Datasets:

ontocord
/

math_permissive

Dataset card Data Studio Files Files and versions Community

Split (1)

train · 27.7k rows

url stringlengths 16 775	text stringlengths 100 1.02M	date timestamp[s]	metadata stringlengths 1.07k 1.1k
https://mooseframework.inl.gov/modules/phase_field/MultiPhase/KKSDerivations.html	(1) (2) (3) # Materials The KKS system (Kim et al. (1999)) uses multiple MOOSE materials to provide values for free energy functions, the switching function , and the double well function . Providing these as materials allows the functions to be bundled in a single place, while being used by multiple kernels. Furthermore the automatic differentiation feature used in the parsed function materials prreplovides the necessary derivatives at no cost to the developer. The derivatives are stored in material properties and follow a naming scheme that is defined in KKSBaseMaterial.C. # Cahn-Hilliard Kernels ## KKSSplitCHCRes KKSSplitCHCRes is the split version. In this kernel, we calculate the chemical potential from . The non-linear variable for this Kernel is the concentration . To calculate and , we use the CoupledTimeDerivative and SplitCHWRes kernels, respectively, as described here. ## Residual In the residual routine we need to calculate the term . We exploit the KKS identity and arbitrarily use the a-phase instead. (4) ### Jacobian #### On-Diagonal Since there is no explicit dependence on the non-linear variable in the residual equation, the diagonal components are zero. #### Off-diagonal We are looking for the derivative of , where . We need to apply the chain rule and will again only keep terms with the derivative. (5) For (6) ## KKSCHBulk KKSCHBulk is the non-split version, which is not fully implemented**. The non-linear variable for this Kernel is the concentration . ### Residual In the residual routine we need to calculate the term . We exploit the KKS identity and arbitrarily use the a-phase instead. The gradient can be calculated through the chain rule (note that is potentially a function of many variables). (7) With being the vector of all arguments to this simplifies to (8) using as a shorthand for the term (and represented in the code as the array _second_derivatives[i]). We do have access to the gradients of through MOOSE (stored in _grad\_args[i]). ### Jacobian The calculation of the Jacobian involves the derivative of the Residual term w.r.t. the individual coefficients of all parameters of . Here can stand for any variable . (9) In the code is given by jvar for the off diagonal case, and (not or !) in the on diagonal case. #### Off-diagonal Let's focus on off diagonal first. Here is zero, if jvar is not equal . Allowing us to remove the sum over and replace it with the single non-zero summand (10) In the first term in the square brackets the derivative is only non-zero if is jvar. We can therefore pull this term out of the sum. (11) With the rules for derivatives we get (12) where is _j in the code. #### On-diagonal For the on diagonal terms we look at the derivative w.r.t. the components of the non-linear variable of this kernel. Note, that is only indirectly a function of . We assume the dependence is given through . The chain rule will thus yield terms of this form (13) which is given as equation (23) in KKS. Following the off-diagonal derivation we get v \frac{d2F_a}{dc_a2}\frac{dc_a}{dc} \nabla \phi_j + \sum_i \nabla a_i \frac {dR_i}{dc_a} \frac{dc_a}{dc} \phi_j #### On-diagonal second approach Let's get back to the original residual with . Then (14) # Allen-Cahn Kernels For the bulk Allen-Cahn residual we need to calculate the term (15) The _chain rule term_ results from the fact that and are dependent on (see eqs. (25) and (26) in KKS). Setting we get (16) Substituting this in we get (17) This simplifies to (18) We split this residual into two kernels to allow for multiple phase concentrations in a multi component system: ## KKSACBulkF KKSACBulkF is the part without a direct composition dependence. (19) ### Jacobian #### On-diagonal We are looking for the derivative of , where . We need to apply the chain rule and will again only keep terms with the derivative. (20) (The implicit dependence of and on through and does not contribute to the Jacobian, so . #### Off-Diagonal The off-diagonal components are calculated for any other variables that and depend on. For example, for : (21) in the KKS formulation, so this term would not need to be included if was the only variable depended on. However, the code calculates derivatives with respect to all variables that and depend on in a general way so that the Jacobian entries for other dependencies are correctly computed using the same piece of code. For example, both and could depend on temperature , in which case (22) which is computed using the same code. The off-diagonal Jacobian contribution is also multiplied by the Allen-Cahn mobility at each point for consistency with the other terms in the Allen-Cahn equation. ## KKSACBulkC KKSACBulkC is the part with a direct composition dependence. An instance of this kernel is needed for each compnent of the problem. (23) ### Jacobian #### On-diagonal We are looking for the derivative of , where . We need to apply the chain rule and will again only keep terms with the derivative. (24) #### Off-diagonal Since and appear in the residual, their effect must be calculated separately from any other variable dependence. For , we are looking for the derivative of , where . We need to apply the chain rule and will again only keep terms with the derivative. (25) Similarly for , (26) For any variable other than or , for example temperature : (27) The off-diagonal Jacobian contributions are again multiplied by the Allen-Cahn mobility at each point for consistency with the other terms in the Allen-Cahn equation. # Constraint Kernels ## KKSPhaseChemicalPotential KKSPhaseChemicalPotential enforces the point wise equality of the phase chemical potentials (28) The non-linear variable of this Kernel is . (29) ### Jacobian For the Jacobian we need to calculate (30) (31) #### Off-Diagonal With the union of the argument vectors of and (represented in the code by _coupled_moose_vars[]) we get (32) Again the is non-zero only if , which is the case if is the argument selected through jvar. (33) Note that in the code jvar is not an index into _coupled_moose_vars[] but has to be resolved through the _jvar_map. ## KKSPhaseConcentration KKSPhaseConcentration enforces the split of the concentration into the phase concentrations, weighted by the switching function. The non-linear variable of this Kernel is . (34) (35) ### Jacobian #### On-Diagonal Since the non-linear variable is , (36) For (37) For (38) For (39)	2019-01-23T15:26:37	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8167209029197693, "perplexity": 1135.3391720958418}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-04/segments/1547584334618.80/warc/CC-MAIN-20190123151455-20190123173455-00107.warc.gz"}
https://arrow.fandom.com/wiki/User_talk:Lorisa214	6,803 Pages Lorisa214 aka Lorisa Content Team Member 0 Discussion posts My favorite wikis • I was born on December 14 • I am Female Welcome Hi, welcome to Arrowverse Wiki! Thanks for your edit to the Oliver Queen page. If you were such a huge fan, I think you'd have done more then 5 edits, also I believe MakeShift considered and declined this, else he would of replied about it ages ago when we were first asked. Wraiyf You never know when life will hit you hard, but then you hit it back. 01:53, February 2, 2014 (UTC) Sorry, but still we're not interested, we only affiliate with the FIRST wikia based on the series, we checked and saw that you made one more recently therefore your request is declined... Also I don't care if you're female, we have a great female editor here, so please don't bring sexism into this. Wraiyf You never know when life will hit you hard, but then you hit it back. 09:38, February 2, 2014 (UTC) RE: Our wikis / Billy Wintergreen In regards to affiliating the wikis, I've already got a strong stance on not. We've begun to incorporate The Flash in to this wiki, as was always the plan, so it's quite silly to affiliate with a wiki that includes the same content as us. I'm always open to discussions on a merge, though affiliation: no. As for Billy Wintergreen, this has been a much-debated topic. In "Damaged" it appears as if in a flashback that Fyers says "Bishop, put him out of his misery" when in fact he says "You should put him out of his misery". It says that on the DVD subtitles, and nowhere else is he ever referred to as Bishop. So that's that! Anything else, just contact me! :) —MakeShift (talk) 04:07, April 6, 2014 (UTC) I really have no problem with Flash Wiki existing, if you guys really want it to exist, though it's the fact that Matt and others seem to think that it's impossible for The Flash to be covered here. He seems to think it necessary that there be a totally new wiki, that it MUST happen, whereas it's truly only optional. As for Billy Wintergreen, sorry about that! I thought you'd sent me a message regarding the character! —MakeShift (talk) 07:51, April 13, 2014 (UTC) Oh and as for cleaning up pages, go right ahead, so long as you feel it's needed! —MakeShift (talk) 08:00, April 13, 2014 (UTC) RE: Tahmoh Penikett Firstly, I just want to say that I love affiliating with other wikis, I really love the sense it gives of being part of a wider community. Though, at the moment, we don't really include stuff like that (particularly as it's so specific, and if anything, advertising-ish). Really, including credits, they'd obviously take way too long to update each actor's page and keep up to date, so for now we don't include that much on the pages apart from the Arrow/Flash content! :) —MakeShift (talk) 10:11, May 3, 2014 (UTC) RE: Affiliation I do appreciate you reaching out for affiliation, though I'd have to decline, cause when it comes down to it, none of our shows are really similar in very many ways, in terms of genre. There's many acting similarities, but the crux of it is really the genres. —MakeShift (talk page) 09:56, October 8, 2014 (UTC) RE Those shows aren't really connected, just same network but we don't need to advertise other shows and wikis in articles. We already use the CW footer on the front page, that's all we need to add.User:TimeShade/sig 08:48, November 20, 2014 (UTC) RE: Affiliation You've asked before, and I've said no. And I'm going to say no again, for the same reasons. The wikis have basically nothing in common except for a couple of actors. —MakeShift (talk page) 07:31, May 13, 2016 (UTC) Admittedly, they would have been a while back. But it was mostly due to their fantastical nature, I believe. —MakeShift (talk page) 07:49, May 13, 2016 (UTC) Promotional stills While I appreciate the effort you've put in, we currently don't include promotional stills on any of our pages, so I've deleted the ones you've uploaded. —MakeShift (talk page) 04:03, October 19, 2017 (UTC) Categories Please consult admins before incorporating such major categories. I know some wikis go really specific into categories but we aren't one of those wikis.User:TimeShade/sig 10:38, November 29, 2017 (UTC) For now, please don't add either. Generally, it'll just clutter the wiki with categories for every single occupation there is and we don't really want that.User:TimeShade/sig 10:47, November 29, 2017 (UTC) Spoiler policy Hey there, if you could read our spoiler policy that'd be great. We only allow future spoilers on production pages, so I've deleted the Brainiac 5 page you created. —MakeShift (talk page) 12:29, November 29, 2017 (UTC) "screenshots from teasers may not be added on production pages." spoiler policy Promotional Images/Stills for the episodes count as teasers. Wraiyf You never know when life will hit you hard, but then you hit it back. 06:57, January 22, 2018 (UTC) RE:Trivia Alright. Sorry. I will stop removing it.Ninja72 (talk) 21:32, November 12, 2019 (UTC) References Because those kind of references are not what we include at this wiki. $\int$ IHH dt 8:25, Dec 10, 2019 (UTC) Infobox formatting Please don't mess with the formatting of infoboxes, particularly the guest sections. We format it a certain way, and just because you believe your way works better, this is not necessarily the case. If you believe something to work better, consult an admin first. —MakeShift (talk page) 08:25, December 10, 2019 (UTC) Community content is available under CC-BY-SA unless otherwise noted.	2019-12-10T15:23:43	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5080695748329163, "perplexity": 2974.853342773194}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-51/segments/1575540528457.66/warc/CC-MAIN-20191210152154-20191210180154-00220.warc.gz"}
https://mfix.netl.doe.gov/doc/mfix/20.1.0/model_setup/fluid.html	4.5. Fluid¶ The fluid pane is used to select the models and parameters defining the fluid phase. The fluid pane is only accessible if the fluid phase is being solved. Name The name used to refer to the continuous phase in the GUI. By default, the continuous phase is termed “fluid”, However, it may be renamed for convenience. 4.5.1. Fluid Model Options¶ Solve Momentum Equation By default, all momentum equations are solved. Individual momentum equations may be disabled by toggling the check box. Solve Species Equations By default, species transport equations are not solved for the fluid phase. If species equations are enabled, species will need to be added to the fluid phase using the fluid species tool. Enable Scalar Equations By default, no additional scalar transport equations are solved with the fluid phase. Additional scalars may be added by toggling the scalar checkbox and specifying the number of additional scalars to track. Energy Equations Energy equations cannot be enabled or disabled on a per-phase basis. As such, they are enabled or disabled for all phases in the Model Setup pane. 4.5.2. Fluid Properties¶ Density has units of $$(\frac{kg}{m^3})$$ and may be specified using one of the following approaches. • Constant: • A positive (non-zero) number must be provided. • Ideal gas law • Requires fluid temperature be specified for the whole domain and all flow boundary conditions. • Requires a fluid molecular weight. • User-Defined Function (UDF) • A custom equation of state must be provided in the usrproperties.f • A custom solver must be built. Viscosity has units of $$(Pa \cdot sec)$$ and may be specified using one of the following approaches. • Constant: • A positive (non-zero) number must be provided. • Sutherland’s law • Requires fluid temperature be specified for the whole domain and all flow boundary conditions. • User-Defined Function (UDF) • A custom equation of state must be provided in the usrproperties.f • A custom solver must be built. Molecular Weight has units of $$(\frac{kg}{kmol})$$ and may be specified using one of the following approaches. • Constant: • A positive (non-zero) number must be provided. • Mixture • Requires fluid species definition. • Requires fluid species mass fractions specification for the whole domain and all flow boundary conditions Specific Heat has units of $$(\frac{J}{kg \cdot K})$$ and may be specified using one of the following approaches. • Constant: • A positive (non-zero) number must be provided. • Mixture • Requires fluid species definition. • Requires fluid species mass fractions specification for the whole domain and all flow boundary conditions • User-Defined Function (UDF) • A custom equation of state must be provided in the usrproperties.f • A custom solver must be built. Thermal Conductivity has units of $$(\frac{W}{m \cdot K})$$ may be specified using one of the following approaches. • Constant: • A non-negative number must be provided. • Dilute Mixture Approximation • Requires fluid temperature be specified for the whole domain and all flow boundary conditions. • User-Defined Function (UDF) • A custom equation of state must be provided in the usrproperties.f • A custom solver must be built. Reference pressure has units of $$(Pa)$$ and is zero by default. A constant value may be specified to shift the simulation pressure prior to scaling. Pressure scale factor is dimensionless and is one by default. A constant value may be specified to scale the simulation pressure. $P_{scaled} = \frac{P_{simulation} - P_{reference} }{ P_{scale factor}}$ 4.5.3. Fluid Model Species¶ Specie that comprise the fluid phase are summarized in the species overview table. New species are added by clicking the add button, , at the top of the species table, and selecting one or more valid regions (see Fig. 4.3).	2022-05-18T17:04:49	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4439258873462677, "perplexity": 1741.2744392886}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662522284.20/warc/CC-MAIN-20220518151003-20220518181003-00689.warc.gz"}
http://trilinos.sandia.gov/packages/docs/r9.0/packages/moocho/src/AbstractLinAlgPack/doc/html/classAbstractLinAlgPack_1_1COOMatrix.html	# AbstractLinAlgPack::COOMatrix Class Reference Sparse Coordinate Matrix abstraction storage class. More... #include <AbstractLinAlgPack_COOMatrixClass.hpp> List of all members. ## {\bf Public Typedefs} typedef AbstractLinAlgPack::size_type size_type typedef AbstractLinAlgPack::indice_type indice_type typedef AbstractLinAlgPack::value_type value_type ## Constructors. The default copy constructor is used since it has the correct implementation (memberwise assignment and not binary copy). In the default copy constructor, initially these objects will share memory for ivect#, jvect#. Initially only val# is allocated and made unique. If the sparsity information of the matrix does not change then the value of the nonzero elements can be changed without further allocations. If however, the row and/or column access in changed, or ivect or jvect is changed then new allocations will be performed. COOMatrix () Consturct with no storage allocated. ## COO matrix representation access. These member functions give access the the val#, ivect# and jvect# arrays used to store the underlying nonzero elements of the full matrix. Since sharing can be used between COOMatrix objects the client should call the 'const_' functions if they are only going to be reading these data since if the others are called on a nonconst object then if ivect# or jvect# is being shared then a freash copy would be made unnecesarily. value_typeval () Return pointer to raw storage array (length nz()#) for the values of the non-zero elements. const value_typeval () const const value_typeconst_val () const indice_typeivect () Return pointer to raw storage array (length nz()#) for the row indices of the non-zero elements. const indice_typeivect () const const indice_typeconst_ivect () const indice_typejvect () Return pointer to raw storage array (length nz()#) for the column indices of the non-zero elements. const indice_typejvect () const const indice_typeconst_jvect () const void initialize (std::istream &istrm) Initialize from an input stream. ## Public Member Functions COOMatrixoperator= (const COOMatrix &coom) Assignment operator. void resize (size_type rows, size_type cols, size_type nz) Resize for a rows# by cols# sparse matrix with nz# elements. size_type rows () const Return the number of rows in the row access view. size_type cols () const Returns the number of columns in the column access view. size_type nz () const ## Detailed Description Sparse Coordinate Matrix abstraction storage class. This class abstracts a fortran style sparse coordinate matrix which is stored is three vectors: (val, ivect, jvect). This class allows direct access to these arrays for integration with fortran function calls. The row and column indices represented by this class must be 1-based. Definition at line 48 of file AbstractLinAlgPack_COOMatrixClass.hpp. ## Member Typedef Documentation Definition at line 59 of file AbstractLinAlgPack_COOMatrixClass.hpp. typedef AbstractLinAlgPack::indice_type AbstractLinAlgPack::COOMatrix::indice_type Definition at line 61 of file AbstractLinAlgPack_COOMatrixClass.hpp. Definition at line 63 of file AbstractLinAlgPack_COOMatrixClass.hpp. ## Constructor & Destructor Documentation AbstractLinAlgPack::COOMatrix::COOMatrix ( ) [inline] Consturct with no storage allocated. Definition at line 185 of file AbstractLinAlgPack_COOMatrixClass.hpp. ## Member Function Documentation COOMatrix& AbstractLinAlgPack::COOMatrix::operator= ( const COOMatrix & coom ) Assignment operator. This function has similar behavior w.r.t sharing that the copy constructor has accept any current storage will be deallocated. void AbstractLinAlgPack::COOMatrix::resize ( size_type rows, size_type cols, size_type nz ) Resize for a rows# by cols# sparse matrix with nz# elements. Any sharing if row or column indices is lost. COOMatrix::size_type AbstractLinAlgPack::COOMatrix::rows ( ) const [inline] Return the number of rows in the row access view. Definition at line 188 of file AbstractLinAlgPack_COOMatrixClass.hpp. COOMatrix::size_type AbstractLinAlgPack::COOMatrix::cols ( ) const [inline] Returns the number of columns in the column access view. Definition at line 191 of file AbstractLinAlgPack_COOMatrixClass.hpp. COOMatrix::value_type * AbstractLinAlgPack::COOMatrix::val ( ) [inline] Return pointer to raw storage array (length nz()#) for the values of the non-zero elements. Definition at line 198 of file AbstractLinAlgPack_COOMatrixClass.hpp. const COOMatrix::value_type * AbstractLinAlgPack::COOMatrix::val ( ) const [inline] Definition at line 201 of file AbstractLinAlgPack_COOMatrixClass.hpp. const COOMatrix::value_type * AbstractLinAlgPack::COOMatrix::const_val ( ) const [inline] Definition at line 204 of file AbstractLinAlgPack_COOMatrixClass.hpp. COOMatrix::indice_type * AbstractLinAlgPack::COOMatrix::ivect ( ) [inline] Return pointer to raw storage array (length nz()#) for the row indices of the non-zero elements. Definition at line 207 of file AbstractLinAlgPack_COOMatrixClass.hpp. const COOMatrix::indice_type * AbstractLinAlgPack::COOMatrix::ivect ( ) const [inline] Definition at line 210 of file AbstractLinAlgPack_COOMatrixClass.hpp. const COOMatrix::indice_type * AbstractLinAlgPack::COOMatrix::const_ivect ( ) const [inline] Definition at line 213 of file AbstractLinAlgPack_COOMatrixClass.hpp. COOMatrix::indice_type * AbstractLinAlgPack::COOMatrix::jvect ( ) [inline] Return pointer to raw storage array (length nz()#) for the column indices of the non-zero elements. Definition at line 216 of file AbstractLinAlgPack_COOMatrixClass.hpp. const COOMatrix::indice_type * AbstractLinAlgPack::COOMatrix::jvect ( ) const [inline] Definition at line 219 of file AbstractLinAlgPack_COOMatrixClass.hpp. const COOMatrix::indice_type * AbstractLinAlgPack::COOMatrix::const_jvect ( ) const [inline] Definition at line 222 of file AbstractLinAlgPack_COOMatrixClass.hpp. void AbstractLinAlgPack::COOMatrix::initialize ( std::istream & istrm ) Initialize from an input stream. The format for the imput is: m n nz#\ a1:i1:j1 a2:i2:j2 .... anz:inz:jnz#\ In the above format, each non-zero element is given as a three item pair: value of the non-zero element, row indice (1-based) of the non-zero element, and the column indice (1-based) of the non-zero element. There must be no spaces between the numbers and the \':\' charachter and there must be at least one whitespace character between elements. The documentation for this class was generated from the following file: Generated on Wed May 12 21:50:52 2010 for AbstractLinAlgPack: C++ Interfaces For Vectors, Matrices And Related Linear Algebra Objects by 1.4.7	2013-12-08T20:45:24	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.23964425921440125, "perplexity": 14409.302316870573}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-48/segments/1386163811461/warc/CC-MAIN-20131204133011-00012-ip-10-33-133-15.ec2.internal.warc.gz"}
https://www.scstatehouse.gov/sess117_2007-2008/bills/4278.htm	South Carolina General Assembly 117th Session, 2007-2008 Indicates Matter Stricken Indicates New Matter H. 4278 STATUS INFORMATION House Resolution Document Path: l:\council\bills\rm\1298ahb07.doc Introduced in the House on June 20, 2007 Adopted by the House on June 20, 2007 Summary: Abbeville Savings and Loan Association HISTORY OF LEGISLATIVE ACTIONS Date Body Action Description with journal page number ------------------------------------------------------------------------------- 6/20/2007 House Introduced and adopted HJ-34 View the latest legislative information at the LPITS web site VERSIONS OF THIS BILL (Text matches printed bills. Document has been reformatted to meet World Wide Web specifications.) ### A HOUSE RESOLUTION TO CONGRATULATE ABBEVILLE SAVINGS & LOAN ASSOCIATION ON ITS ONE HUNDREDTH ANNIVERSARY OF OUTSTANDING SERVICE TO THE CITIZENS OF ABBEVILLE COUNTY, AND TO WISH ITS STAFF AND CUSTOMERS MANY MORE YEARS OF SUCCESSFUL PARTNERSHIP. Whereas, the House of Representatives is pleased to learn that Abbeville Savings & Loan Association is celebrating its one hundredth anniversary of outstanding service to the citizens of Abbeville County; and Whereas, to give special recognition to this milestone in its distinguished history, Abbeville Savings & Loan Association will hold a gala one-hundredth anniversary celebration on Monday, June 25, 2007; and Whereas, the day-long celebration will include drawings for prizes every half hour for the entire day, giveaways for customers, games offering prizes to winners, and cake and other refreshments. An afternoon ribbon-cutting ceremony commemorating the institution's first hundred years and launching its second century of service also will mark this festive occasion; and Whereas, during its first hundred years, in addition to supplying trustworthy financial services to the County of Abbeville and beyond, Abbeville Savings & Loan Association has been an excellent corporate citizen in its support of a multitude of charitable and philanthropic causes. As a result, this large community employer has deservedly earned the respect of its customers and the citizens of the County of Abbeville at large. The House of Representatives, therefore, takes great pleasure in joining with the friends of Abbeville Savings & Loan Association in congratulating the institution on the occasion of its centennial. Now, therefore, Be it resolved by the House of Representatives: That the members of the South Carolina House of Representatives, by this resolution, congratulate Abbeville Savings & Loan Association on its one hundredth anniversary of outstanding service to the citizens of Abbeville County, and wish its staff and customers many more years of successful partnership. Be it further resolved that a copy of this resolution be presented to Abbeville Savings & Loan Association. ----XX---- This web page was last updated on Wednesday, December 2, 2009 at 3:43 P.M.	2023-02-05T10:16:41	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.20457293093204498, "perplexity": 12279.68755952052}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500251.38/warc/CC-MAIN-20230205094841-20230205124841-00025.warc.gz"}
https://zims-en.kiwix.campusafrica.gos.orange.com/wikipedia_en_all_nopic/A/Van_der_Waals_equation	# Van der Waals equation The van der Waals equation (or van der Waals equation of state; named after Johannes Diderik van der Waals) is an equation of state that generalizes the ideal gas law based on plausible reasons that real gases do not act ideally. The ideal gas law treats gas molecules as point particles that interact with their containers but not each other, meaning they neither take up space nor change kinetic energy during collisions.[1] The ideal gas law states that volume (V) occupied by n moles of any gas has a pressure (P) at temperature (T) in kelvins given by the following relationship, where R is the gas constant: PV = nRT, To account for the volume that a real gas molecule takes up, the van der Waals equation replaces V in the ideal gas law with ${\displaystyle (V_{m}-b)}$, where Vm is the molar volume of the gas and b is the volume that is occupied by one mole of the molecules. This leads to:[1] ${\displaystyle P(V_{m}-b)=RT}$ The second modification made to the ideal gas law accounts for the fact that gas molecules do in fact attract each other and that real gases are therefore more compressible than ideal gases. Van der Waals provided for intermolecular attraction by adding to the observed pressure P in the equation of state a term ${\displaystyle a/V_{m}^{2}}$, where a is a constant whose value depends on the gas. The van der Waals equation is therefore written as:[1] ${\displaystyle \left(P+a{\frac {1}{V_{m}^{2}}}\right)(V_{m}-b)=RT}$ and can also be written as the equation below ${\displaystyle \left(P+a{\frac {n^{2}}{V^{2}}}\right)(V-nb)=nRT}$ where Vm is the molar volume of the gas, R is the universal gas constant, T is temperature, P is pressure, and V is volume. When the molar volume Vm is large, b becomes negligible in comparison with Vm, a/Vm2 becomes negligible with respect to P, and the van der Waals equation reduces to the ideal gas law, PVm=RT.[1] It is available via its traditional derivation (a mechanical equation of state), or via a derivation based in statistical thermodynamics, the latter of which provides the partition function of the system and allows thermodynamic functions to be specified. It successfully approximates the behavior of real fluids above their critical temperatures and is qualitatively reasonable for their liquid and low-pressure gaseous states at low temperatures. However, near the transitions between gas and liquid, in the range of p, V, and T where the liquid phase and the gas phase are in equilibrium, the van der Waals equation fails to accurately model observed experimental behaviour, in particular that p is a constant function of V at given temperatures. As such, the van der Waals model is not useful only for calculations intended to predict real behavior in regions near the critical point. Corrections to address these predictive deficiencies have since been made e.g., equal area rule, principle of corresponding states. ## Overview and history The van der Waals equation is a thermodynamic equation of state based on the theory that fluids are composed of particles with non-zero volumes, and subject to a (not necessarily pairwise) inter-particle attractive force. It was based on work in theoretical physical chemistry performed in the late 19th century by Johannes Diderik van der Waals, who did related work on the attractive force that also bears his name. The equation is known to be based on a traditional set of derivations deriving from van der Waals' and related efforts, as well as a set of derivation based in statistical thermodynamics, see below. Van der Waals' early interests were primarily in the field of thermodynamics, where a first influence was Rudolf Clausius's published work on heat in 1857; other significant influences were the writings by James Clerk Maxwell, Ludwig Boltzmann, and Willard Gibbs.[2] After initial pursuit of teaching credentials, van der Waals' undergraduate coursework in mathematics and physics at the University of Leiden in the Netherlands led (with significant hurdles) to his acceptance for doctoral studies at Leiden under Pieter Rijke. While his dissertation helps to explain the experimental observation in 1869 by Irish professor of chemistry Thomas Andrews (Queen's University Belfast) of the existence of a critical point in fluids,[3] science historian Martin J. Klein states that it is not clear whether van der Waals was aware of Andrews' results when he began his doctorate work.[4] Van der Waals' doctoral research culminated in an 1873 dissertation that provided a semi-quantitative theory describing the gas-liquid change of state and the origin of a critical temperature, Over de Continuïteit van den Gas-en Vloeistof[-]toestand (Dutch; in English, On the Continuity of the Gas- and Liquid-State); it was in this dissertation that the first derivations of what we now refer to as the van der Waals equation appeared.[5] James Clerk Maxwell reviewed and lauded its published content in the British science journal Nature,[6][7] and van der Waals began independent work that would result in his receipt of the Nobel Prize in 1910, which emphasized the contribution of his formulation of this "equation of state for gases and liquids."[2] ## Equation The equation relates four state variables: the pressure of the fluid p, the total volume of the fluid's container V, the number of particles N, and the absolute temperature of the system T. The intensive, microscopic form of the equation is: ${\displaystyle \left(p+{\frac {a'}{v^{2}}}\right)\left(v-b'\right)=k_{\text{B}}T}$[2] where ${\displaystyle v=V/N}$ is the volume of the container occupied by each particle (not the velocity of a particle), and kB is the Boltzmann constant. It introduces two new parameters: a′, a measure of the average attraction between particles, and b′, the volume excluded from v by one particle. The equation can be also written in extensive, molar form: ${\displaystyle \left(p+{\frac {n^{2}a}{V^{2}}}\right)\left(V-nb\right)=nRT}$[8] where ${\displaystyle a=N_{A}^{2}a'}$ is a measure of the average attraction between particles, ${\displaystyle b=N_{\text{A}}b'}$ is the volume excluded by a mole of particles, ${\displaystyle n=N/N_{\text{A}}}$ is the number of moles, ${\displaystyle R=N_{\text{A}}k_{\text{B}}}$ is the universal gas constant, kB is the Boltzmann constant, and NA is the Avogadro constant. A careful distinction must be drawn between the volume available to a particle and the volume of a particle. In the intensive equation, v equals the total space available to each particle, while the parameter b′ is proportional to the proper volume of a single particle – the volume bounded by the atomic radius. This is subtracted from v because of the space taken up by one particle. In van der Waals' original derivation, given below, b' is four times the proper volume of the particle. Observe further that the pressure p goes to infinity when the container is completely filled with particles so that there is no void space left for the particles to move; this occurs when V = nb.[9] ### Gas mixture If a mixture of ${\displaystyle n}$ gases is being considered, and each gas has its own ${\displaystyle a}$ (attraction between molecules) and ${\displaystyle b}$ (volume occupied by molecules) values, then ${\displaystyle a}$ and ${\displaystyle b}$ for the mixture can be calculated as ${\displaystyle m}$ = total number of moles of gas present, for each ${\displaystyle i}$, ${\displaystyle m_{i}}$ = number of moles of gas ${\displaystyle i}$ present, and ${\displaystyle x_{i}={\frac {m_{i}}{m}}}$ ${\displaystyle a=\sum _{i=1}^{i=n}\sum _{j=1}^{i=n}(x_{i}x_{j}{\sqrt {a_{i}a_{j}}})}$[10][11] ${\displaystyle b=\sum _{i=1}^{i=n}\sum _{j=1}^{i=n}(x_{i}x_{j}{\sqrt {b_{i}b_{j}}})}$[10][11] and the rule of adding partial pressures becomes invalid if the numerical result of the equation ${\displaystyle \left(p+({n^{2}a}/{V^{2}})\right)\left(V-nb\right)=nRT}$ is significantly different from the ideal gas equation ${\displaystyle pV=nRT}$ . ### Reduced form The van der Waals equation can also be expressed in terms of reduced properties: ${\displaystyle \left(P_{r}+{\frac {3}{V_{r}^{2}}}\right)\left(V_{r}-{\frac {1}{3}}\right)={\frac {8}{3}}T_{r}}$ This yields a critical compressibility factor of 3/8. Reasons for modification of ideal gas equation: The equation state for ideal gas is PV=RT. In the derivation of ideal gas laws on the basis of kinetic theory of gases some assumption have been made. ## Validity The van der Waals equation is mathematically simple, but it nevertheless predicts the experimentally observed transition between vapor and liquid, and predicts critical behaviour.[12]:289 It also adequately predicts and explains the Joule–Thomson effect, which is not possible in ideal gas. Above the critical temperature, TC, the van der Waals equation is an improvement over the ideal gas law, and for lower temperatures, i.e., T < TC, the equation is also qualitatively reasonable for the liquid and low-pressure gaseous states; however, with respect to the first-order phase transition, i.e., the range of (p, V, T) where a liquid phase and a gas phase would be in equilibrium, the equation appears to fail to predict observed experimental behaviour, in the sense that p is typically observed to be constant as a function of V for a given temperature in the two-phase region. This apparent discrepancy is resolved in the context of vapour–liquid equilibrium: at a particular temperature, there exist two points on the van der Waals isotherm that have the same chemical potential, and thus a system in thermodynamic equilibrium will appear to traverse a straight line on the pV diagram as the ratio of vapour to liquid changes. However, in such a system, there are really only two points present (the liquid and the vapour) rather than a series of states connected by a line, so connecting the locus of points is incorrect: it is not an equation of multiple states, but an equation of (a single) state. It is indeed possible to compress a gas beyond the point at which it would typically condense, given the right conditions, and it is also possible to expand a liquid beyond the point at which it would usually boil. Such states are called "metastable" states. Such behaviour is qualitatively (though perhaps not quantitatively) predicted by the van der Waals equation of state.[13] However, the values of physical quantities as predicted with the van der Waals equation of state "are in very poor agreement with experiment", so the model's utility is limited to qualitative rather than quantitative purposes.[12]:289 Empirically-based corrections can easily be inserted into the van der Waals model (see Maxwell's correction, below), but in so doing, the modified expression is no longer as simple an analytical model; in this regard, other models, such as those based on the principle of corresponding states, achieve a better fit with roughly the same work. Even with its acknowledged shortcomings, the pervasive use of the van der Waals equation in standard university physical chemistry textbooks makes clear its importance as a pedagogic tool to aid understanding fundamental physical chemistry ideas involved in developing theories of vapour–liquid behavior and equations of state.[14][15][16] In addition, other (more accurate) equations of state such as the Redlich–Kwong and Peng–Robinson equation of state are essentially modifications of the van der Waals equation of state. ## Derivation Textbooks in physical chemistry generally give two derivations of the title equation. One is the conventional derivation that goes back to van der Waals, a mechanical equation of state that cannot be used to specify all thermodynamic functions; the other is a statistical mechanics derivation that makes explicit the intermolecular potential neglected in the first derivation. A particular advantage of the statistical mechanical derivation is that it yields the partition function for the system, and allows all thermodynamic functions to be specified (including the mechanical equation of state). ### Conventional derivation Consider one mole of gas composed of non-interacting point particles that satisfy the ideal gas law:(see any standard Physical Chemistry text, op. cit.) ${\displaystyle p={\frac {RT}{V_{\mathrm {m} }}}.}$ Next, assume that all particles are hard spheres of the same finite radius r (the van der Waals radius). The effect of the finite volume of the particles is to decrease the available void space in which the particles are free to move. We must replace V by V b, where b is called the excluded volume or "co-volume". The corrected equation becomes ${\displaystyle p={\frac {RT}{V_{\mathrm {m} }-b}}.}$ The excluded volume ${\displaystyle b}$ is not just equal to the volume occupied by the solid, finite-sized particles, but actually four times that volume. To see this, we must realize that a particle is surrounded by a sphere of radius 2r (two times the original radius) that is forbidden for the centers of the other particles. If the distance between two particle centers were to be smaller than 2r, it would mean that the two particles penetrate each other, which, by definition, hard spheres are unable to do. The excluded volume for the two particles (of average diameter d or radius r) is ${\displaystyle b'_{2}=4\pi d^{3}/3=8\times (4\pi r^{3}/3)}$, which, divided by two (the number of colliding particles), gives the excluded volume per particle: ${\displaystyle b'=b'_{2}/2\quad \rightarrow \quad b'=4\times (4\pi r^{3}/3)}$, So b is four times the proper volume of the particle. It was a point of concern to van der Waals that the factor four yields an upper bound; empirical values for b are usually lower. Of course, molecules are not infinitely hard, as van der Waals thought, and are often fairly soft. Next, we introduce a (not necessarily pairwise) attractive force between the particles. van der Waals assumed that, notwithstanding the existence of this force, the density of the fluid is homogeneous; furthermore, he assumed that the range of the attractive force is so small that the great majority of the particles do not feel that the container is of finite size. Given the homogeneity of the fluid, the bulk of the particles do not experience a net force pulling them to the right or to the left. This is different for the particles in surface layers directly adjacent to the walls. They feel a net force from the bulk particles pulling them into the container, because this force is not compensated by particles on the side where the wall is (another assumption here is that there is no interaction between walls and particles, which is not true, as can be seen from the phenomenon of droplet formation; most types of liquid show adhesion). This net force decreases the force exerted onto the wall by the particles in the surface layer. The net force on a surface particle, pulling it into the container, is proportional to the number density ${\displaystyle C=N_{\mathrm {A} }/V_{\mathrm {m} }}$. The number of particles in the surface layers is, again by assuming homogeneity, also proportional to the density. In total, the force on the walls is decreased by a factor proportional to the square of the density, and the pressure (force per unit surface) is decreased by ${\displaystyle a'C^{2}=a'\left({\frac {N_{\mathrm {A} }}{V_{\mathrm {m} }}}\right)^{2}={\frac {a}{V_{\mathrm {m} }^{2}}}}$, so that ${\displaystyle p={\frac {RT}{V_{\mathrm {m} }-b}}-{\frac {a}{V_{\mathrm {m} }^{2}}}\Rightarrow \left(p+{\frac {a}{V_{\mathrm {m} }^{2}}}\right)(V_{\mathrm {m} }-b)=RT.}$ Upon writing n for the number of moles and nVm = V, the equation obtains the second form given above, ${\displaystyle \left(p+{\frac {n^{2}a}{V^{2}}}\right)(V-nb)=nRT.}$ It is of some historical interest to point out that van der Waals, in his Nobel prize lecture, gave credit to Laplace for the argument that pressure is reduced proportional to the square of the density. ### Statistical thermodynamics derivation The canonical partition function Z of an ideal gas consisting of N = nNA identical (non-interacting) particles, is:[17][18] ${\displaystyle Z={\frac {z^{N}}{N!}}\quad {\hbox{with}}\quad z={\frac {V}{\Lambda ^{3}}}}$ where ${\displaystyle \Lambda }$ is the thermal de Broglie wavelength, ${\displaystyle \Lambda ={\sqrt {\frac {h^{2}}{2\pi mkT}}}}$ with the usual definitions: h is Planck's constant, m the mass of a particle, k Boltzmann's constant and T the absolute temperature. In an ideal gas z is the partition function of a single particle in a container of volume V. In order to derive the van der Waals equation we assume now that each particle moves independently in an average potential field offered by the other particles. The averaging over the particles is easy because we will assume that the particle density of the van der Waals fluid is homogeneous. The interaction between a pair of particles, which are hard spheres, is taken to be ${\displaystyle u(r)={\begin{cases}\infty &{\hbox{when}}\quad r r is the distance between the centers of the spheres and d is the distance where the hard spheres touch each other (twice the van der Waals radius). The depth of the van der Waals well is ${\displaystyle \epsilon }$. Because the particles are not coupled under the mean field Hamiltonian, the mean field approximation of the total partition function still factorizes, ${\displaystyle Z=z^{N}/N!}$, but the intermolecular potential necessitates two modifications to z. First, because of the finite size of the particles, not all of V is available, but only V − Nb', where (just as in the conventional derivation above) ${\displaystyle b'=2\pi d^{3}/3}$. Second, we insert a Boltzmann factor exp[ - ϕ/2kT] to take care of the average intermolecular potential. We divide here the potential by two because this interaction energy is shared between two particles. Thus ${\displaystyle z={\frac {(V-Nb')\,e^{-\phi /(2kT)}}{\Lambda ^{3}}}.}$ The total attraction felt by a single particle is ${\displaystyle \phi =\int _{d}^{\infty }u(r){\frac {N}{V}}4\pi r^{2}dr,}$ where we assumed that in a shell of thickness dr there are N/V 4π r2dr particles. This is a mean field approximation; the position of the particles is averaged. In reality the density close to the particle is different than far away as can be described by a pair correlation function. Furthermore, it is neglected that the fluid is enclosed between walls. Performing the integral we get ${\displaystyle \phi =-2a'{\frac {N}{V}}\quad {\hbox{with}}\quad a'=\epsilon {\frac {2\pi d^{3}}{3}}=\epsilon b'.}$ Hence, we obtain, ${\displaystyle \ln Z=N\ln {(V-Nb')}+{\frac {N^{2}a'}{VkT}}-N\ln {(\Lambda ^{3})}-\ln {N!}}$ From statistical thermodynamics we know that ${\displaystyle p=kT{\frac {\partial \ln Z}{\partial V}}}$, so that we only have to differentiate the terms containing V. We get ${\displaystyle p={\frac {NkT}{V-Nb'}}-{\frac {N^{2}a'}{V^{2}}}\Rightarrow \left(p+{\frac {N^{2}a'}{V^{2}}}\right)(V-Nb')=NkT\Rightarrow \left(p+{\frac {n^{2}a}{V^{2}}}\right)(V-nb)=nRT.}$ ## Maxwell equal area rule Below the critical temperature, the van der Waals equation seems to predict qualitatively incorrect relationships. Unlike for ideal gases, the p-V isotherms oscillate with a relative minimum (d) and a relative maximum (e). Any pressure between pd and pe appears to have 3 stable volumes, contradicting the experimental observation that two state variables completely determine a one-component system's state.[19] Moreover, the isothermal compressibility is negative between d and e (equivalently ${\displaystyle \scriptstyle \left({{\partial P}/{\partial V}}\right)_{T,N}>0}$), which cannot describe a system at equilibrium.[20] To address these problems, James Clerk Maxwell replaced the isotherm between points a and c with a horizontal line positioned so that the areas of the two shaded regions would be equal (replacing the a-d-b-e-c curve with a straight line from a to c); this portion of the isotherm corresponds to the liquid-vapor equilibrium. The regions of the isotherm from ad and from ce are interpreted as metastable states of super-heated liquid and super-cooled vapor, respectively.[21] [22] The equal area rule can be expressed as: ${\displaystyle p_{V}(V_{G}-V_{L})=\int _{V_{L}}^{V_{G}}p\,dV}$ where pV is the vapor pressure (flat portion of the curve), VL is the volume of the pure liquid phase at point a on the diagram, and VG is the volume of the pure gas phase at point c on the diagram. A two-phase mixture at pV will occupy a total volume between VL and VG, as determined by Maxwell's lever rule. Maxwell justified the rule based on the fact that the area on a pV diagram corresponds to mechanical work, saying that work done on the system in going from c to b should equal work released on going from a to b. This is because the change in free energy A(T,V) equals the work done during a reversible process, and, as a state variable, the free energy must be path-independent. In particular, the value of A at point b should be the same regardless of whether the path taken is from left or right across the horizontal isobar, or follows the original van der Waals isotherm. This derivation is not entirely rigorous, since it requires a reversible path through a region of thermodynamic instability, while b is unstable. Nevertheless, modern derivations from chemical potential reach the same conclusion, and it remains a necessary modification to the van der Waals and to any other analytic equation of state.[19] ### From chemical potential The Maxwell equal area rule can also be derived from an assumption of equal chemical potential μ of coexisting liquid and vapour phases.[23] On the isotherm shown in the above plot, points a and c are the only pair of points which fulfill the equilibrium condition of having equal pressure, temperature and chemical potential. It follows that systems with volumes intermediate between these two points will consist of a mixture of the pure liquid and gas with specific volumes equal to the pure liquid and gas phases at points a and c. The van der Waals equation may be solved for VG and VL as functions of the temperature and the vapor pressure pV. Since: ${\displaystyle p=-\left({\frac {\partial A}{\partial V}}\right)_{T,N}}$ where A is the Helmholtz free energy, it follows that the equal area rule can be expressed as: ${\displaystyle p_{V}={\frac {A(V_{L},T,N)-A(V_{G},T,N)}{V_{G}-V_{L}}}}$is Since the gas and liquid volumes are functions of pV and T only, this equation is then solved numerically to obtain pV as a function of temperature (and number of particles N), which may then be used to determine the gas and liquid volumes. A pseudo-3D plot of the locus of liquid and vapor volumes versus temperature and pressure is shown in the accompanying figure. One sees that the two locii meet at the critical point (1,1,1) smoothly. An isotherm of the van der Waals fluid taken at T r = 0.90 is also shown where the intersections of the isotherm with the loci illustrate the construct's requirement that the two areas (red and blue, shown) are equal. ## Other parameters, forms and applications ### Other thermodynamic parameters We reiterate that the extensive volume V is related to the volume per particle v=V/N where N = nNA is the number of particles in the system. The equation of state does not give us all the thermodynamic parameters of the system. We can take the equation for the Helmholtz energy A [24] ${\displaystyle A=-kT\ln Q.\,}$ From the equation derived above for lnQ, we find ${\displaystyle A(T,V,N)=-NkT\left[1+\ln \left({\frac {(V-Nb')T^{3/2}}{N\Phi }}\right)\right]-{\frac {a'N^{2}}{V}}.}$ Where Φ is an undetermined constant, which may be taken from the Sackur–Tetrode equation for an ideal gas to be: ${\displaystyle \Phi =T^{3/2}\Lambda ^{3}=\left({\frac {h}{\sqrt {2\pi mk}}}\right)^{3}}$ This equation expresses A in terms of its natural variables V and T , and therefore gives us all thermodynamic information about the system. The mechanical equation of state was already derived above ${\displaystyle p=-\left({\frac {\partial A}{\partial V}}\right)_{T}={\frac {NkT}{V-Nb'}}-{\frac {a'N^{2}}{V^{2}}}.}$ The entropy equation of state yields the entropy (S ) ${\displaystyle S=-\left({\frac {\partial A}{\partial T}}\right)_{V}=Nk\left[\ln \left({\frac {(V-Nb')T^{3/2}}{N\Phi }}\right)+{\frac {5}{2}}\right]}$ from which we can calculate the internal energy ${\displaystyle U=A+TS={\frac {3}{2}}\,NkT-{\frac {a'N^{2}}{V}}.}$ Similar equations can be written for the other thermodynamic potential and the chemical potential, but expressing any potential as a function of pressure p will require the solution of a third-order polynomial, which yields a complicated expression. Therefore, expressing the enthalpy and the Gibbs energy as functions of their natural variables will be complicated. ### Reduced form Although the material constant a and b in the usual form of the van der Waals equation differs for every single fluid considered, the equation can be recast into an invariant form applicable to all fluids. Defining the following reduced variables (fR, fC are the reduced and critical variable versions of f, respectively), ${\displaystyle p_{R}={\frac {p}{p_{C}}},\qquad v_{R}={\frac {v}{v_{C}}},\quad {\hbox{and}}\quad T_{R}={\frac {T}{T_{C}}}}$, where ${\displaystyle p_{C}={\frac {a'}{27b'^{2}}},\qquad \displaystyle {v_{C}=3b'},\quad {\hbox{and}}\quad kT_{C}={\frac {8a'}{27b'}}}$ as shown by Salzman.[25] The first form of the van der Waals equation of state given above can be recast in the following reduced form: ${\displaystyle \left(p_{R}+{\frac {3}{v_{R}^{2}}}\right)(3v_{R}-1)=(8T_{R}}$) This equation is invariant for all fluids; that is, the same reduced form equation of state applies, no matter what a and b may be for the particular fluid. This invariance may also be understood in terms of the principle of corresponding states. If two fluids have the same reduced pressure, reduced volume, and reduced temperature, we say that their states are corresponding. The states of two fluids may be corresponding even if their measured pressure, volume, and temperature are very different. If the two fluids' states are corresponding, they exist in the same regime of the reduced form equation of state. Therefore, they will respond to changes in roughly the same way, even though their measurable physical characteristics may differ significantly. ### Cubic equation The van der Waals equation is a cubic equation of state; in the reduced formulation the cubic equation is: ${\displaystyle {v_{R}^{3}}-{\frac {1}{3}}\left({1+{\frac {8T_{R}}{p_{R}}}}\right){v_{R}^{2}}+{\frac {3}{p_{R}}}v_{R}-{\frac {1}{p_{R}}}=0}$ At the critical temperature, where ${\displaystyle T_{R}=p_{R}=1}$ we get as expected ${\displaystyle {v_{R}^{3}}-3v_{R}^{2}+3v_{R}-1=\left(v_{R}-1\right)^{3}=0\quad \Longleftrightarrow \quad v_{R}=1}$ For TR < 1, there are 3 values for vR. For TR > 1, there is 1 real value for vR. The solution of this equation for the case where there are three separate roots may be found at Maxwell construction ### Application to compressible fluids The equation is also usable as a PVT equation for compressible fluids (e.g. polymers). In this case specific volume changes are small and it can be written in a simplified form: ${\displaystyle (p+A)(V-B)=CT,\,}$ where p is the pressure, V is specific volume, T is the temperature and A, B, C are parameters. ## References 1. Silbey, Robert J.; Alberty, Robert A.; Bawendi, Moungi G. (2004). Physical Chemistry (4th ed.). Wiley. ISBN 978-0471215042. 2. "J. D. Van der Waals, The equation of state for gases and liquids" (PDF). Nobel Lectures, Physics 1901–1921. Amsterdam: Elsevier Publishing Company. 1967. pp. 254–265. 3. Andrews, T. (1869). "The Bakerian Lecture: On the Gaseous State of Matter". Philosophical Transactions of the Royal Society of London. 159: 575–590. doi:10.1098/rstl.1869.0021. 4. Klein, M. J. (1974). "The Historical Origins of the van der Waals Equation". Physica. 73 (1): 31. Bibcode:1974Phy....73...28K. doi:10.1016/0031-8914(74)90224-9. 5. van der Waals; J. D. (1873). Over de Continuiteit van den Gas- en Vloeistoftoestand. University of Leiden. 6. Maxwell, J.C. (1874). "Over de Continuïteit van den Gas-en Vloeistof[-]toestand, Academisch Proefschrift". Nature. 10 (259): 477–480. Bibcode:1874Natur..10..477C. doi:10.1038/010477a0. 7. Maxwell, J.C. (1890). "LXIX. Van der Waals on the Continuity of the Gaseous and Liquid States". In Niven, W. D. (ed.). The scientific papers of James Clerk Maxwell, vol II. Cambridge University Press. pp. 407–415. 8. Chang, Raymond (2014). Physical Chemistry for the Chemical Sciences. University Science Books. p. 14. ISBN 978-1891389696. 9. "Deviations from Ideal Gas Law Behavior". Purdue University. 10. Who was Van der Waals anyway and what has he to do with my Nitrox fill? 11. Mixing Rules for Simple Equations of State 12. Terrell L. Hill, 2012 [1960], "An Introduction to Statistical Thermodynamics" [Dover Books on Physics], Chicago: R.R. Donnelly (Courier/Dover), ISBN 0486130908. Note, this Donnelly edition is a reprint of the 1986 Dover edition, which itself reprinted the 1962 corrected version of the original 1960 text [Addison Wesley Series in Chemistry, Francis T. Bonner & George C. Pimentel, Eds.], Reading, MS: Addison-Wesley. 13. S. I. Sandler, "Chemical and Engineering Thermodynamics", Third Edition. New York: Wiley, 1999, p. 273. 14. Peter Atkins & Julio de Paula, 2006, "Physical chemistry", 8th Edn., pp. 17–22, 104f, 632–641, New York: Macmillan, ISBN 0716787598. 15. R. Stephen Berry, Stuart A. Rice & John Ross, 2000, "Physical Chemistry", pp. 298–306 and passim, Oxford: Oxford University Press, ISBN 0195105893 16. Ken A. Dill & Sarina Bromberg, 2003, "Molecular Driving Forces: Statistical Thermodynamics in Chemistry and Biology", pp. 457–462, New York: Garland Science, ISBN 0815320515. 17. Hill, Terrell L. (1960). An Introduction to Statistical Thermodynamics. Courier Corporation. p. 77. 18. Denker, John (2014). "Chapter 26.9, Derivation: Particle in a Box". Modern Thermodynamics. CreateSpace Independent Publishing Platform. ISBN 978-1502530356. 19. Sandler, Stanley I. (2006). Chemical, Biochemical, and Engineering Thermodynamics (4th ed.). New York: John Wiley & Sons. p. 284. ISBN 978-0-471-66174-0. 20. Sandler, Stanley I. (2006). Chemical, Biochemical, and Engineering Thermodynamics (4th ed.). New York: John Wiley & Sons. p. 287. ISBN 978-0-471-66174-0. 21. Clerk-Maxwell, J. (1875). "On the Dynamical Evidence of the Molecular Constitution of Bodies". Nature. 11 (279): 357–359. Bibcode:1875Natur..11..357C. doi:10.1038/011357a0. ISSN 0028-0836. 22. Maxwell, J.C. (1890). "LXXI. On the Dynamical Evidence of the Molecular Constitution of Bodies". In Niven, W. D. (ed.). The scientific papers of James Clerk Maxwell, vol II. Cambridge University Press. pp. 418–438. 23. Elhassan, A. E.; Craven, R.J.B.; de Reuck, K. M. (1997). "The area method for pure fluids and an analysis of the two-phase region". Fluid Phase Equilibria. 130 (1–2): 167–187. doi:10.1016/S0378-3812(96)03222-0. 24. Michael Gershenson, Date Unknown, "Lecture 16. The van der Waals Gas (Ch. 5)," unpublished course slide set from prior teaching of Physics 351, Thermal Physics (Statistics and Thermodynamics), Rutgers University, Department of Physics and Astronomy, see , accessed 25 June 2015. Possibly sourced from Daniel V. Schroeder, 2013, "An Introduction to Thermal Physics," New York: Pearson Education, ISBN 1292026219. 25. Salzman, W. R. (2004). "Critical Constants of the van der Waals Gas". Chemical Thermodynamics. Arizona State University. Retrieved 2015-07-07. • Michael Cross, 2004, Lecture 3: First Order Phase Transitions, in Physics 127: Statistical Mechanics (Second Term), Pasadena, CA: Division of Physics, Mathematics, and Astronomy, California Institute of Technology. • David Chandler, 1987, Introduction to Modern Statistical Mechanics, pp. 287–295, Oxford: Oxford University Press, ISBN 0195042778. • Charles Kittel & Herbert Kroemer, 1980, Thermal Physics, Rev. Edn., pp. 287–295, New York: Macmillan, ISBN 0716710889. • A. Dalgarno & W.D. Davison, 1966, "The calculation of van der Waals interactions," in Advances in Atomic and Molecular Physics, 1, 195. This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.	2021-01-23T12:02:23	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 66, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8328786492347717, "perplexity": 1120.079678114456}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-04/segments/1610703537796.45/warc/CC-MAIN-20210123094754-20210123124754-00510.warc.gz"}
http://dlmf.nist.gov/23.5	§23.5 Special Lattices §23.5(i) Real-Valued Functions The Weierstrass functions take real values on the real axis iff the lattice is fixed under complex conjugation: ; equivalently, when . This happens in the cases treated in the following four subsections. §23.5(ii) Rectangular Lattice This occurs when both and are real and positive. Then and the parallelogram with vertices at 0, , , is a rectangle. In this case the lattice roots , , and are real and distinct. When they are identified as in (23.3.9) 23.5.1 Also, and have opposite signs unless , in which event both are zero. As functions of , and are decreasing and is increasing. §23.5(iii) Lemniscatic Lattice This occurs when is real and positive and . The parallelogram 0, , , is a square, and 23.5.2 23.5.3 Note also that in this case . In consequence, §23.5(iv) Rhombic Lattice This occurs when is real and positive, , , and . The parallelogram 0, , , , is a rhombus: see Figure 23.5.1. The lattice root is real, and , with . and have the same sign unless when both are zero: the pseudo-lemniscatic case. As a function of the root is increasing. For the case see §23.5(v). §23.5(v) Equianharmonic Lattice This occurs when is real and positive and . The rhombus 0, , , can be regarded as the union of two equilateral triangles: see Figure 23.5.2. Figure 23.5.1: Rhombic lattice. . Symbols: : real part and , , : lattice generators Referenced by: §23.5(iv) Permalink: http://dlmf.nist.gov/23.5.F1 Encodings: pdf, png Figure 23.5.2: Equianharmonic lattice. , . Symbols: : base of exponential function and , , : lattice generators Referenced by: §23.5(v) Permalink: http://dlmf.nist.gov/23.5.F2 Encodings: pdf, png and the lattice roots and invariants are given by	2013-05-19T20:43:15	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9458032250404358, "perplexity": 2087.2867326627015}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368698080772/warc/CC-MAIN-20130516095440-00047-ip-10-60-113-184.ec2.internal.warc.gz"}
https://wikimili.com/en/Bisection	# Bisection Last updated In geometry, bisection is the division of something into two equal or congruent parts, usually by a line, which is then called a bisector. The most often considered types of bisectors are the segment bisector (a line that passes through the midpoint of a given segment) and the angle bisector (a line that passes through the apex of an angle, that divides it into two equal angles). ## Contents In three-dimensional space, bisection is usually done by a plane, also called the bisector or bisecting plane. ## Line segment bisector A line segment bisector passes through the midpoint of the segment. Particularly important is the perpendicular bisector of a segment, which, according to its name, meets the segment at right angles. The perpendicular bisector of a segment also has the property that each of its points is equidistant from the segment's endpoints. Therefore, Voronoi diagram boundaries consist of segments of such lines or planes. In classical geometry, the bisection is a simple compass and straightedge construction, whose possibility depends on the ability to draw circles of equal radii and different centers. The segment is bisected by drawing intersecting circles of equal radius, whose centers are the endpoints of the segment and such that each circle goes through one endpoint. The line determined by the points of intersection of the two circles is the perpendicular bisector of the segment, since it crosses the segment at its center. This construction is in fact used when constructing a line perpendicular to a given line at a given point: drawing an arbitrary circle whose center is that point, it intersects the line in two more points, and the perpendicular to be constructed is the one bisecting the segment defined by these two points. Brahmagupta's theorem states that if a cyclic quadrilateral is orthodiagonal (that is, has perpendicular diagonals), then the perpendicular to a side from the point of intersection of the diagonals always bisects the opposite side. Algebraically, the perpendicular bisector of a line segment with endpoints ${\displaystyle P_{1}(x_{1},y_{1})}$ and ${\displaystyle P_{2}(x_{2},y_{2})}$ is given by the equation ${\displaystyle y=m(x-x_{3})+y_{3}}$, where ${\displaystyle m=-{\frac {x_{2}-x_{1}}{y_{2}-y_{1}}}}$, ${\displaystyle x_{3}={\tfrac {1}{2}}(x_{1}+x_{2})}$, and ${\displaystyle y_{3}={\tfrac {1}{2}}(y_{1}+y_{2})}$. ## Angle bisector An angle bisector divides the angle into two angles with equal measures. An angle only has one bisector. Each point of an angle bisector is equidistant from the sides of the angle. The interior or internal bisector of an angle is the line, half-line, or line segment that divides an angle of less than 180° into two equal angles. The exterior or external bisector is the line that divides the supplementary angle (of 180° minus the original angle), formed by one side forming the original angle and the extension of the other side, into two equal angles. [1] To bisect an angle with straightedge and compass, one draws a circle whose center is the vertex. The circle meets the angle at two points: one on each leg. Using each of these points as a center, draw two circles of the same size. The intersection of the circles (two points) determines a line that is the angle bisector. The proof of the correctness of this construction is fairly intuitive, relying on the symmetry of the problem. The trisection of an angle (dividing it into three equal parts) cannot be achieved with the compass and ruler alone (this was first proved by Pierre Wantzel). The internal and external bisectors of an angle are perpendicular. If the angle is formed by the two lines given algebraically as ${\displaystyle l_{1}x+m_{1}y+n_{1}=0}$ and ${\displaystyle l_{2}x+m_{2}y+n_{2}=0,}$ then the internal and external bisectors are given by the two equations [2] :p.15 ${\displaystyle {\frac {l_{1}x+m_{1}y+n_{1}}{\sqrt {l_{1}^{2}+m_{1}^{2}}}}=\pm {\frac {l_{2}x+m_{2}y+n_{2}}{\sqrt {l_{2}^{2}+m_{2}^{2}}}}.}$ ### Triangle #### Concurrencies and collinearities The interior angle bisectors of a triangle are concurrent in a point called the incenter of the triangle, as seen in the diagram at right. The bisectors of two exterior angles and the bisector of the other interior angle are concurrent. [3] :p.149 Three intersection points, each of an external angle bisector with the opposite extended side, are collinear (fall on the same line as each other). [3] :p. 149 Three intersection points, two of them between an interior angle bisector and the opposite side, and the third between the other exterior angle bisector and the opposite side extended, are collinear. [3] :p. 149 #### Angle bisector theorem The angle bisector theorem is concerned with the relative lengths of the two segments that a triangle's side is divided into by a line that bisects the opposite angle. It equates their relative lengths to the relative lengths of the other two sides of the triangle. #### Lengths If the side lengths of a triangle are ${\displaystyle a,b,c}$, the semiperimeter ${\displaystyle s=(a+b+c)/2,}$ and A is the angle opposite side ${\displaystyle a}$, then the length of the internal bisector of angle A is [3] :p. 70 ${\displaystyle {\frac {2{\sqrt {bcs(s-a)}}}{b+c}},}$ or in trigonometric terms, [4] ${\displaystyle {\frac {2bc}{b+c}}\cos {\frac {A}{2}}.}$ If the internal bisector of angle A in triangle ABC has length ${\displaystyle t_{a}}$ and if this bisector divides the side opposite A into segments of lengths m and n, then [3] :p.70 ${\displaystyle t_{a}^{2}+mn=bc}$ where b and c are the side lengths opposite vertices B and C; and the side opposite A is divided in the proportion b:c. If the internal bisectors of angles A, B, and C have lengths ${\displaystyle t_{a},t_{b},}$ and ${\displaystyle t_{c}}$, then [5] ${\displaystyle {\frac {(b+c)^{2}}{bc}}t_{a}^{2}+{\frac {(c+a)^{2}}{ca}}t_{b}^{2}+{\frac {(a+b)^{2}}{ab}}t_{c}^{2}=(a+b+c)^{2}.}$ No two non-congruent triangles share the same set of three internal angle bisector lengths. [6] [7] #### Integer triangles There exist integer triangles with a rational angle bisector. ### Quadrilateral The internal angle bisectors of a convex quadrilateral either form a cyclic quadrilateral (that is, the four intersection points of adjacent angle bisectors are concyclic), [8] or they are concurrent. In the latter case the quadrilateral is a tangential quadrilateral. #### Rhombus Each diagonal of a rhombus bisects opposite angles. #### Ex-tangential quadrilateral The excenter of an ex-tangential quadrilateral lies at the intersection of six angle bisectors. These are the internal angle bisectors at two opposite vertex angles, the external angle bisectors (supplementary angle bisectors) at the other two vertex angles, and the external angle bisectors at the angles formed where the extensions of opposite sides intersect. ### Parabola The tangent to a parabola at any point bisects the angle between the line joining the point to the focus and the line from the point and perpendicular to the directrix. ## Bisectors of the sides of a polygon ### Triangle #### Medians Each of the three medians of a triangle is a line segment going through one vertex and the midpoint of the opposite side, so it bisects that side (though not in general perpendicularly). The three medians intersect each other at a point which is called the centroid of the triangle, which is its center of mass if it has uniform density; thus any line through a triangle's centroid and one of its vertices bisects the opposite side. The centroid is twice as close to the midpoint of any one side as it is to the opposite vertex. #### Perpendicular bisectors The interior perpendicular bisector of a side of a triangle is the segment, falling entirely on and inside the triangle, of the line that perpendicularly bisects that side. The three perpendicular bisectors of a triangle's three sides intersect at the circumcenter (the center of the circle through the three vertices). Thus any line through a triangle's circumcenter and perpendicular to a side bisects that side. In an acute triangle the circumcenter divides the interior perpendicular bisectors of the two shortest sides in equal proportions. In an obtuse triangle the two shortest sides' perpendicular bisectors (extended beyond their opposite triangle sides to the circumcenter) are divided by their respective intersecting triangle sides in equal proportions. [9] :Corollaries 5 and 6 For any triangle the interior perpendicular bisectors are given by ${\displaystyle p_{a}={\tfrac {2aT}{a^{2}+b^{2}-c^{2}}},}$${\displaystyle p_{b}={\tfrac {2bT}{a^{2}+b^{2}-c^{2}}},}$ and ${\displaystyle p_{c}={\tfrac {2cT}{a^{2}-b^{2}+c^{2}}},}$ where the sides are ${\displaystyle a\geq b\geq c}$ and the area is ${\displaystyle T.}$ [9] :Thm 2 ### Quadrilateral The two bimedians of a convex quadrilateral are the line segments that connect the midpoints of opposite sides, hence each bisecting two sides. The two bimedians and the line segment joining the midpoints of the diagonals are concurrent at a point called the "vertex centroid" and are all bisected by this point. [10] :p.125 The four "maltitudes" of a convex quadrilateral are the perpendiculars to a side through the midpoint of the opposite side, hence bisecting the latter side. If the quadrilateral is cyclic (inscribed in a circle), these maltitudes are concurrent at (all meet at) a common point called the "anticenter". Brahmagupta's theorem states that if a cyclic quadrilateral is orthodiagonal (that is, has perpendicular diagonals), then the perpendicular to a side from the point of intersection of the diagonals always bisects the opposite side. The perpendicular bisector construction forms a quadrilateral from the perpendicular bisectors of the sides of another quadrilateral. ## Area bisectors and perimeter bisectors ### Triangle There are an infinitude of lines that bisect the area of a triangle. Three of them are the medians of the triangle (which connect the sides' midpoints with the opposite vertices), and these are concurrent at the triangle's centroid; indeed, they are the only area bisectors that go through the centroid. Three other area bisectors are parallel to the triangle's sides; each of these intersects the other two sides so as to divide them into segments with the proportions ${\displaystyle {\sqrt {2}}+1:1}$. [11] These six lines are concurrent three at a time: in addition to the three medians being concurrent, any one median is concurrent with two of the side-parallel area bisectors. The envelope of the infinitude of area bisectors is a deltoid (broadly defined as a figure with three vertices connected by curves that are concave to the exterior of the deltoid, making the interior points a non-convex set). [11] The vertices of the deltoid are at the midpoints of the medians; all points inside the deltoid are on three different area bisectors, while all points outside it are on just one. The sides of the deltoid are arcs of hyperbolas that are asymptotic to the extended sides of the triangle. [11] The ratio of the area of the envelope of area bisectors to the area of the triangle is invariant for all triangles, and equals ${\displaystyle {\tfrac {3}{4}}\log _{e}(2)-{\tfrac {1}{2}},}$ i.e. 0.019860... or less than 2%. A cleaver of a triangle is a line segment that bisects the perimeter of the triangle and has one endpoint at the midpoint of one of the three sides. The three cleavers concur at (all pass through) the center of the Spieker circle, which is the incircle of the medial triangle. The cleavers are parallel to the angle bisectors. A splitter of a triangle is a line segment having one endpoint at one of the three vertices of the triangle and bisecting the perimeter. The three splitters concur at the Nagel point of the triangle. Any line through a triangle that splits both the triangle's area and its perimeter in half goes through the triangle's incenter (the center of its incircle). There are either one, two, or three of these for any given triangle. A line through the incenter bisects one of the area or perimeter if and only if it also bisects the other. [12] ### Parallelogram Any line through the midpoint of a parallelogram bisects the area [13] and the perimeter. ### Circle and ellipse All area bisectors and perimeter bisectors of a circle or other ellipse go through the center, and any chords through the center bisect the area and perimeter. In the case of a circle they are the diameters of the circle. ## Bisectors of diagonals ### Parallelogram The diagonals of a parallelogram bisect each other. ### Quadrilateral If a line segment connecting the diagonals of a quadrilateral bisects both diagonals, then this line segment (the Newton Line) is itself bisected by the vertex centroid. ## Volume bisectors A plane that divides two opposite edges of a tetrahedron in a given ratio also divides the volume of the tetrahedron in the same ratio. Thus any plane containing a bimedian (connector of opposite edges' midpoints) of a tetrahedron bisects the volume of the tetrahedron [14] [15] :pp.89–90 ## Related Research Articles A quadrilateral is a polygon in Euclidean plane geometry with four edges (sides) and four vertices (corners). Other names for quadrilateral include quadrangle, tetragon, and 4-gon. A quadrilateral with vertices , , and is sometimes denoted as . A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted . In elementary geometry, the property of being perpendicular (perpendicularity) is the relationship between two lines which meet at a right angle. The property extends to other related geometric objects. In Euclidean geometry, a parallelogram is a simple (non-self-intersecting) quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure. The congruence of opposite sides and opposite angles is a direct consequence of the Euclidean parallel postulate and neither condition can be proven without appealing to the Euclidean parallel postulate or one of its equivalent formulations. In plane Euclidean geometry, a rhombus is a quadrilateral whose four sides all have the same length. Another name is equilateral quadrilateral, since equilateral means that all of its sides are equal in length. The rhombus is often called a diamond, after the diamonds suit in playing cards which resembles the projection of an octahedral diamond, or a lozenge, though the former sometimes refers specifically to a rhombus with a 60° angle, and the latter sometimes refers specifically to a rhombus with a 45° angle. In mathematics and physics, the centroid or geometric center of a plane figure is the arithmetic mean position of all the points in the figure. Informally, it is the point at which a cutout of the shape could be perfectly balanced on the tip of a pin. In Euclidean geometry, a cyclic quadrilateral or inscribed quadrilateral is a quadrilateral whose vertices all lie on a single circle. This circle is called the circumcircle or circumscribed circle, and the vertices are said to be concyclic. The center of the circle and its radius are called the circumcenter and the circumradius respectively. Other names for these quadrilaterals are concyclic quadrilateral and chordal quadrilateral, the latter since the sides of the quadrilateral are chords of the circumcircle. Usually the quadrilateral is assumed to be convex, but there are also crossed cyclic quadrilaterals. The formulas and properties given below are valid in the convex case. In Euclidean geometry, a convex quadrilateral with at least one pair of parallel sides is referred to as a trapezium in English outside North America, but as a trapezoid in American and Canadian English. The parallel sides are called the bases of the trapezoid and the other two sides are called the legs or the lateral sides. A scalene trapezoid is a trapezoid with no sides of equal measure, in contrast to the special cases below. In geometry, the Euler line, named after Leonhard Euler, is a line determined from any triangle that is not equilateral. It is a central line of the triangle, and it passes through several important points determined from the triangle, including the orthocenter, the circumcenter, the centroid, the Exeter point and the center of the nine-point circle of the triangle. In geometry, the midpoint is the middle point of a line segment. It is equidistant from both endpoints, and it is the centroid both of the segment and of the endpoints. It bisects the segment. In geometry, a set of points are said to be concyclic if they lie on a common circle. All concyclic points are at the same distance from the center of the circle. Three points in the plane that do not all fall on a straight line are concyclic, but four or more such points in the plane are not necessarily concyclic. In Euclidean geometry, an isosceles trapezoid is a convex quadrilateral with a line of symmetry bisecting one pair of opposite sides. It is a special case of a trapezoid. Alternatively, it can be defined as a trapezoid in which both legs and both base angles are of the same measure. Note that a non-rectangular parallelogram is not an isosceles trapezoid because of the second condition, or because it has no line of symmetry. In any isosceles trapezoid, two opposite sides are parallel, and the two other sides are of equal length. The diagonals are also of equal length. The base angles of an isosceles trapezoid are equal in measure. In geometry, a square is a regular quadrilateral, which means that it has four equal sides and four equal angles. It can also be defined as a rectangle in which two adjacent sides have equal length. A square with vertices ABCD would be denoted ABCD. In geometry, a median of a triangle is a line segment joining a vertex to the midpoint of the opposite side, thus bisecting that side. Every triangle has exactly three medians, one from each vertex, and they all intersect each other at the triangle's centroid. In the case of isosceles and equilateral triangles, a median bisects any angle at a vertex whose two adjacent sides are equal in length. Lines in a plane or higher-dimensional space are said to be concurrent if they intersect at a single point. In geometry, collinearity of a set of points is the property of their lying on a single line. A set of points with this property is said to be collinear. In greater generality, the term has been used for aligned objects, that is, things being "in a line" or "in a row". In Euclidean geometry, a tangential quadrilateral or circumscribed quadrilateral is a convex quadrilateral whose sides all can be tangent to a single circle within the quadrilateral. This circle is called the incircle of the quadrilateral or its inscribed circle, its center is the incenter and its radius is called the inradius. Since these quadrilaterals can be drawn surrounding or circumscribing their incircles, they have also been called circumscribable quadrilaterals, circumscribing quadrilaterals, and circumscriptible quadrilaterals. Tangential quadrilaterals are a special case of tangential polygons. Varignon's theorem is a statement in Euclidean geometry, that deals with the construction of a particular parallelogram, the Varignon parallelogram, from an arbitrary quadrilateral (quadrangle). It is named after Pierre Varignon, whose proof was published posthumously in 1731. In geometry, a line segment is a part of a line that is bounded by two distinct end points, and contains every point on the line between its endpoints. A closed line segment includes both endpoints, while an open line segment excludes both endpoints; a half-open line segment includes exactly one of the endpoints. In geometry, a line segment is often denoted using a line above the symbols for the two endpoints. In Euclidean geometry, an orthodiagonal quadrilateral is a quadrilateral in which the diagonals cross at right angles. In other words, it is a four-sided figure in which the line segments between non-adjacent vertices are orthogonal (perpendicular) to each other. ## References 1. Spain, Barry. Analytical Conics, Dover Publications, 2007 (orig. 1957). 2. Johnson, Roger A., Advanced Euclidean Geometry, Dover Publ., 2007 (orig. 1929). 3. Oxman, Victor. "On the existence of triangles with given lengths of one side and two adjacent angle bisectors", Forum Geometricorum 4, 2004, 215–218. http://forumgeom.fau.edu/FG2004volume4/FG200425.pdf 4. Simons, Stuart. Mathematical Gazette 93, March 2009, 115-116. 5. Mironescu, P., and Panaitopol, L., "The existence of a triangle with prescribed angle bisector lengths", American Mathematical Monthly 101 (1994): 58–60. 6. Weisstein, Eric W. "Quadrilateral." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/Quadrilateral.html 7. Mitchell, Douglas W. (2013), "Perpendicular Bisectors of Triangle Sides", Forum Geometricorum 13, 53-59. http://forumgeom.fau.edu/FG2013volume13/FG201307.pdf 8. Altshiller-Court, Nathan, College Geometry, Dover Publ., 2007. 9. Dunn, J. A., and Pretty, J. E., "Halving a triangle," Mathematical Gazette 56, May 1972, 105-108. 10. Kodokostas, Dimitrios, "Triangle Equalizers," Mathematics Magazine 83, April 2010, pp. 141-146. 11. Dunn, J. A., and J. E. Pretty, "Halving a triangle", Mathematical Gazette 56, May 1972, p. 105. 12. Weisstein, Eric W. "Tetrahedron." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/Tetrahedron.html 13. Altshiller-Court, N. "The tetrahedron." Ch. 4 in Modern Pure Solid Geometry: Chelsea, 1979. • The Angle Bisector at cut-the-knot • Angle Bisector definition. Math Open Reference With interactive applet • Line Bisector definition. Math Open Reference With interactive applet • Perpendicular Line Bisector. With interactive applet • Animated instructions for bisecting an angle and bisecting a line Using a compass and straightedge • Weisstein, Eric W. "Line Bisector". MathWorld . This article incorporates material from Angle bisector on PlanetMath, which is licensed under the Creative Commons Attribution/Share-Alike License.	2021-04-10T11:56:17	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 26, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5656726360321045, "perplexity": 416.8709978857605}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618038056869.3/warc/CC-MAIN-20210410105831-20210410135831-00315.warc.gz"}
https://libstdc.com/us/q/stats/29325	### What is the difference between linear regression and logistic regression? • What is the difference between linear regression and logistic regression? When would you use each? In the linear regression model the dependent variable $y$ is considered continuous, whereas in logistic regression it is categorical, i.e., discrete. In application, the former is used in regression settings while the latter is used for binary classification or multi-class classification (where it is called multinomial logistic regression). Although written in a different context, it may help you to read my answer here: Difference between logit and probit models, which contains a lot of information about what's happening in logistic regression that may help you understand these better. All the previous answers are right, but there are reasons you might favor a linear regression model even when your outcome is a dichotomy. I've written about these reasons here: http://statisticalhorizons.com/linear-vs-logistic • DocBuckets Correct answer 8 years ago Linear regression uses the general linear equation $Y=b_0+∑(b_i X_i)+\epsilon$ where $Y$ is a continuous dependent variable and independent variables $X_i$ are usually continuous (but can also be binary, e.g. when the linear model is used in a t-test) or other discrete domains. $\epsilon$ is a term for the variance that is not explained by the model and is usually just called "error". Individual dependent values denoted by $Y_j$ can be solved by modifying the equation a little: $Y_j=b_0 + \sum{(b_i X_{ij})+\epsilon_j}$ Logistic regression is another generalized linear model (GLM) procedure using the same basic formula, but instead of the continuous $Y$, it is regressing for the probability of a categorical outcome. In simplest form, this means that we're considering just one outcome variable and two states of that variable- either 0 or 1. The equation for the probability of $Y=1$ looks like this: $$P(Y=1) = {1 \over 1+e^{-(b_0+\sum{(b_iX_i)})}}$$ Your independent variables $X_i$ can be continuous or binary. The regression coefficients $b_i$ can be exponentiated to give you the change in odds of $Y$ per change in $X_i$, i.e., $Odds={P(Y=1) \over P(Y=0)}={P(Y=1) \over 1-P(Y=1)}$ and ${\Delta Odds}= e^{b_i}$. $\Delta Odds$ is called the odds ratio, $Odds(X_i+1)\over Odds(X_i)$. In English, you can say that the odds of $Y=1$ increase by a factor of $e^{b_i}$ per unit change in $X_i$. Example: If you wanted to see how body mass index predicts blood cholesterol (a continuous measure), you'd use linear regression as described at the top of my answer. If you wanted to see how BMI predicts the odds of being a diabetic (a binary diagnosis), you'd use logistic regression. This looks like a fine answer, but could you explain what the $\epsilon_i$ stand for and--in particular--why you include them within the summations? (What is being summed over, anyway?) It looks to me Bill that he meant to write i.e. (Latin abbreviation for that is) rather than e. i. But the εi in the summation of the exponent shouldn't be there. It looks like the noise term in the model was accidentally carried there. The only summing should be over the bis that represent the p coefficients for the p covariates. Oops, you're right. Fixing it now. There's an error in your expression for $P(Y=1)$. You should have $$P(Y=1) = \frac{1}{1 + \exp \{-X \boldsymbol{\beta} \} },$$ not $$P(Y=1) = \frac{1}{1 + \exp \{ -(X \boldsymbol{\beta}+\varepsilon) \} }$$ The randomness in a logistic regression model comes from the fact that these are bernoulli trials, not from there being errors in the success probabilities (which is how you're written it). For logistic regression, shouldn't the GLM stand for generalized linear model, not general? its unclear to me why logistic regression is necessarily binary while linear is continuous. Any explanation? @samthebrand logistic regression is not binary per se. It can be used to model data with a binary response via probabilities that range between 0 and 1. Going to shamelessly plug my blog post on this which should clear your confusion. • Linear Regression is used to establish a relationship between Dependent and Independent variables, which is useful in estimating the resultant dependent variable in case independent variable change. For example: Using a Linear Regression, the relationship between Rain (R) and Umbrella Sales (U) is found to be - U = 2R + 5000 This equation says that for every 1mm of Rain, there is a demand for 5002 umbrellas. So, using Simple Regression, you can estimate the value of your variable. Logistic Regression on the other hand is used to ascertain the probability of an event. And this event is captured in binary format, i.e. 0 or 1. Example - I want to ascertain if a customer will buy my product or not. For this, I would run a Logistic Regression on the (relevant) data and my dependent variable would be a binary variable (1=Yes; 0=No). In terms of graphical representation, Linear Regression gives a linear line as an output, once the values are plotted on the graph. Whereas, the logistic regression gives an S-shaped line Reference from Mohit Khurana. Re: "Linear Regression is used to establish a relationship between Dependent and Indipendent variables" - this is also true about logistic regression - it's just that the dependent variable is binary. Logistic Regression isn't only for predicting a binary event ($2$ classes). It can be generalized to $k$ classes (multinomial logistic regression) • The differences have been settled by DocBuckets and Pardis, but I want to add one way to compare their performance not mentioned. Linear regression is usually solved by minimizing the least squares error of the model to the data, therefore large errors are penalized quadratically. Logistic regression is just the opposite. Using the logistic loss function causes large errors to be penalized to an asymptotically constant. Consider linear regression on a categorical {0,1} outcomes to see why this is a problem. If your model predicts the outcome is 38 when truth is 1, you've lost nothing. Linear regression would try to reduce that 38, logistic wouldn't (as much). Wre then, the situations/cases that _are_ penalized in a logistic, i.e., in what cases would we have a poor fit? Just the opposite: whenever larger deviations from the fit actually do incur worse results. For instance, logistic regression is good at keeping you at hitting a dart board, but can't make a bullseye look nice. Or, similarly, thinks that a near miss of the board is the same as sticking your neighbor. Great answer. Was there any research done how much does it hurt model's performance? I mean if a linear regression was used to predict response={0,1} instead of a logistic regression. License under CC-BY-SA with attribution Content dated before 6/26/2020 9:53 AM • {{ error }}	2021-04-11T12:39:28	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7146804332733154, "perplexity": 538.3805509209683}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618038062492.5/warc/CC-MAIN-20210411115126-20210411145126-00023.warc.gz"}
https://www.mcs.anl.gov/research/projects/otc/InteriorPoint/abstracts/Yao-Zhang-Zhou-1.html	## LQ Control without Riccati Equations: Stochastic Systems ### David D. Yao, Shuzhong Zhang, Xun Yu Zhou We study stochastic linear-quadratic (LQ) optimal control problems over an infinite horizon, allowing the cost matrices to be indefinite. We develop a systematic approach based on semidefinite programming (SDP). A central issue is the stability of the feedback control; and we show this can be effectively examined through the complementary duality of the SDP. Furthermore, we establish several implication relations among the SDP complementary duality, the (generalized) Riccati equation, and the optimality of the LQ control problem. Based on these relations, we propose a numerical procedure that provides a thorough treatment of the LQ control problem via SDP: it identifies a stabilizing feedback control that is optimal or determines that the problem possesses no optimal solution. For the latter case, we develop an $\epsilon$-approximation scheme that is asymptotically optimal. Econometric Institute Report EI9920/A, Erasmus University Rotterdam, P.O. Box 1738, 3000 DR Rotterdam, The Netherlands, April, 1999. Contact: [email protected]	2021-09-19T16:10:36	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.692857027053833, "perplexity": 1058.1506567450813}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780056892.13/warc/CC-MAIN-20210919160038-20210919190038-00355.warc.gz"}
https://par.nsf.gov/biblio/10390096-jwst-imaging-cartwheel-galaxy-reveals-dust-associated-sn	JWST Imaging of the Cartwheel Galaxy Reveals Dust Associated with SN 2021afdx Abstract We present near- and mid-infrared (0.9–18μm) photometry of supernova (SN) 2021afdx, which was imaged serendipitously with the James Webb Space Telescope (JWST) as part of its Early Release Observations of the Cartwheel Galaxy. Our ground-based optical observations show it is likely to be a Type IIb SN, the explosion of a yellow supergiant, and its infrared spectral energy distribution (SED) ≈200 days after explosion shows two distinct components, which we attribute to hot ejecta and warm dust. By fitting models of dust emission to the SED, we derive a dust mass of$(3.8−0.3+0.5)×10−3M⊙$, which is the highest yet observed in a Type IIb SN but consistent with other Type II SNe observed by the Spitzer Space Telescope. We also find that the radius of the dust is significantly larger than the radius of the ejecta, as derived from spectroscopic velocities during the photospheric phase, which implies that we are seeing an infrared echo off of preexisting dust in the progenitor environment, rather than dust newly formed by the SN. Our results show the power of JWST to address questions of dust formation in SNe, and therefore the presence of dust in the early universe, more » Authors: ; ; ; ; ; ; ; ; ; ; ; ; ; ; Publication Date: NSF-PAR ID: 10390096 Journal Name: The Astrophysical Journal Letters Volume: 942 Issue: 1 Page Range or eLocation-ID: Article No. L18 ISSN: 2041-8205 Publisher: DOI PREFIX: 10.3847 National Science Foundation ##### More Like this 1. Abstract We present maps tracing the fraction of dust in the form of polycyclic aromatic hydrocarbons (PAHs) in IC 5332, NGC 628, NGC 1365, and NGC 7496 from JWST/MIRI observations. We trace the PAH fraction by combining the F770W (7.7μm) and F1130W (11.3μm) filters to track ionized and neutral PAH emission, respectively, and comparing the PAH emission to F2100W, which traces small, hot dust grains. We find the averageRPAH= (F770W + F1130W)/F2100W values of 3.3, 4.7, 5.1, and 3.6 in IC 5332, NGC 628, NGC 1365, and NGC 7496, respectively. We find that Hiiregions traced by MUSE Hαshow a systematically low PAH fraction. The PAH fraction remains relatively constant across other galactic environments, with slight variations. We use CO+Hi+Hαto trace the interstellar gas phase and find that the PAH fraction decreases above a value of$IHα/ΣHI+H2∼1037.5ergs−1kpc−2(M⊙pc−2)−1$in all four galaxies. Radial profiles also show a decreasing PAH fraction with increasing radius, correlated with lower metallicity, in line with previous results showing a strong metallicity dependence to the PAH fraction. Our results suggest that the process of PAH destruction in ionized gas operates similarlymore » 2. Abstract We present a multiwavelength analysis of the galaxy cluster SPT-CL J0607-4448 (SPT0607), which is one of the most distant clusters discovered by the South Pole Telescope atz= 1.4010 ± 0.0028. The high-redshift cluster shows clear signs of being relaxed with well-regulated feedback from the active galactic nucleus (AGN) in the brightest cluster galaxy (BCG). Using Chandra X-ray data, we construct thermodynamic profiles and determine the properties of the intracluster medium. The cool-core nature of the cluster is supported by a centrally peaked density profile and low central entropy ($K0=18−9+11$keV cm2), which we estimate assuming an isothermal temperature profile due to the limited spectral information given the distance to the cluster. Using the density profile and gas cooling time inferred from the X-ray data, we find a mass-cooling rate$Ṁcool=100−60+90M⊙$yr−1. From optical spectroscopy and photometry around the [Oii] emission line, we estimate that the BCG star formation rate is$SFR[OII]=1.7−0.6+1.0M⊙$yr−1, roughly two orders of magnitude lower than the predicted mass-cooling rate. In addition, using ATCA radio data at 2.1 GHz, we measure a radio jet power$Pcav=3.2−1.3+2.1×1044$erg s−1, which is consistent withmore » 3. Abstract We present the characteristics of 2 mm selected sources from the largest Atacama Large Millimeter/submillimeter Array (ALMA) blank-field contiguous survey conducted to date, the Mapping Obscuration to Reionization with ALMA (MORA) survey covering 184 arcmin2at 2 mm. Twelve of 13 detections above 5σare attributed to emission from galaxies, 11 of which are dominated by cold dust emission. These sources have a median redshift of$〈z2mm〉=3.6−0.3+0.4$primarily based on optical/near-infrared photometric redshifts with some spectroscopic redshifts, with 77% ± 11% of sources atz> 3 and 38% ± 12% of sources atz> 4. This implies that 2 mm selection is an efficient method for identifying the highest-redshift dusty star-forming galaxies (DSFGs). Lower-redshift DSFGs (z< 3) are far more numerous than those atz> 3 yet are likely to drop out at 2 mm. MORA shows that DSFGs with star formation rates in excess of 300Myr−1and a relative rarity of ∼10−5Mpc−3contribute ∼30% to the integrated star formation rate density at 3 <z< 6. The volume density of 2 mm selected DSFGs is consistent with predictions from some cosmological simulations and is similar to the volume density of their hypothesized descendants: massive, quiescent galaxies atz> 2. Analysis of MORA sources’more » 4. Abstract The genericity of Arnold diffusion in the analytic category is an open problem. In this paper, we study this problem in the followinga prioriunstable Hamiltonian system with a time-periodic perturbation$Hε(p,q,I,φ,t)=h(I)+∑i=1n±12pi2+Vi(qi)+εH1(p,q,I,φ,t),$where$(p,q)∈Rn×Tn$,$(I,φ)∈Rd×Td$withn,d⩾ 1,Viare Morse potentials, andɛis a small non-zero parameter. The unperturbed Hamiltonian is not necessarily convex, and the induced inner dynamics does not need to satisfy a twist condition. Using geometric methods we prove that Arnold diffusion occurs for generic analytic perturbationsH1. Indeed, the set of admissibleH1isCωdense andC3open (a fortiori,Cωopen). Our perturbative technique for the genericity is valid in theCktopology for allk∈ [3, ∞) ∪ {∞,ω}. 5. Abstract We present the discovery of the first millimeter afterglow of a short-durationγ-ray burst (SGRB) and the first confirmed afterglow of an SGRB localized by the GUANO system on Swift. Our Atacama Large Millimeter/Sub-millimeter Array (ALMA) detection of SGRB 211106A establishes an origin in a faint host galaxy detected in Hubble Space Telescope imaging at 0.7 ≲z≲ 1.4. From the lack of a detectable optical afterglow, coupled with the bright millimeter counterpart, we infer a high extinction,AV≳ 2.6 mag along the line of sight, making this one of the most highly dust-extincted SGRBs known to date. The millimeter-band light curve captures the passage of the synchrotron peak from the afterglow forward shock and reveals a jet break at$tjet=29.2−4.0+4.5$days. For a presumed redshift ofz= 1, we infer an opening angle,θjet= (15.°5 ± 1.°4), and beaming-corrected kinetic energy of$log(EK/erg)=51.8±0.3$, making this one of the widest and most energetic SGRB jets known to date. Combining all published millimeter-band upper limits in conjunction with the energetics for a large sample of SGRBs, we find that energetic outflows in high-density environments are more likely to have detectable millimeter counterparts. Concerted afterglow searches with ALMA shouldmore »	2023-03-22T14:14:48	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 14, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5849252343177795, "perplexity": 4447.690855039798}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296943809.76/warc/CC-MAIN-20230322114226-20230322144226-00131.warc.gz"}
http://pdglive.lbl.gov/Particle.action?init=0&node=M166&home=MXXX005	LIGHT UNFLAVORED MESONS($\boldsymbol S$ = $\boldsymbol C$ = $\boldsymbol B$ = 0) For $\mathit I = 1$ (${{\mathit \pi}}$, ${{\mathit b}}$, ${{\mathit \rho}}$, ${{\mathit a}}$): ${\mathit {\mathit u}}$ ${\mathit {\overline{\mathit d}}}$, ( ${\mathit {\mathit u}}$ ${\mathit {\overline{\mathit u}}}−$ ${\mathit {\mathit d}}$ ${\mathit {\overline{\mathit d}}})/\sqrt {2 }$, ${\mathit {\mathit d}}$ ${\mathit {\overline{\mathit u}}}$;for $\mathit I = 0$ (${{\mathit \eta}}$, ${{\mathit \eta}^{\,'}}$, ${{\mathit h}}$, ${{\mathit h}^{\,'}}$, ${{\mathit \omega}}$, ${{\mathit \phi}}$, ${{\mathit f}}$, ${{\mathit f}^{\,'}}$): ${\mathit {\mathit c}}_{{\mathrm {1}}}$( ${{\mathit u}}{{\overline{\mathit u}}}$ $+$ ${{\mathit d}}{{\overline{\mathit d}}}$ ) $+$ ${\mathit {\mathit c}}_{{\mathrm {2}}}$( ${{\mathit s}}{{\overline{\mathit s}}}$ ) INSPIRE search # ${{\boldsymbol h}_{{1}}{(1595)}}$ $I^G(J^{PC})$ = $0^-(1^{+ -})$ Seen in a partial-wave analysis of the ${{\mathit \omega}}{{\mathit \eta}}$ system produced in the reaction ${{\mathit \pi}^{-}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit \omega}}{{\mathit \eta}}{{\mathit n}}$ at 18$~$GeV/$\mathit c$. ${{\mathit h}_{{1}}{(1595)}}$ MASS $1594 {}^{+18}_{-60}$ MeV ${{\mathit h}_{{1}}{(1595)}}$ WIDTH $384 {}^{+90}_{-120}$ MeV $\Gamma_{1}$ ${{\mathit \omega}}{{\mathit \eta}}$ seen 434	2020-02-27T06:26:22	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9955834150314331, "perplexity": 634.5067429529372}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-10/segments/1581875146647.82/warc/CC-MAIN-20200227033058-20200227063058-00172.warc.gz"}
https://www.usgs.gov/center-news/volcano-watch-light-shed-many-mauna-loas-mysteries-under-sea	# Volcano Watch — Light is shed on many of Mauna Loa's mysteries from under the sea Release Date: Earth scientists know a lot about Mauna Loa above sea level but much less about it under water. Studies have naturally focused on the easily accessible island, where one can directly observe and sample rock exposures, gauge the time between eruptions, and trace evolutionary changes in the chemical makeup of the lava flows. Earth scientists know a lot about Mauna Loa above sea level but much less about it under water. Studies have naturally focused on the easily accessible island, where one can directly observe and sample rock exposures, gauge the time between eruptions, and trace evolutionary changes in the chemical makeup of the lava flows. Unfortunately, though, such exposures are rarely more than 300 m (1,000 ft) thick. Consequently we can easily study only the most recent activity--that of the past few thousand years. To learn about most of Mauna Loa's history, we must go under water. The submarine flanks of Mauna Loa have received little attention, because of their difficult access. That is changing, however, as technology advances. Early this year, scientists from the Universities of Hawaii, Massachusetts, and Tasmania teamed up with colleagues from Woods Hole Oceanographic Institute and the Hawaiian Volcano Observatory to look at Mauna Loa's submarine flanks, using an oceanographic research vessel. Some readers may have noticed a ship cruising back and forth off South Point and south Kona during mid-January. The ship was the modern, fully equipped research vessel, Moana Wave, owned by the University of Hawaii. What do the researchers hope to discover? Some want to determine the chemical composition of the plume that carries magma from its deep mantle source up into Mauna Loa. Others are interested in the shallow volcanic plumbing system and the movement of magma within Mauna Loa. Still others are interested in comparing and contrasting the development of the submarine flanks to that of the on-land portion. Are the flanks below sea level comprised of broken rubble that may favor the development of large landslides? The ship-board scientists dredged the flanks of the volcano in order to collect rock samples for chemical analysis and volcanologic study. Previous investigators discovered giant submarine landslides on Mauna Loa. The slides give us an opportunity to sample the interior of a Hawaiian volcano by, in essence, bringing the mountain piecemeal to Mohammed. From outcrops made by the landslides, we collected samples that will enable us to explore Mauna Loa's history for 200,000 years earlier than we now can. What did the scientists find? In ten days, 27 dredge hauls were recovered at water depths from 1,600 m (5,250 ft) to over 4,500 m (14,750 ft) on the south and west flanks. In general, rocks collected from the submarine extension of the southwest rift zone are rich in the heavy green mineral olivine. As we moved west and northwest, away from the rift zone, the olivine abundance decreases in the lava flows. Landslide debris was dredged on the south and west flanks of the volcano; this debris includes parts of lava flows that had been erupted on land and carried out to sea by the slides. We also dredged samples that probably erupted from nearby vents far from a rift zone. Several preliminary interpretations have been reached. Olivine-rich lava off South Point is supplied from deep within Mauna Loa's plumbing system. There the magma is hotter than that above and may contain heavy crystals of olivine that sank to those depths before erupting. The rest of the remaining lava, cooler before eruption and poorer in olivine because of settling, is supplied from higher levels in the magma storage system. The recovery of rocks erupted above sea level but collected on the sea floor far from shoreline verifies that landslides have carried parts of the island into the sea. From this research, the scientific team will gain greater appreciation for how Hawaiian volcanoes grow and develop. Laboratory work on the recovered samples is underway to disclose Mauna Loa's secrets more fully. Comment: Three incorrect changes were made by the Trib to last week's Volcano Watch. The distance that imposes the natural quarantine is 2000 miles. The non-native bird is spelled mejiro. The third felt earthquake, also a magnitude-4.0, was felt at 12:52 p.m. by residents of Hilo, Papaikou, and Puna on March 18. ### Volcano Activity Update Eruptive activity from the Puu O`o vent of Kīlauea Volcano continued unabated during the past week. Lava is flowing away from the vent through a network of tubes to the ocean near Kamokuna and extending the coastline. The public is reminded that the ocean entry areas are extremely hazardous, with frequent explosive activity and occasional collapse of the new land. The steam clouds are highly acidic and laced with glass particles. There were no felt earthquakes since March 18.	2020-08-04T12:14:42	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.27438825368881226, "perplexity": 4854.223805510468}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-34/segments/1596439735867.93/warc/CC-MAIN-20200804102630-20200804132630-00026.warc.gz"}
http://dlmf.nist.gov/23.18	§23.18 Modular Transformations Elliptic Modular Function $\lambda\left(\mathcal{A}\tau\right)$ equals 23.18.1 $\lambda\left(\tau\right),$ $1-\lambda\left(\tau\right),$ $\frac{1}{\lambda\left(\tau\right)},$ $\frac{1}{1-\lambda\left(\tau\right)},$ $\frac{\lambda\left(\tau\right)}{\lambda\left(\tau\right)-1},$ $1-\frac{1}{\lambda\left(\tau\right)},$ ⓘ Symbols: $\lambda\left(\NVar{\tau}\right)$: elliptic modular function and $\tau$: complex variable Permalink: http://dlmf.nist.gov/23.18.E1 Encodings: TeX, TeX, TeX, TeX, TeX, TeX, pMML, pMML, pMML, pMML, pMML, pMML, png, png, png, png, png, png See also: Annotations for 23.18, 23.18 and 23 according as the elements $\begin{bmatrix}a&b\\ c&d\end{bmatrix}$ of $\mathcal{A}$ in (23.15.3) have the respective forms 23.18.2 $\begin{bmatrix}\mathrm{o}&\mathrm{e}\\ \mathrm{e}&\mathrm{o}\end{bmatrix},$ $\begin{bmatrix}\mathrm{e}&\mathrm{o}\\ \mathrm{o}&\mathrm{e}\end{bmatrix},$ $\begin{bmatrix}\mathrm{o}&\mathrm{e}\\ \mathrm{o}&\mathrm{o}\end{bmatrix},$ $\begin{bmatrix}\mathrm{e}&\mathrm{o}\\ \mathrm{o}&\mathrm{o}\end{bmatrix},$ $\begin{bmatrix}\mathrm{o}&\mathrm{o}\\ \mathrm{e}&\mathrm{o}\end{bmatrix},$ $\begin{bmatrix}\mathrm{o}&\mathrm{o}\\ \mathrm{o}&\mathrm{e}\end{bmatrix}.$ ⓘ Symbols: e: even integers and o: odd integers Permalink: http://dlmf.nist.gov/23.18.E2 Encodings: TeX, TeX, TeX, TeX, TeX, TeX, pMML, pMML, pMML, pMML, pMML, pMML, png, png, png, png, png, png See also: Annotations for 23.18, 23.18 and 23 Here e and o are generic symbols for even and odd integers, respectively. In particular, if $a-1,b,c$, and $d-1$ are all even, then 23.18.3 $\lambda\left(\mathcal{A}\tau\right)=\lambda\left(\tau\right),$ ⓘ Symbols: $\lambda\left(\NVar{\tau}\right)$: elliptic modular function, $\tau$: complex variable and $\mathcal{A}$: bilinear transformation Permalink: http://dlmf.nist.gov/23.18.E3 Encodings: TeX, pMML, png See also: Annotations for 23.18, 23.18 and 23 and $\lambda\left(\tau\right)$ is a cusp form of level zero for the corresponding subgroup of SL$(2,\mathbb{Z})$. Klein’s Complete Invariant 23.18.4 $J\left(\mathcal{A}\tau\right)=J\left(\tau\right).$ ⓘ Symbols: $J\left(\NVar{\tau}\right)$: Klein’s complete invariant, $\tau$: complex variable and $\mathcal{A}$: bilinear transformation Referenced by: §23.18 Permalink: http://dlmf.nist.gov/23.18.E4 Encodings: TeX, pMML, png See also: Annotations for 23.18, 23.18 and 23 $J\left(\tau\right)$ is a modular form of level zero for SL$(2,\mathbb{Z})$. Dedekind’s Eta Function 23.18.5 $\eta\left(\mathcal{A}\tau\right)=\varepsilon(\mathcal{A})\left(-i(c\tau+d)% \right)^{1/2}\eta\left(\tau\right),$ where the square root has its principal value and 23.18.6 $\varepsilon(\mathcal{A})=\exp\left(\pi i\left(\frac{a+d}{12c}+s(-d,c)\right)% \right),$ 23.18.7 ${s(d,c)=\sum_{r=1}^{c-1}\frac{r}{c}\left(\frac{dr}{c}-\left\lfloor\frac{dr}{c}% \right\rfloor-\frac{1}{2}\right),}$ $c>0$. ⓘ Symbols: $\left\lfloor\NVar{x}\right\rfloor$: floor of $x$, $\left(\NVar{m},\NVar{n}\right)$: greatest common divisor (gcd), $c$: integer and $d$: integer Referenced by: §23.18, Equation (23.18.7) Permalink: http://dlmf.nist.gov/23.18.E7 Encodings: TeX, pMML, png Errata (effective with 1.0.11): Originally the sum $\sum_{r=1}^{c-1}$ was written with an additional constraint on the summation, that $\left(r,c\right)=1$. This additional condition was incorrect and has been removed. Reported 2015-10-05 by Howard Cohl and Tanay Wakhare See also: Annotations for 23.18, 23.18 and 23 Here $s(d,c)$ is a Dedekind sum. See (27.14.11), §27.14(iii), §27.14(iv) and Apostol (1990, pp. 48 and 51–53). Note that $\eta\left(\tau\right)$ is of level $\tfrac{1}{2}$.	2017-09-21T17:47:23	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 58, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9835489988327026, "perplexity": 13106.713077480095}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-39/segments/1505818687834.17/warc/CC-MAIN-20170921172227-20170921192227-00157.warc.gz"}
https://www.itl.nist.gov/div898/software/dataplot/refman2/auxillar/aadmed.htm	Dataplot Vol 2 Vol 1 Name: Type: Let Subcommand Purpose: Compute the coefficient of dispersion based on the average absolute deviation (AAD) and the median of a variable. Description: There are a number of definitions for the coefficient of dispersion. Dataplot uses the definition based on the ratio of the median absolute deviation (MAD) to the median. An alternative definition is based on the AAD and the median. Specifically, $$\mbox{d} = \frac{\mbox{AAD}}{\tilde{x}}$$ where AAD and $$\tilde{x}$$ denote the average absolute deviation and the median, respectively. This is the statistic computed by this command. Note that the AAD used here is defined as $$\mbox{AAD} = \frac{\sum_{i=1}^{n}{\|X_{i} - \tilde{x}\|}} {n}$$ That is, we compute the deviations from the median rather than the mean. This statistic is a robust alternative to the coefficient of variation. Syntax 1: LET <par> = AAD TO MEDIAN <y> <SUBSET/EXCEPT/FOR qualification> where <y> is a response variable; <par> is a parameter where the AAD TO MEDIAN value is saved; and where the <SUBSET/EXCEPT/FOR qualification> is optional. Syntax 2: LET <par> = DIFFERENCE OF AAD TO MEDIAN <y1> <y2> <SUBSET/EXCEPT/FOR qualification> where <y1> is the first response variable; <y2> is the second response variable; <par> is a parameter where the AAD TO MEDIAN value is saved; and where the <SUBSET/EXCEPT/FOR qualification> is optional. Examples: LET D = AAD TO MEDIAN Y1 LET D = AAD TO MEDIAN Y1 SUBSET TAG > 2 LET D = DIFFERENCE OF AAD TO MEDIAN Y1 Note: Dataplot statistics can be used in a number of commands. For details, enter Default: None Synonyms: None Related Commands: COEFFICIENT OF DISPERSION = Compute the coefficient of dispersion of a variable. QUARTILE COEFFICIENT OF DISPERSION = Compute the quartile coefficient of dispersion of a variable. COEFFICIENT OF VARIATION = Compute the coefficient of variation. RELATIVE STANDARD DEVIATION = Compute the relative standard deviation of a variable. MEDIAN = Compute the median of a variable. MEAN = Compute the mean of a variable. AVERAGE ABSOLUTE DEVIATION = Compute the average absolute deviation of a variable. STANDARD DEVIATION = Compute the standard deviation of a variable. Applications: Data Analysis Implementation Date: 2017/01 Program 1: LET Y1 = DOUBLE EXPONENTIAL NUMBERS FOR I = 1 1 100 LET D = AAD TO MEDIAN Y1 Program 2: . Step 1: Create the data . skip 25 skip 0 set write decimals 6 . . Step 2: Define plot control . title case asis title offset 2 label case asis . y1label Coefficient of Dispersion (AAD to Median) x1label Group title AAD to Median for GEAR.DAT let ngroup = unique x xlimits 1 ngroup major x1tic mark number ngroup minor x1tic mark number 0 tic mark offset units data x1tic mark offset 0.5 0.5 y1tic mark label decimals 3 . character X line blank . set statistic plot reference line average aad to median plot y x . tabulate aad to median y x (Response Variables: Y ) --------------------------------------------- --------------------------------------------- 1.000000 \| 0.003405 2.000000 \| 0.003704 3.000000 \| 0.002811 4.000000 \| 0.003210 5.000000 \| 0.006134 6.000000 \| 0.007419 7.000000 \| 0.005497 8.000000 \| 0.002800 9.000000 \| 0.003106 10.000000 \| 0.003815 Program 3: SKIP 25 READ IRIS.DAT Y1 TO Y4 X . LET A = DIFFERENCE OF AAD TO MEDIAN Y1 Y2 SET WRITE DECIMALS 4 TABULATE DIFFERENCE OF AAD TO MEDIAN Y1 Y2 X Cross Tabulate DIFFERENCE OF AAD TO MEDIAN (Response Variables: Y1 Y2 ) --------------------------------------------- X \| DIFFERENCE OF A --------------------------------------------- 1.0000 \| -0.0295 2.0000 \| -0.0181 3.0000 \| -0.0036 . XTIC OFFSET 0.2 0.2 X1LABEL GROUP ID Y1LABEL DIFFERENCE OF AAD TO MEDIAN CHAR X LINE BLANK DIFFERENCE OF AAD TO MEDIAN PLOT Y1 Y2 X CHAR X ALL LINE BLANK ALL BOOTSTRAP DIFFERENCE OF AAD TO MEDIAN PLOT Y1 Y2 X NIST is an agency of the U.S. Commerce Department. Date created: 01/24/2017 Last updated: 06/30/2017	2018-06-24T07:06:10	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6627038717269897, "perplexity": 10643.8597298869}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-26/segments/1529267866888.20/warc/CC-MAIN-20180624063553-20180624083553-00234.warc.gz"}
https://humancommunications.fandom.com/wiki/User_blog:Jamessungjin.kim/Lagrange_Multiplier	186 Pages Even if Lagrange multiplier is an important mathematical tool, I haven't been used it up to now. It is simple than its look. When we need to optimize two variables with conditioning on the combination of the two variables. ## An Example of Lagrange Multiplier I describe the contents of video to help readers' understanding. We want to minimize subject to . By Lagrange multiplier, we can write the Lagrange multiplier equation as . Use the property of Lagrange multiplier that the partial derivatives of the above Lagrange multiplier equation should be equal to zero From the first and the second equations, we will have and . Putting these results to the third equation, we find , which result that and . Thus, the minimum of becomes . Community content is available under CC-BY-SA unless otherwise noted.	2021-06-20T02:44:51	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8953946828842163, "perplexity": 556.6161319366041}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623487655418.58/warc/CC-MAIN-20210620024206-20210620054206-00097.warc.gz"}
https://www.aimsciences.org/article/doi/10.3934/dcdsb.2020263	Article Contents Article Contents # Chaotic dynamics in a simple predator-prey model with discrete delay • * Corresponding author: Gail S. K. Wolkowicz • A discrete delay is included to model the time between the capture of the prey and its conversion to viable biomass in the simplest classical Gause type predator-prey model that has equilibrium dynamics without delay. As the delay increases from zero, the coexistence equilibrium undergoes a supercritical Hopf bifurcation, two saddle-node bifurcations of limit cycles, and a cascade of period doublings, eventually leading to chaos. The resulting periodic orbits and the strange attractor resemble their counterparts for the Mackey-Glass equation. Due to the global stability of the system without delay, this complicated dynamics can be solely attributed to the introduction of the delay. Since many models include predator-prey like interactions as submodels, this study emphasizes the importance of understanding the implications of overlooking delay in such models on the reliability of the model-based predictions, especially since temperature is known to have an effect on the length of certain delays. Mathematics Subject Classification: 34K18, 34K23, 34K60, 37D45, 37G15, 37G35, 92D25, 92D40. Citation: • Figure 1. Intersections of $\theta(\tau)+2n\pi$ and $\tau \omega_+(\tau), \ n = 0,1,\dots,$. Values of $\tau$ at which the characteristic equation has pure imaginary eigenvalues, and hence candidates for critical values of $\tau$ at which there could be Hopf bifurcations. In both graphs, at all such intersections, transversality holds, since the slope of these curves at these intersections are different. Parameters: $m = 1,\ r = 1,\ K = 1, \ Y = 0.6 .$ (LEFT) $s = 0.02$. For $n = 0$ there are two intersections (i.e. $j_0 = 2$), at $\tau_0^1$ and $\tau_0^2$, but for $n = 1$, and hence $n\geqslant 1$, there are no intersections. (RIGHT) $s = 0.007$. There are two intersections each (i.e. $j_n = 2, \ n = 0,1,2$), at $\tau_n^1$ and $\tau_n^2$, for $n = 0,1$ and $2$, but for $n = 3$, and hence $n\geqslant 3$, there are no intersections. In both (LEFT) and (RIGHT), $E_+$ is asymptotically stable for $\tau\in[0,\tau_0^1)\cup(\tau_0^2,\tau_c)$ and unstable for $\tau\in(\tau_0^1,\tau_0^2)$. Figure 2. Orbit diagrams. Initial data was taken to be $x(t) = y(t) = 0.1$ for $t\in[-\tau,0]$. However, we found bistability in the portion of the diagram beween the vertical dots and varied the initial data as explained below. Except for the portion between the vertical dots, the rest of the diagram was the same for all of the initial conditions we tried (not shown). (TOP) All local maxima and minima for the $y(t)$ coordinate of the attractor as $\tau$ varies, including kinks. (BOTTOM) Diagram including local maxes and mins for the $y(t)$ coordinate as $\tau$ varies, but with kinks eliminated. There are two saddle-node of limit cycle bifurcations. They occur for $\tau$ approximately equal to 76 and 82, where the curves in the orbit diagrams stop abruptly and there appear to be vertical dots. For $\tau$ between these values, there is is bistability. Two orbitally asymptotically stable periodic orbits (with their maximum and minimum amplitudes shown) and an unstable periodic orbit with amplitudes between them (not shown). The two stable periodic orbits were found by producing this part of the orbit diagram varying $\tau$ forward and then varying it backwards but startng at the last point of the attractor for the previous value of $\tau$ Figure 3. The time series for $y(t)$ when $\tau = 70$, depicting kinks. There are two local maxima and two local minima over each period as shown in Figure 2 (TOP), but only one local maxima and one local minima in Figure 2 (BOTTOM) in which kinks have been removed Figure 4. Zoom-in of orbit diagram shown in Figure 2 for $\tau\in[75,100]$ including kinks. The vertical dots indicate the boundary of the region of bistability, where the two saddle-node of limit cycle bifurcations occur Figure 5. Time delay embedding of two orbitally asymptotically stable periodic orbits demonstrating bistability for $\tau = 81$. The one with larger amplitude (dashed) has initial data $x(t) = y(t) = 0.1$, for $t \in [-\tau,0]$, and period approximately $345$. The one with smaller amplitude (solid) has initial data $x(t) = y(t) = 0.1$, for $t \in [-\tau,0)$ and $x(0) = 0.3, \ y(0) = 0.83$ and has period approximately $273.7$ Figure 6. (LEFT) Time series starting from the initial data $x(t) = y(t) = 0.1, t\in[-\tau,0]$ indicating how quickly the orbit gets close to the periodic attractor and (RIGHT) time delay embeddings of the periodic attractors, demonstrating the sequence of period doubling bifurcations initiating from the left at $\tau\approx 83,\ 86$, and $86.6$. Values of $\tau$ selected between these bifurcations: $\tau = 82,\ 85,\ 86.3$, and $86.8$, with periods of the periodic attractor approximately equal to: $340.2,\ 564.6,\ 1144.5$, and $2298.3$, respectively, are shown Figure 7. (LEFT) Time series starting from the initial data $x(t) = y(t) = 0.1, t\in[-\tau,0]$ indicating how quickly the orbit gets close to the periodic attractor and (RIGHT) time delay embeddings of the periodic attractors, demonstrating the sequence of period halfing bifurcations initiating from the left for values of $\tau$ between $91.5$ and $92$, and at $\tau\approx 92.2, \ 93.2, \ 98.3$. Graphs shown are for values of $\tau$ between these bifurcations: $\tau = 91.95,\ 92,\ 93,\ 96$, and $100$, with periods approximately equal to: $4794.3, \ 2398.3, \ 1211.2,\ 557.6,$ and $295.3$, respectively Figure 8. Time delay embedding starting at initial data $x(t) = y(t) = 0.1, t\in[\tau,0]$ for $\tau = 90.7$ showing a periodic attractor with period approximately $1800$, having $6(\neq2^n)$ loops for some integer $n$ Figure 9. (LEFT) Time series for $\tau = 90$ starting from the initial data $x(t) = y(t) = 0.1, t\in[-\tau,0]$. (RIGHT) Time delay embedding of the strange attractor for $\tau = 90$. Only the portion of the orbit from $t = 240,000-260,000$ is shown Figure 10. The strange attractor, for $\tau = 90$, shown in Figure 9 in $(x,y)$-space. Only the portion of the orbit from $t = 240,000$ to $260,000$ is shown Figure 11. The return map for $\tau = 90$, computing the minimum value of $y(t)$ as a function of the preceding minimum value of $y(t)$ for $y(t)<0.7$ in both cases, using the data in Figure 9 Figure 12. Time series (LEFT) for the solution that converges to a periodic attractor when $\tau = 92$, and (RIGHT) for the solution that converges to a strange attractor when $\tau = 90$, demonstrating that there is no sensitivity to initial data in the former case, but that there is sensitivity in the latter case. Initial data used for the solid curves: $x(t) = y(t) = 0.1$ for $t\in[-\tau,0]$, and for the dotted curves: $x(t) = 0.11$ and $y(t) = 0.1$ for $t\in[\tau,0]$ • [1] J. Arino, L. Wang and G. S. K. Wolkowicz, An alternative formulation for a delayed logistic equation, J. Theoret. Biol., 241 (2006), 109-119. doi: 10.1016/j.jtbi.2005.11.007. [2] A. D. Bazykin, Nonlinear Dynamics of Interacting Populations, vol. 11 of A, World Scientific Series on Nonlinear Science, Singapore, 1998. doi: 10.1142/9789812798725. [3] E. Beretta and Y. Kuang, Geometric stability switch criteria in delay differential systems with delay dependent parameters, SIAM J. Math. Anal., 33 (2002), 1144-1165. doi: 10.1137/S0036141000376086. [4] K. L. Cooke, R. H. Elderkin and W. Huang, Predator-prey interactions with delays due to juvenile maturation, SIAM J. Appl. Math., 66 (2006), 1050-1079. doi: 10.1137/05063135. [5] R. Driver, Existence and stability of solutions of a delay-differential system, Arch. Ration. Mech. Anal., 10 (1962), 401-426. doi: 10.1007/BF00281203. [6] B. Ermentrout, Simulating, Analyzing, and Animating Dynamical Systems: A Guide to XPPAUT for Researchers and Students, SIAM, 2002. doi: 10.1137/1.9780898718195. [7] G. Fan and G. S. K. Wolkowicz, A predator-prey model in the chemostat with time delay, Int. J. Differ. Equ., (2010), Art. ID 287969, 41pp. doi: 10.1155/2010/287969. [8] J. E. Forde, Delay Differential Equation Models in Mathematical Biology, PhD thesis, University of Michigan, 2005. [9] H. I. Freedman, Deterministic Mathematical Models in Population Ecology, Marcel Dekker, New York, 1980. [10] F. R. Gantmacher, Applications of the Theory of Matrices, Trans. J. L. Brenner et al., New York: Interscience, 1959. [11] A.-M. Ginoux, B. Rossetto and J.-L. Jamet, Chaos in a three-dimensional Volterra-Gause model of predator-prey type, Internat. J. of Bifur. Chaos Appl. Sci. Engrg., 15 (2005), 1689-1708. doi: 10.1142/S0218127405012934. [12] S. A. Gourley and Y. Kuang, A stage structured predator-prey model and its dependence on maturation delay and death rate, J. Math. Biol., 49 (2004), 188-200. doi: 10.1007/s00285-004-0278-2. [13] J. K. Hale and V. L. S. M., Introduction to Functional-Differential Equations, vol. 99 of Applied Mathematical Sciences, Springer-Verlag, New York, 1993. doi: 10.1007/978-1-4612-4342-7. [14] M. A. Haque, A predator-prey model with discrete time delay considering different growth function of prey, Adv. Appl. Math. Biosci., 2 (2011), 1-16. [15] A. Hastings and T. Powell, Chaos in a three-species food chain, Ecology, 72 (1991), 896-903. [16] W. M. Hirsch, H. Hanisch and J.-P. Gabriel, Differential equation models of some parasitic infections: methods for the study of asymptotic behavior, Comm. Pure Appl. Math., 38 (1985), 733-753. doi: 10.1002/cpa.3160380607. [17] Y. Kuang, Delay Differential Equations with Applications in Population Dynamics, vol. 191 of Mathematics in Science and Engineering, Academic Press Inc., Boston, MA, 1993. [18] V. Lakshmikantham and S. Leela, Differential and Integral Inequalities: Theory and Applications, vol. 55-Ⅰ, Academic Press, New York, 1969. [19] M. Y. Li, X. Lin and H. Wang, Global Hopf branches and multiple limit cycles in a delayed Lotka-Volterra predator-prey model, Discrete Contin. Dyn. Syst. Ser. B, 19 (2014), 747-760. doi: 10.3934/dcdsb.2014.19.747. [20] M. C. Mackey and L. Glass, Oscillations and chaos in physiological control, Science, 197 (1977), 287-289. [21] _____, Mackey-Glass equation, Scholarpedia, 4 (2009), p. 6908. [22] MAPLE, Maplesoft, A Division of Waterloo Maple Inc., Waterloo, Ontario, 2017. [23] MATLAB, Version 9.5.0 (R2018b), The MathWorks Inc., Natick, Massachusetts, 2018. [24] A. Morozov, S. Petrovskii and B.-L. Li, Bifurcations and chaos in a predator-prey system with the allee effect, P Roy. Soc. B-Biol. Sci., 271 (2004), 1407-1414. [25] M. L. Rosenzweig, Paradox of enrichment: Destabilization of exploitation ecosystems in ecological time, Science, 171 (1971), 385-387. [26] H. L. Smith, An Introduction to Delay Differential Equations with Applications to the Life Sciences, vol. 57 of Texts in Applied Mathematics, Springer, New York, 2011. doi: 10.1007/978-1-4419-7646-8. [27] H. L. Smith and H. R. Thieme, Dynamical Systems and Population Persistence, vol. 118 of Graduate Studies in Mathematics, American Mathematical Society, Providence, RI, 2011. [28] J. Wang and W. Jiang, Bifurcation and chaos of a delayed predator-prey model with dormancy of predators, Nonlinear Dynam., 69 (2012), 1541-1558. doi: 10.1007/s11071-012-0368-4. Open Access Under a Creative Commons license Figures(12)	2023-03-23T04:26:40	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 1, "x-ck12": 0, "texerror": 0, "math_score": 0.826853334903717, "perplexity": 778.3788959448652}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296944996.49/warc/CC-MAIN-20230323034459-20230323064459-00330.warc.gz"}
https://par.nsf.gov/biblio/10131146-inferring-parallax-westerlund-from-gaia-dr2	Inferring the parallax of Westerlund 1 from Gaia DR2 ABSTRACT Westerlund 1 (Wd1) is potentially the largest star cluster in the Galaxy. That designation critically depends upon the distance to the cluster, yet the cluster is highly obscured, making luminosity-based distance estimates difficult. Using Gaia Data Release 2 (DR2) parallaxes and Bayesian inference, we infer a parallax of $0.35^{+0.07}_{-0.06}$ mas corresponding to a distance of $2.6^{+0.6}_{-0.4}$ kpc. To leverage the combined statistics of all stars in the direction of Wd1, we derive the Bayesian model for a cluster of stars hidden among Galactic field stars; this model includes the parallax zero-point. Previous estimates for the distance to Wd1 ranged from 1.0 to 5.5 kpc, although values around 5 kpc have usually been adopted. The Gaia DR2 parallaxes reduce the uncertainty from a factor of 3 to 18 per cent and rules out the most often quoted value of 5 kpc with 99 per cent confidence. This new distance allows for more accurate mass and age determinations for the stars in Wd1. For example, the previously inferred initial mass at the main-sequence turn-off was around 40 M⊙; the new Gaia DR2 distance shifts this down to about 22 M⊙. This has important implications for our understanding of the late stages of stellar evolution, including the initial mass more » Authors: ; ; ; ; ; ; ; ; Publication Date: NSF-PAR ID: 10131146 Journal Name: Monthly Notices of the Royal Astronomical Society Volume: 492 Issue: 2 Page Range or eLocation-ID: p. 2497-2509 ISSN: 0035-8711 Publisher: Oxford University Press National Science Foundation ##### More Like this 1. ABSTRACT With Gaia parallaxes, it is possible to study the stellar populations associated with individual Galactic supernova remnants (SNRs) to estimate the mass of the exploding star. Here, we analyse the luminous stars near the Vela pulsar and SNR to find that its progenitor was probably ($\mathrel {\raise.3ex\rm{\gt }\lower0.6ex\rm{\sim }}90\rm \,per\,cent$) low mass (8.1–$10.3\, {\rm M}_\odot$). The presence of the O star γ2 Vel a little over 100 pc from Vela is the primary ambiguity, as including it in the analysis volume significantly increases the probability (to 5 per cent) of higher mass ($\gt 20\, {\rm M}_\odot$) progenitors. However, to be a high-mass star associated with γ2 Vel’s star cluster at birth, the progenitor would have to be a runaway star from an unbound binary with an unusually high velocity. The primary impediment to analysing large numbers of Galactic SNRs in this manner is the lack of accurate distances. This can likely be solved by searching for absorption lines from the SNR in stars as a function of distance, a method which yielded a distance to Vela in agreement with the direct pulsar parallax. If Vela was a $10\, {\rm M}_\odot$ supernova in an external galaxy, the 50-pc search region used in extragalactic studies wouldmore » 2. Context. Stars evolving along the asymptotic giant branch (AGB) can become carbon rich in the final part of their evolution. The detailed description of their spectra has led to the definition of several spectral types: N, SC, J, and R. To date, differences among them have been partially established only on the basis of their chemical properties. Aims. An accurate determination of the luminosity function (LF) and kinematics together with their chemical properties is extremely important for testing the reliability of theoretical models and establishing on a solid basis the stellar population membership of the different carbon star types. Methods. Using Gaia Data Release 2 ( Gaia DR2) astrometry, we determine the LF and kinematic properties of a sample of 210 carbon stars with different spectral types in the solar neighbourhood with measured parallaxes better than 20%. Their spatial distribution and velocity components are also derived. Furthermore, the use of the infrared Wesenheit function allows us to identify the different spectral types in a Gaia -2MASS diagram. Results. We find that the combined LF of N- and SC-type stars are consistent with a Gaussian distribution peaking at M bol ∼ −5.2 mag. The resulting LF, however, shows two tails at lowermore » 3. ABSTRACT Westerlund 1 (Wd 1) is one of the most relevant star clusters in the Milky Way to study massive star formation, although it is still poorly known. Here, we used photometric and spectroscopic data to model the eclipsing binary W36, showing that its spectral type is O6.5 III + O9.5 IV, hotter and more luminous than thought before. Its distance dW36 = 4.03 ± 0.25 kpc agrees, within the errors, with three recent Gaia-EDR3-based distances reported in Paper I, Beasor & Davies, and by Negueruela’s group. However, they follow different approaches to fix the zero-points for red sources such as those in Wd 1, and to select the best approach, we used an accurate modelling of W36. The weighted mean distance of our parallax (Paper I) and binary distances results in dwd1 = 4.05 ± 0.20 kpc, with an unprecedented accuracy of 5 per cent. We adopted isochrones based on the Geneva code with supersolar abundances to infer the age of W36B as 6.4 ± 0.7 Myr. This object seems to be part of the prolific star formation burst represented by OB giants and supergiants that occurred at 7.1 ± 0.5 Myr ago, which coincides with the recently published PMS isochrone with age 7.2 Myr. Other BA-type luminous evolved stars and yellow hypergiants spread in the age range of 8–11 Myr. The four redmore » 4. ABSTRACT We construct from Gaia eDR3 an extensive catalogue of spatially resolved binary stars within ≈1 kpc of the Sun, with projected separations ranging from a few au to 1 pc. We estimate the probability that each pair is a chance alignment empirically, using the Gaia catalogue itself to calculate the rate of chance alignments as a function of observables. The catalogue contains 1.3 (1.1) million binaries with >90 per cent (>99 per cent) probability of being bound, including 16 000 white dwarf – main-sequence (WD + MS) binaries and 1400 WD + WD binaries. We make the full catalogue publicly available, as well as the queries and code to produce it. We then use this sample to calibrate the published Gaia DR3 parallax uncertainties, making use of the binary components’ near-identical parallaxes. We show that these uncertainties are generally reliable for faint stars (G ≳ 18), but are underestimated significantly for brighter stars. The underestimates are generally $\leq30{{\ \rm per\ cent}}$ for isolated sources with well-behaved astrometry, but are larger (up to ∼80 per cent) for apparently well-behaved sources with a companion within ≲4 arcsec, and much larger for sources with poor astrometric fits. We provide an empirical fitting function to inflate published σϖ values for isolated sources. The publicmore » 5. ABSTRACT We report the discovery of 74 new pulsating DA white dwarf stars, or ZZ Cetis, from the data obtained by the Transiting Exoplanet Survey Satellite mission, from Sectors 1 to 39, corresponding to the first 3 cycles. This includes objects from the Southern hemisphere (Sectors 1–13 and 27–39) and the Northern hemisphere (Sectors 14–26), observed with 120 s- and 20 s-cadence. Our sample likely includes 13 low-mass and one extremely low-mass white dwarf candidate, considering the mass determinations from fitting Gaia magnitudes and parallax. In addition, we present follow-up time series photometry from ground-based telescopes for 11 objects, which allowed us to detect a larger number of periods. For each object, we analysed the period spectra and performed an asteroseismological analysis, and we estimate the structure parameters of the sample, i.e. stellar mass, effective temperature, and hydrogen envelope mass. We estimate a mean asteroseismological mass of 〈Msis〉 = 0.635 ± 0.015 M⊙, excluding the candidate low or extremely low-mass objects. This value is in agreement with the mean mass using estimates from Gaia data, which is 〈Mphot〉 = 0.631 ± 0.040 M⊙, and with the mean mass of previously known ZZ Cetis of 〈M*〉 = 0.644 ± 0.034 M⊙. Our sample of 74 new bright ZZ Cetis increases the number of known ZZ Cetis by ∼20 per cent.	2022-11-27T14:34:40	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6416680812835693, "perplexity": 1771.8177286941946}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446710409.16/warc/CC-MAIN-20221127141808-20221127171808-00436.warc.gz"}
http://dlmf.nist.gov/22.5	# §22.5 Special Values ## §22.5(i) Special Values of Table 22.5.1 gives the value of each of the 12 Jacobian elliptic functions, together with its -derivative (or at a pole, the residue), for values of that are integer multiples of , . For example, at , , . (The modulus is suppressed throughout the table.) Table 22.5.1: Jacobian elliptic function values, together with derivatives or residues, for special values of the variable. 0 , , , Table 22.5.2 gives , , for other special values of . For example, . For the other nine functions ratios can be taken; compare (22.2.10). ## §22.5(ii) Limiting Values of If , then and ; if , then and . In these cases the elliptic functions degenerate into elementary trigonometric and hyperbolic functions, respectively. See Tables 22.5.3 and 22.5.4. Table 22.5.3: Limiting forms of Jacobian elliptic functions as . 1 1 Expansions for as or 1 are given in §§19.5, 19.12. For values of when (lemniscatic case) see §23.5(iii), and for (equianharmonic case) see §23.5(v).	2013-06-20T11:59:21	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8629493117332458, "perplexity": 2287.750231480054}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368711515185/warc/CC-MAIN-20130516133835-00086-ip-10-60-113-184.ec2.internal.warc.gz"}
https://zbmath.org/authors/?q=ai%3Apah.chin-hee	# zbMATH — the first resource for mathematics ## Pah, Chin Hee Compute Distance To: Author ID: pah.chin-hee Published as: Pah, C. H.; Pah, Chin Hee External Links: MGP · Wikidata Documents Indexed: 9 Publications since 2003 all top 5 #### Co-Authors 2 single-authored 4 Ganikhodjaev, Nasir Nabievich 4 Mukhamedov, Farruh Maksutovich 2 Wahiddin, M. R. B. 1 Jamil, Hasan M. 1 Rosli, Azizi 1 Saburov, Mansoor all top 5 #### Serials 2 Theoretical and Mathematical Physics 1 Journal of Mathematical Physics 1 Journal of Statistical Physics 1 Physics Letters. A 1 Southeast Asian Bulletin of Mathematics 1 Journal of Physics A: Mathematical and General 1 Qualitative Theory of Dynamical Systems 1 Bulletin of the Malaysian Mathematical Sciences Society. Second Series #### Fields 7 Statistical mechanics, structure of matter (82-XX) 2 Combinatorics (05-XX) 1 Number theory (11-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Operator theory (47-XX) #### Citations contained in zbMATH 5 Publications have been cited 23 times in 17 Documents Cited by Year Exact solution of an Ising model with competing interactions on a Cayley tree. Zbl 1168.82316 Ganikhodjaev, N. N.; Pah, C. H.; Wahiddin, M. R. B. 2003 An Ising model with three competing interactions on a Cayley tree. Zbl 1071.82015 Ganikhodjaev, N. N.; Pah, C. H.; Wahiddin, M. R. B. 2004 Phase diagram of the three states Potts model with next nearest neighbour interactions on the Bethe lattice. Zbl 1227.82044 Ganikhodjaev, Nasir; Mukhamedov, Farrukh; Pah, Chin Hee 2008 On non-ergodic Volterra cubic stochastic operators. Zbl 1443.37005 Mukhamedov, Farrukh; Pah, Chin Hee; Rosli, Azizi 2019 An application of Catalan numbers on Cayley tree of order 2: Single polygon counting. Zbl 1214.82018 Pah, C. H. 2008 On non-ergodic Volterra cubic stochastic operators. Zbl 1443.37005 Mukhamedov, Farrukh; Pah, Chin Hee; Rosli, Azizi 2019 Phase diagram of the three states Potts model with next nearest neighbour interactions on the Bethe lattice. Zbl 1227.82044 Ganikhodjaev, Nasir; Mukhamedov, Farrukh; Pah, Chin Hee 2008 An application of Catalan numbers on Cayley tree of order 2: Single polygon counting. Zbl 1214.82018 Pah, C. H. 2008 An Ising model with three competing interactions on a Cayley tree. Zbl 1071.82015 Ganikhodjaev, N. N.; Pah, C. H.; Wahiddin, M. R. B. 2004 Exact solution of an Ising model with competing interactions on a Cayley tree. Zbl 1168.82316 Ganikhodjaev, N. N.; Pah, C. H.; Wahiddin, M. R. B. 2003 all top 5 #### Cited by 27 Authors 5 Ganikhodjaev, Nasir Nabievich 5 Mukhamedov, Farruh Maksutovich 5 Rozikov, Utkir A. 3 Pah, Chin Hee 2 Akin, Hasan 2 Embong, Ahmad Fadillah 2 Khakimov, Otabek N. 1 Barhoumi, Abdessatar 1 de la Rubia, F. Javier 1 Dragovich, Branko 1 Fernández, Miguel Ángel 1 Han, Qing 1 Haydarov, Farhod Halimjonovich 1 Jamilov, Uygun U. 1 Khrennikov, Andreĭ Yur’evich 1 Korutcheva, Elka R. 1 Kozyrev, Sergeĭ Vladimirovich 1 Ladra González, Manuel 1 Li, Cuiling 1 Liu, Yongjun 1 Mendes, José F. F. 1 Souissi, Abdessatar 1 Temir, Seyit 1 Uǧuz, Selman 1 Volovich, Igor’ Vasil’evich 1 Wahiddin, M. R. B. 1 Zelenov, Evgenii I. all top 5 #### Cited in 12 Serials 4 Journal of Statistical Physics 2 Theoretical and Mathematical Physics 2 Mathematical Physics, Analysis and Geometry 1 Acta Mechanica 1 Journal of Mathematical Physics 1 Nonlinearity 1 Physica A 1 Reviews in Mathematical Physics 1 Journal of Difference Equations and Applications 1 Qualitative Theory of Dynamical Systems 1 Journal of Statistical Mechanics: Theory and Experiment 1 $$p$$-Adic Numbers, Ultrametric Analysis, and Applications all top 5 #### Cited in 12 Fields 12 Statistical mechanics, structure of matter (82-XX) 4 Combinatorics (05-XX) 3 Dynamical systems and ergodic theory (37-XX) 3 Probability theory and stochastic processes (60-XX) 2 Functional analysis (46-XX) 2 Operator theory (47-XX) 2 Biology and other natural sciences (92-XX) 1 Number theory (11-XX) 1 Mechanics of deformable solids (74-XX) 1 Quantum theory (81-XX) 1 Relativity and gravitational theory (83-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) #### Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata.	2021-02-28T20:36:48	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.22011679410934448, "perplexity": 12367.172837260185}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178361723.15/warc/CC-MAIN-20210228175250-20210228205250-00124.warc.gz"}
https://pos.sissa.it/301/663/	Volume 301 - 35th International Cosmic Ray Conference (ICRC2017) - Session Gamma-Ray Astronomy. GA-extra-galactic Constrains on the extragalactic origin of IceCube's neutrinos using HAWC I. Taboada,* C.F. Tung, J. Wood on behalf of the HAWC Collaboration *corresponding author Full text: pdf Pre-published on: August 16, 2017 Published on: August 03, 2018 Abstract IceCube has discovered an unresolved and isotropic flux of neutrinos between 10 TeV and 8 PeV. Extragalactic origin for this flux is usually assumed, as well as a correlation with the sources of cosmic rays. To date, no clear association with a class of objects has been made. HAWC is a very-high-energy (VHE, or $\gtrsim$100~GeV) gamma ray observatory in operation in central Mexico. HAWC has studied 2/3 of the entire sky ($\sim8~sr)$. We use this survey to search for optically thin sources of cosmic rays and neutrinos, responsible for IceCube's observations. We have written a simulation of the cosmological properties of neutrino sources, FIRESONG, to show that under certain conditions, HAWC should be observing multiple sources. However, HAWC has only detected 2 extragalactic objects in 760 days of livetime: Mrk 421 and Mrk 501. This deficiency of detected sources in the extragalactic sky can be used to constrain the properties of neutrino sources, such as their density in the local universe. The case HAWC restricts the most is for no evolution in the density of sources, in which at least 8 objects should have been detected for the cases not excluded already by IceCube. DOI: https://doi.org/10.22323/1.301.0663 How to cite Metadata are provided both in "article" format (very similar to INSPIRE) as this helps creating very compact bibliographies which can be beneficial to authors and readers, and in "proceeding" format which is more detailed and complete. Open Access Copyright owned by the author(s) under the term of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.	2020-12-04T01:05:38	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5010379552841187, "perplexity": 3116.705450688198}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-50/segments/1606141733120.84/warc/CC-MAIN-20201204010410-20201204040410-00558.warc.gz"}
https://large-numbers.fandom.com/wiki/Second_factorial	## FANDOM 1,079 Pages The "2nd factorial" is defined as $$n§ = \prod^{n}_{i = 1} i^i^2 = 1^1^2 \cdot 2^2^2 \cdot 3^3^2 \cdot 4^4^2 \cdot \ldots \cdot n^n^2$$.[1] The first few values of $$n§$$ for $$n = 1, 2, 3, 4, \ldots$$ are 1, 16, 314,928, 1,352,605,460,594,688, 403,107,840,000,000,000,000,000,000,000,000, 4,157,825,501,361,955,044,460,594,652,554,199,040,000,000,000,000,000,000,000,000, ... (OEIS A051675). The sum of the reciprocals of these numbers is 2.2592954398150629.... ## Sources Edit 1. Hyperfactorial from Wolfram MathWorld Community content is available under CC-BY-SA unless otherwise noted.	2019-12-14T07:55:26	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8344272971153259, "perplexity": 4768.25057505172}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-51/segments/1575540585566.60/warc/CC-MAIN-20191214070158-20191214094158-00354.warc.gz"}
https://wiki.cosmos.esa.int/planckpla2015/index.php?title=LFI-Validation&oldid=2660	# LFI-Validation ## Overview Data validation is a step of paramount importance in the complex process of data analysis and the extraction of the final scientific goals of an experiment. The LFI approach to data validation is based upon null-tests approach and here we present the rationale behind envisaged/performed null-tests and the actual results for the present data release. Also we will provide results of the same kind of tests performed on previous release to show the overall improvements in the data quality. ## Null-tests approach In general null-tests are performed in order to highlight possible issues in the data related to instrumental systematic effect not properly accounted for within the processing pipeline and related to known events of the operational conditions (e.g. switch-over of the sorption coolers) or to intrinsic instrument properties coupled with sky signal like stray-light contamination. Such null-tests are expected to be performed considering data on different time scales ranging from 1-minute to one year of observations, at different unit level (radiometer, horn, horn-pair, within frequency and cross-frequency both in total intensity and, when applicable, to polarisation. This is quite demanding in terms of all possible combinations. In addition some tools are already available and can be properly used for this kind of analysis. However it may be possible that on some specific time-scale, detailed tools have to be developed in order to produce the desired null-test results. In this respect the actual half-ring jack-knives are suitable to track any effects on pointing period times scales. On time-scales between half-ring and survey there are lot of possibilities. It has to be verified if the actual code producing half-ring jack-knives (madam) can handle data producing jack-knives of larger (e.g. 1 hour) times scales. It is fundamental that such test have to be performed on DPC data product with clear and identified properties (e.g. single $R$, $DV/V$ single fit, etc.) in order to avoid any possible mis-understanding due to usage of non homogeneous data sets. Many of the null-tests proposed are done at map level with sometime compression of their statistical information into an angular power spectrum. However together with full-sky maps it is interesting to have a closer look on some specific sources. I would be important to compare fluxes from both polarized and un-polarized point sources with different radiometers in order to asses possible calibration mis-match and/or polarization leakage issues. Such comparison will also possibly indicate problems related to channel central frequencies. The proposed set of sources would be: M42, Tau A, Cas A and Cyg A. However other H{\sc II} regions like Perseus are valuable. One can compare directly their fluxes from different sky surveys and/or the flux of the difference map and how this is consistent with instrumental noise. Which kind of effect is probed with a null-test on a specific time scale? Here it is a simple list. At survey time scale it is possible to underlying any side-lobes effects, while on time scales of full-mission, it is possible to have an indication of calibration problems when observing the sky with the same S/C orientation. Differences at this time scale between horns at the same frequency may also reveal central frequency and beam issues. ### Total Intensity Null Tests In order to highlight different issues, several time scales and data combinations are considered. The following table is a sort of null-test matrix to be filled with test results. It should be important to try to set a sort of pass/fail criteria for each of the tests and to be prepared to detailed actions in order to avoid and correct any failure of the tests. To assess the results an idea could be to proceed as in the nominal pipeline $i.e.$ to compare the angular power spectra of null test maps with a fiducial angular power spectrum of a white noise map. This could be made automatic and, in case the test does not pass then a more thorough investigation could be performed. This will provide an overall indication of the residuals. However structures in the residual are important as well as the overall average level and visual inspection of the data is therefore fundamental. Concerning null-tests on various time scales a comment is in order. At large time scales (i.e. of the order of a survey or more) it is clear that the basic data set will be made of the single survey maps at radiometer/horn/frequency level that will be properly combined to obtain the null-test under consideration. For example at 6 months time scale we will analysis maps of the difference between different surveys for the radiometer/horn/frequency under test. On the other hand at 12 months time scale we will combine surveys 1 and 2 together to be compared with the same combination for surveys 3 and 4. At full-mission time scale, the analysis it is not always possible e.g. at radiometer level we have only one full-mission data set. However it would be interesting to combine odd surveys together and compare them with even surveys again combined together. On shorter time scales (i.e. less than a survey) the data products to be considered are different and will be the output of the jack-knives code when different time scales are considered: the usual half-ring JK on pointing period time scale and the new, if possible, jack-knives on 1 minute time scale. Therefore null-tests will use both surveys/full-mission maps as well as tailored jack-knives maps. The following table reports our total intensity null-tests matrix with a $\checkmark$ where tests are possible. Data Set 1minute 1 hour Survey Full Mission Radiometer (M/S) $\checkmark$ $\checkmark$ $\checkmark$ $\checkmark$ Horn (M+S) $\checkmark$ $\checkmark$ $\checkmark$ $\checkmark$ Horn Pair$^1$ $\checkmark$ $\checkmark$ Frequency $\checkmark$ $\checkmark$ $\checkmark$ $\checkmark$ Cross-Frequency $\checkmark$ $\checkmark$ $^1$ this is (M+S)/2 and differences are between couple of horns (e.g. (28M+28S)/2- (27M+27S)/2) ### Polarisation Null Tests The same arguments applies also for polarization analysis with only some differences regarding the possible combination producing polarized data. Radiometer will not be available, instead of sum between M and S radiometer we will consider their difference. Data Set 1minute 1 hour Survey Full Mission Horn (M-S) $\checkmark$ $\checkmark$ $\checkmark$ $\checkmark$ Horn Pair$^1$ $\checkmark$ $\checkmark$ Frequency $\checkmark$ $\checkmark$ $\checkmark$ $\checkmark$ Cross-Frequency $\checkmark$ $\checkmark$ $^1$ this is difference between couple of horns (e.g. (28M-28S)/2- (27M-27S)/2) ### Practical Considerations For practical purposed and visual inspection of the null-tests results it would be useful to produce results smoothed at $3^\circ$ (and at $10^\circ$ for highlight larger angular scales) for all the total intensity maps. For polarization, as we already did several times when comparing to $WMAP$ data, a downgrade of the product at $N_{\rm side}=128$ would be useful to highlight large scale residuals. These considerations are free to evolve according to our needs. Due to large possibilities and number of data sets to be considered, it would be desirable to have sort of automatic tools that ingest two, or more, inputs maps and produce difference map(s) and corresponding angular power spectrum(spectra). This has been implemented using Python language and interacting directly with FITS files of a specific data release. The code is parallel and can run both at NERSC and at DPC producing consistent results. In addition for each null-tests performed a JSON DB file is produced in which main test informations are stored together with interesting computed quantities like mean, standard deviation of the residual maps. Beside JSON files also GIF images of the null-test are produced. Such JSON and GIF files are used to create (both with Python again and with Scheme) a report in form of an HTML page from the LFI Wiki. Together with images, power spectra of the residual are also produced and compared with the expected level of white noise derived from the half-ring jack-knifes. With these quantities are combined to produce a sort of $\chi^2$. This gives an indication of the deviation of the residuals with respect to the white noise level. Of course underlying signal does not posses a Gaussian statistic and therefore with non-Gaussian data, the $\chi^2$ tests is less meaningful. However this gives an hint on the presence of residuals which in some cases are indeed expected: in fact making difference between odd and even survey at horn and frequency level, is a way to show the signature of the external stray-light which, although properly accounted for during the calibration procedure, has not been removed from the data. ## Data Release Results ### Impact on cosmology (Planck) Low Frequency Instrument Data Processing Center Spacecraft Flexible Image Transfer Specification	2022-09-29T18:04:39	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5548908710479736, "perplexity": 1320.6220216744196}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030335362.18/warc/CC-MAIN-20220929163117-20220929193117-00726.warc.gz"}
http://dlmf.nist.gov/22.11	# §22.11 Fourier and Hyperbolic Series Throughout this section $q$ and $\zeta$ are defined as in §22.2. If $q\mathop{\exp\/}\nolimits\!\left(2\|\Im{\zeta}\|\right)<1$, then 22.11.1 $\displaystyle\mathop{\mathrm{sn}\/}\nolimits\left(z,k\right)$ $\displaystyle=\frac{2\pi}{Kk}\sum_{n=0}^{\infty}\frac{q^{n+\frac{1}{2}}\mathop% {\sin\/}\nolimits\!\left((2n+1)\zeta\right)}{1-q^{2n+1}},$ 22.11.2 $\displaystyle\mathop{\mathrm{cn}\/}\nolimits\left(z,k\right)$ $\displaystyle=\frac{2\pi}{Kk}\sum_{n=0}^{\infty}\frac{q^{n+\frac{1}{2}}\mathop% {\cos\/}\nolimits\!\left((2n+1)\zeta\right)}{1+q^{2n+1}},$ 22.11.3 $\displaystyle\mathop{\mathrm{dn}\/}\nolimits\left(z,k\right)$ $\displaystyle=\frac{\pi}{2K}+\frac{2\pi}{K}\sum_{n=1}^{\infty}\frac{q^{n}% \mathop{\cos\/}\nolimits\!\left(2n\zeta\right)}{1+q^{2n}}.$ 22.11.4 $\displaystyle\mathop{\mathrm{cd}\/}\nolimits\left(z,k\right)$ $\displaystyle=\frac{2\pi}{Kk}\sum_{n=0}^{\infty}\frac{(-1)^{n}q^{n+\frac{1}{2}% }\mathop{\cos\/}\nolimits\!\left((2n+1)\zeta\right)}{1-q^{2n+1}},$ 22.11.5 $\displaystyle\mathop{\mathrm{sd}\/}\nolimits\left(z,k\right)$ $\displaystyle=\frac{2\pi}{Kkk^{\prime}}\sum_{n=0}^{\infty}\frac{(-1)^{n}q^{n+% \frac{1}{2}}\mathop{\sin\/}\nolimits\!\left((2n+1)\zeta\right)}{1+q^{2n+1}},$ 22.11.6 $\displaystyle\mathop{\mathrm{nd}\/}\nolimits\left(z,k\right)$ $\displaystyle=\frac{\pi}{2Kk^{\prime}}+\frac{2\pi}{Kk^{\prime}}\sum_{n=1}^{% \infty}\frac{(-1)^{n}q^{n}\mathop{\cos\/}\nolimits\!\left(2n\zeta\right)}{1+q^% {2n}}.$ Next, if $q\mathop{\exp\/}\nolimits\!\left(\|\Im{\zeta}\|\right)<1$, then 22.11.7 $\displaystyle\mathop{\mathrm{ns}\/}\nolimits\left(z,k\right)-\frac{\pi}{2K}% \mathop{\csc\/}\nolimits\zeta$ $\displaystyle=\frac{2\pi}{K}\sum_{n=0}^{\infty}\frac{q^{2n+1}\mathop{\sin\/}% \nolimits\!\left((2n+1)\zeta\right)}{1-q^{2n+1}},$ 22.11.8 $\displaystyle\mathop{\mathrm{ds}\/}\nolimits\left(z,k\right)-\frac{\pi}{2K}% \mathop{\csc\/}\nolimits\zeta$ $\displaystyle=-\frac{2\pi}{K}\sum_{n=0}^{\infty}\frac{q^{2n+1}\mathop{\sin\/}% \nolimits\!\left((2n+1)\zeta\right)}{1+q^{2n+1}},$ 22.11.9 $\displaystyle\mathop{\mathrm{cs}\/}\nolimits\left(z,k\right)-\frac{\pi}{2K}% \mathop{\cot\/}\nolimits\zeta$ $\displaystyle=-\frac{2\pi}{K}\sum_{n=1}^{\infty}\frac{q^{2n}\mathop{\sin\/}% \nolimits\!\left(2n\zeta\right)}{1+q^{2n}},$ 22.11.10 $\mathop{\mathrm{dc}\/}\nolimits\left(z,k\right)-\frac{\pi}{2K}\mathop{\sec\/}% \nolimits\zeta=\frac{2\pi}{K}\sum_{n=0}^{\infty}\frac{(-1)^{n}q^{2n+1}\mathop{% \cos\/}\nolimits\!\left((2n+1)\zeta\right)}{1-q^{2n+1}},$ 22.11.11 $\mathop{\mathrm{nc}\/}\nolimits\left(z,k\right)-\frac{\pi}{2Kk^{\prime}}% \mathop{\sec\/}\nolimits\zeta=-\frac{2\pi}{Kk^{\prime}}\sum_{n=0}^{\infty}% \frac{(-1)^{n}q^{2n+1}\mathop{\cos\/}\nolimits\!\left((2n+1)\zeta\right)}{1+q^% {2n+1}},$ 22.11.12 $\mathop{\mathrm{sc}\/}\nolimits\left(z,k\right)-\frac{\pi}{2Kk^{\prime}}% \mathop{\tan\/}\nolimits\zeta=\frac{2\pi}{Kk^{\prime}}\sum_{n=1}^{\infty}\frac% {(-1)^{n}q^{2n}\mathop{\sin\/}\nolimits\!\left(2n\zeta\right)}{1+q^{2n}}.$ In (22.11.7)–(22.11.12) the left-hand sides are replaced by their limiting values at the poles of the Jacobian functions. Next, with $\mathop{E\/}\nolimits=\mathop{E\/}\nolimits\!\left(k\right)$ denoting the complete elliptic integral of the second kind (§19.2(ii)) and $q\mathop{\exp\/}\nolimits\!\left(2\|\Im{\zeta}\|\right)<1$, 22.11.13 ${\mathop{\mathrm{sn}\/}\nolimits^{2}}\left(z,k\right)=\frac{1}{k^{2}}\left(1-% \frac{E}{K}\right)-\frac{2\pi^{2}}{k^{2}K^{2}}\sum_{n=1}^{\infty}\frac{nq^{n}}% {1-q^{2n}}\mathop{\cos\/}\nolimits\!\left(2n\zeta\right).$ Similar expansions for ${\mathop{\mathrm{cn}\/}\nolimits^{2}}\left(z,k\right)$ and ${\mathop{\mathrm{dn}\/}\nolimits^{2}}\left(z,k\right)$ follow immediately from (22.6.1). For further Fourier series see Oberhettinger (1973, pp. 23–27). A related hyperbolic series is 22.11.14 $k^{2}{\mathop{\mathrm{sn}\/}\nolimits^{2}}\left(z,k\right)=\frac{\mathop{{E^{% \prime}}\/}\nolimits}{\mathop{{K^{\prime}}\/}\nolimits}-\left(\frac{\pi}{2\!% \mathop{{K^{\prime}}\/}\nolimits}\right)^{2}\sum_{n=-\infty}^{\infty}\left({% \mathop{\mathrm{sech}\/}\nolimits^{2}}\!\left(\frac{\pi}{2\!\mathop{{K^{\prime% }}\/}\nolimits}(z-2n\!\mathop{K\/}\nolimits)\right)\right),$ where $\mathop{{E^{\prime}}\/}\nolimits=\mathop{{E^{\prime}}\/}\nolimits\!\left(k\right)$ is defined by §19.2.9. Again, similar expansions for ${\mathop{\mathrm{cn}\/}\nolimits^{2}}\left(z,k\right)$ and ${\mathop{\mathrm{dn}\/}\nolimits^{2}}\left(z,k\right)$ may be derived via (22.6.1). See Dunne and Rao (2000).	2017-05-30T12:55:26	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 156, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9539922475814819, "perplexity": 1655.5105377767438}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-22/segments/1495463615105.83/warc/CC-MAIN-20170530124450-20170530144450-00151.warc.gz"}
https://indico.fnal.gov/event/20381/contributions	# New Perspectives 2019 10-11 June 2019 Fermi National Accelerator Laboratory US/Central timezone Home > Contribution List ## Contribution List Displaying 59 contributions out of 59 Type: Oral Session: Monday Afternoon I SBND is a Liquid Argon Time Projection Chamber (LArTPC) experiment and the near detector in the Short Baseline Neutrino (SBN) program at Fermilab. With a 110 m baseline and a 112 tonne active mass, the detector will observe ~5,000,000 charged current muon neutrino ($\nu_{\mu}$ CC) interactions at energies of <$E_{\nu}$> $\sim$ 650 MeV in its 6.6 $\times 10^{20}$ POT (3 year) exposure. SBND will co ... More Presented by Rhiannon JONES on 10 Jun 2019 at 3:30 PM Type: Oral Session: Monday Afternoon II The Accelerator Neutrino Neutron Interaction Experiment (ANNIE) is a gadolinium-doped water Cherenkov detector located in the Fermilab Booster Neutrino Beam line. Many long-baseline neutrino measurements rely on efficient reconstruction of charged-current quasi-elastic (CCQE) neutrino interactions, whose final-state particles include only the recoiling nucleus, a proton, and an outgoing lepton. O ... More Presented by Teal PERSHING on 10 Jun 2019 at 5:15 PM Type: Oral Session: Monday Afternoon II The Accelerator Neutrino Neutron Interaction Experiment (ANNIE) is a gadolinium-loaded water Cherenkov detector located on the Booster Neutrino Beam at Fermilab. The experiment seeks to better understand neutrino-nucleus interactions by studying the number of final state neutrons produced in charged current interactions. It will be the first experiment testing Large Area Picosecond Photodetectors ... More Presented by Dr. Emrah TIRAS on 10 Jun 2019 at 5:30 PM Type: Oral Session: Tuesday Afternoon II Despite that the Standard Model has been put through many stringent tests, it still can not be the full picture of particle physics. In this short talk, we give an overview of the motivations to go beyond the Standard Model and discuss a few plausible scenarios in its extension. Presented by Yang GAO on 11 Jun 2019 at 4:30 PM The LHC is the worlds highest energy proton-proton collider with a center-of-mass energy of 13 TeV. The world's largest machine is currently running at twice its designed luminosity and represents forefront of the energy frontier. The CMS detector is a multipurpose detector that features a 4 Tesla magnet and over a 100 million active channels taking data every 25 ns. It, along with its sister expe ... More Presented by Cristina Ana MANTILLA SUAREZ on 11 Jun 2019 at 9:00 AM Type: Oral Session: Monday Afternoon I MicroBooNE is a short baseline neutrino oscillation experiment based at Fermilab that employs a Liquid Argon Time Projection Chamber (LArTPC) to investigate the excess of low energy events observed by MiniBooNE, study neutrino-argon cross-sections, and perform detector R&D for future LArTPC experiments. The MicroBooNE detector lies along the Booster Neutrino Beamline, which produces neutrinos with ... More Presented by Polina ABRATENKO on 10 Jun 2019 at 2:45 PM Presented by Michael WALLBANK on 11 Jun 2019 at 5:45 PM Type: Oral Session: Tuesday Morning II The Deep Underground Neutrino Experiment (DUNE) is an international long-baseline neutrino experiment. DUNE will consist of an intense neutrino beam produced at Fermi National Accelerator Laboratory in Batavia, Illinois. The far detector will comprise of four Liquid Argon Time Projection Chambers (LArTPC) holding in total around 40 ktons of fiducial mass and will be placed at the Sanford Undergro ... More Presented by Mrs. Maura SPANU on 11 Jun 2019 at 12:00 PM Type: Oral Session: Monday Afternoon II As the SBN far-detector, the ICARUS T600, a set of liquid argon time-projection chambers (TPC), will operate at shallow depth and therefore be exposed to the full surface flux of cosmic rays. This poses a problematic background to the neutrino oscillation search, especially photons produced by muons passing in close proximity to, but not through, the active volume. A direct way to reject this back ... More Presented by Mr. Christopher HILGENBERG on 10 Jun 2019 at 4:15 PM Type: Oral Session: Tuesday Afternoon I NOvA is a long baseline neutrino experiment based at Fermilab that studies neutrino oscillation parameters via electron neutrino appearance and muon neutrino disappearance. The oscillation measurements compare the Far Detector data to an oscillated prediction which accounts for the Near Detector (ND) data and our understanding of neutrino interactions and cross-sections by using GENIE simulation. ... More Presented by Maria MARTINEZ-CASALES on 11 Jun 2019 at 3:35 PM Type: Oral Session: Monday Morning I The Dark Energy Survey (DES) is a deep, wide-area optical imaging survey in the southern hemisphere. The unprecedented photometry from DES has allowed for exciting science results on topics ranging from cosmology to our Galaxy. I will discuss details of the survey -- which completed its 5.5-year observations in January 2019 -- and highlight some recent science results from the collaboration. Presented by Nora SHIPP on 10 Jun 2019 at 9:10 AM Type: Oral Session: Tuesday Morning II A brief talk on the updates and technical details of DUNE in a concentrated format. Presented by Richard DIURBA on 11 Jun 2019 at 11:45 AM Type: Oral Session: Monday Morning II A large dynamical-range diagnostics (LDRD) design at Jefferson Lab will be used at the FAST-IOTA injector to measure the transverse distribution of halo associated with a high-charge electron beam. One important aspect of this work is to explore the halo distribution when the beam has significant angular momentum (i.e. is magnetized). The beam distribution is measured by recording radiation produc ... More Presented by Mr. Christopher MARSHALL on 10 Jun 2019 at 11:30 AM Type: Oral Session: Tuesday Afternoon II The Mu2e experiment at Fermilab will search for the charged-lepton flavour violating neutrino-less conversion of a negative muon into an electron in the field of an aluminum nucleus. The Mu2e detector is composed of a tracker and an electromagnetic calorimeter and an external veto for cosmic rays. The calorimeter plays an important role in providing excellent particle identification capabilitie ... More Presented by Dr. Raffaella DONGHIA on 11 Jun 2019 at 5:30 PM Type: Oral Session: Monday Morning I Charge Coupled Devices and MKIDs are pixelated imaging sensors used for astronomy. FNAL in involved in the development of instruments using these sensors. I will describe the development of a novel micro-mirror array projector for the characterization of these imaging sensors. The CCD require tight control of the light intensity and the exposure time, and the micromirror array allow to also contro ... More Presented by Brody OLESON on 10 Jun 2019 at 9:55 AM Type: Oral Session: Monday Morning II E1039/SpinQuest is the first transversally-polarized Drell-Yan experiment at Fermilab. SpinQuest data-taking is anticipated to begin this coming fall 2019. In SpinQuest, a transversely-polarized NH3 or ND3 target is employed with the unpolarized 120-GeV extracted proton beam from Fermilab Main Injector to obtain various measurements of transverse single spin asymmetries in J/psi, psi’, lambda, d ... More Presented by Dr. Chun-Min JEN on 10 Jun 2019 at 12:00 PM Type: Oral Session: Monday Afternoon II Elastic neutrino-electron scattering provides an important tool for normalizing neutrino flux in modern experiments. This process is subject to large radiative corrections. We determine the Fermi effective theory performing the one-loop matching to the Standard model at the electroweak scale with subsequent running down to GeV scale. Based on this theory, we analytically evaluate virtual correcti ... More Presented by Oleksandr TOMALAK on 10 Jun 2019 at 4:45 PM Presented by Dr. Deepika JENA on 11 Jun 2019 at 2:00 PM Type: Oral Session: Monday Afternoon II We propose a low-cost and movable setup to probe minicharged particles (or milli-charged particles) using high-intensity proton fixed-target facilities. This proposal, FerMINI, consists of a milliQan-type detector, requiring multi-coincident (nominally, triple-coincident) scintillation signatures within a small time window, located downstream of the proton target of a neutrino experiment. During t ... More Presented by Dr. Yu-Dai TSAI on 10 Jun 2019 at 6:00 PM Type: Oral Session: Monday Morning II The SpinQuest collaboration will measure the sea quark Sivers asymmetry using Drell-Yan production from the 120 GeV proton beam of the Fermilab Main Injector incident on transversely polarized proton and deuteron targets. Measuring a nonzero Sivers asymmetry would provide strong evidence for nonzero orbital angular momentum of sea quarks. The use of both polarized hydrogen and deuterium targets wi ... More Presented by Joshua HOSKINS on 10 Jun 2019 at 11:45 AM Type: Oral Session: Monday Morning I This project was realized primarily to test and improve the spatial tracking resolution of the ANL (Argonne National Laboratory) telescope consisting of the ATLAS IBL silicon pixel sensors and FE-I4 chips by making use of the test beam at Fermilab. In this paper, we will discuss the overall performance of the modules and how it can be improved. We will also discuss efforts made to improve the spat ... More Presented by Spoorthi NAGASAMUDRAM on 10 Jun 2019 at 10:25 AM Type: Oral Session: Monday Afternoon II Liquid Argon Time Projection Chambers (LArTPCs) are currently being used extensively for neutrino physics due to their excellent capabilities in performing particle identification, and precise 3D and calorimetric energy reconstruction. The Liquid Argon In A Test Beam (LArIAT) experiment was located at the Test Beam Facility where it was exposed to a known charged particle beam. The capability of ... More Presented by Vincent BASQUE on 10 Jun 2019 at 4:30 PM Type: Oral Session: Tuesday Morning I In this talk I summarize the current status of the field in lattice QCD. My goal will be to provide an accessible overview. I will emphasize work done at Fermilab and work affecting Fermilab experiments. Presented by William JAY on 11 Jun 2019 at 9:30 AM Type: Oral Session: Tuesday Morning I The CMS Muon group has proposed the use of Gas Electron Multiplier (GEM) technology to maintain an efficient and reliable operation during the High Luminosity phase of the LHC (HL-LHC). This is particularly important to study many physics processes with muons in the final state. The CMS GEM chambers will cover eta region 1.6 to 2.2 of the endcap. We report on the GE1/1 layout and their performance ... More Presented by Mr. Aashaq SHAH on 11 Jun 2019 at 10:00 AM Type: Oral Session: Monday Afternoon II Based in the NuMI beamline at Fermi National Laboratory, the on-axis MINERvA experiment is focused on reaching precision measurements of neutrino and antineutrino interactions in diverse nuclei materials for energies up to 50 GeV. The results support the current and future oscillation experiments as well as to provide information about the structure of nuclei. A look at the latest results from the ... More Presented by Ms. Barbara YAEGGY on 10 Jun 2019 at 5:00 PM Type: Oral Session: Monday Morning I Dark matter halos are the fundamental building blocks of cosmic large-scale structure. Improving our theoretical understanding of their structure, evolution and formation is an essential step towards understanding how galaxies form, which in turn will allow us to fully exploit the large amount of data from future galaxy surveys. I will present a machine learning approach which aims to provide new ... More Presented by Ms. Luisa LUCIE-SMITH on 10 Jun 2019 at 10:10 AM Type: Oral Session: Tuesday Morning II The Deep Underground Neutrino Experiment (DUNE) is a leading-edge experiment for neutrino science and proton decay studies. The single-phase liquid argon prototype detector at CERN is a crucial milestone for the DUNE that will inform the construction and operation of the far detector modules. In this talk, I will present the current status of reconstructing Michel electrons from cosmic-ray muons i ... More Presented by Dr. Aleena RAFIQUE on 11 Jun 2019 at 12:15 PM Type: Oral Session: Monday Afternoon I MicroBooNE is one of three liquid argon time projection chambers (LArTPCs) making up the Short-Baseline Neutrino Program at FNAL. Located on the Booster Neutrino Beamline, MicroBooNE has been collecting data since October 2015 to determine the source of the low-energy electromagnetic event excess previously reported by MiniBooNE and LSND. In addition to its signature analysis, MicroBooNE is employ ... More Presented by Ms. Katrina MILLER on 10 Jun 2019 at 2:00 PM Type: Oral Session: Tuesday Afternoon II The discovery of neutrino oscillation manifests the violation of lepton number conservation. It further indicates Charged Lepton Flavor Violation (CLFV) is not explicitly forbidden in the Standard Model (SM), although it is dynamically suppressed which remain unobserved. Many well-motivated physics models predict rates for CLFV processes that are within a few orders of magnitude of the current exp ... More Presented by Yujing SUN on 11 Jun 2019 at 5:15 PM Type: Oral Session: Tuesday Afternoon II The Muon $g-2$ Experiment (E989) is measuring the magnetic anomaly, $a_\mu$, of the muon to 140 parts per billion (ppb) to resolve the outstanding discrepancy between the value predicted by the Standard Model and the best measurement to date. The magnetic anomaly receives contributions from loops of any particle type in the muon-photon vertex, so a discrepancy between theory and experiment is a st ... More Presented by Jason HEMPSTEAD on 11 Jun 2019 at 4:45 PM Type: Oral Session: Tuesday Afternoon I The long-baseline neutrino oscillation experiment named NOvA is comprised of two detectors utilizing liquid scintillator tracking calorimeters. Both are positioned 14 mrad off-axis with respect to the NuMI beam with the near detector being at Fermilab. The far detector, at 14 kton, can be found approximately 810 km away in Ash River, Minnesota. The main physics goals of NOvA include, but are not l ... More Presented by Miranda ELKINS on 11 Jun 2019 at 2:20 PM Type: Oral Session: Tuesday Afternoon I NOvA continues as one of the leading long-baseline neutrino experiments, thanks to Fermilab's powerful 700 kW NuMI beam, which provides NOvA with a beam of predominantly muon neutrinos or antineutrinos. NOvA studies neutrino oscillations using two detectors, both constructed from plastic extrusions filled with liquid scintillator, placed 810 km apart and both slightly off-axis from the beam c ... More Presented by Dr. Ashley BACK on 11 Jun 2019 at 3:05 PM Type: Oral Session: Tuesday Afternoon I NOvA is a long-baseline neutrino experiment with two functionally identical liquid scintillator detectors 809 km apart, off-axis from the NuMI beam. The main goal of this experiment is to determine the mass hierarchy and precise measurement of several neutrino oscillation parameters. To measure these parameters precisely we need to have a correct estimate of the neutrino and antineutrino compositi ... More Presented by Mr. abhilash DOMBARA on 11 Jun 2019 at 3:20 PM Type: Oral Session: Tuesday Afternoon I Deep learning has aided the NOvA experiment in selection of NuMI beam neutrino events. Low statistics makes enhancements in signal efficiency especially critical to the success of the NOvA analysis. Use of convolutional neural networks (CNNs) for event and particle identification has led to significant gains in signal efficiency for neutrino event selection while also reducing the complexity of th ... More Presented by Grant NIKSERESHT on 11 Jun 2019 at 2:50 PM Type: Oral Session: Monday Afternoon I I will discuss the current state of neutrino theory work, specifically focusing on how we interface with interpretations of current experiments and predictions for upcoming experiments. I will discuss ideas that Fermilab theorists are currently exploring regarding the experimental neutrino program at Fermilab, from the SBN experiments to DUNE. Presented by Kevin KELLY on 10 Jun 2019 at 1:45 PM Type: Oral Session: Tuesday Afternoon I Muon monitors are a very important diagnostic tool for the NOvA experiment at Fermilab. With the MINOS experiment decommissioned, MM are the only detectors to indicate and help mitigate the issues with the NuMI beam. The goal of our study is to maintain the quality of the MM signal and to establish the neutrino beam profile and MM signal correlations. This study could also inform the LBNF decision ... More Presented by Yiding YU on 11 Jun 2019 at 2:35 PM Type: Oral Session: Tuesday Morning II The expected precision of current long-baseline neutrino oscillation experiments (T2K, NO$\nu$A) will be limited by uncertainties in neutrino interaction models in addition to sample statistics. The interaction uncertainties will also play a significant role in next-generation experiments (DUNE, Hyper-K), which aim to collect much larger samples of oscillated neutrinos. Without significant advance ... More Presented by Dr. Luke PICKERING on 11 Jun 2019 at 12:30 PM Type: Oral Session: Monday Afternoon I The Short-Baseline Near Detector (SBND) will be one of three liquid argon neutrino detectors sitting in the Booster Neutrino Beam (BNB) at Fermilab as part of the Short-Baseline Neutrino (SBN) Program. SBND is a 112-ton active mass liquid argon time projection chamber (LArTPC) to be located only 110 m from the BNB neutrino source. An important aspect of LArTPC detector design is that the readout a ... More Presented by Ryan LAZUR on 10 Jun 2019 at 3:15 PM Type: Oral Session: Tuesday Morning I A brief overview of perturbative QCD and its role in precision measurements at the LHC. There will be a focus on efforts that are being done here at Fermilab. Here at Fermilab, the QCD group focuses on three distinct topics. Therefore, the talk will focus on the importance of improving precision for measurements at the LHC, through the use of higher order corrections, analytic resummation, and par ... More Presented by Joshua ISAACSON on 11 Jun 2019 at 9:15 AM Type: Oral Session: Tuesday Afternoon II The Muon g-2 experiment at Fermilab (E989) aims to measure the anomalous magnetic moment of the muon, $a_{\mu}$, to a precision of $140$ ppb, a four-fold increase in precision over the previous experiment at Brookhaven National Laboratory (BNL). The value of $a_{\mu}$ from BNL currently differs from the Standard Model prediction by $\sim 3.5$ standard deviations or higher, suggesting the potential ... More Presented by Ms. Meghna BHATTACHARYA on 11 Jun 2019 at 5:00 PM Type: Oral Session: Monday Morning II This study is focused on the development of an in-situ plasma cleaning procedure for 1.3GHz 9-cell TESLA shaped SRF cavities. The goal of this technique is to reduce field emission through the removal of adsorbed hydrocarbons that lower the work function of the cavity surface. In this work I present the first results of plasma processing applied to LCLS-II cavities focusing on plasma ignition an ... More Presented by Bianca GIACCONE on 10 Jun 2019 at 11:00 AM Type: Oral Session: Monday Afternoon I Next generation neutrino oscillation experiments aim towards high-precision extraction of oscillation parameters, which in turn requires an unprecedented understanding of neutrino-nucleus interactions. Neutrino processes producing a charged lepton and a single intact nucleon in the final state can offer an important window into the dynamics of neutrino interactions with direct importance for ac ... More Presented by Ms. Afroditi PAPADOPOULOU on 10 Jun 2019 at 2:15 PM Type: Oral Session: Tuesday Morning I Clustering of charged particle tracks along the beam axis is the first step in reconstructing the positions of proton-proton (p-p) collisions at Large Hadron Collider (LHC) experiments. In this talk, we formulate this problem for a 2048 qubit D-Wave quantum computer that works by quantum annealing. We show the performance of the quantum annealer on artificial events generated from p-p collision an ... More Presented by Andrew WILDRIDGE, Souvik DAS, Mr. Sachin VAIDYA on 11 Jun 2019 at 10:15 AM Type: Oral Session: Monday Afternoon I The Short-Baseline Near Detector (SBND) will be a 112 ton liquid argon time projection chamber devoted to researching neutrino oscillations. Located 110 m downstream from the Booster Neutrino Beam (BNB) target, SBND will be the near detector of the three-detector Short Baseline Neutrino (SBN) program at Fermilab. The SBN program will probe neutrino oscillations at the $\sim \! 1 \textrm{eV}^2$ sca ... More Presented by Iker DE ICAZA ASTIZ on 10 Jun 2019 at 3:00 PM Type: Oral Session: Tuesday Morning I The CMS Phase II upgrade, High Granularity Calorimeter (HGCal) will have fine transverse and longitudinal segmentation to allow for superior particle identification and pileup rejection in the high radiation and large event pileup environment of the endcap region. A significant portion of the hadronic portion of the HGCal will be instrumented with scintillator tiles directly coupled to Silicon Pho ... More Presented by Ramanpreet SINGH on 11 Jun 2019 at 9:45 AM Type: Oral Session: Tuesday Morning II In traditional searches for physics beyond the standard model, a requirement of high missing transverse momentum (MET) is often used. However, without any signs of significant deviations from the standard model expectations, we decided to relax this requirement for the search reported in this talk. Many new physics models, including versions of supersymmetry (SUSY) characterized by R-parity violat ... More Presented by Christopher MADRID on 11 Jun 2019 at 11:15 AM Type: Oral Session: Tuesday Morning II Searches for dark matter in the past two decades have largely focused on Weakly Interacting Massive Particles (WIMPs). But what if instead of just one type of dark matter particle, there exists a richer dark sector hidden from ordinary view? This opens up a whole new paradigm for dark matter searches, allowing us to focus not only on the coupling between dark matter and the Standard Model, but als ... More Presented by Andre STERENBERG FRANKENTHAL on 11 Jun 2019 at 11:30 AM Type: Oral Session: Tuesday Morning II Most theories that predict dark matter production at colliders rely on weakly coupled dark matter and the existence of WIMPs, or weakly interacting massive particles; however, there can be dark matter signatures in colliders that emerge from strongly coupled dark matter. These signatures are varied, ranging from emerging jets to Stealth Dark Matter. Another possible signature is semi-visible jets. ... More Presented by Colin FALLON on 11 Jun 2019 at 11:00 AM Type: Oral Session: Monday Morning I The Milky Way satellites are among the least luminous and most dark matter-dominated galaxies in the known universe. I present on a search for low-luminosity dwarf galaxy companions of the Milky Way in three years of data from the Dark Energy Survey (DES) and the Panoramic Survey Telescope and Rapid Response System (Pan-STARRS PS1). Together, these two surveys cover roughly three-quarters of the s ... More Presented by Sidney MAU on 10 Jun 2019 at 9:25 AM Type: Oral Session: Tuesday Morning II ProtoDUNE-SP, the prototype of the single-phase DUNE far detector, is constructed and operated at the CERN Neutrino Platform with total liquid argon (LAr) mass of 0.77 kt and using full-scale components of the design for DUNE. The physics program of protoDUNE-SP aims to understand and control the systematic uncertainties for future oscillation measurements at DUNE, the charged-particle beam test a ... More Presented by Carlos SARASTY SEGURA Type: Oral Session: Monday Morning II The Muon Campus at Fermilab presently houses two experiments that aim to find discrepancies (if any) in the Standard Model. The Delivery Ring is a 500m circumference storage ring which is used to deliver protons to muon experiments Muon g-2 and Mu2e. Although these experiments are based on the same particle, they require different intensities because of their detector constraints. For the Mu2e cas ... More Presented by Mr. Prudhvi Raj Varma CHINTALAPATI on 10 Jun 2019 at 11:15 AM Type: Oral Session: Monday Morning I Modern cosmic sky surveys (e.g., CMB S4, DES, LSST) collect a complex diversity of astronomical objects. Each of class of objects presents different requirements for observation time and sensitivity. For determining the best sequence of exposures for mapping the sky systematically, conventional scheduling methods do not optimize the use of survey time and resources. We present an alternative sched ... More Presented by Mr. Andres Felipe ALBA HERNANDEZ Type: Oral Session: Monday Morning I Strong gravitational lenses are cosmic magnifying glasses that can be used as a probe of cosmic phenomena, like dark energy and dark matter. However, strong lensing systems are rare and complex, which means they are both hard to find and analyze. We present two important results in strong lensing science: 1) new deep learning techniques for finding and measuring strong lenses; and 2) dark energy f ... More Presented by Jason POH on 10 Jun 2019 at 9:40 AM Type: Oral Session: Monday Afternoon II The Super Cryogenic Dark Matter Search (SuperCDMS) is at the low-threshold frontier. Our detector technology can detect nuclear recoils at the eV-scale energies necessary for generation-two low-mass dark matter searches. The SNOLAB installation, which will be commissioned in the next two years, will produce world-class limits on the presence of low-mass (between 0.5 and 10\,GeV/c$^2$) dark matter. ... More Presented by Dr. Anthony VILLANO on 10 Jun 2019 at 5:45 PM Type: Oral Session: Tuesday Afternoon I NOvA is a two-detector long-baseline neutrino oscillation experiment which aims to make a determination of the neutrino mass hierarchy, the octant of ${\theta}_{23}$, and measure possible CP violation. The NOvA Test Beam program consists of a scaled-down NOvA detector placed in a beamline capable of delivering 0.3 - 2.0 GeV/c protons, electrons, pions, and kaons. The beamline detectors provide us ... More Presented by Teresa LACKEY on 11 Jun 2019 at 3:50 PM Type: Oral Session: Monday Afternoon I The MicroBooNE experiment is an 87 t active mass Liquid Argon Time Projection Chamber (LArTPC) located on the Booster Neutrino Beam (BNB) at Fermilab, Chicago. The primary physics goals of this experiment are to investigate the excess of low energy electron-like events observed by MiniBooNE, perform precise measurements of neutrino on argon cross sections, and provide research and development for ... More Presented by Mr. Krishan MISTRY on 10 Jun 2019 at 2:30 PM Presented by Dr. Gavin S. DAVIES on 11 Jun 2019 at 2:10 PM Session: Monday Morning I Presented by Andrew FURMANSKI, Andrew FURMANSKI on 10 Jun 2019 at 9:00 AM	2019-12-07T18:54:54	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5265907049179077, "perplexity": 5934.012272415839}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-51/segments/1575540501887.27/warc/CC-MAIN-20191207183439-20191207211439-00505.warc.gz"}
https://wiki.cosmos.esa.int/planckpla/index.php?title=HFI/LFI_joint_data_processing&oldid=7165	# HFI/LFI joint data processing (diff) ← Older revision \| Latest revision (diff) \| Newer revision → (diff) Jump to: navigation, search / common processing uses as basic input the maps at the nine frequencies covered by the two instruments. The goal is to obtain various catalogues, identify the different astrophysical components whose superposition leads to the observed sky, and provides a statistical characterisation of the , in particular through a likelihood code (of a particular theoretical $C(\ell)$ given Planck data).	2017-12-18T20:19:56	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8200778961181641, "perplexity": 6341.85009930046}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-51/segments/1512948623785.97/warc/CC-MAIN-20171218200208-20171218222208-00783.warc.gz"}
https://indico.fnal.gov/event/19348/contributions/186302/	# Neutrino 2020 June 22, 2020 to July 2, 2020 US/Central timezone ## The NEXT-100 neutrinoless double beta decay experiment Not scheduled 10m Poster Jonathan Haefner ### Description The NEXT experiment is searching for neutrinoless double beta decay ($0\nu\beta\beta$) in an electroluminescent high pressure gaseous $^{136}$Xe time projection chamber (HPGXeTPC). Positive detection would indicate that the neutrino, unlike all other fundamental leptons, has a Majorana mass term, and that lepton number is not conserved. The NEXT experiment leverages several advantages of the HPGXeTPC technology, including excellent energy resolution (<1% FWHM at the decay energy) and background rejection through track reconstruction. The detector is under construction with installation and commissioning planned for late 2020 or early 2021. NEXT-100 is expected to reach a sensitivity of $1 \times 10^{26}$ years (90% CL) for an exposure of 400 kg$\cdot$year. ### Mini-abstract Design, plans, and expected performance of the upcoming 100 kg gaseous xenon NEXT detector. Experiment/Collaboration NEXT Collaboration	2022-11-28T11:57:31	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6620216965675354, "perplexity": 5886.882133196179}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446710503.24/warc/CC-MAIN-20221128102824-20221128132824-00020.warc.gz"}
https://portlandpress.com/clinsci/article/134/20/2729/226790/fiddle-a-tool-to-combat-publication-bias-by	Statistically significant findings are more likely to be published than non-significant or null findings, leaving scientists and healthcare personnel to make decisions based on distorted scientific evidence. Continuously expanding ´file drawers’ of unpublished data from well-designed experiments waste resources creates problems for researchers, the scientific community and the public. There is limited awareness of the negative impact that publication bias and selective reporting have on the scientific literature. Alternative publication formats have recently been introduced that make it easier to publish research that is difficult to publish in traditional peer reviewed journals. These include micropublications, data repositories, data journals, preprints, publishing platforms, and journals focusing on null or neutral results. While these alternative formats have the potential to reduce publication bias, many scientists are unaware that these formats exist and don’t know how to use them. Our open source file drawer data liberation effort (fiddle) tool (RRID:SCR_017327 available at: http://s-quest.bihealth.org/fiddle/) is a match-making Shiny app designed to help biomedical researchers to identify the most appropriate publication format for their data. Users can search for a publication format that meets their needs, compare and contrast different publication formats, and find links to publishing platforms. This tool will assist scientists in getting otherwise inaccessible, hidden data out of the file drawer into the scientific community and literature. We briefly highlight essential details that should be included to ensure reporting quality, which will allow others to use and benefit from research published in these new formats. Many laboratories have a ´file drawer’ [1] of unpublished data from well-designed experiments. There are many reasons why data may end up in the file drawer [2,3]. For example, the research team may not have the time or expertise required to analyze the entire data set. Lower priority datasets may remain unpublished, as lab members focus on preparing manuscripts containing the results of high priority experiments. Parts of the study may be missing or incomplete. The study may be a failed replication attempt. Personnel responsible for the project may have left the laboratory before writing a manuscript, or the authors may have published some parts from a larger study, but not others. Alternatively, editors may have rejected the manuscript because the findings were not exciting enough for publication in the authors’ journal of choice. Regardless of the reasons, failing to publish data from well-designed experiments creates problems for individual researchers, the scientific community and the public. Scientists in preclinical and translational research have invested time and research funds to design and conduct studies yielding valuable data that they have either chosen not to publish, have not been able to publish, or have only partially published [4–6]. Funding agencies and the public do not learn anything from research that is not shared; hence the resources used to complete the work are wasted [7]. Other laboratories, who have no way of knowing that the research was ever conducted, may invest additional time and funding to repeat the same types of studies. Additional problems depend on the type of study. When data from animal studies are not published or shared, animals suffer or are killed without benefits to scientists or society [8–10]. Publication bias can also create risks for patients. Unpublished preclinical data can lead to flawed decisions about whether a potential therapy should advance to clinical trials, exposing patients to unnecessary burdens and risks [11]. When results from neutral or negative clinical trials are not published, clinicians’ decisions and recommendations about patient care are based on incomplete evidence [11]. Studies with neutral and null results are more likely to end up in the file drawer than studies with statistically significant findings [12]. This publication bias (Box 1) leaves scientists, funding agencies and clinicians with a distorted view of the scientific evidence, which can lead to poor decisions about what research directions are most promising and should be funded or what medical treatments should be recommended to patients [13]. Such practices can have detrimental consequences. During the 1980s, over 100,000 people died after receiving lorcainide-class like drugs. These antiarrhythmic medications were routinely prescribed to patients after a heart attack. A publication with data on the lethal side effects of lorcainide was repeatedly rejected and ultimately not published for 13 years, as the authors did not interpret the death rates in their small study as conclusive evidence and journals repeatedly refused to publish these null results [14–16]. While this example is extreme, it illustrates the potential harmful effects of publication bias. Selective reporting of results can create similar problems. Box 1 Publication bias and selective reporting • Publication bias occurs when study results influence decisions by authors, reviewers or editors about whether to publish a study, independent of the quality of the research. • Publication bias distorts scientists’ perception of the evidence. When studies showing an effect are more likely to be published than those with null results, a meta-analysis may incorrectly conclude that there is an effect, or may overestimate the effect size [17]. The potential for distortion increases as the probability of publishing null or neutral results decreases. • Several factors contribute to publication bias, and influence the degree to which publication bias distorts the scientific evidence [13]. • Prioritizing statistical significance: The incorrect belief that statistically significant findings are important and relevant, whereas findings that are not statistically significant are less important and less relevant, contributes to publication bias. These beliefs can affect authors’ decisions about whether to submit a manuscript, or editors’ and reviewers’ decisions to recommend publication of the manuscript. • Prior publications: Researchers who hypothesized that there was an effect based on published studies may erroneously conclude that their study design, methods or results were faulty if the hypothesized effect is not found and avoid submitting their study for publication. These beliefs emphasize statistical significance and agreement with previous results over effect sizes and study quality. • Effect size: When the effect is large, most studies will yield statistically significant results. Studies with null or neutral results will be uncommon; hence fewer studies will remain unpublished due to publication bias. When the effect size is small, publication bias is a bigger problem. Many studies will yield negative or neutral results and may be subject to publication bias [2]. • Statistical power: Publication bias may be a greater problem in fields where researchers typically conduct small, underpowered studies [2]. Assuming that there is an effect, high-powered studies are more likely to detect this effect than low powered studies. • Another related problem is selective reporting. Publication bias occurs when scientists make decisions about whether to publish an entire study based on the results. Selective reporting occurs when authors, reviewers or editors make decisions about whether to publish particular outcome variables based on the results. Authors may decide, for example, to ´selectively report’ measurements with statistically significant differences and omit variables that were not statistically different. Alternatively, authors may be more likely to report parts of an experiment that support their hypothesis and less likely to publish parts of an experiment that do not support their hypothesis. • Selective reporting can also occur when authors provide more information about statistically significant results, compared to non-significant results. For example, authors may report detailed information about statistically significant findings in tables and figures, but state that data were not shown for non-significant findings. When summary statistics and sample sizes are not available, data cannot be replicated or included in a meta-analysis. • Determinants of selective reporting include a focus on preferred findings, poor or flexible research design, publishing in fields with a high risk of selective reporting, dependence upon sponsors, prejudice, and other factors [3]. Unfortunately, scientists don’t know what proportion of data are never published because there is no comprehensive registry of all planned studies. A study in social science found that two thirds of survey-based experiments that produced null results ended up in the file drawer, whereas nearly all experiments with statistically significant results supporting the underlying hypothesis were published [18]. Many reports confirm the same phenomenon in the medical field, where negative results are less likely to be published [12,19,20]. Clinical trials offer another unique opportunity to assess publication bias, as journal editors began requiring trial registration in 2005 [21,22]. Estimates from AllTrials (http://www.alltrials.net/), based on comparisons of registered versus published trials, suggest that approximately 50% of clinical trials results remain unpublished [23,24]. New publication formats (Box 2) make it easier for scientists to share research, regardless of the outcome (Table 1), while also ensuring that the data become a part of the permanent scientific record. Tables 1 and 2 and fiddle explain and compare these different formats. fiddle also provides links to websites for publishers of each publication format, which researchers can use to find sample publications that may be relevant to their field. Fiddle focuses on generalist publishers that publish papers from many different fields; it does not provide a comprehensive list of discipline specific publishers. The tool does include links to curated lists designed to help readers identify specialized repositories and discipline-specific databases (i.e. re3data.org, fairsharing.org, and Nature’s list of recommended repositories). Users who are interested in discipline specific repositories or databases can use these links to identify suitable options once they have chosen a publication format. Table 1 fiddle allows authors to quickly compare and contrast different publication formats Data RepositoryMicropublicationPreprint publicationData journalsPublishing platformJournal open to null results Description Platforms that allow upload of research datasets to make them citable and reusable. Designed for unpublished observations, negative/neutral results that do not require a scientific narrative. Platforms for unpublished research manuscripts that allow others to immediately view the manuscript. Journal article that focuses on presenting a dataset with metadata and the methods used to aquire the dataset. Articles are published without editorial filtering; peer-review happens after (immediate) publication of the article. Traditional journals that also publish null results. Providers Zenodo, FigShare or Dryad; to search for disciplinary repositories use re3data, fairsharing, or Nature's list ScienceMatters, BMC Research Notes biorxiv, medRxiv, osf.io Scientific Data, Data, Data in Brief, F1000 Data Note, many disciplinary journals (e.g. GigaScience) F1000Research, Open Research Central PeerJ, PLoS One, Scientific Reports, multiple BMC journals and many other disciplinary journals Effort low effort low effort medium effort some effort to prepare manuscript/data some effort to prepare manuscript/data some effort to prepare manuscript/data Costs in EUR free of charge 600 - 1300 € free of charge up to 1500 € up to 1000 € up to 1600 € Costs in US$free of charge 670 - 1440$ free of charge up to 1670 $up to 1100$ up to 1780 $Time to publication immediate typically 1-3 months immediate typically 1-4 months immediate typically 1-6 months Recognition citations of the dataset citations of article, article can be listed in CV (future handling of such articles is open) citations of article, article can be listed in CV (not universally accepted at this point) citations of article, article can be listed in CV citations of article, article can be listed in CV (not universally accepted at this point) citations of article, article can be listed in CV Publishing venue can have Impact Factor no yes no yes no yes Peer-review no peer-review post-publication review possible peer-review peer-review peer-review DOI yes yes yes yes yes yes Versioning yes no yes yes yes no Indexing: Pubmed no no no yes yes yes Pubmed Central no some no some yes Yes Web of Science no some no most no yes Scopus no some no some no yes CrossRef no some yes some yes yes Google Scholar no yes yes yes yes yes Additional information integrated open data upload, reviewer compensation, often only one reviewer preprint deposit accepted by large majority of journals and often offered as integral steps in submission process (see Sherpa/ROMeO) Data RepositoryMicropublicationPreprint publicationData journalsPublishing platformJournal open to null results Description Platforms that allow upload of research datasets to make them citable and reusable. Designed for unpublished observations, negative/neutral results that do not require a scientific narrative. Platforms for unpublished research manuscripts that allow others to immediately view the manuscript. Journal article that focuses on presenting a dataset with metadata and the methods used to aquire the dataset. Articles are published without editorial filtering; peer-review happens after (immediate) publication of the article. Traditional journals that also publish null results. Providers Zenodo, FigShare or Dryad; to search for disciplinary repositories use re3data, fairsharing, or Nature's list ScienceMatters, BMC Research Notes biorxiv, medRxiv, osf.io Scientific Data, Data, Data in Brief, F1000 Data Note, many disciplinary journals (e.g. GigaScience) F1000Research, Open Research Central PeerJ, PLoS One, Scientific Reports, multiple BMC journals and many other disciplinary journals Effort low effort low effort medium effort some effort to prepare manuscript/data some effort to prepare manuscript/data some effort to prepare manuscript/data Costs in EUR free of charge 600 - 1300 € free of charge up to 1500 € up to 1000 € up to 1600 € Costs in US$ free of charge 670 - 1440 $free of charge up to 1670$ up to 1100 $up to 1780$ Time to publication immediate typically 1-3 months immediate typically 1-4 months immediate typically 1-6 months Recognition citations of the dataset citations of article, article can be listed in CV (future handling of such articles is open) citations of article, article can be listed in CV (not universally accepted at this point) citations of article, article can be listed in CV citations of article, article can be listed in CV (not universally accepted at this point) citations of article, article can be listed in CV Publishing venue can have Impact Factor no yes no yes no yes Peer-review no peer-review post-publication review possible peer-review peer-review peer-review DOI yes yes yes yes yes yes Versioning yes no yes yes yes no Indexing: Pubmed no no no yes yes yes Pubmed Central no some no some yes Yes Web of Science no some no most no yes Scopus no some no some no yes CrossRef no some yes some yes yes Google Scholar no yes yes yes yes yes Additional information integrated open data upload, reviewer compensation, often only one reviewer preprint deposit accepted by large majority of journals and often offered as integral steps in submission process (see Sherpa/ROMeO) The first two rows of fiddle describe each publication format and offer links to providers or publishers. The remaining columns allow users to compare publication formats according to different characteristics (required effort, cost, whether materials are peer reviewed, what databases index materials, etc.) Table 2 What do different publication formats include? InformationData RepositoryMicropublicationPreprintData JournalPublishing platformJournal Open to Null Results Abstract ✓ ✓ ✓ ✓ ✓ ✓ Introduction Brief ✓ ✓ ✓ ✓ Methods Brief ✓ ✓ ✓ ✓ Results Brief ✓ ✓ ✓ Discussion and interpretation ✓ ✓ ✓ Raw data ✓ ✓ Peer reviewed No Yes No* Yes Yes Yes InformationData RepositoryMicropublicationPreprintData JournalPublishing platformJournal Open to Null Results Abstract ✓ ✓ ✓ ✓ ✓ ✓ Introduction Brief ✓ ✓ ✓ ✓ Methods Brief ✓ ✓ ✓ ✓ Results Brief ✓ ✓ ✓ Discussion and interpretation ✓ ✓ ✓ Raw data ✓ ✓ Peer reviewed No Yes No* Yes Yes Yes The table provides a rough overview of what different publishing formats include, as well as information on whether the format is typically peer reviewed. Check marks indicate that the publication format traditionally includes the item, whereas blank spaces indicates that the publication format does not traditionally include this item. ´Brief’ indicates that the publication includes a condensed version of this item. See Table 1 and fiddle for additional information on each format. * Post-publication peer review of pre-prints is possible Peer review for publishing platforms happens after immediate posting of the article These article types do not traditionally include raw data or metadata, however raw data and metadata can be deposited in a data repository and cited in preprints, or papers posted on publishing platforms and in journals open to null results. Box 2 What counts as publication? • In this paper, “publication” refers to any documented product derived from research data that is in the public domain. The various publication formats described in fiddle differ in the degree of documentation and intellectual reflection. A traditional journal article accompanied by archived raw data has the highest degree of data set enrichment, whereas data deposited in a repository contains the smallest degree of enrichment. The six publication formats described in fiddle have four things in common. They are all: 1. Assigned a permanent digital object identifier (DOI), 2. Findable via different scholarly indexing tools and many provide open access availability 3. Citable and 4. Attributable to an author or originator. • Some of the publication formats in fiddle complement one another, or can be used to enhance traditional publications. For instance, datasets deposited in repositories complement traditional research articles published as preprints, on publishing platforms, or in peer reviewed journals. An increasing number of peer-reviewed journals simplify the submission process by allowing authors to directly submit preprints to the journal for consideration. • As the use of preprints and other alternative publication formats continues to grow, the incentives for avoiding publication bias and using new publication formats will continue to shift [25]. The Declaration of Helsinki notes that all researchers have an ethical obligation to disseminate research results [26]. Funders have highlighted the importance of ensuring that research outputs, including negative results, are published [7,27,28]. Funding agencies such as the National Institutes of Health in the United States allow researchers to cite preprints in grant applications [29]. Papers that deposit open data accumulate up to 25% more citations than papers that do not have open data [30,31]. Some of the new publication formats follow the same format as traditional peer-reviewed research articles, but make it easier to publish manuscripts that would typically be rejected from journals where editorial and peer review often prioritizes exciting results. Preprints, for example, are unpublished manuscripts that have not been peer-reviewed and are shared immediately with the scientific community. Platforms that publish preprints include bioRxiv, medRxiv, and Open Science Framework Preprint Services. Publication platforms, such as F1000 Research and Open Research Central, publish articles immediately without editorial filtering. Open peer review occurs after publication. Journals that are open to null results are traditional journals that publish peer-reviewed manuscripts but welcome all studies regardless of outcome. Such journals have clear public policies to publish manuscripts describing well-designed studies with null results, results that appear to contradict those of previous publications [32] or other research outcomes that are hard to publish. Examples include PeerJ and PLOS ONE. Other new publication formats facilitate publication of data or results that would be difficult to share in an Introduction-Method-Results-Discussion format. Micropublications, for example, are very short publications designed for unpublished observations, neutral or null results or other research that does not require a scientific narrative [33]. Platforms that publish micropublications include Science Matters and BMC Research Notes. Data repositories, such as figshare, Zenodo or Dryad, allow scientists to upload small or large research datasets to make them citable and reusable. Data journals, such as Scientific Data or Data, publish journal articles that present a dataset, metadata explaining the dataset and the data collection methods. As the use of preprints [25] and other alternative publication formats continues to grow, even researchers who choose not to use these formats will benefit from understanding how they work. Knowing where these research outputs are indexed and whether they are peer reviewed, for example, is essential to finding and evaluating materials that are relevant to one’s area of research. Scientists who are unaware of data repositories and data journals may miss opportunities to use datasets relevant to their work. Researchers who don’t know about rapidly growing preprint servers may not find out about important studies until papers are published, often many months after the preprints were first posted. Tools that help researchers to understand different publication formats and identify those formats that are most appropriate for the dissemination of their data are thus urgently needed [34]. fiddle is a free, open source ´matchmaking’ tool designed to help researchers to identify the publication format that will work best for a particular dataset or study that may be hard to publish in traditional journals (RRID:SCR_017327, available at: http://s-quest.bihealth.org/fiddle/). The tool includes a link to a brief video tutorial. Researchers can use this shiny (RRID:SCR_001626) [35] app to quickly compare characteristics of different publications formats and search for a format that best meets their needs. Fiddle is not discipline-specific and can be used for any life science field where publication occurs and where research results from well designed and executed studies remain hidden in the file drawer. Once users have identified a publication format in fiddle, they can click on links to visit websites of relevant publishers or platforms, or see examples of this particular format. There are two ways to search for publication formats (Figure 1). The first filtering option is to search by important characteristics describing the dataset and the researcher's publishing-related preferences. Users can find suitable publishing platforms by answering the questions below that are most relevant to them: 1. What type of unpublished information do you have (unanalyzed dataset, rejected manuscript, etc.)? 2. Amount of funding available for publication costs 3. Where should the publication or dataset be indexed? 4. Do you want the publication or dataset to be peer reviewed? 5. Do you want the publication or dataset to appear immediately? ### Search strategies in fiddle Figure 1 Search strategies in fiddle Authors can identify publication formats that meet their needs by selecting either characteristics that are most important or relevant to them (Search by Options) or by selecting the scenario that best describes their situation (Search by Scenarios). Figure 1 Search strategies in fiddle Authors can identify publication formats that meet their needs by selecting either characteristics that are most important or relevant to them (Search by Options) or by selecting the scenario that best describes their situation (Search by Scenarios). Close modal The other, alternative filtering option is to search by scenarios that describe the reason why the information is unpublished. Example scenarios include ´I don’t have enough time to prepare a publication’, ´I have data that may be useful to others, but am not able to analyze everything’, and ´My study is completed, but the findings aren’t novel or exciting’. The tool highlights publication formats that meet the user's requirements. Users can review detailed information on each type of publication format and then click on links to visit websites for different publishers. Users can also compare all publication formats. All options in fiddle provide a permanent, citable and findable link to the data or manuscript. Many formats are also peer-reviewed. The source code for fiddle is available at https://github.com/quest-bih/fiddle. Scientists should focus on the quality of the study methods, rather than the desirability of the results, when deciding which file drawer data to publish. While data from well-designed experiments often ends up in the file drawer, many file drawers also contain data from poorly designed, badly conducted or insufficiently documented experiments that are unlikely to be reproducible or useful. fiddle and other efforts to reduce publication bias and selective reporting encourage authors to publish data from well-designed experiments that may be useful to the scientific community or the public, regardless of whether the findings were statistically significant. This applies also for datasets that are too small to yield reliable conclusions, however may be informative when combined with many other datasets using techniques such as meta-analysis. fiddle is not intended to promote publication of data from poor quality studies that are unlikely to be useful or informative. Authors should consult study design and reporting guidelines when designing studies and preparing publications to increase the likelihood that data will be transparent, rigorous and reproducible. Table 3 lists guidelines for common types of studies in many fields, including observational studies, animal studies, randomized controlled trials, and systematic reviews and meta-analyses. Guidelines for other types of studies can be found through the EQUATOR network website (RRID:SCR_012861). Table 3 Guidelines for conducting transparent, rigorous and reproducible research Guidelines for common types of studies Study typeGuideline acronymRRID or CitationLink Observational studies STROBE RRID: SCR_018788 https://www.strobe-statement.org/ Animal studies - planning PREPARE RRID:SCR_018787 https://norecopa.no/PREPARE Animal studies - reporting ARRIVE 2.0 RRID:SCR_018719 https://arriveguidelines.org/arrive-guidelines Randomized controlled trials CONSORT RRID:SCR_018720 http://www.consort-statement.org/ Systematic review and meta-analysis PRISMA RRID:SCR_018721 http://www.prisma-statement.org/ Systematic review and meta-analysis of observational studies MOOSE Stroup et al., 2000 [36https://jamanetwork.com/journals/jama/fullarticle/192614 Guidelines for common types of studies Study typeGuideline acronymRRID or CitationLink Observational studies STROBE RRID: SCR_018788 https://www.strobe-statement.org/ Animal studies - planning PREPARE RRID:SCR_018787 https://norecopa.no/PREPARE Animal studies - reporting ARRIVE 2.0 RRID:SCR_018719 https://arriveguidelines.org/arrive-guidelines Randomized controlled trials CONSORT RRID:SCR_018720 http://www.consort-statement.org/ Systematic review and meta-analysis PRISMA RRID:SCR_018721 http://www.prisma-statement.org/ Systematic review and meta-analysis of observational studies MOOSE Stroup et al., 2000 [36https://jamanetwork.com/journals/jama/fullarticle/192614 Consult these resources to find guidelines for other types of studies Guidelines for many different types of studies EQUATOR network RRID:SCR_012861 https://www.equator-network.org/ Consult these resources to find guidelines for other types of studies Guidelines for many different types of studies EQUATOR network RRID:SCR_012861 https://www.equator-network.org/ The table provides information on guidelines for specific types of studies that are common in many fields, as well as resources that will allow researchers to find guidelines for less common types of studies. The goal of publishing file drawer data is to make these research outputs available to the scientific community; therefore, scientists should ensure that the information is shared in a form that others can understand and use. The list below outlines some important features that should be reported for most, if not all, formats listed in fiddle. Additional information may be needed, depending on the publication format, study design, experimental methods, and type of data that is generated. The lack of time is one reason for not publishing file drawer data [3]; therefore there may be trade-offs between efforts to reduce publication bias by introducing shorter publication formats that take less time to prepare and attempts to improve transparency and reproducibility by encouraging authors to report detailed information required to assess study quality. Information that scientists need to interpret and use scientific data include the following: 1. Research question: The material provided should clearly specify the research question that the study was designed to answer, along with any hypotheses. 2. Participants, subjects, specimens or samples: The material should specify who the participants or subjects were, and how specimens or samples were obtained. When appropriate, the authority that gave regulatory study approval should be stated (i.e. institutional review board, animal care and use committee, etc.). Human studies should state how patients were consented. 3. Study design: The material should specify the study design, and state whether the study was exploratory or confirmatory. Important design features needed to assess the risk of bias should be reported. These include whether the measurements and analyses were performed in a blinded fashion, whether participants or subjects were randomized to the different conditions and how randomization was performed, a power calculation or sample size justification, and details on the number of excluded observations and reasons for exclusion [37,38]. 4. Data: A scientist without prior knowledge of the experiment should be able to interpret and use the dataset based on the meta-data provided. The dataset should be compliant with the respective Minimum Information for Biological and Biomedical Investigations (RRID:SCR_002042, https://fairsharing.org/collection/MIBBI) and include a data dictionary that clearly explains what each variable is, what the measurement units are and how the variables were measured (https://dataedo.com/blog/different-types-of-tools-you-can-use-to-create-data-dictionary). Data should have a license specifying any conditions for re-use. Authors who share data should consult the FAIR data principles [39] and plan their data documentation [40]. When depositing data obtained from human samples or patient data, regional data protection laws and legislations apply and need to be considered prior to the start of the project to found out which form of consent, de-identification procedures or data access restrictions may apply. Some research institutions employ a data protection or open data specialist to help researchers with open data issues. Investigators working with patient data should contact their institutional review board for guidance. 5. Results: Readers should know what was measured, be able to determine sample sizes for each group and/or analysis and know what summary statistics are reported. 6. Analysis: If the data were analyzed, the material should provide enough information to determine how the analysis was conducted. This could include code for the analysis. The SAMPL guidelines [41] recommend providing enough detail so that a reader who understands statistics could reproduce the analysis if he or she had access to the data. 7. Limitations: The limitations of the data or study should be clearly explained. 8. Contact person: If the uploading author is not the best person to answer additional questions, the name and contact information for one or two people with such knowledge should be provided. Researchers can take several steps to reduce publication bias and accelerate scientific discovery. The first step is to plan ahead. Research teams should ask all collaborators to commit to publishing all study results, regardless of the perceived importance of the results and whether the results support the hypothesis. An additional strategy is to pre-register a study by posting a publicly available, time stamped protocol that outlines the study objectives and hypotheses, data collection procedures and planned analyses. Cite this pre-registration when publishing the study, regardless of which publication format is used, and provide an explanation if the final study differs from the pre-registered protocol. Pre-registration addresses publication bias by allowing researchers to identify studies that were conducted, but not published. Studies can be pre-registered on sites like AsPredicted (RRID:SCR_018789, https://aspredicted.org) and the Open Science Framework (RRID:SCR_003238, https://osf.io) Once the study is complete, researchers should share all findings with the scientific community using traditional peer-reviewed publications or alternative publication formats described in fiddle. Specific actions that researchers can take include using repositories and other platforms to share data and protocols, and avoiding ´data not shown’ statements. Scientists who have a sound scientific reason not to report data should specify this when publishing or sharing such study results. Investigators might report, for example, that one variable measured was not reported due to device malfunctioning on the day the test was performed. Finally, scientists should talk to their colleagues about the consequences of publication bias and selective reporting. These conversations are especially important when co-authors, reviewers or editors encourage selective reporting. The open source fiddle tool is a match-making Shiny app designed to help researchers identify the publication format that is most appropriate for their publication or dataset. Users can search for a publication format that meets their needs, compare and contrast different publication formats, and find links to publishers and examples. This tool will assist scientists in getting otherwise inaccessible data from well-designed experiments out of the file drawer and into the scientific community to reduce bias in the scientific literature. Finally, funding agencies, journals, and hiring and promotion committees need to incentivize and reward publication of all research from well-designed experiments, regardless of the form of publication. Some investigators may be reluctant to publish studies that are unlikely to be accepted by journals with high impact factors due to concerns that funding agencies or promotion and tenure committees may devalue this work, adversely affecting career advancement. This perception bolsters publication bias by encouraging scientists to publish only their most interesting and impactful research, to the detriment of the scientific community and the public. We hope that this paper and the tool will raise awareness of the negative consequences of publication bias and selective reporting, and encourage the scientific community to work towards individual and systemic change. The authors declare that there are no competing interests associated with the manuscript. R.B. was funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy – EXC-2049 – 390688087. T.L.W. was funded by American Heart Association [grant number 16GRNT30950002]. This publication was made possible by CTSA [grant number UL1 TR000135] from the National Center for Advancing Translational Sciences, a component of the National Institutes of Health. The content is solely the authors’ responsibility and does not necessarily represent the official views of the NIH. The writing of the manuscript and the decision to submit it for publication were solely the authors’ responsibilities. • fiddle file drawer data liberation effort 1. Rosenthal R. ( 1979 ) The file drawer problem and tolerance for null results . Psychol. Bull. 86 , 638 641 2. Song F. et al. ( 2010 ) Dissemination and publication of research findings: an updated review of related biases . Health Technol. Assess. (Rockv.) 14 , 1 193 3. van der Steen J.T. et al. ( 2018 ) Determinants of selective reporting: A taxonomy based on content analysis of a random selection of the literature . PLoS ONE 13 , e0188247 [PubMed] 4. Chiu K. and Grundy Q. Bero L. ( 2017 ) Spin’ in published biomedical literature: A methodological systematic review . PLoS Biol. 15 , e2002173 [PubMed] 5. Matosin N. et al. ( 2014 ) Negativity towards negative results: a discussion of the disconnect between scientific worth and scientific culture . Dis. Model Mech 7 , 171 3 [PubMed] 6. McElreath R. and Smaldino P.E. ( 2015 ) Replication, Communication, and the Population Dynamics of Scientific Discovery . PLoS ONE 10 , e0136088 [PubMed] 7. Collins E. ( 2013 ) Publishing priorities of biomedical research funders . BMJ Open 3 , e004171 [PubMed] 8. U. and Joffe A.R. ( 2017 ) Publication bias in animal research presented at the 2008 Society of Critical Care Medicine Conference . BMC Res. Notes 10 , 262 [PubMed] 9. Strech D. and Dirnagl U. ( 2019 ) 3Rs missing: animal research without scientific value is unethical . BMJ Open Sci. 3 , bmjos 2018-000048 10. Wieschowski S. et al. ( 2019 ) Publication rates in animal research. Extent and characteristics of published and non-published animal studies followed up at two German university medical centres . PLoS ONE 14 , e0223758 [PubMed] 11. Yarborough M. et al. ( 2018 ) The bench is closer to the bedside than we think: Uncovering the ethical ties between preclinical researchers in translational neuroscience and patients in clinical trials . PLoS Biol. 16 , e2006343 [PubMed] 12. Fanelli D. ( 2012 ) Negative Results Are Disappearing from Most Disciplines and Countries . Scientometrics 90 , 891 904 13. Mlinaric A. and Horvat M. Supak Smolcic V. ( 2017 ) Dealing with the positive publication bias: Why you should really publish your negative results . Biochem Med. (Zagreb) 27 , 030201 [PubMed] 14. Bruckner T. and Ellis B. ( 2017 ) Clinical Trial Transparency: A Key to Better and Safer Medicines . 15. Dickersin K. and Rennie D. ( 2003 ) Registering clinical trials . JAMA 290 , 516 23 [PubMed] 16. Moor T. ( 1995 ) Deadly Medicine: Why Tens of Thousands of Heart Patients Died in America's Worst Drug Disaster , 1st edn., p. 352 , Simon & Schuster , New York 17. Michel M.C. and Murphy T.J. Motulsky H.J. ( 2020 ) New Author Guidelines for Displaying Data and Reporting Data Analysis and Statistical Methods in Experimental Biology . Drug Metab. Dispos. 48 , 64 74 [PubMed] 18. Franco A. Malhotra N. and Simonovits G. ( 2014 ) Publication bias in the social sciences: Unlocking the file drawer . Science 345 , 1502 1505 [PubMed] 19. Duyx B. et al. ( 2019 ) The strong focus on positive results in abstracts may cause bias in systematic reviews: a case study on abstract reporting bias . Syst Rev 8 , 174 [PubMed] 20. Jannot A.S. et al. ( 2013 ) Citation bias favoring statistically significant studies was present in medical research . J. Clin. Epidemiol. 66 , 296 301 [PubMed] 21. ( 2004 ) Clinical trial registration: a statement from the International Committee of Medical Journal Editors . 22. Laine C. et al. ( 2007 ) Update on Trials Registration: Clinical Trial Registration: Looking Back and Moving Ahead . 23. AllTrials. How many clinical trials are left unpublished? . 24. Sena E.S. et al. ( 2010 ) Publication bias in reports of animal stroke studies leads to major overstatement of efficacy . PLoS Biol. 8 , e1000344 [PubMed] 25. Abdill R.J. and Blekhman R. ( 2019 ) Tracking the popularity and outcomes of all bioRxiv preprints . Elife 8 , e45133 [PubMed] 26. World Medical Association. ( 2013 ) World Medical Association Declaration of Helsinki: ethical principles for medical research involving human subjects . JAMA 310 , 2191 4 [PubMed] 27. Galsworthy M.J. et al. ( 2012 ) Academic output of 9 years of EU investment into health research . Lancet 380 , 971 2 [PubMed] 28. Riley W.T. and Riddle M. Lauer M. ( 2018 ) NIH Policies on Experimental Studies with Humans . Nat. Hum. Behav. 2 , 103 106 [PubMed] 29. Kaiser J. ( 2017 ) NIH enables investigators to include draft preprints in grant proposals . Science n.pag 30. Piwowar H.A. and Vision T.J. ( 2013 ) Data reuse and the open data citation advantage . PeerJ 1 , e175 [PubMed] 31. Colavizza G. et al. ( 2019 ) The citation advantage of linking publications to research data . [cited 2019 12.31.2019]; Available from: https://arxiv.org/abs/1907.02565v2 32. Kannan S. and Gowri S. ( 2014 ) Contradicting/negative results in clinical research: Why (do we get these)? Why not (get these published)? Where (to publish)? Perspect. Clin. Res. 5 , 151 3 [PubMed] 33. Raciti D , Yook K. , Harris TW , Schedl T and Sternberg PW ( 2018 ) Micropublication: incentivizing community curation and placing unpublished data into the public domain . Database (Oxford) volume 2018 bay013 34. Iwema C.L. et al. ( 2016 ) search.bioPreprint: a discovery tool for cutting edge, preprint biomedical research articles . F1000Res 5 , 1396 [PubMed] 35. Chang W. et al. ( 2018 ) shiny: Web Application Framework for R . R package version 1.1.0. 36. Stroup D.F. et al. ( 2000 ) Meta-analysis of Observational Studies in EpidemiologyA Proposal for Reporting . JAMA 283 , 2008 2012 [PubMed] 37. ( 2019 ) Reviewer Guidance on Rigor and Transparency: Research Project Grant and Mentored Career Development Applications . NIH Peer Rev. 38. Landis S.C. et al. ( 2012 ) A call for transparent reporting to optimize the predictive value of preclinical research . Nature 490 , 187 91 [PubMed] 39. Wilkinson M.D. et al. ( 2016 ) The FAIR Guiding Principles for scientific data management and stewardship . Sci. Data 3 , 160018 [PubMed] 40. Hart E.M. et al. ( 2016 ) Ten Simple Rules for Digital Data Storage . PLoS Comput. Biol. 12 , e1005097 [PubMed] 41. Lang T. and Altman D. ( 2013 ) Basic statistical reporting for articles published in clinical medical journals: the Statistical Analyses and Methods in the Published Literature, or SAMPL guidelines . ## Author notes * These authors contributed equally to this work. This is an open access article published by Portland Press Limited on behalf of the Biochemical Society and distributed under the Creative Commons Attribution License 4.0 (CC BY-NC-ND).	2022-07-03T04:58:51	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.19318194687366486, "perplexity": 2731.2193138079037}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656104215790.65/warc/CC-MAIN-20220703043548-20220703073548-00693.warc.gz"}
http://smai-jcm.cedram.org/smai-jcm-bin/fitem?id=SMAI-JCM_2018__4__225_0	Avec cedram.org english version Accueil Présentation Recherche avancée Tous les articles en ligne Derniers articles Rechercher un article Table des matières de ce volume \| Article précédent \| Article suivant Ralf Hiptmair; Cecilia PagliantiniSplitting-Based Structure Preserving Discretizations for MagnetohydrodynamicsSMAI-Journal of computational mathematics, 4 (2018), p. 225-257, doi: 10.5802/smai-jcm.34 Article PDF Class. Math.: 76W05, 65M60, 65M08, 65M12Mots clés: Magnetohydrodynamics (MHD), discrete differential forms, Finite Element Exterior Calculus (FEEC), extrusion contraction, upwinding, extended Euler equations, Orszag-Tang vortex, rotor problem AbstractWe start from the splitting of the equations of single-fluid magnetohydrodynamics (MHD) into a magnetic induction part and a fluid part. We design novel numerical methods for the MHD system based on the coupling of Galerkin schemes for the electromagnetic fields via finite element exterior calculus (FEEC) with finite volume methods for the conservation laws of fluid mechanics. Using a vector potential based formulation, the magnetic induction problem is viewed as an instance of a generalized transient advection problem of differential forms. For the latter, we rely on an Eulerian method of lines with explicit Runge–Kutta timestepping and on structure preserving spatial upwind discretizations of the Lie derivative in the spirit of finite element exterior calculus. The balance laws for the fluid constitute a system of conservation laws with the magnetic induction field as a space and time dependent coefficient, supplied at every time step by the structure preserving discretization of the magnetic induction problem. We describe finite volume schemes based on approximate Riemann solvers adapted to accommodate the electromagnetic contributions to the momentum and energy conservation. A set of benchmark tests for the two-dimensional planar ideal MHD equations provide numerical evidence that the resulting lowest order coupled scheme has excellent conservation properties, is first order accurate for smooth solutions, conservative and stable. Bibliographie[1] D. N. Arnold & G. Awanou, “Finite element differential forms on cubical meshes”, Math. Comp. 83 (2014) no. 288, p. 1551-1570 [2] D. N. Arnold, D. Boffi & F. Bonizzoni, “Finite element differential forms on curvilinear cubic meshes and their approximation properties”, Numer. Math. 129 (2015) no. 1, p. 1-20 [3] D. N. Arnold, R. S. Falk & R. Winther, “Finite element exterior calculus, homological techniques, and applications”, Acta Numer. 15 (2006), p. 1-155 [4] D. N. Arnold, R. S. Falk & R. Winther, “Finite element exterior calculus: from Hodge theory to numerical stability”, Bull. Amer. Math. Soc. (N.S.) 47 (2010) no. 2, p. 281-354 [5] D. S. Balsara, “Total variation diminishing scheme for adiabatic and isothermal magnetohydrodynamics”, The Astrophysical Journal Supplement Series 116 (1998) no. 1, p. 133-153 [6] D. S. Balsara, “Second-order-accurate schemes for magnetohydrodynamics with divergence-free reconstruction”, The Astrophysical Journal Supplement Series 151 (2004) no. 1, p. 149-184 [7] D. S. Balsara & D. S. Spicer, “A staggered mesh algorithm using high order Godunov fluxes to ensure solenoidal magnetic fields in magnetohydrodynamic simulations”, J. Comput. Phys. 149 (1999) no. 2, p. 270-292 [8] A. Bossavit, “Extrusion, contraction: their discretization via Whitney forms”, COMPEL 22 (2003) no. 3, p. 470-480 [9] M. Brio & C.-C. Wu, “An upwind differencing scheme for the equations of ideal magnetohydrodynamics”, J. Comput. Phys. 75 (1988) no. 2, p. 400-422 [10] P. G. Ciarlet, The finite element method for elliptic problems, North-Holland Publishing Co., Amsterdam-New York-Oxford, 1978 [11] B. Einfeldt, “On Godunov-type methods for gas dynamics”, SIAM J. Numer. Anal. 25 (1988) no. 2, p. 294-318 [12] F. G. Fuchs, K. H. Karlsen, S. Mishra & N. H. Risebro, “Stable upwind schemes for the magnetic induction equation”, M2AN Math. Model. Numer. Anal. 43 (2009) no. 5, p. 825-852 [13] F. G. Fuchs, A. D. McMurry, S. Mishra, N. H. Risebro & K. Waagan, “Approximate Riemann solvers and robust high-order finite volume schemes for multi-dimensional ideal MHD equations”, Commun. Comput. Phys. 9 (2011) no. 2, p. 324-362 [14] Franz G. Fuchs, S. Mishra & N. H. Risebro, “Splitting based finite volume schemes for ideal MHD equations”, J. Comput. Phys. 228 (2009) no. 3, p. 641-660 [15] H. Goedbloed & S. Poedts, Principles of Magnetohydrodynamics, Cambridge University Press, 2004 [16] S. Gottlieb, C.-W. Shu & E. Tadmor, “Strong stability-preserving high-order time discretization methods”, SIAM Rev. 43 (2001) no. 1, p. 89-112 [17] J.-L. Guermond & R. Pasquetti, “Entropy-based nonlinear viscosity for Fourier approximations of conservation laws”, C. R. Math. Acad. Sci. Paris 346 (2008) no. 13-14, p. 801-806 [18] J.-L. Guermond, R. Pasquetti & B. Popov, “Entropy viscosity method for nonlinear conservation laws”, J. Comput. Phys. 230 (2011) no. 11, p. 4248-4267 [19] A. Harten, B. Engquist, S. Osher & S. R. Chakravarthy, “Uniformly high-order accurate essentially nonoscillatory schemes. III”, J. Comput. Phys. 71 (1987) no. 2, p. 231-303 [20] A. Harten, P. D. Lax & B. van Leer, “On upstream differencing and Godunov-type schemes for hyperbolic conservation laws”, SIAM Rev. 25 (1983) no. 1, p. 35-61 [21] H. Heumann & R. Hiptmair, “Extrusion contraction upwind schemes for convection-diffusion problems”, SAM Report 2008-30, Seminar for Applied Mathematics, ETH Zürich, 2008 [22] H. Heumann & R. Hiptmair, “Convergence of lowest order semi-Lagrangian schemes”, Found. Comput. Math. 13 (2013) no. 2, p. 187-220 [23] H. Heumann, R. Hiptmair & C. Pagliantini, “Stabilized Galerkin for transient advection of differential forms”, Discrete Contin. Dyn. Syst. Ser. S 9 (2016) no. 1, p. 185-214 [24] R. Hiptmair, “Canonical construction of finite elements”, Math. Comp. 68 (1999) no. 228, p. 1325-1346 [25] R. Hiptmair, “Finite elements in computational electromagnetism”, Acta Numer. 11 (2002), p. 237-339 [26] K. Hu, Y. Ma & J. Xu, “Stable finite element methods preserving $\nabla \cdot \mathbf{B}=0$ exactly for MHD models”, Numer. Math. 135 (2017) no. 2, p. 371-396 [27] R. Käppeli, S. C. Whitehouse, S. Scheidegger, U.-L. Pen & M. Liebendörfer, “FISH: a three-dimensional parallel magnetohydrodynamics code for astrophysical applications”, The Astrophysical Journal Supplement Series 195 (2011) no. 20, p. 1-16 [28] K. H. Karlsen, S. Mishra & N. H. Risebro, “Semi-Godunov schemes for multiphase flows in porous media”, Appl. Numer. Math. 59 (2009) no. 9, p. 2322-2336 [29] T. J. Linde, A three-dimensional adaptive multifluid MHD model of the heliosphere, Ph. D. Thesis, University of Michigan, Ann Arbor, MI, 1998 [30] T. Miyoshi & K. Kusano, “A multi-state HLL approximate Riemann solver for ideal magnetohydrodynamics”, J. Comput. Phys. 208 (2005) no. 1, p. 315-344 [31] P. Mullen, A. McKenzie, D. Pavlov, L. Durant, Y. Tong, E. Kanso, J. E. Marsden & M. Desbrun, “Discrete Lie advection of differential forms”, Found. Comput. Math. 11 (2011) no. 2, p. 131-149 [32] S. A. Orszag & C.-M. Tang, “Small-scale structure of two-dimensional magnetohydrodynamic turbulence”, J. Fluid Mech. 90 (1979) no. 1, p. 129-143 [33] C. Pagliantini, Computational Magnetohydrodynamics with Discrete Differential Forms, Ph. D. Thesis, Dis. no 23781, ETH Zürich, 2016 [34] P.-A. Raviart & J.-M. Thomas, A mixed finite element method for 2nd order elliptic problems, Mathematical aspects of finite element methods (Proc. Conf., Consiglio Naz. delle Ricerche (C.N.R.), Rome, 1975), Springer, Berlin, 1977 [35] H.-G. Roos, M. Stynes & L. Tobiska, Robust numerical methods for singularly perturbed differential equations, Springer-Verlag, Berlin, 2008 [36] D. Schötzau, “Mixed finite element methods for stationary incompressible magneto-hydrodynamics”, Numer. Math. 96 (2004) no. 4, p. 771-800 [37] C.-W. Shu & S. Osher, “Efficient implementation of essentially nonoscillatory shock-capturing schemes. II”, J. Comput. Phys. 83 (1989) no. 1, p. 32-78 [38] M. Tabata, “A finite element approximation corresponding to the upwind finite differencing”, Mem. Numer. Math. 4 (1977), p. 47-63 [39] E. F. Toro, M. Spruce & W. Speares, “Restoration of the contact surface in the HLL-Riemann solver”, Shock Waves 4 (1994) no. 1, p. 25-34 [40] G. Tóth, “The $\nabla \cdot B=0$ constraint in shock-capturing magnetohydrodynamics codes”, J. Comput. Phys. 161 (2000) no. 2, p. 605-652 [41] K. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media”, IEEE Transactions on Antennas and Propagation 14 (1966) no. 3, p. 302-30 © 2015SMAI Journal of Computational Mathematics ISSN 2426-8399 Les articles sont publiés sous licence Creative Commons CC BY-NC-ND 3.0	2019-02-18T22:06:01	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.42180079221725464, "perplexity": 4469.826397843573}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-09/segments/1550247488490.40/warc/CC-MAIN-20190218220415-20190219002415-00276.warc.gz"}
http://philfsis.psa.gov.ph/index.php/id/16/meta/EPR	Employment rate Definition Employment Rate is defined as the percentage of the total number of employed persons to the total number of persons in the labor force. Computational formula $$\table EPR = ( \table {\text" Total number of employed persons" / \text"Total number of persons in the labor force"},),100$$ Basic data Number of employed persons Source Philippine Statistics Authority (PSA) Definition Employed persons --- include all persons 15 years old and over as of their last birthday and during the basic survey reference period are reported as either: At work Those who do any work even for one hour during the reference period for pay or profit, or work without pay on the farm or business interprise operated by a member of the same household related by blood, marriage, or adoption; or, With a job but not at work Those who have a job or business but not at work because of temporary illness/injury, vacation, or other reasons. Likewise, persons who expect to report for work or to start operation of a farm or business interprise within two weeks from the date of the enumerator's visit, are considered employed. Frequency of collection Quarterly Frequency of dissemination Quarterly Temporal disaggregation Quarterly/Annual Spatial disaggregation National/Regional Basic data Number of persons in the labor force Source Philippine Statistics Authority (PSA) Definition Persons in the Labor Force or Economically Active Population refers to all persons 15 years old and over as of their last birthday who are either employed and unemployed. Frequency of collection Quarterly Frequency of dissemination Quarterly Temporal disaggregation Quarterly/Annual Spatial disaggregation National/Regional Key Indicators Support Indicators Economic Access Key Indicators Economic conditions Key Indicators Support Indicators Demographic conditions Key Indicators Support Indicators Environmental conditions Key Indicators Support Indicators Political conditions Key Indicators Risks, hazards, shocks Key Indicators Support Indicators	2019-01-19T07:22:21	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.1791301667690277, "perplexity": 7935.774722887997}, "config": {"markdown_headings": false, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-04/segments/1547583662690.13/warc/CC-MAIN-20190119054606-20190119080606-00578.warc.gz"}
https://www.zbmath.org/authors/?q=ai%3Aalon.noga	zbMATH — the first resource for mathematics Alon, Noga M. Compute Distance To: Author ID: alon.noga Published as: Alon, Noga; Alon, N.; Nilli, A.; Nilli, Alon; Along, Noga Homepage: http://www.tau.ac.il/~nogaa/ External Links: MGP · Wikidata · dblp · GND Documents Indexed: 634 Publications since 1981, including 11 Books Reviewing Activity: 20 Reviews all top 5 Co-Authors 103 single-authored 40 Krivelevich, Michael 37 Sudakov, Benny 22 Yuster, Raphael 20 Shapira, Asaf 17 Azar, Yossi 13 Kleitman, Daniel J. 12 Spencer, Joel H. 11 Bollobás, Béla 11 Lubetzky, Eyal 11 Rodl, Vojtech 9 Caro, Yair 9 Milman, Vitali D. 9 Tennenholtz, Moshe 8 Feldman, Michal 8 Kostochka, Aleksandr Vasil’evich 7 Asodi, Vera 7 Fischer, Eldar 7 Furedi, Zoltan 7 Gutin, Gregory Z. 7 Kalai, Gil 7 Kaufman, Tali 7 Seymour, Paul D. 7 Stav, Uri 7 Szegedy, Mario 6 Balogh, József 6 Gutner, Shai 6 Naor, Moni 6 Zwick, Uri 5 Awerbuch, Baruch 5 Bourgain, Jean 5 Capalbo, Michael 5 Erdős, Pál 5 Grytczuk, Jarosław 5 Haeupler, Bernhard 5 Kaplan, Haim 5 Katchalski, Meir 5 Linial, Nathan 5 Litsyn, Simon N. 5 Newman, Ilan I. 5 Ron, Dana 5 Sharir, Micha 5 West, Douglas Brent 5 Woeginger, Gerhard Johannes 4 Bruck, Jehoshua 4 Chung Graham, Fan-Rong King 4 Connes, Alain 4 Demaine, Erik D. 4 Emek, Yuval 4 Frankl, Péter 4 Gromov, Mikhael Leonidovich 4 Hajiaghayi, Mohammad Taghi 4 Hefetz, Dan 4 Huang, Hao 4 Naor, Assaf 4 Naor, Joseph Seffi 4 Peleg, David 4 Pinchasi, Rom 4 Ruciński, Andrzej 4 Ruzsa, Imre Z. 4 Saurabh, Saket 4 Shikhelman, Clara 4 Smorodinsky, Shakhar 4 Tarsi, Michael 4 Zaks, Ayal 3 Afek, Yehuda 3 Aharoni, Ron 3 Bar-Joseph, Ziv 3 Ben-Eliezer, Omri 3 Benjamini, Itai 3 Berger, Eli 3 Buchbinder, Niv 3 Efremenko, Klim 3 Feldheim, Ohad Noy 3 Fomin, Fedor V. 3 Friedland, Shmuel 3 Galil, Zvi 3 Goldreich, Oded 3 Graham, Ronald Lewis 3 Hod, Rani 3 Kahale, Nabil 3 Kim, Jeong Han 3 Kohayakawa, Yoshiharu 3 Krasikov, Ilia 3 Lefmann, Hanno 3 Malkhi, Dahlia 3 Mansour, Yishay 3 Matias, Yossi 3 McDiarmid, Colin J. H. 3 Meshulam, Roy 3 Morris, Robert D. 3 Nathanson, Melvyn Bernard 3 Orlitsky, Alon 3 Peres, Yuval 3 Prałat, Paweł 3 Procaccia, Ariel D. 3 Pudlák, Pavel 3 Ruszinkó, Miklós 3 Samotij, Wojciech 3 Scheinerman, Edward R. 3 Shraibman, Adi ...and 391 more Co-Authors all top 5 Serials 33 Journal of Graph Theory 33 Combinatorics, Probability and Computing 32 Discrete Mathematics 30 SIAM Journal on Discrete Mathematics 27 Combinatorica 26 Random Structures & Algorithms 25 Journal of Combinatorial Theory. Series B 23 Graphs and Combinatorics 20 Journal of Combinatorial Theory. Series A 17 Israel Journal of Mathematics 17 SIAM Journal on Computing 15 IEEE Transactions on Information Theory 15 European Journal of Combinatorics 11 Discrete & Computational Geometry 11 The Electronic Journal of Combinatorics 10 Journal of Computer and System Sciences 9 Algorithmica 8 Journal of Algorithms 7 Discrete Applied Mathematics 7 Information Processing Letters 7 Geometric and Functional Analysis. GAFA 6 ACM Transactions on Algorithms 5 Journal of Number Theory 5 Theoretical Computer Science 4 Proceedings of the American Mathematical Society 4 Acta Mathematica Hungarica 4 Journal of the ACM 4 Journal of Combinatorics 3 Advances in Mathematics 3 Ars Combinatoria 3 Journal of the Association for Computing Machinery 3 Proceedings of the London Mathematical Society. Third Series 3 Advances in Applied Mathematics 3 Order 3 Information and Computation 3 Linear Algebra and its Applications 3 Distributed Computing 3 Computational Complexity 3 Theory of Computing 2 American Mathematical Monthly 2 Journal of the London Mathematical Society. Second Series 2 The Annals of Applied Probability 2 Journal of Algebraic Combinatorics 2 Annals of Combinatorics 2 Oberwolfach Reports 2 Modern Birkhäuser Classics 1 Letters in Mathematical Physics 1 Mathematical Proceedings of the Cambridge Philosophical Society 1 Mathematics Magazine 1 Acta Arithmetica 1 The Annals of Probability 1 Bulletin of the London Mathematical Society 1 Inventiones Mathematicae 1 Journal of Computational and Applied Mathematics 1 Mathematics of Operations Research 1 Mathematica Scandinavica 1 Mathematika 1 Operations Research 1 Studia Scientiarum Mathematicarum Hungarica 1 Transactions of the American Mathematical Society 1 Annales Societatis Mathematicae Polonae. Series IV 1 SIAM Journal on Algebraic and Discrete Methods 1 Social Choice and Welfare 1 Journal of the American Mathematical Society 1 Publicacions Matemàtiques 1 International Journal of Computational Geometry & Applications 1 Computational Geometry 1 Designs, Codes and Cryptography 1 SIAM Review 1 Bulletin of the American Mathematical Society. New Series 1 Notices of the American Mathematical Society 1 Mathematical Programming. Series A. Series B 1 Nordic Journal of Computing 1 Journal of Combinatorial Designs 1 Electronic Communications in Probability 1 Sbornik: Mathematics 1 Theory of Computing Systems 1 Journal of Scheduling 1 Annals of Mathematics. Second Series 1 Journal of the European Mathematical Society (JEMS) 1 Communications in Contemporary Mathematics 1 Integers 1 ACM Transactions on Computational Logic 1 Internet Mathematics 1 Discrete Optimization 1 Science 1 Journal of Topology and Analysis 1 Moscow Journal of Combinatorics and Number Theory 1 Discrete Analysis 1 Advances in Combinatorics all top 5 Fields 437 Combinatorics (05-XX) 209 Computer science (68-XX) 52 Information and communication theory, circuits (94-XX) 42 Number theory (11-XX) 34 Operations research, mathematical programming (90-XX) 29 Convex and discrete geometry (52-XX) 29 Probability theory and stochastic processes (60-XX) 29 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 14 Linear and multilinear algebra; matrix theory (15-XX) 10 Biology and other natural sciences (92-XX) 9 General and overarching topics; collections (00-XX) 7 History and biography (01-XX) 7 Order, lattices, ordered algebraic structures (06-XX) 7 Group theory and generalizations (20-XX) 7 Numerical analysis (65-XX) 6 Mathematical logic and foundations (03-XX) 4 Geometry (51-XX) 2 Field theory and polynomials (12-XX) 2 Commutative algebra (13-XX) 2 Algebraic geometry (14-XX) 2 Functional analysis (46-XX) 2 Algebraic topology (55-XX) 2 Statistics (62-XX) 2 Statistical mechanics, structure of matter (82-XX) 1 Topological groups, Lie groups (22-XX) 1 Special functions (33-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Sequences, series, summability (40-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 General topology (54-XX) 1 Manifolds and cell complexes (57-XX) 1 Global analysis, analysis on manifolds (58-XX) Citations contained in zbMATH Open 538 Publications have been cited 8,759 times in 6,381 Documents Cited by Year Eigenvalues and expanders. Zbl 0661.05053 Alon, Noga 1986 Combinatorial Nullstellensatz. Zbl 0920.05026 Alon, Noga 1999 $$\lambda_ 1$$, isoperimetric inequalities for graphs, and superconcentrators. Zbl 0549.05051 Alon, N.; Milman, V. D. 1985 Color-coding. Zbl 0885.68116 Alon, Noga; Yuster, Raphael; Zwick, Uri 1995 The probabilistic method. With an appendix on the life and work of Paul Erdős. 3rd ed. Zbl 1148.05001 Alon, Noga; Spencer, Joel H. 2008 The probabilistic method. With an appendix on the life and work of Paul Erdős. 2nd ed. Zbl 0996.05001 Alon, Noga; Spencer, Joel H. 2000 Colorings and orientations of graphs. Zbl 0756.05049 Alon, N.; Tarsi, M. 1992 The probabilistic method. 4th edition. Zbl 1333.05001 Alon, Noga; Spencer, Joel H. 2016 A fast and simple randomized parallel algorithm for the maximal independent set problem. Zbl 0631.68063 Alon, Noga; Babai, László; Itai, Alon 1986 Acyclic coloring of graphs. Zbl 0735.05036 Alon, Noga; McDiarmid, Colin; Reed, Bruce 1991 The probabilistic method. With an appendix on open problems by Paul Erdős. Zbl 0767.05001 Alon, Noga; Spencer, Joel H. 1992 The space complexity of approximating the frequency moments. Zbl 0938.68153 Alon, Noga; Matias, Yossi; Szegedy, Mario 1999 Efficient testing of large graphs. Zbl 1052.68096 Alon, Noga; Fischer, Eldar; Krivelevich, Michael; Szegedy, Mario 2000 Simple constructions of almost $$k$$-wise independent random variables. Zbl 0755.60002 Alon, Noga; Goldreich, Oded; Håstad, Johan; Peralta, René 1992 Explicit construction of linear sized tolerant networks. Zbl 0657.05068 Alon, N.; Chung, F. R. K. 1988 The monotone circuit complexity of Boolean functions. Zbl 0631.68041 Alon, N.; Boppana, R. B. 1987 Acyclic edge colorings of graphs. Zbl 0996.05050 Alon, Noga; Sudakov, Benny; Zaks, Ayal 2001 Finding and counting given length cycles. Zbl 0865.68093 Alon, N.; Yuster, R.; Zwick, U. 1997 $$H$$-factors in dense graphs. Zbl 0855.05085 Alon, Noga; Yuster, Raphael 1996 Algorithmic construction of sets for $$k$$-restrictions. Zbl 1321.68445 Alon, Noga; Moshkovitz, Dana; Safra, Shmuel 2006 Scale-sensitive dimensions, uniform convergence, and learnability. Zbl 0891.68086 Alon, Noga; Ben-David, Shai; Cesa-Bianchi, Nicolò; Haussler, David 1997 The algorithmic aspects of the regularity lemma. Zbl 0794.05119 Alon, N.; Duke, Richard A.; Lefmann, Hanno; Rödl, Vojtěch; Yuster, R. 1994 On the second eigenvalue of a graph. Zbl 0771.05064 Nilli, A. 1991 Nonrepetitive colorings of graphs. Zbl 1018.05032 Alon, Noga; Grytczuk, Jarosław; Hałuszczak, Mariusz; Riordan, Oliver 2002 The polynomial method and restricted sums of congruence classes. Zbl 0861.11006 Alon, Noga; Nathanson, Melvyn B.; Ruzsa, Imre 1996 Piercing convex sets and the Hadwiger-Debrunner $$(p,q)$$-problem. Zbl 0768.52001 Alon, Noga; Kleitman, Daniel J. 1992 Dense graphs are antimagic. Zbl 1055.05132 Alon, N.; Kaplan, G.; Lev, A.; Roditty, Y.; Yuster, R. 2004 A separator theorem for nonplanar graphs. Zbl 0747.05051 Alon, Noga; Seymour, Paul; Thomas, Robin 1990 Ranking tournaments. Zbl 1112.05043 Alon, Noga 2006 Transversal numbers of uniform hypergraphs. Zbl 0742.05065 Alon, Noga 1990 A lower bound for radio broadcast. Zbl 0753.68006 Alon, Noga; Bar-Noy, Amotz; Linial, Nathan; Peleg, David 1991 Restricted colorings of graphs. Zbl 0791.05034 Alon, Noga 1993 Random Cayley graphs and expanders. Zbl 0798.05048 Alon, Noga; Roichman, Yuval 1994 Norm-graphs: Variations and applications. Zbl 0935.05054 Alon, Noga; Rónyai, Lajos; Szabó, Tibor 1999 Approximation schemes for scheduling on parallel machines. Zbl 0909.90168 Alon, Noga; Azar, Yossi; Woeginger, Gerhard J.; Yadid, Tal 1998 Approximating the cut-norm via Grothendieck’s inequality. Zbl 1096.68163 Alon, Noga; Naor, Assaf 2006 Independent sets in regular graphs and sum-free subsets of finite groups. Zbl 0762.05050 Alon, Noga 1991 Problems and results in extremal combinatorics. I. Zbl 1033.05060 Alon, Noga 2003 The star arboricity of graphs. Zbl 0684.05033 Algor, I.; Alon, N. 1989 The chromatic number of Kneser hypergraphs. Zbl 0605.05033 Alon, N.; Frankl, P.; Lovász, László 1986 Large matchings in uniform hypergraphs and the conjectures of Erdős and samuels. Zbl 1242.05189 Alon, Noga; Frankl, Peter; Huang, Hao; Rödl, Vojtech; Ruciński, Andrzej; Sudakov, Benny 2012 The linear arboricity of graphs. Zbl 0673.05019 Alon, N. 1988 Multilinear polynomials and Frankl-Ray-Chaudhuri-Wilson type intersection theorems. Zbl 0751.05009 Alon, N.; Babai, L.; Suzuki, H. 1991 Splitting necklaces. Zbl 0635.05008 Alon, Noga 1987 Non-backtracking random walks mix faster. Zbl 1140.60301 Alon, Noga; Benjamini, Itai; Lubetzky, Eyal; Sodin, Sasha 2007 The Moore bound for irregular graphs. Zbl 0990.05075 Alon, Noga; Hoory, Shlomo; Linial, Nathan 2002 Zero-sum sets of prescribed size. Zbl 0823.11006 Alon, N.; Dubiner, M. 1993 A graph-theoretic game and its application to the $$k$$-server problem. Zbl 0818.90147 Alon, Noga; Karp, Richard M.; Peleg, David; West, Douglas 1995 Bipartite subgraphs. Zbl 0860.05043 Alon, Noga 1996 Many $$T$$ copies in $$H$$-free graphs. Zbl 1348.05100 Alon, Noga; Shikhelman, Clara 2016 Point selections and weak $$\varepsilon$$-nets for convex hulls. Zbl 0797.52004 Alon, Noga; Bárány, Imre; Füredi, Zoltán; Kleitman, Daniel J. 1992 Crossing patterns of semi-algebraic sets. Zbl 1099.14048 Alon, Noga; Pach, János; Pinchasi, Rom; Radoičić, Radoš; Sharir, Micha 2005 Finding a large hidden clique in a random graph. Zbl 0959.05082 Alon, Noga; Krivelevich, Michael; Sudakov, Benny 1998 On a conjecture of Erdoes, Simonovits and Sos concerning anti-Ramsey theorems. Zbl 0456.05038 Alon, Noga 1983 Coloring graphs with sparse neighborhoods. Zbl 1026.05043 Alon, Noga; Krivelevich, Michael; Sudakov, Benny 1999 Eigenvalues, geometric expanders, sorting in rounds, and Ramsey theory. Zbl 0625.05026 Alon, N. 1986 The space complexity of approximating the frequency moments. Zbl 0922.68057 Alon, Noga; Matias, Yossi; Szegedy, Mario 1996 Covering multigraphs by simple circuits. Zbl 0581.05046 Alon, N.; Tarsi, M. 1985 Regular subgraphs of almost regular graphs. Zbl 0527.05059 Alon, N.; Friedland, S.; Kalai, G. 1984 Percolation on finite graphs and isoperimetric inequalities. Zbl 1046.05071 Alon, Noga; Benjamini, Itai; Stacey, Alan 2004 Degrees and choice numbers. Zbl 0958.05049 Alon, Noga 2000 A spectral technique for coloring random 3-colorable graphs. Zbl 0884.05042 Alon, Noga; Kahale, Nabil 1997 Ramsey-type theorems with forbidden subgraphs. Zbl 0989.05124 Alon, Noga; Pach, János; Solymosi, József 2001 Turán numbers of bipartite graphs and related Ramsey-type questions. Zbl 1060.05050 Alon, Noga; Krivelevich, Michael; Sudakov, Benny 2003 A characterization of the (natural) graph properties testable with one-sided error. Zbl 1152.05055 Alon, Noga; Shapira, Asaf 2008 Homomorphisms of edge-colored graphs and Coxeter groups. Zbl 0911.05034 Alon, N.; Marshall, T. H. 1998 A lattice point problem and additive number theory. Zbl 0838.11020 Alon, Noga; Dubiner, Moshe 1995 The number of edge colorings with no monochromatic cliques. Zbl 1060.05049 Alon, Noga; Balogh, József; Keevash, Peter; Sudakov, Benny 2004 A combinatorial characterization of the testable graph properties, it’s all about regularity. Zbl 1301.05354 Alon, Noga; Fischer, Eldar; Newman, Ilan; Shapira, Asaf 2006 On the concentration of eigenvalues of random symmetric matrices. Zbl 1014.15016 Alon, Noga; Krivelevich, Michael; Vu, Van H. 2002 Maximum cuts and judicious partitions in graphs without short cycles. Zbl 1030.05060 Alon, Noga; Bollobás, Béla; Krivelevich, Michael; Sudakov, Benny 2003 A parallel algorithmic version of the local lemma. Zbl 0768.05086 Alon, Noga 1991 Explicit construction of exponential sized families of k-independent sets. Zbl 0588.05003 Alon, N. 1986 Testing subgraphs in directed graphs. Zbl 1084.68087 Alon, Noga; Shapira, Asaf 2004 Derandomization, witnesses for Boolean matrix multiplication and construction of perfect hash functions. Zbl 0857.68055 Alon, N.; Naor, M. 1996 Graphs with integral spectrum. Zbl 1178.05060 Ahmadi, Omran; Alon, Noga; Blake, Ian F.; Shparlinski, Igor E. 2009 On the density of sets of vectors. Zbl 0514.05003 Alon, Noga 1983 Testing subgraphs in large graphs. Zbl 1027.68095 Alon, Noga 2002 Partitioning into graphs with only small components. Zbl 1023.05045 Alon, Noga; Ding, Guoli; Oporowski, Bogdan; Vertigan, Dirk 2003 Measures of pseudorandomness for finite sequences: typical values. Zbl 1124.68084 Alon, N.; Kohayakawa, Y.; Mauduit, C.; Moreira, C. G.; Rödl, V. 2007 Fast FAST. Zbl 1248.68547 Alon, Noga; Lokshtanov, Daniel; Saurabh, Saket 2009 Adding distinct congruence classes modulo a prime. Zbl 0849.11081 Alon, Noga; Nathanson, Melvyn B.; Ruzsa, Imre 1995 Graph products, Fourier analysis and spectral techniques. Zbl 1056.05104 Alon, N.; Dinur, I.; Friedgut, E.; Sudakov, B. 2004 Properly colored subgraphs and rainbow subgraphs in edge-colorings with local constraints. Zbl 1037.05033 Alon, Noga; Jiang, Tao; Miller, Zevi; Pritikin, Dan 2003 A nowhere-zero point in linear mappings. Zbl 0717.05021 Alon, N.; Tarsi, M. 1989 On the exponent of all pairs shortest path problem. Zbl 0877.68090 Alon, Noga; Galil, Zvi; Margalit, Oded 1997 Derandomized graph products. Zbl 0816.60070 Alon, Noga; Feige, Uriel; Wigderson, Avi; Zuckerman, David 1995 Solving MAX-$$r$$-SAT above a tight lower bound. Zbl 1242.68118 Alon, Noga; Gutin, Gregory; Kim, Eun Jung; Szeider, Stefan; Yeo, Anders 2011 A combinatorial characterization of the testable graph properties: it’s all about regularity. Zbl 1197.05159 Alon, Noga; Fischer, Eldar; Newman, Ilan; Shapira, Asaf 2009 Construction of asymptotically good low-rate error-correcting codes through pseudo-random graphs. Zbl 0744.94023 Alon, Noga; Bruck, Jehoshua; Naor, Joseph; Naor, Moni; Roth, Ron M. 1992 A note on the decomposition of graphs into isomorphic matchings. Zbl 0535.05047 Alon, N. 1983 Nearly perfect matchings in regular simple hypergraphs. Zbl 0882.05107 Alon, Noga; Kim, Jeong-Han; Spencer, Joel 1997 Properly colored Hamilton cycles in edge-colored complete graphs. Zbl 0882.05084 Alon, N.; Gutin, Gregory 1997 Approximating the independence number via the $$\vartheta$$-function. Zbl 0895.90169 Alon, Noga; Kahale, Nabil 1998 Covering the cube by affine hyperplanes. Zbl 0773.52011 Alon, Noga; Füredi, Zoltán 1993 An extremal problem for sets with applications to graph theory. Zbl 0578.05002 Alon, Noga 1985 Approximation schemes for scheduling. Zbl 1321.90051 Alon, Noga; Azar, Yossi; Woeginger, Gerhard J.; Yadid, Tal 1997 Algorithmic aspects of acyclic edge colorings. Zbl 1009.68100 Alon, N.; Zaks, A. 2002 The Borsuk-Ulam theorem and bisection of necklaces. Zbl 0614.05005 Alon, Noga; West, Douglas B. 1986 On the number of subgraphs of prescribed type of graphs with a given number of edges. Zbl 0472.05034 Alon, Noga 1981 The hat guessing number of graphs. Zbl 1443.05123 Alon, Noga; Ben-Eliezer, Omri; Shangguan, Chong; Tamo, Itzhak 2020 Isoperimetry, stability, and irredundance in direct products. Zbl 1440.05171 Alon, Noga; Defant, Colin 2020 Lovász, vectors, graphs and codes. Zbl 1443.05088 Alon, Noga 2019 Optimal induced universal graphs for bounded-degree graphs. Zbl 1404.05032 Alon, Noga; Nenadov, Rajko 2019 List-decodable zero-rate codes. Zbl 1431.94199 Alon, Noga; Bukh, Boris; Polyanskiy, Yury 2019 Private PAC learning implies finite Littlestone dimension. Zbl 1434.68149 Alon, Noga; Livni, Roi; Malliaris, Maryanthe; Moran, Shay 2019 Clique coloring of dense random graphs. Zbl 1393.05103 Alon, Noga; Krivelevich, Michael 2018 Many cliques in $$H$$-free subgraphs of random graphs. Zbl 1401.05266 Alon, Noga; Kostochka, Alexandr; Shikhelman, Clara 2018 Random subgraphs of properly edge-coloured complete graphs and long rainbow cycles. Zbl 1378.05180 Alon, Noga; Pokrovskiy, Alexey; Sudakov, Benny 2017 Asymptotically optimal induced universal graphs. Zbl 1358.05143 Alon, Noga 2017 More on the bipartite decomposition of random graphs. Zbl 1354.05120 Alon, Noga; Bohman, Tom; Huang, Hao 2017 Fair representation by independent sets. Zbl 1387.05170 Aharoni, Ron; Alon, Noga; Berger, Eli; Chudnovsky, Maria; Kotlar, Dani; Loebl, Martin; Ziv, Ran 2017 Optimal induced universal graphs for bounded-degree graphs. Zbl 1410.05097 Alon, Noga; Nenadov, Rajko 2017 Counting contours on trees. Zbl 1362.05034 Alon, Noga; Bissacot, Rodrigo; Endo, Eric Ossami 2017 Testing equality in communication graphs. Zbl 1390.94957 Alon, Noga; Efremenko, Klim; Sudakov, Benny 2017 The probabilistic method. 4th edition. Zbl 1333.05001 Alon, Noga; Spencer, Joel H. 2016 Many $$T$$ copies in $$H$$-free graphs. Zbl 1348.05100 Alon, Noga; Shikhelman, Clara 2016 Coloring, sparseness and girth. Zbl 1344.05058 Alon, Noga; Kostochka, Alexandr; Reiniger, Benjamin; West, Douglas B.; Zhu, Xuding 2016 Reliable communication over highly connected noisy networks. Zbl 1373.68033 Alon, Noga; Braverman, Mark; Efremenko, Klim; Gelles, Ran; Haeupler, Bernhard 2016 Eigenvalues of $$K_{1,k}$$-free graphs and the connectivity of their independence complexes. Zbl 1350.05089 Aharoni, Ron; Alon, Noga; Berger, Eli 2016 Problems and results in extremal combinatorics. III. Zbl 1336.05144 Alon, Noga 2016 On the maximum quartet distance between phylogenetic trees. Zbl 1338.92084 Alon, Noga; Naves, Humberto; Sudakov, Benny 2016 Linear Boolean classification, coding and the critical problem. Zbl 1359.94928 Abbe, Emmanuel; Alon, Noga; Bandeira, Afonso S.; Sandon, Colin 2016 On active and passive testing. Zbl 1371.68319 Alon, Noga; Hod, Rani; Weinstein, Amit 2016 Chasing a fast robber on planar graphs and random graphs. Zbl 1305.05142 Alon, Noga; Mehrabian, Abbas 2015 Easily testable graph properties. Zbl 1371.05136 Alon, Noga; Fox, Jacob 2015 Bipartite decomposition of random graphs. Zbl 1315.05122 Alon, Noga 2015 Separation dimension of bounded degree graphs. Zbl 1327.05245 Alon, Noga; Basavaraju, Manu; Chandran, L. Sunil; Mathew, Rogers; Rajendraprasad, Deepak 2015 Practically stabilizing SWMR atomic memory in message-passing systems. Zbl 1320.68042 Alon, Noga; Attiya, Hagit; Dolev, Shlomi; Dubois, Swan; Potop-Butucaru, Maria; Tixeuil, Sébastien 2015 Many $$T$$ copies in $$H$$-free graphs. Zbl 1346.05127 Alon, Noga; Shikhelman, Clara 2015 Comparable pairs in families of sets. Zbl 1319.05130 Alon, Noga; Das, Shagnik; Glebov, Roman; Sudakov, Benny 2015 Approximating sparse binary matrices in the cut-norm. Zbl 1327.15044 Alon, Noga 2015 Local correction with constant error rate. Zbl 1315.68277 Alon, Noga; Weinstein, Amit 2015 Size and degree anti-Ramsey numbers. Zbl 1327.05224 Alon, Noga 2015 On rigid matrices and $$U$$-polynomials. Zbl 1333.68120 Alon, Noga; Cohen, Gil 2015 Counting sum-free sets in abelian groups. Zbl 1332.11030 Alon, Noga; Balogh, József; Morris, Robert; Samotij, Wojciech 2014 A refinement of the Cameron-Erdős conjecture. Zbl 1284.05024 Alon, Noga; Balogh, József; Morris, Robert; Samotij, Wojciech 2014 Two notions of unit distance graphs. Zbl 1295.05092 Alon, Noga; Kupavskii, Andrey 2014 Additive patterns in multiplicative subgroups. Zbl 1377.11013 Alon, Noga; Bourgain, Jean 2014 Correction: “Basic network creation games”. Zbl 1302.90163 Alon, Noga; Demaine, Erik D.; Hajiaghayi, Mohammadtaghi; Kanellopoulos, Panagiotis; Leighton, Tom 2014 Economical graph discovery. Zbl 1327.90345 Alon, Noga; Emek, Yuval; Feldman, Michal; Tennenholtz, Moshe 2014 Maximizing the number of nonnegative subsets. Zbl 1301.05346 Alon, Noga; Aydinian, Harout; Huang, Hao 2014 On the compatibility of quartet trees. Zbl 1349.92102 Alon, Noga; Snir, Sagi; Yuster, Raphael 2014 A note on general sliding window processes. Zbl 1300.60043 Alon, Noga; Feldheim, Ohad Noy 2014 The cover number of a matrix and its algorithmic applications. Zbl 1359.68297 Alon, Noga; Lee, Troy; Shraibman, Adi 2014 Basic network creation games. Zbl 1273.90167 Alon, Noga; Demaine, Erik D.; Hajiaghayi, Mohammad T.; Leighton, Tom 2013 On sunflowers and matrix multiplication. Zbl 1268.05223 Alon, Noga; Shpilka, Amir; Umans, Christopher 2013 Beeping a maximal independent set. Zbl 1311.68024 Afek, Yehuda; Alon, Noga; Bar-Joseph, Ziv; Cornejo, Alejandro; Haeupler, Bernhard; Kuhn, Fabian 2013 The chromatic number of random Cayley graphs. Zbl 1295.05206 Alon, Noga 2013 The approximate rank of a matrix and its algorithmic applications: approximate rank. Zbl 1293.68136 Alon, Noga; Lee, Troy; Shraibman, Adi; Vempala, Santosh 2013 The Turán number of sparse spanning graphs. Zbl 1301.05201 Alon, Noga; Yuster, Raphael 2013 Restricted integer partition functions. Zbl 1294.11157 Alon, Noga 2013 Almost $$k$$-wise vs. $$k$$-wise independent permutations, and uniformity for general group actions. Zbl 1297.68183 Alon, Noga; Lovett, Shachar 2013 Nearly tight bounds for testing function isomorphism. Zbl 1275.68072 Alon, Noga; Blais, Eric; Chakraborty, Sourav; García-Soriano, David; Matsliah, Arie 2013 A note on degenerate and spectrally degenerate graphs. Zbl 1259.05111 Alon, Noga 2013 The asymmetric matrix partition problem. Zbl 1388.68078 Alon, Noga; Feldman, Michal; Gamzu, Iftah; Tennenholtz, Moshe 2013 Minimizing the number of carries in addition. Zbl 1321.11010 Alon, Noga 2013 How to put through your agenda in collective binary decisions. Zbl 1406.91099 Alon, Noga; Bredereck, Robert; Chen, Jiehua; Kratsch, Stefan; Niedermeier, Rolf; Woeginger, Gerhard J. 2013 Matrix sparsification and nested dissection over arbitrary fields. Zbl 1281.65074 Alon, Noga; Yuster, Raphael 2013 Paul Erdős and probabilistic reasoning. Zbl 1293.05387 Alon, Noga 2013 Two notions of unit distance graphs. Zbl 1293.05230 Alon, Noga; Kupavskii, Andrey 2013 Large matchings in uniform hypergraphs and the conjectures of Erdős and samuels. Zbl 1242.05189 Alon, Noga; Frankl, Peter; Huang, Hao; Rödl, Vojtech; Ruciński, Andrzej; Sudakov, Benny 2012 Nonnegative $$k$$-sums, fractional covers, and probability of small deviations. Zbl 1241.05100 Alon, Noga; Huang, Hao; Sudakov, Benny 2012 A non-linear lower bound for planar epsilon-nets. Zbl 1232.68161 Alon, Noga 2012 Sums and products along sparse graphs. Zbl 1288.05124 Alon, Noga; Angel, Omer; Benjamini, Itai; Lubetzky, Eyal 2012 Nearly complete graphs decomposable into large induced matchings and their applications. Zbl 1286.05128 Alon, Noga; Moitra, Ankur; Sudakov, Benny 2012 Dense uniform hypergraphs have high list chromatic number. Zbl 1244.05156 Alon, Noga; Kostochka, Alexandr 2012 Almost $$k$$-wise vs. $$k$$-wise independent permutations, and uniformity for general group actions. Zbl 1297.68182 Alon, Noga; Lovett, Shachar 2012 Space-efficient local computation algorithms. Zbl 1422.68263 Alon, Noga; Rubinfeld, Ronitt; Vardi, Shai; Xie, Ning 2012 Local correction of juntas. Zbl 1242.94044 Alon, Noga; Weinstein, Amit 2012 The de Bruijn-Erdős theorem for hypergraphs. Zbl 1254.05026 Alon, Noga; Mellinger, Keith E.; Mubayi, Dhruv; Verstraëte, Jacques 2012 Solving MAX-$$r$$-SAT above a tight lower bound. Zbl 1242.68118 Alon, Noga; Gutin, Gregory; Kim, Eun Jung; Szeider, Stefan; Yeo, Anders 2011 The structure of almost all graphs in a hereditary property. Zbl 1217.05193 Alon, Noga; Balogh, József; Bollobás, Béla; Morris, Robert 2011 Many random walks are faster than one. Zbl 1223.05284 Alon, Noga; Avin, Chen; Koucký, Michal; Kozma, Gady; Lotker, Zvi; Tuttle, Mark R. 2011 A biological solution to a fundamental distributed computing problem. Zbl 1226.92001 Afek, Yehuda; Alon, Noga; Barad, Omer; Hornstein Eran; Barkai, Naama; Bar-Joseph, Ziv 2011 Beeping a maximal independent set. Zbl 1311.68023 Afek, Yehuda; Alon, Noga; Bar-Joseph, Ziv; Cornejo, Alejandro; Haeupler, Bernhard; Kuhn, Fabian 2011 On a generalization of Meyniel’s conjecture on the Cops and Robbers game. Zbl 1205.05159 Alon, Noga; Mehrabian, Abbas 2011 Multicolored matchings in hypergraphs. Zbl 1255.05144 Alon, Noga 2011 Hypergraph list coloring and Euclidean Ramsey theory. Zbl 1232.05146 Alon, Noga; Kostochka, Alexandr 2011 Modular orientations of random and quasi-random regular graphs. Zbl 1226.05222 Alon, Noga; Prałat, Paweł 2011 The number of $$F$$-matchings in almost every tree is a zero residue. Zbl 1213.05130 Alon, Noga; Haber, Simi; Krivelevich, Michael 2011 Sparse balanced partitions and the complexity of subgraph problems. Zbl 1229.05125 Alon, Noga; Marx, Dániel 2011 Strategyproof approximation of the minimax on networks. Zbl 1232.91015 Alon, Noga; Feldman, Michal; Procaccia, Ariel D.; Tennenholtz, Moshe 2010 A note on competitive diffusion through social networks. Zbl 1197.91057 Alon, Noga; Feldman, Michal; Procaccia, Ariel D.; Tennenholtz, Moshe 2010 Quasi-randomness and algorithmic regularity for graphs with general degree distributions. Zbl 1227.05225 Alon, Noga; Coja-Oghlan, Amin; Hàn, Hiệp; Kang, Mihyun; Rödl, Vojtěch; Schacht, Mathias 2010 The inverse Banzhaf problem. Zbl 1201.91045 Alon, Noga; Edelman, Paul H. 2010 Solving MAX-$$r$$-SAT above a tight lower bound. Zbl 1288.68099 Alon, Noga; Gutin, Gregory; Kim, Eun Jung; Szeider, Stefan; Yeo, Anders 2010 High degree graphs contain large-star factors. Zbl 1255.05145 Along, Noga; Wormald, Nicholas 2010 A note on regular Ramsey graphs. Zbl 1208.05084 Alon, Noga; Ben-Shimon, Sonny; Krivelevich, Michael 2010 Testing Boolean function isomorphism. Zbl 1305.68327 Alon, Noga; Blais, Eric 2010 The number of sumsets in a finite field. Zbl 1223.11028 Alon, Noga; Granville, Andrew; Ubis, Adrián 2010 Typical peak sidelobe level of binary sequences. Zbl 1366.94440 Alon, Noga; Litsyn, Simon; Shpunt, Alexander 2010 Balanced families of perfect hash functions and their applications. Zbl 1300.68062 Alon, Noga; Gutner, Shai 2010 Increasing the chromatic number of a random graph. Zbl 1244.05194 Alon, Noga; Sudakov, Benny 2010 On constant time approximation of parameters of bounded degree graphs. Zbl 1309.68213 Alon, Noga 2010 Walking in circles. Zbl 1228.05099 Alon, Noga; Feldman, Michal; Procaccia, Ariel D.; Tennenholtz, Moshe 2010 Bayesian ignorance. Zbl 1315.91012 Alon, Noga; Emek, Yuval; Feldman, Michal; Tennenholtz, Moshe 2010 Choice-memory tradeoff in allocations. Zbl 1205.60023 Alon, Noga; Gurel-Gurevich, Ori; Lubetzky, Eyal 2010 Playing to retain the advantage. Zbl 1198.05112 Alon, Noga; Hefetz, Dan; Krivelevich, Michael 2010 Visions in mathematics. GAFA 2000 special volume, Part II. Proceedings of the meeting “Visions in Mathematics – Towards 2000, Tel Aviv, Israel, August 25–September 3, 1999. Special volume of the journal Geometric and Functional Analysis – GAFA. Reprint of the 2000 original. Zbl 1185.00038 Alon, Noga; Bourgain, Jean; Connes, Alain; Gromov, Mikhael; Milman, Vitali D. 2010 ...and 438 more Documents all top 5 Cited by 6,693 Authors 209 Alon, Noga M. 106 Sudakov, Benny 52 Krivelevich, Michael 48 Fox, Jacob 46 Rodl, Vojtech 45 Saurabh, Saket 43 Zhu, Xuding 41 Pach, János 40 Kohayakawa, Yoshiharu 39 Yuster, Raphael 38 Bollobás, Béla 36 Balogh, József 36 Kostochka, Aleksandr Vasil’evich 34 Fomin, Fedor V. 34 Goldreich, Oded 33 Wang, Guanghui 32 Gutin, Gregory Z. 31 Yeo, Anders 29 Mubayi, Dhruv 28 Shapira, Asaf 27 Furedi, Zoltan 27 Zehavi, Meirav 26 Hou, Jianfeng 26 Linial, Nathan 26 Wu, Jian-Liang 25 Osthus, Deryk 25 Peres, Yuval 25 Thomassé, Stéphan 24 Conlon, David 24 Kühn, Daniela 24 Lefmann, Hanno 24 Mohar, Bojan 23 Lokshtanov, Daniel 23 Matoušek, Jiří 23 Pelc, Andrzej 23 Prałat, Paweł 23 Vu, Van H. 22 Cioabă, Sebastian M. 22 Hoppen, Carlos 22 Tuza, Zsolt 21 Naor, Assaf 21 Scott, Alexander D. 20 Golovach, Petr A. 20 Grytczuk, Jarosław 20 Nešetřil, Jaroslav 20 Ron, Dana 19 Benjamini, Itai 19 Caro, Yair 19 Gao, Weidong 19 Han, Jie 19 Kang, Ross J. 19 Lubetzky, Eyal 19 Verstraëte, Jacques 19 West, Douglas Brent 18 Henning, Michael Anthony 18 Keevash, Peter 18 Schacht, Mathias 18 Zhang, Shenggui 17 Bang-Jensen, Jørgen 17 Dondi, Riccardo 17 Morris, Robert D. 17 Rautenbach, Dieter 17 Soberón, Pablo 17 Wang, Wei-Fan 17 Wigderson, Avi 16 Frankl, Péter 16 Kalai, Gil 16 Kowalski, Dariusz R. 16 Lingas, Andrzej 16 McDiarmid, Colin J. H. 16 Pilipczuk, Michał 16 Raĭgorodskiĭ, Andreĭ Mikhaĭlovich 16 Tardos, Gábor 16 Wong, Tsai-Lien 16 Yu, Xingxing 16 Yukna, Stasys P. 15 Esperet, Louis 15 Ferber, Asaf 15 Peleg, David 15 Raspaud, André 15 Samotij, Wojciech 15 Shabanov, Dmitry A. 15 Zhukovskiĭ, Maksim Evgen’evich 14 Böttcher, Julia 14 Bukh, Boris 14 Chudnovsky, Maria 14 Coja-Oghlan, Amin 14 Dudek, Andrzej 14 Marx, Dániel 14 Raman, Venkatesh 14 Szemerédi, Endre 14 Tao, Terence 14 Treglown, Andrew 14 Yu, Xiaowei 14 Zhao, Yi 13 Akbari, Saieed 13 Bolla, Marianna 13 Chandran, L. Sunil 13 Epstein, Leah 13 Frieze, Alan Michael ...and 6,593 more Authors all top 5 Cited in 445 Serials 478 Discrete Mathematics 339 Theoretical Computer Science 316 Discrete Applied Mathematics 219 Journal of Combinatorial Theory. Series B 215 European Journal of Combinatorics 184 Combinatorics, Probability and Computing 181 Journal of Combinatorial Theory. Series A 180 Algorithmica 169 SIAM Journal on Discrete Mathematics 157 Graphs and Combinatorics 144 Information Processing Letters 143 Combinatorica 137 Journal of Graph Theory 127 Random Structures & Algorithms 125 Journal of Computer and System Sciences 103 Discrete & Computational Geometry 101 Israel Journal of Mathematics 95 The Electronic Journal of Combinatorics 86 Journal of Combinatorial Optimization 83 Linear Algebra and its Applications 77 SIAM Journal on Computing 63 Advances in Mathematics 61 Theory of Computing Systems 56 Distributed Computing 52 Information and Computation 52 Computational Complexity 44 Proceedings of the American Mathematical Society 41 The Annals of Probability 39 Designs, Codes and Cryptography 36 Journal of Number Theory 36 Computational Geometry 35 Transactions of the American Mathematical Society 29 Advances in Applied Mathematics 29 Journal of Mathematical Sciences (New York) 27 Mathematical Programming. Series A. Series B 27 Journal of Discrete Algorithms 26 Probability Theory and Related Fields 25 European Journal of Operational Research 23 Applied Mathematics and Computation 22 The Annals of Applied Probability 22 Discussiones Mathematicae. Graph Theory 21 Mathematical Notes 21 Acta Mathematica Sinica. English Series 20 Discrete Optimization 19 Journal of Statistical Physics 19 The Annals of Statistics 18 Problems of Information Transmission 18 Geometric and Functional Analysis. GAFA 17 Doklady Mathematics 17 Journal of Scheduling 16 Order 15 Bulletin of the American Mathematical Society. New Series 15 Journal of Algebraic Combinatorics 14 Operations Research Letters 14 Acta Mathematicae Applicatae Sinica. English Series 14 Journal of the American Mathematical Society 14 Finite Fields and their Applications 14 Annals of Combinatorics 13 Artificial Intelligence 13 Communications in Mathematical Physics 13 Inventiones Mathematicae 13 Mathematical Social Sciences 13 Annals of Pure and Applied Logic 13 Journal of Cryptology 13 Annals of Mathematics. Second Series 13 Journal of the European Mathematical Society (JEMS) 12 Bulletin of the Australian Mathematical Society 12 Journal of Mathematical Physics 12 Computers & Operations Research 12 Annals of Operations Research 11 Czechoslovak Mathematical Journal 11 Duke Mathematical Journal 11 Mathematics of Operations Research 11 Applied Mathematics Letters 11 Journal of Combinatorial Designs 11 International Journal of Number Theory 11 Computer Science Review 10 Journal of Algebra 10 Networks 10 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 10 Bernoulli 10 Science China. Mathematics 10 Forum of Mathematics, Sigma 9 Linear and Multilinear Algebra 9 Journal of Functional Analysis 9 Journal of Complexity 9 Journal of Machine Learning Research (JMLR) 9 Discrete Mathematics, Algorithms and Applications 8 Statistics & Probability Letters 8 Acta Mathematica Hungarica 8 International Journal of Computational Geometry & Applications 8 International Journal of Foundations of Computer Science 8 Discrete Mathematics and Applications 8 Integers 8 Internet Mathematics 7 Computers & Mathematics with Applications 7 Mathematical Proceedings of the Cambridge Philosophical Society 7 Periodica Mathematica Hungarica 7 The Journal of Symbolic Logic 7 Mathematika ...and 345 more Serials all top 5 Cited in 56 Fields 4,064 Combinatorics (05-XX) 1,962 Computer science (68-XX) 503 Operations research, mathematical programming (90-XX) 433 Probability theory and stochastic processes (60-XX) 415 Number theory (11-XX) 337 Information and communication theory, circuits (94-XX) 290 Convex and discrete geometry (52-XX) 245 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 179 Linear and multilinear algebra; matrix theory (15-XX) 164 Group theory and generalizations (20-XX) 134 Statistics (62-XX) 94 Mathematical logic and foundations (03-XX) 93 Statistical mechanics, structure of matter (82-XX) 90 Numerical analysis (65-XX) 81 Functional analysis (46-XX) 79 Order, lattices, ordered algebraic structures (06-XX) 72 Geometry (51-XX) 56 Biology and other natural sciences (92-XX) 54 Quantum theory (81-XX) 44 Commutative algebra (13-XX) 35 Algebraic geometry (14-XX) 27 Dynamical systems and ergodic theory (37-XX) 25 Algebraic topology (55-XX) 24 Harmonic analysis on Euclidean spaces (42-XX) 24 Manifolds and cell complexes (57-XX) 22 Field theory and polynomials (12-XX) 21 Measure and integration (28-XX) 21 Operator theory (47-XX) 21 General topology (54-XX) 20 Global analysis, analysis on manifolds (58-XX) 19 Partial differential equations (35-XX) 18 Differential geometry (53-XX) 17 Systems theory; control (93-XX) 12 General and overarching topics; collections (00-XX) 12 Approximations and expansions (41-XX) 11 Functions of a complex variable (30-XX) 10 History and biography (01-XX) 10 Topological groups, Lie groups (22-XX) 9 Real functions (26-XX) 9 Ordinary differential equations (34-XX) 9 Abstract harmonic analysis (43-XX) 6 Difference and functional equations (39-XX) 5 Associative rings and algebras (16-XX) 5 Sequences, series, summability (40-XX) 5 Calculus of variations and optimal control; optimization (49-XX) 4 Integral transforms, operational calculus (44-XX) 3 Nonassociative rings and algebras (17-XX) 2 Special functions (33-XX) 2 Fluid mechanics (76-XX) 2 Relativity and gravitational theory (83-XX) 2 Mathematics education (97-XX) 1 General algebraic systems (08-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Integral equations (45-XX) 1 Mechanics of deformable solids (74-XX) 1 Classical thermodynamics, heat transfer (80-XX) Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata.	2021-07-26T20:46:23	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5220569372177124, "perplexity": 14929.057451018116}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046152144.92/warc/CC-MAIN-20210726183622-20210726213622-00198.warc.gz"}
https://par.nsf.gov/biblio/10366606-preparing-low-surface-brightness-science-vera-rubin-observatory-characterization-tidal-features-from-mock-images	Preparing for low surface brightness science with the Vera C. Rubin Observatory: Characterization of tidal features from mock images ABSTRACT Tidal features in the outskirts of galaxies yield unique information about their past interactions and are a key prediction of the hierarchical structure formation paradigm. The Vera C. Rubin Observatory is poised to deliver deep observations for potentially millions of objects with visible tidal features, but the inference of galaxy interaction histories from such features is not straightforward. Utilizing automated techniques and human visual classification in conjunction with realistic mock images produced using the NewHorizon cosmological simulation, we investigate the nature, frequency, and visibility of tidal features and debris across a range of environments and stellar masses. In our simulated sample, around 80 per cent of the flux in the tidal features around Milky Way or greater mass galaxies is detected at the 10-yr depth of the Legacy Survey of Space and Time (30–31 mag arcsec−2), falling to 60 per cent assuming a shallower final depth of 29.5 mag arcsec−2. The fraction of total flux found in tidal features increases towards higher masses, rising to 10 per cent for the most massive objects in our sample (M⋆ ∼ 1011.5 M⊙). When observed at sufficient depth, such objects frequently exhibit many distinct tidal features with complex shapes. The interpretation and characterization of such features varies significantly with more » Authors: ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; more » Publication Date: NSF-PAR ID: 10366606 Journal Name: Monthly Notices of the Royal Astronomical Society Volume: 513 Issue: 1 Page Range or eLocation-ID: p. 1459-1487 ISSN: 0035-8711 Publisher: Oxford University Press 1. ABSTRACT Core formation and runaway core collapse in models with self-interacting dark matter (SIDM) significantly alter the central density profiles of collapsed haloes. Using a forward modelling inference framework with simulated data-sets, we demonstrate that flux ratios in quadruple image strong gravitational lenses can detect the unique structural properties of SIDM haloes, and statistically constrain the amplitude and velocity dependence of the interaction cross-section in haloes with masses between 106 and 1010 M⊙. Measurements on these scales probe self-interactions at velocities below $30 \ \rm {km} \ \rm {s^{-1}}$, a relatively unexplored regime of parameter space, complimenting constraints at higher velocities from galaxies and clusters. We cast constraints on the amplitude and velocity dependence of the interaction cross-section in terms of σ20, the cross-section amplitude at $20 \ \rm {km} \ \rm {s^{-1}}$. With 50 lenses, a sample size available in the near future, and flux ratios measured from spatially compact mid-IR emission around the background quasar, we forecast $\sigma _{20} \lt 11\rm {\small {--}}23 \ \rm {cm^2} \rm {g^{-1}}$ at $95 {{\ \rm per\ cent}}$ CI, depending on the amplitude of the subhalo mass function, and assuming cold dark matter (CDM). Alternatively, if $\sigma _{20} = 19.2 \ \rmmore » 2. ABSTRACT We present a pilot study to assess the potential of Hyper Suprime-Cam Public Data Release 2 (HSC-PDR2) images for the analysis of extended faint structures within groups of galaxies. We examine the intragroup light (IGL) of the group 400138 (Mdyn = 1.3 ± 0.5 × 1013 M⊙, z ∼ 0.2) from the Galaxy And Mass Assembly (GAMA) survey using Hyper Suprime-Cam Subaru Strategic Program Public Data Release 2 (HSC-SSP PDR2) images in g, r, and i bands. We present the most extended IGL measurement to date, reaching down to$\mu _{g}^{\rm {lim}}=30.76$mag arcsec−2 (3σ; 10 × 10 arcsec2) at a semimajor axis of 275 kpc. The IGL shows mean colour values of g − i = 0.92, g − r = 0.60, and r − i = 0.32 (±0.01). The IGL stellar populations are younger (2–2.5 Gyr) and less metal rich ([Fe/H] ∼ −0.4) than those of the host group galaxies. We find a range of IGL fractions as a function of total group luminosity of${\sim} 2\!-\!36 {{\ \rm per\ cent}}$depending on the definition of IGL, with larger fractions the bluer the observation wavelength. The early-type to late-type galaxy ratio suggests that 400138 is a more evolved group, dominated by early-type galaxies, and the IGL fraction agrees with that of other similarly evolved groups.more » 3. ABSTRACT We present a detailed visual morphological classification for the 4614 MaNGA galaxies in SDSS Data Release 15, using image mosaics generated from a combination of r band (SDSS and deeper DESI Legacy Surveys) images and their digital post-processing. We distinguish 13 Hubble types and identify the presence of bars and bright tidal debris. After correcting the MaNGA sample for volume completeness, we calculate the morphological fractions, the bi-variate distribution of type and stellar mass M* – where we recognize a morphological transition ‘valley’ around S0a-Sa types – and the variations of the g − i colour and luminosity-weighted age over this distribution. We identified bars in 46.8 per cent of galaxies, present in all Hubble types later than S0. This fraction amounts to a factor ∼2 larger when compared with other works for samples in common. We detected 14 per cent of galaxies with tidal features, with the fraction changing with M* and morphology. For 355 galaxies, the classification was uncertain; they are visually faint, mostly of low/intermediate masses, low concentrations, and discy in nature. Our morphological classification agrees well with other works for samples in common, though some particular differences emerge, showing that our image procedures allow us to identify a wealthmore » 4. ABSTRACT Globular clusters are prone to lose stars while moving around the Milky Way. These stars escape the clusters and are distributed throughout extended envelopes or tidal tails. However, such extra-tidal structures are not observed in all globular clusters, and yet there are no structural or dynamical parameters that can predict their presence or absence. NGC 6864 is an outer halo globular cluster with reported no observed tidal tails. We used Dark Energy Camera photometry reaching ∼4 mag underneath its main-sequence turnoff to confidently detect an extra-tidal envelope, and stellar debris spread across the cluster outskirts. These features emerged once robust field star filtering techniques were applied to the fainter end of the observed cluster main sequence. NGC 6864 is associated to the Gaia-Enceladus dwarf galaxy, among others 28 globular clusters. Up-to-date, nearly 64${{\ \rm per\,cent}}$of them have been targeted looking for tidal tails and most of them have been confirmed to exhibit tidal tails. Thus, the present outcomes allow us to speculate on the possibility that Gaia-Enceladus globular clusters share a common pattern of mass loss by tidal disruption. 5. ABSTRACT We present a sample of 446 galaxy pairs constructed using the cosmological simulation IllustrisTNG-100 at z = 0, with M$_{\rm FoF,dm} = 10^{11}\!-\!10^{13.5}\$ M⊙. We produce ideal mock SDSS g-band images of all pairs to test the reliability of visual classification schema employed to produce samples of interacting galaxies. We visually classify each image as interacting or not based on the presence of a close neighbour, the presence of stellar debris fields, disturbed discs, and/or tidal features. By inspecting the trajectories of the pairs, we determine that these indicators correctly identify interacting galaxies ∼45 per cent of the time. We subsequently split the sample into the visually identified interacting pairs (VIP; 38 pairs) and those which are interacting but are not visually identified (nonVIP; 47 pairs). We find that VIP have undergone a close passage nearly twice as recently as the non-VIP, and typically have higher stellar masses. Further, the VIP sit in dark matter haloes that are approximately 2.5 times as massive, in environments nearly 2 times as dense, and are almost a factor of 10 more affected by the tidal forces of their surroundings than the nonVIP. These factors conspire to increase the observability of tidal features and disturbed morphologies, making themore »	2023-03-21T01:14:24	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7460521459579468, "perplexity": 4085.845659528399}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296943589.10/warc/CC-MAIN-20230321002050-20230321032050-00195.warc.gz"}
http://legisquebec.gouv.qc.ca/en/showversion/cs/B-1?code=se:78&pointInTime=20200529	### B-1 - Act respecting the Barreau du Québec 78. (1) The board of directors may, if it considers it expedient, appoint persons to assist the syndic in the performance of his duties. (2) Within the limits of their mandate, these persons shall have the same powers as the syndic. 1973, c. 44, s. 36; 1975, c. 81, s. 22; 2008, c. 11, s. 212; 2014, c. 13, s. 17. 78. (1) The executive committee may, if it considers it expedient, appoint persons to assist the syndic in the performance of his duties. (2) Within the limits of their mandate, these persons shall have the same powers as the syndic. 1973, c. 44, s. 36; 1975, c. 81, s. 22; 2008, c. 11, s. 212. 78. (1) The Executive Committee may, if it considers it expedient, appoint persons to assist the syndic in the performance of his duties. (2) Within the limits of their mandate, these persons shall have the same powers as the syndic. 1973, c. 44, s. 36; 1975, c. 81, s. 22.	2020-07-14T20:56:34	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8339182138442993, "perplexity": 10567.174340330386}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-29/segments/1593657151197.83/warc/CC-MAIN-20200714181325-20200714211325-00592.warc.gz"}
https://zbmath.org/authors/?q=rv%3A7137	## Naniewicz, Zdzisław Compute Distance To: Author ID: naniewicz.zdzislaw Published as: Naniewicz, Zdzisław; Naniewicz, Z.; Naniewicz, Zdzislaw; Naniewicz, Zdisław; Naniewicz, Zdizsław more...less External Links: Wikidata · IdRef Documents Indexed: 53 Publications since 1977, including 1 Book Reviewing Activity: 25 Reviews Co-Authors: 10 Co-Authors with 22 Joint Publications 193 Co-Co-Authors all top 5 ### Co-Authors 31 single-authored 7 Woźniak, Czesław 5 Panagiotopoulos, Panagiotis D. 4 Gałka, Andrzej 4 Motreanu, Dumitru 2 Nockowska, Magdalena 1 Carl, Siegfried 1 Chełmiński, Krzysztof 1 Halidias, Nikolaos 1 Pop, Gabriela 1 Puchała, Piotr all top 5 ### Serials 7 Bulletin of the Polish Academy of Sciences. Technical Sciences 6 Control and Cybernetics 5 Archives of Mechanics 3 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 3 Journal of Global Optimization 3 Bulletin de l’Académie Polonaise des Sciences, Série des Sciences Techniques 3 Nonlinear Analysis. Theory, Methods & Applications 2 Applicable Analysis 2 Ingenieur-Archiv 2 Journal of Mathematical Analysis and Applications 1 Mechanika Teoretyczna i Stosowana 1 Journal of Optimization Theory and Applications 1 Mathematics of Operations Research 1 Numerical Functional Analysis and Optimization 1 Optimization 1 Differential and Integral Equations 1 Nonlinear World 1 Journal of Applied Analysis 1 Annales Mathematicae Silesianae 1 Pure and Applied Mathematics, Marcel Dekker 1 Set-Valued and Variational Analysis all top 5 ### Fields 37 Calculus of variations and optimal control; optimization (49-XX) 23 Mechanics of deformable solids (74-XX) 11 Partial differential equations (35-XX) 7 Operator theory (47-XX) 7 Operations research, mathematical programming (90-XX) 5 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Mathematical logic and foundations (03-XX) 1 Functional analysis (46-XX) 1 Numerical analysis (65-XX) 1 Fluid mechanics (76-XX) 1 Statistical mechanics, structure of matter (82-XX) ### Citations contained in zbMATH Open 35 Publications have been cited 546 times in 453 Documents Cited by Year Mathematical theory of hemivariational inequalities and applications. Zbl 0968.49008 Naniewicz, Z.; Panagiotopoulos, P. D. 1994 On some nonconvex variational problems related to hemivariational inequalities. Zbl 0696.49018 Naniewicz, Zdzisław 1989 Hemivariational inequality approach to constrained problems for star- shaped admissible sets. Zbl 0808.49019 Naniewicz, Z. 1994 On some nonmonotone subdifferential boundary conditions in elastostatics. Zbl 0698.73009 Naniewicz, Z. 1989 On a quasi-stationary model of debonding processes in layered composites. Zbl 0675.73006 Naniewicz, Z.; Woźniak, Cz. 1988 Hemivariational inequalities with functions fulfilling directional growth condition. Zbl 0835.49008 Naniewicz, Zdzisław 1994 A topological approach to hemivariational inequalities with unilateral growth condition. Zbl 0994.49008 Motreanu, D.; Naniewicz, Z. 2001 On the pseudo-monotonicity of generalized gradients of nonconvex functions. Zbl 0724.49011 Naniewicz, Zdzisław 1992 Hemivariational inequalities with functionals which are not locally Lipschitz. Zbl 0849.49013 Naniewicz, Zdzisław 1995 Coercive limits for constitutive equations of monotone-gradient type. Zbl 1056.35146 Chełmiński, Krzysztof; Naniewicz, Zdzisław 2002 Semicoercive variational-hemivariational inequalities with unilateral growth conditions. Zbl 1055.49005 Naniewicz, Z. 2000 Discontinuous semilinear problems in vector-valid function spaces. Zbl 0848.35051 Motreanu, D.; Naniewicz, Z. 1996 Hemivariational inequalities as necessary conditions for optimality for a class of nonsmooth nonconvex functionals. Zbl 0910.49010 Naniewicz, Zdzisław 1997 Vector quasi-hemivariational inequalities and discontinuous elliptic systems. Zbl 1090.49005 Carl, S.; Naniewicz, Z. 2006 Pseudomonotonicity and economic equilibrium problem in reflexive Banach space. Zbl 1276.91071 Naniewicz, Zdzislaw 2007 Systems of variational inequalities related to economic equilibrium. Zbl 1227.91026 Naniewicz, Zdzisław; Nockowska, Magdalena 2007 On economic equilibrium type problems with applications. Zbl 1251.49011 Naniewicz, Zdzisław 2011 On variational aspects of some nonconvex nonsmooth global optimization problem. Zbl 0839.49009 Naniewicz, Z. 1995 On the existence of solutions to the continuum model of delamination. Zbl 0770.73003 Naniewicz, Zdisław 1993 Semilinear hemivariational inequalities with Dirichlet boundary condition. Zbl 1053.49007 Motreanu, Dumitru; Naniewicz, Zdzisław 2003 On some optimization problem related to economic equilibrium. Zbl 1169.91408 Naniewicz, Zdzisław 2002 Hemivariational inequalities governed be the $$p$$-Laplacian Dirichlet problem. Zbl 1166.49301 Naniewicz, Zdzisław 2004 Variational-hemivariational inequalities for multidimensional superpotential laws. Zbl 0894.49005 Pop, G.; Panagiotopoulos, P. D.; Naniewicz, Z. 1997 A minimax approach to semicoercive hemivariational inequalities. Zbl 1044.49006 Motreanu, Dumitru; Naniewicz, Zdzisław 2003 On stationary unilateral problems. Zbl 0617.73004 Naniewicz, Z.; Woźniak, Cz. 1985 Some existence results in stationary problems of solid mechanics with unilateral constraints for displacements and stresses. Zbl 0612.73018 Naniewicz, Z. 1986 On a class of hemivariational inequalities at resonance. Zbl 1041.49007 Halidias, N.; Naniewicz, Z. 2004 Pareto optimality and Walrasian equilibria. Zbl 1148.90013 Naniewicz, Zdzisław 2008 On regularity results for variational-hemivariational inequalities. Zbl 0968.49009 Naniewicz, Z.; Panagiotopoulos, P. D. 2000 Hemivariational inequalities governed by the $$p$$-Laplacian Neumann problem. Zbl 1168.49010 Naniewicz, Zdzisław 2007 On ideal textile-type materials. IV: Examples of solutions. Zbl 0568.73040 Gałka, Andrzej; Naniewicz, Zdzisław; Woźniak, Czesław 1985 On some class of problems of linear elasticity with constraints for displacements and stresses. Zbl 0569.73018 Naniewicz, Z. 1983 Minimization and min-max problems in elastostatics with unilateral constraints for displacements and stresses. Zbl 0612.73017 Naniewicz, Z. 1985 Economic equilibrium problems in reflexive Banach spaces. Zbl 1102.90071 Naniewicz, Zdzisław 2006 Pseudomonotone semicoercive variational-hemivariational inequalities with unilateral growth condition. Zbl 1136.49305 Naniewicz, Zdzisław 2003 On economic equilibrium type problems with applications. Zbl 1251.49011 Naniewicz, Zdzisław 2011 Pareto optimality and Walrasian equilibria. Zbl 1148.90013 Naniewicz, Zdzisław 2008 Pseudomonotonicity and economic equilibrium problem in reflexive Banach space. Zbl 1276.91071 Naniewicz, Zdzislaw 2007 Systems of variational inequalities related to economic equilibrium. Zbl 1227.91026 Naniewicz, Zdzisław; Nockowska, Magdalena 2007 Hemivariational inequalities governed by the $$p$$-Laplacian Neumann problem. Zbl 1168.49010 Naniewicz, Zdzisław 2007 Vector quasi-hemivariational inequalities and discontinuous elliptic systems. Zbl 1090.49005 Carl, S.; Naniewicz, Z. 2006 Economic equilibrium problems in reflexive Banach spaces. Zbl 1102.90071 Naniewicz, Zdzisław 2006 Hemivariational inequalities governed be the $$p$$-Laplacian Dirichlet problem. Zbl 1166.49301 Naniewicz, Zdzisław 2004 On a class of hemivariational inequalities at resonance. Zbl 1041.49007 Halidias, N.; Naniewicz, Z. 2004 Semilinear hemivariational inequalities with Dirichlet boundary condition. Zbl 1053.49007 Motreanu, Dumitru; Naniewicz, Zdzisław 2003 A minimax approach to semicoercive hemivariational inequalities. Zbl 1044.49006 Motreanu, Dumitru; Naniewicz, Zdzisław 2003 Pseudomonotone semicoercive variational-hemivariational inequalities with unilateral growth condition. Zbl 1136.49305 Naniewicz, Zdzisław 2003 Coercive limits for constitutive equations of monotone-gradient type. Zbl 1056.35146 Chełmiński, Krzysztof; Naniewicz, Zdzisław 2002 On some optimization problem related to economic equilibrium. Zbl 1169.91408 Naniewicz, Zdzisław 2002 A topological approach to hemivariational inequalities with unilateral growth condition. Zbl 0994.49008 Motreanu, D.; Naniewicz, Z. 2001 Semicoercive variational-hemivariational inequalities with unilateral growth conditions. Zbl 1055.49005 Naniewicz, Z. 2000 On regularity results for variational-hemivariational inequalities. Zbl 0968.49009 Naniewicz, Z.; Panagiotopoulos, P. D. 2000 Hemivariational inequalities as necessary conditions for optimality for a class of nonsmooth nonconvex functionals. Zbl 0910.49010 Naniewicz, Zdzisław 1997 Variational-hemivariational inequalities for multidimensional superpotential laws. Zbl 0894.49005 Pop, G.; Panagiotopoulos, P. D.; Naniewicz, Z. 1997 Discontinuous semilinear problems in vector-valid function spaces. Zbl 0848.35051 Motreanu, D.; Naniewicz, Z. 1996 Hemivariational inequalities with functionals which are not locally Lipschitz. Zbl 0849.49013 Naniewicz, Zdzisław 1995 On variational aspects of some nonconvex nonsmooth global optimization problem. Zbl 0839.49009 Naniewicz, Z. 1995 Mathematical theory of hemivariational inequalities and applications. Zbl 0968.49008 Naniewicz, Z.; Panagiotopoulos, P. D. 1994 Hemivariational inequality approach to constrained problems for star- shaped admissible sets. Zbl 0808.49019 Naniewicz, Z. 1994 Hemivariational inequalities with functions fulfilling directional growth condition. Zbl 0835.49008 Naniewicz, Zdzisław 1994 On the existence of solutions to the continuum model of delamination. Zbl 0770.73003 Naniewicz, Zdisław 1993 On the pseudo-monotonicity of generalized gradients of nonconvex functions. Zbl 0724.49011 Naniewicz, Zdzisław 1992 On some nonconvex variational problems related to hemivariational inequalities. Zbl 0696.49018 Naniewicz, Zdzisław 1989 On some nonmonotone subdifferential boundary conditions in elastostatics. Zbl 0698.73009 Naniewicz, Z. 1989 On a quasi-stationary model of debonding processes in layered composites. Zbl 0675.73006 Naniewicz, Z.; Woźniak, Cz. 1988 Some existence results in stationary problems of solid mechanics with unilateral constraints for displacements and stresses. Zbl 0612.73018 Naniewicz, Z. 1986 On stationary unilateral problems. Zbl 0617.73004 Naniewicz, Z.; Woźniak, Cz. 1985 On ideal textile-type materials. IV: Examples of solutions. Zbl 0568.73040 Gałka, Andrzej; Naniewicz, Zdzisław; Woźniak, Czesław 1985 Minimization and min-max problems in elastostatics with unilateral constraints for displacements and stresses. Zbl 0612.73017 Naniewicz, Z. 1985 On some class of problems of linear elasticity with constraints for displacements and stresses. Zbl 0569.73018 Naniewicz, Z. 1983 all top 5 ### Cited by 290 Authors 74 Migórski, Stanisław 39 Sofonea, Mircea 33 Han, Weimin 29 Papageorgiou, Nikolaos S. 26 Liu, Zhenhai 24 Xiao, Yibin 23 Motreanu, Dumitru 23 Zeng, Shengda 21 Carl, Siegfried 21 Panagiotopoulos, Panagiotis D. 20 Gasiński, Leszek 19 Ochal, Anna 16 Naniewicz, Zdzisław 16 Noor, Muhammad Aslam 14 Huang, Nan-Jing 12 Kalita, Piotr 11 Bartosz, Krzysztof 11 Goeleven, Daniel 11 Peng, Zijia 11 Zeng, Biao 9 Chadli, Ouayl 9 Costea, Nicuşor 9 Le, Vy Khoi 9 Verma, Ram U. 9 Yao, Jen-Chih 8 Filippakis, Michael E. 7 Gwinner, Joachim 7 Rădulescu, Vicenţiu D. 6 Barboteu, Mikaël 6 Denkowski, Zdzislaw 6 Dudek, Sylwia 6 Han, Jiangfeng 6 Kasyanov, Pavlo O. 6 Miettinen, Markku 5 Kristály, Alexandru 5 Kyritsi, Sophia Th. 5 Li, Yunxiang 5 Matei, Andaluzia Cristina 5 Ovcharova, Nina 4 Hu, Shouchuan 4 Kolumbán, József 4 Kulig, Anna 4 Kuttler, Kenneth L. jun. 4 Noor, Khalida Inayat 4 Pączka, Dariusz 4 Shillor, Meir 4 Stavroulakis, Georgios E. 4 Tang, Guoji 4 Tarzia, Domingo Alberto 4 Teng, Kaimin 3 Alleche, Boualem 3 Asfaw, Teffera M. 3 Gamorski, Piotr 3 Halidias, Nikolaos 3 Haslinger, Jaroslav 3 Huang, Jianguo 3 Khan, Akhtar Ali 3 Li, Xiuwen 3 Liu, Xiaoyou 3 Mistakidis, E. S. 3 Nguyen Van Thien 3 Staicu, Vasile 3 Szafraniec, Paweł 3 Tzaferopoulos, Michael Ap. 3 Varga, Csaba György 3 Wang, Zhongbao 3 Wen, Chingfeng 3 Winkert, Patrick 3 Zadoianchuk, Nina V. 3 Zeng, Huidan 3 Zgurovsky, Mikhail Z. 2 Addi, Khalid 2 Adly, Samir 2 Akhlil, Khalid 2 Alves, Claudianor Oliveira 2 Andrade Santos, Sandrina Rafaela 2 Andrews, Kevin T. 2 Bai, Yunru 2 Baiz, Othmane 2 Ben Aadi, Sultana 2 Benaissa, Hicham 2 Bocea, Marian F. 2 Bogdan, Marcel 2 Brogliato, Bernard 2 Cai, Dong-ling 2 Ceng, Lu-Chuan 2 Chełmiński, Krzysztof 2 Chen, Wenbin 2 Cheng, Xiaoliang 2 Chu, Xu 2 Cocou, Marius 2 Danan, David 2 Dong, Ge 2 El Moutawakil, Driss 2 Faiz, Zakaria 2 Fang, Changjie 2 Feng, Fang 2 Gariboldi, Claudia M. 2 Abreu Goncalves, Jose Valdo 2 Han, Danfu ...and 190 more Authors all top 5 ### Cited in 114 Serials 50 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 29 Journal of Mathematical Analysis and Applications 24 Nonlinear Analysis. Real World Applications 18 Journal of Global Optimization 15 Journal of Optimization Theory and Applications 14 Computers & Mathematics with Applications 14 Communications in Nonlinear Science and Numerical Simulation 12 ZAMP. Zeitschrift für angewandte Mathematik und Physik 12 Journal of Computational and Applied Mathematics 10 Applicable Analysis 10 Applied Mathematics and Optimization 10 Numerical Functional Analysis and Optimization 10 Applied Mathematics Letters 9 Optimization 8 Applied Mathematics and Computation 7 Nonlinear Analysis. Theory, Methods & Applications 6 Journal of Elasticity 6 Mathematics and Mechanics of Solids 5 Journal of Differential Equations 5 SIAM Journal on Mathematical Analysis 5 Set-Valued Analysis 5 Journal of Inequalities and Applications 5 Journal of Applied Mathematics and Computing 5 Optimization Letters 5 Set-Valued and Variational Analysis 4 Results in Mathematics 4 SIAM Journal on Control and Optimization 4 Acta Applicandae Mathematicae 4 Mathematical and Computer Modelling 4 Journal of Scientific Computing 4 Mathematical Programming. Series A. Series B 4 Abstract and Applied Analysis 4 Evolution Equations and Control Theory 4 Fixed Point Theory and Algorithms for Sciences and Engineering 3 Computer Methods in Applied Mechanics and Engineering 3 Czechoslovak Mathematical Journal 3 Mathematische Nachrichten 3 Proceedings of the American Mathematical Society 3 Journal of Applied Analysis 3 Positivity 3 Minimax Theory and its Applications 2 Ingenieur-Archiv 2 Israel Journal of Mathematics 2 Mathematical Methods in the Applied Sciences 2 Monatshefte für Mathematik 2 Numerische Mathematik 2 SIAM Journal on Numerical Analysis 2 Applied Mathematics and Mechanics. (English Edition) 2 European Journal of Applied Mathematics 2 Applications of Mathematics 2 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 2 Electronic Journal of Differential Equations (EJDE) 2 Acta Mathematica Sinica. English Series 2 Nonlinear Analysis. Modelling and Control 2 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 2 Analysis and Applications (Singapore) 2 Nonlinear Analysis. Hybrid Systems 2 Journal of Nonlinear Science and Applications 2 Science China. Mathematics 2 Advances in Nonlinear Analysis 2 Journal of Function Spaces 1 Acta Mechanica 1 Bulletin of the Australian Mathematical Society 1 Inverse Problems 1 Rocky Mountain Journal of Mathematics 1 Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM) 1 Annali di Matematica Pura ed Applicata. Serie Quarta 1 Mathematische Annalen 1 Mathematica Slovaca 1 Rendiconti del Circolo Matemàtico di Palermo. Serie II 1 Tôhoku Mathematical Journal. Second Series 1 Transactions of the American Mathematical Society 1 Operations Research Letters 1 Chinese Annals of Mathematics. Series B 1 Bulletin of the Iranian Mathematical Society 1 Applied Numerical Mathematics 1 Acta Mathematicae Applicatae Sinica. English Series 1 Computational Mechanics 1 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 1 Numerical Algorithms 1 Journal of Dynamics and Differential Equations 1 Archive of Applied Mechanics 1 SIAM Journal on Optimization 1 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 1 Cybernetics and Systems Analysis 1 Continuum Mechanics and Thermodynamics 1 Topological Methods in Nonlinear Analysis 1 Journal of Inverse and Ill-Posed Problems 1 NoDEA. Nonlinear Differential Equations and Applications 1 Bulletin des Sciences Mathématiques 1 Advances in Computational Mathematics 1 Discrete and Continuous Dynamical Systems 1 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 1 Vietnam Journal of Mathematics 1 Journal of Mathematical Fluid Mechanics 1 Communications in Contemporary Mathematics 1 Optimization and Engineering 1 Discrete and Continuous Dynamical Systems. Series B 1 Journal of Applied Mathematics 1 Acta Mathematica Scientia. Series B. (English Edition) ...and 14 more Serials all top 5 ### Cited in 24 Fields 283 Calculus of variations and optimal control; optimization (49-XX) 191 Partial differential equations (35-XX) 169 Operator theory (47-XX) 157 Mechanics of deformable solids (74-XX) 56 Numerical analysis (65-XX) 38 Operations research, mathematical programming (90-XX) 37 Ordinary differential equations (34-XX) 26 Global analysis, analysis on manifolds (58-XX) 21 Fluid mechanics (76-XX) 7 Functional analysis (46-XX) 7 Systems theory; control (93-XX) 6 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 4 Dynamical systems and ergodic theory (37-XX) 4 Probability theory and stochastic processes (60-XX) 3 General topology (54-XX) 2 Real functions (26-XX) 2 Integral equations (45-XX) 1 Measure and integration (28-XX) 1 Sequences, series, summability (40-XX) 1 Approximations and expansions (41-XX) 1 Computer science (68-XX) 1 Mechanics of particles and systems (70-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Information and communication theory, circuits (94-XX) ### Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata.	2023-03-24T19:36:39	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2872485816478729, "perplexity": 13594.447683794691}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296945288.47/warc/CC-MAIN-20230324180032-20230324210032-00674.warc.gz"}
https://publons.com/publon/2802/	0 pre-pub reviews 4 post-pub reviews ##### Abstract We present a new BSSRDF for rendering images of translucent materials. Previous diffusion BSSRDFs are limited by the accuracy of classical diffusion theory. We introduce a modified diffusion theory that is more accurate for highly absorbing materials and near the point of illumination. The new diffusion solution accurately decouples single and multiple scattering. We then derive a novel, analytic, extended-source solution to the multilayer search-light problem by quantizing the diffusion Green's function. This allows the application of the diffusion multipole model to material layers several orders of magnitude thinner than previously possible and creates accurate results under high-frequency illumination. Quantized diffusion provides both a new physical foundation and a variable-accuracy construction method for sum-of-Gaussians BSSRDFs, which have many useful properties for efficient rendering and appearance capture. Our BSSRDF maps directly to previous real-time rendering algorithms. For film production rendering, we propose several improvements to previous hierarchical point cloud algorithms by introducing a new radial-binning data structure and a doubly-adaptive traversal strategy. ##### Authors Eugene D'Eon; Geoffrey Irving • 1 author • 2 reviewers • Review of ### A quantized-diffusion model for rendering translucent materials Following presentation of the paper at SIGGRAPH 2011 I can only recall one question from Wenzel Jakob: "How were the parameters of the BSSRDF derived when rendering a textured surface, like the face images?" Response: A pre-computed lookup table is used to map a requested diffuse albedo to a single-scattering albedo such that normally incident illumination of a semi-infinite material produces the desired diffuse albedo. For the skin renders, this was done for a fixed index of refraction (1.4). How this is applied during rendering using the radial binning acceleration method is explained further in the paper. Published in Reviewed by • Review of ### A quantized-diffusion model for rendering translucent materials On page 4 the footnote incorrectly states that equation (5) is not absolutely convergent. Equation (5) provides the convergent form that separates the ballistic fluence from the scattered fluence and does converge. It is the alternative form $$\phi(r) = \frac{\mu_t^2}{2 \pi^2 r} \int_0^\infty \frac{\text{arctan}\, u}{\mu_t-\mu_s \, \frac{\text{arctan} \, u}{u}} \, \sin (r \, \mu_t \, u) \, du.$$ that does not separate the ballistic fluence explicitly and only converges in the sense of Cesaro summability. Published in Reviewed by • Review of ### A quantized-diffusion model for rendering translucent materials Let $\tau_0:=\frac{1}{s}\tau_1$, then $\tau_i=s^{i-1}\tau_1$ and $v_i=D(\tau_{i+1}+\tau_i)=s^i v_0$ $$\int\limits_{0}^{\infty} G_{3D}(2D\tau,r)e^{-\mu_a\tau}d\tau \approx \sum\limits_{i=0}^{k-1}\int\limits_{\tau_i}^{\tau_{i+1}} G_{3D}(2D\tau,r)e^{-\mu_a\tau}d\tau = \sum\limits_{i=0}^{k-1}(\tau_{i+1}-\tau_i) G_{3D}(D(\tau_{i+1}+\tau_i),r)e^{-\mu_a\frac{\tau_{i+1}+\tau_i}{2}} = \frac{s-1}{s+1}\sum\limits_{i=0}^{k-1}(\tau_{i+1}+\tau_i) G_{3D}(D(\tau_{i+1}+\tau_i),r)e^{-\mu_a\frac{\tau_{i+1}+\tau_i}{2}} = \frac{s-1}{s+1}\sum\limits_{i=0}^{k-1}\frac{s^i v_0}{D} G_{3D}(s^i v_0,r)e^{-\mu_a\frac{s^i v_0}{2D}}$$ Given $s=\frac{1+\sqrt{5}}{2}$, $\frac{s-1}{s+1} \approx 0.236068$ rather than $0.240606$ in the paper. Can someone tell me how to get that magic number? And why $v_0$ is specified in terms of $\mu_a$? Thanks for your kindness. Published in Reviewed by • Review of ### A quantized-diffusion model for rendering translucent materials The equation between (19) and (20) has incorrect indices on the $\tau$s and should read: $$w_i = \int_{\tau_i}^{\tau_{i+1}} e^{-\tau \mu_a} d\tau = \frac{e^{-\tau_i \mu_a} - e^{-\tau_{i+1} \mu_a }}{\mu_a}$$ (thanks to Toshiya Hachisuka for bringing this to my attention) Published in Reviewed by All peer review content displayed here is covered by a Creative Commons CC BY 4.0 license.	2021-04-20T13:32:33	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3091563582420349, "perplexity": 3339.802375361528}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618039398307.76/warc/CC-MAIN-20210420122023-20210420152023-00557.warc.gz"}
https://par.nsf.gov/biblio/10273153	Cryogenic spectrometer for measuring the far-IR to millimeter-wave absorptivity of cosmic analog dusts We report on the design, construction, and performance of a custom apparatus built to measure the frequency- and temperature-dependent absorptivity of millimeter-wave light by cosmic analog dusts. We highlight the unique challenges faced as well as a few key innovations that are part of the instrument. Among those is an ultra-compact Fourier transform spectrometer. We have measured its effective frequency range and FWHM resolution to be 150–2100 GHz and$∼<#comment/>45GHz$, respectively. Another innovation is a cold sample positioner whose temperature can be controlled within the range of 3.7–50 K. The use of a pulse-tube cryocooler results in a pulse-synchronous signal that dominates the detector (bolometer) signal. Methods used to address that challenge are also presented. Authors: ; ; ; ; ; ; ; ; ; ; Publication Date: NSF-PAR ID: 10273153 Journal Name: Applied Optics Volume: 60 Issue: 20 Page Range or eLocation-ID: Article No. 5880 ISSN: 1559-128X; APOPAI Publisher: Optical Society of America 1. An optical parametric oscillator (OPO) is developed and characterized for the simultaneous generation of ultraviolet (UV) and near-UV nanosecond laser pulses for the single-shot Rayleigh scattering and planar laser-induced-fluorescence (PLIF) imaging of methylidyne (CH) and nitric oxide (NO) in turbulent flames. The OPO is pumped by a multichannel, 8-pulse Nd:YAG laser cluster that produces up to 225 mJ/pulse at 355 nm with pulse spacing of 100 µs. The pulsed OPO has a conversion efficiency of 9.6% to the signal wavelength of$∼<#comment/>430nm$when pumped by the multimode laser. Second harmonic conversion of the signal, with 3.8% efficiency, is used for the electronic excitation of the A-X (1,0) band of NO at$∼<#comment/>215nm$, while the residual signal at 430 nm is used for direct excitation of the A-X (0,0) band of the CH radical and elastic Rayleigh scattering. The section of the OPO signal wavelength for simultaneous CH and NO PLIF imaging is performed with consideration of the pulse energy, interference from the reactant and product species, and the fluorescence signal intensity. The excitation wavelengths of 430.7 nm and 215.35 nm are studied in a laminar, premixed–air flame. Single-shot CH and NO PLIF and Rayleigh scatter imaging is demonstrated in a turbulent$CH4−<#comment/>H2−<#comment/>NH3$diffusion flame using a high-speed intensified CMOS camera. Analysis of the complementary Rayleigh scattering and CH and NO PLIF enables identification and quantification of the high-temperature flame layers, the combustion product zones, and the fuel-jet core. Considerations for extension to simultaneous, 10-kHz-rate acquisition are discussed. 3. Electro-optic (EO) modulators rely on the interaction of optical and electrical signals with second-order nonlinear media. For the optical signal, this interaction can be strongly enhanced using dielectric slot–waveguide structures that exploit a field discontinuity at the interface between a high-index waveguide core and the low-index EO cladding. In contrast to this, the electrical signal is usually applied through conductive regions in the direct vicinity of the optical waveguide. To avoid excessive optical loss, the conductivity of these regions is maintained at a moderate level, thus leading to inherentRClimitations of the modulation bandwidth. In this paper, we show that these limitations can be overcome by extending the slot–waveguide concept to the modulating radio-frequency (RF) signal. Our device combines an RF slotline that relies on$BaTiO3$as a high-k dielectric material with a conventional silicon photonic slot waveguide and a highly efficient organic EO cladding material. In a proof-of-concept experiment, we demonstrate a 1 mm long Mach–Zehnder modulator that offers a 3 dB bandwidth of 76 GHz and a 6 dB bandwidth of 110 GHz along with a small$π<#comment/>$voltage of 1.3 V ($Uπ<#comment/>L=1.3Vmm$). Wemore » 4. We experimentally demonstrate tunable optical single-sideband (SSB) generation using a tapped-delay-line (TDL) optical filter for 10 and 20 Gbit/s on/off-keying (OOK) signals and a 20 Gbit/s four-level pulse-amplitude-modulated (PAM4) signal. The optical SSB filter is realized by using an optical frequency comb, wavelength-dependent delay, and nonlinear wave-mixing to achieve the TDL function. Moreover, SSB tunability is achieved by adjusting the amplitude, phase, frequency spacing, and number of selected optical frequency comb lines. We show that the one-sideband suppression of a double-sideband (DSB) channel can be enhanced as the number of taps is increased; however, we do measure a$∼<#comment/>1.5%<#comment/>$error-vector-magnitude penalty. Furthermore, we demonstrate that the chromatic-dispersion-induced penalty after 80 km standard-single-mode-fiber transmission of a 10 Gbit/s SSB OOK signal without chromatic dispersion compensation has been reduced by$><#comment/>3dB$when compared to DSB. 5. Electro-optic quantum coherent interfaces map the amplitude and phase of a quantum signal directly to the phase or intensity of a probe beam. At terahertz frequencies, a fundamental challenge is not only to sense such weak signals (due to a weak coupling with a probe in the near-infrared) but also to resolve them in the time domain. Cavity confinement of both light fields can increase the interaction and achieve strong coupling. Using this approach, current realizations are limited to low microwave frequencies. Alternatively, in bulk crystals, electro-optic sampling was shown to reach quantum-level sensitivity of terahertz waves. Yet, the coupling strength was extremely weak. Here, we propose an on-chip architecture that concomitantly provides subcycle temporal resolution and an extreme sensitivity to sense terahertz intracavity fields below 20 V/m. We use guided femtosecond pulses in the near-infrared and a confinement of the terahertz wave to a volume of$VTHz∼<#comment/>10−<#comment/>9(λ<#comment/>THz/2)3$in combination with ultraperformant organic molecules ($r33=170pm/V$) and accomplish a record-high single-photon electro-optic coupling rate of, 10,000 times higher than in recent reports of sensing vacuum field fluctuations in bulk media. Via homodyne detection implemented directly on chip, the interaction results into an intensity modulation of the femtosecond pulses. The single-photon cooperativity is$C0=1.6×<#comment/>10−<#comment/>8$, and the multiphoton cooperativity is$C=0.002$at room temperature. We show$><#comment/>70dB$dynamic range in intensity at 500 ms integration under irradiation with a weak coherent terahertz field. Similar devices could be employed in future measurements of quantum states in the terahertz at the standard quantum limit, or for entanglement of subsystems on subcycle temporal scales, such as terahertz and near-infrared quantum bits.	2022-11-30T07:37:43	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 16, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5446091890335083, "perplexity": 3632.021911547743}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446710733.87/warc/CC-MAIN-20221130060525-20221130090525-00141.warc.gz"}
https://www.legisquebec.gouv.qc.ca/en/version/cr/Q-2,%20r.%2017.1?code=se:88&historique=20210920	Q-2, r. 17.1 - Regulation respecting the regulatory scheme applying to activities on the basis of their environmental impact 88. The construction and operation of a sawmill are eligible for a declaration of compliance on the following conditions: (1) the sawmill’s annual production capacity is equal to or less than 25,000 m3; (2) the sawmill’s activities are carried on (a) 100 m or more from a category 1 or 2 water withdrawal site and 30 m or more from a category 3 groundwater withdrawal site; (b) 30 m or more from a watercourse, lake or wetland; (3) the storage areas for biomass used for energy production and bulk timber, and the crosscutting area, are watertight; (4) the boundaries of the bulk storage areas are identified using visual markers or posts; (5) the sawmill’s operating area is located 15 m or more from the boundary of the land where the activity is carried on; (6) the operating area is equipped with a storm water management system to evacuate storm water from the site; (7) the discharge point for wastewater is not located in the littoral zone or on the shore of a lake; (8) the wastewater cannot come into contact with a wetland. O.C. 871-2020, s. 88. In force: 2020-12-31 88. The construction and operation of a sawmill are eligible for a declaration of compliance on the following conditions: (1) the sawmill’s annual production capacity is equal to or less than 25,000 m3; (2) the sawmill’s activities are carried on (a) 100 m or more from a category 1 or 2 water withdrawal site and 30 m or more from a category 3 groundwater withdrawal site; (b) 30 m or more from a watercourse, lake or wetland; (3) the storage areas for biomass used for energy production and bulk timber, and the crosscutting area, are watertight; (4) the boundaries of the bulk storage areas are identified using visual markers or posts; (5) the sawmill’s operating area is located 15 m or more from the boundary of the land where the activity is carried on; (6) the operating area is equipped with a storm water management system to evacuate storm water from the site; (7) the discharge point for wastewater is not located in the littoral zone or on the shore of a lake; (8) the wastewater cannot come into contact with a wetland. O.C. 871-2020, s. 88.	2022-05-24T02:47:41	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8066551089286804, "perplexity": 4225.830492301836}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662562410.53/warc/CC-MAIN-20220524014636-20220524044636-00627.warc.gz"}
https://lammps.sandia.gov/doc/pair_spin_exchange.html	pair_style spin/exchange command Syntax pair_style spin/exchange cutoff • cutoff = global cutoff pair (distance in metal units) Examples pair_style spin/exchange 4.0 pair_coeff * * exchange 4.0 0.0446928 0.003496 1.4885 pair_coeff 1 2 exchange 6.0 -0.01575 0.0 1.965 Description Style spin/exchange computes the exchange interaction between pairs of magnetic spins: where si and sj are two neighboring magnetic spins of two particles, rij = ri - rj is the inter-atomic distance between the two particles, and J(rij) is a function defining the intensity and the sign of the exchange interaction for different neighboring shells. This function is defined as: where a, b and d are the three constant coefficients defined in the associated “pair_coeff” command (see below for more explanations). The coefficients a, b, and d need to be fitted so that the function above matches with the value of the exchange interaction for the N neighbor shells taken into account. Examples and more explanations about this function and its parameterization are reported in (Tranchida). From this exchange interaction, each spin i will be submitted to a magnetic torque omega, and its associated atom can be submitted to a force F for spin-lattice calculations (see fix_nve_spin), such as: with h the Planck constant (in metal units), and eij = (ri - rj)/\|ri-rj\| the unit vector between sites i and j. More details about the derivation of these torques/forces are reported in (Tranchida). For the spin/exchange pair style, the following coefficients must be defined for each pair of atoms types via the pair_coeff command as in the examples above, or in the data file or restart files read by the read_data or read_restart commands, and set in the following order: • rc (distance units) • a (energy units)	2019-03-23T22:59:59	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8302903771400452, "perplexity": 2250.9730989814993}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-13/segments/1552912203093.63/warc/CC-MAIN-20190323221914-20190324003914-00426.warc.gz"}
https://openastronomy.org/rcsc18/chapters/03-fundamentals-of-python/05-making-choices	# Making Choices In our last lesson, we discovered something suspicious was going on in our inflammation data by drawing some plots. How can we use Python to automatically recognize the different features we saw, and take a different action for each? In this lesson, we’ll learn how to write code that runs only when certain conditions are true. ## Conditionals We can ask Python to take different actions, depending on a condition, with an if statement: num = 37 if num > 100: print('greater') else: print('not greater') print('done') not greater done The second line of this code uses the keyword if to tell Python that we want to make a choice. If the test that follows the if statement is true, the body of the if (i.e., the lines indented underneath it) are executed. If the test is false, the body of the else is executed instead. Only one or the other is ever executed: Conditional statements don’t have to include an else. If there isn’t one, Python simply does nothing if the test is false: num = 53 print('before conditional...') if num > 100: print(num,' is greater than 100') print('...after conditional') before conditional... ...after conditional We can also chain several tests together using elif, which is short for “else if”. The following Python code uses elif to print the sign of a number. num = -3 if num > 0: print(num, 'is positive') elif num == 0: print(num, 'is zero') else: print(num, 'is negative') -3 is negative Note that to test for equality we use a double equals sign == rather than a single equals sign = which is used to assign values. We can also combine tests using and and or. and is only true if both parts are true: if (1 > 0) and (-1 > 0): print('both parts are true') else: print('at least one part is false') at least one part is false while or is true if at least one part is true: if (1 < 0) or (-1 < 0): print('at least one test is true') at least one test is true ## True and False True and False are special words in Python called booleans, which represent truth values. A statement such as 1 < 0 returns the value False, while -1 < 0 returns the value True. callout ## Checking our Data Now that we’ve seen how conditionals work, we can use them to check for the suspicious features we saw in our inflammation data. We are about to use functions provided by the numpy module again. Therefore, if you’re working in a new Python session, make sure to load the module with: import numpy as np data = np.loadtxt(fname='inflammation-01.csv', delimiter=',') From the first couple of plots, we saw that maximum daily inflammation exhibits a strange behavior and raises one unit a day. Wouldn’t it be a good idea to detect such behavior and report it as suspicious? Let’s do that! However, instead of checking every single day of the study, let’s merely check if maximum inflammation in the beginning (day 0) and in the middle (day 20) of the study are equal to the corresponding day numbers. max_inflammation_0 = np.max(data, axis=0)[0] max_inflammation_20 = np.max(data, axis=0)[20] if max_inflammation_0 == 0 and max_inflammation_20 == 20: print('Suspicious looking maxima!') Suspicious looking maxima! We also saw a different problem in the third dataset; the minima per day were all zero (looks like a healthy person snuck into our study). We can also check for this with an elif condition: if max_inflammation_0 == 0 and max_inflammation_20 == 20: print('Suspicious looking maxima!') elif np.sum(np.min(data, axis=0)) == 0: Suspicious looking maxima! And if neither of these conditions are true, we can use else to give the all-clear: if max_inflammation_0 == 0 and max_inflammation_20 == 20: print('Suspicious looking maxima!') elif np.sum(np.min(data, axis=0)) == 0: else: print('Seems OK!') Suspicious looking maxima! In this way, we have asked Python to do something different depending on the condition of our data. Here we printed messages in all cases, but we could also imagine not using the else catch-all so that messages are only printed when something is wrong, freeing us from having to manually examine every plot for features we’ve seen before. ## How Many Paths? Consider this code: if 4 > 5: print('A') elif 4 == 5: print('B') elif 4 < 5: print('C') C ## Challenge: Which of the following would be printed if you were to run this code? Why did you pick this answer? 1. A 2. B 3. C 4. B and C ## Solution C gets printed because the first two conditions, 4 > 5 and 4 == 5, are not true, but 4 < 5 is true. ## Challenge: What Is Truth? True and False booleans are not the only values in Python that are true and false. In fact, any value can be used in an if or elif. After reading and running the code below, explain what the rule is for which values are considered true and which are considered false. if '': print('empty string is true') if 'word': print('word is true') if []: print('empty list is true') if [1, 2, 3]: print('non-empty list is true') if 0: print('zero is true') if 1: print('one is true') word is true non-empty list is true one is true ## Challenge: That's Not Not What I Meant Sometimes it is useful to check whether some condition is not true. The Boolean operator not can do this explicitly. After reading and running the code below, write some if statements that use not to test the rule that you formulated in the previous challenge. if not '': print('empty string is not true') if not 'word': print('word is not true') if not not True: print('not not True is true') empty string is not true not not True is true ## Challenge: Close Enough Write some conditions that print True if the variable a is within 10% of the variable b and False otherwise. Compare your implementation with your partner's: do you get the same answer for all possible pairs of numbers? ## Solution 1 a = 5 b = 5.1 if abs(a - b) < 0.1 * abs(b): print('True') else: print('False') True ## Solution 2 print(abs(a - b) < 0.1 * abs(b)) True This works because the Booleans True and False have string representations which can be printed. ## In-Place Operators Python (and most other languages in the C family) provides in-place operators that work like this: x = 1 # original value x += 1 # add one to x, assigning result back to x x *= 3 # multiply x by 3 print(x) 6 ## Challenge: Write some code that sums the positive and negative numbers in a list separately, using in-place operators. Do you think the result is more or less readable than writing the same without in-place operators? ## Solution positive_sum = 0 negative_sum = 0 test_list = [3, 4, 6, 1, -1, -5, 0, 7, -8] for num in test_list: if num > 0: positive_sum += num elif num == 0: pass else: negative_sum += num print(positive_sum, negative_sum) 21 -14 Here pass means “don’t do anything”. In this particular case, it’s not actually needed, since if num == 0 neither sum needs to change, but it illustrates the use of elif and pass. ## Sorting a List Into Buckets In our data folder, large data sets are stored in files whose names start with “inflammation-“ and small data sets – in files whose names start with “small-“. We also have some other files that we do not care about at this point. We’d like to break all these files into three lists called large_files, small_files, and other_files, respectively. ## Challenge: Add code to the template below to do this. Note that the string method startswith returns True if and only if the string it is called on starts with the string passed as an argument, that is: "String".startswith("Str") True But "String".startswith("str") False Use the following Python code as your starting point: files = ['inflammation-01.csv', 'myscript.py', 'inflammation-02.csv', 'small-01.csv', 'small-02.csv'] large_files = [] small_files = [] other_files = [] 1. loop over the names of the files 2. figure out which group each filename belongs 3. append the filename to that list In the end the three lists should be: large_files = ['inflammation-01.csv', 'inflammation-02.csv'] small_files = ['small-01.csv', 'small-02.csv'] other_files = ['myscript.py'] ## Solution for file in files: if file.startswith('inflammation-'): large_files.append(file) elif file.startswith('small-'): small_files.append(file) else: other_files.append(file) print('large_files:', large_files) print('small_files:', small_files) print('other_files:', other_files) large_files: ['inflammation-01.csv', 'inflammation-02.csv'] small_files: ['small-01.csv', 'small-02.csv'] other_files: ['myscript.py'] ## Challenge: Counting Vowels 1. Write a loop that counts the number of vowels in a character string. 2. Test it on a few individual words and full sentences. 3. Once you are done, compare your solution to your neighbor's. Did you make the same decisions about how to handle the letter 'y' (which some people think is a vowel, and some do not)? ## Solution vowels = 'aeiouAEIOU' sentence = 'Mary had a little lamb.' count = 0 for char in sentence: if char in vowels: count += 1 print("The number of vowels in this string is " + str(count)) The number of vowels in this string is 6 The material in this notebook is derived from the Software Carpentry lessons © Software Carpentry under the terms of the CC-BY 4.0 license.	2022-01-21T08:15:07	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.19033844769001007, "perplexity": 2622.1815398329677}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320302740.94/warc/CC-MAIN-20220121071203-20220121101203-00077.warc.gz"}
https://www.usgs.gov/center-news/state-hawaii-geologic-map-available-online	# State of Hawaii geologic map available online Release Date: A new geologic map of the State of Hawaii became publicly available this week. The publication is free online as U.S. Geological Survey Open-File Report 2007-1089. The compilation was done primarily by Dave Sherrod, former staff member of HVO. Chief sources of mapping used in compilation of digital geologic map of State of Hawai'i. See References Cited in the pamphlet for full bibliographic citation (from figure 1). (Public domain.) The State's geology is presented on eight full-color map sheets, one for each of the major islands. These map sheets, the illustrative meat of the publication, can be downloaded in pdf format, ready to print. The map's scale is 1:100,000 (1 inch on the map equals about 1.6 miles on the ground), so that each map is about 27 inches by 36 inches. The island of Hawaii, largest of the islands, is depicted at a smaller scale, 1:250,000 (1 in. = 4 mi), so that it, too, can be shown on 36-inch-wide paper. The new publication isn't limited strictly to its map depictions. Twenty years have passed since David Clague and Brent Dalrymple published a comprehensive USGS report on the Hawaiian-Emperor volcanic chain that summarized the geology of all the islands, and it has been even longer since Gordon Macdonald's 1970 book, Volcanoes in the Sea (revised in 1983). The new statewide geologic map thus includes a lengthy pamphlet that revisits many of the concepts that have evolved in our geologic understanding of the eight main islands. The pamphlet includes simplified page-sized geologic maps for each island, summaries of all the ages from samples gathered since about 1960, generalized depictions of geochemical analyses for each volcano's eruptive stages, and discussion of some outstanding topics that remain controversial or warrant additional research. The pamphlet also contains a complete description of map units, which enumerates the characteristics for each of the State's many rock layers shown on the map sheets. Since the late 1980s, the audience for geologic maps has grown as desktop computers and map-based software have become increasingly powerful. Those who prefer the convenience and access offered by Geographic Information Systems (GIS) can also feast on this publication. An electronic database, suitable for most GIS software applications, is available for downloading. The GIS database is in an Earth projection widely employed throughout the State of Hawaii, using the North American datum of 1983 and the Universal Transverse Mercator system projection to zone 4. "This digital statewide map allows engineers, consultants, and scientists from many different fields to take advantage of the geologic database," said John Sinton, a geology professor at the University of Hawaii, whose new mapping of the Waianae Range (West Oahu) appears on the map. Indeed, when a test version was first made available, most requests came from biologists, archaeologists, and soil scientists interested in applying the map's GIS database to their ongoing investigations. Another area newly depicted on the map, in addition to the Waianae Range, is Haleakalā Volcano, East Maui. Also updated are the boundaries of lava flows on Kīlauea Volcano, Hawaii Island, where the landscape has continued to evolve in the 10 years since publication of the previous geologic map of the Big Island by Wolfe and Morris in 1996. For the other islands, much of the map is compiled from mapping published in the 1930s-1960s. This reliance stems partly from shortage of funding to undertake entirely new mapping but is warranted by the exemplary mapping of those early experts. The boundaries of all map units are digitized to show correctly on modern topographic maps. Those unprepared to print the maps themselves will be able to buy the map as a printed product in the future. For now, however, the preliminary version bridges the two-year gap required to edit and print a formal USGS Scientific Investigations map. In this way, scientists, engineers, land-use planners, and anyone interested in the geologic history of Hawaii can begin using the data and interpretations it contains. To obtain a copy online, reach for the link on the USGS publications Web site, http://pubs.usgs.gov/ofr/2007/1089. Be advised: a rapid data-transfer connection is helpful, because the explanatory pamphlet (pdf format) is 8 megabytes, and the map sheets (also in pdf) range from 5 to 40 megabytes. ———————————————————————————————————————————————————————————————— ### Volcano Activity Update This past week, activity levels at the summit of Kīlauea Volcano have been elevated above background levels. The summit caldera has been expanding, indicating inflation, since the beginning of 2007. The number of earthquakes located in the summit area increased from typical levels of less than 10 per day to nearly 20 per day on May 12. The earthquakes were concentrated in the upper southwest and east rift zones. A magnitude-4.7 earthquake, along with a number of aftershocks, occurred on the morning of May 24. Eruptive activity at Puu Oo continues. On clear nights, glow is visible from vents within the eastern half of the crater. Lava continues to flow through the upper portion of the PKK lava tube to where the Campout tube branches off about 1 km south of Puu Oo. A new breakout from this section of the PKK tube has been sending lava down-slope onto the upper flow field for the last few weeks. This breakout is upslope from the Campout tube branch and may be the start of a new tube system. Though the new breakout is robbing part of the lava supply, the Campout tube continues to carry lava downslope, where it is feeding breakouts on the coastal plain near the base of the Royal Gardens subdivision, and possibly inland from East Laeapuki. The lava ponding near the base of Royal Gardens, ongoing for the last several months, finally advanced across the coastal plain and reached the ocean at Poupou on May 16. This new ocean entry continues to be active, though the entry has not yet become well established. It is located within Hawaii Volcanoes National Park. To the west, the Kamokuna entry, fed by the main branch of the Campout tube, appears to no longer be active. Access to the sea cliff at the ocean entries is closed, due to significant hazards. The surrounding area, however, is open. If you visit the eruption site, check with the rangers for current updates, and remember to carry lots of water when venturing out onto the flow field. Seven earthquakes beneath Hawai`i Island were reported felt within the past week. A magnitude-2.0 earthquake occurred at 1:02 a.m. H.s.t. on Thursday, May 17, and was located 5 km (3 miles) west of Kīlauea summit at a depth of 6 km (4 miles). A magnitude-2.0 earthquake occurred at 5:17 p.m. later that day and was located 1 km (1 mile) northeast of Captain Cook at a depth of 12 km (8 miles). A magnitude-3.3 earthquake occurred at 5:59 a.m. on Friday, May 18, and was located 3 km (2 miles) northwest of Pahala at a depth of 6 km (4 miles). A magnitude-2.2 earthquake occurred at 11:36 a.m. on Monday, May 21, and was located 4 km (2 miles) northwest of Captain Cook at a depth of 12 km (7 miles). A magnitude-4.7 earthquake occurred at 9:13 a.m. on Thursday, May 24, and was located 3 km southeast of Kīlauea summit at a depth of 2 km (1 mile). A magnitude 4.1 aftershock occurred 20 minutes later at 9:33 a.m. and was located 5 km (3 miles) southeast of Kīlauea summit at a depth of 4 km (2 miles). A magnitude-3.9 aftershock occurred at 10:51 a.m. on Thursday and was located 6 km (4 miles) southeast of Kīlauea summit at a depth of 1 km (1 mile). Mauna Loa is not erupting. Two earthquakes were located beneath the summit. Extension of distances between locations spanning the summit, indicating inflation, continues at steady, slow rates.	2020-01-19T20:19:56	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.42562371492385864, "perplexity": 2767.671882600671}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-05/segments/1579250594705.17/warc/CC-MAIN-20200119180644-20200119204644-00076.warc.gz"}
https://pdglive.lbl.gov/Particle.action?init=0&node=B127&home=BXXX010	${{\boldsymbol \Delta}}$ BARYONS($\boldsymbol S$ = 0, $\boldsymbol I$ = 3/2) ${{\mathit \Delta}^{++}}$ = ${{\mathit u}}{{\mathit u}}{{\mathit u}}$ , ${{\mathit \Delta}^{+}}$ = ${\mathit {\mathit u}}$ ${\mathit {\mathit u}}$ ${\mathit {\mathit d}}$, ${{\mathit \Delta}^{0}}$ = ${\mathit {\mathit u}}$ ${\mathit {\mathit d}}$ ${\mathit {\mathit d}}$, ${{\mathit \Delta}^{-}}$ = ${\mathit {\mathit d}}$ ${\mathit {\mathit d}}$ ${\mathit {\mathit d}}$ INSPIRE search # ${{\boldsymbol \Delta}{(\sim3000 \text{ Region})}}$ Partial-Wave Analyses We list here miscellaneous high-mass candidates for isospin-${}^{}3/2{}^{}$ resonances found in partial-wave analyses. Our 1982 edition also had a ${{\mathit \Delta}{(2850)}}$ and a ${{\mathit \Delta}{(3230)}}$. The evidence for them was deduced from total cross-section and 180$^\circ{}$ elastic cross-section measurements. The ${{\mathit \Delta}{(2850)}}$ has been resolved into the ${{\mathit \Delta}{(2750)}}{\mathit I}_{\mathrm 3,13}$ and ${{\mathit \Delta}{(2950)}}{\mathit K}_{\mathrm 3,15}$. The ${{\mathit \Delta}{(3230)}}$ is perhaps related to the ${\mathit K}_{\mathrm 3,13}$ of HENDRY 1978 and to the ${\mathit L}_{\mathrm 3,17}$ of KOCH 1980 . ${{\mathit \Delta}{(\sim3000)}}$ BREIT-WIGNER MASS ${{\mathit \Delta}{(\sim3000)}}$ BREIT-WIGNER WIDTH	2020-11-29T07:51:20	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8909150958061218, "perplexity": 983.1507877909203}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-50/segments/1606141197278.54/warc/CC-MAIN-20201129063812-20201129093812-00508.warc.gz"}
http://pdglive.lbl.gov/DataBlock.action?node=S044DZ	# AVERAGE PARTICLE MULTIPLICITIES IN HADRONIC ${{\boldsymbol Z}}$ DECAY Summed over particle and antiparticle, when appropriate. # $\langle{}\boldsymbol N_{{{\boldsymbol D}^{0}}}\rangle{}$ INSPIRE search VALUE DOCUMENT ID TECN COMMENT $\bf{ 0.462 \pm0.026}$ OUR AVERAGE $0.465$ $\pm0.017$ $\pm0.027$ 1996 R OPAL ${\it{}E}^{\it{}ee}_{\rm{}cm}$= $91.2$ GeV $0.518$ $\pm0.052$ $\pm0.035$ 1994 J ALEP ${\it{}E}^{\it{}ee}_{\rm{}cm}$= $91.2$ GeV $0.403$ $\pm0.038$ $\pm0.044$ 1 1993 I DLPH ${\it{}E}^{\it{}ee}_{\rm{}cm}$= $91.2$ GeV 1 See ABREU 1995 (erratum). References: ALEXANDER 1996R ZPHY C72 1 A Study of Charm Hadron Production in ${{\mathit Z}}$ $\rightarrow$ ${\mathit {\mathit c}}$ ${\mathit {\overline{\mathit c}}}$ and ${{\mathit Z}}$ $\rightarrow$ ${\mathit {\mathit b}}$ ${\mathit {\overline{\mathit b}}}$ Decays at LEP BUSKULIC 1994J ZPHY C62 1 Production of Charmed Mesons in ${{\mathit Z}^{0}}$ Decays ABREU 1993I ZPHY C59 533 A Measurement of ${{\mathit D}}$ Meson Production in ${{\mathit Z}^{0}}$ Hadronic Decays	2019-01-18T03:15:12	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9713935852050781, "perplexity": 14523.879357517902}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-04/segments/1547583659677.17/warc/CC-MAIN-20190118025529-20190118051529-00457.warc.gz"}
https://par.nsf.gov/biblio/10272409	Integrated assessment modeling reveals near-channel management as cost-effective to improve water quality in agricultural watersheds Despite decades of policy that strives to reduce nutrient and sediment export from agricultural fields, surface water quality in intensively managed agricultural landscapes remains highly degraded. Recent analyses show that current conservation efforts are not sufficient to reverse widespread water degradation in Midwestern agricultural systems. Intensifying row crop agriculture and increasing climate pressure require a more integrated approach to water quality management that addresses diverse sources of nutrients and sediment and off-field mitigation actions. We used multiobjective optimization analysis and integrated three biophysical models to evaluate the cost-effectiveness of alternative portfolios of watershed management practices at achieving nitrate and suspended sediment reduction goals in an agricultural basin of the Upper Midwestern United States. Integrating watershed-scale models enabled the inclusion of near-channel management alongside more typical field management and thus directly the comparison of cost-effectiveness across portfolios. The optimization analysis revealed that fluvial wetlands (i.e., wide, slow-flowing, vegetated water bodies within the riverine corridor) are the single-most cost-effective management action to reduce both nitrate and sediment loads and will be essential for meeting moderate to aggressive water quality targets. Although highly cost-effective, wetland construction was costly compared to other practices, and it was not selected in portfolios at low investment levels. more » Authors: ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; Publication Date: NSF-PAR ID: 10272409 Journal Name: Proceedings of the National Academy of Sciences Volume: 118 Issue: 28 Page Range or eLocation-ID: Article No. e2024912118 ISSN: 0027-8424 Publisher: Proceedings of the National Academy of Sciences Excessive phosphorus (P) export to aquatic ecosystems can lead to impaired water quality. There is a growing interest among watershed managers in using restored wetlands to retain P from agricultural landscapes and improve water quality. We develop a novel framework for prioritizing wetland restoration at a regional scale. The framework uses an ecosystem service model and an optimization algorithm that maximizes P reduction for given levels of restoration cost. Applying our framework in the Lake Champlain Basin, we find that wetland restoration can reduce P export by 2.6% for a budget of $50 M and 5.1% for a budget of$200 M. Sensitivity analysis shows that using finer spatial resolution data for P sources results in twice the P reduction benefits at a similar cost by capturing hot-spots on the landscape. We identify 890 wetlands that occur in more than 75% of all optimal scenarios and represent priorities for restoration. Most of these wetlands are smaller than 7 ha with contributing area less than 100 ha and are located within 200 m of streams. Our approach provides a simple yet robust tool for targeting restoration efforts at regional scales and is readily adaptable to other restoration strategies.	2023-02-06T16:51:46	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.1968180388212204, "perplexity": 6800.76413830865}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500356.92/warc/CC-MAIN-20230206145603-20230206175603-00364.warc.gz"}
https://survivor.togaware.com/datascience/remove-punctuation.html	## 21.12 Remove Punctuation docs <- tm_map(docs, removePunctuation) viewDocs(docs, 16) ## hybrid weighted random forests for ## classifying very highdimensional data ## baoxun xu joshua zhexue huang graham williams and ## yunming ye ## ## ## department of computer science harbin institute of technology shenzhen graduate ## school shenzhen china ## ## shenzhen institutes of advanced technology chinese academy of sciences shenzhen ## china ## email amusing gmailcom ## random forests are a popular classification method based on an ensemble of a ## single type of decision trees from subspaces of data in the literature there ## are many different types of decision tree algorithms including c cart and ## chaid each type of decision tree algorithm may capture different information ## and structure this paper proposes a hybrid weighted random forest algorithm ## simultaneously using a feature weighting method and a hybrid forest method to ## classify very high dimensional data the hybrid weighted random forest algorithm ## can effectively reduce subspace size and improve classification performance ## without increasing the error bound we conduct a series of experiments on eight ## high dimensional datasets to compare our method with traditional random forest ## methods and other classification methods the results show that our method ## consistently outperforms these traditional methods ## keywords random forests hybrid weighted random forest classification decision tree ## ## ## ## introduction ## ## random forests are a popular classification ## method which builds an ensemble of a single type ## of decision trees from different random subspaces of ## data the decision trees are often either built using ## c or cart but only one type within ## a single random forest in recent years random ## forests have attracted increasing attention due to ## its competitive performance compared with other ## classification methods especially for highdimensional ## data algorithmic intuitiveness and simplicity and ## its most important capability ensemble using ## bagging and stochastic discrimination ## several methods have been proposed to grow random ## forests from subspaces of data in ## these methods the most popular forest construction ## procedure was proposed by breiman to first use ## bagging to generate training data subsets for building ## individual trees ## a subspace of features is then ## randomly selected at each node to grow branches of ## a decision tree the trees are then combined as an ## ensemble into a forest as an ensemble learner the ## performance of a random forest is highly dependent ## on two factors the performance of each tree and the ## diversity of the trees in the forests breiman ## formulated the overall performance of a set of trees as ## the average strength and proved that the generalization ## ## error of a random forest is bounded by the ratio of the ## average correlation between trees divided by the square ## of the average strength of the trees ## for very high dimensional data such as text data ## there are usually a large portion of features that are ## uninformative to the classes during this forest building ## process informative features would have the large ## chance to be missed if we randomly select a small ## subspace breiman suggested selecting log m ## features in a subspace where m is the number of ## independent features in the data from high dimensional ## data as a result weak trees are created from these ## subspaces the average strength of those trees is reduced ## and the error bound of the random forest is enlarged ## therefore when a large proportion of such weak ## trees are generated in a random forest the forest has a ## large likelihood to make a wrong decision which mainly ## results from those weak trees classification power ## to address this problem we aim to optimize decision ## trees of a random forest by two strategies one ## straightforward strategy is to enhance the classification ## performance of individual trees by a feature weighting ## method for subspace sampling in this ## method feature weights are computed with respect ## to the correlations of features to the class feature ## and regarded as the probabilities of the feature to ## be selected in subspaces this method obviously ## increases the classification performance of individual ## ## the computer journal vol ## ## no ## ## ## ## ## ## baoxun xu joshua zhexue huang graham williams yunming ye ## ## trees because the subspaces will be biased to contain ## more informative features however the chance of more ## correlated trees is also increased since the features with ## large weights are likely to be repeatedly selected ## the second strategy is more straightforward use ## several different types of decision trees for each training ## data subset to increase the diversity of the trees ## and then select the optimal tree as the individual ## tree classifier in the random forest model the work ## presented here extends the algorithm developed in ## specifically we build three different types of tree ## classifiers c cart and chaid for each ## training data subset we then evaluate the performance ## of the three classifiers and select the best tree in ## this way we build a hybrid random forest which may ## include different types of decision trees in the ensemble ## the added diversity of the decision trees can effectively ## improve the accuracy of each tree in the forest and ## hence the classification performance of the ensemble ## however when we use this method to build the best ## random forest model for classifying high dimensional ## data we can not be sure of what subspace size is best ## in this paper we propose a hybrid weighted random ## forest algorithm by simultaneously using a new feature ## weighting method together with the hybrid random ## forest method to classify high dimensional data in ## this new random forest algorithm we calculate feature ## weights and use weighted sampling to randomly select ## features for subspaces at each node in building different ## types of trees classifiers c cart and chaid for ## each training data subset and select the best tree as ## the individual tree in the final ensemble model ## experiments were performed on high dimensional ## text datasets with dimensions ranging from to ## we compared the performance of eight random ## forest methods and wellknown classification methods ## c random forest cart random forest chaid ## random forest hybrid random forest c weighted ## random forest cart weighted random forest chaid ## weighted random forest hybrid weighted random ## forest support vector machines naive bayes ## and knearest neighbors ## the experimental ## results show that our hybrid weighted random forest ## achieves improved classification performance over the ## ten competitive methods ## the remainder of this paper is organized as follows ## in section we introduce a framework for building ## a hybrid weighted random forest and describe a new ## random forest algorithm section summarizes four ## measures to evaluate random forest models we present ## experimental results on high dimensional text datasets ## in section section contains our conclusions ## ## table contingency table of input feature a and class ## feature y ## y y ## y yj ## y yq total ## a a ## ## ## j ## ## q ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## a ai ## i ## ## ij ## ## iq ## i ## ## ## ## ## ## ## ## ## ## ## ## ## ## a ap ## p ## ## pj ## ## pq ## p ## total ## ## ## j ## ## q ## ## ## general framework for building hybrid random forests ## by integrating these two methods we propose a novel ## hybrid weighted random forest algorithm ## ## ## let y be the class or target feature with q distinct ## class labels yj for j q for the purposes of ## our discussion we consider a single categorical feature ## a in dataset d with p distinct category values we ## denote the distinct values by ai for i p ## numeric features can be discretized into p intervals with ## a supervised discretization method ## assume d has val objects the size of the subset of ## d satisfying the condition that a ai and y yj is ## denoted by ij considering all combinations of the ## categorical values of a and the labels of y we can ## obtain a contingency table of a against y as shown ## in table the far right column contains the marginal ## totals for feature a ## ## hybrid ## forests ## ## weighted ## ## random ## ## in this section we first introduce a feature weighting ## method for subspace sampling then we present a ## ## q ## ## ## i ## ## ij ## ## for i p ## ## ## ## j ## ## and the bottom row is the marginal totals for class ## feature y ## j ## ## p ## ## ## ij ## ## for j q ## ## ## ## i ## ## the grand total the total number of samples is in ## the bottom right corner ## ## ## q ## p ## ## ## ij ## ## ## ## j i ## ## given a training dataset d and feature a we first ## compute the contingency table the feature weights are ## then computed using the two methods to be discussed ## in the following subsection ## ## ## ## ## notation ## ## feature weighting method ## ## in this subsection we give the details of the feature ## weighting method for subspace sampling in random ## forests consider an mdimensional feature space ## a a am we present how to compute the ## ## the computer journal vol ## ## no ## ## ## ## hybrid weighted random forests for classifying very highdimensional data ## weights w w wm for every feature in the space ## these weights are then used in the improved algorithm ## to grow each decision tree in the random forest ## feature weight computation ## the weight of feature a represents the correlation ## between the values of feature a and the values of the ## class feature y a larger weight will indicate that the ## class labels of objects in the training dataset are more ## correlated with the values of feature a indicating that ## a is more informative to the class of objects thus it ## is suggested that a has a stronger power in predicting ## the classes of new objects ## in the following we propose to use the chisquare ## statistic to compute feature weights because this ## method can quantify the correspondence between two ## categorical variables ## given the contingency table of an input feature a and ## the class feature y of dataset d the chisquare statistic ## of the two features is computed as ## corra y ## ## q ## p ## ## ij tij ## tij ## i j ## ## ## ## where ij is the observed frequency from the ## contingency table and tij is the expected frequency ## computed as ## i x j ## tij ## ## ## ## ## the larger the measure corra y the more ## informative the feature a is in predicting class y ## normalized feature weight ## in practice feature weights are normalized for feature ## subspace sampling we use corra y to measure the ## informativeness of these features and consider them ## as feature weights however to treat the weights as ## probabilities of features we normalize the measures to ## ensure the sum of the normalized feature weights is ## equal to let corrai y i m be the set ## of m feature measures we compute the normalized ## weights as ## ## corrai y ## wi n ## ## i corrai y ## here we use the square root to smooth the values of ## the measures wi can be considered as the probability ## that feature ai is randomly sampled in a subspace the ## more informative a feature is the larger the weight and ## the higher the probability of the feature being selected ## ## diversity is commonly obtained by using bagging and ## random subspace sampling we introduce a further ## element of diversity by using different types of trees ## considering an analogy with forestry the different data subsets from bagging represent the soil structures different decision tree algorithms represent different tree species our approach has two key aspects ## one is to use three types of decision tree algorithms to ## generate three different tree classifiers for each training data subset the other is to evaluate the accuracy ## of each tree as the measure of tree importance in this ## paper we use the outofbag accuracy to assess the importance of a tree ## following breiman we use bagging to generate ## a series of training data subsets from which we build ## trees for each tree the data subset used to grow ## the tree is called the inofbag iob data and the ## remaining data subset is called the outofbag oob ## data since oob data is not used for building trees ## we can use this data to objectively evaluate each trees ## accuracy and importance the oob accuracy gives an ## unbiased estimate of the true accuracy of a model ## given n instances in a training dataset d and a tree ## classifier hk iobk built from the kth training data ## subset iobk we define the oob accuracy of the tree ## hk iobk for di d as ## n ## oobacck ## ## framework for building a hybrid random ## forest ## ## as an ensemble learner the performance of a random ## forest is highly dependent on two factors the diversity ## among the trees and the accuracy of each tree ## ## i ## ## ihk di yi di oobk ## n ## i idi oobk ## ## ## ## where i is an indicator function the larger the ## oobacck the better the classification quality of a tree ## we use the outofbag data subset oobi to calculate ## the outofbag accuracies of the three types of trees ## c cart and chaid with evaluation values e ## e and e respectively ## fig illustrates the procedure for building a hybrid ## random forest model firstly a series of iob oob ## datasets are generated from the entire training dataset ## by bagging then three types of tree classifiers c ## cart and chaid are built using each iob dataset ## the corresponding oob dataset is used to calculate the ## oob accuracies of the three tree classifiers finally ## we select the tree with the highest oob accuracy as ## the final tree classifier which is included in the hybrid ## random forest ## building a hybrid random forest model in this ## way will increase the diversity among the trees ## the classification performance of each individual tree ## classifier is also maximized ## ## ## ## ## ## ## decision tree algorithms ## ## the core of our approach is the diversity of decision ## tree algorithms in our random forest different decision ## tree algorithms grow structurally different trees from ## the same training data selecting a good decision tree ## algorithm to grow trees for a random forest is critical ## ## the computer journal vol ## ## no ## ## ## ## ## ## baoxun xu joshua zhexue huang graham williams yunming ye ## the difference lies in the way to split a node such ## as the split functions and binary branches or multibranches in this work we use these different decision ## tree algorithms to build a hybrid random forest ## ## ## ## figure the hybrid random forests framework ## ## for the performance of the random forest few studies ## have considered how different decision tree algorithms ## affect a random forest we do so in this paper ## the common decision tree algorithms are as follows ## classification trees c is a supervised ## learning classification algorithm used to construct ## decision trees given a set of preclassified objects each ## described by a vector of attribute values we construct ## a mapping from attribute values to classes c uses ## a divideandconquer approach to grow decision trees ## beginning with the entire dataset a tree is constructed ## by considering each predictor variable for dividing the ## dataset the best predictor is chosen at each node ## using a impurity or diversity measure the goal is ## to produce subsets of the data which are homogeneous ## with respect to the target variable c selects the test ## that maximizes the information gain ratio igr ## classification and regression tree cart is ## a recursive partitioning method that can be used for ## both regression and classification the main difference ## between c and cart is the test selection and ## evaluation process ## chisquared automatic interaction detector ## chaid method is based on the chisquare test of ## association a chaid decision tree is constructed ## by repeatedly splitting subsets of the space into two ## or more nodes to determine the best split at any ## node any allowable pair of categories of the predictor ## variables is merged until there is no statistically ## significant difference within the pair with respect to the ## target variable ## from these decision tree algorithms we can see that ## ## hybrid weighted random forest algorithm ## ## in this subsection we present a hybrid weighted ## random forest algorithm by simultaneously using the ## feature weights and a hybrid method to classify high ## dimensional data the benefits of our algorithm has ## two aspects firstly compared with hybrid forest ## method we can use a small subspace size to ## create accurate random forest models ## secondly ## compared with building a random forest using feature ## weighting we can use several different types of ## decision trees for each training data subset to increase ## the diversities of trees the added diversity of the ## decision trees can effectively improve the classification ## performance of the ensemble model the detailed steps ## are introduced in algorithm ## input parameters to algorithm include a training ## dataset d the set of features a the class feature y ## the number of trees in the random forest k and the ## size of subspaces m the output is a random forest ## model m lines form the loop for building k ## decision trees in the loop line samples the training ## data d by sampling with replacement to generate an ## inofbag data subset iobi for building a decision tree ## line build three types of tree classifiers c ## cart and chaid in this procedure line calls ## the function createt reej to build a tree classifier ## line calculates the outofbag accuracy of the tree ## classifier after this procedure line selects the tree ## classifier with the maximum outofbag accuracy k ## decision tree trees are thus generated to form a hybrid ## weighted random forest model m ## generically function createt reej first creates a ## new node then it tests the stopping criteria to decide ## whether to return to the upper node or to split this ## node if we choose to split this node then the feature ## weighting method is used to randomly select m features ## as the subspace for node splitting these features ## are used as candidates to generate the best split to ## partition the node for each subset of the partition ## createt reej is called again to create a new node under ## the current node if a leaf node is created it returns to ## the parent node this recursive process continues until ## a full tree is generated ## ## the computer journal vol ## ## no ## ## ## ## hybrid weighted random forests for classifying very highdimensional data ## algorithm new random forest algorithm ## input ## d the training dataset ## a the features space a a am ## y the class features space y y yq ## k the number of trees ## m the size of subspaces ## output a random forest m ## method ## for i to k do ## ## draw a bootstrap sample inofbag data subset ## iobi and outofbag data subset oobi from ## training dataset d ## ## for j to do ## ## hij iobi createt reej ## use outofbag data subset oobi to calculate ## ## the outofbag accuracy oobacci j of the tree ## classifier hij iobi by equation ## ## end for ## ## select hi iobi with the highest outofbag ## accuracy oobacci as optimal tree i ## end for ## combine ## the ## k ## tree ## classifiers ## h iob h iob hk iobk into a random ## forest m ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## function createtree ## create a new node n ## if stopping criteria is met then ## return n as a leaf node ## else ## for j to m do ## compute ## the ## informativeness ## measure ## corraj y by equation ## end for ## compute feature weights w w wm by ## equation ## use the feature weighting method to randomly ## select m features ## use these m features as candidates to generate ## the best split for the node to be partitioned ## call createtree for each split ## end if ## return n ## evaluation measures ## ## in this paper we use five measures ie strength ## correlation error bound c s test accuracy and f ## metric to evaluate our random forest models strength ## measures the collective performance of individual trees ## in a random forest and the correlation measures the ## diversity of the trees the ratio of the correlation ## over the square of the strength c s indicates the ## generalization error bound of the random forest model ## these three measures were introduced in the ## accuracy measures the performance of a random forest ## model on unseen test data the f metric is a ## ## ## ## commonly used measure of classification performance ## ## ## strength and correlation measures ## ## we follow breimans method described in to ## calculate the strength correlation and the ratio c s ## following breimans notation we denote strength as ## s and correlation as let hk iobk be the kth ## tree classifier grown from the kth training data iobk ## sampled from d with replacement ## assume the ## random forest model contains k trees the outofbag ## proportion of votes for di d on class j is ## k ## ihk di j di ## iobk ## qdi j kk ## ## iobk ## k idi ## this is the number of trees in the random forest ## which are trained without di and classify di into class ## j divided by the number of training datasets not ## containing di ## the strength s is computed as ## ## qdi yi maxjyi qdi j ## n i ## n ## ## s ## ## ## ## where n is the number of objects in d and yi indicates ## the true class of di ## the correlation is computed as ## n ## ## ## ## i qdi yi maxjyi qdi j s ## n ## ## ## ## ## k ## ## k ## k pk pk ## k pk p ## where ## ## n ## pk ## ## i ## ## ihk di yi di ## iobk ## n ## iobk ## i idi ## ## ## ## and ## n ## pk ## ## i ## ## ihk di jdi y di ## iobk ## n ## id ## ## ## iob ## ## i ## k ## i ## ## ## ## where ## jdi y argmaxjyi qd j ## ## ## ## is the class that obtains the maximal number of votes ## among all classes but the true class ## ## ## general error bound measure c s ## ## given the strength and correlation the outofbag ## estimate of the c s measure can be computed ## an important theoretical result in breimans method ## is the upper bound of the generalization error of the ## random forest ensemble that is derived as ## p e s s ## ## ## ## where is the mean value of correlations between all ## pairs of individual classifiers and s is the strength of ## the set of individual classifiers that is estimated as the ## ## the computer journal vol ## ## no ## ## ## ## ## ## baoxun xu joshua zhexue huang graham williams yunming ye ## ## average accuracy of individual classifiers on d with ## outofbag evaluation this inequality shows that the ## generalization error of a random forest is affected by ## the strength of individual classifiers and their mutual ## correlations therefore breiman defined the c s ratio ## to measure a random forest as ## c s s ## ## ## ## the smaller the ratio the better the performance of ## the random forest as such c s gives guidance for ## reducing the generalization error of random forests ## ## ## test accuracy ## ## the test accuracy measures the classification performance of a random forest on the test data set let ## dt be a test data and yt be the class labels given ## di dt the number of votes for di on class j is ## n di j ## ## k ## ## ## ihk di j ## ## ## ## table ## summary statistic of highdimensional ## datasets ## name ## features ## instances ## classes minority ## fbis ## ## ## ## ## re ## ## ## ## ## re ## ## ## ## ## tr ## ## ## ## ## wap ## ## ## ## ## tr ## ## ## ## ## las ## ## ## ## ## las ## ## ## ## ## ## it emphasizes the performance of a classifier on rare ## categories define and as follows ## ## i ## ## t pi ## t pi ## i ## t pi f pi ## t pi f ni ## ## ## ## f for each category i and the macroaveraged f ## are computed as ## ## k ## ## the test accuracy is calculated as ## f i ## ## in di yi maxjyi n di j ## n i ## ## i i ## m acrof ## i i ## ## q ## i ## ## q ## ## f i ## ## ## ## n ## ## acc ## ## where n is the number of objects in dt and yi indicates ## the true class of di ## ## ## f metric ## ## to evaluate the performance of classification methods ## in dealing with an unbalanced class distribution we use ## the f metric introduced by yang and liu this ## measure is equal to the harmonic mean of recall ## and precision the overall f score of the entire ## classification problem can be computed by a microaverage and a macroaverage ## microaveraged f is computed globally over all ## classes and emphasizes the performance of a classifier ## on common classes define and as follows ## q ## ## q ## t pi ## i t pi ## q i ## q ## ## i t pi f pi ## i t pi f ni ## where q is the number of classes t pi true positives ## is the number of objects correctly predicted as class i ## f pi false positives is the number of objects that are ## predicted to belong to class i but do not the microaveraged f is computed as ## m icrof ## ## ## ## ## ## ## macroaveraged f is first computed locally over ## each class and then the average over all classes is taken ## ## the larger the microf and macrof values are the ## higher the classification performance of the classifier ## ## ## experiments ## ## in this section we present two experiments that ## demonstrate the effectiveness of the new random ## forest algorithm for classifying high dimensional data ## high dimensional datasets with various sizes and ## characteristics were used in the experiments the ## first experiment is designed to show how our proposed ## method can reduce the generalization error bound ## c s and improve test accuracy when the size of ## the selected subspace is not too large the second ## experiment is used to demonstrate the classification ## performance of our proposed method in comparison to ## other classification methods ie svm nb and knn ## ## ## datasets ## ## in the experiments we used eight realworld high ## dimensional datasets these datasets were selected ## due to their diversities in the number of features the ## number of instances and the number of classes their ## dimensionalities vary from to instances ## vary from to and the minority class rate varies ## from to in each dataset we randomly ## select of instances as the training dataset and ## the remaining data as the test dataset detailed ## information of the eight datasets is listed in table ## the fbis re re tr wap tr las ## and las datasets are classical text classification ## benchmark datasets which were carefully selected and ## ## the computer journal vol ## ## no ## ## ## ## hybrid weighted random forests for classifying very highdimensional data ## preprocessed by han and karypis dataset fbis ## was compiled from the foreign broadcast information ## service trec the datasets re and re were ## selected from the reuters text categorization test ## collection distribution the datasets tr and ## tr were derived from trec trec ## and trec dataset wap is from the webace ## project wap the datasets las and las were ## selected from the los angeles times for trec ## the classes of these datasets were generated from the ## relevance judgment provided in these collections ## ## ## performance comparisons between random forest methods ## ## the purpose of this experiment was to evaluate ## the effect of the hybrid weighted random forest ## method h w rf on strength correlation c s ## and test accuracy ## the eight high dimensional ## datasets were analyzed and results were compared ## with seven other random forest methods ie c ## random forest c rf cart random forest ## cart rf chaid random forest chaid rf ## hybrid random forest h rf c weighted random ## forest c w rf cart weighted random forest ## cart w rf chaid weighted random forest ## chaid w rf for each dataset we ran each ## random forest algorithm against different sizes of the ## feature subspaces since the number of features in these ## datasets was very large we started with a subspace ## of features and increased the subspace by more ## features each time for a given subspace size we built ## trees for each random forest model in order to ## obtain a stable result we built random forest models ## for each subspace size each dataset and each algorithm ## and computed the average values of the four measures ## of strength correlation c s and test accuracy as the ## final results for comparison the performance of the ## eight random forest algorithms on the four measures ## for each of the datasets is shown in figs and ## ## fig plots the strength for the eight methods against ## different subspace sizes on each of the datasets ## in the same subspace the higher the strength the ## better the result from the curves we can see that ## the new algorithm h w rf consistently performs ## better than the seven other random forest algorithms ## the advantages are more obvious for small subspaces ## the new algorithm quickly achieved higher strength ## as the subspace size increases ## the seven other ## random forest algorithms require larger subspaces to ## achieve a higher strength these results indicate that ## the hybrid weighted random forest algorithm enables ## random forest models to achieve a higher strength ## for small subspace sizes compared to the seven other ## random forest algorithms ## fig plots the curves for the correlations for the ## eight random forest methods on the datasets for ## ## ## ## small subspace sizes h rf c rf cart rf ## and chaid rf produce higher correlations between ## the trees on all datasets the correlation decreases ## as the subspace size increases for the random forest ## models the lower the correlation between the trees ## then the better the final model ## with our new ## random forest algorithm h w rf a low correlation ## level was achieved with very small subspaces in all ## datasets we also note that as the subspace size ## increased the correlation level increased as well this is ## understandable because as the subspace size increases ## the same informative features are more likely to be ## selected repeatedly in the subspaces increasing the ## similarity of the decision trees therefore the feature ## weighting method for subspace selection works well for ## small subspaces at least from the point of view of the ## correlation measure ## fig shows the error bound indicator c s for the ## eight methods on the datasets from these figures ## we can observe that as the subspace size increases c s ## consistently reduces the behaviour indicates that a ## subspace size larger than log m benefits all eight ## algorithms however the new algorithm h w rf ## achieved a lower level of c s at subspace size of ## log m than the seven other algorithms ## fig plots the curves showing the accuracy of the ## eight random forest models on the test datasets from ## the datasets we can clearly see that the new random ## forest algorithm h w rf outperforms the seven ## other random forest algorithms in all eight data sets ## it can be seen that the new method is more stable ## in classification performance than other methods in ## all of these figures it is observed that the highest test ## accuracy is often obtained with the default subspace size ## of log m this implies that in practice large ## size subspaces are not necessary to grow highquality ## trees for random forests ## ## ## performance comparisons ## classification methods ## ## with ## ## other ## ## we conducted a further experimental comparison ## against three other widely used text classification ## methods support vector machines svm naive ## bayes nb and knearest neighbor knn the ## support vector machine used a linear kernel with a ## regularization parameter of which was often ## used in text categorization for naive bayes we ## adopted the multivariate bernoulli event model that ## is frequently used in text classification for knearest neighbor knn we set the number k of ## neighbors to in the experiments we used wekas ## implementation for these three text classification ## methods we used a single subspace size of ## features in all eight datasets to run the random forest ## algorithms for h rf c rf cart rf and ## chaid rf we used a subspace size of features in ## the first datasets ie fbis re re tr wap and ## ## the computer journal vol ## ## no ## ## ## ## ## ## baoxun xu joshua zhexue huang graham williams yunming ye ## fbis ## ## re ## ## ## ## ## ## ## ## ## ## ## ## strength ## ## strength ## ## ## ## ## ## ## ## hwrf ## ## ## ## cwrf ## cartwrf ## ## ## ## hwrf ## cwrf ## ## ## ## cartwrf ## ## chaidwrf ## ## chaidwrf ## ## ## ## hrf ## ## ## ## hrf ## ## crf ## ## crf ## ## ## ## cartrf ## ## ## ## cartrf ## ## chaidrf ## ## chaidrf ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## number of features ## ## number of features ## ## re ## ## ## ## ## ## tr ## ## ## ## ## ## ## ## ## ## ## ## ## hwrf ## cwrf ## ## ## ## cartwrf ## ## strength ## ## strength ## ## ## ## hwrf ## cwrf ## ## ## ## cartwrf ## ## chaidwrf ## ## ## ## chaidwrf ## ## hrf ## ## hrf ## ## ## ## crf ## ## ## ## crf ## ## cartrf ## ## cartrf ## ## ## ## chaidrf ## ## chaidrf ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## number of features ## ## number of features ## ## wap ## ## tr ## ## ## ## ## ## ## ## ## ## ## strength ## ## hwrf ## ## ## ## cwrf ## cartwrf ## ## ## ## strength ## ## ## ## ## ## ## hwrf ## cwrf ## ## ## ## cartwrf ## chaidwrf ## ## chaidwrf ## hrf ## ## ## ## hrf ## ## ## ## crf ## ## crf ## ## cartrf ## ## cartrf ## ## ## ## ## ## chaidrf ## ## chaidrf ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## las ## ## ## ## ## ## ## ## ## ## ## ## las ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## hwrf ## ## ## ## cwrf ## cartwrf ## chaidwrf ## ## ## ## strength ## ## strength ## ## ## ## number of features ## ## number of features ## ## ## ## ## ## hwrf ## ## ## ## cwrf ## cartwrf ## ## ## ## chaidwrf ## ## hrf ## crf ## ## ## ## hrf ## ## ## ## crf ## ## cartrf ## chaidrf ## ## cartrf ## ## ## ## chaidrf ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## number of features ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## number of features ## ## figure strength changes against the number of features in the subspace on the high dimensional datasets ## ## tr to run the random forest algorithms and used ## a subspace size of features in the last datasets ## las and las to run these random forest algorithms ## for h w rf c w rf cart w rf and ## chaid w rf we used breimans subspace size of ## ## log m to run these random forest algorithms ## this number of features provided a consistent result as ## shown in fig in order to obtain stable results we ## built random forest models for each random forest ## algorithm and each dataset and present the average ## ## the computer journal vol ## ## no ## ## ## ## hybrid weighted random forests for classifying very highdimensional data ## fbis ## ## ## ## re ## ## ## ## ## ## ## ## ## ## correlation ## ## correlation ## ## ## ## ## ## ## ## ## hwrf ## cwrf ## ## ## ## cartwrf ## chaidwrf ## ## ## ## hwrf ## ## ## ## cwrf ## cartwrf ## ## ## ## chaidwrf ## ## hrf ## crf ## ## ## ## hrf ## ## ## ## crf ## ## cartrf ## chaidrf ## ## cartrf ## ## ## ## chaidrf ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## number of features ## ## ## ## ## ## ## ## ## ## ## ## ## ## number of features ## ## re ## ## ## ## ## ## tr ## ## ## ## ## ## ## ## ## ## hwrf ## cwrf ## ## ## ## cartwrf ## chaidwrf ## ## ## ## correlation ## ## correlation ## ## ## ## ## ## hwrf ## ## ## ## cwrf ## cartwrf ## ## ## ## chaidwrf ## hrf ## ## hrf ## crf ## ## ## ## crf ## ## ## ## cartrf ## ## cartrf ## ## ## ## chaidrf ## ## chaidrf ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## number of features ## ## number of features ## ## wap ## ## tr ## ## ## ## ## ## ## ## ## correlation ## ## ## ## ## ## hwrf ## cwrf ## ## ## ## cartwrf ## chaidwrf ## ## ## ## correlation ## ## ## ## ## ## hwrf ## cwrf ## ## ## ## cartwrf ## chaidwrf ## ## ## ## hrf ## ## hrf ## ## crf ## ## ## ## crf ## ## cartrf ## ## cartrf ## ## ## ## chaidrf ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## chaidrf ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## number of features ## ## number of features ## ## las ## ## las ## ## ## ## ## ## ## ## ## ## ## ## ## ## hwrf ## ## ## ## cwrf ## cartwrf ## ## ## ## chaidwrf ## ## ## ## correlation ## ## correlation ## ## ## ## ## ## ## ## hwrf ## cwrf ## ## ## ## cartwrf ## chaidwrf ## ## ## ## hrf ## ## hrf ## crf ## ## ## ## crf ## ## ## ## cartrf ## ## cartrf ## chaidrf ## ## chaidrf ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## number of features ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## number of features ## ## figure correlation changes against the number of features in the subspace on the high dimensional datasets ## ## results noting that the range of values are less than ## and the hybrid trees are always more accurate ## the comparison results of classification performance ## of eleven methods are shown in table ## the ## performance is estimated using test accuracy acc ## ## micro f mic and macro f mac boldface ## denotes best results between eleven classification ## methods ## while the improvement is often quite ## small there is always an improvement demonstrated ## we observe that our proposed method h w rf ## ## the computer journal vol ## ## no ## ## ## ## ## ## baoxun xu joshua zhexue huang graham williams yunming ye ## fbis ## ## ## ## re ## ## ## ## ## log m ## ## ## ## ## ## ## ## ## ## ## ## cwrf ## ## ## ## ## ## ## ## hwrf ## ## c s ## ## c s ## ## ## ## ## ## cartwrf ## ## hwrf ## cwrf ## ## ## ## cartwrf ## ## chaidwrf ## ## ## ## chaidwrf ## ## ## ## hrf ## ## hrf ## ## log m ## ## ## crf ## ## ## ## crf ## ## ## ## cartrf ## ## cartrf ## ## chaidrf ## ## ## ## chaidrf ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## number of features ## ## ## ## ## ## ## ## ## ## ## ## ## ## log m ## ## ## ## ## ## ## ## c s ## ## hwrf ## ## ## ## ## ## ## ## ## ## ## ## tr ## ## ## ## ## ## c s ## ## ## ## number of features ## ## re ## ## ## ## ## ## cwrf ## ## ## ## ## ## hwrf ## cwrf ## ## ## ## cartwrf ## ## cartwrf ## ## chaidwrf ## ## ## ## chaidwrf ## ## ## ## hrf ## ## hrf ## ## crf ## ## log m ## ## ## ## ## ## crf ## ## ## ## cartrf ## ## cartrf ## ## chaidrf ## ## ## ## chaidrf ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## number of features ## ## number of features ## ## wap ## ## tr ## ## ## ## ## ## ## ## log m ## ## log m ## ## ## ## ## ## ## ## ## cwrf ## ## c s ## ## ## ## c s ## ## hwrf ## ## ## ## ## ## ## ## ## ## hwrf ## ## ## ## cwrf ## cartwrf ## ## cartwrf ## ## ## chaidwrf ## ## ## ## chaidwrf ## hrf ## ## hrf ## crf ## ## ## ## crf ## ## ## ## cartrf ## ## cartrf ## chaidrf ## ## chaidrf ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## number of features ## ## number of features ## ## las ## ## las ## ## ## ## ## ## ## ## ## ## ## ## cwrf ## cartwrf ## ## ## ## ## ## hrf ## ## ## ## crf ## cartwrf ## ## ## ## chaidrf ## ## ## ## ## ## ## ## ## ## hwrf ## ## ## ## cwrf ## cartwrf ## ## ## ## chaidwrf ## ## log m ## ## ## ## c s ## ## c s ## ## ## ## ## hwrf ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## chaidwrf ## ## log m ## ## ## ## ## hrf ## crf ## ## ## ## cartrf ## chaidrf ## ## ## ## ## ## ## ## ## ## number of features ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## number of features ## ## figure c s changes against the number of features in the subspace on the high dimensional datasets ## ## outperformed the other classification methods in all ## datasets ## ## ## ## conclusions ## ## in this paper we presented a hybrid weighted random ## forest algorithm by simultaneously using a feature ## weighting method and a hybrid forest method to classify ## the computer journal vol ## ## no ## ## ## ## hybrid weighted random forests for classifying very highdimensional data ## fbis ## ## ## ## ## ## re ## ## ## ## ## ## ## ## ## ## ## hwrf ## cwrf ## ## ## ## cartwrf ## ## accuracy ## ## accuracy ## ## ## ## chaidwrf ## hrf ## ## ## ## ## hwrf ## ## ## ## cwrf ## cartwrf ## ## ## ## chaidwrf ## hrf ## ## ## ## crf ## ## crf ## ## log m ## ## cartrf ## ## ## ## ## ## cartrf ## ## log m ## ## ## ## ## ## chaidrf ## ## chaidrf ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## number of features ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## number of features ## ## re ## ## tr ## ## ## ## ## ## ## ## ## log m ## ## ## ## ## ## ## ## ## hwrf ## cwrf ## ## ## ## cartwrf ## ## ## ## accuracy ## ## accuracy ## ## ## ## chaidwrf ## ## ## ## hwrf ## ## ## ## cwrf ## cartwrf ## ## ## ## chaidwrf ## hrf ## ## hrf ## ## ## ## log m ## ## ## ## crf ## ## crf ## ## ## ## cartrf ## ## cartrf ## ## ## ## ## ## chaidrf ## ## chaidrf ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## number of features ## ## number of features ## ## wap ## ## ## ## ## ## tr ## ## ## ## ## ## ## ## ## ## ## ## ## ## hwrf ## cwrf ## ## ## ## cartwrf ## ## accuracy ## ## accuracy ## ## ## ## ## ## ## ## hwrf ## cwrf ## ## ## ## cartwrf ## chaidwrf ## ## chaidwrf ## ## ## ## hrf ## ## log m ## ## ## ## ## hrf ## ## crf ## ## ## ## cartrf ## ## ## ## crf ## ## log m ## ## ## ## ## cartrf ## chaidrf ## ## chaidrf ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## number of features ## ## number of features ## ## las ## ## ## ## ## ## las ## ## ## ## ## ## ## ## accuracy ## ## ## hwrf ## cwrf ## ## ## ## cartwrf ## chaidwrf ## ## ## ## accuracy ## ## ## ## ## ## ## ## hwrf ## cwrf ## cartwrf ## ## ## ## chaidwrf ## hrf ## ## hrf ## ## log m ## ## ## ## crf ## ## ## ## crf ## ## log m ## ## ## ## ## ## cartrf ## ## cartrf ## chaidrf ## ## chaidrf ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## number of features ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## number of features ## ## figure test accuracy changes against the number of features in the subspace on the high dimensional datasets ## ## high dimensional data our algorithm not only retains ## a small subspace size breimans formula log m ## for determining the subspace size to create accurate ## random forest models but also effectively reduces ## the upper bound of the generalization error and ## ## improves classification performance from the results of ## experiments on various high dimensional datasets the ## random forest generated by our new method is superior ## to other classification methods we can use the default ## log m subspace size and generally guarantee ## ## the computer journal vol ## ## no ## ## ## ## ## ## baoxun xu joshua zhexue huang graham williams yunming ye ## ## table the comparison of results ## datasets ## dataset ## fbis ## measures ## acc ## mic ## svm ## ## knn ## ## ## nb ## ## h rf ## ## c rf ## ## cart rf ## ## chaid rf ## ## h w rf ## ## c w rf ## ## cart w rf ## ## chaid w rf ## ## dataset ## wap ## measures ## acc ## mic ## svm ## ## ## knn ## ## nb ## ## h rf ## ## c rf ## ## cart rf ## ## chaid rf ## ## h w rf ## ## c w rf ## ## cart w rf ## ## ## chaid w rf ## ## ## best accuracy micro f and macro f results of the eleven methods on the ## re ## mic ## ## ## ## ## ## ## ## ## ## ## ## tr ## mac ## acc ## mic ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## mac ## ## ## ## ## ## ## ## ## ## ## ## ## acc ## ## ## ## ## ## ## ## ## ## ## ## ## to always produce the best models on a variety of ## measures by using the hybrid weighted random forest ## algorithm ## acknowledgements ## this research is supported in part by nsfc under ## grant no and shenzhen new industry development fund under grant nocxba ## references ## breiman l random forests machine learning ## ## ho t random subspace method for constructing decision forests ieee transactions on pattern ## analysis and machine intelligence ## quinlan j c programs for machine ## learning morgan kaufmann ## breiman l classification and regression trees ## chapman hall crc ## breiman l bagging predictors ## machine ## learning ## ho t random decision forests proceedings ## of the third international conference on document ## analysis and recognition pp ieee ## dietterich t an experimental comparison of ## three methods for constructing ensembles of decision ## trees bagging boosting and randomization machine ## learning ## ## mac ## ## ## ## ## ## ## ## ## ## ## ## mac ## ## ## ## ## ## ## ## ## ## ## ## ## re ## mic ## ## ## ## ## ## ## ## ## ## ## ## las ## acc ## mic ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## acc ## ## ## ## ## ## ## ## ## ## ## ## ## tr ## mic ## ## ## ## ## ## ## ## ## ## ## ## las ## mac ## acc ## mic ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## mac ## ## ## ## ## ## ## ## ## ## ## ## ## acc ## ## ## ## ## ## ## ## ## ## ## ## ## mac ## ## ## ## ## ## ## ## ## ## ## ## mac ## ## ## ## ## ## ## ## ## ## ## ## ## banfield r hall l bowyer k and kegelmeyer w ## a comparison of decision tree ensemble creation ## techniques ieee transactions on pattern analysis ## and machine intelligence ## ## robniksikonja ## m improving random forests ## proceedings of the th european conference on ## machine learning pp springer ## ho t c decision forests proceedings of ## the fourteenth international conference on pattern ## recognition pp ieee ## dietterrich t machine learning research four ## current direction artificial intelligence magzine ## ## amaratunga d cabrera j and lee y ## enriched random forests bioinformatics ## ## ye y li h deng x and huang j ## feature weighting random forest for detection of hidden ## web search interfaces the journal of computational ## linguistics and chinese language processing ## ## xu b huang j williams g wang q and ## ye y classifying very highdimensional data ## with random forests built from small subspaces ## international journal of data warehousing and ## mining ## xu b huang j williams g li j and ye y ## hybrid random forests advantages of mixed ## trees in classifying text data proceedings of the th ## pacificasia conference on knowledge discovery and ## data mining springer ## ## the computer journal vol ## ## no ## ## ## ## hybrid weighted random forests for classifying very highdimensional data ## biggs d de ville b and suen e a method ## of choosing multiway partitions for classification and ## decision trees journal of applied statistics ## ture m kurt i turhan kurum a and ozdamar ## k comparing classification techniques for ## predicting essential hypertension expert systems with ## applications ## begum n ma f and ren f automatic text summarization using support vector machine ## international journal of innovative computing information and control ## chen j huang h tian s and qu y ## feature selection for text classification with naive ## bayes expert systems with applications ## ## tan s neighborweighted knearest neighbor ## for unbalanced text corpus ## expert systems with ## applications ## pearson k on the theory of contingency and ## its relation to association and normal correlation ## cambridge university press ## yang y and liu x a reexamination of ## text categorization methods proceedings of the th ## international conference on research and development ## in information retrieval pp acm ## han e and karypis g centroidbased ## document classification analysis and experimental ## results proceedings of the th european conference on ## principles of data mining and knowledge discovery ## pp springer ## trec ## ## text ## retrieval ## conference ## http trecnistgov ## lewis ## d ## ## reuters ## text ## categorization ## test ## collection ## distribution ## ## http wwwresearchattcom lewis ## han e boley d gini m gross r hastings ## k karypis g kumar v mobasher b and ## moore j webace a web agent for document ## categorization and exploration proceedings of the nd ## international conference on autonomous agents pp ## acm ## mccallum a and nigam k a comparison of ## event models for naive bayes text classification aaai workshop on learning for text categorization pp ## ## witten i frank e and hall m data mining ## practical machine learning tools and techniques ## morgan kaufmann ## ## the computer journal vol ## ## no Punctuation can provide gramatical context which supports understanding. Often for initial analyses we ignore the punctuation. Later we will use punctuation to support the extraction of meaning. Your donation will support ongoing availability and give you access to the PDF version of this book. Desktop Survival Guides include Data Science, GNU/Linux, and MLHub. Books available on Amazon include Data Mining with Rattle and Essentials of Data Science. Popular open source software includes rattle, wajig, and mlhub. Hosted by Togaware, a pioneer of free and open source software since 1984. Copyright © 1995-2021 [email protected] Creative Commons Attribution-ShareAlike 4.0	2022-01-29T11:19:34	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.49444591999053955, "perplexity": 11600.780373785825}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320304883.8/warc/CC-MAIN-20220129092458-20220129122458-00561.warc.gz"}
https://ftp.aimsciences.org/article/doi/10.3934/ipi.2009.3.487	Article Contents Article Contents # Coordinate descent optimization for l1 minimization with application to compressed sensing; a greedy algorithm • We propose a fast algorithm for solving the Basis Pursuit problem, minu $\{\|u\|_1\: \Au=f\}$, which has application to compressed sensing. We design an efficient method for solving the related unconstrained problem minu $E(u) = \|u\|_1 + \lambda \\|\|Au-f\\|\|^2_2$ based on a greedy coordinate descent method. We claim that in combination with a Bregman iterative method, our algorithm will achieve a solution with speed and accuracy competitive with some of the leading methods for the basis pursuit problem. Mathematics Subject Classification: Primary: 90C25; Secondary: 65K05. Citation: Open Access Under a Creative Commons license	2023-04-01T17:52:57	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 1, "x-ck12": 0, "texerror": 0, "math_score": 0.26180583238601685, "perplexity": 606.1946669550734}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296950110.72/warc/CC-MAIN-20230401160259-20230401190259-00289.warc.gz"}
http://pdglive.lbl.gov/Particle.action?init=0&node=M161&home=MXXX005	LIGHT UNFLAVORED MESONS($\boldsymbol S$ = $\boldsymbol C$ = $\boldsymbol B$ = 0) For $\mathit I = 1$ (${{\mathit \pi}}$, ${{\mathit b}}$, ${{\mathit \rho}}$, ${{\mathit a}}$): ${\mathit {\mathit u}}$ ${\mathit {\overline{\mathit d}}}$, ( ${\mathit {\mathit u}}$ ${\mathit {\overline{\mathit u}}}−$ ${\mathit {\mathit d}}$ ${\mathit {\overline{\mathit d}}})/\sqrt {2 }$, ${\mathit {\mathit d}}$ ${\mathit {\overline{\mathit u}}}$;for $\mathit I = 0$ (${{\mathit \eta}}$, ${{\mathit \eta}^{\,'}}$, ${{\mathit h}}$, ${{\mathit h}^{\,'}}$, ${{\mathit \omega}}$, ${{\mathit \phi}}$, ${{\mathit f}}$, ${{\mathit f}^{\,'}}$): ${\mathit {\mathit c}}_{{\mathrm {1}}}$( ${{\mathit u}}{{\overline{\mathit u}}}$ $+$ ${{\mathit d}}{{\overline{\mathit d}}}$ ) $+$ ${\mathit {\mathit c}}_{{\mathrm {2}}}$( ${{\mathit s}}{{\overline{\mathit s}}}$ ) INSPIRE search ${{\boldsymbol a}_{{1}}{(1640)}}$ $I^G(J^{PC})$ = $1^-(1^{+ +})$ Possibly seen in the study of the hadronic structure in decay ${{\mathit \tau}}$ $\rightarrow$ 3 ${{\mathit \pi}}{{\mathit \nu}_{{\tau}}}$ (ABREU 1998G and ASNER 2000 ). ${{\mathit a}_{{1}}{(1640)}}$ MASS $1655 \pm16$ MeV (S = 1.2) ${{\mathit a}_{{1}}{(1640)}}$ WIDTH $254 \pm40$ MeV (S = 1.8)	2020-07-03T14:50:17	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9972923994064331, "perplexity": 857.2199743959706}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-29/segments/1593655882051.19/warc/CC-MAIN-20200703122347-20200703152347-00489.warc.gz"}
https://www.itl.nist.gov/div898/handbook/pmc/section3/pmc321.htm	6. Process or Product Monitoring and Control 6.3. Univariate and Multivariate Control Charts 6.3.2. What are Variables Control Charts? ## Shewhart X-bar and R and S Control Charts $$\bar{X}$$ and $$s$$ Charts $$\bar{X}$$ and $$s$$ Shewhart Control Charts We begin with $$\bar{X}$$ and $$s$$ charts. We should use the $$s$$ chart first to determine if the distribution for the process characteristic is stable. Let us consider the case where we have to estimate $$\sigma$$ by analyzing past data. Suppose we have $$m$$ preliminary samples at our disposition, each of size $$n$$, and let $$s_i$$ be the standard deviation of the ith sample. Then the average of the $$m$$ standard deviations is $$\bar{s} = \frac{1}{m} \sum_{i=1}^m s_i \, .$$ Control Limits for $$\bar{X}$$ and $$s$$ Control Charts We make use of the factor $$c_4$$ described on the previous page. The statistic $$\bar{s}/c_4$$ is an unbiased estimator of $$\sigma$$. Therefore, the parameters of the $$s$$ chart would be $$\begin{eqnarray} UCL & = & \bar{s} + 3\frac{\bar{s}} {c_4} \sqrt{1 - c_4^2} \\ \mbox{Center Line} & = & \bar{s} \\ LCL & = & \bar{s} - 3\frac{\bar{s}} {c_4} \sqrt{1 - c_4^2} \, . \end{eqnarray}$$ Similarly, the parameters of the $$\bar{X}$$ chart would be $$\begin{eqnarray} UCL & = & \bar{\bar{x}} + 3\frac{\bar{s}}{c_4\sqrt{n}} \\ \mbox{Center Line} & = & \bar{\bar{x}} \\ LCL & = & \bar{\bar{x}} - 3\frac{\bar{s}}{c_4\sqrt{n}} \, . \end{eqnarray}$$ $$\bar{\bar{x}}$$, the "grand" mean, is the average of all the observations. It is often convenient to plot the $$\bar{X}$$ and $$s$$ charts on one page. $$\bar{X}$$ and $$R$$ Control Charts $$\bar{X}$$ and $$R$$ control charts If the sample size is relatively small (say equal to or less than 10), we can use the range instead of the standard deviation of a sample to construct control charts on $$\bar{X}$$ and the range, $$R$$. The range of a sample is simply the difference between the largest and smallest observation. There is a statistical relationship (Patnaik, 1946) between the mean range for data from a normal distribution and $$\sigma$$, the standard deviation of that distribution. This relationship depends only on the sample size, $$n$$. The mean of $$R$$ is $$d_2 \sigma$$, where the value of $$d_2$$ is also a function of $$n$$. An estimator of $$\sigma$$ is therefore $$R / d_2$$. Armed with this background we can now develop the $$\bar{X}$$ and $$R$$ control chart. Let $$R_1, \, R_2, \, \ldots, R_k$$, be the ranges of $$k$$ samples. The average range is $$\bar{R} = \frac{R_1 + R_2 + ... + R_k} {k} \, .$$ Then an estimate of $$\sigma$$ can be computed as $$\hat{\sigma} = \frac{\bar{R}} {d_2} \, .$$ $$\bar{X}$$ control charts So, if we use $$\bar{\bar{x}}$$ (or a given target) as an estimator of $$\mu$$ and $$\bar{R} / d_2$$ as an estimator of $$\sigma$$, then the parameters of the $$\bar{X}$$ chart are $$\begin{eqnarray} UCL & = & \bar{\bar{x}} + \frac{3}{d_2\sqrt{n}} \bar{R} \\ \mbox{Center Line} & = & \bar{\bar{x}} \\ LCL & = & \bar{\bar{x}} - \frac{3}{d_2\sqrt{n}} \bar{R} \, . \end{eqnarray}$$ The simplest way to describe the limits is to define the factor $$A_2 = 3 / (d_2 \sqrt{n})$$ and the construction of the $$\bar{X}$$ becomes $$\begin{eqnarray} UCL & = & \bar{\bar{x}} + A_2 \bar{R} \\ \mbox{Center Line} & = & \bar{\bar{x}} \\ LCL & = & \bar{\bar{x}} - A_2 \bar{R} \, . \\ \end{eqnarray}$$ The factor $$A_2$$ depends only on $$n$$, and is tabled below. The $$R$$ chart $$R$$ control charts This chart controls the process variability since the sample range is related to the process standard deviation. The center line of the $$R$$ chart is the average range. To compute the control limits we need an estimate of the true, but unknown standard deviation $$W = R/\sigma$$. This can be found from the distribution of $$W = R/\sigma$$ (assuming that the items that we measure follow a normal distribution). The standard deviation of $$W$$ is $$d_3$$, and is a known function of the sample size, $$n$$. It is tabulated in many textbooks on statistical quality control. Therefore since $$R = W \sigma$$, the standard deviation of $$R$$ is $$\sigma_R = d_3 \sigma$$. But since the true $$\sigma$$ is unknown, we may estimate $$\sigma_R$$ by $$\hat{\sigma}_{R} = d_3\frac{\bar{R}} {d_2} \, .$$ As a result, the parameters of the $$R$$ chart with the customary 3-sigma control limits are $$\begin{eqnarray} UCL & = & \bar{R} + 3\hat{\sigma_R} = \bar{R} + 3d_3\frac{\bar{R}}{d_2} \\ \mbox{Center Line} & = & \bar{R} \\ LCL & = & \bar{R} - 3\hat{\sigma_R} = \bar{R} - 3d_3\frac{\bar{R}}{d_2} \, . \end{eqnarray}$$ As was the case with the control chart parameters for the subgroup averages, defining another set of factors will ease the computations, namely: $$D_3 = 1 - 3 d_3/d_2 \,\, \mbox{ and } \,\, D_4 = 1 + 3 d_3/d_2 \, .$$ These yield $$\begin{eqnarray} UCL & = & \bar{R} D_4 \\ \mbox{Center Line} & = & \bar{R} \\ LCL & = & \bar{R} D_3 \, . \end{eqnarray}$$ The factors $$D_3$$ and $$D_4$$ depend only on $$n$$, and are tabled below. Factors for Calculating Limits for $$\bar{X}$$ and $$R$$ Charts $$n$$ $$A_2$$ $$D_3$$ $$D_4$$ 2 1.880 0 3.267 3 1.023 0 2.575 4 0.729 0 2.282 5 0.577 0 2.115 6 0.483 0 2.004 7 0.419 0.076 1.924 8 0.373 0.136 1.864 9 0.337 0.184 1.816 10 0.308 0.223 1.777 In general, the range approach is quite satisfactory for sample sizes up to around 10. For larger sample sizes, using subgroup standard deviations is preferable. For small sample sizes, the relative efficiency of using the range approach as opposed to using standard deviations is shown in the following table. Efficiency of $$R$$ versus $$s/c_4$$ $$n$$ Relative Efficiency 2 1.000 3 0.992 4 0.975 5 0.955 6 0.930 10 0.850 A typical sample size is 4 or 5, so not much is lost by using the range for such sample sizes. Time To Detection or Average Run Length (ARL) Waiting time to signal "out of control" Two important questions when dealing with control charts are: 1. How often will there be false alarms where we look for an assignable cause but nothing has changed? 2. How quickly will we detect certain kinds of systematic changes, such as mean shifts? The ARL tells us, for a given situation, how long on the average we will plot successive control charts points before we detect a point beyond the control limits. For an $$\bar{X}$$ chart, with no change in the process, we wait on the average $$1/p$$ points before a false alarm takes place, with $$p$$ denoting the probability of an observation plotting outside the control limits. For a normal distribution, $$p = 0.0027$$ and the ARL is approximately 371. A table comparing Shewhart $$\bar{X}$$ chart ARLs to Cumulative Sum (CUSUM) ARLs for various mean shifts is given later in this section. There is also (currently) a web site developed by Galit Shmueli that will do ARL calculations interactively with the user, for Shewhart charts with or without additional (Western Electric) rules added.	2018-04-24T06:22:30	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.831689178943634, "perplexity": 339.22110116493764}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-17/segments/1524125946565.64/warc/CC-MAIN-20180424061343-20180424081343-00522.warc.gz"}
https://indico.bnl.gov/event/1800/contributions/3483/	# 11th international workshop on High-pT Physics in the RHIC & LHC Era 12-15 April 2016 BNL Physics Building US/Eastern timezone ## Elimination of pQCD renormalization scale ambiguities for collider reactions 12 Apr 2016, 09:05 30m Large Seminar Room (BNL Physics Building) ### Speaker Prof. Stanley Brodsky (SLAC National Accelerator Laboratory) ### Description A primary problem for perturbative QCD analyses is how to set the renormalization scale of the QCD running coupling in order to achieve maximally precise fixed-order predictions for physical observables. The Principle of Maximum Conformality (PMC) eliminates the ambiguities associated with the conventional renormalization scale-setting procedure, giving predictions which are independent of the choice of the renormalization scheme. The scales of the QCD couplings and the effective number of quark flavors are set order-by-order in the pQCD series. The PMC has a rigorous theoretical foundation, satisfying renormalization group invariance and all of the self-consistency conditions derived from the renormalization group. The PMC scales at each order are obtained by shifting the arguments of $\alpha_s$ to eliminate all non-conformal $\{\beta_i\}$-terms in the pQCD series. The $\{\beta_i\}$ terms are determined from renormalization group equations without ambiguity. One then obtains the correct scale of the running coupling at each order and at each phase-space point. The PMC reduces in the $N_C \to 0$ Abelian limit to the Gell-Mann-Low method. In this talk, I will summarize recent PMC applications for a number of collider processes. If one applies the PMC to compute the top-quark pair forward-backward asymmetry at the next-to-next-to-leading order level, one obtains a comprehensive, self-consistent pQCD explanation for the Tevatron measurements of the asymmetry, accounting for the increasing-decreasing" behavior observed by D0 collaboration as the $t \bar t$ invariant mass is increased. In the case of hadronic $Z$ decay, one can achieve precise scheme-independent predictions for the decay widths at each order without scale ambiguities by applying the PMC. The application of the PMC systematically eliminates a major theoretical uncertainty for pQCD predictions, thus increasing the sensitivity of the colliders to possible new physics beyond the Standard Model. ### Primary author Prof. Stanley Brodsky (SLAC National Accelerator Laboratory) Slides	2020-11-29T17:12:27	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.76584392786026, "perplexity": 2395.943897772759}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-50/segments/1606141201836.36/warc/CC-MAIN-20201129153900-20201129183900-00491.warc.gz"}
https://zbmath.org/authors/?q=ai%3Abertoin.jean	## Bertoin, Jean Compute Distance To: Author ID: bertoin.jean Published as: Bertoin, Jean; Bertoin, J. External Links: MGP · Wikidata · GND Documents Indexed: 171 Publications since 1986, including 5 Books 4 Contributions as Editor Reviewing Activity: 97 Reviews Co-Authors: 56 Co-Authors with 74 Joint Publications 1,700 Co-Co-Authors all top 5 ### Co-Authors 101 single-authored 12 Yor, Marc 8 Doney, Ronald Arthur 6 Le Gall, Jean-François 4 Baur, Erich 4 Kortchemski, Igor 4 Miermont, Grégory 4 Pitman, Jim William 3 Caballero, María Emilia 3 Curien, Nicolas 3 Mallein, Bastien 3 Watson, Alexander R. 3 Werner, Wendelin 2 Berestycki, Julien 2 Chaumont, Loïc 2 Haas, Bénédicte 2 Jacod, Jean 2 Le Jan, Yves 2 Maller, Ross Arthur 2 Martinez Aguilera, Servet 2 Shi, Zhan 2 Sidoravicius, Vladas 1 Barczy, Mátyás 1 Barndorff-Nielsen, Ole Eiler 1 Barral, Julien 1 Biane, Philippe 1 Bretagnolle, Jean L. 1 Budd, Timothy G. 1 Cortines, Aser 1 Dufresne, Daniel 1 Fan, Ai Hua 1 Fontbona, Joaquin 1 Fujita, Takahiko 1 Giraud, Christophe 1 Gnedin, Alexander V. 1 Goldschmidt, Christina 1 Ibragimov, Il’dar Abdullovich 1 Isozaki, Yasuki 1 Jaffard, Stéphane 1 Jeanblanc, Monique 1 Klüppelberg, Claudia 1 Lindner, Alexander M. 1 Marsalle, Laurence 1 Martinelli, Fabio 1 Norris, James R. 1 Peres, Yuval 1 Peyrière, Jacques 1 Rouault, Alain 1 Roynette, Bernard 1 Ruiz de Chavez, Juan 1 Savov, Mladen Svetoslavov 1 Stephenson, Robin 1 Steutel, Fred Willem 1 Uribe Bravo, Gerónimo 1 van Harn, Klaas 1 Vares, Maria Eulalia 1 Wagner, Wolfgang all top 5 ### Serials 15 Probability Theory and Related Fields 14 The Annals of Probability 11 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 8 Stochastic Processes and their Applications 8 Electronic Communications in Probability 7 Journal of Applied Probability 6 The Annals of Applied Probability 6 Electronic Journal of Probability 5 Advances in Applied Probability 5 Communications in Mathematical Physics 4 Random Structures & Algorithms 3 Journal of Statistical Physics 3 Bulletin of the London Mathematical Society 3 Statistics & Probability Letters 3 Journal of Theoretical Probability 3 Bulletin des Sciences Mathématiques 2 Stochastics 2 Journal of Functional Analysis 2 Japan Journal of Applied Mathematics 2 Forum Mathematicum 2 Stochastics and Stochastics Reports 2 Potential Analysis 2 Bernoulli 2 Journal of the European Mathematical Society (JEMS) 2 Cambridge Tracts in Mathematics 2 Lecture Notes in Mathematics 1 Bulletin des Sciences Mathématiques. Deuxième Série 1 Canadian Journal of Mathematics 1 Gazette des Mathématiciens 1 Illinois Journal of Mathematics 1 Journal of the London Mathematical Society. Second Series 1 Journal of Mathematics of Kyoto University 1 Probability and Mathematical Statistics 1 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 1 Revista Matemática Iberoamericana 1 Journal de Mathématiques Pures et Appliquées. Neuvième Série 1 Comptes Rendus de l’Académie des Sciences. Série I 1 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 1 Combinatorics, Probability and Computing 1 European Series in Applied and Industrial Mathematics (ESAIM): Probability and Statistics 1 Markov Processes and Related Fields 1 Oberwolfach Reports 1 Cambridge Studies in Advanced Mathematics 1 Panoramas et Synthèses 1 ALEA. Latin American Journal of Probability and Mathematical Statistics 1 Probability Surveys 1 Annales Henri Lebesgue all top 5 ### Fields 171 Probability theory and stochastic processes (60-XX) 11 Combinatorics (05-XX) 9 Partial differential equations (35-XX) 8 Biology and other natural sciences (92-XX) 7 Statistical mechanics, structure of matter (82-XX) 5 General and overarching topics; collections (00-XX) 4 Measure and integration (28-XX) 4 Dynamical systems and ergodic theory (37-XX) 3 History and biography (01-XX) 3 Real functions (26-XX) 3 Operator theory (47-XX) 3 Statistics (62-XX) 2 Ordinary differential equations (34-XX) 2 Integral equations (45-XX) 1 Number theory (11-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Functions of a complex variable (30-XX) 1 Abstract harmonic analysis (43-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Fluid mechanics (76-XX) 1 Relativity and gravitational theory (83-XX) ### Citations contained in zbMATH Open 151 Publications have been cited 2,919 times in 1,891 Documents Cited by Year Lévy processes. Zbl 0861.60003 Bertoin, Jean 1996 Random fragmentation and coagulation processes. Zbl 1107.60002 Bertoin, Jean 2006 Subordinators: Examples and applications. Zbl 0955.60046 Bertoin, Jean 1999 Exponential functionals of Lévy processes. Zbl 1189.60096 Bertoin, Jean; Yor, Marc 2005 Exponential decay and ergodicity of completely asymmetric Lévy processes in a finite interval. Zbl 0880.60077 Bertoin, Jean 1997 On conditioning a random walk to stay nonnegative. Zbl 0834.60079 Bertoin, J.; Doney, R. A. 1994 Self-similar fragmentations. Zbl 1002.60072 Bertoin, Jean 2002 Stochastic flows associated to coalescent processes. Zbl 1023.92018 Bertoin, Jean; Le Gall, Jean-François 2003 Lévy processes. Zbl 0938.60005 Bertoin, Jean 1998 Cramér’s estimate for Lévy processes. Zbl 0809.60085 Bertoin, J.; Doney, R. A. 1994 Stochastic flows associated to coalescent processes. III: Limit theorems. Zbl 1110.60026 Bertoin, Jean; Le Gall, Jean-Francois 2006 Some asymptotic results for transient random walks. Zbl 0854.60069 Bertoin, J.; Doney, R. A. 1996 The Bolthausen-Sznitman coalescent and the genealogy of continuous-state branching processes. Zbl 0963.60086 Bertoin, Jean; Le Gall, Jean-François 2000 On subordinators, self-similar Markov processes and some factorizations of the exponential variable. Zbl 1024.60030 Bertoin, Jean; Yor, Marc 2001 Homogeneous fragmentation processes. Zbl 0992.60076 Bertoin, Jean 2001 The entrance laws of self-similar Markov processes and exponential functionals of Lévy processes. Zbl 1004.60046 Bertoin, Jean; Yor, Marc 2002 The asymptotic behavior of fragmentation processes. Zbl 1042.60042 Bertoin, Jean 2003 Splitting at the infimum and excursions in half-lines for random walks and Lévy processes. Zbl 0786.60101 Bertoin, Jean 1993 On the entire moments of self-similar Markov processes and exponential functionals of Lévy processes. Zbl 1031.60038 Bertoin, Jean; Yor, Marc 2002 The inviscid Burgers equation with Brownian initial velocity. Zbl 0917.60063 Bertoin, Jean 1998 On the first exit time of a completely asymmetric stable process from a finite interval. Zbl 0863.60068 Bertoin, Jean 1996 Path transformations connecting Brownian bridge, excursion and meander. Zbl 0805.60076 Bertoin, Jean; Pitman, Jim 1994 On continuity properties of the law of integrals of Lévy processes. Zbl 1180.60042 Bertoin, Jean; Lindner, Alexander; Maller, Ross 2008 Asymptotic laws for nonconservative self-similar fragmentations. Zbl 1064.60075 Bertoin, Jean; Gnedin, Alexander V. 2004 Les processus de Dirichlet en tant qu’espace de Banach. (Dirichlet processes as Banach spaces). Zbl 0602.60069 Bertoin, Jean 1986 Discretization methods for homogeneous fragmentations. Zbl 1077.60053 Bertoin, Jean; Rouault, Alain 2005 Entrance from $$0+$$ for increasing semi-stable Markov processes. Zbl 1002.60032 Bertoin, Jean; Caballero, Maria-Emilia 2002 On prolific individuals in a supercritical continuous-state branching process. Zbl 1154.60066 Bertoin, Jean; Fontbona, Joaquin; Martínez, Servet 2008 Spitzer’s condition for random walks and Lévy processes. Zbl 0880.60078 Bertoin, J.; Doney, R. A. 1997 Renewal theory and level passage by subordinators. Zbl 0965.60053 Bertoin, J.; van Harn, K.; Steutel, F. W. 1999 Martingales in self-similar growth-fragmentations and their connections with random planar maps. Zbl 1451.60047 Bertoin, Jean; Budd, Timothy; Curien, Nicolas; Kortchemski, Igor 2018 Markovian growth-fragmentation processes. Zbl 1375.60129 Bertoin, Jean 2017 Passage of Lévy processes across power law boundaries at small times. Zbl 1140.60025 Bertoin, J.; Doney, R. A.; Maller, R. A. 2008 Stochastic flows associated to coalescent processes. II: Stochastic differential equations. Zbl 1119.60024 Bertoin, Jean; Le Gall, Jean-François 2005 Some applications of duality for Lévy processes in a half-line. Zbl 1213.60090 2011 Random planar maps and growth-fragmentations. Zbl 1447.60058 Bertoin, Jean; Curien, Nicolas; Kortchemski, Igor 2018 An extension of Pitman’s theorem for spectrally positive Lévy processes. Zbl 0760.60068 Bertoin, Jean 1992 Path transformations of first passage bridges. Zbl 1061.60083 Bertoin, Jean; Chaumont, Loïc; Pitman, Jim 2003 A probabilistic approach to spectral analysis of growth-fragmentation equations. Zbl 1384.35132 Bertoin, Jean; Watson, Alexander R. 2018 Fires on trees. Zbl 1263.60083 Bertoin, Jean 2012 Regularity of the half-line for Lévy processes. Zbl 0883.60069 Bertoin, Jean 1997 Poissonian exponential functionals, $$q$$-series, $$q$$-integrals, and the moment problem for log-normal distributions. Zbl 1056.60046 Bertoin, Jean; Biane, Philippe; Yor, Marc 2004 A fragmentation process connected to Brownian motion. Zbl 0965.60072 Bertoin, Jean 2000 Iterated Brownian motion and stable $$(1/4)$$ subordinator. Zbl 0854.60082 Bertoin, Jean 1996 Eternal solutions to Smoluchowski’s coagulation equation with additive kernel and their probabilistic interpretations. Zbl 1030.60036 Bertoin, Jean 2002 Sur une intégrale pour les processus à $$\alpha$$-variation bornée. (On an integral for processes with bounded $$\alpha$$-variation). Zbl 0687.60054 Bertoin, Jean 1989 The cut-tree of large Galton-Watson trees and the Brownian CRT. Zbl 1279.60035 Bertoin, Jean; Miermont, Grégory 2013 The structure of the allelic partition of the total population for Galton-Watson processes with neutral mutations. Zbl 1180.92063 Bertoin, Jean 2009 Representation of measures by balayage from a regular recurrent point. Zbl 0749.60038 Bertoin, J.; Le Jan, Yves 1992 Sur la décomposition de la trajectoire d’un processus de Lévy spectralement positif en son infimum. (On the path decomposition at the infimum for a spectrally positive Lévy process). Zbl 0758.60073 Bertoin, Jean 1991 On a particular class of self-decomposable random variables: the durations of Bessel excursions straddling independent exponential times. Zbl 1123.60063 Bertoin, J.; Fujita, T.; Roynette, B.; Yor, M. 2006 Self-similar scaling limits of Markov chains on the positive integers. Zbl 1352.60103 Bertoin, Jean; Kortchemski, Igor 2016 Fragmentation energy. Zbl 1080.60080 Bertoin, Jean; Martínez, Servet 2005 Stable windings. Zbl 0867.60045 Bertoin, Jean; Werner, Wendelin 1996 Spatial branching processes and subordination. Zbl 0921.60078 Bertoin, Jean; Le Gall, Jean-François; Le Jan, Yves 1997 The convex minorant of the Cauchy process. Zbl 0954.60042 Bertoin, Jean 2000 Compensated fragmentation processes and limits of dilated fragmentations. Zbl 1344.60033 Bertoin, Jean 2016 The structure of typical clusters in large sparse random configurations. Zbl 1168.82028 2009 Reflecting a Langevin process at an absorbing boundary. Zbl 1132.60057 Bertoin, Jean 2007 Clustering statistics for sticky particles with Brownian initial velocity. Zbl 0959.60074 Bertoin, Jean 2000 Two coalescents derived from the ranges of stable subordinators. Zbl 0949.60034 Bertoin, Jean; Pitman, Jim 2000 Eternal additive coalescents and certain bridges with exchangeable increments. Zbl 1019.60072 Bertoin, Jean 2001 On a Feynman-Kac approach to growth-fragmentation semigroups and their asymptotic behaviors. Zbl 1433.35414 Bertoin, Jean 2019 Sizes of the largest clusters for supercritical percolation on random recursive trees. Zbl 1280.05117 Bertoin, Jean 2014 On the maximal offspring in a critical branching process with infinite variance. Zbl 1223.60020 Bertoin, Jean 2011 A limit theorem for trees of alleles in branching processes with rare neutral mutations. Zbl 1193.60099 Bertoin, Jean 2010 On small masses in self-similar fragmentations. Zbl 1075.60092 Bertoin, Jean 2004 Dual random fragmentation and coagulation and an application to the genealogy of Yule processes. Zbl 1064.60177 Bertoin, Jean; Goldschmidt, Christina 2004 Regenerative embedding of Markov sets. Zbl 0895.60011 Bertoin, Jean 1997 Complements on the Hilbert transform and the fractional derivative of Brownian local times. Zbl 0725.60084 Bertoin, Jean 1990 The fragmentation process of an infinite recursive tree and Ornstein-Uhlenbeck type processes. Zbl 1333.60186 Baur, Erich; Bertoin, Jean 2015 Local explosion in self-similar growth-fragmentation processes. Zbl 1346.60038 Bertoin, Jean; Stephenson, Robin 2016 Probabilistic aspects of critical growth-fragmentation equations. Zbl 1426.35213 Bertoin, Jean; Watson, Alexander R. 2016 Excursions of a $$BES_ o(d)$$ and its drift term $$(0<d<1)$$. Zbl 0665.60073 Bertoin, J. 1990 Sur la mesure d’occupation d’une classe de fonctions self-affines. (On the occupation measure of a class of self-affine functions). Zbl 0685.26007 Bertoin, Jean 1988 Almost giant clusters for percolation on large trees with logarithmic heights. Zbl 1283.60119 Bertoin, Jean 2013 Two-parameter Poisson-Dirichlet measures and reversible exchangeable fragmentation-coalescence processes. Zbl 1165.60032 Bertoin, Jean 2008 Homogeneous multitype fragmentations. Zbl 1153.60046 Bertoin, Jean 2008 Asymptotic windings of planar Brownian motion revisited via the Ornstein- Uhlenbeck process. Zbl 0814.60080 Bertoin, Jean; Werner, Wendelin 1994 Large-deviations estimates in Burgers turbulence with stable noise initial data. Zbl 0927.60039 Bertoin, Jean 1998 Supercritical percolation on large scale-free random trees. Zbl 1309.60094 Bertoin, Jean; Bravo, Gerónimo Uribe 2015 Infinitely ramified point measures and branching Lévy processes. Zbl 1456.60225 Bertoin, Jean; Mallein, Bastien 2019 Temps locaux et intégration stochastique pour les processus de Dirichlet. (Local time and stochastic integration for Dirichlet processes). Zbl 0616.60073 Bertoin, Jean 1987 Applications de la théorie spectral des cordes vibrantes aux fonctionnelles additives principales d’un brownien réfléchi. (Applications of the spectral theory of vibrating strings to principal additive functionals of a reflected Brownian motion). Zbl 0694.60070 Bertoin, Jean 1989 On largest offspring in a critical branching process with finite variance. Zbl 1277.60045 Bertoin, Jean 2013 Asymptotic regimes for the occupancy scheme of multiplicative cascades. Zbl 1148.60013 Bertoin, Jean 2008 Increase of a Lévy process with no positive jumps. Zbl 0739.60065 Bertoin, Jean 1991 Some aspects of additive coalescents. Zbl 1007.60101 Bertoin, Jean 2002 On the local behaviour of ladder height distributions. Zbl 0815.60065 Bertoin, J.; Doney, R. A. 1994 Constructions of a Brownian path with a given minimum. Zbl 1021.60060 Bertoin, Jean; Pitman, Jim; Ruiz de Chavez, Juan 1999 Darling-Erdős theorems for normalized sums of i. i. d. variables close to a stable law. Zbl 0943.60041 Bertoin, Jean 1998 Structure of shocks in Burgers turbulence with stable noise initial data. Zbl 0943.60055 Bertoin, Jean 1999 The cut-tree of large recursive trees. Zbl 1351.60010 Bertoin, Jean 2015 Biggins’ martingale convergence for branching Lévy processes. Zbl 1402.60051 Bertoin, Jean; Mallein, Bastien 2018 Some two-dimensional extensions of Bougerol’s identity in law for the exponential functional of linear Brownian motion. Zbl 1303.60073 Bertoin, Jean; Dufresne, Daniel; Yor, Marc 2013 A second order SDE for the Langevin process reflected at a completely inelastic boundary. Zbl 1169.60009 Bertoin, Jean 2008 Decomposition of Brownian motion with derivation in a local minimum by the juxtaposition of its positive and negative excursions. (Décomposition du mouvement brownien avec dérive en un minimum local par juxtaposition de ses excursions positives et négatives.) Zbl 0741.60077 Bertoin, Jean 1991 Increase of stable processes. Zbl 0809.60050 Bertoin, Jean 1994 Asymptotic behavior of the number of windings of the planar Brownian path. (Comportement asymptotique du nombre de tours effectués par la trajectoire brownienne plane.) Zbl 0810.60077 Bertoin, Jean; Werner, Wendelin 1994 On the local rate of growth of Lévy processes with no positive jumps. Zbl 0816.60072 Bertoin, Jean 1995 Universality of noise reinforced Brownian motions. Zbl 1469.60253 Bertoin, Jean 2021 Scaling exponents of step-reinforced random walks. Zbl 1483.60065 Bertoin, Jean 2021 On conditioning a self-similar growth-fragmentation by its intrinsic area. Zbl 1484.60045 Bertoin, Jean; Curien, Nicolas; Kortchemski, Igor 2021 The strong Malthusian behavior of growth-fragmentation processes. (Comportement Malthusien fort des processus de croissance-fragmentation.) Zbl 1451.35229 Bertoin, Jean; Watson, Alexander R. 2020 Noise reinforcement for Lévy processes. Zbl 1477.60069 Bertoin, Jean 2020 How linear reinforcement affects Donsker’s theorem for empirical processes. Zbl 1478.60108 Bertoin, Jean 2020 On a Feynman-Kac approach to growth-fragmentation semigroups and their asymptotic behaviors. Zbl 1433.35414 Bertoin, Jean 2019 Infinitely ramified point measures and branching Lévy processes. Zbl 1456.60225 Bertoin, Jean; Mallein, Bastien 2019 A version of Herbert A. Simon’s model with slowly fading memory and its connections to branching processes. Zbl 1481.60184 Bertoin, Jean 2019 Martingales in self-similar growth-fragmentations and their connections with random planar maps. Zbl 1451.60047 Bertoin, Jean; Budd, Timothy; Curien, Nicolas; Kortchemski, Igor 2018 Random planar maps and growth-fragmentations. Zbl 1447.60058 Bertoin, Jean; Curien, Nicolas; Kortchemski, Igor 2018 A probabilistic approach to spectral analysis of growth-fragmentation equations. Zbl 1384.35132 Bertoin, Jean; Watson, Alexander R. 2018 Biggins’ martingale convergence for branching Lévy processes. Zbl 1402.60051 Bertoin, Jean; Mallein, Bastien 2018 Markovian growth-fragmentation processes. Zbl 1375.60129 Bertoin, Jean 2017 Weak limits for the largest subpopulations in Yule processes with high mutation probabilities. Zbl 1425.60066 Baur, Erich; Bertoin, Jean 2017 Self-similar scaling limits of Markov chains on the positive integers. Zbl 1352.60103 Bertoin, Jean; Kortchemski, Igor 2016 Compensated fragmentation processes and limits of dilated fragmentations. Zbl 1344.60033 Bertoin, Jean 2016 Local explosion in self-similar growth-fragmentation processes. Zbl 1346.60038 Bertoin, Jean; Stephenson, Robin 2016 Probabilistic aspects of critical growth-fragmentation equations. Zbl 1426.35213 Bertoin, Jean; Watson, Alexander R. 2016 On the destruction of large random recursive trees. (Sur la destruction de grands arbres alétoires récursifs.) Zbl 1358.05253 Baur, E.; Bertoin, J. 2016 The fragmentation process of an infinite recursive tree and Ornstein-Uhlenbeck type processes. Zbl 1333.60186 Baur, Erich; Bertoin, Jean 2015 Supercritical percolation on large scale-free random trees. Zbl 1309.60094 Bertoin, Jean; Bravo, Gerónimo Uribe 2015 The cut-tree of large recursive trees. Zbl 1351.60010 Bertoin, Jean 2015 Sizes of the largest clusters for supercritical percolation on random recursive trees. Zbl 1280.05117 Bertoin, Jean 2014 On the non-Gaussian fluctuations of the giant cluster for percolation on random recursive trees. Zbl 1292.60095 Bertoin, Jean 2014 Local times for functions with finite variation: two versions of Stieltjes change-of-variables formula. Zbl 1295.26011 Bertoin, Jean; Yor, Marc 2014 Cutting edges at random in large recursive trees. Zbl 1390.60043 Baur, Erich; Bertoin, Jean 2014 The cut-tree of large Galton-Watson trees and the Brownian CRT. Zbl 1279.60035 Bertoin, Jean; Miermont, Grégory 2013 Almost giant clusters for percolation on large trees with logarithmic heights. Zbl 1283.60119 Bertoin, Jean 2013 On largest offspring in a critical branching process with finite variance. Zbl 1277.60045 Bertoin, Jean 2013 Some two-dimensional extensions of Bougerol’s identity in law for the exponential functional of linear Brownian motion. Zbl 1303.60073 Bertoin, Jean; Dufresne, Daniel; Yor, Marc 2013 Retrieving information from subordination. Zbl 1284.60084 Bertoin, Jean; Yor, Marc 2013 Pure jump increasing processes and the change of variables formula. Zbl 1306.60120 Bertoin, Jean; Yor, Marc 2013 Fires on trees. Zbl 1263.60083 Bertoin, Jean 2012 The area of a self-similar fragmentation. Zbl 1277.60070 Bertoin, Jean 2012 Lévy processes at Saint-Flour. Reprint of lectures originally published in the Lecture Notes in Mathematics volumes 307 (1973), 1117 (1985), 1717 (1999) and 1897 (2007). Zbl 1254.60004 Bertoin, Jean; Bretagnolle, Jean L.; Doney, Ronald A.; Ibragimov, Ildar A.; Jacod, Jean 2012 Some applications of duality for Lévy processes in a half-line. Zbl 1213.60090 2011 On the maximal offspring in a critical branching process with infinite variance. Zbl 1223.60020 Bertoin, Jean 2011 Functional limit theorems for Lévy processes satisfying Cramér’s condition. Zbl 1244.60049 Barczy, Matyas; Bertoin, Jean 2011 A limit theorem for trees of alleles in branching processes with rare neutral mutations. Zbl 1193.60099 Bertoin, Jean 2010 A system of grabbing particles related to Galton-Watson trees. Zbl 1209.60048 Bertoin, Jean; Sidoravicius, Vladas; Vares, Maria Eulalia 2010 Asymptotic regimes for the partition into colonies of a branching process with emigration. Zbl 1215.60049 Bertoin, Jean 2010 Some interactions between analysis, probability theory and fractals. To Benoît Mandelbrot, in memoriam. (Quelques interactions entre analyse, probabilités et fractals. A Benoît Mandelbrot, in memoriam.) Zbl 1308.28002 Barral, Julien; Berestycki, Julien; Bertoin, Jean; Fan, Aihua; Haas, Bénédicte; Jaffard, Stéphane; Miermont, Grégory; Peyrière, Jacques 2010 A two-time-scale phenomenon in a fragmentation-coagulation process. Zbl 1226.60028 Bertoin, Jean 2010 The structure of the allelic partition of the total population for Galton-Watson processes with neutral mutations. Zbl 1180.92063 Bertoin, Jean 2009 The structure of typical clusters in large sparse random configurations. Zbl 1168.82028 2009 Two solvable systems of coagulation equations with limited aggregations. Zbl 1179.82180 Bertoin, Jean 2009 On continuity properties of the law of integrals of Lévy processes. Zbl 1180.60042 Bertoin, Jean; Lindner, Alexander; Maller, Ross 2008 On prolific individuals in a supercritical continuous-state branching process. Zbl 1154.60066 Bertoin, Jean; Fontbona, Joaquin; Martínez, Servet 2008 Passage of Lévy processes across power law boundaries at small times. Zbl 1140.60025 Bertoin, J.; Doney, R. A.; Maller, R. A. 2008 Two-parameter Poisson-Dirichlet measures and reversible exchangeable fragmentation-coalescence processes. Zbl 1165.60032 Bertoin, Jean 2008 Homogeneous multitype fragmentations. Zbl 1153.60046 Bertoin, Jean 2008 Asymptotic regimes for the occupancy scheme of multiplicative cascades. Zbl 1148.60013 Bertoin, Jean 2008 A second order SDE for the Langevin process reflected at a completely inelastic boundary. Zbl 1169.60009 Bertoin, Jean 2008 Reflecting a Langevin process at an absorbing boundary. Zbl 1132.60057 Bertoin, Jean 2007 Random fragmentation and coagulation processes. Zbl 1107.60002 Bertoin, Jean 2006 Stochastic flows associated to coalescent processes. III: Limit theorems. Zbl 1110.60026 Bertoin, Jean; Le Gall, Jean-Francois 2006 On a particular class of self-decomposable random variables: the durations of Bessel excursions straddling independent exponential times. Zbl 1123.60063 Bertoin, J.; Fujita, T.; Roynette, B.; Yor, M. 2006 Asymptotics in Knuth’s parking problem for caravans. Zbl 1102.60006 Bertoin, Jean; Miermont, Grégory 2006 Different aspects of a model for random fragmentation processes. Zbl 1137.60045 Bertoin, J. 2006 Exponential functionals of Lévy processes. Zbl 1189.60096 Bertoin, Jean; Yor, Marc 2005 Discretization methods for homogeneous fragmentations. Zbl 1077.60053 Bertoin, Jean; Rouault, Alain 2005 Stochastic flows associated to coalescent processes. II: Stochastic differential equations. Zbl 1119.60024 Bertoin, Jean; Le Gall, Jean-François 2005 Fragmentation energy. Zbl 1080.60080 Bertoin, Jean; Martínez, Servet 2005 Asymptotic laws for nonconservative self-similar fragmentations. Zbl 1064.60075 Bertoin, Jean; Gnedin, Alexander V. 2004 Poissonian exponential functionals, $$q$$-series, $$q$$-integrals, and the moment problem for log-normal distributions. Zbl 1056.60046 Bertoin, Jean; Biane, Philippe; Yor, Marc 2004 On small masses in self-similar fragmentations. Zbl 1075.60092 Bertoin, Jean 2004 Dual random fragmentation and coagulation and an application to the genealogy of Yule processes. Zbl 1064.60177 Bertoin, Jean; Goldschmidt, Christina 2004 Random covering of an interval and a variation of Kingman’s coalescent. Zbl 1063.60009 Bertoin, Jean 2004 Stochastic flows associated to coalescent processes. Zbl 1023.92018 Bertoin, Jean; Le Gall, Jean-François 2003 The asymptotic behavior of fragmentation processes. Zbl 1042.60042 Bertoin, Jean 2003 Path transformations of first passage bridges. Zbl 1061.60083 Bertoin, Jean; Chaumont, Loïc; Pitman, Jim 2003 Self-similar fragmentations. Zbl 1002.60072 Bertoin, Jean 2002 The entrance laws of self-similar Markov processes and exponential functionals of Lévy processes. Zbl 1004.60046 Bertoin, Jean; Yor, Marc 2002 On the entire moments of self-similar Markov processes and exponential functionals of Lévy processes. Zbl 1031.60038 Bertoin, Jean; Yor, Marc 2002 Entrance from $$0+$$ for increasing semi-stable Markov processes. Zbl 1002.60032 Bertoin, Jean; Caballero, Maria-Emilia 2002 Eternal solutions to Smoluchowski’s coagulation equation with additive kernel and their probabilistic interpretations. Zbl 1030.60036 Bertoin, Jean 2002 Some aspects of additive coalescents. Zbl 1007.60101 Bertoin, Jean 2002 Self-attracting Poisson clouds in an expanding universe. Zbl 1016.83043 Bertoin, Jean 2002 On subordinators, self-similar Markov processes and some factorizations of the exponential variable. Zbl 1024.60030 Bertoin, Jean; Yor, Marc 2001 Homogeneous fragmentation processes. Zbl 0992.60076 Bertoin, Jean 2001 Eternal additive coalescents and certain bridges with exchangeable increments. Zbl 1019.60072 Bertoin, Jean 2001 Some properties of Burgers turbulence with white or stable noise initial data. Zbl 0984.60078 Bertoin, Jean 2001 Statistics of a flux in Burgers turbulence with one-sided Brownian initial data. Zbl 0993.60067 Bertoin, J.; Giraud, C.; Isozaki, Y. 2001 Some elements on Lévy processes. Zbl 0982.60042 Bertoin, Jean 2001 The Bolthausen-Sznitman coalescent and the genealogy of continuous-state branching processes. Zbl 0963.60086 Bertoin, Jean; Le Gall, Jean-François 2000 A fragmentation process connected to Brownian motion. Zbl 0965.60072 Bertoin, Jean 2000 The convex minorant of the Cauchy process. Zbl 0954.60042 Bertoin, Jean 2000 Clustering statistics for sticky particles with Brownian initial velocity. Zbl 0959.60074 Bertoin, Jean 2000 Two coalescents derived from the ranges of stable subordinators. Zbl 0949.60034 Bertoin, Jean; Pitman, Jim 2000 Subordinators: Examples and applications. Zbl 0955.60046 Bertoin, Jean 1999 Renewal theory and level passage by subordinators. Zbl 0965.60053 Bertoin, J.; van Harn, K.; Steutel, F. W. 1999 Constructions of a Brownian path with a given minimum. Zbl 1021.60060 Bertoin, Jean; Pitman, Jim; Ruiz de Chavez, Juan 1999 Structure of shocks in Burgers turbulence with stable noise initial data. Zbl 0943.60055 Bertoin, Jean 1999 Intersection of independent regenerative sets. Zbl 0937.60043 Bertoin, Jean 1999 Regularity of the Cauchy principal value of the local times of some Lévy processes. Zbl 0922.60073 Bertoin, Jean; Caballero, Maria-Emilia 1999 Renewal theory for embedded regenerative sets. Zbl 0961.60082 Bertoin, Jean 1999 Lectures on probability theory and statistics. Ecole d’eté de Probabilités de Saint-Flour XXVII–1997, Saint-Flour, France, July 7–23, 1997. Zbl 0930.00052 1999 On overshoots and hitting times for random walks. Zbl 0942.60032 Bertoin, Jean 1999 Lévy processes. Zbl 0938.60005 Bertoin, Jean 1998 ...and 51 more Documents all top 5 ### Cited by 1,756 Authors 58 Bertoin, Jean 54 Kyprianou, Andreas E. 29 Maller, Ross Arthur 27 Palmowski, Zbigniew 27 Zhou, Xiaowen 25 Pitman, Jim William 24 Pardo, Juan Carlos 23 Yor, Marc 22 Lambert, Amaury 20 Patie, Pierre 19 Iksanov, Aleksander M. 19 Winkel, Matthias 18 Chaumont, Loïc 18 Curien, Nicolas 17 Rivero, Víctor Manuel 17 Simon, Thomas 16 Khoshnevisan, Davar 16 Pistorius, Martijn R. 16 Song, Renming 15 Delmas, Jean-François 15 Haas, Bénédicte 15 Mandjes, Michel Robertus Hendrikus 15 Meerschaert, Mark Marvin 15 Vondraček, Zoran 14 Berestycki, Julien 14 Li, Zenghu 14 Möhle, Martin 14 Savov, Mladen Svetoslavov 13 Xiao, Yimin 12 Avram, Florin 12 Chen, Zhen-Qing 12 Doney, Ronald Arthur 12 Gnedin, Alexander V. 12 Ivanovs, Jevgeņijs 12 Kuznetsov, Alexey 12 Leonenko, Nikolai N. 12 Russo, Francesco 12 Shi, Zhan 12 Wang, Yuebao 12 Zwart, Bert P. 11 Griffin, Philip S. 11 Nane, Erkan 11 Uribe Bravo, Gerónimo 11 Vallois, Pierre 10 Abraham, Romain 10 Döring, Leif 10 Kim, Panki 9 Berestycki, Nathanaël 9 Crane, Harry 9 Foucart, Clément 9 Huillet, Thierry E. 9 Le Gall, Jean-François 9 Lindner, Alexander M. 9 Mallein, Bastien 9 Pérez Garmendia, Jose Luis 8 Buchmann, Boris 8 D’Ovidio, Mirko 8 Kella, Offer 8 Salminen, Paavo H. 8 Toaldo, Bruno 8 Yin, Chuancun 7 Aurzada, Frank 7 Bansaye, Vincent 7 Behme, Anita Diana 7 Czarna, Irmina 7 Escobedo Martínez, Miguel 7 Forman, Noah Mills 7 Grzywny, Tomasz 7 He, Hui 7 James, Lancelot F. 7 Klüppelberg, Claudia 7 Limic, Vlada 7 Loeffen, Ronnie L. 7 Magdziarz, Marcin 7 Miermont, Grégory 7 Mijatović, Aleksandar 7 Schilling, René Leander 7 Schweinsberg, Jason Ross 7 Straka, Peter 7 Van Schaik, Kees 7 Watson, Alexander R. 7 Yamazaki, Kazutoshi 6 Baurdoux, Erik Jan 6 Boxma, Onno Johan 6 Broutin, Nicolas 6 Caballero, María Emilia 6 Doumic, Marie 6 Hu, Ze-Chun 6 Janson, Svante 6 Kersting, Götz-Dietrich 6 Kortchemski, Igor 6 Kumar, Amit N. 6 Laurençot, Philippe 6 Le Jan, Yves 6 Mai, Jan-Frederik 6 Marynych, Alexander V. 6 Mimica, Ante 6 Mischler, Stéphane 6 Pego, Robert L. 6 Pirozzi, Enrica ...and 1,656 more Authors all top 5 ### Cited in 270 Serials 208 Stochastic Processes and their Applications 143 The Annals of Probability 94 The Annals of Applied Probability 87 Journal of Applied Probability 80 Probability Theory and Related Fields 75 Journal of Theoretical Probability 73 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 65 Statistics & Probability Letters 60 Advances in Applied Probability 51 Bernoulli 48 Electronic Journal of Probability 43 Journal of Statistical Physics 33 Transactions of the American Mathematical Society 30 Potential Analysis 28 Journal of Mathematical Analysis and Applications 25 Insurance Mathematics & Economics 19 Stochastics 18 Journal of Differential Equations 17 Finance and Stochastics 15 Journal of Functional Analysis 15 Queueing Systems 15 Electronic Communications in Probability 14 ALEA. Latin American Journal of Probability and Mathematical Statistics 13 Communications in Mathematical Physics 11 Acta Applicandae Mathematicae 11 European Series in Applied and Industrial Mathematics (ESAIM): Probability and Statistics 11 Scandinavian Actuarial Journal 10 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 10 Bulletin des Sciences Mathématiques 9 Physica A 9 Applied Mathematics and Computation 9 Theory of Probability and Mathematical Statistics 9 Methodology and Computing in Applied Probability 8 Journal of Computational and Applied Mathematics 8 Stochastic Analysis and Applications 8 Random Structures & Algorithms 7 Chaos, Solitons and Fractals 7 Advances in Mathematics 7 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 7 Proceedings of the American Mathematical Society 7 SIAM Journal on Mathematical Analysis 7 Comptes Rendus. Mathématique. Académie des Sciences, Paris 7 North American Actuarial Journal 7 Probability Surveys 7 Science China. Mathematics 6 Journal of Econometrics 6 Physica D 6 Combinatorics, Probability and Computing 6 Fractional Calculus & Applied Analysis 5 Journal of Mathematical Biology 5 Mathematische Zeitschrift 5 Osaka Journal of Mathematics 5 Journal de Mathématiques Pures et Appliquées. Neuvième Série 5 Extremes 5 Acta Mathematica Sinica. English Series 5 Stochastic Models 5 Stochastics and Dynamics 5 Frontiers of Mathematics in China 4 Lithuanian Mathematical Journal 4 Theory of Probability and its Applications 4 Applied Mathematics and Optimization 4 Journal of Mathematical Psychology 4 Journal of Statistical Planning and Inference 4 European Journal of Operational Research 4 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 4 International Journal of Theoretical and Applied Finance 4 Statistical Inference for Stochastic Processes 4 Journal of Evolution Equations 4 Discrete and Continuous Dynamical Systems. Series B 4 Boundary Value Problems 4 Kinetic and Related Models 4 Modern Stochastics. Theory and Applications 4 Annales Henri Lebesgue 3 Archive for Rational Mechanics and Analysis 3 Israel Journal of Mathematics 3 Journal of Mathematical Physics 3 Rocky Mountain Journal of Mathematics 3 Annals of the Institute of Statistical Mathematics 3 The Annals of Statistics 3 Journal of Optimization Theory and Applications 3 Memoirs of the American Mathematical Society 3 Publications of the Research Institute for Mathematical Sciences, Kyoto University 3 Japan Journal of Applied Mathematics 3 Revista Matemática Iberoamericana 3 Mathematical and Computer Modelling 3 Communications in Statistics. Theory and Methods 3 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 3 Mathematical Methods of Operations Research 3 Journal of the European Mathematical Society (JEMS) 3 SIAM Journal on Financial Mathematics 3 Journal of Theoretical Biology 3 Stochastic and Partial Differential Equations. Analysis and Computations 3 Journal de l’École Polytechnique – Mathématiques 3 European Series in Applied and Industrial Mathematics (ESAIM): Proceedings and Surveys 3 AIMS Mathematics 2 Applicable Analysis 2 Communications on Pure and Applied Mathematics 2 Discrete Mathematics 2 Journal d’Analyse Mathématique 2 Metrika ...and 170 more Serials all top 5 ### Cited in 52 Fields 1,653 Probability theory and stochastic processes (60-XX) 217 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 204 Partial differential equations (35-XX) 124 Statistical mechanics, structure of matter (82-XX) 121 Statistics (62-XX) 115 Biology and other natural sciences (92-XX) 101 Combinatorics (05-XX) 73 Operator theory (47-XX) 61 Numerical analysis (65-XX) 50 Real functions (26-XX) 47 Integral equations (45-XX) 41 Measure and integration (28-XX) 40 Operations research, mathematical programming (90-XX) 31 Systems theory; control (93-XX) 30 Potential theory (31-XX) 28 Ordinary differential equations (34-XX) 23 Dynamical systems and ergodic theory (37-XX) 21 Functional analysis (46-XX) 19 Computer science (68-XX) 17 Special functions (33-XX) 17 Calculus of variations and optimal control; optimization (49-XX) 16 Fluid mechanics (76-XX) 15 Integral transforms, operational calculus (44-XX) 13 Number theory (11-XX) 13 Harmonic analysis on Euclidean spaces (42-XX) 12 Mechanics of particles and systems (70-XX) 11 Functions of a complex variable (30-XX) 11 Global analysis, analysis on manifolds (58-XX) 11 Quantum theory (81-XX) 7 General topology (54-XX) 5 Sequences, series, summability (40-XX) 5 Convex and discrete geometry (52-XX) 4 Mathematical logic and foundations (03-XX) 3 History and biography (01-XX) 3 Linear and multilinear algebra; matrix theory (15-XX) 3 Differential geometry (53-XX) 3 Manifolds and cell complexes (57-XX) 3 Classical thermodynamics, heat transfer (80-XX) 2 Algebraic geometry (14-XX) 2 Difference and functional equations (39-XX) 2 Approximations and expansions (41-XX) 2 Mechanics of deformable solids (74-XX) 2 Relativity and gravitational theory (83-XX) 2 Information and communication theory, circuits (94-XX) 1 General and overarching topics; collections (00-XX) 1 Nonassociative rings and algebras (17-XX) 1 Group theory and generalizations (20-XX) 1 Topological groups, Lie groups (22-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Abstract harmonic analysis (43-XX) 1 Astronomy and astrophysics (85-XX) 1 Geophysics (86-XX) ### Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata.	2022-08-09T17:59:18	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5175356864929199, "perplexity": 7264.063157623597}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882571056.58/warc/CC-MAIN-20220809155137-20220809185137-00039.warc.gz"}
https://en.wikibooks.org/wiki/High_School_Chemistry/Electron_Affinity	# High School Chemistry/Electron Affinity The final periodic trend for our discussion is electron affinity. We have talked about atomic structure, electronic configurations, size of the atoms and ionization energy. And now, the final periodic trend we will study is how an atom can gain an electron and the trends that exist in the Periodic Table. ## Lesson Objectives • Define electron affinity. • Describe the trend for electron affinity on the Periodic Table. ## The Energy Process When an Electron is Added to an Atom Atoms can gain or lose electrons. When an atom gains an electron, energy is given off and is known as the electron affinity. Electron affinity is defined as the energy released when an electron is added to a gaseous atom or ion. ${\displaystyle {\text{T}}+e^{-}\rightarrow {\text{T}}^{-}\,\!}$ When most reactions occur that involve the addition of an electron to a gaseous atom, potential energy is released. ${\displaystyle {\text{Br}}+e^{-}\,\!}$ ${\displaystyle \rightarrow \,\!}$ ${\displaystyle {\text{Br}}^{1-}\,\!}$ ${\displaystyle [{\text{Ar}}]4s^{2}4p^{5}\,\!}$ ${\displaystyle [{\text{Ar}}]4s^{2}4p^{6}\,\!}$ Let's look at the electron configurations of a few of the elements and the trend that develops within groups and periods. Take a look at Table 10.10, the electron affinity for the Halogen family. Table 10.10: Electron Affinities for Group 17 Element Electron Configuration Electron Affinity, kJ/mol Fluorine (F) [He]2s22p5 −328 Chlorine (Cl) [Ne]3s23p5 −349 Bromine (Br) [Ar]4s24p5 −325 Iodine (I) [Kr]5s25p5 −295 As you can see, the electron affinity generally decreases (becomes less negative) going down a group because of the increase in size of the atoms. Remember that the atoms located within a family but lower on the periodic table are larger since there are more electrons filling more energy levels. For example, an atom of chlorine is smaller than iodine; or, an atom of oxygen is smaller than sulfur. When an electron is added to a large atom, less energy is released because the electron cannot move as close to the nucleus as it can in a smaller atom. Therefore, as the atoms in a family get larger, the electron affinity gets smaller. There is an exception to this when it involves certain small atoms. Electron affinity for fluorine is less than chlorine most likely due to the electron-electron repulsions that occur between the electrons where n = 2. This phenomenon is observed in other families as well. For instance, the electron affinity for oxygen is less than the electron affinity for sulfur. Electron affinity of all of the elements in the second period is less than the ones below them due to the fact that the elements in the second period have such small electron clouds that electron repulsion is greater than that of the rest of the family. ## Nonmetals Tend to Have the Highest Electron Affinity Overall, the Periodic Table shows the general trend similar to the one below. Electron Affinities for Period 4 Main Group Elements Element Electron Configuration Electron Affinity Potassium (K) [Ar]4s1 −48 kJ/mol Calcium (Ca) [Ar]4s2 −2.4 kJ/mol Gallium (Ga) [Ar]4s24p1 −29 kJ/mol Germanium (Ge) [Ar]4s24p2 −118 kJ/mol Arsenic (As) [Ar]4s24p3 −77 kJ/mol Selenium (Se) [Ar]4s24p4 −195 kJ/mol Bromine (Br) [Ar]4s24p5 −325 kJ/mol Krypton (Kr) [Ar]4s24p6 0 kJ/mol The general trend in the electron affinity for atoms is almost the same as the trend for ionization energy. This is because both electron affinity and ionization energy are highly related to atomic size. Large atoms have low ionization energy and low electron affinity. Therefore, they tend to lose electrons and do not tend to gain electrons. Small atoms, in general, are the opposite. Since they are small, they have high ionization energies and high electron affinities. Therefore, the small atoms tend to gain electrons and tend not to lose electrons. The major exception to this rule are the noble gases. They are small atoms and do follow the general trend for ionization energies. The noble gases, however, do not follow the general trend for electron affinities. Even though the noble gases are small atoms, their outer energy levels are completely filled with electrons and therefore, an added electron cannot enter their outer most energy level. Any electrons added to a noble gas would have to be the first electron in a new (larger) energy level. This causes the noble gases to have essentially zero electron affinity. This concept is discussed more thoroughly in the next chapter. When atoms become ions, the process involves either the energy released through electron affinity or energy being absorbed with ionization energy. Therefore, the atoms that require a large amount of energy to release an electron will most likely be the atoms that give off the most energy while accepting an electron. In other words, non-metals will most easily gain electrons since they have large electron affinities and large ionization energies; and, metals will lose electrons since they have the low ionization energies and low electron affinities. Now let's add this last periodic trend to our Periodic Table representation and our periodic trends are complete. The development and arrangement of the Periodic Table of Elements is examined (free registration required). Video on Demand – The World of Chemistry – The Periodic Table. ## Lesson Summary • Electron affinity is the energy required (or released) when an electron is added to a gaseous atom or ion. Electron affinity generally increases going up a group and increases left to right across a period. • Non-metals tend to have the highest electron affinities. ## Review Questions 1. Define electron affinity and show an example equation. 2. Choose the element in each pair that has the lower electron affinity: (a) Li or N (b) Na or Cl (c) Ca or K (d) Mg or F 3. Why is the electron affinity for calcium much higher than that of potassium? 4. Draw a visual representation of the periodic table describing the trend of electron affinity. 5. Which of the following would have the largest electron affinity? (a) Se (b) F (c) Ne (d) Br 6. Which of the following would have the smallest electron affinity? (a) Na (b) Ne (c) Al (d) Rb 7. Place the following elements in order of increasing electron affinity: Te, Br, S, K, Ar. 8. Place the following elements in order of decreasing electron affinity: S, Sn, Pb, F, Cs. 9. Describe the trend that would occur for electron affinities for elements in Period 3. Are there any anomalies? Explain. 10. Comparing the electron affinity (EA) of sulfur, S, and phosphorus, P: (a) S has a higher EA because its radius is smaller. (b) P has a higher EA because its radius is smaller. (c) S has a higher EA because its p sub-shell is half full. (d) P has a higher EA because its p sub-shell is half full. (e) they have the same EA because they are next to each other in the Periodic Table. ## Vocabulary electron affinity The energy required to add an electron to a gaseous atom or ion. This material was adapted from the original CK-12 book that can be found here. This work is licensed under the Creative Commons Attribution-Share Alike 3.0 United States License	2023-03-23T08:17:03	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 6, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5767496228218079, "perplexity": 1194.6280295684232}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296945030.59/warc/CC-MAIN-20230323065609-20230323095609-00545.warc.gz"}
https://notes.aquiles.me/simoa/	# Simoa First published: Last Edited: Number of edits: Simoa stands for single-molecule arrays[] and essentially consists of an essay to detect very small concentrations of antigens, following protocols very similar to those of the Elisa tests. The general principle is like in the image below: Paramagnetic beads, coated with a known antibody can diffuse in the medium, capturing antigens. The process is the same as in the Sandwich ELISA (see: Elisa tests). They are later precipitated onto specific arrays in which only one bead fits. By looking at each well with and without the beads and with or without fluorescence, it is possible to conduct a digital elisa test. The method can detect as little as $$10^{-19}M$$under special conditions, or $$10^{-15}M = 10fM$$ in clinical conditions. See: why pushing sensitivity of assays. One of the core aspects of the Simoa devices is how to know if you have double binding events. In [], the authors present a statistical argument in which double binding events is almost negligible if binding (overall) is below 50%, as it follows a poissonian distribution. #### Backlinks These are the other notes that link to this one. #### Newsletter Join my experiment of better thinking and interesting discussions Aquiles Carattino This note you are reading is part of my digital garden. Follow the links to learn more, and remember that these notes evolve over time. After all, this website is not a blog. © 2021 Aquiles Carattino This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License Privacy Policy	2022-11-27T15:09:59	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.25704458355903625, "perplexity": 2530.657752945969}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446710409.16/warc/CC-MAIN-20221127141808-20221127171808-00392.warc.gz"}
https://www.legisquebec.gouv.qc.ca/en/version/cs/M-19%20?code=se:32_0_3&history=20211126	### M-19 - Act respecting the Ministère de la Justice 32.0.3. The following are credited to the Fund: (1) the sums transferred to it by the Minister of Justice out of the appropriations granted for that purpose by Parliament; (2) the sums collected under article 8.1 of the Code of Penal Procedure (chapter C-25.1), to the extent determined in that article; (2.1) the amount of the fines paid under sections 24 to 26 of the Act to promote access to justice through the establishment of the Service administratif de rajustement des pensions alimentaires pour enfants (chapter A-2.02); (3) the sums transferred to it by the Minister of Justice out of the sums credited to the general fund up to the amount of the sums paid by the Government of Canada under cost-sharing agreements related to projects or activities financed by the Fund; (4) the sums transferred to it by the Minister of Finance under section 53 or 54 of the Financial Administration Act (chapter A-6.001); (5) the gifts, legacies and other contributions paid into it to further the purpose of the Fund; and (6) the revenues generated by the sums credited to the Fund. 2012, c. 3, s. 1; 2012, c. 20, s. 51; 2015, c. 8, s. 346. 32.0.3. The following are credited to the Fund: (1) the sums transferred to it by the Minister of Justice out of the appropriations granted for that purpose by Parliament; (2) the sums collected under article 8.1 of the Code of Penal Procedure (chapter C-25.1), in the proportion determined in that article; (2.1) the amount of the fines paid under sections 24 to 26 of the Act to promote access to justice through the establishment of the Service administratif de rajustement des pensions alimentaires pour enfants (chapter A-2.02); (3) the sums transferred to it by the Minister of Justice out of the sums credited to the general fund up to the amount of the sums paid by the Government of Canada under cost-sharing agreements related to projects or activities financed by the Fund; (4) the sums transferred to it by the Minister of Finance under section 53 or 54 of the Financial Administration Act (chapter A-6.001); (5) the gifts, legacies and other contributions paid into it to further the purpose of the Fund; and (6) the revenues generated by the sums credited to the Fund. 2012, c. 3, s. 1; 2012, c. 20, s. 51. 32.0.3. The following are credited to the Fund: (1) the sums transferred to it by the Minister of Justice out of the appropriations granted for that purpose by Parliament; (2) the sums collected under article 8.1 of the Code of Penal Procedure (chapter C-25.1), in the proportion determined in that article; (3) the sums transferred to it by the Minister of Justice out of the sums credited to the general fund up to the amount of the sums paid by the Government of Canada under cost-sharing agreements related to projects or activities financed by the Fund; (4) the sums transferred to it by the Minister of Finance under section 53 or 54 of the Financial Administration Act (chapter A-6.001); (5) the gifts, legacies and other contributions paid into it to further the purpose of the Fund; and (6) the revenues generated by the sums credited to the Fund. 2012, c. 3, s. 1. 32.0.3. The following are credited to the Fund: (1) the sums transferred to it by the Minister of Justice out of the appropriations granted for that purpose by Parliament; Not in force (2) the sums collected under article 8.1 of the Code of Penal Procedure (chapter C-25.1), in the proportion determined in that article; (3) the sums transferred to it by the Minister of Justice out of the sums credited to the general fund up to the amount of the sums paid by the Government of Canada under cost-sharing agreements related to projects or activities financed by the Fund; (4) the sums transferred to it by the Minister of Finance under section 53 or 54 of the Financial Administration Act (chapter A-6.001); (5) the gifts, legacies and other contributions paid into it to further the purpose of the Fund; and (6) the revenues generated by the sums credited to the Fund. 2012, c. 3, s. 1.	2022-05-20T04:53:29	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8087486028671265, "perplexity": 5731.105375987686}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662531352.50/warc/CC-MAIN-20220520030533-20220520060533-00594.warc.gz"}
https://indico.fnal.gov/event/ANLHEP8/other-view?fr=no&detailLevel=contribution&view=standard&showSession=all&showDate=all	# Deficit Spending and the Cluster Baryon Budget chaired by Thursday, February 28, 2013 from to (US/Central) at Building 362 ( F-108 ) Description The deep gravitational potential wells of clusters of galaxies should capture fair samples of the total baryon fraction of the Universe, unless other physical processes drive baryons out of clusters. Thus precision measurements of the baryon fraction, particularly as a function of cluster halo mass, can reveal the history of baryon flux into and out of clusters. How those baryons are then apportioned between stars and intracluster gas --- the star formation efficiency --- informs models of cluster assembly and massive galaxy evolution, as well as efforts to use the cluster gas fraction to constrain the mass density and dark energy equation of state parameters. Even the partitioning of the stellar baryons alone, in and out of galaxies, tests models of cluster galaxy evolution, as intracluster stars are the final, unambiguous signature of stars stripped from cluster galaxies. We have discovered that intracluster stars are a significant part of the stellar baryons in clusters and poorer groups of galaxies. I will present new work characterizing the properties of this previously unexplored component, as well as the consequences for the cluster baryon budget and its relationship to the Universal WMAP value. Material: Go to day	2019-10-23T19:03:29	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4842695891857147, "perplexity": 1850.4761925908406}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570987835748.66/warc/CC-MAIN-20191023173708-20191023201208-00344.warc.gz"}
https://www.bnl.gov/event.php?q=15852	# CFNS seminar ## "Era of Jet-SubStructure and its utility in high energy collisions" #### Presented by Raghav Kunnawalkam Elayavalli, Wayne State University Thursday, August 6, 2020, 4:00 pm — https://bluejeans.com/494177937 Jets, originating from hard scatterings of quarks/gluons (partons), have been established as a very powerful tool of study in high energy colliders. Measurements utilizing jets have been performed at nearly all major collider experiments as probes of the standard model (and BSM), spin, polarization, fundamental QCD and also played an important role in studies of the Quark-Gluon Plasma (QGP) via parton energy loss or jet quenching. Since jet evolution in vacuum is intimately dependent on both the momentum and angular scales, disentangling these scales via jet substructure (JSS) tools can lead to a more differential study of the parton shower. In essence, understanding parton evolution and JSS in vacuum is a necessary prerequisite for qualitatively describing how jets are quenched in the QGP, which in turn leads to extracting the QGP microscopic properties via jet-tomography. In this talk, I will introduce JSS and present recent measurements from the STAR collaboration of JSS observables in p-p, p+Au and Au-Au collisions at $\sqrt{s_{NN}} = 200$ GeV. These results are aimed at describing the vacuum parton shower and study the impact of cold and hot nuclear matter effects differentially with jet topology. I will also discuss an important application JSS whereby we isolated a special selection of jets in heavy ion collisions who's energy loss mechanism can then be further studied in a differential fashion. I will conclude the talk by contextualizing these measurements and briefly discuss some ongoing work related to upcoming heavy ion runs at RHIC and at the recently approved EIC, where JSS can contribute towards studies of quantum entanglement and hadronization within jets in a clean environment. Hosted by: Jinlong Zhang 15852 \| INT/EXT \| Events Calendar	2021-06-13T17:57:09	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.650912880897522, "perplexity": 2410.0673637342875}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623487610196.46/warc/CC-MAIN-20210613161945-20210613191945-00340.warc.gz"}
https://www.zbmath.org/authors/?q=ai%3Amuller.stefan.1	## Müller, Stefan Compute Distance To: Author ID: muller.stefan.1 Published as: Müller, Stefan; Müller, S. Homepage: http://www.hcm.uni-bonn.de/people/profile/stefan-mueller/ External Links: MGP · Wikidata · Google Scholar · dblp · GND · IdRef Awards: EMS Prize (1992) Documents Indexed: 138 Publications since 1987 5 Contributions as Editor · 1 Further Contribution Co-Authors: 74 Co-Authors with 122 Joint Publications 1,949 Co-Co-Authors all top 5 ### Co-Authors 20 single-authored 17 Conti, Sergio 11 Dolzmann, Georg 11 Šverák, Vladimír 10 DeSimone, Antonio 9 Mora, Maria Giovanna 8 James, Richard D. 8 Kohn, Robert Vita 7 Garroni, Adriana 7 Otto, Felix 6 Fonseca, Irene 5 Friesecke, Gero 5 Kirchheim, Bernd 5 Struwe, Michael 4 Ortiz, Michael 4 Spector, Scott J. 3 Abels, Helmut 3 Ball, John MacLeod 3 Chaudhuri, Nirmalendu 3 De Lellis, Camillo 3 Flucher, Martin 3 Hungerbuhler, Norbert 3 Kienzler, Reinhold 3 McDowell, David L. 3 Palombaro, Mariapia 3 Werner, Ewald A. 2 Ben Belgacem, Hafedh 2 Freire, Alexandre 2 Geymonat, Giuseppe 2 Kopecká, Eva 2 Lewicka, Marta 2 Maggi, Francesco 2 Müller, Paul F. X. 2 Olbermann, Heiner 2 Pakzad, Mohammad Reza 2 Schweiger, Florian 2 Tang, Qi 2 Triantafyllidis, Nicolas 2 Yan, Baisheng 1 Adams, Stefan 1 Alberti, Giovanni 1 Bourne, David P. 1 Carstensen, Carsten 1 Cotar, Codina 1 Dacorogna, Bernard 1 Deuschel, Jean-Dominique 1 Dmitrieva, Olga 1 Dondl, Patrick Werner 1 Esteban, Maria J. 1 Faraco, Daniel 1 Francfort, Gilles A. 1 Fusco, Nicola 1 Giuliani, Alessandro 1 Koop, Andreas 1 Kotecký, Roman 1 Kröner, Dietmar 1 Lecumberry, Myriam 1 Lee, Jihoon 1 Leoni, Giovanni 1 Lewintan, Peter 1 Lienstromberg, Christina 1 Marcellini, Paolo 1 Mielke, Alexander 1 Neff, Patrizio 1 Neukamm, Stefan 1 Pedregal, Pablo 1 Raabe, Dierk 1 Rieger, Marc Oliver 1 Röger, Matthias 1 Romeo, Mario 1 Scardia, Lucia 1 Schäfer, Rudolf 1 Schlömerkemper, Anja 1 Schroeter, Brian M. 1 Schultz, M. G. 1 Schupp, Bernhard 1 Sivaloganathan, Jeyabal 1 Süli, Endre E. 1 Sychev, Mikhail A. 1 Zeppieri, Caterina Ida all top 5 ### Serials 15 Archive for Rational Mechanics and Analysis 15 Calculus of Variations and Partial Differential Equations 11 SIAM Journal on Mathematical Analysis 8 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 6 Comptes Rendus. Mathématique. Académie des Sciences, Paris 5 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 5 Oberwolfach Reports 4 Communications on Pure and Applied Mathematics 4 Comptes Rendus de l’Académie des Sciences. Série I 3 Indiana University Mathematics Journal 3 Journal of Differential Geometry 3 Journal of Functional Analysis 3 Journal für die Reine und Angewandte Mathematik 3 Communications in Partial Differential Equations 3 Journal of Nonlinear Science 2 Communications in Mathematical Physics 2 Mathematische Zeitschrift 2 Topological Methods in Nonlinear Analysis 2 Journal of the European Mathematical Society (JEMS) 1 Computer Methods in Applied Mechanics and Engineering 1 Journal of Mathematical Analysis and Applications 1 Journal of the Mechanics and Physics of Solids 1 Mitteilungen der Deutschen Mathematiker-Vereinigung (DMV) 1 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 1 Inventiones Mathematicae 1 Journal of Differential Equations 1 Manuscripta Mathematica 1 Mathematische Annalen 1 Meccanica 1 Numerische Mathematik 1 Rendiconti del Seminario Matemàtico e Fisico di Milano 1 SIAM Journal on Numerical Analysis 1 Transactions of the American Mathematical Society 1 Revista Matemática Iberoamericana 1 Journal of the American Mathematical Society 1 IMRN. International Mathematics Research Notices 1 The Journal of Geometric Analysis 1 Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences 1 Bulletin of the American Mathematical Society. New Series 1 Continuum Mechanics and Thermodynamics 1 Tatra Mountains Mathematical Publications 1 NoDEA. Nonlinear Differential Equations and Applications 1 Documenta Mathematica 1 Vietnam Journal of Mathematics 1 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 1 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 Annals of Mathematics. Second Series 1 Multiscale Modeling & Simulation 1 GAMM-Mitteilungen 1 Lecture Notes in Mathematics 1 Bollettino dell’Unione Matematica Italiana all top 5 ### Fields 76 Mechanics of deformable solids (74-XX) 57 Partial differential equations (35-XX) 51 Calculus of variations and optimal control; optimization (49-XX) 16 Statistical mechanics, structure of matter (82-XX) 12 Functional analysis (46-XX) 8 Real functions (26-XX) 7 General and overarching topics; collections (00-XX) 7 Global analysis, analysis on manifolds (58-XX) 6 Differential geometry (53-XX) 5 Harmonic analysis on Euclidean spaces (42-XX) 4 Ordinary differential equations (34-XX) 4 Numerical analysis (65-XX) 4 Fluid mechanics (76-XX) 3 Convex and discrete geometry (52-XX) 2 Potential theory (31-XX) 2 Operator theory (47-XX) 2 Probability theory and stochastic processes (60-XX) 2 Optics, electromagnetic theory (78-XX) 1 Measure and integration (28-XX) 1 Functions of a complex variable (30-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Difference and functional equations (39-XX) 1 Geometry (51-XX) ### Citations contained in zbMATH Open 131 Publications have been cited 3,780 times in 2,192 Documents Cited by Year A theorem on geometric rigidity and the derivation of nonlinear plate theory from three-dimensional elasticity. Zbl 1021.74024 Friesecke, Gero; James, Richard D.; Müller, Stefan 2002 A hierarchy of plate models derived from nonlinear elasticity by gamma-convergence. Zbl 1100.74039 Friesecke, Gero; James, Richard D.; Müller, Stefan 2006 Variational models for microstructure and phase transitions. Zbl 0968.74050 Müller, Stefan 1999 Homogenization of nonconvex integral functionals and cellular elastic materials. Zbl 0629.73009 Müller, Stefan 1987 $$\mathcal A$$-quasiconvexity, lower semicontinuity, and Young measures. Zbl 0940.49014 Fonseca, Irene; Müller, Stefan 1999 Homogenization of nonlinearly elastic materials, microscopic bifurcation and macroscopic loss of rank-one convexity. Zbl 0801.73008 Geymonat, Giuseppe; Müller, Stefan; Triantafyllidis, Nicolas 1993 Convex integration for Lipschitz mappings and counterexamples to regularity. Zbl 1083.35032 Müller, S.; Šverák, V. 2003 Surface energy and microstructure in coherent phase transitions. Zbl 0803.49007 Kohn, Robert V.; Müller, Stefan 1994 An existence theory for nonlinear elasticity that allows for cavitation. Zbl 0836.73025 Müller, Stefan; Spector, Scott J. 1995 Higher integrability of determinants and weak convergence in $$L^ 1$$. Zbl 0713.49004 Müller, Stefan 1990 A uniqueness proof for the Wulff theorem. Zbl 0752.49019 Fonseca, Irene; Müller, Stefan 1991 Derivation of nonlinear bending theory for shells from three-dimensional nonlinear elasticity by Gamma-convergence. Zbl 1140.74481 Friesecke, Gero; James, Richard D.; Mora, Maria Giovanna; Müller, Stefan 2003 Quasi-convex integrands and lower semicontinuity in $$L^ 1$$. Zbl 0764.49012 Fonseca, Irene; Müller, Stefan 1992 Analysis of concentration and oscillation effects generated by gradients. Zbl 0920.49009 Fonseca, Irene; Müller, Stefan; Pedregal, Pablo 1998 Relaxation of quasiconvex functionals in $$BV(\Omega, \mathbb{R}^ N)$$ for integrands $$f(x, u, \bigtriangledown u)$$. Zbl 0788.49039 Fonseca, Irene; Müller, Stefan 1993 Singular perturbations as a selection criterion for periodic minimizing sequences. Zbl 0821.49015 Müller, Stefan 1993 $$\Gamma$$-limit of a phase-field model of dislocations. Zbl 1094.82008 Garroni, A.; Müller, S. 2005 On a new class of elastic deformations not allowing for cavitation. Zbl 0863.49002 Müller, S.; Qi, Tang; Yan, B. S. 1994 A reduced theory for thin-film micromagnetics. Zbl 1027.82042 DeSimone, Antonio; Kohn, Robert V.; Müller, Stefan; Otto, Felix 2002 Convex integration with constraints and applications to phase transitions and partial differential equations. Zbl 0953.35042 Müller, S.; Šverák, V. 1999 Uniqueness and maximal regularity for nonlinear elliptic systems of $$n$$-Laplace type with measure valued right hand side. Zbl 0937.35065 Dolzmann, Georg; Hungerbühler, Norbert; Müller, Stefan 2000 A variational model for dislocations in the line tension limit. Zbl 1158.74365 2006 Derivation of the nonlinear bending-torsion theory for inextensible rods by $$\Gamma$$-convergence. Zbl 1053.74027 Mora, Maria Giovanna; Müller, Stefan 2003 A compactness result in the gradient theory of phase transitions. Zbl 0986.49009 DeSimone, Antonio; Müller, Stefan; Kohn, Robert V.; Otto, Felix 2001 Det$$=\det$$. A remark on the distributional determinant. Zbl 0717.46033 Müller, Stefan 1990 Optimal rigidity estimates for nearly umbilical surfaces. Zbl 1087.53004 de Lellis, Camillo; Müller, Stefan 2005 Microstructures with finite surface energy: The two-well problem. Zbl 0846.73054 Dolzmann, Georg; Müller, Stefan 1995 Estimates for Green’s matrices of elliptic systems by $$L^ p$$ theory. Zbl 0846.35040 Dolzmann, G.; Müller, S. 1995 Studying nonlinear PDE by geometry in matrix space. Zbl 1290.35097 Kirchheim, Bernd; Müller, Stefan; Šverák, Vladimír 2003 Nonlinear elliptic systems with measure-valued right hand side. Zbl 0895.35029 Dolzmann, Georg; Hungerbühler, Norbert; Müller, Stefan 1997 Recent analytical developments in micromagnetics. Zbl 1151.35426 DeSimone, Antonio; Kohn, Robert V.; Müller, Stefan; Otto, Felix 2006 Attainment results for the two-well problem by convex integration. Zbl 0930.35038 1996 On surfaces of finite total curvature. Zbl 0853.53003 Müller, S.; Šverák, V. 1995 A new approach to variational problems with multiple scales. Zbl 1021.49012 Alberti, Giovanni; Müller, Stefan 2001 Energy scaling of compressed elastic films – three-dimensional elasticity and reduced theories. Zbl 1041.74048 Ben Belgacem, Hafedh; Conti, Sergio; DeSimone, Antonio; Müller, Stefan 2002 Lower semicontinuity and existence of minimizers in incremental finite-strain elastoplasticity. Zbl 1102.74006 Mielke, Alexander; Müller, Stefan 2006 Optimal existence theorems for nonhomogeneous differential inclusions. Zbl 0989.49012 Müller, S.; Sychev, M. A. 2001 Hardy spaces and the two-dimensional Euler equations with nonnegative vorticity. Zbl 0802.35120 Evans, L. C.; Müller, S. 1994 Rigorous derivation of nonlinear plate theory and geometric rigidity. Zbl 1012.74043 Friesecke, Gero; Müller, Stefan; James, Richard D. 2002 Rank-one convexity implies quasiconvexity on diagonal matrices. Zbl 1055.49506 Müller, Stefan 1999 Rigourous bounds for the Föppl-von Kármán theory of isotropically compressed plates. Zbl 1015.74029 Ben Belgacem, H.; Conti, S.; DeSimone, A.; Müller, S. 2000 Invertibility and a topological property of Sobolev maps. Zbl 0855.73028 Müller, Stefan; Spector, Scott J.; Tang, Qi 1996 Weak continuity of determinants and nonlinear elasticity. (Continuité faible des déterminants et applications à l’élasticité non linéaire). Zbl 0679.34051 Müller, Stefan 1988 Local stress regularity in scalar nonconvex variational problems. Zbl 1012.49027 Carstensen, Carsten; Müller, Stefan 2002 A nonlinear model for inextensible rods as a low energy $$\varGamma$$-limit of three-dimensional nonlinear elasticity. Zbl 1109.74028 Mora, Maria Giovanna; Müller, Stefan 2004 The $$p$$-harmonic system with measure-valued right hand side. Zbl 0879.35052 Dolzmann, Georg; Hungerbühler, Norbert; Müller, Stefan 1997 Magnetic microstructures – a paradigm of multiscale problems. Zbl 0991.82038 DeSimone, Antonio; Kohn, Robert V.; Müller, Stefan; Otto, Felix 2000 The uniform Korn-Poincaré inequality in thin domains. Zbl 1253.74055 Lewicka, Marta; Müller, Stefan 2011 A surprising higher integrability property of mappings with positive determinant. Zbl 0689.49006 Müller, Stefan 1989 Data-driven problems in elasticity. Zbl 1402.35276 Conti, S.; Müller, S.; Ortiz, M. 2018 The Föppl-von Kármán plate theory as a low energy $$\Gamma$$-limit of nonlinear elasticity. Zbl 1041.74043 Friesecke, Gero; James, Richard D.; Müller, Stefan 2002 Hardy space methods for nonlinear partial differential equations. Zbl 0811.35025 Müller, Stefan 1994 Sufficient conditions for the validity of the Cauchy-Born rule close to $$\mathrm{SO}(n)$$. Zbl 1146.74006 Conti, Sergio; Dolzmann, Georg; Kirchheim, Bernd; Müller, Stefan 2006 Regularity properties of isometric immersions. Zbl 1082.58010 2005 A $$C^{0}$$ estimate for nearly umbilical surfaces. Zbl 1100.53005 De Lellis, Camillo; Müller, Stefan 2006 Internal variables and fine-scale oscillations in micromagnetics. Zbl 0814.73054 James, R. D.; Müller, Stefan 1994 Unexpected solutions of first and second order partial differential equations. Zbl 0896.35029 1998 Singular kernels, multiscale decomposition of microstructure, and dislocation models. Zbl 1251.74006 Conti, Sergio; Garroni, Adriana; Müller, Stefan 2011 Stability of slender bodies under compression and validity of the von Kármán theory. Zbl 1200.74060 Lecumberry, Myriam; Müller, Stefan 2009 On quasiconvex functions which are homogeneous of degree 1. Zbl 0736.26006 Müller, Stefan 1992 On the $$\Gamma$$-convergence of discrete dynamics and variational integrators. Zbl 1136.37350 Müller, S.; Ortiz, M. 2004 Convergence of equilibria of three-dimensional thin elastic beams. Zbl 1142.74022 Mora, M. G.; Müller, S. 2008 On the singular support of the distributional determinant. Zbl 0792.46027 Müller, Stefan 1993 A sharp version of Zhang’s theorem on truncating sequences of gradients. Zbl 0942.49013 Müller, Stefan 1999 The time-dependent von Kármán plate equation as a limit of 3d nonlinear elasticity. Zbl 1346.74110 Abels, Helmut; Mora, Maria Giovanna; Müller, Stefan 2011 Convergence of equilibria of thin elastic plates – the von Kármán case. Zbl 1141.74034 2008 Two-dimensional modelling of soft ferromagnetic films. Zbl 1065.74028 DeSimone, Antonio; Kohn, Robert V.; Müller, Stefan; Otto, Felix; Schäfer, Rudolf 2001 Rigidity estimate for two incompatible wells. Zbl 1086.49010 Chaudhuri, Nirmalendu; Müller, Stefan 2004 Conical singularities in thin elastic sheets. Zbl 1285.49031 Müller, Stefan; Olbermann, Heiner 2014 The div-curl lemma for sequences whose divergence and curl are compact in $$W^{-1,1}$$. Zbl 1235.46034 Conti, Sergio; Dolzmann, Georg; Müller, Stefan 2011 Korn’s second inequality and geometric rigidity with mixed growth conditions. Zbl 1295.35369 Conti, Sergio; Dolzmann, Georg; Müller, Stefan 2014 Strict convexity of the free energy for a class of non-convex gradient models. Zbl 1173.82010 Cotar, Codina; Deuschel, Jean-Dominique; Müller, Stefan 2009 Parabolic systems with nowhere smooth solutions. Zbl 1116.35059 Müller, Stefan; Rieger, Marc Oliver; Šverák, Vladimír 2005 Sobolev maps with integer degree and applications to Skyrme’s problem. Zbl 0757.49010 Esteban, Maria J.; Müller, Stefan 1992 $$\mathcal A$$-quasiconvexity: weak-star convergence and the gap. Zbl 1064.49016 Fonseca, Irene; Leoni, Giovanni; Müller, Stefan 2004 Weak compactness of wave maps and harmonic maps. Zbl 0924.58011 Freire, Alexandre; Müller, Stefan; Struwe, Michael 1998 The influence of surface energy on stress-free microstructures in shape memory alloys. Zbl 0835.73061 Dolzmann, Georg; Müller, Stefan 1995 Rigorous derivation of Föppl’s theory for clamped elastic membranes leads to relaxation. Zbl 1146.74025 Conti, Sergio; Maggi, Francesco; Müller, Stefan 2007 Convergence of equilibria of planar thin elastic beams. Zbl 1125.74026 Mora, M. G.; Müller, S.; Schultz, M. G. 2007 Combined effects of homogenization and singular perturbations in elasticity. Zbl 0802.35007 Francfort, G. A.; Müller, S. 1994 Repulsive interaction of Néel walls, and the internal length scale of the cross-tie wall. Zbl 1059.82046 DeSimone, Antonio; Kohn, Robert V.; Müller, Stefan; Otto, Felix 2003 Rank-one convex functions on $$2\times 2$$ symmetric matrices and laminates on rank-three lines. Zbl 1135.26301 Conti, S.; Faraco, D.; Maggi, F.; Müller, S. 2005 Global existence of wave maps in 1+2 dimensions with finite energy data. Zbl 0896.35086 Müller, Stefan; Struwe, Michael 1996 Weak convergence of wave maps from $$(1+2)$$-dimensional Minkowski space to Riemannian manifolds. Zbl 0906.35061 Freire, Alexandre; Müller, Stefan; Struwe, Michael 1997 Radial symmetry and decay rate of variational ground states in the zero mass case. Zbl 0908.35005 Flucher, M.; Müller, S. 1998 On the commutability of homogenization and linearization in finite elasticity. Zbl 1262.74029 Müller, Stefan; Neukamm, Stefan 2011 On the optimal constants in Korn’s and geometric rigidity estimates in bounded and unbounded domains, under Neumann boundary conditions. Zbl 1405.74010 Lewicka, Marta; Müller, Stefan 2016 Large time existence for thin vibrating plates. Zbl 1247.74019 Abels, Helmut; Mora, Maria Giovanna; Müller, Stefan 2011 Concentration of low energy extremals: Identification of concentration points. Zbl 1004.35040 Flucher, M.; Garroni, A.; Müller, S. 2002 Sharp stability results for almost conformal maps in even dimensions. Zbl 0966.35016 Müller, Stefan; Šverák, Vladimir; Yan, Baisheng 1999 The two-well problem in three dimensions. Zbl 0956.74039 Dolzmann, Georg; Kirchheim, Bernd; Müller, Stefan; Šverák, Vladimir 2000 Striped periodic minimizers of a two-dimensional model for martensitic phase transitions. Zbl 1448.74082 Giuliani, Alessandro; Müller, Stefan 2012 Existence of minimizers for a polyconvex energy in a crystal with dislocations. Zbl 1134.74015 Müller, Stefan; Palombaro, Mariapia 2008 Mathematical problems in thin elastic sheets: scaling limits, packing, crumpling and singularities. Zbl 1372.35003 Müller, Stefan 2017 Concentration of low energy extremals. Zbl 0938.35042 Flucher, M.; Müller, S. 1999 An isoperimetric estimate and $$W^{1,p}$$-quasiconvexity in nonlinear elasticity. Zbl 0929.74013 Müller, Stefan; Sivaloganathan, Jeyabal; Spector, Scott J. 1999 Confined structures of least bending energy. Zbl 1296.53127 Müller, Stefan; Röger, Matthias 2014 Compensated compactness, separately convex functions and interpolatory estimates between Riesz transforms and Haar projections. Zbl 1230.49009 Lee, Jihoon; Müller, Paul F. X.; Müller, Stefan 2011 Derivation of a rod theory for biphase materials with dislocations at the interface. Zbl 1274.74064 Müller, Stefan; Palombaro, Mariapia 2013 Data-driven finite elasticity. Zbl 1437.35654 Conti, S.; Müller, S.; Ortiz, M. 2020 Korn inequalities for incompatible tensor fields in three space dimensions with conformally invariant dislocation energy. Zbl 1471.35009 Lewintan, Peter; Müller, Stefan; Neff, Patrizio 2021 Data-driven finite elasticity. Zbl 1437.35654 Conti, S.; Müller, S.; Ortiz, M. 2020 Optimal-order finite difference approximation of generalized solutions to the biharmonic equation in a cube. Zbl 1471.65172 Müller, Stefan; Schweiger, Florian; Süli, Endre 2020 Local strong solutions to a quasilinear degenerate fourth-order thin-film equation. Zbl 1445.35198 Lienstromberg, Christina; Müller, Stefan 2020 Symmetric div-quasiconvexity and the relaxation of static problems. Zbl 1434.74010 Conti, S.; Müller, S.; Ortiz, M. 2020 Estimates for the Green’s function of the discrete Bilaplacian in dimensions 2 and 3. Zbl 1422.65324 Müller, Stefan; Schweiger, Florian 2019 Data-driven problems in elasticity. Zbl 1402.35276 Conti, S.; Müller, S.; Ortiz, M. 2018 Mathematical problems in thin elastic sheets: scaling limits, packing, crumpling and singularities. Zbl 1372.35003 Müller, Stefan 2017 Energy bounds for a compressed elastic film on a substrate. Zbl 1387.74069 Bourne, David P.; Conti, Sergio; Müller, Stefan 2017 Homogenization of vector-valued partition problems and dislocation cell structures in the plane. Zbl 1469.74095 Conti, Sergio; Garroni, Adriana; Müller, Stefan 2017 On the optimal constants in Korn’s and geometric rigidity estimates in bounded and unbounded domains, under Neumann boundary conditions. Zbl 1405.74010 Lewicka, Marta; Müller, Stefan 2016 Gradient theory for geometrically nonlinear plasticity via the homogenization of dislocations. Zbl 1456.74018 Müller, Stefan; Scardia, Lucia; Zeppieri, Caterina Ida 2015 Microstructure in plasticity, a comparison between theory and experiment. Zbl 1370.74026 Dmitrieva, Olga; Raabe, Dierk; Müller, Stefan; Dondl, Patrick W. 2015 Conical singularities in thin elastic sheets. Zbl 1285.49031 Müller, Stefan; Olbermann, Heiner 2014 Korn’s second inequality and geometric rigidity with mixed growth conditions. Zbl 1295.35369 Conti, Sergio; Dolzmann, Georg; Müller, Stefan 2014 Confined structures of least bending energy. Zbl 1296.53127 Müller, Stefan; Röger, Matthias 2014 Almost conical deformations of thin sheets with rotational symmetry. Zbl 1290.49087 Müller, Stefan; Olbermann, Heiner 2014 On a differential inclusion related to the Born-Infeld equations. Zbl 1301.35226 Müller, Stefan; Palombaro, Mariapia 2014 Derivation of a rod theory for biphase materials with dislocations at the interface. Zbl 1274.74064 Müller, Stefan; Palombaro, Mariapia 2013 Finite range decomposition for families of gradient Gaussian measures. Zbl 1263.60047 Adams, Stefan; Kotecký, Roman; Müller, Stefan 2013 Striped periodic minimizers of a two-dimensional model for martensitic phase transitions. Zbl 1448.74082 Giuliani, Alessandro; Müller, Stefan 2012 The uniform Korn-Poincaré inequality in thin domains. Zbl 1253.74055 Lewicka, Marta; Müller, Stefan 2011 Singular kernels, multiscale decomposition of microstructure, and dislocation models. Zbl 1251.74006 Conti, Sergio; Garroni, Adriana; Müller, Stefan 2011 The time-dependent von Kármán plate equation as a limit of 3d nonlinear elasticity. Zbl 1346.74110 Abels, Helmut; Mora, Maria Giovanna; Müller, Stefan 2011 The div-curl lemma for sequences whose divergence and curl are compact in $$W^{-1,1}$$. Zbl 1235.46034 Conti, Sergio; Dolzmann, Georg; Müller, Stefan 2011 On the commutability of homogenization and linearization in finite elasticity. Zbl 1262.74029 Müller, Stefan; Neukamm, Stefan 2011 Large time existence for thin vibrating plates. Zbl 1247.74019 Abels, Helmut; Mora, Maria Giovanna; Müller, Stefan 2011 Compensated compactness, separately convex functions and interpolatory estimates between Riesz transforms and Haar projections. Zbl 1230.49009 Lee, Jihoon; Müller, Paul F. X.; Müller, Stefan 2011 Monotone curves. Zbl 1238.46017 Kirchheim, Bernd; Kopecká, Eva; Müller, Stefan 2011 Stability of slender bodies under compression and validity of the von Kármán theory. Zbl 1200.74060 Lecumberry, Myriam; Müller, Stefan 2009 Strict convexity of the free energy for a class of non-convex gradient models. Zbl 1173.82010 Cotar, Codina; Deuschel, Jean-Dominique; Müller, Stefan 2009 Do projections stay close together? Zbl 1160.51016 Kirchheim, Bernd; Kopecká, Eva; Müller, Stefan 2009 Convergence of equilibria of three-dimensional thin elastic beams. Zbl 1142.74022 Mora, M. G.; Müller, S. 2008 Convergence of equilibria of thin elastic plates – the von Kármán case. Zbl 1141.74034 2008 Existence of minimizers for a polyconvex energy in a crystal with dislocations. Zbl 1134.74015 Müller, Stefan; Palombaro, Mariapia 2008 Rigorous derivation of Föppl’s theory for clamped elastic membranes leads to relaxation. Zbl 1146.74025 Conti, Sergio; Maggi, Francesco; Müller, Stefan 2007 Convergence of equilibria of planar thin elastic beams. Zbl 1125.74026 Mora, M. G.; Müller, S.; Schultz, M. G. 2007 Derivation of a rod theory for multiphase materials. Zbl 1105.74016 Mora, Maria Giovanna; Müller, Stefan 2007 Scaling of the energy for thin martensitic films. Zbl 1108.74039 Chaudhuri, Nirmalendu; Müller, Stefan 2007 A hierarchy of plate models derived from nonlinear elasticity by gamma-convergence. Zbl 1100.74039 Friesecke, Gero; James, Richard D.; Müller, Stefan 2006 A variational model for dislocations in the line tension limit. Zbl 1158.74365 2006 Recent analytical developments in micromagnetics. Zbl 1151.35426 DeSimone, Antonio; Kohn, Robert V.; Müller, Stefan; Otto, Felix 2006 Lower semicontinuity and existence of minimizers in incremental finite-strain elastoplasticity. Zbl 1102.74006 Mielke, Alexander; Müller, Stefan 2006 Sufficient conditions for the validity of the Cauchy-Born rule close to $$\mathrm{SO}(n)$$. Zbl 1146.74006 Conti, Sergio; Dolzmann, Georg; Kirchheim, Bernd; Müller, Stefan 2006 A $$C^{0}$$ estimate for nearly umbilical surfaces. Zbl 1100.53005 De Lellis, Camillo; Müller, Stefan 2006 $$\Gamma$$-limit of a phase-field model of dislocations. Zbl 1094.82008 Garroni, A.; Müller, S. 2005 Optimal rigidity estimates for nearly umbilical surfaces. Zbl 1087.53004 de Lellis, Camillo; Müller, Stefan 2005 Regularity properties of isometric immersions. Zbl 1082.58010 2005 Parabolic systems with nowhere smooth solutions. Zbl 1116.35059 Müller, Stefan; Rieger, Marc Oliver; Šverák, Vladimír 2005 Rank-one convex functions on $$2\times 2$$ symmetric matrices and laminates on rank-three lines. Zbl 1135.26301 Conti, S.; Faraco, D.; Maggi, F.; Müller, S. 2005 Self-similar folding patterns and energy scaling in compressed elastic sheets. Zbl 1082.74030 Conti, Sergio; DeSimone, Antonio; Müller, Stefan 2005 A nonlinear model for inextensible rods as a low energy $$\varGamma$$-limit of three-dimensional nonlinear elasticity. Zbl 1109.74028 Mora, Maria Giovanna; Müller, Stefan 2004 On the $$\Gamma$$-convergence of discrete dynamics and variational integrators. Zbl 1136.37350 Müller, S.; Ortiz, M. 2004 Rigidity estimate for two incompatible wells. Zbl 1086.49010 Chaudhuri, Nirmalendu; Müller, Stefan 2004 $$\mathcal A$$-quasiconvexity: weak-star convergence and the gap. Zbl 1064.49016 Fonseca, Irene; Leoni, Giovanni; Müller, Stefan 2004 Convex integration for Lipschitz mappings and counterexamples to regularity. Zbl 1083.35032 Müller, S.; Šverák, V. 2003 Derivation of nonlinear bending theory for shells from three-dimensional nonlinear elasticity by Gamma-convergence. Zbl 1140.74481 Friesecke, Gero; James, Richard D.; Mora, Maria Giovanna; Müller, Stefan 2003 Derivation of the nonlinear bending-torsion theory for inextensible rods by $$\Gamma$$-convergence. Zbl 1053.74027 Mora, Maria Giovanna; Müller, Stefan 2003 Studying nonlinear PDE by geometry in matrix space. Zbl 1290.35097 Kirchheim, Bernd; Müller, Stefan; Šverák, Vladimír 2003 Repulsive interaction of Néel walls, and the internal length scale of the cross-tie wall. Zbl 1059.82046 DeSimone, Antonio; Kohn, Robert V.; Müller, Stefan; Otto, Felix 2003 Rank-one convexity implies quasi-convexity on certain hypersurfaces. Zbl 1054.49018 Chaudhuri, Nirmalendu; Müller, Stefan 2003 Multiscale modeling of materials – the role of analysis. Zbl 1065.74056 Conti, Sergio; DeSimone, Antonio; Dolzmann, Georg; Müller, Stefan; Otto, Felix 2003 Concentration phenomena for the volume functional in unbounded domains: identification of concentration points. Zbl 1161.49305 Garroni, A.; Müller, S. 2003 Polyconvexity equals rank-one convexity for connected isotropic sets in $$\mathbb M^{2\times 2}$$. Zbl 1050.49010 Conti, Sergio; De Lellis, Camillo; Müller, Stefan; Romeo, Mario 2003 A theorem on geometric rigidity and the derivation of nonlinear plate theory from three-dimensional elasticity. Zbl 1021.74024 Friesecke, Gero; James, Richard D.; Müller, Stefan 2002 A reduced theory for thin-film micromagnetics. Zbl 1027.82042 DeSimone, Antonio; Kohn, Robert V.; Müller, Stefan; Otto, Felix 2002 Energy scaling of compressed elastic films – three-dimensional elasticity and reduced theories. Zbl 1041.74048 Ben Belgacem, Hafedh; Conti, Sergio; DeSimone, Antonio; Müller, Stefan 2002 Rigorous derivation of nonlinear plate theory and geometric rigidity. Zbl 1012.74043 Friesecke, Gero; Müller, Stefan; James, Richard D. 2002 Local stress regularity in scalar nonconvex variational problems. Zbl 1012.49027 Carstensen, Carsten; Müller, Stefan 2002 The Föppl-von Kármán plate theory as a low energy $$\Gamma$$-limit of nonlinear elasticity. Zbl 1041.74043 Friesecke, Gero; James, Richard D.; Müller, Stefan 2002 Concentration of low energy extremals: Identification of concentration points. Zbl 1004.35040 Flucher, M.; Garroni, A.; Müller, S. 2002 Discrete-to-continuum limit of magnetic forces. Zbl 1038.74018 Müller, Stefan; Schlömerkemper, Anja 2002 A compactness result in the gradient theory of phase transitions. Zbl 0986.49009 DeSimone, Antonio; Müller, Stefan; Kohn, Robert V.; Otto, Felix 2001 A new approach to variational problems with multiple scales. Zbl 1021.49012 Alberti, Giovanni; Müller, Stefan 2001 Optimal existence theorems for nonhomogeneous differential inclusions. Zbl 0989.49012 Müller, S.; Sychev, M. A. 2001 Two-dimensional modelling of soft ferromagnetic films. Zbl 1065.74028 DeSimone, Antonio; Kohn, Robert V.; Müller, Stefan; Otto, Felix; Schäfer, Rudolf 2001 Uniqueness and maximal regularity for nonlinear elliptic systems of $$n$$-Laplace type with measure valued right hand side. Zbl 0937.35065 Dolzmann, Georg; Hungerbühler, Norbert; Müller, Stefan 2000 Rigourous bounds for the Föppl-von Kármán theory of isotropically compressed plates. Zbl 1015.74029 Ben Belgacem, H.; Conti, S.; DeSimone, A.; Müller, S. 2000 Magnetic microstructures – a paradigm of multiscale problems. Zbl 0991.82038 DeSimone, Antonio; Kohn, Robert V.; Müller, Stefan; Otto, Felix 2000 The two-well problem in three dimensions. Zbl 0956.74039 Dolzmann, Georg; Kirchheim, Bernd; Müller, Stefan; Šverák, Vladimir 2000 Quasiconvexity is not invariant under transposition. Zbl 0980.49017 Müller, Stefan 2000 Variational models for microstructure and phase transitions. Zbl 0968.74050 Müller, Stefan 1999 $$\mathcal A$$-quasiconvexity, lower semicontinuity, and Young measures. Zbl 0940.49014 Fonseca, Irene; Müller, Stefan 1999 Convex integration with constraints and applications to phase transitions and partial differential equations. Zbl 0953.35042 Müller, S.; Šverák, V. 1999 Rank-one convexity implies quasiconvexity on diagonal matrices. Zbl 1055.49506 Müller, Stefan 1999 A sharp version of Zhang’s theorem on truncating sequences of gradients. Zbl 0942.49013 Müller, Stefan 1999 Sharp stability results for almost conformal maps in even dimensions. Zbl 0966.35016 Müller, Stefan; Šverák, Vladimir; Yan, Baisheng 1999 Concentration of low energy extremals. Zbl 0938.35042 Flucher, M.; Müller, S. 1999 An isoperimetric estimate and $$W^{1,p}$$-quasiconvexity in nonlinear elasticity. Zbl 0929.74013 Müller, Stefan; Sivaloganathan, Jeyabal; Spector, Scott J. 1999 Analysis of concentration and oscillation effects generated by gradients. Zbl 0920.49009 Fonseca, Irene; Müller, Stefan; Pedregal, Pablo 1998 Unexpected solutions of first and second order partial differential equations. Zbl 0896.35029 1998 Weak compactness of wave maps and harmonic maps. Zbl 0924.58011 Freire, Alexandre; Müller, Stefan; Struwe, Michael 1998 Radial symmetry and decay rate of variational ground states in the zero mass case. Zbl 0908.35005 Flucher, M.; Müller, S. 1998 Spatially discrete wave maps on (1+2)-dimensional space-time. Zbl 0933.58020 Müller, Stefan; Struwe, Michael 1998 Microstructures, phase transitions and geometry. Zbl 0908.49014 Müller, Stefan 1998 Nonlinear elliptic systems with measure-valued right hand side. Zbl 0895.35029 Dolzmann, Georg; Hungerbühler, Norbert; Müller, Stefan 1997 The $$p$$-harmonic system with measure-valued right hand side. Zbl 0879.35052 Dolzmann, Georg; Hungerbühler, Norbert; Müller, Stefan 1997 Weak convergence of wave maps from $$(1+2)$$-dimensional Minkowski space to Riemannian manifolds. Zbl 0906.35061 Freire, Alexandre; Müller, Stefan; Struwe, Michael 1997 Harmonic maps on planar lattices. Zbl 1004.58007 Müller, Stefan; Struwe, Michael; Šverák, Vladimir 1997 Attainment results for the two-well problem by convex integration. Zbl 0930.35038 1996 ...and 31 more Documents all top 5 ### Cited by 1,923 Authors 70 Conti, Sergio 59 Müller, Stefan 35 Fonseca, Irene 30 Ortiz, Michael 27 Ciarlet, Philippe Gaston 25 Iwaniec, Tadeusz 24 Mardare, Cristinel 22 Dolzmann, Georg 22 Kružík, Martin 21 Braides, Andrea 21 Otto, Felix 20 Hornung, Peter 20 Mingione, Giuseppe 19 Garroni, Adriana 19 Yan, Baisheng 19 Yang, Dachun 18 DeSimone, Antonio 18 Ignat, Radu 18 Mora, Maria Giovanna 17 Bartels, Sören 17 De Lellis, Camillo 16 Kohn, Robert Vita 16 Lewicka, Marta 16 Paroni, Roberto 16 Pedregal, Pablo 16 Ponte Castañeda, Pedro 16 Schmidt, Bernd 16 Stefanelli, Ulisse 15 Fusco, Nicola 15 Harutyunyan, Davit 15 Mora-Corral, Carlos 15 Onninen, Jani 15 Pruchnicki, Erick 15 Rindler, Filip 15 Rivière, Tristan 15 Velčić, Igor 15 Zhang, Kewei 14 Carstensen, Carsten 14 Henao, Duvan A. 14 Lopez-Pamies, Oscar 13 De Philippis, Guido 13 Faraco, Daniel 13 Friedrich, Manuel 13 Kristensen, Jan 13 Krömer, Stefan 13 Mielke, Alexander 13 Neff, Patrizio 13 Schlömerkemper, Anja 13 Sivaloganathan, Jeyabal 13 Székelyhidi, László jun. 12 Dacorogna, Bernard 12 Dal Maso, Gianni 12 Griso, Georges 12 Hencl, Stanislav 12 Leoni, Giovanni 12 Malý, Jan 12 Palombaro, Mariapia 12 Ponsiglione, Marcello 12 Serfaty, Sylvia 12 Spector, Scott J. 12 Zappale, Elvira 11 Azroul, Elhoussine 11 Cianchi, Andrea 11 James, Richard D. 11 Muratov, Cyrill B. 11 Neukamm, Stefan 11 Olbermann, Heiner 11 Rüland, Angkana 10 Blanchard, Dominique 10 Focardi, Matteo 10 Kreisbeck, Carolin 10 Miehe, Christian 10 Roubíček, Tomáš 10 Steigmann, David J. 10 Triantafyllidis, Nicolas 10 Zeppieri, Caterina Ida 10 Zwicknagl, Barbara Maria 9 Alicandro, Roberto 9 Balaadich, Farah 9 Bella, Peter 9 Bevan, Jonathan J. 9 Cicalese, Marco 9 Friesecke, Gero 9 Gaudiello, Antonio 9 Gloria, Antoine 9 Kim, Seick 9 Lorent, Andrew 9 Maggi, Francesco 9 Mandallena, Jean-Philippe 9 Marcellini, Paolo 9 Pakzad, Mohammad Reza 9 Rumpf, Martin 9 Schikorra, Armin 8 Agostiniani, Virginia 8 Benešová, Barbora 8 Davoli, Elisa 8 Della Porta, Francesco 8 Francfort, Gilles A. 8 Grabovsky, Yury 8 Jiu, Quansen ...and 1,823 more Authors all top 5 ### Cited in 279 Serials 192 Archive for Rational Mechanics and Analysis 148 Calculus of Variations and Partial Differential Equations 97 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 73 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 69 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 68 Journal of the Mechanics and Physics of Solids 59 Journal of Elasticity 53 Journal de Mathématiques Pures et Appliquées. Neuvième Série 51 Computer Methods in Applied Mechanics and Engineering 51 Journal of Differential Equations 50 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 50 SIAM Journal on Mathematical Analysis 48 Comptes Rendus. Mathématique. Académie des Sciences, Paris 40 Mathematics and Mechanics of Solids 37 Journal of Nonlinear Science 36 Journal of Mathematical Analysis and Applications 36 Journal of Functional Analysis 26 Communications in Mathematical Physics 25 Advances in Calculus of Variations 23 Communications on Pure and Applied Mathematics 23 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 21 The Journal of Geometric Analysis 19 Proceedings of the American Mathematical Society 19 Continuum Mechanics and Thermodynamics 16 Transactions of the American Mathematical Society 15 Communications in Partial Differential Equations 14 Annali di Matematica Pura ed Applicata. Serie Quarta 14 Mathematische Annalen 14 NoDEA. Nonlinear Differential Equations and Applications 13 Advances in Mathematics 13 Physica D 12 Applicable Analysis 12 Mathematical Methods in the Applied Sciences 12 Manuscripta Mathematica 12 Bulletin of the American Mathematical Society. New Series 12 Journal of the European Mathematical Society (JEMS) 12 Communications in Contemporary Mathematics 12 Communications on Pure and Applied Analysis 12 Analysis and Applications (Singapore) 11 Journal of Computational Physics 11 Inventiones Mathematicae 11 Discrete and Continuous Dynamical Systems. Series S 10 International Journal of Engineering Science 10 Applied Mathematics and Optimization 10 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V 9 Journal of Mathematical Physics 9 Nonlinearity 9 Ricerche di Matematica 9 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 8 Journal d’Analyse Mathématique 8 Journal of Statistical Physics 8 ZAMP. Zeitschrift für angewandte Mathematik und Physik 8 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 8 Meccanica 8 SIAM Journal on Numerical Analysis 8 Discrete and Continuous Dynamical Systems 8 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 8 GAMM-Mitteilungen 8 Science China. Mathematics 7 The Annals of Probability 7 Mathematische Zeitschrift 7 Zeitschrift für Analysis und ihre Anwendungen 7 Computational Mechanics 7 Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni 7 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 6 Duke Mathematical Journal 6 International Journal for Numerical Methods in Engineering 6 Journal of Optimization Theory and Applications 6 Numerische Mathematik 6 Quarterly of Applied Mathematics 6 Acta Mathematicae Applicatae Sinica. English Series 6 European Journal of Mechanics. A. Solids 6 Nonlinear Analysis. Real World Applications 6 Multiscale Modeling & Simulation 5 Mathematics of Computation 5 Journal für die Reine und Angewandte Mathematik 5 Chinese Annals of Mathematics. Series B 5 Revista Matemática Iberoamericana 5 Journal of the American Mathematical Society 5 Journal of Scientific Computing 5 SIAM Journal on Applied Mathematics 5 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 5 Acta Mathematica Sinica. English Series 5 Oberwolfach Reports 5 Networks and Heterogeneous Media 5 Analysis & PDE 5 Nonlinear Analysis. Theory, Methods & Applications 4 Computers & Mathematics with Applications 4 International Journal of Solids and Structures 4 Annals of Global Analysis and Geometry 4 Probability Theory and Related Fields 4 Asymptotic Analysis 4 Potential Analysis 4 Revista Matemática Complutense 4 Journal of Mathematical Fluid Mechanics 4 Annals of Mathematics. Second Series 4 Interfaces and Free Boundaries 4 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics 4 Advanced Nonlinear Studies 4 Journal of Fixed Point Theory and Applications ...and 179 more Serials all top 5 ### Cited in 50 Fields 960 Mechanics of deformable solids (74-XX) 934 Partial differential equations (35-XX) 734 Calculus of variations and optimal control; optimization (49-XX) 197 Statistical mechanics, structure of matter (82-XX) 158 Differential geometry (53-XX) 151 Functional analysis (46-XX) 121 Fluid mechanics (76-XX) 112 Real functions (26-XX) 102 Numerical analysis (65-XX) 87 Global analysis, analysis on manifolds (58-XX) 62 Functions of a complex variable (30-XX) 59 Optics, electromagnetic theory (78-XX) 58 Operator theory (47-XX) 55 Harmonic analysis on Euclidean spaces (42-XX) 55 Probability theory and stochastic processes (60-XX) 48 Measure and integration (28-XX) 35 Potential theory (31-XX) 27 Dynamical systems and ergodic theory (37-XX) 27 Convex and discrete geometry (52-XX) 24 Ordinary differential equations (34-XX) 20 Biology and other natural sciences (92-XX) 18 Mechanics of particles and systems (70-XX) 17 Quantum theory (81-XX) 14 Computer science (68-XX) 13 Classical thermodynamics, heat transfer (80-XX) 11 Operations research, mathematical programming (90-XX) 9 Linear and multilinear algebra; matrix theory (15-XX) 9 Approximations and expansions (41-XX) 9 Manifolds and cell complexes (57-XX) 9 Systems theory; control (93-XX) 8 General and overarching topics; collections (00-XX) 8 Information and communication theory, circuits (94-XX) 7 Integral equations (45-XX) 7 Relativity and gravitational theory (83-XX) 6 Difference and functional equations (39-XX) 6 Algebraic topology (55-XX) 6 Geophysics (86-XX) 5 Statistics (62-XX) 5 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 4 History and biography (01-XX) 4 Several complex variables and analytic spaces (32-XX) 3 Abstract harmonic analysis (43-XX) 2 Combinatorics (05-XX) 2 Geometry (51-XX) 2 General topology (54-XX) 1 Nonassociative rings and algebras (17-XX) 1 Special functions (33-XX) 1 Sequences, series, summability (40-XX) 1 Integral transforms, operational calculus (44-XX) 1 Astronomy and astrophysics (85-XX) ### Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata.	2022-06-28T12:25:09	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5928621888160706, "perplexity": 10205.62589630901}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656103516990.28/warc/CC-MAIN-20220628111602-20220628141602-00354.warc.gz"}
http://lammps.sandia.gov/doc/fix_gravity.html	# fix gravity/omp command ## Syntax fix ID group gravity magnitude style args • ID, group are documented in fix command • gravity = style name of this fix command • magnitude = size of acceleration (force/mass units) • magnitude can be a variable (see below) • style = chute or spherical or gradient or vector chute args = angle angle = angle in +x away from -z or -y axis in 3d/2d (in degrees) angle can be a variable (see below) spherical args = phi theta phi = azimuthal angle from +x axis (in degrees) theta = angle from +z or +y axis in 3d/2d (in degrees) phi or theta can be a variable (see below) vector args = x y z x y z = vector direction to apply the acceleration x or y or z can be a variable (see below) ## Examples fix 1 all gravity 1.0 chute 24.0 fix 1 all gravity v_increase chute 24.0 fix 1 all gravity 1.0 spherical 0.0 -180.0 fix 1 all gravity 10.0 spherical v_phi v_theta fix 1 all gravity 100.0 vector 1 1 0 ## Description Impose an additional acceleration on each particle in the group. This fix is typically used with granular systems to include a “gravity” term acting on the macroscopic particles. More generally, it can represent any kind of driving field, e.g. a pressure gradient inducing a Poiseuille flow in a fluid. Note that this fix operates differently than the fix addforce command. The addforce fix adds the same force to each atom, independent of its mass. This command imparts the same acceleration to each atom (force/mass). The magnitude of the acceleration is specified in force/mass units. For granular systems (LJ units) this is typically 1.0. See the units command for details. Style chute is typically used for simulations of chute flow where the specified angle is the chute angle, with flow occurring in the +x direction. For 3d systems, the tilt is away from the z axis; for 2d systems, the tilt is away from the y axis. Style spherical allows an arbitrary 3d direction to be specified for the acceleration vector. Phi and theta are defined in the usual spherical coordinates. Thus for acceleration acting in the -z direction, theta would be 180.0 (or -180.0). Theta = 90.0 and phi = -90.0 would mean acceleration acts in the -y direction. For 2d systems, phi is ignored and theta is an angle in the xy plane where theta = 0.0 is the y-axis. Style vector imposes an acceleration in the vector direction given by (x,y,z). Only the direction of the vector is important; it’s length is ignored. For 2d systems, the z component is ignored. Any of the quantities magnitude, angle, phi, theta, x, y, z which define the gravitational magnitude and direction, can be specified as an equal-style variable. If the value is a variable, it should be specified as v_name, where name is the variable name. In this case, the variable will be evaluated each timestep, and its value used to determine the quantity. You should insure that the variable calculates a result in the appropriate units, e.g. force/mass or degrees. Equal-style variables can specify formulas with various mathematical functions, and include thermo_style command keywords for the simulation box parameters and timestep and elapsed time. Thus it is easy to specify a time-dependent gravitational field. Styles with a gpu, intel, kk, omp, or opt suffix are functionally the same as the corresponding style without the suffix. They have been optimized to run faster, depending on your available hardware, as discussed in Section 5 of the manual. The accelerated styles take the same arguments and should produce the same results, except for round-off and precision issues. These accelerated styles are part of the GPU, USER-INTEL, KOKKOS, USER-OMP and OPT packages, respectively. They are only enabled if LAMMPS was built with those packages. See the Making LAMMPS section for more info. You can specify the accelerated styles explicitly in your input script by including their suffix, or you can use the -suffix command-line switch when you invoke LAMMPS, or you can use the suffix command in your input script. See Section 5 of the manual for more instructions on how to use the accelerated styles effectively. Restart, fix_modify, output, run start/stop, minimize info:	2018-03-19T10:46:08	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.768120527267456, "perplexity": 2223.8839692652764}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-13/segments/1521257646875.28/warc/CC-MAIN-20180319101207-20180319121207-00090.warc.gz"}
https://lammps.sandia.gov/doc/fix_bond_swap.html	# fix bond/swap command ## Syntax fix ID group-ID bond/swap Nevery fraction cutoff seed • ID, group-ID are documented in fix command • bond/swap = style name of this fix command • Nevery = attempt bond swapping every this many steps • fraction = fraction of group atoms to consider for swapping • cutoff = distance at which swapping will be considered (distance units) • seed = random # seed (positive integer) ## Examples fix 1 all bond/swap 50 0.5 1.3 598934 ## Description In a simulation of polymer chains, this command attempts to swap bonds between two different chains, effectively grafting the end of one chain onto another chain and vice versa. This is done via Monte Carlo rules using the Boltzmann acceptance criterion. The purpose is to equilibrate the polymer chain conformations more rapidly than dynamics alone would do it, by enabling instantaneous large conformational changes in a dense polymer melt. The polymer chains should thus more rapidly converge to the proper end-to-end distances and radii of gyration. It is designed for use with systems of FENE or harmonic bead-spring polymer chains where each polymer is a linear chain of monomers, but LAMMPS does not enforce this requirement, i.e. any bond_style can be used. A schematic of the kinds of bond swaps that can occur is shown here: On the left, the red and blue chains have two monomers A1 and B1 close to each other, which are currently bonded to monomers A2 and B2 respectively within their own chains. The bond swap operation will attempt to delete the A1-A2 and B1-B2 bonds and replace them with A1-B2 and B1-A2 bonds. If the swap is energetically favorable, the two chains on the right are the result and each polymer chain has undergone a dramatic conformational change. This reference, (Sides) provides more details on how the algorithm works and its application: The bond swapping operation is invoked every Nevery timesteps. If any bond is swapped, a re-build of the neighbor lists is triggered, since a swap alters the list of which neighbors are considered for pairwise interaction. At each invocation, each processor considers a random specified fraction of its atoms as potential swapping monomers for this timestep. Choosing a small fraction value can reduce the likelihood of a reverse swap occurring soon after an initial swap. For each monomer A1, its neighbors are examined to find a possible B1 monomer. Both A1 and B1 must be in the fix group, their separation must be less than the specified cutoff, and the molecule IDs of A1 and B1 must be the same (see below). If a suitable partner is found, the energy change due to swapping the 2 bonds is computed. This includes changes in pairwise, bond, and angle energies due to the altered connectivity of the 2 chains. Dihedral and improper interactions are not allowed to be defined when this fix is used. If the energy decreases due to the swap operation, the bond swap is accepted. If the energy increases it is accepted with probability exp(-delta/kT) where delta is the increase in energy, k is the Boltzmann constant, and T is the current temperature of the system. Whether the swap is accepted or rejected, no other swaps are attempted by this processor on this timestep. The criterion for matching molecule IDs is how bond swaps performed by this fix conserve chain length. To use this features you must setup the molecule IDs for your polymer chains in a certain way, typically in the data file, read by the read_data command. Consider a system of 6-mer chains. You have 2 choices. If the molecule IDs for monomers on each chain are set to 1,2,3,4,5,6 then swaps will conserve chain length. For a particular momoner there will be only one other monomer on another chain which is a potential swap partner. If the molecule IDs for monomers on each chain are set to 1,2,3,3,2,1 then swaps will conserve chain length but swaps will be able to occur at either end of a chain. Thus for a particular monomer there will be 2 possible swap partners on another chain. In this scenario, swaps can also occur within a single chain, i.e. the two ends of a chain swap with each other. Note If your simulation uses molecule IDs in the usual way, where all monomers on a single chain are assigned the same ID (different for each chain), then swaps will only occur within the same chain. If you assign the same molecule ID to all monomers in all chains then inter-chain swaps will occur, but they will not conserve chain length. Neither of these scenarios is probably what you want for this fix. Note When a bond swap occurs the image flags of monomers in the new polymer chains can become inconsistent. See the dump command for a discussion of image flags. This is not an issue for running dynamics, but can affect calculation of some diagnostic quantities or the printing of unwrapped coordinates to a dump file. This fix computes a temperature each time it is invoked for use by the Boltzmann criterion. To do this, the fix creates its own compute of style temp, as if this command had been issued: compute fix-ID_temp all temp See the compute temp command for details. Note that the ID of the new compute is the fix-ID with underscore + “temp” appended and the group for the new compute is “all”, so that the temperature of the entire system is used. Note that this is NOT the compute used by thermodynamic output (see the thermo_style command) with ID = thermo_temp. This means you can change the attributes of this fix’s temperature (e.g. its degrees-of-freedom) via the compute_modify command or print this temperature during thermodynamic output via the thermo_style custom command using the appropriate compute-ID. It also means that changing attributes of thermo_temp will have no effect on this fix. Restart, fix_modify, thermo output, run start/stop, minimize info: No information about this fix is written to binary restart files. Because the state of the random number generator is not saved in restart files, this means you cannot do “exact” restarts with this fix, where the simulation continues on the same as if no restart had taken place. However, in a statistical sense, a restarted simulation should produce the same behavior. Also note that each processor generates possible swaps independently of other processors. Thus if you repeat the same simulation on a different number of processors, the specific swaps performed will be different. The fix_modify temp option is supported by this fix. You can use it to assign a compute you have defined to this fix which will be used to compute the temperature for the Boltzmann criterion. This fix computes two statistical quantities as a global 2-vector of output, which can be accessed by various output commands. The first component of the vector is the cumulative number of swaps performed by all processors. The second component of the vector is the cumulative number of swaps attempted (whether accepted or rejected). Note that a swap “attempt” only occurs when swap partners meeting the criteria described above are found on a particular timestep. The vector values calculated by this fix are “intensive”. No parameter of this fix can be used with the start/stop keywords of the run command. This fix is not invoked during energy minimization. ## Restrictions This fix is part of the MC package. It is only enabled if LAMMPS was built with that package. See the Making LAMMPS section for more info. The settings of the “special_bond” command must be 0,1,1 in order to use this fix, which is typical of bead-spring chains with FENE or harmonic bonds. This means that pairwise interactions between bonded atoms are turned off, but are turned on between atoms two or three hops away along the chain backbone. Currently, energy changes in dihedral and improper interactions due to a bond swap are not considered. Thus a simulation that uses this fix cannot use a dihedral or improper potential.	2018-07-19T09:43:04	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.589625895023346, "perplexity": 1545.5932999103409}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-30/segments/1531676590794.69/warc/CC-MAIN-20180719090301-20180719110301-00376.warc.gz"}
https://www.itl.nist.gov/div898/handbook/pmc/section3/pmc3231.htm	6. Process or Product Monitoring and Control 6.3. Univariate and Multivariate Control Charts 6.3.2. What are Variables Control Charts? 6.3.2.3. Cusum Control Charts ## Cusum Average Run Length The Average Run Length of Cumulative Sum Control Charts The ARL of CUSUM The operation of obtaining samples to use with a cumulative sum (CUSUM) control chart consists of taking samples of size $$n$$ and plotting the cumulative sums $$S_r = \sum_{i=1}^{r}{(\bar{x}_i - k)} \;\;\; \mbox{or} \;\;\; S_r = \sum_{i=1}^{r}{(\bar{x}_i - k)/\sigma_{\bar{x}}} \;\;\; \mbox{(standardized)}$$ versus the sample number $$r$$, where $$\bar{x}_i$$ is the sample mean and $$k$$ is a reference value. In practice, $$k$$ might be set equal to $$(\hat{\mu}_0 + \mu_1)/2$$, where $$\hat{\mu}_0$$ is the estimated in-control mean, which is sometimes known as the acceptable quality level, and $$\mu_1$$ is referred to as the rejectable quality level. If the distance between a plotted point and the lowest previous point is equal to or greater than $$h$$, one concludes that the process mean has shifted (increased). $$h$$ is decision limit Hence, $$h$$ is referred to as the decision limit. Thus the sample size $$n$$, reference value $$k$$, and decision limit $$h$$ are the parameters required for operating a one-sided CUSUM chart. If one has to control both positive and negative deviations, as is usually the case, two one-sided charts are used, with respective values $$k_1, \, k_2, \, (k_1 > k_2)$$ and respective decision limits $$h$$ and $$-h$$. Standardizing shift in mean and decision limit The shift in the mean can be expressed as $$\mu -k$$. If we are dealing with normally distributed measurements, we can standardize this shift by $$k_s = \frac{(\mu -k)}{\sigma/\sqrt{n}} \,\,\,\,\, \mbox{or} \,\,\,\,\, ((\mu - k)\sqrt{n})/\sigma \, .$$ Similarly, the decision limit can be standardized by $$h_s = \frac{h}{\sigma / \sqrt{n}} = (h \sqrt{n})/\sigma \, .$$ Determination of the ARL, given $$h$$ and $$k$$ The average run length (ARL) at a given quality level is the average number of samples (subgroups) taken before an action signal is given. The standardized parameters $$k_s$$ and $$h_s$$ together with the sample size $$n$$ are usually selected to yield approximate ARLs $$L_0$$ and $$L_1$$ at acceptable and rejectable quality levels $$\mu_0$$ and $$\mu_1$$ respectively. We would like to see a high ARL, $$L_0$$, when the process is on target, (i.e. in control), and a low ARL, $$L_1$$, when the process mean shifts to an unsatisfactory level. In order to determine the parameters of a CUSUM chart, the acceptable and rejectable quality levels along with the desired respective ARLs are usually specified. The design parameters can then be obtained by a number of ways. Unfortunately, the calculations of the ARL for CUSUM charts are quite involved. There are several nomographs available from different sources that can be utilized to find the ARLs when the standardized $$h$$ and $$k$$ are given. Some of the nomographs solve the unpleasant integral equations that form the basis of the exact solutions, using an approximation of Systems of Linear Algebraic Equations (SLAE). This Handbook used a computer program that furnished the required ARLs given the standardized $$h$$ and $$k$$. An example is given below. Example of finding ARLs given the standardized $$h$$ and $$k$$ mean shift $$(h\sqrt{n})/\sigma$$ Shewart ($$k = 0.5$$) 4 5 $$\bar{X}$$ 0.00 336 930 371.00 0.25 74.2 140 281.14 0.50 26.6 30.0 155.22 0.75 13.3 17.0 81.22 1.00 8.38 10.4 44.0 1.50 4.75 5.75 14.97 2.00 3.34 4.01 6.30 2.50 2.62 3.11 3.24 3.00 2.19 2.57 2.00 4.00 1.71 2.01 1.19 Using the table If $$k = 0.5$$, then the shift of the mean (in multiples of the standard deviation of the mean) is obtained by adding 0.5 to the first column. For example to detect a mean shift of $$1 \sigma$$ at $$h = 4$$, the ARL = 8.38 (at first column entry of 0.5). The last column of the table contains the ARLs for a Shewhart control chart at selected mean shifts. The ARL for Shewhart is $$1/p$$, where $$p$$ is the probability for a point to fall outside established control limits. Thus, for 3-sigma control limits and assuming normality, the probability to exceed the upper control limit is 0.00135 and to fall below the lower control limit is also 0.00135 and their sum is 0.0027. (These numbers come from standard normal distribution tables or computer programs, setting $$z = 3$$. Then the ARL = 1/0.0027 = 370.37. This says that when a process is in control one expects an out-of-control signal (false alarm) each 371 runs. ARL if a 1 sigma shift has occurred When the means shifts up by $$1 \sigma$$, then the distance between the upper control limit and the shifted mean is $$2 \sigma$$ (instead of $$3 \sigma$$. Entering normal distribution tables with $$z = 2$$ yields a probability of $$p = 0.02275$$ to exceed this value. The distance between the shifted mean and the lower limit is now $$4 \sigma$$ and the probability of $$\bar{X} < -4$$ is only 0.000032 and can be ignored. The ARL is 1/0.02275 = 43.96. Shewhart is better for detecting large shifts, CUSUM is faster for small shifts The conclusion can be drawn that the Shewhart chart is superior for detecting large shifts and the CUSUM scheme is faster for small shifts. The break-even point is a function of $$h$$, as the table shows.	2018-05-24T04:18:12	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8451546430587769, "perplexity": 540.4947039569149}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-22/segments/1526794865913.52/warc/CC-MAIN-20180524033910-20180524053910-00427.warc.gz"}
https://badpiggies.fandom.com/wiki/Thread:Chiachichang/@comment-5056828-20140809102033/@comment-5056828-20140908113508?diff=prev&oldid=8089	## FANDOM 245 Pages Thanks to your math, we then have something more to put on the trivia sections! And that would mean that $2.2 * 1.375 = 3.025$ Greens is equivalent to one Reds! Community content is available under CC-BY-SA unless otherwise noted.	2020-09-21T19:50:26	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8850736021995544, "perplexity": 2572.4773671757384}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-40/segments/1600400202007.15/warc/CC-MAIN-20200921175057-20200921205057-00360.warc.gz"}
https://indico.fnal.gov/event/53004/contributions/244169/	# NuFact 2022: The 23rd International Workshop on Neutrinos from Accelerators July 30, 2022 to August 6, 2022 Cliff Lodge US/Mountain timezone ## The search for the muon EDM at the Fermilab $g-2$ experiment and beyond Aug 5, 2022, 2:20 PM 30m Magpie A ### Magpie A Talk WG4: Muon Physics ### Speaker Samuel Grant (University College London) ### Description The observation of a non-zero permanent electric dipole moment (EDM) of an elementary particle would break both parity and time-reversal symmetries, implying the violation of charge-parity (CP) symmetry under CPT invariance. The Standard Model (SM) predicts subatomic particle EDMs which are so small as to be out of reach of current experiments, such that any observation of a non-zero EDM would indicate a source of CP violation arising from new physics beyond the SM (BSM). Presently, a measurement of muon EDM at the Fermilab $g-2$ experiment is well underway, aiming to exceed the current upper limit – set by the Brookhaven $g-2$ experiment – by two orders of magnitude at $\sim10^{-21}$ $e\cdot$cm; providing a unique opportunity to investigate BSM sources of CP violation in the second generation of leptons. This talk will provide an overview of the muon EDM search at Fermilab, as well as future search experiments. Attendance type Virtual presentation ### Primary author Samuel Grant (University College London)	2023-01-28T20:56:56	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6576056480407715, "perplexity": 3372.388859823234}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764499654.54/warc/CC-MAIN-20230128184907-20230128214907-00015.warc.gz"}
https://www.rba.gov.au/publications/rdp/2020/2020-04/non-technical-summary.html	# RDP 2020-04: The Apartment Shortage The Apartment Shortage Planning regulations restrict the supply of apartments and hence drive up their price. This effect can be measured by the difference between the price of new apartments and the cost of supplying them. We estimate this gap to be large, especially in Sydney. Specifically, planning restrictions increase the cost of apartments by 68 per cent in Sydney, by 20 per cent in Melbourne and 2 per cent in Brisbane. One way of supplying extra apartments is to build taller buildings. This increases per-apartment construction costs but means that extra land is not required. Our estimates allow for these higher construction costs, together with costs of finance, marketing, professional fees, infrastructure contributions and developer's margins. Results are in the following table. Table 1: Average Apartment Prices and Costs $000, 2018 Sydney Melbourne Brisbane Average sale price 873 588 470 Cost of supply 519 491 460 Effect of planning restrictions ($′000) 355 97 10 Effect of planning restrictions (per cent of costs) 68 20 2 We also estimate the effect of planning restrictions at a more detailed level within capital cities for a slightly earlier period – from 2011 to 2016. In Sydney, the effect of restrictions increases strongly as you get closer to the centre of the city. The largest effects – averaging more than \$450,000 per apartment in 2011 to 2016 – occur in inner-ring areas like the eastern suburbs, Leichhardt and North Sydney. However, even though the excess demand for apartments is greatest near the centre, building patterns do not reflect this. Recent and planned construction in Sydney is located predominantly in middle and outer suburbs. In Melbourne and Brisbane the effect was unevenly spread throughout the metropolitan areas. While we focus on the cost of adding additional floors to apartment buildings, an alternative way of supplying apartments would be to construct more buildings. This requires the purchase of land, which is expensive, especially in Sydney. For short buildings, land costs amount to hundreds of thousands of dollars per apartment. For this reason, medium-density housing in the form of low-rise apartment buildings is much more expensive to provide than high-density housing. As building height increases, however, the per-apartment cost of land declines while construction costs increase. So, above a certain height, tall buildings become more costly to build than more, shorter buildings. In Sydney, under central assumptions and on average across the metropolitan area, this crossover point occurs at 20 storeys, much higher than the typical apartment building, which is 10 storeys. This cost advantage of taller buildings is largest in Sydney's inner suburbs, where land costs are very high and where, in the absence of height restrictions, it would be economic to raise building heights by 20 storeys or more above their current heights. In contrast, the benefits of raising building heights in Melbourne and Brisbane are smaller. This is partly because land is less expensive, so it does not need to be used so intensively. And partly because apartment buildings in those cities are already close to the economically efficient height.	2023-03-31T22:26:46	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.35043540596961975, "perplexity": 2476.6494433885655}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296949689.58/warc/CC-MAIN-20230331210803-20230401000803-00206.warc.gz"}
https://pdglive.lbl.gov/DataBlock.action?node=S020AV&home=sumtabB	#### ${{\mathit \Sigma}^{-}}$ DECAY PARAMETERS See the Note on Baryon Decay Parameters'' in the neutron Listings. Older, outdated results have been omitted. #### ${\mathit g}_{{{\mathit V}}}/{\mathit g}_{{{\mathit A}}}$ FOR ${{\mathit \Sigma}^{-}}$ $\rightarrow$ ${{\mathit \Lambda}}{{\mathit e}^{-}}{{\overline{\mathit \nu}}_{{e}}}$ For the sign convention, see the Note on Baryon Decay Parameters'' in the neutron Listings. The value is predicted to be zero by conserved vector current theory. The values averaged assume CVC-SU(3) weak magnetism term. VALUE EVTS DOCUMENT ID TECN COMMENT $\bf{ 0.01 \pm0.10}$ OUR AVERAGE Error includes scale factor of 1.5. See the ideogram below. $-0.034$ $\pm0.080$ 1620 1 1982 SPEC SPS hyperon beam $-0.29$ $\pm0.29$ 114 1980 ASPK BNL hyperon beam $-0.17$ $\pm0.35$ 55 1975 B SPEC BNL hyperon beam $+0.45$ $\pm0.20$ 186 2, 1 1972 HBC 1 The sign has been changed to agree with our convention. 2 The FRANZINI 1972 value includes the events of earlier papers. ${\mathit g}_{{{\mathit V}}}/{\mathit g}_{{{\mathit A}}}$ for ${{\mathit \Sigma}^{-}}$ $\rightarrow$ ${{\mathit \Lambda}}{{\mathit e}^{-}}{{\overline{\mathit \nu}}_{{e}}}$ References: BOURQUIN 1982 ZPHY C12 307 Measurements of Hyperon Semileptonic Decays at the CERN Super Proton Synchrotron. 1. The ${{\mathit \Sigma}^{-}}$ $\rightarrow$ ${{\mathit \Lambda}}{{\mathit e}^{-}}{{\overline{\mathit \nu}}_{{e}}}$ Decay Mode THOMPSON 1980 PR D21 25 Studies in the BNL 21 ${\mathrm {GeV/}}\mathit c$ Negative Hyperon Beam. II. Leptonic Decays of ${{\mathit \Sigma}}$ and ${{\mathit \Xi}}$ TANENBAUM 1975B PR D12 1871 Leptonic Decays of the ${{\mathit \Sigma}^{-}}$ and ${{\mathit \Xi}^{-}}$ Hyperons FRANZINI 1972 PR D6 2417 Decay ${{\mathit \Sigma}^{\pm}}$ $\rightarrow$ ${{\mathit \Lambda}}{{\mathit e}^{\pm}}{{\mathit \nu}}$	2022-09-26T10:19:50	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8343075513839722, "perplexity": 10926.43508553371}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030334855.91/warc/CC-MAIN-20220926082131-20220926112131-00443.warc.gz"}
https://pdglive.lbl.gov/DataBlock.action?node=S011M&home=sumtabM	# ${{\boldsymbol K}^{0}}$ MASS INSPIRE search VALUE (MeV) EVTS DOCUMENT ID TECN COMMENT $\bf{ 497.611 \pm0.013}$ OUR FIT Error includes scale factor of 1.2. $\bf{ 497.611 \pm0.013}$ OUR AVERAGE Error includes scale factor of 1.2. $497.607$ $\pm0.007$ $\pm0.015$ 261k 1 2014 ${{\mathit \psi}{(2S)}}$ $\rightarrow$ ${{\mathit K}_S^0}$ ${{\mathit X}}$ $497.583$ $\pm0.005$ $\pm0.020$ 35k 2007 B KLOE ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit K}_L^0}$ ${{\mathit K}_S^0}$ $497.625$ $\pm0.001$ $\pm0.031$ 655k 2002 NA48 ${{\mathit K}_L^0}$ beam $497.661$ $\pm0.033$ 3713 1987 B CMD ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit K}_L^0}$ ${{\mathit K}_S^0}$ $497.742$ $\pm0.085$ 780 1985 B CMD ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit K}_L^0}$ ${{\mathit K}_S^0}$ • • • We do not use the following data for averages, fits, limits, etc. • • • $497.44$ $\pm0.50$ 1967 OSPK $498.9$ $\pm0.5$ 4500 1966 HBC ${{\mathit K}^{0}}$ from ${{\overline{\mathit p}}}{{\mathit p}}$ $497.44$ $\pm0.33$ 2223 1965 B HBC ${{\mathit K}^{0}}$ from ${{\overline{\mathit p}}}{{\mathit p}}$ $498.1$ $\pm0.4$ 1964 OSPK 1 Obtained by analyzing CLEO-c data but not authored by the CLEO Collaboration. References: PR D89 031501 High Precision Measurement of the Masses of the ${{\mathit D}^{0}}$ and ${{\mathit K}_S^0}$ mesons AMBROSINO 2007B JHEP 0712 073 Precise Measurements of the ${{\mathit \eta}}$ Meson and the Neutral Kaon Masses with the KLOE Detector LAI 2002 PL B533 196 New Measurements of the ${{\mathit \eta}}$ and ${{\mathit K}^{0}}$ Masses BARKOV 1987B SJNP 46 630 The Precision Neutral Kaon Mass Measurement BARKOV 1985B JETPL 42 138 Measurement of the Neutral Kaon Mass FITCH 1967 PR 164 1711 Studies of ${{\mathit K}_{{2}}^{0}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ Decay and Interference BALTAY 1966 PR 142 932 Study of Antiproton Proton Annihilations into ${{\mathit K}}$ and ${{\mathit \pi}}$ Mesons at 3.7 ${\mathrm {GeV/}}\mathit c$ KIM 1965B PR 140 B1334 Measurement of the ${{\mathit K}^{0}}$ Mass and the ${{\mathit K}^{0}}{{\mathit K}^{-}}$ Mass Difference CHRISTENSON 1964 PRL 13 138 Evidence for the 2${{\mathit \pi}}$ Decay of the ${{\mathit K}_L^0}$ Meson	2021-02-28T22:25:41	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6662235856056213, "perplexity": 4908.937903899611}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178361776.13/warc/CC-MAIN-20210228205741-20210228235741-00208.warc.gz"}
https://www-cdf.fnal.gov/physics/new/top/publications.html	Measurement of the Top Pair Production Cross Section in the Dilepton Decay Channel in p anti-p Collisions at sqrt(s) = 0.96 TeV T. Aaltonen et al., The CDF Collaboration, Phys. Rev. D82, 052002 (2010). Abstract, PDF Exclusion of an Exotic Top Quark with -4/3 Electric Charge Using Soft Lepton Tagging T. Aaltonen et al., The CDF Collaboration, Phys. Rev. Lett. 105, 101801 (2010). Abstract, PDF Measurement of W-Boson Polarization in Top-quark Decay in ppbar Collisions at sqrt(s) = 1.96 TeV T. Aaltonen et al., The CDF Collaboration, Phys.Rev.Lett.105 042002 (2010) Abstract, PDF First Measurement of the Ratio sigma_(t-tbar) / sigma_(Z/\gamma->ll) and Precise Extraction of the t-tbar Cross Section. T. Aaltonen et al., The CDF Collaboration, Phys.Rev.Lett.105 012001 (2010) Abstract PDF Measurement of the ttbar Production Cross Section in ppbar Collisions at sqrt(s)=1.96 TeV using Soft Electron b-Tagging T. Aaltonen et al., The CDF Collaboration, Phys.Rev.D81 092002 (2010) Abstract, PDF Search for Pair Production of Supersymmetric Top Quarks in Dilepton Events from p anti-p Collisions at S(1/2) = 1.96 TeV. T. Aaltonen et al., The CDF Collaboration, Phys.Rev.Lett.104 251801 (2010) Abstract, PDF Search for single top quark production in pbar p collisions at sqrt{s}=1.96 TeV in the missing transverse energy plus jets topology T. Aaltonen et al., The CDF Collaboration, Phys. Rev. D81, 072003 (2010) Abstract, PDF Measurement of the Top Quark Mass and ppbar -> ttbar Cross Section in the All-Hadronic Mode with the CDFII Detector T. Aaltonen et al., The CDF Collaboration, Phys. Rev. D81, 052011 (2010) Abstract, PDF Measurements of the top-quark mass using charged particle tracking T. Aaltonen et al., The CDF Collaboration, Phys. Rev. D81, 032002 (2010) Abstract, PDF Measurement of the Top Quark Mass in the Dilepton Channel using m_T2 at CDF T. Aaltonen et al., The CDF Collaboration, Phys. Rev. D81, 031102 (2010) Abstract, PDF Measurement of the t-tbar Production Cross Section in 2 fb-1 of p anti-p Collisions at sqrt(s) = 1.96 TeV Using Lepton Plus Jets Events with Soft Muon Tagging T. Aaltonen et al., The CDF Collaboration, Phys. Rev. D79, 052007 (2009) Abstract, PDF Search for charged Higgs bosons in decays of top quarks in p-pbar collisions at sqrt(s) = 1.96 TeV T. Aaltonen et al., The CDF Collaboration, Phys. Rev. Lett. 103 101803 (2009), FERMILAB-PUB-09-343-E Abstract, PDF Measurement of the Top Quark Mass Using the Invariant Mass of Lepton Pairs in Soft Muon b-tagged Events T. Aaltonen et al., The CDF Collaboration, Phys. Rev. D80 051104 (2009), FERMILAB-PUB-09-332-E Abstract, PDF Searching the Inclusive Lepton + Photon + Missing E(T) + b-quark Signature for Radiative Top Quark Decay and Non-Standard-Model Processes. T. Aaltonen et al., The CDF Collaboration, Phys.Rev.D80 011102 (2009) Abstract PDF First Observation of Electroweak Single Top Quark Production T. Aaltonen et al., The CDF Collaboration, Phys. Rev. Lett. 103 092002(2009), Fermilab-Pub-09-059-E. Abstract, PDF A Measurement of the tt-bar Cross Section in p anti-p Collisions at sqrt s= 1.96 TeV using Dilepton Events with a Lepton plus Track Selections T. Aaltonen et al., The CDF Collaboration, Fermilab-Pub-09-091-E. Phys. Rev. D79 112007 (2009). Abstract, PDF First Measurement of the tt-bar Differential Cross Section d sigma/dM_tt-bar in pp-bar Collisions at sqrt s= 1.96 TeV T. Aaltonen et al., The CDF Collaboration, Phys. Rev. Lett. 102 222003 (2009). Fermilab-Pub-09-079-E. Abstract, PDF Search for the Production of Narrow tb-bar Resonances in 1.9 fb-1 of p anti-p Collisions at sqrt s= 1.96 Tev T. Aaltonen et al., The CDF Collaboration, Phys. Rev. Lett. 103 041801 (2009). Fermilab-Pub-09-048-E. Abstract, PDF Top quark mass measurement in the lepton plus jets channel using a modified matrix element method T. Aaltonen et al., The CDF Collaboration, Phys. Rev. D 79, 072001 (2009). Abstract, PDF Measurement of the top quark mass at CDF using the "Neutrino Phi Weighing" template method on a lepton plus isolated track sample T. Aaltonen et al., The CDF Collaboration, Phys. Rev. D 79, 072005 (2009). Abstract, PDF Search for top-quark production via flavor-changing neutral currents in W+1 jet events at CDF T. Aaltonen et al., The CDF Collaboration, Phys. Rev. Lett. 102, 151801 (2009). Abstract, PDF Measurement of W-Boson Helicity Fractions in Top-Quark Decays Using costheta. T. Aaltonen et al., The CDF Collaboration, Physics Letters B, Volume 674, Issue 3, 20 April 2009, Pages 160-167. Abstract, PDF Top Quark Mass Measurement in the tt-bar All Hadronic Channel using a Matrix Element Technique in ppbar Collisions at sqrt s= 1.96 TeV T. Aaltonen et al., The CDF Collaboration, Phys. Rev. D79, 072101 (2009). Abstract, PDF. The First measurement of the top quark mass at CDF II in the lepton+jets and dilepton channels simultaneously. T. Aaltonen et al., The CDF Collaboration, Phys. Rev. D79, 072009 (2009). Abstract, PDF. Measurement of the Single Top Quark Production Cross Section at CDF T. Aaltonen et al., The CDF Collaboration, Phys. Rev. Lett. 101, 252001 (2008). Abstract, PDF. Direct Bound on the Total Width of the Top Quark in p anti-p Collisions at sqrt s = 1.96-TeV. T. Aaltonen et al., The CDF Collaboration, Phys. Rev. Lett. 102, 042001 (2009). Abstract, PDF. Measurement of the top quark mass with dilepton events selected using neuroevolution at CDF T. Aaltonen et al., The CDF Collaboration, Phys. Rev. Lett. 102, 152001 (2009) Abstract, PDF. Measurement of the ttbar production cross section in 2fb-1 of ppbar collisions at sqrt[s] =1.96 TeV using lepton plus jets events with soft muon b tagging T. Aaltonen et al., The CDF Collaboration, Phys. Rev. D 79, 052007 (2009) Abstract, PDF. Measurement of the fraction of t anti-t production via gluon-gluon fusion in p anti-p collisions at s(1/2) = 1.96-TeV T. Aaltonen et al., The CDF Collaboration, Phys. Rev. D79, 031101 (2009) Abstract, PDF. Forward-Backward Asymmetry in Top Quark Production in ppbar Collisions at sqrt{s}=1.96 TeV T. Aaltonen et al., The CDF Collaboration, Fermilab-Pub-08-171-E, Phys. Rev. Lett. 101, 202001 (2008) Abstract, PDF. Search for the Flavor Changing Neutral Current Decay t -->Zq in p anti-p Collisions at s(1/2) = 1.96 TeV T. Aaltonen et al., The CDF Collaboration, Phys. Rev. Lett. 101, 192002, (2008). Abstract, PDF (213KiB). Search for Heavy Top-like Quarks Using Lepton Plus Jets Events in 1.96 TeV p anti-p Collisions T. Aaltonen et al., The CDF Collaboration, Phys. Rev. Lett. 100, 161803 (2008). Abstract, PDF (257KiB). First Measurement of the Fraction of Top Quark Pair Production Through Gluon-Gluon Fusion T. Aaltonen et al., The CDF Collaboration, Phys. Rev. D. 78, 111101, (2008). Abstract, PDF (418KiB). First Measurement of the Production of a W Boson in Association with a Single Charm Quark in p anti-p Collisions at s(1/2) = 1.96 TeV T. Aaltonen et al., The CDF Collaboration, Phys. Rev. Lett. 100, 091803 (2008). Abstract, PostScript (418KiB). Precise Measurement of the Top Quark Mass in the Lepton+Jets Topology at CDF II A. Abulencia et al., The CDF Collaboration, Phys. Rev. Lett. 99, 182002 (2007). Abstract, PostScript (418KiB). Cross Section Constrained Top Quark Mass Measurement from Dilepton Events at the Tevatron T. Aaltonen et al., The CDF Collaboration, Phys. Rev. Lett. 100, 062005 (2008) Abstract, PostScript (313KiB). Limits on the Production of Narrow tt-bar Resonances in p anti-p Collisions at s(1/2) = 1.96 TeV T. Aaltonen et al., The CDF Collaboration, Phys. Rev. D77, 051102 (2008). Abstract, PDF (204KiB). Measurement of the p anti-p --> tt-bar Production Cross Section and the Top Quark Mass at s(1/2) = 1.96 TeV in the All-Hadronic Decay Mode T. Aaltonen et al., The CDF Collaboration, Phys. Rev. D76, 072009 (2007). Abstract, PostScript (693KiB). Search for Resonant tt-bar Production in p anti-p Collisions at s(1/2) = 1.96 TeV T. Aaltonen et al., The CDF Collaboration, Phys. Rev. Lett. 100, 231801 (2008). Abstract, PDF (184KiB). Measurement of the Top-Quark Mass using Missing E(t) + Jets Events with Secondary Vertex b-tagging at CDF II T. Aaltonen et al., The CDF Collaboration, Phys. Rev. D75, 111103 (2007). Abstract, PostScript (273KiB). Measurement of the Top Quark Mass in p anti-p Collisions at s(1/2) = 1.96 TeV using the Decay Length Technique A. Abulencia et al., The CDF Collaboration, Phys. Rev. D75, 071102 (2007) Abstract, PDF (233KiB). Measurement of the Top-Quark Mass in All-Hadronic Decays in p anti-p Collisions at CDF II A. Aaltonen et al., The CDF Collaboration, Phys. Rev. Lett. 98, 142001 (2007) Abstract, PDF (207KiB). Search for anomalous semileptonic decay of heavy flavor hadrons produced in association with a W boson at CDF II. A. Abulencia et al., The CDF Collaboration, Phys. Rev. D73, 051101 (2006). Abstract, PDF (418KiB). Measurement of the Helicity Fractions of W Bosons from Top Quark Decays using Fully Reconstructed tt-bar Events with CDF II A. Abulencia et al., The CDF Collaboration, Phys. Rev. D75, 052001 (2007). Abstract, PostScript (464KiB). Precision Measurement of the Top-Quark Mass from Dilepton Events at CDF II A. Abulencia et al., The CDF Collaboration, Phys. Rev. D75, 031105 (2007). Abstract, PDF (236KiB). Search for V + A Current in Top Quark Decay in p anti-p Collisions at s(1/2) = 1.96 TeV A. Abulencia et al., The CDF Collaboration, Phys. Rev. Lett. 98, 072001 (2007) Abstract, PostScript (295KiB). Cross Section Measurements of High-p(t) Dilepton Final-State Processes Using a Global Fitting Method A. Abulencia et al., The CDF Collaboration, Phys. Rev. D 78, 012003, (2008). Abstract, PostScript (457KiB). Top Quark Mass Measurement from Dilepton Events at CDF II with the Matrix-Element Method A. Abulencia et al., The CDF Collaboration, Phys. Rev. D74, 032009 (2006). Abstract, PDF (553KiB). Measurement of the tt-bar Production Cross Section in p anti-p Collisions at s(1/2) = 1.96 TeV using Lepton + Jets Events with Jet Probability b-tagging A. Abulencia et al., The CDF Collaboration, Phys. Rev. D74, 072006 (2006). Abstract, PostScript (2364KiB). Measurement of the tt-bar Production Cross Section in p anti-p Collisions at s(1/2) = 1.96 TeV in the all Hadronic Decay Mode A. Abulencia et al., The CDF Collaboration, Phys. Rev. D74, 072005 (2006). Abstract, PostScript (436KiB). Measurement of the tt-bar Production Cross Section in p anti-p Collisions at s(1/2) = 1.96 TeV A. Abulencia et al., The CDF Collaboration, Phys. Rev. Lett. 97, 082004 (2006). Abstract, PDF (150KiB). A Search for t --> tau nu q in tt-bar Production A. Abulencia et al., The CDF Collaboration, Phys. Lett. B 639, 172-178 (2006). Abstract, PDF (178KiB). Search for Charged Higgs Bosons from Top Quark Decays in p anti-p Collisions at s(1/2) = 1.96 TeV A. Abulencia et al., The CDF Collaboration, Phys. Rev. Lett. 96, 042003 (2006). Measurement of the tt-bar Production Cross Section in p anti-p Collisions at s(1/2) = 1.96 TeV using Missing E(t) + jets Events with Secondary Vertex b-Tagging A. Abulencia et al., The CDF Collaboration, Phys. Rev. Lett. 96, 202002 (2006). Abstract, PostScript (254KiB). Measurement of the Top Quark Mass using Template Methods on Dilepton Events in p anti-p Collisions at s(1/2) = 1.96 TeV A. Abulencia et al., The CDF Collaboration, Phys. Rev. D73, 112006 (2006). Abstract, PostScript (1589KiB). Measurement of the Helicity of W Bosons in Top-Quark Decays A. Abulencia et al., The CDF Collaboration, Phys. Rev. D73, 111103 (2006). Abstract, PDF (196KiB). Measurement of the Top Quark Mass with the Dynamical Likelihood Method using Lepton plus Jets Events with b-tags in p anti-p Collisions at sqrt s = 1.96 TeV A. Abulencia et al., The CDF Collaboration, Phys. Rev. D73, 092002 (2006). Abstract, PostScript (1191KiB). Top Quark Mass Measurement from Dilepton Events at CDF II A. Abulencia et al., The CDF Collaboration, Phys. Rev. Lett. 96, 152002 (2006). Abstract, PDF (186KiB). Precision Top Quark Mass Measurement in the Lepton + Jets Topology in p anti-p Collisions at s(1/2) = 1.96 TeV A. Abulencia et al., The CDF Collaboration, Phys. Rev. Lett. 96, 022004 (2006). Abstract, PDF (197KiB). Top Quark Mass Measurement Using the Template Method in the Lepton + Jets Channel at CDF II A. Abulencia et al., The CDF Collaboration, Phys. Rev. D73, 032003 (2006). Abstract, PDF (825KiB). Measurement of the Cross Section for tt-bar Production in pp-bar Collisions using the Kinematics of Lepton + Jets Events D. Acosta et al., The CDF Collaboration, Phys. Rev. D72, 052003 (2005). Abstract, PDF (1294KiB). Measurement of the tt-bar Production Cross Section in pp-bar Collisions at s(1/2) = 1.96 TeV using Lepton Plus Jets events with Semileptonic B Decays to Muons D. Acosta et al., The CDF Collaboration, Phys. Rev. D72, 032002 (2005) Abstract, PDF (785KiB). Measurement of B(t --> Wb)/B(t --> Wq) at the Collider Detector at Fermilab D. Acosta et al., The CDF Collaboration, Phys. Rev. Lett. 95, 102002 (2005) Abstract, PDF (580KiB). Search for Anomalous Kinematics in tt-bar Dilepton Events at CDF II D. Acosta et al., The CDF Collaboration, Phys. Rev. Lett. 95, 022001 (2005). Abstract, PostScript (290KiB). Measurement of the tt-bar Production Cross Section in pp-bar Collisions at s(1/2) = 1.96 TeV Using Lepton + Jets Events with Secondary Vertex b-Tagging D. Acosta et al., The CDF Collaboration, Phys. Rev. D71, 052003 (2005). Abstract, PostScript (775KiB). Measurement of the tt-bar Production Cross Section in p-bar p Collisions at sqrt s = 1.96 TeV using Kinematic Fitting of b-tagged Lepton + Jet Events D. Acosta et al., The CDF Collaboration, Phys. Rev. D71, 072005 (2005). Abstract, PostScript (546KiB). Measurement of the W Boson Polarization in Top Decay at CDF at sqrt s = 1.8 TeV D. Acosta et al., The CDF Collaboration, Phys. Rev. D71, 031101(R) (2005). Abstract, PostScript (352KiB). Search for Electroweak Single Top Quark Production in p anti-p Collisions at s(1/2) = 1.96 TeV D. Acosta et al., The CDF Collaboration, Phys. Rev. D71, 012005 (2005). Abstract, PDF (149KiB). Measurement of the tt-bar Production Cross Section in pp-bar Collisions at s(1/2) = 1.96 TeV Using Dilepton Events D. Acosta et al., The CDF Collaboration, Phys. Rev. Lett. 93, 142001 (2004). Abstract, PostScript (220KiB). Optimized Search for Single-Top-Quark Production at the Tevatron D. Acosta et al., The CDF Collaboration, Phys. Rev. D69, 052003 (2004). Abstract, PostScript (1729KiB). Search for W' Boson Decaying to a Top and Bottom Quark Pair in 1.8 TeV p anti-p Collisions D. Acosta et al., The CDF Collaboration, Phys. Rev. Lett. 90, 081802 (2003). Abstract, PostScript (107KiB). Search for Single-Top-Quark Production in p anti-p Collisions at s(1/2) = 1.8 TeV D. Acosta et al., The CDF Collaboration, Phys. Rev. D65, 091120 (2002). Abstract, PostScript (113KiB). Measurement of the tt-bar Production Cross Section in p anti-p Collisions at s(1/2) = 1.8 TeV T. Affolder et al., The CDF Collaboration, Phys. Rev. D64, 032002 (2001). Abstract, PostScript (379KiB). Measurement of the Top Quark p(t) Distribution T. Affolder et al., The CDF Collaboration, Phys. Rev. Lett. 87, 102001 (2001). Abstract, PostScript (89865). Measurement of the Top Quark Mass with the Collider Detector at Fermilab T. Affolder et al., The CDF Collaboration, Phys. Rev. D63, 032003 (2001). Abstract, PostScript (682KiB). Measurement of the Helicity of W Bosons in Top Quark Decays T. Affolder et al., The CDF Collaboration, Phys. Rev. Lett. 84, 216 (2000). Abstract, PostScript (57697). Kinematics of t anti-t Events at CDF F. Abe et al., The CDF Collaboration, Phys. Rev. D59, 092001 (1999) Abstract, PostScript (231KiB). Measurement of the Top Quark Mass with the Collider Detector F. Abe et al., The CDF Collaboration, Phys. Rev. Lett. 82, 271 (1999) Abstract, PostScript (80081). Measurement of the Top Quark Mass F. Abe et al., The CDF Collaboration, Phys. Rev. Lett. 80, 2767 (1998). Abstract, PostScript (69528). Search for Flavor-Changing Neutral Current Decays of the Top Quark in p anti-p Collisions at s(1/2) = 1.8 TeV F. Abe et al., The CDF Collaboration, Phys. Rev. Lett. 80, 2525, (1998). Abstract, PostScript (66979). Measurement of the t anti-t Production Cross Section in p anti-p Collisions at s(1/2) = 1.8 TeV F. Abe et al., The CDF Collaboration, Phys. Rev. Lett. 80, 2773 (1998). Abstract, PostScript (51190). Measurement of the Top Quark Mass and t anti-t Production Cross Section from Dilepton Events at the Collider Detector at Fermilab F. Abe et al., The CDF Collaboration, Phys. Rev. Lett. 80, 2779 (1998) Abstract, PostScript (61114). Observation of Hadronic W Decays in t anti-t Events with the Collider Detector at Fermilab F. Abe et al., The CDF Collaboration, Phys. Rev. Lett.80, 5720-5725, (1998). Abstract, PostScript (58034). First Observation of the All Hadronic Decay of tt-bar Pairs F. Abe et al., The CDF Collaboration, Phys. Rev. Lett. 79, 1992 (1997). Abstract, PostScript (61930). Study of t anti-t Production in p anti-p Collisions Using Total Transverse Energy F. Abe et al., The CDF Collaboration, Phys. Rev. Lett. 75, 3997 (1995). FERMILAB-PUB-95/149-E. Abstract, PostScript (144KiB). Measurement of the B Meson Differential Cross Section, d sigma/d p(t), in p anti-p Collisions at s(1/2) = 1.8 TeV F. Abe et al., The CDF Collaboration, Phys. Rev Lett. 75, 1451 (1995). Abstract, PostScript (89147). Kinematics of the t anti-t Events in W + Jets at CDF A. Beretvas, The CDF Collaboration, Int. J. Mod. Phys. A11, 2233-2252, (1996). Abstract, PostScript (680KiB). CDF Results on Top A. Beretvas, The CDF Collaboration, Int. J. Mod. Phys. A11, 2045-2064, (1996). Abstract, PostScript (458KiB). Observation of Top Quark Production in p anti-p Collisions with the Collider Detector at Fermilab F. Abe et al., The CDF Collaboration, Phys. Rev. Lett. 74, 2626 (1995). Abstract, PostScript (52506). Kinematic evidence for top quark pair production in W+multijet events in p anti-p collisions at s(1/2) = 1.8 TeV F. Abe et al., The CDF Collaboration, Phys. Rev. D (b>51, 4623 (1995). Abstract, PostScript (123KiB). Identification of top quarks using kinematic variables F. Abe et al., The CDF Collaboration, Phys. Rev. D 52, 2605 (1995). Evidence for Top Production in p anti-p Collisions at s(1/2) = 1.8 TeV F. Abe et al., Phys. Rev. Lett. 73, 225 (1994). Abstract, PostScript (57820). Evidence for Top Quark Production in p anti-p Collisions at s(1/2) = 1.8 TeV F. Abe et al., Phys. Rev. D50, 2966 (1994). Abstract, PostScript (670KiB). Search for the Top Quark Decaying to a Charged Higgs Boson in p anti-p Collisions at s(1/2)=1.8 TeV F. Abe et al., Phys. Rev. Lett. 72, 1977 (1994). Abstract, PostScript (59364). Limit on the top-quark mass from proton-antiproton collisions at s(1/2) = 1.8 TeV F. Abe et al., The CDF Collaboration, Phys. Rev. D 45, 3921 (1992). Search for W' --> e nu and W' --> mu nu in p anti-p collisions at s(1/2) = 1.8 TeV F. Abe et al., The CDF Collaboration, Phys. Rev. Lett. 67, 2609 (1991). Abstract, PostScript (1436KiB). Top-quark search in the electron+jets channel in proton-antiproton collisions at s(1/2) = 1.8 TeV F. Abe et al., The CDF Collaboration, Phys. Rev. D 43, 664 (1991). Search for the top quark in the reaction p anti-p --> electron + jets at s**(1/2) = 1.8 TeV F. Abe et al., The CDF Collaboration, Phys. Rev. Lett. 64, 142 (1990). Search for new heavy quarks in electron-muon events at the Fermilab Tevatron Collider F. Abe et al., The CDF Collaboration, Phys. Rev. Lett. 64, 147 (1990).	2019-03-23T21:03:43	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9904398322105408, "perplexity": 6441.245219063044}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-13/segments/1552912203021.14/warc/CC-MAIN-20190323201804-20190323223804-00100.warc.gz"}
https://us.edugain.com/questions/A-number-is-increased-by-40-and-then-the-increased-number-is-decreased-by-40-Find-the-net-increase-or-decrease-percent	### A number is increased by $40\%$ and then the increased number is decreased by $40\%$. Find the net increase or decrease percent. Answer: $16\%$ Step by Step Explanation: 1. Let the number be $x$. We are given that a number is increased by $40\%$. So, increased percentage = $(100+40)\%$ = $140\%$ Then, \begin{aligned} \text{ Increased number } =& \space 140\% \text{ of } x = \bigg( \dfrac { 140 } { 100 } \times x \bigg) = \dfrac { 7 } { 5 } x \\ \end{aligned} Now, the number is decreased by $40 \%$. So, the decreased number will be $(100-40)\%$ = $60\%$ of the increased number. \begin{aligned} \text{ Decreased number } =& \space 60\% \text{ of } \dfrac { 7 } { 5 } x = \bigg( \dfrac { 60 } { 100 } \times \dfrac { 7 } { 5 } x \bigg) = \dfrac { 420 } { 500 } x \\ \therefore \text{ Net decrease } =& \text{ Original Number - Decreased Number } = \bigg( x - \dfrac { 420 } { 500 } x \bigg) = \dfrac { 80 } { 500 } x \\ \end{aligned} 2. Therefore, \begin{aligned} \text{ Net decrease }\% =& \dfrac { \text{ Net decrease } } { \text{ Original number } } \times 100\% \\ =& \bigg( \dfrac { 80 x } { 500 } \div { x } \times 100 \bigg)\% \\ = & \bigg( \dfrac { 80 x } { 500 } \times \dfrac { 1 } { x } \times 100 \bigg)\% = 16\% \end{aligned} Hence, the net decrease is $16\%$. You can reuse this answer Creative Commons License	2022-11-29T15:42:25	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 1.0000041723251343, "perplexity": 1035.1175680534157}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446710698.62/warc/CC-MAIN-20221129132340-20221129162340-00749.warc.gz"}
https://zbmath.org/authors/?q=ai%3Achen.yangquan	# zbMATH — the first resource for mathematics ## Chen, Yangquan Compute Distance To: Author ID: chen.yangquan Published as: Chen, Yangquan; Chen, YangQuan; Chen, Yang Quan; Chen, Y.; Chen, Y. Q.; Chen, Yang-quan; Chen, Yang-Quan External Links: ORCID · Wikidata · Google Scholar · ResearchGate · dblp · IdRef · theses.fr Documents Indexed: 170 Publications since 1997, including 15 Books all top 5 #### Co-Authors 2 single-authored 16 Ahn, Hyo-Sung 16 Ge, Fudong 16 Podlubny, Igor 15 Li, Yan 13 Li, Changpin 13 Xue, Dingyu 12 Moore, Kevin L. 10 Vinagre, Blas Manuel 9 Kou, Chunhai 9 Sheng, Hu 8 Zeng, Caibin 5 Jiao, Zhuang 5 Lu, Junguo 5 Luo, Ying 5 Sun, Hongguang 5 Wen, Changyun 5 Yang, Qigui 4 Chen, Dali 4 Yin, Chun 4 Zhong, Shou-Ming 3 Bai, Zhanbing 3 Liang, Jinsong 3 Liu, Lu 3 Petras, Ivo 3 Qiu, Tianshuang 3 Sun, Mingxuan 3 Sun, Sujing 2 Băleanu, Dumitru I. 2 Cai, Ruiyang 2 Cao, Jianxiong 2 Cao, Kecai 2 Chen, Weidong 2 Chen, Wen 2 Cheng, Yuhua 2 Dadras, Sara 2 Ding, Hengfei 2 Domański, Paweł D. 2 Feliu, Vicente 2 Jiang, Ping 2 Monje, Concepción Alicia 2 Qian, Deliang 2 Skovranek, Tomas 2 Tian, Guohui 2 Tricaud, Christophe 2 Vinagre Jara, Blas Manuel 2 Zhang, Shuo 1 Agarwal, Praveen 1 Ashurov, Ravshan R. 1 Atherton, Derek P. 1 Aziz, T. Z. 1 Bahl, Vikas 1 Bao, Bocheng 1 Bao, Han 1 Bhambhani, Varsha 1 Bigoni, Daniele 1 Calderon, Antonio J. 1 Cao, Junyi 1 Cao, Lili 1 Chao, Haiyang 1 Chechkin, Aleksei V. 1 Chen, Diyi 1 Chen, Liping 1 Chen, Mo 1 Chen, Wen 1 Chen, Xiaolu 1 Cheng, Heng-Da 1 Dehghan, Sina 1 Deshpande, Vikram S. 1 Dharmasena, K. P. 1 Dou, Huifang 1 Du, Zengji 1 Dudt, P. 1 Evans, Anthony G. 1 Fei, Shumin 1 Fullmer, Rees 1 Ghosh, Mohua 1 Gong, Zhiming 1 Gong, Ziqing 1 Guo, Bao-Zhu 1 Guo, Lihong 1 Guo, Peng 1 Huang, Jiacai 1 Huang, Jianhua 1 Huang, Ruoyun 1 Huang, Xuegang 1 Ionescu, Clara Mihaela 1 Jiang, Bin 1 Kim, Youngsoo 1 Kiryakova, Virginia S. 1 Kurths, Jürgen 1 Lee, Tong Heng 1 Li, Chunhao 1 Li, Hongsheng 1 Li, Zhuo 1 Li, Ziyu 1 Lian, Hairong 1 Lian, Zhigang 1 Liao, Xiaozhong 1 Liu, Baodong 1 Lv, Chunwan ...and 67 more Co-Authors all top 5 #### Serials 20 Fractional Calculus & Applied Analysis 14 Automatica 10 Nonlinear Dynamics 8 Signal Processing 7 Computers & Mathematics with Applications 5 International Journal of Control 5 Journal of the Franklin Institute 5 International Journal of Robust and Nonlinear Control 5 Abstract and Applied Analysis 4 Applied Mathematics and Computation 4 IEEE Transactions on Automatic Control 4 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 4 Communications in Nonlinear Science and Numerical Simulation 4 Asian Journal of Control 3 Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 3 Control Theory & Applications 2 Journal of Computational Physics 2 IMA Journal of Mathematical Control and Information 2 Applied Mathematical Modelling 2 Journal of Vibration and Control 2 Chaos 2 International Journal of Differential Equations 2 International Journal of Systems Science. Principles and Applications of Systems and Integration 1 Inverse Problems 1 Journal of Mathematical Analysis and Applications 1 Mathematical Methods in the Applied Sciences 1 Physics Letters. A 1 Chaos, Solitons and Fractals 1 Information Sciences 1 Journal of Optimization Theory and Applications 1 Meccanica 1 Systems & Control Letters 1 International Journal of Adaptive Control and Signal Processing 1 IEEE Transactions on Circuits and Systems. I: Fundamental Theory and Applications 1 International Journal of Computer Mathematics 1 The Journal of Artificial Intelligence Research (JAIR) 1 Complexity 1 Mathematical Problems in Engineering 1 European Journal of Control 1 Discrete Dynamics in Nature and Society 1 European Journal of Mechanics. A. Solids 1 International Journal of Applied Mathematics and Computer Science 1 Entropy 1 Sādhanā 1 Control and Intelligent Systems 1 New Mathematics and Natural Computation 1 Lecture Notes in Control and Information Sciences 1 Advances in Design and Control 1 Numerical Mathematics: Theory, Methods and Applications 1 IET Control Theory & Applications 1 Scientia Iranica. Transaction B: Mechanical Engineering 1 Algorithms 1 Fluctuation and Noise Letters (FNL) 1 Mathematical Control and Related Fields 1 Springer Proceedings in Mathematics & Statistics 1 Signals and Communication Technology 1 Fractional Calculus in Applied Sciences and Engineering 1 SpringerBriefs in Electrical and Computer Engineering 1 Advances in Industrial Control 1 Communications and Control Engineering 1 Encyclopedia of Complexity and Systems Science Series all top 5 #### Fields 102 Systems theory; control (93-XX) 53 Ordinary differential equations (34-XX) 45 Real functions (26-XX) 26 Partial differential equations (35-XX) 21 Numerical analysis (65-XX) 18 Computer science (68-XX) 14 Information and communication theory, circuits (94-XX) 13 Probability theory and stochastic processes (60-XX) 7 General and overarching topics; collections (00-XX) 6 Calculus of variations and optimal control; optimization (49-XX) 4 Special functions (33-XX) 4 Dynamical systems and ergodic theory (37-XX) 4 Statistics (62-XX) 4 Mechanics of particles and systems (70-XX) 4 Mechanics of deformable solids (74-XX) 4 Operations research, mathematical programming (90-XX) 4 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 4 Biology and other natural sciences (92-XX) 3 Optics, electromagnetic theory (78-XX) 3 Statistical mechanics, structure of matter (82-XX) 2 Integral transforms, operational calculus (44-XX) 2 Integral equations (45-XX) 1 History and biography (01-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Functions of a complex variable (30-XX) 1 Approximations and expansions (41-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Functional analysis (46-XX) 1 Quantum theory (81-XX) #### Citations contained in zbMATH Open 139 Publications have been cited 3,453 times in 2,263 Documents Cited by Year Mittag-Leffler stability of fractional order nonlinear dynamic systems. Zbl 1185.93062 Li, Yan; Chen, Yangquan; Podlubny, Igor 2009 Stability of fractional-order nonlinear dynamic systems: Lyapunov direct method and generalized Mittag-Leffler stability. Zbl 1189.34015 Li, Yan; Chen, Yangquan; Podlubny, Igor 2010 Fractional-order systems and controls. Fundamentals and applications. Zbl 1211.93002 Monje, Concepción Alicia; Chen, YangQuan; Vinagre, Blas Manuel; Xue, Dingyü; Feliu, Vicente 2010 Numerical approximation of nonlinear fractional differential equations with subdiffusion and superdiffusion. Zbl 1228.65190 Li, Changpin; Zhao, Zhengang; Chen, Yangquan 2011 Matrix approach to discrete fractional calculus. II: Partial fractional differential equations. Zbl 1160.65308 Podlubny, Igor; Chechkin, Aleksei; Skovranek, Tomas; Chen, Yangquan; Vinagre Jara, Blas M. 2009 Robust stability and stabilization of fractional-order interval systems with the fractional order $$\alpha$$: the $$0<\alpha<1$$ case. Zbl 1368.93506 Lu, Jun-Guo; Chen, Yang-Quan 2010 Discretization schemes for fractional-order differentiators and integrators. Zbl 1368.65035 Chen, Yang Quan; Moore, Kevin L. 2002 Analytical stability bound for a class of delayed fractional-order dynamic systems. Zbl 1020.34064 Chen, Yangquan; Moore, Kevin L. 2002 Necessary and sufficient stability condition of fractional-order interval linear systems. Zbl 1152.93455 Ahn, Hyo-Sung; Chen, Yangquan 2008 Two direct Tustin discretization methods for fractional-order differentiator/integrator. Zbl 1051.93031 Vinagre, Blas M.; Chen, Yang Quan; Petráš, Ivo 2003 Fractional-order sliding mode based extremum seeking control of a class of nonlinear systems. Zbl 1309.93041 Yin, Chun; Chen, YangQuan; Zhong, Shou-ming 2014 An approximate method for numerically solving fractional order optimal control problems of general form. Zbl 1189.49045 Tricaud, Christophe; Chen, Yangquan 2010 Robust stability check of fractional order linear time invariant systems with interval uncertainties. Zbl 1172.94385 Chen, Yangquan; Ahn, Hyo-Sung; Podlubny, Igor 2006 Continued fraction expansion approaches to discretizing fractional order derivatives-an expository review. Zbl 1134.93300 Chen, Yangquan; Vinagre, Blas M.; Podlubny, Igor 2004 High-order algorithms for Riesz derivative and their applications. II. Zbl 1349.65284 Ding, Hengfei; Li, Changpin; Chen, YangQuan 2015 Fractional-order iterative learning control for fractional-order linear systems. Zbl 1248.93085 Li, Yan; Chen, YangQuan; Ahn, Hyo-Sung 2011 Robust stability test of a class of linear time-invariant interval fractional-order system using Lyapunov inequality. Zbl 1123.93074 Ahn, Hyo-Sung; Chen, Yangquan; Podlubny, Igor 2007 A new collection of real world applications of fractional calculus in science and engineering. Zbl 07265270 Sun, HongGuang; Zhang, Yong; Baleanu, Dumitru; Chen, Wen; Chen, YangQuan 2018 Distributed-order dynamic systems. Stability, simulation, applications and perspectives. Zbl 1401.93005 Jiao, Zhuang; Chen, YangQuan; Podlubny, Igor 2012 Using fractional order adjustment rules and fractional order reference models in model-reference adaptive control. Zbl 1031.93110 Vinagre, B. M.; Petráš, I.; Podlubny, I.; Chen, Y. Q. 2002 Finite difference schemes for variable-order time fractional diffusion equation. Zbl 1258.65079 Sun, Hongguang; Chen, Wen; Li, Changpin; Chen, Yangquan 2012 Iterative learning control. Robustness and monotonic convergence for interval systems. Zbl 1162.93025 Ahn, Hyo-Sung; Moore, Kevin L.; Chen, YangQuan 2007 A new IIR-type digital fractional order differentiator. Zbl 1145.93423 Chen, Yangquan; Vinagre, Blas M. 2003 Robust controllability of interval fractional order linear time invariant systems. Zbl 1172.94386 Chen, Yangquan; Ahn, Hyo-Sung; Xue, Dingyü 2006 Fractional order [proportional derivative] controller for a class of fractional order systems. Zbl 1183.93053 Luo, Ying; Chen, Yangquan 2009 Adaptive fractional-order switching-type control method design for 3D fractional-order nonlinear systems. Zbl 1348.93216 Yin, Chun; Cheng, Yuhua; Chen, Yangquan; Stark, Brandon; Zhong, Shouming 2015 Control of a novel class of fractional-order chaotic systems via adaptive sliding mode control approach. Zbl 1349.93237 Yin, Chun; Dadras, Sara; Zhong, Shou-Ming; Chen, Yangquan 2013 Fractional processes and fractional-order signal processing. Techniques and applications. Zbl 1245.94004 Sheng, Hu; Chen, YangQuan; Qiu, TianShuang 2012 On Riemann-Liouville and Caputo derivatives. Zbl 1213.26008 Li, Changpin; Qian, Deliang; Chen, Yangquan 2011 On fractional $$PI^{\lambda }$$ controllers: Some tuning rules for robustness to plant uncertainties. Zbl 1134.93338 Monje, Concepción A.; Calderon, Antonio J.; Vinagre, Blas M.; Chen, Yangquan; Feliu, Vicente 2004 On the existence of blow up solutions for a class of fractional differential equations. Zbl 1312.34007 Bai, Zhanbing; Chen, YangQuan; Lian, Hairong; Sun, Sujing 2014 Analysis of a high-order iterative learning control algorithm for uncertain nonlinear systems with state delays. Zbl 0912.93031 Chen, Yangquan; Gong, Zhiming; Wen, Changyun 1998 High-order approximation to Caputo derivatives and Caputo-type advection-diffusion equations. II. Zbl 1325.65121 Cao, Jianxiong; Li, Changpin; Chen, YangQuan 2015 Application of numerical inverse Laplace transform algorithms in fractional calculus. Zbl 1210.65201 Sheng, Hu; Li, Yan; Chen, YangQuan 2011 An iterative learning controller with initial state learning. Zbl 1056.93646 Chen, Y.; Wen, C.; Gong, Z.; Sun, M. 1999 Random-order fractional differential equation models. Zbl 1203.94056 Sun, HongGuang; Chen, YangQuan; Chen, Wen 2011 Stability analysis of discrete-time iterative learning control systems with interval uncertainty. Zbl 1117.93075 Ahn, Hyo-Sung; Moore, Kevin L.; Chen, Yangquan 2007 Iterative learning control and repetitive control in hard disk drive industry – a tutorial. Zbl 1284.93269 Chen, YangQuan; Moore, Kevin L.; Yu, Jie; Zhang, Tao 2008 Trajectory-keeping in satellite formation flying via robust periodic learning control. Zbl 1204.93082 Ahn, Hyo-Sung; Moore, Kevin L.; Chen, Yangquan 2010 Iterative learning control. Convergence, robustness and applications. Zbl 0949.93002 Chen, Yangquan; Wen, Changyun 1999 On mean square displacement behaviors of anomalous diffusions with variable and random orders. Zbl 1235.82018 Sun, Hongguang; Chen, Wen; Sheng, Hu; Chen, Yangquan 2010 Matrix approach to discrete fractional calculus. III: Non-equidistant grids, variable step length and distributed orders. Zbl 1339.65094 Podlubny, Igor; Skovranek, Tomas; Vinagre Jara, Blas M.; Petras, Ivo; Verbitsky, Viktor; Chen, YangQuan 2013 On the bound of the Lyapunov exponents for the fractional differential systems. Zbl 1311.34016 Li, Changpin; Gong, Ziqing; Qian, Deliang; Chen, YangQuan 2010 Asymptotical stability of nonlinear fractional differential system with Caputo derivative. Zbl 1239.34008 Zhang, Fengrong; Li, Changpin; Chen, Yangquan 2011 Convergence speed of a fractional order consensus algorithm over undirected scale-free networks. Zbl 1263.93013 Sun, Wei; Li, Yan; Li, Changpin; Chen, Yangquan 2011 Time-optimal control of systems with fractional dynamics. Zbl 1203.49031 Tricaud, Christophe; Chen, Yangquan 2010 Stability and stabilization of fractional-order linear systems with convex polytopic uncertainties. Zbl 1312.93081 Lu, Jun-Guo; Chen, YangQuan 2013 A survey on fractional-order iterative learning control. Zbl 1263.93100 Li, Yan; Chen, YangQuan; Ahn, Hyo-Sung; Tian, Guohui 2013 A fractional adaptation scheme for lateral control of an AGV. Zbl 1229.70086 Suárez, José I.; Vinagre, Blas M.; Chen, Yangquan 2008 Terminal iterative learning control with an application to RTPCVD thickness control. Zbl 0953.93508 Xu, Jian-Xin; Chen, Yangquan; Lee, Tong Heng; Yamamoto, Shigehiko 1999 Stabilizing and robust fractional order PI controller synthesis for first order plus time delay systems. Zbl 1257.93039 Luo, Ying; Chen, Yangquan 2012 Synthesis of multifractional Gaussian noises based on variable-order fractional operators. Zbl 1213.94049 Sheng, Hu; Sun, Hongguang; Chen, Yangquan; Qiu, Tianshuang 2011 Monotonically convergent iterative learning control for linear discrete-time systems. Zbl 1086.93066 Moore, Kevin L.; Chen, Yangquan; Bahl, Vikas 2005 Fractional calculus in image processing: a review. Zbl 06663383 Yang, Qi; Chen, Dali; Zhao, Tiebiao; Chen, YangQuan 2016 Numerics for the fractional Langevin equation driven by the fractional Brownian motion. Zbl 1312.34093 Guo, Peng; Zeng, Caibin; Li, Changpin; Chen, YangQuan 2013 Iteration domain $$H_{\infty }$$-optimal iterative learning controller design. Zbl 1284.93104 Moore, Kevin L.; Ahn, Hyo-Sung; Chen, Yang Quan 2008 Hybrid symbolic and numerical simulation studies of time-fractional order wave-diffusion systems. Zbl 1125.65364 Liang, J.; Chen, Y. Q. 2006 Analytical stability bound for delayed second-order systems with repeating poles using Lambert function $$W$$. Zbl 1020.93019 Chen, Yang Quan; Moore, Kevin L. 2002 Global Padé approximations of the generalized Mittag-Leffler function and its inverse. Zbl 1333.26007 Zeng, Caibin; Chen, Yang Quan 2015 Solving nonlinear stochastic differential equations with fractional Brownian motion using reducibility approach. Zbl 1246.60084 Zeng, Caibin; Yang, Qigui; Chen, Yang Quan 2012 Fractional-order total variation image denoising based on proximity algorithm. Zbl 1338.68273 Chen, Dali; Chen, YangQuan; Xue, Dingyu 2015 Linear feedback control. Analysis and design with Matlab. Zbl 1143.93002 Xue, Dingyü; Chen, YangQuan; Atherton, Derek P. 2007 The fBm-driven Ornstein-Uhlenbeck process: probability density function and anomalous diffusion. Zbl 1274.60127 Zeng, Caibin; Chen, Yangquan; Yang, Qigui 2012 Boundary stabilization and disturbance rejection for time fractional order diffusion-wave equations. Zbl 1094.74042 Liang, Jinsong; Chen, Yangquan; Fullmer, Rees 2004 A robust high-order $$P$$-type iterative learning controller using current iteration tracking error. Zbl 0886.93036 Chen, Yangquan; Wen, Changyun; Sun, Mingxuan 1997 Compact difference method for solving the fractional reaction-subdiffusion equation with Neumann boundary value condition. Zbl 1308.65140 Cao, Jianxiong; Li, Changpin; Chen, Yangquan 2015 Stability analysis of fractional-order systems with double noncommensurate orders for matrix case. Zbl 1273.93143 Jiao, Zhuang; Chen, Yangquan 2011 A review and evaluation of numerical tools for fractional calculus and fractional order controls. Zbl 1367.93205 Li, Zhuo; Liu, Lu; Dehghan, Sina; Chen, Yangquan; Xue, Dingyü 2017 Regional analysis of time-fractional diffusion processes. Zbl 1382.93002 Ge, Fudong; Chen, YangQuan; Kou, Chunhai 2018 High-order algorithms for Riesz derivative and their applications. I. Zbl 1434.65113 Ding, Hengfei; Li, Changpin; Chen, YangQuan 2014 Almost sure and moment stability properties of fractional order Black-Scholes model. Zbl 1333.60132 Zeng, Caibin; Chen, YangQuan; Yang, Qigui 2013 Fractional-order total variation image restoration based on primal-dual algorithm. Zbl 1364.94091 Chen, Dali; Chen, Yang Quan; Xue, Dingyu 2013 Monotonic convergent iterative learning controller design based on interval model conversion. Zbl 1366.93714 Ahn, Hyo-Sung; Moore, Kevin L.; Chen, YangQuan 2006 Fractional-order exponential switching technique to enhance sliding mode control. Zbl 1443.93023 Yin, Chun; Huang, Xuegang; Chen, Yangquan; Dadras, Sara; Zhong, Shou-ming; Cheng, Yuhua 2017 FARIMA with stable innovations model of Great Salt Lake elevation time series. Zbl 1203.94053 Sheng, Hu; Chen, YangQuan 2011 Fractional calculus and its applications. Zbl 1338.00072 Li, Changpin (ed.); Chen, YangQuan (ed.); Kurths, Jürgen (ed.) 2013 Dynamic multi-attribute decision making model based on triangular intuitionistic fuzzy numbers. Zbl 1277.91035 Chen, Y.; Li, B. 2011 On distributed order integrator/differentiator. Zbl 1219.94039 Li, Yan; Sheng, Hu; Chen, Yang Quan 2011 Robust asymptotical stability of fractional-order linear systems with structured perturbations. Zbl 1345.93125 Lu, Jun-Guo; Chen, Yangquan; Chen, Weidong 2013 On the regional gradient observability of time fractional diffusion processes. Zbl 1348.93054 Ge, Fudong; Chen, Yang Quan; Kou, Chunhai 2016 On the regional controllability of the sub-diffusion process with Caputo fractional derivative. Zbl 06663385 Ge, Fudong; Chen, YangQuan; Kou, Chunhai; Podlubny, Igor 2016 Analytical impulse response of a fractional second order filter and its impulse response invariant discretization. Zbl 1203.94039 Li, Yan; Sheng, Hu; Chen, YangQuan 2011 Optimal observation for cyber-physical systems. A Fisher-information-matrix-based approach. Zbl 1219.93002 Song, Zhen; Chen, YangQuan; Sastry, Chellury Ram; Tas, Nazif Cihan 2009 Robust stability bounds of uncertain fractional-order systems. Zbl 1312.34021 Ma, YingDong; Lu, Jun-Guo; Chen, WeiDong; Chen, YangQuan 2014 Regional gradient controllability of sub-diffusion processes. Zbl 1339.93025 Ge, Fudong; Chen, YangQuan; Kou, Chunhai 2016 Genetic algorithm-based identification of fractional-order systems. Zbl 1297.93062 Zhou, Shengxi; Cao, Junyi; Chen, Yangquan 2013 Robust position control of PMSM using fractional-order sliding mode controller. Zbl 1256.93053 Huang, Jiacai; Li, Hongsheng; Chen, Yangquan; Xu, Qinghong 2012 Robust stability analysis for fractional-order systems with time delay based on finite spectrum assignment. Zbl 1418.93213 Liu, Lu; Zhang, Shuo; Xue, Dingyu; Chen, Yangquan 2019 Stability analysis of nonlinear Hadamard fractional differential system. Zbl 1418.34111 Wang, Guotao; Pei, Ke; Chen, YangQuan 2019 Robust decentralized control of perturbed fractional-order linear interconnected systems. Zbl 1345.93140 Li, Jun; Lu, Jun-Guo; Chen, Yangquan 2013 Optimal random search, fractional dynamics and fractional calculus. Zbl 1305.26021 Zeng, Caibin; Chen, Yangquan 2014 Fractional order signal processing of electrochemical noises. Zbl 1229.78018 Chen, Yangquan; Sun, Rongtao; Zhou, Anhong; Zaveri, Nikita 2008 Stability of fractional-order linear time-invariant systems with multiple noncommensurate orders. Zbl 1268.34018 Jiao, Zhuang; Chen, Yang Quan 2012 Impulse response of a generalized fractional second order filter. Zbl 1269.93121 Jiao, Zhuang; Chen, Yangquan 2012 Fractional-order variational optical flow model for motion estimation. Zbl 1342.49028 Chen, Dali; Sheng, Hu; Chen, YangQuan; Xue, Dingyü 2013 Exact maximum singular value calculation of an interval matrix. Zbl 1367.65054 Ahn, Hyo-Sung; Chen, YangQuan 2007 An interval Kalman filtering with minimal conservatism. Zbl 1245.93128 Ahn, Hyo-Sung; Kim, Young-Soo; Chen, Yangquan 2012 Fractional order disturbance observer for robust vibration suppression. Zbl 1142.74334 Chen, Yangquan; Vinagre, Blas M.; Podlubny, Igor 2004 Suboptimum $$H_2$$ pseudo-rational approximations to fractional-order linear time invariant systems. Zbl 1127.65044 Xue, Dingyü; Chen, Yangquan 2007 Robustness of fractional-order boundary control of time fractional wave equations with delayed boundary measurement using the simple predictor. Zbl 1125.93029 Liang, Jinsong; Zhang, Weiwei; Chen, Yangquan; Podlubny, Igor 2007 Stability and resonance analysis of a general non-commensurate elementary fractional-order system. Zbl 1441.93211 Zhang, Shuo; Liu, Lu; Xue, Dingyu; Chen, YangQuan 2020 Data-driven forward discretizations for Bayesian inversion. Zbl 1450.62136 Bigoni, D.; Chen, Y.; Trillos, N. Garcia; Marzouk, Y.; Sanz-Alonso, D. 2020 Distribution consensus of nonlinear stochastic multi-agent systems based on sliding-mode control with probability density function compensation. Zbl 1448.93306 Wang, Jing; Zhang, Xuerou; Zhou, Jinglin; Chen, Yangquan 2020 The Green function for a class of Caputo fractional differential equations with a convection term. Zbl 07268202 Bai, Zhanbing; Sun, Sujing; Du, Zengji; Chen, YangQuan 2020 Robust stability analysis for fractional-order systems with time delay based on finite spectrum assignment. Zbl 1418.93213 Liu, Lu; Zhang, Shuo; Xue, Dingyu; Chen, Yangquan 2019 Stability analysis of nonlinear Hadamard fractional differential system. Zbl 1418.34111 Wang, Guotao; Pei, Ke; Chen, YangQuan 2019 Fractional calculus. Selected papers from the international conference on fractional differentiation and its applications (ICFDA 2018), Amman, Jordan, July 16–18, 2018. Zbl 1444.26001 Agarwal, Praveen; Baleanu, Dumitru; Chen, YangQuan; Momani, Shaher; Tenreiro Machado, José António 2019 Finite energy Lyapunov function candidate for fractional order general nonlinear systems. Zbl 07264511 Li, Yan; Zhao, Daduan; Chen, YangQuan; Podlubny, Igor; Zhang, Chenghui 2019 Mittag-Leffler stabilization for an unstable time-fractional anomalous diffusion equation with boundary control matched disturbance. Zbl 1426.93310 Zhou, Hua-Cheng; Lv, Chunwan; Guo, Bao-Zhu; Chen, Yangquan 2019 Complex dynamical behaviors of a fractional-order system based on a locally active memristor. Zbl 1435.34057 Yu, Yajuan; Bao, Han; Shi, Min; Bao, Bocheng; Chen, Yangquan; Chen, Mo 2019 Regional observability for Hadamard-Caputo time fractional distributed parameter systems. Zbl 1428.34011 Cai, Ruiyang; Ge, Fudong; Chen, YangQuan; Kou, Chunhai 2019 Event-triggered boundary feedback control for networked reaction-subdiffusion processes with input uncertainties. Zbl 1457.93057 Ge, Fudong; Chen, YangQuan 2019 Robust dissipativity and dissipation of a class of fractional-order uncertain linear systems. Zbl 1432.93297 Chen, Liping; Yin, Hao; Wu, Ranchao; Yin, Lisheng; Chen, Yangquan 2019 State-of-art survey of fractional order modeling and estimation methods for Lithium-ion batteries. Zbl 1436.78006 Wang, YaNan; Chen, YangQuan; Liao, XiaoZhong 2019 A new collection of real world applications of fractional calculus in science and engineering. Zbl 07265270 Sun, HongGuang; Zhang, Yong; Baleanu, Dumitru; Chen, Wen; Chen, YangQuan 2018 Regional analysis of time-fractional diffusion processes. Zbl 1382.93002 Ge, Fudong; Chen, YangQuan; Kou, Chunhai 2018 A novel method for control performance assessment with fractional order signal processing and its application to semiconductor manufacturing. Zbl 1461.94039 Liu, Kai; Chen, Yangquan; Domański, Paweł D.; Zhang, Xi 2018 Mittag-Leffler convergent backstepping observers for coupled semilinear subdiffusion systems with spatially varying parameters. Zbl 1408.93097 Ge, Fudong; Meurer, Thomas; Chen, YangQuan 2018 A review and evaluation of numerical tools for fractional calculus and fractional order controls. Zbl 1367.93205 Li, Zhuo; Liu, Lu; Dehghan, Sina; Chen, Yangquan; Xue, Dingyü 2017 Fractional-order exponential switching technique to enhance sliding mode control. Zbl 1443.93023 Yin, Chun; Huang, Xuegang; Chen, Yangquan; Dadras, Sara; Zhong, Shou-ming; Cheng, Yuhua 2017 Regional controllability analysis of fractional diffusion equations with Riemann-Liouville time fractional derivatives. Zbl 1352.93022 Ge, Fudong; Chen, YangQuan; Kou, Chunhai 2017 Actuator characterisations to achieve approximate controllability for a class of fractional sub-diffusion equations. Zbl 1367.93069 Ge, Fudong; Chen, Yangquan; Kou, Chunhai 2017 Special issue: Applied fractional calculus in modelling, analysis and design of control systems. Zbl 1368.00050 Chen, Yangquan; Ionescu, Clara 2017 Regional boundary controllability of time fractional diffusion processes. Zbl 1417.93069 Ge, Fudong; Chen, YangQuan; Kou, Chunhai 2017 Reply to “Comments on ‘Mittag-Leffler stability of fractional order nonlinear dynamic systems’ [Automatica 45(8) (2009) 1965-1969]”. Zbl 1351.93074 Li, Yan; Chen, YangQuan; Podlubny, Igor 2017 Extended Luenberger-type observer for a class of semilinear time fractional diffusion systems. Zbl 1374.93170 Ge, Fudong; Chen, YangQuan 2017 Fractional calculus in image processing: a review. Zbl 06663383 Yang, Qi; Chen, Dali; Zhao, Tiebiao; Chen, YangQuan 2016 On the regional gradient observability of time fractional diffusion processes. Zbl 1348.93054 Ge, Fudong; Chen, Yang Quan; Kou, Chunhai 2016 On the regional controllability of the sub-diffusion process with Caputo fractional derivative. Zbl 06663385 Ge, Fudong; Chen, YangQuan; Kou, Chunhai; Podlubny, Igor 2016 Regional gradient controllability of sub-diffusion processes. Zbl 1339.93025 Ge, Fudong; Chen, YangQuan; Kou, Chunhai 2016 Bifurcation dynamics of the tempered fractional Langevin equation. Zbl 1378.60066 Zeng, Caibin; Yang, Qigui; Chen, YangQuan 2016 Scientific computing with MATLAB. 2nd edition. Zbl 1344.65001 Xue, Dingyü; Chen, YangQuan 2016 High-order algorithms for Riesz derivative and their applications. II. Zbl 1349.65284 Ding, Hengfei; Li, Changpin; Chen, YangQuan 2015 Adaptive fractional-order switching-type control method design for 3D fractional-order nonlinear systems. Zbl 1348.93216 Yin, Chun; Cheng, Yuhua; Chen, Yangquan; Stark, Brandon; Zhong, Shouming 2015 High-order approximation to Caputo derivatives and Caputo-type advection-diffusion equations. II. Zbl 1325.65121 Cao, Jianxiong; Li, Changpin; Chen, YangQuan 2015 Global Padé approximations of the generalized Mittag-Leffler function and its inverse. Zbl 1333.26007 Zeng, Caibin; Chen, Yang Quan 2015 Fractional-order total variation image denoising based on proximity algorithm. Zbl 1338.68273 Chen, Dali; Chen, YangQuan; Xue, Dingyu 2015 Compact difference method for solving the fractional reaction-subdiffusion equation with Neumann boundary value condition. Zbl 1308.65140 Cao, Jianxiong; Li, Changpin; Chen, Yangquan 2015 Output consensus for multiple non-holonomic systems under directed communication topology. Zbl 1316.93010 Xu, Yaojin; Tian, Yu-Ping; Chen, Yangquan 2015 Cooperative control design for non-holonomic chained-form systems. Zbl 1332.93009 Cao, Ke-Cai; Jiang, Bin; Chen, Yangquan 2015 Modeling, analysis and design of control systems in MATLAB and Simulink. Zbl 1305.93005 Xue, Dingyü; Chen, YangQuan 2015 Fractional-order sliding mode based extremum seeking control of a class of nonlinear systems. Zbl 1309.93041 Yin, Chun; Chen, YangQuan; Zhong, Shou-ming 2014 On the existence of blow up solutions for a class of fractional differential equations. Zbl 1312.34007 Bai, Zhanbing; Chen, YangQuan; Lian, Hairong; Sun, Sujing 2014 High-order algorithms for Riesz derivative and their applications. I. Zbl 1434.65113 Ding, Hengfei; Li, Changpin; Chen, YangQuan 2014 Robust stability bounds of uncertain fractional-order systems. Zbl 1312.34021 Ma, YingDong; Lu, Jun-Guo; Chen, WeiDong; Chen, YangQuan 2014 Optimal random search, fractional dynamics and fractional calculus. Zbl 1305.26021 Zeng, Caibin; Chen, Yangquan 2014 The existence and uniqueness of a class of fractional differential equations. Zbl 07022469 Bai, Zhanbing; Sun, Sujing; Chen, YangQuan 2014 Control of a novel class of fractional-order chaotic systems via adaptive sliding mode control approach. Zbl 1349.93237 Yin, Chun; Dadras, Sara; Zhong, Shou-Ming; Chen, Yangquan 2013 Matrix approach to discrete fractional calculus. III: Non-equidistant grids, variable step length and distributed orders. Zbl 1339.65094 Podlubny, Igor; Skovranek, Tomas; Vinagre Jara, Blas M.; Petras, Ivo; Verbitsky, Viktor; Chen, YangQuan 2013 Stability and stabilization of fractional-order linear systems with convex polytopic uncertainties. Zbl 1312.93081 Lu, Jun-Guo; Chen, YangQuan 2013 A survey on fractional-order iterative learning control. Zbl 1263.93100 Li, Yan; Chen, YangQuan; Ahn, Hyo-Sung; Tian, Guohui 2013 Numerics for the fractional Langevin equation driven by the fractional Brownian motion. Zbl 1312.34093 Guo, Peng; Zeng, Caibin; Li, Changpin; Chen, YangQuan 2013 Almost sure and moment stability properties of fractional order Black-Scholes model. Zbl 1333.60132 Zeng, Caibin; Chen, YangQuan; Yang, Qigui 2013 Fractional-order total variation image restoration based on primal-dual algorithm. Zbl 1364.94091 Chen, Dali; Chen, Yang Quan; Xue, Dingyu 2013 Fractional calculus and its applications. Zbl 1338.00072 Li, Changpin; Chen, YangQuan; Kurths, Jürgen 2013 Robust asymptotical stability of fractional-order linear systems with structured perturbations. Zbl 1345.93125 Lu, Jun-Guo; Chen, Yangquan; Chen, Weidong 2013 Genetic algorithm-based identification of fractional-order systems. Zbl 1297.93062 Zhou, Shengxi; Cao, Junyi; Chen, Yangquan 2013 Robust decentralized control of perturbed fractional-order linear interconnected systems. Zbl 1345.93140 Li, Jun; Lu, Jun-Guo; Chen, Yangquan 2013 Fractional-order variational optical flow model for motion estimation. Zbl 1342.49028 Chen, Dali; Sheng, Hu; Chen, YangQuan; Xue, Dingyü 2013 Stability analysis of linear time-invariant distributed-order systems. Zbl 1327.93340 Jiao, Zhuang; Chen, YangQuan; Zhong, Yisheng 2013 Fractional order adaptive feed-forward cancellation for periodic disturbances. Zbl 1327.93140 Luo, Ying; Chen, YangQuan; Pi, YouGuo 2013 Time domain analysis of the fractional order weighted distributed parameter Maxwell model. Zbl 1381.74037 Cao, Lili; Li, Yan; Tian, Guohui; Liu, Baodong; Chen, YangQuan 2013 Distributed-order dynamic systems. Stability, simulation, applications and perspectives. Zbl 1401.93005 Jiao, Zhuang; Chen, YangQuan; Podlubny, Igor 2012 Finite difference schemes for variable-order time fractional diffusion equation. Zbl 1258.65079 Sun, Hongguang; Chen, Wen; Li, Changpin; Chen, Yangquan 2012 Fractional processes and fractional-order signal processing. Techniques and applications. Zbl 1245.94004 Sheng, Hu; Chen, YangQuan; Qiu, TianShuang 2012 Stabilizing and robust fractional order PI controller synthesis for first order plus time delay systems. Zbl 1257.93039 Luo, Ying; Chen, Yangquan 2012 Solving nonlinear stochastic differential equations with fractional Brownian motion using reducibility approach. Zbl 1246.60084 Zeng, Caibin; Yang, Qigui; Chen, Yang Quan 2012 The fBm-driven Ornstein-Uhlenbeck process: probability density function and anomalous diffusion. Zbl 1274.60127 Zeng, Caibin; Chen, Yangquan; Yang, Qigui 2012 Robust position control of PMSM using fractional-order sliding mode controller. Zbl 1256.93053 Huang, Jiacai; Li, Hongsheng; Chen, Yangquan; Xu, Qinghong 2012 Stability of fractional-order linear time-invariant systems with multiple noncommensurate orders. Zbl 1268.34018 Jiao, Zhuang; Chen, Yang Quan 2012 Impulse response of a generalized fractional second order filter. Zbl 1269.93121 Jiao, Zhuang; Chen, Yangquan 2012 An interval Kalman filtering with minimal conservatism. Zbl 1245.93128 Ahn, Hyo-Sung; Kim, Young-Soo; Chen, Yangquan 2012 A fractional order universal high gain adaptive stabilizer. Zbl 1258.93095 Li, Yan; Chen, Yangquan 2012 Convergence analysis of fractional-order iterative learning control. Zbl 1274.93196 Li, Yan; Chen, Yangquan; Ahn, Hyo-Sung 2012 Numerical approximation of nonlinear fractional differential equations with subdiffusion and superdiffusion. Zbl 1228.65190 Li, Changpin; Zhao, Zhengang; Chen, Yangquan 2011 Fractional-order iterative learning control for fractional-order linear systems. Zbl 1248.93085 Li, Yan; Chen, YangQuan; Ahn, Hyo-Sung 2011 On Riemann-Liouville and Caputo derivatives. Zbl 1213.26008 Li, Changpin; Qian, Deliang; Chen, Yangquan 2011 Application of numerical inverse Laplace transform algorithms in fractional calculus. Zbl 1210.65201 Sheng, Hu; Li, Yan; Chen, YangQuan 2011 Random-order fractional differential equation models. Zbl 1203.94056 Sun, HongGuang; Chen, YangQuan; Chen, Wen 2011 Asymptotical stability of nonlinear fractional differential system with Caputo derivative. Zbl 1239.34008 Zhang, Fengrong; Li, Changpin; Chen, Yangquan 2011 Convergence speed of a fractional order consensus algorithm over undirected scale-free networks. Zbl 1263.93013 Sun, Wei; Li, Yan; Li, Changpin; Chen, Yangquan 2011 Synthesis of multifractional Gaussian noises based on variable-order fractional operators. Zbl 1213.94049 Sheng, Hu; Sun, Hongguang; Chen, Yangquan; Qiu, Tianshuang 2011 Stability analysis of fractional-order systems with double noncommensurate orders for matrix case. Zbl 1273.93143 Jiao, Zhuang; Chen, Yangquan 2011 FARIMA with stable innovations model of Great Salt Lake elevation time series. Zbl 1203.94053 Sheng, Hu; Chen, YangQuan 2011 Dynamic multi-attribute decision making model based on triangular intuitionistic fuzzy numbers. Zbl 1277.91035 Chen, Y.; Li, B. 2011 On distributed order integrator/differentiator. Zbl 1219.94039 Li, Yan; Sheng, Hu; Chen, Yang Quan 2011 Analytical impulse response of a fractional second order filter and its impulse response invariant discretization. Zbl 1203.94039 Li, Yan; Sheng, Hu; Chen, YangQuan 2011 Heavy-tailed distribution and local long memory in time series of molecular motion on the cell membrane. Zbl 1271.62210 Sheng, Hu; Chen, Yang Quan; Qiu, Tianshuang 2011 A novel noise removal method based on fractional anisotropic diffusion and subpixel approach. Zbl 1216.65032 Zhang, Yingtao; Cheng, H. D.; Chen, Yangquan; Huang, Jianhua 2011 Stability of fractional-order nonlinear dynamic systems: Lyapunov direct method and generalized Mittag-Leffler stability. Zbl 1189.34015 Li, Yan; Chen, Yangquan; Podlubny, Igor 2010 Fractional-order systems and controls. Fundamentals and applications. Zbl 1211.93002 Monje, Concepción Alicia; Chen, YangQuan; Vinagre, Blas Manuel; Xue, Dingyü; Feliu, Vicente 2010 Robust stability and stabilization of fractional-order interval systems with the fractional order $$\alpha$$: the $$0<\alpha<1$$ case. Zbl 1368.93506 Lu, Jun-Guo; Chen, Yang-Quan 2010 An approximate method for numerically solving fractional order optimal control problems of general form. Zbl 1189.49045 Tricaud, Christophe; Chen, Yangquan 2010 Trajectory-keeping in satellite formation flying via robust periodic learning control. Zbl 1204.93082 Ahn, Hyo-Sung; Moore, Kevin L.; Chen, Yangquan 2010 On mean square displacement behaviors of anomalous diffusions with variable and random orders. Zbl 1235.82018 Sun, Hongguang; Chen, Wen; Sheng, Hu; Chen, Yangquan 2010 On the bound of the Lyapunov exponents for the fractional differential systems. Zbl 1311.34016 Li, Changpin; Gong, Ziqing; Qian, Deliang; Chen, YangQuan 2010 Time-optimal control of systems with fractional dynamics. Zbl 1203.49031 Tricaud, Christophe; Chen, Yangquan 2010 Mittag-Leffler stability of fractional order nonlinear dynamic systems. Zbl 1185.93062 Li, Yan; Chen, Yangquan; Podlubny, Igor 2009 Matrix approach to discrete fractional calculus. II: Partial fractional differential equations. Zbl 1160.65308 Podlubny, Igor; Chechkin, Aleksei; Skovranek, Tomas; Chen, Yangquan; Vinagre Jara, Blas M. 2009 Fractional order [proportional derivative] controller for a class of fractional order systems. Zbl 1183.93053 Luo, Ying; Chen, Yangquan 2009 ...and 39 more Documents all top 5 all top 5 #### Cited in 245 Serials 160 Nonlinear Dynamics 112 Fractional Calculus & Applied Analysis 96 Applied Mathematics and Computation 88 Journal of the Franklin Institute 88 Advances in Difference Equations 79 Computers & Mathematics with Applications 79 Mathematical Problems in Engineering 73 Automatica 69 Asian Journal of Control 65 Communications in Nonlinear Science and Numerical Simulation 44 International Journal of Control 44 Chaos, Solitons and Fractals 42 Abstract and Applied Analysis 41 Journal of Computational Physics 39 Journal of Computational and Applied Mathematics 38 Numerical Algorithms 36 Applied Numerical Mathematics 31 Applied Mathematical Modelling 29 Complexity 29 Chaos 28 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 28 International Journal of Systems Science. Principles and Applications of Systems and Integration 26 Journal of Vibration and Control 25 Computational and Applied Mathematics 23 Journal of Scientific Computing 23 Discrete Dynamics in Nature and Society 22 Systems & Control Letters 21 International Journal of Robust and Nonlinear Control 19 Circuits, Systems, and Signal Processing 19 Applied Mathematics Letters 18 International Journal of Applied Mathematics and Computer Science 17 Advances in Mathematical Physics 15 Signal Processing 15 International Journal of Adaptive Control and Signal Processing 15 Journal of Applied Mathematics and Computing 14 Mathematics and Computers in Simulation 13 Nonlinear Analysis. Modelling and Control 12 International Journal of Systems Science 12 Journal of Optimization Theory and Applications 12 Journal of Function Spaces 11 European Journal of Control 11 Journal of Applied Mathematics 10 Engineering Analysis with Boundary Elements 9 Information Sciences 9 Automation and Remote Control 9 International Journal of Computer Mathematics 9 Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 8 Mathematical Methods in the Applied Sciences 8 SIAM Journal on Control and Optimization 8 SIAM Journal on Scientific Computing 8 Turkish Journal of Mathematics 8 Journal of Systems Science and Complexity 8 Journal of Nonlinear Science and Applications 8 Journal of Control Science and Engineering 8 International Journal of Applied and Computational Mathematics 7 Journal of Mathematical Analysis and Applications 7 Neural Networks 7 Archives of Control Sciences 7 Journal of Mathematics 7 Mathematics 6 Optimal Control Applications & Methods 6 Entropy 6 Nonlinear Analysis. Hybrid Systems 6 Mathematical Modelling of Natural Phenomena 6 East Asian Journal on Applied Mathematics 5 Applicable Analysis 5 Physica A 5 BIT 5 Calcolo 5 Multidimensional Systems and Signal Processing 5 Fractals 5 Soft Computing 5 Discrete and Continuous Dynamical Systems. Series B 5 Mediterranean Journal of Mathematics 5 Journal of Applied Analysis and Computation 4 Computational Mechanics 4 Numerical Methods for Partial Differential Equations 4 Linear Algebra and its Applications 4 International Journal of Nonlinear Sciences and Numerical Simulation 4 Journal of Control Theory and Applications 4 Boundary Value Problems 4 Computational & Mathematical Methods in Medicine 4 Discrete and Continuous Dynamical Systems. Series S 4 International Journal of Biomathematics 4 Algorithms 4 International Journal of Differential Equations 4 Advances in Applied Mathematics and Mechanics 4 Axioms 4 Communications on Applied Mathematics and Computation 3 International Journal of Modern Physics B 3 International Journal of Theoretical Physics 3 Fuzzy Sets and Systems 3 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 3 Acta Applicandae Mathematicae 3 Optimization 3 Mathematical and Computer Modelling 3 Stochastic Processes and their Applications 3 Journal of Difference Equations and Applications 3 Mathematical Communications 3 Differential Equations and Dynamical Systems ...and 145 more Serials all top 5 #### Cited in 43 Fields 1,013 Systems theory; control (93-XX) 945 Ordinary differential equations (34-XX) 542 Real functions (26-XX) 536 Numerical analysis (65-XX) 454 Partial differential equations (35-XX) 187 Computer science (68-XX) 127 Biology and other natural sciences (92-XX) 107 Dynamical systems and ergodic theory (37-XX) 96 Calculus of variations and optimal control; optimization (49-XX) 86 Information and communication theory, circuits (94-XX) 76 Probability theory and stochastic processes (60-XX) 65 Special functions (33-XX) 64 Integral equations (45-XX) 52 Operator theory (47-XX) 50 Operations research, mathematical programming (90-XX) 40 Fluid mechanics (76-XX) 39 Difference and functional equations (39-XX) 37 Mechanics of particles and systems (70-XX) 35 Mechanics of deformable solids (74-XX) 28 Integral transforms, operational calculus (44-XX) 24 Classical thermodynamics, heat transfer (80-XX) 24 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 20 Linear and multilinear algebra; matrix theory (15-XX) 19 Statistical mechanics, structure of matter (82-XX) 18 Statistics (62-XX) 17 Approximations and expansions (41-XX) 16 Harmonic analysis on Euclidean spaces (42-XX) 9 Quantum theory (81-XX) 8 Combinatorics (05-XX) 8 Optics, electromagnetic theory (78-XX) 8 Geophysics (86-XX) 7 Functional analysis (46-XX) 6 Functions of a complex variable (30-XX) 5 General and overarching topics; collections (00-XX) 5 Global analysis, analysis on manifolds (58-XX) 4 Measure and integration (28-XX) 3 History and biography (01-XX) 3 Number theory (11-XX) 2 Relativity and gravitational theory (83-XX) 1 Mathematical logic and foundations (03-XX) 1 Potential theory (31-XX) 1 Sequences, series, summability (40-XX) 1 General topology (54-XX) #### Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata.	2021-10-17T10:19:07	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6900295615196228, "perplexity": 11470.329870515898}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323585171.16/warc/CC-MAIN-20211017082600-20211017112600-00162.warc.gz"}
https://www.usgs.gov/news/usgs-collaborates-fema-national-earthquake-loss-estimate	Due to a lapse in appropriations, the majority of USGS websites may not be up to date and may not reflect current conditions. Websites displaying real-time data, such as Earthquake and Water and information needed for public health and safety will be updated with limited support. Additionally, USGS will not be able to respond to inquiries until appropriations are enacted. For more information, please see www.doi.gov/shutdown # USGS Collaborates with FEMA on National Earthquake Loss Estimate Release Date: Earthquakes are estimated to cost the nation $6.1 billion annually in building stock losses according to an updated report published today by FEMA. Earthquakes are estimated to cost the nation$6.1 billion annually in building stock losses according to an updated report published today by FEMA. USGS science on earthquake hazards was a critical component to this analysis. The new loss estimate represent a 10% increase over the previous estimate in 2008, but when accounting for inflation changes there is a net small decrease (when both the 2008 and new report results adjusted to 2014 dollars). The changes in loss estimates are mainly due to changes in population and building exposure, estimate of long term earthquake hazard and an improved site soil characterization adopted in the present study. Figure 3-4 This map depicts annualized earthquake loss by county. The estimated losses consider the value of buildings in each specific area. (Public domain.) In 2014, the USGS released an updated assessment of earthquake hazards and potential ground shaking across the nation. This was used as an essential piece to inform the FEMA analysis, which combines that insight with consequences in terms of physical damage and economic loss. USGS earthquake science is vital because you can’t plan for earthquakes if you don’t know precisely what you are planning for. Those USGS maps reflect the best and most current understanding of where future earthquakes will occur, how often they will occur, and how hard the ground will likely shake as a result. The USGS regularly updates the national seismic hazard models and maps, typically every 6 years, in sync with the building code updates. In addition, the USGS provided new insight on soil characteristics across the nation to help understand the intensity of ground motion following an earthquake. If a structure is built on soft soil, it is more likely to have stronger shaking compared to harder bedrock. With limited data available, the 2008 FEMA analysis assumed the worst case scenario and considered the nation uniformly as if it was on soft soil. For this new report, the USGS produced preliminary maps to estimate soil classifications in different areas. Further research and testing will allow for more precise maps of soil characteristics. The USGS is the only federal agency with responsibility for recording and reporting earthquake activity nationwide and providing a seismic hazard assessment. These USGS earthquake hazard maps are part of contributions to the National Earthquake Hazards Reduction Program (NEHRP), which is a congressionally established partnership of four federal agencies with the purpose of reducing risks to life and property in the United States that result from earthquakes. The main updates to earthquake hazards since the 2008 FEMA report include: • Significant change in the hazard in the western United States, except for some parts of Washington and Oregon where the changes are small. • A slight change in the hazard in the Great Plains. • A slight change in hazard in the Southeast, except for modest changes in some areas of Virginia, North Carolina, and a significant decrease in the Charleston, South Carolina area. • Significant decrease in hazard in the central region, which includes the New Madrid seismic zone (shown in blue), with a small increase in parts of Tennessee. • A slight change in hazard in the Northeast, except for some areas of New York and New Jersey, where the hazard has gone down. Induced Seismicity Earthquake hazard has remained relatively stable except for the regions of induced seismicity. Induced seismicity is not included in this report because it can increase or decrease over a short period of time and is subject to commercial and policy decisions that could change rapidly. This report looks at the long term while USGS induced seismicity maps are one-year forecasts. Therefore earthquake hazards and losses are currently higher than what is reflected in this report for Oklahoma, Kansas, Colorado, New Mexico, Texas, and Arkansas where there have been recent occurrences of induced seismicity. Need for Loss and Hazard Estimates Earthquakes in the last decade alone have claimed tens of thousands of lives and caused hundreds of billion dollars of economic impact throughout the globe. In the United States, earthquake risk continues to grow with increased exposure of population and development. While there is constantly improved understanding of high hazard and risk areas such as Los Angeles, San Francisco and Seattle, there is also high risk of significant damage and loss in regions such as Salt Lake City, St. Louis, Memphis, Charleston, New York City and Boston even though they have low or moderate earthquake hazards. This high level of risk reflects dense concentrations of buildings and infrastructure. Understanding earthquake hazards is critical for informed policies, priorities, strategies, and funding decisions to protect the most at-risk communities. Figure 4-1 This map depicts the difference in USGS estimates of earthquake hazards across the nation in 2002 and 2014. The new FEMA earthquake loss report includes the 2014 data, while the previous 2008 report includes the 2002 data. The negative values represent a decrease in estimated hazard since 2002 and the positive values represent an increase. (Public domain.)	2019-01-20T16:50:04	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.27402135729789734, "perplexity": 2640.028647547025}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-04/segments/1547583728901.52/warc/CC-MAIN-20190120163942-20190120185942-00618.warc.gz"}
https://pdglive.lbl.gov/Particle.action?node=S016&init=0&home=sumtabB	${{\boldsymbol N}}$ BARYONS($\boldsymbol S$ = 0, $\boldsymbol I$ = 1/2) ${{\mathit p}}$, ${{\mathit N}^{+}}$ = ${\mathit {\mathit u}}$ ${\mathit {\mathit u}}$ ${\mathit {\mathit d}}$; ${{\mathit n}}$, ${{\mathit N}^{0}}$ = ${\mathit {\mathit u}}$ ${\mathit {\mathit d}}$ ${\mathit {\mathit d}}$ INSPIRE search # ${{\boldsymbol p}}$ $I(J^P)$ = $1/2(1/2^{+})$ ${{\mathit p}}$ MASS (atomic mass units u) $1.00727646662 \pm0.00000000009$ u (S = 3.1) ${{\mathit p}}$ MASS (MeV) $938.272081 \pm0.000006$ MeV $\vert {\mathit m}_{{{\mathit p}}}−{\mathit m}_{{{\overline{\mathit p}}}}\vert /{\mathit m}_{{{\mathit p}}}$ $<7 \times 10^{-10}$ CL=90.0% ${{\overline{\mathit p}}}/{{\mathit p}}$ CHARGE-TO-MASS RATIO, $\vert {\mathit q_{{{\overline{\mathit p}}}}\over {\mathit m}_{{{\overline{\mathit p}}}}}\vert /({\mathit q_{{{\mathit p}}}\over {\mathit m}_{{{\mathit p}}}}$) $1.00000000000 \pm0.00000000007$ ($\vert {\mathit q_{{{\overline{\mathit p}}}}\over {\mathit m}_{{{\overline{\mathit p}}}}}\vert -{\mathit q_{p}\over {\mathit m}_{{{\mathit p}}}})/{\mathit q_{{{\mathit p}}}\over {\mathit m}_{{{\mathit p}}}}$ $(0.1 \pm6.9) \times 10^{-11}$ $\vert \mathit q_{{{\mathit p}}}~+~\mathit q_{{{\overline{\mathit p}}}}\vert /{{\mathit e}}$ $<7 \times 10^{-10}$ CL=90.0% $\vert {{\mathit q}_{{p}}}+{{\mathit q}_{{e}}}\vert /{{\mathit e}}$ $<1 \times 10^{-21}$ ${{\mathit p}}$ MAGNETIC MOMENT $2.7928473446 \pm0.0000000008$ $\mu _{\mathit N}$ ${{\overline{\mathit p}}}$ MAGNETIC MOMENT $-2.792847344 \pm0.000000004$ $\mu _{\mathit N}$ (${\mathit \mu}_{{{\mathit p}}}$ $+$ ${\mathit \mu}_{{{\overline{\mathit p}}}}$) $/$ $\mu _{{{\mathit p}}}$ $(2 \pm4) \times 10^{-9}$ ${{\mathit p}}$ ELECTRIC DIPOLE MOMENT $<2.1 \times 10^{-25}$ $\mathit e~$cm ${{\mathit p}}$ ELECTRIC POLARIZABILITY ${{\mathit \alpha}_{{p}}}$ $0.00112 \pm0.00004$ fm${}^{3}$ ${{\mathit p}}$ MAGNETIC POLARIZABILITY ${{\mathit \beta}_{{p}}}$ $(2.5 \pm0.4) \times 10^{-4}$ fm${}^{3}$ (S = 1.2) ${{\mathit p}}$ CHARGE RADIUS $0.8409 \pm0.0004$ fm ${{\mathit p}}$ MAGNETIC RADIUS $0.851 \pm0.026$ fm ${{\mathit p}}$ MEAN LIFE $>3.6 \times 10^{29}$ years CL=90.0% ${{\overline{\mathit p}}}$ MEAN LIFE See the Note on Nucleon Decay'' in our 1994 edition (Phys. Rev. $\mathbf {D50}$, 1173) for a short review. The partial mean life'' limits tabulated here are the limits on ${{\mathit \tau}}/B_{\mathit i}$, where ${{\mathit \tau}}$ is the total mean life and B$_{\mathit i}$ is the branching fraction for the mode in question. For ${{\mathit N}}$ decays, ${{\mathit p}}$ and ${{\mathit n}}$ indicate proton and neutron partial lifetimes.	2021-03-02T21:32:57	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9440034627914429, "perplexity": 1137.308810650322}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178364764.57/warc/CC-MAIN-20210302190916-20210302220916-00315.warc.gz"}
https://pvpmc.sandia.gov/modeling-steps/1-weather-design-inputs/sun-position/	The position of the sun relative to an observer on the surface of the Earth is an important input needed to model PV system performance. The convention used to describe solar position includes: • Zenith angle ($\theta&space;_{Z}$) • Azimuth angle ($\theta&space;_{A}$) • Solar elevation angle ($\theta&space;_{el}$) is equal to $90^{\circ}&space;-&space;\theta_{Z}$ The figure below shows how these angles are defined.	2018-08-16T05:52:02	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 4, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8003911972045898, "perplexity": 376.70248026307655}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-34/segments/1534221210463.30/warc/CC-MAIN-20180816054453-20180816074453-00642.warc.gz"}
https://www.abs.gov.au/statistics/research/measuring-digital-activities-australian-economy	# Measuring Digital Activities in the Australian Economy This paper outlines the ABS application of the BEA approach, and presents preliminary and experimental estimates of digital activity in Australia Release date and time By Pengfei Zhao, Research Hub ## Summary Rapid advancements in digital technologies in recent years have transformed the ways in which households, firms and governments interact with each other. Digital activities have grown rapidly and become an important contributor to economies around the world. This dynamic shift has increased the demand for statistical insights into digital activities in Australia for analytical and policy purposes. While the Australian Bureau of Statistics (ABS) captures many aspects of the Australian digital economy in the National Accounts, it does not separately identify all digital activities, nor trace the estimated aggregate economic performance to its digital origins. In particular, measuring digital activities in official statistics has been challenging due to definitional, classification and measurement issues. To guide estimation and comparability in official statistics, a framework for measuring a digital economy has been developed by the Organisation for Economic Co-operation and Development (OECD). The framework has been partially implemented by the Bureau of Economic Analysis (BEA) and Statistics New Zealand to gain insights into digital activities relative to the U.S. and New Zealand economy, respectively (Barefoot et al., 2018; Millar & Grant, 2017). In this paper, ABS has applied the BEA approach to estimate digital activity in Australia using selected separately identifiable digital products from the ABS supply-use tables. The preliminary estimates provide insights into digital activities through a National Accounts lens. Applying the BEA approach enables Australia to engage in policy debate and international discussions of digital activities in a timely and responsive manner. This paper outlines the ABS application of the BEA approach, and presents preliminary and experimental estimates of digital activity in Australia. The results indicate that information and telecommunication services, while a relatively small share of total Australian production, are an increasing driver of Australian economic growth. The paper also acknowledges the limitations of the approach and highlights areas for potential future developments. The ABS welcomes feedback and comments on the preliminary work, which can be directed to: Lauren Ford, Director, Economic Research Section, email: [email protected]. The ABS Privacy Policy outlines how the ABS will handle any personal information that you provide to us. ## 1. Introduction In recent years, digital activities have grown rapidly and become an important economic contributor. Across major economies, including the U.S., U.K., France and Germany, expenditure on digital skills, digital equipment, software and intermediate digital goods and services are significant sources of economic activity (Watson, 2018). In New Zealand, digitally ordered products were estimated to account for around 20% of total gross output over the period 2007-2015. Further, the annual growth of digitally delivered products outpaced that of total gross output (Millar & Grant, 2017). In Canada, over half of the country’s population purchased music and video downloads, and streaming services in 2017-2018 (Statistics Canada, 2018). Such results have increased the demand for insights into digital activities in Australia for analytical and policy purposes. While the ABS captures many aspects of the Australian digital economy, the ABS National Accounts do not separately identify digital activities nor trace the estimated aggregate economic performance to its digital origins. Feedback from stakeholders and policy makers noted that this lack of visibility in official statistics hampers analysis and discussion. Estimating digital activity in the economy presents many definitional, classification and measurement challenges. One main issue is the absence of a well-accepted definition of a digital economy. Variation in measurement and conceptual scope between countries can make comparisons difficult, and there are further difficulties in keeping conceptual and measurement pace with the rapid pace of digitalisation. Furthermore, the estimation and conceptual treatment of growing digital activities – such as “free” services and information, and the shared economy – remain in ongoing development and debate. To enable estimation and comparison in official statistics, a framework for measuring a digital economy has been developed by OECD. The framework characterises digital economic activities around the System of National Accounts (SNA) production boundary by Producers, Product, Nature, Users and Enablers (Ahmad & Ribarsky, 2018). The framework has been partially implemented in case studies. For example, Statistics New Zealand measured digital activities as “digitally ordered” and “digitally delivered” goods and services produced in New Zealand (Millar & Grant, 2017). In contrast, the BEA measured digital activities in the U.S. as the production of information and communications technology and selected “primarily digital” products, based upon multiple dimensions of the digital economy framework (Barefoot et al., 2018). Both case studies have revealed that digital activities are an important contributor to their respective total economies. To address the visibility gap, the ABS has developed preliminary experimental estimates of digital activity in the Australian economy. Using the BEA approach, digital products were selected from ABS supply-use tables. This means that for the first time, the Australian production of some digital products can be ‘seen’ through a National Accounts lens. Applying the BEA approach will enable Australia to engage in policy debate and international comparisons of digital activities. This paper outlines the ABS application of the BEA approach, and presents the preliminary experimental estimates. Section Two summarises data compilation in current price and volume, and acknowledges the limitations in the current approach. Section Three provides insights into digital activities value added relative to the total Australian economy. Section Four concludes with areas for potential future developments. ## 2. ABS application of the BEA approach ### Concept Under the BEA approach, the ABS measured the digital activities in Australia as the production of: • #### Digital enabling infrastructure: computer hardware, software, telecommunications equipment and support services that form and facilitate the use of computer networks; • #### Digital media: digital audio, video and advertisement broadcasting services that can be created, accessed, stored or viewed on digital devices; and • #### E-commerce: retail and wholesale services and margins from digitally ordered or platform enabled online transactions. In the production approach, digital activity value added is the gross output of the selected digital products less the value of products consumed in production. For simplicity, the measurement focused on products that were “primarily digital” in nature, and separately identifiable in the supply-use tables. The ABS acknowledges that this digital activity measurement is limited in scope. For example, peer-to-peer transactions and emerging digitalised products (such as UBER transport services, financial services and “smart” household electronic goods) are not included in the estimates. While the production of these digitalised products are embedded in the supply-use source data under existing product classifications, they are not separately identified and it would be resource intensive to unembed. Also, digital trade is not visible from the production approach. Exports and imports through digital networks can be estimated with components of final demand¹. Hence, the measurement in this paper provides “lower-bound” insights into digital activities in Australia for analytical and policy purposes. ### Methodology The Australian preliminary experimental estimates of digital activities were estimated using ABS supply-use data (ABS Cat. no. 5217.0). The following steps were undertaken: 1. Products (Supply-Use Product Classification, or SUPC) selected for the three broad digital activities outlined above. 2. Industry sources (Supply-Use Industry Classification, or SUIC) identified for the selected digital products. 3. Inputs and outputs of digital activities estimated. #### Step 1: Selecting the digital products To represent each of the three broad digital activities (digital enabling infrastructure, digital media and e-commerce), the SUPCs were selected in alignment with Barefoot et al (2018) and shown in Table 1. Infrastructure was divided into Hardware, Software, Support Services and Telecommunications. E-commerce consisted of Wholesale and Retail services. Within some of the selected SUPCs, only the listed Input-Output Product Classifications (IOPC) were relevant to the current measurement of digital activities². Table 1: Selected supply-use and input-output products by digital activity Digital ActivitySUPCProduct DescriptionRelevant IOPCProduct Description Digital media Digital media 56010Cable (pay TV) & other subscription broadcasting services 56010Cable (pay TV) & other subscription broadcasting services E-commerce - wholesale33005Wholesale margin E-commerce - retail39005Retail margin Infrastructure - hardware16015Recorded media reproduction 24005Photographic goods (incl. optical fibres) & ophthalmic equipment (excl. spectacles)24110050Ophthalmic instruments & appliances 24110090Cameras, image projectors & parts, photographic goods nec. (excl. sensitised photographic film, paper, plates and chemicals) 24190090Optical fibres, fibre bundles & cables (excl. insulated) 24025Computer hardware & peripherals (incl. photocopiers & parts) 24035Vending, video, monetary, office & other electronic hardware nec. Infrastructure - software54010Software publishing Infrastructure - support services57020Data processing & information storage services 70005Computer consultancy, systems design & related services 94010Machinery & equipment repair & maintenance services94220010Electronic & precision equipment repair & maintenance (excl. domestic appliance) Infrastructure - telecommunications24030Telecommunication & audio visual equipment 24040Electric lights (incl. torches), cables and24310010Uninsulated copper & aluminium stranded wire, ropes, cable, plaited bands and slings 24310090Cable, wire & strip 57015Internet services 58005Telecommunication services (excl. equipment) #### Step 2: Identifying the industry sources Both the primary and secondary industries producing the selected SUPCs were identified from the Australian production matrix within the supply-use table. The matrix shows the estimated value of goods and services produced by SUIC, which can be aggregated in concordance with the Australian and New Zealand Standard Industrial Classification (ANZSIC). In recent years, the Australian digital products were primarily produced in the following ANZSIC divisions: • J Information, Media and Telecommunications; and • M Professional, Scientific and Technical Services. #### Step 3: Estimating the inputs and outputs of the digital activities Gross output, intermediate consumption and value added of the digital activities were estimated with established assumptions and simple modelling. The estimation was firstly in current price, followed by volume and then contribution to total digital and economic growth. ##### Current price estimation The current price estimation of the digital activities involved modelling the relevant digital products; compiling the gross output, intermediate consumption and value added of the digital activities within the source SUICs; and aggregating the estimated inputs and outputs across the industries. Within some of the selected SUPCs, only certain components were relevant to the conceptual measurement of digital activities. To ensure consistency within the established scope, the supply-use gross output of such components were modelled using other data sources. The underlying model by digital product (and caveats in the estimated Wholesale E-commerce outputs) are highlighted in Appendix A. Next, the digital activities were estimated in each of the identified primary and secondary industries. In a particular SUIC, digital gross output was estimated as the sum of the selected and modelled products. Due to the lack of information on the production processes, the industry production function for the digital products was assumed to be identical to the “non-digital” counterpart. Hence, the associated digital value added was estimated as the total value added weighted by the share of the estimated digital output in total output. Total intermediate consumption for the production of the digital products was calculated as the difference between the digital gross output and digital value added, which was then proportionately split amongst SUPCs. Gross output, intermediate consumption and value added by digital activity were estimated as the sum of the relevant products across the source SUICs. ##### Volume estimation In volume terms, value added by digital activity was estimated with double deflation on a chain volume basis. A chain volume measure shows change in quantity over time by holding the price constant at a reference year. The derivation of a chain volume measure separates the annual price effect from quantity, through dividing the current price measure by the corresponding price movement – the implicit price deflator. This deflation process yields a quantity estimate at constant prices³. As prices for value added were unavailable, constant price value added by digital activity was estimated as the difference between the total digital output in constant prices and the total intermediate consumption in constant prices (double deflation). To derive the constant price digital output and intermediate consumption, each of the underlying products were deflated with the corresponding price movement. Next, the volume movement of digital activity value added was estimated by accounting for the annual growth over time. The annual volume growth of the digital value added was calculated as the ratio of the constant price measure to the current price measure in the previous period. Then, the volume growth of the digital value added over time (the chain volume index) was derived as the cumulative multiplication (or ‘chaining’) of the annual volume movement across the time series. The chain volume digital activity value added was estimated by converting the chain volume index into the dollar value of a selected reference year. Further information on the chain volume calculations is provided in Appendix B. Double deflation and the estimation of chain volume value added are demonstrated with a numerical example in Appendix C. ##### Estimating aggregate growth and contribution to growth The aggregate digital activity value added growth was defined as the Laspeyres aggregation (ABS cat.no. 5206.0 feature article, 2012) of the underlying digital activities, where the activity contribution was the annual value added volume growth weighted by the corresponding lagged share in the total digital activity value added. The total economy value added growth was estimated as the Laspeyres aggregation of all SUICs. ## 3. Results The preliminary estimates of Australian digital activities, from 2011-12 to 2016-17, are summarised in this section. In recent years, domestic production of the selected digital products had grown relative to the total Australian economy, from 5.4% ($75.6 billion) of aggregate value added in 2011-12 to 5.7% ($93.5 billion) in 2016-17 (Figure 1). The relative size (and trend) of digital activities in Australia has been broadly similar to, albeit slightly less than, that seen in the U.S. (6.5% in 2016), as published in Barefoot et al (2018). From a context perspective, noting the industries shown in Figure 2 include digital activities, the selected digital activities represented higher aggregate value added than 12 industry divisions, but were behind traditional drivers such as Finance, Construction, Health and Mining (Figure 2)⁴. In both current price and volume terms, apart from current price growth in 2016-17, growth in the digital activities significantly outpaced growth in total production (Figures 3 and 4). The rapid expansion in digital activities was driven by strong demand for more advanced telecommunication and support services, and further digitalisation of wholesale trade in the Australian economy. From 2012-13 to 2016-17, digital activities accounted for almost one sixth of the total economic growth in Australia (0.4% of the total 2.6%), due to the rapid growth proportional to the digital activities’ moderate size (Figure 5). The level contribution of the digital activities in Australia was similar to the counterpart in the U.S. (0.4% in 2016), as published in Barefoot et al (2018). The figures hereafter explore the drivers of the digital activity value added. Within the digital activities, production was dominated by Support Services, Telecommunications and Wholesale E-commerce (Figure 6). Support Services and Telecommunications were driven by strong demand for high speed and volume internet services, and increased commercial adoption of new technologies (such as Cloud computing and storage, remote data access and multi-platform networking) under the ongoing rollout of the National Broadband Network (NBN). Wholesale E-commerce was relatively significant due to intensified digitalisation, and a high commercial reliance on imported necessities in response to the limited domestic supply of manufactured goods (Table 8, Appendix D). In contrast, Hardware and Retail E-commerce were overshadowed by low-cost imported computer products (Lo, 2017) and traditional retail sales (National Australia Bank Online Retail Sales Index or NORSI) January 2010 – January 2012 and June 2017), respectively. Looking at volume, the estimated value added growth in most of the digital activities significantly outpaced that in the total Australian economy (Figure 7). Hardware experienced the highest growth, followed by Retail E-commerce, Wholesale E-commerce and Telecommunications. Hardware was driven by depreciation in the Australian dollar, efficiency improvements and increased focus on local customisation and support for businesses and governments (Lo, 2017). Retail E-commerce thrived on the affordability and convenience of online shopping, and the integration of “Click and Collect” and physical retail presence. The growth in Wholesale E-commerce primarily reflects significant digitalisation within the Wholesale Trade division. In response to strong downward pressure on profits⁵, wholesalers could cut costs by replacing labour with advanced automated systems for order, inventory and customer service management⁶. Digital Media experienced the lowest growth due an ongoing shift in consumer viewing trend, from free-to-air digital TV and radio to on-demand internet streaming services. Overall, the digital activity value added grew by 7.5% per annum primarily due to the production in Telecommunications (2.7%) and Support Services (2.4%); and the intensified digitalisation of Wholesale Trade (1.3%) (Figure 8). The contribution from Hardware and Retail E-commerce was minor, as the high value added growth rate was offset by the relatively small production. In summary, information and communication technologies were a growing engine of the Australian economy. Characterised by rapid growth and relatively significant production, telecommunication and support services were significant direct contributors to the aggregate digital activities and economic growth. Further, technological innovation and increased commercial adoption of new ICT amongst producers enables vital productivity gains. For example, the intensified automation within Wholesale Trade significantly reduced labour costs and, in turn, allowed wholesalers to confront declining profitability. Maintaining competitive supply channels through Wholesale E-commerce will be important as Australia continues to transition towards a services economy. The results also indicate that Retail E-commerce is currently a relatively minor contributor to the Australian digital activities and aggregate economy. However, the activity has demonstrated much potential for future growth. ## 4. Conclusion Rapid progress in digitalisation has increased the demand for statistical insights into digital activities in the Australian economy. In response, the ABS has measured selected domestic digital activities under the BEA approach. Adopting the BEA approach enables Australia to engage in policy debate and international comparisons of digital activities in a timely and responsive manner. While representing a relatively small share of total Australian production (behind traditional economic drivers such as Mining, Finance, Health and Construction), the selected digital activities contributed significantly to the aggregate economic growth in recent years. In current price and volume terms, the selected digital activities grew rapidly, primarily due to strong demand for more advanced telecommunications and support services. The results also highlight the economic importance of Wholesale E-commerce in Australia’s ongoing economic structural change. The ABS acknowledges the scope limitations in the current approach to measuring digital activities in the Australian economy. Potential areas for future research and development include: • Measurement of emerging digitalised services, such as finance (particularly Financial Intermediation Services Indirectly Measured, or FISIM) and UBER transport; • Digitalisation in products across time, including improvements in modelling Wholesale E-commerce; • Outsourcing of digital activities across time; and The ABS will consider any future research in this area in conjunction with broader organisational forward work program priorities. ## References ### Show all Ahmad, N. and Ribarsky, J. 2018, 'Towards a Framework for Measuring the Digital Economy'. Prepared for the 16th Conference of the International Association of Official Statisticians (IAOS), OECD Headquarters, Paris, France, 19-21 September 2018. ABS (Australian Bureau of Statistics) 2012, 'Feature article: Forthcoming Changes to the Calculation of Contributions to Growth in the National Accounts', in Australian National Accounts: National Income, Expenditure and Product, Jun 2012, cat. no. 5206.0, ABS, Canberra. ABS 2018, Australian National Accounts: Supply Use Tables, 2016-17, cat. no. 5217.0, ABS, Canberra. ABS 2018, Retail Trade, Australia, Jul 2018, cat. no. 8501.0, ABS, Canberra. Barefoot, K., Curtis, D., Jolliff, W.A., Nicholson, J.R. & R. Omohundro 2018, 'Defining and Measuring the Digital Economy', Working Paper, BEA (Bureau of Economic Analysis), Washington, D.C.. Lo, B. 2017, Computer and Electronic Office Equipment Manufacturing (C2421) - Australia. IBISWorld Industry Report, Melbourne. Millar, J. & H. Grant 2017, 'Valuing New Zealand's Digital Economy', Paper presented to Working Party on National Accounts, OECD Conference Centre (November), Statistics New Zealand, Wellington. NAB (National Australia Bank) Online Retail Sales Index, Quarterly Series, NAB, Melbourne. Statistics Canada 2018, Results from the Digital Economy Survey, July 2017 to June 2018, cat. no. 11-627-M. Infographics, Stats Canada, Ottawa. Watson, T. 2018, 'Digital Economy Measurement and Digital Policy', G20 and Economic Policy Branch, Economic Division, PM&C (Department of the Prime Minister and Cabinet of Australia), Canberra. ## Appendix A Appendix A highlights the underlying model by digital product, and provides caveats in the current modelled Wholesale E-commerce activities. To ensure consistency within the established scope, the supply-use industry output of certain digital elements is modelled with existing data sources (Table 2). Infrastructure, ophthalmic instruments, cameras, optical fibres, software copyright leasing, metal wires and electronic equipment repair were estimated using the individual product’s share in the corresponding SUPC from the ABS Input-output table. In wholesale and retail trade activities, however, E-commerce is not well represented by the underlying IOPCs. Hence, retail E-commerce margin and trade services were estimated using the share of Australian online retail sales (NORSI) in the total Australian retail turnover (ABS Cat. no. 8501.0). Wholesale E-commerce margin and trade services were based on the share of internet income (unpublished experimental data from the ABS Business Characteristics Survey (BCS)) in the total sales of goods not produced (Economic Activity Survey) for the Wholesale Trade division. For simplicity, the estimated shares of E-commerce activity were assumed to be identical across all SUICs. The significance of E-commerce relative to total wholesale trade may be overestimated due to the scope and limitations of the estimated internet income. Internet income was derived from the reported proportion of online sales in business income from the BCS. The BCS definition of online sales accounts for all internet business-to-business (from a producer to a wholesaler, and from a wholesaler to a retailer etc.) and business-to-consumer transactions on any particular good. Moreover, the current estimated internet income cannot be traced to non-wholesale business activities and the underlying goods traded between businesses. Table 2: Data sources for modelling the relevant digital products Data SourceFrequencyAvailability ABS Input-output tableAnnual (financial year)1994-95 to 2015-16 NAB online retail sales index (NORSI)MonthlyJanuary 2010 to December 2018 Retail turnover by industry group ABS Cat. no. 8501.0 Table 1MonthlyApril 1982 to December 2018 ABS Business Characteristics Survey (BCS)Annual (financial year)2004-05 to 2016-17 ## Appendix B Appendix B formulaically shows the final stages in the estimation of the chain volume digital activity value added. The chain volume index of digital activity value added $$\Large \left( {\left. {\frac{{{Q_{i,t}}}}{{{Q_{i,0}}}}} \right)} \right.$$was calculated as the cumulative multiplication of the annual volume movement across time: $$\Large\frac{{{Q_{i,t}}}}{{{Q_{i,0}}}} = \frac{{{P_{i,t - 1}}{Q_{i,t}}}}{{{P_{i,t - 1}}{Q_{i,t - 1}}}} \times \frac{{{P_{i,t - 2}}{Q_{i,t - 1}}}}{{{P_{i,t - 2}}{Q_{i,t - 2}}}} \times \frac{{{P_{i,t - 3}}{Q_{i,t - 2}}}}{{{P_{i,t - 3}}{Q_{i,t - 3}}}} \times .......\frac{{{P_{i,0}}{Q_{i,]}}}}{{{P_{i,0}}{Q_{i,0}}}}$$ --------- (1) Where: $${Q_{i,t}}$$ is the quantity of value added in digital activity i at time t, $${P_{i,t - 1}}$$ is the price of value added in digital activity i at time t-1, $${P_{i,t - 1}}{Q_{i,t}}$$ is the constant price value added in digital activity i at time t, and $${P_{i,t - 1}}{Q_{i,t - 1}}$$ is the current price value added in digital activity i at time t-1. The chain volume digital activity value added $$\Large({P_{i,ref}}{Q_{i,t}})$$ was estimated by converting the chain volume index into the dollar value of a selected reference year: $$\Large{P_{i,ref}}{Q_{i,ref}} = \frac{{{Q_{i,t}}}}{{{Q_{i,0}}}}x{P_{i,ref}}{Q_{i,ref}} \div \frac{{{Q_{i,ref}}}}{{{Q_{i,0}}}}$$ --------- (2) Where: $${P_{i,ref}}{Q_{i,ref}}$$ is the current price value added in digital activity i at a selected reference year, and $$\Large\frac{{{Q_{i,ref}}}}{{{Q_{i,0}}}}$$ is the chain volume index in digital activity i at a selected reference year. ## Appendix C Appendix C numerically demonstrates double deflation and the estimation of chain volume value added. In this example, an industry produces products one and two through the intermediate consumption of three other products. The industry’s current price gross output and intermediate consumption by product, as well as the corresponding annual change in price (the implicit price deflator, or IPD), are shown in Tables 3. The current price value added is the difference between the gross output and intermediate consumption. Table 3: The industry’s gross output, intermediate consumption and value added in current prices Current price ($m)Year 1Year 2Year 3Year 4Implicit Price DeflatorYear 1Year 2Year 3Year 4 Gross Output Gross Output Product 11,0001,1001,2001,300Product 11.011.011.031.02 Product 2100110120130Product 21.021.011.021.01 Total 1,1001,2101,3201,430 Intermediate ConsumptionIntermediate Consumption Product 3500510530550Product 31.021.011.011.03 Product 4100110120130Product 41.031.011.021.01 Product 510203040Product 51.011.021.021.01 Total610640680720 Value Added Total490570640710 To remove the price effect from quantity of value added, the current price gross output and intermediate consumption were separately deflated at each individual product (Table 4). The double deflation involved dividing the current price measure by the corresponding IPD. The industry’s value added at constant prices was estimated as the difference between the total deflated gross output and the total deflated intermediate consumption. Table 4: Estimating the constant price value added with double deflation Constant price ($m)Year 1Year 2Year 3Year 4 Gross Output Product 1990.11,089.11,165.01,274.5 Product 298.0108.9117.6128.7 Total 1,088.11,198.01,282.71,403.2 Intermediate Consumption Product 3490.2505.0524.8534.0 Product 497.1108.9117.6128.7 Product 59.919.629.439.6 Total597.2633.5671.8702.3 Total491.0564.6610.9700.9 The chain volume value added shows change in quantity by accounting for the annual growth rate over time. For a particular year, the annual value added volume growth was calculated as the ratio of the industry’s constant price value added to the industry’s current price value added in the previous year (Table 5). The quantity of value added has not grown at the beginning of the time series (Year 1). Table 5: The industry’s annual value added growth rate Year 1Year 2Year 3Year 4 Value Added (constant price, $m)491.0564.6610.9700.9 Value Added (current price,$m)490.0570.0640.0710.0 The chain volume value added shows change in quantity by accounting for the annual growth rate over time. For a particular year, the annual value added volume growth was calculated as the ratio of the industry’s constant price value added to the industry’s current price value added in the previous year (Table 5). The quantity of value added has not grown at the beginning of the time series (Year 1). Table 6: The chain volume index of value added Year 1Year 2Year 3Year 4 Cumulative (Chain) Volume Index1.001.151.231.35 For example, setting Year 1 as the reference year, the chain volume index of value added from Year 1 to Year 4 $$\Large\left( {{\textstyle{{{Q_{VA,Year4}}} \over {{Q_{VA,Year1}}}}}} \right)$$ is calculated as: $$\Large\begin{array}{l} {\textstyle{{{Q_{VA,Year4}}} \over {{Q_{VA,Year1}}}}} = {\textstyle{{{P_{VA,Year1}}{Q_{VA,Year2}}} \over {{P_{VA,Year1}}{Q_{VA,Year1}}}}} \times {\textstyle{{{P_{VA,Year2}}{Q_{VA,Year3}}} \over {{P_{VA,Year2}}{Q_{VA,Year2}}}}} \times {\textstyle{{{P_{VA,Year3}}{Q_{VA,Year4}}} \over {{P_{VA,Year3}}{Q_{VA,Year3}}}}}\\ \end{array}$$ = 1.15 * 1.07 * 1.10 = 1.35 The chain volume measure of value added was estimated by converting the chain volume index into the dollar value of the selected reference year (Year 1) (equation 2). The estimated chain volume measure is shown in Table 7. Table 7: Estimating the chain volume value added Reference year = Year 1Year 1Year 2Year 3Year 4 Current Price Value Added ($m)490 Cumulative (Chain) Volume Growth1.001.151.231.35 Chain Volume Value Added ($m)490565605663 As an example, the chain volume value added in Year 4 $${(^{{P_{VA,Year1}}{Q_{VA,Year4}}}})$$ is calculated as: $$\Large\begin{array}{l} {P_{VA,Year1}}{Q_{VA,Year4}} = {\textstyle{{{Q_{VA,Year4}}} \over {{Q_{VA,Year1}}}}} \times {P_{VA,Year1}}{Q_{VA,Year1}} \div {\textstyle{{{Q_{VA,Year1}}} \over {{Q_{VA,Year1}}}}}\\ \end{array}$$ = 1.35 * 490 / 1 = 663⁸ ## Appendix D Appendix D summarises the common elements in the top 15 imported and wholesale margin products, from 2011-12 to 2016-17 (Table 8). The imports, wholesale margin and Australian production by product were estimated as the current price summation across the established timeframe. As indicated by the high ratios of imports to Australian production, the main products sold for commercial purposes were significantly sourced from abroad. The high levels of import were consistent with the slowing domestic sources of manufactured goods under Australia’s ongoing structural change. Table 8 – The common elements in the top 15 imported and wholesale margin products, 2011-12 to 2016-17, current prices SUPCSUPC descriptionImportWholesale marginAustralian production (Basic prices)Ratio of imports to Australian production $m$ m\$ mNumber 23005Motor cars119,34025,76323,5845.1 17015Automotive petroleum and coal products91,34326,447129,0720.7 24030Telecommunication and audio visual equipment79,07719,1997,59710.4 24065Specialised machinery and equipment69,33433,35136,4991.9 13070Clothing (excluding knitted or crocheted)67,24828,2245,56612.1 24025Computer hardware and peripherals (incl photocopiers and parts)63,97218,47414,5644.4 24075Other machinery and equipment57,30027,12331,0331.8 18025Medicinal and pharmaceutical products51,33532,21052,5191.0 23060Motor vehicle parts (excluding engines and panels) and accessories34,15319,39321,5531.6 Total633,102230,184321,9872.0 Grand total of goods¹⁰1,846,104670,6863,453,4660.5 Percentage of the top products in the grand total34.334.39.3 ## Endnotes ### Show all 1. The ABS is separately investigating the estimation of imported digital products. 2. The IOPC represents a detailed decomposition of the SUPC. 3. In this paper, a constant price measure is referred to as the current quantity valued at the corresponding price in the previous period (Pt-1Qt). 4. Note that the production of the digital products has not been removed from the existing industries for which it is partially embedded. Therefore, the shares add to more than 100% of aggregate value added. 5. Profitability in wholesale trade activities sharply diminished in recent years due to the depreciation of the Australian dollar, decrease in oil prices and intensified competition from overseas. 6. One example of such systems is the radio-frequency identification (RFID). 7. Unpublished experimental internet income for the Wholesale Trade division. 8. Includes minor rounding error. 9. The wholesale margin by SUPC is derived with an experimental product allocation from the ABS Retail Industry and Wholesale Industry surveys (RIS/WIS). Hence, ranking the estimate by size would reasonably indicate the main underlying products in wholesale trade. 10. The grand total estimate only includes goods that attract wholesale margin in the source supply-use table.	2021-03-04T04:17:43	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.17230264842510223, "perplexity": 6677.351808139108}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178368431.60/warc/CC-MAIN-20210304021339-20210304051339-00536.warc.gz"}
https://par.nsf.gov/biblio/10203338-high-frequency-atomic-tunneling-yields-ultralow-glass-like-thermal-conductivity-chalcogenide-single-crystals	High frequency atomic tunneling yields ultralow and glass-like thermal conductivity in chalcogenide single crystals Abstract Crystalline solids exhibiting glass-like thermal conductivity have attracted substantial attention both for fundamental interest and applications such as thermoelectrics. In most crystals, the competition of phonon scattering by anharmonic interactions and crystalline imperfections leads to a non-monotonic trend of thermal conductivity with temperature. Defect-free crystals that exhibit the glassy trend of low thermal conductivity with a monotonic increase with temperature are desirable because they are intrinsically thermally insulating while retaining useful properties of perfect crystals. However, this behavior is rare, and its microscopic origin remains unclear. Here, we report the observation of ultralow and glass-like thermal conductivity in a hexagonal perovskite chalcogenide single crystal, BaTiS 3 , despite its highly symmetric and simple primitive cell. Elastic and inelastic scattering measurements reveal the quantum mechanical origin of this unusual trend. A two-level atomic tunneling system exists in a shallow double-well potential of the Ti atom and is of sufficiently high frequency to scatter heat-carrying phonons up to room temperature. While atomic tunneling has been invoked to explain the low-temperature thermal conductivity of solids for decades, our study establishes the presence of sub-THz frequency tunneling systems even in high-quality, electrically insulating single crystals, leading to anomalous transport properties well above cryogenic more » Authors: ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; more » Award ID(s): Publication Date: NSF-PAR ID: 10203338 Journal Name: Nature Communications Volume: 11 Issue: 1 ISSN: 2041-1723	2022-10-07T11:43:15	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8060113191604614, "perplexity": 3496.5183628957834}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030338073.68/warc/CC-MAIN-20221007112411-20221007142411-00789.warc.gz"}
https://par.nsf.gov/biblio/10004874-insensitivity-pressure-dependences-characteristic-energy-scales-ce-coin-yb-gd-electronic-configuration-rare-earth-ion	Insensitivity of the pressure dependences of characteristic energy scales in Ce $1−xRx$ CoIn $5$ ( $R=Yb,Y,Gd$ ) to the electronic configuration of the rare-earth ion Authors: ; ; ; ; ; ; ; Publication Date: NSF-PAR ID: 10004874 Journal Name: Physical Review B Volume: 86 Issue: 10 ISSN: 1098-0121 Publisher: American Physical Society	2022-07-01T10:15:18	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 15, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8850913643836975, "perplexity": 7756.778041139911}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656103940327.51/warc/CC-MAIN-20220701095156-20220701125156-00314.warc.gz"}
https://par.nsf.gov/biblio/10324376-learning-hierarchically-structured-concepts	Learning Hierarchically Structured Concepts We use a recently developed synchronous Spiking Neural Network (SNN) model to study the problem of learning hierarchically-structured concepts. We introduce an abstract data model that describes simple hierarchical concepts. We define a feed-forward layered SNN model, with learning modeled using Oja’s local learning rule, a well known biologically-plausible rule for adjusting synapse weights. We define what it means for such a network to recognize hierarchical concepts; our notion of recognition is robust, in that it tolerates a bounded amount of noise. Then, we present a learning algorithm by which a layered network may learn to recognize hierarchical concepts according to our robust definition. We analyze correctness and performance rigorously; the amount of time required to learn each concept, after learning all of the sub-concepts, is approximately O ( 1ηk(max log(k) + 1ε) + b log(k)), where k is the number of sub-concepts per concept, max is the maximum hierarchical depth, η is the learning rate, ε describes the amount of uncertainty allowed in robust recognition, and b describes the amount of weight decrease for "irrelevant" edges. An interesting feature of this algorithm is that it allows the network to learn sub-concepts in a highly interleaved manner. This algorithm assumes that more » Authors: ; Award ID(s): Publication Date: NSF-PAR ID: 10324376 Journal Name: Neural networks Volume: 143 Page Range or eLocation-ID: 798-817 ISSN: 0893-6080	2023-03-21T17:51:09	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8935351371765137, "perplexity": 2000.7236473489836}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296943704.21/warc/CC-MAIN-20230321162614-20230321192614-00155.warc.gz"}
http://www.itl.nist.gov/div898/handbook/ppc/section2/ppc22.htm	3. Production Process Characterization 3.2. Assumptions / Prerequisites ## Continuous Linear Model Description The continuous linear model (CLM) is probably the most commonly used model in PPC. It is applicable in many instances ranging from simple control charts to response surface models. The CLM is a mathematical function that relates explanatory variables (either discrete or continuous) to a single continuous response variable. It is called linear because the coefficients of the terms are expressed as a linear sum. The terms themselves do not have to be linear. Model The general form of the CLM is: $$y = a_{0} + \sum_{i=1}^{p}{a_{i} f(x_{i})} + \epsilon$$ This equation just says that if we have p explanatory variables then the response is modeled by a constant term plus a sum of functions of those explanatory variables, plus some random error term. This will become clear as we look at some examples below. Estimation The coefficients for the parameters in the CLM are estimated by the method of least squares. This is a method that gives estimates which minimize the sum of the squared distances from the observations to the fitted line or plane. See the chapter on Process Modeling for a more complete discussion on estimating the coefficients for these models. Testing The tests for the CLM involve testing that the model as a whole is a good representation of the process and whether any of the coefficients in the model are zero or have no effect on the overall fit. Again, the details for testing are given in the chapter on Process Modeling. Assumptions For estimation purposes, there are no additional assumptions necessary for the CLM beyond those stated in the assumptions section. For testing purposes, however, it is necessary to assume that the error term is adequately modeled by a Gaussian distribution. Uses The CLM has many uses such as building predictive process models over a range of process settings that exhibit linear behavior, control charts, process capability, building models from the data produced by designed experiments, and building response surface models for automated process control applications. Examples Shewhart Control Chart - The simplest example of a very common usage of the CLM is the underlying model used for Shewhart control charts. This model assumes that the process parameter being measured is a constant with additive Gaussian noise and is given by: $$y = a_{0} + \epsilon$$ Diffusion Furnace - Suppose we want to model the average wafer sheet resistance as a function of the location or zone in a furnace tube, the temperature, and the anneal time. In this case, let there be 3 distinct zones (front, center, back) and temperature and time are continuous explanatory variables. This model is given by the CLM: $y = a_{0} + \left\{ \begin{array}{ll} a_{1} & \mbox{if front} \\ a_{2} + a_{4}\mbox{temp} + a_{5} \mbox{time} + \epsilon & \mbox{if center} \\ a_{3} & \mbox{if back} \end{array} \right.$ Diffusion Furnace (cont.) - Usually, the fitted line for the average wafer sheet resistance is not straight but has some curvature to it. This can be accommodated by adding a quadratic term for the time parameter as follows: $y = a_{0} + \left\{ \begin{array}{ll} a_{1} & \mbox{if front} \\ a_{2} + a_{4}\mbox{temp} + a_{5} \mbox{time} + a_{6} \mbox{time}^2 + \epsilon & \mbox{if center} \\ a_{3} & \mbox{if back} \end{array} \right.$	2017-10-24T00:14:16	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7648727893829346, "perplexity": 432.24852945757704}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-43/segments/1508187827662.87/warc/CC-MAIN-20171023235958-20171024015958-00332.warc.gz"}
https://xmm-tools.cosmos.esa.int/external/sas/current/doc/epexposure/node8.html	XMM-Newton Science Analysis System epexposure (epexposure-0.16) [xmmsas_20211130_0941-20.0.0] ### Chopper dependent livetime factor FC3 Because of telemetry limits an exposure might be programmed such that not all frames will be transmitted. This info is stored as quadrant specific periodic housekeeping parameters An_CHOP (see Table 1). These chopper parameters (normally 0) control the number of frames excluded from the onboard analysis before one is analysed and sent to telemetry. The livetime due to such discarded frames is represented by the factor (3) As the chopper parameter and thus the associated livetime is constant for a specific exposure the values be stored in the keywords An_CHOP and AX_FC3 by epframes in the CCD specific EXPOSURE extension to be addressed by higher SAS tasks. If one is just interested in a correct count rate then it is sufficient to divide the rate by FC3. XMM-Newton SOC -- 2021-11-30	2022-05-26T10:14:29	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8626317381858826, "perplexity": 4187.570909196072}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662604794.68/warc/CC-MAIN-20220526100301-20220526130301-00620.warc.gz"}
https://www.rba.gov.au/publications/bulletin/2018/dec/understanding-demand-for-australias-banknotes.html	# Bulletin – December 2018 Payments Understanding Demand for Australia's Banknotes ## Abstract As the sole issuer of the nation's banknotes, the Reserve Bank knows how many banknotes it prints, issues to the public and destroys. However, much less is known about how these banknotes are used. This is particularly true for the $50 and$100 banknotes, which, by value, account for more than 90 per cent of banknotes on issue. To help address this, we describe in this article the various components of Australian cash demand and use a range of techniques to estimate how much each category contributes to total demand. Our key findings include that non-transactional demand for cash (e.g. hoarding for store-of-value purposes) has likely been the driving force of recent growth in the value of outstanding banknotes, and that a small but non-trivial portion of cash demand comes from the shadow economy. As at June 2018 the total value of outstanding Australian banknotes was $76 billion, or roughly$3,000 per Australian. Although this figure might seem high, Australia is by no means an outlier amongst other comparable countries (Graph 1). The vast majority of the value of these outstanding banknotes – 93 per cent – is accounted for by the $50 and$100 denominations, split roughly evenly between the two. By contrast, $5 banknotes represent just 1 per cent of outstanding value,$10 banknotes represent 2 per cent and $20 banknotes represent 4 per cent. (By number, the lower three denominations constitute a higher share at around 30 per cent of total banknotes outstanding.) The value of banknotes on issue has continued to grow over recent years despite a shift away from cash as a means of payment, a phenomenon observed in many countries.[1] To explain these diverging trends, it has been argued that the share of cash used for non-transactional purposes, particularly as a store of value, must be increasing.[2] This article seeks to investigate the sources of demand for Australian banknotes. This is a worthwhile exercise for a few reasons. Different sources of demand may be affected by different variables and so, understanding the relative importance of each, may help in forecasting overall future banknote demand, thereby assisting with banknote print orders for example. The use of banknotes to facilitate illegal activity and avoid tax obligations has also been widely discussed in Australia and internationally in recent years, including in the final report of the Black Economy Taskforce (BETF 2017), and we aim to contribute to this discussion by providing estimates of the amount of cash used in Australia's shadow economy. At any point in time, outstanding banknotes can be considered to fall into one of the following categories: 1. banknotes that, while still recorded as outstanding, have actually been lost or destroyed; 2. banknotes used to facilitate legitimate day-to-day transactions in Australia; 3. banknotes that are held, either domestically or overseas, as a store of value, for emergency liquidity, or for other such purposes (referred to as hoarding); and 4. banknotes used in the shadow economy (either to conceal legal transactions to avoid tax, to pay for illegal goods or to store wealth generated by the sale of illegal goods). While individual banknotes move between these categories every day, the share of banknotes committed to each category is likely to be relatively stable over the short run and we aim to estimate these shares. It is important to acknowledge, however, that cash is anonymous and hard to trace. Thus, any attempt to estimate where outstanding banknotes are and what they are used for, including that made here, is bound to be an approximation at best. To mitigate this, where possible, we use a variety of techniques to estimate the same quantity, with the hope that if the errors of each technique are imperfectly correlated, then the range of estimates produced will provide a better indication of the truth than any individual method could. ## Lost Banknotes A certain portion of banknotes, while still recorded as being outstanding, are likely to have been lost, destroyed, forgotten about, or are sitting in numismatic collections and otherwise unavailable for spending. For the purposes of this article, we will refer to all such banknotes as ‘lost’. To estimate the value of lost banknotes, we assume that all still-outstanding paper banknotes – which were last issued more than 20 years ago – are lost, calculate an implied annual loss rate, and then apply this rate to outstanding polymer banknotes. Graph 2 shows estimated annual paper loss rates for currently issued denominations (loss rates for paper$1 and $2 banknotes are much higher, at around 4 and 2 per cent respectively). A couple of features are worth noting. First, for low-denomination banknotes (less than$50), there is a rough inverse relationship between the value of the banknote and the loss rate. This makes sense: people are likely to show greater care towards banknotes of greater value. For high-denomination banknotes ($50 and$100) we see the opposite: the relationship between the value of the banknote and the loss rate is positive. This is most easily explained by hoarding: these banknotes are likely either still hoarded, or have been forgotten about or lost during the hoarding process. While the loss rates of paper banknotes serve as an indicator for polymer banknotes, there are some important reasons why they may differ. For example, polymer banknotes are more durable than paper banknotes, which suggests that they should be inadvertently destroyed less often. On the other hand, increased international travel has probably resulted in a greater flow of Australian banknotes leaving the country in recent years. Some of these banknotes are unlikely to return. As it is difficult to know the net effect of these factors, we use the minimum and maximum loss rates of the paper denominations to estimate a loss range. Applying these to polymer banknotes suggests that $4–8 billion, or roughly 5–10 per cent of all banknotes on issue, have been lost, destroyed, forgotten about or are sitting in numismatic collections. ## Cash Used in Legitimate Transactions The most visible source of banknote demand is for banknotes that are used to facilitate legitimate transactions in Australia, which we call ‘transactional demand’. These are the banknotes that Australians use daily to purchase goods and services. Transactional demand is also the easiest to estimate since transactional banknotes continuously flow through the cash distribution system. As a result, we are able to employ a number of different methods to estimate the size of this source of demand. Most of our methods distinguish between cash used for legitimate transactions and cash used for shadow-economy activity, although some do not, and where this is the case we adjust our numbers by subtracting estimates of the share of banknotes used transactionally in the shadow economy (5 per cent). We first describe each method and then present a summary of our combined results at the end of this section. ### The counting method Our first approach is to estimate the stock of cash held in various physical locations that are part of the transactional stock, including banknotes in wallets, ATMs and bank branches, cash depots, tills and self-service checkouts and gaming machines, and banknotes held by tourists. These figures are added up to form an economy-wide estimate. This calculation by necessity relies on a number of assumptions, and will miss any cash held in locations not directly considered. Despite these limitations, the approach is useful as it provides a broad sense-check on other estimates arrived at through more abstract means and also offers a tangible basis from which to think about the transactional stock of cash. We use two approaches to estimate the stock of cash held in each of these locations: • estimating the number of a given location (e.g. the number of tills) and multiplying this by an estimated average amount held per location; and • converting flow data to a stock by making assumptions about the velocity of cash through a particular location. This method suggests that the transactional stock of cash has risen from around$9 billion at the end of 2002 to around $13 billion as at June 2018. This corresponds to an annualised growth rate of around 2 per cent, which is well below the 6 per cent growth rate in total outstanding banknotes over the same period. As a result, the transactional stock's share of the total is estimated to have fallen from 30 per cent to around 20 per cent according to this method (Graph 7). ### The banknote life method and the banknote processing methods We now assume that the non-transactional stock of cash consists only of hoarded$50 and $100 banknotes. While this may not be exactly true, it is probably not far off the mark: for example, almost all large claims for damaged banknotes that are submitted to the Reserve Bank are for the$50 and $100 denominations. We then try to find some data affected by this hoarding. In each of the methods below, this involves data where the$50 and $100 banknotes behave very differently to the other denominations. This difference can then be used to estimate transactional demand for the$50 and $100. Adding this to the value of outstanding$5, $10 and$20 banknotes, less our estimates of lost banknotes, gives an estimate of overall transactional demand. (Note that neither of these methods will distinguish between banknotes used for legal and shadow-economy transactions.) #### The banknote life method Banknotes reach the end of their lives (become ‘unfit’) for two main reasons: excessive inkwear, which will tend to increase in a relatively linear fashion with banknote use; and mechanical defects such as tears, which can be thought of as random events that can occur at any stage, but whose cumulative probability of having occurred also increases with use. Given that all denominations of banknotes are initially of similar quality, the speed at which certain denominations become unfit is closely related to the frequency with which they are handled. Since banknotes are most commonly handled when used as a means of payment, banknotes used in transactions should have a shorter lifespan than banknotes not used in transactions. Graph 3 shows estimated banknote life, from which one can observe that: polymer banknotes have a much longer lifespan than paper banknotes; low-denomination banknotes ($5,$10, and $20) have broadly similar banknote lives; and high-denomination banknotes ($50 and $100) have a longer lifespan than low-denomination banknotes.[3] Further, one can see that the lifespan of all banknotes has increased in recent years, which could reflect improvements in banknote handling; a decline in the velocity of transactional cash; and/or the after-effects of previous banknote cleansing programs, which replaced unfit banknotes with new ones, reducing measured banknote life at the time and increasing the quality (and remaining life) of the outstanding stock. Finally, we note that low-denomination banknotes all having similar lifespans supports the assumption that most hoarding occurs with high-denomination banknotes. For example, if the$20 was hoarded significantly more than the $10, we would expect that to show up in a longer life for$20 banknotes, whereas this is not the case. If we assume that all banknotes used in transactions wear out at a similar rate, then the ‘excess life’ of high-denomination banknotes relative to low-denomination banknotes can be attributed to hoarding. Based on this insight, we estimate that over the past three decades, the share of $100 banknotes used for transactions has fallen from around 20 per cent to just 3 per cent; the share of$50 banknotes used for transactions has fallen from around 35 per cent to 25 per cent; and the transactional share by value of all banknotes has fallen from around 45 per cent to around 20 per cent, or 15 per cent after subtracting our estimate of cash used in the shadow economy (Graph 7). #### The banknote processing method One can apply the same idea to data on the frequency with which different banknote denominations are processed by cash depots. In particular, cash depots process and fitness-sort banknotes lodged by commercial banks and large retailers, but do not process any banknotes that are hoarded or otherwise are not part of the transactional stock of cash. Thus, broadly speaking, only the transactional stock of banknotes passes through cash depots, and the rate at which banknotes pass through depots is an indication of transactional cash use. Graph 4 shows the average number of times each banknote denomination passes through a cash depot per year. A few features are worth observing. First, in recent years there has been a general decline in the processing frequencies of all denominations. This is consistent with a fall in the speed with which cash flows through the economy and/or consumers substituting away from cash as a means of payment, both of which result in banknotes passing through depots less frequently. Second, we see that the $50 and$100 banknotes pass through depots less frequently than $20 banknotes, which is indicative of non-transactional demand for these denominations given that, once spent, they are very likely to be banked (retailers don't keep$100 banknotes to use as change). Conversely, the low processing frequency of the $5 and$10 banknotes is most likely due to their use as change – that is, they cycle between consumers and retailers many times before being returned to a cash depot for processing. Given this, if we assume that the processing frequency of transactional $50 and$100 banknotes is equal to the processing frequency of the $20 banknote, then the difference between the observed processing frequency of$50 and $100 banknotes and that of the$20 is the result of hoarding. In fact the true processing frequency of transactional $50 and$100 banknotes is likely to be higher than the $20 denomination as almost all$50 and $100 banknotes received by retailers will be banked, whereas some$20 banknotes will be given as change. This suggests that this method will deliver an upwardly biased transactional share estimate. Applying the same technique used in the banknote life calculations suggests that the transactional stock has fallen from around 55 per cent of total outstanding banknotes in the late 1990s to around 40 per cent now (or 35 per cent after subtracting cash used in shadow-economy transactions; Graph 7). ### The velocity method Another way to estimate the stock of cash used for transactions is to first estimate the flow of cash payments made by consumers, and then convert this flow into a stock. The flow of cash payments and the stock of banknotes used to make them are related, but one banknote can be used in multiple transactions; banknote velocity ties the two concepts together, as described in Equation 1 below. Equation 1 $Flow of cash payments=Velocity of transactional stock×Value of transactional stock.$ We estimate the flow of cash payments through time by scaling the value of card payments with the cash-to-card payment ratio as recorded periodically in the Reserve Bank's Consumer Payment Survey (CPS; Graph 5).[4] To estimate the velocity of transactional cash, we map out the cash cycle: banknotes start at a cash depot, are transported to an ATM or bank branch, pass to a consumer's wallet or purse, get spent at a business, and then get returned to a bank and/or cash depot. For some legs of this journey we have accurate data – for example, we know the flow into and out of cash depots, and so can calculate the average time a banknote spends in a depot – whereas for other aspects we need to use judgement. Because of this, we estimate a range for the velocity of cash rather than a single number (Graph 5). Our estimates suggest that the velocity of transactional cash has declined over the past decade, and that, on average, a transactional banknote takes a little over one month to complete a full cycle. To estimate the transactional stock of cash we divide our estimates of cash payments by our estimates of velocity. With cash payments estimated to be broadly stable and velocity estimated to be falling, we estimate the transactional stock to be gradually increasing over recent years and in the range of $15–25 billion currently. These results suggest that transactional cash accounts for around 20–30 per cent of total outstanding banknotes (Graph 7). ### The seasonality method The final way we estimate the transactional share of banknotes is via the seasonality present in banknote demand. The logic works as follows: demand for cash displays a predictable seasonal pattern, with a peak around Christmas and a trough in the winter months. This seasonality resembles that of consumer spending, which suggests that it is driven by seasonality in transactional cash demand. On the other hand, non-transactional cash demand (for example, hoarding for store-of-value or numismatic purposes) is unlikely to contain significant seasonality. As a result, if most cash is transactional, then the seasonality of cash demand should closely match the seasonality of cash spending; conversely, if non-transactional demand is more important, then there will be less seasonality in cash demand than in spending. As such, and similar to the banknote life and banknote processing methods, the degree of seasonality present in cash demand, when compared with the seasonality of cash spending, is an indication of the share of cash used for transactional purposes. Graph 6 shows original and seasonally adjusted data for the stock of outstanding banknotes, as well as the monthly flow of banknote lodgements to cash depots – the latter being a proxy for cash spending.[5] The degree of seasonality in each series can be seen in the extent to which the ‘original’ line deviates from the ‘seasonally adjusted’ line; it is clear that cash lodgements are the more seasonal series. To account for the stock/flow mismatch between outstanding banknotes and cash lodgements, we adjust the seasonality of the lodgement data with three estimates of the seasonality present in the velocity of transactional cash, and then average over the three estimates.[6] Our results suggest the transactional stock of cash has been largely unchanged over the past decade. Converting to a share of total banknotes outstanding suggests that transactional demand has declined from around 40 per cent of outstanding banknotes in 2009 to 25 per cent currently, or 20 per cent after subtracting cash used in shadow-economy transactions (Graph 7). ### Overview of cash used in legitimate transactions Overall, the methods that we employ suggest that somewhere between 15 and 35 per cent of outstanding banknotes are used to facilitate non shadow-economy transactions within Australia (Graph 7). Notably, all methods show that this share is in decline. Although each estimation method is imperfect, we take comfort from the fact that a number of different methods yield a broadly similar trend. ## Hoarding Another major component of currency demand is hoarding, which can be done either by Australian residents (domestic hoarding) or by foreigners (international hoarding). Hoarding refers to banknotes actively held by people for reasons other than to finance everyday payments, and so excludes the transactional stock of banknotes (both legitimate and shadow economy), and banknotes that have been lost. Evidence from the 2016 CPS suggests that around 70 per cent of Australians hold cash outside of their wallets, and that they do so for a variety of reasons, including as a store of wealth, for use in emergencies, a desire for privacy and as a back-up in case of problems with electronic payment systems. The existence of asset means-testing for various social benefits in Australia, and more generally the desire to hide assets from tax authorities, also provides an incentive for Australians to hold assets in a form that is hard to trace. ### Estimates of total hoarding: the residual While we presented the banknote life, banknote processing and seasonality estimates above as indirect estimates of transactional cash demand, they can equally be seen as indirect estimates of hoarding demand. For instance, the banknote life method suggested that 20–40 per cent of outstanding banknotes were used to facilitate transactions (legal and shadow economy), implying that 60–80 per cent are used for non-transactional purposes. Subtracting our estimates of lost banknotes (5–10 per cent) suggests hoarding in the range of roughly half to three-quarters of total outstanding banknotes. The other indirect estimates of transactional demand give broadly similar results. ### Domestic hoarding In the 2013 and 2016 CPSs, respondents were asked to select a range that described the amount of cash they held outside their wallets. Scaling these results to economy-wide levels, we estimate that domestic cash hoarding is in the range of roughly 10–20 per cent of total outstanding banknotes.[7] While this represents a material share of Australian banknotes, it is still likely to be an underestimate. This is because those with large physical cash holdings are probably less likely to participate in a survey than others and, even if they do, might be hesitant to respond with the true extent of their cash holdings. ### International hoarding The Bank has previously noted that foreign demand for banknotes is an increasingly important component of currency demand, both in Australia and overseas (Flannigan and Parsons 2018). This is highlighted by a historically strong relationship between the exchange rate and demand for$100 banknotes: depreciations in the Australian dollar are associated with an increase in demand, although the relationship appears to have weakened somewhat of late (Graph 8). To estimate overseas hoarding, we first estimate the value of Australian banknotes flowing out of Australia; such outflows can occur via a number of channels, although the most significant appears to be international wholesale currency shipments that transport Australian banknotes to foreign banks and bureaux de change. From this gross outflow, we deduct an estimate of Australian currency that re-enters Australia; the largest component here is banknotes brought back into Australia by tourists, which we estimate as total tourist spending in Australia less the estimated portion of spending done using electronic means of payment or via banknotes obtained in Australia. There is considerable judgement involved in these calculations, and reasonable assumptions lead to an estimate of net banknote outflows over the past decade (i.e. additions to the stock of internationally hoarded Australian banknotes) of between zero and 15 per cent of total outstanding banknotes. It is important to note, however, that even this large range could be wrong as it is calculated as the residual of two imprecisely estimated quantities. ### Overall assessment of hoarding Overall, we estimate that between half and three-quarters of the value of outstanding banknotes are hoarded in some form. Of this, we can attribute 10–20 percentage points to domestic hoarding and up to 15 percentage points to international hoarding. However, this does not necessarily mean that total hoarding is overestimated. As discussed, there are limitations to the estimates of domestic and international hoarding. In particular, domestic hoarding is likely to be higher than estimated, while international hoarding could also be higher. ## Banknotes Used in the Shadow Economy A source of currency demand that continues to attract considerable attention in Australia and internationally is the use of cash to facilitate activity in the ‘shadow’ or ‘black’ economy. Borrowing from the Australian Bureau of Statistics (ABS, 2013) we define the shadow economy as consisting of: • underground production (the deliberate concealment of legal activities to avoid tax payments); and • illegal production (activities forbidden by law where there is mutual consent, such as illegal drug production and sale). To estimate the stock of banknotes used in the shadow economy, we first estimate the size of the shadow economy (a flow of spending) and then use our estimate of banknote velocity to convert this into a stock of cash required to facilitate these transactions. The assumption that most shadow-economy transactions are made with cash is implicit. While this may not be exactly true, it is probably a reasonable approximation of reality.[8] By its very nature, the shadow economy is difficult to measure. To ensure our results are as robust as possible, we use various estimates of its overall size. Our baseline approach is to scale estimates made in ABS (2013) for 2009/10 to 2017/18 levels. Our second approach is to combine results from the ABS with the Australian Criminal Intelligence Commission's (ACIC) estimates of the size of the illicit drug market in Australia. In both methods we assume that the only material component of illegal production is illegal drug production; this may downwardly bias our estimates slightly, although illegal drug production is likely to be the largest component of total illegal production by some margin (the ABS also took this approach when estimating illegal production for 2009/10). ### ABS estimates for 2009/10 applied to 2017/18 GDP figures ABS (2013) estimated underground production to be 1.5 per cent of nominal GDP and household expenditure on illegal drugs to be 0.8 per cent of total household consumption in 2009/10. In 2017/18, nominal GDP was $1,848 billion, while nominal household consumption was$1,044 billion; applying the same 1.5 and 0.8 per cent estimates as for 2009/10 implies annual underground production of $27½ billion and annual nominal spending on illegal drugs of$8½ billion in 2017/18. ### New estimates of cash used in the drug trade We next modify these results to incorporate ACIC's estimates of the size of the Australian drug market, which are made via wastewater analysis (see below). This allows us to re-estimate the value of banknotes used to purchase illicit drugs, as well as to estimate the value of cash hoarded by drug suppliers. #### Estimates of cash used to purchase illicit drugs Wastewater analysis is a standard method used to measure drug consumption. The method is based on ‘the principle that any given compound that is consumed will subsequently be excreted’ (ACIC 2018b) and end up in the sewer system. Calculating the amount of a given compound in wastewater allows for a back-calculation to estimate the amount of drug that was used by the population connected to the wastewater. National estimates of annual drug consumption are then made by scaling the results to population levels. This method suggests annual illicit drug expenditure of roughly $13½ billion, with methylamphetamine and cannabis accounting for more than 70 per cent of this value. Because a single banknote can make multiple payments, we convert the annual flow of purchases to a stock using our earlier velocity estimates. This suggests that, for the year ending August 2017, the stock of cash used to facilitate purchases of illicit drugs was a little more than$1 billion, or almost 2 per cent of the total value of banknotes on issue. #### Estimates of cash held by drug suppliers Evidence from AFP drug raids suggests that suppliers of illicit drugs often hold large volumes of cash. To estimate total cash held by drug suppliers, we combine our previous estimates of the illicit drug market with data released by the AFP and the ACIC detailing annual cash and drug seizure quantities (ACIC 2017). By comparing the value of cash seized with the value of illicit drugs confiscated, we can estimate how much cash the average drug supplier holds relative to their illicit drug stock. Scaling this number by our estimates of the size of the domestic drug market gives economy-wide estimates of the cash stock hoarded by drug suppliers, although we note that our estimates will only be reliable if those who have drugs and cash seized by the police are representative of all those involved in the illicit drug supply chain. Data from cash and drug seizures suggests that drug suppliers maintain cash holdings of around 2 per cent of the value of their stock of drugs, on average.[10] By comparison, the same data suggest that seized proceeds of crime (that is, all assets gained through crime, not just cash) equated to approximately 11 per cent of the value of drugs seized. This implies that criminals convert a large share of their cash profits into other assets, and do not solely hoard cash. Combining this with our earlier assumptions suggests that total cash hoarding by the illicit drug supply chain is in the range of $40 million to$1 billion, or somewhere between 0 and 1 per cent of all banknotes on issue.[11] ### Overall assessment of cash used in the shadow economy Our estimates suggest that between roughly $3½ and$6 billion worth of Australian banknotes are used in the shadow economy, split between underground production ($2½–$4 billion), purchases of illegal drugs (around $1 billion), and storing the profits of criminal activity (up to$1 billion). This represents between 4 and 8 per cent of all banknotes on issue. ## Conclusion This article uses a range of techniques to estimate where Australian banknotes are and what they are used for. Our results suggest that of total outstanding banknotes: 5–10 per cent are lost; 15–35 per cent are used to facilitate legitimate transactions; half to three-quarters are hoarded, of which we can allocate 10–20 percentage points to domestic hoarding and up to 15 percentage points to international hoarding; and 4–8 per cent are used in the shadow economy. Our best guess of point estimates for each of the above categories are broadly the midpoints of the ranges given, with the exceptions of the subcategories of hoarding: even the upper estimate of 20 per cent of outstanding banknotes being used for domestic hoarding is likely too low, while international hoarding and the hoarding of profits from criminal activity may also be higher than suggested by the estimation techniques that we employ. In addition, our results suggest that the share of banknotes used in transactions has fallen by around 1–1½ percentage points per year over the past few decades. This is consistent with the Reserve Bank's CPSs, which show that debit and credit cards have recently overtaken cash as the most frequently used means of payment. Consequently, it is likely that non transactional demand has been the driving force of recent growth in the value of banknotes on issue. Despite constituting a declining share of transactions, however, we estimate that the value of banknotes used to facilitate legitimate transactions in Australia has increased slightly over recent years, and is currently around $15–20 billion. ## Footnotes The authors are from Note Issue Department; this article summarises a longer paper and interested readers should refer to Finlay, Staib and Wakefield (2018) for further details on the estimation methods employed. [*] For example Doyle et al (2017) document that, in 2016, electronic payments surpassed cash as the most common payment method; we will use the terms ‘banknotes’, ‘currency’ and ‘cash’ interchangeably throughout this paper. [1] See for example Davies et al (2016) and Flannigan and Staib (2017), as well as Flannigan and Parsons (2018) for a comparison of trends in Australia, Canada and the UK. [2] We measure banknote life as the average number of banknotes outstanding over a given period, divided by the number of banknotes that have been deemed unfit over the same period, and choose a five-year period to average over in order to reduce undue volatility. This is the ‘steady-state method’ described in Rush (2014). [3] The card payment data are from RBA Statistical Tables C1 and C5, which are available at <https://www.rba.gov.au/statistics/tables/>. The CPS was conducted in 2007, 2010, 2013 and 2016 and provides the Bank with a nationally representative dataset of the payment habits of Australian consumers; the next survey is planned for 2019. We interpolate between survey years and extrapolate the 2013–16 trend for 2017 and 2018. [4] We use lodgement data as a proxy rather than card spending data here to avoid possible seasonal variation in consumers' payment preferences, which may mean that the seasonal pattern of card spending differs from that of cash spending. [5] We approximate the seasonality of velocity as: unchanging (that is, we assume that velocity is non-seasonal); as the seasonality present in the number of ATM withdrawals per person per month; and as the seasonality present in our estimate of velocity presented previously. [6] The CPS asks respondents to select a bucket that their cash holdings fall into, from ‘$1–$100’ through to ‘more than$5,000’. We take the midpoint of each value bucket, or $10,000 for the top, open-ended bucket, as the average hoarding of each respondent within each bucket, and scale up the results to be representative of the adult population. For those who did not answer (2013 and 2016) or chose ‘prefer not to answer’ (2016 only), we set their cash hoarding as the weighted average of those who did answer. For 2013, we estimate cash hoarding of 20 per cent of outstanding banknotes, while for 2016 the estimate is lower at roughly 10 per cent, suggesting that a large degree of sampling error exists in these estimates. [7] For example, despite anecdotal reports suggesting that an increasing number of illicit drug purchases are made online using digital currencies such as bitcoin, survey results from the National Drug and Alcohol Research Centre's Illicit Drug Reporting System (Karlsson and Burns 2017) indicate that most drug users still purchase their drugs face to face. [8] The difference can, in part, be explained by the BETF including a wider range of shadow-economy activities in their analysis (some of which are unlikely to involve material amounts of cash). [9] In particular, over the five years to 2016/17, the ACIC reports total drug seizures worth$6.1 billion and total cash seizures of \$100 million (ACIC 2017). [10] See Finlay et al (2018) for details of the other assumptions underlying these calculations. [11] ## References ABS (Australian Bureau of Statistics) (2013), ‘Information Paper: The Non-Observed Economy and Australia's GDP, 2012’, ABS Cat No 5204.0.55.008, viewed 4 July 2018. ACIC (Australian Criminal Intelligence Commission) (2017), 2016–17 Annual Report. ACIC (2018a), Illicit Drug Data Report 2016–17. ACIC (2018b), National Wastewater Drug Monitoring Program, Report 4, March. BETF (Black Economy Taskforce) (2017), Black Economy Taskforce: Final Report – October 2017, (M Andrew, Chair), Australian Treasury, Canberra. Davies C, M-A Doyle, C Fisher and S Nightingale (2016), ‘The Future of Cash’, RBA Bulletin, December, pp 43–52. Doyle M-A, C Fisher, E Tellez and A Yadav (2017), ‘How Australians Pay: Evidence from the 2016 Consumer Payments Survey’, RBA Research Discussion Paper No 2017-04. Finlay R, A Staib and M Wakefield (2018), ‘Where's the money? An investigation into the whereabouts and uses of Australian banknotes’, RBA Research Discussion Paper No 2018-12. Flannigan G and S Parsons (2018), ‘High-Denomination Banknotes in Circulation: A Cross-Country Analysis’, RBA Bulletin, March, viewed 4 July 2018. Available at <https://www.rba.gov.au/publications/bulletin/2018/mar/high-denomination-banknotes-in-circulation-a-cross-country-analysis.html>. Flannigan G and A Staib (2017), ‘The Growing Demand for Cash’, RBA Bulletin, September, pp 63–74. Karlsson A and L Burns (2017), Australian Drug Trends 2017: Findings from the Illicit Drug Reporting System (IDRS), Australian Drug Trends Series No 181, National Drug and Alcohol Research Centre, Sydney. Available at <https://ndarc.med.unsw.edu.au/resource/illicit-drug-reporting-system-idrs-national-report-2017>. Rush A (2015), ‘The Life of Australian Banknotes’, RBA Research Discussion Paper No 2015-10.	2021-09-28T05:35:24	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 1, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4994301199913025, "perplexity": 3054.4583563235565}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780060201.9/warc/CC-MAIN-20210928032425-20210928062425-00609.warc.gz"}
https://finalfantasy.fandom.com/wiki/Edge_Geraldine/Gameplay	## FANDOM 37,127 Pages Edge is a playable character in the Final Fantasy IV series. He is a ninja-type character who can dual-wield weapons and use Ninjutsu skills in battle. ## Final Fantasy IVEdit ### Stats Edit Edge has high Speed and physical stats, but has low Defense. This is counteracted by his high physical evasion. #### 2D statsEdit Edge (2D)data extracted from the PSP version Level HP MP Strength Speed Stamina Intellect Spirit 25 790 60 20 23 17 12 12 30 1077 80 25 27 21 14 14 40 1714 120 35 34 27 19 17 50 2441 160 45 41 34 24 20 60 3286 200 52 47 41 29 22 70At random afterward, see table below 4270 240 59 54 47 34 25 80 5316 280 rdm rdm rdm rdm rdm 90 6343 320 rdm rdm rdm rdm rdm 997641892 exp 7268 356 rdm rdm rdm rdm rdm Level up possibilities -Edge-Data extracted from the PSP version Possibility Strength Speed Stamina Intellect Spirit 1 -1 -1 0 -1 0 2 +1 0 0 0 0 3 0 +1 0 0 0 4 +1 0 +1 0 0 5 +1 +1 0 +1 0 6 +2 0 +2 0 0 7 0 +3 0 +3 0 #### 3D statsEdit Edge (3D) Level HP MP Strength Speed Stamina Intellect Spirit 35 1215 100 32 39 26 20 14 40 1476 120 36 43 29 22 15 50 2078 160 45 53 35 27 18 60 2781 200 53 62 42 31 21 70Depend on augments in character's battle menu afterward 3584 240 61 72 48 35 24 To reach 99 points in his stats, Edge needs 38 points in Strength, 27 in Speed, 51 in Stamina, 64 in Intellect and 75 in Spirit. ### AbilitiesEdit Edge is a Ninja, allowing him to dual wield weapons. If Edge has two weapons equipped, the damage he deals from the Attack command is equal to the attack power of his left weapon plus the attack power of the right weapon plus Edge's Strength divided by 4, added together with Edge's Level divided by 4, multiplied by 2. $Base Attack Power = Weapon on Left Hand's Attack Power + Weapon on Right Hand's Attack Power + (Str/4 + Level/4)2$ However, if Edge is only equipped with one weapon, the damage he deals from the Attack command is equal to just the attack power of the weapon. $Base Attack Power = Weapon's Attack Power$ After calculating the base attack power for a physical attack, several modifiers are brought into play, such as Critical Hits, elements, and status effects. Edge's Throw command allows him to throw weapons at his opponents for high damage. His Steal allows him to steal items from his opponents and Ninjutsu allows him to cast special Ninja spells. In the Advance and Final Fantasy IV: The Complete Collection releases, Edge gains the Hanzo Gloves for completing his Lunar Trial that upgrades Steal to Plunder. With Plunder, Edge will attack if he successfully steals. In all 2D versions of the game, Edge takes some damage if he fails to steal an item. In the 3D releases Edge learns more Ninjutsu skills. skill Level Learned 2D versionsSNES, PS, GBA, PSP 3D versionsDS, Mobile Flame Known Known FloodLearned at Tower of Babil Event Event BlitzLearned at Tower of Babil Event Event Smoke 33 Known Mirage 38 Known Tremor 40 Gale 50 Frost 60 ### EquipmentEdit Edge can equip katanas, boomerangs, daggers and claws, although he can no longer equip claws in the 3D remake version. He may also equip hats, clothes, the Genji equipment, armlets, some gloves and rings. In all versions, Edge joins with 2 Kunais, a Green Beret, a Black Belt Gi and Mythril Gloves. Weapons 2D & 3D Katanas Daggers Boomerangs Claws Armor 2D & 3D ## Final Fantasy IV -Interlude-Edit Edge is playable alone during a short section after the Sealed Cave. He joins the party after Rydia? disappears. ### StatsEdit Edge starts at level 39. Edge has the same stats table and level up possibilities as he did in Final Fantasy IV. Edge Level HP MP Strength Speed Stamina Intellect Spirit 39 1630 128 34 33 27 19 16 ### AbilitiesEdit Edge retains his Ninjutsu, Throw, and Steal commands that function the same way they did in Final Fantasy IV. He already knows all his six Ninjutsu spells. Spell Level Learned Flame Known Smoke Known Mirage Known Flood Known Blitz Known ### EquipmentEdit Edge may equip katanas, daggers, Claws, hats, clothes, the genji equipment, armlets, some gloves and rings. He comes equipped with a Kotetsu, a Ashura, a Green Beret, a Black Belt Gi, and Giant's Gloves. Weapons Katanas Daggers Claws ## Final Fantasy IV: The After YearsEdit ### StatsEdit Edge and the Eblan Four have a level cap of 40 in his chapter. Edge has all around decent stats with the exception of his low Spirit, and while he is primarily a physical attacker he can be a somewhat effective Black Mage with Ninjutsu. Edge's greatest asset is his high Speed, and he is the second-fastest character in the game after Tsukinowa. Stats Level HP MP Strength Speed Stamina Intelligence Spirit 15 550 72 15 19 13 10 9 20 787 92 17 21 15 12 12 30 1376 132 25 27 21 18 17 40 2166 172 35 34 27 25 22 50 3160 227 45 44 36 34 25 60 4157 282 52 49 43 44 26 70 5130 336 61 54 50 54 27 80 5553 369 64 56 52 55 29 90 5994 405 66 58 54 56 31 99 6373 438 68 59 56 58 31 ### AbilitiesEdit Edge retains his Ninjutsu techniques, and learns a much larger variety of them than his apprentices do. He also has the Throw ability and Mug (Smash & Grab in the WiiWare version), which lets him attack enemies and attempt to steal from them. Spell Level Learned Flame Known Flood Known Shock Known Gale Known Smoke Known Heal Pill 17 Spell Level Learned Mirage 32 Blast 42 Frost 45 Blitz 48 Tremor 50 Band Abilities Ability Members MP Effect Wild Moon • Edge (Attack) • Tsukinowa (Attack) 12 Attack all enemies with a pincer attack. Blazing Moon Ring • Edge (Ninjutsu) • Gekkou (Shuriken) 7 Attack a single enemy with a flaming body slam. Frozen Moon Dance • Edge (Ninjutsu) • Izayoi (Ninjutsu) 8 Freeze and shatter a single enemy. Gale Twin Break • Edge (Ninjutsu) • Zangetsu (Human Kite) 14 Attack all enemies from above. Broken Heart • Edge (Attack) • Rydia (Attack, Bow) 25 Attack all enemies with emotion-charged arrows. Inferno • Edge • Rydia (Event) 40 Create a tornado of flame to attack all enemies. Mirage Dive • Edge (Ninjutsu) • Kain (Jump) 32 Create illusions to attack an enemy • Edge (Ninjutsu) • Luca (Big Throw) • Rydia (Black Magic) 15 Create a flaming whirlwind that strikes all enemies. Oboro Strike • Edge • Yang (Event) 25 Strike an enemy with a flurry of attacks. • Edge (Attack) • Cecil (Attack) • Edward (Bardsong) • Yang (Attack) 30 Combo attack on one enemy with the power of four monarchs. Final Fantasy • Edge (Throw) • Cecil (Fight) • Kain (Jump) • Rosa (White Magic) • Rydia (Black Magic) 75 Attack all enemies and heal party with a powerful combination. Ultimate Art: Advent of the Phoenix • Edge (Mug) • Gekkou (Shuriken) • Izayoi (Illusions) • Tsukinowa (Steal) • Zangetsu (Human Kite) 20 Create a flaming phoenix to damage all enemies equivalent to lost HP of party. ### EquipmentEdit Edge may equip katanas, boomerangs, daggers, claws, hats, clothes, the Genji equipment, armlets, some gloves and rings. His equipment has expanded in Final Fantasy IV: The After Years. The most significant item is Rubicante's cloak, the Fire Scarf. It provides adequate Defense and can absorb all Fire-elemental attacks and when combined with a Protect Ring can give him absorption to Ice and Lightning additionally. He starts with 2 Kodachis, a Green Beret, a Shinobi Gear and a Silver Armlet. Community content is available under CC-BY-SA unless otherwise noted.	2020-01-25T16:30:37	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.23123565316200256, "perplexity": 13142.769461448144}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-05/segments/1579251678287.60/warc/CC-MAIN-20200125161753-20200125190753-00268.warc.gz"}
https://www.nist.gov/pml/sensor-science/fluid-metrology/database-thermophysical-properties-gases-used-semiconductor-3	An official website of the United States government The .gov means it’s official. Federal government websites often end in .gov or .mil. Before sharing sensitive information, make sure you’re on a federal government site. The site is secure. The https:// ensures that you are connecting to the official website and that any information you provide is encrypted and transmitted securely. # Index of Semiconductor Process Gases - Boron Trichloride ## Share BORON TRICHLORIDE M.W. [1] 117.169 N.B.P [2] 285.65 K T.P [3] 166.15 K BCl3 Pc [4] 3.87 MPa Tc [4] 451.95 K Vc [5] 0.1483 m3/kmol Note: In the tables, is used for properties obtained from estimation methods. * and + are used to distinguish between differing data sets within a single column. If no uncertainty is specified, then no uncertainty was provided by the reference. T K $$\frac{C_P^0(T)} {R}$$ Vapor Pressure kPa B(T) cm3· mol-1 dB/dT·T cm3· mol-1 C(T) cm6· mol-2 dC/dT·T cm6· mol-2 λ mW/ (m·K) η µPa·s Estimated Uncertainty 1%/+0.1% 1% Gas densities are calculated to better than 0.1% over the temperature and pressure ranges of the reference. 10% 10% Reference 6/+7 8 7 7 7 7 7 7 290 +7.45 119 -780.9 1760.5 -138842 1531523 #7.4 #12.0 295 +7.49 141 -751.4 1685.1 -114510 1320367 #7.5 #12.2 300 +7.53 166 -723.7 1614.9 -93866 1140490 #7.7 #12.3 305 +7.57 195 -697.5 1549.6 -76314 986761 #7.8 #12.5 310 +7.62 227 -672.8 1488.6 -61365 854979 #7.9 #12.6 315 +7.66 263 -649.5 1431.6 -48611 741684 #8.1 #12.8 320 +7.70 303 -627.4 1378.2 -37717 644020 #8.2 #13.0 340 +7.85 508 -549.5 1195.3 -7749 367768 #8.8 #13.6 360 +7.99 799 -485.5 1050.6 8360 208501 #9.4 #14.2 380 +8.12 1195 -431.9 934.1 16889 114183 #9.9 #14.9 400 +8.25 1719 -386.5 838.6 21178 57261 #10.5 #15.5 420 +8.36 2397 -347.5 759.1 23062 22529 #11.0 #16.2 440 +8.46 3264 -313.8 692.2 23580 1292 #11.6 #16.8 450 +8.51 3781 -298.6 662.6 23524 -5958 #11.9 #17.1 460 +8.55 - -284.3 635.2 23329 -11574 #12.1 #17.4 480 8.66 - -258.4 586.2 22661 -19171 #12.7 #18.1 500 8.74 - -235.3 543.6 21784 -23414 #13.3 #18.7 550 8.91 - -187.7 458.6 19357 -26247 #14.6 #20.3 600 9.05 - -150.7 395.2 17136 -24375 #16.0 #21.9 650 9.17 - -121.0 346.2 15307 -21206 #17.3 #23.4 700 9.26 - -96.8 307.5 13856 -17943 #18.6 #25.0 750 9.34 - -76.7 276.1 12722 -14986 #19.9 #26.5 800 9.41 - -59.8 250.2 11838 -12436 #21.2 #28.0 850 9.47 - -45.3 228.4 11151 -10284 #22.4 #29.5 900 9.52 - -32.8 210.0 10615 -8485 #23.6 #30.9 950 9.56 - -21.8 194.1 10198 -6987 #24.8 #32.3 1000 9.60 - -12.3 180.3 9872 -5739 #26.0 #33.7 References: 1. IUPAC, "Atomic Weights of the Elements 1993," J. Phys. Chem. Ref. Data (1995, 24, 1561). 2. "Handbook of Chemistry and Physics," 62nd ed., the Chemical Rubber Co., Cleveland, OH (1981). 3. "Predicted by Project Staff at The Pennsylvania State University using either published or internal methods. 4. Lynn, Jr., R.E., and Kobe, K.A., "The Critical Properties of Elements and Compounds," Chem. Rev. (1953, 52, 117). 5. Matheson Gas Data Book, unabridged ed., Matheson Company, Inc. East Rutherford, NJ (1974, 4 vols.) 6. "JANAF Thermochemical Tables," J. Phys. Chem. Ref. Data (1978, 7, 793). 1978 Supplement 7. Hurly, J.J., "Thermophysical Properties of Gaseous HBr and BCl3 from Speed-of-Sound Measurements," Int. J. Thermophys. (2000, 21/4). 8. Stull, D.R., "Vapor Pressure of Pure Substances," Ind. Eng. Chem. (1947, 39, 517). Footnote: # is used for properties obtained from estimation methods. * and + are used to distinguish between differing data sets within a single column. ## Contacts Created December 18, 2009, Updated December 5, 2019	2020-08-09T16:26:11	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2288604974746704, "perplexity": 12713.21656425211}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-34/segments/1596439738562.5/warc/CC-MAIN-20200809162458-20200809192458-00152.warc.gz"}
https://zbmath.org/authors/?q=ai%3Agangbo.wilfrid	# zbMATH — the first resource for mathematics ## Gangbo, Wilfrid Compute Distance To: Author ID: gangbo.wilfrid Published as: Gangbo, Wilfrid; Gangbo, W.; Gangbo, Wilfried External Links: MGP · Wikidata · GND Documents Indexed: 57 Publications since 1990, including 3 Books all top 5 #### Co-Authors 6 single-authored 9 Dacorogna, Bernard 7 Tudorascu, Adrian 5 Świȩch, Andrzej 3 Li, Wuchen 3 McCann, Robert J. 2 Brenier, Yann 2 Carlen, Eric Anders 2 Cullen, Mike 2 Evans, Lawrence Craig 2 Fonseca, Irene 2 Kneuss, Olivier 2 Osher, Stanley Joel 2 Westdickenberg, Michael 1 Ambrosio, Luigi 1 Awi, Roméo 1 Banyaga, Augustin 1 Bouchitté, Guy 1 Buttazzo, Giuseppe 1 Cardaliaguet, Pierre 1 Chayes, Lincoln 1 Chipot, Michel 1 Chow, Yat Tin 1 Cordero-Erausquin, Dario 1 Douchet, Jacques 1 Figalli, Alessio 1 Georgy, Nicolas 1 Haskovec, Jan 1 Houdré, Christian 1 Kawohl, Bernd 1 Kim, Hwa Kil 1 Lei, Helen K. 1 Luca, Florian 1 Markowich, Peter Alexander 1 Mayorga, Sergio 1 Mou, Chenchen 1 Neudauer, Nancy Ann 1 Nguyen, Truyen Van 1 Nguyen, Van Truyen 1 Oliker, Vladimir I. 1 Pacini, Tommaso 1 Pisante, Giovanni 1 Puthawala, Michael A. 1 Rappaz, Jacques 1 Ryu, Ernest K. 1 Savaré, Giuseppe 1 Savin, Ovidiu V. 1 Seppecher, Pierre 1 Shubin, Carol Ann 1 Sierra, Jesús 1 Subia, Nelson 1 Van der Putten, Roberto 1 Villani, Cédric 1 Waldschmidt, Michel 1 Yin, Wotao 1 Yolcu, Turkay all top 5 #### Serials 7 Archive for Rational Mechanics and Analysis 4 Journal de Mathématiques Pures et Appliquées. Neuvième Série 4 SIAM Journal on Mathematical Analysis 3 Communications on Pure and Applied Mathematics 3 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 3 Calculus of Variations and Partial Differential Equations 2 Advances in Mathematics 2 Journal of Differential Equations 2 Memoirs of the American Mathematical Society 2 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 2 Notices of the American Mathematical Society 2 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 1 Journal of Computational Physics 1 Acta Mathematica 1 Quarterly of Applied Mathematics 1 Journal of Scientific Computing 1 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 1 Communications in Partial Differential Equations 1 Comptes Rendus de l’Académie des Sciences. Série I 1 Bollettino della Unione Matemàtica Italiana. Serie VII. B 1 Journal of Mathematical Sciences (New York) 1 Methods and Applications of Analysis 1 Discrete and Continuous Dynamical Systems 1 Annals of Mathematics. Second Series 1 Comptes Rendus. Mathématique. Académie des Sciences, Paris 1 Communications in Mathematical Sciences 1 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V 1 Analysis and Applications (Singapore) 1 Oxford Lecture Series in Mathematics and its Applications all top 5 #### Fields 41 Calculus of variations and optimal control; optimization (49-XX) 24 Partial differential equations (35-XX) 10 Mechanics of deformable solids (74-XX) 6 Dynamical systems and ergodic theory (37-XX) 5 Measure and integration (28-XX) 5 Functional analysis (46-XX) 5 Statistical mechanics, structure of matter (82-XX) 5 Operations research, mathematical programming (90-XX) 4 Operator theory (47-XX) 4 Probability theory and stochastic processes (60-XX) 4 Fluid mechanics (76-XX) 3 Real functions (26-XX) 2 Integral equations (45-XX) 2 Differential geometry (53-XX) 2 Global analysis, analysis on manifolds (58-XX) 2 Geophysics (86-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 History and biography (01-XX) 1 Functions of a complex variable (30-XX) 1 Ordinary differential equations (34-XX) 1 General topology (54-XX) 1 Algebraic topology (55-XX) 1 Manifolds and cell complexes (57-XX) 1 Numerical analysis (65-XX) 1 Quantum theory (81-XX) 1 Information and communication theory, circuits (94-XX) #### Citations contained in zbMATH Open 47 Publications have been cited 1,175 times in 852 Documents Cited by Year The geometry of optimal transportation. Zbl 0887.49017 Gangbo, Wilfrid; McCann, Robert J. 1996 Differential equations methods for the Monge-Kantorovich mass transfer problem. Zbl 0920.49004 Evans, L. C.; Gangbo, W. 1999 Degree theory in analysis and applications. Zbl 0852.47030 Fonseca, Irene; Gangbo, Wilfrid 1995 Optimal maps for the multidimensional Monge-Kantorovich problem. Zbl 0889.49030 Gangbo, Wilfrid; Świȩch, Andrzej 1998 Hamiltonian ODEs in the Wasserstein space of probability measures. Zbl 1132.37028 Ambrosio, Luigi; Gangbo, Wilfrid 2008 Hamilton-Jacobi equations in the Wasserstein space. Zbl 1171.49308 Gangbo, Wilfrid; Nguyen, Truyen; Tudorascu, Adrian 2008 Optimal maps in Monge’s mass transport problem. Zbl 0858.49002 Gangbo, Wilfried; McCann, Robert J. 1995 Shape recognition via Wasserstein distance. Zbl 1039.49038 Gangbo, Wilfrid; McCann, Robert J. 2000 Inequalities for generalized entropy and optimal transportation. Zbl 1135.49026 Cordero-Erausquin, Dario; Gangbo, Wilfrid; Houdré, Christian 2004 An elementary proof of the polar factorization of vector-valued functions. Zbl 0828.57021 Gangbo, Wilfrid 1994 Constrained steepest descent in the 2-Wasserstein metric. Zbl 1038.49040 Carlen, E. A.; Gangbo, W. 2003 Solution of a model Boltzmann equation via steepest descent in the 2-Wasserstein metric. Zbl 1182.76944 Carlen, E. A.; Gangbo, W. 2004 Euler-Poisson systems as action-minimizing paths in the Wasserstein space. Zbl 1171.76047 Gangbo, W.; Nguyen, Van Truyen; Tudorascu, A. 2009 Existence of a solution to an equation arising from the theory of mean field games. Zbl 1359.35221 Gangbo, Wilfrid; Święch, Andrzej 2015 Diffeomorphisms and nonlinear heat flows. Zbl 1096.35061 Evans, L. C.; Savin, O.; Gangbo, W. 2005 Sticky particle dynamics with interactions. Zbl 1282.35236 Brenier, Y.; Gangbo, W.; Savaré, G.; Westdickenberg, M. 2013 Optimal transport for the system of isentropic Euler equations. Zbl 1182.35161 Gangbo, Wilfrid; Westdickenberg, Michael 2009 Metric viscosity solutions of Hamilton-Jacobi equations depending on local slopes. Zbl 1355.49024 Gangbo, Wilfrid; Świȩch, Andrzej 2015 On differentiability in the Wasserstein space and well-posedness for Hamilton-Jacobi equations. Zbl 1419.35234 2019 A variational approach for the 2-dimensional semi-geostrophic shallow water equations. Zbl 0985.76008 Cullen, Mike; Gangbo, Wilfrid 2001 Sur une généralisation de l’inégalité de Wirtinger. (A generalization of Wirtinger’s inequality). Zbl 0764.49009 Dacorogna, B.; Gangbo, W.; Subía, N. 1992 Local invertibility of Sobolev functions. Zbl 0839.30018 Fonseca, I.; Gangbo, W. 1995 Optimal transport and large number of particles. Zbl 1277.35129 Gangbo, Wilfrid; Świȩch, Andrzej 2014 Lagrangian dynamics on an infinite-dimensional torus; a weak KAM theorem. Zbl 1186.49031 Gangbo, W.; Tudorascu, A. 2010 A parallel method for Earth mover’s distance. Zbl 1398.65124 Li, Wuchen; Ryu, Ernest K.; Osher, Stanley; Yin, Wotao; Gangbo, Wilfrid 2018 Weak KAM theory on the Wasserstein torus with multidimensional underlying space. Zbl 1321.37074 2014 Some examples of rank one convex functions in dimension two. Zbl 0722.49018 Dacorogna, B.; Douchet, J.; Gangbo, W.; Rappaz, J. 1990 Differential forms on Wasserstein space and infinite-dimensional Hamiltonian systems. Zbl 1221.53001 Gangbo, Wilfrid; Kim, Hwa Kil; Pacini, Tommaso 2011 Michell trusses and lines of principal action. Zbl 1151.49019 Bouchitté, Guy; Gangbo, Wilfrid; Seppecher, Pierre 2008 On the weak lower semicontinuity of energies with polyconvex integrands. Zbl 0829.49011 Gangbo, W. 1994 Existence of optimal maps in the reflector-type problems. Zbl 1136.49015 2007 Geometric restrictions for the existence of viscosity solutions. Zbl 0927.35021 Cardaliaguet, P.; Dacorogna, B.; Gangbo, W.; Georgy, N. 1999 The semigeostrophic equations discretized in reference and dual variables. Zbl 1139.86003 Cullen, Mike; Gangbo, Wilfrid; Pisante, Giovanni 2007 Optimal transport of closed differential forms for convex costs. (Transport optimal des formes fermées pour des coûts convexes.) Zbl 1334.49142 Dacorogna, Bernard; Gangbo, Wilfrid; Kneuss, Olivier 2015 The Monge mass transfer problem and its applications. Zbl 0930.49025 Gangbo, Wilfrid 1999 On the envelopes of functions depending on singular values of matrices. Zbl 0803.49014 Buttazzo, G.; Dacorogna, B.; Gangbo, W. 1994 A weak KAM theorem; from finite to infinite dimension. Zbl 1196.37114 2010 Homogenization for a class of integral functionals in spaces of probability measures. Zbl 1248.35015 2012 On some nonlocal variational problems. Zbl 1115.49007 Chipot, Michel; Gangbo, Wilfrid; Kawohl, Bernd 2006 $$L^p$$ approximation of maps by diffeomorphisms. Zbl 1055.26008 Brenier, Yann; Gangbo, Wilfrid 2003 A variational method for a class of parabolic PDEs. Zbl 1239.35074 Figalli, Alessio; Gangbo, Wilfrid; Yolcu, Turkay 2011 Uniqueness of equilibrium configurations in solid crystals. Zbl 0984.49017 Gangbo, Wilfrid; Van der Putten, Roberto 2000 On the continuity of the polyconvex, quasiconvex and rank-one-convex envelopes with respect to growth condition. Zbl 0818.49012 Gangbo, Wilfrid 1993 A polyconvex integrand; Euler-Lagrange equations and uniqueness of equilibrium. Zbl 1297.35009 Awi, Roméo; Gangbo, Wilfrid 2014 Extension theorems for vector valued maps. Zbl 1101.46016 Dacorogna, Bernard; Gangbo, Wilfrid 2006 A partial Laplacian as an infinitesimal generator on the Wasserstein space. Zbl 1422.60119 Chow, Yat Tin; Gangbo, Wilfrid 2019 Unnormalized optimal transport. Zbl 1453.49016 Gangbo, Wilfrid; Li, Wuchen; Osher, Stanley; Puthawala, Michael 2019 On differentiability in the Wasserstein space and well-posedness for Hamilton-Jacobi equations. Zbl 1419.35234 2019 A partial Laplacian as an infinitesimal generator on the Wasserstein space. Zbl 1422.60119 Chow, Yat Tin; Gangbo, Wilfrid 2019 Unnormalized optimal transport. Zbl 1453.49016 Gangbo, Wilfrid; Li, Wuchen; Osher, Stanley; Puthawala, Michael 2019 A parallel method for Earth mover’s distance. Zbl 1398.65124 Li, Wuchen; Ryu, Ernest K.; Osher, Stanley; Yin, Wotao; Gangbo, Wilfrid 2018 Existence of a solution to an equation arising from the theory of mean field games. Zbl 1359.35221 Gangbo, Wilfrid; Święch, Andrzej 2015 Metric viscosity solutions of Hamilton-Jacobi equations depending on local slopes. Zbl 1355.49024 Gangbo, Wilfrid; Świȩch, Andrzej 2015 Optimal transport of closed differential forms for convex costs. (Transport optimal des formes fermées pour des coûts convexes.) Zbl 1334.49142 Dacorogna, Bernard; Gangbo, Wilfrid; Kneuss, Olivier 2015 Optimal transport and large number of particles. Zbl 1277.35129 Gangbo, Wilfrid; Świȩch, Andrzej 2014 Weak KAM theory on the Wasserstein torus with multidimensional underlying space. Zbl 1321.37074 2014 A polyconvex integrand; Euler-Lagrange equations and uniqueness of equilibrium. Zbl 1297.35009 Awi, Roméo; Gangbo, Wilfrid 2014 Sticky particle dynamics with interactions. Zbl 1282.35236 Brenier, Y.; Gangbo, W.; Savaré, G.; Westdickenberg, M. 2013 Homogenization for a class of integral functionals in spaces of probability measures. Zbl 1248.35015 2012 Differential forms on Wasserstein space and infinite-dimensional Hamiltonian systems. Zbl 1221.53001 Gangbo, Wilfrid; Kim, Hwa Kil; Pacini, Tommaso 2011 A variational method for a class of parabolic PDEs. Zbl 1239.35074 Figalli, Alessio; Gangbo, Wilfrid; Yolcu, Turkay 2011 Lagrangian dynamics on an infinite-dimensional torus; a weak KAM theorem. Zbl 1186.49031 Gangbo, W.; Tudorascu, A. 2010 A weak KAM theorem; from finite to infinite dimension. Zbl 1196.37114 2010 Euler-Poisson systems as action-minimizing paths in the Wasserstein space. Zbl 1171.76047 Gangbo, W.; Nguyen, Van Truyen; Tudorascu, A. 2009 Optimal transport for the system of isentropic Euler equations. Zbl 1182.35161 Gangbo, Wilfrid; Westdickenberg, Michael 2009 Hamiltonian ODEs in the Wasserstein space of probability measures. Zbl 1132.37028 Ambrosio, Luigi; Gangbo, Wilfrid 2008 Hamilton-Jacobi equations in the Wasserstein space. Zbl 1171.49308 Gangbo, Wilfrid; Nguyen, Truyen; Tudorascu, Adrian 2008 Michell trusses and lines of principal action. Zbl 1151.49019 Bouchitté, Guy; Gangbo, Wilfrid; Seppecher, Pierre 2008 Existence of optimal maps in the reflector-type problems. Zbl 1136.49015 2007 The semigeostrophic equations discretized in reference and dual variables. Zbl 1139.86003 Cullen, Mike; Gangbo, Wilfrid; Pisante, Giovanni 2007 On some nonlocal variational problems. Zbl 1115.49007 Chipot, Michel; Gangbo, Wilfrid; Kawohl, Bernd 2006 Extension theorems for vector valued maps. Zbl 1101.46016 Dacorogna, Bernard; Gangbo, Wilfrid 2006 Diffeomorphisms and nonlinear heat flows. Zbl 1096.35061 Evans, L. C.; Savin, O.; Gangbo, W. 2005 Inequalities for generalized entropy and optimal transportation. Zbl 1135.49026 Cordero-Erausquin, Dario; Gangbo, Wilfrid; Houdré, Christian 2004 Solution of a model Boltzmann equation via steepest descent in the 2-Wasserstein metric. Zbl 1182.76944 Carlen, E. A.; Gangbo, W. 2004 Constrained steepest descent in the 2-Wasserstein metric. Zbl 1038.49040 Carlen, E. A.; Gangbo, W. 2003 $$L^p$$ approximation of maps by diffeomorphisms. Zbl 1055.26008 Brenier, Yann; Gangbo, Wilfrid 2003 A variational approach for the 2-dimensional semi-geostrophic shallow water equations. Zbl 0985.76008 Cullen, Mike; Gangbo, Wilfrid 2001 Shape recognition via Wasserstein distance. Zbl 1039.49038 Gangbo, Wilfrid; McCann, Robert J. 2000 Uniqueness of equilibrium configurations in solid crystals. Zbl 0984.49017 Gangbo, Wilfrid; Van der Putten, Roberto 2000 Differential equations methods for the Monge-Kantorovich mass transfer problem. Zbl 0920.49004 Evans, L. C.; Gangbo, W. 1999 Geometric restrictions for the existence of viscosity solutions. Zbl 0927.35021 Cardaliaguet, P.; Dacorogna, B.; Gangbo, W.; Georgy, N. 1999 The Monge mass transfer problem and its applications. Zbl 0930.49025 Gangbo, Wilfrid 1999 Optimal maps for the multidimensional Monge-Kantorovich problem. Zbl 0889.49030 Gangbo, Wilfrid; Świȩch, Andrzej 1998 The geometry of optimal transportation. Zbl 0887.49017 Gangbo, Wilfrid; McCann, Robert J. 1996 Degree theory in analysis and applications. Zbl 0852.47030 Fonseca, Irene; Gangbo, Wilfrid 1995 Optimal maps in Monge’s mass transport problem. Zbl 0858.49002 Gangbo, Wilfried; McCann, Robert J. 1995 Local invertibility of Sobolev functions. Zbl 0839.30018 Fonseca, I.; Gangbo, W. 1995 An elementary proof of the polar factorization of vector-valued functions. Zbl 0828.57021 Gangbo, Wilfrid 1994 On the weak lower semicontinuity of energies with polyconvex integrands. Zbl 0829.49011 Gangbo, W. 1994 On the envelopes of functions depending on singular values of matrices. Zbl 0803.49014 Buttazzo, G.; Dacorogna, B.; Gangbo, W. 1994 On the continuity of the polyconvex, quasiconvex and rank-one-convex envelopes with respect to growth condition. Zbl 0818.49012 Gangbo, Wilfrid 1993 Sur une généralisation de l’inégalité de Wirtinger. (A generalization of Wirtinger’s inequality). Zbl 0764.49009 Dacorogna, B.; Gangbo, W.; Subía, N. 1992 Some examples of rank one convex functions in dimension two. Zbl 0722.49018 Dacorogna, B.; Douchet, J.; Gangbo, W.; Rappaz, J. 1990 all top 5 #### Cited by 988 Authors 26 Gangbo, Wilfrid 20 McCann, Robert J. 20 Rossi, Julio Daniel 15 Dacorogna, Bernard 15 Li, Wuchen 13 Ghoussoub, Nassif A. 13 Tudorascu, Adrian 12 Ambrosio, Luigi 12 Carrillo de la Plata, José Antonio 12 Kim, Young-Heon 11 Carlier, Guillaume 11 De Pascale, Luigi 11 Santambrogio, Filippo 10 Hencl, Stanislav 10 Pass, Brendan 10 Rossi, Francesco 9 Beiglböck, Mathias 9 Cardaliaguet, Pierre 9 Chen, Yongxin 9 Feldman, Mikhail 9 Figalli, Alessio 8 Brenier, Yann 8 Friesecke, Gero 8 Malý, Jan 8 Mazón Ruiz, José M. 8 Moameni, Abbas 8 Moroşanu, Costică 8 Osher, Stanley Joel 8 Westdickenberg, Michael 7 Agueh, Martial 7 Bouchitté, Guy 7 Fonseca, Irene 7 Georgiou, Tryphon T. 7 Igbida, Noureddine 7 Piccoli, Benedetto 7 Pratelli, Aldo 7 Savaré, Giuseppe 7 Wolansky, Gershon 6 Champion, Thierry 6 Dweik, Samer 6 Granieri, Luca 6 Müller, Stefan 6 Palmer, Aaron Zeff 6 Villani, Cédric 6 Wang, Xu-Jia 5 Bertrand, Jérôme 5 Bessi, Ugo 5 Bevan, Jonathan J. 5 Gentil, Ivan 5 Jimenez, Chloé 5 Kitagawa, Jun 5 Kolesnikov, Alexander V. 5 Marcellini, Paolo 5 Marigonda, Antonio 5 Matthes, Daniel 5 Nguyen, Truyen Van 5 Olbermann, Heiner 5 Pavon, Michele 5 Peletier, Mark Adriaan 5 Świȩch, Andrzej 4 Benamou, Jean-David 4 Blanchet, Adrien 4 Caffarelli, Luis Ángel 4 Cavalletti, Fabio 4 Crasta, Graziano 4 Croce, Gisella 4 Di Marino, Simone 4 Feng, Jin 4 Fragalà, Ilaria 4 Gigli, Nicola 4 Glimm, James G. 4 Gozlan, Nathael 4 Heinich, Henri 4 Henao, Duvan A. 4 Huesmann, Martin 4 Hynd, Ryan 4 Jacobs, Matthew 4 Kim, Hwa Kil 4 Kneuss, Olivier 4 Liu, Jiakun 4 Loeper, Grégoire 4 Manfredi, Juan J. 4 Mérigot, Quentin 4 Pedregal, Pablo 4 Pham, Huyên 4 Pisante, Giovanni 4 Puel, Marjolaine 4 Takatsu, Asuka 4 Wong, Mu Ming 4 Xia, Qinglan 4 Yan, Baisheng 4 Yin, Wotao 3 Averboukh, Yuriĭ Vladimirovich 3 Bonnet, Benoît 3 Brasco, Lorenzo 3 Buffoni, Boris 3 Cavagnari, Giulia 3 Chen, Gui-Qiang G. 3 Chow, Shui-Nee 3 Chow, Yat Tin ...and 888 more Authors all top 5 #### Cited in 198 Serials 58 Calculus of Variations and Partial Differential Equations 53 Archive for Rational Mechanics and Analysis 38 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 30 SIAM Journal on Mathematical Analysis 26 Journal of Mathematical Analysis and Applications 25 Journal of Differential Equations 25 Journal of Functional Analysis 24 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 20 Discrete and Continuous Dynamical Systems 18 Journal de Mathématiques Pures et Appliquées. Neuvième Série 15 Advances in Mathematics 14 Transactions of the American Mathematical Society 13 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 11 Journal of Optimization Theory and Applications 11 Communications in Partial Differential Equations 10 Communications in Mathematical Physics 10 Proceedings of the American Mathematical Society 10 Journal of Scientific Computing 10 Comptes Rendus. Mathématique. Académie des Sciences, Paris 9 SIAM Journal on Scientific Computing 9 Journal of Mathematical Sciences (New York) 8 Journal of Computational Physics 8 The Annals of Probability 8 SIAM Journal on Control and Optimization 8 Probability Theory and Related Fields 8 Advances in Calculus of Variations 7 Communications on Pure and Applied Mathematics 7 Journal of Statistical Physics 7 Applied Mathematics and Optimization 7 NoDEA. Nonlinear Differential Equations and Applications 6 Physica D 6 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 6 Stochastic Processes and their Applications 5 Journal of Mathematical Physics 5 SIAM Journal on Numerical Analysis 5 Acta Applicandae Mathematicae 5 European Journal of Applied Mathematics 5 Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni 5 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 5 Economic Theory 4 ZAMP. Zeitschrift für angewandte Mathematik und Physik 4 Applied Mathematics and Computation 4 Journal of Multivariate Analysis 4 Mathematische Zeitschrift 4 Journal of Global Optimization 4 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 4 Potential Analysis 4 Bulletin des Sciences Mathématiques 4 Journal of the European Mathematical Society (JEMS) 4 Discrete and Continuous Dynamical Systems. Series S 4 Kinetic and Related Models 3 Journal d’Analyse Mathématique 3 Mathematical Notes 3 Nonlinearity 3 Mathematics of Computation 3 Acta Mathematica 3 Annali di Matematica Pura ed Applicata. Serie Quarta 3 Duke Mathematical Journal 3 Journal of Computational and Applied Mathematics 3 Journal of Economic Theory 3 Manuscripta Mathematica 3 Mathematische Annalen 3 Memoirs of the American Mathematical Society 3 Quarterly of Applied Mathematics 3 Rendiconti del Seminario Matematico della Università di Padova 3 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 3 Journal of Elasticity 3 SIAM Journal on Applied Mathematics 3 SIAM Journal on Optimization 3 Journal of Mathematical Imaging and Vision 3 Journal of Nonlinear Science 3 Bernoulli 3 Revista Matemática Complutense 3 Communications in Contemporary Mathematics 3 Nonlinear Analysis. Real World Applications 3 Journal of Evolution Equations 3 Foundations of Computational Mathematics 3 Communications on Pure and Applied Analysis 3 Analysis and Applications (Singapore) 3 Boundary Value Problems 3 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 3 SIAM Journal on Imaging Sciences 3 Analysis & PDE 3 Bulletin of Mathematical Sciences 3 Information Geometry 2 Computer Methods in Applied Mechanics and Engineering 2 Inverse Problems 2 Israel Journal of Mathematics 2 Mathematical Methods in the Applied Sciences 2 Automatica 2 Inventiones Mathematicae 2 Journal of the Mathematical Society of Japan 2 Journal für die Reine und Angewandte Mathematik 2 Statistics & Probability Letters 2 Revista Matemática Iberoamericana 2 Applied Mathematics Letters 2 The Annals of Applied Probability 2 Computational Geometry 2 The Journal of Geometric Analysis 2 Geometric and Functional Analysis. GAFA ...and 98 more Serials all top 5 #### Cited in 48 Fields 418 Calculus of variations and optimal control; optimization (49-XX) 376 Partial differential equations (35-XX) 113 Probability theory and stochastic processes (60-XX) 85 Numerical analysis (65-XX) 70 Mechanics of deformable solids (74-XX) 69 Operations research, mathematical programming (90-XX) 62 Global analysis, analysis on manifolds (58-XX) 54 Differential geometry (53-XX) 54 Fluid mechanics (76-XX) 51 Real functions (26-XX) 50 Functional analysis (46-XX) 49 Measure and integration (28-XX) 48 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 44 Statistical mechanics, structure of matter (82-XX) 42 Dynamical systems and ergodic theory (37-XX) 41 Operator theory (47-XX) 34 Systems theory; control (93-XX) 22 Ordinary differential equations (34-XX) 19 Statistics (62-XX) 16 Computer science (68-XX) 16 Mechanics of particles and systems (70-XX) 16 Information and communication theory, circuits (94-XX) 15 Convex and discrete geometry (52-XX) 14 Functions of a complex variable (30-XX) 14 Biology and other natural sciences (92-XX) 13 Quantum theory (81-XX) 11 Geophysics (86-XX) 10 Classical thermodynamics, heat transfer (80-XX) 9 Combinatorics (05-XX) 9 Integral equations (45-XX) 7 General topology (54-XX) 7 Optics, electromagnetic theory (78-XX) 6 Several complex variables and analytic spaces (32-XX) 6 Difference and functional equations (39-XX) 4 Approximations and expansions (41-XX) 4 Manifolds and cell complexes (57-XX) 3 Linear and multilinear algebra; matrix theory (15-XX) 3 Topological groups, Lie groups (22-XX) 3 Abstract harmonic analysis (43-XX) 3 Geometry (51-XX) 3 Algebraic topology (55-XX) 2 General and overarching topics; collections (00-XX) 2 History and biography (01-XX) 2 Algebraic geometry (14-XX) 2 Potential theory (31-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Relativity and gravitational theory (83-XX) 1 Astronomy and astrophysics (85-XX) #### Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata.	2021-07-29T16:36:02	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.47716930508613586, "perplexity": 8155.961940196131}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046153860.57/warc/CC-MAIN-20210729140649-20210729170649-00659.warc.gz"}
https://www.gfdl.noaa.gov/blog_held/58-addicted-to-global-mean-temperature/	# 58. Addicted to global mean temperature Posted on March 31st, 2015 in Isaac Held's Blog Traditional “lapse rate feedback” in CMIP3 models, over the 21st century in the A1B scenario, plotted against the degree of polar amplification of surface warming in those models (tropical – 30S-30N divided by global mean warming). From Soden and Held 2006. “Everything should be made as simple as possible, but not simpler.” There is evidently no record of Einstein having actually used these words , and a quote of his that may be the source of this aphorism has a somewhat different resonance to my ear. In any case, I want to argue here that thinking about the global mean temperature in isolation or working with simple globally averaged box models that ignore the spatial structure of the response is very often “too simple”. I am reiterating some points made in earlier posts, especially #5, #7, and #44, but maybe it is useful to gather these together for emphasis. Consider two regions A and B which together cover the globe. Suppose that we have excellent observations of the mean temperature of A over time and relatively few of B. Let’s also consider the admittedly extreme case with negligible internal variability and CO2 the only external agent causing change. Now assume that some new observations of the evolution of temperatures in B are obtained, resulting in larger trends in B and therefore in the global mean as well. The result is an increase in the estimate of climate sensitivity (transient climate response to be precise) since this quantity is traditionally defined using the global mean temperature. Which is OK, but someone living in A might read of this upward revision of climate sensitivity and mistakenly conclude that the projected response to CO2 in A has increased. Of course, given this setup what the new observations are telling us is that the response to CO2 has a different pattern than what we had thought, not that the response to CO2 is everywhere larger than previously estimated. This scenario is meant to be reminiscent of some of the reaction to the recent work of Cowtan and Way 2014. Putting aside the question of the quantitative implications of that particular study for estimates of the transient climate response, I think this is an example of how the emphasis on the global mean in isolation can be misleading. Suppose more realistically that there is substantial internal variability, plus other forcing agents, as well as uncertainty in the pattern of the response to CO2 to deal with. Then it is possible that observations in B could modify estimates of the change in A attributable to CO2, depending on how the covariability in A and B intersects with what we know and don’t know about these various factors. The effect on the attributable A response might be positive or negative however. Or consider the connection between global mean surface temperatures and the Earth’s energy balance. This has become a hot topic, with a number of perspectives on this emerging, some of which I have talked about in previous posts In the simplest box model, perturbations to the global mean energy flux at the top of the atmosphere (TOA) — or what is essentially the same thing on the time scales of interest, perturbations to the heat uptake $H$ by the oceans — are assumed to be a simple function of the radiative forcing $F$ and perturbations in global mean surface temperature $T$, ie $H = F - \beta T$. But, among other issues, different spatial patterns of warming with the same global mean can produce different spatially integrated responses in the TOA energy flux. You might be able to get away with the simplest of models, dealing only with global means, when the spatial structure of the temperature response is self-similar: $\delta T \propto f(x,y) g(t)$. But you cannot expect it to be accurate in general. In models, the effective strength of the radiative restoring is stronger for perturbations in tropical temperatures than for perturbations in high latitude temperatures. In addition, temperature responses are less polar amplified in the initial as compared to the final stages of the approach to a new equilibrium with elevated CO2. So equilibrium climate sensitivity is increased beyond what you would expect from fitting heat uptake, forcing, and temperature responses during the initial stage — when the stronger radiative restoring at lower latitudes plays a bigger role. This is sometimes referred to as the difference between “effective climate sensitivity” and equilibrium climate sensitivity. But beyond this distinction in the global mean response, there is the tendency to miss the point that this enhanced climate sensitivity due to the structure of the slow response has larger consequences for polar than for equatorial regions. Trying to think about these issues while focusing on the global mean in isolation tempts people to think about nonlinearity to explain this behavior, whereas the explanation seems to be primarily that the spatial structure of the linear response is a function of frequency. As another example, one approach to thinking about the recent hiatus is to focus on the energy balance of the Earth, asking where the energy has gone. But suppose we are looking at some superposition of forced and internal variability (a safe assumption). Both affect the global mean surface temperature and both affect the global mean TOA energy balance (and heat uptake by the oceans), but not necessarily with the same restoring strength $\beta$. The forced response and internal variability can have very different spatial structures after all. You can’t go back and forth from global mean energy balance to global mean temperature that easily. Additionally, the hiatus is mostly reflecting temperature evolution in northern hemisphere winter, where there has been a cooling trend over the past one or two decades (Cohen et al 2012) The global and annual mean receives so much emphasis that the important constraint this seasonal and spatial structure imposes on explanations for the temperature evolution is often ignored. Take for instance the idea that an increase in heat uptake in the south Atlantic is important for closure of the energy budget in recent years (Chen and Tung 2014). Suppose you could rerun the climate over the past couple of decades and command the South Atlantic not to increase its heat uptake (this is what models are for) — how would surface temperatures respond? I could be wrong, but I suspect that most of the warming would be in the southern hemisphere, with much of the excess heat radiated away in the southern hemisphere as well, with minimal impact on temperatures in northern winter. If this is the way to close the Earth’s energy budget, it does not strike me as plausible that there is a tight connection to the recent hiatus. (I hasten to add that there are other reasons to want to close the Earth’s energy budget.) As another example, consider the accumulated emission perspective on long-term climate change after emissions cease, in which slow carbon uptake over centuries compensates approximately for the slow equilibration of the climate to the evolving CO2 levels. The southern ocean plays a leading role for both carbon and heat uptake. And from a global perspective these are competing to change the same global mean temperature. But CO2 is well mixed in the atmosphere on time scales longer than a year or two, so any uptake of carbon affects both hemispheres with roughly equal radiative forcing. But uptake of heat in the Southern Oceans affects the southern more strongly than the northern hemisphere. This distinction can get lost when discussing this accumulated emission perspective. Finally, I’ve included a figure illustrating the spread in the strength of the lapse rate feedback in GCMs at the top of this post. This term measures how much the global mean TOA flux is modified by the fact that temperature changes aloft are not the same as at the surface, holding water vapor and clouds fixed. It is negative in models because it is dominated by the tropics where temperature changes are larger aloft than at the surface. The resulting change in the TOA flux is normalized by the global mean surface temperature change because this is a term in a feedback analysis that focuses on explaining the value of $\beta$ in the simplest global mean energy balance model. One gets a big spread across models in the strength of this term, which can be (mis)interpreted as evidence that the models differ a lot in the physics determining the vertical structure of the response. But as the figure makes clear much of this spread is due to differences in the polar amplification of the surface warming — since most of this feedback is coming from the tropics it scales with the tropical, not the global mean, surface change. This is not to say that the remaining spread is not interesting, but the normalization by the global mean temperature change evidently disguises a major source of the difference across models. I make these points in large part as self-criticism. The simple global mean perspective is addictive and I am sure that I’ll succumb again sooner rather than later. [The views expressed on this blog are in no sense official positions of the Geophysical Fluid Dynamics Laboratory, the National Oceanic and Atmospheric Administration, or the Department of Commerce.] ## 4 thoughts on “58. Addicted to global mean temperature” 1. Chett Mitchell says: I appreciate your willingness to engage in self-criticism about focus on undue attention to global mean temperature. It is certainly true that many different patterns of local temperature could yield the same average, and that the differences between the northern and southern hemispheres get washed out in the averaging process. Nonetheless, there is a real need for some “master number” to use as a universally agreed standard of climate change. Body temperature is a good analogy. Though there are many physiological pathways to fever, the existence of a fever and its severity is a key sign that something isn’t right. No competent physician would focus only on fever, or completely ignore it. It matters, even if the underlying disease process matters more. Thank you for your blog. Though I don’t always understand it, I appreciate the effort to show what climate modelling looks like from the inside. 2. Consider two regions A and B which together cover the globe. Suppose that we have excellent observations of the mean temperature of A over time and relatively few of B. Something I have wanted to ask a modeller for some time. Let’s see A as the land and B as the ocean. The temperature trend over land is about twice as large as the trend over the ocean. In the models (CMIP ensemble) this ratio is about 1.6 (Sutton et al., 2007; Laine et al., 2009). Is this an indication that one of the observed trends is wrong or would it be easy to change a climate model to give another ratio? More related to the above post, could this have consequences for the climate sensitivity? 1. Isaac Held says: If there is a difference in the modeled and observed land/ocean warming ratio then it is interesting to ask how well the atmosphere/land component of these same models do in generating land temperature trends when forced with observed sea surface temperatures and the same external forcings as used in the coupled models. (See post #32 — where the land temperatures in the AMIP simulations over 1980-2008 from the CMIP5 models are compared to observations.) Seeing if these AMIP simulations correct any bias in the warming ratio would help in determining if the problem is in the forced response or if internal variability plays a role. 3. Paul S says: Victor, I think part of the issue is a domain difference between observations and models. The 1.6 figure comes from a comparison of landSAT/oceanSAT whereas our observations are LandSAT and SST. Using MPI-ESM-LR RCP8.5 experiments and instead comparing model LandSAT to SST trends over 1950-2014 I get ratios of 2.15, 1.96 and 2.2 from the three runs available. That’s comfortably compatible with long term modelled ratios. There is a case that slightly shorter trend ratios may be greater than typically modelled – 1979-2014 gives a ratio of about 2.4. The high SSTs of 2014 also make a big difference – 1979-2013 gives a ratio of about 2.6 (these come from comparison of BEST against ERSSTv4). Even over same length periods in models I think these high ratios are very unusual. Given the reasonable match over a longer term I would guess the higher ratio over 1979-2013 is a manifestation of internal variability with diverse regional effects which is perhaps not well-modelled	2021-05-13T07:22:03	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 14, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.662841260433197, "perplexity": 919.1723042165303}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243991537.32/warc/CC-MAIN-20210513045934-20210513075934-00213.warc.gz"}
https://math.libretexts.org/TextMaps/Number_Theory/Book%3A_Elementary_Number_Theory_(Raji)/5%3A_Primitive_Roots_and_Quadratic_Residues/5.6%3A_The_Law_of_Quadratic_Reciprocity	5.6: The Law of Quadratic Reciprocity $$\newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} }$$ $$\newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}}$$ Given that $$p$$ and $$q$$ are odd primes. Suppose we know whether $$q$$ is a quadratic residue of $$p$$ or not. The question that this section will answer is whether $$p$$ will be a quadratic residue of $$q$$ or not. Before we state the law of quadratic reciprocity, we will present a Lemma of Eisenstein which will be used in the proof of the law of reciprocity. The following lemma will relate Legendre symbol to the counting lattice points in the triangle. Lemma of Eisenstein If $$p\neq 2$$ is a prime and $$a$$ is an odd integer such that $$p\nmid a$$, then $\left(\frac{a}{p}\right)=(-1)^{\sum_{i=1}^{(p-1)/2}[ia/p]}.$ Consider the least positive residues of the integers $$a, 2a,...,((p-1)/2)a$$; let $$m_1,m_2,...,m_s$$ be integers of this set such that $$m_i>p/2$$ for all $$i$$ and let $$n_1,n_2,...,n_t$$ be those integers where $$n_i<p/2$$. Using the division algorithm, we see that $ia=p[ia/p]+r$ where $$r$$ is one of the $$m_i$$ or $$n_i$$. By adding the $$(p-1)/2$$ equations, we obtain $\label{qr1} \sum_{i=1}^{(p-1)/2}ia=\sum_{i=1}^{(p-1)/2}p[ia/p]+\sum_{i=1}^sm_i+\sum_{i=1}^tn_i.$ As in the proof of Gauss’s Lemma, we see that $p-m_1,p-m_2,...,p-m_s,p-n_1,p-n_2,...,p-n_t$ are precisely the integers $$1,2,...,(p-1)/2$$, in the same order. Now we obtain $\label{qr2} \sum_{i=1}^{(p-1)/2}i=\sum_{i=1}^s(p-m_i)+\sum_{i=1}^tn_i=ps-\sum_{i=1}^sm_i+\sum_{i=1}^tn_i.$ We subtract $$(\ref{qr2})$$ from $$(\ref{qr1})$$ to get $\sum_{i=1}^{(p-1)/2}ia-\sum_{i=1}^{(p-1)/2}i=\sum_{i=1}^{(p-1)/2}p[ia/p]-ps+2\sum_{i=1}^sm_i.$ Now since we are taking the following as exponents for $$-1$$, it suffice to look at them modulo 2. Thus $0\equiv \sum_{i=1}^{(p-1)/2}[ia/p]-s(mod \ 2).$ $\sum_{i=1}^{(p-1)/2}[ia/p]\equiv s(mod \ 2)$ Using Gauss’s lemma, we get $\left(\frac{a}{p}\right)=(-1)^s=(-1)^{\sum_{i=1}^{(p-1)/2}[ia/p]}.$ Let $$p$$ and $$q$$ be distinct odd primes. Then $\left(\frac{p}{q}\right)\left(\frac{q}{p}\right)=(-1)^{\frac{p-1}{2}.\frac{q-1}{2}}$ We consider now the pairs of integers also known as lattice points $$(x,y)$$ with $1\leq x\leq (p-1)/2 \mbox{and} \ \ 1\leq y\leq (q-1)/2.$ The number of such pairs is $$\frac{p-1}{2}.\frac{q-1}{2}$$. We divide these pairs into two groups depending on the sizes of $$qx$$ and $$py$$. Note that $$qx\neq py$$ for all pairs because $$p$$ and $$q$$ are distinct primes. We now count the pairs of integers $$(x,y)$$ with $1\leq x\leq (p-1)/2, \ \ 1\leq y\leq (q-1)/2 \mbox{and} \ \ qx>py.$ Note that these pairs are precisely those where $1\leq x\leq (p-1)/2 \mbox{and} \ \ 1\leq y\leq qx/p.$ For each fixed value of $$x$$ with $$1\leq x\leq (p-1)/2$$, there are $$[qx/p]$$ integers satisfying $$1\leq y\leq qx/p$$. Consequently, the total number of pairs with are $1\leq x\leq (p-1)/2, \ \ 1\leq y\leq qx/p, \mbox{and} \ \ qx>py$ is $\sum_{i=1}^{(p-1)/2}[qi/p].$ Consider now the pair of integers $$(x,y)$$ with $1\leq x\leq (p-1)/2, \ \ 1\leq y\leq (q-1)/2, \mbox{and} \ \ qx<py.$ Similarly, we find that the total number of such pairs of integers is $\sum_{i=1}^{(q-1)/2}[pi/q].$ Adding the numbers of pairs in these classes, we see that $\sum_{i=1}^{(p-1)/2}[qi/p]+ \sum_{i=1}^{(q-1)/2}[pi/q]=\frac{p-1}{2}.\frac{q-1}{2},$ and hence using Lemma 14, we get that $\left(\frac{p}{q}\right)\left(\frac{p}{q}\right)=(-1)^{\frac{p-1}{2}.\frac{q-1}{2}}$ Exercises 1. Evaluate $$\left(\frac{3}{53}\right)$$. 2. Evaluate $$\left(\frac{31}{641}\right)$$. 3. Using the law of quadratic reciprocity, show that if $$p$$ is an odd prime, then $\left(\frac{3}{p}\right)=\left\{\begin{array}{lcr} \ 1 &{\mbox{if}\ p\equiv \pm1(mod \ 12)} \\ \ -1 &{\mbox{if}\ p\equiv \pm 5(mod \ 12)}. \\ \end{array}\right .$ 4. Show that if $$p$$ is an odd prime, then $\left(\frac{-3}{p}\right)=\left\{\begin{array}{lcr} \ 1 &{\mbox{if}\ p\equiv 1(mod \ 6)} \\ \ -1 &{\mbox{if}\ p\equiv -1 (mod \ 6)}. \\ \end{array}\right .$ 5. Find a congruence describing all primes for which 5 is a quadratic residue. Contributors • Dr. Wissam Raji, Ph.D., of the American University in Beirut. His work was selected by the Saylor Foundation’s Open Textbook Challenge for public release under a Creative Commons Attribution (CC BY) license.	2018-06-22T03:33:34	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9036094546318054, "perplexity": 110.56096287570014}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-26/segments/1529267864343.37/warc/CC-MAIN-20180622030142-20180622050142-00271.warc.gz"}
https://www.usgs.gov/media/images/tassel-cap-planes-landsat-mss-and-tm-images	# Tassel Cap Planes for Landsat MSS and TM images ## Detailed Description The top row of this image shows the Tassel Cap (TC) planes for a Landat MSS image, while the bottom row are the TC planes for the coincident TM image. The distribution of pixel values between the images for each TC plane are very similar. The greatest deviation is for TC wetness, which is heavily weighted by short-wave infrared, which MSS data does not contain (is it modeled in the LLR process).	2021-06-21T13:11:47	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8067423701286316, "perplexity": 4262.06714936005}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623488273983.63/warc/CC-MAIN-20210621120456-20210621150456-00468.warc.gz"}
https://phys.libretexts.org/Bookshelves/College_Physics/Book%3A_College_Physics_(OpenStax)/03._Two-Dimensional_Kinematics/3.3%3A__Vector_Addition_and_Subtraction%3A_Analytical_Methods	$$\require{cancel}$$ # 3.3: Vector Addition and Subtraction: Analytical Methods Analytical methods of vector addition and subtraction employ geometry and simple trigonometry rather than the ruler and protractor of graphical methods. Part of the graphical technique is retained, because vectors are still represented by arrows for easy visualization. However, analytical methods are more concise, accurate, and precise than graphical methods, which are limited by the accuracy with which a drawing can be made. Analytical methods are limited only by the accuracy and precision with which physical quantities are known. # Resolving a Vector into Perpendicular Components Analytical techniques and right triangles go hand-in-hand in physics because (among other things) motions along perpendicular directions are independent. We very often need to separate a vector into perpendicular components. For example, given a vector like $$\displaystyle A$$ in Figure, we may wish to find which two perpendicular vectors, $$\displaystyle A_x$$ and $$\displaystyle A_y$$, add to produce it. Figure $$\PageIndex{1}$$:The vector $$\displaystyle A$$, with its tail at the origin of an x, y-coordinate system, is shown together with its x- and y-components, $$\displaystyle A_x$$ and $$\displaystyle A_y$$. These vectors form a right triangle. The analytical relationships among these vectors are summarized below. $$\displaystyle A_x$$ and $$\displaystyle A_y$$ are defined to be the components of $$\displaystyle A$$ along the x- and y-axes. The three vectors $$\displaystyle A, A_x$$, and $$\displaystyle A_y$$ form a right triangle: $$\displaystyle A_x + A_y = A.$$ Note that this relationship between vector components and the resultant vector holds only for vector quantities (which include both magnitude and direction). The relationship does not apply for the magnitudes alone. For example, if $$\displaystyle A_x=3 m$$ east, $$\displaystyle A_y=4 m$$ north, and $$\displaystyle A=5 m$$north-east, then it is true that the vectors $$\displaystyle A_x + A_y = A$$. However, it is not true that the sum of the magnitudes of the vectors is also equal. That is, $$\displaystyle 3 m+4 m ≠ 5 m$$ Thus, $$\displaystyle A_x+A_y≠A$$ If the vector $$\displaystyle A$$ is known, then its magnitude $$\displaystyle A$$ (its length) and its angle $$\displaystyle θ$$ (its direction) are known. To find $$\displaystyle A_x$$ and $$\displaystyle A_y$$, its x- and y-components, we use the following relationships for a right triangle. $$\displaystyle A_x=Acosθ$$ and $$\displaystyle A_y=Asinθ.$$ Figure $$\PageIndex{2}$$: The magnitudes of the vector components $$\displaystyle A_x$$ and $$\displaystyle A_y$$ can be related to the resultant vector $$\displaystyle A$$ and the angle $$\displaystyle θ$$ with trigonometric identities. Here we see that $$\displaystyle A_x=Acosθ$$ and $$\displaystyle A_y=Asinθ.$$ Suppose, for example, that A is the vector representing the total displacement of the person walking in a city considered in Kinematics in Two Dimensions: An Introduction and Vector Addition and Subtraction: Graphical Methods. Figure $$\PageIndex{3}$$: We can use the relationships $$\displaystyle A_x=Acosθ$$ and $$\displaystyle A_y=Asinθ$$ to determine the magnitude of the horizontal and vertical component vectors in this example. Then $$\displaystyle A=10.3$$ blocks and $$\displaystyle θ=29.1º$$ , so that $$\displaystyle A_x=A\cos θ=(10.3 blocks)(\cos 29.1º)=9.0$$ blocks $$\displaystyle A_y=A\sin θ=(10.3 blocks)(\sin 29.1º)=5.0$$ blocks. # Calculating a Resultant Vector If the perpendicular components $$\displaystyle A_x$$ and $$\displaystyle A_y$$ of a vector $$\displaystyle A$$ are known, then A can also be found analytically. To find the magnitude $$\displaystyle A$$ and direction $$\displaystyle θ$$ of a vector from its perpendicular components $$\displaystyle A_x$$ and $$\displaystyle A_y$$, we use the following relationships: $$\displaystyle A=\sqrt{A_{x^2}+A_{y^2}}$$ $$\displaystyle θ=tan^{−1}(A_y/A_x)$$. Figure $$\PageIndex{4}$$: The magnitude and direction of the resultant vector can be determined once the horizontal and vertical components $$\displaystyle A_x$$ and $$\displaystyle A_y$$ have been determined. Note that the equation $$\displaystyle A=\sqrt{A^2_x+A^2_y}$$ is just the Pythagorean theorem relating the legs of a right triangle to the length of the hypotenuse. For example, if $$\displaystyle A_x$$ and $$\displaystyle A_y$$ are 9 and 5 blocks, respectively, then $$\displaystyle A=\sqrt{9^2+5^2}=10.3$$ blocks, again consistent with the example of the person walking in a city. Finally, the direction is $$\displaystyle θ=tan^{–1}(5/9)=29.1º$$ , as before. DETERMINING VECTORS AND VECTOR COMPONENTS WITH ANALYTICAL METHODS Equations $$\displaystyle A_x=Acosθ$$ and $$\displaystyle A_y=Asinθ$$ are used to find the perpendicular components of a vector—that is, to go from $$\displaystyle A$$ and $$\displaystyle θ$$ to $$\displaystyle A_x$$ and $$\displaystyle A_y$$. Equations $$\displaystyle A=\sqrt{A^2_x+A^2_y}$$ and $$\displaystyle θ=tan^{–1}(A_y/A_x)$$ are used to find a vector from its perpendicular components—that is, to go from $$\displaystyle A_x$$ and $$\displaystyle A_y$$ to $$\displaystyle A$$ and $$\displaystyle θ$$. Both processes are crucial to analytical methods of vector addition and subtraction. # Adding Vectors Using Analytical Methods To see how to add vectors using perpendicular components, consider Figure, in which the vectors $$\displaystyle A$$ and $$\displaystyle B$$ are added to produce the resultant $$\displaystyle R$$. Figure $$\PageIndex{5}$$: Vectors $$\displaystyle A$$ and$$\displaystyle B$$ are two legs of a walk, and $$\displaystyle R$$ is the resultant or total displacement. You can use analytical methods to determine the magnitude and direction of $$\displaystyle R$$. If $$\displaystyle A$$ and $$\displaystyle B$$ represent two legs of a walk (two displacements), then $$\displaystyle R$$ is the total displacement. The person taking the walk ends up at the tip of R. There are many ways to arrive at the same point. In particular, the person could have walked first in the x-direction and then in the y-direction. Those paths are the x- and y-components of the resultant, $$\displaystyle R_x$$ and $$\displaystyle R_y$$. If we know $$\displaystyle R_x$$ and $$\displaystyle R_y$$, we can find $$\displaystyle R$$ and $$\displaystyle θ$$ using the equations $$\displaystyle A=\sqrt{A_x^2+A_y^2}$$ and $$\displaystyle θ=tan^{–1}(A_y/A_x)$$. When you use the analytical method of vector addition, you can determine the components or the magnitude and direction of a vector. Step 1. Identify the x- and y-axes that will be used in the problem. Then, find the components of each vector to be added along the chosen perpendicular axes. Use the equations $$\displaystyle A_x=Acosθ$$ and $$\displaystyle A_y=Asinθ$$ to find the components. In Figure, these components are $$\displaystyle A_x, A_y, B_x$$, and $$\displaystyle B_y$$. The angles that vectors $$\displaystyle A$$ and $$\displaystyle B$$ make with the x-axis are $$\displaystyle θ_A$$ and $$\displaystyle θ_B$$, respectively. Figure $$\PageIndex{6}$$: To add vectors $$\displaystyle A$$ and $$\displaystyle B$$, first determine the horizontal and vertical components of each vector. These are the dotted vectors $$\displaystyle A_x, A_y, B_x$$ and $$\displaystyle B-y$$ shown in the image. Step 2. Find the components of the resultant along each axis by adding the components of the individual vectors along that axis. That is, as shown in Figure, $$\displaystyle R_x=A_x+B_x$$ and $$\displaystyle R_y=A_y+B_y.$$ Figure $$\PageIndex{7}$$: The magnitude of the vectors $$\displaystyle A_x$$ and $$\displaystyle B_x$$ add to give the magnitude $$\displaystyle R_x$$ of the resultant vector in the horizontal direction. Similarly, the magnitudes of the vectors $$\displaystyle A_y$$ and $$\displaystyle B_y$$ add to give the magnitude $$\displaystyle R_y$$ of the resultant vector in the vertical direction. Components along the same axis, say the x-axis, are vectors along the same line and, thus, can be added to one another like ordinary numbers. The same is true for components along the y-axis. (For example, a 9-block eastward walk could be taken in two legs, the first 3 blocks east and the second 6 blocks east, for a total of 9, because they are along the same direction.) So resolving vectors into components along common axes makes it easier to add them. Now that the components of R are known, its magnitude and direction can be found. Step 3. To get the magnitude $$\displaystyle R$$ of the resultant, use the Pythagorean theorem: $$\displaystyle R=\sqrt{R^2_x+R^2_y}$$. Step 4. To get the direction of the resultant: $$\displaystyle θ=tan^{−1}(R_y/R_x)$$. The following example illustrates this technique for adding vectors using perpendicular components. Example $$\displaystyle \PageIndex{1}$$: Adding Vectors Using Analytical Methods Add the vector $$\displaystyle A$$ to the vector $$\displaystyle B$$ shown in Figure, using perpendicular components along the x- and y-axes. The x- and y-axes are along the east–west and north–south directions, respectively. Vector $$\displaystyle A$$ represents the first leg of a walk in which a person walks $$\displaystyle 53.0 m$$ in a direction $$\displaystyle 20.0º$$ north of east. Vector $$\displaystyle B$$ represents the second leg, a displacement of $$\displaystyle 34.0 m$$ in a direction $$\displaystyle 63.0º$$ north of east. Figure $$\PageIndex{8}$$: Vector $$\displaystyle A$$ has magnitude $$\displaystyle 53.0 m$$ and direction $$\displaystyle 20.0º$$ north of the x-axis. Vector B has magnitude $$\displaystyle 34.0 m$$ and direction $$\displaystyle 63.0º$$ north of the x-axis. You can use analytical methods to determine the magnitude and direction of $$\displaystyle R$$. Strategy The components of $$\displaystyle A$$ and $$\displaystyle B$$ along the x- and y-axes represent walking due east and due north to get to the same ending point. Once found, they are combined to produce the resultant. Solution Following the method outlined above, we first find the components of $$\displaystyle A$$ and $$\displaystyle B$$ along the x- and y-axes. Note that $$\displaystyle A=53.0 m, θ_A=20.0º, B=34.0 m,$$ and $$\displaystyle θ_B=63.0º$$. We find the x-components by using $$\displaystyle A_x=Acosθ$$, which gives $$\displaystyle A_x=Acosθ_A=(53.0 m)(cos 20.0º)(53.0 m)(0.940)=49.8 m$$ and $$\displaystyle B_x=Bcosθ_B=(34.0 m)(cos 63.0º)(34.0 m)(0.454)=15.4 m.$$ Similarly, the y-components are found using $$\displaystyle A_y=Asinθ_A$$: $$\displaystyle A_y=Asinθ_A=(53.0 m)(sin 20.0º)(53.0 m)(0.342)=18.1 m$$ and $$\displaystyle B_y=Bsinθ_B=(34.0 m)(sin 63.0º)(34.0 m)(0.891)=30.3 m.$$ The x- and y-components of the resultant are thus $$\displaystyle R_x=A_x+B_x=49.8 m+15.4 m=65.2 m$$ and $$\displaystyle R_y=A_y+B_y=18.1 m+30.3 m=48.4 m.$$ Now we can find the magnitude of the resultant by using the Pythagorean theorem: $$\displaystyle R=\sqrt{R^2_x+R^2_y}=\sqrt{(65.2)^2+(48.4)^2m}$$ so that $$\displaystyle R=81.2 m.$$ Finally, we find the direction of the resultant: $$\displaystyle θ=tan^{−1}(R_y/R_x)=+tan^{−1}(48.4/65.2).$$ Thus, $$\displaystyle θ=tan^{−1}(0.742)=36.6º.$$ Figure $$\PageIndex{9}$$: Using analytical methods, we see that the magnitude of $$\displaystyle R$$ is $$\displaystyle 81.2 m$$ and its direction is $$\displaystyle 36.6º$$ north of east. Discussion This example illustrates the addition of vectors using perpendicular components. Vector subtraction using perpendicular components is very similar—it is just the addition of a negative vector. Subtraction of vectors is accomplished by the addition of a negative vector. That is, $$\displaystyle A−B≡A+(–B)$$. Thus, the method for the subtraction of vectors using perpendicular components is identical to that for addition. The components of $$\displaystyle –B$$ are the negatives of the components of $$\displaystyle B$$. The x- and y-components of the resultant $$\displaystyle A−B = R$$ are thus $$\displaystyle R_x=A_x+(–B_x)$$ and $$\displaystyle R_y=A_y+(–B_y)$$ and the rest of the method outlined above is identical to that for addition. (See Figure.) Analyzing vectors using perpendicular components is very useful in many areas of physics, because perpendicular quantities are often independent of one another. The next module, Projectile Motion, is one of many in which using perpendicular components helps make the picture clear and simplifies the physics. Figure $$\PageIndex{10}$$:The subtraction of the two vectors shown in Figure. The components of $$\displaystyle –B$$ are the negatives of the components of $$\displaystyle B$$. The method of subtraction is the same as that for addition. Learn how to add vectors. Drag vectors onto a graph, change their length and angle, and sum them together. The magnitude, angle, and components of each vector can be displayed in several formats. Figure $$\PageIndex{11}$$: Vector Addition # Summary • The analytical method of vector addition and subtraction involves using the Pythagorean theorem and trigonometric identities to determine the magnitude and direction of a resultant vector. • The steps to add vectors $$\displaystyle A$$ and $$\displaystyle B$$ using the analytical method are as follows: Step 1: Determine the coordinate system for the vectors. Then, determine the horizontal and vertical components of each vector using the equations $$\displaystyle A_x=Acosθ$$ $$\displaystyle B_x=Bcosθ$$ and $$\displaystyle A_y=Asinθ$$ $$\displaystyle B_y=Bsinθ.$$ Step 2: Add the horizontal and vertical components of each vector to determine the components Rx and Ry of the resultant vector, R: $$\displaystyle R_x=A_x+B_x$$ and $$\displaystyle R_y=A_y+B_y$$. Step 3: Use the Pythagorean theorem to determine the magnitude, R, of the resultant vector R: $$\displaystyle R=\sqrt{R^2_x+R^2_y}$$. Step 4: Use a trigonometric identity to determine the direction, $$\displaystyle θ$$, of R: $$\displaystyle θ=tan^{−1}(R_y/R_x)$$. # Glossary analytical method the method of determining the magnitude and direction of a resultant vector using the Pythagorean theorem and trigonometric identities ### Contributors • Paul Peter Urone (Professor Emeritus at California State University, Sacramento) and Roger Hinrichs (State University of New York, College at Oswego) with Contributing Authors: Kim Dirks (University of Auckland) and Manjula Sharma (University of Sydney). This work is licensed by OpenStax University Physics under a Creative Commons Attribution License (by 4.0).	2019-10-21T00:32:46	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6880160570144653, "perplexity": 236.91230906291145}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570987750110.78/warc/CC-MAIN-20191020233245-20191021020745-00191.warc.gz"}
https://www.federalreserve.gov/econres/notes/feds-notes/historical-proxies-for-the-secured-overnight-financing-rate-20190715.htm	July 15, 2019 ### Historical Proxies for the Secured Overnight Financing Rate David Bowman This note was revised on September 16, 2019 to add the note below Table 1. The Federal Reserve Board and Federal Reserve Bank of New York (FRBNY) convened the Alternative Reference Rates Committee (ARRC) to recommend an alternative rate to U.S. dollar LIBOR and to develop plans to promote its use. In June 2017, as part of this mandate, the ARRC selected the Secured Overnight Financing Rate (SOFR) as its recommended alternative. In this note, I describe the available history of SOFR data and argue that other historical data published by FRBNY can act as a reasonable proxy for SOFR going back to 1998. SOFR is the broadest available measure of rates in the overnight repurchase agreement (repo) market in which Treasury securities are posted as collateral. It includes transactions in the tri-party repo market from Bank of New York Mellon, General Collateral Finance Repo Service (GCF Repo®) transactions, and bilaterally settled transactions cleared by the Fixed Income Clearing Corporation (FICC).1 FRBNY, in cooperation with the Office of Financial Research, began publishing SOFR on April 3, 2018.2 Prior to the start of official publication, FRBNY also released data from August 2014 to March 2018 representing modeled, pre-production estimates of SOFR that are based on the same basic underlying transaction data and methodology that now underlie the official publication. While the data required to calculate SOFR do not exist prior to August 2014, FRBNY has also separately released a much longer historical data series based on primary dealers' overnight Treasury repo borrowing activity. Since the late 1990s, the Open Market Trading Desk at FRBNY has conducted a survey of primary dealers each morning covering their borrowing activity that day in the Treasury general collateral (GC) repo market. Using this survey, FRBNY released a time series, going back to February 1998, of the volume-weighted mean rate of the primary dealers' overnight Treasury GC repo borrowing activity. It is important to note that there are a number of technical differences between SOFR and the primary dealer survey rate (survey rate). The survey rate is calculated as a volume-weighted mean whereas as SOFR is calculated as a volume-weighted median. In addition, the transactions underlying the survey rate are not as broad as those underlying SOFR, as the survey collects only the GC segments of the repo market and does not capture borrowing activity conducted by non-primary dealer market participants. Nonetheless, despite these differences, this note argues that the historical survey data is an adequate proxy for SOFR for risk modelling or other purposes. In order to understand why this could be the case, it is useful to first cover some details about the structure of Treasury repo markets. The tri-party repo market is based on clearing and settlement infrastructure provided by the Bank of New York Mellon.3 Tri-party transactions are secured by GC pools of accepted Treasury securities, any of which can be delivered as collateral by the cash borrower. Repo transactions facilitated by the tri-party infrastructure fall into two segments: Tri-party ex-GCF transactions, which are tri-party transactions not cleared through FICC, and GCF transactions, which are cleared through FICC's GCF repo service. The tri-party ex-GCF segment predominantly involves institutional investors--such as money market funds--lending cash to broker-dealers. The GCF segment is largely an inter-dealer market where cash raised from institutional investors is reallocated among broker-dealers. Unlike GC repo, bilateral repo trades can designate specific securities as collateral.4 The majority of netting members in the FICC-cleared bilateral market are broker-dealers, so, like the GCF segment of tri-party repo, the FICC-cleared bilateral market mostly consists of trades among dealers, as opposed to trades between dealers and their clients. Bowman et al. (2017) show that, apart from the lower tail of bilateral trades that are omitted from SOFR, bilateral repo transactions are generally distributed fairly similarly to GCF transactions, as both are essentially inter-dealer markets.5 Many dealers may move with some fluidity between the two market segments depending on relative transactions costs--for example, activity moved from the GCF to the bilateral portion of the market as JPMorgan prepared to exit its government securities settlement services. Over the past several years, inter-dealer transactions have tended to be at higher rates, associated with the higher balance sheet cost of repo transactions following post-crisis reforms. Thus, as shown in Figure 1, DTCC's GCF rate (which is based on inter-dealer GCF transactions) or a similar series produced by ICAP (based on brokered repo transactions and quantitatively very similar to the GCF rate) are generally higher than available measures of tri-party ex GCF rates (the Tri-party General Collateral rate produced by FRBNY or a separately produced tri-party rate published by Bank of New York Mellon (BNYM), the BNY Mellon Treasury Tri-Party Repo Index).6 7 Because SOFR is not purely an inter-dealer rate but does include a sizeable proportion of inter-dealer trades, it has tended to be higher than either of the tri-party ex GCF rates but below the GCF and ICAP rates. The historical primary dealer survey rate that FRBNY has released includes both dealer-to-customer and inter-dealer tri-party trades reported by primary dealers, and so likewise tends to lie between the tri-party ex GCF rates and the GCF and ICAP rates. Because SOFR includes both GCF and bilateral trades, it has a higher proportion of interdealer trades and tends to trade close to or a bit above the survey rate. However, as can also be seen, the differences between all of these rates were smaller prior to 2015. Interdealer spreads widened as post-crisis regulations were implemented and became binding, but prior to that time, those spreads were narrower. Figure 2 plots the spread between the GCF and BNYM repo series going back to 2012 (the starting point of the BNYM series), and shows that spreads were clearly lower prior to 2015. Similarly the spread between the GCF rate and the survey rate was notably lower before 2015 as well (Table 1). If we go back before 2009 using the ICAP brokered rate rather than the GCF rate, the spread was lower still, averaging only 2 basis points. #### Table 1: Average Differences between Repo Rates (Basis Points) GCF - BNYM Spread GCF - P.D. Survey Spread ICAP - P.D. Survey Spread 12 8 9 4 3 3 --- 2 2 2 Note: Primary Dealer Survey data is only available through February 2018. The historical behavior of the spread between inter-dealer and more general repo rates matters because it appears to be a main determinant (or at least highly correlated with the determinants) of the difference between SOFR and the survey rate. In fact, SOFR can be very closely modeled by the following simple regression $$SOFR = {Survey\ Rate} + .38*(GCF - {Survey\ Rate} - .05)$$ Despite its simplicity, this regression has an R2 of 99.8 percent (Figure 3). Using this regression, one can model a fitted SOFR for the longer history, which is shown in Figure 4. With smaller differences between interdealer rates and dealer-to-customer rates prior to 2015, the repo market was more homogeneous, and SOFR was quite close to the survey rate. The fitted SOFR is in fact extraordinarily close to the survey rate, which argues that the survey rate should be considered as a reasonable proxy for a longer history of SOFR. There is no way to know for sure how SOFR would have behaved historically, but it appears that the survey is likely to be fairly close given the greater homogeneity of repo markets before 2015. It should certainly be close enough to be a reasonable proxy for risk modeling or other purposes, especially given that historical data always has limitations for forward-looking modeling--even if we had a longer series for SOFR itself, there would be no guarantee that SOFR would behave in exactly the same way going forward as it has in the past. Using this longer historical series, we can gain a greater understanding as to how a rate like SOFR should be expected to behave. As shown in Figure 5, a compound average of the SOFR/P.D. Survey rate has tended to be very close to a compound average of the effective federal funds rate (EFFR), the rate that the Federal Reserve bases its policy target on. Thus, despite the fact that it is a secured rate and has some day-to-day fluctuations, SOFR should be expected to move very closely with Federal Reserve policy and very closely with overnight unsecured rates like EFFR over time. Similarly, the indicative forward-looking term SOFR rates produced by Heitfield and Park (2019) are very close to EFFR OIS rates (Figure 6).8 Over the period shown, SOFR term rate was 3.2 basis points above the EFFR OIS rate, which is very close to the 2.8 basis point difference between compound SOFR and compound EFFR during the same time. Thus, based on the historical data, it seems reasonable to model SOFR OIS rates as likely to be very close to EFFR OIS rates. #### Figure 6: Comparing an Indicative SOFR Term Rate to EFFR OIS 1. SOFR and other repo reference rates published by FRBNY exclude repo transactions with the Federal Reserve. Additional information on SOFR can be found at www.newyorkfed.org/markets/treasury-repo-reference-rates-information Return to text 2. FRBNY also began publication of two other repo reference rates at this time: the Broad General Collateral Rate (BGCR) is based on transactions in the tri-party repo market from Bank of New York Mellon, including GCF Repo transactions, while the Tri-party General Collateral Rate (TGCR) excludes GCF repo transactions. Both rates exclude bilateral repo transactions. Return to text 3. JPMorgan Chase had previously offered similar infrastructure but announced on July 21, 2016 that it would end its business as a clearing bank for broker-dealer government security services by the end of 2018. Return to text 4. If particular securities are in high demand in the bilateral repo market, then they may trade "special" with much lower rates than other Treasury repo transactions. FRBNY deals with this by filtering the lower quartile of all bilateral trades in its calculation of SOFR. Return to text 5. Further information can be found in see Bowman, Louria, McCormick, and Styczynski (2017), The Cleared Bilateral Repo Market and Proposed Repo Benchmark Rates, February 27, 2017. Return to text 6. Neither DTCC Solutions LLC nor any of its affiliates shall be responsible for any errors or omissions in any DTCC data included in this publication, regardless of the cause and, in no event, shall DTCC or any of its affiliates be liable for any direct, indirect, special or consequential damages, costs, expenses, legal fees, or losses (including lost income or lost profit, trading loses and opportunity costs) in connection with this publication. Return to text 7. BNY Mellon Tri-Party Repo Indices, the data contained therein and any related trademarks and service marks are the sole and exclusive property of The Bank of New York Mellon (the "Company") and its suppliers. The information and data appearing on this site regarding BNY Mellon Tri-Party Repo Indices is for internal use only by the recipient, and may not be modified, copied, redistributed, retransmitted, reproduced, published, or otherwise used in whole or in part for any purpose without the Company's prior written consent. THE COMPANY AND ITS AFFILIATES MAKE NO EXPRESS OR IMPLIED WARRANTIES, AND EXPRESSLY DISCLAIM, ALL WARRANTIES OF ACCURACY, TIMELINESS, COMPLETENESS, NON-INFRINGEMENT MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE OR USE WITH RESPECT TO THE BNY MELLON TRI-PARTY REPO INDICES AND ANY INFORMATION, DATA OR MATERIALS INCLUDED THEREIN OR FOR ANY DELAYS OR INTERRUPTIONS IN PROVIDING THE BNY MELLON TRI-PARTY REPO INDICES OR ANY DATA INCLUDED THEREIN. WITHOUT LIMITING ANY OF THE FOREGOING, IN NO EVENT SHALL THE COMPANY OR ANY OF ITS AFFILIATES HAVE ANY LIABILITY FOR DIRECT, INDIRECT, SPECIAL, PUNITIVE, OR CONSEQUENTIAL DAMAGES (INCLUDING LOST PROFITS), EVEN IF NOTIFIED OF THE POSSIBILITY OF SUCH DAMAGES AND REGARDLESS OF THE FORM OF ACTION. The information appearing on this site is presented as general information and not in connection with any sale or offer to sell, or solicitation of an offer to buy, securities or other financial instruments. Any decisions regarding any use of the information included in this site, including but not limited to any transaction or trading decisions based on such information, are the sole and exclusive responsibility of the recipient and the Company shall incur no liability whatsoever in connection therewith. Neither the Company nor any of its subsidiaries or affiliates is acting as an advisor or fiduciary by providing information contained in this site. Return to text 8. Heitfield and Park (2019) Indicative Forward-Looking SOFR Term Rates April 19, 2019. Return to text	2022-07-01T03:10:29	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2188996970653534, "perplexity": 4665.111682746857}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656103917192.48/warc/CC-MAIN-20220701004112-20220701034112-00344.warc.gz"}
https://malegislature.gov/Bills/BillHtml/133874?generalCourtId=11	HOUSE . . . . . . . . . . . . . . . No. 4143 The Commonwealth of Massachusetts House of Representatives, June 04, 2014. Ordered, That the committee on State Administration and Regulatory Oversight be authorized to sit during a recess of the General Court to make an investigation and study of Senate documents numbered 1459, 1461, 1462, 1467, 1468, 1482, 1483, 1486, 1487, 1489, 1490, 1491, 1493, 1496, 1497, 1500, 1501, 1503, 1504, 1505, 1506, 1509, 1510, 1512, 1513, 1515, 1516, 1518, 1524, 1525, 1528, 1529, 1530, 1534, 1536, 1537, 1538, 1539, 1540, 1541, 1542, 1543, 1544, 1545, 1546, 1547, 1548, 1549, 1550, 1551, 1552, 1553, 1554, 1555, 1556, 1558, 1559, and 1562 and House documents numbered 4, 769, 770, 771, 2772, 2773, 2776, 2777, 2780, 2782, 2785, 2786, 2788, 2789, 2790, 2791, 2795, 2796, 2798, 2799, 2801, 2802, 2803, 2809, 2810, 2811, 2815, 2817, 2818, 2820, 2821, 2823, 2824, 2825, 2826, 2827, 2828, 2829, 2833, 2840, 2848, 2849, 2850, 2851, 2852, 2854, 2855, 2860, 2866, 2867, 2872, 2873, 2875, 2885, 2887, 2888, 2893, 2894, 2896, 2897, 2900, 2903, 2906, 2907, 2908, 2909, 3322, 3365, 3366, 3404, 3405, 3435, 3497, and 3597, relative to State Administration. Said committee shall report to the General Court the results of its investigation and study and its recommendations, if any, together with drafts of legislation necessary to carry such recommendations into effect, by filing the same with the Clerk of the House of Representatives on or before December 31, 2014. The information contained in this website is for general information purposes only. The General Court provides this information as a public service and while we endeavor to keep the data accurate and current to the best of our ability, we make no representations or warranties of any kind, express or implied, about the completeness, accuracy, reliability, suitability or availability with respect to the website or the information contained on the website for any purpose. Any reliance you place on such information is therefore strictly at your own risk.	2016-06-26T19:50:40	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8046348094940186, "perplexity": 171.44464947006225}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-26/segments/1466783395548.53/warc/CC-MAIN-20160624154955-00052-ip-10-164-35-72.ec2.internal.warc.gz"}
http://www.itl.nist.gov/div898/handbook/pri/section5/pri544.htm	5. Process Improvement 5.5.4. What is a mixture design? Constrained mixture designs Upper and/or lower bound constraints may be present In mixture designs when there are constraints on the component proportions, these are often upper and/or lower bound constraints of the form LixiUi, i = 1, 2,..., q, where Li is the lower bound for the i-th component and Ui the upper bound for the i-th component. The general form of the constrained mixture problem is x1 + x2 + ... + xq = 1 Li xi Ui, for i = 1, 2,..., q with Li ≥ 0 and Ui ≤ 1. Example using only lower bounds Consider the following case in which only the lower bounds in the above equation are imposed, so that the constrained mixture problem becomes x1 + x2 + ... + xq = 1 Lixi ≤ 1, for i = 1, 2,..., q Assume we have a three-component mixture problem with constraints 0.3 ≤ x1 0.4 ≤ x2 0.1 ≤ x3 Feasible mixture region The feasible mixture space is shown in the figure below. Note that the existence of lower bounds does not affect the shape of the mixture region, it is still a simplex region. In general, this will always be the case if only lower bounds are imposed on any of the component proportions. Diagram showing the feasible mixture space FIGURE 5.12: The Feasible Mixture Space (Shaded Region) for Three Components with Lower Bounds A simple transformation helps in design construction and analysis Since the new region of the experiment is still a simplex, it is possible to define a new set of components that take on the values from 0 to 1 over the feasible region. This will make the design construction and the model fitting easier over the constrained region of interest. These new components ( $$x_{i}^{\star}$$ ) are called pseudo components and are defined using the following formula Formula for pseudo components $x_{i}^{\star} = \frac{x_{i} - L_{i}} {1 - L}$ with $L = \sum_{i=1}^{q}{L_{i}} < 1$ denoting the sum of all the lower bounds. Computation of the pseudo components for the example In the three component example above, the pseudo components are $$x_{1}^{\star} = \frac{x_{1} - 0.3}{0.2} \hspace{.3in} x_{2}^{\star} = \frac{x_{2} - 0.4}{0.2} \hspace{.3in} x_{3}^{\star} = \frac{x_{3} - 0.1}{0.2} \hspace{.3in}$$ Constructing the design in the pseudo components Constructing a design in the pseudo components is accomplished by specifying the design points in terms of the and then converting them to the original component settings using xi = Li + (1 - L)$$x_{i}^{\star}$$ Select appropriate design In terms of the pseudo components, the experimenter has the choice of selecting a Simplex-Lattice or a Simplex-Centroid design, depending on the objectives of the experiment. Simplex-centroid design example (after transformation) Suppose, we decided to use a Simplex-centroid design for the three-component experiment. The table below shows the design points in the pseudo components, along with the corresponding setting for the original components. Table showing the design points in both the pseudo components and the original components TABLE 5.5: Pseudo Component Settings and Original Component Settings, Three-Component Simplex-Centroid Design Pseudo Components Original Components X1 X2 X3 $$x_{1}^{\star}$$ $$x_{2}^{\star}$$ $$x_{3}^{\star}$$ 1 0 0 0.5 0.4 0.1 0 1 0 0.3 0.6 0.1 0 0 1 0.3 0.4 0.3 0.5 0.5 0 0.4 0.5 0.1 0.5 0 0.5 0.4 0.4 0.2 0 0.5 0.5 0.3 0.5 0.2 0.3333 0.3333 0.3333 0.3667 0.4667 0.1666 Use of pseudo components (after transformation) is recommended It is recommended that the pseudo components be used to fit the mixture model. This is due to the fact that the constrained design space will usually have relatively high levels of multicollinearity among the predictors. Once the final predictive model for the pseudo components has been determined, the equation in terms of the original components can be determined by substituting the relationship between xi and $$x_{i}^{\star}$$. D-optimal designs can also be used Computer-aided designs (D-optimal, for example) can be used to select points for a mixture design in a constrained region. See Myers and Montgomery (1995) for more details on using D-optimal designs in mixture experiments. Extreme vertice designs are another option Note: There are other mixture designs that cover only a sub-portion or smaller space within the simplex. These types of mixture designs (not covered here) are referred to as extreme vertices designs. (See chapter 11 of Myers and Montgomery (1995) or Cornell (1990).	2017-10-21T22:59:38	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6533596515655518, "perplexity": 956.8356722531787}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-43/segments/1508187824899.75/warc/CC-MAIN-20171021224608-20171022004608-00636.warc.gz"}
http://pdglive.lbl.gov/DataBlock.action?node=S022ACP&home=BXXX030	# ${{\boldsymbol \Xi}^{-}}$ DECAY PARAMETERS See the Note on Baryon Decay Parameters'' in the neutron Listings. # ${[\alpha\mathrm {({{\boldsymbol \Xi}^{-}})}\alpha_-({{\boldsymbol \Lambda}}) − \alpha\mathrm {({{\overline{\boldsymbol \Xi}}^{+}})}\alpha_+({{\overline{\boldsymbol \Lambda}}})]\over [\alpha\mathrm {({{\boldsymbol \Xi}^{-}})}\alpha_-({{\boldsymbol \Lambda}}) + \alpha\mathrm {({{\overline{\boldsymbol \Xi}}^{+}})}\alpha_+({{\overline{\boldsymbol \Lambda}}})]}$ INSPIRE search This is zero if $\mathit CP$ is conserved. The $\alpha$'s are the decay-asymmetry parameters for ${{\mathit \Xi}^{-}}$ $\rightarrow$ ${{\mathit \Lambda}}{{\mathit \pi}^{-}}$ and ${{\mathit \Lambda}}$ $\rightarrow$ ${{\mathit p}}{{\mathit \pi}^{-}}$ and for ${{\overline{\mathit \Xi}}^{+}}$ $\rightarrow$ ${{\overline{\mathit \Lambda}}}{{\mathit \pi}^{+}}$ and ${{\overline{\mathit \Lambda}}}$ $\rightarrow$ ${{\overline{\mathit p}}}{{\mathit \pi}^{+}}$ . VALUE ($10^{-4}$) EVTS DOCUMENT ID TECN COMMENT $0.0$ $\pm5.1$ $\pm4.4$ 158M 2004 HYCP ${{\mathit p}}$ Cu, 800 GeV • • • We do not use the following data for averages, fits, limits, etc. • • • $+120$ $\pm140$ 252k 2000 E756 ${{\mathit p}}$ Be, 800 GeV Conservation Laws: $\mathit CP$ INVARIANCE References: HOLMSTROM 2004 PRL 93 262001 Search for $\mathit CP$ Violation in Charged-${{\mathit \Xi}}$ and ${{\mathit \Lambda}}$ Hyperon Decays LUK 2000 PRL 85 4860 Search for Direct $\mathit CP$ Violation in Nonleptonic Decays of Charged ${{\mathit \Xi}}$ and ${{\mathit \Lambda}}$ Hyperons	2019-12-09T05:18:57	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.944989025592804, "perplexity": 5732.203961458543}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-51/segments/1575540517557.43/warc/CC-MAIN-20191209041847-20191209065847-00244.warc.gz"}
https://zbmath.org/authors/?q=ai%3Agrubb.gerd	## Grubb, Gerd Compute Distance To: Author ID: grubb.gerd Published as: Grubb, Gerd; Grubb, G. External Links: MGP · Wikidata · IdRef Documents Indexed: 117 Publications since 1968, including 3 Books 1 Contribution as Editor Co-Authors: 25 Co-Authors with 26 Joint Publications 777 Co-Co-Authors all top 5 ### Co-Authors 91 single-authored 7 Solonnikov, Vsevolod Alekseevich 3 Geymonat, Giuseppe 3 Seeley, Robert Thomas 2 Kokholm, Niels Jørgen 2 Schrohe, Elmar 2 Wood, Ian Geoffrey 1 Abels, Helmut 1 Atiyah, Michael Francis 1 Behrndt, Jussi 1 Boman, Jan 1 Bony, Jean-Michel 1 Booss-Bavnbek, Bernhelm 1 Broström, Sofia 1 Brown, B. Malcolm 1 Demailly, Jean-Pierre 1 Gaarde, Anders 1 Gilkey, Peter B. 1 Gimperlein, Heiko 1 Helgason, Sigurdur 1 Hörmander, Lars Valter 1 Kiselman, Christer Oscar 1 Langer, Matthias 1 Lerner, Nicolas 1 Lotoreichik, Vladimir 1 Sigurðsson, Ragnar 1 Trèves, François 1 Wojciechowski, Krzysztof P. all top 5 ### Serials 9 Communications in Partial Differential Equations 7 Comptes Rendus de l’Académie des Sciences. Série I 7 Comptes Rendus Hebdomadaires des Séances de l’Académie des Sciences, Série A 6 Mathematica Scandinavica 4 Journal of Mathematical Analysis and Applications 4 Journal of Functional Analysis 3 Journal of Differential Equations 2 Communications in Mathematical Physics 2 Annales de l’Institut Fourier 2 Journal of Soviet Mathematics 2 Mathematische Annalen 2 Mathematische Nachrichten 2 Bollettino della Unione Matematica Italiana. Series V. B 2 Bulletin of the American Mathematical Society 2 Progress in Mathematics 2 Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta Imeni V. A. Steklova 2 Journal of Spectral Theory 1 Applicable Analysis 1 Israel Journal of Mathematics 1 Jahresbericht der Deutschen Mathematiker-Vereinigung (DMV) 1 Arkiv för Matematik 1 Acta Mathematica 1 Advances in Mathematics 1 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 1 Bulletin des Sciences Mathématiques. Deuxième Série 1 Duke Mathematical Journal 1 Inventiones Mathematicae 1 Journal für die Reine und Angewandte Mathematik 1 Mathematische Zeitschrift 1 Journal of Operator Theory 1 Annals of Global Analysis and Geometry 1 Differential and Integral Equations 1 The Journal of Geometric Analysis 1 Bulletin of the American Mathematical Society. New Series 1 Notices of the American Mathematical Society 1 Séminaire Équations aux Dérivées Partielles 1 Discrete and Continuous Dynamical Systems 1 Journal of Mathematical Fluid Mechanics 1 Journal of Evolution Equations 1 Annali della Scuola Normale Superiore di Pisa. Scienze Fisiche e Matematiche. III. Ser 1 Rendiconti del Seminario Matematico. Universitá e Politecnico di Torino 1 Contemporary Mathematics 1 Graduate Texts in Mathematics 1 Analysis & PDE 1 Mathematics in Engineering all top 5 ### Fields 100 Partial differential equations (35-XX) 39 Global analysis, analysis on manifolds (58-XX) 37 Operator theory (47-XX) 11 Functional analysis (46-XX) 4 Fluid mechanics (76-XX) 3 Probability theory and stochastic processes (60-XX) 2 Approximations and expansions (41-XX) 2 Differential geometry (53-XX) 2 Quantum theory (81-XX) 1 General and overarching topics; collections (00-XX) 1 History and biography (01-XX) ### Citations contained in zbMATH Open 93 Publications have been cited 1,391 times in 774 Documents Cited by Year Fractional Laplacians on domains, a development of Hörmander’s theory of $$\mu$$-transmission pseudodifferential operators. Zbl 1318.47064 Grubb, Gerd 2015 Distributions and operators. Zbl 1171.47001 Grubb, Gerd 2009 Functional calculus of pseudodifferential boundary problems. 2nd ed. Zbl 0844.35002 Grubb, Gerd 1996 A characterization of the non-local boundary value problems associated with an elliptic operator. Zbl 0182.14501 Grubb, G. 1968 Weakly parametric pseudodifferential operators and Atiyah-Patodi-Singer boundary problems. Zbl 0851.58043 Grubb, Gerd; Seeley, Robert T. 1995 Boundary value problems for the nonstationary Navier-Stokes equations treated by pseudo-differential methods. Zbl 0766.35034 Grubb, Gerd; Solonnikov, Vsevolod A. 1991 Functional calculus of pseudo-differential boundary problems. Zbl 0622.35001 Grubb, Gerd 1986 Pseudo-differential boundary problems in $$L_ p$$ spaces. Zbl 0723.35091 Grubb, Gerd 1990 Local and nonlocal boundary conditions for $$\mu$$-transmission and fractional elliptic pseudodifferential operators. Zbl 1317.35310 Grubb, Gerd 2014 $$M$$-functions for closed extensions of adjoint pairs of operators with applications to elliptic boundary problems. Zbl 1167.47057 Brown, B. M.; Grubb, G.; Wood, I. G. 2009 A global calculus of parameter-dependent pseudodifferential boundary problems in $$L_ p$$ Sobolev spaces. Zbl 0811.35176 Grubb, Gerd; Kokholm, Niels Jørgen 1993 Zeta and eta functions for Atiyah-Patodi-Singer operators. Zbl 0858.58050 Grubb, Gerd; Seeley, Robert T. 1996 Regularity of spectral fractional Dirichlet and Neumann problems. Zbl 1448.47062 Grubb, Gerd 2016 The essential spectrum of elliptic systems of mixed order. Zbl 0361.35050 Grubb, Gerd; Geymonat, Giuseppe 1977 Singular Green operators and their spectral asymptotics. Zbl 0553.58034 Grubb, Gerd 1984 Trace expansions for pseudodifferential boundary problems for Dirac-type operators and more general systems. Zbl 1021.35046 Grubb, Gerd 1999 Trace expansions and the noncommutative residue for manifolds with boundary. Zbl 0980.58017 Grubb, Gerd; Schrohe, Elmar 2001 Spectral asymptotics for the ”soft” selfadjoint extension of a symmetric elliptic differential operator. Zbl 0559.47035 Grubb, Gerd 1983 Krein resolvent formulas for elliptic boundary problems in nonsmooth domains. Zbl 1206.35090 Grubb, G. 2008 Parameter-elliptic and parabolic pseudodifferential boundary problems in global $$L_ p$$ Sobolev spaces. Zbl 0877.35142 Grubb, Gerd 1995 On coerciveness and semiboundedness of general boundary problems. Zbl 0231.35027 Grubb, Gerd 1971 Extension theory and Kreĭn-type resolvent formulas for nonsmooth boundary value problems. Zbl 1312.47019 Abels, Helmut; Grubb, Gerd; Wood, Ian Geoffrey 2014 Nonhomogeneous Dirichlet Navier-Stokes problems in low regularity $$L_p$$ Sobolev spaces. Zbl 0992.35065 Grubb, Gerd 2001 Heat kernel estimates for pseudodifferential operators, fractional Laplacians and Dirichlet-to-Neumann operators. Zbl 1432.35107 Gimperlein, Heiko; Grubb, Gerd 2014 Solution of parabolic pseudo-differential initial-boundary value problems. Zbl 0713.35109 Grubb, Gerd; Solonnikov, Vsevolod A. 1990 Properties of normal boundary problems for elliptic even-order systems. Zbl 0309.35034 Grubb, Gerd 1975 Heat operator trace expansions and index for general Atiyah-Patodi-Singer boundary problems. Zbl 0773.58025 Grubb, Gerd 1992 Spectral results for mixed problems and fractional elliptic operators. Zbl 1302.35279 Grubb, Gerd 2015 A resolvent approach to traces and zeta Laurent expansions. Zbl 1073.58021 Grubb, Gerd 2005 The transmission property. Zbl 0766.35088 Grubb, Gerd; Hörmander, Lars 1990 Spectral asymptotics for Robin problems with a discontinuous coefficient. Zbl 1223.35146 Grubb, Gerd 2011 Boundary problems for systems of partial differential operators of mixed order. Zbl 0368.35030 Grubb, Gerd 1977 Spectral asymptotics for nonsmooth singular Green operators. Zbl 1290.35057 Grubb, Gerd 2014 Les problèmes aux limites généraux d’un opérateur elliptique, provenant de la théorie variationnelle. Zbl 0201.46502 Grubb, G. 1970 Traces and quasi-traces on the Boutet de Monvel algebra. Zbl 1078.58015 Grubb, Gerd; Schrohe, Elmar 2004 The mixed boundary value problem, Krein resolvent formulas and spectral asymptotic estimates. Zbl 1223.47050 Grubb, Gerd 2011 Integration by parts and Pohozaev identities for space-dependent fractional-order operators. Zbl 1375.35600 Grubb, Gerd 2016 Weakly semi-bounded boundary problems and sesquilinear forms. Zbl 0261.35011 Grubb, Gerd 1973 Spectral boundary conditions for generalizations of Laplace and Dirac operators. Zbl 1039.58027 Grubb, Gerd 2003 Regularity in $$L_{p}$$ Sobolev spaces of solutions to fractional heat equations. Zbl 1396.35022 Grubb, Gerd 2018 Fractional-order operators: boundary problems, heat equations. Zbl 1414.35099 Grubb, Gerd 2018 Spectral asymptotics for Douglis-Nirenberg elliptic and pseudo- differential boundary problems. Zbl 0381.35034 Grubb, Gerd 1978 Logarithmic terms in asymptotic expansions of heat operator traces. Zbl 0911.35128 Gilkey, Peter B.; Grubb, Gerd 1998 The local and global parts of the basic zeta coefficient for operators on manifolds with boundary. Zbl 1147.58028 Grubb, Gerd 2008 Spectral asymptotics for resolvent differences of elliptic operators with $$\delta$$ and $$\delta^{'}$$-interactions on hypersurfaces. Zbl 1353.47090 Behrndt, Jussi; Grubb, Gerd; Langer, Matthias; Lotoreichik, Vladimir 2015 Perturbation of essential spectra of exterior elliptic problems. Zbl 1208.35094 Grubb, Gerd 2011 Kreĭn-like extensions and the lower boundedness problem for elliptic operators. Zbl 1242.47041 Grubb, Gerd 2012 Poles of zeta and eta functions for perturbations of the Atiyah-Patodi-Singer problem. Zbl 0976.58018 Grubb, G. 2001 Complex powers of resolvents of pseudodifferential operators. Zbl 1129.58304 Grubb, Gerd; Hansen, Lars 2002 Known and unknown results on elliptic boundary problems. Zbl 1159.35004 Grubb, Gerd 2006 Nonhomogeneous time-dependent Navier-Stokes problems in $$L_ p$$ Sobolev spaces. Zbl 0831.35126 Grubb, Gerd 1995 Remainder estimates for eigenvalues and kernels of pseudo-differential elliptic systems. Zbl 0407.35075 Grubb, Gerd 1978 Green’s formula and a Dirichlet-to-Neumann operator for fractional-order pseudodifferential operators. Zbl 1409.35216 Grubb, Gerd 2018 A weakly polyhomogeneous calculus for pseudodifferential boundary problems. Zbl 0998.58017 Grubb, Gerd 2001 Remarks on trace estimates for exterior boundary problems. Zbl 0553.35022 Grubb, Gerd 1984 The sectorial projection defined from logarithms. Zbl 1270.58016 Grubb, Gerd 2012 On the logarithm component in trace defect formulas. Zbl 1087.35100 Grubb, Gerd 2005 Limited regularity of solutions to fractional heat and Schrödinger equations. Zbl 1415.35142 Grubb, Gerd 2019 Logarithms and sectorial projections for elliptic boundary problems. Zbl 1189.35347 Gaarde, Anders; Grubb, Gerd 2008 Estimation du reste dans l’étude des valeurs propres des problèmes aux limites pseudo-différentiels auto-adjoints. Zbl 0399.58019 Grubb, Gerd 1978 Reduction of basic initial-boundary value problems for the Stokes equations to initial-boundary value problems for parabolic systems of pseudodifferential equations. Zbl 0655.35065 Grubb, Gerd; Solonnikov, V. A. 1987 Parabolic pseudo-differential boundary problems and applications. Zbl 0763.35116 Grubb, Gerd 1991 Extension theory for elliptic partial differential operators with pseudodifferential methods. Zbl 1331.47069 Grubb, Gerd 2012 Initial value problems for the Navier-Stokes equations with Neumann conditions. Zbl 0781.35051 Grubb, Gerd 1992 Nonhomogeneous Navier-Stokes problems in $$L_p$$ Sobolev spaces over exterior and interior domains. Zbl 0934.35119 Grubb, G. 1998 Integration by parts for nonsymmetric fractional-order operators on a halfspace. Zbl 1473.35629 Grubb, Gerd 2021 Asymptotic expansions for the Atiyah-Patodi-Singer operator. (Développements asymptotiques pour l’opérateur d’Atiyah-Patodi-Singer.) Zbl 0813.58059 Grubb, Gerd; Seeley, Robert T. 1993 Eigenvalue asymptotics for selfadjoint elliptic mixed order systems with nonempty essential spectrum. Zbl 0423.35071 Grubb, Gerd; Geymonat, Giuseppe 1979 Parametrized pseudodifferential operators and geometric invariants. Zbl 0873.35116 Grubb, Gerd 1997 Problèmes aux limites semi-bornes pour les systèmes elliptiques. Zbl 0243.35032 Grubb, Gerd 1972 Inequalities for boundary value problems for systems of partial differential operators. Zbl 0267.35026 Grubb, Gerd 1973 Spectral theory for boundary value problems for elliptic systems of mixed order. Zbl 0301.35071 Geymonat, Giuseppe; Grubb, Gerd 1974 Analysis of invariants associated with spectral boundary problems for elliptic operators. Zbl 1077.58014 Grubb, Gerd 2005 Une condition necessaire et suffisante pour la m-coercivite des problèmes aux limites elliptiques. Zbl 0192.49301 Grubb, G. 1970 Logarithmic terms in trace expansions of Atiyah-Patodi-Singer problems. Zbl 1048.35095 Grubb, Gerd 2003 On coerciveness of Douglis-Nirenberg elliptic boundary value problems. Zbl 0456.35015 Grubb, Gerd 1979 Reduction of the basic initial-boundary value problems for the Navier- Stokes equations to initial-boundary value problems for nonlinear parabolic systems of pseudodifferential equations. Zbl 0729.35102 Grubb, G.; Solonnikov, V. A. 1991 Problèmes aux limites pseudodifférentiels dependant d’un paramètre. Zbl 0492.35079 Grubb, Gerd 1981 A pseudo-differential treatment of general inhomogeneous initial-boundary value problems for the Navier-Stokes equation. Zbl 0675.76028 Grubb, Gerd; Solonnikov, Vsevolod A. 1988 Exact Green’s formula for the fractional Laplacian and perturbations. Zbl 1453.35051 Grubb, Gerd 2020 Trace defect formulas and zeta values for boundary problems. Zbl 1154.35103 Grubb, Gerd 2008 Pseudodifferential boundary problems and applications. Zbl 0873.35117 Grubb, G. 1997 A resolvent construction for pseudo-differential boundary value problems, with applications. Zbl 0471.35064 Grubb, Gerd 1981 Le spectre négatif des problèmes aux limites auto-adjoints fortement elliptiques. (The negative spectrum of strongly elliptic selfadjoint boundary value problems). Zbl 0234.35075 Grubb, Gerd 1972 Caractérisation de quelques propriétés des problèmes aux limites pour les systèmes elliptiques: Problèmes aux limites variationnels. Zbl 0278.35035 Grubb, G. 1972 Coerciveness of the normal boundary problems for an elliptic operator. Zbl 0188.16902 Grubb, G. 1970 Complex powers of pseudo-differential boundary value problems with the transmission property. Zbl 0623.47068 Grubb, Gerd 1987 Comportement asymptotique du spectre des opérateurs de Green singuliers. Zbl 0553.35066 Grubb, Gerd 1983 Une méthode pseudo-différentielle pour les perturbations singulières elliptiques. (A pseudo-differential method for elliptic singular perturbation problems). Zbl 0595.35045 Grubb, Gerd 1985 Remarks on nonlocal trace expansion coefficients. Zbl 1119.58019 Grubb, Gerd 2006 Reduction of basic initial-boundary value problems for Navier-Stokes equations to initial-boundary value problems for nonlinear parabolic systems of pseudo-differential equations. Zbl 0717.35069 Grubb, G.; Solonnikov, V. A. 1989 Solution dans les espaces de Sobolev $$L_ p$$ anisotropes des problèmes aux limites pseudo-différentiels paraboliques et des problèmes de Stokes. (Solution in anisotropic $$L_ p$$ Sobolev spaces of parabolic pseudo-differential boundary value problems and Stokes problems). Zbl 0723.35093 Grubb, Gerd 1991 La resolvante d’un problème aux limites pseudo-différentiel elliptique. Zbl 0489.35083 Grubb, Gerd 1981 Integration by parts for nonsymmetric fractional-order operators on a halfspace. Zbl 1473.35629 Grubb, Gerd 2021 Exact Green’s formula for the fractional Laplacian and perturbations. Zbl 1453.35051 Grubb, Gerd 2020 Limited regularity of solutions to fractional heat and Schrödinger equations. Zbl 1415.35142 Grubb, Gerd 2019 Regularity in $$L_{p}$$ Sobolev spaces of solutions to fractional heat equations. Zbl 1396.35022 Grubb, Gerd 2018 Fractional-order operators: boundary problems, heat equations. Zbl 1414.35099 Grubb, Gerd 2018 Green’s formula and a Dirichlet-to-Neumann operator for fractional-order pseudodifferential operators. Zbl 1409.35216 Grubb, Gerd 2018 Regularity of spectral fractional Dirichlet and Neumann problems. Zbl 1448.47062 Grubb, Gerd 2016 Integration by parts and Pohozaev identities for space-dependent fractional-order operators. Zbl 1375.35600 Grubb, Gerd 2016 Fractional Laplacians on domains, a development of Hörmander’s theory of $$\mu$$-transmission pseudodifferential operators. Zbl 1318.47064 Grubb, Gerd 2015 Spectral results for mixed problems and fractional elliptic operators. Zbl 1302.35279 Grubb, Gerd 2015 Spectral asymptotics for resolvent differences of elliptic operators with $$\delta$$ and $$\delta^{'}$$-interactions on hypersurfaces. Zbl 1353.47090 Behrndt, Jussi; Grubb, Gerd; Langer, Matthias; Lotoreichik, Vladimir 2015 Local and nonlocal boundary conditions for $$\mu$$-transmission and fractional elliptic pseudodifferential operators. Zbl 1317.35310 Grubb, Gerd 2014 Extension theory and Kreĭn-type resolvent formulas for nonsmooth boundary value problems. Zbl 1312.47019 Abels, Helmut; Grubb, Gerd; Wood, Ian Geoffrey 2014 Heat kernel estimates for pseudodifferential operators, fractional Laplacians and Dirichlet-to-Neumann operators. Zbl 1432.35107 Gimperlein, Heiko; Grubb, Gerd 2014 Spectral asymptotics for nonsmooth singular Green operators. Zbl 1290.35057 Grubb, Gerd 2014 Kreĭn-like extensions and the lower boundedness problem for elliptic operators. Zbl 1242.47041 Grubb, Gerd 2012 The sectorial projection defined from logarithms. Zbl 1270.58016 Grubb, Gerd 2012 Extension theory for elliptic partial differential operators with pseudodifferential methods. Zbl 1331.47069 Grubb, Gerd 2012 Spectral asymptotics for Robin problems with a discontinuous coefficient. Zbl 1223.35146 Grubb, Gerd 2011 The mixed boundary value problem, Krein resolvent formulas and spectral asymptotic estimates. Zbl 1223.47050 Grubb, Gerd 2011 Perturbation of essential spectra of exterior elliptic problems. Zbl 1208.35094 Grubb, Gerd 2011 Distributions and operators. Zbl 1171.47001 Grubb, Gerd 2009 $$M$$-functions for closed extensions of adjoint pairs of operators with applications to elliptic boundary problems. Zbl 1167.47057 Brown, B. M.; Grubb, G.; Wood, I. G. 2009 Krein resolvent formulas for elliptic boundary problems in nonsmooth domains. Zbl 1206.35090 Grubb, G. 2008 The local and global parts of the basic zeta coefficient for operators on manifolds with boundary. Zbl 1147.58028 Grubb, Gerd 2008 Logarithms and sectorial projections for elliptic boundary problems. Zbl 1189.35347 Gaarde, Anders; Grubb, Gerd 2008 Trace defect formulas and zeta values for boundary problems. Zbl 1154.35103 Grubb, Gerd 2008 Known and unknown results on elliptic boundary problems. Zbl 1159.35004 Grubb, Gerd 2006 Remarks on nonlocal trace expansion coefficients. Zbl 1119.58019 Grubb, Gerd 2006 A resolvent approach to traces and zeta Laurent expansions. Zbl 1073.58021 Grubb, Gerd 2005 On the logarithm component in trace defect formulas. Zbl 1087.35100 Grubb, Gerd 2005 Analysis of invariants associated with spectral boundary problems for elliptic operators. Zbl 1077.58014 Grubb, Gerd 2005 Traces and quasi-traces on the Boutet de Monvel algebra. Zbl 1078.58015 Grubb, Gerd; Schrohe, Elmar 2004 Spectral boundary conditions for generalizations of Laplace and Dirac operators. Zbl 1039.58027 Grubb, Gerd 2003 Logarithmic terms in trace expansions of Atiyah-Patodi-Singer problems. Zbl 1048.35095 Grubb, Gerd 2003 Complex powers of resolvents of pseudodifferential operators. Zbl 1129.58304 Grubb, Gerd; Hansen, Lars 2002 Trace expansions and the noncommutative residue for manifolds with boundary. Zbl 0980.58017 Grubb, Gerd; Schrohe, Elmar 2001 Nonhomogeneous Dirichlet Navier-Stokes problems in low regularity $$L_p$$ Sobolev spaces. Zbl 0992.35065 Grubb, Gerd 2001 Poles of zeta and eta functions for perturbations of the Atiyah-Patodi-Singer problem. Zbl 0976.58018 Grubb, G. 2001 A weakly polyhomogeneous calculus for pseudodifferential boundary problems. Zbl 0998.58017 Grubb, Gerd 2001 Trace expansions for pseudodifferential boundary problems for Dirac-type operators and more general systems. Zbl 1021.35046 Grubb, Gerd 1999 Logarithmic terms in asymptotic expansions of heat operator traces. Zbl 0911.35128 Gilkey, Peter B.; Grubb, Gerd 1998 Nonhomogeneous Navier-Stokes problems in $$L_p$$ Sobolev spaces over exterior and interior domains. Zbl 0934.35119 Grubb, G. 1998 Parametrized pseudodifferential operators and geometric invariants. Zbl 0873.35116 Grubb, Gerd 1997 Pseudodifferential boundary problems and applications. Zbl 0873.35117 Grubb, G. 1997 Functional calculus of pseudodifferential boundary problems. 2nd ed. Zbl 0844.35002 Grubb, Gerd 1996 Zeta and eta functions for Atiyah-Patodi-Singer operators. Zbl 0858.58050 Grubb, Gerd; Seeley, Robert T. 1996 Weakly parametric pseudodifferential operators and Atiyah-Patodi-Singer boundary problems. Zbl 0851.58043 Grubb, Gerd; Seeley, Robert T. 1995 Parameter-elliptic and parabolic pseudodifferential boundary problems in global $$L_ p$$ Sobolev spaces. Zbl 0877.35142 Grubb, Gerd 1995 Nonhomogeneous time-dependent Navier-Stokes problems in $$L_ p$$ Sobolev spaces. Zbl 0831.35126 Grubb, Gerd 1995 A global calculus of parameter-dependent pseudodifferential boundary problems in $$L_ p$$ Sobolev spaces. Zbl 0811.35176 Grubb, Gerd; Kokholm, Niels Jørgen 1993 Asymptotic expansions for the Atiyah-Patodi-Singer operator. (Développements asymptotiques pour l’opérateur d’Atiyah-Patodi-Singer.) Zbl 0813.58059 Grubb, Gerd; Seeley, Robert T. 1993 Heat operator trace expansions and index for general Atiyah-Patodi-Singer boundary problems. Zbl 0773.58025 Grubb, Gerd 1992 Initial value problems for the Navier-Stokes equations with Neumann conditions. Zbl 0781.35051 Grubb, Gerd 1992 Boundary value problems for the nonstationary Navier-Stokes equations treated by pseudo-differential methods. Zbl 0766.35034 Grubb, Gerd; Solonnikov, Vsevolod A. 1991 Parabolic pseudo-differential boundary problems and applications. Zbl 0763.35116 Grubb, Gerd 1991 Reduction of the basic initial-boundary value problems for the Navier- Stokes equations to initial-boundary value problems for nonlinear parabolic systems of pseudodifferential equations. Zbl 0729.35102 Grubb, G.; Solonnikov, V. A. 1991 Solution dans les espaces de Sobolev $$L_ p$$ anisotropes des problèmes aux limites pseudo-différentiels paraboliques et des problèmes de Stokes. (Solution in anisotropic $$L_ p$$ Sobolev spaces of parabolic pseudo-differential boundary value problems and Stokes problems). Zbl 0723.35093 Grubb, Gerd 1991 Pseudo-differential boundary problems in $$L_ p$$ spaces. Zbl 0723.35091 Grubb, Gerd 1990 Solution of parabolic pseudo-differential initial-boundary value problems. Zbl 0713.35109 Grubb, Gerd; Solonnikov, Vsevolod A. 1990 The transmission property. Zbl 0766.35088 Grubb, Gerd; Hörmander, Lars 1990 Reduction of basic initial-boundary value problems for Navier-Stokes equations to initial-boundary value problems for nonlinear parabolic systems of pseudo-differential equations. Zbl 0717.35069 Grubb, G.; Solonnikov, V. A. 1989 A pseudo-differential treatment of general inhomogeneous initial-boundary value problems for the Navier-Stokes equation. Zbl 0675.76028 Grubb, Gerd; Solonnikov, Vsevolod A. 1988 Reduction of basic initial-boundary value problems for the Stokes equations to initial-boundary value problems for parabolic systems of pseudodifferential equations. Zbl 0655.35065 Grubb, Gerd; Solonnikov, V. A. 1987 Complex powers of pseudo-differential boundary value problems with the transmission property. Zbl 0623.47068 Grubb, Gerd 1987 Functional calculus of pseudo-differential boundary problems. Zbl 0622.35001 Grubb, Gerd 1986 Une méthode pseudo-différentielle pour les perturbations singulières elliptiques. (A pseudo-differential method for elliptic singular perturbation problems). Zbl 0595.35045 Grubb, Gerd 1985 Singular Green operators and their spectral asymptotics. Zbl 0553.58034 Grubb, Gerd 1984 Remarks on trace estimates for exterior boundary problems. Zbl 0553.35022 Grubb, Gerd 1984 Spectral asymptotics for the ”soft” selfadjoint extension of a symmetric elliptic differential operator. Zbl 0559.47035 Grubb, Gerd 1983 Comportement asymptotique du spectre des opérateurs de Green singuliers. Zbl 0553.35066 Grubb, Gerd 1983 Problèmes aux limites pseudodifférentiels dependant d’un paramètre. Zbl 0492.35079 Grubb, Gerd 1981 A resolvent construction for pseudo-differential boundary value problems, with applications. Zbl 0471.35064 Grubb, Gerd 1981 La resolvante d’un problème aux limites pseudo-différentiel elliptique. Zbl 0489.35083 Grubb, Gerd 1981 Eigenvalue asymptotics for selfadjoint elliptic mixed order systems with nonempty essential spectrum. Zbl 0423.35071 Grubb, Gerd; Geymonat, Giuseppe 1979 On coerciveness of Douglis-Nirenberg elliptic boundary value problems. Zbl 0456.35015 Grubb, Gerd 1979 Spectral asymptotics for Douglis-Nirenberg elliptic and pseudo- differential boundary problems. Zbl 0381.35034 Grubb, Gerd 1978 Remainder estimates for eigenvalues and kernels of pseudo-differential elliptic systems. Zbl 0407.35075 Grubb, Gerd 1978 Estimation du reste dans l’étude des valeurs propres des problèmes aux limites pseudo-différentiels auto-adjoints. Zbl 0399.58019 Grubb, Gerd 1978 The essential spectrum of elliptic systems of mixed order. Zbl 0361.35050 Grubb, Gerd; Geymonat, Giuseppe 1977 Boundary problems for systems of partial differential operators of mixed order. Zbl 0368.35030 Grubb, Gerd 1977 Properties of normal boundary problems for elliptic even-order systems. Zbl 0309.35034 Grubb, Gerd 1975 Spectral theory for boundary value problems for elliptic systems of mixed order. Zbl 0301.35071 Geymonat, Giuseppe; Grubb, Gerd 1974 Weakly semi-bounded boundary problems and sesquilinear forms. Zbl 0261.35011 Grubb, Gerd 1973 Inequalities for boundary value problems for systems of partial differential operators. Zbl 0267.35026 Grubb, Gerd 1973 Problèmes aux limites semi-bornes pour les systèmes elliptiques. Zbl 0243.35032 Grubb, Gerd 1972 Le spectre négatif des problèmes aux limites auto-adjoints fortement elliptiques. (The negative spectrum of strongly elliptic selfadjoint boundary value problems). Zbl 0234.35075 Grubb, Gerd 1972 Caractérisation de quelques propriétés des problèmes aux limites pour les systèmes elliptiques: Problèmes aux limites variationnels. Zbl 0278.35035 Grubb, G. 1972 On coerciveness and semiboundedness of general boundary problems. Zbl 0231.35027 Grubb, Gerd 1971 Les problèmes aux limites généraux d’un opérateur elliptique, provenant de la théorie variationnelle. Zbl 0201.46502 Grubb, G. 1970 Une condition necessaire et suffisante pour la m-coercivite des problèmes aux limites elliptiques. Zbl 0192.49301 Grubb, G. 1970 Coerciveness of the normal boundary problems for an elliptic operator. Zbl 0188.16902 Grubb, G. 1970 A characterization of the non-local boundary value problems associated with an elliptic operator. Zbl 0182.14501 Grubb, G. 1968 all top 5 ### Cited by 814 Authors 46 Grubb, Gerd 20 Behrndt, Jussi 19 Schulze, Bert-Wolfgang 18 Schrohe, Elmar 14 Loya, Paul A. 12 Malamud, Mark M. 12 Ros-Oton, Xavier 12 Warma, Mahamadi 11 Abels, Helmut 11 Seiler, Jörg 10 Gesztesy, Fritz 10 Lesch, Matthias 10 Mitrea, Marius 10 Raymond, Jean-Pierre 9 Abatangelo, Nicola 9 Kirsten, Klaus 9 Lee, Yoonweon 9 Natroshvili, David 8 Antil, Harbir 8 Borthagaray, Juan Pablo 8 Johnsen, Jon 8 Lotoreichik, Vladimir 8 Neidhardt, Hagen 8 Rohleder, Jonathan 8 Solonnikov, Vsevolod Alekseevich 7 Dipierro, Serena 7 Faierman, Melvin 7 Geymonat, Giuseppe 7 Jarohs, Sven 7 Kozhevnikov, Alexander 7 Michelangeli, Alessandro 7 Park, Jinsung 7 Scott, Simon G. 7 Uhlmann, Gunther Alberto 7 Wang, Yong 7 Wood, Ian Geoffrey 6 Coriasco, Sandro 6 Denk, Robert 6 Fall, Mouhamed Moustapha 6 Gimperlein, Heiko 6 Liu, Genqian 6 Rüland, Angkana 6 Saldaña, Alberto 6 Valdinoci, Enrico 5 Acosta, Gabriel 5 Amann, Herbert 5 Booss-Bavnbek, Bernhelm 5 Brown, B. Malcolm 5 Fahrenwaldt, Matthias Albrecht 5 Gallone, Matteo 5 Ghosh, Tuhin 5 Gilkey, Peter B. 5 Krupchyk, Katsiaryna 5 Langer, Matthias 5 Posilicano, Andrea 5 Rabinovich, Vladimir Samuilovich 5 Seeley, Robert Thomas 5 Serra Montolí, Joaquim 5 ter Elst, Antonius Frederik Maria 5 Wang, Jian 5 Zakora, Dmitriĭ Aleksandrovich 4 Battisti, Ubertino 4 Chang, Tongkeun 4 Dappiaggi, Claudio 4 Fernández-Real, Xavier 4 Fischbacher, Christoph 4 Goffeng, Magnus 4 Huang, Rung-Tzung 4 Iochum, Bruno 4 Jin, Bumja 4 Krainer, Thomas 4 Levendorskiĭ, Sergeĭ Zakharovich 4 Naboko, Serguei N. 4 Nistor, Victor 4 Otárola, Enrique 4 Ponge, Raphaël S. 4 Salo, Mikko 4 Shibata, Yoshihiro 4 Sire, Yannick 4 Zhu, Chaofeng 3 Ainsworth, Mark 3 Ashbaugh, Mark S. 3 Bersetche, Francisco M. 3 Biccari, Umberto 3 Bonforte, Matteo 3 Brüning, Jochen 3 Buchukuri, Tengiz 3 Burkovska, Olena 3 Cardona, Duván 3 Chang, Der-Chen E. 3 Chen, Guoyuan 3 Del Corral, César 3 D’Elia, Marta 3 Dias, Nuno Costa 3 Duduchava, Roland 3 Evans, William Desmond 3 Farwig, Reinhard 3 Glusa, Christian 3 Hieber, Matthias 3 Kamocki, Rafal ...and 714 more Authors all top 5 ### Cited in 197 Serials 40 Journal of Functional Analysis 31 Journal of Differential Equations 30 Integral Equations and Operator Theory 26 Communications in Partial Differential Equations 25 Journal of Mathematical Analysis and Applications 22 Mathematische Nachrichten 18 Advances in Mathematics 15 Journal of Pseudo-Differential Operators and Applications 14 Journal of Geometry and Physics 14 Journal of Mathematical Sciences (New York) 12 Communications in Mathematical Physics 12 Journal of Mathematical Physics 11 Mathematische Annalen 11 Transactions of the American Mathematical Society 11 The Journal of Geometric Analysis 10 Annals of Global Analysis and Geometry 9 Archive for Rational Mechanics and Analysis 9 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 9 SIAM Journal on Numerical Analysis 9 Journal of Evolution Equations 8 Applicable Analysis 8 Journal d’Analyse Mathématique 8 Proceedings of the American Mathematical Society 8 Calculus of Variations and Partial Differential Equations 7 Reviews in Mathematical Physics 7 Journal de Mathématiques Pures et Appliquées. Neuvième Série 7 Discrete and Continuous Dynamical Systems 6 Letters in Mathematical Physics 6 Mathematical Methods in the Applied Sciences 6 Duke Mathematical Journal 6 Journal of Soviet Mathematics 6 Mathematische Zeitschrift 6 Russian Journal of Mathematical Physics 6 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 6 Complex Analysis and Operator Theory 6 Journal of Spectral Theory 5 Journal of Computational Physics 5 Mathematical Notes 5 Annali di Matematica Pura ed Applicata. Serie Quarta 5 Applied Mathematics and Optimization 5 Functional Analysis and its Applications 5 Journal für die Reine und Angewandte Mathematik 5 Numerische Mathematik 5 Annales Henri Poincaré 5 Communications on Pure and Applied Analysis 5 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 4 Inverse Problems 4 Indiana University Mathematics Journal 4 Monatshefte für Mathematik 4 SIAM Journal on Control and Optimization 4 International Journal of Mathematics 4 Differential Geometry and its Applications 4 SIAM Journal on Mathematical Analysis 4 Fractional Calculus & Applied Analysis 4 Journal of Mathematical Fluid Mechanics 4 Journal of Noncommutative Geometry 3 Computers & Mathematics with Applications 3 Israel Journal of Mathematics 3 Mathematics of Computation 3 Annales de l’Institut Fourier 3 Applied Mathematics and Computation 3 Journal of Computational and Applied Mathematics 3 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 3 Journal of Integral Equations and Applications 3 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 3 Potential Analysis 3 St. Petersburg Mathematical Journal 3 The Journal of Fourier Analysis and Applications 3 Mathematical Physics, Analysis and Geometry 3 Nonlinear Analysis. Real World Applications 3 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V 3 Annali dell’Università di Ferrara. Sezione VII. Scienze Matematiche 3 Mathematical Control and Related Fields 3 Journal of Elliptic and Parabolic Equations 2 International Journal of Modern Physics A 2 Computer Methods in Applied Mechanics and Engineering 2 Communications on Pure and Applied Mathematics 2 Nonlinearity 2 ZAMP. Zeitschrift für angewandte Mathematik und Physik 2 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 2 The Annals of Statistics 2 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 2 Manuscripta Mathematica 2 Memoirs of the American Mathematical Society 2 Rendiconti del Seminario Matematico della Università di Padova 2 Siberian Mathematical Journal 2 Transactions of the Moscow Mathematical Society 2 Journal of Scientific Computing 2 Computational Mathematics and Mathematical Physics 2 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 2 SIAM Journal on Scientific Computing 2 Opuscula Mathematica 2 Electronic Research Announcements of the American Mathematical Society 2 Matematychni Metody ta Fizyko-Mekhanichni Polya 2 Journal of Nonlinear Mathematical Physics 2 Advanced Nonlinear Studies 2 Comptes Rendus. Mathématique. Académie des Sciences, Paris 2 Bulletin of the American Mathematical Society 2 Annali della Scuola Normale Superiore di Pisa. Scienze Fisiche e Matematiche. III. Ser 2 Inverse Problems and Imaging ...and 97 more Serials all top 5 ### Cited in 46 Fields 522 Partial differential equations (35-XX) 217 Operator theory (47-XX) 207 Global analysis, analysis on manifolds (58-XX) 74 Fluid mechanics (76-XX) 71 Functional analysis (46-XX) 65 Numerical analysis (65-XX) 58 Quantum theory (81-XX) 39 Mechanics of deformable solids (74-XX) 37 Differential geometry (53-XX) 25 Ordinary differential equations (34-XX) 24 Systems theory; control (93-XX) 23 Real functions (26-XX) 22 Probability theory and stochastic processes (60-XX) 21 Integral equations (45-XX) 20 Calculus of variations and optimal control; optimization (49-XX) 19 Potential theory (31-XX) 14 Harmonic analysis on Euclidean spaces (42-XX) 11 Statistical mechanics, structure of matter (82-XX) 10 Functions of a complex variable (30-XX) 10 Several complex variables and analytic spaces (32-XX) 9 Approximations and expansions (41-XX) 8 $$K$$-theory (19-XX) 8 Dynamical systems and ergodic theory (37-XX) 8 Biology and other natural sciences (92-XX) 7 Number theory (11-XX) 6 Algebraic geometry (14-XX) 6 Optics, electromagnetic theory (78-XX) 5 Abstract harmonic analysis (43-XX) 5 Integral transforms, operational calculus (44-XX) 5 Manifolds and cell complexes (57-XX) 5 Mechanics of particles and systems (70-XX) 5 Relativity and gravitational theory (83-XX) 4 Topological groups, Lie groups (22-XX) 4 Statistics (62-XX) 3 Linear and multilinear algebra; matrix theory (15-XX) 3 Classical thermodynamics, heat transfer (80-XX) 3 Geophysics (86-XX) 2 General and overarching topics; collections (00-XX) 2 Measure and integration (28-XX) 2 Special functions (33-XX) 2 Operations research, mathematical programming (90-XX) 1 Associative rings and algebras (16-XX) 1 Difference and functional equations (39-XX) 1 Sequences, series, summability (40-XX) 1 Convex and discrete geometry (52-XX) 1 Algebraic topology (55-XX) ### Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata.	2022-10-01T18:48:53	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4795979857444763, "perplexity": 4280.594811831358}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030336880.89/warc/CC-MAIN-20221001163826-20221001193826-00756.warc.gz"}
https://www.p2psp.org/en/p2psp-protocol?cap=indexsu4.html	P2PSP (Peer-to-Peer “Straightforward” Protocol) 4.4 IMS (IP Multicast Set of rules) This set of rules implements the most basic behaviour of the protocol that can be used when IP multicast is available. This mode can be useful in local area networks where this transmission mode usually works properly. 1. IP multicast address: The splitter uses an IP multicast address (and a port) where all peers of the team wait for receiving chunks. Notice that the peers only receive chunks (never send them to the multicast channel because the splitter does all the work). 2. Peer arrival: An incoming peer must contact with the splitter in order to join the team. After that, the splitter sends to the peer the stream header over the TCP using a temporal unicast connection. 3. Buﬀering in peers: Packets in transit can suﬀer diﬀerent transmission delays due to the jitter Variations in the network latency. , even producing that they arrive out of order. For this reason, the splitter enumerates every chunk of stream with a 16-bit counter, producing a packet with the format: IMS_packet = [chunk_number, chunk] Peers store the received IMS_packets in a buﬀer whose size $b$ can be diﬀerent in each peer depending on the maximun tolerated delay. 4. Relation between the buﬀer size $B$ and chunk number upper bound $M$: Due to practical reasons, the upper bound for the chunk number should be a power of two. In order to minimize the probability of receiving two or more chunks with the same number (remember that chunks can be reordered in transit), $M$ must be a multiple of $B$, i.e.: $M=pB,$ (1) where $p\in ℕ$. P2PSP (Peer-to-Peer Straightforward Protocol) by Cristobal Medina-López, J. A. M. Naranjo, L. G. Casado and Vicente González-Ruiz is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.	2019-01-19T07:25:38	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 7, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2941974997520447, "perplexity": 3070.23185302855}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-04/segments/1547583662690.13/warc/CC-MAIN-20190119054606-20190119080606-00122.warc.gz"}
http://www.scstatehouse.gov/sess118_2009-2010/sj10/20100429.htm	South Carolina General Assembly 118th Session, 2009-2010 Journal of the Senate Thursday, April 29, 2010 (Statewide Session) Indicates Matter Stricken Indicates New Matter The Senate assembled at 10:00 A.M., the hour to which it stood adjourned, and was called to order by the PRESIDENT Pro Tempore. A quorum being present, the proceedings were opened with a devotion by the Chaplain as follows: "Gold there is, and rubies in abundance, but lips that speak knowledge are a rare jewel." (Proverbs 20:15) We fail to see sacks of gold and rubies stacked up here in this State House, dear Lord. We wish there were plenty of material resources with which to solve many of the problems which face these leaders. But we will settle for knowledge and wisdom on the part of each one of these Senators, O God. Enable them and their able staff members to use that precious gift of knowledge in ways which benefit both South Carolina and her citizens. In Your loving name we pray, dear Lord. Amen. The PRESIDENT Pro Tempore called for Petitions, Memorials, Presentments of Grand Juries and such like papers. MESSAGE FROM THE GOVERNOR The following appointments were transmitted by the Honorable Mark C. Sanford: Local Appointments Reappointment, Lancaster County Magistrate, with the term to commence April 30, 2010, and to expire April 30, 2014 Jaqueline M. Pope, P.O. Box 66, Kershaw, SC 29067 Reappointment, Lancaster County Magistrate, with the term to commence April 30, 2010, and to expire April 30, 2014 Van K. Richardson, 3611 Kershaw Camden Highway, Heath Springs, SC 29058 Reappointment, Lancaster County Magistrate, with the term to commence April 30, 2010, and to expire April 30, 2014 Fredrick Asgill Thomas, P. O. Box 3222, Lancaster, SC 29721 Doctor of the Day Senator LOURIE introduced Dr. Brian Huff of Columbia, S.C., Doctor of the Day. Leave of Absence At 11:25 A.M., Senator THOMAS requested a leave of absence from 12:30 - 2:00 P.M. Leave of Absence At 3:30 P.M., Senator COURSON requested a leave of absence beginning at 6:00 P.M. and lasting until 10:00 A.M. in the morning. Leave of Absence At 3:30 P.M., Senator FORD requested a leave of absence from 5:30 - 8:30 P.M. Leave of Absence At 5:30 P.M., Senator SHOOPMAN requested a leave of absence from 5:40 - 8:40 P.M. Leave of Absence At 10:10 P.M., Senator RYBERG requested a leave of absence beginning at 4:00 A.M. and lasting until 7:00 P.M. on Friday. Leave of Absence Requested, Objection At 12:28 A.M., Senator FORD requested a leave of absence until 10:00 A.M. Senator KNOTTS objected. Leave of Absence On motion of Senator JACKSON, at 12:30 A.M., Senator FORD was granted a leave of absence until 10:00 A.M. next Tuesday. Leave of Absence At 4:00 A.M., Senator CLEARY requested a leave of absence until 8:00 A.M. Leave of Absence At 4:50 P.M., Senator ROSE requested a leave of absence from 12:00 Noon until 3:00 P.M. next Tuesday. Leave of Absence At 4:50 A.M., Senator LOURIE requested a leave of absence for next Tuesday. Expression of Personal Interest Senator LEVENTIS rose for an Expression of Personal Interest. SENSE OF THE SENATE MOTION ADOPTED On motion of Senators LEVENTIS, COURSON and SHEHEEN, with unanimous consent, it was agreed to take up a Sense of the Senate motion for consideration. Senators LEVENTIS, COURSON and SHEHEEN moved that it be the Sense of the Senate that the Senate must move more aggressively to live up to its self-imposed obligation to the state's school children by finding additional funds for public education. The "ayes" and "nays" were demanded and taken, resulting as follows: Ayes 46; Nays 0 AYES Alexander Anderson Bright Bryant Campbell Campsen Cleary Coleman Courson Cromer Davis Elliott Fair Ford Grooms Hayes Hutto Jackson Knotts Land Leatherman Leventis Lourie Malloy Martin, Larry Martin, Shane Massey Matthews McConnell McGill Mulvaney Nicholson O'Dell Peeler Pinckney Rankin Reese Rose Ryberg Scott Setzler Sheheen Shoopman Thomas Verdin Williams Total--46 The Sense of the Senate motion was unanimously adopted. H. 4779 (Word version) -- Rep. Bales: A CONCURRENT RESOLUTION TO REQUEST THAT THE DEPARTMENT OF TRANSPORTATION NAME THE PORTION OF GARNERS FERRY ROAD BEGINNING AT INTERSTATE 77 INTERCHANGE CONTINUING TO THE INTERSECTION OF PINEVIEW ROAD THE "CAPTAIN L. D. 'DOUG' BARDEN MEMORIAL HIGHWAY" AND ERECT APPROPRIATE MARKERS OR SIGNS ALONG THIS PORTION OF HIGHWAY THAT CONTAIN THE WORDS "CAPTAIN L. D. 'DOUG' BARDEN MEMORIAL HIGHWAY". Senator LOURIE asked unanimous consent to make a motion to recall the Concurrent Resolution from the Committee on Transportation. The Concurrent Resolution was recalled from the Committee on Education. Senator LOURIE asked unanimous consent to make a motion to take the Concurrent Resolution up for immediate consideration. There was no objection. The Senate proceeded to a consideration of the Concurrent Resolution. The question then was the adoption of the Concurrent Resolution. On motion of Senator LOURIE, with unanimous consent, the Concurrent Resolution was adopted, ordered returned to the House. INTRODUCTION OF BILLS AND RESOLUTIONS The following were introduced: S. 1405 (Word version) -- Senator Coleman: A BILL TO PROVIDE FOR THE TRANSFER OF QUALIFYING STUDENTS FROM FAIRFIELD COUNTY SCHOOL DISTRICT TO CHESTER COUNTY SCHOOL DISTRICT; TO REQUIRE THE TREASURER OF FAIRFIELD COUNTY TO REMIT CERTAIN FUNDS PER TRANSFERRING PUPIL TO CHESTER COUNTY SCHOOL DISTRICT ON BEHALF OF FAIRFIELD COUNTY SCHOOL DISTRICT; TO PROVIDE FOR THE TIMING OF THE PAYMENT, AND TO REQUIRE THE STATE DEPARTMENT OF EDUCATION TO PAY THE AMOUNT DUE TO CHESTER COUNTY SCHOOL DISTRICT OUT OF FUNDS OTHERWISE ALLOCATED TO THE FAIRFIELD COUNTY SCHOOL DISTRICT PURSUANT TO THE EDUCATION FINANCE ACT IF THE TREASURER OF FAIRFIELD COUNTY FAILS TO PAY CHESTER COUNTY SCHOOL DISTRICT; TO ALLOW THE CHESTER COUNTY SCHOOL DISTRICT TO CONSIDER THESE PAYMENTS ANTICIPATED AD VALOREM TAXATION; TO REQUIRE THE STATE SUPERINTENDENT OF EDUCATION TO SETTLE ANY DISPUTE THAT ARISES BETWEEN THE DISTRICTS UPON THE IMPLEMENTATION AND ADMINISTRATION OF THE PROVISIONS OF THIS ACT; AND TO PROVIDE FOR THE PAYMENT OF MONIES PREVIOUSLY OWED TO CHESTER COUNTY SCHOOL DISTRICT. l:\council\bills\agm\19999bh10.docx Read the first time and referred to the Committee on Education. S. 1405--Recalled Senator COLEMAN asked unanimous consent to make a motion to recall the Bill from the Committee on Education. The Bill was recalled from the Committee on Education and ordered placed on the Calendar for consideration tomorrow. S. 1405--Ordered to a Second and Third Reading On motion of Senator COLEMAN, with unanimous consent, S. 1405 was ordered to receive a second and third reading on the next two consecutive legislative days. S. 1406 (Word version) -- Senator Fair: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING SECTION 63-1-60 SO AS TO ESTABLISH THE JOINT COUNCIL ON CHILDREN AND ADOLESCENTS, TO PROVIDE FOR ITS MEMBERS, POWERS, AND DUTIES, INCLUDING, BUT NOT LIMITED TO, PROMOTING AND FACILITATING ACTIVITIES TO IMPROVE ACCESS TO SERVICES FOR CHILDREN, ADOLESCENTS, AND THEIR FAMILIES, TO PROVIDE THAT CLIENT RECORDS ARE CONFIDENTIAL AND TO PROVIDE CIRCUMSTANCES UNDER WHICH RECORDS MAY BE RELEASED. l:\council\bills\nbd\12272ac10.docx Read the first time and referred to the Committee on Judiciary. S. 1407 (Word version) -- Senators Knotts, Alexander, Anderson, Bright, Bryant, Campbell, Campsen, Cleary, Coleman, Courson, Cromer, Davis, Elliott, Fair, Ford, Grooms, Hayes, Hutto, Jackson, Land, Leatherman, Leventis, Lourie, Malloy, L. Martin, S. Martin, Massey, Matthews, McConnell, McGill, Mulvaney, Nicholson, O'Dell, Peeler, Pinckney, Rankin, Reese, Rose, Ryberg, Scott, Setzler, Sheheen, Shoopman, Thomas, Verdin and Williams: A SENATE RESOLUTION TO CONGRATULATE MASTER CHIEF CHARLES N. MCKENZIE, UPON THE OCCASION OF HIS RETIREMENT FROM THE UNITED STATES NAVY, AND TO COMMEND HIM FOR MANY YEARS OF DEDICATED SERVICE TO OUR NATION, AND TO WISH HIM CONTINUED SUCCESS AND HAPPINESS IN ALL HIS FUTURE ENDEAVORS. l:\council\bills\gm\24496ab10.docx S. 1408 (Word version) -- Senator Coleman: A SENATE RESOLUTION TO RECOGNIZE AND CONGRATULATE WINNSBORO FIRST CHURCH OF THE NAZARENE ON THE OCCASION OF ITS SEVENTY-FIFTH ANNIVERSARY, AND TO COMMEND THE CHURCH FOR THREE QUARTERS OF A CENTURY'S SERVICE TO THE COMMUNITY. l:\council\bills\rm\1229bh10.docx S. 1409 (Word version) -- Senator S. Martin: A BILL TO AMEND SECTION 56-15-10 OF THE 1976 CODE, RELATING TO THE REGULATION OF MANUFACTURERS, DISTRIBUTORS, AND DEALERS OF MOTOR VEHICLES, TO PROVIDE THAT BUSINESSES WHICH OPERATE AS WHOLESALE MOTOR VEHICLE AUCTIONS ARE NOT MOTOR VEHICLE DEALERS. l:\s-res\srm\015car.ebd.srm.docx Read the first time and referred to the Committee on Transportation. S. 1410 (Word version) -- Senators Williams and Elliott: A SENATE RESOLUTION TO HONOR MR. BURNIE BELL, PRINCIPAL OF CREEK BRIDGE HIGH SCHOOL IN MARION, SOUTH CAROLINA, UPON THE OCCASION OF HIS RETIREMENT AND TO EXTEND BEST WISHES FOR MUCH SUCCESS AND HAPPINESS IN ALL HIS FUTURE ENDEAVORS. l:\s-res\kmw\007bell.mrh.kmw.docx H. 3748 (Word version) -- Reps. Duncan, Clemmons, Chalk and Erickson: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING SECTION 59-20-24 SO AS TO PROVIDE THAT THE VALUE OF OWNER OCCUPIED PROPERTY MUST BE INCLUDED IN THE CALCULATION OF THE INDEX OF TAXPAYING ABILITY UNTIL A PERMANENT CHANGE IN THE METHOD OF ITS CALCULATION IS ENACTED; AND TO CREATE THE INDEX OF TAXPAYING ABILITY STUDY COMMITTEE, TO PROVIDE FOR ITS MEMBERSHIP AND ITS PURPOSE, AND TO REQUIRE THE COMMITTEE TO REPORT ITS FINDINGS TO THE GENERAL ASSEMBLY BY JANUARY 10, 2010, UPON WHICH DATE THE COMMITTEE SHALL DISSOLVE. Read the first time and referred to the Committee on Finance. H. 3815 (Word version) -- Rep. Haley: A BILL TO AMEND SECTION 40-13-20, AS AMENDED, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE DEFINITION OF TERMS PERTAINING TO THE LICENSURE AND REGULATION OF COSMETOLOGISTS, SO AS TO SPECIFICALLY EXCLUDE FROM THE DEFINITION OF "SALON" A RENTAL BOOTH AND THE SPACE IN A SALON OCCUPIED BY AN INDEPENDENT CONTRACTOR; AND BY ADDING SECTION 40-13-255 SO AS TO PROVIDE THAT A PERSON PRACTICING UNDER AN INDIVIDUAL COSMETOLOGY LICENSE IN A BOOTH RENTAL OR AS AN INDEPENDENT CONTRACTOR MAY NOT BE CHARGED A LICENSURE OR LICENSURE RENEWAL FEE OTHER THAN THE FEE CHARGED FOR INDIVIDUAL LICENSURE OR LICENSURE RENEWAL. Read the first time and referred to the Committee on Labor, Commerce and Industry. H. 4049 (Word version) -- Reps. Nanney and Loftis: A BILL TO AMEND SECTION 29-3-330, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO ENTERING A SATISFACTION OF MORTGAGE IN THE PUBLIC RECORD, SO AS TO INCLUDE A PROBATE AND ACKNOWLEDGEMENT FORM IN THE SATISFACTION AFFIDAVIT. Read the first time and referred to the Committee on Banking and Insurance. H. 4215 (Word version) -- Reps. Harrison, McLeod and Weeks: A BILL TO AMEND SECTION 18-3-30, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE APPEAL OF A DECISION OF A MAGISTRATE, SO AS TO PROVIDE THAT AN APPELLANT MUST SERVE A NOTICE OF APPEAL OF A DECISION OF A MAGISTRATE UPON THE OFFICER OR ATTORNEY WHO PROSECUTED THE CASE IN ADDITION TO THE MAGISTRATE WHO TRIED THE CASE. Read the first time and referred to the Committee on Judiciary. H. 4243 (Word version) -- Reps. Owens, Harrell, Cato, Duncan, Harrison, Sandifer, Whitmire, Allison, Skelton, E. H. Pitts, Bowen, Wylie, Rice, G. R. Smith, Limehouse, Daning, Long, Littlejohn, Hutto, A. D. Young, Simrill, Loftis, Stewart, D. C. Smith, Bedingfield and Haley: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING SECTION 59-40-55 SO AS TO PROVIDE CHARTER SCHOOL POWERS AND DUTIES AND TO ALLOW A SPONSOR TO RETAIN CERTAIN FUNDS FOR OVERSEEING THE CHARTER SCHOOL; BY ADDING SECTION 59-40-175 SO AS TO CREATE THE CHARTER SCHOOL FACILITY REVOLVING LOAN PROGRAM; TO AMEND SECTION 59-40-20, AS AMENDED, RELATING TO THE PURPOSE OF THE CHARTER SCHOOL ACT, SO AS TO INCLUDE AN ADDITIONAL PURPOSE; TO AMEND SECTION 59-40-40, AS AMENDED, RELATING TO DEFINITIONS, SO AS TO AMEND EXISTING DEFINITIONS AND ADD NEW DEFINITIONS; TO AMEND SECTION 59-40-50, AS AMENDED, RELATING TO CHARTER SCHOOL POWERS AND DUTIES, SO AS TO PROVIDE FOR THE ELECTION OF A CHARTER SCHOOL BOARD OF DIRECTORS, ALLOW A CHARTER SCHOOL TO CONTRACT WITH PROVIDERS FOR STUDENT TRANSPORTATION, AND ALLOW CHARTER SCHOOL STUDENTS TO PARTICIPATE IN CERTAIN EXTRACURRICULAR ACTIVITIES UNDER CERTAIN CONDITIONS; TO AMEND SECTION 59-40-60, AS AMENDED, RELATING TO APPLICATION TO CREATE A CHARTER SCHOOL, SO AS TO CLARIFY WHAT MUST BE INCLUDED IN THE CONTRACT, TO REQUIRE THE DEPARTMENT OF EDUCATION TO CREATE A CONTRACT TEMPLATE; TO AMEND SECTION 59-40-70, AS AMENDED, RELATING TO THE CHARTER SCHOOL ADVISORY COMMITTEE, SO AS TO REVISE ITS MEMBERSHIP AND TO EXTEND THE TIME PERIOD IN WHICH THE COMMITTEE MUST DETERMINE APPLICATION COMPLIANCE; TO AMEND SECTION 59-40-100, AS AMENDED, RELATING TO CHARTER SCHOOL CONVERSION, SO AS TO ALLOW A CONVERTED CHARTER SCHOOL TO RETAIN FACILITIES AND EQUIPMENT AVAILABLE BEFORE CONVERSION; TO AMEND SECTION 59-40-110, RELATING TO THE DURATION OF A CHARTER, SO AS TO ALLOW A SPONSOR TO IMMEDIATELY REVOKE A CHARTER AND CLOSE THE SCHOOL UPON CERTAIN CONDITIONS; TO AMEND SECTION 59-40-140, AS AMENDED, RELATING TO DISTRIBUTION OF RESOURCES, SO AS TO PROVIDE FOR THE DISTRIBUTION OF FUNDS TO CHARTER SCHOOLS, TO REVISE WHAT THE SOUTH CAROLINA PUBLIC CHARTER SCHOOL DISTRICT SHALL RECEIVE, TO ALLOW THE DEPARTMENT OF EDUCATION TO FINE SPONSORS THAT FAIL TO DISTRIBUTE CERTAIN FUNDS TO CHARTER SCHOOLS, AND TO REVISE REPORTING REQUIREMENTS; TO AMEND SECTION 59-40-210, AS AMENDED, RELATING TO CONVERSION OF A PRIVATE SCHOOL TO A CHARTER SCHOOL, SO AS TO ALLOW A PRIVATE SCHOOL TO DISSOLVE AND IMMEDIATELY SEEK TO FORM A CHARTER SCHOOL; AND TO AMEND SECTION 59-40-230, RELATING TO THE BOARD OF TRUSTEES OF THE SOUTH CAROLINA PUBLIC CHARTER SCHOOL, SO AS TO REVISE ITS MEMBERSHIP. Read the first time and referred to the Committee on Education. H. 4350 (Word version) -- Reps. Limehouse, Sottile, Gilliard and Mack: A BILL TO AMEND SECTION 40-29-340, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO CRITERIA REQUIRED FOR A MANUFACTURED HOME, SO AS TO PROVIDE THAT FOR A SALE OF A PREVIOUSLY OWNED MANUFACTURED HOME, THE BUYER MUST CERTIFY HE HAS DETERMINED AT LEAST TWO FUNCTIONING SMOKE DETECTORS ARE IN THE HOME. Read the first time and referred to the Committee on Labor, Commerce and Industry. H. 4352 (Word version) -- Reps. Hodges and Dillard: A JOINT RESOLUTION TO ESTABLISH A STUDY COMMITTEE TO REVIEW, STUDY, AND MAKE RECOMMENDATIONS CONCERNING THE NEED TO FOSTER THE DEVELOPMENT OF MICROENTERPRISES IN THIS STATE, TO PROVIDE FOR THE STUDY COMMITTEE'S MEMBERSHIP, AND TO REQUIRE THE STUDY COMMITTEE TO REPORT ITS FINDINGS AND RECOMMENDATIONS TO THE GENERAL ASSEMBLY NO LATER THAN JANUARY 20, 2011, AT WHICH TIME THE STUDY COMMITTEE IS ABOLISHED. Read the first time and, on motion of Senator RYBERG, with unanimous consent, H. 4352 was ordered placed on the Calendar without reference. H. 4413 (Word version) -- Reps. Chalk, Gunn, Hardwick, Clemmons, Lowe, Crawford, Long, J. M. Neal, G. R. Smith, Harrison, A. D. Young, Horne, Brady, Erickson, Herbkersman, Millwood, Allison, Parker, Duncan, M. A. Pitts, Harvin, Williams, Neilson, Battle, Miller, Huggins, Spires, Willis, Hearn, Scott, Daning, J. E. Smith, Vick and H. B. Brown: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING CHAPTER 70 TO TITLE 44 TO ENACT THE "LICENSURE OF IN-HOME CARE PROVIDER ACT" SO AS TO REQUIRE A BUSINESS TO BE LICENSED TO PROVIDE, OR TO MAKE PROVISIONS FOR, IN-HOME CARE SERVICES THROUGH ITS EMPLOYEES OR AGENTS OR THROUGH CONTRACTUAL ARRANGEMENTS; TO PROVIDE THAT THE DEPARTMENT OF HEALTH AND ENVIRONMENTAL CONTROL SHALL PROMULGATE REGULATIONS FOR LICENSURE IN ACCORDANCE WITH REQUIREMENTS PROVIDED FOR IN THIS ACT, INCLUDING, BUT NOT LIMITED TO, CRIMINAL BACKGROUND CHECKS; TO REQUIRE CRIMINAL BACKGROUND CHECKS FOR IN-HOME CAREGIVERS EMPLOYED BY IN-HOME CARE PROVIDERS; AND TO PROVIDE THAT THE DEPARTMENT SHALL RETAIN ALL FEES COLLECTED PURSUANT TO THIS CHAPTER TO BE USED EXCLUSIVELY TO CARRY OUT THE DEPARTMENT'S RESPONSIBILITIES UNDER THIS CHAPTER. Read the first time and referred to the Committee on Medical Affairs. H. 4505 (Word version) -- Rep. Nanney: A BILL TO AMEND SECTION 14-1-214, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO PAYMENT OF FINES, FEES, AND COURT COSTS BY CREDIT OR DEBIT CARD, SO AS TO INCLUDE REGISTERS OF DEEDS IN THE LIST OF PERSONS ASSOCIATED WITH THE COURTS WHO MAY ACCEPT PAYMENT BY CREDIT OR DEBIT CARD. Read the first time and referred to the Committee on Judiciary. H. 4589 (Word version) -- Reps. Gambrell, D. C. Moss, Frye, V. S. Moss and White: A BILL TO AMEND SECTION 46-7-110, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO ANIMAL FACILITY WASTE MANAGEMENT TRAINING AND CERTIFICATION PROGRAMS, SO AS TO EXEMPT CATTLE STOCKYARD OWNERS AND OPERATORS AND CATTLE PRODUCERS FROM THESE TRAINING AND CERTIFICATION REQUIREMENTS. Read the first time and referred to the Committee on Agriculture and Natural Resources. Read the first time and referred to the Committee on Banking and Insurance. H. 4663 (Word version) -- Reps. Sandifer, Bales, Cato, McEachern, Hamilton, Loftis, G. R. Smith, Wylie, Stringer, Willis, Clemmons, Barfield, Ballentine, Whitmire, White, Toole, Huggins, Pinson, Gunn, Norman, Millwood, Simrill, Delleney, Owens, Bannister, Rice, Erickson, D. C. Moss, Stewart, Mitchell, Bowen, J. E. Smith, Dillard, Herbkersman, Chalk, Haley, Viers, Anderson, T. R. Young, Nanney and Vick: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING SECTION 6-9-55 SO AS TO PROVIDE THAT A BUILDING CODE PROVISION THAT REQUIRES AN AUTOMATIC RESIDENTIAL FIRE SPRINKLER SYSTEM BE INSTALLED IN A NEW ONE-FAMILY OR TWO-FAMILY DWELLING MAY NOT BE ENFORCED, TO PROVIDE CERTAIN PROSPECTIVE HOMEOWNERS MAY CHOOSE WHETHER TO HAVE AN AUTOMATIC SPRINKLER SYSTEM INSTALLED, TO MAKE THE INSTALLATION OF AN AUTOMATIC SPRINKLER SYSTEM APPROVED BY THE INTERNATIONAL RESIDENTIAL CODE AVAILABLE WHERE REQUIRED BY THAT CODE, AND TO PROVIDE WHERE THE PROVISIONS OF THIS SECTION CONTROL EVEN WHEN THEY CONFLICT WITH ANOTHER LAW OR LOCAL ORDINANCE. Read the first time and referred to the Committee on Labor, Commerce and Industry. H. 4838 (Word version) -- Rep. Cooper: A JOINT RESOLUTION TO PROVIDE THAT A LOCAL SCHOOL DISTRICT MAY PAY TEACHERS BASED ON THE EDUCATION LEVEL AND YEARS OF EXPERIENCE THE TEACHERS POSSESSED IN FISCAL YEAR 2009-2010 WITHOUT NEGATIVE IMPACT TO THEIR EXPERIENCE CREDIT; TO PROVIDE VOTING AND NOTICE REQUIREMENTS FOR THIS DECISION; TO REQUIRE THAT PAYMENT ACCORDING TO THE 2009-2010 DATA BE APPLIED UNIFORMLY; TO PROVIDE THAT A LOCAL SCHOOL DISTRICT MAY NOT PAY DISTRICT OR SCHOOL ADMINISTRATORS MORE THAN THEY RECEIVED IN FISCAL YEAR 2009-2010; AND TO DEFINE CERTAIN TERMS. Read the first time and referred to the Committee on Education. H. 4885 (Word version) -- Agriculture, Natural Resources and Environmental Affairs Committee: A JOINT RESOLUTION TO APPROVE REGULATIONS OF THE DEPARTMENT OF NATURAL RESOURCES, RELATING TO REGULATIONS OF REAL PROPERTY OWNED AND LEASED BY THE DEPARTMENT, DESIGNATED AS REGULATION DOCUMENT NUMBER 4110, PURSUANT TO THE PROVISIONS OF ARTICLE 1, CHAPTER 23, TITLE 1 OF THE 1976 CODE. Read the first time and referred to the Committee on Fish, Game and Forestry. H. 4887 (Word version) -- Rep. Stavrinakis: A JOINT RESOLUTION TO PROVIDE THAT THE SCHOOL DISTRICT OF CHARLESTON COUNTY FOR FISCAL YEARS 2010-2011 AND 2011-2012 MAY EXPEND FUNDS GENERATED FROM A GENERAL OBLIGATION DEBT BOND ISSUED FOR SCHOOL OPERATING PURPOSES, IN ORDER TO DEAL WITH A SHORTAGE OF SCHOOL OPERATING FUNDS, IF PERMITTED BY THE FEDERAL LAW APPLICABLE TO THE PARTICULAR TYPES OF BONDS ISSUED AND IF IT DOES NOT VIOLATE ANY PROVISIONS OF THE BOND INDENTURE APPLICABLE TO THE ISSUANCE AND SALE OF THOSE BONDS. Read the first time and ordered placed on the Local and Uncontested Calendar. H. 4912 (Word version) -- Rep. McLeod: A CONCURRENT RESOLUTION TO DESIGNATE THE MONTH OF MAY 2010 AS "MENTAL HEALTH MONTH" IN SOUTH CAROLINA AND TO ENCOURAGE COMMUNITY AWARENESS AND UNDERSTANDING OF MENTAL ILLNESS AND THE NEED FOR APPROPRIATE AND ACCESSIBLE SERVICES FOR ALL PEOPLE WITH MENTAL ILLNESS. The Concurrent Resolution was adopted, ordered returned to the House. H. 4913 (Word version) -- Rep. Clyburn: A CONCURRENT RESOLUTION TO RECOGNIZE AND CONGRATULATE FIRST PROVIDENCE CHURCH OF NORTH AUGUSTA ON THE OCCASION OF ITS HISTORIC ONE HUNDRED FIFTIETH ANNIVERSARY, AND TO COMMEND THE CHURCH FOR A CENTURY AND A HALF OF SERVICE TO GOD AND THE COMMUNITY. The Concurrent Resolution was adopted, ordered returned to the House. H. 4914 (Word version) -- Reps. Haley, Agnew, Alexander, Allen, Allison, Anderson, Anthony, Bales, Ballentine, Bannister, Barfield, Battle, Bedingfield, Bingham, Bowen, Bowers, Brady, Branham, Brantley, G. A. Brown, H. B. Brown, R. L. Brown, Cato, Chalk, Clemmons, Clyburn, Cobb-Hunter, Cole, Cooper, Crawford, Daning, Delleney, Dillard, Duncan, Edge, Erickson, Forrester, Frye, Funderburk, Gambrell, Gilliard, Govan, Gunn, Hamilton, Hardwick, Harrell, Harrison, Hart, Harvin, Hayes, Hearn, Herbkersman, Hiott, Hodges, Horne, Hosey, Howard, Huggins, Hutto, Jefferson, Jennings, Kelly, Kennedy, King, Kirsh, Knight, Limehouse, Littlejohn, Loftis, Long, Lowe, Lucas, Mack, McEachern, McLeod, Merrill, Miller, Millwood, Mitchell, D. C. Moss, V. S. Moss, Nanney, J. H. Neal, J. M. Neal, Neilson, Norman, Ott, Owens, Parker, Parks, Pinson, E. H. Pitts, M. A. Pitts, Rice, Rutherford, Sandifer, Scott, Sellers, Simrill, Skelton, D. C. Smith, G. M. Smith, G. R. Smith, J. E. Smith, J. R. Smith, Sottile, Spires, Stavrinakis, Stewart, Stringer, Thompson, Toole, Umphlett, Vick, Viers, Weeks, Whipper, White, Whitmire, Williams, Willis, Wylie, A. D. Young and T. R. Young: A CONCURRENT RESOLUTION TO RECOGNIZE AND COMMEND THE LEXINGTON HIGH SCHOOL GIRLS GOLF TEAM FOR CAPTURING THE 2009 CLASS AAAA STATE CHAMPIONSHIP TITLE, AND TO HONOR THE TEAM'S SUPERLATIVE PLAYERS, COACHES, AND STAFF. The Concurrent Resolution was adopted, ordered returned to the House. H. 4924 (Word version) -- Reps. Edge, Crawford, Agnew, Alexander, Allen, Allison, Anderson, Anthony, Bales, Ballentine, Bannister, Barfield, Battle, Bedingfield, Bingham, Bowen, Bowers, Brady, Branham, Brantley, G. A. Brown, H. B. Brown, R. L. Brown, Cato, Chalk, Clemmons, Clyburn, Cobb-Hunter, Cole, Cooper, Daning, Delleney, Dillard, Duncan, Erickson, Forrester, Frye, Funderburk, Gambrell, Gilliard, Govan, Gunn, Haley, Hamilton, Hardwick, Harrell, Harrison, Hart, Harvin, Hayes, Hearn, Herbkersman, Hiott, Hodges, Horne, Hosey, Howard, Huggins, Hutto, Jefferson, Jennings, Kelly, Kennedy, King, Kirsh, Knight, Limehouse, Littlejohn, Loftis, Long, Lowe, Lucas, Mack, McEachern, McLeod, Merrill, Miller, Millwood, Mitchell, D. C. Moss, V. S. Moss, Nanney, J. H. Neal, J. M. Neal, Neilson, Norman, Ott, Owens, Parker, Parks, Pinson, E. H. Pitts, M. A. Pitts, Rice, Rutherford, Sandifer, Scott, Sellers, Simrill, Skelton, D. C. Smith, G. M. Smith, G. R. Smith, J. E. Smith, J. R. Smith, Sottile, Spires, Stavrinakis, Stewart, Stringer, Thompson, Toole, Umphlett, Vick, Viers, Weeks, Whipper, White, Whitmire, Williams, Willis, Wylie, A. D. Young and T. R. Young: A CONCURRENT RESOLUTION TO DESIGNATE MAY 5, 2010, AS "SOUTH CAROLINA CLEAN HANDS DAY", AND TO ENCOURAGE ALL SOUTH CAROLINIANS TO RECOGNIZE DAILY THE IMPORTANCE OF PROPER HAND HYGIENE TO REDUCE AND PREVENT THE SPREAD OF INFECTIONS AND TO DISCUSS PROPER HAND HYGIENE WITH FAMILIES, FRIENDS, AND HEALTH CARE PROVIDERS. The Concurrent Resolution was adopted, ordered returned to the House. Message from the House Columbia, S.C., April 28, 2010 Mr. President and Senators: The House respectfully informs your Honorable Body that it has reconsidered the vote whereby the House sustained the veto and has overridden the veto by the Governor on R. 140, S. 191 by a vote of 74 to 37: (R140, S191 (Word version)) -- Senators McConnell, Malloy, Campsen, Sheheen, Rose, Campbell and Knotts: AN ACT TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ENACTING THE "SOUTH CAROLINA REDUCTION OF RECIDIVISM ACT OF 2010" SO AS TO PROVIDE LAW ENFORCEMENT OFFICERS WITH THE STATUTORY AUTHORITY TO REDUCE RECIDIVISM RATES, APPREHEND CRIMINALS AND PROTECT POTENTIAL VICTIMS FROM CRIMINAL ENTERPRISES BY AUTHORIZING WARRANTLESS SEARCHES AND SEIZURES OF PROBATIONERS AND PAROLEES; TO AMEND SECTION 63-19-1820, RELATING TO THE BOARD OF JUVENILE PAROLE, SO AS TO PROVIDE THAT BEFORE A JUVENILE MAY BE CONDITIONALLY RELEASED, THE JUVENILE MUST AGREE TO BE SUBJECT TO SEARCH OR SEIZURE WITH OR WITHOUT A SEARCH WARRANT AND WITH OR WITHOUT CAUSE; TO AMEND SECTION 63-19-1850, RELATING TO CONDITIONAL RELEASE, SO AS TO PROVIDE THAT BEFORE A JUVENILE MAY BE CONDITIONALLY RELEASED, THE JUVENILE MUST AGREE TO BE SUBJECT TO SEARCH OR SEIZURE WITH OR WITHOUT A SEARCH WARRANT AND WITH OR WITHOUT CAUSE; TO AMEND SECTION 24-19-110, RELATING TO THE PROCEDURE FOR CONDITIONAL RELEASE OF YOUTHFUL OFFENDERS, SO AS TO PROVIDE THAT BEFORE A YOUTHFUL OFFENDER MAY BE CONDITIONALLY RELEASED, THE YOUTHFUL OFFENDER MUST AGREE TO BE SUBJECT TO SEARCH OR SEIZURE WITH OR WITHOUT A SEARCH WARRANT AND WITH OR WITHOUT CAUSE; TO AMEND SECTION 24-13-710, RELATING TO THE GUIDELINES, ELIGIBILITY CRITERIA, AND IMPLEMENTATION OF A SUPERVISED FURLOUGH PROGRAM, SO AS TO PROVIDE THAT BEFORE AN INMATE MAY BE RELEASED ON SUPERVISED FURLOUGH, THE INMATE MUST AGREE TO BE SUBJECT TO SEARCH OR SEIZURE WITH OR WITHOUT A SEARCH WARRANT AND WITH OR WITHOUT CAUSE; TO AMEND SECTION 24-13-720, RELATING TO INMATES WHO MAY BE PLACED WITHIN CERTAIN PROGRAMS, SO AS TO PROVIDE THAT BEFORE AN INMATE MAY BE RELEASED ON SUPERVISED FURLOUGH, THE INMATE MUST AGREE TO BE SUBJECT TO SEARCH OR SEIZURE WITH OR WITHOUT A SEARCH WARRANT AND WITH OR WITHOUT CAUSE; TO AMEND SECTION 24-13-1330, RELATING TO AN ELIGIBLE INMATE'S AGREEMENT TO TERMS AND CONDITIONS, SO AS TO PROVIDE THAT BEFORE AN INMATE MAY BE RELEASED ON PAROLE, THE INMATE MUST AGREE TO BE SUBJECT TO SEARCH OR SEIZURE WITH OR WITHOUT A SEARCH WARRANT AND WITH OR WITHOUT CAUSE; TO AMEND SECTION 24-21-410, RELATING TO THE COURT BEING AUTHORIZED TO SUSPEND IMPOSITION OF SENTENCE FOR PROBATION AFTER CONVICTION, SO AS TO PROVIDE THAT BEFORE A DEFENDANT MAY BE PLACED ON PROBATION, THE DEFENDANT MUST AGREE TO BE SUBJECT TO SEARCH OR SEIZURE WITH OR WITHOUT A SEARCH WARRANT BASED ON REASONABLE SUSPICIONS; TO AMEND SECTION 24-21-430, RELATING TO THE CONDITIONS OF PROBATION, SO AS TO PROVIDE THAT THE CONDITIONS IMPOSED MUST INCLUDE THE REQUIREMENT THAT THE PROBATIONER MUST PERMIT SEARCH OR SEIZURE WITH OR WITHOUT A SEARCH WARRANT BASED ON REASONABLE SUSPICIONS; TO AMEND SECTION 24-21-560, RELATING TO COMMUNITY SUPERVISION PROGRAMS, SO AS TO PROVIDE THAT THE CONDITIONS OF PARTICIPATION MUST INCLUDE THE REQUIREMENT THAT THE OFFENDER MUST PERMIT SEARCH OR SEIZURE WITH OR WITHOUT A SEARCH WARRANT; TO AMEND SECTION 24-21-640, RELATING TO THE CIRCUMSTANCES WARRANTING PAROLE, SO AS TO PROVIDE THAT BEFORE AN INMATE MAY BE RELEASED ON PAROLE, THE INMATE MUST AGREE TO SEARCH AND SEIZURE WITH OR WITHOUT A SEARCH WARRANT AND WITH OR WITHOUT CAUSE; AND TO AMEND SECTION 24-21-645, RELATING TO THE ORDER AUTHORIZING PAROLE, SO AS TO PROVIDE THAT THE CONDITIONS OF PAROLE MUST INCLUDE THE REQUIREMENT THAT THE PAROLEE MUST PERMIT SEARCH OR SEIZURE WITH OR WITHOUT A SEARCH WARRANT AND WITH OR WITHOUT CAUSE. Very respectfully, Speaker of the House Message from the House Columbia, S.C., April 29, 2010 Mr. President and Senators: The House respectfully informs your Honorable Body that it has appointed Reps. Frye, Vick and D. Moss to the Committee of Conference on the part of the House on: S. 328 (Word version) -- Senators Verdin, Grooms, Campbell, Bright, Bryant and Campsen: A BILL TO AMEND SECTION 47-5-60 OF THE 1976 CODE, RELATING TO INOCULATING PETS AGAINST RABIES, SO AS TO PROVIDE THAT THESE INOCULATIONS MUST BE ADMINISTERED BY A LICENSED VETERINARIAN OR SOMEONE UNDER THE DIRECT SUPERVISION OF A LICENSED VETERINARIAN. Very respectfully, Speaker of the House HOUSE CONCURRENCE S. 1401 (Word version) -- Senators Anderson, Reese, Peeler, Scott, Malloy, Leatherman, Ryberg, Ford, Nicholson, Elliott, Setzler, Land, Williams, Jackson, Leventis, L. Martin, Hayes, Cromer, McGill, Rankin, Alexander and Coleman: A CONCURRENT RESOLUTION TO DESIGNATE MAY 5, 2010, AS "SOUTH CAROLINA CLEAN HANDS DAY", AND TO ENCOURAGE ALL SOUTH CAROLINIANS TO RECOGNIZE DAILY THE IMPORTANCE OF PROPER HAND HYGIENE TO REDUCE AND PREVENT THE SPREAD OF INFECTIONS AND TO DISCUSS PROPER HAND HYGIENE WITH FAMILIES, FRIENDS, AND HEALTH CARE PROVIDERS. Returned with concurrence. S. 1402 (Word version) -- Senator Verdin: A CONCURRENT RESOLUTION TO RECOGNIZE AND HONOR DR. PEGGY C. PRESCOTT UPON THE OCCASION OF HER RETIREMENT FROM PIEDMONT TECHNICAL COLLEGE, AND TO WISH HER MUCH HAPPINESS IN ALL HER FUTURE ENDEAVORS. Returned with concurrence. THE SENATE PROCEEDED TO A CALL OF THE UNCONTESTED LOCAL AND STATEWIDE CALENDAR. The following Bills were read the third time and ordered sent to the House of Representatives: S. 1296 (Word version) -- Senator S. Martin: A BILL TO AMEND SECTION 50-11-710 OF THE 1976 CODE, RELATING TO NIGHT HUNTING, TO PROVIDE THAT COYOTES MAY BE HUNTED AT NIGHT, TO PROVIDE EXCEPTIONS, AND TO PROVIDE PENALTIES. S. 1296--Recorded Vote Senators RYBERG and BRYANT desired to be recorded as voting in favor of the third reading of the Bill. S. 1051 (Word version) -- Senator Davis: A BILL TO AMEND SECTION 48-39-290, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO RESTRICTIONS, EXCEPTIONS, AND SPECIAL PERMITS CONCERNING CONSTRUCTION AND RECONSTRUCTION SEAWARD OF THE BASELINE OR BETWEEN THE BASELINE AND THE SET BACK LINE, SO AS TO REVISE THE DESCRIPTION OF A PRIVATE ISLAND WITH AN ATLANTIC SHORELINE THAT IS EXEMPT FROM THE PROVISIONS OF THIS SECTION AND THE FORTY-YEAR RETREAT POLICY. S. 1051--Recorded Vote Senators RYBERG and BRYANT desired to be recorded as voting in favor of the third reading of the Bill. S. 1025 (Word version) -- Senator Cromer: A BILL TO AMEND SECTION 38-73-737 OF THE 1976 CODE, RELATING TO DRIVER TRAINING COURSE CREDIT TOWARD LIABILITY AND COLLISION INSURANCE COVERAGE, TO REDUCE THE INITIAL COURSE FROM EIGHT TO SIX HOURS, TO ALLOW FOR A FOUR HOUR REFRESHER COURSE EVERY THREE YEARS, AND TO ALLOW THE DEPARTMENT OF INSURANCE TO PROMULGATE REGULATIONS FOR FIFTY-FIVE YEARS AND OLDER DRIVER SAFETY INTERNET COURSES. S. 1025--Recorded Vote Senators RYBERG and BRYANT desired to be recorded as voting in favor of the third reading of the Bill. S. 1088 (Word version) -- Senators Matthews, O'Dell, Jackson and Hutto: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING SECTION 40-43-70 SO AS TO DEFINE CERTAIN TERMS, AND TO PROVIDE FOR THE DISPENSING OF CERTAIN DRUGS OR DEVICES AT A FEDERALLY QUALIFIED HEALTH CENTER. Motion Under Rule 26B Senator HUTTO asked unanimous consent to make a motion to take up further amendments pursuant to the provisions of Rule 26B. There was no objection. Senator CROMER proposed the following amendment (DKA\4002AB10), which was adopted: Amend the bill, as and if amended, by deleting all after the enacting words and inserting: / SECTION 1. Chapter 43, Title 40 of the 1976 Code is amended by adding: "Section 40-43-70. (A) For purposes of this section: (1) 'Federally qualified health center' or 'FQHC' means an entity funded by the Bureau of Primary Health Care (BPHC) under Section 330 of the Public Health Service Act as amended by the Health Centers Consolidation Act of 1996. (2) 'Health center delivery site' means a physical location where a licensed practitioner duly employed by or under contract with an FQHC provides primary and preventative health care services to patients of that FQHC. An FQHC may have multiple health center delivery sites. (3) 'Board' means the South Carolina Board of Pharmacy. (B) This section does not prevent a licensed practitioner, as defined in Section 40-43-30(45), from dispensing a drug or device for a patient of a FQHC if: (1) a drug dispensed by the FQHC is properly labeled in accordance with state and federal law; (2) the patient is given a choice of receiving the drug or device from the FQHC or from another provider; (3) as it pertains to an FQHC without a retail pharmacy, the FQHC must obtain and maintain an FQHC permit as designated by this section; and (a) monthly shall conduct and submit to the Board of Pharmacy self inspections and maintain written checklists that are readily available to the Board of Pharmacy for on-site visits; and (b) designate a pharmacist duly licensed by and in good standing with the Board of Pharmacy as a consultant pharmacist to be responsible for the duties stated in this section at the FQHC permit holder's location. A consultant pharmacist shall sign a new or renewal application along with the FQHC permit holder and agree in writing to assume the responsibilities of a consultant pharmacist. The consultant pharmacist shall perform and maintain written quarterly inspections that are readily available. The FQHC permit holder and consultant pharmacist shall notify the board in writing within ten days of a change of consultant pharmacist. A designation of an individual as a consultant pharmacist or delegation of duties to a consultant pharmacist by a holder of a FQHC permit may not relieve the permit holder of the FQHC permit holder's duties under state or federal laws or regulations; (4) as it pertains to a health center delivery site established after January 1, 2011 by an FQHC without a retail pharmacy, as a condition of permitting by the Board pursuant to section 40-43-70(B)(2), this FQHC must certify to the Board that it made a good faith effort but was unable to reach an agreement with an existing retail pharmacy located within five miles of the FQHC health center delivery site pursuant to which the existing retail pharmacy would provide prescription drugs to all FQHC patients at the same cost, convenience, and efficacy provided by the proposed new FQHC health center delivery site; (5) as it pertains to an FQHC with a permitted retail pharmacy: (a) the FQHC's retail pharmacy must be permitted pursuant to Section 40-43-83; (b) the FQHC must obtain and maintain a FQHC permit for its affiliated health center delivery sites without an on-site pharmacy; and (i) those affiliated delivery sites will be subject to the inspection requirements outlined in item (3) of this subsection; and (ii) the FQHC pharmacist may serve as the consultant pharmacist for the FQHC's affiliated delivery sites. (c) with prior approval of the Board of Pharmacy, the FQHC pharmacist may serve as the pharmacist in charge for more than one pharmacy at a time and need not be physically present in the pharmacy to serve as its pharmacist in charge. (C) The Board of Pharmacy shall issue rules and promulgate regulations needed to effectuate the purposes of this section." SECTION 2. This act takes effect upon approval by the Governor. / Renumber sections to conform. Amend title to conform. Senator HUTTO explained the amendment. There being no further amendments, the Bill was read the third time, passed and ordered sent to the House of Representatives with amendments. S. 1148 (Word version) -- Senator Cleary: A BILL TO AMEND CHAPTER 65, TITLE 40, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE LICENSURE AND REGULATION OF PROFESSIONAL SOIL CLASSIFIERS, SO AS TO CONFORM THIS CHAPTER TO THE ORGANIZATIONAL STATUTORY FRAMEWORK ESTABLISHED FOR PROFESSIONS AND OCCUPATIONS UNDER THE ADMINISTRATION OF THE DEPARTMENT OF LABOR, LICENSING AND REGULATION; TO PROVIDE THAT PERSONS ENGAGING IN PROFESSIONAL SOIL CLASSIFICATION MUST BE LICENSED, RATHER THAN REGISTERED; TO REVISE QUALIFICATIONS FOR LICENSURE; TO PROVIDE GRANDFATHERING PROVISIONS FOR REGISTERED PROFESSIONAL SOIL CLASSIFIERS TO BECOME LICENSED PROFESSIONAL SOIL CLASSIFIERS UPON THE NEXT RENEWAL OF THE PERSON'S REGISTRATION; AND TO FURTHER PROVIDE FOR THE LICENSURE AND REGULATION OF PROFESSIONAL SOIL CLASSIFIERS. The Senate proceeded to a consideration of the Bill, the question being the third reading of the Bill. Motion Under Rule 26B Senator LEVENTIS asked unanimous consent to make a motion to take up further amendments pursuant to the provisions of Rule 26B. There was no objection. Senator LEVENTIS proposed the following amendment (1148R005.PPL), which was adopted: Amend the bill, as and if amended, page 15, on line 16 by inserting: / Section 40-65-45. An applicant otherwise qualified shall be admitted to registration as a professional soil classifier without examination if he holds a certificate of registration in the practice of soil classifying awarded on the basis of comparable qualifications and issued to him by a proper authority of another state, possession, or territory of the United States and who in the opinion of the department meets the requirements of this chapter. / Renumber sections to conform. Amend title to conform. Senator LEVENTIS explained the amendment. There being no further amendments, the Bill was read the third time, passed and ordered sent to the House of Representatives with amendments. S. 1148--Recorded Vote Senators RYBERG and BRYANT desired to be recorded as voting in favor of the third reading of the Bill. S. 1367 (Word version) -- Senator Cromer: A BILL TO AMEND SECTION 50-23-295, AS AMENDED, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO TRANSFER OF TITLE TO WATERCRAFT OR OUTBOARD MOTOR ON WHICH PROPERTY TAXES ARE OWED, SO AS TO REMOVE THE PENALTY IMPOSED FOR SELLING A WATERCRAFT WITH PERSONAL PROPERTY TAXES OWED AND TO ADD PROVISIONS REGARDING CIVIL ACTIONS AGAINST SELLERS FOR SELLING A WATERCRAFT OR OUTBOARD MOTOR WITH TAXES OWED. The Senate proceeded to a consideration of the Bill, the question being the third reading of the Bill. Motion Under Rule 26B Senator CROMER asked unanimous consent to make a motion to take up further amendments pursuant to the provisions of Rule 26B. There was no objection. Senators KNOTTS and CROMER proposed the following amendment (1367R003.JMK), which was adopted: Amend the bill, as and if amended, page 1, by striking lines 28-36 and inserting: / "(B) A person who knowingly sells a watercraft on which he owes unpaid and outstanding property taxes, or on which he knows there is a property tax lien, is guilty of a misdemeanor and, upon conviction, must be fined not more than one thousand dollars or imprisoned not more than thirty days. In addition to any applicable criminal penalties, falsely signing such a certification subjects the person signing the certification to a fee of five hundred dollars and suspension of any title issued in the applicant's name by the department. The title can be reinstated upon proof to the department of payment of all taxes due and payment of the five-hundred-dollar fee to the department a seller who falsely signs the certification required by subsection (A) that property taxes are current and paid on a watercraft transferred to the buyer is liable to the buyer for three times the amount of damages directly associated with the false certification, as well as applicable costs and reasonable attorney's fees." / Renumber sections to conform. Amend title to conform. Senator CROMER explained the amendment. There being no further amendments, the Bill was read the third time, passed and ordered sent to the House of Representatives with amendments. S. 1367--Recorded Vote Senators RYBERG and BRYANT desired to be recorded as voting in favor of the third reading of the Bill. The following Bills, having been read the second time, were ordered placed on the Third Reading Calendar: S. 1323 (Word version) -- Senators Matthews, Elliott, Malloy, Leventis, Leatherman, Land, McGill and Williams: A BILL TO AMEND TITLE 11 OF THE 1976 CODE, RELATING TO PUBLIC FINANCE, BY ADDING CHAPTER 54 TO ESTABLISH THE "I-95 CORRIDOR AUTHORITY ACT" AND TO PROVIDE FOR THE COMPOSITION, DUTIES, AND POWERS OF THE AUTHORITY. Senator LAND asked unanimous consent to take the Bill up for immediate consideration. There was no objection. The Bill was read the second time, passed and ordered to a third reading. S. 1323--Recorded Vote Senator DAVIS desired to be recorded as voting against the second reading of the Bill. S. 1323--Ordered to a Third Reading On motion of Senator LAND, with unanimous consent, S. 1323, was ordered to receive a third reading on Friday, April 30, 2010. H. 4343 (Word version) -- Reps. Wylie, Harrell, Cooper, Stringer, Merrill, Allen, Allison, Ballentine, Bannister, Bedingfield, Bowen, Cato, Cole, Daning, Dillard, Erickson, Forrester, Gunn, Hamilton, Hardwick, Hearn, Hiott, Horne, Huggins, Kelly, Kirsh, Littlejohn, Loftis, Millwood, Mitchell, Nanney, Norman, Owens, Parker, Scott, G.R. Smith, Sottile, Umphlett, White, Willis, T.R. Young, Lucas, Neilson, Bales, Clemmons, Weeks, Stavrinakis, Hutto and Viers: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING CHAPTER 19 TO TITLE 55 SO AS TO ESTABLISH THE SOUTH CAROLINA AIR SERVICE INCENTIVE AND DEVELOPMENT FUND UNDER THE SOUTH CAROLINA AERONAUTICS COMMISSION TO PROVIDE GRANTS TO REGIONAL ECONOMIC DEVELOPMENT ENTITIES OR AIR SERVICE DEVELOPMENT TASK FORCES TO PROVIDE MORE FLIGHT OPTIONS, MORE COMPETITION FOR AIR TRAVEL AND MORE AFFORDABLE AIR FARES FOR THE CITIZENS OF THE REGION AND THIS STATE, AND TO PROVIDE THE SELECTION CRITERIA AND SELECTION PROCESS FOR THESE GRANTS TO BE MADE FROM FUNDS PROVIDED TO OR APPROPRIATED FOR THE FUND BY THE GENERAL ASSEMBLY. Senator GROOMS asked unanimous consent to take the Bill up for immediate consideration. There was no objection. The Senate proceeded to a consideration of the Bill, the question being the second reading of the Bill. Senator GROOMS asked unanimous consent to give the Bill a second reading, carrying over all amendments on third reading. There was no objection. The Bill was given a second reading and placed on the third reading Calendar. S. 958 (Word version) -- Senators Knotts, Davis and Rose: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING SECTION 47-1-45 SO AS TO MAKE IT UNLAWFUL TO KNOWINGLY OR INTENTIONALLY CONFINE OR RESTRAIN AN ANIMAL IN A CRUEL MANNER OR KNOWINGLY OR INTENTIONALLY CAUSE SUCH CRUEL CONFINEMENT OR RESTRAINING OF AN ANIMAL, TO DEFINE CERTAIN TERMS IN REGARD TO THE ABOVE, TO PROVIDE PENALTIES FOR VIOLATION, AND TO PROVIDE THAT LOCAL GOVERNMENTS MAY ADOPT MORE STRINGENT LOCAL ORDINANCES GOVERNING THE CONFINEMENT OR RESTRAINING OF AN ANIMAL WITH CIVIL PENALTIES FOR VIOLATIONS. The Senate proceeded to a consideration of the Bill, the question being the adoption of the amendment proposed by the Committee on Agriculture and Natural Resources. The Committee on Agriculture and Natural Resources proposed the following amendment (958R001.DBV), which was adopted: Amend the bill, as and if amended, page 3, by striking lines 20 - 23 and inserting: / (E) It is the intent of the General Assembly to occupy the field of regulation of cruel restraint of animals. All local laws and ordinances related to the regulation of cruel restraint of animals in this State are preempted and superseded by laws enacted by the General Assembly and regulations promulgated by state agencies pursuant to those laws." Renumber sections to conform. Amend title to conform. There being no further amendments, the Bill was read the second time, passed and ordered to a third reading. S. 958--Ordered to a Third Reading On motion of Senator VERDIN, with unanimous consent, S. 958 was ordered to receive a third reading on Friday, April 30, 2010. S. 1390 (Word version) -- Senator Peeler: A BILL TO AMEND SECTION 8-13-1308, RELATING TO INFORMATION REGARDING EXPENDITURES THAT MUST BE CONTAINED IN A CERTIFIED CAMPAIGN REPORT, TO DELETE A REFERENCE TO CAMPAIGN FUNDS AND REQUIRE THAT ALL EXPENDITURES BE LISTED IN THE REPORT. Senator PEELER asked unanimous consent to take the Bill up for immediate consideration. There was no objection. The Senate proceeded to a consideration of the Bill, the question being the second reading of the Bill. Senators HUTTO, ALEXANDER, ANDERSON, BRIGHT, BRYANT, CAMPBELL, CAMPSEN, CLEARY, COLEMAN, COURSON, CROMER, DAVIS, ELLIOTT, FAIR, FORD, GROOMS, HAYES, JACKSON, KNOTTS, LAND, LEATHERMAN, LEVENTIS, LOURIE, MALLOY, LARRY MARTIN, SHANE MARTIN, MASSEY, MATTHEWS, McCONNELL, MCGILL, MULVANEY, NICHOLSON, O'DELL, PEELER, PINCKNEY, RANKIN, REESE, ROSE, RYBERG, SCOTT, SETZLER, SHEHEEN, SHOOPMAN, THOMAS, VERDIN and WILLIAMS proposed the following amendment (JUD1390.001), which was adopted: Amend the bill, as and if amended, by striking SECTION 2 and inserting: SECTION 2. The 1976 Code is amended by adding: "Section 8-13-1339. A political action committee organized by or on behalf of the Governor, the Lieutenant Governor, any other statewide constitutional officer, a member of the General Assembly, a director or deputy director of a state department appointed by the Governor is prohibited. Any political action committee prohibited by this section in existence on the effective date of this act must distribute all unexpended contributions in the manner provided for in Section 8-13-1370(C). A political action committee does not include a candidate committee." SECTION 3. Section 8-13-1340 of the 1976 Code is amended to read: "Section 8-13-1340. (A) Except as provided in subsections subsection (B) and (E), a candidate or public official shall not make a contribution to another candidate or make an independent expenditure on behalf of another candidate or public official from the candidate's or public official's campaign account or through a committee, except legislative caucus committees, directly or indirectly established, financed, maintained, or controlled by the candidate or public official. (B) This section does not prohibit a candidate from: (1) making a contribution from the candidate's own personal funds on behalf of the candidate's candidacy or to another candidate for a different office; or (2) providing the candidate's surplus funds or material assets upon final disbursement to a legislative caucus committee or party committee in accordance with the procedures for the final disbursement of a candidate under Section 8-13-1370 of this article. (C) Assets or funds which are the proceeds of a campaign contribution and which are held by or under the control of a public official or a candidate for public office on January 1, 1992, are considered to be funds held by a candidate and subject to subsection (A). (D) A committee is considered to be directly or indirectly established, financed, maintained, or controlled by a candidate or public official if any of the following are applicable: (1) the candidate or public official, or an agent of either, has signature authority on the committee's checks; (2) funds contributed or disbursed by the committee are authorized or approved by the candidate or public official; (3) the candidate or public official is clearly identified on either the stationery or letterhead of the committee; (4) the candidate or public official signs solicitation letters or other correspondence on behalf of the entity; (5) the candidate, public official, or his campaign staff, office staff, or immediate family members, or any other agent of either, has the authority to approve, alter, or veto the committee's solicitations, contributions, donations, disbursements, or contracts to make disbursements; or (6) the committee pays for travel by the candidate or public official, his campaign staff or office staff, or any other agent of the candidate or public official, in excess of one hundred dollars per calendar year. (E) The provisions of subsection (A) do not apply to a committee directly or indirectly established, financed, maintained, or controlled by a candidate or public official if the candidate or public official directly or indirectly establishes, finances, maintains, or controls only one committee in addition to any committee formed by the candidate or public official to solely promote his own candidacy and one legislative caucus committee. (F) No committee operating under the provisions of Section 8-13-1340(E) may: (1) solicit or accept a contribution from a registered lobbyist if that lobbyist engages in lobbying the public office or public body for which the candidate is seeking election; or (2) transfer anything of value to any other committee except as a contribution under the limitations of Section 8-13-1314(A) or the dissolution provisions of Section 8-13-1370." SECTION 4. This act takes effect upon approval by the Governor. Renumber sections to conform. Amend title to conform. Senator HUTTO explained the amendment. The question then was the second reading of the Bill. The "ayes" and "nays" were demanded and taken, resulting as follows: Ayes 46; Nays 0 AYES Alexander Anderson Bright Bryant Campbell Campsen Cleary Coleman Courson Cromer Davis Elliott Fair Ford Grooms Hayes Hutto Jackson Knotts Land Leatherman Leventis Lourie Malloy Martin, Larry Martin, Shane Massey Matthews McConnell McGill Mulvaney Nicholson O'Dell Peeler Pinckney Rankin Reese Rose Ryberg Scott Setzler Sheheen Shoopman Thomas Verdin Williams Total--46 NAYS Total--0 The Bill was read the second time, passed and ordered to a third reading. S. 1390--Ordered to a Third Reading On motion of Senator PEELER, with unanimous consent, S. 1390 was ordered to receive a third reading on Friday, April 30, 2010. S. 1392 (Word version) -- Transportation Committee: A BILL TO AMEND CHAPTER 3, TITLE 56 OF THE 1976 CODE, RELATING TO MOTOR VEHICLE REGISTRATION AND LICENSING, TO PROVIDE FOR CERTAIN SPECIALTY LICENSE PLATES; TO AMEND SECTION 56-3-10810, RELATING TO 'BOY SCOUTS OF AMERICA' SPECIAL LICENSE PLATES, TO PROVIDE FOR 'EAGLE SCOUT' SPECIAL LICENSE PLATES; TO AMEND SECTION 56-3-2150, RELATING TO SPECIAL LICENSE PLATES FOR CERTAIN ELECTED OFFICIALS, TO PROVIDE THAT CORONERS MAY BE PROVIDED WITH TWO LICENSE PLATES; TO AMEND SECTION 56-3-1240, RELATING TO THE LOCATION ON VEHICLES WHERE LICENSE PLATES MUST BE ATTACHED, TO PROVIDE THAT A FRAME MAY BE PLACED AROUND A LICENSE PLATE UNDER CERTAIN CIRCUMSTANCES; AND TO AMEND SECTION 56-3-10410, RELATING TO A SPECIAL MOTOR VEHICLE LICENSE PLATE FOR VETERANS, TO PROVIDE FOR A DISABLED VETERAN SPECIAL LICENSE PLATE. Senator SCOTT asked unanimous consent to take the Bill up for immediate consideration. There was no objection. The Senate proceeded to a consideration of the Bill, the question being the second reading of the Bill. Senator LARRY MARTIN explained the Bill. Senator VERDIN proposed the following amendment (1392R002.DBV), which was adopted: Amend the bill, as and if amended, page 9, by striking lines 31 - 41 and inserting: Section 56-3-___. (A) The Department of Motor Vehicles may issue special motor vehicle license plates to owners of private passenger carrying motor vehicles, as defined in Section 56-3-630, or motorcycles registered in their names which must have imprinted on the plate 'Coon Hunters'. This special license plate must be of the same size and general design of regular motor vehicle license plates. This special license plate must be issued or revalidated for a biennial period which expires twenty-four months from the month it is issued./ Renumber sections to conform. Amend title to conform. Senator BRIGHT proposed the following amendment (1392R003.LB), which was adopted: Amend the bill, as and if amended, page 14, after line 5, by adding an appropriately numbered new SECTION to read: / SECTION ___. Chapter 3, Title 56 of the 1976 Code is amended by adding: "Article ___ Section 56-3-___. (A) The Department of Motor Vehicles may issue to owners of private passenger motor vehicles special motor vehicle license plates which may have imprinted on them an emblem, a seal, or other symbol the department considers appropriate of a public or independent high school located in this State. A school may submit to the department for its approval the emblem, seal, or other symbol it desires to be used for its respective special license plate. A school also may request a change in the emblem, seal, or other symbol once the existing inventory of the license plate has been exhausted. The fee for this special license plate is seventy dollars every two years in addition to the regular motor vehicle registration fee set forth in Article 5, Chapter 3 of this title. This special license plate must be of the same size and general design of regular motor vehicle license plates. The special license plates must be issued or revalidated for a biennial period which expires twenty-four months from the month they are issued. (B) The fees collected pursuant to this section must be distributed to a separate fund for each of the respective high schools. Each fund must be administered by the school and may be used only for academic scholarships. Funds collected for state schools must be deposited with the State Treasurer. Funds collected for independent institutions must be deposited in an account designated by the respective school. The distribution is thirty dollars to the department and forty dollars to the school for each special license plate sold for the respective school. (C) The guidelines for the production of a special license plate under this section must meet the requirements of Section 56-3-8100."/ Renumber sections to conform. Amend title to conform. Senator BRIGHT explained the amendment. The question then was the adoption of the amendment. The "ayes" and "nays" were demanded and taken, resulting as follows: Ayes 25; Nays 14 AYES Alexander Anderson Bright Bryant Campbell Courson Cromer Davis Fair Grooms Hayes Leatherman Martin, Shane Massey McGill Mulvaney Nicholson Peeler Reese Ryberg Setzler Shoopman Thomas Verdin Williams Total--25 NAYS Campsen Cleary Coleman Elliott Knotts Land Leventis Lourie Malloy Martin, Larry McConnell Rose Scott Sheheen Total--14 Senator GROOMS proposed the following amendment (1392R005.LKG), which was adopted: Amend the bill, as and if amended, page 14, after line 31, by adding an appropriately numbered new SECTION to read: / SECTION 15. Chapter 3, Title 56 of the 1976 Code is amended by adding an appropriately numbered new article to read: "Article ___ 'South Carolina Wildlife Federation' Special License Plates Section 56-3-___. (A) The Department of Motor Vehicles may issue 'South Carolina Wildlife Federation' special motor vehicle license plates to owners of private passenger motor vehicles as defined in Section 56-3-630 registered in their names which may have imprinted on them an emblem, seal, symbol, or design of the South Carolina South Carolina Wildlife Federation. The South Carolina South Carolina Wildlife Federation must submit to the department for its approval the emblem, seal, symbol, or design it wishes to display on the plates. The South Carolina South Carolina Wildlife Federation must submit to the department written authorization for use of any copyrighted or registered logos, trademarks, or designs. The South Carolina South Carolina Wildlife Federation may request a change in the emblem, seal, or symbol not more than once every five years. The plates must be issued or revalidated for a biennial period which expires twenty-four months from the month they are issued. The fee for the plate is the regular motor vehicle registration fee contained in Article 5, Chapter 3 of this title and a special motor vehicle license fee of thirty dollars. (B) Notwithstanding any other provision of law, from the fees collected pursuant to this section, the Comptroller General shall place sufficient funds into a special restricted account to be used by the department to defray the expenses of the department in producing and administering the plates. The remaining funds collected from the special motor vehicle license fee must be distributed to the South Carolina South Carolina Wildlife Federation for conservation programs in South Carolina. (C) The guidelines for the production of a special license plate under this section must meet the requirements of Section 56-3-8100."/ Renumber sections to conform. Amend title to conform. Senator GROOMS explained the amendment. Senator GROOMS proposed the following amendment (1392R004.LKG), which was adopted: Amend the bill, as and if amended, by striking SECTION 15 in its entirety and inserting: / SECTION 15. Chapter 3, Title 56 of the 1976 Code is amended by adding an appropriately numbered new article to read: "Article ___ 'Large Mouth Bass' Special License Plates Section 56-3-____. (A) The Department of Motor Vehicles may issue 'Large Mouth Bass' special motor vehicle license plates to owners of private passenger carrying motor vehicles, as defined in Section 56-3-630, or motorcycles registered in their names. The license plate shall have the image of a large mouth bass imprinted on it. The design of the plate and the large mouth bass image utilized must be selected through a public process conducted by the Department of Natural Resources. This special license plate must be of the same size and general design of regular motor vehicle license plates. The special license plates must be issued or revalidated for a biennial period which expires twenty-four months from the month they are issued. (B) The fees collected pursuant to this section above the cost of the regular motor vehicle registration fee must be distributed to the Department of Natural Resources, which shall only use the funds to promote bass fishing throughout the State. (C) The guidelines for the production of a special license plate under this section must meet the requirements of Section 56-3-8100."/ Renumber sections to conform. Amend title to conform. There being no further amendments, the question then was the second reading of the Bill. The "ayes" and "nays" were demanded and taken, resulting as follows: Ayes 46; Nays 0 AYES Alexander Anderson Bright Bryant Campbell Campsen Cleary Coleman Courson Cromer Davis Elliott Fair Ford Grooms Hayes Hutto Jackson Knotts Land Leatherman Leventis Lourie Malloy Martin, Larry Martin, Shane Massey Matthews McConnell McGill Mulvaney Nicholson O'Dell Peeler Pinckney Rankin Reese Rose Ryberg Scott Setzler Sheheen Shoopman Thomas Verdin Williams Total--46 NAYS Total--0 There being no further amendments, the Bill was read the second time, passed and ordered to a third reading. S. 1392--Ordered to a Third Reading On motion of Senator SCOTT, with unanimous consent, S. 1392 was ordered to receive a third reading on Friday, April 30, 2010. S. 1321 (Word version) -- Senators Scott, Alexander, Anderson, Bright, Bryant, Campbell, Campsen, Cleary, Coleman, Courson, Cromer, Davis, Elliott, Fair, Ford, Grooms, Hayes, Hutto, Jackson, Knotts, Land, Leatherman, Leventis, Lourie, Malloy, L. Martin, S. Martin, Massey, Matthews, McConnell, McGill, Mulvaney, Nicholson, O'Dell, Peeler, Pinckney, Rankin, Reese, Rose, Ryberg, Setzler, Sheheen, Shoopman, Thomas, Verdin and Williams: A CONCURRENT RESOLUTION TO DECLARE THE MONTH OF SEPTEMBER 2010 YOUTH AWARENESS MONTH IN SOUTH CAROLINA AND TO ENCOURAGE ALL CITIZENS OF THIS GREAT STATE TO PROMOTE STRONG FAMILIES AND PARENTING, ALONG WITH YOUTH PROGRAMS AND JOBS. The Concurrent Resolution was adopted, ordered sent to the House. S. 1324 (Word version) -- Senators Scott, Alexander, Anderson, Bright, Bryant, Campbell, Campsen, Cleary, Coleman, Courson, Cromer, Davis, Elliott, Fair, Ford, Grooms, Hayes, Hutto, Jackson, Knotts, Land, Leatherman, Leventis, Lourie, Malloy, L. Martin, S. Martin, Massey, Matthews, McConnell, McGill, Mulvaney, Nicholson, O'Dell, Peeler, Pinckney, Rankin, Reese, Rose, Ryberg, Setzler, Sheheen, Shoopman, Thomas, Verdin and Williams: A CONCURRENT RESOLUTION TO DECLARE THE MONTH OF OCTOBER 2010 AS GANG AWARENESS MONTH IN SOUTH CAROLINA IN ORDER TO RAISE PUBLIC AWARENESS OF THE INCREASING PROBLEM OF CRIMINAL GANG ACTIVITY IN OUR STATE. The Concurrent Resolution was adopted, ordered sent to the House. S. 1403 (Word version) -- Senators Rose, Grooms and Matthews: A CONCURRENT RESOLUTION TO REQUEST THAT THE DEPARTMENT OF TRANSPORTATION NAME THE INTERSECTION OF ORANGEBURG ROAD AND CENTRAL AVENUE IN DORCHESTER COUNTY AS "KNIGHT CROSSROADS" AND ERECT APPROPRIATE MARKERS OR SIGNS AT THIS INTERSECTION THAT CONTAIN THE WORDS "KNIGHT CROSSROADS". The Concurrent Resolution was adopted, ordered sent to the House. H. 4771 (Word version) -- Rep. Cato: A CONCURRENT RESOLUTION TO REQUEST THAT THE DEPARTMENT OF TRANSPORTATION NAME THE BRIDGE LOCATED ON SOUTH CAROLINA HIGHWAY 253 BETWEEN CAMP CREEK ROAD AND MUSH CREEK ROAD IN GREENVILLE COUNTY "JOHN T. WOOD BRIDGE", AND NAME THE PORTION OF SOUTH CAROLINA HIGHWAY 253 FROM THIS BRIDGE TO ITS INTERSECTION WITH SOUTH CAROLINA HIGHWAY 414 "JOHN T. WOOD ROAD", ERECT APPROPRIATE MARKERS OR SIGNS AT THE BRIDGE THAT CONTAIN THE WORDS "JOHN T. WOOD BRIDGE" AND ERECT APPROPRIATE MARKERS OR SIGNS ALONG THIS PORTION OF HIGHWAY THAT CONTAIN THE WORDS "JOHN T. WOOD ROAD". The Concurrent Resolution was adopted, ordered returned to the House. OBJECTION S. 1353 (Word version) -- Senators Ryberg, Rose and Campsen: A BILL TO AMEND CHAPTER 31, TITLE 41 OF THE 1976 CODE, RELATING TO CONTRIBUTIONS AND PAYMENTS TO THE UNEMPLOYMENT TRUST FUND, TO PROVIDE FOR CONTRIBUTIONS TO THE UNEMPLOYMENT TRUST FUND AND THE MANNER IN WHICH THOSE CONTRIBUTIONS ARE CALCULATED, TO PROVIDE NECESSARY DEFINITIONS, AND TO MAKE TECHNICAL AND CONFORMING AMENDMENTS. Senator RYBERG asked unanimous consent to take the Bill up for immediate consideration. There was no objection. The Senate proceeded to a consideration of the Bill, the question being the adoption of the amendment proposed by the Committee on Labor, Commerce and Industry. Senator MULVANEY proposed the following amendment (1353R002.WGR), which was adopted: Amend the committee amendment, as and if amended, page [1353-1] by striking lines 27 - 42, and on page [1353-2], by striking lines 1 - 11 and inserting: / (1) 'Benefit ratio' means: (a) for the period of January 1, 2011, through December 31, 2011, the number calculated by dividing the average of all benefits charged to an employer during the forty calendar quarters immediately preceding the calculation date by the employer's average taxable payroll during the same period. If fewer than forty but more than four calendar quarters of data are available, the data from those available calendar quarters shall be used in the calculation. The benefit ratio must be calculated annually on July first to the sixth decimal place; (b) for the period of January 1, 2012, through December 31, 2014, the number calculated by dividing the average of all benefits charged to an employer during the twenty-four calendar quarters immediately preceding the calculation date by the employer's average taxable payroll during the same period. If fewer than twenty-four but more than four calendar quarters of data are available, the data from those available calendar quarters shall be used in the calculation. The benefit ratio must be calculated annually on July first to the sixth decimal place; and (c) from January 1, 2015, the number calculated by dividing the average of all benefits charged to an employer during the twelve calendar quarters immediately preceding the calculation date by the employer's average taxable payroll during the same period. If fewer than twelve but more than four calendar quarters of data are available, the data from those available calendar quarters shall be used in the calculation. The benefit ratio must be calculated annually on July first to the sixth decimal place. / Amend the committee amendment further, as and if amended, page [1353-2], by inserting after line 11: // Amend the bill further, as and if amended, by striking Section 41-31-45, found on page 3, lines 36-43, page 4, lines 1-43, and on page 5, lines 1-2 and inserting: / Section 41-31-45. (A) For the purposes of this section: (1) 'Average high cost multiple' means the number of years the department could pay unemployment compensation, based upon the statewide reserve ratio, if the department paid the compensation at a rate equivalent to the average benefit cost rate in the three calendar years during the previous twenty calendar years, or the last three recessions, in which the benefit cost rates were the highest. (2) 'Benefit cost rate' means the rate determined by dividing the unemployment compensation benefits paid during a calendar year by the total covered wages in the state during that year. The calculation of the benefit cost rate may not include the wages and unemployment compensation paid by employers covered under Section 3309 of the Internal Revenue Code of 1986. (3) 'Income needed to pay benefits' means the estimate of benefit payable in a given calendar year less the estimate of interest to be earned by the unemployment insurance trust fund for that calendar year. (4) 'Statewide reserve ratio' means the ratio determined by dividing the balance in the trust fund reserve at the end of the calendar year by the total covered wages in the State for that year. The calculation of the statewide reserve ratio may not include the wages and unemployment compensation paid by employers covered under Section 3309 of the Internal Revenue Code of 1986. (5) 'Fund adequacy target' means an average high-cost multiple of one. (6) 'Trust fund reserve' excludes distributions from the federal government pursuant to 42 U.S.C. 1103, commonly referred to as the Reed Act. (B)(1) For each calendar year during the state Unemployment Insurance Trust Fund is in debt status, the department must estimate the amount of income necessary to pay benefits for that year, the amount of income necessary to avoid automatic FUTA credit reductions, and an amount of income necessary to repay all outstanding federal loans within five years. Additional estimates of interest costs shall be determined concurrently. (i) Estimates of the revenue needed to pay benefits will be based on Congressional Budget Office projections for the subsequent calendar year's total unemployment rate. This total unemployment rate will be adjusted for South Carolina based on the historic relationship between the unemployment rate in South Carolina and the national unemployment rate calculated from 1980 to present. (ii) The historic relationship, calculated from 1980 to present, between the total unemployment rate and the insured unemployment rate in South Carolina will be used to adjust the projected total unemployment rate to the rate of insured unemployment. (iii) An estimate of the relationship between the amount of benefits paid and the level of the insured rate of unemployment will be used to project the total level of benefits to be paid in the upcoming year. (iv) Estimates of amounts to pay to avoid FUTA credit reductions and amount of repayments on the loan will be projected through consultation with officials at the US Department of Labor. (2) The executive director may make reasonable adjustments to the contribution rates set for a calendar year to prevent significant rate variations between calendar years. (C) After the fund returns to solvency, the department must promulgate regulations concerning the income needed to pay benefits in each year and return the trust fund to an adequate level as defined in 41-35-45(5). / Amend the bill further, as and if amended, page 9, by striking lines 26 - 37 and inserting: / (b) The estimated revenues necessary, as computed in Section 41-35-45(B)(1) must be divided by the estimated taxable wages for the calendar year. The result rounded to the next higher one-hundredth of one percent is the average required rate needed to pay benefits and achieve solvency targets. (c) The rate for class twenty will be set by multiplying the statewide average tax rate by twenty and dividing by the sum of the experience factors in the third column in the table provided in this subitem from both sections. To determine the remaining rates, multiply each experience factor in the table by the rate for class twenty. Rate Class Less than 5.4% Greater than 5.4% (Section 1) 1 0.000000 0.000000 2 0.348678 0.087170 3 0.387420 0.096855 4 0.430467 0.107617 5 0.478297 0.119574 6 0.531441 0.132860 7 0.590490 0.147623 8 0.656100 0.164025 9 0.729000 0.182250 10 0.810000 0.202500 11 0.900000 0.225000 12 1.000000 0.250000 13 1.200000 0.478297 (Section 2) 14 0.590490 0.531441 15 0.656100 0.590490 16 0.729000 0.656100 17 0.810000 0.729000 18 0.900000 0.810000 19 1.000000 0.900000 20 ---- 1.000000 / Amend the bill further, as and if amended, page 9, by striking lines 38-42, and on page 10, by striking lines 1-17 and inserting: / (2)(a)(i) If the computed rate necessary for class twenty is less than five and four-tenths percent, then the rate for class twenty shall be set at five and four-tenths percent. (ii) The rates for the remaining classes will be calculated by multiplying the statewide average tax rate by 20 and subtracting from this quotient five and four-tenths percent. This amount shall then be divided by 19. This is the tax rate for class twelve. (iii) To determine the rates for classes one through thirteen, multiply the experience factors in the second column of first section of the table in subitem (A)(1)(c) by the rate for class twelve. (iv) To determine the rates for classes fourteen through nineteen, multiply the statewide average tax rate by twenty and subtract five and four-tenths percent and the sum of the tax rates for classes one through thirteen. Divide this result by nineteen. This is the average tax rate needed for the remaining classes. (v) The rate for class nineteen is determined by multiplying the result in subitem (iv) by six and dividing by the sum of the experience factors in second column of the second section of the table in subitem (A)(1)(c). The remaining rates are determined by multiplying the appropriate experience factor by the rate for class nineteen. Section 41-31-55. (A) In any calendar year in which the state Unemployment Insurance trust fund is insolvent, the state shall impose additional surcharges on all employers to pay interest on the outstanding debt. The amount of interest to be paid will be divided by the estimated taxable payroll for the calendar year to determine the statewide average surcharge. (1) The statewide average surcharge shall be multiplied by twenty and divided by the sum of the experience factors in the second column of the table in subsection (B). This is the surcharge applied to rate class twenty. (2) The remaining class surcharges shall be calculated by multiplying each experience factor in the second column of the table in subsection (B) by the rate for class twenty. (3) Funds collected for interest payments shall be deposited in an account separate from regular collections and shall be transferred to the federal government in the manner required by the United States Department of Labor's regulations. (B) The table contained in this subsection shall be used for calculations required in subsection (A): Rate Class Experience Factor 1 0.78453 2 0.087170 3 0.096855 4 0.107617 5 0.119574 6 0.132860 7 0.147623 8 0.164025 9 0.182250 10 0.202500 11 0.225000 12 0.250000 13 0.478297 14 0.531441 15 0.590490 16 0.656100 17 0.729000 18 0.810000 19 0.900000 20 1.000000 Amend the bill further, as and if amended, page 10, by striking lines 42 - 43, and on page 11, by striking lines 1 - 17: / Section 41-31-70. If the Commission department finds that an employer ceased to render employment solely due to the closing of the business because of the entrance of one or more of the owners, officers, partners, or the majority stockholders into the armed forces of the United States, or any of its allies, or of the United Nations after January 1, 1951, such employer's account shall not be terminated; and, if the business is resumed and employment rendered within two years after the discharge or release from active duty in the armed forces of such the person or persons, the employer's experience shall be deemed to have been continuous throughout such that period. The reserve benefit ratio of any such the employer shall be the total contributions paid by such employer minus all benefits average annual benefits charged to the employer during the twenty-four calendar quarters immediately preceding the calculation date, including benefits paid to any individual during the period such the employer was in the armed forces, charged against such employer's account, divided by his average annual payroll for the most recent year during the whole of which such the employer has been in business and has rendered employment. This provision shall not be construed to authorize cash refunds and any adjustments required hereunder shall be only by credit certificate. Amend the bill further, as and if amended, page 14, by striking line 9 and inserting: / reserve account benefit experience attributable to an identifiable portion of the / Amend the bill further, as and if amended, page 17, by striking lines 39 - 43, and on page 18, by striking lines 1 - 4 and inserting: / Section 41-31-170. The Commission department shall report annually to any employer the status of his account showing his reserve balance at the beginning of the period, total contributions he has made and total charges against it for benefits paid during the annual period and the twenty-four calendar quarters prior to the computation date, as applicable, and his reserve balance at the end of such period. No employer may contest any charge against his account or the status of his account unless he makes protest within thirty days after such report has been mailed by the Commission department. / // Renumber sections to conform. Amend title to conform. Senator MULVANEY explained the amendment. Senators LEVENTIS, RYBERG and SCOTT proposed the following amendment (1353R005.WGR), which was adopted: Amend the committee amendment, as and if amended, page [1353-4], by striking line 37 and inserting: / SECTION 7. Article 5, Chapter 27, Title 41 of the 1976 Code is amended by adding: "Section 41-27-525. (A) A part-time worker is considered to be able and available for work if he is monetarily eligible based on wages that were predominantly earned from part-time work, is actively seeking part-time work, is available for part-time work for at least the number of restrictions on his ability to work or availability for work, and is in a labor market in which a reasonable demand exists for part-time work. A part time worker is not considered to be unemployed, and therefore not entitled to benefits, if the part-time worker is working all hours for which he is available regardless of the amount of money earned. (B) An individual who is otherwise eligible for benefits under this title may not be considered ineligible for those benefits solely on the basis that he seeks, applies for, or is willing to accept only part-time employment." SECTION 8. Section 41-27-150, as last amended by an act bearing ratification number 159 of 2010, is further amended to read: "Section 41-27-150. (A) Except as provided in subsection (B), 'base period' means the first four of the last five completed calendar quarters immediately preceding the first day of an individual's benefit year. However, in the case of a combined wage claim filed by an individual in accord with an arrangement entered into by the department pursuant to the provisions of Section 41-29-140(2), the base period is that applicable provided by the law of the paying state. (B)(1) 'Alternate base period' means for benefits years effective after May 31, 2010, if an individual does not have sufficient wages in the base period defined in subsection (A) to qualify for benefits, his base period must be the four calendar quarters completed most recently before the individual's benefit year if this period qualifies him for benefits, provided these quarters were not previously used to establish a prior valid benefit year. (2) If the wage information for an individual's most recently completed calendar quarter is not available to the department from regular quarterly reports of systematically accessible wage information, the department promptly must contact the individual's employer to establish such wage information. The director shall establish rules necessary to implement this subsection. (C) Wages that fall within the base period, if claims established under this section, must not be available for use in qualifying for a subsequent benefit year." SECTION 9. This act takes effect January 1, 2011. / Renumber sections to conform. Amend title to conform. Senator LEVENTIS explained the amendment. The Committee on Labor, Commerce and Industry proposed the following amendment (1353R001.WGR), which was adopted: Amend the bill, as and if amended, page 1, by striking lines 37 - 42, and on page 2, by striking lines 1 - 3 and inserting: / (1) 'Benefit ratio' means: (a) for the period of January 1, 2011, through December 31, 2011, the number calculated by dividing the average of all benefits charged to an employer during the forty calendar quarters immediately preceding the calculation date by the employer's annual taxable payroll during the same period. If fewer than forty but more than four calendar quarters of data are available, the data from those available calendar quarters shall be used in the calculation. The benefit ratio must be calculated annually on July first to the sixth decimal place; (b) for the period of January 1, 2012, through December 31, 2014, the number calculated by dividing the average of all benefits charged to an employer during the twenty-four calendar quarters immediately preceding the calculation date by the employer's annual taxable payroll during the same period. If fewer than twenty-four but more than four calendar quarters of data are available, the data from those available calendar quarters shall be used in the calculation. The benefit ratio must be calculated annually on July first to the sixth decimal place; and (c) from January 1, 2015, the number calculated by dividing the average of all benefits charged to an employer during the twelve calendar quarters immediately preceding the calculation date by the employer's annual taxable payroll during the same period. If fewer than twelve but more than four calendar quarters of data are available, the data from those available calendar quarters shall be used in the calculation. The benefit ratio must be calculated annually on July first to the sixth decimal place. / Amend the bill further, as and if amended, page 33, by striking SECTION 2 and inserting: / SECTION 2. Section 41-27-310 of the 1976 Code is amended to read: "Section 41-27-310. An 'insured worker' is an individual who has been paid wages in his base period for insured work equal to or exceeding one and one-half times the total of his wages paid in the quarter of such base period in which his wages for insured work were highest; provided, however, that no individual shall qualify as an insured worker unless he has been paid at least nine hundred four thousand four hundred fifty five dollars in his base period for insured work and five hundred forty one thousand ninety-two dollars in that quarter of his base period in which such wages were highest." SECTION 3. Section 41-27-380(2) of the 1976 Code is amended to read: "(2) For the purpose of Chapter 31, Article 1, of this title, 'wages' does not include that part of remuneration which, after remuneration equal to seven ten thousand dollars for the period of January 1, 2011, through December 31, 2011, twelve thousand dollars for the period of January 1, 2012, through December 31, 2014, and fourteen thousand dollars from January 1, 2015 has been paid in a calendar year to an individual by an employer or his predecessor or with respect to employment during any calendar year, is paid to the individual by the employer during the calendar year unless that part of the remuneration is subject to a tax under a federal law imposing a tax against which credit may be taken for contributions required to be paid into a state unemployment fund. For the purposes of this subsection, employment includes service constituting employment under any unemployment compensation law of another state." SECTION 4. Section 41-35-40 of the 1976 Code is amended to read: "Section 41-35-40. An insured worker's weekly benefit amount is fifty percent of his weekly average wage, as defined in Section 41-27-140, and the weekly benefit amount, if not a multiple of one dollar, must be computed to the next lower multiple of one dollar. However, no insured worker's weekly benefit amount may be less than twenty forty-two dollars nor greater than sixty-six and two-thirds percent of the statewide average weekly wage most recently computed before the beginning of the individual's benefit year." SECTION 5. Article 7, Chapter 27, Title 41 of the 1976 Code, as added by Act 146 of 2010, is amended by adding: "Section 41-27-760. (A) No candidate for or person intending to become a candidate for the Department of Workforce Appellate Panel may seek, directly or indirectly, the pledge of a member of the General Assembly's vote or contact, directly or indirectly, a member of the General Assembly or the review committee regarding screening for the Department of Workforce Appellate Panel, until the qualifications of all candidates for that office have been determined by the Department of Workforce Review Committee, and the review committee has formally released its report as to the qualifications of all candidates for the office to the General Assembly. For purposes of this section, 'indirectly seeking a pledge' means the candidate, or someone acting on behalf of or at the request of the candidate, requests a person to contact a member of the General Assembly on behalf of the candidate before the review committee has formally released its report as to the qualifications of all candidates to the General Assembly. The prohibitions of this section do not extend to an announcement of candidacy by the candidate or statement by the candidate detailing the candidate's qualifications. (B)(1) No member of the General Assembly may pledge or offer his pledge his vote for a candidate until the qualifications of all candidates for the Department of Workforce Appellate Panel have been determined by the Department of Workforce Review Committee, and the review committee has formally released its report as to the qualifications of all candidates to the General Assembly. The formal release of the report of qualifications must occur no earlier than forty-eight hours after the names of all candidates found qualified by the review committee have been initially released to members of the General Assembly. (2) No member of the review committee may pledge or offer his pledge to find a candidate qualified prior to the review committee's determination of qualifications. (C) No member of the General Assembly may trade anything of value, including pledges to vote for legislation or for other candidates, in exchange for another member's pledge to vote for a candidate for the Department of Workforce Appellate Panel. (D)(1) Violations of this section may be considered by the Department of Workforce Review Committee when it considers the candidate's qualifications. (2) Violations of this section by members of the General Assembly must be reported by the review committee to the House or Senate Ethics Committee, as may be applicable. (3) Violations of this section by incumbent appellate panelists seeking reelection must be reported by the Department of Workforce and the Department of Workforce Appellate Panel to the State Ethics Commission. A violation of this section is a misdemeanor and, upon conviction, the violator must be fined not more than one thousand dollars or imprisoned not more than ninety days, or both. Cases tried under this section may not be transferred from general sessions court pursuant to Section 22-3-545." SECTION 6. Section 41-29-40 of the 1976 Code, as last amended by Act 146 of 2010, is further amended to read: "Section 41-29-40. There are created under the department two coordinate divisions, the South Carolina State Employment Service Division created pursuant to Section 41-5-10, and a division to be known as the Unemployment Compensation Division. Each division must be administered by a full-time salaried director, who is subject to the supervision and direction of the department. The department may appoint, fix the compensation of, and prescribe the duties of the directors of these divisions. These appointments must be made on a nonpartisan merit basis in accordance with the provisions of Section 41-29-90. The director of each division shall be responsible to the department for the administration of his respective division and has the power and authority as vested in him by the department." SECTION 7. This act takes effect January 1, 2011. / Renumber sections to conform. Amend title to conform. Senator RYBERG explained the committee amendment. Senator O'DELL proposed the following amendment (1353R003.WHO), which was tabled: Amend the bill, as and if amended, page 9, by striking lines 32 - 42, and on page 10, by striking lines 1 - 17 and inserting: / (c) The rate for class twenty will be set such that the entire schedule raises the income required to pay benefits for the year, as well as the income necessary to move the trust fund toward the solvency target, subject to the structure defined in this chapter. However, the rate for class twenty must be a least five and four-tenths percent. For calendar year 2011, the rate for class one shall not be lower than one percent. For each ensuing year, the director must, when calculating the rate for class one, take into consideration the solvency of the Unemployment Insurance Trust Fund and the funds necessary to cover the claims from unemployed individuals from failed businesses. (2)(a) If the calculated rate necessary for benefit rate class twenty exceeds five and four-tenths percent, then the rate for each succeeding benefit rate class shall be equal to ninety percent of the rate calculated for the preceding class. (b)(i) If the computed rate necessary for class twenty is less than five and four-tenths percent, then the rate for class twenty shall be set at five and four-tenths percent. (ii) The contribution rate for rate classes nineteen through one shall be set at a consistent percentage of the rate of the preceding class so that the entire schedule raises the income required to pay benefits for the year, as well as the income necessary to move the trust fund toward the solvency target, subject to the structure defined in chapter. / Renumber sections to conform. Amend title to conform. Renumber sections to conform. Amend title to conform. Senator O'DELL explained the amendment. Senator RYBERG argued contra to the adoption of the amendment. Senator RYBERG moved to lay the amendment on the table. The amendment was laid on the table. Senator THOMAS objected to further consideration of the Bill. CARRIED OVER S. 642 (Word version) -- Senators Alexander, Ford and Knotts: A BILL TO AMEND ARTICLE 31, CHAPTER 5, TITLE 56, CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING SECTION 56-5-3890 TO PROVIDE THAT A PERSON UNDER THE AGE OF EIGHTEEN MAY NOT OPERATE A MOTOR VEHICLE WHILE USING A CELL PHONE OR OTHER WIRELESS COMMUNICATIONS DEVICE AND TO PROVIDE FOR PENALTIES AND EXCEPTIONS. On motion of Senator LARRY MARTIN, the Bill was carried over. H. 3964 (Word version) -- Reps. Duncan, Ott, Vick, Loftis and Bales: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING ARTICLE 13 TO CHAPTER 21, TITLE 46 SO AS TO UPDATE AND CLARIFY SEED ARBITRATION PROCEDURES; TO AMEND ARTICLE 1, CHAPTER 21, TITLE 46, RELATING TO GENERAL PROVISIONS OF SEED AND PLANT CERTIFICATION, SO AS TO REPLACE OBSOLETE DEFINITIONS, TO REVISE ENFORCEMENT MECHANISMS, TO CLARIFY LICENSING PROCEDURES, AND TO PROVIDE EXEMPTIONS; TO AMEND ARTICLE 3, CHAPTER 21, TITLE 46, RELATING TO LABELS AND TAGS REGARDING SEEDS AND PLANTS, SO AS TO REVISE THE LABELING REQUIREMENTS FOR SEED PRODUCTS, AND TO IMPOSE ADDITIONAL PROHIBITIONS; TO AMEND ARTICLE 5, CHAPTER 21, TITLE 46, RELATING TO ANALYSES AND TESTS REGARDING SEEDS AND PLANTS, SO AS TO DELETE REDUNDANT PROVISIONS, TO PROVIDE THAT DEPARTMENT OF AGRICULTURE OFFICIALS SHALL HAVE ACCESS TO SEED RECORDS AND SAMPLES, TO PROVIDE THAT SEED RECORDS SHALL BE MAINTAINED FOR TWO YEARS, AND TO CLARIFY WHO IS ENTITLED TO FREE SEED TESTING AT THE STATE SEED LABORATORY; TO AMEND ARTICLE 7, CHAPTER 21, TITLE 46, RELATING TO WITHDRAWAL, CONFISCATION, AND SALE OF SEEDS REGARDING SEEDS AND PLANTS, SO AS TO INCREASE PENALTIES FOR VIOLATIONS FROM A MAXIMUM OF ONE HUNDRED DOLLARS FOR EACH VIOLATION TO ONE THOUSAND DOLLARS FOR EACH VIOLATION, TO CLARIFY THE ROLE OF THE ATTORNEY GENERAL IN PROSECUTING VIOLATIONS, AND TO PROVIDE FOR INJUNCTIVE RELIEF TO PREVENT VIOLATIONS; TO AMEND ARTICLE 9, CHAPTER 21, TITLE 46, RELATING TO SEED AND PLANT CERTIFICATION, SO AS TO CLARIFY CLEMSON UNIVERSITY'S SEED AND PLANT CERTIFICATION AUTHORITY; AND TO REPEAL ARTICLE 11, CHAPTER 21, TITLE 46 RELATING TO SEED IRISH POTATOES IN CHARLESTON COUNTY. On motion of Senator VERDIN, the Bill was carried over. AMENDED, CARRIED OVER S. 1322 (Word version) -- Senators O'Dell, Verdin and Rose: A CONCURRENT RESOLUTION TO ADMONISH THE ATTORNEY GENERAL OF SOUTH CAROLINA TO DETERMINE AND CARRY OUT THE MOST EXPEDITIOUS STRATEGY TO ASSURE THAT "BIG RED," THE CITADEL BATTLE FLAG, SHALL REMAIN IN SOUTH CAROLINA PERMANENTLY AS AN IMPORTANT HISTORICAL ASSET OF SOUTH CAROLINA. The Senate proceeded to a consideration of the Resolution, the question being the adoption of the Resolution. Senators SHOOPMAN, O'DELL, VERDIN and ROSE proposed the following amendment (1322R001.PWS), which was adopted: Amend the concurrent resolution, as and if amended, page 1, by striking lines 11-16 and inserting: / TO URGE THE ATTORNEY GENERAL OF SOUTH CAROLINA TO TAKE SWIFT AND APPROPRIATE ACTION TO ASSURE THAT "BIG RED," THE CITADEL BATTLE FLAG AND A SIGNIFICANT ARTIFACT REPRESENTING THIS STATE'S RICH HISTORY, REMAINS PERMANENTLY IN SOUTH CAROLINA. / Amend the concurrent resolution further, as and if amended, page 2, by striking lines 28-32 and inserting: / Be it further resolved that the South Carolina General Assembly urges the Attorney General of South Carolina to take swift and appropriate action to assure that "Big Red," the Citadel battle flag and a significant artifact representing this state's rich history, remains permanently in South Carolina. / Renumber sections to conform. Amend title to conform. Senator SHOOPMAN explained the amendment. Senator LEATHERMAN spoke on the amendment. On motion of Senator SHOOPMAN, the Concurrent Resolution was carried over, as amended. THE SENATE PROCEEDED TO A CONSIDERATION OF H. 4657, THE GENERAL APPROPRIATIONS BILL. RETURNED TO THE HOUSE WITH AMENDMENTS H. 4657--GENERAL APPROPRIATIONS BILL The Senate proceeded to a consideration of the Bill, the question being the third reading of the Bill. Amendment No. 27A Senators BRYANT and BRIGHT proposed the following Amendment No. 27A (4657R035.KLB.DOCX), which was ruled out of order: Amend the bill, as and if amended, Part IB, Section 1, DEPARTMENT OF EDUCATION, by adding an appropriately numbered new proviso to read: / 1. (SDE: Additional Classroom Funding) From the funds appropriated to or carried forward by the Commission on Higher Education for the Endowed Chairs, $108,000,000 must be credited to the Department of Education to be distributed to school districts pursuant to the EFA formula. From the funds appropriated to or carried forward by the University of South Carolina for the Innovista Project,$58, 000,000 must be credited to the Department of Education to be distributed to the school districts pursuant to the EFA formula. From funds carried forward by the Budget and Control Board, $65,777,139 must be credited to the Department of Education to be distributed to the school districts pursuant to the EFA formula. / Renumber sections to conform. Amend sections, totals and title to conform. Senator BRYANT explained the amendment. Point of Order Senator COURSON raised a Point of Order that the amendment was out of order inasmuch as it was violative of Rule 24A. Senator BRYANT spoke on the Point of Order. Senator MULVANEY spoke on the Point of Order. The PRESIDENT Pro Tempore sustained the Point of Order. Amendment No. 27A was ruled out of order. Senator BRYANT moved to divide the amendment. Point of Order Senator SETZLER raised a Point of Order that the motion was out of order as the motion came too late inasmuch as the amendment had been ruled out of order and was not before the Senate for consideration. The PRESIDENT Pro Tempore sustained the Point of Order. Objection Senator BRYANT asked unanimous consent to make a motion to divide the amendment. Senator LEATHERMAN objected. Point of Order Senator MASSEY raised a Point of Order that Proviso 76.14 of Part 1B was out of order inasmuch as it was violative of Rule 24A. 76.14. (TREAS: Assessments & Filing Fees) The State Treasurer shall retain an amount equal to one percent of that portion of assessments in Municipal, Magistrate, Family, and General Sessions Courts and filing fees in courts of record which must be credited to the General Fund of the State and require that those retained revenues must be used for training local governments and to defray the administrative expenses of the collection and distribution of these revenues. Further, the State Treasurer's Office shall identify any jurisdiction that it believes is not timely transmitting assessments and filing fees required to be paid to the State Treasurer and follow-up with the County Treasurer to determine why the appropriate amounts have not been remitted. The PRESIDENT Pro Tempore sustained the Point of Order. Proviso 76.14 of Part 1B was ruled out of order. Point of Order Senator MASSEY raised a Point of Order that Proviso 82.2 of Part 1B was out of order inasmuch as it was violative of Rule 24A. 82.2. (ETHICS: Lobbying Fee Increase) The State Ethics Commission is authorized to increase lobbyist and lobbyist's principal registration fees to one hundred fifty dollars to be used to offset costs associated with the administration and enforcement of Chapter 17 of Title 2 and Chapter 13 of Title 8 of the South Carolina Code of Laws, 1976, as amended. Any excess funds may be carried forward into the current fiscal year to be used for the same purpose. The PRESIDENT Pro Tempore sustained the Point of Order. Proviso 82.2 of Part 1B was ruled out of order. Point of Order Senator MULVANEY raised a Point of Order that Proviso 1.41 of Part 1B was out of order inasmuch as it was violative of Rule 24A. 1.41. (SDE: Alternative Certification/Displaced Employees) The Department of Education is directed to give priority in the Program for Alternative Certification for Educators (PACE) to the recruitment of qualified state employees impacted by reduction in force actions of agencies. The Student Loan Corporation is directed to give priority in the Career-Changer Loan program to qualified state employees. The Department of Education shall provide information to the Office of Human Resources and the personnel offices of state agencies instituting a reduction in force to advertise and inform employees of this program and state agencies shall work with the department in this effort. The PRESIDENT Pro Tempore overruled the Point of Order. Amendment No. 58A Senator RYBERG proposed the following Amendment No. 58A (4657R048.WGR.DOCX), which was ruled out of order: Amend the bill, as and if amended, Part IB, Section 1, DEPARTMENT OF EDUCATION, by adding an appropriately numbered new proviso to read: / 1. . (SDE: ___) The Department of Education must withhold ten percent of the funds to be distributed pursuant to the EFA formula from school districts that reject a contract from a charter school pursuant Section 59-40-50(C)(3). / Renumber sections to conform. Amend sections, totals and title to conform. Senator RYBERG explained the amendment. Point of Order Senator LARRY MARTIN raised a Point of Order that the amendment was out of order inasmuch as it was violative of Rule 24A. The PRESIDENT Pro Tempore sustained the Point of Order. Amendment No. 58A was ruled out of order. RECESS At 12:25 P.M., on motion of Senator LEATHERMAN, the Senate receded from business until 1:15 P.M. AFTERNOON SESSION The Senate reassembled at 1:29 P.M. and was called to order by the PRESIDENT Pro Tempore. THE SENATE RESUMED CONSIDERATION OF H. 4657, THE GENERAL APPROPRIATIONS BILL. The Senate resumed consideration of the Bill, the question being the third reading of the Bill. Point of Quorum At 1:30 P.M., Senator LEATHERMAN made the point that a quorum was not present. It was ascertained that a quorum was present. Amendment No. 60 Senator ROSE proposed the following Amendment No. 60 (4657R040.MTR.DOCX), which was adopted (#10): Amend the bill, as and if amended, Part IB, Section 1, DEPARTMENT OF EDUCATION, page 352, after line 29, by adding a new unnumbered paragraph to read: / The commission shall also determine how to best provide for the state's portion of education funding to flow down to the schools and shall examine all state and local sources of funding K-12 education. The commission shall study a weighted pupil formula or any other formula the committee finds appropriate. The commission shall consider the following specific questions, but may consider other questions it finds appropriate in order to achieve its purpose: (1) how to reform funding for educational programs in South Carolina, mainly in the seventy-four funding categoricals in the Education Finance Act , in an effort to see that more educational dollars make it to the schools; (2) how to provide for flexibility in spending these dollars; (3) how to emphasize allowing school principals budgetary input for spending in the areas where principals see need, thus matching funds to students' needs; (4) how to provide for the state's educators' use of state funding in ways that produce the best results for students; and (5) how to expend the Education Finance Act's weighting system to include additional groups of students not currently weighted, including: (a) low income or poverty weightings; (b) gifted and talented program children; (c) special needs children; and (d) a base weight for all children. / Renumber sections to conform. Amend sections, totals and title to conform. Senator ROSE explained the amendment. The amendment was adopted. Amendment No. 97 Senator MULVANEY proposed the following Amendment No. 97 (DAD AMEND AM16A), which was adopted (#11): Amend the bill, as and if amended, Part IB, Section 1, DEPARTMENT OF EDUCATION, page 353,by amending previously adopted Amendment 16A which added a new proviso entitled (SDE: Salary Increase Suspension) to read as follows: // 1xx (SDE: Salary Increase Suspension) For Fiscal Year 2010-11, the requirement that school districts provide a salary step increase pursuant to Section 59-20-50 is suspended provided that the school district desiring to suspend the salary step increase provide in their Fiscal Year 2010-11 budget for at least two furlough days for school administrators. Said skip, if implemented, shall not negatively impact the experience credit of teachers to who skip applies. Nothing herein shall be deemed to mandate that step increases be skipped. / Renumber sections to conform. Amend sections, totals and title to conform. Senator MULVANEY explained the amendment. The amendment was adopted. Amendment No. 98 Senators DAVIS, McCONNELL, CLEARY, ELLIOTT, RANKIN, FORD, CAMPSEN and McGILL proposed the following Amendment No. 98 (DKA\4000BH10), which was ruled out of order: Amend the bill, as and if amended, Part IB, Section 1, DEPARTMENT OF EDUCATION, page 353, after line 32, by adding an appropriately numbered new proviso to read: /1.__ (SDE: Additional Classroom Funding) From the funds appropriated to or carried forward by the State Budget and Control Board,$21,515,400 must be credited to the Department of Education to be distributed to school districts receiving less than thirty-five percent of state support as computed in Section 59-20-40(1), with each district to receive a pro rata share of said amount determined in accordance with the district's number of weighted students, which must be subject to adjustment for student attendance. / Renumber sections to conform. Amend sections, totals and title to conform. Senator DAVIS explained the amendment. Senator HAYES spoke on the amendment. Senator LEATHERMAN spoke on the amendment. Point of Order Senator LEATHERMAN raised a Point of Order that the amendment was out of order inasmuch as it was violative of Rule 24A. Senator DAVIS spoke on the Point of Order. Senator SETZLER spoke on the Point of Order. Senator CAMPSEN spoke on the Point of Order. The PRESIDENT Pro Tempore sustained the Point of Order. Amendment No. 98 was ruled out of order. Amendment No. 108 Senator SETZLER proposed the following Amendment No. 108 (4657 SETZLEREXCAPP.DOCX), which was ruled out of order: Amend the bill, as and if amended, Part IB, Section 1, DEPARTMENT OF EDUCATION, page 353, after line 32, by adding an appropriately numbered new proviso to read: /1.xx Any revenue collections in the current fiscal year that are used as a source of funds for appropriations within any of the Parts contained in this Act, whether recurring or nonrecurring sources of revenue, that are above the level of appropriation for the source shall be transferred to the State Department of Education and distributed to school districts based on the Education Finance Act formula. / Renumber sections to conform. Amend sections, totals and title to conform. Senator SETZLER explained the amendment. Point of Order Senator GROOMS raised a Point of Order that the amendment was out of order inasmuch as it was violative of Rule 24A. Senator MASSEY spoke on the Point of Order. The PRESIDENT Pro Tempore sustained the Point of Order. Amendment No. 108 was ruled out of order. Amendment No. 81 Senator ROSE proposed the following Amendment No. 81 (4657R049.MTR.DOCX), which was tabled: Amend the bill, as and if amended, Part IB, Section 6, COMMISSION ON HIGHER EDUCATION, page 378, after line 29, by adding an appropriately numbered new proviso to read: /6.__ (CHE: Transaction Register ) For fiscal year 2010-2011, each public institution of higher learning shall maintain a transaction register that includes a complete record of all funds expended over one thousand dollars, from whatever source for whatever purpose. The register must be prominently posted on the institution's internet website and made available for public viewing and downloading. The register must include the transaction amount, name of payee, the identification number of the transaction, and a statement providing a detailed description of the expenditure. The description must include the source of funds, a category title, and an object title for the expenditure. The register must include all reimbursements for expenses, but must not include an entry for salary, wages, or other compensation paid to individual employees. The register must not include a social security number. At the option of the public institution, the register may exclude any information that can be used to identify an individual employee or student. The register must be accompanied by a complete explanation of any codes or acronyms used to identify a payee or an expenditure, and must be searchable and updated at least once a month. Each monthly register must be maintained on the internet during fiscal year 2010-2011. Each public institution of higher learning shall be responsible for providing on its Internet website a link to the Internet website of any agency, other than the individual institution, that posts on its Internet website the institution's monthly state procurement card statements or monthly reports containing all or substantially all of the same information contained in the monthly state procurement card statements. The link must be to the specific webpage or section on the website of the agency where the state procurement card information for the institution can be found. The information posted may not contain the state procurement card number. Any information that is expressly prohibited from public disclosure by federal or state law or regulation must be redacted from any posting required by this section. / Renumber sections to conform. Amend sections, totals and title to conform. Senator ROSE explained the amendment. Senator LEATHERMAN spoke on the amendment. Senator LEATHERMAN moved to lay the amendment on the table. A roll call vote was ordered. With unanimous consent, Senator RYBERG was recognized to speak in favor of the adoption of the amendment. With unanimous consent, Senator BRYANT was recognized to speak in favor of the adoption of the amendment. The "ayes" and "nays" were demanded and taken, resulting as follows: Ayes 22; Nays 21 AYES Alexander Anderson Campbell Coleman Elliott Fair Ford Hutto Jackson Land Leatherman Leventis Lourie Malloy Martin, Larry McGill Nicholson Pinckney Reese Scott Sheheen Williams Total--22 NAYS Bright Bryant Campsen Cleary Courson Cromer Davis Grooms Hayes Knotts Martin, Shane Massey McConnell Mulvaney O'Dell Peeler Rankin Rose Ryberg Shoopman Verdin Total--21 The amendment was laid on the table. Amendment No. 82 Senators ROSE and BRIGHT proposed the following Amendment No. 82 (4657R047.MTR.DOCX), which was carried over and subsequently tabled: Amend the bill, as and if amended, Part IB, Section 6, COMMISSION ON HIGHER EDUCATION, page 378, after line 29, by adding an appropriately numbered new proviso to read: /6.__ (CHE: Transaction Register ) For fiscal year 2010-2011, institutions of higher learning must maintain a transaction register that includes a complete record of all funds expended over one hundred dollars, from whatever source, for whatever purpose. The register must be prominently posted on the instiution's internet website and made available for public viewing and downloading. The register must include for each expenditure: (i) the transaction amount; (ii) the name of the payee; and (iii) a statement providing a detailed description of the expenditure. The register must not include an entry for salary, wages, or other compensation paid to individual employees. The register must not include any information that can be used to identify an individual employee. The register must be accompanied by a complete explanation of any codes or acronyms used to identify a payee or an expenditure. The register must be searchable and updated at least once a month. Each public institution of higher learning shall be responsible for providing on its Internet website a link to the Internet website of any agency, other than the individual institution, that posts on its Internet website the institution's monthly state procurement card statements or monthly reports containing all or substantially all of the same information contained in the monthly state procurement card statements. The link must be to the specific webpage or section on the website of the agency where the state procurement card information for the institution can be found. The information posted may not contain the state procurement card number. Any information that is expressly prohibited from public disclosure by federal or state law or regulation must be redacted from any posting required by this section. / Renumber sections to conform. Amend sections, totals and title to conform. Senator ROSE explained the amendment. Objection Senator SHEHEEN asked unanimous consent to make a motion to perfect the amendment to reflect an expenditure of $1,000 in lieu of$100. Senator FORD objected. Senator ROSE explained the amendment. Objection Senator ROSE asked unanimous consent to make a motion to withdraw Amendment No. 82. Senator BRIGHT objected. On motion of Senator ROSE, the Amendment No. 82 was carried over and subsequently tabled. PRESIDENT PRESIDES At 3:27 P.M., the PRESIDENT assumed the Chair. Point of Order Senator CAMPSEN raised a Point of Order that Proviso 51.29 of Part 1B was out of order inasmuch as it was violative of Rule 24A. 51.29 (CORR: Legal Fees) For the current fiscal year, the Department of Corrections shall submit a report to the Senate Finance Committee and the House Ways and Means Committee detailing the expenditure of all funds, including expenditures from the Insurance Reserve Fund or any prepaid legal account, within the last four fiscal years for private lawyers to defend actions for wrongful termination or other personnel matters against the department's employees or former employees. At a minimum, the report must provide a detailed accounting of the expenditures to include the names of parties to the lawsuits, the cause(s) of action, the date of the alleged wrongdoing, name of private lawyers engaged, amount paid to each private lawyer, status of all pending lawsuits, and outcome of any order or judgment. The report must be submitted by October 1 of the current fiscal year. Senator LEVENTIS spoke on the Point of Order. The PRESIDENT overruled the Point of Order. Amendment No. 83 Senator ROSE proposed the following Amendment No. 83 (4657R045.MTR.DOCX), which was adopted (#12): Amend the bill, as and if amended, Part IB, Section 6, COMMISSION ON HIGHER EDUCATION, page 378, after line 29, by adding an appropriately numbered new proviso to read: /6.__ (CHE: Transaction Register ) For fiscal year 2010-2011, each public institution of higher learning shall post on its website the institution's annual and periodic financial statements. Each public institution of higher learning shall be responsible for providing on its Internet website a link to the Internet website of any agency, other than the individual institution, that posts on its Internet website the institution's monthly state procurement card statements or monthly reports containing all or substantially all of the same information contained in the monthly state procurement card statements. The link must be to the specific webpage or section on the website of the agency where the state procurement card information for the institution can be found. The information posted may not contain the state procurement card number. Any information that is expressly prohibited from public disclosure by federal or state law or regulation must be redacted from any posting required by this section. / Renumber sections to conform. Amend sections, totals and title to conform. Senator ROSE explained the amendment. Senator ROSE moved that the amendment be adopted. The "ayes" and "nays" were demanded and taken, resulting as follows: Ayes 32; Nays 11 AYES Alexander Anderson Campbell Campsen Cleary Courson Cromer Fair Ford Hayes Hutto Jackson Knotts Land Leatherman Leventis Lourie Malloy Martin, Larry McGill Nicholson O'Dell Peeler Pinckney Rankin Reese Rose Ryberg Scott Setzler Sheheen Williams Total--32 NAYS Bright Bryant Davis Elliott Grooms Martin, Shane Massey McConnell Mulvaney Shoopman Verdin Total--11 Statement by Senator ROSE I voted for Amendment No. 83 because it would require, for the first time, each institution of higher learning to post on its website a link to what will be the Comptroller General's website, which will contain all of each institution's monthly state procurement card statements or reports. That would enable the public to see, for the first time, on the Internet all credit card expenditures by all higher learning institutions. Further, this amendment requires, for the first time, that each institution post on line all its financial statements. All of that will be a victory for transparency and accountability by institutions of higher learning. I preferred the passage of two more comprehensive transparency amendments, No. 81 and No. 45, that I introduced previously, but they were tabled. I requested withdrawal of a third proviso, Amendment No. 82, because it appeared it would not pass and to obtain, in return, the votes necessary to obtain passage of Amendment No. 83. Objection Senator ROSE asked unanimous consent to make a motion to take up Amendment No. 82 for immediate consideration. Senator BRIGHT objected. Amendment No. 120 Senator BRYANT proposed the following Amendment No. 120 (4657R064.KLB.DOCX), which was substituted with Amendment No. 120A: Amend the bill, as and if amended, Part IB, SECTION 6, COMMISSION ON HIGHER EDUCATION, page 378, after line 28, by adding an appropriately numbered new proviso to read: / 6. . (CHE: ) From the funds appropriated to the Commission on Higher Education, $108,000,000 must be credited to the Department of Education to be distributed to school districts pursuant to the EFA formula. / Amend the bill further, as and if amended, Part IB, SECTION 15, UNIVERSITY OF SOUTH CAROLINA, page 379, after line 24, by adding an appropriately numbered new proviso to read: /15.__. (USC: ) From the funds appropriated to the University of South Carolina,$58,000,000 must be credited to the Department of Education to be distributed to the school districts pursuant to the EFA formula. / Renumber sections to conform. Amend sections, totals and title to conform. Senator BRYANT explained the amendment. Point of Order Senator LARRY MARTIN raised a Point of Order that the amendment was out of order inasmuch as it was violative of Rule 24A. Senator BRYANT spoke on the Point of Order. The PRESIDENT overruled the Point of Order. Senator BRYANT explained the amendment. Senator BRYANT asked unanimous consent to make a motion to perfect the amendment. There was no objection. Amendment No. 120A Senator BRYANT proposed the following Amendment No. 120A, which was carried over, but subsequently withdrawn: Amend the bill, as and if amended, Part IB, SECTION 6, Amend the bill further, as and if amended, Part IB, SECTION 15, UNIVERSITY OF SOUTH CAROLINA, page 379, after line 24, by adding an appropriately numbered new proviso to read: /15.__. (USC: ) From the funds appropriated to the University of South Carolina, $58,000,000 must be credited to the Department of Education to be distributed to the school districts pursuant to the EFA formula. / Renumber sections to conform. Amend sections, totals and title to conform. Senator BRYANT explained the amendment. On motion with Senator BRYANT, Amendment No. 120A was carried over. With unanimous consent, Senator SHANE MARTIN was recognized to speak on Amendment No. 120A. Amendment No. 118 Senator ELLIOTT proposed the following Amendment No. 118 (AS MULTI-STATE DRUG PURCHASING POOL), which was adopted (#13): Amend the bill, as and if amended, Part IB, Section 21, DEPARTMENT OF HEALTH AND HUMAN SERVICES, page 390, after line 18, by adding an appropriately numbered new proviso to read: /21. (Medicaid Pooling Initiative) The Department of Health and Human Services' Medicaid Pharmacy and Therapeutics Committee shall conduct a cost-benefit analysis of the National Medicaid Pooling Initiative (NMPI) and the state's participation in the NMPI. The analysis shall include a review of all other multi-state Medicaid drug purchasing pools that have been approved by the Centers for Medicare and Medicaid Services to compare the NMPI to other available plans to identify the initiative that provides the greatest opportunity to achieve maximum savings for the state. The department shall provide a report on the results of the analysis to the Chairman of the Senate Finance Committee and the Chairman of the House Ways & Means Committee no later than January 14, 2011. / Renumber sections to conform. Amend sections, totals and title to conform. Senator ELLIOTT explained the amendment. Senator CROMER moved that the amendment be adopted. The amendment was adopted. Amendment No. 92 Senator BRIGHT proposed the following Amendment No. 92 (DAD 31.9 RENT PAYMENT SUSPENSION), which was tabled: Amend the bill, as and if amended, Part IB, Section 31, STATE MUSEUM COMMISSION, page 410, paragraph 31.9, by striking lines 8-10, by inserting: / 31.9. (MUSM: Rent Payment Suspension) For Fiscal Year 2009-10 2010-11 the State Museum is not required to pay rent or maintenance expenses, including all utilities, operations, maintenance and repairs to General Services for the premises it leases in the Columbia Mills Building. / Renumber sections to conform. Amend sections, totals and title to conform. Senator BRIGHT explained the amendment. Senator KNOTTS moved to lay the amendment on the table. The "ayes" and "nays" were demanded and taken, resulting as follows: Ayes 31; Nays 11 AYES Alexander Anderson Campbell Campsen Cleary Coleman Courson Cromer Davis Elliott Fair Ford Grooms Hayes Jackson Knotts Land Leatherman Leventis Lourie Malloy Martin, Larry McGill Nicholson O'Dell Pinckney Rankin Ryberg Scott Shoopman Williams Total--31 NAYS Bryant Martin, Shane Massey McConnell Mulvaney Peeler Reese Rose Setzler Sheheen Verdin Total--11 The amendment was laid on the table. Point of Order Senator MASSEY raised a Point of Order that Proviso 37.14 of Part 1B was out of order inasmuch as it was violative of Rule 24A. 37.14. (DNR: Watercraft Title and Registration Fees Surcharge) For Fiscal Year 2010-11, the Department of Natural Resources shall be authorized to charge a five dollar administrative surcharge on each watercraft and outboard motor title, title transfer and duplicate title, and on each watercraft registration, watercraft registration transfer, and duplicate registration document. The revenue collected must be deposited into the Drew's Law/Boat Titling Fund of which forty percent must be utilized for law enforcement operations and the balance utilized for administration of the provisions of Title 50. No funds generated from this administrative surcharge may be used to provide pay increases. Unexpended revenue must be retained by the department and carried forward from the prior fiscal year into the current fiscal year and used for the same purposes The PRESIDENT took the Point of Order under advisement. The Point of Order was subsequently withdrawn. Point of Order Senator MASSEY raised a Point of Order that Proviso 37.15 of Part 1B was out of order inasmuch as it was violative of Rule 24A. 37.15. (DNR: Hunting and Fishing License Surcharge) For Fiscal Year 2010-11, the Department of Natural Resources shall be authorized to impose a two dollar administrative surcharge on each license, permit, stamp, and tag issued to engage in any hunting or fishing activity. The surcharge shall not apply where no fee is charged. The revenue collected must be deposited into the Fish & Wildlife Protection Fund and be expended for the purposes of the Fish and Wildlife Protection Fund as defined in statute. No funds generated from this administrative surcharge may be used to provide pay increases. Unexpended funds must be retained by the department and carried forward from the prior fiscal year into the current fiscal year and used for the same purpose. The PRESIDENT took the Point of Order under advisement. The Point of Order was subsequently withdrawn. Amendment No. 101 Senator MASSEY proposed the following Amendment No. 101 (4657R052.ASM.DOCX), which was laid on the table: Amend the bill, as and if amended, Part IB, SECTION 44, JUDICIAL DEPARTMENT, page 424, after line 2, by adding an appropriately numbered new proviso to read: / 44.__. (JUD: Rent Payments) The Judicial Department is not required to pay rent to the Budget and Control Board for Fiscal Year 2010-2011. The Judicial Department is entitled to retain those funds to cover the Department's operating expenses for Fiscal Year 2010-2011./ Renumber sections to conform. Amend sections, totals and title to conform. Senator MASSEY explained the amendment. Senator LEATHERMAN spoke on the amendment. Senator LEATHERMAN moved to lay the amendment on the table. The amendment was laid on the table. Amendment No. 31 Senator MASSEY proposed the following Amendment No. 31 (4657R022.ASM), which was not adopted: Amend the bill, as and if amended, page 445, by striking Proviso 62.2 and inserting: / 62.2. (INS: Reimbursement Carry Forward) Reimbursements received for Data Processing Services, Revenue, Miscellaneous Revenue and Sale of Listings and Labels shall be retained for use by the department. These funds may be carried forward in the current fiscal year. The Department of Insurance is authorized to pay the annual dues, not to exceed$10,000 for the South Carolina Senate and the South Carolina House of Representatives for membership in the National Council of Insurance Legislators from funds collected under this proviso. / Renumber sections to conform. Amend title to conform. Senator MASSEY explained the amendment. Senator LEATHERMAN moved to lay the amendment on the table. PRESIDENT Pro Tempore PRESIDES At 4:50 P.M., Senator McCONNELL assumed the Chair. The Senate refused to table the amendment. The question then was the adoption of the amendment. Amendment No. 31 was not adopted. Amendment No. 31--Recorded Vote Senators MASSEY and SHEHEEN desired to be recorded as voting in favor of the adoption of Amendment No. 31. Amendment No. 122 Senator FAIR proposed the following Amendment No. 122 (4657R059.MLF.DOCX), which was adopted (#14): Amend the bill, as and if amended, Part IB, Section 80C, BUDGET AND CONTROL BOARD, EMPLOYEE BENEFITS, page 482, by striking Proviso 80C.2 in its entirety and inserting: / 80C.2. (BCB/EB: Funding Abortions Prohibited) No funds appropriated for employer contributions to the State Health Insurance Plan may be expended to reimburse the expenses of an abortion, except in cases of rape, incest or where the life of the mother is in jeopardy mother's medical condition is one which, on the basis of the physician's good faith judgment, so complicates the pregnancy as to necessitate an immediate abortion to avert the risk of her death or for which a delay will create serious risk of substantial and irreversible impairment of major bodily function, and the State Health Plan may not offer coverage for abortion services, including ancillary services provided contemporaneously with abortion services. / Renumber sections to conform. Amend sections, totals and title to conform. Senator FAIR explained the amendment. Amendment No. 122--Recorded Vote Senator KNOTTS desired to be recorded as voting in favor of the adoption of Amendment No. 122. Amendment No. 68 Senators CLEARY and ROSE proposed the following Amendment No. 68 (4657R043.REC.DOCX), which was adopted (#15): Amend the bill, as and if amended, Part IB, Section 81, DEPARTMENT OF REVENUE, page 484, after line 8, by adding an appropriately numbered new proviso to read: / 81. . (DOR: Bingo Licenses) The provisions of Section 12-21-3940(D) of the 1976 Code are suspended for the current fiscal year. / Renumber sections to conform. Amend sections, totals and title to conform. Senator CLEARY explained the amendment. Senator GROOMS asked unanimous consent to make a motion to take up Amendment No. 114A for immediate consideration. There was no objection. Amendment No. 114A Senators KNOTTS and SETZLER proposed the following Amendment No. 114A (4657R065.JMK.DOCX), which was adopted (#16): Amend the bill, as and if amended, Part IB, Section 37, DEPARTMENT OF NATURAL RESOURCES, page 415, after line 30, by adding an appropriately numbered new proviso to read: / 37. . (DNR: County Funds) Funds belonging to each of the counties of the State, now on hand or hereafter accruing to the counties, shall be expended by the department on recommendation of the respective county delegation, including the resident senator or senators, if any. An annual accounting for all such funds and expenditures shall be furnished by the department to each member of each county delegation; it being the intent of the General Assembly that the appropriations made in this section are conditioned upon compliance with this requirement. In addition to the annual accounting required above, the department shall make a proposal for expenditures of such funds in the succeeding fiscal year in each county to the members of the respective county legislative delegation, including the resident senator or senators, if any, and upon approval thereby shall proceed with the use of such funds in compliance with the finalized and approved plan as approved by each legislative delegation. If no plan is approved, the expenditure of such funds is to be administered as determined by the various legislative delegations. / Renumber sections to conform. Amend sections, totals and title to conform. Senator KNOTTS explained the amendment. Senator KNOTTS moved that the amendment be adopted. Senator GROOMS asked unanimous consent to make a motion to take up Amendment No. 115 for immediate consideration. There was no objection. Amendment No. 115 Senator KNOTTS proposed the following Amendment No. 115 (4657R062.JMK.DOCX), which was adopted (#17): Amend the bill, as and if amended, Part IB, Section 37, DEPARTMENT OF NATURAL RESOURCES, page 415, after line 30, by adding an appropriately numbered new proviso to read: / 37. . (DNR: County Game Funds/Equipment Purchase) Any equipment purchased by the department from county game funds upon recommendation of a county delegation, including the resident senator or senators, if any, shall remain in that county upon the request of a majority of the respective county delegation, including the resident senator or senators, if any, and if sold by the department, the proceeds of such sale shall be credited to such county game fund. Expenditures from the County Game Fund and the Water Recreation Resource Fund which have the approval of the county delegation shall be exempt from the provisions of Act 651 of 1978, as amended. // Renumber sections to conform. Amend sections, totals and title to conform. Senator KNOTTS explained the amendment. Amendment No. 19 Senators ROSE and MULVANEY proposed the following Amendment No. 19 (4657R012.MTR.DOCX), which was ruled out of order: Amend the bill, as and if amended, Part IB, Section 86, AID TO SUBDIVISIONS-STATE TREASURER, page 486, after line 8, by adding an appropriately numbered new proviso to read: /86._(AS-TREAS: Flexibility) For fiscal year 2010-2011, a political subdivision receiving aid from the Local Government Fund may reduce its support to any state mandated program or requirement by up to a percentage equal to the percentage reduction in the actual amount appropriated to the Local Government Fund as compared to the last completed fiscal year. / Renumber sections to conform. Amend sections, totals and title to conform. Senator ROSE explained the amendment. Point of Order Senator LEATHERMAN raised a Point of Order that the amendment was out of order inasmuch as it was violative of Rule 24A. Senator ROSE spoke on the Point of Order. Senator LAND spoke on the Point of Order. Senator MULVANEY spoke on the Point of Order. The PRESIDENT Pro Tempore sustained the Point of Order. Amendment No. 19 was ruled out of order. Amendment No. 72A Senator GROOMS proposed the following Amendment No. 72A (AS COMMUNITY HEALTH PLANS), which was adopted (#18): Amend the bill, as and if amended, Part IB, Section 21, DEPARTMENT OF HEALTH AND HUMAN SERVICES, page 390, after line 18, by adding an appropriately numbered new proviso to read: /21. (DHHS: Community Health Plan Grants) From funds appropriated to the Department of Health and Human Services, the department shall allocate grants to community health plans approved pursuant to proviso 21.40 of this act and to Access HealthSC community health plans. The total amount of the grants shall not exceed $300,000. / Renumber sections to conform. Amend sections, totals and title to conform. Senator GROOMS explained the amendment. The amendment was adopted. Amendment No. 110 Senator BRIGHT proposed the following Amendment No. 110 (4657R057.LB.DOCX), which was tabled: Amend the bill, as and if amended, Part IB, SECTION 89, GENERAL PROVISIONS, page 517, Proviso 89.104, by striking line 9 and inserting: / resources of the Division of Aeronautics in the Department of Commerce are transferred to the Budget and Control Board Department of Transportation. / Renumber sections to conform. Amend sections, totals and title to conform. Senator BRIGHT explained the amendment. Point of Order Withdrawn Senator LAND raised a Point of Order that the amendment was out of order inasmuch as it was violative of Rule 24A. Senator LEATHERMAN spoke on the Point of Order. Senator MULVANEY spoke on the Point of Order. On motion of Senator LAND, with unanimous consent, the Point of Order was withdrawn. Point of Order Withdrawn Senator BRIGHT raised a Point of Order that Proviso 89.104 of Part 1B was out of order inasmuch as it was violative of Rule 24A. 89.104. (GP: Transfer Division of Aeronautics) Effective July 1, 2009, or as soon as practicable, the duties, functions, responsibilities, personnel, equipment, supplies, appropriated and authorized funds, carry forward funds and all other assets and resources of the Division of Aeronautics in the Department of Commerce are transferred to the Budget and Control Board. Objection Senator SHEHEEN asked unanimous consent to withdraw the Point of Order and withdraw the amendment. Senator BRIGHT objected. Senator MULVANEY asked unanimous consent to withdraw the Point of Order. There was no objection and the Point of Order was withdrawn. Senator BRIGHT explained the amendment. Senator BRIGHT moved to carry over the amendment. Senator SHEHEEN moved to table the motion to carry over the amendment. Parliamentary Inquiry Senator MASSEY made a Parliamentary Inquiry as to whether or not the Senator who made the motion to carry over the Bill loses the floor after disposal of the motion. The PRESIDENT Pro Tempore stated that the Senator does not lose the floor if the motion to carry over fails. The motion to carry over the amendment was tabled. Senator LEATHERMAN moved to lay the amendment on the table. The amendment was laid on the table. Amendment No. 7 Senator ROSE proposed the following Amendment No. 7 (4657R013.MTR.DOCX), which was not adopted: Amend the bill, as and if amended, Part IB, Section 89, GENERAL PROVISIONS, page 522, after line 10, by adding an appropriately numbered new proviso to read: /89._(GP: Tobacco Funds) With the exception of provisos 89.59 and 90.3 of this appropriations bill, any funds appropriated from the Healthcare Tobacco Settlement Trust Fund, established pursuant to Section 11-11-170, must be appropriated for use by the Department of Health and Human Services to fund programs eligible for federal Medicaid matching assistance. / Renumber sections to conform. Amend sections, totals and title to conform. Senator ROSE explained the amendment. Point of Order Withdrawn Senator SHEHEEN raised a Point of Order that the amendment was out of order inasmuch as it was violative of Rule 24A. On motion of Senator LAND, with unanimous consent, the Point of Order was withdrawn. Senator ROSE explained the amendment. The amendment was not adopted. Amendment No. 23 Senator ROSE proposed the following Amendment No. 23 (4657R017.MTR.DOCX), which was adopted (#19): Amend the bill, as and if amended, Part IB, Section 89, page 522, after line 10, by adding an appropriately numbered new proviso to read: /89._ (GP: Websites) All agencies, departments, and institutions of state government shall be responsible for providing on its Internet website a link to the Internet website of any agency, other than the individual agency, department, or institution, that posts on its Internet website that agency, department, or institution's monthly state procurement card statements or monthly reports containing all or substantially all the same information contained in the monthly state procurement card statements. The link must be to the specific webpage or section on the website of the agency where the state procurement card information for the state agency, department, or institution can be found. The information posted may not contain the state procurement card number. Any information that is expressly prohibited from public disclosure by federal or state law or regulation must be redacted from any posting required by this section. Renumber sections to conform. Amend sections, totals and title to conform. Senator ROSE explained the amendment. Senator LEATHERMAN moved that the amendment be adopted. The amendment was adopted. Point of Order Senator BRIGHT raised a Point of Order that Proviso 89.97 of Part 1B was out of order inasmuch as it was violative of Rule 24A. The PRESIDENT Pro Tempore overruled the Point of Order. Point of Order Withdrawn The PRESIDENT Pro Tempore took up the Point of Order raised by Senator BRIGHT on Wednesday, April 28, 2010, that Proviso 18.5 of Part 1B was out of order inasmuch as it was violative of Rule 24A. 18.5. (TEC: Caterpillar Dealer Academy) The area commission for the Florence-Darlington Technical College may waive the requirements of Chapter 112 of Title 59 for student participants in the Caterpillar Dealer Academy operated by Florence-Darlington Technical College. On motion of Senator BRIGHT, with unanimous consent, the Point of Order was withdrawn. Amendment No. 26 Senator SCOTT proposed the following Amendment No. 26 (SWB\8069CM10), which was adopted (#20): Amend the bill, as and if amended, Part IB, Section 89, GENERAL PROVISIONS, page 522, after line 10, by adding an appropriately numbered new proviso to read: / 89.__(GP: Mayor and Councilman Study Committee) There is created a study committee to study all relevant provisions of law and make recommendations to the members of the General Assembly regarding the issues of when does a mayor or councilman forfeit his office, and how should a vacancy in the office of mayor or councilman be filled. The study committee shall be composed of the: Director of the South Carolina Election Commission, or her designee who shall serve as chairperson; President Pro Tempore of the Senate, or his designee; Speaker of the House of Representatives, or his designee; Chairman of the Senate Judiciary Committee, or his designee; Chairman of the House of Representatives Judiciary Committee, or his designee; two members selected by the President of the Association of Counties; two members selected by the President of the Municipal Association; and President of the South Carolina Association of Registration and Election Officials. The study committee shall accept committee staffing and coordination from the appropriate committees of the Senate and House of Representatives. The members of the study committee shall serve without mileage, per diem, and subsistence. The study committee shall meet as often as is necessary, and shall convene no later than sixty days after the effective date of this act. The study committee shall submit its recommendations to the Chairman of the Senate Judiciary Committee, Chairman of the House of Representatives Judiciary Committee, and the members of the Senate and House of Representatives no later than January 1, 2011, at which point the study committee will dissolve. / Renumber sections to conform. Amend sections, totals and title to conform. Senator SCOTT explained the amendment. The amendment was adopted. Amendment No. 49 Senator MULVANEY proposed the following Amendment No. 49 (DKA\3998DW10), which was adopted (#21): Amend the bill, as and if amended, Part IB, Section 89, GENERAL PROVISIONS, page 522, after line 10, by adding an appropriately numbered new proviso to read: / 89.__ (GP: Regulations) For the current fiscal year, if a state agency proposes a regulation that levies or increases a fee, fine, or that otherwise generates revenues, the title to the Joint Resolution which proposes the regulation must indicate that a fee, fine, or revenue source is being proposed. / Renumber sections to conform. Amend sections, totals and title to conform. Senator LEATHERMAN spoke on the amendment. Senator LEATHERMAN moved that the amendment be adopted. The amendment was adopted. Amendment No. 55 Senator MULVANEY proposed the following Amendment No. 55 (DAD SUSPEND ETV2), which was tabled: Amend the bill, as and if amended, Part IB, Section 89, GENERAL PROVISIONS, page 522, after line 10, by adding an appropriately numbered new proviso to read: / (GP: Suspend Operations of ETV) Operation of the Educational Television Commission shall be suspended for Fiscal Year 2010-11 and all of their general fund appropriation and all other funds carried forward from the prior fiscal year, excluding federal funds and donations or gifts bound by donor stipulation shall be transferred to the Department of Public Safety for law enforcement officers. / Renumber sections to conform. Amend sections, totals and title to conform. Senator MULVANEY explained the amendment. Senator HAYES spoke on the amendment. Point of Order Senator PEELER raised a Point of Order that the amendment was out of order inasmuch as it was violative of Rule 24A. The PRESIDENT Pro Tempore overruled the Point of Order. Senator MULVANEY resumed explaining the amendment. Remarks by Senator MULVANEY Gentlemen, I have one amendment -- one real amendment. We have had some small ones, some less controversial ones, but I want to warn you, this one is controversial. So I want to talk a little bit about why I am doing this, because on its face, it seems fairly hard-hearted. This budget amendment is fairly simple. It takes all of the money from Educational Television this year -- all of it -- every single penny and gives it to the Department of Public Safety for law enforcement officers. That's about it. What's the argument in favor? You know what the argument is and I guess we'll get a chance to talk about it with some questions. The argument is -- what's the priority? What's the priority as a State when we're as short as we are with funding our law enforcement officers? Do we really need to be in the television business? I'll be happy to take some questions. Senator LEATHERMAN: Senator, are you aware that ETV supports K-12 beyond belief? Throughout the schools are we proposing that we shut them down for one year and not allow those programs to be broadcast in the classrooms? Senator MULVANEY: Yes, sir. Senator LEATHERMAN: Senator, we are trying to improve education. Are you opposed to little Johnny and little Suzy out there getting those ETV programs to help to them learn to read and write? Are you opposed to that? Senator MULVANEY: I'm not opposed to education, Mr. Chairman. You know that I am not. You also know you may be aware that the next amendment in line actually takes the money from ETV and gives a portion of it to EFA, so we can have more discussions about how to best spend money for education in a few minutes but the bottom line is that we are in the television business -- the State of South Carolina is in the television business. You can go home any night. I do. I watch ETV, and you can't tell the difference most of the time between ETV and regular television. This amendment has nothing to do with an attack on ETV. It is simply, in my mind, sir, a prioritization. Is ETV more important than putting more law enforcement officers on the roads? Senator LEATHERMAN: Senator, I thought I heard you say just now "take a part of the money" and transfer it. What I am reading here is that it suspends operation and transfers all of their General Funds and other funds. Senator MULVANEY: Yes, sir, but, Mr. Chairman, what I had mentioned was that the next amendment in line actually does the same thing. It takes all of the money away from ETV and splits it into three pieces, one of which is for EFA funding. Senator HAYES: I just wanted to follow up with what the Senator from Florence was telling you. Not only does ETV provide distance learning for K-12, but, also, it is an integral part of higher education and also for law enforcement. They do training for law enforcement as well. So the very people you are trying to help with this, once again, are being hurt. It's not just your public television or public radio; it's a very small part. We have invested a great deal of money and effort to get these programs out to the colleges and the K-12 and law enforcement all over the State. Certainly, as well-intentioned as your priorities are, I think this is against some of the priorities that you claim to be seeking. Senator MULVANEY: I appreciate that Senator. I do accept that reasonable minds can disagree on this, but I would suggest to you that if your interest is really in public safety then the top priority should be officers. While ETV certainly does play a public safety role, it's a very attenuated role -- it's not a direct or primary role -- and that the best way to deal with public safety would be with more officers. By the same token, ETV has an attenuated role in education. Certainly the best way to impact education would be to get more teachers in the classroom, which will be in the next amendment. So, I hear what you are saying. I think we will have to respectfully disagree on this one, but, I think your point is well-made. Senator PINCKNEY: What do you have against Big Bird? I mean, did Elmo do something to you or did Oscar the Grouch say something wrong? Senator MULVANEY: Senator, you make an excellent point. You can get that on regular television these days. When you and I were young men that was not the case. When ETV was started, it was what? One of three or four channels and there was no outlet for that kind of educational programming. Senator PINCKNEY: But, now Senator, you can't get Big Bird on anyplace but public television. Now how am I going to explain to my one-year old that she can no longer watch Barney and I tell her that my seatmate from Lancaster said that public TV is no longer worth funding? How do we tell teachers in the classroom that they can no longer have the science shows. What about Great Performances for our fellow lovers of classical music. How do we not have these wonderful shows that really add to the life of our children and bring families together? I can't go home and tell my daughter that I cancelled Big Bird. I just can't do that. Help me explain to her why we are cancelling Big Bird. Senator MULVANEY: Let me answer this way, Senator. My 10-year old triplets are at the point where they are not watching many -- if not any -- of those shows, but they used to just the same as all the rest of our children did. We were big into Blues Clues, that was the big one for us and then there was Where in the World is Carmen San Diego, I think, was another one, all right? Those are all available on regular television. The history shows that you talked about are excellent programming which is another part of ETV. There's the History Channel, there's a National Geographic Channel, there are literally dozens of channels that are privately owned and not funded by the State. Senator PINCKNEY: Now Senator, I don't mind if you cancel Barney and I take away all the funding in the world from Barney. I don't mind that. Now, if you are going to cancel all of public television, that becomes almost as silly as my questions. I mean public television is a vital part of what we do as a State and, I mean, law enforcement is important but wouldn't you agree that for preschoolers and their parents and the rest of us -- don't you see any real benefit for public television? Senator MULVANEY: Absolutely I do. This is not about whether or not there is a benefit here. Absolutely, that is not the debate. The debate is the priorities. We have heard so much for the last several months about how we are cutting through fat, we're cutting through muscle, all the way down to the bone. We have heard that we cannot provide the most basic essential services. And my point is simply, that in this circumstance, educational television is not an essential service. Senator PINCKNEY: Senator from Lancaster, if we don't fund public television, you are going to need to help me explain it to a six-year old why we cancelled Barney and Sesame Street, and Cailliou and Word Girl, and Between the Lions, and I know all of that because I have young children so I am going to need you to help me understand if we are going to pass your amendment. Senator MULVANEY: We have been down that road together. This past summer a tremendous series -- Ken Burns' baseball series -- was available on ETV and regular television. It is almost impossible these days, aside from the pledge drive and the special programming that usually focuses on this Chamber and the House Chamber, to tell the difference in what we are doing in educational television and what you can get on regular TV. Again, this amendment is not about the benefits of ETV, it's not about the fact that ETV does not provide something valuable to the community; certainly, it does. It's simply about priorities in an unusually desperate financial situation. Senator BRYANT: Isn't it true that there is a lot of private support for Educational Television? Senator MULVANEY: It is my understanding that there is. I have contributed to it in the past in this State and in other states. My understanding is that there is a lot of private support. Senator BRYANT: They'll say brought to you by and they'll name a corporation or foundation, whatever. So your amendment wouldn't necessarily shut down ETV, would it? It would just shut down the state portion and it might even increase private investment. And maybe they might want to sponsor "This Week in the Senate," the President Pro Tempore show. I don't know. Senator MULVANEY: And maybe the Senator from Jasper would be the first in line to increase his donation so that his child can continue to watch Sesame Street. If it is valuable enough to the community, they will support it. That is the whole concept behind regular television. And, if you do believe that ETV does provide a valuable service, let it stand on its own. What I really think we are saying, what we are hearing in here from folks opposed to this amendment, is that it doesn't provide enough of a service to stand on its own. We can't afford that this year. I think it is time for it to go on its own for this year. Senator BRYANT: And, Senator, if this does pass, I would tell constituents that are disappointed, if they can't see Big Bird -- and we don't know that -- but, that we could tell them that the roads are safer because we are putting the funds toward law enforcement. Did you know that if this passes that I plan to tell folks that are disappointed if their favorite shows are discontinued, that the roads are a little bit safer now because we put this money in law enforcement? Senator MULVANEY: I think that would make sense, yes, sir. Senator PEELER: Senator from Lancaster, did you know that a group of Representatives meet every Thursday morning about 9:30 in 5-1A Blatt Building to watch "This week in the Senate," -- the President Pro Tempore calls it "The Senate Speaks," I think, and if this amendment passed, it would be dead on arrival in the House because they have nothing else to do on Thursday morning and it would eliminate this show. I can't imagine the House going along with you doing away with ETV. Senator MULVANEY: I would have you know that my first introduction to the Senate -- actually my first two formal introductions to the Senate were thanks to ETV. Number one, I was amongst that group that used to sit in Jimmy Merrill's office and watch that program -- all five of us in the State who were doing that. And, then my first formal introduction as a member of the Senate was on the President Pro Tempore's show with the Senator from Lexington. I can tell you that was a very interesting introduction to the Senate when you come over from the House. Senator PEELER: I'll have to get the archives and look at that one, and, when everyone else gets through with their humor, Mr. PRESIDENT, I remember either you or the other presiding officer ruled yesterday that a similar amendment was ruled out of order because it violated Rule 24 and this would be the same thing. This amendment suspends permanent law and transfers so I would make that Point of Order that it is in violation of Rule 24. Senator MULVANEY: I think it's pretty straightforward that it does none of those things. It simply takes, for one year, the money from ETV. It does not change any permanent law in any fashion. It simply takes the funding and then moves it over to other line items and in this case another line item in the budget. It is exactly the type of amendment that I think is well within the lines of Rule 24. There is no permanent law affected in any fashion and it deals with the expenditure of funds. Senator CAMPSEN: Senator, I applaud your efforts to try to focus the budget on the core functions of government, but, I am sure you would agree, that one core function of government is legislating. Wouldn't you agree with that? What we do in the General Assembly, that's a core function of government, isn't it? Senator MULVANEY: I would think so, yes sir. Senator CAMPSEN: And you would also agree that since the House does watch the President Pro Temporepore's show every week, since they began that, that the quality of their legislative product has gone up dramatically has it not? Senator, would you agree with that one? Senator MULVANEY: (Laughing) Can I pass on that one? Senator CAMPSEN: As a recent former House member, you can pass on that one. But, my concern is that they are not watching it just for entertainment value, but, also to be enlightened. And my only concern, my only concern with your amendment is that if we cut out that show and we have that educational opportunity no longer available to the House that a core function of government, dealing with lawmaking, may go down dramatically -- the quality of the work product. Senator MULVANEY: Let's talk about that, because I use this service. In fact, often times I know many of us, we will sit at our desk and watch what's happening in the House on the ETV link that is available on the website. To that extent, it is used. There is no question. First, I would say that that is easily enough done without ETV. We could simply wire this room up to do a live feed on the Internet without ETV's intervention and still allow that information to get out. Secondly, with all due respect to the group that watched this on Thursday morning -- and I was one of them -- there were maybe half a dozen of us on a really, really good day. Senator CAMPSEN: No, I'm trying to be funny. Senator MULVANEY: The point is that a lot of the things that ETV does, including coverage of the State House, both Chambers, could be done in another fashion without spending the taxpayer's dollars. Senator CAMPSEN: I agree with that. Senator MASSEY: Senator, tell us again how much money we are talking about here from ETV, do you know? Senator MULVANEY: I do, I think it's about$9.9 million plus whatever is in the appropriate carry forward funds which, I think, was another $2 or$3 million. It translated, by the way, roughly into someplace between 175 and 190 additional law enforcement officers on the roads next year. Senator MASSEY: And that was going to be my next question. We're talking to somewhere between probably $12 and$13 million and how many troopers are we talking about with that? Senator MULVANEY: 175 to 190 are the numbers I was given by staff. Senator MASSEY: Senator, my good friend, the birthday boy, over here, asked me if public radio is included in this? Do you know anything about that? Senator MULVANEY: I believe that it is, but, again, I don't want to say something that is inaccurate from the dais. I believe that it is a line item from within the ETV section. Senator MASSEY: So, what you are trying to do is to give more money Public Safety to put troopers on the road, is that right? Senator MULVANEY: That is the intent of what this amendment does. Yes, sir. Senator MASSEY: Senator, are you aware that and I hope that everybody will listen to this, because there are probably some people who don't know this; but, are you aware that there is hidden within the provisos of this budget an increase in registration fees for motor vehicles? Senator MASSEY: Well, every year we have to register our cars, are you aware of that? Senator MULVANEY: Are you talking about Proviso number 89.135? Senator MASSEY: Sounds like you are familiar with it. Senator MULVANEY: This is the proviso that raises the registration fees for automobiles by $6? Senator MASSEY: That's right. And are you aware that this fee is being increased in order to give money to troopers, a bunch of it. Senator MULVANEY: I think that the proviso specifically says that the money that is used from that car registration fee, or the increase in the car registration fee, will be used for law enforcement officers, yes sir. Senator MASSEY: All right then. Are you aware that what we are talking about with that increase in registration fees is somewhere a little over$22 million? Senator MULVANEY: I had heard that, yes, sir. Senator MASSEY: All right, now, Senator, you were here last week, when we had a pretty spirited debate on legislation that the Chief Justice asked for regarding court fees. Do you remember that? Senator MULVANEY: I was here for that. Senator MASSEY: Do you remember us having a debate about whether we should raise fees $22 million in order to help the highway patrol? Senator MULVANEY: I don't remember any debate as to whether or not we should raise taxes$22 million for the highway patrol. Senator MASSEY: Do you remember us having any debate at all on this floor about what kind of position the highway patrol was in, the financial position the highway patrol was in and whether we actually need to, let's call it what it is -- we are raising taxes on everybody across the State pretty much, on people who own cars, isn't that right? Senator MULVANEY: We are. Senator MASSEY: Do you remember hearing any type of debate in this body about what the financial situation was with the patrol and why we needed to raise that amount of money? Senator MULVANEY: Nope. Senator MASSEY: Are you aware, Senator, that there are several people in here who believe that that proviso potentially violates the Rules of the Senate? Senator MULVANEY: I am aware of that, yes sir. Senator MASSEY: Now tell us, Senator, what happens, if that Point of Order is made and sustained -- as I believe that it probably would be -- and the patrol loses that amount of money and they are not getting the $9 million that you are asking for here. What's going to happen to the patrol? Senator MULVANEY: They are going to lose several hundred positions. What you are talking about is Proviso 89.135 which proposes to raise registration fees on automobiles by about$22 million. There has been some discussion, I have been aware of some discussion, as whether that proviso violates Rule 24. If it goes away, wouldn't it be nice to have the additional money here to keep those officers on the road? If that is what you are getting at, I tend to agree with you Senator. Senator MASSEY: Now tell me, I know you are not opposed to education. You probably even like Big Bird. Is that right? Senator MULVANEY: I was a Grover fan, myself. But, that probably is getting more information than most people need, but, I was a big Grover fan. Senator MASSEY: Senator, do you believe like I do that at some point this State is going to have to make responsible budget decisions and going to have to start prioritizing the things that are core essentials for government as opposed to the things that we want? Senator MULVANEY: Well, let's talk about that. Why would somebody, by the way, who is running for Congress get up and do something as unpopular as this? Why would I do that? Because I believe that we are making some mistakes here in this process. What I have not seen -- and with all due respect to the Finance Committee -- what I have not seen are the really, really difficult cuts. I know that there have been cuts. I know that there have been cuts through fat, through muscle, down to the bone. But, when I see a budget that still has ETV services in it, what that tells me is that we are in a state of denial. Senator MASSEY: How about the Arts Commission, Senator? Senator MULVANEY: And the Human Rights Commission and the various other groups? What that tells me is that we have not come to grips with what is going to happen next year when the stimulus money is gone. We are simply kicking the can down the road for another year saying that, "Well, we hope it gets better next year." We really are in a position to make the really, really unpopular decisions this year by looking at things that are very popular like the Arts Commission and like Educational Television. So, yes, sir. That is the root of what is getting ready to happen here. Senator MASSEY: So when that Point of Order is made and it is sustained and we lose that money and then we also don't have the $9 million or actually$12 or $13 million from here, then we are talking about the patrol having some real problems because this body, and lets include the House in this, failed to budget in a responsible manner, isn't that right? Senator MULVANEY: I tend to agree, yes, sir. Senator MASSEY: I appreciate your amendment. Thank you. Senator RANKIN: Is this a sincere amendment where you genuinely want to take the money that is operating ETV away from them and let them rest solely on sponsorships? Senator MULVANEY: Well, Senator, I have not been in the body very long -- you and I don't know each other extraordinarily well -- but I think it would be entirely consistent with everything you have seen out of me for the last year and a half to say that I am very interested as to what the core function of government is. So, I think that, yes, it is absolutely a sincere motion. In fact, I am at somewhat of a loss as what you think it might be other than that. Senator RANKIN: Well, I wonder. Do you have an educational radio or television satellite within Lancaster? Do they broadcast in Lancaster? Senator MULVANEY: I think that the nearest broadcast is in Rock Hill. Senator RANKIN: Is that part of your district? Senator MULVANEY: It's not. I believe that the actual facility itself lies in the other Senator from York's district, but, it is very close to the boundary between my district and his. My guess is that I probably have folks in my district who work for educational television. Senator RANKIN: OK. Are you aware of what the State appropriated to modernize the technology for ETV? Perhaps, when you were in the House? Do you recall? Senator MULVANEY: That number does not ring a bell for me, Senator. I'm sorry. Senator RANKIN: OK. We appropriated a huge expense of money that we as a State advanced to modernizing the satellites and the broadcast and broadband. Senator MULVANEY: Wasn't there something there for broadband as well? Yes, I remember that. Senator RANKIN: And so, would you have that money and that expense effectively shut down or were you just saying you can exist, but you are not going to exist with state dollars. Senator MULVANEY: I don't think it's wasted, if that's your point. I mean it is certainly an asset. It can still function. Again, if ETV offers something worthwhile to the public, it would strike me that the public would support it and it would continue to work and that the money we have expended as a State would not go to waste. You could see it being privatized possibly and sold off. Senator RANKIN: So, you would want to sell ETV? Senator MULVANEY: I would want ETV to make its own decisions. What I am trying to do is to simply say, "Listen, we can no longer afford in this economic environment to make ETV a priority." Senator RANKIN: Do you know that they are actually making money, when they produce locally within South Carolina, both music and television programming? Are you aware that they make money? Senator MULVANEY: I have no reason to believe that is false, no, sir. Senator RANKIN: Are you a listener, by chance, of either the radio or do you watch ETV? Senator MULVANEY: I listen to more public radio than folks on my side of the aisle would probably be comfortable with. Senator RANKIN: Are you aware of the fundraising efforts that they have where they will give you a cup, give you music, give you a T-shirt if you give$100 or higher? Senator MULVANEY: Yes, sir. Senator RANKIN: Have you ever contributed to that? Senator MULVANEY: You probably can tell from my political philosophy that I am a big fan of the Prairie Home Companion, which I do listen to religiously on Saturday. Senator RANKIN: Have you ever contributed to ETV as a member? Senator MULVANEY: I don't know if I gave to the channel in North Carolina when I lived in North Carolina, or if I do now. Senator RANKIN: You know, in fact, there is talk about people like you. I'm not talking about North Carolina ETV, I'm talking about your own State. You are a taker and not a giver. Senator MULVANEY: The point is there were several gentlemen who got beat up last week for telling things that were not exactly 100% accurate from the dais, but what I'm telling you is that I have supported public television and public radio in the past. In my district we get both TV and radio from North Carolina, and I am not precisely sure to which I have given. Senator MULVANEY: There were checks, there was no question about that. Senator RANKIN: All right, is that SC ETV or is that North Carolina? Senator MULVANEY: Where I live, it is always hard to tell. Senator RANKIN: I am genuinely concerned because it is not just about what we have spent and the federal money that is also appropriated that we get as a result of a product that we generate here. Marian McPartland's show is made here. It is a product produced out of South Carolina. She is a world-renowned pianist. Have you ever heard of her? Senator MULVANEY: I have, yes. Senator RANKIN: And there are others, many others, that they produce that are making money for us. I wonder for not just the Barney's and the other great programs that are now leaving my mind because my children now are ages 9 and 12 -- I wonder for the young families who not only are getting the benefit of all this, but also, for those in the classroom -- whether you would tell the teachers that this is positive for them? That we are going to shut the lights off at ETV. Senator MULVANEY: Absolutely I would. I would not hesitate to tell teachers that this is good for them. Because what I would tell them is, "Listen, we had a choice in Columbia between continuing ETV and putting 180 additional police officers on the streets." Now, I could have that conversation straight in the face with any teacher in this State. So, yes, sir. I could not be up here making this amendment in good faith if I could not have that exact conversation. Senator RANKIN: So, you are taking this money and putting this to hiring more police officers for the streets and highway patrolmen? Senator MULVANEY: That's exactly right. Senator RANKIN: And your support -- and I don't know if there are efforts to increase within the budget by the agency responsible for that or the subcommittee -- are you saying that you are taking ETV off the TV and putting more cars and troopers on the road and that's for one year? Senator MULVANEY: Yes, I can only do it for one year without violating Rule 24. Senator RANKIN: And you would hire somebody and you as a potential employee would take a job that you knew had a shelf life of only one year? Senator MULVANEY: I think I took a job like that in the House, didn't I? Senator RANKIN: That's a two-year job. Senator MULVANEY: OK. Is that what it was? Senator RANKIN: And sincerely, there is no way you are going to train, the police academy is going to train these folks... Senator MULVANEY: This body can see the benefit of having the additional 180 officers on the road. Actually we can do this again next year, can't we? This a recurring line at ETV. So we can be right back up again next year and have this same conversation and you can vote for it again next year if you want to. Senator RANKIN: To delete ETV, but increase law enforcement? Senator MULVANEY: Yes, sir. Senator RANKIN: Now, that is a great argument and I hope you get to make that somewhere beyond the Senate. Perhaps you'll get to make that in Congress. I am curious though, in all sincerity, with all that you've got that are the benefits of ETV and you have heard smatterings of the offerings that they have -- radio, television, broadcasting, production -- I guess, perhaps, if there is one show that you might not like, perhaps not the Senate or the House, but maybe you would like to delete the State of the State Address? Because, surely there are fewer people watching that than watch the .... Senator MULVANEY: You are barking up the wrong tree on that one, Senator. I would have no difficulty cutting out the State of the State Address. Senator RANKIN: And I am curious, have you ever, after the State of the State Address, gotten in the line-up as a House member, Senator, to speak about the comments of the Governor? Senator MULVANEY: No, sir. Senator RANKIN: You have not? Senator MULVANEY: No, sir. Senator RANKIN: You ought to try it. You get a lot of points at home if you do. Senator MULVANEY: No, sir. I don't have the patience for that. Senator SHEHEEN: Mr. PRESIDENT, has the PRESIDENT ruled on the Point of Order? Senator McCONNELL: No, I am getting ready to. Senator SHEHEEN: I would love to hear it before we have a lot more dialogue. Senator McCONNELL: Alright, I have looked very carefully at this. It was probably one of the most difficult Points of Order, Senator from Cherokee. And, at first glance it raises serious questions under Rule 24. We looked at the statute on ETV. The statute on ETV is loosely drawn and only uses precatory language regarding decision-making. The amendment has been carefully worded to use the word "spend" for the fiscal year and the appropriation and then has excepted out from coverage all the funds that are otherwise directed in the statute. For that reason, it appears to fit. It does not conflict with, amend or add to the permanent law. It very neatly fits into an exception to suspend for a year. So for that reason we will have to overrule the Point of Order. But, I tell you it was a very difficult Point of Order. Senator FAIR: Senator, did the Senator from Aiken when he was questioning you ask if you knew that there was a proviso hidden in the budget? Did he say "hidden" in the budget. Senator MULVANEY: No. What I heard was there was a tax increase hidden in the budget. If he had said there was a proviso hidden in this budget, obviously -- we don't "hide" provisos in the budget. Senator FAIR: He was referring to the $6 tag saying that you subsequently talked about? Senator MULVANEY: Yes, sir. Senator FAIR: Did you have any trouble finding it? Senator MULVANEY: No, sir. I sat down to read it. Senator FAIR: Would you say that it was hidden? Senator MULVANEY: As a tax, yes, sir, I think that it is. Because it doesn't use the word "tax." It doesn't pass nearly, for example, the level of debate that we had last week on something that was one tenth the size. Senator FAIR: Putting semantics aside, wouldn't you agree that it was not hidden? And, did you know Senate Finance and maybe three subcommittees debated that with the leadership with the public present? To suggest to the public that it was hidden I think is an attack really on what we were trying to get done --what we are trying to get done with that and we will have to live with the consequences of what comes in the hours ahead. But, one of the questions that you asked, I have the answers to. What will happen if that$6 additional tax -- although it is not a tax -- on tags, doesn't come to fruition? The House, by the way -- with the House version of the budget when it came over here had already cut the Highway Patrol by 90 officers without any further reductions, the Department of Public Safety has to lay off an additional 152 officers and not all of those are highway patrolmen. Anyway, without this money, it gets down to 654 which is roughly half of what the highway patrol will be. Do you know which counties they are coming to Senator, to do away with the third shift first? I'm just kidding. There are a lot of us -- I have a smile on my face -- but I am very, very concerned about what is going to happen to Public Safety of South Carolina. Now, we have the option in the Senate, did you know, to pull the trigger on what we think is an "ought to be" situation and override a circumstance that we refer to as "what is"? And we are talking about "what is". We are looking at a reduction in force in the Highway Patrol, did you know that? Let me suggest something. You may get some more votes if you were to carry this over. Because if the attack on the Highway Patrol continues, and that funding source is removed, then eliminating ETV becomes an option along with eliminating libraries in Clarendon County and other things because we have to have the Highway Patrol. Senator MULVANEY: Well, it's not true, because what you are getting ready to say is that the funding source we have is the tax, and it's not true. The funding source we have is the General Fund. And we made a decision not to fund the officers fully. Senator FAIR: That's correct, and you are trying to offer something by replacing it. At least that is better than what some will do and I am suggesting to you that you don't have a chance of passage, in my opinion, with this right now. And, whereas later, if the attack on the Highway Patrol continues and if successful, then you might have a chance in passing your desire. Senator MULVANEY: Thank you, Senator. Senator MASSEY: Senator, I want to see if you heard what I just heard? Did you just hear that if we actually follow the rules, imagine that, if we actually follow the rules, that we will actually be responsible and find money to fund the Highway Patrol? Did you just hear that? Senator MULVANEY: I could see how you could have heard that, yes, sir. Senator MASSEY: That if we actually follow the rules, that we will start prioritizing in funding the core essentials of government. By cutting things like -- unfortunately and I would hate to do this -- but if we have to start ranking the Highway Patrol and ETV, the patrol is going to win out for me. But that we will start ranking things and we are going to start funding the core essentials of government. Senator MULVANEY: That's what this is. This is ranking. Face it. That's what we're doing. That's what this entire process is about. How are we going to rank the priorities of the State of South Carolina? I think this amendment simply looks at the budget and says, I think, that a small piece of it is out of whack. $9 million is not properly spent. It has nothing to do with ETV. Gentlemen, I appreciate your time. I also appreciate your questions and I move adoption. *** On motion of Senator LEVENTIS, with unanimous consent, the remarks of Senator MULVANEY were ordered printed in the Journal. Senator HAYES moved to lay the amendment on the table. The "ayes" and "nays" were demanded and taken, resulting as follows: Ayes 28; Nays 14 AYES Alexander Campbell Coleman Cromer Elliott Fair Hayes Hutto Jackson Knotts Land Leatherman Leventis Lourie Malloy Martin, Larry McConnell McGill Nicholson O'Dell Peeler Pinckney Rankin Reese Scott Setzler Sheheen Williams Total--28 NAYS Anderson Bright Bryant Campsen Cleary Davis Grooms Martin, Shane Massey Mulvaney Rose Ryberg Thomas Verdin Total--14 The amendment was laid on the table. Expression of Personal Interest Senator LEVENTIS rose for an Expression of Personal Interest. Remarks by Senator LEVENTIS Mr. PRESIDENT, I ask that the remarks of Senator MULVANEY, the Senator from Lancaster, be placed in the Journal and, when I finish, I will ask that my remarks be placed there as well. I do this not as a tete-a-tete--mine against his--not at all. I consider the Senator from Lancaster to be a friend. But I see an emerging pattern that goes into two camps. One being that the reason we are not funding education properly is because we are squandering money in other areas. The other I see is that the reason we are not funding education properly is because we have not prioritized matters. Senator from Lancaster, I have always been against--and will remain against--fiscal autonomy for school districts because the school boards are charged with a very serious and important matter of education that, by nature, is fairly narrow. We, on the other hand, are charged with shaping a budget that balances all of the demands of 4.6 million South Carolinians and education. While I believe education is an absolute priority, I believe just as strongly that quality of life is a priority that reflects directly upon whether business, industry and individuals come and/or remain in South Carolina. Therefore, I cannot be forced to say that we could take all those small agencies at the bottom and eliminate them in order to fund education or law enforcement, and then, at the end of the day, say that I've done a good day's work. If we eliminate parts--and no one is suggesting that, nor am I suggesting that they have--but if we eliminate agencies such as SCETV (which has been suggested), Vocational Rehabilitation and a lot of the agencies that are not too large just because they are not our priorities, then our actions virtually impact the quality of life in South Carolina in a way that will undermine our efforts to grow the state's economy, population and the young citizens we will look toward to take care of us in our later years. To sum up, we need for people to know not only what we end up with as a budget based on the leadership of our Finance Chairman, Senator LEATHERMAN, and members of this Senate; but, we also need them to understand some of these proposals so that they can make up their minds as to whether or not we have secured a legitimate way to fund the core functions of government--and one of those core functions is providing a quality of life for all of our citizens that will help South Carolina grow and prosper. Thank you. On motion of Senator LEVENTIS, with unanimous consent, the remarks of Senator LEVENTIS were ordered printed in the Journal. Expression of Personal Interest Senator MULVANEY rose for an Expression of Personal Interest. Point of Order Senator CLEARY raised a Point of Order that Proviso 90.5 of Part 1B was out of order inasmuch as it was a revenue raising measure and must originate in the House of Representatives. 90.5. (SR: Criminal Justice Academy Funding) (A) In addition to all other assessments and surcharges, during the current fiscal year, a five dollar surcharge to fund training at the South Carolina Criminal Justice Academy is also levied on all fines, forfeitures, escheatments, or other monetary penalties imposed in the general sessions court or in magistrates' or municipal court for misdemeanor traffic offenses or for nontraffic violations. No portion of the surcharge may be waived, reduced, or suspended. (B) The revenue collected pursuant to subsection (A) must be retained by the jurisdiction, which heard or processed the case and paid to the State Treasurer within thirty days after receipt. The State Treasurer shall transfer the revenue quarterly to the South Carolina Criminal Justice Academy. (C) The State Treasurer may request the State Auditor to examine the financial records of any jurisdiction which he believes is not timely transmitting the funds required to be paid to the State Treasurer pursuant to subsection (B). The State Auditor is further authorized to conduct these examinations and the local jurisdiction is required to participate in and cooperate fully with the examination. The PRESIDENT Pro Tempore overruled the Point of Order. RECESS At 7:15 P.M., on motion of Senator LEATHERMAN, the Senate receded from business until 8:15 P.M. NIGHT SESSION The Senate reassembled at 8:34 P.M. and was called to order by the PRESIDENT Pro Tempore. THE SENATE RESUMED CONSIDERATION OF H. 4657, THE GENERAL APPROPRIATIONS BILL. The Senate resumed consideration of the Bill, the question being the third reading of the Bill. Amendment No. 56 Senator MULVANEY proposed the following Amendment No. 56 (DAD SUSPEND ETV), which was tabled: Amend the bill, as and if amended, Part IB, Section 89, GENERAL PROVISIONS, page 522, after line 10, by adding an appropriately numbered new proviso to read: / (GP: Suspend Operations of ETV) Operation of the Educational Television Commission shall be suspended for Fiscal Year 2010-11. Of their general fund appropriation and all other funds carried forward from the prior fiscal year, excluding federal funds and donations or gifts bound by donor stipulation, one-third of the funds shall be transferred to the Department of Public Safety for law enforcement officers, one-third of the funds shall be transferred to the Department of Disabilities and Special Needs for in-home services, and one-third of the funds shall be transferred to the Department of Education to be distributed to local school districts based on the Education Finance Act formula. / Renumber sections to conform. Amend sections, totals and title to conform. Senator MULVANEY explained the amendment. Senator LOURIE moved to lay the amendment on the table. The amendment was laid on the table. Amendment No. 61 Senators MASSEY and BRIGHT proposed the following Amendment No. 61 (DG ASMBILLFEE), which was tabled: Amend the bill, as and if amended, Part IB, Section 89, GENERAL PROVISIONS, page 522, after line 10, by adding an appropriately numbered new proviso to read: / 89.___ (GP: Bill Fee) For fiscal year 2010-2011, each member of the General Assembly shall pay a fee of$50 for every bill or resolution introduced in which the member is the primary sponsor. The fee shall be paid to the member's respective house. The revenue raised pursuant to this proviso shall be transferred to the Department of Education to be transferred to school districts based on the Education Finance Act formula. / Renumber sections to conform. Amend sections, totals and title to conform. Senator MASSEY explained the amendment. Objection Senator LOURIE asked unanimous consent to make a motion to perfect the amendment by charging $100 per amendment to be offered on the General Appropriations Bill. Senator MULVANEY objected. Senator MASSEY resumed explaining the amendment. Senator LEATHERMAN moved to lay the amendment on the table. The amendment was laid on the table. Amendment No. 88 Senators PEELER, KNOTTS and ROSE proposed the following Amendment No. 88 (DG HSPSUSPREN), which was adopted (#22): Amend the bill, as and if amended, Part IB, Section 89, GENERAL PROVISIONS, page 522, after line 10, by adding an appropriately numbered new proviso to read: / /89.___. (GP: Beach Renourishment Suspension) For fiscal year 2010-2011, Chapter 40 of Title 48 of the 1976 Code is suspended. / Renumber sections to conform. Amend sections, totals and title to conform. Senator PEELER explained the amendment. Remarks by Senator PEELER Yesterday, there was a Point of Order on a proviso on residential care homes and their inspections. Our committee, two or three months ago, rejected a request to increase fees to inspect residential homes and facilities. This was a way to pay for that without a fee increase, but it was ruled out of order under Rule 24. This kind of surprised me--that it was ruled out of order under Rule 24. It wasn't a Rule 24 violation to stop funding ETV and shift the money to DPS? I understand that was a tough ruling, but I thought it was about the same. Anyway, this amendment I have before you now just suspends the beach nourishment program for one year and here's why. I'm serious about this when I tell you about this. Don't let this be you in a few years: "Granddaddy," "Yes son." "My teacher tells me that you were a South Carolina State Senator." "Well, yes son, I was." "I understand you were a Senator in 2010." "Yes, son, I was." "Our teacher told us that it was the toughest economic time in the State of South Carolina since the War and since a thing called the Great Depression." "Yes, son, it was a very, very tough time in the State of South Carolina. It was a terrible recession. People were out of work. School teachers were losing their jobs. Sick, hungry children were left unattended. Mean people were walking the streets." "Well, Granddaddy, what did you do when you were in the Senate?" "Well, let me tell you what I did, son. I paid millions of dollars to dump sand into the ocean." "You did what, Granddaddy?" "I spent millions of dollars of hard earned, tax payers' money to dump sand into the ocean." "Granddaddy, you mean like when we go to the beach and we make this thing called a sandcastle and it's so pretty and then after a few hours, no matter how hard we work and no matter how hard we try to protect that castle, that ocean comes up and washes that sand away?" "Millions of dollars, in the toughest economic time in the State and we dumped sand into the ocean." "Well, Granddaddy, why aren't you still in the Senate?" "Well, son, I think I just gave you the answer." Now, you're going to hear how great dumping sand in the ocean is and what it's going to do to our tourism in the State of South Carolina. I don't care how pretty a sandcastle you build tonight; that ocean's going to wash it away. I've put that just as plain as I can put it. If you can vote against this amendment and get re-elected, I'll worry about your constituents. Thank you. On motion of Senator ROSE, with unanimous consent, the remarks of Senator PEELER were ordered printed in the Journal. Objection Senator LOURIE asked unanimous consent to make a motion to perfect the amendment by directing any funds realized by the adoption of this amendment to the Education Finance Act funding formula. Senator CAMPSEN objected. Objection Senator LOURIE asked unanimous consent to make a motion to perfect the amendment by directing any funds realized by the adoption of this amendment to the Education Improvement Act funding formula. Senator HUTTO objected. Objection Senator LOURIE asked unanimous consent to make a motion to perfect the amendment by directing any funds realized by the adoption of this amendment to the Department of Public Safety. Senator KNOTTS objected. Objection Senator KNOTTS asked unanimous consent to make a motion to perfect the amendment by directing any funds realized by the adoption of this amendment to the Criminal Justice Academy. Senator LOURIE objected. Objection Senator BRIGHT asked unanimous consent to make a motion to perfect the amendment by directing any funds realized by the adoption of this amendment to the Department of Disability and Special Needs. Senator MALLOY objected. Objection Senator ALEXANDER asked unanimous consent to make a motion to perfect the amendment by directing$790,000 realized by the adoption of this amendment to the Residential Care Facilities Inspection Program. Senator CAMPSEN objected. Senator PEELER resumed explaining the amendment. The "ayes" and "nays" were demanded and taken, resulting as follows: Ayes 28; Nays 14 AYES Alexander Anderson Bright Bryant Cleary Coleman Courson Hayes Jackson Knotts Land Lourie Malloy Martin, Larry Martin, Shane Massey Mulvaney Nicholson Peeler Reese Rose Ryberg Scott Setzler Sheheen Shoopman Thomas Williams Total--28 NAYS Campbell Campsen Cromer Davis Elliott Fair Ford Grooms Hutto Leventis McConnell McGill Pinckney Rankin Total--14 Amendment No. 131 Senators MALLOY, CAMPSEN and KNOTTS proposed the following Amendment No. 131 (4657R066.GM.DOCX), which was adopted (#23): Amend the bill, as and if amended, Part IB, SECTION 89, GENERAL PROVISIONS, page 522, after line 10, by adding an appropriately numbered proviso to read: / 89. . (GP: Drug Court Program Funds) (A) During the current fiscal year, a Drug Court Program Fund is established within the State Treasurer's Office separate and distinct from the State's General Fund for the purpose of funding drug court programs. (B) Solicitors who received drug court funds during prior fiscal years pursuant to Section 14-1-213, Section 8-21-320, or a General Appropriations bill who have not used the funds to establish or administer a drug court program by January 1, 2011, shall transfer such funds to the State Treasurer's Office by February 1, 2011, to be deposited in the Drug Court Program Fund. (C) Solicitors who receive drug court funds during the current fiscal year pursuant to Section 14-1-213, Section 8-21-320, or the General Appropriations bill who are not using the funds for the establishment or operation of a drug court program shall transfer such funds to the State Treasurer's Office within thirty days of receipt, to be deposited in the Drug Court Program Fund. (D) A person who is convicted, pleads guilty, or pleads nolo contendere for a drug offense in general sessions court, magistrates court, or municipal court during the current fiscal year must pay a fifty dollar drug court fee. No portion of the fee may be waived, reduced, or suspended, except in cases of indigency. If the court determines that a person is indigent, the court may partially or totally waive, reduce, or suspend the fee. The revenue collected pursuant to this provision must be retained by the jurisdiction that heard or processed the case and paid to the State Treasurer's Office within thirty days of receipt, to be deposited in the Drug Court Program Fund. If the drug surcharge established by Section 14-1-213 is increased by a separate act of the General Assembly, this provision is null and void. (E) Before a person may be discharged and the proceedings dismissed during the current fiscal year pursuant to Section 44-53-450, the person must pay a three hundred fifty dollar fee if the person is in a general sessions court and a one hundred fifty dollar fee if the person is in a summary court. No portion of the fee may be waived, reduced, or suspended, except in cases of indigency. If the court determines that a person is indigent, the court may partially or totally waive, reduce, or suspend the fee. The revenue collected pursuant to this provision must be retained by the jurisdiction that heard or processed the case and paid to the State Treasurer's Office within thirty days of receipt, to be deposited in the Drug Court Program Fund. If a fee is established by a separate act of the General Assembly for a conditional discharge as contained in Section 44-53-450, this provision is null and void. (F) The funds and revenue deposited in the Drug Court Program Fund during the current fiscal year pursuant to this proviso may be distributed pursuant to a resolution of the General Assembly passed during the current fiscal year. / Renumber sections to conform. Amend sections, totals and title to conform. Senator MALLOY explained the amendment. Senator LEATHERMAN spoke on the amendment. Senator MALLOY moved that the amendment be adopted. Amendment No. 76 Senator BRIGHT proposed the following Amendment No. 76 (DG LBARTDB), which was tabled: Amend the bill, as and if amended, Part IB, Section 89, GENERAL PROVISIONS, page 522, after line 10, by adding an appropriately numbered new proviso to read: / 89.___ (Art Commission Suspension) For fiscal year 2010-2011, state funding for the Arts Commission is suspended. The state funds that otherwise would have been appropriated to the Arts Commission shall be transferred to the School for the Deaf and the Blind. The Department of Education shall administer any grant program that the Arts Commission otherwise would have administered. / Renumber sections to conform. Amend sections, totals and title to conform. Objection Senator RYBERG asked unanimous consent to make a motion to consider Amendment Nos. 76, 77, 78, 84, 85, 86 and 87 en banc. Senator BRIGHT objected. Senator BRIGHT explained Amendment No. 76. Senator HAYES moved to lay the amendment on the table. The amendment was laid on the table. Amendment No. 77 Senator BRIGHT proposed the following Amendment No. 77 (DG LBARTDPS), which was tabled: Amend the bill, as and if amended, Part IB, Section 89, GENERAL PROVISIONS, page 522, after line 10, by adding an appropriately numbered new proviso to read: / 89.__ (Art Commission Suspension) For fiscal year 2010-2011, state funding for the Arts Commission is suspended. The state funds that otherwise would have been appropriated to the Arts Commission shall be transferred to the Department of Public Safety for the Highway Patrol. The Department of Education shall administer any grant program that the Arts Commission otherwise would have administered./ Renumber sections to conform. Amend sections, totals and title to conform. Senator BRIGHT explained the amendment. Senator SHEHEEN moved to lay the amendment on the table. The amendment was laid on the table. Amendment No. 78 Senator BRIGHT proposed the following Amendment No. 78 (DG LBARTDDSN), which was tabled: Amend the bill, as and if amended, Part IB, Section 89, GENERAL PROVISIONS, page 522, after line 10, by adding an appropriately numbered new proviso to read: / 89.___ (Art Commission Suspension) For fiscal year 2010-2011, state funding for the Arts Commission is suspended. The state funds that otherwise would have been appropriated to the Arts Commission shall be transferred to the Department of Disabilities and Special Needs. The Department of Education shall administer any grant program that the Arts Commission otherwise would have administered./ Renumber sections to conform. Amend sections, totals and title to conform. Senator BRIGHT explained the amendment. Senator SHEHEEN moved to lay the amendment on the table. The amendment was laid on the table. Amendment No. 84 Senator BRIGHT proposed the following Amendment No. 84 (DAD SUSPEND COMM ON WOMEN FOR DDSN), which was tabled: Amend the bill, as and if amended, Part IB, Section 89, GENERAL PROVISIONS, page 522, after line 10, by adding an appropriately numbered new proviso to read: / (Suspend Commission on Women State Funds) For Fiscal Year 2010-11, state funding for the Commission on Women is suspended. The state funds that otherwise would have been appropriated to the Commission on Women shall be redirected to the Department of Disabilities and Special Needs. / Renumber sections to conform. Amend sections, totals and title to conform. Senator BRIGHT explained the amendment. Senator HUTTO moved to lay the amendment on the table. The amendment was laid on the table. Amendment No. 85 Senator BRIGHT proposed the following Amendment No. 85 (DAD SUSPEND MINORITY AFF FOR DDSN), which was tabled: Amend the bill, as and if amended, Part IB, Section 89, GENERAL PROVISIONS, page 522, after line 10, by adding an appropriately numbered new proviso to read: / (Suspend Commission for Minority Affairs State Funds) For Fiscal Year 2010-11, state funding for the Commission for Minority Affairs is suspended. The state funds that otherwise would have been appropriated to the Commission for Minority Affairs shall be redirected to the Department of Disabilities and Special Needs. / Renumber sections to conform. Amend sections, totals and title to conform. Senator BRIGHT explained the amendment. Senator PINCKNEY moved to lay the amendment on the table. The amendment was laid on the table. Amendment No. 86 Senator BRIGHT proposed the following Amendment No. 86 (DAD SUSPEND CONSUMER AFFAIRS FOR DDSN), which was tabled: Amend the bill, as and if amended, Part IB, Section 89, GENERAL PROVISIONS, page 522, after line 10, by adding an appropriately numbered new proviso to read: / (Suspend Department of Consumer Affairs State Funds) For Fiscal Year 2010-11, state funding for the Department of Consumer Affairs is suspended. The state funds that otherwise would have been appropriated to the Department of Consumer Affairs shall be redirected to the Department of Disabilities and Special Needs. / Renumber sections to conform. Amend sections, totals and title to conform. Senator BRIGHT explained the amendment. Senator HUTTO moved to lay the amendment on the table. The amendment was laid on the table. Statement by Senators RYBERG, ROSE, BRIGHT, DAVIS VERDIN, BRYANT and MULVANEY We voted against tabling Amendment Nos. 76, 77, 78, 84, 85 and 86. Senator BRIGHT offered good faith proposals to move money from certain state agencies into services for the children and the disabled. While each of the agencies in question provides a service of value, we believe that services to children and the disabled reflect the core mission of government. This budget calls for prioritization, and these amendments made the right priorities with taxpayer dollars. Amendment No. 87 Senator BRIGHT proposed the following Amendment No. 87 (DAD SUSPEND HUMAN AFF FOR DDSN), which was tabled: Amend the bill, as and if amended, Part IB, Section 89, GENERAL PROVISIONS, page 522, after line 10, by adding an appropriately numbered new proviso to read: / (Suspend Human Affairs Commission State Funds) For Fiscal Year 2010-11, state funding for the Human Affairs Commission is suspended. The state funds that otherwise would have been appropriated to the Human Affairs Commission shall be redirected to the Department of Disabilities and Special Needs. / Renumber sections to conform. Amend sections, totals and title to conform. Senator BRIGHT explained the amendment. Senator PINCKNEY spoke on the amendment. Senator PINCKNEY moved to lay the amendment on the table. The "ayes" and "nays" were demanded and taken, resulting as follows: Ayes 30; Nays 12 AYES Alexander Anderson Campbell Campsen Cleary Courson Cromer Elliott Fair Grooms Hayes Hutto Jackson Knotts Land Leventis Lourie Malloy Martin, Larry McConnell McGill Nicholson O'Dell Pinckney Rankin Scott Setzler Sheheen Shoopman Williams Total--30 NAYS Bright Bryant Davis Martin, Shane Massey Mulvaney Peeler Reese Rose Ryberg Thomas Verdin Total--12 The amendment was laid on the table. Point of Order Senator MULVANEY raised a Point of Order that Proviso 64.1 of Part 1B was out of order inasmuch as it was violative of Rule 24A. 64.1. (CA: Consumer Protection Code Violations Revenue) Funds, paid to the department in settlement of cases involving violations of the South Carolina Consumer Protection Code and other statutes enforced by the department be retained and expended within the agency's budget to help offset the costs of investigating, prosecuting, and the administrative costs associated with these violations, may be carried forward and expended for the same purposes in the current fiscal year. The PRESIDENT Pro Tempore overruled the Point of Order. Point of Order Senator MULVANEY raised a Point of Order that Proviso 64.2 of Part 1B was out of order inasmuch as it was violative of Rule 24A. 64.2. (CA: Student Athlete/Agents Registration) Funds received by the department of Consumer Affairs pursuant to registrations under Chapter 102 of Title 59 of the 1976 Code may be retained by the department for its enforcement duties relating to athlete agents and student athletes under that chapter. The PRESIDENT Pro Tempore overruled the Point of Order. Point of Order Senator MULVANEY raised a Point of Order that Proviso 64.3 of Part 1B was out of order inasmuch as it was violative of Rule 24A. 64.3. (CA: Expert Witness/Assistance Carry Forward) Unexpended encumbered appropriated funds for the Consumer Advocacy expert witness/assistance program (under Section 37-6-603) may be carried forward into the next fiscal year to meet contractual obligations existing at June 30 and not paid by July 31. The PRESIDENT Pro Tempore overruled the Point of Order. Point of Order Senator MULVANEY raised a Point of Order that Proviso 64.4 of Part 1B was out of order inasmuch as it was violative of Rule 24A. 64.4. (CA: Registered Credit Grantor Notification and Maximum Rate Filing Fees Retention) The Department of Consumer Affairs may retain all Consumer Credit Grantor Notification filing fees collected under Section 37-6-203 and all Maximum Rate Schedules filing fees collected under Section 37-2-305 and Section 37-3-305. These fees shall be used to offset the cost of administering and enforcing Chapters 2 and 3 of Title 37 of the 1976 Code and may be applied to the cost of operations. Unexpended balances may be carried forward for the prior fiscal year into the current fiscal year and be utilized for the same purposes. The PRESIDENT Pro Tempore overruled the Point of Order. Point of Order Senator MULVANEY raised a Point of Order that Proviso 64.5 of Part 1B was out of order inasmuch as it was violative of Rule 24A. 64.5. (CA: Retention of Fees) For Fiscal Year 2010-11, the department may retain all fees collected pursuant to Sections 39-61-80, 39-61-120, 40-39-120, and 44-79-80 of the 1976 Code. The funds retained shall be utilized to implement the requirements of the programs mandated by those sections of the code. The PRESIDENT Pro Tempore overruled the Point of Order. Amendment No. 89 Senator FAIR proposed the following Amendment No. 89 (DC JOINT CHILDREN'S COMMITTEE), which was adopted (#24): Amend the bill, as and if amended, Part IB, Section 89, GENERAL PROVISIONS, page 522, after line 11, by adding an appropriately numbered new proviso to read: / 89.___ (GP: Joint Children's Committee) For the current fiscal year, the Department of Revenue is directed to reduce the rate of interest paid on eligible refunds by one percentage point. Of the revenue resulting from this reduction, $250,000 shall be transferred to the Senate for the Joint Citizens and Legislative Committee on Children to provide the report, research, and other operating expenses as directed in Section 63-1-50 of the 1976 Code. The remaining revenue resulting from this reduction shall be transferred to the Department of Juvenile Justice to be used for mentoring or alternatives to incarceration programs. Unexpended funds authorized by this provision may be retained and carried forward by the Senate or the Department of Juvenile Justice, respectively, and used for the same purposes. The rate of reduction authorized in this provision shall be in addition to the reduction authorized in Proviso 72.17. / Renumber sections to conform. Amend sections, totals and title to conform. Senator FAIR explained the amendment. The amendment was adopted. Recorded Vote Senator MULVANEY desired to be recorded as voting against the adoption of the amendment. Amendment No. 96 Senator MULVANEY proposed the following Amendment No. 96 (DG MMOFFROAD), which was ruled out of order: Amend the bill, as and if amended, Part IB, Section 89, GENERAL PROVISIONS, page 522, after line 10, by adding an appropriately numbered proviso to read: / 89.___. (GP: Off-Road Diesel) For fiscal year 2010-2011, political subdivisions of this state may purchase "off-road diesel" for the purpose of operating fire service vehicles. / Renumber sections to conform. Amend sections, totals and title to conform. Senator MULVANEY explained the amendment. Point of Order Senator LEATHERMAN raised a Point of Order that the amendment was out of order inasmuch as it was violative of Rule 24A. The PRESIDENT Pro Tempore sustained the Point of Order. Amendment No. 96 was ruled out of order. Amendment No. 28 Senator MASSEY proposed the following Amendment No. 28 (4657R026.ASM), which was adopted (#25): Amend the bill, as and if amended, pages 523-524, by striking Proviso 90.5 and inserting: / 90.5. (SR: Criminal Justice Academy Funding) (A) In addition to all other assessments and surcharges, during the current fiscal year, a five dollar surcharge to fund training at the South Carolina Criminal Justice Academy is also levied on all fines, forfeitures, escheatments, or other monetary penalties imposed in the general sessions court or in magistrates' or municipal court for misdemeanor traffic offenses or for nontraffic violations. No portion of the surcharge may be waived, reduced, or suspended. The additional surcharge imposed by this section does not apply to parking citations. / Renumber sections to conform. Amend title to conform. Senator MASSEY explained the amendment. The amendment was adopted. Amendment No. 67 Senators BRIGHT and BRYANT proposed the following Amendment No. 67 (4657R037.LB.DOCX), which was ruled out of order: Amend the bill, as and if amended, Part IB, SECTION 90, by adding an appropriately numbered new proviso to read: / 90.___. (SR: Business Tax Relief) (A) The source of the revenue to fund the suspensions in subsection (B) and the tax credit established in subsection (C) is: (1) Office of the State Treasurer 7,629,566 (2) Office of the Attorney General 7,347,697 (3) The Budget and Control Board 65,777,139 (4) The Commission on Higher Education 126,006,811 (5) Higher Education Tuition Grants Commission 1,872,348 (6) University of South Carolina 206,987,199 (7) University of South Carolina - Salkehatchie Campus 2,426,959 (8) Medical University of South Carolina 43,023,796 (9) State Board for Technical and Comprehensive Education 6,508,376 (10) Educational Television Commission 6,084,514 (11) Department of Health and Environmental Control 39,758,780 (12) Commission for the Blind 642,511 (13) Clemson University 7,200,991 (14) Division of Aeronautics 995,595 (B) The taxes levied in the following code sections are suspended for tax year 2010: (1) Section 12-6-530, related to corporate income tax; (2) Chapter 20, Title 12, related to corporate license fees; (3) Chapter 11, Title 12, related to income tax on banks; (4) Chapter 21, Title 12, related to stamp and business license tax; (5) Chapter 7, Title 38, related to insurance fees and taxes; (6) Chapter 13, Title 12, related to income tax on building and loan associations; (7) Article 16, Chapter 37, Title 12, related to taxes levied against the assessed value of cars in private car line companies; and (8) Article 5, Chapter 36 of Title 12, related to retail license taxes. (C) Funds remaining after the suspension in subsection (B) must be used to fund a tax credit pass through businesses, as defined in Section 12-6-545(A)(2). The tax credit shall be equal to the amount of available revenue divided by the number of pass through businesses filing income tax returns. / Renumber sections to conform. Amend sections, totals and title to conform. Senator BRIGHT explained the amendment. Point of Order Senator LOURIE raised a Point of Order that the amendment was out of order inasmuch as it was violative of Rule 24A. The PRESIDENT Pro Tempore sustained the Point of Order. Amendment No. 67 was ruled out of order. Amendment No. 106 Senators BRIGHT and BRYANT proposed the following Amendment No. 106 (4657R042.LB.DOCX), which was ruled out of order: Amend the bill, as and if amended, Part IB, SECTION 90, by adding an appropriately numbered new proviso to read: / 90.___. (SR: Business Tax Relief) (A) The source of the revenue to fund the tax credit established in subsection (B) is: (1) Office of the State Treasurer 7,629,566 (2) Office of the Attorney General 7,347,697 (3) The Budget and Control Board 65,777,139 (4) The Commission on Higher Education 126,006,811 (5) Higher Education Tuition Grants Commission 1,872,348 (6) University of South Carolina 206,987,199 (7) University of South Carolina - Salkehatchie Campus 2,426,959 (8) Medical University of South Carolina 43,023,796 (9) State Board for Technical and Comprehensive Education 6,508,376 (10) Educational Television Commission 6,084,514 (11) Department of Health and Environmental Control 39,758,780 (12) Commission for the Blind 642,511 (13) Clemson University 7,200,991 (14) Division of Aeronautics 995,595 (B) There is created a refundable income tax credit for pass through businesses, as defined in Section 12-6-545(A)(2). The tax credit shall be equal to the amount of available revenue divided by the number of pass through businesses filing income tax returns during the previous year. / Renumber sections to conform. Amend sections, totals and title to conform. Point of Order Senator LOURIE raised a Point of Order that the amendment was out of order inasmuch as it was violative of Rule 24A. The PRESIDENT Pro Tempore sustained the Point of Order. Amendment No. 106 was ruled out of order. Amendment No. 104B Senators REESE, DAVIS and RANKIN proposed the following Amendment No. 104B (4657 REESE.FTE.2.DOCX), which was adopted (#26): Amend the bill, as and if amended, Part IB, Section 1, DEPARTMENT OF EDUCATION, page 353, after line 32, by adding an appropriately numbered new proviso to read: / 1.__ From the funds appropriated, all certified public school teachers, certified special school classroom teachers, certified media specialists, certified guidance counselors, certified full time athletic directors, certified principals, certified assistant principals, certified school district administrators that are employed by a school district must teach at least two classes per week within the school district they are employed. / Renumber sections to conform. Amend sections, totals and title to conform. Senator REESE explained the amendment. PRESIDENT PRESIDES At 10:28 P.M., the PRESIDENT assumed the Chair. Senator REESE resumed explaining the amendment. Senator LEATHERMAN spoke on the amendment. The amendment was adopted. Amendment No. 82 Senators ROSE and BRIGHT proposed the following Amendment No. 82 (4657R047.MTR.DOCX), which was tabled: Amend the bill, as and if amended, Part IB, Section 6, COMMISSION ON HIGHER EDUCATION, page 378, after line 29, by adding an appropriately numbered new proviso to read: /6.__ (CHE: Transaction Register ) For fiscal year 2010-2011, institutions of higher learning must maintain a transaction register that includes a complete record of all funds expended over one hundred dollars, from whatever source, for whatever purpose. The register must be prominently posted on the instiution's internet website and made available for public viewing and downloading. The register must include for each expenditure: (i) the transaction amount; (ii) the name of the payee; and (iii) a statement providing a detailed description of the expenditure. The register must not include an entry for salary, wages, or other compensation paid to individual employees. The register must not include any information that can be used to identify an individual employee. The register must be accompanied by a complete explanation of any codes or acronyms used to identify a payee or an expenditure. The register must be searchable and updated at least once a month. Each public institution of higher learning shall be responsible for providing on its Internet website a link to the Internet website of any agency, other than the individual institution, that posts on its Internet website the institution's monthly state procurement card statements or monthly reports containing all or substantially all of the same information contained in the monthly state procurement card statements. The link must be to the specific webpage or section on the website of the agency where the state procurement card information for the institution can be found. The information posted may not contain the state procurement card number. Any information that is expressly prohibited from public disclosure by federal or state law or regulation must be redacted from any posting required by this section. / Renumber sections to conform. Amend sections, totals and title to conform. Senator BRIGHT explained the amendment. Senator KNOTTS moved to lay the amendment on the table. The "ayes" and "nays" were demanded and taken, resulting as follows: Ayes 24; Nays 20 AYES Alexander Anderson Campbell Coleman Fair Hayes Hutto Jackson Knotts Land Leatherman Leventis Lourie Malloy Martin, Larry McGill Nicholson O'Dell Pinckney Rankin Scott Setzler Sheheen Williams Total--24 NAYS Bright Bryant Campsen Cleary Cromer Davis Elliott Ford Grooms Martin, Shane Massey McConnell Mulvaney Peeler Reese Rose Ryberg Shoopman Thomas Verdin Total--20 The amendment was laid on the table. Statement by Senators LARRY MARTIN and ALEXANDER We support the move toward greater transparency with the expenditure of public funds. There is, however, a cost associated with complying with Senator ROSE's Amendment No. 82, and the colleges and universities have asked for a year to ramp up to meet these requirements. We sat in on a Higher Education Subcommittee meeting where Senator ROSE's separate legislation was considered. We are convinced that the colleges and universities will take steps to address this issue over the coming year and for that reason cannot support these amendments. Amendment No. 1 Senator CAMPBELL proposed the following Amendment No. 1 (DG DNREXPO50), which was adopted (#27): Amend the bill, as and if amended, Part IB, Section 37, DEPARTMENT OF NATURAL RESOURCES, page 415, after line 30, by adding an appropriately numbered proviso to read: / 37.___. (DNR: Wildlife Expo) For the current fiscal year, from the funds appropriated to the Department of Natural Resources, the department shall expend fifty thousand dollars on the Southeastern Wildlife Expo. / Renumber sections to conform. Amend sections, totals and title to conform. Senator CAMPBELL explained the amendment. The amendment was adopted. Recorded Vote Senators MASSEY and MULVANEY desired to be recorded as voting against the adoption of the amendment. Recorded Vote Senator LEVENTIS desired to be recorded as voting in favor of the adoption of the amendment. Amendment No. 132 Senator MALLOY proposed the following Amendment No. 132 (DAD DEPOSITION FEE), which was adopted (#28): Amend the bill, as and if amended, Part IB, Section 44, JUDICIAL DEPARTMENT, page 424, after line 2, by adding an appropriately numbered new proviso to read: / 44.___ (JUD: Deposition Fee) For the current fiscal year, there is assessed a fee of fifty dollars for every deposition conducted as part of any proceeding in a Family Court or Circuit Court in this State. No later than ten days after the taking of a deposition, the attorney who initiated a deposition must file notice of the deposition with the clerk of court in the county in which the proceeding is pending and pay the fee with the filing of the notice. The revenue from this fee must be collected by the clerk of court in each county and remitted to the State Treasurer and credited to a separate judicial department support fund for the exclusive use of the Judicial Department for court administration. / Renumber sections to conform. Amend sections, totals and title to conform. Senator MALLOY explained the amendment. Senator MASSEY spoke on the amendment. Senator MASSEY moved to carry over the amendment. Senator MALLOY moved to table the motion to carry over the amendment. The "ayes" and "nays" were demanded and taken, resulting as follows: Ayes 23; Nays 21 AYES Anderson Campbell Cleary Coleman Ford Hutto Jackson Knotts Land Leventis Lourie Malloy McConnell McGill Nicholson O'Dell Pinckney Rankin Reese Scott Setzler Sheheen Williams Total--23 NAYS Alexander Bright Bryant Campsen Cromer Davis Elliott Fair Grooms Hayes Leatherman Martin, Larry Martin, Shane Massey Mulvaney Peeler Rose Ryberg Shoopman Thomas Verdin Total--21 The motion to carry over the amendment was tabled. Senator KNOTTS spoke on the amendment. Senator MALLOY moved that the amendment be adopted. Senator MASSEY argued contra to the adoption of the amendment. The "ayes" and "nays" were demanded and taken, resulting as follows: Ayes 27; Nays 15 AYES Alexander Campbell Coleman Cromer Elliott Ford Hayes Hutto Jackson Knotts Land Leatherman Leventis Lourie Malloy Martin, Larry McConnell McGill Nicholson O'Dell Pinckney Rankin Reese Scott Setzler Sheheen Williams Total--27 NAYS Bright Bryant Campsen Cleary Davis Fair Martin, Shane Massey Mulvaney Peeler Rose Ryberg Shoopman Thomas Verdin Total--15 The amendment was adopted. Expression of Personal Interest Senator FORD rose for an Expression of Personal Interest. Remarks by Senator FORD Mr. PRESIDENT, I do not like the way that we treated Senator MASSEY, the Senator from Aiken, when he had the floor. Under the Rules of the Senate, he has a right to speak. Now, after four hours, then we have the right to sit him down if we choose to do so. To take his rights away like that, I disagree and I don't like that at all. Senator MARTIN from Pickens and other Senators told him to sit down when he was not ready. He has a right to speak if he chooses to and I do not like anyone messing with another's Constitutional right and that's what we did. We violated the man's rights and we were totally wrong for doing so and that's not the Senate. You do not question a man -- saying the Senate has decided on what their position might be. Anyone can change their position on an issue. He might have changed my vote, because I don't like the fact that we are using fees to fund all of these different things in the first place. So, in the future let people speak and if we want to vote to sit them down, then we can vote to sit them down. But don't force the man to sit down. I do not like that. He's a Senator just like the rest of us. I know some you feel you have the right to do whatever you want to do, but everyone has the same rights and I resent the fact that you all did that to this young man. Now he may disagree--and he has the right to do so--but I think it was totally unfair for us to do that. On motion of Senator BRIGHT, with unanimous consent, the remarks of Senator FORD were ordered printed in the Journal. Expression of Personal Interest Senator PEELER rose for an Expression of Personal Interest. Senator MASSEY moved that the Senate stand adjourned. The "ayes" and "nays" were demanded and taken, resulting as follows: Ayes 4; Nays 39 AYES Bryant Ford Massey Sheheen Total--4 NAYS Alexander Bright Campbell Campsen Cleary Coleman Cromer Davis Elliott Fair Grooms Hayes Hutto Jackson Knotts Land Leatherman Leventis Lourie Malloy Martin, Larry Martin, Shane McConnell McGill Mulvaney Nicholson O'Dell Peeler Pinckney Rankin Reese Rose Ryberg Scott Setzler Shoopman Thomas Verdin Williams Total--39 The Senate refused to adjourn. Objection Senator JACKSON asked unanimous consent to make a motion that the pages be compensated at time and a half their hourly wage from midnight until the Senate adjourns today. Senator McCONNELL objected. Expression of Personal Interest Senator LOURIE rose for an Expression of Personal Interest. Amendment No. 94 Senator MASSEY proposed the following Amendment No. 94 (4657R054.), which was tabled: Amend the bill, as and if amended, page 424, by striking Proviso 45.6 and inserting: / 45.6. (AG: Auction Rate Securities Settlement/Water Rights) The Attorney General's Office is authorized to utilize up to$2,200,000 of retain and expend funds received in Fiscal Year 2009-10 and in Fiscal Year 2010-11 from the "Auction Rate Securities Settlement" to pay for expenses and fees associated with the South Carolina vs. North Carolina water lawsuit (United States Supreme Court original Jurisdiction Case Number 138.) The $2,200,000 shall not include the$750,000 the Attorney General's Office currently allocates for securities enforcement expenses. The Attorney General's Office is authorized to use a portion of the $2,200,000 these funds to reimburse Water Litigation expenses incurred in the prior fiscal year. These funds may be carried forward from the prior fiscal year into the current fiscal year and be utilized for the same purpose. Upon satisfaction of the South Carolina vs. North Carolina water lawsuit, any remaining Auction Rate Securities Settlement funds shall be transferred to the Judicial Department to fund nonrecurring expenses. This paragraph takes effect on the earlier of July 1, 2010, or the date on which Auction Rate Securities Settlement funds in Fiscal Year 2009-10 exceeded$2,200,000. / Renumber sections to conform. Amend title to conform. Senator MASSEY explained the amendment. Senator SHEHEEN moved to lay the amendment on the table. The amendment was laid on the table. Amendment No. 95 Senator GROOMS proposed the following Amendment No. 95 (4657R044.LKG.DOCX), which was withdrawn: Amend the bill, as and if amended, Part IB, Section 81, DEPARTMENT OF REVENUE, by adding an appropriately numbered new proviso to read: / 81.___. (DOR: Illegal Alien Registration Fee) Each person in South Carolina that is in the United States illegally must register with the Department of Revenue. The department must collect a fifty dollar registration fee and provide proof that the person has paid the fee. All state and local law enforcement agencies are authorized to question people in South Carolina for whom there is a reasonable suspicion that the person is in the United States illegally to determine whether the person has paid the registration fee. A person that cannot produce proof that the registration fee has been paid or that the person is legally present in the United States must be detained for a period not to exceed ten days or until proof is presented to the detaining law enforcement agency that the fee has been paid. A person may be released prior to the expiration of ten days and prior to the presentment of proof that the registration fee has been paid if the person or someone on the person's behalf posts a $5,000 cash bond with the magistrate having jurisdiction over the area where the person is detained. The person then has five days to provide proof to the magistrate that the fee has been paid. If proof is not provided within five days, then the bond is forfeit and must be transferred to the detaining law enforcement agency. The authority to question and detain a person pursuant to this section expires June 15, 2011. / Renumber sections to conform. Amend sections, totals and title to conform. Senator GROOMS explained the amendment. Point of Order Senator HUTTO raised a Point of Order that the amendment was out of order inasmuch as it was violative of Rule 24A. Senator GROOMS spoke on the Point of Order. The PRESIDENT overruled the Point of Order. Senator HUTTO moved to lay the amendment on the table. The "ayes" and "nays" were demanded and taken, resulting as follows: Ayes 9; Nays 32 AYES Coleman Hutto Jackson Land Leventis Malloy Nicholson Pinckney Scott Total--9 NAYS Alexander Bright Bryant Campbell Campsen Cleary Cromer Davis Elliott Fair Grooms Hayes Knotts Leatherman Lourie Martin, Larry Martin, Shane Massey McConnell McGill Mulvaney O'Dell Peeler Rankin Reese Rose Ryberg Setzler Shoopman Thomas Verdin Williams Total--32 The Senate refused to table the amendment. The question then was the adoption of the amendment. Senator LEVENTIS argued contra to the adoption of the amendment. On motion of Senator GROOMS, with unanimous consent, Amendment No. 95 was withdrawn. Amendment No. 130 Senator ROSE proposed the following Amendment No. 130 (4657R067.MTR.DOCX), which was adopted (#29): Amend the bill, as and if amended, Part IB, Section 86, AID TO SUBDIVISIONS-STATE TREASURER, page 486, after line 8, by adding an appropriately numbered new proviso to read: /86.__(AS-TREAS: Flexibility) For fiscal year 2010-2011, a political subdivision receiving aid from the Local Government Fund may reduce its support to any state mandated program or requirement, for which a specific level or amount of support or funding is not provided by law, by up to a percentage equal to the percentage reduction in the actual amount appropriated to the Local Government Fund as compared to the last completed fiscal year. / Renumber sections to conform. Amend sections, totals and title to conform. Senator ROSE explained the amendment. Senator LEATHERMAN moved to lay the amendment on the table. The "ayes" and "nays" were demanded and taken, resulting as follows: Ayes 20; Nays 22 AYES Alexander Campbell Coleman Elliott Hutto Jackson Knotts Land Leatherman Leventis Lourie Malloy Martin, Larry McConnell Pinckney Rankin Reese Scott Setzler Williams Total--20 NAYS Bright Bryant Campsen Cleary Cromer Davis Fair Grooms Hayes Martin, Shane Massey McGill Mulvaney Nicholson O'Dell Peeler Rose Ryberg Sheheen Shoopman Thomas Verdin Total--22 The Senate refused to table the amendment. The question then was the adoption of the amendment. The amendment was adopted. Recorded Vote Senators MULVANEY and SHOOPMAN desired to be recorded as voting in favor of the adoption of the amendment. Amendment No. 62 Senator MASSEY proposed the following Amendment No. 62 (DG ASMDEPO), which was tabled: Amend the bill, as and if amended, Part IB, Section 89, GENERAL PROVISIONS, page 522, after line 10, by adding an appropriately numbered new proviso to read: / 89.___ (GP: Suspend Deposition Fee) For fiscal year 2010-2011, Section 8-21-330 as contained in H. 3161 of 2009, is suspended. / Renumber sections to conform. Amend sections, totals and title to conform. Senator MASSEY explained the amendment. Senator MALLOY moved to lay the amendment on the table. The amendment was laid on the table. Amendment No. 66 Senators LEATHERMAN and LAND proposed the following Amendment No. 66 (DG HKL95), which was adopted (#30): Amend the bill, as and if amended, Part IB, Section 89, GENERAL PROVISIONS, page 522, after line 10, by adding an appropriately numbered proviso to read: / 89.__. (GP: I-95 Corridor) For the current fiscal year, from the funds available in the Healthcare Tobacco Settlement Trust Fund, there is appropriated three million dollars to the South Carolina Research Authority. The funds shall be used for a grant program to promote health related issues, pursuant to Section 11-11-170(B)(1)(g), along the I-95 Corridor. Any grant awarded pursuant to this proviso shall be matched on a two-to-one basis by the grant recipient. / Renumber sections to conform. Amend sections, totals and title to conform. Senator LEATHERMAN explained the amendment. By a division vote of 26-10, the amendment was adopted. Recorded Vote Senators CROMER and ROSE desired to be recorded as voting against the adoption of Amendment No. 66. Point of Order Senator MULVANEY raised a Point of Order that Amendment No. 66 was out of order inasmuch as it was violative of Rule 24A. Point of Order Senator LAND raised a Point of Order that the Point of Order comes too late. The PRESIDENT sustained the Point of Order of Senator LAND and stated that the Point of Senator MULVANEY came too late. Parliamentary Inquiry Senator MULVANEY made a Parliamentary Inquiry as to whether or not an adopted amendment would still be considered a proviso within the General Appropriations Bill and subject to Points of Order. Senator LARRY MARTIN stated that the custom and practice of the Senate has been that an amendment is not subject to further Points of Order once it has been disposed of. Amendment No. 90 Senator BRIGHT proposed the following Amendment No. 90 (DG LBSECTOR), which was tabled: Amend the bill, as and if amended, Part IB, Section 89, GENERAL PROVISIONS, page 522, after line 10, by adding an appropriately numbered new proviso to read: / 89.___. (GP: University Funding Redistribution) Notwithstanding the appropriation of state funds in Part 1A of this act, no institution of higher learning within the comprehensive university sector shall receive less than the sector's average level of funding as determined by the Mission Resource Requirement Calculation of Need calculated in the preceding fiscal year by the Commission on Higher Education. To the extent necessary, funds shall be redistributed to and among the institutions to accomplish the provisions of this paragraph. / Renumber sections to conform. Amend sections, totals and title to conform. Senator BRIGHT explained the amendment. Senator LEATHERMAN spoke on the amendment. Senator LEATHERMAN moved to lay the amendment on the table. The "ayes" and "nays" were demanded and taken, resulting as follows: Ayes 30; Nays 12 AYES Alexander Campbell Campsen Coleman Cromer Fair Grooms Hayes Hutto Jackson Knotts Land Leatherman Leventis Lourie Malloy Martin, Larry McConnell McGill Nicholson O'Dell Pinckney Rankin Rose Scott Setzler Sheheen Thomas Verdin Williams Total--30 NAYS Bright Bryant Cleary Davis Elliott Martin, Shane Massey Mulvaney Peeler Reese Ryberg Shoopman Total--12 The amendment was laid on the table. Amendment No. 99A Senators DAVIS, McCONNELL, CLEARY, ELLIOTT, RANKIN, FORD, CAMPSEN, McGILL and PINCKNEY proposed the following amendment (DAD DAVIS FILLED VACANT 40%), which was adopted (#31): Amend the bill, as and if amended, Part IB, Section 89, GENERAL PROVISIONS, page 522, after line 10, by adding an appropriately numbered new proviso to read: / (GP: Additional Classroom Funding) Agencies are directed to determine the amount of unencumbered funds, as of September 1, 2010, resulting from the difference between the number of filled and authorized FTE's funded by general funds existing within their budget as delineated in this act. Agencies shall report their findings to the Budget and Control Board, Office of State Budget by September 15, 2010. Based on these findings the Office of State Budget shall direct agencies to transfer, on a pro-rata basis, up to$21,515,400 of these identified funds to the Department of Education to be distributed to school districts receiving less than forty percent of state support as computed in Section 59-20-40(1) of the 1976 Code, with each district to receive a pro-rata share of said amount determined in accordance with the district's number of weighted students, which must be subject to adjustment for student attendance. / Renumber sections to conform. Amend sections, totals and title to conform. Senator DAVIS explained the amendment. Senator LEATHERMAN spoke on the amendment. Senator LEATHERMAN moved that the amendment be adopted. Point of Order Senator BRYANT raised a Point of Order that Proviso 89.135 of Part 1B was out of order inasmuch as it was violative of Rule 24A. 89.135. (GP: Public Safety Service Charge) At the time of collection of the registration fee for a motor vehicle, the Department of Motor Vehicles shall collect a six dollar annual public safety service charge on all vehicles required to be registered in this state, in addition to the registration fees prescribed by law. Of the funds collected pursuant to this provision for property carrying vehicles, two dollars shall be deposited into a special restricted account of the Department of Transportation to be used for operating expenses of commercial motor vehicle rest areas. The remaining funds collected pursuant to this provision for property carrying vehicles and all service charges collected for other motor vehicles required to be registered shall be deposited into a special restricted account for the Department of Public Safety to be used specifically for personnel and operating expenses for sworn law enforcement officers of the South Carolina Highway Patrol and State Transport Police. All unexpended funds collected under this provision may be retained and carried forward by the Department of Transportation or the Department of Public Safety and used for the same purposes. Senator FAIR spoke on the Point of Order. Senator MASSEY spoke on the Point of Order. Senator LAND spoke on the Point of Order. Senator McCONNELL spoke on the Point of Order. The PRESIDENT took the Point of Order under advisement. The Point of Order was subsequently sustained. The Decision of the PRESIDENT was appealed and the Point of Order was overridden. Expression of Personal Interest Senator LEVENTIS rose for an Expression of Personal Interest. Amendment No. 113 Senators CAMPSEN, McCONNELL, LAND, LEATHERMAN, RANKIN, McGILL, HUTTO, PINCKNEY, SETZLER, LARRY MARTIN, NICHOLSON, CROMER, CLEARY, REESE, CAMPBELL, KNOTTS, O'DELL, DAVIS, ALEXANDER and MALLOY proposed the following Amendment No. 113 (DAD CONSERV BNK MPWR), which was adopted (#32): Amend the bill, as and if amended, Part IB, Section 89, GENERAL PROVISIONS, page 522, after line 10, by adding an appropriately numbered new proviso to read: / (GP: General Fund Transfer to Conservation Bank) The Department of Revenue is directed to transfer to the South Carolina Conservation Bank, $1,500,000 of the increased general fund revenue resulting from the motion picture wage rebate of fifteen percent as required by Section 12-62-50 of the 1976 Code, rather than twenty percent as authorized in prior appropriation acts. / Renumber sections to conform. Amend sections, totals and title to conform. Senator CAMPSEN explained the amendment. The "ayes" and "nays" were demanded and taken, resulting as follows: Ayes 31; Nays 11 AYES Alexander Campbell Campsen Cleary Coleman Cromer Davis Elliott Grooms Hayes Hutto Jackson Knotts Land Leatherman Leventis Lourie Malloy Martin, Larry McConnell McGill Nicholson O'Dell Pinckney Rankin Reese Scott Setzler Sheheen Verdin Williams Total--31 NAYS Bright Bryant Fair Martin, Shane Massey Mulvaney Peeler Rose Ryberg Shoopman Thomas Total--11 The amendment was adopted. Amendment No. 41 Senator MASSEY proposed the following Amendment No. 41 (DG DGASMJUDTRANS), which was tabled: Amend the bill, as and if amended, Part IB, Section 90, STATEWIDE REVENUE, page 534, after line 23, by adding an appropriately numbered proviso to read: / 90.___. (SR: Judicial Transfer) The Educational Television Commission and the Department of Natural Resources shall transfer$500,000 to the Judicial Department. The Department of Health and Human Services, the Department of Parks, Recreation and Tourism, The Department of Alcohol and Other Drug Abuse Services, and the Forestry Commission shall transfer $250,000 to the Judicial Department. The Department of Health and Human Service's transfer must be from its administration budget. The Department of Health and Environmental Control and the Budget and Control Board shall transfer$1,000,000 to the Judicial Department. The Department of Archives and History, the State Museum Commission, the Commission on Human Affairs, the Public Service Commission, the Office of Regulatory Staff, the Department of Consumer Affairs, the Department of Motor Vehicles, and the Department of Insurance shall transfer $125,000 to the Judicial Department. / Renumber sections to conform. Amend sections, totals and title to conform. Senator MASSEY explained the amendment. Senator ALEXANDER moved to lay the amendment on the table. The amendment was laid on the table. Recorded Vote Senator RYBERG desired to be recorded as voting against the motion to table the amendment. Amendment No. 133 Senator BRIGHT proposed the following Amendment No. 133 (4657R068.LB.DOCX), which was tabled: Amend the bill, as and if amended, Part IB, SECTION 90, by adding an appropriately numbered new proviso to read: / 90.___. (SR: Business Tax Relief) (A) The source of the revenue to fund the suspensions in subsection (B) and the tax credit established in subsection (C) is: (1) Office of the State Treasurer 1,596,170 (2) Office of the Attorney General 3,700,380 (3) The Budget and Control Board 25,234,009 (4) The Commission on Higher Education 118,942,833 (5) Higher Education Tuition Grants Commission 1,872,348 (6) University of South Carolina 101,531,435 (7) University of South Carolina - Salkehatchie Campus 1,302,879 (8) Medical University of South Carolina 43,023,796 (9) State Board for Technical and Comprehensive Education 6,508,376 (10) Educational Television Commission 6,084,514 (11) Department of Health and Environmental Control 39,758,780 (12) Commission for the Blind 642,511 (13) Clemson University 7,200,991 (14) Division of Aeronautics 995,595 (B) The taxes levied in the following code sections are suspended for tax year 2010: (1) Section 12-6-530, related to corporate income tax; (2) Chapter 20, Title 12, related to corporate license fees; (3) Chapter 11, Title 12, related to income tax on banks; (4) Chapter 21, Title 12, related to stamp and business license tax; (5) Chapter 13, Title 12, related to income tax on building and loan associations; (6) Article 16, Chapter 37, Title 12, related to taxes levied against the assessed value of cars in private car line companies; and (7) Article 5, Chapter 36 of Title 12, related to retail license taxes. (C) Funds remaining after the suspension in subsection (B) must be used to fund a tax credit pass through businesses, as defined in Section 12-6-545(A)(2). The tax credit shall be equal to the amount of available revenue divided by the number of pass through businesses filing income tax returns. / Renumber sections to conform. Amend sections, totals and title to conform. Senator BRIGHT explained the amendment. Senator LEATHERMAN spoke on the amendment. Senator BRIGHT spoke on the amendment. Senator LEATHERMAN moved to lay the amendment on the table. The "ayes" and "nays" were demanded and taken, resulting as follows: Ayes 39; Nays 2 AYES Alexander Campbell Campsen Cleary Coleman Cromer Davis Elliott Fair Grooms Hayes Hutto Jackson Knotts Land Leatherman Leventis Lourie Malloy Martin, Larry Martin, Shane Massey McConnell McGill Nicholson O'Dell Peeler Pinckney Rankin Reese Rose Ryberg Scott Setzler Sheheen Shoopman Thomas Verdin Williams Total--39 NAYS Bright Bryant Total--2 The amendment was laid on the table. Motion Under Rule 15A Adopted At 2:13 A.M., Senator LARRY MARTIN moved under the provisions of Rule 15A to vote on the entire matter of H.4657, the General Appropriations Bill. The "ayes" and "nays" were demanded and taken, resulting as follows: Ayes 30; Nays 12 AYES Alexander Campbell Campsen Cleary Coleman Cromer Elliott Fair Grooms Hayes Hutto Jackson Knotts Land Leatherman Leventis Lourie Martin, Larry McConnell McGill Nicholson O'Dell Peeler Pinckney Rankin Reese Rose Scott Setzler Williams Total--30 NAYS Bright Bryant Davis Malloy Martin, Shane Massey Mulvaney Ryberg Sheheen Shoopman Thomas Verdin Total--12 Having received the necessary vote, the motion under Rule 15A was adopted, with proponents and opponents each being allowed ten minutes to debate the amendments currently on the desk. Amendment No. 74 Senator BRIGHT proposed the following Amendment No. 74 (DAD TRANSFER 1ST STEPS$ TO DDSN), which was tabled: Amend the bill, as and if amended, Part IA, Section 1, DEPARTMENT OF EDUCATION, page 14, line 13, by: COLUMN 7 COLUMN 8 / STRIKING: 645,828 348,005 and INSERTING: 297,823 0/ Amend the bill further, as and if amended, Part IA, Section 1, DEPARTMENT OF EDUCATION, page 14, line 15, by: COLUMN 7 COLUMN 8 / STRIKING: 74,336 74,336 and INSERTING: 0 0/ Amend the bill further, as and if amended, Part IA, Section 1, DEPARTMENT OF EDUCATION, page 14, line 21, by: COLUMN 7 COLUMN 8 / STRIKING: 14,549,603 11,549,603 and INSERTING: 3,000,000 0/ Amend the bill further, as and if amended, Part IA, Section 24, DEPARTMENT OF DISABILITIES AND SPECIAL NEEDS, page 108, line 3 by: COLUMN 7 COLUMN 8 / STRIKING: 33,843,258 11,374,997 and INSERTING: 37,833,906 15,365,645/ Amend the bill further, as and if amended, Part IA, Section 24, DEPARTMENT OF DISABILITIES AND SPECIAL NEEDS, page 109, line 9 by: COLUMN 7 COLUMN 8 / STRIKING: 15,580,669 952,499 and INSERTING: 19,571,317 4,943,147/ Amend the bill further, as and if amended, Part IA, Section 24, DEPARTMENT OF DISABILITIES AND SPECIAL NEEDS, page 110, line 4 by: COLUMN 7 COLUMN 8 / STRIKING: 200,607,765 31,854,595 and INSERTING: 204,598,413 35,845,243/ Renumber sections to conform. Amend sections, totals and title to conform. Senator BRIGHT explained the amendment. Senator LOURIE moved to lay the amendment on the table. The "ayes" and "nays" were demanded and taken, resulting as follows: Ayes 38; Nays 4 AYES Alexander Campbell Campsen Cleary Coleman Davis Elliott Fair Grooms Hayes Hutto Jackson Knotts Land Leatherman Leventis Lourie Malloy Martin, Larry Massey McConnell McGill Mulvaney Nicholson O'Dell Peeler Pinckney Rankin Reese Rose Ryberg Scott Setzler Sheheen Shoopman Thomas Verdin Williams Total--38 NAYS Bright Bryant Cromer Martin, Shane Total--4 The amendment was laid on the table. Amendment No. 79 Senator BRIGHT proposed the following amendment (DAD TRANSFER 1ST STEPS $TO DPS), which was tabled: Amend the bill, as and if amended, Part IA, Section 1, DEPARTMENT OF EDUCATION, page 14, line 13, by: COLUMN 7 COLUMN 8 / STRIKING: 645,828 348,005 and INSERTING: 297,823 0/ Amend the bill further, as and if amended, Part IA, Section 1, DEPARTMENT OF EDUCATION, page 14, line 15, by: COLUMN 7 COLUMN 8 / STRIKING: 74,336 74,336 and INSERTING: 0 0/ Amend the bill further, as and if amended, Part IA, Section 1, DEPARTMENT OF EDUCATION, page 14, line 21, by: COLUMN 7 COLUMN 8 / STRIKING: 14,549,603 11,549,603 and INSERTING: 3,000,000 0/ Amend the bill further, as and if amended, Part IA, Section 49, DEPARTMENT OF PUBLIC SAFETY, page 199, line 23 by: COLUMN 7 COLUMN 8 / STRIKING: 45,596,435 31,447,232 and INSERTING: 52,596,435 38,447,232 Amend the bill further, as and if amended, Part IA, Section 49, DEPARTMENT OF PUBLIC SAFETY, page 199, line 33 by: COLUMN 7 COLUMN 8 / STRIKING: 20,166,517 177,660 and INSERTING: 23,166,517 3,177,660 Amend the bill further, as and if amended, Part IA, Section 49, DEPARTMENT OF PUBLIC SAFETY, page 201, line 16 by: COLUMN 7 COLUMN 8 / STRIKING: 26,953,594 14,600,684 and INSERTING: 28,925,538 16,572,628 Renumber sections to conform. Amend sections, totals and title to conform. Senator BRIGHT explained the amendment. Senator KNOTTS moved to lay the amendment on the table. The "ayes" and "nays" were demanded and taken, resulting as follows: Ayes 37; Nays 4 AYES Alexander Campbell Campsen Cleary Coleman Cromer Davis Fair Grooms Hayes Hutto Jackson Knotts Land Leatherman Leventis Lourie Malloy Martin, Larry Massey McConnell McGill Mulvaney Nicholson O'Dell Pinckney Rankin Reese Rose Ryberg Scott Setzler Sheheen Shoopman Thomas Verdin Williams Total--37 NAYS Bright Bryant Martin, Shane Peeler Total--4 The amendment was laid on the table. Amendment No. 117B Senators ROSE and DAVIS proposed the following Amendment No. 117B (DG MTRTRANS70B), which was tabled: Amend the bill, as and if amended, Part IA, Section 44, JUDICIAL DEPARTMENT, page 186, line 14, by: COLUMN 7 COLUMN 8 / STRIKING: 6,597,914 4,817,177 and INSERTING: 7,237,230 5,456,493/ Amend the bill further, as and if amended, Part IA, Section 1, DEPARTMENT OF EDUCATION, page 6, line 5, by: COLUMN 7 COLUMN 8 / STRIKING: 136,163,204 0 and INSERTING: 136,802,520 639,316/ Amend the bill further, as and if amended, Part IA, Section 49, DEPARTMENT OF PUBLIC SAFETY, page 199, line 23, by: COLUMN 7 COLUMN 8 / STRIKING: 45,596,435 31,447,232 and INSERTING: 46,235,751 32,086,548/ Amend the bill further, as and if amended, Part IA, Section 70A, LEG. DEPT.-THE SENATE, page 254, line 7, by: COLUMN 7 COLUMN 8 / STRIKING: 7,003,610 7,003,610 and INSERTING: 5,085,662 5,085,662/ Renumber sections to conform. Amend sections, totals and title to conform. Senator ROSE explained the amendment. Remarks by Senator ROSE Members of the Senate, last year this Senate's budget was$8.43 million in recurring funds. This year's budget for the Senate has been increased 46% to $12.3 million. So, we're going to go up in this agency -- the SC Senate --$3.89 million at 46% according to the Senate Finance Committee, while all these other agencies are being cut. An agency losing $75 million this year may lose$175 million next year. Other agencies have been using reserve funds to fund current operations -- like the Department of Juvenile Justice and the Department of Public Safety. I have received some explanation as to why the State Senate's budget has to go up so much this year -- that it was underfunded in past years and its reserves last year. What I have here is a list of our Senate budgeted funds for the last ten years. In 1999, the Senate had $10.6 million, and in successive years had$10 million, $11million,$9 million, $9 million,$10 million, $11 million, and, last year,$8.6 million. So within the last ten years last year's $8.6 million has been the Senate's lowest budget amount. But now we're going to spike up this budget again -- 46% to$12.3 million. What I propose instead is that we take the amount of the increase, $3.89 million, and cut it in half so that the Senate budget increases by 23% not 46%. Frankly, I'm going to have to go home to auditoriums filled with parents of disabled children, people in the PTA and teachers whose budgets are being cut, and try to justify to them why the Senate's budget is going up and everyone else is being cut. But at least this is a compromise. Instead of going up 46%, which is$3.89 million, under my proposed amendment we will go up 23%, which is $1.94 million. I figure that the Senate will just have to learn to do with some cuts just like everyone else. I'm directing in this proviso that this$1.94 million saved go in three directions, a third, a third, a third -- $600 something thousand each, to the judiciary,$600 something thousand to the EIA and a third to the Department of Public Safety. So, there will be to each of those three agencies $648,570.30 of new money -- by the Senate giving up half of its 46% increase. Thank you. On motion of Senator MULVANEY, with unanimous consent, the remarks of Senator ROSE were ordered printed in the Journal. Senator McCONNELL spoke on the amendment. Remarks by Senator McCONNELL Mr. PRESIDENT, ladies and gentlemen of the Senate, I know it's late, and I will be brief. You only got a piece of the picture. Let me go back and tell you the history of the Senate and what the Senate has done budgetarily and the challenges that are ahead. First of all, our budget back in 2008 was$12,295,008. Our adjusted base right now is down to $7,693,171. We have been through almost all of our reserves to make up the deficit. Rather than take new money last year, like the House did, we went into our reserves, tightened our belt and didn't ask for money so as to keep this Senate as frugal as we could be. Ninety percent or thereabouts of our costs are personnel costs. There's very little in operating costs here in the South Carolina Senate. So, what the Senator from Dorchester, Senator ROSE, and his allies would propose is that we cut staff. Because the personnel expenses in this body right now are$12,213,234, it won't take you long to understand. We cannot cut the Senators' pay. I could go through all of the expenses here today. I am not going to go through all of that. That's a very small part of this budget. This Senate is driven by employee cost -- the staff that we have. If you think we have too much staff here, if you want the staff cut, if you want to furlough them -- and to furlough all of the staff, it will amount to $24,000 per day. If we furlough them for about one hundred and something days, the budget can be balanced. Senator from Dorchester, you are one of the biggest demands on the staff. I think you would starve for information if we started furloughing the staff or cutting back. Let me give you some of the other challenges ahead. The Senator from Florence, Senator LEATHERMAN, can tell you. Most of you know, and I'm not going to go into too much public detail about the challenges facing the Gressette Building. We are in the process now of engineers testing over there. We are going to have to make some changes over there. The question is whether we can make them or whether or not we will have to find another place to do business. The building may require seismic changes in addition to new walls being erected up five stories into the building in order to secure it. We are meeting with those engineers and taking the tests on it. The House, last year, added, I think it was close to about$5 million to their budget, and I didn't hear a peep over here about it. Now, when the Senate has gone through its reserves and asks to restore the monies, there is opposition. All I've heard this week is core function, core function, core function. The legislative branch is a core function of government. Why would you on one hand say we need to fund core function and then on the next hand tell me we need to cut it? On top of that, reapportionment is coming. I have been in reapportionment now since I've served on the Judiciary Committee close to 30 years. Every time we get sued. Every time we are in federal court. We have to have computers and we have to have personnel to handle that. We have to have lawyers to represent us. There will be costs in advice going forward. So the Senator from Dorchester wants to cut the budget right as our expenses are going up -- not of our own making but because of the cyclical spot that we are in trying to balance reapportionment with the other challenges ahead. I'm not going to take long except to tell you that all we are doing is trying to keep this Senate about where it is, and that is to keep the personnel on board and maintain our ability to pay our bills to cover reapportionment and other things. There is no fat in this budget. We have been able to economize. The Clerk has done an excellent job with technology by reducing our telephone costs. I think it was once way, way over what it is today. We have cut, and we have cut, and we have cut. There is nowhere else to cut except the staff. Let me give you an example. I've heard complaints this year. We have not gotten a hearing in the Judiciary Committee on this Bill, and we haven't gotten a hearing on that Bill. Why can't we have hearings? Because we didn't have the money last year to have the subcommittees of the Judiciary Committee meet in the interim, take up Bills, and bring them back to this General Assembly. We had to cram it all into this Session. In past years, we have been able to go out and have public hearings, have subcommittee meetings and get major pieces of legislation ready to come to this floor. I suspect the Finance Committee and similar other committees are in similar shape. So, in a nutshell, there is not surplus money. There is no bloated budget. We have coasted on surplus reserve. This is not an increase. It's putting back into the line what is needed to pay the personnel here. I will close by saying this Senate has always prided itself in having a good legislative product. We have tried to hire the best people. The people of South Carolina deserve that. Every one of you in here knows we cannot function without staff. Look at it this week with all of us asking them questions. Where does this money come from? How do I fashion an amendment? On Judiciary Committee Bills, ask the Senator from Darlington, the Senator from Orangeburg, the Senator from Charleston, etc. about the technical things that need to be asked on Constitutional matters. You have to have good lawyers. You have to have good staff. You have to have people you can depend on. The quality of life of the people of this State is affected by what we do. I'll close by telling you, in addition to that, we have to make do as best we can with this budget in covering our legal expenses when this Senate gets sued for some of the Bills that passed. We have money that we have to set aside in other funds for the education lawsuit and for reapportionment but there is no more reserve. There is no more coasting on the reserves. So, you can vote it up or down. You are not voting for a fat budget, you're voting for a lean operating budget for a core function; and I would urge you to vote with me to table this amendment, and I move to table the amendment. On motion of Senator PEELER, with unanimous consent, the remarks of Senator McConnell were ordered printed in the Journal. Senator McCONNELL moved to lay the amendment on the table. The "ayes" and "nays" were demanded and taken, resulting as follows: Ayes 33; Nays 7 AYES Alexander Campbell Campsen Cleary Coleman Cromer Fair Grooms Hayes Hutto Jackson Knotts Land Leatherman Leventis Lourie Malloy Martin, Larry Martin, Shane McConnell McGill Nicholson O'Dell Peeler Pinckney Rankin Reese Scott Setzler Shoopman Thomas Verdin Williams Total--33 NAYS Bright Bryant Davis Massey Mulvaney Rose Sheheen Total--7 The amendment was laid on the table. Amendment No. 70 Senators LEATHERMAN, McCONNELL, LAND, SETZLER, MALLOY, KNOTTS and SCOTT proposed the following Amendment No. 70 (DG JUDINC), which was adopted (#33): Amend the bill, as and if amended, Part IA, Section 44, JUDICIAL DEPARTMENT, page 186, line 14, by: COLUMN 7 COLUMN 8 / STRIKING: 6,597,914 4,817,177 and INSERTING: 8,378,651 6,597,914/ Amend the bill further, as and if amended, Part IA, Section 44, JUDICIAL DEPARTMENT, page 188, line 16, by: COLUMN 7 COLUMN 8 / STRIKING: 15,880,462 0 and INSERTING: 17,599,725 1,719,263/ Renumber sections to conform. Amend sections, totals and title to conform. Senator LAND explained the amendment. Recorded Vote Senator KNOTTS desired to be recorded as voting in favor of the adoption of the amendment. Point of Order Senator BRIGHT raised a Point of Order that Proviso 2.6 of Part 1B was out of order inasmuch as it was violative of Rule 24A. 2.6. (LEA: FY 10-11 Lottery Funding) There is appropriated from the Education Lottery Account for the following education purposes and programs and funds for these programs and purposes shall be transferred by the Budget and Control Board as directed below. These appropriations must be used to supplement and not supplant existing funds for education. The Budget and Control Board is directed to prepare the subsequent Lottery Expenditure Account detail budget to reflect the appropriations of the Education Lottery Account as provided in this section. All Education Lottery Account revenue shall be carried forward from the prior fiscal year into the current fiscal year including any interest earnings, which shall be used to support the appropriations contained below. For Fiscal Year 2010-11 certified net lottery proceeds and investment earnings and any other proceeds identified by this provision are appropriated as follows: (1) Commission on Higher Education--Tuition Assistance Two-Year Institutions 47,000,000; (2) Commission on Higher Education--LIFE Scholarships as provided in Chapter 149 of Title 59 $87,370,916; (3) Commission on Higher Education--HOPE Scholarships as provided in Section 59-150-370$ 7,823,474; (4) Commission on Higher Education--Palmetto Fellows Scholarships as provided in Section 59-104-20 $30,277,240; (5) Commission on Higher Education--Need-Based Grants$11,631,566; (6) Tuitions Grants Commission--Tuition Grants $7,766,604; (7) Commission on Higher Education--National Guard Tuition Repayment Program as provided in Section 59-111-75$ 1,700,000; (8) South Carolina State University $2,500,000; (9) Technology--Public 4-Year Universities, 2-Year Institutions, and State Technical Colleges$ 4,154,702; (10) Department of Education--K-5 Reading, Math, Science & Social Studies Program as provided in Section 59-1-525 $41,891,798; (11) Department of Education--Grades 6-8 Reading, Math, Science & Social Studies Program$ 2,000,000; (12) Commission on Higher Education--Higher Education Excellence Enhancement Program $3,000,000; and. (13) School for the Deaf and the Blind--Technology Replacement 200,000. Fiscal Year 2010-11 funds appropriated to the Commission on Higher Education for Tuition Assistance must be distributed to the technical colleges and 2-year institutions as provided in Section 59-150-360. Of the funds appropriated to South Carolina State University,$250,000 may be used for the BRIDGE Program. The provisions of Section 2-75-30 of the 1976 Code regarding the aggregate amount of funding provided for the Centers of Excellence Matching Endowment are suspended for the current fiscal year. The Commission on Higher Education is authorized to temporarily transfer funds between appropriated line items in order to ensure the timely receipt of scholarships and tuition assistance. It is the goal of the General Assembly to fund the Tuition Assistance program at such a level to support at least $996 per student per term for full time students. Fiscal Year 2010-11 net lottery proceeds and investment earnings in excess of the certified net lottery proceeds and investment earnings for this period are appropriated and must be used to ensure that all LIFE, HOPE, and Palmetto Fellows Scholarships for Fiscal Year 2010-11 are fully funded. If the lottery revenue received for Fiscal Year 2010-11 is less than the amounts appropriated, the projects and programs receiving appropriations for any such year shall have their appropriations reduced on a pro rata basis, except that a reduction must not be applied to the funding of LIFE, HOPE, and Palmetto Fellows Scholarships. The Commission on Higher Education is authorized to use up to$260,000 of the funds appropriated in this provision for LIFE, HOPE, and Palmetto Fellows scholarships to provide the necessary level of program support for the scholarship award process. For Fiscal Year 2010-11, $8,400,000 certified from unclaimed prizes shall be appropriated as follows:$5,722,729 to the Department of Education for K-5 Reading, Math, Science & Social Studies Program as provided in Section 59-1-525 and $2,677,271 for Technology: Public 4-Year Universities, 2-Year Institutions, and State Technical Colleges. The allocations of Section 59-150-230(I) of the 1976 Code are suspended for the current fiscal year. Of any unclaimed prize funds available in excess of the Board of Economic Advisors estimate, the first$7,618,477 shall be directed to the Commission on Higher Education for LIFE, HOPE, and Palmetto Fellows Scholarships. The next $100,000 shall be directed to the Department of Alcohol and Other Drug Abuse Services for Prevention/Treatment of Gambling Disorders. The next$2,000,000 shall be directed to the State Library for Aid to County Libraries. The next $1,500,000 shall be directed to the Commission on Higher Education for the Partnership Among South Carolina Academic Libraries (PASCAL) Program. The next$1,000,000 shall be directed to the Commission on Higher Education for the Higher Education Excellence Enhancement Program. The next $4,000,000 shall be directed to the State Board for Technical and Comprehensive Education for the Allied Health Initiative. The next$5,470,093 shall be directed for Technology: Public 4-Year Universities, 2-Year Institutions, and State Technical Colleges. The next $1,000,000 shall be directed to the Commission on Higher Education for the Critical Needs Nursing. All additional revenue in excess of the amount certified by the Board of Economic Advisors for unclaimed prizes shall be distributed to the Commission on Higher Education for LIFE, HOPE, and Palmetto Fellows Scholarships. Notwithstanding the provisions of Section 59-150-355 of the 1976 Code or any other provision of law, the Budget and Control Board may distribute funds from the Education Lottery Account on a monthly basis during the final quarter of the fiscal year. The PRESIDENT Pro Tempore overruled the Point of Order. Point of Order Withdrawn The PRESIDENT took up the Point of Order raised by Senator MASSEY that Proviso 37.14 of Part 1B was out of order inasmuch as it was violative of Rule 24A. 37.14. (DNR: Watercraft Title and Registration Fees Surcharge) For Fiscal Year 2010-11, the Department of Natural Resources shall be authorized to charge a five dollar administrative surcharge on each watercraft and outboard motor title, title transfer and duplicate title, and on each watercraft registration, watercraft registration transfer, and duplicate registration document. The revenue collected must be deposited into the Drew's Law/Boat Titling Fund of which forty percent must be utilized for law enforcement operations and the balance utilized for administration of the provisions of Title 50. No funds generated from this administrative surcharge may be used to provide pay increases. Unexpended revenue must be retained by the department and carried forward from the prior fiscal year into the current fiscal year and used for the same purposes On motion of Senator MASSEY, with unanimous consent, the Point of Order was withdrawn. Point of Order Withdrawn The PRESIDENT took up the Point of Order raised by Senator MASSEY that Proviso 37.15 of Part 1B was out of order inasmuch as it was violative of Rule 24A. 37.15. (DNR: Hunting and Fishing License Surcharge) For Fiscal Year 2010-11, the Department of Natural Resources shall be authorized to impose a two dollar administrative surcharge on each license, permit, stamp, and tag issued to engage in any hunting or fishing activity. The surcharge shall not apply where no fee is charged. The revenue collected must be deposited into the Fish & Wildlife Protection Fund and be expended for the purposes of the Fish and Wildlife Protection Fund as defined in statute. No funds generated from this administrative surcharge may be used to provide pay increases. Unexpended funds must be retained by the department and carried forward from the prior fiscal year into the current fiscal year and used for the same purpose. On motion of Senator MASSEY, with unanimous consent, the Point of Order was withdrawn. Decision of the PRESIDENT Appealed and Overruled The PRESIDENT took up the Point of Order raised by Senator BRYANT that Proviso 89.135 of Part 1B was out of order inasmuch as it was violative of Rule 24A. 89.135. (GP: Public Safety Service Charge) At the time of collection of the registration fee for a motor vehicle, the Department of Motor Vehicles shall collect a six dollar annual public safety service charge on all vehicles required to be registered in this state, in addition to the registration fees prescribed by law. Of the funds collected pursuant to this provision for property carrying vehicles, two dollars shall be deposited into a special restricted account of the Department of Transportation to be used for operating expenses of commercial motor vehicle rest areas. The remaining funds collected pursuant to this provision for property carrying vehicles and all service charges collected for other motor vehicles required to be registered shall be deposited into a special restricted account for the Department of Public Safety to be used specifically for personnel and operating expenses for sworn law enforcement officers of the South Carolina Highway Patrol and State Transport Police. All unexpended funds collected under this provision may be retained and carried forward by the Department of Transportation or the Department of Public Safety and used for the same purposes. The PRESIDENT sustained the Point of Order. Proviso 89.135 was ruled out of order. Senator FAIR appealed the Decision of the PRESIDENT. PRESIDENT Pro Tempore PRESIDES At 3:21 A.M., Senator McCONNELL assumed the Chair. The PRESIDENT Pro Tempore stated that under the provisions of Rule 7, proponents and opponents would have a total of one-half hour to debate the Decision of the PRESIDENT, fifteen minutes each for proponents and opponents. Senator LAND was recognized to speak in favor of overriding the Decision of the PRESIDENT. Senator MASSEY was recognized to argue contra to overriding the Decision of the PRESIDENT. The question then was "Shall the ruling of the PRESIDENT be overridden?" The "ayes" and "nays" were demanded and taken, resulting as follows: Ayes 28; Nays 14 AYES Alexander Campbell Campsen Cleary Coleman Cromer Elliott Fair Hayes Hutto Jackson Land Leatherman Leventis Lourie Malloy Martin, Larry McConnell McGill Nicholson O'Dell Pinckney Rankin Reese Scott Setzler Sheheen Williams Total--28 NAYS Bright Bryant Davis Grooms Knotts Martin, Shane Massey Mulvaney Peeler Rose Ryberg Shoopman Thomas Verdin Total--14 The decision of the PRESIDENT was overridden. Statement by Senators GROOMS, SHOOPMAN, MULVANEY SHANE MARTIN, ROSE, BRYANT, BRIGHT and VERDIN We voted to sustain the PRESIDENT's decision that Proviso 89.135 was out of order. It was argued that this proviso did not violate Senate Rule 24 as there was no increase in the current registration fee for motor vehicles. It was our position that this assumption was wrong because the registration fee was increased by six dollars per vehicle. Just because the fee increase was called a "public safety service charge" does not change the fact that the motor vehicle registration was increased. This fee will look like a registration fee. It will be billed like a registration fee and will be collected like a registration fee. When exercising common sense, one can only conclude that this proviso is a fee increase and that it did violate Senate Rule 24. Amendment No. 71 Senators LEATHERMAN, LAND and SCOTT proposed the following Amendment No. 71 (DG HKLDRUGCT), which was adopted (#34): Amend the bill, as and if amended, Part IA, Section 46, PROSECUTION COORDINATION COMMISSION, page 190, line 27, by: COLUMN 7 COLUMN 8 / STRIKING: 0 0 and INSERTING: 56,436 56,436/ Amend the bill further, as and if amended, Part IA, Section 46, PROSECUTION COORDINATION COMMISSION, page 190, line 28, by: COLUMN 7 COLUMN 8 / STRIKING: 0 0 and INSERTING: 52,965 52,965/ Amend the bill further, as and if amended, Part IA, Section 46, PROSECUTION COORDINATION COMMISSION, page 190, line 29, by: COLUMN 7 COLUMN 8 / STRIKING: 0 0 and INSERTING: 38,000 38,000/ Amend the bill further, as and if amended, Part IA, Section 46, PROSECUTION COORDINATION COMMISSION, page 190, line 38, by: COLUMN 7 COLUMN 8 / STRIKING: 0 0 and INSERTING: 150,000 150,000/ Renumber sections to conform. Amend sections, totals and title to conform. Senator LAND explained the amendment. The amendment was adopted. Amendment No. 105 Senator MASSEY proposed the following Amendment No. 105 (DG ASM3CJ), which was tabled: Amend the bill, as and if amended, Part III, Section 2, page 537, by striking lines 16 and 17 and inserting: / (40) K05 - Department of Public Safety - Highway Patrol$500,000 / Renumber sections to conform. Amend sections, totals and title to conform. Senator MASSEY explained the amendment. Senator HAYES spoke on the amendment. Senator HAYES moved to lay the amendment on the table. The amendment was laid on the table. On motion of Senator MALLOY, with unanimous consent, Amendment No. 116 was taken up for immediate consideration. Amendment No. 116 Senator MASSEY proposed the following Amendment No. 116 (4657R063.ASM.DOCX), which was tabled: Amend the bill as and if amended, Part IB, Page 450, DEPARTMENT OF EMPLOYMENT AND WORKFORCE, by adding an appropriately numbered new Proviso to read: / 67. . (ESC: Unemployed Tax Credit (A) As used in this section, 'creditable employee' means an employee of a taxpayer employer who (1) was unemployed for four consecutive weeks immediately before being hired by the employer, (2) is first employed by the employer before December 1, 2010, and (3) the employer executes and provides a notarized affidavit swearing or affirming that the employee is eligible to work in the United States because the person is either a United States citizen or a lawfully present alien according to federal law. (B) An employer who has one or more creditable employees and who provides a notarized affidavit attesting to use of the federal employment verification system now known as 'E-Verify' or any future federal employment verification system is eligible to apply for and receive a credit against these taxes as provided in subsection (C) of this section. The amount of the credit is one thousand dollars for each creditable employee. Eligibility for the credit must be established as of the time the creditable employee completes thirty consecutive days of employment and the credit must be claimed for the 2010 taxable year. (C) The credit allowed pursuant to subsection (C) of this section may be taken against income taxes, the bank tax imposed pursuant to Chapter 11 of Title 12, the savings and loan association tax imposed pursuant to Chapter 13 of Title 12, the corporate license tax imposed pursuant to Chapter 20 of Title 12, and insurance premium taxes imposed pursuant to Chapter 7 of Title 38. (E) The total amount of any tax credit for the 2010 taxable year may not exceed the taxpayer's tax liability. Any unused tax may not be carried over to apply to the taxpayer's succeeding year's liability./ Renumber sections to conform. Amend sections, totals and title to conform. Senator MASSEY explained the amendment. Point of Order Senator LOURIE raised a Point of Order that the amendment was out of order inasmuch as it was violative of Rule 24B. The PRESIDENT Pro Tempore overruled the Point of Order. Senator MASSEY resumed explaining the amendment. Senator MASSEY resumed explaining the amendment. Senator LEATHERMAN moved to lay the amendment on the table. The "ayes" and "nays" were demanded and taken, resulting as follows: Ayes 23; Nays 15 AYES Alexander Fair Hayes Hutto Jackson Knotts Land Leatherman Leventis Lourie Malloy Martin, Larry McConnell McGill Nicholson O'Dell Pinckney Rankin Reese Scott Setzler Sheheen Williams Total--23 NAYS Bright Bryant Campbell Campsen Cromer Davis Grooms Martin, Shane Massey Mulvaney Peeler Rose Shoopman Thomas Verdin Total--15 The amendment was laid on the table. On motion of Senator MALLOY, with unanimous consent, Amendment No. 119 was taken up for immediate consideration. Amendment No. 119 Senator JACKSON proposed the following Amendment No. 119 (DAD 1A.17 TCHR SPLY2), which was adopted (#35): Amend the bill, as and if amended, Part IB, Section 1A, DEPARTMENT OF EDUCATION - EIA, page 358, by amending previously adopted amendment #3 (Amendment 51) which amended proviso 1A.17, by adding the following at the end of the proviso: / School districts utilizing this provision to retain the teaching supplies funding for purposes other than reimbursement to the teacher must publicly display on the school district's website the number of jobs saved through the use of these funds and to electronically forward the report on jobs saved to the Department of Education no later than December 31 of the current fiscal year to be compiled in a report for electronic presentation to the General Assembly by January 15 of the current fiscal year. / Renumber sections to conform. Amend sections, totals and title to conform. Senator JACKSON explained the amendment. Senator LEATHERMAN moved that the amendment be adopted. On motion of Senator MALLOY, with unanimous consent, Amendment No. 134 was taken up for immediate consideration. Amendment No. 134 Senator BRYANT proposed the following Amendment No. 134 (4657R069.KLB), which was tabled: Amend the bill, as and if amended, Page 500, GENERAL PROVISIONS, by striking lines 28-34 and inserting: / Violation of the above provisions of this section is prima facie evidence of a violation of Section 8-13-410(1) of the 1976 Code and shall subject a violating member of the General Assembly to the ethics procedure of his appropriate house and shall subject a violating member of a state board, commission or committee, or a state official to the applicable ethics procedure relating to them as provided by law. The above provisions do not apply to aircraft of the Division of Aeronautics when used by the Medical University of South Carolina, nor to aircraft of the athletic department or the educational foundations of any state-supported institution of higher education to law enforcement officers when flying on state owned aircraft in pursuit of fugitives, missing persons, or felons or for investigation of gang, drug, or other violent crimes. / Renumber sections to conform. Amend title to conform. Senator BRYANT explained the amendment. Point of Order Senator LEVENTIS raised a Point of Order that the amendment was out of order inasmuch as it was violative of Rule 24A. The PRESIDENT Pro Tempore overruled the Point of Order. Senator BRYANT explained the amendment. Senator LEATHERMAN moved to lay the amendment on the table. The amendment was laid on the table. Recorded Vote Senator MULVANEY desired to be recorded as voting against the motion to table the amendment. Amendment No. 150 Senator LEATHERMAN proposed the following Amendment No. 150 (DAD BALAMEND), which was adopted (#36): Amend the bill, as and if amended, Part IA, Section 80C, B&C BD-EMPLOYEE BENEFITS, page 304, line 26, by: COLUMN 7 COLUMN 8 / STRIKING: 53,855,589 53,855,589 and INSERTING: 50,058,188 50,058,188/ Renumber sections to conform. Amend sections, totals and title to conform. The question then was the third reading of the Bill. The "ayes" and "nays" were demanded and taken, resulting as follows: Ayes 29; Nays 9 AYES Alexander Campbell Campsen Cromer Elliott Fair Grooms Hayes Hutto Jackson Knotts Land Leatherman Leventis Lourie Malloy Martin, Larry McConnell McGill Nicholson O'Dell Peeler Pinckney Rankin Reese Scott Setzler Verdin Williams Total--29 NAYS Bright Bryant Davis Martin, Shane Massey Mulvaney Rose Sheheen Shoopman Total--9 There being no further amendments, the Bill was read the third time, passed and ordered returned to the House of Representatives with amendments. Statement by Senator LAND Under the provisions of Section 8-13-745, S. C. Code of Laws, I abstained from consideration of and voting on matters pertaining to the Workers' Compensation Commission, Probation, Parole and Pardon Services, and the Employment Security Commission. Statement by Senator HUTTO Under the provisions of Section 8-13-745, S. C. Code of Laws, I abstained from consideration of and voting on matters pertaining to the Workers' Compensation Commission, the Department of Motor Vehicles, the Probation, Parole and Pardon Services, the Employment Security Commission, the Administrative Law Court, DHEC, Public Service Commission, Department of Transportation and the Election Commission. Statement by Senator RANKIN Under the provisions of Section 8-13-745, S. C. Code of Laws, I abstained from consideration of and voting on matters pertaining to the Workers' Compensation Commission. Statement by Senator HAYES Under the provisions of Section 8-13-745, S. C. Code of Laws, I abstained from consideration of and voting on matters pertaining to the Workers' Compensation Commission. Statement by Senator MALLOY Under the provisions of Section 8-13-745, S. C. Code of Laws, I abstained from consideration of and voting on matters pertaining to the Workers' Compensation Commission, the Department of Motor Vehicles, the Probation, Parole and Pardon Services, the Public Service Commission, the Employment Security Commission, the Administrative Law Court and DHEC. I also abstained from the vote on the Insurance Reserve Fund. Statement by Senator SHEHEEN Under the provisions of Section 8-13-745, S. C. Code of Laws, I abstained from consideration of and voting on matters pertaining to the Workers' Compensation Commission, the Department of Motor Vehicles, the Department of Probation, Parole and Pardon Services, the Employment Security Commission, the Administrative Law Court and DHEC. I also abstained from the Guardian ad Litem Program. Statement by Senator THOMAS Under the provisions of Section 8-13-745, S. C. Code of Laws, I abstained from consideration of and voting on any matters pertaining to the Workers' Compensation Commission each year since obtaining a law license. Statement by Senator MASSEY Under the provisions of Section 8-13-745, S. C. Code of Laws, I abstained from consideration of and voting on matters pertaining to the Workers' Compensation Commission. Statement by Senator COLEMAN Under the provisions of Section 8-13-745, S. C. Code of Laws, I abstained from consideration of and voting on matters pertaining to the Workers' Compensation Commission. I also abstained from the vote on Aid to Subdivisions. Statement by Senator DAVIS Under the provisions of Section 8-13-745, S. C. Code of Laws, I abstained from consideration of and voting on matters pertaining to the Workers' Compensation Commission, the Department of Motor Vehicles, the Department of Probation, Parole and Pardon Services, the Employment Security Commission, the Administrative Law Court, DHEC, Public Service Commission, S.C. Department of Transportation, the Department of Health and Human Services and the Election Commission. Statement by Senator SETZLER Under the provisions of Section 8-13-745, S. C. Code of Laws, I abstained from consideration of and voting on matters pertaining to DHEC, the Administrative Law Court, Department of Motor Vehicles, Employment Security Commission, Labor, Licensing and Regulation, the Workers' Compensation Commission and Department of Revenue. Statement by Senator COURSON Due to physical therapy necessitated by rotator cuff surgery, I requested and received leave from the Senate for the late evening of April 29, 2010, and early morning of April 30, 2010. I would have voted in favor of third reading of the 2010-2011 Appropriations Bill. Statement by Senator RYBERG Had I been present in the Chamber when the vote was taken, I would have voted against the 2010-2011 Appropriations Bill. The Bill fails to prioritize spending for the core functions of government. The debate on this Bill, moreover, saw efforts to reorient funding to the core functions denied and dismissed on an interpretation of Senate rules that merely avoided the tough decisions required to fund schools and law enforcement. This budget, moreover, raises a bevy of fees that not only fund something other than the services from which they arise but also received very little debate and in some cases none at all. This method of budgeting is not only unfair to the citizens of South Carolina but also is unsustainable. The 2010-2011 Appropriations Bill denies South Carolinians the full funding of core services that they deserve. We must do things differently and more transparently. Statement by Senator MALLOY I have serious misgivings related to the spending priorities set in H.4657, the General Appropriations Bill. The Bill contains an unprecedented amount of fee increases, which must be paid by the citizens of South Carolina. I feel strongly that essential functions of government must be funded through our appropriations instead of relying on the ability of the branch of government or agency to impose fees on its users to cover its operations. All citizens of South Carolina, regardless of the level of direct use or interaction with state government, benefit from having a functioning government. Furthermore, not all departments and agencies are equal in their abilities to impose fees; however, they all need additional funding. Moreover, these fees are even less appealing given their regressive nature. We, as members of the General Assembly, have a duty to appropriate the funds of this State to ensure that government is able to function properly. I can think of no greater dereliction of our duties as a General Assembly than failing to properly fund the Judiciary and, instead, relying on fee increases to fill the gap between needs and haves in order to keep the Judiciary functioning. These increases jeopardize the ability of the most needy in South Carolina to avail themselves of rights and protections that are only available inside of the court house doors. Despite these concerns, I am cognizant of the dire financial condition and extreme need for additional funding of the Judiciary and agencies and departments that provide other core governmental functions. Our current budget crises and the urgency with which additional funds must be made available have prevented in-depth considerations of options for new means of appropriations to fully fund essential functions of government without relying on fee increases. In order to keep government operating and performing its essential functions, I am reluctantly voting for this budget as written because it is the best option given the circumstances we face. However, I call on all members of the General Assembly to apply all means of thought and deliberation during the next year toward new approaches for taxation and appropriating funds to essential governmental functions. I hope, and strongly believe, that we can avoid a repeat of our current situation by timely, thoughtful deliberation and consideration of new taxation and appropriation systems. On motion of Senator LARRY MARTIN, with unanimous consent, the Senate agreed that, when the Senate adjourns today, it stand adjourned to meet Friday, April 30, 2010, at 11:00 A.M., under the provisions of Rule 1 for the purpose of taking up local matters and uncontested matters which have previously received unanimous consent to be taken up. STATEWIDE APPOINTMENT Confirmation Having received a favorable report from the Labor, Commerce and Industry Committee, the following appointment was taken up for immediate consideration in open session: Initial Appointment, Director of the Department of Employment and Workforce, with the term to commence April 27, 2010, and to expire March 31, 2011 Director: Gen. John L. Finan, USAF (Ret.), 220 Holliday Rd., Columbia, SC 29223 The question then was the confirmation of the appointment. The "ayes" and "nays" were demanded and taken, resulting as follows: Ayes 46; Nays 0 AYES Alexander Anderson Bright Bryant Campbell Campsen Cleary Coleman Courson Cromer Davis Elliott Fair Ford Grooms Hayes Hutto Jackson Knotts Land Leatherman Leventis Lourie Malloy Martin, Larry Martin, Shane Massey Matthews McConnell McGill Mulvaney Nicholson O'Dell Peeler Pinckney Rankin Reese Rose Ryberg Scott Setzler Sheheen Shoopman Thomas Verdin Williams Total--46 NAYS Total--0 The appointment was confirmed. LOCAL APPOINTMENTS Confirmations Having received a favorable report from the Senate, the following appointments were confirmed in open session: Reappointment, Lancaster County Magistrate, with the term to commence April 30, 2010, and to expire April 30, 2014 Fredrick Asgill Thomas, P. O. Box 3222, Lancaster, SC 29721 Reappointment, Lancaster County Magistrate, with the term to commence April 30, 2010, and to expire April 30, 2014 Van K. Richardson, 3611 Kershaw Camden Highway, Heath Springs, SC 29058 Reappointment, Lancaster County Magistrate, with the term to commence April 30, 2010, and to expire April 30, 2014 Jaqueline M. Pope, P.O. Box 66, Kershaw, SC 29067 At 4:50 A.M., on motion of Senator LARRY MARTIN, the Senate adjourned to meet tomorrow at 11:00 A.M. under the provisions of Rule 1 for the purpose of taking up local matters and uncontested matters which have previously received unanimous consent to be taken up. * * * This web page was last updated on Tuesday, February 22, 2011 at 11:46 A.M.	2017-10-20T16:02:39	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3259927034378052, "perplexity": 7672.946115475546}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-43/segments/1508187824226.31/warc/CC-MAIN-20171020154441-20171020174441-00123.warc.gz"}
https://control.com/textbook/chemistry/electronic-structure/	# Electronic Structure ## Chapter 3 - Chemistry in Industrial Instrumentation Earlier in this chapter you were shown a model of a nitrogen atom with a dense nucleus (comprised of protons and neutrons) surrounded by electrons whirling around like satellites around a planet. While there are some useful features of this model, it is largely in error. A more realistic view of atomic structure begins with the realization that electrons do not exist as discrete particles, but rather as wave packets. In a sense, they orbit the nucleus within certain areas of probability, as described by the principles of quantum mechanics. One way to envision this is to think of an electron’s placement around the nucleus in the same way you might picture a city shrouded by a layer of fog. The electron does not have a discrete location (even though there is a discrete number of them found in every atom), but rather may be found anywhere within a certain region to varying degrees of probability. Things get even stranger the more electrons there are in an atom. No two electrons may share the same quantum states in the same atom – a principle called the Pauli Exclusion Principle. This means the electrons surrounding a nucleus must exist in distinct patterns. Just a few of these patterns are shown here as orbitals (regions of high probability where up to two electrons may be found surrounding a nucleus): Electrons situate themselves around the nucleus of any atom according to one basic rule: the minimization of potential energy. That is, the electrons seek the lowest-energy positions available around the nucleus. Given the electrostatic attraction between negative electrons and the positive nucleus of an atom, there is potential energy stored in the “elevation” between an orbiting electron and the nucleus, just as there is gravitational potential energy in any object orbiting a planet. Electrons lose energy as they situate themselves closer to the nucleus, and it requires an external input of energy to move an electron farther away from its parent nucleus. In a sense, most of chemistry may be explained by this principle of minimized potential energy. Electrons “want” to “fall” as close as they can to the positively-charged nucleus. However, there is limited “seating” around the nucleus. As described by Pauli’s Exclusion Principle, electrons cannot simply pile on top of each other in their quest for minimum energy, but rather must occupy certain regions of space allowed by their unique quantum states. An analogy for visualizing this is to picture an atom as if it were an amphitheater, with the stage being the nucleus and the concentric array of seats being places where electrons may reside. All spectators (electrons) desire to be as close to the stage (nucleus) in an amphitheater (atom) as possible, but since everyone cannot occupy the best seat, people are forced to choose seats at different positions around the stage. As a result, the inner seats fill first, with most empty seats being furthest away from the stage. The concept of energy fits neatly into this analogy as well: just as electrons give up energy to “fall into” lower-energy regions around the nucleus, people must give up money to purchase seats closest to the action on stage. The energy levels available for orbiting electrons are divided into categories of shells and subshells. A “shell” (or, principal quantum number, $$n$$) describes the main energy level of an electron. In our amphitheater analogy, this is equivalent to a tier or seating level. A “subshell” (or, subsidiary quantum number, $$l$$) further divides the energy levels within each electron shell, and assigns different shapes to the electrons’ probability “clouds.” In the amphitheater analogy, a subshell would be a row of seats within a particular tier. To make the analogy accurate, we would have to imagine each row of seats in a tier having a different shape (not all arcs or straight lines), with varying degrees of viewing comfort afforded by each shape. The first row in each tier faces uniformly toward the stage, allowing easy viewing. Successive rows (subshells) in each tier (shell) contain more seats, but are bent in such a way that the stage is not as easy to view, making these rows less desirable to occupy. Electron subshells always have an even-numbered electron capacity, analogous to theater rows containing even-numbered quantities of seats, because atomic electrons tend to gather in pairs called orbitals. Chemists identify electron shells both by number (the value of the quantum number $$n$$) and/or by capital letters: the first shell by the letter K, the second by L, the third by M, and the fourth by N. Higher-order shells exist for atoms requiring many electrons (high atomic number), and the lettering pattern is alphabetic (fifth shell is O, sixth is P, etc.). Each successive shell has a greater number of subshells available, like successive amphitheater tiers having more rows: the low-level tiers closest to the stage having the fewest rows, and the high-level tiers furthest from the stage having the most rows. A numbering and lettering system is also used by chemists to identify subshells within each shell (the $$l$$ quantum number value starting with zero, and lower-case letters beginning with “s”): the first subshell ($$l = 0$$) in any shell represented by the letter s, the second ($$l = 1$$) by p, the third ($$l = 2$$) by d, the fourth ($$l = 3$$) by f, and all others by successive lower-case letters of the alphabet. Each subshell of each shell has an even-numbered capacity for electrons, since the electrons in each subshell are organized in “orbital” regions, each orbital handling a maximum of two electrons. The number of orbitals per shell is equal to twice the $$l$$ value plus one. An “s” subshell has one orbital holding up to two electrons. A “p” subshell has three orbitals holding up to six electrons total. A “d” subshell has five orbitals holding up to ten electrons total. An “f” subshell has seven orbitals holding up to 14 electrons total. A “g” subshell has nine orbitals holding up to 18 electrons total. The number of subshells in any shell is the same as that shell’s $$n$$ value. Thus, the first (K) shell has only one subshell, “s”. The second (L) shell has two subshells, an “s” and a “p”. The third (M) shell has three subshells available, an “s”, a “p”, and a “d”; and so on. This table shows the first few shells, their subshells, and electron capacities of each: ($n$ value) & ($l$ value) & $=2(2l + 1)$ \cr \noalign{\hrule \vskip 10pt \hrule} \noalign{\hrule \vskip 10pt \hrule} \noalign{\hrule \vskip 10pt \hrule} \noalign{\hrule \vskip 10pt \hrule} Shell Subshell Subshell electron capacity $n = 1$ ; K $l = 0$ ; s $2 \times (2 \times 0 + 1) = 2$ $n = 2$ ; L $l = 0$ ; s $2 \times (2 \times 0 + 1) = 2$ $l = 1$ ; p $2 \times (2 \times 1 + 1) = 6$ $n = 3$ ; M $l = 0$ ; s $2 \times (2 \times 0 + 1) = 2$ $l = 1$ ; p $2 \times (2 \times 1 + 1) = 6$ $l = 2$ ; d $2 \times (2 \times 2 + 1) = 10$ $n = 4$ ; N $l = 0$ ; s $2 \times (2 \times 0 + 1) = 2$ $l = 1$ ; p $2 \times (2 \times 1 + 1) = 6$ $l = 2$ ; d $2 \times (2 \times 2 + 1) = 10$ $l = 3$ ; f $2 \times (2 \times 3 + 1) = 14$ Reviewing our amphitheater analogy, atomic shells are like seating tiers (levels), subshells are like rows of seats within each tier, and subshell electron capacity is like the number of seats in each row. This simple illustration shows an atom with three shells (K, L, and M) with the respective subshells (s, p, and d) represented by differently-shaded rings within each shell, having different numbers of places for electrons within each one: This illustration is vastly over-simplified, failing to show the diverse shapes of each subshell, serving only to show how each successive shell grows in subshells and electron capacities. The complete electron configuration for an atom may be expressed using spectroscopic notation, showing the shell numbers, subshell letters, and number of electrons residing within each subshell as a superscript. For example, the element helium (with an atomic number of 2) would be expressed as 1s$$^{2}$$, with just two electrons in the “s” subshell of the first shell. The following table shows the electron structures of the first nineteen elements in the periodic table, from the element hydrogen (atomic number = 1) to potassium (atomic number = 19): Element Atomic number Electron configuration Hydrogen 1 1s$^{1}$ Helium 2 1s$^{2}$ Lithium 3 1s$^{2}$2s$^{1}$ Beryllium 4 1s$^{2}$2s$^{2}$ Boron 5 1s$^{2}$2s$^{2}$2p$^{1}$ Carbon 6 1s$^{2}$2s$^{2}$2p$^{2}$ Nitrogen 7 1s$^{2}$2s$^{2}$2p$^{3}$ Oxygen 8 1s$^{2}$2s$^{2}$2p$^{4}$ Fluorine 9 1s$^{2}$2s$^{2}$2p$^{5}$ Neon 10 1s$^{2}$2s$^{2}$2p$^{6}$ Sodium 11 1s$^{2}$2s$^{2}$2p$^{6}$3s$^{1}$ Magnesium 12 1s$^{2}$2s$^{2}$2p$^{6}$3s$^{2}$ Aluminum 13 1s$^{2}$2s$^{2}$2p$^{6}$3s$^{2}$3p$^{1}$ Silicon 14 1s$^{2}$2s$^{2}$2p$^{6}$3s$^{2}$3p$^{2}$ Phosphorus 15 1s$^{2}$2s$^{2}$2p$^{6}$3s$^{2}$3p$^{3}$ Sulfur 16 1s$^{2}$2s$^{2}$2p$^{6}$3s$^{2}$3p$^{4}$ Chlorine 17 1s$^{2}$2s$^{2}$2p$^{6}$3s$^{2}$3p$^{5}$ Argon 18 1s$^{2}$2s$^{2}$2p$^{6}$3s$^{2}$3p$^{6}$ Potassium 19 1s$^{2}$2s$^{2}$2p$^{6}$3s$^{2}$3p$^{6}$4s$^{1}$ In order to avoid having to write unwieldy spectroscopic descriptions of each element’s electron structure, it is customary to write the notation only for subshells that are unfilled. For example, instead of writing the electron structure of the element aluminum as 1s$$^{2}$$2s$$^{2}$$2p$$^{6}$$3s$$^{2}$$3p$$^{1}$$, we might just as well write a condensed version showing only the last subshell (3p$$^{1}$$), since all the previous subshells are completely full. Another way to abbreviate the spectroscopic notation for elements is to condense all the shells below the newest (unfilled) shell as the corresponding noble element, in brackets. To use the example of aluminum again, we could write its spectroscopic notation as [Ne]3s$$^{2}$$3p$$^{1}$$ since its shell 1 and shell 2 configurations are completely described by the electron configuration of Neon. Re-writing our electron shell table for the first nineteen elements using this condensed notation: Element Atomic number Electron configuration Hydrogen 1 1s$^{1}$ Helium 2 1s$^{2}$ Lithium 3 [He]2s$^{1}$ Beryllium 4 [He]2s$^{2}$ Boron 5 [He]2s$^{2}$2p$^{1}$ Carbon 6 [He]2s$^{2}$2p$^{2}$ Nitrogen 7 [He]2s$^{2}$2p$^{3}$ Oxygen 8 [He]2s$^{2}$2p$^{4}$ Fluorine 9 [He]2s$^{2}$2p$^{5}$ Neon 10 [He]2s$^{2}$2p$^{6}$ Sodium 11 [Ne]3s$^{1}$ Magnesium 12 [Ne]3s$^{2}$ Aluminum 13 [Ne]3s$^{2}$3p$^{1}$ Silicon 14 [Ne]3s$^{2}$3p$^{2}$ Phosphorus 15 [Ne]3s$^{2}$3p$^{3}$ Sulfur 16 [Ne]3s$^{2}$3p$^{4}$ Chlorine 17 [Ne]3s$^{2}$3p$^{5}$ Argon 18 [Ne]3s$^{2}$3p$^{6}$ Potassium 19 [Ar]4s$^{1}$ If we progress from element to element in increasing atomic number, we see that no new shell begins to form until after we reach the noble element for that period at the far right-hand column. With the beginning of each new period at the far-left end of the Table, we see the beginning of the next higher-order electron shell. The shell(s) below are represented by whichever noble element shares that same configuration, indicating a “noble core” of electrons residing in extremely stable (low-energy) regions around the nucleus. The beginning of the next higher-order shell is what accounts for the periodic cycle of ionization energies we see in elements of progressing atomic number. The first electron to take residence in a new shell is very easy to remove, unlike the electrons residing in the “noble” configuration shell(s) below: Not only is the “noble core” notation convenient for tersely describing the electron structure of an element, but it also reveals an important concept in chemistry: the idea of valence. Electrons residing in lower-order shells are, by definition, at lower energy states than electrons residing in higher-order shells and are therefore much more difficult to dislodge. Therefore, the electrons in unfilled shells, being easier to dislodge, play a far greater role in chemical bonds than electrons residing in filled shells below. These “outer” electrons are called valence electrons, and their number determines how readily an atom will chemically interact with another atom. This is why elements found in the same group (having similar outer-electron configurations) bear similar chemical characteristics: the electrons lying below in the “noble core” configurations have little effect on how the atom will bond with other atoms. A lithium atom, with its outer-most electron configuration being 2s$$^{1}$$, reacts in much the same way as an atom of sodium having an outer-most configuration of 3s$$^{1}$$, and much the same as a potassium atom having an outer-most configuration of 4s$$^{1}$$, all because those outer-shell electrons are the most available for interaction with electrons of other atoms. If we examine the electron structures of atoms with successively greater atomic numbers (more protons in the nucleus, therefore more electrons in orbit to balance the electrical charge), we notice that the shells and subshells fill up in an interesting pattern. One might think that all the lower-order shells get completely filled before any electrons go into a higher-order shell – just as we might expect people to fill every seat in all the lower tiers of an amphitheater before filling seats in any of the higher tiers – but this is not always the case. Instead, the energy levels of subshells within shells is split, such that certain subshells within a higher shell will have a lower energy value than certain subshells within a lower shell. Referring back to our amphitheater analogy, where seating tiers represented shells and seat rows of various shape represented subshells, it is as though people choose to fill the more comfortable rows in higher-level tiers before sitting in the less-comfortable rows in lowest available tiers, the desire for comfort trumping the desire for proximity to the stage. A rule commonly taught in introductory chemistry courses called the Madelung rule (also referred to as Aufbau order, after the German verb aufbauen meaning “to build up”) is that subshells fill with increasing atomic number in such an order that the subshell with the lowest $$n + l$$ value, in the lowest shell, gets filled before any others. The following graphic illustrates this ordering: Madelung filling order: 1s $$\rightarrow$$ 2s $$\rightarrow$$ 2p $$\rightarrow$$ 3s $$\rightarrow$$ 3p $$\rightarrow$$ 4s $$\rightarrow$$ 3d $$\rightarrow$$ 4p $$\rightarrow$$ 5s $$\rightarrow$$ 4d $$\rightarrow$$ 5p $$\rightarrow$$ 6s $$\rightarrow$$ 4f $$\rightarrow$$ 5d $$\rightarrow$$ 6p $$\rightarrow$$ 7s $$\rightarrow$$ 5f $$\rightarrow$$ 6d $$\rightarrow$$ 7p $$\rightarrow$$ 8s $$\rightarrow$$ (etc.) It should be noted that exceptions exist for this rule. We see one of those exceptions with the element chromium ($$_{24}$$Cr). Strictly following the Madelung rule in progressing from vanadium (atomic number = 23, valence electron structure 3d$$^{3}$$4s$$^{2}$$) to chromium (atomic number = 24), we would expect the next electron to take residence in the “3d” subshell making chromium’s valence structure be 3d$$^{4}$$4s$$^{2}$$, but instead we find two more electrons residing in chromium’s 3d subshell with one less in the 4s subshell (3d$$^{5}$$4s$$^{1}$$). The sequence resumes its expected progression with the next element, manganese (atomic number = 25, valence electron structure 3d$$^{5}$$4s$$^{2}$$). The general principle of energy minimization still holds true . . . it’s just that the relative energies of succeeding subshells do not follow a simple rule structure. In other words, the Aufbau order is an over-simplified view of reality. To use the amphitheater analogy again, it’s as if someone gave up one of the nice chairs in tier 4 to sit next to a friend who just occupied one of the less comfortable chairs in tier 3. The practical importance of electron configurations in chemistry is the potential energy possessed by electrons as they reside in different shells and subshells. This is extremely important in the formation and breaking of chemical bonds, which occur due to the interaction of electrons between two or more atoms. A chemical bond occurs between atoms when the outer-most (valence) electrons of those atoms mutually arrange themselves in energy states that are collectively lower than they would be individually. The ability for different atoms to join in chemical bonds completely depends upon the default energy states of electrons in each atom, as well as the next available energy states in the other atoms. Atoms will form stable bonds only if the union allows electrons to assume stable (low-energy) levels. This is why different elements are very selective regarding which elements they will chemically bond with to form compounds: not all combinations of atoms result in favorable potential energy levels. The amount of energy required to break a chemical bond (i.e. separate the atoms from each other) is the same amount of energy required to restore the atoms’ electrons to their previous (default) states before they joined. This is the same amount of energy released by the atoms as they come together to form the bond. Thus, we see the foundation of the general principle in chemistry that forming chemical bonds releases energy, while breaking chemical bonds requires an input of energy from an external source. We also see in this fact an expression of the Conservation of Energy: the amount of energy “invested” in breaking bonds is precisely the same as the amount of energy “returned” when those same bonds re-form. In summary, the whole of chemistry is a consequence of electrons not being able to assume arbitrary positions around the nucleus of an atom. Instead, they seek the lowest possible energy levels within a framework allowing them to retain unique quantum states. Atoms with mutually agreeable electron structures readily bond together to form molecules, and they release energy in the process of joining. Molecules may be broken up into their constituent atoms, if sufficient energy is applied to overcome the bond. Atoms with incompatible electron structures do not form stable bonds with each other. Published under the terms and conditions of the Creative Commons Attribution 4.0 International Public License	2022-01-27T02:49:20	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5038368105888367, "perplexity": 1409.9512070861836}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320305052.56/warc/CC-MAIN-20220127012750-20220127042750-00696.warc.gz"}
https://zbmath.org/authors/?q=ai%3Agugat.martin	## Gugat, Martin Compute Distance To: Author ID: gugat.martin Published as: Gugat, Martin; Gugat, M. External Links: MGP · ORCID · Wikidata · IdRef Documents Indexed: 105 Publications since 1992, including 1 Book Reviewing Activity: 35 Reviews Co-Authors: 47 Co-Authors with 64 Joint Publications 1,410 Co-Co-Authors all top 5 ### Co-Authors 41 single-authored 24 Leugering, Günter 14 Herty, Michael Matthias 7 Dick, Markus 5 Wintergerst, David 4 Schultz, Rüdiger 4 Schuster, Michael J. 3 Hante, Falk M. 3 Klar, Axel 3 Schleper, Veronika 3 Steffensen, Sonja 3 Zuazua, Enrique 2 Giesselmann, Jan 2 Grimm, Volker 2 Heitsch, Holger 2 Henrion, René 2 Keimer, Alexander 2 Martin, Alexander 2 Schmidt, E. J. P. Georg 2 Schmidt, Martin 2 Sirvent, Mathias 2 Tröltzsch, Fredi 2 Ulbrich, Stefan 1 Adelhütte, Dennis 1 Aßmann, Denis 1 Farshbaf-Shaker, Mohammad Hassan 1 Gerster, Stephan 1 Grandòn, Tatiana Gonzàlez 1 Hettich, Rainer 1 Hirsch-Dick, Markus 1 Kunkel, Teresa 1 Liers, Frauke 1 Mateos, Mariano 1 Müller, Siegfried 1 Nitsche, Sabrina 1 Perrollaz, Vincent 1 Pfeiffer, Barbara 1 Rosier, Lionel 1 Schittkowski, Klaus 1 Sigalotti, Mario 1 Sklyar, Grigory Mikhailovitch 1 Sokołowski, Jan 1 Stingl, Michael 1 Strauch, Elisa 1 Tamasoiu, Simona Oana 1 Trélat, Emmanuel 1 Tucsnak, Marius 1 Weber, Gerhard-Wilhelm 1 Yu, Hui all top 5 ### Serials 9 SIAM Journal on Control and Optimization 6 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 6 Networks and Heterogeneous Media 5 Journal of Optimization Theory and Applications 4 Systems & Control Letters 4 Optimization 3 Mathematical Methods in the Applied Sciences 3 IMA Journal of Mathematical Control and Information 3 Computational Optimization and Applications 3 Computational and Applied Mathematics 3 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 2 Applicable Analysis 2 Control and Cybernetics 2 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 2 MCSS. Mathematics of Control, Signals, and Systems 2 Mathematical Programming. Series A. Series B 2 Mathematical Problems in Engineering 2 Vietnam Journal of Mathematics 2 Mathematical Control and Related Fields 1 International Journal of Control 1 Journal of Mathematical Analysis and Applications 1 Automatica 1 Journal of Computational and Applied Mathematics 1 Management Science 1 Networks 1 SIAM Journal on Numerical Analysis 1 Optimal Control Applications & Methods 1 Chinese Annals of Mathematics. Series B 1 Constructive Approximation 1 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 1 Numerical Algorithms 1 SIAM Journal on Applied Mathematics 1 Optimization Methods & Software 1 Mathematical Methods of Operations Research 1 International Journal of Applied Mathematics and Computer Science 1 Optimization and Engineering 1 Journal of Evolution Equations 1 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 1 Advanced Modeling and Optimization 1 Numerical Algebra, Control and Optimization 1 Arabian Journal of Mathematics 1 Pure and Applied Functional Analysis 1 SpringerBriefs in Electrical and Computer Engineering all top 5 ### Fields 56 Partial differential equations (35-XX) 52 Systems theory; control (93-XX) 45 Calculus of variations and optimal control; optimization (49-XX) 31 Operations research, mathematical programming (90-XX) 25 Fluid mechanics (76-XX) 12 Numerical analysis (65-XX) 10 Mechanics of deformable solids (74-XX) 2 Approximations and expansions (41-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Combinatorics (05-XX) 1 Operator theory (47-XX) 1 Probability theory and stochastic processes (60-XX) 1 Mechanics of particles and systems (70-XX) ### Citations contained in zbMATH Open 96 Publications have been cited 791 times in 408 Documents Cited by Year Existence of classical solutions and feedback stabilization for the flow in gas networks. Zbl 1429.76090 Gugat, Martin; Herty, Michaël 2011 Global boundary controllability of the de St. Venant equations between steady states. Zbl 1032.93030 Gugat, M.; Leugering, G. 2003 Optimal control for traffic flow networks. Zbl 1079.49024 Gugat, M.; Herty, M.; Klar, A.; Leugering, G. 2005 Gas flow in fan-shaped networks: classical solutions and feedback stabilization. Zbl 1237.35107 Gugat, Martin; Dick, Markus; Leugering, Günter 2011 Flow control in gas networks: exact controllability to a given demand. Zbl 1394.76112 Gugat, M.; Herty, M.; Schleper, V. 2011 Global controllability between steady supercritical flows in channel networks. Zbl 1047.93028 Gugat, Martin; Leugering, Günter; Schmidt, E. J. P. Georg 2004 Stationary states in gas networks. Zbl 1332.93154 Gugat, Martin; Hante, Falk M.; Hirsch-Dick, Markus; Leugering, Günter 2015 Classical solutions and feedback stabilization for the gas flow in a sequence of pipes. Zbl 1263.76059 Dick, Markus; Gugat, Martin; Leugering, Günter 2010 Optimal Neumann control for the 1D wave equation: finite horizon, infinite horizon, boundary tracking terms and the turnpike property. Zbl 1335.49012 Gugat, Martin; Trélat, Emmanuel; Zuazua, Enrique 2016 Stars of vibrating strings: switching boundary feedback stabilization. Zbl 1258.93088 Gugat, Martin; Sigalotti, Mario 2010 Global boundary controllability of the Saint-Venant system for sloped canals with friction. Zbl 1154.76009 Gugat, M.; Leugering, G. 2009 Boundary feedback stabilization by time delay for one-dimensional wave equations. Zbl 1198.93177 Gugat, Martin 2010 Optimal switching boundary control of a string to rest in finite time. Zbl 1242.49008 Gugat, Martin 2008 $$L^{p}$$-optimal boundary control for the wave equation. Zbl 1083.49017 Gugat, M.; Leugering, G.; Sklyar, G. 2005 Analysis of a system of nonlocal conservation laws for multi-commodity flow on networks. Zbl 1335.49011 Gugat, Martin; Keimer, Alexander; Leugering, Günter; Wang, Zhiqiang 2015 $$L^\infty$$-norm minimal control of the wave equation: on the weakness of the bang-bang principle. Zbl 1133.49006 Gugat, Martin; Leugering, Gunter 2008 Prox-regularization methods for generalized fractional programming. Zbl 0973.90078 Gugat, M. 1998 MIP-based instantaneous control of mixed-integer PDE-constrained gas transport problems. Zbl 1391.49040 Gugat, Martin; Leugering, Günter; Martin, Alexander; Schmidt, Martin; Sirvent, Mathias; Wintergerst, David 2018 Optimal boundary control and boundary stabilization of hyperbolic systems. Zbl 1328.49001 Gugat, Martin 2015 Optimal nodal control of networked hyperbolic systems: evaluation of derivatives. Zbl 1165.49307 Gugat, Martin 2005 The smoothed-penalty algorithm for state constrained optimal control problems for partial differential equations. Zbl 1201.90186 Gugat, Martin; Herty, Michael 2010 An example for the switching delay feedback stabilization of an infinite dimensional system: the boundary stabilization of a string. Zbl 1216.93084 Gugat, Martin; Tucsnak, Marius 2011 $$H^2$$-stabilization of the isothermal Euler equations: a Lyapunov function approach. Zbl 1253.76112 Gugat, Martin; Leugering, Günter; Tamasoiu, Simona 2012 Optimal distributed control of the wave equation subject to state constraints. Zbl 1176.35176 Gugat, Martin; Keimer, Alexander; Leugering, Günter 2009 A strict $$H^1$$-Lyapunov function and feedback stabilization for the isothermal Euler equations with friction. Zbl 1242.76296 Dick, Markus; Gugat, Martin; Leugering, Günter 2011 On the turnpike phenomenon for optimal boundary control problems with hyperbolic systems. Zbl 1418.35252 Gugat, Martin; Hante, Falk M. 2019 Well-posedness of networked hyperbolic systems of balance laws. Zbl 1356.49004 Gugat, Martin; Herty, Michael; Klar, Axel; Leugering, Günther; Schleper, Veronika 2012 Modelling, stabilization, and control of flow in networks of open channels. Zbl 0987.93056 Gugat, Martin; Leugering, Günter; Schittkowski, Klaus; Schmidt, E. J. P. Georg 2001 Neumann boundary feedback stabilization for a nonlinear wave equation: A strict $$H^2$$-Lyapunov function. Zbl 1366.76079 Gugat, Martin; Leugering, Günter; Wang, Ke 2017 Boundary feedback stabilization of the Schlögl system. Zbl 1309.93121 Gugat, Martin; Tröltzsch, Fredi 2015 Boundary feedback stabilization of the telegraph equation: decay rates for vanishing damping term. Zbl 1288.93066 Gugat, Martin 2014 Time-delayed boundary feedback stabilization of the isothermal Euler equations with friction. Zbl 1368.76010 Gugat, Martin; Dick, Markus 2011 Approximation of semigroups and related operator functions by resolvent series. Zbl 1222.65052 Grimm, Volker; Gugat, Martin 2010 One-sided derivatives for the value function in convex parametric programming. Zbl 0822.90130 Gugat, M. 1994 A fast algorithm for a class of generalized fractional programs. Zbl 0881.90113 Gugat, Martin 1996 Controllability of a slowly rotating Timoshenko beam. Zbl 1031.93103 Gugat, Martin 2001 The isothermal Euler equations for ideal gas with source term: product solutions, flow reversal and no blow up. Zbl 1372.35224 Gugat, Martin; Ulbrich, Stefan 2017 Optimal boundary feedback stabilization of a string with moving boundary. Zbl 1141.93047 Gugat, Martin 2008 Boundary stabilization of quasilinear hyperbolic systems of balance laws: exponential decay for small source terms. Zbl 1421.35213 Gugat, Martin; Perrollaz, Vincent; Rosier, Lionel 2018 Networks of pipelines for gas with nonconstant compressibility factor: stationary states. Zbl 1416.76253 Gugat, Martin; Schultz, Rüdiger; Wintergerst, David 2018 Weber problems with mixed distances and regional demand. Zbl 1146.90464 Gugat, Martin; Pfeiffer, Barbara 2007 Penalty techniques for state constrained optimal control problems with the wave equation. Zbl 1202.49037 Gugat, Martin 2010 Boundary controllability between sub- and supercritical flow. Zbl 1047.35087 Gugat, Martin 2003 Towards simulation based mixed integer optimization with differential equations. Zbl 1397.90308 Gugat, Martin; Leugering, Günter; Martin, Alexander; Schmidt, Martin; Sirvent, Mathias; Wintergerst, David 2018 Parametric disjunctive programming: One-sided differentiability of the value function. Zbl 0886.90113 Gugat, M. 1997 Solutions of $$L^p$$-norm-minimal control problems for the wave equation. Zbl 1119.90353 Gugat, Martin; Leugering, G. 2002 Contamination source determination in water distribution networks. Zbl 1260.49005 Gugat, Martin 2012 Analytic solutions of $$L^{\infty}$$ optimal control problems for the wave equation. Zbl 1012.49025 Gugat, M. 2002 Exponential stabilization of the wave equation by Dirichlet integral feedback. Zbl 1339.35156 Gugat, Martin 2015 Optimal boundary control of the wave equation with pointwise control constraints. Zbl 1226.49023 Gugat, Martin; Grimm, Volker 2011 Regularization of $$L^\infty$$-optimal control problems for distributed parameter systems. Zbl 1015.49020 Gugat, M.; Leugering, G. 2002 Norm-minimal Neumann boundary control of the wave equation. Zbl 1314.35205 Gugat, Martin 2015 Exact penalization of terminal constraints for optimal control problems. Zbl 1353.49005 Gugat, Martin; Zuazua, Enrique 2016 A note on the approximation of Dirichlet boundary control problems for the wave equation on curved domains. Zbl 1273.49009 Gugat, M.; Sokolowski, J. 2013 A parametric view on the Mangasarian-Fromovitz constraint qualification. Zbl 0976.90111 Gugat, Martin 1999 Optimal energy control in finite time by varying the length of the string. Zbl 1144.49016 Gugat, Martin 2007 Conservation law constrained optimization based upon Front-Tracking. Zbl 1116.65079 Gugat, Martin; Herty, Michaël; Klar, Axel; Leugering, Gunter 2006 Optimal boundary control of a string to rest in finite time with continuous state. Zbl 1092.49020 Gugat, Martin 2006 An algorithm for Chebyshev approximation by rationals with constrained denominators. Zbl 0886.41013 Gugat, M. 1996 Coupling conditions for the transition from supersonic to subsonic fluid states. Zbl 1379.35241 Gugat, Martin; Herty, Michael; Müller, Siegfried 2017 Lipschitz continuity of the value function in mixed-integer optimal control problems. Zbl 1439.49047 Gugat, Martin; Hante, Falk M. 2017 Transient flow in gas networks: traveling waves. Zbl 1442.35316 Gugat, Martin; Wintergerst, David 2018 Lavrentiev-prox-regularization for optimal control of PDEs with state constraints. Zbl 1200.65051 Gugat, Martin 2009 Optimization under functional constraints (semi-infinite programming) and applications. Zbl 0770.90070 Hettich, Rainer; Gugat, Martin 1992 $$L^1$$-optimal boundary control of a string to rest in finite time. Zbl 1108.49017 Gugat, Martin 2006 Time-parametric control: Uniform convergence of the optimal value functions of discretized problems. Zbl 0951.49032 Gugat, Martin 1999 A Newton method for the computation of time-optimal boundary controls of one-dimensional vibrating systems. Zbl 0953.93042 Gugat, Martin 2000 The Newton differential correction algorithm for rational Chebyshev approximation with constrained denominators. Zbl 0860.65006 Gugat, M. 1996 Erratum to: “Flow control in gas networks: exact controllability to a given demand”. Zbl 1464.76183 Gugat, M.; Herty, M.; Schleper, V. 2015 Stabilization of networked hyperbolic systems with boundary feedback. Zbl 1327.93312 Dick, Markus; Gugat, Martin; Herty, Michael; Leugering, Günter; Steffensen, Sonja; Wang, Ke 2014 Lipschitz solutions of initial boundary value problems for balance laws. Zbl 1394.35261 Gugat, Martin; Ulbrich, Stefan 2018 Stationary gas networks with compressor control and random loads: optimization with probabilistic constraints. Zbl 1427.76234 Gugat, Martin; Schuster, Michael 2018 On the limits of stabilizability for networks of strings. Zbl 1425.93229 Gugat, Martin; Gerster, Stephan 2019 Error bounds for infinite systems of convex inequalities without Slater’s condition. Zbl 0997.90090 Gugat, Martin 2000 Optimal boundary control in flood management. Zbl 1239.49030 Gugat, Martin 2007 Computation of lower bounds for spectra via fractional semi-infinite programming. Zbl 0841.65091 Gugat, Martin 1995 Convex semi-infinite parametric programming: Uniform convergence of the optimal value functions of discretized problems. Zbl 0956.90054 Gugat, M. 1999 A turnpike result for convex hyperbolic optimal boundary control problems. Zbl 1458.35259 Gugat, Martin 2019 Optimal Neumann boundary control of a vibrating string with uncertain initial data and probabilistic terminal constraints. Zbl 1446.49004 Farshbaf-Shaker, M. Hassan; Gugat, Martin; Heitsch, Holger; Henrion, René 2020 A smoothed penalty iteration for state constrained optimal control problems for partial differential equations. Zbl 1290.90072 Gugat, Martin; Herty, Michael 2013 Exact boundary controllability for free traffic flow with Lipschitz continuous state. Zbl 1400.90098 Gugat, Martin 2016 Joint model of probabilistic-robust (probust) constraints applied to gas network optimization. Zbl 1477.90012 Adelhütte, Dennis; Aßmann, Denis; Grandòn, Tatiana Gonzàlez; Gugat, Martin; Heitsch, Holger; Henrion, René; Liers, Frauke; Nitsche, Sabrina; Schultz, Rüdiger; Stingl, Michael; Wintergerst, David 2021 Lavrentiev prox-regularization methods for optimal control problems with pointwise state constraints. Zbl 1197.49042 Gugat, Martin 2009 On the relaxation approximation for $$2\times 2$$ hyperbolic balance laws. Zbl 1407.65105 Gugat, Martin; Herty, Michael; Yu, Hui 2018 Nodal control of conservation laws on networks. Sensitivity calculations for the control of systems of conservation laws with source terms on networks. Zbl 1097.65071 Gugat, Martin 2005 Parametric convex optimization: One-sided derivatives of the value function in singular parameters. Zbl 0961.90114 Gugat, Martin 1998 Corrigendum: One-sided derivatives for the value function in convex parametric programming. Zbl 0864.90113 Gugat, M. 1996 Semi-infinite terminal problems: A Newton type method. Zbl 0916.65066 Gugat, Martin 1998 Exponential stability for the Schlögl system by Pyragas feedback. Zbl 1462.35079 Gugat, Martin; Mateos, Mariano; Tröltzsch, Fredi 2020 Convexity and starshapedness of feasible sets in stationary flow networks. Zbl 1441.90108 Gugat, Martin; Schultz, Rüdiger; Schuster, Michael 2020 Boundary feedback stabilization of the isothermal Euler equations with uncertain boundary data. Zbl 1391.76673 Gugat, Martin; Schultz, Rüdiger 2018 Time delay in optimal control loops for wave equations. Zbl 1356.49005 Gugat, Martin; Leugering, Günter 2017 On the relaxation approximation of boundary control of the isothermal Euler equations. Zbl 1253.93110 Dick, M.; Gugat, M.; Herty, M.; Steffensen, S. 2012 Stabilization of the gas flow in star-shaped networks by feedback controls with varying delay. Zbl 1264.93206 Gugat, Martin; Dick, Markus; Leugering, Günter 2013 Exact controllability of a string to rest with a moving boundary. Zbl 1453.93017 Gugat, Martin 2019 Dynamic boundary control games with networks of strings. Zbl 1415.49026 Gugat, Martin; Steffensen, Sonja 2018 Joint model of probabilistic-robust (probust) constraints applied to gas network optimization. Zbl 1477.90012 Adelhütte, Dennis; Aßmann, Denis; Grandòn, Tatiana Gonzàlez; Gugat, Martin; Heitsch, Holger; Henrion, René; Liers, Frauke; Nitsche, Sabrina; Schultz, Rüdiger; Stingl, Michael; Wintergerst, David 2021 Optimal Neumann boundary control of a vibrating string with uncertain initial data and probabilistic terminal constraints. Zbl 1446.49004 Farshbaf-Shaker, M. Hassan; Gugat, Martin; Heitsch, Holger; Henrion, René 2020 Exponential stability for the Schlögl system by Pyragas feedback. Zbl 1462.35079 Gugat, Martin; Mateos, Mariano; Tröltzsch, Fredi 2020 Convexity and starshapedness of feasible sets in stationary flow networks. Zbl 1441.90108 Gugat, Martin; Schultz, Rüdiger; Schuster, Michael 2020 On the turnpike phenomenon for optimal boundary control problems with hyperbolic systems. Zbl 1418.35252 Gugat, Martin; Hante, Falk M. 2019 On the limits of stabilizability for networks of strings. Zbl 1425.93229 Gugat, Martin; Gerster, Stephan 2019 A turnpike result for convex hyperbolic optimal boundary control problems. Zbl 1458.35259 Gugat, Martin 2019 Exact controllability of a string to rest with a moving boundary. Zbl 1453.93017 Gugat, Martin 2019 MIP-based instantaneous control of mixed-integer PDE-constrained gas transport problems. Zbl 1391.49040 Gugat, Martin; Leugering, Günter; Martin, Alexander; Schmidt, Martin; Sirvent, Mathias; Wintergerst, David 2018 Boundary stabilization of quasilinear hyperbolic systems of balance laws: exponential decay for small source terms. Zbl 1421.35213 Gugat, Martin; Perrollaz, Vincent; Rosier, Lionel 2018 Networks of pipelines for gas with nonconstant compressibility factor: stationary states. Zbl 1416.76253 Gugat, Martin; Schultz, Rüdiger; Wintergerst, David 2018 Towards simulation based mixed integer optimization with differential equations. Zbl 1397.90308 Gugat, Martin; Leugering, Günter; Martin, Alexander; Schmidt, Martin; Sirvent, Mathias; Wintergerst, David 2018 Transient flow in gas networks: traveling waves. Zbl 1442.35316 Gugat, Martin; Wintergerst, David 2018 Lipschitz solutions of initial boundary value problems for balance laws. Zbl 1394.35261 Gugat, Martin; Ulbrich, Stefan 2018 Stationary gas networks with compressor control and random loads: optimization with probabilistic constraints. Zbl 1427.76234 Gugat, Martin; Schuster, Michael 2018 On the relaxation approximation for $$2\times 2$$ hyperbolic balance laws. Zbl 1407.65105 Gugat, Martin; Herty, Michael; Yu, Hui 2018 Boundary feedback stabilization of the isothermal Euler equations with uncertain boundary data. Zbl 1391.76673 Gugat, Martin; Schultz, Rüdiger 2018 Dynamic boundary control games with networks of strings. Zbl 1415.49026 Gugat, Martin; Steffensen, Sonja 2018 Neumann boundary feedback stabilization for a nonlinear wave equation: A strict $$H^2$$-Lyapunov function. Zbl 1366.76079 Gugat, Martin; Leugering, Günter; Wang, Ke 2017 The isothermal Euler equations for ideal gas with source term: product solutions, flow reversal and no blow up. Zbl 1372.35224 Gugat, Martin; Ulbrich, Stefan 2017 Coupling conditions for the transition from supersonic to subsonic fluid states. Zbl 1379.35241 Gugat, Martin; Herty, Michael; Müller, Siegfried 2017 Lipschitz continuity of the value function in mixed-integer optimal control problems. Zbl 1439.49047 Gugat, Martin; Hante, Falk M. 2017 Time delay in optimal control loops for wave equations. Zbl 1356.49005 Gugat, Martin; Leugering, Günter 2017 Optimal Neumann control for the 1D wave equation: finite horizon, infinite horizon, boundary tracking terms and the turnpike property. Zbl 1335.49012 Gugat, Martin; Trélat, Emmanuel; Zuazua, Enrique 2016 Exact penalization of terminal constraints for optimal control problems. Zbl 1353.49005 Gugat, Martin; Zuazua, Enrique 2016 Exact boundary controllability for free traffic flow with Lipschitz continuous state. Zbl 1400.90098 Gugat, Martin 2016 Stationary states in gas networks. Zbl 1332.93154 Gugat, Martin; Hante, Falk M.; Hirsch-Dick, Markus; Leugering, Günter 2015 Analysis of a system of nonlocal conservation laws for multi-commodity flow on networks. Zbl 1335.49011 Gugat, Martin; Keimer, Alexander; Leugering, Günter; Wang, Zhiqiang 2015 Optimal boundary control and boundary stabilization of hyperbolic systems. Zbl 1328.49001 Gugat, Martin 2015 Boundary feedback stabilization of the Schlögl system. Zbl 1309.93121 Gugat, Martin; Tröltzsch, Fredi 2015 Exponential stabilization of the wave equation by Dirichlet integral feedback. Zbl 1339.35156 Gugat, Martin 2015 Norm-minimal Neumann boundary control of the wave equation. Zbl 1314.35205 Gugat, Martin 2015 Erratum to: “Flow control in gas networks: exact controllability to a given demand”. Zbl 1464.76183 Gugat, M.; Herty, M.; Schleper, V. 2015 Boundary feedback stabilization of the telegraph equation: decay rates for vanishing damping term. Zbl 1288.93066 Gugat, Martin 2014 Stabilization of networked hyperbolic systems with boundary feedback. Zbl 1327.93312 Dick, Markus; Gugat, Martin; Herty, Michael; Leugering, Günter; Steffensen, Sonja; Wang, Ke 2014 A note on the approximation of Dirichlet boundary control problems for the wave equation on curved domains. Zbl 1273.49009 Gugat, M.; Sokolowski, J. 2013 A smoothed penalty iteration for state constrained optimal control problems for partial differential equations. Zbl 1290.90072 Gugat, Martin; Herty, Michael 2013 Stabilization of the gas flow in star-shaped networks by feedback controls with varying delay. Zbl 1264.93206 Gugat, Martin; Dick, Markus; Leugering, Günter 2013 $$H^2$$-stabilization of the isothermal Euler equations: a Lyapunov function approach. Zbl 1253.76112 Gugat, Martin; Leugering, Günter; Tamasoiu, Simona 2012 Well-posedness of networked hyperbolic systems of balance laws. Zbl 1356.49004 Gugat, Martin; Herty, Michael; Klar, Axel; Leugering, Günther; Schleper, Veronika 2012 Contamination source determination in water distribution networks. Zbl 1260.49005 Gugat, Martin 2012 On the relaxation approximation of boundary control of the isothermal Euler equations. Zbl 1253.93110 Dick, M.; Gugat, M.; Herty, M.; Steffensen, S. 2012 Existence of classical solutions and feedback stabilization for the flow in gas networks. Zbl 1429.76090 Gugat, Martin; Herty, Michaël 2011 Gas flow in fan-shaped networks: classical solutions and feedback stabilization. Zbl 1237.35107 Gugat, Martin; Dick, Markus; Leugering, Günter 2011 Flow control in gas networks: exact controllability to a given demand. Zbl 1394.76112 Gugat, M.; Herty, M.; Schleper, V. 2011 An example for the switching delay feedback stabilization of an infinite dimensional system: the boundary stabilization of a string. Zbl 1216.93084 Gugat, Martin; Tucsnak, Marius 2011 A strict $$H^1$$-Lyapunov function and feedback stabilization for the isothermal Euler equations with friction. Zbl 1242.76296 Dick, Markus; Gugat, Martin; Leugering, Günter 2011 Time-delayed boundary feedback stabilization of the isothermal Euler equations with friction. Zbl 1368.76010 Gugat, Martin; Dick, Markus 2011 Optimal boundary control of the wave equation with pointwise control constraints. Zbl 1226.49023 Gugat, Martin; Grimm, Volker 2011 Classical solutions and feedback stabilization for the gas flow in a sequence of pipes. Zbl 1263.76059 Dick, Markus; Gugat, Martin; Leugering, Günter 2010 Stars of vibrating strings: switching boundary feedback stabilization. Zbl 1258.93088 Gugat, Martin; Sigalotti, Mario 2010 Boundary feedback stabilization by time delay for one-dimensional wave equations. Zbl 1198.93177 Gugat, Martin 2010 The smoothed-penalty algorithm for state constrained optimal control problems for partial differential equations. Zbl 1201.90186 Gugat, Martin; Herty, Michael 2010 Approximation of semigroups and related operator functions by resolvent series. Zbl 1222.65052 Grimm, Volker; Gugat, Martin 2010 Penalty techniques for state constrained optimal control problems with the wave equation. Zbl 1202.49037 Gugat, Martin 2010 Global boundary controllability of the Saint-Venant system for sloped canals with friction. Zbl 1154.76009 Gugat, M.; Leugering, G. 2009 Optimal distributed control of the wave equation subject to state constraints. Zbl 1176.35176 Gugat, Martin; Keimer, Alexander; Leugering, Günter 2009 Lavrentiev-prox-regularization for optimal control of PDEs with state constraints. Zbl 1200.65051 Gugat, Martin 2009 Lavrentiev prox-regularization methods for optimal control problems with pointwise state constraints. Zbl 1197.49042 Gugat, Martin 2009 Optimal switching boundary control of a string to rest in finite time. Zbl 1242.49008 Gugat, Martin 2008 $$L^\infty$$-norm minimal control of the wave equation: on the weakness of the bang-bang principle. Zbl 1133.49006 Gugat, Martin; Leugering, Gunter 2008 Optimal boundary feedback stabilization of a string with moving boundary. Zbl 1141.93047 Gugat, Martin 2008 Weber problems with mixed distances and regional demand. Zbl 1146.90464 Gugat, Martin; Pfeiffer, Barbara 2007 Optimal energy control in finite time by varying the length of the string. Zbl 1144.49016 Gugat, Martin 2007 Optimal boundary control in flood management. Zbl 1239.49030 Gugat, Martin 2007 Conservation law constrained optimization based upon Front-Tracking. Zbl 1116.65079 Gugat, Martin; Herty, Michaël; Klar, Axel; Leugering, Gunter 2006 Optimal boundary control of a string to rest in finite time with continuous state. Zbl 1092.49020 Gugat, Martin 2006 $$L^1$$-optimal boundary control of a string to rest in finite time. Zbl 1108.49017 Gugat, Martin 2006 Optimal control for traffic flow networks. Zbl 1079.49024 Gugat, M.; Herty, M.; Klar, A.; Leugering, G. 2005 $$L^{p}$$-optimal boundary control for the wave equation. Zbl 1083.49017 Gugat, M.; Leugering, G.; Sklyar, G. 2005 Optimal nodal control of networked hyperbolic systems: evaluation of derivatives. Zbl 1165.49307 Gugat, Martin 2005 Nodal control of conservation laws on networks. Sensitivity calculations for the control of systems of conservation laws with source terms on networks. Zbl 1097.65071 Gugat, Martin 2005 Global controllability between steady supercritical flows in channel networks. Zbl 1047.93028 Gugat, Martin; Leugering, Günter; Schmidt, E. J. P. Georg 2004 Global boundary controllability of the de St. Venant equations between steady states. Zbl 1032.93030 Gugat, M.; Leugering, G. 2003 Boundary controllability between sub- and supercritical flow. Zbl 1047.35087 Gugat, Martin 2003 Solutions of $$L^p$$-norm-minimal control problems for the wave equation. Zbl 1119.90353 Gugat, Martin; Leugering, G. 2002 Analytic solutions of $$L^{\infty}$$ optimal control problems for the wave equation. Zbl 1012.49025 Gugat, M. 2002 Regularization of $$L^\infty$$-optimal control problems for distributed parameter systems. Zbl 1015.49020 Gugat, M.; Leugering, G. 2002 Modelling, stabilization, and control of flow in networks of open channels. Zbl 0987.93056 Gugat, Martin; Leugering, Günter; Schittkowski, Klaus; Schmidt, E. J. P. Georg 2001 Controllability of a slowly rotating Timoshenko beam. Zbl 1031.93103 Gugat, Martin 2001 A Newton method for the computation of time-optimal boundary controls of one-dimensional vibrating systems. Zbl 0953.93042 Gugat, Martin 2000 Error bounds for infinite systems of convex inequalities without Slater’s condition. Zbl 0997.90090 Gugat, Martin 2000 A parametric view on the Mangasarian-Fromovitz constraint qualification. Zbl 0976.90111 Gugat, Martin 1999 Time-parametric control: Uniform convergence of the optimal value functions of discretized problems. Zbl 0951.49032 Gugat, Martin 1999 Convex semi-infinite parametric programming: Uniform convergence of the optimal value functions of discretized problems. Zbl 0956.90054 Gugat, M. 1999 Prox-regularization methods for generalized fractional programming. Zbl 0973.90078 Gugat, M. 1998 Parametric convex optimization: One-sided derivatives of the value function in singular parameters. Zbl 0961.90114 Gugat, Martin 1998 Semi-infinite terminal problems: A Newton type method. Zbl 0916.65066 Gugat, Martin 1998 Parametric disjunctive programming: One-sided differentiability of the value function. Zbl 0886.90113 Gugat, M. 1997 A fast algorithm for a class of generalized fractional programs. Zbl 0881.90113 Gugat, Martin 1996 An algorithm for Chebyshev approximation by rationals with constrained denominators. Zbl 0886.41013 Gugat, M. 1996 The Newton differential correction algorithm for rational Chebyshev approximation with constrained denominators. Zbl 0860.65006 Gugat, M. 1996 Corrigendum: One-sided derivatives for the value function in convex parametric programming. Zbl 0864.90113 Gugat, M. 1996 Computation of lower bounds for spectra via fractional semi-infinite programming. Zbl 0841.65091 Gugat, Martin 1995 One-sided derivatives for the value function in convex parametric programming. Zbl 0822.90130 Gugat, M. 1994 Optimization under functional constraints (semi-infinite programming) and applications. Zbl 0770.90070 Hettich, Rainer; Gugat, Martin 1992 all top 5 ### Cited by 530 Authors 57 Gugat, Martin 24 Leugering, Günter 19 Herty, Michael Matthias 13 Keimer, Alexander 11 Kunisch, Karl 10 Roubi, Ahmed 10 Schmidt, Martin 9 Coron, Jean-Michel 9 Göttlich, Simone 9 Hante, Falk M. 9 Prieur, Christophe 8 Krstić, Miroslav 8 Pflug, Lukas 8 Zuazua, Enrique 7 Li, Tatsien 5 Aamo, Ole Morten 5 Bastin, Georges 5 Grüne, Lars 5 Hayat, Amaury 5 Klar, Axel 5 Schewe, Lars 5 Shang, Peipei 4 Alvarez-Vázquez, Lino Jose 4 Bayen, Alexandre M. 4 Bermúdez, Alfredo 4 Boufi, Karima 4 Clason, Christian 4 Grimm, Volker 4 Gu, Qilong 4 Kmit, Irina 4 Kröner, Axel 4 López, Xián 4 Martinez, Aurea 4 Nicaise, Serge 4 Piccoli, Benedetto 4 Pignotti, Cristina 4 Schultz, Rüdiger 4 Schuster, Michael J. 4 Sirvent, Mathias 4 Sun, Hailin 4 Trélat, Emmanuel 4 Vázquez-Cendón, María Elena 4 Wintergerst, David 4 Xu, Huifu 3 Banda, Mapundi Kondwani 3 Chitour, Yacine 3 D’Apice, Ciro 3 Delle Monache, Maria Laura 3 El Alami, Abdessamad 3 El Haffari, Mostafa 3 Garavello, Mauro 3 García-Chan, Néstor 3 Girard, Antoine 3 Goatin, Paola 3 Heitsch, Holger 3 Maksimov, Vyacheslav Ivanovich 3 Manita, Larissa A. 3 Martin, Alexander 3 Mazanti, Guilherme 3 Mehrmann, Volker 3 Rodriguez, Charlotte 3 Rosier, Lionel 3 Saraç, Yeşim 3 Schaller, Manuel 3 Schiela, Anton 3 Schillen, Peter 3 Schleper, Veronika 3 Spinola, Michele 3 Steinbach, Marc Christian 3 Strecker, Timm 3 Tröltzsch, Fredi 3 Ulbrich, Stefan 3 Vázquez-Méndez, Miguel Ernesto 3 Wang, Ji 3 Wang, Yue 3 Wehbe, Ali 3 Wollner, Winnifried 3 Xie, Yaru 3 Xu, Gen-Qi 3 Zelikin, Mikhail Il’ich 3 Zhang, Liguo 3 Zhuang, Kaili 2 Addoune, Smail 2 Barnard, Richard C. 2 Benharrat, Mohammed 2 Benner, Peter 2 Borsche, Raul 2 Boutoulout, Ali 2 Bressan, Alberto 2 Briani, Maya 2 Burlacu, Robert 2 Cantoni, Michael 2 Chang, Ching-Ter 2 Colombo, Rinaldo M. 2 Corli, Andrea 2 Crouzeix, Jean-Pierre 2 Elosmani, Mohamed 2 Espejo, Inmaculada 2 Fardigola, Larissa V. 2 Ferland, Jacques A. ...and 430 more Authors all top 5 ### Cited in 119 Serials 24 Automatica 22 SIAM Journal on Control and Optimization 19 Systems & Control Letters 17 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 15 Journal of Optimization Theory and Applications 15 Networks and Heterogeneous Media 12 Mathematical Control and Related Fields 11 Optimization 10 Mathematical Methods in the Applied Sciences 9 Journal of Differential Equations 8 Computational Optimization and Applications 8 Optimization and Engineering 7 Journal of Computational and Applied Mathematics 7 SIAM Journal on Scientific Computing 6 Journal of Mathematical Analysis and Applications 6 Journal de Mathématiques Pures et Appliquées. Neuvième Série 6 Mathematical Programming. Series A. Series B 6 Vietnam Journal of Mathematics 5 International Journal of Control 5 European Journal of Operational Research 5 European Journal of Control 4 Computers & Mathematics with Applications 4 Journal of Computational Physics 4 Applied Mathematics and Optimization 4 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 4 Chinese Annals of Mathematics. Series B 4 MCSS. Mathematics of Control, Signals, and Systems 4 Journal of Scientific Computing 4 Journal of Global Optimization 4 Mathematical Methods of Operations Research 4 International Journal of Applied Mathematics and Computer Science 4 Journal of Hyperbolic Differential Equations 3 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 3 SIAM Journal on Mathematical Analysis 3 SIAM Journal on Optimization 3 Top 3 Mathematical Problems in Engineering 3 Optimization Methods & Software 2 Computers and Fluids 2 Journal of the Franklin Institute 2 Ukrainian Mathematical Journal 2 Applied Mathematics and Computation 2 Numerical Functional Analysis and Optimization 2 SIAM Journal on Numerical Analysis 2 Optimal Control Applications & Methods 2 Acta Applicandae Mathematicae 2 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 2 Computers & Operations Research 2 Asymptotic Analysis 2 Journal of Dynamics and Differential Equations 2 Journal of Computer and Systems Sciences International 2 Journal of Mathematical Sciences (New York) 2 Discrete and Continuous Dynamical Systems 2 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 2 Journal of the European Mathematical Society (JEMS) 2 Journal of Dynamical and Control Systems 2 RAIRO. Operations Research 2 Nonlinear Analysis. Real World Applications 2 Journal of Evolution Equations 2 Discrete and Continuous Dynamical Systems. Series B 2 Journal of Applied Mathematics 2 SIAM Journal on Applied Dynamical Systems 2 Journal of Industrial and Management Optimization 2 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 2 Proceedings of the Steklov Institute of Mathematics 2 Optimization Letters 2 Discrete and Continuous Dynamical Systems. Series S 1 Applicable Analysis 1 Journal of Engineering Mathematics 1 Journal of Mathematical Physics 1 Journal of Statistical Physics 1 ZAMP. Zeitschrift für angewandte Mathematik und Physik 1 Mathematics of Computation 1 Chaos, Solitons and Fractals 1 BIT 1 Canadian Mathematical Bulletin 1 International Journal for Numerical Methods in Engineering 1 Journal of Approximation Theory 1 Mathematics and Computers in Simulation 1 Opsearch 1 Quarterly of Applied Mathematics 1 Rendiconti del Circolo Matemàtico di Palermo. Serie II 1 Transactions of the American Mathematical Society 1 Constructive Approximation 1 Numerical Methods for Partial Differential Equations 1 Asia-Pacific Journal of Operational Research 1 Mathematical and Computer Modelling 1 Numerical Algorithms 1 International Journal of Computer Mathematics 1 Pattern Recognition 1 SIAM Journal on Applied Mathematics 1 Set-Valued Analysis 1 Numerical Linear Algebra with Applications 1 Computational and Applied Mathematics 1 Journal of Inverse and Ill-Posed Problems 1 ETNA. Electronic Transactions on Numerical Analysis 1 NoDEA. Nonlinear Differential Equations and Applications 1 Advances in Computational Mathematics 1 Discrete Dynamics in Nature and Society 1 Journal of Systems Science and Complexity ...and 19 more Serials all top 5 ### Cited in 33 Fields 209 Partial differential equations (35-XX) 183 Systems theory; control (93-XX) 130 Operations research, mathematical programming (90-XX) 115 Calculus of variations and optimal control; optimization (49-XX) 65 Numerical analysis (65-XX) 54 Fluid mechanics (76-XX) 16 Mechanics of deformable solids (74-XX) 8 Dynamical systems and ergodic theory (37-XX) 8 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 7 Operator theory (47-XX) 5 Approximations and expansions (41-XX) 4 Ordinary differential equations (34-XX) 4 Probability theory and stochastic processes (60-XX) 4 Biology and other natural sciences (92-XX) 3 Statistical mechanics, structure of matter (82-XX) 2 General and overarching topics; collections (00-XX) 2 Combinatorics (05-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Real functions (26-XX) 2 Difference and functional equations (39-XX) 2 Integral equations (45-XX) 2 Functional analysis (46-XX) 1 Functions of a complex variable (30-XX) 1 Potential theory (31-XX) 1 Special functions (33-XX) 1 Sequences, series, summability (40-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Integral transforms, operational calculus (44-XX) 1 General topology (54-XX) 1 Computer science (68-XX) 1 Mechanics of particles and systems (70-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Information and communication theory, circuits (94-XX) ### Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata.	2022-08-11T01:57:56	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6188340783119202, "perplexity": 7095.306991951529}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882571232.43/warc/CC-MAIN-20220811012302-20220811042302-00317.warc.gz"}
https://par.nsf.gov/biblio/10367625-new-eclipsing-binary-candidates-from-tess-sectors	370 New Eclipsing Binary Candidates from TESS Sectors 1–26 Abstract We present 370 candidate eclipsing binaries (EBs), identified from ∼510,000 short cadence TESS light curves. Our statistical criteria identify 5105 light curves with features consistent with eclipses (∼1% of the initial sample). After visual confirmation of the light curves, we have a final sample of 2288 EB candidates. Among these, we find 370 sources that were not included in the catalog recently published by Prša et al. We publish our full sample of 370 new EB candidates, and statistical features used for their identification, reported per observation sector. Authors: ; ; Publication Date: NSF-PAR ID: 10367625 Journal Name: Research Notes of the AAS Volume: 6 Issue: 5 Page Range or eLocation-ID: Article No. 96 ISSN: 2515-5172 Publisher: DOI PREFIX: 10.3847 National Science Foundation ##### More Like this 1. ABSTRACT The period-change rate (PCR) of pulsating variable stars is a useful probe of changes in their interior structure, and thus of their evolutionary stages. So far, the PCRs of classical Cepheids in the Large Magellanic Cloud (LMC) have been explored in a limited sample of the total population of these variables. Here, we use a template-based method to build observed-minus-computed (O − C) period diagrams, from which we can derive PCRs for these stars by taking advantage of the long time baseline afforded by the Digital Access to a Sky Century @ Harvard light curves, combined with additional data from the Optical Gravitational Lensing Experiment, the MAssive Compact Halo Object project, Gaia’s Data Release 2, and in some cases the All-Sky Automated Survey. From an initial sample of 2315 sources, our method provides an unprecedented sample of 1303 LMC classical Cepheids with accurate PCRs, the largest for any single galaxy, including the Milky Way. The derived PCRs are largely compatible with theoretically expected values, as computed by our team using the Modules for Experiments in Stellar Astrophysics code, as well as with similar previous computations available in the literature. Additionally, five long-period ($P\,\gt\, 50\, \rm {d}$) sources display a cyclic behaviourmore » 2. ABSTRACT We present the results of the analysis of Type II and anomalous Cepheids using the data from the Kepler K2 mission. The precise light curves of these pulsating variable stars are the key to study the details of their pulsation, such as the period-doubling effect or the presence of additional modes. We applied the Automated Extended Aperture Photometry (autoEAP) to obtain the light curves of the targeted variable stars which were observed. The light curves were Fourier analysed. We investigated 12 stars observed by the K2 mission, seven Type II, and five anomalous Cepheids. Among the Type II Cepheids, EPIC 210622262 shows period-doubling, and four stars have modulation present in their light curves which are different from the period-doubling effect. We calculated the high-order Fourier parameters for the short-period Cepheids. We also determined physical parameters by fitting model atmospheres to the spectral energy distributions. The determined distances using the parallaxes measured by the Gaia space telescope have limited precision below 16 mag for these types of pulsating stars, regardless if the inverse method is used or the statistical method to calculate the distances. The BaSTI evolutionary models were compared to the luminosities and effective temperatures. Most of the Type IImore » 3. Abstract Using ultraviolet (UV) light curves, we constrain the circumstellar environments of 1080 Type Ia supernovae (SNe Ia) withinz< 0.5 from archival Galaxy Evolution Explorer (GALEX) observations. All SNe Ia are required to have pre- and post-explosion GALEX observations to ensure adequate subtraction of the host-galaxy flux. Using the late-time GALEX observations, we look for the UV excess expected from any interaction between the SN ejecta and circumstellar material (CSM). Four SNe Ia are detected near maximum light, and we compare the GALEX photometry to archival data. However, we find that none of our targets show convincing evidence of CSM interaction. A recent Hubble Space Telescope (HST) survey estimates that ∼6% of SNe Ia may interact with distant CSM, but statistical inferences are complicated by the small sample size and selection effects. By injecting model light curves into our data and then recovering them, we constrain a broad range of CSM interactions based on the CSM interaction start time and the maximum luminosity. Combining our GALEX nondetections with the HST results, we constrain occurrence of late-onset CSM interaction among SNe Ia with moderate CSM interaction, similar to that observed in PTF11kx, tofCSM≲ 5.1% between 0 and 500 days after discoverymore » 4. ABSTRACT We present the results of a search for binary hot subdwarf stars in photometric data from the Transiting Exoplanet Survey Satellite (TESS). The sample of objects used in this work was a byproduct of another search for pulsating hot subdwarfs, which resulted in the discovery of nearly 400 non-pulsating variable candidates. The periodogram for each object was calculated and a frequency signal with one or more harmonics above the 4 σ detection threshold was used to consider the candidate as a possible binary system. The type of variability was subsequently confirmed by visual inspection. We present a list of 46 binary system candidates that were not previously known as binaries. We also analysed a few example light curves to demonstrate the importance of double checking the variability of the source in the TESS light curves corrected for instrumental signatures. Four objects, TIC 55753808, TIC 118412596, TIC 4999380, and TIC 68834079, which show variations in the TESS-calibrated fluxes, were actually found to be constant. We also found that it might be more appropriate to increase the commonly used 4σ detection threshold in order to avoid the detection of multiple spurious peaks in the periodograms or Fourier transform of the TESS light curves. 5. Abstract Type Ia supernovae (SNe Ia) are more precise standardizable candles when measured in the near-infrared (NIR) than in the optical. With this motivation, from 2012 to 2017 we embarked on the RAISIN program with the Hubble Space Telescope (HST) to obtain rest-frame NIR light curves for a cosmologically distant sample of 37 SNe Ia (0.2 ≲z≲ 0.6) discovered by Pan-STARRS and the Dark Energy Survey. By comparing higher-zHST data with 42 SNe Ia atz< 0.1 observed in the NIR by the Carnegie Supernova Project, we construct a Hubble diagram from NIR observations (with only time of maximum light and some selection cuts from optical photometry) to pursue a unique avenue to constrain the dark energy equation-of-state parameter,w. We analyze the dependence of the full set of Hubble residuals on the SN Ia host galaxy mass and find Hubble residual steps of size ∼0.06-0.1 mag with 1.5σ−2.5σsignificance depending on the method and step location used. Combining our NIR sample with cosmic microwave background constraints, we find 1 +w= −0.17 ± 0.12 (statistical + systematic errors). The largest systematic errors are the redshift-dependent SN selection biases and the properties of the NIR mass step. We also use these data to measureH0=more »	2023-01-27T12:20:52	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.45390012860298157, "perplexity": 2540.3845768566225}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764494976.72/warc/CC-MAIN-20230127101040-20230127131040-00593.warc.gz"}
https://pdglive.lbl.gov/DataBlock.action?node=M300J48&home=sumtabM	# $\mathbf {{{\boldsymbol \eta}{(2100)}}}$ $\boldsymbol I\boldsymbol G(\boldsymbol J{}^{PC}) = 0{}^{+}(0{}^{-+})$ INSPIRE search MASS ${\mathrm {(MeV)}}$ WIDTH ${\mathrm {(MeV)}}$ EVTS DOCUMENT ID TECN COMMENT $2050 {}^{+30}_{-24} {}^{+75}_{-26}$ 250+36-30+181-164 1 2016 N BES3 ${{\mathit J / \psi}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit K}^{+}}$ ${{\mathit K}^{-}}{{\mathit K}^{+}}{{\mathit K}^{-}}$ $2103 \pm50$ 187+-75 586 2 1989 B DM2 ${{\mathit J / \psi}}$ $\rightarrow$ 4 ${{\mathit \pi}}{{\mathit \gamma}}$ 1 From a partial wave analysis of ${{\mathit J / \psi}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit \phi}}{{\mathit \phi}}$ , for which the primary signal is ${{\mathit \eta}{(2225)}}$ $\rightarrow$ ${{\mathit \phi}}{{\mathit \phi}}$ , and that also finds significant signals for for ${}^{}0{}^{-+}$ phase space, ${{\mathit f}_{{0}}{(2100)}}$, ${{\mathit f}_{{2}}{(2010)}}$, ${{\mathit f}_{{2}}{(2300)}}$, ${{\mathit f}_{{2}}{(2340)}}$, and a previously unseen ${}^{}0{}^{-+}$ state ${{\mathit X}{(2500)}}$ (M = $2470$ ${}^{+15}_{-19}{}^{+101}_{-23}$ MeV, $\Gamma$ = $230$ ${}^{+64}_{-35}{}^{+56}_{-33}$ MeV). 2 ASTON 1981B sees no peak, has 850 events in Ajinenko+Barth bins. ARESTOV 1980 sees no peak. References: ABLIKIM 2016N PR D93 112011 Observation of Pseudoscalar and tensor Resonances in ${{\mathit J / \psi}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit \phi}}{{\mathit \phi}}$ BISELLO 1989B PR D39 701 First Observation of Three Pseudoscalar States in the ${{\mathit J / \psi}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit \rho}}{{\mathit \rho}}$ Decay	2021-03-02T20:30:29	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8479606509208679, "perplexity": 3834.5149210144327}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178364764.57/warc/CC-MAIN-20210302190916-20210302220916-00472.warc.gz"}
https://www.zbmath.org/authors/?q=ai%3Akudryashov.nikolai-a	## Kudryashov, Nikolaĭ Alekseevich Compute Distance To: Author ID: kudryashov.nikolai-a Published as: Kudryashov, Nikolay A.; Kudryashov, N. A.; Kudryashov, Nikolai A.; Kudryashov, Nicolai A.; Kudryashov, Nick A. Homepage: https://primat.mephi.ru/~kudryashov/ External Links: ORCID · Wikidata · Google Scholar · ResearchGate · Math-Net.Ru · dblp Documents Indexed: 218 Publications since 1980, including 1 Book Co-Authors: 66 Co-Authors with 135 Joint Publications 503 Co-Co-Authors all top 5 ### Co-Authors 83 single-authored 34 Sinelshchikov, Dmitry I. 21 Demina, Maria V. 12 Ryabov, Pavel N. 5 Alekseev, Alexander A. 5 Kolobashkin, V. M. 4 Kochanov, Mark B. 4 Murzenko, V. V. 4 Soukharev, Mikhail B. 4 Zakharchenko, Anastasia S. 3 Bondarenko, A. G. 3 Chmykhov, Mikhail A. 3 Efimova, Olga Yu. 3 Gordeev, Yu. N. 3 Safonova, Dariya V. 3 Shilnikov, Kirill E. 3 Tutnov, An. A. 3 Volkov, Alexandr K. 2 Basanskij, E. G. 2 Chernyavsky, Igor L. 2 Fedyanin, Timofey E. 2 Gaiur, Ilia Yu. 2 Garashchuk, Ivan R. 2 Ghose Choudhury, Anindya 2 Guha, Partha 2 Korotkov, Eugene V. 2 Kucherenko, Sergei S. 2 Loguinova, Nadejda B. 2 Muratov, R. V. 2 Pickering, Andrew 1 Antonova, Anastasia O. 1 Biswas, Anjan 1 Borisov, Alekseĭ Vladimirovich 1 Crepin, Kofane Timoleon 1 Doka, Serge Yamigno 1 Gabbasov, M. N. 1 Gaiur, Ilya Y. 1 Gavrikov, M. B. 1 Gordeev, Yu. I. 1 Hubert, Malwe Boudoue 1 Ivanova, Yulia S. 1 Kazakov, Alexey O. 1 Khlunov, Aleksandr V. 1 Kolobanov, S. N. 1 Korotkova, M. A. 1 Koshkin, V. I. 1 Kutukov, Alexandr A. 1 Laskin, Andrew A. 1 Lavrova, S. F. 1 Migita, A. V. 1 Minaev, V. S. 1 Nikitin, V. A. 1 Petrov, B. A. 1 Prilipko, Svetlana G. 1 Rybka, Roman B. 1 Savatorova, Viktoria L. 1 Savel’ev, V. V. 1 Savina, Tatiana V. 1 Sboev, Aleksandr Georgievich 1 Skryabin, Konstantin Georgievich 1 Sukharev, M. B. 1 Sytsko, Yu. I. 1 Tala-Tebué, Éric 1 Teterev, N. A. 1 Urbain, Fibay 1 Vigdorowitsch, Michael V. 1 Zargaryan, Evgenia D. all top 5 ### Serials 29 Applied Mathematics and Computation 24 Regular and Chaotic Dynamics 23 Communications in Nonlinear Science and Numerical Simulation 19 Physics Letters. A 17 Fluid Dynamics 12 Chaos, Solitons and Fractals 12 Applied Mathematics Letters 11 Journal of Physics A: Mathematical and General 11 Matematicheskoe Modelirovanie 9 Theoretical and Mathematical Physics 5 Journal of Applied Mathematics and Mechanics 3 Journal of Mathematical Analysis and Applications 3 Mathematical Methods in the Applied Sciences 3 Zhurnal Vychislitel’noĭ Matematiki i Matematicheskoĭ Fiziki 3 Prikladnaya Matematika i Mekhanika 3 Journal of Computational and Applied Mathematics 3 Computational Mathematics and Mathematical Physics 3 Applied Mathematical Modelling 3 Soviet Physics. Doklady 2 Journal of Mathematical Physics 2 Reports on Mathematical Physics 2 Sorosovskiĭ Obrazovatel’nyĭ Zhurnal 2 Physica Scripta 2 Journal of Physics A: Mathematical and Theoretical 1 International Journal of Heat and Mass Transfer 1 Magnetohydrodynamics 1 Wave Motion 1 Acta Applicandae Mathematicae 1 Nonlinear Dynamics 1 Chaos 1 The ANZIAM Journal 1 Journal of Nonlinear Mathematical Physics 1 Computational Biology and Chemistry 1 Nelineĭnaya Dinamika all top 5 ### Fields 113 Partial differential equations (35-XX) 68 Ordinary differential equations (34-XX) 48 Fluid mechanics (76-XX) 34 Dynamical systems and ergodic theory (37-XX) 19 Special functions (33-XX) 13 Classical thermodynamics, heat transfer (80-XX) 12 Biology and other natural sciences (92-XX) 9 Numerical analysis (65-XX) 9 Mechanics of deformable solids (74-XX) 7 Optics, electromagnetic theory (78-XX) 4 Global analysis, analysis on manifolds (58-XX) 4 Statistical mechanics, structure of matter (82-XX) 3 Mechanics of particles and systems (70-XX) 3 Geophysics (86-XX) 2 General and overarching topics; collections (00-XX) 2 Real functions (26-XX) 2 Operations research, mathematical programming (90-XX) 1 History and biography (01-XX) 1 Field theory and polynomials (12-XX) 1 Commutative algebra (13-XX) 1 Difference and functional equations (39-XX) 1 Computer science (68-XX) 1 Quantum theory (81-XX) 1 Relativity and gravitational theory (83-XX) 1 Astronomy and astrophysics (85-XX) ### Citations contained in zbMATH Open 173 Publications have been cited 1,984 times in 786 Documents Cited by Year Simplest equation method to look for exact solutions of nonlinear differential equations. Zbl 1069.35018 Kudryashov, Nikolai A. 2005 One method for finding exact solutions of nonlinear differential equations. Zbl 1250.35055 Kudryashov, Nikolay A. 2012 Seven common errors in finding exact solutions of nonlinear differential equations. Zbl 1221.35342 Kudryashov, Nikolai A. 2009 Exact solitary waves of the Fisher equation. Zbl 1222.35054 Kudryashov, Nikolai A. 2005 Be careful with the Exp-function method. Zbl 1221.35344 Kudryashov, Nikolai A.; Loguinova, Nadejda B. 2009 Extended simplest equation method for nonlinear differential equations. Zbl 1168.34003 Kudryashov, Nikolai A.; Loguinova, Nadejda B. 2008 On “new travelling wave solutions” of the KdV and the KdV-Burgers equations. Zbl 1221.35343 Kudryashov, Nikolai A. 2009 The first and second Painlevé equations of higher order and some relations between them. Zbl 0962.35504 Kudryashov, Nicolai A. 1996 Meromorphic solutions of nonlinear ordinary differential equations. Zbl 1222.35160 Kudryashov, Nikolai A. 2010 A note on the $$G'/G$$-expansion method. Zbl 1203.35228 Kudryashov, Nikolai A. 2010 From Laurent series to exact meromorphic solutions: The Kawahara equation. Zbl 1238.34020 Demina, Maria V.; Kudryashov, Nikolay A. 2010 Popular ansatz methods and solitary wave solutions of the Kuramoto-Sivashinsky equation. Zbl 1229.34008 Kudryashov, N. A.; Soukharev, M. B. 2009 Rational solutions for Schwarzian integrable hierarchies. Zbl 0985.37073 Kudryashov, Nicolai A.; Pickering, Andrew 1998 Explicit expressions for meromorphic solutions of autonomous nonlinear ordinary differential equations. Zbl 1221.34233 Demina, Maria V.; Kudryashov, Nikolay A. 2011 Exact solutions of the Burgers-Huxley equation. Zbl 1092.35084 Efimova, O. Yu.; Kudryashov, N. A. 2004 Two hierarchies of ordinary differential equations and their properties. Zbl 0948.34069 Kudryashov, Nicolai A. 1999 Polygons of differential equations for finding exact solutions. Zbl 1133.35084 Kudryashov, Nikolai A.; Demina, Maria V. 2007 Solitary and periodic solutions of the generalized Kuramoto-Sivashinsky equation. Zbl 1229.35229 Kudryashov, N. A. 2008 A note on solutions of the generalized Fisher equation. Zbl 1327.35165 Kudryashov, N. A.; Zakharchenko, A. S. 2014 Solitary waves in active-dissipative dispersive media. Zbl 0901.35090 Kudryashov, Nicolai A.; Zargaryan, Evgenia D. 1996 Nonlinear waves in bubbly liquids with consideration for viscosity and heat transfer. Zbl 1236.76075 Kudryashov, Nikolai A.; Sinelshchikov, Dmitry I. 2010 Transcendents defined by nonlinear fourth-order ordinary differential equations. Zbl 0930.34004 Kudryashov, Nicolai A. 1999 Uniformization and transcendence of solutions for the first and second Painlevé hierarchies. Zbl 0941.34077 Kudryashov, Nicolai A.; Soukharev, Mikhail B. 1998 Amalgamations of the Painlevé equations. Zbl 1063.34085 Kudryashov, Nikolai A. 2003 Traveling wave solutions of the generalized nonlinear evolution equations. Zbl 1170.35514 Kudryashov, Nikolai A.; Demina, Maria V. 2009 Painlevé analysis and exact solutions of the Korteweg-de Vries equation with a source. Zbl 1321.35203 Kudryashov, Nikolay A. 2015 Polynomials in logistic function and solitary waves of nonlinear differential equations. Zbl 1297.35076 Kudryashov, Nikolay A. 2013 Exact solutions of the Swift-Hohenberg equation with dispersion. Zbl 1245.35095 Kudryashov, Nikolai A.; Sinelshchikov, Dmitry I. 2012 Exact solutions of the generalized Bretherton equation. Zbl 1242.37054 Kudryashov, Nikolai A.; Sinelshchikov, Dmitry I.; Demina, Maria V. 2011 Higher Painlevé transcendents as special solutions of some nonlinear integrable hierarchies. Zbl 1328.35193 Kudryashov, Nikolay A. 2014 One generalization of the second Painlevé hierarchy. Zbl 1007.34083 Kudryashov, Nikolai A. 2002 The second Painlevé equation as a model for the electric field in a semiconductor. Zbl 1044.82573 Kudryashov, Nicolai A. 1997 Fourth-order analogies to the Painlevé equations. Zbl 1066.34086 Kudryashov, Nikolai A. 2002 Comment on: “A novel approach for solving the Fisher equation using exp-function method” [Phys. Lett. A 372 (2008) 3836]. Zbl 1228.83031 Kudryashov, Nikolai A. 2009 Exact solutions of equations for the Burgers hierarchy. Zbl 1176.35146 Kudryashov, Nikolai A.; Sinelshchikov, Dmitry I. 2009 On the criteria for integrability of the Liénard equation. Zbl 1343.34005 Kudryashov, Nikolay A.; Sinelshchikov, Dmitry I. 2016 Paul Painlevé and his contribution to science. Zbl 1333.01025 Borisov, Alexey V.; Kudryashov, Nikolay A. 2014 Exact solutions of the nonlinear wave equations arising in mechanics. Zbl 0736.76009 Kudryashov, N. A. 1990 Highly dispersive solitary wave solutions of perturbed nonlinear Schrödinger equations. Zbl 1433.35367 Kudryashov, Nikolay A. 2020 Double Bäcklund transformations and special integrals for the $$K_{II}$$ hierarchy. Zbl 1115.37355 Kudryashov, Nikolai A. 2000 On elliptic solutions of nonlinear ordinary differential equations. Zbl 1220.65090 Demina, Maria V.; Kudryashov, Nikolai A. 2011 On the connection of the quadratic Liénard equation with an equation for the elliptic functions. Zbl 1383.34003 Kudryashov, Nikolay A.; Sinelshchikov, Dmitry I. 2015 On the integrability conditions for a family of Liénard-type equations. Zbl 1355.34006 Kudryashov, N. A.; Sinelshchikov, D. I. 2016 On new transcendents defined by nonlinear ordinary differential equations. Zbl 0906.34005 Kudryashov, Nicolai A. 1998 Nonlinear waves in liquids with gas bubbles with account of viscosity and heat transfer. Zbl 1215.76103 Kudryashov, N. A.; Sinel’shchikov, D. I. 2010 Hyperchaos and multistability in the model of two interacting microbubble contrast agents. Zbl 1416.37069 Garashchuk, Ivan R.; Sinelshchikov, Dmitry I.; Kazakov, Alexey O.; Kudryashov, Nikolay A. 2019 Solitary wave solutions of hierarchy with non-local nonlinearity. Zbl 1440.35028 Kudryashov, Nikolay A. 2020 Exact solutions of the equation for surface waves in a convecting fluid. Zbl 1428.35454 Kudryashov, Nikolay A. 2019 Analytical properties of the perturbed FitzHugh-Nagumo model. Zbl 1379.35050 Kudryashov, Nikolay A.; Rybka, Roman B.; Sboev, Aleksander G. 2018 Special polynomials and rational solutions of the hierarchy of the second Painlevé equation. Zbl 1138.35388 Demina, M. V.; Kudryashov, N. A. 2007 A note on new exact solutions for the Kawahara equation using Exp-function method. Zbl 1194.65119 Kudryashov, Nikolai A. 2010 Nonlinear evolution equations for describing waves in bubbly liquids with viscosity and heat transfer consideration. Zbl 1273.76407 Kudryashov, Nikolai A.; Sinelshchikov, Dmitry I. 2010 Point vortices and polynomials of the Sawada-Kotera and Kaup-Kupershmidt equations. Zbl 1264.35186 Demina, Maria V.; Kudryashov, Nikolai A. 2011 Self-similar solutions of the Burgers hierarchy. Zbl 1178.35321 Kudryashov, Nikolai A. 2009 Analytical solutions of the Rayleigh equation for empty and gas-filled bubble. Zbl 1298.76190 Kudryashov, Nikolay A.; Sinelshchikov, Dmitry I. 2014 Power and non-power expansions of the solutions for the fourth-order analogue to the second Painlevé equation. Zbl 1141.34058 Demina, Maria V.; Kudryashov, Nikolai A. 2007 The Yablonskii-Vorob’ev polynomials for the second Painlevé hierarchy. Zbl 1132.33339 Demina, Maria V.; Kudryashov, Nikolai A. 2007 The generalized Yablonskii-Vorob’ev polynomials and their properties. Zbl 1221.33033 Kudryashov, Nikolai A.; Demina, Maria V. 2008 Vortices and polynomials: non-uniqueness of the Adler-Moser polynomials for the Tkachenko equation. Zbl 1245.35016 Demina, Maria V.; Kudryashov, Nikolai A. 2012 Special polynomials associated with some hierarchies. Zbl 1220.34111 Kudryashov, Nikolai A. 2008 Information decomposition method to analyze symbolical sequences. Zbl 1041.68073 Korotkov, E. V.; Korotkova, M. A.; Kudryashov, N. A. 2003 Elliptic traveling waves of the Olver equation. Zbl 1248.35162 Kudryashov, Nikolai A.; Soukharev, Mikhail B.; Demina, Maria V. 2012 A note on the Lie symmetry analysis and exact solutions for the extended mKdV equation. Zbl 1209.34111 Kudryashov, Nikolay A.; Sinelshchikov, Dmitry I. 2011 Asymptotic and exact solutions of the Fitzhugh-Nagumo model. Zbl 1401.34004 Kudryashov, Nikolay A. 2018 Nonlinear waves in fluid flow through a viscoelastic tube. Zbl 1198.76167 Kudryashov, N. A.; Chernyavskij, I. L. 2006 From singular manifold equations to integrable evolution equations. Zbl 0839.35119 Kudryashov, Nick A. 1994 Some fourth-order ordinary differential equations which pass the Painlevé test. Zbl 0982.34077 Kudryashov, Nicolai A. 2001 Quasi-exact solutions of the dissipative Kuramoto-Sivashinsky equation. Zbl 1290.35228 Kudryashov, Nikolay A. 2013 Nonlinear differential equations of the second, third and fourth order with exact solutions. Zbl 1259.34006 Kudryashov, Nikolai A.; Sinelshchikov, Dmitry I. 2012 Analytical solutions of the Lorenz system. Zbl 1331.34005 Kudryashov, Nikolay A. 2015 Exact solutions and integrability of the Duffing-van der Pol equation. Zbl 1425.34105 Kudryashov, Nikolay A. 2018 Soliton, rational and special solutions of the Korteweg-de Vries hierarchy. Zbl 1203.35229 Kudryashov, Nikolai A. 2010 Refinement of the Korteweg-de Vries equation from the Fermi-pasta-Ulam model. Zbl 1361.35157 Kudryashov, Nikolay A. 2015 Analytical properties of nonlinear dislocation equation. Zbl 1376.82102 Kudryashov, Nikolay A. 2017 Equation for the three-dimensional nonlinear waves in liquid with gas bubbles. Zbl 1263.76073 Kudryashov, Nikolay A.; Sinelshchikov, Dmitry I. 2012 Fuchs indices and the first integrals of nonlinear differential equations. Zbl 1076.34500 Kudryashov, Nikolai A. 2005 Quasi-exact solutions of nonlinear differential equations. Zbl 1295.34005 Kudryashov, Nikolay A.; Kochanov, Mark B. 2012 Nonlinear waves in media with fifth order dispersion. Zbl 1242.74002 Kudryashov, Nikolai A.; Ryabov, Pavel N.; Sinelshchikov, Dmitry I. 2011 Relations between zeros of special polynomials associated with the Painlevé equations. Zbl 1209.33007 Kudryashov, Nikolai A.; Demina, Maria V. 2007 Power expansions for solution of the fourth-order analog to the first Painlevé equation. Zbl 1157.34066 Kudryashov, Nikolai A.; Efimova, Olga Yu. 2006 On the Jacobi last multipliers and Lagrangians for a family of Liénard-type equations. Zbl 1411.34115 Sinelshchikov, Dmitry I.; Kudryashov, Nikolay A. 2017 Nonlinear differential equations associated with the first Painlevé hierarchy. Zbl 1414.34071 Kudryashov, Nikolay A. 2019 Lax pair and first integrals of the traveling wave reduction for the KdV hierarchy. Zbl 1428.35455 Kudryashov, Nikolay A. 2019 On connections of the Liénard equation with some equations of Painlevé-Gambier type. Zbl 1362.34004 Kudryashov, Nikolai A.; Sinelshchikov, Dmitry I. 2017 A note on “Abundant new exact solutions for the $$(3+1)$$-dimensional Jimbo-Miwa equation”. Zbl 1204.35071 Kudryashov, Nikolay A.; Sinelshchikov, Dmitry I. 2010 Bäcklund transformation for a fourth-order partial differential equation with the Burgers-Korteweg-de Vries nonlinearity. Zbl 0678.35082 Kudryashov, N. A. 1988 Exact solutions of the generalized Ginzburg-Landau equation. Zbl 0972.35524 Kudryashov, N. A. 1989 Painlevé analysis and a solution to the traveling wave reduction of the Radhakrishnan-Kundu-Lakshmanan equation. Zbl 1434.78022 Kudryashov, Nikolay A.; Safonova, Dariya V.; Biswas, Anjan 2019 Exact solutions of the generalized $$K(m, m)$$ equations. Zbl 1221.35345 Kudryashov, Nikolay A.; Prilipko, Svetlana G. 2011 Approximate solutions to one-dimensional nonlinear heat conduction problems with a given flux. Zbl 1210.80009 Kudryashov, N. A.; Chmykhov, M. A. 2007 Logistic function as solution of many nonlinear differential equations. Zbl 1443.34004 Kudryashov, Nikolay A. 2015 Integrable nonautonomous Liénard-type equations. Zbl 1403.34003 Sinelshchikov, D. I.; Kudryashov, N. A. 2018 Rational and special solutions for some Painlevé hierarchies. Zbl 1415.34132 Kudryashov, Nikolay A. 2019 A note on “New kink-shaped solutions and periodic wave solutions for the $$(2 + 1)$$-dimensional sine-Gordon equation”. Zbl 1200.35262 Kudryashov, Nikolay A.; Ryabov, Pavel N.; Sinelshchikov, Dmitry I. 2010 Special polynomials associated with the fourth order analogue to the Painlevé equations. Zbl 1197.33015 Kudryashov, Nikolai A.; Demina, Maria V. 2007 Solitary waves in dissipative-dispersive systems with instability. Zbl 0691.76017 Gordeev, Yu. N.; Kudryashov, N. A. 1989 Point vortices and classical orthogonal polynomials. Zbl 1257.33048 Demina, Maria V.; Kudryashov, Nikolai A. 2012 Self-similar solution of the problem of gas flow through a porous medium under the conditions of turbulent filtration. Zbl 0484.76104 Bondarenko, A. G.; Kolobashkin, V. M.; Kudryashov, N. A. 1980 Exact solutions of a family of Fisher equations. Zbl 0799.35112 Kudryashov, N. A. 1993 The generalized Duffing oscillator. Zbl 07274921 Kudryashov, Nikolay A. 2021 The generalized Duffing oscillator. Zbl 07274921 Kudryashov, Nikolay A. 2021 Analytical features of the SIR model and their applications to COVID-19. Zbl 1481.92146 Kudryashov, Nikolay A.; Chmykhov, Mikhail A.; Vigdorowitsch, Michael 2021 Lax pairs for one of hierarchies similar to the first Painlevé hierarchy. Zbl 1469.34117 Kudryashov, Nikolay A. 2021 Lax pairs and rational solutions of similarity reductions for Kupershmidt and Sawada-Kotera hierarchies. Zbl 1475.34055 Kudryashov, Nikolay A. 2021 Highly dispersive solitary wave solutions of perturbed nonlinear Schrödinger equations. Zbl 1433.35367 Kudryashov, Nikolay A. 2020 Solitary wave solutions of hierarchy with non-local nonlinearity. Zbl 1440.35028 Kudryashov, Nikolay A. 2020 Lax pairs and special polynomials associated with self-similar reductions of Sawada – Kotera and Kupershmidt equations. Zbl 1441.34096 Kudryashov, Nikolay A. 2020 First integrals and general solution of the complex Ginzburg-Landau equation. Zbl 07323469 Kudryashov, Nikolay A. 2020 Highly dispersive optical solitons of an equation with arbitrary refractive index. Zbl 1471.35251 Kudryashov, Nikolay A. 2020 Rational solutions of equations associated with the second Painlevé equation. Zbl 1451.34004 Kudryashov, Nikolay A. 2020 Hyperchaos and multistability in the model of two interacting microbubble contrast agents. Zbl 1416.37069 Garashchuk, Ivan R.; Sinelshchikov, Dmitry I.; Kazakov, Alexey O.; Kudryashov, Nikolay A. 2019 Exact solutions of the equation for surface waves in a convecting fluid. Zbl 1428.35454 Kudryashov, Nikolay A. 2019 Nonlinear differential equations associated with the first Painlevé hierarchy. Zbl 1414.34071 Kudryashov, Nikolay A. 2019 Lax pair and first integrals of the traveling wave reduction for the KdV hierarchy. Zbl 1428.35455 Kudryashov, Nikolay A. 2019 Painlevé analysis and a solution to the traveling wave reduction of the Radhakrishnan-Kundu-Lakshmanan equation. Zbl 1434.78022 Kudryashov, Nikolay A.; Safonova, Dariya V.; Biswas, Anjan 2019 Rational and special solutions for some Painlevé hierarchies. Zbl 1415.34132 Kudryashov, Nikolay A. 2019 Lax representation and quadratic first integrals for a family of non-autonomous second-order differential equations. Zbl 1440.34003 Sinelshchikov, Dmitry I.; Gaiur, Ilia Yu.; Kudryashov, Nikolay A. 2019 Traveling wave reduction of the modified KdV hierarchy: the Lax pair and the first integrals. Zbl 1464.35299 Kudryashov, Nikolay A. 2019 On integrability of the FitzHugh-Rinzel model. Zbl 1416.37055 Kudryashov, Nikolay A. 2019 Analytical properties of the perturbed FitzHugh-Nagumo model. Zbl 1379.35050 Kudryashov, Nikolay A.; Rybka, Roman B.; Sboev, Aleksander G. 2018 Asymptotic and exact solutions of the Fitzhugh-Nagumo model. Zbl 1401.34004 Kudryashov, Nikolay A. 2018 Exact solutions and integrability of the Duffing-van der Pol equation. Zbl 1425.34105 Kudryashov, Nikolay A. 2018 Integrable nonautonomous Liénard-type equations. Zbl 1403.34003 Sinelshchikov, D. I.; Kudryashov, N. A. 2018 Meromorphic solutions in the Fitzhugh-Nagumo model. Zbl 1394.34184 Demina, Maria V.; Kudryashov, Nikolay A. 2018 Nonlinear dynamics of a bubble contrast agent oscillating near an elastic wall. Zbl 1400.37106 Garashchuk, Ivan R.; Sinelshchikov, Dmitry I.; Kudryashov, Nikolay A. 2018 The collective behavior of shear strain localizations in dipolar materials. Zbl 1427.74009 Kudryashov, N. A.; Muratov, R. V.; Ryabov, P. N. 2018 Analytical properties of nonlinear dislocation equation. Zbl 1376.82102 Kudryashov, Nikolay A. 2017 On the Jacobi last multipliers and Lagrangians for a family of Liénard-type equations. Zbl 1411.34115 Sinelshchikov, Dmitry I.; Kudryashov, Nikolay A. 2017 On connections of the Liénard equation with some equations of Painlevé-Gambier type. Zbl 1362.34004 Kudryashov, Nikolai A.; Sinelshchikov, Dmitry I. 2017 New non-standard Lagrangians for the Liénard-type equations. Zbl 1356.34045 Kudryashov, Nikolai A.; Sinelshchikov, Dmitry I. 2017 Weak nonlinear asymptotic solutions for the fourth order analogue of the second Painlevé equation. Zbl 1387.34124 Gaiur, Ilia Yu.; Kudryashov, Nikolay A. 2017 On the criteria for integrability of the Liénard equation. Zbl 1343.34005 Kudryashov, Nikolay A.; Sinelshchikov, Dmitry I. 2016 On the integrability conditions for a family of Liénard-type equations. Zbl 1355.34006 Kudryashov, N. A.; Sinelshchikov, D. I. 2016 Analytical and numerical solutions of the generalized dispersive Swift-Hohenberg equation. Zbl 1410.35174 Kudryashov, Nikolay A.; Ryabov, Pavel N. 2016 From the Fermi-Pasta-Ulam model to higher-order nonlinear evolution equations. Zbl 1378.35269 Kudryashov, Nikolay A. 2016 Painlevé analysis and exact solutions for the modified Korteweg-de Vries equation with polynomial source. Zbl 1410.35172 Kudryashov, Nikolay A.; Ivanova, Yulia S. 2016 Nonlinear waves described by a fifth-order equation derived from the Fermi-Pasta-Ulam system. Zbl 1352.35155 Volkov, Alexander K.; Kudryashov, N. A. 2016 Multi-particle dynamical systems and polynomials. Zbl 1377.35006 Demina, Maria V.; Kudryashov, Nikolai A. 2016 On solutions of generalized modified Korteweg-de Vries equation of the fifth order with dissipation. Zbl 1410.35171 Kudryashov, Nikolay A. 2016 Painlevé analysis and exact solutions of the Korteweg-de Vries equation with a source. Zbl 1321.35203 Kudryashov, Nikolay A. 2015 On the connection of the quadratic Liénard equation with an equation for the elliptic functions. Zbl 1383.34003 Kudryashov, Nikolay A.; Sinelshchikov, Dmitry I. 2015 Analytical solutions of the Lorenz system. Zbl 1331.34005 Kudryashov, Nikolay A. 2015 Refinement of the Korteweg-de Vries equation from the Fermi-pasta-Ulam model. Zbl 1361.35157 Kudryashov, Nikolay A. 2015 Logistic function as solution of many nonlinear differential equations. Zbl 1443.34004 Kudryashov, Nikolay A. 2015 Painlevé analysis and exact solutions of the fourth-order equation for description of nonlinear waves. Zbl 07246001 Kudryashov, Nikolay A. 2015 Analytical properties and exact solutions of the Lotka-Volterra competition system. Zbl 1410.35018 Kudryashov, Nikolay A.; Zakharchenko, Anastasia S. 2015 Numerical modeling and optimization of the cryosurgery operations. Zbl 1323.80005 Kudryashov, Nikolay A.; Shilnikov, Kirill E. 2015 Painlevé analysis and exact solutions of a predator-prey system with diffusion. Zbl 1318.35136 Kudryashov, N. A.; Zakharchenko, A. S. 2015 On nonlinear differential equation with exact solutions having various pole orders. Zbl 1352.34117 Kudryashov, N. A. 2015 A note on solutions of the generalized Fisher equation. Zbl 1327.35165 Kudryashov, N. A.; Zakharchenko, A. S. 2014 Higher Painlevé transcendents as special solutions of some nonlinear integrable hierarchies. Zbl 1328.35193 Kudryashov, Nikolay A. 2014 Paul Painlevé and his contribution to science. Zbl 1333.01025 Borisov, Alexey V.; Kudryashov, Nikolay A. 2014 Analytical solutions of the Rayleigh equation for empty and gas-filled bubble. Zbl 1298.76190 Kudryashov, Nikolay A.; Sinelshchikov, Dmitry I. 2014 The Cauchy problem for the equation of the Burgers hierarchy. Zbl 1319.35220 Kudryashov, Nikolai A.; Sinelshchikov, Dmitry I. 2014 Special solutions of a high-order equation for waves in a liquid with gas bubbles. Zbl 1307.35229 Kudryashov, Nikolay A.; Sinelshchikov, Dmitry I. 2014 Exact solutions of one pattern formation model. Zbl 1410.35173 Kudryashov, Nikolay A.; Ryabov, Pavel N. 2014 Analytical and numerical studying of the perturbed Korteweg-de Vries equation. Zbl 1366.35158 Kudryashov, Nikolai A.; Sinelshchikov, Dmitry I. 2014 Quasi-exact solutions of the equation for description of nonlinear waves in a liquid with gas bubbles. Zbl 1310.76165 Kochanov, Mark B.; Kudryashov, Nikolay A. 2014 Painlevé analysis and exact solutions for the Belousov-Zhabotinskii reaction-diffusion system. Zbl 1348.35112 Kudryashov, Nikolay A.; Zakharchenko, Anastasia S. 2014 Elliptic solutions in the Hénon-Heiles model. Zbl 1470.34003 Demina, Maria V.; Kudryashov, Nikolay A. 2014 Generalization of the simplest equation method for nonlinear non-autonomous differential equations. Zbl 1470.34002 Antonova, Anastasia O.; Kudryashov, Nikolay A. 2014 Polynomials in logistic function and solitary waves of nonlinear differential equations. Zbl 1297.35076 Kudryashov, Nikolay A. 2013 Quasi-exact solutions of the dissipative Kuramoto-Sivashinsky equation. Zbl 1290.35228 Kudryashov, Nikolay A. 2013 Relative equilibrium configurations of point vortices on a sphere. Zbl 1274.76178 Demina, Maria V.; Kudryashov, Nikolai A. 2013 An extended equation for the description of nonlinear waves in a liquid with gas bubbles. Zbl 1454.76097 Kudryashov, Nikolai A.; Sinelshchikov, Dmitry I. 2013 Non-linear waves on shallow water under an ice cover. Higher order expansions. Zbl 1282.76077 Kochanov, M. B.; Kudryashov, N. A.; Sinel’shchikov, D. I. 2013 One method for finding exact solutions of nonlinear differential equations. Zbl 1250.35055 Kudryashov, Nikolay A. 2012 Exact solutions of the Swift-Hohenberg equation with dispersion. Zbl 1245.35095 Kudryashov, Nikolai A.; Sinelshchikov, Dmitry I. 2012 Vortices and polynomials: non-uniqueness of the Adler-Moser polynomials for the Tkachenko equation. Zbl 1245.35016 Demina, Maria V.; Kudryashov, Nikolai A. 2012 Elliptic traveling waves of the Olver equation. Zbl 1248.35162 Kudryashov, Nikolai A.; Soukharev, Mikhail B.; Demina, Maria V. 2012 Nonlinear differential equations of the second, third and fourth order with exact solutions. Zbl 1259.34006 Kudryashov, Nikolai A.; Sinelshchikov, Dmitry I. 2012 Equation for the three-dimensional nonlinear waves in liquid with gas bubbles. Zbl 1263.76073 Kudryashov, Nikolay A.; Sinelshchikov, Dmitry I. 2012 Quasi-exact solutions of nonlinear differential equations. Zbl 1295.34005 Kudryashov, Nikolay A.; Kochanov, Mark B. 2012 Point vortices and classical orthogonal polynomials. Zbl 1257.33048 Demina, Maria V.; Kudryashov, Nikolai A. 2012 Special polynomials associated with the Burgers hierarchy. Zbl 1430.35198 Kudryashov, Nikolay A. 2012 Elliptic solutions for a family of fifth order nonlinear evolution equations. Zbl 1246.35079 Kudryashov, Nikolai A.; Sinelshchikov, Dmitry I. 2012 Explicit expressions for meromorphic solutions of autonomous nonlinear ordinary differential equations. Zbl 1221.34233 Demina, Maria V.; Kudryashov, Nikolay A. 2011 Exact solutions of the generalized Bretherton equation. Zbl 1242.37054 Kudryashov, Nikolai A.; Sinelshchikov, Dmitry I.; Demina, Maria V. 2011 On elliptic solutions of nonlinear ordinary differential equations. Zbl 1220.65090 Demina, Maria V.; Kudryashov, Nikolai A. 2011 Point vortices and polynomials of the Sawada-Kotera and Kaup-Kupershmidt equations. Zbl 1264.35186 Demina, Maria V.; Kudryashov, Nikolai A. 2011 A note on the Lie symmetry analysis and exact solutions for the extended mKdV equation. Zbl 1209.34111 Kudryashov, Nikolay A.; Sinelshchikov, Dmitry I. 2011 Nonlinear waves in media with fifth order dispersion. Zbl 1242.74002 Kudryashov, Nikolai A.; Ryabov, Pavel N.; Sinelshchikov, Dmitry I. 2011 Exact solutions of the generalized $$K(m, m)$$ equations. Zbl 1221.35345 Kudryashov, Nikolay A.; Prilipko, Svetlana G. 2011 Nonlinear evolution equation for describing waves in a viscoelastic tube. Zbl 1221.74044 Kudryashov, Nikolai A.; Sinelshchikov, Dmitry I. 2011 Comment on: “Application of the $$(\frac{G'}{G})$$-expansion method for the complex KdV equation” [Huiqun Zhang, Commun. Nonlinear Sci. Numer. Simul. 15; 2010:1700-1704]. Zbl 1222.35171 Kudryashov, Nikolay A.; Ryabov, Pavel N. 2011 Properties of nonlinear waves in an actively-dissipative dispersive medium. Zbl 1235.76031 Kudryashov, N. A.; Ryabov, P. N. 2011 Redundant exact solutions of nonlinear differential equations. Zbl 1244.35030 Kudryashov, Nikolay A. 2011 A note on solutions of the Korteweg-de Vries hierarchy. Zbl 1222.65086 Kudryashov, Nikolay A. 2011 Meromorphic solutions of nonlinear ordinary differential equations. Zbl 1222.35160 Kudryashov, Nikolai A. 2010 A note on the $$G'/G$$-expansion method. Zbl 1203.35228 Kudryashov, Nikolai A. 2010 From Laurent series to exact meromorphic solutions: The Kawahara equation. Zbl 1238.34020 Demina, Maria V.; Kudryashov, Nikolay A. 2010 Nonlinear waves in bubbly liquids with consideration for viscosity and heat transfer. Zbl 1236.76075 Kudryashov, Nikolai A.; Sinelshchikov, Dmitry I. 2010 Nonlinear waves in liquids with gas bubbles with account of viscosity and heat transfer. Zbl 1215.76103 Kudryashov, N. A.; Sinel’shchikov, D. I. 2010 A note on new exact solutions for the Kawahara equation using Exp-function method. Zbl 1194.65119 Kudryashov, Nikolai A. 2010 Nonlinear evolution equations for describing waves in bubbly liquids with viscosity and heat transfer consideration. Zbl 1273.76407 Kudryashov, Nikolai A.; Sinelshchikov, Dmitry I. 2010 Soliton, rational and special solutions of the Korteweg-de Vries hierarchy. Zbl 1203.35229 Kudryashov, Nikolai A. 2010 A note on “Abundant new exact solutions for the $$(3+1)$$-dimensional Jimbo-Miwa equation”. Zbl 1204.35071 Kudryashov, Nikolay A.; Sinelshchikov, Dmitry I. 2010 A note on “New kink-shaped solutions and periodic wave solutions for the $$(2 + 1)$$-dimensional sine-Gordon equation”. Zbl 1200.35262 Kudryashov, Nikolay A.; Ryabov, Pavel N.; Sinelshchikov, Dmitry I. 2010 A new note on exact complex travelling wave solutions for $$(2+1)$$-dimensional B-type Kadomtsev-Petviashvili equation. Zbl 1202.35230 Kudryashov, Nikolay A. 2010 Seven common errors in finding exact solutions of nonlinear differential equations. Zbl 1221.35342 Kudryashov, Nikolai A. 2009 ...and 73 more Documents all top 5 ### Cited by 840 Authors 136 Kudryashov, Nikolaĭ Alekseevich 34 Sinelshchikov, Dmitry I. 29 Khalique, Chaudry Masood 28 Biswas, Anjan 22 Demina, Maria V. 15 Vitanov, Nikolay K. 14 Bruzón, Maria Santos 14 Yuan, Wenjun 12 Adem, Abdullahi Rashid 12 Dimitrova, Zlatinka I. 12 Gandarias Núñez, Maria Luz 12 Zayed, Elsayed M. E. 11 Kara, Abdul Hamid 11 Pickering, Andrew 11 Ryabov, Pavel N. 10 Aslan, İsmail 10 Navickas, Zenonas 10 Ragulskis, Minvydas 9 Gordoa, Pilar Ruiz 9 Gu, Yongyi 9 Kashchenko, Sergeĭ Aleksandrovich 8 Belić, Milivoj R. 7 Ekici, Mehmet 7 Mirzazadeh, Mohammad 7 Muatjetjeja, Ben 7 Wu, Yonghong 6 Alquran, Marwan Taiseer 6 Gromak, Valeriĭ Ivanovich 6 Meng, Fanning 6 Parkes, E. John 6 Polyanin, Andrei Dmitrievich 6 Telksnys, Tadas 6 Zhou, Qin 5 Alurrfi, Khaled A. E. 5 Băleanu, Dumitru I. 5 Bulut, Hasan 5 Conte, Robert Maurice 5 Doka, Serge Yamigno 5 Guha, Partha 5 Huang, Yong 5 Kazakov, Aleksandr Leonidovich 5 Kazakov, Alexey O. 5 Kochanov, Mark B. 5 Lu, Dianchen 5 Muriel, Concepción 5 Rezazadeh, Hadi 5 Vitanov, Kaloyan N. 5 Yaşar, Emrullah 5 Yıldırım, Yakup 4 Arnous, Ahmed H. 4 Bekir, Ahmet 4 Betchewe, Gambo 4 Chen, Cheng 4 Clarkson, Peter A. 4 Coclite, Giuseppe Maria 4 Dai, Chaoqing 4 Di Ruvo, Lorenzo 4 Efimova, Olga Yu. 4 Eslami, Mostafa 4 Garashchuk, Ivan R. 4 Ghose Choudhury, Anindya 4 Gordeev, Yu. N. 4 Gurefe, Yusuf 4 Jaradat, Imad 4 Jiang, Yaolin 4 Li, Jibin 4 Liu, Qian 4 Long, Yao 4 Mhlanga, Isaiah Elvis 4 Misirli, Emine E. 4 Moleleki, Letlhogonolo Daddy 4 Murzenko, V. V. 4 Ng, Tuen-Wai 4 Pandir, Yusuf 4 Qin, Yupeng 4 Sönmezoğlu, Abdullah 4 Tian, Shoufu 4 van Gorder, Robert Ashton 4 Wang, Gangwei 4 Wang, Zhen 4 Zakharchenko, Anastasia S. 4 Zhang, Tiantian 4 Zhao, Yunmei 4 Zhou, Yuqian 4 Zou, Li 3 Adem, Khadijo Rashid 3 Alzahrani, Abdullah Kamis 3 Aminakbari, Najva 3 Anghel, Nicolae 3 Baskonus, Haci Mehmet 3 Bochkarev, Andrey V. 3 Crepin, Kofane Timoleon 3 Fahmy, E. S. 3 Garrido, Tamara Maria 3 He, Yinghui 3 Khater, Mostafa M. A. 3 Kim, Hyunsoo 3 Korotkov, Eugene V. 3 Kuznetsov, Pavel Aleksandrovich 3 Layeni, Olawanle P. ...and 740 more Authors all top 5 ### Cited in 157 Serials 116 Applied Mathematics and Computation 61 Communications in Nonlinear Science and Numerical Simulation 32 Regular and Chaotic Dynamics 27 Nonlinear Dynamics 26 Chaos, Solitons and Fractals 25 Computers & Mathematics with Applications 22 Applied Mathematics Letters 18 Fluid Dynamics 17 Mathematical Methods in the Applied Sciences 15 Journal of Mathematical Analysis and Applications 15 Mathematical Problems in Engineering 14 International Journal of Applied and Computational Mathematics 13 Physics Letters. A 13 Abstract and Applied Analysis 13 Advances in Mathematical Physics 12 Chaos 10 Theoretical and Mathematical Physics 9 Journal of Mathematical Physics 9 Computational Mathematics and Mathematical Physics 9 Journal of Nonlinear Mathematical Physics 9 Advances in Difference Equations 8 Journal of Computational and Applied Mathematics 7 Journal of Applied Mathematics and Mechanics 6 Reports on Mathematical Physics 6 Applied Mathematical Modelling 6 Differential Equations 6 Journal of Applied Mathematics 5 Studies in Applied Mathematics 5 Physica D 5 Numerical Methods for Partial Differential Equations 5 Computational and Applied Mathematics 5 Journal of the Egyptian Mathematical Society 5 Nonlinear Analysis. Real World Applications 5 Discrete and Continuous Dynamical Systems. Series S 5 Nelineĭnaya Dinamika 4 Physica A 4 Journal of Geometry and Physics 4 Journal of Theoretical and Applied Mechanics (Sofia) 4 Prikladnaya Matematika i Mekhanika 4 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 4 Complexity 4 Qualitative Theory of Dynamical Systems 4 Discrete and Continuous Dynamical Systems. Series B 4 Proceedings of the Steklov Institute of Mathematics 4 Journal of Function Spaces 3 Journal of Fluid Mechanics 3 Mathematics and Computers in Simulation 3 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 3 Ricerche di Matematica 3 International Journal of Computer Mathematics 3 Fractals 3 Journal of Mathematical Chemistry 3 Doklady Mathematics 3 Differential Equations and Dynamical Systems 3 International Journal of Nonlinear Sciences and Numerical Simulation 3 Entropy 3 Analysis and Mathematical Physics 3 East Asian Journal on Applied Mathematics 3 Open Mathematics 3 AIMS Mathematics 2 Computers and Fluids 2 Nonlinearity 2 Wave Motion 2 Zhurnal Vychislitel’noĭ Matematiki i Matematicheskoĭ Fiziki 2 Journal of Differential Equations 2 Proceedings of the Japan Academy. Series A 2 Publications of the Research Institute for Mathematical Sciences, Kyoto University 2 Siberian Mathematical Journal 2 Acta Applicandae Mathematicae 2 Acta Mathematicae Applicatae Sinica. English Series 2 Journal of Scientific Computing 2 Numerical Algorithms 2 Russian Mathematics 2 Journal of Mathematical Sciences (New York) 2 Engineering Analysis with Boundary Elements 2 Discrete and Continuous Dynamical Systems 2 Journal of Inequalities and Applications 2 Nonlinear Analysis. Modelling and Control 2 Journal of Applied Mathematics and Computing 2 Statistical Applications in Genetics and Molecular Biology 2 Computational Biology and Chemistry 2 International Journal of Computational Methods 2 Mediterranean Journal of Mathematics 2 Boundary Value Problems 2 Asian-European Journal of Mathematics 2 Communications in Theoretical Physics 2 Symmetry 2 Journal of Theoretical Biology 2 Izvestiya Irkutskogo Gosudarstvennogo Universiteta. Seriya Matematika 2 Applied Mathematics and Nonlinear Sciences 1 Astrophysics and Space Science 1 Bulletin of the Australian Mathematical Society 1 Communications in Mathematical Physics 1 Israel Journal of Mathematics 1 Journal of Computational Physics 1 Journal of Engineering Mathematics 1 Journal of Mathematical Biology 1 Journal of Statistical Physics 1 Mathematical Biosciences 1 Rocky Mountain Journal of Mathematics ...and 57 more Serials all top 5 ### Cited in 44 Fields 556 Partial differential equations (35-XX) 167 Ordinary differential equations (34-XX) 134 Dynamical systems and ergodic theory (37-XX) 94 Fluid mechanics (76-XX) 79 Numerical analysis (65-XX) 43 Biology and other natural sciences (92-XX) 28 Special functions (33-XX) 28 Optics, electromagnetic theory (78-XX) 20 Functions of a complex variable (30-XX) 19 Mechanics of deformable solids (74-XX) 19 Statistical mechanics, structure of matter (82-XX) 15 Quantum theory (81-XX) 14 Mechanics of particles and systems (70-XX) 13 Classical thermodynamics, heat transfer (80-XX) 10 Probability theory and stochastic processes (60-XX) 10 Computer science (68-XX) 9 Real functions (26-XX) 6 Difference and functional equations (39-XX) 5 Topological groups, Lie groups (22-XX) 5 Relativity and gravitational theory (83-XX) 4 Nonassociative rings and algebras (17-XX) 4 Harmonic analysis on Euclidean spaces (42-XX) 3 Approximations and expansions (41-XX) 3 Integral equations (45-XX) 3 Operator theory (47-XX) 3 Calculus of variations and optimal control; optimization (49-XX) 3 Differential geometry (53-XX) 3 Global analysis, analysis on manifolds (58-XX) 3 Geophysics (86-XX) 3 Systems theory; control (93-XX) 2 Commutative algebra (13-XX) 2 Several complex variables and analytic spaces (32-XX) 2 Manifolds and cell complexes (57-XX) 2 Statistics (62-XX) 2 Operations research, mathematical programming (90-XX) 1 General and overarching topics; collections (00-XX) 1 History and biography (01-XX) 1 Field theory and polynomials (12-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Associative rings and algebras (16-XX) 1 Measure and integration (28-XX) 1 Integral transforms, operational calculus (44-XX) 1 Functional analysis (46-XX) 1 Astronomy and astrophysics (85-XX) ### Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata.	2022-05-16T05:41:46	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5995326042175293, "perplexity": 8190.251503749047}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662509990.19/warc/CC-MAIN-20220516041337-20220516071337-00224.warc.gz"}
https://par.nsf.gov/biblio/10285278-multi-objective-logarithmic-extremum-seeking-wind-turbine-power-capture-load-reduction	Multi-Objective Logarithmic Extremum Seeking for Wind Turbine Power Capture with Load Reduction This paper describes a multi-objective ESC strategy that determines Pareto-optimal control parameters to jointly optimize wind turbine loads and power capture. The method uses two optimization objectives calculated in real time: (a) the logarithm of the average power and (b) the logarithm of the standard deviation of a measurable blade load, tower load or the combination of these loads. These two objectives are weighted in real-time to obtain a solution that is Pareto optimal with respect to the power average and the standard deviation of chosen load metric. The method is evaluated using NREL FAST simulations of the 5-MW reference turbine. The results are then evaluated using energy capture over the duration of the simulation and damage equivalent loads (DEL) calculated with MLife. Authors: ; ; Award ID(s): Publication Date: NSF-PAR ID: 10285278 Journal Name: Multi-Objective Logarithmic Extremum Seeking for Wind Turbine Power Capture with Load Reduction Page Range or eLocation-ID: 533 to 538	2022-07-03T11:31:19	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8782633543014526, "perplexity": 1939.8535702166946}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656104240553.67/warc/CC-MAIN-20220703104037-20220703134037-00690.warc.gz"}
http://montessorimuddle.org/category/mathematics/	# Getting Data into R #### December 14, 2017 One of my students is taking an advanced statistics course–mostly online–and it introduced her to the statistical package R. I’ve been meaning to learn how to use R for a while, so I had her show me how use it. This allowed me to give her a final exam that used some PEW survey data for analysis. (I used the data for the 2013 LGBT survey). These are my notes on getting the PEW data, which is in SPSS format, into R. ## Instructions on Getting PEW data into R Go to the link for the 2013 LGBT survey“>2013 LGBT survey and download the data (you will have to set up an account if you have not used their website before). • There should be two files. • The .sav file contains the data (in SPSS format) • The .docx file contains the metadata (what is metadata?). • Load the data into R. • To load this data type you will need to let R know that you are importing a foreign data type, so execute the command: • > library(foreign) • To get the file’s name and path execute the command: • > file.choose() • The file.choose() command will give you a long string for the file’s path and name: it should look something like “C:\\Users\…” Copy the name and put it in the following command to read the file (Note 1: I’m naming the data “dataset” but you can call it anything you like; Note 2: The string will look different based on which operating system you use. The one you see below is for Windows): • > dataset = read.spss(“C:\\Users\...”) • To see what’s in the dataset you can use the summary command: • > summary(dataset) • To draw a histogram of the data in column “Q39” (which is the age at which the survey respondents realized they were LGBT) use: • > hist(dataset$Q35) • If you would like to export the column of data labeled “Q39” as a comma delimited file (named “helloQ39Data.csv”) to get it into Excel, use: • > write.csv(dataset$Q39, ”helloQ39Data.csv”) This should be enough to get started with R. One problem we encountered was that the R version on Windows was able to produce the histogram of the dataset, while the Mac version was not. I have not had time to look into why, but my guess is that the Windows version is able to screen out the non-numeric values in the dataset while the Mac version is not. But that’s just a guess. Histogram showing the age at which LGBT respondents first felt that they might be something other than heterosexual. Citing this post: Urbano, L., 2017. Getting Data into R, Retrieved February 26th, 2018, from Montessori Muddle: http://MontessoriMuddle.org/ . Attribution (Curator's Code ): Via: Montessori Muddle; Hat tip: Montessori Muddle. # Liquid Chessboard #### March 1, 2017 Chessboard under regular (day) light. I used the computer controlled (CNC) Shopbot machine at the Techshop to drill out 64 square pockets in the shape of a chessboard. One of my students (Kathryn) designed and printed the pieces as part of an extra credit project for her Geometry class. The pockets were then filled with a clear eqoxy to give a liquid effect. However, I mixed in two colors of pigmented powder to make the checkerboard. The powder was uv reactive so it fluoresces under black (ultra-violet) light. Under a black (ultra violet) light bulb. The powder also glows in the dark. Glowing in the dark. Citing this post: Urbano, L., 2017. Liquid Chessboard, Retrieved February 26th, 2018, from Montessori Muddle: http://MontessoriMuddle.org/ . Attribution (Curator's Code ): Via: Montessori Muddle; Hat tip: Montessori Muddle. # Demonstrating Taylor Series Approximations with Graphs #### January 31, 2017 This little embeddable, interactive app uses nth order polynomials to approximate a few curves to demonstrate the Taylor Series. Citing this post: Urbano, L., 2017. Demonstrating Taylor Series Approximations with Graphs, Retrieved February 26th, 2018, from Montessori Muddle: http://MontessoriMuddle.org/ . Attribution (Curator's Code ): Via: Montessori Muddle; Hat tip: Montessori Muddle. # Maximum Range of a Potato Gun #### December 18, 2016 One of the middle schoolers built a potato gun for his math class. He was looking a the mathematical relationship between the amount of fuel (hair spray) and the hang-time of the potato. To augment this work, I had my Numerical Methods class do the math and create analytical and numerical models of the projectile motion. One of the things my students had to figure out was what angle would give the maximum range of the projectile? You can figure this out analytically by finding the function for how the horizontal distance (x) changes as the angle (theta) changes (i.e. x(theta)) and then finding the maximum of the function. Initial velocity vector (v) and its component vectors in the x and y directions for a given angle. ## Distance as a function of the angle In a nutshell, to find the distance traveled by the potato we break its initial velocity into its x and y components (vx and vy), use the y component to find the flight time of the projectile (tf), and then use the vx component to find the distance traveled over the flight time. Starting with the diagram above we can separate the initial velocity of the potato into its two components using basic trigonometry: $\cos{\theta} = \frac{v_x}{v}$ $\sin{\theta} = \frac{v_y}{v}$, so, $v_x = v \cos{\theta}$, $v_y = v \sin{\theta}$ Now we know that the height of a projectile (y) is given by the function: $y(t) = \frac{a t^2}{2} + v_0 t + y_0$ (you can figure this out by assuming that the acceleration due to gravity (a) is constant and acceleration is the second differential of position with respect to time.) To find the flight time we assume we’re starting with an initial height of zero (y0 = 0), and that the flight ends when the potato hits the ground which is also at zero ((yt = 0), so: $0 = \frac{a t^2}{2} + v_0 t + 0$ $0 = \frac{a t^2}{2} + v_0 t$ Factoring out t gives: $0 = t ( \frac{a t}{2} + v_0)$ Looking at the two factors, we can now see that there are two solutions to this problem, which should not be too much of a surprise since the height equation is parabolic (a second order polynomial). The solutions are when: $t = 0$ $\frac{a t}{2} + v_0 = 0$ The first solution is obviously the initial launch time, while the second is going to be the flight time (tf). $\frac{a t_f}{2} + v_0 = 0$ $t_f = - \frac{2 v_0}{a}$ You might think it’s odd to have a negative in the equation, but remember, the acceleration is negative so it’ll cancel out. Now since we’re working with the y component of the velocity vector, the initial velocity in this equation (v0) is really just vy: $v_0 = v_y$ so we can substitute in the trig function for vy to get: $t_f = - \frac{2 v \sin{\theta}}{a}$ Our horizontal distance is simply given by the velocity in the x direction (vx) times the flight time: $x = v_x t_f$ which becomes: $x = v_x \left(- \frac{2 v \sin{\theta}}{a}\right)$ and substituting in the trig function for vx (just to make things look more complicated): $x = \left( v \cos{\theta} \right) \left(- \frac{2 v \sin{\theta}}{a}\right)$ and factoring out some of the constants gives: $x = -\frac{v^2}{a} 2 \sin{\theta}\cos{theta}$ Now we have distance as a function of the launch angle. We can simplify this a little by using the double-angle formula: $\sin{2\theta} = 2 \sin{\theta}\cos{theta}$ to get: $x = -\frac{v^2}{a} \sin{2\theta}$ ## Finding the maximum distance How do we find the maxima for this function. Sketching the curve should be easy enough, but because we know a little calculus we know that the maximum will occur when the first differential is equal to zero. So we differentiate with respect to the angle to get: $\frac{dx}{d\theta} = -\frac{v^2}{a} 2 \cos{2\theta}$ and set the differential equal to zero: $0 = -\frac{v^2}{a} 2 \cos{2\theta}$ and solve to get: $\cos{2\theta} = 0$ $2\theta = \cos^{-1}{(0)}$ Since we remember that the arccosine of 0 is 90 degrees: $2\theta = 90^{\circ}$ $\theta = 45^{\circ}$ And thus we’ve found the angle that gives the maximum launch distance for a potato gun. Citing this post: Urbano, L., 2016. Maximum Range of a Potato Gun, Retrieved February 26th, 2018, from Montessori Muddle: http://MontessoriMuddle.org/ . Attribution (Curator's Code ): Via: Montessori Muddle; Hat tip: Montessori Muddle. # Spurious Correlations #### November 18, 2016 Tyler Vigen has a great website Spurious Correlations that shows graphs of exactly that. A spurious correlation. Great for explaining what correlation means, and why correlation does not necessarily mean causation. Citing this post: Urbano, L., 2016. Spurious Correlations, Retrieved February 26th, 2018, from Montessori Muddle: http://MontessoriMuddle.org/ . Attribution (Curator's Code ): Via: Montessori Muddle; Hat tip: Montessori Muddle. # Numerical and Analytical Solutions 2: Constant Acceleration #### November 3, 2016 Previously, I showed how to solve a simple problem of motion at a constant velocity analytically and numerically. Because of the nature of the problem both solutions gave the same result. Now we’ll try a constant acceleration problem which should highlight some of the key differences between the two approaches, particularly the tradeoffs you must make when using numerical approaches. The Problem • A ball starts at the origin and moves horizontally with an acceleration of 0.2 m/s2. Print out a table of the ball’s position (in x) with time (every second) for the first 20 seconds. Analytical Solution We know that acceleration (a) is the change in velocity with time (t): $a = \frac{dv}{dt}$ so if we integrate acceleration we can find the velocity. Then, as we saw before, velocity (v) is the change in position with time: $v = \frac{dx}{dt}$ which can be integrated to find the position (x) as a function of time. So, to summarize, to find position as a function of time given only an acceleration, we need to integrate twice: first to get velocity then to get x. For this problem where the acceleration is a constant 0.2 m/s2 we start with acceleration: $\frac{dv}{dt} = 0.2$ which integrates to give the general solution, $v = 0.2 t + c$ To find the constant of integration we refer to the original question which does not say anything about velocity, so we assume that the initial velocity was 0: i.e.: at t = 0 we have v = 0; which we can substitute into the velocity equation to find that, for this problem, c is zero: $v = 0.2 t + c$ $0 = 0.2 (0) + c$ $0 = c$ making the specific velocity equation: $v = 0.2 t$ we replace v with dx/dt and integrate: $\frac{dx}{dt} = 0.2 t$ $x = \frac{0.2 t^2}{2} + c$ $x = 0.1 t^2 + c$ This constant of integration can be found since we know that the ball starts at the origin so at t = 0 we have x = 0, so; $x = 0.1 t^2 + c$ $0 = 0.1 (0)^2 + c$ $0 = c$ Therefore our final equation for x is: $x = 0.1 t^2$ ### Summarizing the Analytical To summarize the analytical solution: $a = 0.2$ $v = 0.2 t$ $x = 0.1 t^2$ These are all a function of time so it might be more proper to write them as: $a(t) = 0.2$ $v(t) = 0.2 t$ $x(t) = 0.1 t^2$ Velocity and acceleration represent rates of change which so we could also write these equations as: $a(t) = \frac{dv}{dt} = 0.2$ $v(t) = \frac{dx}{dt} = 0.2 t$ $x(t) = x = 0.1 t^2$ or we could even write acceleration as the second differential of the position: $a(t) = \frac{d^2x}{dt^2} = 0.2$ $v(t) = \frac{dx}{dt} = 0.2 t$ $x(t) = x = 0.1 t^2$ or, if we preferred, we could even write it in prime notation for the differentials: $a(t) = x$ $v(t) = x$ $x(t) = x(t) =0.1 t^2$ ## As we saw before we can determine the position of a moving object if we know its old position (xold) and how much that position has changed (dx).$x_{new} = x_{old} + dx$where the change in position is determined from the fact that velocity (v) is the change in position with time (dx/dt):$v = \frac{dx}{dt}$which rearranges to:$dx = v dt$So to find the new position of an object across a timestep we need two equations:$dx = v dt$ $x_{new} = x_{old} + dx$In this problem we don’t yet have the velocity because it changes with time, but we could use the exact same logic to find velocity since acceleration (a) is the change in velocity with time (dv/dt):$a = \frac{dv}{dt}$which rearranges to:$dv = a dt$and knowing the change in velocity (dv) we can find the velocity using:$v_{new} = v_{old} + dv$Therefore, we have four equations to find the position of an accelerating object (note that in the third equation I’ve replaced v with vnew which is calculated in the second equation):$dv = a dt$ $v_{new} = v_{old} + dv$ $dx = v_{new} dt$ $x_{new} = x_{old} + dx$These we can plug into a python program just so:motion-01-both.pyfrom visual import * # Initialize x = 0.0 v = 0.0 a = 0.2 dt = 1.0 # Time loop for t in arange(dt, 20+dt, dt): # Analytical solution x_a = 0.1 * t*2 # Numerical solution dv = a dt v = v + dv dx = v * dt x = x + dx # Output print t, x_a, x which give output of: >>> 1.0 0.1 0.2 2.0 0.4 0.6 3.0 0.9 1.2 4.0 1.6 2.0 5.0 2.5 3.0 6.0 3.6 4.2 7.0 4.9 5.6 8.0 6.4 7.2 9.0 8.1 9.0 10.0 10.0 11.0 11.0 12.1 13.2 12.0 14.4 15.6 13.0 16.9 18.2 14.0 19.6 21.0 15.0 22.5 24.0 16.0 25.6 27.2 17.0 28.9 30.6 18.0 32.4 34.2 19.0 36.1 38.0 20.0 40.0 42.0 Here, unlike the case with constant velocity, the two methods give slightly different results. The analytical solution is the correct one, so we’ll use it for reference. The numerical solution is off because it does not fully account for the continuous nature of the acceleration: we update the velocity ever timestep (every 1 second), so the velocity changes in chunks. To get a better result we can reduce the timestep. Using dt = 0.1 gives final results of:18.8 35.344 35.532 18.9 35.721 35.91 19.0 36.1 36.29 19.1 36.481 36.672 19.2 36.864 37.056 19.3 37.249 37.442 19.4 37.636 37.83 19.5 38.025 38.22 19.6 38.416 38.612 19.7 38.809 39.006 19.8 39.204 39.402 19.9 39.601 39.8 20.0 40.0 40.2 which is much closer, but requires a bit more runtime on the computer. And this is the key tradeoff with numerical solutions: greater accuracy requires smaller timesteps which results in longer runtimes on the computer. ### Post Script To generate a graph of the data use the code: from visual import * from visual.graph import * # Initialize x = 0.0 v = 0.0 a = 0.2 dt = 1.0 analyticCurve = gcurve(color=color.red) numericCurve = gcurve(color=color.yellow) # Time loop for t in arange(dt, 20+dt, dt): # Analytical solution x_a = 0.1 * t*2 # Numerical solution dv = a dt v = v + dv dx = v * dt x = x + dx # Output print t, x_a, x analyticCurve.plot(pos=(t, x_a)) numericCurve.plot(pos=(t,x)) which gives: Comparison of numerical and analytical solutions using a timestep (dt) of 1.0 seconds. Citing this post: Urbano, L., 2016. Numerical and Analytical Solutions 2: Constant Acceleration, Retrieved February 26th, 2018, from Montessori Muddle: http://MontessoriMuddle.org/ . Attribution (Curator's Code ): Via: Montessori Muddle; Hat tip: Montessori Muddle. # Numerical versus Analytical Solutions #### November 3, 2016 We’ve started working on the physics of motion in my programming class, and really it boils down to solving differential equations using numerical methods. Since the class has a calculus co-requisite I thought a good way to approach teaching this would be to first have the solve the basic equations for motion (velocity and acceleration) analytically–using calculus–before we took the numerical approach. ## Constant velocity • Question 1. A ball starts at the origin and moves horizontally at a speed of 0.5 m/s. Print out a table of the ball’s position (in x) with time (t) (every second) for the first 20 seconds. Analytical Solution: Well, we know that speed is the change in position (in the x direction in this case) with time, so a constant velocity of 0.5 m/s can be written as the differential equation: $\frac{dx}{dt} = 0.5$ To get the ball’s position at a given time we need to integrate this differential equation. It turns out that my calculus students had not gotten to integration yet. So I gave them the 5 minute version, which they were able to pick up pretty quickly since integration’s just the reverse of differentiation, and we were able to move on. Integrating gives: $x = 0.5t + c$ which includes a constant of integration (c). This is the general solution to the differential equation. It’s called the general solution because we still can’t use it since we don’t know what c is. We need to find the specific solution for this particular problem. In order to find c we need to know the actual position of the ball is at one point in time. Fortunately, the problem states that the ball starts at the origin where x=0 so we know that: • at t = 0, x = 0 So we plug these values into the general solution to get: $0 = 0.5(0) + c$ solving for c gives: $c = 0$ Therefore our specific solution is simply: $x = 0.5t$ And we can write a simple python program to print out the position of the ball every second for 20 seconds: motion-01-analytic.py for t in range(21): x = 0.5 * t print t, x which gives the result: >>> 0 0.0 1 0.5 2 1.0 3 1.5 4 2.0 5 2.5 6 3.0 7 3.5 8 4.0 9 4.5 10 5.0 11 5.5 12 6.0 13 6.5 14 7.0 15 7.5 16 8.0 17 8.5 18 9.0 19 9.5 20 10.0 Numerical Solution: Finding the numerical solution to the differential equation involves not integrating, which is particularly good if the differential equation can’t be integrated. We start with the same differential equation for velocity: $\frac{dx}{dt} = 0.5$ but instead of trying to solve it we’ll just approximate a solution by recognizing that we use dx/dy to represent when the change in x and t are really, really small. If we were to assume they weren’t infinitesimally small we would rewrite the equations using deltas instead of d’s: $\frac{\Delta x}{\Delta t} = 0.5$ now we can manipulate this equation using algebra to show that: $\Delta x = 0.5 \Delta t$ so the change in the position at any given moment is just the velocity (0.5 m/s) times the timestep. Therefore, to keep track of the position of the ball we need to just add the change in position to the old position of the ball: $x_{new} = x_{old} + \Delta x$ Now we can write a program to calculate the position of the ball using this numerical approximation. motion-01-numeric.py from visual import * # Initialize x = 0.0 dt = 1.0 # Time loop for t in arange(dt, 21, dt): v = 0.5 dx = v * dt x = x + dx print t, x I’m sure you’ve noticed a couple inefficiencies in this program. Primarily, that the velocity v, which is a constant, is set inside the loop, which just means it’s reset to the same value every time the loop loops. However, I’m putting it in there because when we get working on acceleration the velocity will change with time. I also import the visual library (vpython.org) because it imports the numpy library and we’ll be creating and moving 3d balls in a little bit as well. Finally, the two statements for calculating dx and x could easily be combined into one. I’m only keeping them separate to be consistent with the math described above. A Program with both Analytical and Numerical Solutions For constant velocity problems the numerical approach gives the same results as the analytical solution, but that’s most definitely not going to be the case in the future, so to compare the two results more easily we can combine the two programs into one: motion-01.py from visual import * # Initialize x = 0.0 dt = 1.0 # Time loop for t in arange(dt, 21, dt): v = 0.5 # Analytical solution x_a = v * t # Numerical solution dx = v * dt x = x + dx # Output print t, x_a, x which outputs: >>> 1.0 0.5 0.5 2.0 1.0 1.0 3.0 1.5 1.5 4.0 2.0 2.0 5.0 2.5 2.5 6.0 3.0 3.0 7.0 3.5 3.5 8.0 4.0 4.0 9.0 4.5 4.5 10.0 5.0 5.0 11.0 5.5 5.5 12.0 6.0 6.0 13.0 6.5 6.5 14.0 7.0 7.0 15.0 7.5 7.5 16.0 8.0 8.0 17.0 8.5 8.5 18.0 9.0 9.0 19.0 9.5 9.5 20.0 10.0 10.0 Solving a problem involving acceleration comes next. Citing this post: Urbano, L., 2016. Numerical versus Analytical Solutions, Retrieved February 26th, 2018, from Montessori Muddle: http://MontessoriMuddle.org/ . Attribution (Curator's Code ): Via: Montessori Muddle; Hat tip: Montessori Muddle. # Model Skate Park #### November 1, 2016 Skate park bowl under construction. After batting around a number of ideas, three of my middle schoolers settled on building a model skate park out of popsicle sticks and cardboard for their interim project. A lot of hot glue was involved. The ramps turned out to be pretty easy, but on the second day they decided that the wanted a bowl, which proved to be much more challenging. They cut out sixteen profiles out of thicker cardboard, made a skeleton out of popsicle sticks, and then coated the top with thin, cereal-box cardboard. When they were done they painted the whole thing grey–to simulate concrete I think–except for the sides, which were a nice flat blue so that they could put their own miniature graffiti over the top. It was a lot of careful, well thought-out work. Getting there: ramps, a rail, and bowl. Citing this post: Urbano, L., 2016. Model Skate Park, Retrieved February 26th, 2018, from Montessori Muddle: http://MontessoriMuddle.org/ . Attribution (Curator's Code ): Via: Montessori Muddle; Hat tip: Montessori Muddle. Montessori Muddle by Montessori Muddle is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 United States License.	2018-02-26T03:44:30	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 77, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6526764035224915, "perplexity": 1058.3565610226165}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-09/segments/1518891817999.51/warc/CC-MAIN-20180226025358-20180226045358-00396.warc.gz"}
https://zbmath.org/authors/?q=ai%3Amorgan.frank	## Morgan, Frank Compute Distance To: Author ID: morgan.frank Published as: Morgan, Frank; Morgan, F. Homepage: http://math.williams.edu/morgan External Links: MGP · Wikidata Documents Indexed: 126 Publications since 1976, including 13 Books 2 Further Contributions Co-Authors: 56 Co-Authors with 45 Joint Publications 1,229 Co-Co-Authors all top 5 ### Co-Authors 82 single-authored 5 Sullivan, John M. jun. 4 Hutchings, Michael Lounsbery 4 Ritoré, Manuel 3 Harvey, Reese 3 Ros, Antonio 2 Adams, Colin C. 2 Gluck, Herman 2 Hass, Joel 2 Howards, Hugh Nelson 2 Lawlor, Gary R. 1 Almgren, Robert F. 1 Bayle, Vincent 1 Bolton, Roger 1 Brakke, Kenneth A. 1 Bray, Hubert L. 1 Brothers, John E. 1 Burger, Edward B. 1 Cañete, Antonio 1 Carozza, Davide 1 Chung, Ping Ngai 1 Cook, Jack S. 1 Corwin, Ivan Z. 1 Cox, Steven J. 1 Dadok, Jiri 1 Epstein, David Bernard Alper 1 Fernández, Miguel Ángel 1 Forman, Robin 1 French, Christopher P. 1 Furedi, Zoltan 1 Graner, François 1 Greenleaf, Scott 1 Gulliver, Robert D. II 1 Hardt, Robert M. 1 Harman, Nate 1 Holmes, Thomas J. 1 Howe, Sean 1 Hsu, Wen-Tai 1 Johnson, David Lewis 1 Johnson, Stewart D. 1 Jones, B. Frank jun. 1 Kern, Norbert 1 Keyfitz, Barbara Lee 1 Kusner, Robert B. 1 Lagarias, Jeffrey C. 1 Larché, Francis 1 Li, Yifei 1 Lieb, Elliott Hershel 1 Lovett, Jonathan 1 Mackenzie, Dana Walter Nance 1 Mara, Michael Kelly 1 Marden, Albert 1 Maurmann, Quinn 1 Miller, Steven J. 1 Newkirk, Edward 1 Pansu, Pierre 1 Pedersen, Lori 1 Plata, Isamar Rosa 1 Pratelli, Aldo 1 Rosales, César 1 Salavessa, Isabel M. C. 1 Seferis, Deividas 1 Shah, Niralee 1 Sordo Vieira, Luis 1 Taylor, Jean Ellen 1 Wichiramala, Wacharin 1 Wikner, Elena 1 Wolf, Michael 1 Ziller, Wolfgang all top 5 ### Serials 11 Proceedings of the American Mathematical Society 10 American Mathematical Monthly 9 Transactions of the American Mathematical Society 6 The Journal of Geometric Analysis 4 The Mathematical Intelligencer 4 Indiana University Mathematics Journal 4 Pacific Journal of Mathematics 3 Archive for Rational Mechanics and Analysis 3 Inventiones Mathematicae 3 Mathematische Annalen 3 Annals of Global Analysis and Geometry 2 Bulletin of the Australian Mathematical Society 2 Duke Mathematical Journal 2 Michigan Mathematical Journal 2 Rendiconti del Circolo Matemàtico di Palermo. Serie II 2 Bulletin of the American Mathematical Society. New Series 2 Notices of the American Mathematical Society 2 Calculus of Variations and Partial Differential Equations 2 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 Mitteilungen der Deutschen Mathematiker-Vereinigung (DMV) 1 Reviews of Modern Physics 1 Mathematics Magazine 1 Advances in Mathematics 1 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 1 Commentarii Mathematici Helvetici 1 Journal of Differential Geometry 1 Journal of Economic Theory 1 Kodai Mathematical Journal 1 Manuscripta Mathematica 1 Mathematische Zeitschrift 1 Revista Matemática Iberoamericana 1 International Journal of Mathematics 1 Aequationes Mathematicae 1 Communications in Partial Differential Equations 1 Linear Algebra and its Applications 1 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 1 SIAM Review 1 Experimental Mathematics 1 Communications in Analysis and Geometry 1 Electronic Research Announcements of the American Mathematical Society 1 Matemática Contemporânea 1 European Mathematical Society Newsletter 1 The Asian Journal of Mathematics 1 Annals of Mathematics. Second Series 1 Interfaces and Free Boundaries 1 Student Mathematical Library 1 Involve 1 São Paulo Journal of Mathematical Sciences 1 Analysis and Geometry in Metric Spaces 1 MAA Spectrum all top 5 ### Fields 87 Calculus of variations and optimal control; optimization (49-XX) 83 Differential geometry (53-XX) 14 Convex and discrete geometry (52-XX) 14 Global analysis, analysis on manifolds (58-XX) 7 Measure and integration (28-XX) 6 General and overarching topics; collections (00-XX) 4 Real functions (26-XX) 4 Geometry (51-XX) 4 Mechanics of deformable solids (74-XX) 4 Fluid mechanics (76-XX) 3 History and biography (01-XX) 3 Relativity and gravitational theory (83-XX) 3 Operations research, mathematical programming (90-XX) 3 Mathematics education (97-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Partial differential equations (35-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Combinatorics (05-XX) 1 Number theory (11-XX) 1 Topological groups, Lie groups (22-XX) 1 Functions of a complex variable (30-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 General topology (54-XX) 1 Algebraic topology (55-XX) 1 Manifolds and cell complexes (57-XX) 1 Probability theory and stochastic processes (60-XX) 1 Numerical analysis (65-XX) 1 Mechanics of particles and systems (70-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Statistical mechanics, structure of matter (82-XX) ### Citations contained in zbMATH Open 105 Publications have been cited 1,391 times in 810 Documents Cited by Year Manifolds with density. Zbl 1118.53022 Morgan, Frank 2005 Geometric measure theory. A beginner’s guide. Zbl 0671.49043 Morgan, Frank 1988 Geometric measure theory. A beginner’s guide. Illustrated by James F. Bredt. 4th ed. Zbl 1179.49050 Morgan, Frank 2009 On the isoperimetric problem in Euclidean space with density. Zbl 1126.49038 Rosales, César; Cañete, Antonio; Bayle, Vincent; Morgan, Frank 2008 Some sharp isoperimetric theorems for Riemannian manifolds. Zbl 1021.53020 Morgan, Frank; Johnson, David L. 2000 Proof of the double bubble conjecture. Zbl 1009.53007 Hutchings, Michael; Morgan, Frank; Ritoré, Manuel; Ros, Antonio 2002 Regularity of isoperimetric hypersurfaces in Riemannian manifolds. Zbl 1063.49031 Morgan, Frank 2003 Geometric measure theory. A beginner’s guide. 3rd ed. Zbl 0974.49025 Morgan, Frank 2000 Paired calibrations applied to soap films, immiscible fluids, and surfaces or networks minimizing other norms. Zbl 0830.49028 Lawlor, Gary; Morgan, Frank 1994 Geometric measure theory. A beginner’s guide. 2nd ed. Zbl 0819.49024 Morgan, Frank 1995 Isoperimetric regions in cones. Zbl 0988.53028 Morgan, Frank; Ritoré, Manuel 2002 Existence of isoperimetric regions in $$\mathbb{R}^{n}$$ with density. Zbl 1263.49049 Morgan, Frank; Pratelli, Aldo 2013 The isoperimetric problem on surfaces. Zbl 1003.52011 Howards, Hugh; Hutchings, Michael; Morgan, Frank 1999 The isoperimetric theorem for general integrands. Zbl 0923.49019 Brothers, John E.; Morgan, Frank 1994 Geometric measure theory. A beginner’s guide. Illustrated by James F. Bredt. 5th edition. Zbl 1338.49089 Morgan, Frank 2016 Soap bubbles in $$\mathbb{R}^ 2$$ and in surfaces. Zbl 0820.53002 Morgan, Frank 1994 Clusters minimizing area plus length of singular curves. Zbl 0805.49025 Morgan, Frank 1994 The isoperimetric problem on surfaces of revolution of decreasing Gauss curvature. Zbl 0976.53082 Morgan, Frank; Hutchings, Michael; Howards, Hugh 2000 Hexagonal economic regions solve the location problem. Zbl 1026.90059 Morgan, Frank; Bolton, Roger 2002 The exterior algebra $$\Lambda ^ kR^ n$$ and area minimization. Zbl 0585.49029 Morgan, Frank 1985 On the singular structure of two-dimensional area minimizing surfaces in $${\mathbb{R}}^ n$$. Zbl 0549.49029 Morgan, Frank 1982 Manifolds with density and Perelman’s proof of the Poincaré conjecture. Zbl 1170.53001 Morgan, Frank 2009 Myer’s theorem with density. Zbl 1132.53306 Morgan, Frank 2006 The cone over the Clifford torus in $$R^ 4$$ is $$\Phi$$-minimizing. Zbl 0725.49013 Morgan, Frank 1991 An isoperimetric comparison theorem for Schwarzschild space and other manifolds. Zbl 0994.53029 Bray, Hubert; Morgan, Frank 2002 Riemannian geometry. A beginner’s guide. 2nd ed. Zbl 0911.53001 Morgan, Frank 1998 On the singular structure of three-dimensional, area-minimizing surfaces. Zbl 0557.49022 Morgan, Frank 1983 Isoperimetric comparison theorems for manifolds with density. Zbl 1175.49042 Maurmann, Quinn; Morgan, Frank 2009 Harnack-type mass bounds and Bernstein theorems for area-minimizing flat chains modulo $$\nu$$. Zbl 0617.49019 Morgan, Frank 1986 Area-minimizing currents bounded by higher multiples of curves. Zbl 0541.49018 Morgan, Frank 1984 Area-minimizing surfaces, faces of Grassmannians, and calibrations. Zbl 0672.49028 Morgan, Frank 1988 Calibrations on $${\mathbb{R}}^ 8$$. Zbl 0666.49015 Dadok, J.; Harvey, R.; Morgan, F. 1988 Minimal surfaces, crystals, shortest networks, and undergraduate research. Zbl 0765.52015 Morgan, Frank 1992 In polytopes, small balls about some vertex minimize perimeter. Zbl 1132.49036 Morgan, Frank 2007 Open problems in soap bubble geometry. Zbl 0867.53009 Sullivan, John M.; Morgan, Frank 1996 Examples of unoriented area-minimizing surfaces. Zbl 0509.53007 Morgan, Frank 1984 The log-convex density conjecture. Zbl 1238.49062 Morgan, Frank 2011 Volume-minimizing cycles in Grassmann manifolds. Zbl 0837.53035 Gluck, Herman; Mackenzie, Dana; Morgan, Frank 1995 The standard double bubble is the unique stable double bubble in $$\mathbb{R}^2$$. Zbl 1003.53010 Morgan, Frank; Wichiramala, Wacharin 2002 Planar Wulff shape is unique equilibrium. Zbl 1071.49025 Morgan, Frank 2005 Stable constant-mean-curvature hypersurfaces are area minimizing in small $$L^1$$ neighborhoods. Zbl 1195.49055 Morgan, Frank; Ros, Antonio 2010 Riemannian geometry. A beginner’s guide. Zbl 0794.53001 Morgan, Frank 1993 The faces of the Grassmannian of 3-planes in $${\mathbb{R}}^ 7$$ (calibrated geometries on $${\mathbb{R}}^ 7)$$. Zbl 0556.53036 Harvey, Reese; Morgan, Frank 1986 Calibrated geometries in Grassmann manifolds. Zbl 0681.53039 Gluck, Herman; Morgan, Frank; Ziler, Wolfgang 1989 Almost every curve in $$R^3$$ bounds a unique area minimizing surface. Zbl 0378.49028 Morgan, Frank 1978 Geodesic nets on the $$2$$-sphere. Zbl 0871.53038 Hass, Joel; Morgan, Frank 1996 Steiner and Schwarz symmetrization in warped products and fiber bundles with density. Zbl 1229.49046 Morgan, Frank; Howe, Sean; Harman, Nate 2011 Isoperimetric estimates in products. Zbl 1097.49027 Morgan, Frank 2006 $$(M,\varepsilon,\delta)$$-minimal curve regularity. Zbl 0804.49033 Morgan, Frank 1994 Size-minimizing rectifiable currents. Zbl 0645.49024 Morgan, Frank 1989 Immiscible fluid clusters in $${\mathbb{R}}^2$$ and $${\mathbb{R}}^3$$. Zbl 0967.49026 Morgan, Frank 1998 Lower semicontinuity of energy clusters. Zbl 0886.49016 Morgan, Frank 1997 Measures on spaces of surfaces. Zbl 0529.58031 Morgan, Frank 1982 The Levy-Gromov isoperimetric inequality in convex manifolds with boundary. Zbl 1149.53021 Morgan, Frank 2008 A regularity theorem for minimizing hypersurfaces modulo $$\nu$$. Zbl 0641.49027 Morgan, Frank 1986 Surfaces minimizing area plus length of singular curves. Zbl 0816.49033 Morgan, Frank 1994 A smooth curve in $$R^4$$ bounding a continuum of area minimizing surfaces. Zbl 0338.53003 Morgan, Frank 1976 On finiteness of the number of stable minimal hypersurfaces with a fixed boundary. Zbl 0592.53004 Morgan, Frank 1986 Singularities of minimal surfaces and networks and related extremal problems in Minkowski space. Zbl 0762.49014 Füredi, Z.; Lagarias, J. C.; Morgan, F. 1991 Calibrations and new singularities in area-minimizing surfaces: A survey. Zbl 0721.53058 Morgan, Frank 1990 Curvy slicing proves that triple junctions locally minimize area. Zbl 0870.53006 Lawlor, Gary; Morgan, Frank 1996 Rotation in a normed plane. Zbl 1140.51013 Cook, Jack; Lovett, Jonathan; Morgan, Frank 2007 Calibrations modulo $$\nu$$. Zbl 0618.49019 Morgan, Frank 1987 Area-minimizing surfaces in cones. Zbl 1035.58011 Morgan, Frank 2002 Wulff clusters in $$\mathbb{R}^2$$. Zbl 0934.49024 Morgan, Frank; French, Christopher; Greenleaf, Scott 1998 Isoperimetric curves on hyperbolic surfaces. Zbl 0992.53048 1999 The hexagonal honeycomb conjecture. Zbl 0932.49032 Morgan, Frank 1999 Proof of the double bubble conjecture. Zbl 0970.53009 Hutchings, Michael; Morgan, Frank; Ritoré, Manuel; Ros, Antonio 2000 Clusters with multiplicities in $$\mathbb R^2$$. Zbl 1108.49034 Morgan, Frank 2005 A round ball uniquely minimizes gravitational potential energy. Zbl 1066.70010 Morgan, Frank 2005 The comass ball in $$\Lambda ^ 3({\mathbb{R}}^ 6)^$$. Zbl 0594.53045 Harvey, Reese; Morgan, Frank 1986 Geodesics and soap bubbles in surfaces. Zbl 0865.53009 Hass, Joel; Morgan, Frank 1996 Hexagonal surfaces of Kapouleas. Zbl 1117.53010 Morgan, Frank 2005 Isoperimetric pentagonal tilings. Zbl 1253.52009 Chung, Ping Ngai; Fernandez, Miguel A.; Li, Yifei; Mara, Michael; Morgan, Frank; Plata, Isamar Rosa; Shah, Niralee; Sordo Vieira, Luis; Wikner, Elena 2012 Proof of the double bubble conjecture. Zbl 0990.49029 Morgan, Frank 2001 Mathematicians, including undergraduates, look at soap bubbles. Zbl 0814.53002 Morgan, Frank 1994 Are large perimeter-minimizing two-dimensional clusters of equal-area bubbles hexagonal or circular? Zbl 1371.74233 Cox, S. J.; Morgan, F.; Graner, F. 2013 Geometric measure theory and the proof of the double bubble conjecture. Zbl 1125.49033 Morgan, Frank; Ritoré, Manuel 2005 The symmetry group of a curve preserves a plane. Zbl 0489.53002 Gulliver, Robert; Morgan, Frank 1982 The Gauss-Bonnet formula on surfaces with densities. Zbl 1251.53002 Corwin, Ivan; Morgan, Frank 2011 When soap bubbles collide. Zbl 1183.52015 Adams, Colin; Morgan, Frank; Sullivan, John M. 2007 A smooth curve in $$R^ 3$$ bounding a continuum of minimal manifolds. Zbl 0453.49027 Morgan, Frank 1981 Regularity of area-minimizing surfaces in 3D polytopes and of invariant hypersurfaces in $$\mathbb R^n$$. Zbl 1085.52501 Morgan, Frank 2005 Perimeter-minimizing curves and surfaces in $$\mathbf R^n$$ enclosing prescribed multi-volume. Zbl 0985.49025 Morgan, Frank 2000 Riemannian geometry. A beginner’s guide. 2nd ed., revised paperback printing. Zbl 1234.53001 Morgan, Frank 2009 On the singular structure of three-dimensional, area-minimizing surfaces. Zbl 0529.49022 Morgan, Frank 1983 Least-volume representatives of homology classes in $$G(2,C^ 4)$$. Zbl 0679.53060 Morgan, Frank 1989 Colloquium: Soap bubble clusters. Zbl 1205.53009 Morgan, Frank 2007 Generic uniqueness for hypersurfaces minimizing the integral of an elliptic integrand with constant coefficients. Zbl 0423.53042 Morgan, Frank 1981 Cylindrical surfaces of Delaunay. Zbl 1097.53003 Morgan, Frank 2004 Streams of cylindrical water. Zbl 1075.53009 Morgan, Frank 2004 An isoperimetric inequality for the thread problem. Zbl 0893.49029 Morgan, Frank 1997 Survey lectures on geometric measure theory. Zbl 0915.49025 Morgan, Frank 1993 Instability of the wet $$X$$ soap film. Zbl 0965.53012 Brakke, Kenneth; Morgan, Frank 1998 Calibrations and the size of Grassmann faces. Zbl 0766.53048 Morgan, Frank 1992 Isoperimetric symmetry breaking: a counterexample to a generalized form of the log-convex density conjecture. Zbl 1355.53005 Morgan, Frank 2016 Strict calibrations, constant mean curvature and triple junctions. Zbl 0867.53008 Morgan, Frank 1995 Soap films and mathematics. Zbl 0804.53009 Morgan, Frank 1993 Optimal city hierarchy: a dynamic programming approach to central place theory. Zbl 1309.91110 Hsu, Wen-Tai; Holmes, Thomas J.; Morgan, Frank 2014 Soap bubbles and soap films. Zbl 0774.53005 Morgan, Frank 1990 The isoperimetric problem with density. Zbl 1386.49061 Morgan, Frank 2017 Geometric measure theory. A beginner’s guide. Illustrated by James F. Bredt. 5th edition. Zbl 1338.49089 Morgan, Frank 2016 Isoperimetric symmetry breaking: a counterexample to a generalized form of the log-convex density conjecture. Zbl 1355.53005 Morgan, Frank 2016 Optimal city hierarchy: a dynamic programming approach to central place theory. Zbl 1309.91110 Hsu, Wen-Tai; Holmes, Thomas J.; Morgan, Frank 2014 Existence of isoperimetric regions in $$\mathbb{R}^{n}$$ with density. Zbl 1263.49049 Morgan, Frank; Pratelli, Aldo 2013 Are large perimeter-minimizing two-dimensional clusters of equal-area bubbles hexagonal or circular? Zbl 1371.74233 Cox, S. J.; Morgan, F.; Graner, F. 2013 Isoperimetric pentagonal tilings. Zbl 1253.52009 Chung, Ping Ngai; Fernandez, Miguel A.; Li, Yifei; Mara, Michael; Morgan, Frank; Plata, Isamar Rosa; Shah, Niralee; Sordo Vieira, Luis; Wikner, Elena 2012 The log-convex density conjecture. Zbl 1238.49062 Morgan, Frank 2011 Steiner and Schwarz symmetrization in warped products and fiber bundles with density. Zbl 1229.49046 Morgan, Frank; Howe, Sean; Harman, Nate 2011 The Gauss-Bonnet formula on surfaces with densities. Zbl 1251.53002 Corwin, Ivan; Morgan, Frank 2011 Stable constant-mean-curvature hypersurfaces are area minimizing in small $$L^1$$ neighborhoods. Zbl 1195.49055 Morgan, Frank; Ros, Antonio 2010 Baserunner’s optimal path. Zbl 1187.00008 Carozza, Davide; Johnson, Stewart; Morgan, Frank 2010 Geometric measure theory. A beginner’s guide. Illustrated by James F. Bredt. 4th ed. Zbl 1179.49050 Morgan, Frank 2009 Manifolds with density and Perelman’s proof of the Poincaré conjecture. Zbl 1170.53001 Morgan, Frank 2009 Isoperimetric comparison theorems for manifolds with density. Zbl 1175.49042 Maurmann, Quinn; Morgan, Frank 2009 Riemannian geometry. A beginner’s guide. 2nd ed., revised paperback printing. Zbl 1234.53001 Morgan, Frank 2009 Isoperimetric balls in cones over tori. Zbl 1171.53040 Morgan, Frank 2009 On the isoperimetric problem in Euclidean space with density. Zbl 1126.49038 Rosales, César; Cañete, Antonio; Bayle, Vincent; Morgan, Frank 2008 The Levy-Gromov isoperimetric inequality in convex manifolds with boundary. Zbl 1149.53021 Morgan, Frank 2008 In polytopes, small balls about some vertex minimize perimeter. Zbl 1132.49036 Morgan, Frank 2007 Rotation in a normed plane. Zbl 1140.51013 Cook, Jack; Lovett, Jonathan; Morgan, Frank 2007 When soap bubbles collide. Zbl 1183.52015 Adams, Colin; Morgan, Frank; Sullivan, John M. 2007 Colloquium: Soap bubble clusters. Zbl 1205.53009 Morgan, Frank 2007 Myer’s theorem with density. Zbl 1132.53306 Morgan, Frank 2006 Isoperimetric estimates in products. Zbl 1097.49027 Morgan, Frank 2006 Manifolds with density. Zbl 1118.53022 Morgan, Frank 2005 Planar Wulff shape is unique equilibrium. Zbl 1071.49025 Morgan, Frank 2005 Clusters with multiplicities in $$\mathbb R^2$$. Zbl 1108.49034 Morgan, Frank 2005 A round ball uniquely minimizes gravitational potential energy. Zbl 1066.70010 Morgan, Frank 2005 Hexagonal surfaces of Kapouleas. Zbl 1117.53010 Morgan, Frank 2005 Geometric measure theory and the proof of the double bubble conjecture. Zbl 1125.49033 Morgan, Frank; Ritoré, Manuel 2005 Regularity of area-minimizing surfaces in 3D polytopes and of invariant hypersurfaces in $$\mathbb R^n$$. Zbl 1085.52501 Morgan, Frank 2005 Cylindrical surfaces of Delaunay. Zbl 1097.53003 Morgan, Frank 2004 Streams of cylindrical water. Zbl 1075.53009 Morgan, Frank 2004 Regularity of isoperimetric hypersurfaces in Riemannian manifolds. Zbl 1063.49031 Morgan, Frank 2003 Proof of the double bubble conjecture. Zbl 1009.53007 Hutchings, Michael; Morgan, Frank; Ritoré, Manuel; Ros, Antonio 2002 Isoperimetric regions in cones. Zbl 0988.53028 Morgan, Frank; Ritoré, Manuel 2002 Hexagonal economic regions solve the location problem. Zbl 1026.90059 Morgan, Frank; Bolton, Roger 2002 An isoperimetric comparison theorem for Schwarzschild space and other manifolds. Zbl 0994.53029 Bray, Hubert; Morgan, Frank 2002 The standard double bubble is the unique stable double bubble in $$\mathbb{R}^2$$. Zbl 1003.53010 Morgan, Frank; Wichiramala, Wacharin 2002 Area-minimizing surfaces in cones. Zbl 1035.58011 Morgan, Frank 2002 Proof of the double bubble conjecture. Zbl 0990.49029 Morgan, Frank 2001 Some sharp isoperimetric theorems for Riemannian manifolds. Zbl 1021.53020 Morgan, Frank; Johnson, David L. 2000 Geometric measure theory. A beginner’s guide. 3rd ed. Zbl 0974.49025 Morgan, Frank 2000 The isoperimetric problem on surfaces of revolution of decreasing Gauss curvature. Zbl 0976.53082 Morgan, Frank; Hutchings, Michael; Howards, Hugh 2000 Proof of the double bubble conjecture. Zbl 0970.53009 Hutchings, Michael; Morgan, Frank; Ritoré, Manuel; Ros, Antonio 2000 Perimeter-minimizing curves and surfaces in $$\mathbf R^n$$ enclosing prescribed multi-volume. Zbl 0985.49025 Morgan, Frank 2000 The isoperimetric problem on surfaces. Zbl 1003.52011 Howards, Hugh; Hutchings, Michael; Morgan, Frank 1999 Isoperimetric curves on hyperbolic surfaces. Zbl 0992.53048 1999 The hexagonal honeycomb conjecture. Zbl 0932.49032 Morgan, Frank 1999 Riemannian geometry. A beginner’s guide. 2nd ed. Zbl 0911.53001 Morgan, Frank 1998 Immiscible fluid clusters in $${\mathbb{R}}^2$$ and $${\mathbb{R}}^3$$. Zbl 0967.49026 Morgan, Frank 1998 Wulff clusters in $$\mathbb{R}^2$$. Zbl 0934.49024 Morgan, Frank; French, Christopher; Greenleaf, Scott 1998 Instability of the wet $$X$$ soap film. Zbl 0965.53012 Brakke, Kenneth; Morgan, Frank 1998 Lower semicontinuity of energy clusters. Zbl 0886.49016 Morgan, Frank 1997 An isoperimetric inequality for the thread problem. Zbl 0893.49029 Morgan, Frank 1997 Open problems in soap bubble geometry. Zbl 0867.53009 Sullivan, John M.; Morgan, Frank 1996 Geodesic nets on the $$2$$-sphere. Zbl 0871.53038 Hass, Joel; Morgan, Frank 1996 Curvy slicing proves that triple junctions locally minimize area. Zbl 0870.53006 Lawlor, Gary; Morgan, Frank 1996 Geodesics and soap bubbles in surfaces. Zbl 0865.53009 Hass, Joel; Morgan, Frank 1996 Geometric measure theory. A beginner’s guide. 2nd ed. Zbl 0819.49024 Morgan, Frank 1995 Volume-minimizing cycles in Grassmann manifolds. Zbl 0837.53035 Gluck, Herman; Mackenzie, Dana; Morgan, Frank 1995 Strict calibrations, constant mean curvature and triple junctions. Zbl 0867.53008 Morgan, Frank 1995 Paired calibrations applied to soap films, immiscible fluids, and surfaces or networks minimizing other norms. Zbl 0830.49028 Lawlor, Gary; Morgan, Frank 1994 The isoperimetric theorem for general integrands. Zbl 0923.49019 Brothers, John E.; Morgan, Frank 1994 Soap bubbles in $$\mathbb{R}^ 2$$ and in surfaces. Zbl 0820.53002 Morgan, Frank 1994 Clusters minimizing area plus length of singular curves. Zbl 0805.49025 Morgan, Frank 1994 $$(M,\varepsilon,\delta)$$-minimal curve regularity. Zbl 0804.49033 Morgan, Frank 1994 Surfaces minimizing area plus length of singular curves. Zbl 0816.49033 Morgan, Frank 1994 Mathematicians, including undergraduates, look at soap bubbles. Zbl 0814.53002 Morgan, Frank 1994 Riemannian geometry. A beginner’s guide. Zbl 0794.53001 Morgan, Frank 1993 Survey lectures on geometric measure theory. Zbl 0915.49025 Morgan, Frank 1993 Soap films and mathematics. Zbl 0804.53009 Morgan, Frank 1993 Minimal surfaces, crystals, shortest networks, and undergraduate research. Zbl 0765.52015 Morgan, Frank 1992 Calibrations and the size of Grassmann faces. Zbl 0766.53048 Morgan, Frank 1992 The cone over the Clifford torus in $$R^ 4$$ is $$\Phi$$-minimizing. Zbl 0725.49013 Morgan, Frank 1991 Singularities of minimal surfaces and networks and related extremal problems in Minkowski space. Zbl 0762.49014 Füredi, Z.; Lagarias, J. C.; Morgan, F. 1991 Calibrations and new singularities in area-minimizing surfaces: A survey. Zbl 0721.53058 Morgan, Frank 1990 Soap bubbles and soap films. Zbl 0774.53005 Morgan, Frank 1990 A sharp counterexample on the regularity of $$\Phi$$-minimizing hypersurfaces. Zbl 0696.49074 Morgan, Frank 1990 Calibrated geometries in Grassmann manifolds. Zbl 0681.53039 Gluck, Herman; Morgan, Frank; Ziler, Wolfgang 1989 Size-minimizing rectifiable currents. Zbl 0645.49024 Morgan, Frank 1989 Least-volume representatives of homology classes in $$G(2,C^ 4)$$. Zbl 0679.53060 Morgan, Frank 1989 Geometric measure theory. A beginner’s guide. Zbl 0671.49043 Morgan, Frank 1988 Area-minimizing surfaces, faces of Grassmannians, and calibrations. Zbl 0672.49028 Morgan, Frank 1988 Calibrations on $${\mathbb{R}}^ 8$$. Zbl 0666.49015 Dadok, J.; Harvey, R.; Morgan, F. 1988 Calibrations modulo $$\nu$$. Zbl 0618.49019 Morgan, Frank 1987 Harnack-type mass bounds and Bernstein theorems for area-minimizing flat chains modulo $$\nu$$. Zbl 0617.49019 Morgan, Frank 1986 The faces of the Grassmannian of 3-planes in $${\mathbb{R}}^ 7$$ (calibrated geometries on $${\mathbb{R}}^ 7)$$. Zbl 0556.53036 Harvey, Reese; Morgan, Frank 1986 A regularity theorem for minimizing hypersurfaces modulo $$\nu$$. Zbl 0641.49027 Morgan, Frank 1986 On finiteness of the number of stable minimal hypersurfaces with a fixed boundary. Zbl 0592.53004 Morgan, Frank 1986 The comass ball in $$\Lambda ^ 3({\mathbb{R}}^ 6)^$$. Zbl 0594.53045 Harvey, Reese; Morgan, Frank 1986 The exterior algebra $$\Lambda ^ kR^ n$$ and area minimization. Zbl 0585.49029 Morgan, Frank 1985 On finiteness of the number of stable minimal hypersurfaces with a fixed boundary. Zbl 0572.49021 Morgan, Frank 1985 Area-minimizing currents bounded by higher multiples of curves. Zbl 0541.49018 Morgan, Frank 1984 Examples of unoriented area-minimizing surfaces. Zbl 0509.53007 Morgan, Frank 1984 On the singular structure of three-dimensional, area-minimizing surfaces. Zbl 0557.49022 Morgan, Frank 1983 On the singular structure of three-dimensional, area-minimizing surfaces. Zbl 0529.49022 Morgan, Frank 1983 On the singular structure of two-dimensional area minimizing surfaces in $${\mathbb{R}}^ n$$. Zbl 0549.49029 Morgan, Frank 1982 Measures on spaces of surfaces. Zbl 0529.58031 Morgan, Frank 1982 ...and 5 more Documents all top 5 ### Cited by 981 Authors 52 Morgan, Frank 16 de Lima, Henrique F. 12 Novaga, Matteo 10 Milman, Emanuel 10 Paolini, Emanuele 10 Pratelli, Aldo 10 Swanepoel, Konrad J. 9 Ambrosio, Luigi 9 Chiacchio, Francesco 9 Rosales, César 8 Brock, Friedemann 8 Garcke, Harald 8 López Camino, Rafael 8 Maggi, Francesco 8 Nardulli, Stefano 8 Ritoré, Manuel 7 Mercaldo, Anna 7 Santos, Márcio S. 6 Lawlor, Gary R. 5 Bellettini, Giovanni 5 Brakke, Kenneth A. 5 Bucur, Dorin 5 Cañete, Antonio 5 Figalli, Alessio 5 Fragalà, Ilaria 5 Hieu, Doan The 5 Hutchings, Michael Lounsbery 5 Liang, Xiangyu 5 Posteraro, Maria Rosaria 5 Ros, Antonio 5 Velásquez, Marco Antonio Lázaro 4 Altin, Mustafa 4 Alvino, Angelo 4 Bouchitté, Guy 4 Bueno, Antonio 4 Buttazzo, Giuseppe 4 Caraballo, David G. 4 Dewar, Sean 4 Giga, Yoshikazu 4 Goldman, Michael 4 Hardt, Robert M. 4 Hass, Joel 4 Karadaǧ, Haci Bayram 4 Katz, Mikhail G. 4 Kazan, Ahmet 4 Koiso, Miyuki 4 Lê Hông Vân 4 Li, Haizhong 4 Marchese, Andrea 4 Mondino, Andrea 4 Mucci, Domenico 4 Neumayer, Robin 4 Oliveira, Arlandson Matheus Silva 4 Paolini, Maurizio 4 Pérez Muñoz, Joaquín 4 Petean, Jimmy 4 Ros-Oton, Xavier 4 Ruiz, Juan Miguel 4 Saracco, Giorgio 4 Stepanov, Eugene 4 Tanaka, Minoru 4 Topaloglu, Ihsan 4 Vernadakis, Efstratios 4 White, Brian Cabell 4 Yoon, Dae Won 3 Abels, Helmut 3 Alama, Stan 3 Alberti, Giovanni 3 Antonelli, Gioacchino 3 Arroja Neves, André 3 Batista, Márcio 3 Bérard, Pierre H. 3 Bronsard, Lia 3 Cabré, Xavier 3 Castro, Katherine 3 Chambolle, Antonin 3 Choksi, Rustum 3 Cinti, Eleonora 3 Conti, Sergio 3 Corneli, Joseph 3 Dadok, Jiri 3 de Lima, Eudes Leite 3 De Philippis, Guido 3 Delladio, Silvano 3 Filliman, Paul 3 Fonseca, Irene 3 Fusco, Nicola 3 Garroni, Adriana 3 Giaquinta, Mariano 3 He, Guoqing 3 Heilman, Steven M. 3 Helffer, Bernard 3 Ilias, Saïd 3 Ivanov, Sergei Vladimirovich 3 Kloeckner, Benoît R. 3 Le Nam, Tran 3 Leonardi, Gian Paolo 3 Li, Xingxiao 3 Lin, Fang Hua 3 Liu, Yangyang ...and 881 more Authors all top 5 ### Cited in 232 Serials 49 The Journal of Geometric Analysis 42 Calculus of Variations and Partial Differential Equations 35 Transactions of the American Mathematical Society 30 Proceedings of the American Mathematical Society 22 Archive for Rational Mechanics and Analysis 21 Advances in Mathematics 20 Duke Mathematical Journal 19 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 18 Annals of Global Analysis and Geometry 17 Journal of Mathematical Analysis and Applications 17 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 15 Inventiones Mathematicae 14 Geometriae Dedicata 14 Mathematische Annalen 14 Mathematische Zeitschrift 10 Journal of Differential Equations 10 Journal of Functional Analysis 10 Manuscripta Mathematica 9 Discrete & Computational Geometry 9 Journal de Mathématiques Pures et Appliquées. Neuvième Série 8 Annali di Matematica Pura ed Applicata. Serie Quarta 8 Journal für die Reine und Angewandte Mathematik 8 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 8 Differential Geometry and its Applications 7 Journal of Geometry and Physics 7 Comptes Rendus. Mathématique. Académie des Sciences, Paris 7 Advances in Calculus of Variations 6 Annales de l’Institut Fourier 6 Revista Matemática Iberoamericana 5 Communications in Mathematical Physics 5 Results in Mathematics 5 Geometric and Functional Analysis. GAFA 5 Experimental Mathematics 5 Bulletin of the Brazilian Mathematical Society. New Series 5 Analysis and Geometry in Metric Spaces 4 Communications on Pure and Applied Mathematics 4 Israel Journal of Mathematics 4 Journal of Computational Physics 4 Kodai Mathematical Journal 4 Memoirs of the American Mathematical Society 4 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 4 SIAM Journal on Mathematical Analysis 4 Journal of Mathematical Sciences (New York) 4 Geometry & Topology 4 Communications in Contemporary Mathematics 4 Communications on Pure and Applied Analysis 3 Bulletin of the Australian Mathematical Society 3 The Mathematical Intelligencer 3 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 3 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 3 Journal of Geometry 3 Mathematika 3 Pacific Journal of Mathematics 3 Acta Applicandae Mathematicae 3 Bulletin of the American Mathematical Society. New Series 3 Journal of Mathematical Imaging and Vision 3 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 3 Discrete and Continuous Dynamical Systems 3 Interfaces and Free Boundaries 3 Journal of the European Mathematical Society (JEMS) 3 Annales Henri Poincaré 3 Journal of Evolution Equations 3 Foundations of Computational Mathematics 3 Missouri Journal of Mathematical Sciences 2 Discrete Mathematics 2 Journal d’Analyse Mathématique 2 Journal of Mathematical Physics 2 Mathematical Proceedings of the Cambridge Philosophical Society 2 Rocky Mountain Journal of Mathematics 2 Acta Mathematica 2 Archiv der Mathematik 2 Illinois Journal of Mathematics 2 Journal of Differential Geometry 2 Journal of Economic Theory 2 Journal of the Mathematical Society of Japan 2 Networks 2 Rendiconti del Circolo Matemàtico di Palermo. Serie II 2 Rendiconti del Seminario Matematico della Università di Padova 2 Tôhoku Mathematical Journal. Second Series 2 European Journal of Combinatorics 2 Advances in Applied Mathematics 2 Ergodic Theory and Dynamical Systems 2 Journal of the American Mathematical Society 2 Annals of Operations Research 2 The Annals of Applied Probability 2 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 2 Communications in Partial Differential Equations 2 Linear Algebra and its Applications 2 Expositiones Mathematicae 2 Potential Analysis 2 Bulletin of the Belgian Mathematical Society - Simon Stevin 2 St. Petersburg Mathematical Journal 2 Electronic Research Announcements of the American Mathematical Society 2 The Journal of Fourier Analysis and Applications 2 Abstract and Applied Analysis 2 Conformal Geometry and Dynamics 2 Journal of Inequalities and Applications 2 Annals of Mathematics. Second Series 2 Acta Mathematica Sinica. English Series 2 Journal of High Energy Physics ...and 132 more Serials all top 5 ### Cited in 51 Fields 418 Differential geometry (53-XX) 343 Calculus of variations and optimal control; optimization (49-XX) 115 Partial differential equations (35-XX) 105 Global analysis, analysis on manifolds (58-XX) 86 Convex and discrete geometry (52-XX) 55 Measure and integration (28-XX) 35 Functional analysis (46-XX) 34 Geometry (51-XX) 31 Probability theory and stochastic processes (60-XX) 29 Manifolds and cell complexes (57-XX) 26 Operations research, mathematical programming (90-XX) 25 Mechanics of deformable solids (74-XX) 23 Statistical mechanics, structure of matter (82-XX) 22 Real functions (26-XX) 22 Numerical analysis (65-XX) 21 Combinatorics (05-XX) 20 Fluid mechanics (76-XX) 17 Dynamical systems and ergodic theory (37-XX) 13 Computer science (68-XX) 12 Potential theory (31-XX) 12 Relativity and gravitational theory (83-XX) 9 Functions of a complex variable (30-XX) 9 Several complex variables and analytic spaces (32-XX) 8 Ordinary differential equations (34-XX) 8 Statistics (62-XX) 8 Quantum theory (81-XX) 7 Algebraic geometry (14-XX) 7 Group theory and generalizations (20-XX) 7 Biology and other natural sciences (92-XX) 6 Linear and multilinear algebra; matrix theory (15-XX) 6 Operator theory (47-XX) 6 General topology (54-XX) 6 Algebraic topology (55-XX) 5 Mechanics of particles and systems (70-XX) 5 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 5 Information and communication theory, circuits (94-XX) 4 Topological groups, Lie groups (22-XX) 4 Difference and functional equations (39-XX) 4 Systems theory; control (93-XX) 2 General and overarching topics; collections (00-XX) 2 Mathematical logic and foundations (03-XX) 2 Approximations and expansions (41-XX) 2 Integral transforms, operational calculus (44-XX) 2 Classical thermodynamics, heat transfer (80-XX) 2 Mathematics education (97-XX) 1 History and biography (01-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Number theory (11-XX) 1 Nonassociative rings and algebras (17-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Integral equations (45-XX) ### Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata.	2022-10-07T09:27:30	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.44622981548309326, "perplexity": 5951.03797885492}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030338001.99/warc/CC-MAIN-20221007080917-20221007110917-00776.warc.gz"}
https://www.rba.gov.au/publications/bulletin/2019/jun/can-structural-change-account-for-the-low-level-of-non-mining-investment.html	# Bulletin – June 2019 Australian Economy Can Structural Change Account for the Low Level of Non-mining Investment? ## Abstract No, it cannot. Non-mining firms have invested less over the past decade, relative to their output, than they did over the previous two decades, and this decline in investment intensity has been broad based across firms. This reduced investment could contribute to slower economic growth, if, for example, it is associated with decreased adoption of new technologies. This article looks into potential driving forces behind the decline in the rate of investment, finding that it cannot be explained by shifts in industry structure, or the composition of firms by age or date of formation. The size of the decline is consistent with what would be expected given slower technological progress and lower depreciation rates. But there might be other, more cyclical reasons for the observed slowdown in non-mining investment. ## Introduction The production of goods and services typically relies on the use of both capital (e.g. buildings, machinery & equipment, computer software) and labour inputs. To expand production, firms can either increase their stock of capital, hire additional workers, or find ways to use existing inputs more efficiently. Since firms' investment decisions affect their stock of capital, investment is a key channel through which the economy can grow its productive capacity. Over the past decade, non-mining firms have tended to invest less intensively than they did in the preceding two decades. In the decade leading up to the Global Financial Crisis (GFC), firms in the non-mining sector invested, on average, between 14 and 16 cents per dollar of output. In the post-GFC period this has declined to between 10 and 12 cents of investment per dollar of output (Graph 1). To put this into context, if non-mining firms invested with a similar intensity today as they did before the GFC, non-mining investment would have been around \$54 billion, or one-third, higher in 2017/18 than was actually observed. The slowdown in investment is not unique to Australia; following the GFC, many advanced economies have recorded weaker capital expenditure than expected (CEA, 2017). The decline in the economy's investment intensity could have wide-ranging consequences. For example, to the extent that lower investment leads to slower growth in the capital stock, growth in output per worker (also known as labour productivity) is also likely to slow unless there are offsetting technological improvements. All things being equal, this would tend to put downward pressure on wage growth. Moreover, if firms tend to invest in new and more productive capital, a decline in the rate of investment could contribute to a lower rate of technological advancement, and therefore slower economic growth. Given the possible consequences, we are interested in understanding what has driven the decline in the economy's investment intensity in the past decade. In doing so, we build on past work by van der Merwe et al (2018), which provided an overview of, and evidence regarding, a wide range of potential explanations for the decline in investment intensity. In the first part of this article, we revisit whether changes in industry structure can explain the decline, as well as examining a potential role for changes in the age and cohort composition of firms in the economy. We do this using firm-level tax data from the Business Longitudinal Analysis Data Environment (BLADE), which is ideally suited to such an analysis.[1] Having demonstrated that compositional change explains only a very small share of the decline in the economy's investment intensity since the GFC, and that the decline is apparent across most firms irrespective of their characteristics, we then consider other explanations. In particular, we present a simple theoretical model of the economy's (long-run) investment intensity. Using this model and aggregate data, we demonstrate that the combination of a slowdown in technological progress and a lower depreciation rate can potentially explain a large share of the decline in the non-mining sector's investment intensity. Throughout this article, we focus on nominal (rather than real) investment as a share of output. Nominal data are considered more appropriate given difficulties in comparing the level of real investment over time and across industries, particularly due to the large changes in technology over recent decades and the significant shifts in the relative prices of investment goods that have accompanied these changes. However, given real investment has also been relatively subdued in recent years, this focus on nominal data is unlikely to substantially affect our conclusions. ## Compositional Change ### Industry structure If economic activity shifts away from investment-intensive sectors, such as manufacturing, to sectors with lower intensities, such as services, then, in principle, this could account for a decline in the overall (non-mining) investment intensity (Adeney, 2018, van der Merwe et al 2018). But although economic activity has shifted in this way over the decades, the shift accounts for only a small part of the more recent decline in investment intensity; most of the decline has occurred within sectors. Previous research showed this for broad sectors such as manufacturing and services, using National Accounts data (van der Merwe et al (2018); Graph 2). We confirm that this finding is also true for more disaggregated industry groupings using firm-level data from BLADE.[2] That is, the decline in investment intensity has not occurred because activity had shifted within sectors to less investment-intensive industries in each sector. To demonstrate this finding, we show results for four sectors that account for much of the decline in the aggregate investment intensity based on firm-level data. These sectors are: transport, ‘rental, hiring and real estate’ (RHRE), construction and manufacturing. We find that for three of the sectors we examine – transport, RHRE and construction – compositional change has actually contributed positively to investment intensity (Table 1). The manufacturing sector is an exception: around one-third of the decline in its investment intensity is explained by changes in the type of manufacturing done now, compared with the pre-GFC period. In particular, shifts away from ‘traditional’ manufacturing industries such as non-ferrous metal manufacturing, aluminium smelting and motor vehicle manufacturing appear to have played some role. Table 1: BLADE Non-mining Investment Intensity Cumulative change from 2007/08 to 2014/15, percentage points Total Within-industry effect Compositional effect Total Non-mining −0.99 −1.21 0.22 Transport −5.50 −7.30 1.80 Rental, hiring & real estate −5.41 −6.12 0.71 Manufacturing −0.84 −0.56 −0.27 Construction −1.27 −1.31 0.03 Sources: ABS; RBA ### Investment intensity over the firm lifecycle At a high level, there are two potential explanations for the broad-based declines in the investment intensities of industries: either they reflect some sort of compositional shift between firms, such as an increase in the prevalence of older, less investment-intensive firms; or they reflect broad-based declines in the investment intensities of all firms. We consider two potential compositional shifts, both of which are motivated by overseas evidence. The first is a shift in the age distribution of firms. As we will show, young firms are typically more investment intensive than mature firms. This finding is intuitive, given young firms need to buy machinery, fit out their shop or purchase other capital goods before they can ramp up production. Accordingly, any shift in economic activity away from young firms, and towards older firms, could weigh on the economy's aggregate investment intensity. Other research has noted a trend of declining firm entry rates both in Australia (Productivity Commission, 2015) and overseas (Pugsley, Sahin & Karahan 2015). Lower firm entry rates will mean fewer young firms and, all else being equal, this could potentially contribute to a decline in the economy's investment intensity. The second compositional shift we consider is a change in the cohort composition of firms. Firms ‘born’ at different points in time could have inherently different investment intensities. For example, firms born during periods of weak economic growth, such as the GFC, may be inherently less investment intensive than firms born during other periods. This would be consistent with evidence from the United States, which shows that firms born during the GFC remained smaller than firms born during other periods (Moreira, 2017). As such, this could contribute to the decline in the economy's investment intensity, if firms from low-intensity cohorts start to make up an increasingly large share of the economy. To quantify age and cohort effects, we use an age-period-cohort (APC) model with firm-level data from BLADE. APC models are useful in this context because they allow us to separately identify the effects of ageing from the effects of belonging to a particular cohort, or of being observed in a particular time period.[3] We start by considering age effects. Our results show that firms are most investment intensive in their first year of life and that the sharpest drop-off occurs as they move from their first to second year of existence (Graph 3). Firms' investment intensities continue to decline for a few years, but then flatten out from the age of five onwards. Moreover, the share of output produced by young firms (defined here as between 1 and 5 years of age) has declined by around 4 percentage points relative to the pre-GFC period. At face value, the two observations together would suggest that age effects could be important in explaining the decline in the economy's investment intensity. However, we estimate that the reduction in the share of output accounted for by young firms explains at most 10 per cent of the total decline.[4] In terms of cohort composition, we want to consider whether firms born or established during periods of low growth, such as in the GFC period, have permanently lower investment intensities. While we do find some weak evidence that firms born during periods of slower economic growth tend to be less investment intensive than other firms, this is not particularly robust to different modelling choices. Further, these ‘cohort’ effects are not economically significant. Firms born during the GFC are estimated to be only slightly less investment intensive than firms established during more normal economic conditions. Further, since firms born during the GFC make up only a very small portion of the economy, their effect on the aggregate non-mining investment intensity is close to zero. Taken together, our results do not provide evidence of significant compositional effects at the firm level. Rather, they suggest that the decline in the non-mining sector's aggregate investment intensity has been broad based across all firms. To demonstrate this further, we can examine the estimated year effects from the model. Year effects capture the (weighted) average investment intensity across all firms in a given period, after we account for other relevant factors such as their age, cohort and industry. As a result, they can be thought of as capturing any aggregate factors that affect all firms equally at a given period in time. The estimated year effects have been consistently negative since 2008/09, suggesting that, on average, all firms have tended to be less investment intensive than expected, given factors such as their age and cohort (Graph 4). Moreover, the magnitude of the effects is similar to the overall decline in the aggregate investment intensity in BLADE (see Graph A1). This is consistent with earlier findings that there is little role for compositional change in explaining the decline in the economy's investment intensity. ## Long-run Determinants of Non-mining (Market Sector) Investment[5] Because the decline in firms' investment intensity appears to be broadly based, there may be some economy-wide factors that have been depressing firms' investment intensity. One useful starting place to look for such factors is to examine the theoretical determinants of an economy's investment intensity – those factors that would be expected to determine the economy's investment intensity in the long run. In this section, we focus our analysis on the non-mining market sector, which excludes health, education and public administration. We do this to avoid complications related to measuring productivity growth in the non-market sector. The trends in investment intensity are similar to those in the overall non-mining sector, although the decline has been more pronounced in the non-mining market sector. As discussed in Jenner et al (2018), using a simple theoretical model, the non-mining economy's long-run investment-to-output ratio should depend on three things: the economy's capital-to-output ratio; the growth rate of output, which in turn will be a function of productivity growth and growth in inputs; and depreciation rates.[6] This reflects the fact that additional investment will be required to both support future economic growth and to replace worn-out capital. Below we consider each of the three factors and how they have changed over time. We note here that this exercise is descriptive in nature and focuses on the long run, and that there may be other factors outside of our stylised model that can help to explain the observed decline in investment intensity. First, we consider the capital-to-output ratio. Economic growth theory suggests that the capital-to-output ratio should be constant over time, which appears to be broadly true in the Australian data, at least over our sample period (Graph 5). This suggests that changes in the ratio cannot explain the decline in the investment-to-output ratio in the past decade. For the rest of the analysis, we assume that the capital-to-output ratio is equal to the average capital-to-output over the sample, which is about 2. A ratio of 2 indicates that, on average, firms require two dollars of capital – such as buildings, motor vehicles or computer hardware – to produce one dollar of output each year. The growth rate of non-mining output is the second determinant of investment intensity in our model. The growth rate of output is important because changes in production and capital must match each other over time if the capital-to-output ratio is to remain constant. Therefore, the faster (slower) that output expands, the more (less) investment will be required to increase the stock of capital. Economic theory suggests that, in the long run, the growth rate of output is determined by growth in productivity and growth in the supply of labour. Graphs 6 and 7 show both determinants, and provide some evidence of lower productivity growth over the past decade, although the precise magnitude of the slowdown is sensitive to the reference period. More generally, a slowdown in productivity growth has been widely documented both in Australian and overseas (D'Arcy and Gustafsson, 2012; McCririck and Rees, 2016), with some overseas research also finding that the decline in productivity growth preceded the GFC (Fernald et al, 2017). The final component of our calculation is the depreciation rate. The depreciation rate measures the amount of firms' capital that is ‘consumed’ or ‘worn out’ in a given period. In our model, some investment is required simply to offset depreciation and to maintain the value of the existing stock of capital. The ABS measure of the depreciation rate for the non-mining market sector has declined notably since the early 2000s, implying that less investment is required to maintain the existing capital stock than used to be the case (Graph 8). The decline in the depreciation rate largely reflects a compositional shift in the capital stock towards longer lived assets, such as buildings & engineering structures (i.e. office towers, roads and railways), which tend to be replaced less often than other types of capital, such as machinery & equipment. To quantify the effects of these three factors, we can use them to construct an estimate of the long-run investment intensity of the non-mining market sector that we would expect the economy to eventually reach over time.[7] We estimate that the non-mining market sector's long-run investment intensity has decreased by about 5 percentage points over the sample, driven by weaker multifactor productivity growth and a lower depreciation rate (Graph 9). This suggests that declining rates of (long-run) output growth and depreciation could explain most of the recent decline in the economy's investment intensity. Despite this, we can't rule out the possibility that other cyclical factors may have also weighed on investment intensity in recent years. For example, an increase in risk premiums or risk aversion may have also depressed firms' investment over the post-GFC period. ## Conclusion We find that the decrease in the economy's investment intensity has been broad based across most firms and that shifts in the industry, age or cohort composition of firms have not had a material impact. This is consistent with a lower long-run investment intensity for the entire non-mining market sector. We estimate that the economy's long-run investment intensity has declined over the past decade, reflecting weak multifactor productivity growth and a lower depreciation rate. ## Appendix A For our analysis of compositional change, we use longitudinal firm-level data from BLADE. Our measures of investment and output are both derived from firms' Business Activity Statements (BAS). We define the investment-to-output ratio as firms' capital expenditure divided by their gross output. The sample covers 2001/02 to 2014/15. For all analysis using BLADE, we exclude firms: • in the finance and utilities divisions due to conceptual issues with the calculation of gross output, as well as public sector organisations; • in a handful of industries where the data appears suspect. For our analysis of firm age and cohort effects, we also exclude firms: • with an investment-to-output ratio above the 99th percentile (around 160 per cent); • born prior to 1980 and after 2013 due to the small sample size of firms born outside of this period. Further, we combine the BAS data with data on the date of firm formation, which we use to calculate firms' ages. One feature of the data, however, is that there is a substantial increase in the coverage of firms born from 2001/02 onwards.[8] This will initially inflate the measured share of output produced by young firms in our sample. Moreover, this bias will tend to decline over time, as additional observations with improved firm coverage become available. The effect of this will be to exaggerate the decline in the share of output produced by young firms from 2001/02 onwards, likely causing us to overstate the effect of an ageing business population. ## Appendix B We want to decompose the decrease in the aggregate investment intensity into: 1. A compositional effect that is due to industries with a low investment intensity growing faster than the average division. 2. Within-industry effects, which are due to investment intensities within industries decreasing. Denoting industries as x, first we note that the aggregate investment intensity, $\frac{{I}_{t}}{{Y}_{t}}$ ,can be expressed as the sum of the individual industries' ratios, ${r}_{x,t}$ , weighted by their shares of total output, ${w}_{x,t}$ : $I t Y t = ∑ x I x , t ∑ x Y x , t$ $I t Y t = ∑ x I x , t Y x , t * Y x , t ∑ x Y x , t$ $I t Y t = ∑ x r x , t w x , t$ The change in the aggregate investment intensity over some period, $j$ , is then: The within-industry effect, $WE$ , is calculated by assuming that the weights are unchanged across the two periods (at their average level): The compositional effect, $C{E}_{t}$ , is calculated similarly, by assuming the industry investment intensities remain unchanged: ## Appendix C To estimate the firm-level effect of age and cohort, we estimate an Age-Period-Cohort (APC) model. In APC models, age effects capture lifecycle patterns, period effects capture aggregate shocks that affect all firms at a given point in time, and birth cohort effects capture differences in investment-intensities across generations. The APC model shows the outcome of interest for firm i at time t as the sum of age, year and cohort dummies, and an error term: Since there is an exact linear relationship between age, time and cohort (i.e. age = year – cohort), all three components cannot be identified at the same time. We take two different approaches to address this issue: 1. Estimate a fixed effects model, which strips out firm-specific time-invariant factors such as their birth cohort. 2. Replace the cohort dummy variable with a proxy variable that captures economic conditions in the year the firm was born. Our main proxy variable is real gross national expenditure growth. For both models, we include an additional control variable for firm size, measured as employment.[9] For the second approach, we also include a number of time-invariant controls, including firm's legal structure (i.e. company or unincorporated), industry (measured at the 4-digit ANZSIC level), and location (at the state level). To calculate the effect of changes in composition of firms' age on the aggregate investment intensity, we need to weight the estimated age coefficients from our regression results by the share of output accounted for by firms of different ages. Doing so gives us a ‘weighted average age coefficient’ (WAAC). We construct this measure for pre- and post-GFC periods. The difference between the pre- and post-GFC WAAC can then be interpreted as the effect of ageing on the aggregate investment intensity, assuming that estimated age coefficients are constant across the two periods. Or more precisely, Where, • $j$ is firm age • $w$ is age j's share of output in the post-GFC period (2012 to 2015) • $\mu$ is age j's share of output in the pre-GFC period (2007 to 2008) ## Appendix D We use a Cobb-Douglas production function to analyse long-run investment intensity in the private non-mining market sector: $Y = A K ( 1 − α ) L α$ Where, • ${Y}_{t}$ is non-mining market sector output • ${A}_{t}$ is non-mining market sector multi-factor productivity (MFP) • ${K}_{t}$ is the non-mining market sector capital stock • ${L}_{t}$ is non-mining market sector labour inputs • $\alpha$ is the labour share of income In the steady state, the above equation becomes:[10] Where, • ${g}_{\alpha }$ is non-mining market sector MFP growth • $\text{Δ}$ indicates growth rates • $$ gives the steady state Over our sample, technological progress seems to have been approximately “neutral” in the sense that it has not changed the capital-to-output ratio. This implies that the steady-state growth rate of both output and capital are equal. This implies that: $Δ Y = Δ K * = g α α + g L$ Where, • ${g}_{L}$ is the exogenous growth rate of labour supply We can now use the capital accumulation identity to relate the potential growth rate of output to the rate of investment. The capital accumulation identity is written as: Where, • ${K}_{t}$ is the non-mining market sector capital stock • ${I}_{t}$ is non-mining market sector gross fixed capital formation • ${\delta }_{t}$ is the depreciation rate We can now use $\text{Δ}{K}_{t}=\frac{{I}_{t}-\delta {K}_{t}}{{K}_{t}}$ to give the long-run investment-to-output ratio: $( I Y ) * = ( K Y ) * × ( I K ) $ We assume that $\alpha =0.60$ in all periods, while all other values are taken directly from the annual national accounts. ## Footnotes The authors completed this work in Economic Analysis Department. We would like to thank Leon Berkelmans, Mark Chambers, Gianni La Cava, Peter Tulip and Michelle van der Merwe for helpful comments and feedback. [] See Appendix A for details on the adjustments we have made to the BLADE data prior to analysis. [1] For evidence that the BLADE data are suitably comparable to the National Accounts data, see Appendix A. We consider changes in industry structure at the 4-digit Australian and New Zealand Standard Industrial Classification (ANZSIC) level. Details of the calculation can be found in Appendix B. [2] More details on this model and its estimation are included in Appendix C. [3] Even this is likely to be an overstatement of the role of ageing, given data coverage issues that we discuss in more detail in Appendix A. [4] This section of the article is an update of previous internal RBA work by Leon Berkelmans and Gareth Spence. [5] For details see Appendix D. [6] In our model, the economy’s long-run investment intensity is calculated as the long-run (or potential) growth rate of output plus the depreciation rate, multiplied by the capital-to-output ratio. The ratio is surprisingly high, reflecting inconsistencies in the coverage of our investment, capital, and output measures. Nevertheless, this is unlikely to substantially affect the changes in the ratio, which tend to broadly track the observed non-mining investment-to-output ratio. [7] The increase in coverage is also non-random in nature; for example, unincorporated firms make up just 5 per cent of firms born in 2000/01 but account for 51 per cent of new firms in 2001/02. [8] Employment is measured as the number of full-time equivalent employees. [9] As we focus on the long-run, we assume that the prices of investment goods, the capital stock, and output all grow at the same rate. Moreover, for ease of exposition we abstract from relative prices, and so the distinction between nominal and real quantities. [10] ## References Adeney R (2018), ‘Structural Change in the Australian Economy’, RBA Bulletin, March, viewed 6 June 2019. CEA (Council of Economic Advisors) (2017), ‘Chapter 2: The Year in Review and the Years Ahead’, Economic Report of the President. D'Arcy P and L Gustafsson (2012), ‘Australia's Productivity Performance and Real Incomes’, RBA Bulletin, June, pp 23–35. Fernald J, R Hall, J Stock and M Watson (2017), ‘The Disappointing Recovery of Output after 2009’, Brookings Papers on Economic Activity, 2017(1), pages 1–81. Jenner K, A Walker, C Close and T Saunders (2018), ‘Mining Investment Beyond the Boom’, RBA Bulletin, March, viewed 6 June 2019. McCririck R and D Rees (2016), ‘The Slowdown in US Productivity Growth: Breaks and Beliefs’, RBA Research Discussion Paper No 2016-08. Moreira, S (2017), ‘Firm Dynamics, Persistent Effects of Entry Conditions, and Business Cycles’, Center for Economic Studies, US Census Bureau. Productivity Commission (2015), ‘Business Set-up, Transfer and Closure’, Inquiry Report, September. Pugsley B, S Aysegul and F Karahan (2015), ‘Understanding the 30 year Decline in Business Dynamism: a General Equilibrium Approach’, 2015 Meeting Papers 1333, Society for Economic Dynamics. van der Merwe M, L Cockerell, M Chambers and J Jääskelä (2018), ‘Private Non-mining Investment in Australia’, RBA Bulletin, June, viewed 6 June 2019.	2020-06-04T22:50:39	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 29, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.47326523065567017, "perplexity": 2664.4784175075083}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-24/segments/1590348492295.88/warc/CC-MAIN-20200604223445-20200605013445-00021.warc.gz"}
https://pdglive.lbl.gov/DataBlock.action?node=S054CTN	# SCALE LIMITS for Contact Interactions: $\Lambda\mathrm {( {{\boldsymbol \ell}} {{\boldsymbol \nu}} {{\boldsymbol \ell}} {{\boldsymbol \nu}} )}$ INSPIRE search VALUE (TeV) CL% DOCUMENT ID TECN COMMENT $\bf{>3.10}$ 90 1 1986 SPEC $\Lambda_{LR}^{\pm}$( ${{\mathit \nu}_{{\mu}}}{{\mathit \nu}_{{e}}}{{\mathit \mu}}{{\mathit e}}$ ) • • • We do not use the following data for averages, fits, limits, etc. • • • $>3.8$ 2 1994 RVUE $\Lambda_{LL}^+$( ${{\mathit \tau}}{{\mathit \nu}_{{\tau}}}{{\mathit e}}{{\mathit \nu}_{{e}}}$ ) $>8.1$ 2 1994 RVUE $\Lambda_{LL}^-$( ${{\mathit \tau}}{{\mathit \nu}_{{\tau}}}{{\mathit e}}{{\mathit \nu}_{{e}}}$ ) $>4.1$ 3 1994 RVUE $\Lambda_{LL}^+$( ${{\mathit \tau}}{{\mathit \nu}_{{\tau}}}{{\mathit \mu}}{{\mathit \nu}_{{\mu}}}$ ) $>6.5$ 3 1994 RVUE $\Lambda_{LL}^-$( ${{\mathit \tau}}{{\mathit \nu}_{{\tau}}}{{\mathit \mu}}{{\mathit \nu}_{{\mu}}}$ ) 1 JODIDIO 1986 limit is from ${{\mathit \mu}^{+}}$ $\rightarrow$ ${{\overline{\mathit \nu}}_{{\mu}}}{{\mathit e}^{+}}{{\mathit \nu}_{{e}}}$ . Chirality invariant interactions $\mathit L$ = ($\mathit g{}^{2}/\Lambda {}^{2}$) $\lbrack{}{{\mathit \eta}}_{\mathit LL}$ (${{\overline{\mathit \nu}}_{{ {{\mathit \mu}} {{\mathit L}} }}}{{\mathit \gamma}}{}^{\alpha }{{\mathit \mu}_{{L}}}$) (${{\overline{\mathit e}}_{{L}}}{{\mathit \gamma}}_{\alpha }{{\mathit \nu}_{{ {{\mathit e}} {{\mathit L}} }}}$) $+$ ${{\mathit \eta}_{{LR}}}$ (${{\overline{\mathit \nu}}_{{ {{\mathit \mu}} {{\mathit L}} }}}{{\mathit \gamma}}{}^{\alpha }{{\mathit \nu}_{{ {{\mathit e}} {{\mathit L}} }}}$ (${{\overline{\mathit e}}_{{R}}}{{\mathit \gamma}_{{\alpha}}}{{\mathit \mu}_{{R}}})\rbrack{}$ with $\mathit g{}^{2}/4{{\mathit \pi}}$ = 1 and (${{\mathit \eta}}_{\mathit LL},{{\mathit \eta}}_{\mathit LR}$) = (0,$\pm{}$1) are taken. No limits are given for $\Lambda {}^{\pm{}}_{\mathit LL}$ with (${{\mathit \eta}}_{\mathit LL},{{\mathit \eta}}_{\mathit LR}$) = ($\pm{}$1,0). For more general constraints with right-handed neutrinos and chirality nonconserving contact interactions, see their text. 2 DIAZCRUZ 1994 limits are from $\Gamma\mathrm {( {{\mathit \tau}} \rightarrow {{\mathit e}} {{\mathit \nu}} {{\mathit \nu}} )}$ and assume flavor-dependent contact interactions with $\Lambda\mathrm {( {{\mathit \tau}} {{\mathit \nu}_{{\tau}}} {{\mathit e}} {{\mathit \nu}_{{e}}} )}{}\ll\Lambda\mathrm {( {{\mathit \mu}} {{\mathit \nu}_{{\mu}}} {{\mathit e}} {{\mathit \nu}_{{e}}} )}$. 3 DIAZCRUZ 1994 limits are from $\Gamma\mathrm {( {{\mathit \tau}} \rightarrow {{\mathit \mu}} {{\mathit \nu}} {{\mathit \nu}} )}$ and assume flavor-dependent contact interactions with $\Lambda\mathrm {( {{\mathit \tau}} {{\mathit \nu}_{{\tau}}} {{\mathit \mu}} {{\mathit \nu}_{{\mu}}} )}{}\ll\Lambda\mathrm {( {{\mathit \mu}} {{\mathit \nu}_{{\mu}}} {{\mathit e}} {{\mathit \nu}_{{e}}} )}$. References: DIAZCRUZ 1994 PR D49 2149 Limits on the Scale of Compositeness from Leptonic ${{\mathit \tau}}$ Decays JODIDIO 1986 PR D34 1967 Search for Right Handed Currents in Muon Decay	2020-11-29T07:52:00	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9557309150695801, "perplexity": 7584.322681227065}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-50/segments/1606141197278.54/warc/CC-MAIN-20201129063812-20201129093812-00460.warc.gz"}

Subsets and Splits

No community queries yet

The top public SQL queries from the community will appear here once available.