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https://large-numbers.fandom.com/wiki/Weak_factorial?oldid=5236
## FANDOM 1,138 Pages The weak factorial is a factorial-related function so-named by Cookie Fonster. It is equal to the least smallest number divisible by all numbers 1 through x. [1] Formally: $$wf(x) = LCM(x, wf(x-1))$$ $$wf(1) = 1$$ The first ten weak factorial numbers are 1, 2, 6, 12, 60, 60, 420, 840, 2520, and 2,520. It can be shown that value of this function increases only at arguments which are prime powers. Because of that, there will be long runs where the function is constant. This function can be shown to be equal to $$e^{\psi(x)}$$, where $$\psi(x)$$ is the second Chebyshev function, so as a collorary from prime number theorem, it can be approximated by ex. ### SourcesEdit 1. Pointless Large Number Stuff by Cookiefonster, entry on 420 Community content is available under CC-BY-SA unless otherwise noted.
2020-08-04T16:56:51
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https://lammps.sandia.gov/doc/pair_resquared.html
# pair_style resquared command Accelerator Variants: resquared/gpu, resquared/omp ## Syntax pair_style resquared cutoff • cutoff = global cutoff for interactions (distance units) ## Examples pair_style resquared 10.0 pair_coeff * * 1.0 1.0 1.7 3.4 3.4 1.0 1.0 1.0 ## Description Style resquared computes the RE-squared anisotropic interaction (Everaers), (Babadi) between pairs of ellipsoidal and/or spherical Lennard-Jones particles. For ellipsoidal interactions, the potential considers the ellipsoid as being comprised of small spheres of size $$\sigma$$. LJ particles are a single sphere of size $$\sigma$$. The distinction is made to allow the pair style to make efficient calculations of ellipsoid/solvent interactions. Details for the equations used are given in the references below and in this supplementary document. Use of this pair style requires the NVE, NVT, or NPT fixes with the asphere extension (e.g. fix nve/asphere) in order to integrate particle rotation. Additionally, atom_style ellipsoid should be used since it defines the rotational state and the size and shape of each ellipsoidal particle. 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: • A12 = Energy Prefactor/Hamaker constant (energy units) • $$\sigma$$ = atomic interaction diameter (distance units) • $$\epsilon_{i,a}$$ = relative well depth of type I for side-to-side interactions • $$\epsilon_{i,b}$$ = relative well depth of type I for face-to-face interactions • $$\epsilon_{i,c}$$ = relative well depth of type I for end-to-end interactions • $$\epsilon_{j,a}$$ = relative well depth of type J for side-to-side interactions • $$\epsilon_{j,b}$$ = relative well depth of type J for face-to-face interactions • $$\epsilon_{j,c}$$ = relative well depth of type J for end-to-end interactions • cutoff (distance units) The parameters used depend on the type of the interacting particles, i.e. ellipsoids or LJ spheres. The type of a particle is determined by the diameters specified for its 3 shape parameters. If all 3 shape parameters = 0.0, then the particle is treated as an LJ sphere. The $$\epsilon_{i,*}$$ or $$\epsilon_{j,*}$$ parameters are ignored for LJ spheres. If the 3 shape parameters are > 0.0, then the particle is treated as an ellipsoid (even if the 3 parameters are equal to each other). A12 specifies the energy prefactor which depends on the types of the two interacting particles. For ellipsoid/ellipsoid interactions, the interaction is computed by the formulas in the supplementary document referenced above. A12 is the Hamaker constant as described in (Everaers). In LJ units: $A_{12} = 4\pi^2\epsilon_{\mathrm{LJ}}(\rho\sigma^3)^2$ where $$\rho$$ gives the number density of the spherical particles composing the ellipsoids and $$\epsilon_{\mathrm{LJ}}$$ determines the interaction strength of the spherical particles. For ellipsoid/LJ sphere interactions, the interaction is also computed by the formulas in the supplementary document referenced above. A12 has a modified form (see here for details): $A_{12} = 4\pi^2\epsilon_{\mathrm{LJ}}(\rho\sigma^3)$ For ellipsoid/LJ sphere interactions, a correction to the distance- of-closest approach equation has been implemented to reduce the error from two particles of disparate sizes; see this supplementary document. For LJ sphere/LJ sphere interactions, the interaction is computed using the standard Lennard-Jones formula, which is much cheaper to compute than the ellipsoidal formulas. A12 is used as epsilon in the standard LJ formula: $A_{12} = \epsilon_{\mathrm{LJ}}$ and the specified $$\sigma$$ is used as the $$\sigma$$ in the standard LJ formula. When one of both of the interacting particles are ellipsoids, then $$\sigma$$ specifies the diameter of the continuous distribution of constituent particles within each ellipsoid used to model the RE-squared potential. Note that this is a different meaning for $$\sigma$$ than the pair_style gayberne potential uses. The $$\epsilon_i$$ and $$\epsilon_j$$ coefficients are defined for atom types, not for pairs of atom types. Thus, in a series of pair_coeff commands, they only need to be specified once for each atom type. Specifically, if any of $$\epsilon_{i,a}$$, $$\epsilon_{i,b}$$, $$\epsilon_{i,c}$$ are non-zero, the three values are assigned to atom type I. If all the $$\epsilon_i$$ values are zero, they are ignored. If any of $$\epsilon_{j,a}$$, $$\epsilon_{j,b}$$, $$\epsilon_{j,c}$$ are non-zero, the three values are assigned to atom type J. If all three $$\epsilon_i$$ values are zero, they are ignored. Thus the typical way to define the $$\epsilon_i$$ and $$\epsilon_j$$ coefficients is to list their values in “pair_coeff I J” commands when I = J, but set them to 0.0 when I != J. If you do list them when I != J, you should insure they are consistent with their values in other pair_coeff commands. Note that if this potential is being used as a sub-style of pair_style hybrid, and there is no “pair_coeff I I” setting made for RE-squared for a particular type I (because I-I interactions are computed by another hybrid pair potential), then you still need to insure the epsilon a,b,c coefficients are assigned to that type in a “pair_coeff I J” command. For large uniform molecules it has been shown that the $$\epsilon_{*,*}$$ energy parameters are approximately representable in terms of local contact curvatures (Everaers): $\epsilon_a = \sigma \cdot { \frac{a}{ b \cdot c } }; \epsilon_b = \sigma \cdot { \frac{b}{ a \cdot c } }; \epsilon_c = \sigma \cdot { \frac{c}{ a \cdot b } }$ where a, b, and c give the particle diameters. The last coefficient is optional. If not specified, the global cutoff specified in the pair_style command is used. 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 on the Speed packages doc page. 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 Build package doc page 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 the Speed packages doc page for more instructions on how to use the accelerated styles effectively. ## Mixing, shift, table, tail correction, restart, rRESPA info For atom type pairs I,J and I != J, the epsilon and sigma coefficients and cutoff distance can be mixed, but only for sphere pairs. The default mix value is geometric. See the “pair_modify” command for details. Other type pairs cannot be mixed, due to the different meanings of the energy prefactors used to calculate the interactions and the implicit dependence of the ellipsoid-sphere interaction on the equation for the Hamaker constant presented here. Mixing of sigma and epsilon followed by calculation of the energy prefactors using the equations above is recommended. This pair style supports the pair_modify shift option for the energy of the Lennard-Jones portion of the pair interaction, but only for sphere-sphere interactions. There is no shifting performed for ellipsoidal interactions due to the anisotropic dependence of the interaction. The pair_modify table option is not relevant for this pair style. This pair style does not support the pair_modify tail option for adding long-range tail corrections to energy and pressure. This pair style writes its information to binary restart files, so pair_style and pair_coeff commands do not need to be specified in an input script that reads a restart file. This pair style can only be used via the pair keyword of the run_style respa command. It does not support the inner, middle, outer keywords of the run_style command. ## Restrictions This style is part of the ASPHERE package. It is only enabled if LAMMPS was built with that package. See the Build package doc page for more info. This pair style requires that atoms be ellipsoids as defined by the atom_style ellipsoid command. Particles acted on by the potential can be finite-size aspherical or spherical particles, or point particles. Spherical particles have all 3 of their shape parameters equal to each other. Point particles have all 3 of their shape parameters equal to 0.0. The distance-of-closest-approach approximation used by LAMMPS becomes less accurate when high-aspect ratio ellipsoids are used. ## Default none (Everaers) Everaers and Ejtehadi, Phys Rev E, 67, 041710 (2003).
2020-12-05T00:24:27
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https://tjyj.stats.gov.cn/CN/Y2014/V31/I9/51
• 论文 • ### 中国高龄人口死亡率随机波动趋势分析 • 出版日期:2014-09-15 发布日期:2014-10-14 ### Analysis of Stochastic Volatility and Trend of Chinese Elderly Mortality Wang Xiaojun & Zhao Ming • Online:2014-09-15 Published:2014-10-14 Abstract: This paper takes the males aged 70 as a representative of the elderly and presents an empirical analysis of stochastic volatility and trend of mortality based on the data of the year 1996-2010 from the National Bureau of Statistics. Considering the limited and incomplete mortality date in China, we give up the traditional Lee-Carter model and use Monte Carlo method to build stochastic mortality models by analyzing the reasons of mortality improvement. By comparing combination models with different mortality improvement reasons, we study on the relationship between stochastic mortality volatility and trend, and then select the best model as mortality projection model. It can overcome the mortality underestimate and makes the future mortality prediction more accurate and reliable.
2022-06-25T19:22:41
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http://www.itl.nist.gov/div898/handbook/ppc/section2/ppc233.htm
3. Production Process Characterization 3.2. Assumptions / Prerequisites 3.2.3. Analysis of Variance Models (ANOVA) ## Two-Way Nested ANOVA Description Sometimes, constraints prevent us from crossing every level of one factor with every level of the other factor. In these cases we are forced into what is known as a nested layout. We say we have a nested layout when fewer than all levels of one factor occur within each level of the other factor. An example of this might be if we want to study the effects of different machines and different operators on some output characteristic, but we can't have the operators change the machines they run. In this case, each operator is not crossed with each machine but rather only runs one machine. Model If Factor B is nested within Factor A, then a level of Factor B can only occur within one level of Factor A and there can be no interaction. This gives the following model: $$y_{ijk} = m + a_{i} + b_{j(i)} + \epsilon_{ijk}$$ This equation indicates that each data value is the sum of a common value (grand mean), the level effect for Factor A, the level effect of Factor B nested within Factor A, and the residual. Estimation For a nested design we typically use variance components methods to perform the analysis.  We can sweep out the common value, the Factor A effects, the Factor B within A effects and the residuals using  value-splitting techniques. Sums of squares can be calculated and summarized in an ANOVA table as shown below. splitting example It is important to note that with this type of layout, since each level of one factor is only present with one level of the other factor, we can't estimate interaction between the two. ANOVA table for nested case Source Sum of Squares DoF Mean Square F0 A $$SSA = JK\sum{(\bar{y}_{i..} - \bar{y}_{...})^2}$$ I - 1 MSA = SSA/(I - 1) MSA/MSB B within A $$SSB = K\sum\sum{(\bar{y}_{ij.} - \bar{y}_{i..})^2}$$ I(J - 1) MSB = SSB/(I(J - 1)) MSB/MSE Residuals $$SSE = \sum\sum\sum{(y_{ijk} - \bar{y}_{ij.})^2}$$ IJ(K - 1) MSE = SSE/(IJ(K - 1)) Corr. Total $$SST = \sum\sum\sum{(y_{ijk} - \bar{y}_{...})^2}$$ IJK - 1 $$\bar{y}_{i..} = \frac{1}{JK} \sum_{j=1}^{J}{\sum_{k=1}^{K}{y_{ijk}}}$$ $$\bar{y}_{ij.} = \frac{1}{K} \sum_{k=1}^{K}{y_{ijk}}$$ $$\bar{y}_{...} = \frac{1}{IJK} \sum_{i=1}^{I}{\sum_{j=1}^{J}{\sum_{k=1}^{K}{y_{ijk}}}}$$ The row labeled, "Corr. Total", in the ANOVA table contains the corrected total sum of squares and the associated degrees of freedom (DoF). As with the crossed layout, we can also use CLM techniques. We still have the problem that the model is saturated and no unique solution exists. We overcome this problem by applying to the model the constraints that the two main effects sum to zero. Testing We are testing that two main effects are zero. Again we just form a ratio (F0) of each main effect mean square to the appropriate mean-squared error term. (Note that the error term for Factor A is not MSE, but is MSB.) If the assumptions stated below are true then those ratios follow an F distribution and the test is performed by comparing the F0 ratios to values in an F table with the appropriate degrees of freedom and confidence level. Assumptions For estimation purposes, we assume the data can be adequately modeled by the model above and that there is more than one variance component. It is assumed that the random component can be modeled with a Gaussian distribution with fixed location and spread. Uses The two-way nested ANOVA is useful when we are constrained from combining all the levels of one factor with all of the levels of the other factor. These designs are most useful when we have what is called a random effects situation. When the levels of a factor are chosen at random rather than selected intentionally, we say we have a random effects model. An example of this is when we select lots from a production run, then select units from the lot. Here the units are nested within lots and the effect of each factor is random. Example Let's change the two-way machining example slightly by assuming that we have five different machines making the same part and each machine has two operators, one for the day shift and one for the night shift. We take five samples from each machine for each operator to obtain the following data: Machine Operator Day 1 2 3 4 5 0.125 0.118 0.123 0.126 0.118 0.127 0.122 0.125 0.128 0.129 0.125 0.120 0.125 0.126 0.127 0.126 0.124 0.124 0.127 0.120 0.128 0.119 0.126 0.129 0.121 Operator Night 0.124 0.116 0.122 0.126 0.125 0.128 0.125 0.121 0.129 0.123 0.127 0.119 0.124 0.125 0.114 0.126 0.125 0.126 0.130 0.124 0.129 0.120 0.125 0.124 0.117 Analyze For analysis details see the nested two-way value splitting example. We can summarize the analysis results in an ANOVA table as follows: F0 Source Sum of Squares Deg. of Freedom Mean Square Machine 3.03e-4 4 7.58e-5 20.38 Operator(Machine) 1.86e-5 5 3.72e-6 0.428 Residuals 3.46e-4 40 8.70e-6 Corrected Total 6.68e-4 49 Test By dividing the mean square for Machine by the mean square for Operator within Machine, or Operator(Machine), we obtain an F0 value of 20.38 which is greater than the critical value of 5.19 for 4 and 5 degrees of freedom at the 0.05 significance level. The F0 value for Operator(Machine), obtained by dividing its mean square by the residual mean square, is less than the critical value of 2.45 for 5 and 40 degrees of freedom at the 0.05 significance level. Conclusion From the ANOVA table we can conclude that the Machine is the most important factor and is statistically significant. The effect of Operator nested within Machine is not statistically significant. Again, any improvement activities should be focused on the tools.
2018-01-16T13:42:19
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https://indico.fnal.gov/event/22303/contributions/241379/
# Seattle Snowmass Summer Meeting 2022 Jul 16 – 26, 2022 US/Pacific timezone ## Quantum Computing Simulation for Collective Neutrino Oscillations Jul 18, 2022, 7:00 PM 2h 20m 211 South Ballroom (HUB) ### Speaker Valentina Amitrano (University of Trento (Italy)) ### Description Studies of neutrinos from astrophysical environments such as core-collapse supernovae, neutron star mergers and the early universe provide a large amount of information about various phenomena occurring in them. The description of the flavor oscillation is a crucial aspect for such studies, since the physics of matter under extreme conditions is strongly flavor-dependents (nucleosynthesis, proton/neutron ratio, spectral splits...). It is well known that the neutrino flavor changes under the effect of 3 contributions: the vacuum oscillation, the interaction with the electrons of the surrounding matter, and the collective oscillations due to interactions between different neutrinos. This last effect adds a non-linear contribution to the equations of motion, making the exact simulation of such a system inaccessible from any current classical computational resource. Our goal is to describe the real time evolution of a system of many neutrinos by implementing the unitary propagator $U(t) = e^{-iHt}$ using quantum computation and paying attention to the fact that the flavor Hamiltonian $H$, in the presence of neutrino-neutrino term, presents an all-to-all interaction that makes the implementation of $U(t)$, into a quantum algorithm, strongly dependent on the qubit topology. In this contribution we present an efficient way to simulate the coherent collective oscillations of a system of $N$ neutrinos motivating the benefits of full-qubit connectivity which allows for more freedom in gate decomposition and a smaller number of quantum gates making simulation on near-term quantum devises more feasible. We present the results obtained from a real quantum simulation on a trapped-ions based quantum machine for the cases of $N=4$ and $N=8$ neutrinos. In-person or Virtual? In-person ### Primary author Valentina Amitrano (University of Trento (Italy)) ### Co-authors Prof. Alessandro Roggero (University of Trento) Prof. Francesco Pederiva (University of Trento) Dr Piero Luchi (University of Trento) Dr Francesco Turro (University of Trento) ### Presentation materials Poster_Neutrini.pdf Video_poster.mp4
2022-11-29T02:11:19
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https://www.mail-archive.com/[email protected]/msg03862.html
# Re: sources errors in advection/diffusion problems, and one solution Interesting. One addition to Zhekai's comment. When I read it, I thought diffusion (as upwind usually does, at least in finite difference codes). However this is not the case. If you keep the advection u and diffusion D the 1D equation is D*psi_xx + u*psi_x =0 and the exponential term of the solution (the one that appears in the error) has the form exp((u/D)*x). An increase in diffusion D would make the error decay more slowly away from the boundary (you can test that this is so by increasing "DiffCoef" in the code). This increase in decay scale is not what appears when UpwindConvectionTerm is used for the convection term. Instead, the solution becomes perfect (Note -- in this context advection and convection are the same thing.) But it does give a hint as to the source of the error. The upwind schemes only use the gradient calculated in the direction the advection the current is coming from -- in this case u is from the positive x direction. This means an advection scheme in a finite-difference code (which is all that I know, I am new to finite element codes) would not usually use the gradient calculate on the x=0 boundary since the current is coming from +x). But the upwindConvection scheme is sensitive to the boundary condition on the x=0 boundary. (change the line "psi.faceGrad.constrain(0.0*faceNorm,where=xeq0bound)" to see this.) And it appears to be doing the right thing when the gradient is set to some other value than 0. So how does the upwind scheme implement the normal gradient boundary condition differently from the other schemes? At this point I should get off my lazy behind and dig through the code, but I have a number of deadlines for the rest of the week as I switch from being an incompetent applied mathematician to an incompetent writer and administrator. But if no one else has an idea, I might look next week. Jamie On Tue, Sep 20, 2016 at 6:52 PM, Zhekai Deng < [email protected]> wrote: > Hi James, > > Thanks for providing this demo to illustrate the problem. I don't have any > particular ideas exactly why the initial value of psi helps to reduce the > error and why transient problem "advect" out. However, I have some > findings that may help on this. > > Finding # 1: I noticed you have tried ExponentialConvectionTerm, > PowerLawConvectionTerm, CentralDifferenceConvectionTerm, all of these > give exponential error. However, if you tried UpwindConvectionTerm, this > will give the right result on the steady state solution. Thus, maybe using > upwind method, the convection does not require the value from downstream, > consequently, the error from the downstream will not excite the error > toward the upstream. However, I am still very surprise with the magnitude > of the error from other methods, and how similar > > Finding # 2: In the transient state problem, if I increase the mesh size > from 50*50 to 100*100. The error actually grows larger for the > ExponentialConvectionTerm, PowerLawConvectionTerm, > CentralDifferenceConvectionTerm. To show this, if I change the mesh size > to 100*100, the max psi value I have is around 1.1 . However, if I change > the mesh size to 50*50, the max psi is 1.005366, which is several orders of > magnitude lower in terms of difference to the exact solution. This is also > the case for the UpwindConvectionTerm, however, the error for both mesh > size are very small (max(psi) = 1e-13 or 1e-14 + 1). So even in the > transient state, the mesh size appears to somehow amplify the error if we > use finer mesh. I am confused by this. > > To now, it seems UpWindConvectionTerm appears to the the work around > other people think on this. > > Best, > > Zhekai > > > > > On Fri, Sep 16, 2016 at 8:53 AM, James Pringle <[email protected]> wrote: > >> No worries -- I had to do it to figure out the problem in my more complex >> domain and equation... The issue which surprised me was that the value the >> variable was initialized to had an effect on the steady solution. >> >> Jamie >> >> On Fri, Sep 16, 2016 at 8:14 AM, Guyer, Jonathan E. Dr. (Fed) < >> [email protected]> wrote: >> >>> James - >>> >>> I think Daniel will have more insight into why this is happening and if >>> there is anything to be done about it besides artificial relaxation, but I >>> just want to say how much I appreciate your putting this together. This is >>> a very lucid illustration. >>> >>> - Jon >>> >>> > On Sep 15, 2016, at 5:13 PM, James Pringle <[email protected]> wrote: >>> > >>> > Dear FiPy users -- >>> > >>> > This is a simple example of how and why fipy may fail to solve a >>> > problem can reduce the error. I also found something that was a >>> > surprise -- the "initial" condition of a steady problem can affect >>> > the solution for some solvers. >>> > >>> > At the end are two interesting questions for those who want to >>> > understand what FiPy is actually doing.... I admit to being a bit >>> > lost >>> > >>> > The equation I am solving is >>> > >>> > \Del\dot (D\del psi + u*psi) =0 >>> > >>> > Where the diffusion D is 1, and u is a vector (1,0) -- so there is >>> > only a flow of speed -1 in the x direction. I solve this equation >>> > on a 10 by 10 grid. The boundary conditions are no normal gradient >>> > on the y=0 and y=10 boundary: >>> > >>> > psi_y =0 at y=0 and y=10 >>> > >>> > For the x boundary, I impose a value of x=1 on the inflow boundary >>> at x=10 >>> > (this is a little tricky -- the way the equation is written, u is >>> > the negative of velocity). >>> > >>> > psi=1 at x=10 >>> > >>> > and a no-normal-gradient condition at x=0. >>> > >>> > psi_x=0 at x=0 >>> > >>> > since all of the domain and boundary is symmetrical with respect to >>> > y, we can assume psi_y=0 is zero everywhere. This reduces the >>> equation to >>> > >>> > psi_xx + psi_x =0 >>> > >>> > The general solution to this equation is >>> > >>> > psi=C1+C2*exp(-x) >>> > >>> > Where C1 and C2 are constants. For these boundary conditions, C1=1 >>> > and C2=0, so psi=1 everywhere. >>> > >>> > Now run the code SquareGrid_HomemadeDelaunay and look at figure(3) >>> > -- this is the plot of psi versus x, and you can see that it does >>> > not match the true solution of psi=1 everywhere! Instead, it >>> > appears to be decaying exponential. The blue line is actually just >>> > (1+exp(-x)). What is going on? It appears that small errors in the >>> > boundary condition at x=0 are allowing C2 to not be exactly 0, and >>> > this error is this exponential mode. The error is the artificial >>> > exiting of a correct mode of the interior equation, albeit one that >>> > should not be excited by these BC's. >>> > >>> > Interestingly, the size of this error depends on the value the psi >>> > is initially set to. If the line >>> > >>> > psi=fipy.CellVariable(name='psi',mesh=mesh,value=0.0) >>> > >>> > is changed so psi is initially 1, the error goes away entirely; if >>> > it is set to some other value, you get different errors. I do not >>> > know if this is a bug, or just numerical error in a well programmed >>> > solver. >>> > >>> > Now if you run SquareGrid_HomemadeDelaunay_transient which >>> implements >>> > >>> > psi_t = \Del\dot (D\del psi + u*psi) >>> > >>> > you can see that the error in the numerical solution is advected >>> > out of the x=0 boundary, and the solution approaches the true >>> > solution of psi=1 rapidly. >>> > >>> > The interesting question is if the formulation of the boundary >>> > condition at x=0 could be altered to less excite the spurious mode? >>> > >>> > Also, why does the "initial" condition have any effect on the >>> > >>> > Cheers, >>> > Jamie >>> > >>> ____________________ >>> > fipy mailing list >>> > [email protected] >>> > https://urldefense.proofpoint.com/v2/url?u=http-3A__www.ctcm >>> s.nist.gov_fipy&d=DQICAg&c=c6MrceVCY5m5A_KAUkrdoA&r=7HJI3EH6 >>> RqKWf16fbYIYKw&m=IaTL4nEetwjm4G4qfj8cwLzvztKzuiFsw_Nhksv_oWQ >>> &s=vG-nxTf76KxE_CqEHTjt2jIkoy0l9M6X8bm01ypXaBQ&e= >>> > [ NIST internal ONLY: https://urldefense.proofpoint. >>> com/v2/url?u=https-3A__email.nist.gov_mailman_listinfo_fipy& >>> d=DQICAg&c=c6MrceVCY5m5A_KAUkrdoA&r=7HJI3EH6RqKWf16fbYIYKw&m >>> =IaTL4nEetwjm4G4qfj8cwLzvztKzuiFsw_Nhksv_oWQ&s=7JGh0Zz82O69c >>> JiLFKmkV3NfW2TLz6KB_ngkAGCrYGI&e= ] >>> >>> >>> _______________________________________________ >>> fipy mailing list >>> [email protected] >>> https://urldefense.proofpoint.com/v2/url?u=http-3A__www.ctcm >>> s.nist.gov_fipy&d=DQICAg&c=c6MrceVCY5m5A_KAUkrdoA&r=7HJI3EH6 >>> RqKWf16fbYIYKw&m=IaTL4nEetwjm4G4qfj8cwLzvztKzuiFsw_Nhksv_oWQ >>> &s=vG-nxTf76KxE_CqEHTjt2jIkoy0l9M6X8bm01ypXaBQ&e= >>> [ NIST internal ONLY: https://urldefense.proofpoint. >>> com/v2/url?u=https-3A__email.nist.gov_mailman_listinfo_fipy& >>> d=DQICAg&c=c6MrceVCY5m5A_KAUkrdoA&r=7HJI3EH6RqKWf16fbYIYKw&m >>> =IaTL4nEetwjm4G4qfj8cwLzvztKzuiFsw_Nhksv_oWQ&s=7JGh0Zz82O69c >>> JiLFKmkV3NfW2TLz6KB_ngkAGCrYGI&e= ] >>> >> >> >> _______________________________________________ >> fipy mailing list >> [email protected] >> http://www.ctcms.nist.gov/fipy >> <https://urldefense.proofpoint.com/v2/url?u=http-3A__www.ctcms.nist.gov_fipy&d=DQMFaQ&c=c6MrceVCY5m5A_KAUkrdoA&r=7HJI3EH6RqKWf16fbYIYKw&m=wuk3Y2LnhuJ3FKIVZDoGdmC1ovFdPfp6lqdOgHdGRec&s=I5wSFuQN45zZ5980JdThYQ0jP6di-SHCdEIFvV4AHnQ&e=> >> [ NIST internal ONLY: https://email.nist.gov/mailman/listinfo/fipy >> <https://urldefense.proofpoint.com/v2/url?u=https-3A__email.nist.gov_mailman_listinfo_fipy&d=DQMFaQ&c=c6MrceVCY5m5A_KAUkrdoA&r=7HJI3EH6RqKWf16fbYIYKw&m=wuk3Y2LnhuJ3FKIVZDoGdmC1ovFdPfp6lqdOgHdGRec&s=AcaNYv0Fm1HLbOqXnEZR-WwegGriQDechAUvW1dhRlU&e=> >> ] >> >> > _______________________________________________ fipy mailing list [email protected] http://www.ctcms.nist.gov/fipy [ NIST internal ONLY: https://email.nist.gov/mailman/listinfo/fipy ]
2016-09-30T19:10:37
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https://ikariam.fandom.com/wiki/Building:Glassblower
## FANDOM 1,483 Pages Glassblower Function: Increases production Requirements: Research: Improved Resource Gathering () Expansion requirements: and Use requirements: Have workers in the Crystal mine ## Description True masters of their art create sparkling pieces at the glassblower's house.  The blow tubes, glasses and all sorts of other apparatuses only our scientists understand.  And they are so handy, that things break only once in a while. Note: • Every level of the Glassblower increases Crystal Glass production by 2% per expansion (only in the town it is built). ## Expansion Details The time (in seconds) it takes to upgrade to the next level is determined by the following formula: ${ \text{Building time (seconds)} = \left \lbrack \cfrac{72,000}{11} \times 1.1^\text{Level} - 6,120\right \rbrack }$ The accumulative time (in seconds) it takes to upgrade up to the next level is determined by the following formula: ${ \text{Accumulative building time (seconds)} = \left \lbrack 72,000 \times \left (\ 1.1^\text{Level} -\ 1\ \right ) - 6,120 \times \text{Level}\right \rbrack}$ ## Other Production Buildings Community content is available under CC-BY-SA unless otherwise noted.
2019-10-24T04:21:44
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https://hrsl.ba.ars.usda.gov/sgp97/explan/section11.html
## Southern Great Plains 1997 (SGP97) Hydrology Experiment Plan Section 11 - Science Investigations Goto Section in Document: 1. Overview 2. Soil Moisture and Temperature 3. Vegetation and Land Cover 4. Soil Physical and Hydraulic Properties 5. Planetary Boundary Layer Studies 6. Satellite Data Acquisition 7. DOE ARM CART Program 8. Oklahoma Mesonet Program 9. Operations 10. Data Management and Availability 11. Science Investigations 12. Sampling Protocols 13. Local Information 14. References 15. List of Participants 11. SCIENTIFIC INVESTIGATIONS Investigators actively participating were asked to submit an abstract describing their planned activities. These are included here as provided. 1. Meyers, Baldrocchi 2. Kustas, Schmugge, Jackson, Prueger, Hatfield, Sauer, Starks, Norman, Diak, Anderson, Doraiswamy 3. Starks 4. Miller, Mohanty, Tsegaye, Rawls 5. Daughtry, Doraiswamy, Hollinger 6. Entekhabi, McLaughlin 7. Entekhabi, Rodriguez­Iturbe 8. Barros, Bindlish, Yanming 9. Peters­Lidard 10. Kumar 11. Chauhan 12. Diak, Norman, Kustas 13. Finch, Burke, Simmonds 14. Browell, Ismail, Lenschow, Davis 15. Salvucci 16. Njoku 17. Houser, Shuttleworth 18. Laymon, Crosson, Fahsi, Tsegaye, Manu 19. van Oevelen, Menenti 20. Mahrt, Sun 21. Valdes, North 22. Mohanty, Shouse, van Genuchten 23. Famiglietti 24. Elliott, Senay 25. Islam 26. Doraiswamy, Daughtry, Jackson, Kustas, Hatfield 27. Wood, Jackson 28. Wetzel 29. Duffy 30. Humes 31. England, Judge, Hornbuckle, Kim, Boprie 32. MacPherson, Mailhot, Strapp, Belair Investigator(s): Tilden P. Meyers and Dennis D. Baldocchi Institutions(s): NOAA/Air Resources Laboratory Atm Turbulence and Diffusion Div: Title:Continuous Long­term Energy Flux Measurements within the GCIP Domain Numerical regional and global scale models will continue to be used for future climate and hydrological assessments. However, predicted climate scenarios are sensitive to the surface layer processes such as evapotranspiration and soil moisture. Preliminary results have shown significant variations in predicted evapotranspiration from the land­surface submodels that are currently used. Observational data sets that allow for detailed testing for an annual cycle are few. The credibility of climate simulations depends on the predictive capabilities of the submodels used in the parameterizations of the physical and biological processes. Long­term continuous measurements of water and heat fluxes are needed to assess and reduce uncertainties in the land­surface models. The results from the proposed work plan will provide a data base that can be used directly to meet the first two objectives of the GCIP scientific plan which are (1) to determine the temporal variability of the hydrological and energy budgets over a continental scale, and (2) to develop and validate coupled atmosphere­surface hydrological models. Continuous measurements of the surface energy balance components (net radiation, sensible heat flux latent heat flux , ground heat flux , and heat storage ) will continue at the Little Washita Watershed Latent energy fluxes from the soil and canopy systems will be determined to provide a complete data set for (1) the evaluation of the surface layer submodels currently used in synoptic scale and general circulation models, and (2) the determination of seasonal probability distributions and statistics for evaluating predictive capabilities of models. Measurements of additional hydrological components include precipitation and soil moisture. Other measurements that will continue to be measured include solar and net radiation, air temperature and humidity, wind speed and direction, and soil temperatures. Biophysical data will include determinations of leaf area indices, stomatal conductance, and surface albedo. Data from these sites will be used to: 1) evaluate the temporal variability of surface fluxes as a function of season; 2) determine daily and weekly probability distributions of energy fluxes; 3) evaluate and test current surface­biosphere submodels that are currently used for both short and long term numerical weather prediction; 4) determine the relative latent energy contributions from the soil and vegetative components as functions of season; and 5) test a hierarchy of models for estimating the surface energy fluxes from standard meteorological data. Tilden P. Meyers 423­576­1245 FAX: 423­576­1245 FED EX: NOAA/ATDD 456 S. Illinois Avenue Oak Ridge, TN Use of Optical and Microwave Remote Sensing for Mapping Surface Fluxes During the SGP Experiment Investigators/Institutions: Bill Kustas, Tom Schmugge & Tom Jackson/USDA­ARS Hydro Lab Beltsville, MD John Prueger & Jerry Hatfield/USDA­ARS Soil Tilth Lab, Ames, IA Tom Sauer/USDA­ARS SPA Fayetteville, AR Pat Starks/USDA­ARS Grazing Lands Res. El Reno, OK John Norman, George Diak & Martha Anderson/Univ. of Wisconsin, Madison WI Paul Doraiswamy/USDA­ARS RS & Modeling Lab, Beltsville, MD Radiometric temperature and passive microwave observations provide unique spatially distributed surface boundary conditions for surface energy balance modeling. Several relatively simple remote sensing models have recently been developed and tested with ground­truth measurements for computing the surface energy balance (Norman et al., 1995; Kustas and Humes, 1996; Anderson et al., 1997; Zhan et al., 1997). There has also been recent applications of remote sensing data from weather satellites in a simple hydrologic model for monitoring vegetation growth and predicting crop yields (Doraiswamy and Cook, 1995). These modeling algorithms will be applied to remote sensing data collected over the whole SGP study area, but with primary focus on the El Reno site where there will be ground truth hydrometeorological data collected by J. Prueger, B. Kustas, T. Sauer and P. Starks. These data will include standard weather data (wind speed, wind direction, air temperature, relative humidity, solar radiation and precipitation), the surface energy balance, and profiles of soil moisture, temperature and soil heat flux. There will be several aircraft flights with the TIMS instrument coordinated by Tom Schmugge for collecting high resolution thermal­IR data in the early and later morning in order to evaluate the Two­Source­Time­Integrated­Model (TSTIM; Anderson et al., 1997) and the Dual­Source­Energy flux­Model (DSEM; Norman et al., 1995) with local flux observations. In particular, the high spatial resolution TIMS data can be used to evaluate how well the TSTIM model performs on small pixels and whether simple methods exist for interpolating 5 km flux estimates from GOES down to the small scale of 10's of meters. The daily surface moisture maps from the ESTAR passive microwave observations on the P­3 aircraft coordinated by Tom Jackson will be used to test a version of DSEM that uses surface moisture for surface energy flux predictions (Zhan et al., 1997). Landsat TM and NOAA AVHRR data for the study sites and surrounding area will be acquired, processed and mapped by Paul Doraiswamy. In addition, the ground­based measurements of evapotranspiration and soil moisture profile changes will be used for testing the hydrologic model predictions (Kalluri and Doraiswmay, 1995; Doraiswamy, et al., 1997). Once model validation/calibration is performed at the El Reno site, the models will be used with satellite data (i.e., LANDSAT, NOAA­AVHRR and GOES) for mapping fluxes over the entire SGP domain. These estimates will be compared to regional fluxes derived from aircraft eddy correlation and LASE measurements. References: Anderson, M.A., J.M. Norman, G.R. Diak, W.P. Kustas and J.R. Mecikalski. 1997. A two­source time­integrated model for estimating surface fluxes using thermal infrared remote sensing. Remote Sensing of Environment [In Press] Doraiswamy, P.C. and P.W. Cook. 1995. Spring Wheat Yield assessment using NOAA AVHRR data. Canadian J Remote Sens. 21:43­51. Doraiswamy, P.C., P. Zara S. Moulin and P.W. Cook 1997. Spring wheat yield assessment using Landsat TM imagery and a crop simulation model. (Submitted to Remote Sensing of the Environ.) Kalluri, S. and P.C. Doraiswamy. 1995. Modelling transpiration and water stress in vegetation from satellite and ground measurements. Presentation at the 1995 International Geoscience and Remote Sensing Symposium. Firenze, Italy , p1483­1487. Kustas, W.P., and K.S. Humes. 1996. Sensible heat flux from remotely­sensed data at different resolutions. Chapter 8. In: Scaling up in Hydrology Using Remote Sensing (J.B. Stewart, E.T. Engman, R.A. Feddes and Y. Kerr editors) John Wiley and Sons London pp. 127­145. Norman, J. M., W. P. Kustas and K. S. Humes. 1995. A two­source approach for estimating soil and vegetation energy fluxes from observations of directional radiometric surface temperature. Agricultural and Forest Meteorology 77:263­293. Zhan, X., W.P. Kustas, T.J. Schmugge and T.J. Jackson. 1997. Mapping surface energy fluxes in a semiarid watershed with remotely sensed surface information. Preprint of the 13th Conference on Hydrology, American Meteorological Society, pp. 194­197. Bill Kustas [email protected] USDA­ARS­Hydrology Lab Beltsville, MD 20705 USA Voice: (301) 504­8498 Fax: (301) 504­8931 Title: Investigation of spatial distribution of soil water and heat flux. Abstract: A series of Soil Heat and Water Measurement Stations (SHAWMS) have been installed on the Little Washita River Watershed (LWRS) which make profile measurements of soil temperature, soil heat flux, the three parameters of soil heat, and soil moisture. Data from the SHAWMS will be used to investigate the temporal and spatial variability of soil water and heat flux under rangeland condtions and to provide another source of ground truth data for the ESTAR instrument. A limited number of SHAWMS will be installed on the Ft. Reno site under both natural rangeland and winter wheat fields to investigate differences in these fluxes for representative ground cover conditions in central Oklahoma. References: Patrick J. Starks [email protected] (405) 262­5291 fax (405) 262­0133 USDA­ARS­GRL 7207 W. Cheyenne St. El Reno, Oklahoma 73036 Investigator: Doug Miller Collaborators: Binayak Mohanty, Teferi Tsegaye, Walter Rawls Title: Combining Soil Survey Information and Point Observations of Soil Physical and Hydraulic Properties to Improve the Extension of Pedo­Transfer Functions to Regional Areas. Abstract: Soil moisture is a much sought after parameter for a wide range of modeling and management applications. Direct measurement of soil water status, however, is an expensive, time-consuming exercise which is largely prohibitive beyond a few select areas. Previous work has shown the utility of "pedo-transfer" functions to predict the water retention curve or unsaturated hydraulic conductivity of the soil. These functions are based on commonly measured soil physical properties such as particle-size distribution, organic matter content, and bulk density. Pedo-transfer functions in combination with routine spatial information from soil survey and spatial information on topographic and land surface characteristics could potentially be used to improve regional estimates of soil moisture. We will focus on combining spatial information from soil survey, topographic and land surface characteristics with point observations of soil physical properties and soil moisture content to improve soil moisture predictions. The Little Washita River Basin in the southwestern portion of the SGP97 operations area will be the location of detailed study and correlation of field observations of soil physical and hydraulic properties. Ground sampling for this work will be performed in conjunction with soil moisture sampling in support of the main remote sensing objectives of SGP97. Manpower for sampling and access to sampling sites may, necessarily, restrict our opportunities to obtain a full range of representative soil map units. However, it is our hope that we can obtain enough samples to be able to characterize several key combinations of soil, topographic, and land surface conditions which in turn may be used to test our ability to "scale up" to larger areas. Sponsor: NASA through the Penn State EOS IDS Investigation of the Global Water Cycle Spatial variability of biomass and fraction of absorbed PAR within the SGP97 site. Craig Daughtry and Paul Doraiswamy, USDA/ARS Remote Sensing and Modeling Lab, Beltsville, MD Steven Hollinger, Illinois State Water Survey, 2204 Griffith Dr., Champaign, IL 61820. Abstract: Relationships between phytomass production and absorbed photosynthetically active radiation (PAR) have been reported for numerous plant species (Daughtry, et al., 1992). The fraction of absorbed PAR (fA) may be estimated from multispectral remotely sensed data (Prince, 1991). Together these two concepts provide a basis for monitoring vegetation production using remotely sensed data. Our primary objective is to characterize the spatial variability of vegetation within the SGP97 site. We will sample fresh and dry phytomass, leaf area index (LAI), and fA in approximately 60 fields and will extract the multispectral data for each field from Landsat TM scenes. Most of the fields for vegetation sampling will also be used for the gravimetric and profile soil moisture sampling. Global positioning system (GPS) data will be used to register the images and locate the sample sites within the images. Various models will be used to relate the multispectral and vegetation data (Moran et al., 1995) and to estimate phytomass in other fields of the SGP97 site. In addition, for selected fields of winter wheat, we will measure crop residue cover using line­transect methods (Morrison et al., 1993) and will estimate residue cover for other fields using multispectral data from Landsat and other sources (Daughtry et al., 1996). Anticipated products include land use/cover maps, maps of vegetation density, and crop residue cover maps for the SGP97 site. These data should be useful for developing and extending various surface energy balance models and vegetation assessment models from local to regional scales. References: Daughtry, C.S.T., K.P. Gallo, S.N. Goward, S.D. Prince, and W.P. Kustas. 1992. Spectral estimates of absorbed radiation and phytomass production in corn and soybean canopies. Remote Sensing Environment 39:141­152. Daughtry, C.S.T., J.E. McMurtrey III, E.W. Chappelle, W.J. Hunter, and J.L. Steiner. 1996. Measuring crop residue cover using remote sensing techniques. Theor. Appl. Climatol. 54:17­26. Morrison Jr, J.E., C Huang, D.T. Lightle, C.S.T. Daughtry. 1993. Residue cover measurement techniques. J. Soil Water Conserv. 48:479­483. Moran. M.S., S.J. Maas, and P.J. Pinter Jr. 1995. Combining remote sensing and modeling for estimating surface evaporation and biomass production. Remote Sensing Reviews 12:335­353. Prince, S.N. 1991. A model of regional primary production for use with coarse­resolution satellite data. Int. J. Remote Sensing 12:1313­1330. Craig Daughtry voice 301­504­5015 USDA­ARS Remote Sensing and Modeling lab fax 301­504­5031 10300 Baltimore Ave email Beltsville, MD 20705 [email protected] Investigators/Institutions: Dara Entekhabi, 48­331, MIT, Cambridge, MA 02139 Tel: (617) 253­9698 Fax: (617) 258­8850 Email: [email protected] Dennis McLaughlin, 48­209, MIT, Cambridge, MA 02139 Tel: (617) 253­7176 Fax: (617) 253­7462 Email: [email protected] Title: Using Data Assimilation to Infer Soil Moisture from Remotely Sensed Observations: A Feasibility Study Abstract: A state­space formulation of the data assimilation problem is developed including the following components: near­surface soil moisture and subsurface profile dynamics, surface energy balance, multispectral radiobrightness, soil type and pedotransfer functions. The data assimilation model will be tested using data from numerical experiments whose statistics are derived from the SPG97 and Washita92 experiments. References: McLaughlin, D. B. , 1996: Recent advances in hydrologic data assimilation, Reviews of Geophysics, 977­984. Investigators/Institutions: Dara Entekhabi, 48­331, MIT, Cambridge, MA 02139 Tel: (617) 253­9698 Fax: (617) 258­8850 Email: [email protected] Ignacio Rodriguez­Iturbe, Dept. Civil Engineering, Texas A&M University, College Station, TX 77843 Tel: (409) 845­7435 Fax: (409) 845­6156 Email: [email protected] Title: On Space­Time Organization of Soil Moisture Fields: Dynamics and Interaction with the Atmosphere Abstract: The decrease in second­order statistics of soil moisture random fields under aggregation may be estimated using scaling functions whose parameters vary in time (during dry­downs) in a predictable manner and whose parameters have known dependencies on soil and climate properties. We plan to use the multiple scale observations of soil moisture fields using a variety of platforms and sensors to characterize the required scaling functions. Next using simple models of dry­down and percolation, we intend to relate the parameters of these functions to soil and climate properties. References: Rodriguez­Iturbe, I., G. K. Vogel, R. Rigon, D. Entekhabi, F. Castelli and A. Rinaldo, 1995: On the spatial organization of soil moisture fields, Geophysical Research Letters, 22(20), 2757­2760. Scaling Issues in the Retrieval and Modeling of Soil Moisture ­­ A Geomorphology Perspective Ana P. Barros, Rajat Bindlish, and Li Yanming The Pennsylvania State University ABSTRACT Remote sensing and the prospect of long­term monitoring of soil moisture over large areas offer unique opportunities in hydrologic science both for climate studies and for operational applications. Pertinent research issues include: 1) the formulation and accuracy of the algorithms used to transform the remotely­sensed signal (i.e. surface radiometric temperature) into estimates of soil moisture; 2) scaling and the relationship between the scale of measurement and data resolution; 3) data assimilation into operational mesoscale models. In this context, the objectives of our research are to: 1) investigate and quantify the functional dependencies between observed soil moisture dynamics at different scales and the forming and development factors that determine the properties of soils in their natural setting­­climate, vegetation, topography and geology; 2) investigate and quantify the functional dependencies between remotely sensed brightness temperatures at different scales and soil forming and development factors; 3) elucidate the scaling mechanisms implicit in remotely sensed brightness temperatures at different resolutions, and determine the effective scale of measurement at each resolution; 4) use the results of 1), 2) and 3) to constrain a transformation model to retrieve soil moisture. Sensitivity analysis to will be conducted to evaluate model's accuracy and transportability; 5) evaluate the skill of a mesoscale model, specifically MM5, when remote­sensing estimates of soil moisture are used as surface boundary conditions in operational mode. The focus is on short to medium­range forecasts of surface temperature, humidity, and precipitation. Multidimensional spectral analysis, system identification techniques such as cluster analysis and self­organizing neural networks, geostatistics and deconvolution methods will be used to identify soil­topography, soil­vegetation, soil­climate and soil­geology relationships. Data from SGP97 will be analyzed along with data from previous field experiments (e.g. Washita­92 and 94). Vertical Profiles of the Atmospheric Boundary Layer and Upper Air for the Southern Great Plains 1997 Field Experiment Principal Investigator: C. D. Peters­Lidard Environmental Hydraulics and Water Resources School of Civil and Environmental Engineering Georgia Institute of Technology, Atlanta, GA 30332­0355 tel: 404­894­5190; fax: 404­894­2677 e­mail: [email protected] Abstract In support of the eventual goal to integrate remotely sensed observations with coupled land­atmosphere models, Georgia Institute of Technology and the National Severe Storms Laboratory propose to provide vertical profiles of atmospheric pressure, temperature, humidity, wind speed and wind direction during the Southern Great Plains 1997 field experiment (June 17­July 11). Our sounding design is based on three science needs directly related to the existing objectives of the experiment: (1) Provide boundary and initial conditions for coupled atmospheric­hydrologic modeling; (2) Provide data necessary for atmospheric correction of thermal remote sensing; and (3) Support water vapor and heat budget computations over the SGP97 domain. In addition to these science needs, surface and boundary layer profiles will provide data to support the estimation of roughness lengths and stability correction functions and to study boundary layer top entrainment processes and vertical structure. We plan to deploy two sounding systems: one boundary layer and upper air sounding system and one tethersonde system collocated within the Little Washita River Watershed in the southern portion of the SGP97 domain. The launch times will coincide with the launch times of the ARM/CART IOP Sounding program, and will therefore provide complete coverage around the boundary of the SGP97 domain to support vapor budget computations. Sponsor: NASA (Program Manager: Ming­Ying Wei) References Betts, A. K. and A. C. M. Beljaars, Estimation of effective roughness length for heat and momentum from FIFE data, Atmos. Res., 30, 251­261, 1993. Peters­Lidard, C. D. and E. F. Wood, Spatial variability and scale in land­atmosphere interactions: 2. Model validation and results, submitted to Water Resour. Res., 1996b. Ziegler, C. L and L. C. Showell, Chapter XII: Atmospheric Soundings in Hydrology Data Report Washita 1994, eds. P. J. Starks and K. S. Humes, NAWQL 96­1, USDA ARS, Durant OK, June 1996. Investigator(s)/Institutions(s): Dr. Praveen Kumar, Hydrosystems Lab. # 2527B, 205 North Matthews Avenue, Department of Civil Engineering, University of Illinois, Urbana, Illinois 61801 (217)­333­4688 Fax (217)­333­0687 email: [email protected] Students: Patricia Saco ([email protected]) Ji Chen ([email protected]) Title: Estimation, Modeling and Simulation of Soil Moisture Variability and Surface Energy Balance Using Multisensor Measurements at Large Scales Abstract: In order to understand the feedback interaction between land and atmosphere we need a method to characterize the near surface soil­moisture variability and surface energy balance at a vast range of scales. Due to the formidable cost of making such measurements the strategy adopted is to make fine scale measurements of limited coverage embedded within coarse scale measurements of larger coverage using instruments on different platforms. The PI has recently developed a multiple scale conditional simulation (MSCS) technique [Kumar, 1996] to obtain soil moisture fields by combining the multisensor measurements (obtained at multiple scales). The technique uses multiple scale Kalman filtering algorithms for the estimation and a conditional simulation technique for obtaining realistic soil­moisture fields. It relies on a fractal model of soil moisture [Iturbe et al., 1995]. The method can be easily extended to multiple variable fields such as the energy balance components at the land surface. The objectives of our participation in the Southern Great Plains Experiment are to: (a) Extensively validate the multiple scale conditional simulation technique for a wide range of scales and soil­moisture conditions; (b) Apply it to multiple variable surface energy fields and assess its performance; © Assess the impact of the conditionally simulated fields on the atmosphere. References: 1. Kumar, P., Application of Multiple Scale Estimation and Conditional Simulation for Characterizing Soil Moisture Variability, submitted to {\em Water Resources Res.}, 1996. 2 Rodriguez­Iturbe, I., G. K. Vogel, R. Rigon, D. Entekhabi, F. Castelli, A. Rinaldo, On the Spatial Organization of Soil Moisture Fields, {\em Geophysical Res. Letters}, 22(20), 2757­2760, 1995. VEGETATION EFFECTS ON SOIL MOISTURE ESTIMATION Narinder Chauhan Code 923 NASA/Goddard Space Flight Center Greenbelt MD 20771 301 286 4840 FAX: 301 286 1757 E­mail: [email protected] The estimation of soil moisture depends strongly on the vegetation and its quantization. I will be working with Paul Doraiswamy of USDA and David LeVine of GSFC/NASA for the characterization of vegetation. The plan is to participate in the collection of gross vegetation parameters such as plant density, LAI, vegetation water content, etc. for most of the vegetation in the area. In addition, specific vegetation types will be targeted for collection of detailed canopy geometry data. This can involve measuring canopy architecture, leaf and stem angle distributions. In the past, the measurement of soil moisture under certain crops, like grass and alfalfa has been a problem. The plan is to characterize such crops with a higher degree of accuracy and to use theory (Discrete Scatter Models) to compare predictions with passive microwave measurements. The goal is to learn how to characterize these vegetation canopies to accurately estimate soil moisture. Investigators: George R. Diak and John M. Norman, University of Wisconsin­Madison William P. Kustas ,USDA­ARS Title of Investigation: Estimation and Validation of Evapotranspiration at 10 km Scales During The SGP­97 Experiment Abstract: We will investigate the performance of a two­source time­integrated model (TSTIM) for evaluating the surface energy balance over the domain of the SGP­97 experiment. This model is comprised of a surface component (describing the relationship between radiometric temperatures, sensible heat flux and the temperatures of the air, canopy and soil surface), coupled with a time­integrated component (connecting the time­integrated surface sensible heat flux with planetary boundary layer development). The required data inputs are radiometric surface temperatures at two times (from GOES), analyzed surface and upper air synoptic data, and vegetation cover estimates from satellite sources. Surface energy balance components will be estimated at approximately a 10­km resolution over the SGP­97 domain. These estimates will be compared with available surface and aircraft­based flux estimates. The TSTIM has the ability to utilize information on soil­surface evapotranpiration from any source. Using the SGP­97 data, we will also investigate how microwave­based near­surface soil moisture estimates from passive microwave sensors can be incorporated into this model. References: Anderson, M. C., J. M. Norman, G. R. Diak and W. P. Kustas, 1996: A two­source time integrated model for estimating surface fluxes for thermal infrared satellite observations. Accepted for publication, Rem. Sens. Environ. Diak, G. R. and M. S. Whipple, 1995: A note on estimating surface sensible heat fluxes using surface temperatures measured from a geostationary satellite during FIFE­1989. J. Geophys. Res. 100, 25,453­25,461. Norman, J. M., W. P, Kustas and K. S. Humes, 1995: A two­source approach for estimating soil and vegetation energy fluxes from observations of directional radiometric surface temperatures, Agric. For. Meteor., 77, 263­293. Contact: Dr. George R. Diak 1225 W. Dayton St., #205 Phone: 608­263­5862 Fax: 608­262­5974 email: [email protected] Title: Estimating Soil Hydraulic Properties from Airborne Passive Microwave Data ­ The Effects of Subpixel Heterogeneity Investigators/Institutions: J. Finch and E. Burke, Institute of Hydrology Abstract: A physically based model that couples a soil water/energy model to a microwave emission model (MICRO­SWEAT) has recently been developed. MICRO­SWEAT predicts the time series of microwave emission from input parameters of the soil properties, soil water status, vegetation parameters and a time series of meteorological data. One application of MICRO­SWEAT has been to successfully estimate soil hydraulic properties from ground­based microwave data, i.e. essentially point measurements, by fitting the model to detailed time series of data. The next step in this line of research is to estimate soil hydraulic properties at the spatial scale of a pixel of remotely sensed data. The proposed research will investigate the effect of sub­pixel heterogeneity in soil hydraulic properties, soil roughness, vegetation water content and soil moisture on microwave data. The objectives of the project will be achieved by using the microwave values predicted from MICRO­SWEAT. The ground and ESTAR data acquired during SGP'97 will provide a data set that contains both the input parameters for MICRO­SWEAT and microwave data that can be used to test the values predicted by the model. The proposed research will make additional measurements on the ground of the soil and vegetation parameters required by MICRO­SWEAT at a series of sites in order to quantify the spatial heterogeneity within a pixel of the ESTAR data. Between 50 and 100 sites will be selected to represent the variations in soil and vegetation and measurements of soil moisture taken daily except during periods of rapid change when a reduced number of sites will be monitored more frequently. Other parameters will be estimated at different periods reflecting their rate of change. The key input and validation parameters which will be measured are: rainfall, plant height, leaf area index and leaf angle, vegetation water content, surface soil moisture, TDR soil water down to 120 cm, surface roughness, soil bulk density. In addition, gravimetric soil moisture samples for calibration will be collected and soil samples will be taken for laboratory analysis. The field data will be analyzed to assess the temporal and spatial variability of the input parameters required by MICRO­SWEAT. The first step of the modelling will be to test the values predicted by MICRO­SWEAT against the values recorded by the ground­based microwave radiometer in order to verify that the model is predicting the values to an acceptable accuracy. The next stage will be to use MICRO­SWEAT to predict the microwave emission from the range of soils and land cover types that occur within a pixel of the airborne remotely sensed data. These values will then be aggregated to produce a time­series of 'averaged' values that will be tested against the values of the airborne remotely sensed data. A sensitivity analysis will be carried out to assess the contribution from the different land surface parameter combinations to the time series of 'averaged' remotely sensed data. Finally, the simulated times series of remotely sensed data will be inverted to estimate the soil hydraulic properties of the pixel and a comparison made between these values and the variability of the values actually occurring within the pixel. Sponsor: UK Natural Environment Research Council Staff: Dr. Jon Finch Institute of Hydrology Wallingford Oxon OX10 8BB UK tel. + 44 (0)1491 838800 fax. + 44 (0)1491 692424 email: [email protected] Dr. Lester Simmonds Soil Science Department UK tel. +44 (0)1189 316557 fax. +44(0)1189 316660 Miss Eleanor Burke Institute of Hydrology Wallingford Oxon OX10 8BB UK tel. + 44 (0)1491 838800 fax. + 44 (0)1491 692424 email: [email protected] Investigator(s)/Institutions(s): Edward V. Browell, PI, NASA Langley Research Center, Syed Ismail, co­I, NASA Langley Research Center, Donald H. Lenschow, co­I, National Center for Atmospheric Research Kenneth J. Davis, co­I, University of Minnesota Title: INVESTIGATION OF MESOSCALE VARIABILITY IN CONVECTIVE BOUNDARY LAYER DEVELOPMENT USING LASE Abstract: One of the four objective of the Southern Great Plains 1997 (SGP97) Experiment is the examination of 'the effect of soil moisture on the evolution of the atmospheric boundary layer and clouds over the southern great plains". This study seeks to advance our understanding of this coupled land­atmosphere system, a fundamental component of the hydrologic, weather and climatic systems. We will study the spatial variability in the development of the convective boundary layer (CBL) over a fairly uniform land surface with spatially varying soil moisture content. Soil moisture will be measured with ESTAR on­board the NASA P­3 aircraft. NASA's Lidar Atmospheric Sensing Experiment (LASE) will also be flow on­board the P­3 aircraft. The LASE instrument, reconfigured to fly on the P­3, will be capable of resolving the vertical and horizontal structure of the developing CBL, including information on the two dimensional moisture structure of the atmospheric boundary layer. LASE and ESTAR together will provide a unique and comprehensive mesoscale remote sensing data set for studying the evolution of the CBL and its relation to the land surface. This study will benefit from complementary data from the Canadian Twin Otter aircraft (real­time images of boundary layer structure obtained by LASE can be used, when appropriate, to guide the Twin Otter). Other in situ surface and tower measurements, and satellite remote sensing data will also be used in this study. The primary goals of this research are: evaluation of the influence of soil moisture on the local surface energy budget (SEB) over the SGP97 region; 2) evaluation of the influence of mesoscale spatial variability in the SEB on CBL development, including CBL depth and cloud cover; 3) quantification of the CBL water vapor budget (advection, entrainment, evapotranspiration) using remotely sensed and in situ data; and investigation of microscale mechanisms responsible for the entrainment of tropospheric air into the CBL. References: Kenneth J. Davis, Assistant Professor phone: 612­625­2774 Department of Soil, Water, and Climate fax: 612­625­2208 University of Minnesota email: [email protected] 1991 Upper Buford Circle St. Paul, MN 55108­6028 Investigator: Guido D. Salvucci, Boston University, Dept. of Geography 675 Commonwealth Ave., Boston, MA 02215 617­353­8344 Fax 617­353­8399 [email protected] Title: Detection and modeling of transitions between atmosphere and soil limited evapotranspiration in the southern great plains summer 1997 experiment Abstract: Salvucci [WRR 33(1), 111­122, 1997] presented a simple diagnostic model of bare soil evaporation which expresses the daily rate of evaporation during soil limited periods as a function of the duration (td) and average rate (ep) of stage­one (potential) evaporation. The model does not require in situ estimates of soil hydraulic properties or initial water content, as these are implicitly related to td and ep. Surface and remote observations of detectable changes in near surface moisture content, temperature, and albedo may be used to estimate the transition time (td). With extensions to estimate stressed transpiration from grasses, the model thus has the potential to yield ET estimates over large areas using satellite data. The microwave estimates of soil moisture collected over the month long SGP experiment will be used in conjunction with concurrent surface flux measurements taken at the ARM sites to further test and develop this methodology, with special emphasis on the detection of transition time via microwave­estimated surface soil moisture dynamics. References: Salvucci, G.D., 1997. Soil and moisture independent estimation of stage­two evaporation from potential evaporation and albedo or surface temperature, Water Resources Research, 33(1), 111­122 Sponsor: NASA Grant NAGW­5255 "Thermal and Hydrologic Signatures of Soil Controls on Evaporation" Investigator: Eni G. Njoku Institution:Jet Propulsion Laboratory Title: Multichannel land parameter retrieval at different spatial scales Abstract: Soil moisture is the dominant effect on microwave emission from soils at L­to C­band for soils with low to moderate vegetation. Surface roughness, temperature, and low­opacity vegetation cover affect soil microwave emission, but to lesser extents than soil moisture. As the opacity of vegetation cover increases it becomes the dominant effect on the microwave emission, and can mask the soil moisture signal. Multifrequency retrieval algorithms are a means for utilizing the varying sensitivity of brightness temperature to the surface parameters at different frequencies to correct for vegetation, roughness, and temperature in retrieving soil moisture. Theoretical simulations using models based on recent empirical data show that multichannel algorithms should work well in practice. However, there have been few opportunities to demonstrate this in actual field experiments. SGP'97 provides an opportunity for such a demonstration. Truck­based L­, S­, and C­band measurements are planned, providing data at a local scale, and L­band aircraft data and AVHRR satellite data will be available at the 1­km resolution scale. SSM/I data will be available at a 50­km resolution scale, providing a historical database of 19.3 and 37 GHz brightness temperatures over the SGP'97 site at that scale. We will provide the AVHRR and SSM/I data to the SGP'97 experiment database as a contribution of this investigation. Soil moisture retrievals will be performed at three scales, using different algorithms and available data sets: (1) local ­ truck­based; (2) regional ­ aircraft microwave/satellite AVHRR; (3) time­series ­ satellite SSM/I. Soil moisture retrievals for these cases will be compared with in­situ observations and output from numerical models over the SGP'97 site, and results of the analyses will be published. Research using the truck­based, aircraft, in­situ, and model data will be performed in collaboration with the data providers. References: Njoku, E.G. and D. Entekhabi (1996): Passive microwave remote sensing of soil moisture. J. Hydrology, 184, 101­129. Njoku, E. G., S. J. Hook, and A. Chehbouni (1996): Effects of surface heterogeneity on thermal remote sensing of land parameters. In: Scaling Up In Hydrology Using Remote Sensing (J. B. Stewart, E. T. Engman, R. A. Feddes, and Y. Kerr, Eds.), Wiley, New York. Investigator(s)/Institutions(s): Paul R. Houser (NASA­GSFC), and Jim Shuttleworth (U. of Arizona) Title: Regional In­Situ Profile Soil Moisture and Surface Energy Flux Observations in support of the 1997 Southern Great Plains Experiment. Abstract: Our contribution to the Southern Great Plains 1997 experiment will be in four areas: (1) general mission support through surface gravimetric sampling and processing, (2) profile soil moisture observations using TDR and gravimetric techniques, (3) Soil characterization at selected sites, and (4) operation of a surface energy and water flux station at the ARM central facility. Observations of Profile Soil Moisture and Characteristics: The primary objective of the Southern Great Plains 1997 (SGP97) Experiment is to map soil moisture using an airborne passive microwave radiometer (ESTAR, LeVine et al., 1992) over a 60 km by 250 km area in central Oklahoma for a one month period during the summer of 1997 (Jackson, 1996). Passive microwave instruments are only sensitive to moisture in the top few centimeters of soil, but knowledge of moisture in the entire soil profile is essential for hydrologic, ecologic, and climatic studies (Wei, 1995; Ragab, 1995; Jackson, 1980). Therefore, profile soil moisture observations will be essential for understanding the relationship between the remotely­sensed measurements and deeper moisture stores. Profile measurements will enable further development and validation of methodologies that extend remotely sensed surface soil moisture estimates to the entire root zone (Jackson, 1980), will enable the definition of vertical soil moisture error correlation structures which are essential in soil moisture data assimilation studies, and will help to calibrate existing profile sensors. Profile soil moisture observations using Campbell heat dissipation probes are currently in place in the SGP97 area at 14 Little Washita Micronet, 5 Oklahoma Mesonet, 2 ARM Central Facility, and 5 El Reno sites. Observations made with these sensors are known to vary with soil characteristics and temperature, therefore each of these sites will be instrumented with an ESI MoisturePoint profile TDR that will be monitored daily during SGP97 (installation done prior to the experiment by Pat Starks, USDA­ARS El Reno), and profile gravimetric observations at selected sites (mostly at El Reno) will be collected as frequently as possible (selected soil cores will be sent to the USSL for water retention, and soil characterization analysis). The TDR probes and MoisturePoint equipment for this plan are currently available (Pat Starks, USDA­ARS, and Ron Elliot, OK Mesonet), and both truck­mounted and hand operated gravimetric sampling equipment is available (USSL­Binayak Mohanty), but truck sampling may be limited to the EL Reno facility. The existing profile soil moisture sensors are located next to weather observation stations that are typically on the edges of fields in non­characteristic soil and vegetation. To assess the representiveness of these observations, additional in­field TDR profile observations will be made at a subset of sites (2 at the ARM Central Facility, 2 at El Reno, and 1 at the Little Washita). It is thought that a minimum of 3 in­field TDR observations will be necessary at each of these sites to assess the field average profile soil moisture. At one site (El Reno) a larger number of in­field TDR observations (9 samples) will be made to determine if 3 samples is adequate for determination of in­field average profile soil moisture. Approximately 4 of these 21 additional probes are currently available (Pat Starks, USDA­ARS), leaving only ~17 to purchase ($350ea * 17probes =$5950)! Observations of Surface Water and Energy Fluxes: The DOE­ARM program has embarked on an extensive environmental observation program in the Oklahoma and Kansas area. As part of this program, observations of surface water and energy fluxes are being performed with eddy correlation and Bowen ratio techniques. To characterize the quality of these observations for use in applications such as validation and calibration of regional land surface and atmospheric modeling projects, a well established eddy correlation system will be co­located with the ARM surface flux measurement sites at the ARM Central Facility. The University of Arizona's CO2/H2O eddy correlation system (Shuttleworth) will initially be co­located with other mobile surface flux measurement systems at the EL Reno Facility for a period of a few days just prior to the SGP97 experiment for intercomparison. During this time, two other Campbell LiCor Bowen Ratio systems may be deployed and maintained at El Reno as part of this project. The UA eddy correlation system will be re­deployed to the ARM Central Facility at the start of the SGP97 experiment. It will be located near the ARM Bowen ratio system in rangeland vegetation for two weeks, and near the ARM eddy correlation system in a winter wheat field for two weeks. The exact location and height of the UA system may vary from the ARM sensors to minimize fetch problems. Personnel: Paul Houser (available for experiment duration) Chawn Harlow (available for experiment duration) Jim Shuttleworth (questionable availability) NASA­GSFC: Houser's salary, computer support, GPS NASA­HQ: Houser's Travel, and hopefully some equipment U of Arizona: NASA Contract NAS­5­3492 will provide salary and travel for 1 student, computer support, 1 flux station Cooperator(s): USDA­ARS (Pat Starks at El Reno): cooperating on MoisturePoint TDR sampling USDA-ARS-SL (Binayak Mohanty): Use of soil sampling equipment, possibly including a hydraulic press for use at El Reno Oklahoma Mesonet (Ron Elliot): Use of 2­3 MoisturePoint "Boxes" References: Jackson, T. J., 1996. Southern Great Plains 1997 (SGP97) Experiment Plan, http://hydrolab.arsusda.gov/~tjackson/. Jackson, T. J., 1980. Profile Soil Moisture from Surface Measurements. Journal of the Irrigation and Drainage Division, June 1980. Le Vine, D. M., A. Griffis, C. T. Swift, ant T. J. Jackson, 1992. ESTAR: A Synthetic Aperture Microwave Radiometer for Measuring Soil Moisture. International Geoscience and Remote Sensing Symposium 1992, Vol 1. Ragab, R., 1995. Towards a continuous operational system to estimate the root­zone soil moisture from intermittent remotely sensed surface moisture. Journal of Hydrology, 173:1­25. Wei, Ming­Ying, editor, 1995. Soil Moisture: Report of a Workshop Held in Tiburon, California, 25­27 January 1994. NASA Conference Publication 3319. Primary Contact: Paul R. Houser [email protected] (301)­286­7702 fax (301) 286­1758 NASA's Goddard Space Flight Center Hydrological Sciences Branch / Data Assimilation Office Code 974 (Bldg. 22, Room C277) Greenbelt, MD 20771 Participation in SGP97 from the Center for Hydrology, Soil Climatology and Remote Sensing The Center for Hydrology, Soil Climatology, and Remote Sensing (HSCaRS) under NASA sponsorship has as one of its objectives to develop a Local­scale Hydrology Model (LHM) and a Regional­scale Hydrology Model (RHM) that can utilize periodic input of remotely­sensed soil moisture data to "adjust" the surface soil moisture field used to calculate root zone moisture. In addition, we recognize the need to address the issue of disaggregating large pixel soil moisture data from satellites to the process­scale represented in the hydrologic models. The Southern Great Plains 1997 (SGP97) Experiment will provide data necessary for HSCaRS to pursue its hydrologic modeling research objectives. HSCaRS will provide support to the SGP97 Experiment and acquire additional characterization information needed for hydrologic modeling by conducting research in the following five areas: 1.) Relate surface soil moisture measurements to the soil moisture profile: We will install and operate a soil profile station (see description below) on each of the two plots in the vicinity of the calibration plots to relate the observed surface soil moisture to the underlying soil moisture profile. One energy balance Bowen ratio (EBBR) station is available for deployment at the SLMR calibration site to relate soil moisture changes to surface energy fluxes. Depending on which site is selected for the calibration site, instead we may choose to deploy the EBBR in the Little Washita River basin. Additional meteorological measurements, including rainfall, air temperature, relative humidity, shortwave and infrared radiation wind direction and speed will be made at the SLMR site. Chip Laymon (GHCC) will service these stations and will also assist Peggy O'Neill in SLMR operation and data acquisition. Up to four additional soil profile stations will be deployed in the Little Washita River watershed to a.) provide additional points for relating remotely­sensed surface soil moisture to the underlying soil moisture profile, b.) to relate SHAWMS soil profile measurements at field borders to measurements within the field, and c.) provide time continuity to periodic manual soil moisture profile measurements to be made at approximately 20­30 sites in the SGP97 study area (coordinated by Paul Houser). Bill Crosson (GHCC) will be the lead on this activity. Description of Soil Profile Stations: Soil moisture and temperature measurements will be made at several depths down to about 75 cm in each pit. Soil moisture will be measured using Water Content Reflectometers (Campbell Scientific, Inc.), a device based on time domain reflectometry, and using Soil Moisture Probes (Radiation and Energy Balance Systems), a device based on electrical resistance. Soil temperature will be measured in each pit using soil thermistors. Ground heat flux will be determined using a heat flux plate installed at 5 cm depth plus the heat storage in the upper 5 cm layer calculated from the time rate of change of temperature, which is measured using 4­sensor averaging thermocouple probes installed at 1, 2, 3 and 4 cm depths. We are currently examining techniques to derive the soil dielectric constant from Water Content Reflectometers or similar sensors. At this point this appears feasible; if so, we will provide dielectric constant profiles at one or more of the profile stations. This information should be valuable in understanding both SLMR and ESTAR measurements vis­a­vis soil moisture measurements in the upper 5 cm as well as in the profile. 2.) Soil hydraulic property characterization: Accurate knowledge of the spatial distribution of soil hydraulic properties is necessary for SGP97 soil moisture retrieval as well as for hydrologic modeling activities. Soil profiles will be described and sampled for texture, hydraulic conductivity, bulk density and porosity at the sites where the HSCaRS soil profile stations are installed. A representative grass and winter wheat field in the Little Washita River watershed will be sampled (up top 100 samples each) for surface hydraulic properties. All soil samples will be analyzed at Alabama A&M University. Teferi Tsegaye (Alabama A&M University) will be lead on this activity. 3.) Classify vegetation: An accurate land cover classification is necessary for the SGP97 soil moisture retrieval algorithm and subsequent hydrologic modeling. Landsat TM data will serve as the basis of the classification. HSCaRS will provide personnel to support this effort being coordinated by other SGP97 team scientists. Ahmed Fahsi (Alabama A&M University) will assist in this activity and coordinate additional student support provided by Alabama A&M University. 4.) Surface soil moisture variability: Some understanding of the spatial variability of surface soil moisture is required to a.) assess the accuracy of using a limited number of gravimetric samples for remote sensing verification, b.) assess the accuracy of the remote sensing technique to represent the mean surface moisture of the field, c.) assess the linearity of integrating moisture variability by the ESTAR instrument within a single pixel, d.) test mixed­pixel algorithms, and e.) evaluate field­ and sub­watershed­scale hydrologic processes. While this activity will be conducted with a large cooperative group from many institutions, HSCaRS scientists from GHCC and Alabama A&M University have contributed significantly to developing the science and implementation plans for this activity. Teferi Tsegaye has particular interest in studying field­scale variability and Chip Laymon and Bill Crosson have interests in the application of these data to remote sensing interpretation and verification of hydrologic models. In addition to field sampling, Chip Laymon is developing a GIS application for rapid mapping and evaluation of the field measurements. Site information and field measurements will be downloaded nightly from portable data recorders to a PC. These data can then be uploaded into a GIS application and for mapping and production of soft and hard copy output and thereby used by the field team leaders in redirecting labor resources the next day. In addition, near "real­time" visualization of the field measurements will contribute greatly to morale by making the science more tangible and understandable to those participating. 5.) Develop and test surface TDR measurement capability: The surface soil moisture variability study (#4 above) is dependent on a portable, rapid measurement technique. Recent advances in time domain reflectometry techniques have resulted in sensors with "on­board" signal processing. We are currently investigating the ability to modify several off­the­shelf products for use in surface (0­5 cm) soil moisture determination. Preliminary results indicate that we will be successful in providing an instrument for use during SGP97. Current research is focusing on sensor intercomparison and calibration. Recommendations on equipment are forthcoming. HSCaRS Participants: Global Hydrology and Climate Center Chip Laymon week 1, 2, 4 [email protected] Bill Crosson week 1, 3, 4 [email protected] Vishwas Soman [email protected] Alabama A&M University Ahmed Fahsi [email protected] Teferi Tsegaye [email protected] Andrew Manu amanu@ asnaam.aamu.edu Rajbhandari Narayan [email protected] ~ 5­8 grad. students 2 week each ? Investigator(s)/Institution: P.J. van Oevelen, Dept. Water Resources, WAU, Wageningen, The Netherlands M. Menenti, Winand Staring Centre, Wageningen, The Netherlands Title of Investigation: Estimation of spatial soil moisture fields estimation using sensor fusion: SSM-I, ERS, Radarsat and ESTAR Abstract: Microwave radiometry has been widely accepted as the most practical tool to estimate spatial soil moisture fields, especially at L-band the results have been encouraging. However, currently there are no spaceborne microwave radiometers available with an acceptable resolution to be used in watershed studies. Therefore, the usefulness of SAR, in particular Radarsat and ERS, to estimate the same type of soil moisture fields as is possible with the airborne ESTAR (at a resolution of 1 km) will be investigated. The combination of data originating from various sensors to estimate the same property is referred to as sensor fusion. Within the EOS framework this study will also investigate the usefulness of low resolution SAR systems such as ASAR and the application of these fields in Numerical Weather Prediction models. To facilitate this study an extensive soil moisture measurement campaign will be set-up using portable TDR's (Time Domain Reflectometry), an FD (frequency domain) sensor along transects/grids and the EM38 instrument to give a more spatially average measurement over the same transect/grid. The grid size and spatial sampling scheme should be set up such that the measurements are representative enough to cover the spatial resolutions of the various sensors (25 m up to 1 km). All these measurements should occur as closely as possible to the overpass times of the various instruments. References: Investigator(s)/Institutions(s): Larry Mahrt (Oregon State University) and Jielun Sun (University of Colorado/NCAR) Title: Aircraft measured surface fluxes and relationship to soil moisture. Abstract: The Canadian Twin Otter and the NOAA LongEZ will be deployed during SGP to measure the spatial variability of fluxes of heat, moisture and carbon dioxide. The LongEZ will fly primarily low level flights below 50 m (subject to final FAA approval) to concentrate on surface flux measurements while the Twin Otter will fly multiple levels to include vertical structure of the boundary layer and assessment of entrainment of dry air. Two principal modes of operation will be "chasing" spatial gradients of surface moisture and coordinated flights with the P3. Additional flights will feature tower-aircraft flux comparisons. The aircraft data, and eventually the tower flux, Mesonet and sounding data will be archived at Oregon State. The aircraft data will be quality controlled and evaluated in terms of flux sampling errors. The analyzed fluxes will be provided to the community along with a suite of other processed parameters such as surface roughness and surface radiation temperature. The analyzed fluxes from the two aircraft will be combined with the sounding data, the Mesonet data, LASE water vapor measurements, ESTAR brightness temperature and the soil moisture estimates to examine the response of the boundary layer to spatial variations of the soil moisture and the feedback of boundary layer evolution on the surface moisture fluxes. For example surface dryer conditions lead to greater heat flux, boundary layer growth and entrainment drying which reduces the surface relative humidity. For a given soil moisture, this enhances the soil moisture loss. Its effect on transpiration depends on stomatal control. Methods are being developed to estimate area averaged moisture fluxes by modelling the evaporative fraction in terms of remotely sensed variables including the surface radiation temperature, red and near infrared channels and microwave band. Larry Mahrt COAS OSU Corvallis, OR 97331 [email protected] 541 737 5691 fax 2540 Jielun Sun MMM NCAR P.O. Box 3000 Boulder, CO 80307 [email protected] 303 497 8994 fax 8171 Space-Time Characterization of Soil Moisture Variability for Assessment of Sampling Errors by Space-Borne Sensors and Related Ground Truth Issues Investigators: Juan B. Valdes, Department of Civil Engineering and Climate System Research Program Gerald R. North, Department of Meteorology and Climate System Research Program Abstract There is a great need of a set of observations of soil moisture that cover large areas and time intervals. The available records of Washita'92 have been extensively analyzed and used in our research but the data set have some limitations both in temporal and in areal extent. The planned experiment would greatly improve the data availability of soil moisture. In our research we are planning to use those measurements to characterize the space-time spectrum of soil moisture to be used in the estimation of sampling errors by sensors that are intermittent in time and/or space. The measurements will also be used to estimate nominal parameters for one-layer/two-layer models of the upper soil zone to carry out controlled experiments of proposed missions. The statistics of the observed point values on the ground and the observed surrogates on the overflights will be used to determine the possible bias in a procedure similar to the one carried out for precipitation. Juan B. Valdes Department of Civil Engineering Texas A&M University College Station TX 77843-3136 (409) 845-1340 (409) 862-1542 FAX e-mail: [email protected] SGP-97: An Integrated Validation Framework Investigators: B.P. Mohanty, P. Shouse, M. Th. van Genuchten (U.S. Salinity Lab) Rationale: The spatio-temporal dynamics of water and energy transport across the soil-atmosphere boundary layer in relation to climate change, hydrology, near-surface thermodynamics, and land use is still poorly understood. The problem of accurately estimating regional-scale soil water contents of the near-surface, variably-saturated (vadose) zone is complicated by the overwhelming heterogeneity of both the soil surface and the subsurface, the highly nonlinear nature of local-scale water and heat transport processes, and the difficulty of measuring or estimating the subsurface unsaturated soil-hydraulic functions (the constitutive functions relating soil water content, soil-water pressure head and the unsaturated hydraulic conductivity) and soil thermal properties (heat capacity and soil thermal conductivity). As remote sensing techniques make it increasingly possible to obtain large-scale soil water content and heat flux measurements, validation of these measurements using ground-based data and/or indirect estimates from relevant soil, landscape, and vegetation parameters is essential. Objective: The overall objective of our project is to develop and evaluate an "integrated validation framework" for remote sensing data of soil moisture content in the shallow subsurface. Specific scopes of our investigation for SGP-97 experiment will include: 1. Coupling of digital soil maps (e.g., SSURGO, STATSGO) with soil hydraulic and thermal property databases (e.g., UNSODA) using ARC/INFO geographical information systems (GIS) and neural network (NN) based pedotransfer functions (PTFs) (in collaboration with Doug Miller, and others). 2. Identification of important soil (e.g., soil type, texture, porosity, bulk density), landscape (e.g., slope, aspect, elevation, depth to water table), and land use/cover (vegetation type, vegetation density, management practice, etc.) parameters for establishing pedotransfer functions to describe soil hydrologic and thermal properties of relatively large land areas (in collaboration with Jay Famiglietti, Charles Laymon, Doug Miller, Paul Houser, and others). 3. Measurement of soil water retention and hydraulic conductivity functions across the space and time domains of SGP-97 experiment (in collaboration with Paul Houser and others). 4. Investigation of the suitability of different exploratory data analyses, Bayesian statistics, spatial statistics, numerical or other up-scaling techniques for estimating effective soil hydraulic and thermal parameters of the larger land areas (pixels) from point measurements in the vadose zone (in collaboration with Dennis McLaughlin, and Dara Entekhabi). The ultimate purpose of this research is to obtain pixel-scale estimates of the soil hydraulic and soil thermal properties for possible use in land-soil-atmospheric interaction simulation models to test space-borne measurements of transient soil moisture and soil temperature data, thereby yielding alternative (provide supplementary data) to ground-truth measurements. Investigator/Institution: Jay Famiglietti, University of Texas at Austin Title: Ground-Based Investigation of Spatial-Temporal Soil Moisture variability in Support of SGP '97 Abstract: Surface (0-5 cm) soil moisture exhibits a high degree of variability in both space and time. However, larger-scale remote sensing integrates over this variability, masking the underlying detail observed at the land surface. Since many earth system processes are nonlinearly dependent upon surface moisture content, this variability must be better understood to enable full utilization of the larger-scale remotely-sensed averages by the earth science community. The overall goals of this investigation are to (a) characterize soil moisture variability at high spatial and temporal frequencies; (b) understand the processes controlling this variability (e.g. precipitation, topography, soils, vegetation); and © determine how well this variability is represented in a time series of 1-km (approximately) remotely-sensed soil moisture maps. Specific tasks are to (a) quantify the spatial-temporal variability of surface moisture content (mean, variance, distributional form, spatial pattern) in selected, representative quarter sections by means of supplementary sampling; (b) assess the accuracy of the remotely-sensed soil moisture maps by comparing ESTAR-derived mean moisture contents to those observed in the field; © assess the representativeness of remotely-sensed maps of mean moisture content with respect to the underlying variance within quarter sections; (d) determine how well larger-scale (full section to small watershed scale) observed patterns of soil moisture are preserved by the remotely-sensed maps; and (e) characterize the processes controlling soil moisture variability from the quarter-section to the small watershed scale, with implications for the environmental factors which influence spatial-temporal variations in the accuracy and representativeness of the remotely-sensed soil moisture maps. A team of seven researchers (listed below) will conduct this investigation and will be on site for the full duration of the experiment. Site selection and the spatial-temporal frequency of intensive sampling are currently under investigation in collaboration with other SGP investigators. A portable sampling methodology, critical to the feasibility of this effort, is also under study at MSFC with promising results to date. Beyond the implications outlined above, the proposed research will also have significance with respect to: sensor sensitivity and the design of future instruments; the potential utility and success of larger-scale remote sensing (i.e. in the presence of greater heterogeneity); improved understanding of soil moisture variability across spatial-temporal scales and its role in land-atmosphere interactions; and the parameterization of soil moisture and related processes in models of land surface hydrology. Sponsors: NASA, NSF, University of Texas Geology Foundation Participants: Stewart Franks Marcia Branstetter Tel: 512-471-8547 [email protected] Johanna Devereaux Tel: 512-471-8547 [email protected] Karen Mohr Tel: 512-471-8547 [email protected] Jay Famiglietti Tel: 512-471-3824 [email protected] Steve Graham Tel: 512-471-5023 [email protected] Matt Rodell Tel: 512-471-5762 [email protected] All at: Department of Geological Sciences, University of Texas at Austin Austin, TX 78712, Fax: 512-471-9425 INVESTIGATORS: Ronald L. Elliott, Professor and Gabriel B. Senay, Post-Doctoral Fellow INSTITUTION: Biosystems & Agricultural Engineering Dept. Oklahoma State University Stillwater, OK TITLE: In-Situ Soil Moisture Intercomparisons and Scale-Based Validation of an T/Soil Moisture Model ABSTRACT: Our investigations will be focused on two topics: (1) intercomparisons of soil moisture measurements; and (2) validation of evapotranspiration/soil moisture modeling at various spatial scales. These investigations will depend on ground and remote sensing data that are collected during the SGP97 experiment, as well as measurements that are made on an ongoing basis in Oklahoma. Analyses related to topic (1) will be conducted in the relatively near term, whereas studies of topic (2) will be longer term in nature. (1) The senior investigator has been directly involved in the addition of soil moisture sensors to 60 of the 114 Mesonet sites across Oklahoma. These sensors include a single TDR (time domain reflectometry) probe that provides layered data from five soil depths down to 90 cm, and four heat dissipation devices which are installed at depths of 5, 25, 60, and 75 cm. The TDR measurements are made periodically and provide data on volumetric water content, whereas the heat dissipation sensors are logged continuously and provide data on soil water potential. We not only seek to check the consistency between these two sources of data, but also to develop a soil- and sensor-specific calibration of the heat dissipation sensors to volumetric water content. The more intensive TDR sampling that will be done as part of SGP97 will enable us to expand these calibration data sets for the Mesonet sites in the study area. Furthermore, the surface (and perhaps profile) gravimetric sampling that will be done as part of SGP97 will provide a third, independent set of soil moisture data. With soil bulk density information from the sampling sites, the gravimetric data will be converted to volumetric water content and compared to the in-situ measurements. The OSU investigators will help to support the gravimetric sampling in the northern part of the SGP97 study area. (2) The investigators and their colleagues are developing a GIS-based simulation model for estimating daily latent heat flux (evapotranspiration) and soil moisture at various scales across a heterogeneous landscape. The model is physically based, tracks the soil water balance, and makes use of three data "layers" -- soil, vegetation, and weather. The highest resolution data layers consist of 4-hectare cells, each of which is considered homogeneous. Mesonet sites are well suited for validating the model at "points", but it becomes much more problematic to validate at larger scales. Soil moisture and surface flux measurements from SGP97 will provide a valuable data set for checking the model at various space (and time) scales. This work will be funded through the combined support of the Oklahoma Agricultural Experiment Station and the Oklahoma NSF and NASA EPSCoR programs. Investigator(s)/Institutions(s): Shafiqul Islam, University of Cincinnati Title: Scaling Properties of Soil Moisture Images Abstract: An outstanding research question critical to the integration of remotely sensed soil moisture into global models is how adequately the inherent spatial heterogeneity is represented at scales commensurate with current generation mesoscale and global climate models. To address this question, a framework is needed that can bridge the scale gap between the scale of remote sensors and large scale model resolution which can take into account the role of spatial heterogeneity. Recent research on spatial rainfall and streamflow has shown that they may exhibit scaling-multi scaling characteristics (Gupta and Waymire 1990). Our analysis of remotely sensed soil moisture images from Washita '92 experiment has shown that soil moisture also exhibits multi scaling properties (Hu et al.,1997). We hypothesize that the soil moisture images can be decomposed into large scale feature parts and small scale fluctuation parts. This decomposition will not make any apriori assumption regarding the structure of the soil moisture fields. Our preliminary results suggest the presence of simple scaling for the small-scale fluctuation parts. The limitations imposed by the data have allowed only three levels of decomposition and it is not clear over what range of scales such simple scaling exists. Using SGP97 data, we will explore and hopefully establish a relationship among the multi scaling properties observed in rainfall, soil moisture, and other land surface variables. References: Gupta, V.K. and E. Waymire (1990): "Multiscaling properties of spatial rainfall and river flow distributions", J. Geophys. Res. 95 (D3), 1999-2009. Hu, Z., S. Islam, and Y. Cheng (1997): "Statistical characterization of remotely sensed soil moisture images", in press, Remote Sensing of Environment. Investigator(s)/Institution(s): Shafiqul Islam, University of Cincinnati, Elfatih Eltahir, Massachusetts Institute of Technology Title: Relative Merits of Microwave Measurements of Soil Wetness and Radar Measurements of Rainfall for the Purpose of Estimating Soil Moisture Profile Abstract: Recent studies in land-atmosphere interactions have shown that large scale soil moisture information as well as estimate of the soil water within the soil column is essential for accurate partitioning of surface fluxes. Current microwave measurements of soil moisture provides an excellent estimate of the soil water content within the top few centimeters. For the first time entire United States will be covered by the NEXRAD systems that would provide very detailed spatial information of rainfall. We plan to explore a fusion approach that combines microwave measurements of soil moisture and radar measurements of rainfall within a coupled land-atmosphere model to infer the soil moisture profile. In this experiment, we would also compare and contrast the relative merits of microwave (for soil moisture) and radar (for rainfall) to infer soil moisture profile within a single- and multi-sensor mode. The planned SGP97 data set would be an ideal test bed to examine the validity of this proposed approach of multi-sensor fusion for soil moisture profile estimation. Sponsors: University of Cincinnati and Massachusetts Institute of Technology ----------------------------------------------------------------------- Shafiqul Islam Cincinnati Earth System Science Program Department of Civil and Environmental Engineering University of Cincinnati Phone: (513) 556-1026 P.O. Box 210071 Fax: (513) 556-2599 Cincinnati, Ohio 45221-0071 email: [email protected] Investigators/Institutions: Paul Doraiswamy and Craig Daughtry, USDA/ARS, Remote Sensing and Modeling Laboratory, Beltsville, MD Tom Jackson and Bill Kustas USDA/ARS, Hydrology Laboratory, Beltsville, MD Jerry Hatfield, USDA/ARS, Soil Tilth Laboratory, Ames, IA Title of Investigation: Study the techniques for retrieval of biophysical parameters from remote sensing and evaluate models for Leaf Area Index, Biomass and Energy balance of different canopies in the SGP experiment site. Abstract The seasonal vegetation dynamics will be monitored, using Landsat TM and NOAA AVHRR imagery acquired between May through July 1997. Ground measurements of LAW and green biomass will be monitored during the June-July period by Craig Daughtry. Several canopy models estimating surface reflectance (Verhoef, W., 1984), LAI (Clevers, J.G.P.W. et al., 1989 & Rahman H. et al., 1993) and biomass (Moran, M.S. et al., 1995) will be tested for their applicability in three major types of vegetative cover in the SGP study area. Biophysical parameters retrieved from remote sensing using several models will be evaluated. The extrapolation of parameters from field to region scales using models will be investigated for monitoring the vegetation dynamics throughout the summer period. Landsat TM and AVHRR data will be processed to provide good registration accuracy for correlation with ground samples collected through the study period. Soil moisture and surface energy balance modeling to extrapolate measurements from aircraft and flux stations to the surrounding areas will be investigated in collaboration with T. Jackson and W. Kustas. Geospatial statistical analysis of soil, vegetation, and atmospheric parameters measured on the ground will be used in developing models to study techniques for extrapolating parameters from small to large areas. References Clevers, J. G. P. W., (1989), "The application of a weighted infrared-red vegetation index for estimating leaf area index by correcting for soil moisture", Rem. Sens. Environ., 29:25-37. Moran, M.S., Maas, S.J., and Pinter, P.J., Jr. (1995). Combining Remote sensing and modeling for estimating surface evaporation and biomass production. Remote Sensing Reviews. 12:335-353. Verhoef, W., (1984), "Light scattering by leaf layers with application to canopy reflectance modeling: the SAIL model", Rem. Sens. Environ., 16:125-141. Utilizing Data from the Southern Great Plains Experiment with RADARSAT Data Eric F. Wood, Princeton University, Princeton, NJ 08544 T. J. Jackson, USDA ARS Hydrology Lab The goal of our participation in the Southern Great Plains Experiment is to develop improved remote sensing techniques for areal estimation of soil moisture, and to demonstrate that RADARSAT, either alone or in conjunction with other satellite and hydrologic observations, can provide soil moisture fields at regional scales. To date, the application of microwave radar remote sensing to soil moisture estimation has been hampered by several difficulties, including its sensitivity to vegetation and surface roughness, and understanding the relationship between observations from remote sensing instruments and point measurement values. The planned research activities are the following: 1. Field data collection. In discussion with Tom Jackson, we plan to participate and focus our collection at the USDA El Reno site. We are assuming that this site will have a surface flux station so point water and energy balance modeling can be carried out, post experiment. We are also planning on utilizing field scale data collected in the Little Washita and point measurements from the CART-ARM sites. These data will help us extend the research to scales more consistent with regional estimation. 2. Soil moisture retrievals. Test and develop calibration strategies for soil moisture retrieval algorithms for the RADARSAT satellite data using the above field data., and estimate spatial maps of soil moisture. This work will build on research developed under our SIR-C funding. 3. Analyses. Intercompare remotely sensed soil moisture maps derived from RADARSAT with those developed from airborne ESTAR passive microwave sensors, and with field data collected at El Reno, Little Washita and CART-Arm sites 4. Scaling. Study the scaling behavior of both airborne and satellite radar and derived soil moisture fields so as to develop strategies for regional soil estimation with lower resolution data than that collected in the SGP Experiment. The anticipated results of the research include an improved understanding of and estimation abilities for soil moisture at catchment to regional scales, and to understand the relationship between remotely sensed soil moisture and ground observations. Eric F. Wood Department of Civil Engineering Princeton University Princeton, NJ 08544 Tel: 609-258-4675 Fax: 609-258-2799 ([email protected]) Investigator/Institution: Peter J. Wetzel/NASA GSFC Title of investigation: Validation of PLACE land surface model using SGP97 observations Abstract: The SGP97 experiment provides a unique opportunity to validate land surface models on scales ranging from point to regional. As part of the ongoing validation of the PLACE (Wetzel and Boone, 1995) model, data from SGP97 will be applied to provide initial conditions for the model and to validate the model's predictions of soil moisture (Wetzel et al 1996; Boone and Wetzel 1996) and of evaporative fluxes. Eventually it is hoped that a data set can be developed which will be used for validation of other land surface models participating in the Project for Intercomparison of Land surface Parameterization Schemes (PILPS). References: Wetzel, P. J., and A. Boone, 1995: A parameterization for land-atmosphere-cloud exchange (PLACE): Documentation and testing of a detailed process model of the partly cloudy boundary layer over heterogeneous land, J. Climate, 8, 1810-1837. Wetzel, P. J., X. Liang, P. Irannejad, A. Boone, J. Noilhan, Y., Shao, C. Skelly, Y. Xue and Z.-L. Yang, 1996: Modeling vadose zone liquid water fluxes: Infiltration, runoff, drainage, interflow, Global and Planetary Change, 13, 57-71. Boone, A., and P. J. Wetzel, 1996: Issues related to low resolution modeling of soil moisture: Experience with the PLACEmodel, Global and Planetary Change, 13, 161-181. Investigator(s)/Institution(s): Christopher J. Duffy Civil and Environmental Engineering Dept., 212 Sackett Bldg Penn State University University Park, PA 16802 (814) 863-4384 (814) 863-7304 fax [email protected] Title of investigation: Hydrogeologic Reconnaissance SG97 Abstract: This investigation will involve field, library and agency (state, federal) research in order to compile available hydrogeologic data for the SG97 study sites. The compiled data will include geologic maps (digital and paper), groundwater level maps, and hopefully a reasonable number of historical well records. Field work will involve 1 week of site reconnaissance during June 97 (to be determined) including photographing all stream gaging stations, soil moisture sites, important landforms, geologic outcrops or other features of hydrologic interest. The hydrogeologic data base along with the site photos will be put on a CD-Rom and made available to all investigators. Christopher Duffy will initially work with Doug Miller who has the soils data compiled. The overall objective is to get at least a baseline of information on groundwater response during the experiment and to get some notion of the historical spatial and temporal variability in groundwater levels. References: A Two-State integral-balance model for soil moisture and groundwater dynamics in complex terrain, WRR, 32(8), 2421-2434, 1996. Ground-Based Visible and Near Infrared Radiometry Karen Humes University of Oklahoma Collaborating with: Bill Kustas and John Preuger (Flux measurements) Craig Daughtry (vegetation sampling and ground radiometry) Ground-based remote sensing measurements will be acquired in conjunction with flux measurements at the El Reno site and vegetation sampling at various sites. These measurements will be used to help develop and validate algorithms for several purposes: a) the estimation of surface fluxes with remotely sensed data; b) atmospheric corrections to satellite and aircraft data; c) the estimation of land cover and biomass from remotely sensed measurements. The radiometers to be used will include the 4-band Exotech radiometers (with bandpasses matching the TM and SPOT sensors) and occasional measurements with the ASD hyperspectral radiometer. Relating 19, 37, and 85 GHz field brightness measurements to SSM/I data during the SGP'97 Hydrology Experiment A.W. England, Jasmeet Judge, Brian Hornbuckle, Ed Kim and David Boprie The University of Michigan, Ann Arbor ABSTRACT We propose to monitor 19, 37, and 85 GHz sky- and ground-brightness and thermal infrared ground-brightness at the ARM SGP'97 site and to relate these observations to contemporaneous SSM/I data. The dominant landcover will be senescent winter wheat or, after the wheat is harvested, wheat stubble. The relatively low canopy column density in either case will allow some sensitivity to surface soil moisture at 19 GHz. Our radiometer system will be on a 10 m tower and will view the winter wheat/stubble at the SSM/I incidence angle of 53o. Data will be collected at half hour intervals for the duration of the experiment. Diurnal vegetation and soil samples will be collected periodically throughout the experiment. SSM/I data will be obtained from NSIDC and will be resampled to the Equal Area SSM/I Earth - grid (EASE - grid) for comparison with the field measurements. We will use our Land Surface Process/Radiobrightness (LSP/R) model to relate brightness at L-, C-, and S-band frequencies, and at the SSM/I frequencies to surface soil moisture and to local stored water. The LSP/R model has been validated in a series of Radiobrightness Energy Balance Experiments (REBEX) for prairie grassland in fall and winter (REBEX-1) and prairie grassland and bare soil in summer (REBEX-4). Our SGP'97 data will be combined with available meteorological and radiant flux data to validate the LSP/R model for winter wheat/stubble. Once validated, the model will be forced by observed weather and downwelling short- and long-wavelength radiance to predict 19, 37, and 85 GHz brightness for each of the dominate terrains within the SGP'97 region. These brightness will be aggregated for each local pixel of EASE-grid according to landcover fractions to yield a pixel brightness that can be compared with the resampled SSM/I data. We are particularly interested in a running comparison during a significant dry down period. -Investigators/Institutions: J. Ian MacPherson, PI, NRC Canada, Jocelyn Mailhot, co-I, AES/MRB, J. Walter Strapp, co-I, AES/MRB, Stephane Belair, co-I, AES/MRB NRC = National Research Council of Canada MRB = Meteorological Research Branch, AES = Atmospheric Environment Service Title: Mesoscale modelling of the convective boundary layer during SGP97 Abstract: The study addresses one of the main objectives of SGP97 "to examine the effect of soil moisture on the evolution of the atmospheric boundary layer and clouds over the southern great plains during the warm season". The investigation will focus on comparisons of detailed observations during SGP97 with mesoscale simulations using the MC2 (Mesoscale Compressible Community) model (Benoit et al. 1997) coupled with advanced land surface schemes, such as ISBA and CLASS (Noilhan and Planton 1989, Verseghy 1991), two models participating in PILPS. The high-resolution (order of a few km) models will be complemented with detailed spatial analyses of soil moisture measured with the ESTAR and SLFMR radiometers. The simulations will be compared with various measurements such as LASE, the Twin Otter aircraft turbulent flux observations, surface and tower measurements, and satellite remote sensing data. This will provide a unique opportunity to investigate various aspects of the structure an devolution of the convective boundary layer (CBL) during SGP97, on a variety of regional and local scales. The study also has some connection with another field study, MERMOZ, having objectives similar to SGP97. MERMOZ took place in Canada during June 1996 and will continue in August 1997, to examine several aspects of the CBL, in particular the influence of soil moisture on CBL evolution and entrainment processes near the CBL top (Mailhot et al. 1997a,b). References: Benoit, R., M. Desgagne, P. Pellerin, S. Pellerin, Y. Chartier, and S. Desjardins, 1997: The Canadian MC2: A semi-Lagrangian, semi-implicit wide-band atmospheric model suited for fine-scale process studies and simulation. Mon. Wea. Rev., (in press) Mailhot, J., and the MERMOZ Scientific Team, 1997a: MERMOZ Project Report. Recherche en prevision numerique, Atmospheric Environment Service, Dorval, Canada, 156 pp. Mailhot, J., R. Benoit, S. Belair, J.W. Strapp, J.I. MacPherson, N.R. Donaldson, J. Goldstein, F. Froude, M. Benjamin, I. Zawadski and R.R. Rogers, 1997b: The Montreal-96 Experiment on Regional Mixing and Ozone (MERMOZ): An overview and some preliminary results. Bull. Amer. Met. Soc. (submitted). Noilhan, J., and S. Planton, 1989: A simple parameterization of land surface processes for meteorological model. Mon. Wea. Rev., 117, 536-549. Verseghy, D.L., 1991: CLASS - A Canadian land surface scheme for GCMs. Soil model. Int. J. Climatol., 11, 111-133. Jocelyn Mailhot, Recherche en Prevision Numerique, Environnement Canada, 2121 Trans-Canada N., Suite 500, Dorval, Quebec, CANADA H9P-1J3. Phone:(514) 421-4760 Fax:(514) 421-2106 e-mail (Internet): [email protected] Stephane Belair Recherche en Prevision Numerique Environnement Canada, 2121 Trans-Canada N., Suite 500, Dorval, Quebec, CANADA H9P-1J3. Ian MacPherson, Flight Research Laboratory, NRC, Ottawa, ON, K1A 0R6 Walter Strapp, Cloud Physics Research Division, AES, Downsview, ON, M3H5T4
2020-02-23T04:36:04
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http://pdglive.lbl.gov/DataBlock.action?node=Q007TP2
# ${{\boldsymbol t}}$-QUARK MASS We first list the direct measurements of the top quark mass which employ the event kinematics and then list the measurements which extract a top quark mass from the measured ${{\mathit t}}{{\overline{\mathit t}}}$ cross-section using theory calculations. A discussion of the definition of the top quark mass in these measurements can be found in the review The Top Quark.'' For earlier search limits see PDG 1996 , Physical Review D54 1 (1996). We no longer include a compilation of indirect top mass determinations from Standard Model Electroweak fits in the Listings (our last compilation can be found in the Listings of the 2007 partial update). For a discussion of current results see the reviews "The Top Quark" and "Electroweak Model and Constraints on New Physics." # ${{\boldsymbol t}}$-Quark Mass from Cross-Section Measurements INSPIRE search The top quark $\overline{\rm{}MS}$ or pole mass can be extracted from a measurement of ${\mathit \sigma (}$ ${{\mathit t}}{{\overline{\mathit t}}}{)}$ by using theory calculations. We quote below the $\overline{\rm{}MS}$ mass. See the review The Top Quark'' and references therein for more information. VALUE (GeV) DOCUMENT ID TECN  COMMENT $160.0$ ${}^{+4.8}_{-4.3}$ 1 2011 S D0 ${\mathit \sigma (}$ ${{\mathit t}}{{\overline{\mathit t}}}{)}$ + theory • • • We do not use the following data for averages, fits, limits, etc. • • • 2 2009 AG D0 cross sects, theory + exp 3 2009 R D0 cross sects, theory + exp 1  Based on 5.3 fb${}^{-1}$ in ${{\mathit p}}{{\overline{\mathit p}}}$ collisions at $\sqrt {s }$ = 1.96 TeV. ABAZOV 2011S uses the measured ${{\mathit t}}{{\overline{\mathit t}}}$ production cross section of $8.13$ ${}^{+1.02}_{-0.90}$ pb [ABAZOV 2011E] in the lepton plus jets channel to obtain the top quark $\overline{\rm{}MS}$ mass by using an approximate NNLO computation (MOCH 2008 , LANGENFELD 2009 ). The corresponding top quark pole mass is $167.5$ ${}^{+5.4}_{-4.9}$ GeV. A different theory calculation (AHRENS 2010 , AHRENS 2010A) is also used and yields m${}^{\overline{\rm{}MS}}_{t}$ = $154.5$ ${}^{+5.0}_{-4.3}$ GeV. 2  Based on 1 fb${}^{-1}$ of data at $\sqrt {s }$ = 1.96 TeV. Uses the ${{\mathit \ell}}$ + jets, ${{\mathit \ell}}{{\mathit \ell}}$ , and ${{\mathit \ell}}{{\mathit \tau}}$ + jets channels. ABAZOV 2009AG extract the pole mass of the top quark using two different calculations that yield $169.1$ ${}^{+5.9}_{-5.2}$ GeV (MOCH 2008 , LANGENFELD 2009 ) and $168.2$ ${}^{+5.9}_{-5.4}$ GeV (KIDONAKIS 2008 ). 3  Based on 1 fb${}^{-1}$ of data at $\sqrt {s }$ = 1.96 TeV. Uses the ${{\mathit \ell}}{{\mathit \ell}}$ and ${{\mathit \ell}}{{\mathit \tau}}$ + jets channels. ABAZOV 2009R extract the pole mass of the top quark using two different calculations that yield $173.3$ ${}^{+9.8}_{-8.6}$ GeV (MOCH 2008 , LANGENFELD 2009 ) and $171.5$ ${}^{+9.9}_{-8.8}$ GeV (CACCIARI 2008 ). References: ABAZOV 2011S PL B703 422 Determination of the Pole and $\overline{\rm{}MS}$ Masses of the top Quark from the ${\mathit {\mathit t}}{\mathit {\overline{\mathit t}}}$ Cross Section ABAZOV 2009AG PR D80 071102 Combination of ${{\mathit t}}{{\overline{\mathit t}}}$ Cross Section Measurements and Constraints on the Mass of the Top Quark and Its Decays into Charged Higgs Bosons ABAZOV 2009R PL B679 177 Measurement of the ${\mathit {\mathit t}}{\mathit {\overline{\mathit t}}}$ Production Cross Section and Top Quark Mass Extraction using Dilepton Events in ${{\mathit p}}{{\overline{\mathit p}}}$ Collisions ABAZOV 2011E PR D84 012008 Measurement of the Top Quark Pair Production Cross Section in the Lepton+Jets Channel in Proton-Antiproton Collisions at $\sqrt {s }$ = 1.96 TeV MOCH 2008 PR D78 034003 Theoretical Status and Prospects for top-Quark Pair Production at Hadron Colliders LANGENFELD 2009 PR D80 054009 Measuring the Running top-Quark Mass
2019-02-21T20:09:41
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https://codereview.stackexchange.com/questions/257486/quicksort-algorithm-speed
# Quicksort Algorithm Speed I have made a sorting algorithm in Python 3. This sorting algorithm is a modified optimized median of 3 quicksort, with network sorting for lists of size up to 16 and for finding the median. I have tried using the O(N) approach to finding the median, but sorting normally was faster. Can I get some advice on how to make this faster? Also, can anyone link fast sorting algorithms? I want to compare them to mine and see if there are faster, and if they are, how I can improve mine. The first like 1000 lines is the network sorting (I made a program to automatically generate code for the network sorting, I am not a madman), and the final 20ish is testing how fast it is. On my laptop, it sorts 100,000 random numbers in about 0.192 seconds and 1,000,000 random numbers in about 2.754 seconds. (Note that python's time is not 100% accurate. I used multiple tests and found the average.) I have compared my code to mergesort, heapsort, other quicksorts, timsort, and radix sort, but none of them seem to be close to beating my code. However, that is likely because they were from how-to sites, and were not optimized. Sadly, most people who care about having a quick sorting algorithm seem to write it in Java, C or C++ which I can't really compare. So, I would appreciate any other optimized sorting algorithms, or even suggestions to my original code. #importing import math import random import time #this is the sorting network (scroll a bunch, this is like 1000 lines) def sorting_network(lst): l = len(lst) if l < 9: if l < 5: if l < 3: if not l or l == 1: return lst else: a = lst[0] b = lst[1] if a > b: a, b = b, a return [a, b] else: if l == 3: a = lst[0] b = lst[1] c = lst[2] if a > b: a, b = b, a if b > c: b, c = c, b if a > b: a, b = b, a return [a, b, c] else: a = lst[0] b = lst[1] c = lst[2] d = lst[3] if a > b: a, b = b, a if c > d: c, d = d, c if a > c: a, c = c, a if b > d: b, d = d, b if b > c: b, c = c, b return [a, b, c, d] else: if l < 7: if l == 5: a = lst[0] b = lst[1] c = lst[2] d = lst[3] e = lst[4] if a > d: a, d = d, a if b > e: b, e = e, b if a > b: a, b = b, a if c > e: c, e = e, c if b > c: b, c = c, b if d > e: d, e = e, d if c > d: c, d = d, c return [a, b, c, d, e] else: a = lst[0] b = lst[1] c = lst[2] d = lst[3] e = lst[4] f = lst[5] if a > f: a, f = f, a if b > d: b, d = d, b if c > e: c, e = e, c if b > c: b, c = c, b if d > e: d, e = e, d if a > d: a, d = d, a if c > f: c, f = f, c if a > b: a, b = b, a if c > d: c, d = d, c if e > f: e, f = f, e if b > c: b, c = c, b if d > e: d, e = e, d return [a, b, c, d, e, f] else: if l == 7: a = lst[0] b = lst[1] c = lst[2] d = lst[3] e = lst[4] f = lst[5] g = lst[6] if a > b: a, b = a, b if c > d: c, d = d, c if e > f: e, f = f, e if a > c: a, c = c, a if b > e: b, e = e, b if d > g: d, g = g, d if a > b: a, b = b, a if c > f: c, f = f, c if d > e: d, e = e, d if b > c: b, c = c, b if e > g: e, g = g, e if c > d: c, d = d, c if e > f: e, f = f, e if b > c: b, c = c, b if d > e: d, e = e, d if f > g: f, g = g, f return [a, b, c, d, e, f, g] else: a = lst[0] b = lst[1] c = lst[2] d = lst[3] e = lst[4] f = lst[5] g = lst[6] h = lst[7] if a > c: a, c = c, a if b > d: b, d = d, b if e > g: e, g = g, e if f > h: f, h = h, f if a > e: a, e = e, a if b > f: b, f = f, b if c > g: c, g = g, c if d > h: d, h = h, d if a > b: a, b = b, a if c > d: c, d = d, c if e > f: e, f = f, e if g > h: g, h = h, g if c > e: c, e = e, c if d > f: d, f = f, d if b > e: b, e = e, b if d > g: d, g = g, d if b > c: b, c = c, b if d > e: d, e = e, d if f > g: f, g = g, f return [a, b, c, d, e, f, g, h] else: if l < 13: if l < 11: if l == 9: a = lst[0] b = lst[1] c = lst[2] d = lst[3] e = lst[4] f = lst[5] g = lst[6] h = lst[7] i = lst[8] if a > d: a, d = d, a if b > h: b, h = h, b if c > f: c, f = f, c if e > i: e, i = i, e if a > h: a, h = h, a if c > e: c, e = e, c if d > i: d, i = i, d if f > g: f, g = g, f if a > c: a, c = c, a if b > d: b, d = d, b if e > f: e, f = f, e if h > i: h, i = i, h if b > e: b, e = e, b if d > g: d, g = g, d if f > h: f, h = h, f if a > b: a, b = b, a if c > e: c, e = e, c if d > f: d, f = f, d if g > i: g, i = i, g if c > d: c, d = d, c if e > f: e, f = f, e if g > h: g, h = h, g if b > c: b, c = c, b if d > e: d, e = e, d if f > g: f, g = g, f return [a, b, c, d, e, f, g, h, i] else: a = lst[0] b = lst[1] c = lst[2] d = lst[3] e = lst[4] f = lst[5] g = lst[6] h = lst[7] i = lst[8] j = lst[9] if a > i: a, i = i, a if b > j: b, j = j, b if c > h: c, h = h, c if d > f: d, f = f, d if e > g: e, g = g, e if a > c: a, c = c, a if b > e: b, e = e, b if f > i: f, i = i, f if h > j: h, j = j, h if a > d: a, d = d, a if c > e: c, e = e, c if f > h: f, h = h, f if g > j: g, j = j, g if a > b: a, b = b, a if d > g: d, g = g, d if i > j: i, j = j, i if b > f: b, f = f, b if c > d: c, d = d, c if e > i: e, i = i, e if g > h: g, h = h, g if b > c: b, c = c, b if d > f: d, f = f, d if e > g: e, g = g, e if h > i: h, i = i, h if c > d: c, d = d, c if e > f: e, f = f, e if g > h: g, h = h, g if d > e: d, e = e, d if f > g: f, g = g, f return [a, b, c, d, e, f, g, h, i, j] else: if l == 11: a = lst[0] b = lst[1] c = lst[2] d = lst[3] e = lst[4] f = lst[5] g = lst[6] h = lst[7] i = lst[8] j = lst[9] k = lst[10] if b > g: b, g = g, b if c > e: c, e = e, c if d > h: d, h = h, d if f > i: f, i = i, f if a > b: a, b = b, a if d > f: d, f = f, d if e > k: e, k = k, e if g > j: g, j = j, g if h > i: h, i = i, h if b > d: b, d = d, b if c > f: c, f = f, c if e > h: e, h = h, e if i > k: i, k = k, i if a > e: a, e = e, a if b > c: b, c = c, b if d > h: d, h = h, d if f > j: f, j = j, f if g > i: g, i = i, g if a > b: a, b = b, a if c > g: c, g = g, c if e > f: e, f = f, e if h > i: h, i = i, h if j > k: j, k = k, j if c > e: c, e = e, c if d > g: d, g = g, d if f > h: f, h = h, f if i > j: i, j = j, i if b > c: b, c = c, b if d > e: d, e = e, d if f > g: f, g = g, f if h > i: h, i = i, h if c > d: c, d = d, c if e > f: e, f = f, e if g > h: g, h = h, g return [a, b, c, d, e, f, g, h, i, j, k] else: a = lst[0] b = lst[1] c = lst[2] d = lst[3] e = lst[4] f = lst[5] g = lst[6] h = lst[7] i = lst[8] j = lst[9] k = lst[10] l = lst[11] if b > h: b, h = h, b if c > g: c, g = g, c if d > l: d, l = l, d if e > k: e, k = k, e if f > j: f, j = j, f if a > b: a, b = b, a if c > f: c, f = f, c if d > e: d, e = e, d if g > j: g, j = j, g if h > i: h, i = i, h if k > l: k, l = l, k if a > c: a, c = c, a if b > g: b, g = g, b if f > k: f, k = k, f if j > l: j, l = l, j if a > d: a, d = d, a if b > c: b, c = c, b if e > g: e, g = g, e if f > h: f, h = h, f if i > l: i, l = l, i if j > k: j, k = k, j if b > e: b, e = e, b if d > f: d, f = f, d if g > i: g, i = i, g if h > k: h, k = k, h if b > d: b, d = d, b if c > f: c, f = f, c if g > j: g, j = j, g if i > k: i, k = k, i if c > d: c, d = d, c if e > f: e, f = f, e if g > h: g, h = h, g if i > j: i, j = j, i if e > g: e, g = g, e if f > h: f, h = h, f if d > e: d, e = e, d if f > g: f, g = g, f if h > i: h, i = i, h return [a, b, c, d, e, f, g, h, i, k, l] else: if l < 15: if l == 13: a = lst[0] b = lst[1] c = lst[2] d = lst[3] e = lst[4] f = lst[5] g = lst[6] h = lst[7] i = lst[8] j = lst[9] k = lst[10] l = lst[11] m = lst[12] if a > m: a, m = m, a if b > k: b, k = k, b if c > j: c, j = j, c if d > h: d, h = h, d if f > l: f, l = l, f if g > i: g, i = i, g if b > g: b, g = g, b if c > d: c, d = d, c if e > l: e, l = l, e if h > j: h, j = j, h if i > k: i, k = k, i if a > e: a, e = e, a if b > c: b, c = c, b if d > g: d, g = g, d if h > i: h, i = i, h if j > k: j, k = k, j if l > m: l, m = m, l if e > g: e, g = g, e if f > j: f, j = j, f if i > l: i, l = l, i if k > m: k, m = m, k if a > f: a, f = f, a if d > i: d, i = i, d if e > h: e, h = h, e if g > l: g, l = l, g if j > k: j, k = k, j if a > b: a, b = b, a if c > f: c, f = f, c if g > j: g, j = j, g if h > i: h, i = i, h if k > l: k, l = l, k if b > d: b, d = d, b if c > e: c, e = e, c if f > g: f, g = g, f if j > k: j, k = k, j if b > c: b, c = c, b if d > e: d, e = e, d if f > h: f, h = h, f if g > i: g, i = i, g if c > d: c, d = d, c if e > f: e, f = f, e if g > h: g, h = h, g if i > j: i, j = j, i if d > e: d, e = e, d if f > g: f, g = g, f return [a, b, c, d, e, f, g, h, i, j, k, l, m] else: a = lst[0] b = lst[1] c = lst[2] d = lst[3] e = lst[4] f = lst[5] g = lst[6] h = lst[7] i = lst[8] j = lst[9] k = lst[10] l = lst[11] m = lst[12] n = lst[13] if a > g: a, g = g, a if b > l: b, l = l, b if c > m: c, m = m, c if d > k: d, k = k, d if e > f: e, f = f, e if h > n: h, n = n, h if i > j: i, j = j, i if b > c: b, c = c, b if d > h: d, h = h, d if e > i: e, i = i, e if f > j: f, j = j, f if g > k: g, k = k, g if l > m: l, m = m, l if a > e: a, e = e, a if b > d: b, d = d, b if f > g: f, g = g, f if h > i: h, i = i, h if j > n: j, n = n, j if k > m: k, m = m, k if a > b: a, b = b, a if c > j: c, j = j, c if d > h: d, h = h, d if e > l: e, l = l, e if g > k: g, k = k, g if m > n: m, n = n, m if c > f: c, f = f, c if e > h: e, h = h, e if g > j: g, j = j, g if i > l: i, l = l, i if b > c: b, c = c, b if d > e: d, e = e, d if g > h: g, h = h, g if j > k: j, k = k, j if l > m: l, m = m, l if b > d: b, d = d, b if c > e: c, e = e, c if f > g: f, g = g, f if h > i: h, i = i, h if j > l: j, l = l, j if k > m: k, m = m, k if c > d: c, d = d, c if e > h: e, h = h, e if g > j: g, j = j, g if k > l: k, l = l, k if e > f: e, f = f, e if g > h: g, h = h, g if i > j: i, j = j, i if d > e: d, e = e, d if f > g: f, g = g, f if h > i: h, i = i, h if j > k: j, k = k, j return [a, b, c, d, e, f, g, h, i, j, k, l, m, n] else: if l == 15: a = lst[0] b = lst[1] c = lst[2] d = lst[3] e = lst[4] f = lst[5] g = lst[6] h = lst[7] i = lst[8] j = lst[9] k = lst[10] l = lst[11] m = lst[12] n = lst[13] o = lst[14] if b > c: b, c = c, b if d > k: d, k = k, d if e > o: e, o = o, e if f > i: f, i = i, f if g > n: g, n = n, g if h > m: h, m = m, h if j > l: j, l = l, j if a > o: a, o = o, a if b > f: b, f = f, b if c > i: c, i = i, c if d > h: d, h = h, d if g > j: g, j = j, g if k > m: k, m = m, k if l > n: l, n = n, l if a > h: a, h = h, a if b > g: b, g = g, b if c > j: c, j = j, c if e > k: e, k = k, e if f > l: f, l = l, f if i > n: i, n = n, i if m > o: m, o = o, m if a > g: a, g = g, a if c > e: c, e = e, c if d > f: d, f = f, d if h > l: h, l = l, h if i > k: i, k = k, i if j > m: j, m = m, j if n > o: n, o = o, n if a > d: a, d = d, a if b > c: b, c = c, b if e > h: e, h = h, e if f > j: f, j = j, f if g > i: g, i = i, g if k > l: k, l = l, k if m > n: m, n = n, m if a > b: a, b = b, a if c > d: c, d = d, c if e > g: e, g = g, e if h > j: h, j = j, h if k > m: k, m = m, k if l > n: l, n = n, l if b > c: b, c = c, b if d > f: d, f = f, d if i > k: i, k = k, i if l > m: l, m = m, l if d > e: d, e = e, d if f > g: f, g = g, f if h > i: h, i = i, h if j > k: j, k = k, j if c > d: c, d = d, c if e > f: e, f = f, e if g > h: g, h = h, g if i > j: i, j = j, i if k > l: k, l = l, k if f > g: f, g = g, f if h > i: h, i = i, h return [a, b, c, d, e, f, g, h, i, j, k, l, m, n, o] else: a = lst[0] b = lst[1] c = lst[2] d = lst[3] e = lst[4] f = lst[5] g = lst[6] h = lst[7] i = lst[8] j = lst[9] k = lst[10] l = lst[11] m = lst[12] n = lst[13] o = lst[14] p = lst[15] if a > n: a, n = n, a if b > m: b, m = m, b if c > p: c, p = p, c if d > o: d, o = o, d if e > i: e, i = i, e if f > g: f, g = g, f if h > l: h, l = l, h if j > k: j, k = k, j if a > f: a, f = f, a if b > h: b, h = h, b if c > j: c, j = j, c if d > e: d, e = e, d if g > n: g, n = n, g if i > o: i, o = o, i if k > p: k, p = p, k if l > m: l, m = m, l if a > b: a, b = b, a if c > d: c, d = d, c if e > f: e, f = f, e if g > i: g, i = i, g if h > j: h, j = j, h if k > l: k, l = l, k if m > n: m, n = n, m if o > p: o, p = p, o if a > c: a, c = c, a if b > d: b, d = d, b if e > k: e, k = k, e if f > l: f, l = l, f if g > h: g, h = h, g if i > j: i, j = j, i if m > o: m, o = o, m if n > p: n, p = p, n if b > c: b, c = c, b if d > m: d, m = m, d if e > g: e, g = g, e if f > h: f, h = h, f if i > k: i, k = k, i if j > l: j, l = l, j if n > o: n, o = o, n if b > e: b, e = e, b if c > g: c, g = g, c if f > i: f, i = i, f if h > k: h, k = k, h if j > n: j, n = n, j if l > o: l, o = o, l if c > e: c, e = e, c if d > g: d, g = g, d if j > m: j, m = m, j if l > n: l, n = n, l if d > f: d, f = f, d if g > i: g, i = i, g if h > j: h, j = j, h if k > m: k, m = m, k if d > e: d, e = e, d if f > g: f, g = g, f if h > i: h, i = i, h if j > k: j, k = k, j if l > m: l, m = m, l if g > h: g, h = h, g if i > j: i, j = j, i return [a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p] #and this is the quicksort algorithm! def swiftsort(lst): l = len(lst) if l < 17: return sorting_network(lst) elif l < 128: a = lst[0] b = lst[l // 2] c = lst[-1] if a <= b <= c or c <= b <= a: split = b elif b <= c <= a or a <= c <= b: split = c else: split = a elif l < 8192: a = [lst[0], lst[l // 8], lst[2 * l // 8], lst[3 * l // 8], lst[4 * l // 8], lst[5 * l // 8], lst[6 * l // 8], lst[7 * l // 8], lst[-1]] split = sorting_network(lst)[4] else: a = [lst[0]] for x in range(1, 32): a.append(lst[x * l // 32]) a.append(lst[-1]) split = swiftsort(a)[16] lst1 = [] lst2 = [] mid = [] for x in lst: if x < split: lst1.append(x) elif x == split: mid.append(x) else: lst2.append(x) return swiftsort(lst1) + mid + swiftsort(lst2) #This is for testing the time of my algorithm. length = 100000 runs = 60 test_list = [random.randint(1, length) for _ in range(length)] t = 0 for _ in range(runs): start = time.time() sort = swiftsort(test_list) end = time.time() t += end - start print(t / runs) • Python is not a good choice for benchmarking algorithms, since it is an interpretive language and slow. I would recommend C or C++ compiled with an optimizing compiler. Mar 21, 2021 at 22:21 • Welcome to Code Review@SE. I have made a sorting algorithm… I don't think so - you tried to implement quicksort, but left out base cases, for starters. Try print(swiftsort(list('abramccarthybra'))). (…made a sorting algorithm in python conventional wordings include coded, implemented, crafted an implementation.) Mar 21, 2021 at 22:41 • Ok, I have edited my title (is it better now?). Also, I have removed the insertion sort part because I wasn't using it anymore, and added the network sorting from 13-16. It should work now! I'll also try to add comments to the code. EDIT: I've added a few comments to seperate my code out. Mar 21, 2021 at 23:10 • I do find the title much improved. Remaining issue with it: There's little need to repeat tags. I have removed the insertion sort part funny - I thought the "almost median of 32" uses it. Mar 21, 2021 at 23:38 • I've changed the insertion sort part to my quicksort algorithm itself because it was faster. Also, I've edited my post. Mar 21, 2021 at 23:45 (This begins with opinions about the way the partition&network sort presented by Sola Sky is coded. I intend to get to comments on resource requirements - don't hold your breath.) In your question, you provide context: the what & why. Do so in the code! Python has got it right providing docstrings, a documentation mechanism succeeding in making it unlikely for code to be separated from its documentation. (It even is available for introspection.) You may find yourself wanting to rename sorting_network() after writing its docstring. Docstrings feature in the Style Guide for Python Code, which you seem aware of. It contains good advice such as comments are unnecessary and in fact distracting if they state the obvious - #importing is a non-comment. math currently is not used. (random and time are "just" used in the benchmark - more on this later.) sorting_network(lst): I notice you do not use Type Hints. In the "decision tree", there is no need for an else following a return. One advantage of doing without is less code indentation. I'd have liked to read, in the code, about the type of comparison network your generator constructs - I didn't try to figure it out, no comment on using networks of optimal depth or comparators(/comparisons?) here. My IDE "counts" 60 for len 16 - best known I find. (and this is the quicksort algorithm! To split a hair, I expect quicksort to sort in-place (and, hopefully, with additional space dominated by the size of input). I'd use partition sort.) swiftsort(lst): return-else, again "Habitually", quicksort is coded with pivot selection and partition factored out. The "between-comparisons" are very readable - split = b if a <= b == b <= c else c if b <= c == c <= a else a repeats one comparison instead of potentially four. Prefer a for in comprehensions over enumerating the elements or appending them in a loop: [lst[l_ * i // 8] for i in range(9) for l_ in (l - 1,)] (The second for just introduces l_ (=l-1) "in-line") "The 8192-limit" looks somewhat arbitrary - how about using one item less than the number of bits in ls representation? samples = (int.bit_length(l) // 2) * 2 - 1 samples = [lst[(l - 1) * i // (samples - 1)] for i in range(samples)] pivot = sorted(samples)[len(samples)//2] (I could write (int.bit_length(l)&~1) - can I read it? You? The maintenance programmer?) (For no more than 16 items, swiftsort()/sorting_network() look advantageous. Not so sure immediately above.) (Oh, look, you could do away with "the 128 comparison", too.) While lst is a so-so name to begin with, lst1/lst2 just don't do: I'd prefer before&after over preceding&following for brevity, and over smaller/bigger for not interpreting the order (which you may want redefinable via mechanisms like an optional comparator or a reverse flag like sorted()). In languages providing a shorter syntax for this, I might prefer the equivalent of (before if x < split else mid if x == split else after).append(x) to stress the difference is in picking the sequence, not in the operation on it or the parameter. In a "production strength sort", I'd try to avoid worst case resource consumption: recurse on the shorter of before&after, iterate on the other. Doesn't look any simpler with three-way partition. With Python code in files, there are named modules: the module name is the file name "without the trailing .py". The module a python interpreter is started to execute has the name "__main__" during execution. This allows keeping short tests or benchmarks in code intended to be used library style: # This is for testing the time of my algorithm. if __name__== '__main__': import random # place "non-library imports" here # some test code Assessing resource usage to expect in general and timing, micro-benchmarking in particular are interesting cans of worms. Let me just mention timeit and Cython. And that the bigger of the problem sizes you chose fits into (L3) cache of contemporary general purpose processors. • The more I think about it, the less I like swiftsort() to use additional lists instead of sorting in-place. Mar 22, 2021 at 20:56 • Ok, thanks! The reason I didn't do in place was because it was harder to code the partitions, and it was almost 2x slower. However, that might be because I'm a beginner coder. If you could help me write quicksort inplace without affecting the speed heavily, I would appreciate it a lot. Also, I'd definitely change the partitions to the bit_length suggestion you made. I'd try to make better variable names, type hints and more. Thanks a lot! Mar 22, 2021 at 21:22 • The main pretext I have for not doing so is that when you are doing three-way partition anyway, you may as well go dual pivot. (Not true by a mile ordering unique values, but then you'd know len(mid) at the outset of partition.) I'd be tempted even more if I could adapt the ordering network code generator too: that would need to generate code ordering in-place, too. Note that posting on SE puts contents under Creative Commons. Mar 23, 2021 at 6:40
2022-05-17T21:46:07
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http://dergipark.gov.tr/ieja/issue/25202/266310
| | | | ## SOME CHARACTERIZATIONS OF ARTINIAN RINGS #### H. Khabazian [1] ##### 65 157 In this paper, we investigate rings in which the prime radical is an annihilator and present a characterization of Artinian rings satisfying this property. We also study rings in which the singular ideal and the prime radical coincide. Finally we show that Artinian rings are the direct product of a semiprime ring and a semiprime-free ring (ring in which every nonzero ideal contains a nonzero nilpotent ideal) and present a result on quasi-Baer Artinian rings. prime, semiprime, semiprime-free, rAI-semiprime, Artinian, quasiBaer, QF, essential, annihilator • W. E. Clark, Twisted matrix units semigroup algebra, Duke Math. J., 34 (1967), 423. • P. M. Cohn, Reversible rings, Bull. London Math. Soc., 31 (1999), 641-648. • H. Khabazian, Primary decomposition for noncommutative rings, Vietnam J. Math., 36(2) (2008), 183-190. • T.Y. Lam, Lectures on Modules and Rings, Springer-Verlag, 1998. • D. S. Passman, Infinite Group Ring, Marcel Dekker Inc, 1971. H. Khabazian • Department of Mathematical Sciences, Isfahan University of Technology Isfahan 84156-83111, Iran. e-mail: [email protected] Konular JA85BD23CD Makaleler Yazar: H. Khabazian Bibtex @ { ieja266310, journal = {International Electronic Journal of Algebra}, issn = {1306-6048}, eissn = {1306-6048}, address = {Prof. Dr. Abdullah HARMANCI}, year = {2011}, volume = {9}, pages = {1 - 9}, doi = {}, title = {SOME CHARACTERIZATIONS OF ARTINIAN RINGS}, key = {cite}, author = {Khabazian, H.} } APA Khabazian, H . (2011). SOME CHARACTERIZATIONS OF ARTINIAN RINGS. International Electronic Journal of Algebra, 9 (9), 1-9. Retrieved from http://dergipark.gov.tr/ieja/issue/25202/266310 MLA Khabazian, H . "SOME CHARACTERIZATIONS OF ARTINIAN RINGS". International Electronic Journal of Algebra 9 (2011): 1-9 Chicago Khabazian, H . "SOME CHARACTERIZATIONS OF ARTINIAN RINGS". International Electronic Journal of Algebra 9 (2011): 1-9 RIS TY - JOUR T1 - SOME CHARACTERIZATIONS OF ARTINIAN RINGS AU - H. Khabazian Y1 - 2011 PY - 2011 N1 - DO - T2 - International Electronic Journal of Algebra JF - Journal JO - JOR SP - 1 EP - 9 VL - 9 IS - 9 SN - 1306-6048-1306-6048 M3 - UR - Y2 - 2019 ER - EndNote %0 International Electronic Journal of Algebra SOME CHARACTERIZATIONS OF ARTINIAN RINGS %A H. Khabazian %T SOME CHARACTERIZATIONS OF ARTINIAN RINGS %D 2011 %J International Electronic Journal of Algebra %P 1306-6048-1306-6048 %V 9 %N 9 %R %U ISNAD Khabazian, H. . "SOME CHARACTERIZATIONS OF ARTINIAN RINGS". International Electronic Journal of Algebra 9 / 9 (Haziran 2011): 1-9.
2019-02-23T06:41:38
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http://home.fnal.gov/~mrenna/lutp0613man2/node118.html
Next: Extended Higgs Sector Up: Supersymmetry Previous: Supersymmetry   Contents ### General Introduction In any () supersymmetric version of the SM there exists a partner to each SM state with the same gauge quantum numbers but whose spin differs by one half unit. Additionally, the dual requirements of generating masses for up- and down-type fermions while preserving SUSY and gauge invariance, require that the SM Higgs sector be enlarged to two scalar doublets, with corresponding spin-partners. After Electroweak symmetry breaking (EWSB), the bosonic Higgs sector contains a quintet of physical states: two CP-even scalars, and , one CP-odd pseudoscalar, , and a pair of charged scalar Higgs bosons, (naturally, this classification is only correct when CP violation is absent in the Higgs sector. Non-trivial phases between certain soft-breaking parameters will induce mixing between the CP eigenstates). The fermionic Higgs (called Higgsino') sector is constituted by the superpartners of these fields, but these are not normally exact mass eigenstates, so we temporarily postpone the discussion of them. In the gauge sector, the spin- partners of the and gauge bosons (called gauginos') are the Bino, , the neutral Wino, , and the charged Winos, and , while the partner of the gluon is the gluino, . After EWSB, the and mix with the neutral Higgsinos, , to form four neutral Majorana fermion mass-eigenstates, the neutralinos, . In addition, the charged Higgsinos, , mix with the charged Winos, and , resulting in two charged Dirac fermion mass eigenstates, the charginos, . Note that the and , which sometimes occur in the literature, are linear combinations of the and , by exact analogy with the mixing giving the and , but these are not normally mass eigenstates after EWSB, due to the enlarged mixing caused by the presence of the Higgsinos. The spin-0 partners of the SM fermions (so-called scalar fermions', or sfermions') are the squarks , sleptons , and sneutrinos . Each fermion (except possibly the neutrinos) has two scalar partners, one associated with each of its chirality states. These are named left-handed and right-handed sfermions, respectively. Due to their scalar nature, it is of course impossible for these particles to possess any intrinsic handedness' themselves, but they inherit their couplings to the gauge sector from their SM partners, so that e.g. a does not couple to while a does. Generically, the KF code numbering scheme used in PYTHIA reflects the relationship between particle and sparticle, so that e.g. for sfermions, the left-handed (right-handed) superpartners have codes 1000000 (2000000) plus the code of the corresponding SM fermion. A complete list of the particle partners and their KF codes is given in Table . Note that, antiparticles of scalar particles are denoted by , i.e. . A gravitino is also included with KF=1000039. The gravitino is only relevant in PYTHIA when simulating models of gauge-mediated SUSY breaking, where the gravitino becomes the lightest superpartner. In practice, the gravitino simulated here is the spin- Goldstino components of the spin- gravitino. The MSSM Lagrangian contains interactions between particles and sparticles, with couplings fixed by SUSY. There are also a number of soft SUSY-breaking mass parameters. Soft' here means that they break the mass degeneracy between SM particles and their SUSY partners without reintroducing quadratic divergences in the theory or destroying its gauge invariance. In the MSSM, the soft SUSY-breaking parameters are extra mass terms for gauginos and sfermions and trilinear scalar couplings. Further soft terms may arise, for instance in models with broken -parity, but we here restrict our attention to the minimal case (for RPV in PYTHIA see section ). The exact number of independent parameters depends on the detailed mechanism of SUSY breaking. The general MSSM model in PYTHIA assumes only a few relations between these parameters which seem theoretically difficult to avoid. Thus, the first two generations of sfermions with otherwise similar quantum numbers, e.g. and , have the same masses. Despite such simplifications, there are a fairly large number of parameters that appear in the SUSY Lagrangian and determine the physical masses and interactions with Standard Model particles, though far less than the which are allowed in all generality. The Lagrangian (and, hence, Feynman rules) follows the conventions set down by Kane and Haber in their Physics Report article [Hab85] and the papers of Gunion and Haber [Gun86a]. Once the parameters of the softly-broken SUSY Lagrangian are specified, the interactions are fixed, and the sparticle masses can be calculated. Note that, when using SUSY Les Houches Accord input, PYTHIA automatically translates between the SLHA conventions and the above, with no action required on the part of the user. Next: Extended Higgs Sector Up: Supersymmetry Previous: Supersymmetry   Contents Stephen Mrenna 2007-10-30
2018-01-23T21:29:50
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https://zbmath.org/authors/?q=ai%3Agorban.alexander-n
# zbMATH — the first resource for mathematics ## Gorban, Alexander N. Compute Distance To: Author ID: gorban.alexander-n Published as: Gorban’, A.; Gorban’, A. N.; Gorban, A.; Gorban, A. N.; Gorban, Alexander; Gorban, Alexander N.; Gorban, Alexandr N. External Links: MGP · Wikidata Documents Indexed: 91 Publications since 1977, including 13 Books all top 5 #### Co-Authors 23 single-authored 14 Karlin, Iliya V. 9 Tyukin, Ivan Yu. 6 Verbitskij, V. I. 4 Cheresiz, Vladimir Mikhaĭlovich 4 Levesley, Jeremy 4 Tyukina, Tatiana A. 3 Mirkes, Evgeny M. 3 Öttinger, Hans Christian 3 Sadovskii, M. G. 3 Smirnova, Elena V. 3 Zinovyev, Andrey Yu. 2 Gorban, Pavel A. 2 Pokidysheva, Lyudmila I. 2 Popova, Tatyana G. 2 Prokhorov, Danil V. 2 Steur, Erik 2 Yablonskij, G. S. 2 Zinovyev, Andrei 1 Al-Ameri, J. M. 1 Boulouchos, Konstantinos 1 Brownlee, Robert 1 Bugaenko, N. N. 1 Burton, Richard M. 1 Bykov, Valeriǐ I. 1 Calvo, Carlos Adolfo 1 Cangiani, Andrea 1 Chiavazzo, Eliodoro 1 Davidchack, Ruslan L. 1 Elkington, Peter A. S. 1 Georgoulis, Emmanuil H. 1 Gilev, S. E. 1 Golubkov, Artem Yu. 1 Grechuk, Bogdan 1 Green, Stephen R. 1 Ilg, Patrick 1 Jarman, N. 1 Judge, George G. 1 Kazantzis, Nikolaos K. 1 Kégl, Balázs 1 Kevrekidis, Ioannis George 1 Khlebopros, Rem G. 1 Kolokoltsov, Vassili N. 1 Korablev, Yu. A. 1 Makarov, Valeri A. 1 Makarova, Yulia 1 Melamed, V. B. 1 Nijmeijer, Henk 1 Okhonin, Victor A. 1 Packwood, D. J. 1 Packwood, David 1 Petrovskii, Sergei V. 1 Romanenko, Ilya 1 Roose, Dirk 1 Rossiev, A. A. 1 Rossiev, D. A. 1 Sargsyan, H. P. 1 Senashova, M. Yu. 1 Shahzad, Muhammad Rizwan 1 Shokin, Yuriĭ Ivanovich 1 Sofeikov, Konstantin I. 1 Sumner, N. R. 1 Tatarinova, Larisa L. 1 Theodoropoulos, Constantinos 1 Tretyakov, Michael V. 1 Tsibul’skij, G. M. 1 Utyubaev, G. Sh. 1 van Leeuwen, Cees 1 Verbitskij, B. I. 1 Wahab, Hafiz Abdul 1 Whetton, James A. 1 Wunsch, Donald C. II 1 Zmievskij, Vladimir B. all top 5 #### Serials 8 Mathematical Modelling of Natural Phenomena 5 Transport Theory and Statistical Physics 4 Information Sciences 3 Bulletin of Mathematical Biology 3 Siberian Mathematical Journal 3 Open Systems & Information Dynamics 3 Sibirskiĭ Zhurnal Industrial’noĭ Matematiki 2 Computers & Mathematics with Applications 2 Physica A 2 Sibirskiĭ Matematicheskiĭ Zhurnal 2 Soviet Mathematics. Doklady 2 Applied Mathematics Letters 2 Neural Networks 2 Journal of Non-Newtonian Fluid Mechanics 2 Doklady Mathematics 2 Entropy 2 Lecture Notes in Computational Science and Engineering 1 Differentsial’nye Uravneniya 1 SIAM Journal on Control and Optimization 1 Soviet Mathematics 1 Advances in Modeling & Simulation 1 Numerical Algorithms 1 Bulletin of the American Mathematical Society. New Series 1 Continuum Mechanics and Thermodynamics 1 Russian Mathematics 1 Journal of Computer and Systems Sciences International 1 Vychislitel’nye Tekhnologii 1 Sorosovskiĭ Obrazovatel’nyĭ Zhurnal 1 Sibirskiĭ Zhurnal Vychislitel’noĭ Matematiki 1 Annalen der Physik. 8th Series 1 Communications in Nonlinear Science and Numerical Simulation 1 SIAM Journal on Applied Dynamical Systems 1 Mathematical Medicine and Biology 1 Journal of Statistical Mechanics: Theory and Experiment 1 Electronic Journal of Differential Equations. Monograph 1 Lecture Notes in Physics 1 Mathematical Geosciences 1 Journal of Theoretical Biology all top 5 #### Fields 24 Biology and other natural sciences (92-XX) 19 Computer science (68-XX) 19 Statistical mechanics, structure of matter (82-XX) 16 Fluid mechanics (76-XX) 13 General and overarching topics; collections (00-XX) 9 Dynamical systems and ergodic theory (37-XX) 7 Ordinary differential equations (34-XX) 7 Classical thermodynamics, heat transfer (80-XX) 6 Probability theory and stochastic processes (60-XX) 6 Statistics (62-XX) 5 Partial differential equations (35-XX) 5 Approximations and expansions (41-XX) 5 Functional analysis (46-XX) 5 General topology (54-XX) 5 Numerical analysis (65-XX) 4 Real functions (26-XX) 4 Operator theory (47-XX) 3 Measure and integration (28-XX) 3 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 3 Systems theory; control (93-XX) 3 Information and communication theory, circuits (94-XX) 2 Global analysis, analysis on manifolds (58-XX) 2 Operations research, mathematical programming (90-XX) 1 History and biography (01-XX) 1 Integral equations (45-XX) 1 Convex and discrete geometry (52-XX) 1 Geophysics (86-XX) #### Citations contained in zbMATH 50 Publications have been cited 255 times in 188 Documents Cited by Year Invariant manifolds for physical and chemical kinetics. Zbl 1086.82009 Gorban, Alexander N.; Karlin, Iliya V. 2005 Hydrodynamics from Grad’s equations: What can we learn from exact solutions? Zbl 1068.76074 Karlin, Iliya V.; Gorban, Alexander N. 2002 Selection theorem for systems with inheritance. Zbl 1337.92150 Gorban, A. N. 2007 Entropy: the Markov ordering approach. Zbl 1229.60085 Gorban, Alexander N.; Gorban, Pavel A.; Judge, George 2010 Hilbert’s 6th problem: exact and approximate hydrodynamic manifolds for kinetic equations. Zbl 1294.35052 Gorban, Alexander N.; Karlin, Ilya 2014 Quasichemical models of multicomponent nonlinear diffusion. Zbl 1234.35131 Gorban, A. N.; Sargsyan, H. P.; Wahab, H. A. 2011 Method of invariant manifolds and regularization of acoustic spectra. Zbl 0812.76077 Gorban, Alexander N.; Karlin, Iliya V. 1994 Stable simulation of fluid flow with high-Reynolds number using Ehrenfest’s steps. Zbl 1121.76049 Brownlee, R.; Gorban, A. N.; Levesley, J. 2007 Structure and approximations of the Chapman-Enskog expansion for the linearized Grad equations. Zbl 0756.76066 Gorban, Alexandr N.; Karlin, Iliya V. 1992 The Michaelis-Menten-Stueckelberg theorem. Zbl 1303.92152 2011 Principal manifolds for data visualization and dimension reduction. Reviews and original papers presented partially at the workshop ‘Principal manifolds for data cartography and dimension reduction’, Leicester, UK, August 24–26, 2006. Zbl 1125.68003 Gorban, Alexander N. (ed.); Kégl, Balázs (ed.); Wunsch, Donald C. (ed.); Zinovyev, Andrei (ed.) 2008 Model reduction and coarse-graining approaches for multiscale phenomena. Selected papers from the workshop held at the University of Leicester, Leicester, UK, August 24–26, 2005. Zbl 1129.82005 Gorban, Alexander N. (ed.); Kazantzis, Nikolaos K. (ed.); Kevrekidis, Ioannis G. (ed.); Öttinger, Hans Christian (ed.); Theodoropoulos, Constantinos (ed.) 2006 Corrections and enhancements of quasi-equilibrium states. Zbl 1060.82520 Gorban, Alexander N.; Karlin, Iliya V.; Ilg, Patrick; Öttinger, Hans Christian 2001 Approximation with random bases: pro et contra. Zbl 1427.68361 Gorban, Alexander N.; Tyukin, Ivan Yu.; Prokhorov, Danil V.; Sofeikov, Konstantin I. 2016 Neural networks on a personal computer. Zbl 0931.68114 Gorban’, A. N.; Rossiev, D. A. 1996 Enhancement of the stability of lattice Boltzmann methods by dissipation control. Zbl 1395.76068 Gorban, A. N.; Packwood, D. J. 2014 Maxallent: maximizers of all entropies and uncertainty of uncertainty. Zbl 1384.62018 Gorban, A. N. 2013 Elastic principal graphs and manifolds and their practical applications. Zbl 1274.62408 Gorban, A.; Zinovyev, A. 2005 Legendre integrators, post-processing and quasi-equilibrium. Zbl 1143.76533 Gorban, Alexander N.; Gorban, Pavel A.; Karlin, Iliya V. 2004 Singularities of transition processes in dynamical systems: Qualitative theory of critical delays. Zbl 1057.54028 Gorban, Alexander N. 2004 Irreversibility in the short memory approximation. Zbl 1031.82020 Karlin, Iliya V.; Tatarinova, Larisa L.; Gorban, Alexander N.; Öttinger, Hans Christian 2003 Neural network iterative method of principal curves for data with gaps. Zbl 1077.68763 Gorban’, A. N.; Rossiev, A. A. 1999 Approximation of continuous functions of several variables by an arbitrary nonlinear continuous function of one variable, linear functions, and their superpositions. Zbl 0940.41017 Gorban, A. N. 1998 Three waves of chemical dynamics. Zbl 1330.92007 Gorban, A. N.; Yablonsky, G. S. 2015 Leaders do not look back, or do they? Zbl 1332.34074 Gorban, A. N.; Jarman, N.; Steur, E.; van Leeuwen, C.; Tyukin, I. Yu. 2015 Lyapunov-like conditions of forward invariance and boundedness for a class of unstable systems. Zbl 1283.34050 Gorban, A. N.; Tyukin, I.; Steur, E.; Nijmeijer, H. 2013 Topological grammars for data approximation. Zbl 1167.68378 Gorban, A. N.; Sumner, N. R.; Zinovyev, A. Y. 2007 Basic types of coarse-graining. Zbl 1141.82012 Gorban, A. N. 2006 Self-organizing approach for automated gene identification. Zbl 1034.92012 Zinovyev, Andrey Yu.; Gorban, Alexander N.; Popova, Tatyana G. 2003 Modified Kirchhoff flow with a partially penetrable obstacle and its application to the efficiency of free flow turbines. Zbl 1076.76516 Gorban, A.; Braverman, M.; Silantyev, V. 2002 Two-step approximation of space-independent relaxation. Zbl 0946.76085 Gorban, Alexander N.; Karlin, Iliya V.; Zmievskij, Vladimir B. 1999 Stochastic separation theorems. Zbl 1429.68217 Gorban, A. N.; Tyukin, I. Y. 2017 Fast sampling of evolving systems with periodic trajectories. Zbl 1390.93238 Tyukin, I. Yu.; Gorban, A. N.; Tyukina, T. A.; Al-Ameri, J. M.; Korablev, Yu. A. 2016 Evolution of adaptation mechanisms: adaptation energy, stress, and oscillating death. Zbl 1343.92344 Gorban, Alexander N.; Tyukina, Tatiana A.; Smirnova, Elena V.; Pokidysheva, Lyudmila I. 2016 Editorial: Grasping complexity. Zbl 1339.00026 Gorban, A. N. (ed.); Yablonski, G. S. (ed.) 2013 Thermodynamic tree: the space of admissible paths. Zbl 1283.37009 Gorban, Alexander N. 2013 A numerical analyst’s view of the lattice Boltzmann method. Zbl 1426.76604 Levesley, Jeremy; Gorban, Alexander N.; Packwood, David 2011 Law of the minimum paradoxes. Zbl 1225.92042 Gorban, Alexander N.; Pokidysheva, Lyudmila I.; Smirnova, Elena V.; Tyukina, Tatiana A. 2011 Coping with complexity: Model reduction and data analysis. Selected papers based on the presentations at the international research workshop, Ambleside, UK, August 31–September 4, 2009. Zbl 1202.00097 Gorban, Alexander N. (ed.); Roose, Dirk (ed.) 2011 Combustion simulation via lattice Boltzmann and reduced chemical kinetics. Zbl 07229872 Chiavazzo, Eliodoro; Karlin, Iliya V.; Gorban, Alexander N.; Boulouchos, Konstantinos 2009 The mystery of two straight lines in bacterial genome statistics. Zbl 1298.92065 Gorban, A. N.; Zinovyev, A. Y. 2007 Riabouchinsky flow with partially penetrable obstacle. Zbl 1027.76006 Gorban’, A.; Silantyev, V. 2002 Classification of symbol sequences over their frequency dictionaries: Towards the connection between structure and natural taxonomy. Zbl 0956.92003 Gorban, A. N.; Popova, T. G.; Sadovsky, M. G. 2000 A generalized approximation theorem and an exact representation of polynomials of several variables by superpositions of polynomials of one variable. Zbl 07091938 Gorban’, A. N. 1998 Maximum entropy method in analysis of genetic text and measurement of its information content. Zbl 0986.92022 Bugaenko, N. N.; Gorban, A. N.; Sadovsky, M. G. 1998 A generalized approximation theorem and computational capabilities of neural networks. Zbl 0903.68152 Gorban’, A. N. 1998 On “solid liquid” limit of hydrodynamic equations. Zbl 0891.76004 Gorban, A. N.; Karlin, I. V. 1995 Nonarbitrary regularization of acoustic spectra. Zbl 0772.76064 Gorban, Alexandr N.; Karlin, Iliya V. 1993 Quasi-equilibrium approximations and nonstandard expansions in the theory of the Boltzmann kinetic equation. Zbl 0820.76074 Gorban’, A. N.; Karlin, I. V. 1992 Thermodynamic constraints and conditions for being quasithermodynamic in chemical kinetics. Zbl 0967.80503 Verbitskij, V. I.; Gorban’, A. N. 1989 Stochastic separation theorems. Zbl 1429.68217 Gorban, A. N.; Tyukin, I. Y. 2017 Approximation with random bases: pro et contra. Zbl 1427.68361 Gorban, Alexander N.; Tyukin, Ivan Yu.; Prokhorov, Danil V.; Sofeikov, Konstantin I. 2016 Fast sampling of evolving systems with periodic trajectories. Zbl 1390.93238 Tyukin, I. Yu.; Gorban, A. N.; Tyukina, T. A.; Al-Ameri, J. M.; Korablev, Yu. A. 2016 Evolution of adaptation mechanisms: adaptation energy, stress, and oscillating death. Zbl 1343.92344 Gorban, Alexander N.; Tyukina, Tatiana A.; Smirnova, Elena V.; Pokidysheva, Lyudmila I. 2016 Three waves of chemical dynamics. Zbl 1330.92007 Gorban, A. N.; Yablonsky, G. S. 2015 Leaders do not look back, or do they? Zbl 1332.34074 Gorban, A. N.; Jarman, N.; Steur, E.; van Leeuwen, C.; Tyukin, I. Yu. 2015 Hilbert’s 6th problem: exact and approximate hydrodynamic manifolds for kinetic equations. Zbl 1294.35052 Gorban, Alexander N.; Karlin, Ilya 2014 Enhancement of the stability of lattice Boltzmann methods by dissipation control. Zbl 1395.76068 Gorban, A. N.; Packwood, D. J. 2014 Maxallent: maximizers of all entropies and uncertainty of uncertainty. Zbl 1384.62018 Gorban, A. N. 2013 Lyapunov-like conditions of forward invariance and boundedness for a class of unstable systems. Zbl 1283.34050 Gorban, A. N.; Tyukin, I.; Steur, E.; Nijmeijer, H. 2013 Editorial: Grasping complexity. Zbl 1339.00026 Gorban, A. N. (ed.); Yablonski, G. S. (ed.) 2013 Thermodynamic tree: the space of admissible paths. Zbl 1283.37009 Gorban, Alexander N. 2013 Quasichemical models of multicomponent nonlinear diffusion. Zbl 1234.35131 Gorban, A. N.; Sargsyan, H. P.; Wahab, H. A. 2011 The Michaelis-Menten-Stueckelberg theorem. Zbl 1303.92152 2011 A numerical analyst’s view of the lattice Boltzmann method. Zbl 1426.76604 Levesley, Jeremy; Gorban, Alexander N.; Packwood, David 2011 Law of the minimum paradoxes. Zbl 1225.92042 Gorban, Alexander N.; Pokidysheva, Lyudmila I.; Smirnova, Elena V.; Tyukina, Tatiana A. 2011 Coping with complexity: Model reduction and data analysis. Selected papers based on the presentations at the international research workshop, Ambleside, UK, August 31–September 4, 2009. Zbl 1202.00097 Gorban, Alexander N. (ed.); Roose, Dirk (ed.) 2011 Entropy: the Markov ordering approach. Zbl 1229.60085 Gorban, Alexander N.; Gorban, Pavel A.; Judge, George 2010 Combustion simulation via lattice Boltzmann and reduced chemical kinetics. Zbl 07229872 Chiavazzo, Eliodoro; Karlin, Iliya V.; Gorban, Alexander N.; Boulouchos, Konstantinos 2009 Principal manifolds for data visualization and dimension reduction. Reviews and original papers presented partially at the workshop ‘Principal manifolds for data cartography and dimension reduction’, Leicester, UK, August 24–26, 2006. Zbl 1125.68003 Gorban, Alexander N. (ed.); Kégl, Balázs (ed.); Wunsch, Donald C. (ed.); Zinovyev, Andrei (ed.) 2008 Selection theorem for systems with inheritance. Zbl 1337.92150 Gorban, A. N. 2007 Stable simulation of fluid flow with high-Reynolds number using Ehrenfest’s steps. Zbl 1121.76049 Brownlee, R.; Gorban, A. N.; Levesley, J. 2007 Topological grammars for data approximation. Zbl 1167.68378 Gorban, A. N.; Sumner, N. R.; Zinovyev, A. Y. 2007 The mystery of two straight lines in bacterial genome statistics. Zbl 1298.92065 Gorban, A. N.; Zinovyev, A. Y. 2007 Model reduction and coarse-graining approaches for multiscale phenomena. Selected papers from the workshop held at the University of Leicester, Leicester, UK, August 24–26, 2005. Zbl 1129.82005 Gorban, Alexander N. (ed.); Kazantzis, Nikolaos K. (ed.); Kevrekidis, Ioannis G. (ed.); Öttinger, Hans Christian (ed.); Theodoropoulos, Constantinos (ed.) 2006 Basic types of coarse-graining. Zbl 1141.82012 Gorban, A. N. 2006 Invariant manifolds for physical and chemical kinetics. Zbl 1086.82009 Gorban, Alexander N.; Karlin, Iliya V. 2005 Elastic principal graphs and manifolds and their practical applications. Zbl 1274.62408 Gorban, A.; Zinovyev, A. 2005 Legendre integrators, post-processing and quasi-equilibrium. Zbl 1143.76533 Gorban, Alexander N.; Gorban, Pavel A.; Karlin, Iliya V. 2004 Singularities of transition processes in dynamical systems: Qualitative theory of critical delays. Zbl 1057.54028 Gorban, Alexander N. 2004 Irreversibility in the short memory approximation. Zbl 1031.82020 Karlin, Iliya V.; Tatarinova, Larisa L.; Gorban, Alexander N.; Öttinger, Hans Christian 2003 Self-organizing approach for automated gene identification. Zbl 1034.92012 Zinovyev, Andrey Yu.; Gorban, Alexander N.; Popova, Tatyana G. 2003 Hydrodynamics from Grad’s equations: What can we learn from exact solutions? Zbl 1068.76074 Karlin, Iliya V.; Gorban, Alexander N. 2002 Modified Kirchhoff flow with a partially penetrable obstacle and its application to the efficiency of free flow turbines. Zbl 1076.76516 Gorban, A.; Braverman, M.; Silantyev, V. 2002 Riabouchinsky flow with partially penetrable obstacle. Zbl 1027.76006 Gorban’, A.; Silantyev, V. 2002 Corrections and enhancements of quasi-equilibrium states. Zbl 1060.82520 Gorban, Alexander N.; Karlin, Iliya V.; Ilg, Patrick; Öttinger, Hans Christian 2001 Classification of symbol sequences over their frequency dictionaries: Towards the connection between structure and natural taxonomy. Zbl 0956.92003 Gorban, A. N.; Popova, T. G.; Sadovsky, M. G. 2000 Neural network iterative method of principal curves for data with gaps. Zbl 1077.68763 Gorban’, A. N.; Rossiev, A. A. 1999 Two-step approximation of space-independent relaxation. Zbl 0946.76085 Gorban, Alexander N.; Karlin, Iliya V.; Zmievskij, Vladimir B. 1999 Approximation of continuous functions of several variables by an arbitrary nonlinear continuous function of one variable, linear functions, and their superpositions. Zbl 0940.41017 Gorban, A. N. 1998 A generalized approximation theorem and an exact representation of polynomials of several variables by superpositions of polynomials of one variable. Zbl 07091938 Gorban’, A. N. 1998 Maximum entropy method in analysis of genetic text and measurement of its information content. Zbl 0986.92022 Bugaenko, N. N.; Gorban, A. N.; Sadovsky, M. G. 1998 A generalized approximation theorem and computational capabilities of neural networks. Zbl 0903.68152 Gorban’, A. N. 1998 Neural networks on a personal computer. Zbl 0931.68114 Gorban’, A. N.; Rossiev, D. A. 1996 On “solid liquid” limit of hydrodynamic equations. Zbl 0891.76004 Gorban, A. N.; Karlin, I. V. 1995 Method of invariant manifolds and regularization of acoustic spectra. Zbl 0812.76077 Gorban, Alexander N.; Karlin, Iliya V. 1994 Nonarbitrary regularization of acoustic spectra. Zbl 0772.76064 Gorban, Alexandr N.; Karlin, Iliya V. 1993 Structure and approximations of the Chapman-Enskog expansion for the linearized Grad equations. Zbl 0756.76066 Gorban, Alexandr N.; Karlin, Iliya V. 1992 Quasi-equilibrium approximations and nonstandard expansions in the theory of the Boltzmann kinetic equation. Zbl 0820.76074 Gorban’, A. N.; Karlin, I. V. 1992 Thermodynamic constraints and conditions for being quasithermodynamic in chemical kinetics. Zbl 0967.80503 Verbitskij, V. I.; Gorban’, A. N. 1989 all top 5 all top 5 #### Cited in 78 Serials 14 Bulletin of Mathematical Biology 11 Mathematical Modelling of Natural Phenomena 9 Computers & Mathematics with Applications 9 Journal of Mathematical Chemistry 7 Journal of Computational Physics 7 Journal of Fluid Mechanics 7 Journal of Mathematical Sciences (New York) 7 Entropy 6 Journal of Statistical Physics 4 Physica A 4 Physica D 4 Journal of Theoretical Biology 3 Fluid Dynamics 3 Information Sciences 3 Bulletin of the American Mathematical Society. New Series 3 Continuum Mechanics and Thermodynamics 3 Communications in Nonlinear Science and Numerical Simulation 2 Computers and Fluids 2 Computer Methods in Applied Mechanics and Engineering 2 Quarterly of Applied Mathematics 2 Systems & Control Letters 2 Mathematical and Computer Modelling 2 Neural Networks 2 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 2 SIAM Journal on Applied Mathematics 2 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 2 Physics of Fluids 2 Mathematical Problems in Engineering 2 European Journal of Control 2 Nonlinear Dynamics 2 Open Systems & Information Dynamics 2 Chaos 2 Combustion Theory and Modelling 2 Nonlinear Analysis. Modelling and Control 2 SIAM Journal on Applied Dynamical Systems 1 International Journal of Modern Physics A 1 Archive for Rational Mechanics and Analysis 1 Computer Physics Communications 1 International Journal of Control 1 International Journal of General Systems 1 Journal of Mathematical Analysis and Applications 1 Journal of Mathematical Biology 1 Journal of Mathematical Physics 1 Journal of the Mechanics and Physics of Solids 1 Nonlinearity 1 Physics Reports 1 Transport Theory and Statistical Physics 1 Applied Mathematics and Computation 1 Computing 1 Journal of Approximation Theory 1 Meccanica 1 Siberian Mathematical Journal 1 Applied Mathematics Letters 1 Journal of Scientific Computing 1 Numerical Algorithms 1 Computational Statistics 1 Computational Mathematics and Mathematical Physics 1 Applied Mathematical Modelling 1 Communications in Statistics. Theory and Methods 1 Journal of Nonlinear Science 1 Computational Optimization and Applications 1 Russian Journal of Mathematical Physics 1 Computer Science Journal of Moldova 1 Discrete and Continuous Dynamical Systems 1 Multibody System Dynamics 1 Sibirskiĭ Zhurnal Industrial’noĭ Matematiki 1 Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 Acta Mathematica Sinica. English Series 1 Doklady Physics 1 International Journal of Modern Physics C 1 Journal of Nonlinear Mathematical Physics 1 Differential Equations 1 Journal of Machine Learning Research (JMLR) 1 Advances in Complex Systems 1 Journal of Statistical Mechanics: Theory and Experiment 1 The Journal of Prime Research in Mathematics 1 Axioms 1 Prikladnaya Diskretnaya Matematika all top 5 #### Cited in 28 Fields 58 Fluid mechanics (76-XX) 56 Biology and other natural sciences (92-XX) 34 Partial differential equations (35-XX) 27 Statistical mechanics, structure of matter (82-XX) 20 Classical thermodynamics, heat transfer (80-XX) 17 Ordinary differential equations (34-XX) 17 Systems theory; control (93-XX) 15 Numerical analysis (65-XX) 13 Dynamical systems and ergodic theory (37-XX) 12 Statistics (62-XX) 12 Computer science (68-XX) 9 Probability theory and stochastic processes (60-XX) 8 Information and communication theory, circuits (94-XX) 6 Mechanics of particles and systems (70-XX) 5 Mechanics of deformable solids (74-XX) 5 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 4 Calculus of variations and optimal control; optimization (49-XX) 3 General and overarching topics; collections (00-XX) 2 Combinatorics (05-XX) 2 Approximations and expansions (41-XX) 2 Optics, electromagnetic theory (78-XX) 2 Quantum theory (81-XX) 2 Operations research, mathematical programming (90-XX) 1 Potential theory (31-XX) 1 Operator theory (47-XX) 1 Differential geometry (53-XX) 1 General topology (54-XX) 1 Manifolds and cell complexes (57-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.
2021-03-04T04:28:08
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http://www.giss.nasa.gov/tools/latex/ltx-117.html
## Hypertext Help with LaTeX ### Math Symbols TeX provides almost any mathematical symbol you're likely to need. Some, like + - = < > | are obtained from the keyboard (the first three can be used in any mode; the last three only in math mode). Others are generated by LaTeX commands and can generally be used only in math mode. The following describe some of the useful symbols • \frac generates fractions (math mode) • \sqrt generates n-th root symbol (math mode) • \stackrel places one item above another (math mode)
2015-07-03T10:37:06
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https://www.usgs.gov/news/technical-announcement/darpa-announces-winners-artificial-intelligence-competition-aid
December 16, 2022 RESTON, Va. — Critical minerals are essential to the U.S. economy and national security; however, their supply is vulnerable to disruption. U.S. production and refining of critical minerals has been declining for decades, while production has become more concentrated in fewer countries. Given the urgency to increase and better secure critical-mineral supply, The Defense Advanced Research Projects Agency (DARPA) partnered with the U.S. Geological Survey (USGS) to launch the Artificial Intelligence for Critical Mineral Assessment Competition in August 2022. The partnership will help the USGS conduct more than 50 assessments of critical-mineral resources to aid in economic planning and land-use decision-making. To do this, the USGS draws from more than a century of accumulated data, contained mostly within geologic maps and reports, that provide the fundamental basis for these resource assessments. Extracting useful and accurate information from these maps is a time-consuming and laborious process involving manual human effort. In fact, a typical assessment for one critical mineral takes approximately two years to prepare. That’s because the USGS map catalog consists of more than 100,000 geologic maps; only about 10% of those are available as georeferenced images and only about half of those are fully digitized vector files needed for analysis. Everything else – 90% of the data – consists of scanned images of paper maps. The goal of the competition was to crowdsource ideas that could drastically reduce the time required to complete parts of the assessment, using AI and machine learning to automate key processes. “The competition has been a valuable opportunity for the USGS to work with leading minds in AI to improve our approach to critical-mineral assessments,” said David Applegate, USGS Director. “It has already led to incredible time savings in how we prepare data in a machine-readable format. Furthermore, these machine-learning models have implications beyond mineral resources into other fields that use map data, including geologic mapping, ecological mapping of species diversity and many other application areas.” “We anticipate our experience will serve as a road map for future interagency collaborations where machine learning can be applied to real-world problems,” said Bart Russell, deputy director of DARPA’s Defense Sciences Office. After analyzing the mineral-assessment workflow, DARPA and its performers MITRE and NASA Jet Propulsion Laboratory recognized the greatest potential for near-term, high impact was in solving the data needs associated with georeferencing and extraction of individual geologic features found on USGS maps. As such, the competition was divided into two distinct sub-challenges. A total of 18 teams from industry, academia and even a high-school junior competed for cash prizes of $10,000 for first place,$3,000 for second and \$1,000 for third. For the Map Georeferencing Challenge, participants were tasked to find a map within a given scanned image and georeference it by aligning reference points to base maps, such as grid lines, topography, administrative boundaries, roads, or towns. A Canadian company, Uncharted, received top prize for their simple, clean and organized solution. U.S. company Jataware received second place, and “Team Ptolemy,” with members from the Massachusetts Institute of Technology, University of Arizona and Pennsylvania State University, received third place. For the Map Feature Extraction Challenge, participants were asked to extract features identified in an image’s map legend. Students and faculty from the University of Southern California Information Sciences Institute and University of Minnesota joined forces, earning first place for their exceptional solution to extract line features as well as polygons and points. “Team ICM” from the University of Illinois received second place, followed by Uncharted in third. Throughout the competition, participants had up to eight weeks to complete each challenge. Each week, they had the option to submit their results for a blind validation dataset to test the accuracy of their code. In the last week of each challenge, participants received a completely blind evaluation dataset and had 24 hours to process and submit their code and detailed documentation of their approach, which was evaluated by experts from USGS, MITRE and NASA Jet Propulsion Laboratory, who reviewed the solutions for accuracy/usability. To meet the high quality standards required by the USGS, the resulting solutions require further evaluation and development to become operational. USGS experts plan to integrate the best elements of the submissions into a workable solution for mineral assessment workflows and potentially for other mission area assessments within the agency. In addition to identifying fresh approaches for this problem, DARPA officials view these competitions as a model for how transition partners can access the agency’s performer base. To hear more about the competition, including insights from members of the winning teams, listen to Voices from DARPA podcast episode 63, “So Many Maps, So Little Time: Using AI to Locate Critical Minerals.” A list of winners can be found on the DARPA website.
2023-02-06T19:54:59
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http://www-minimax.fnal.gov/Internal/archives/minimax/0565.html
# Proposed Revisions to MiniMax paper Cyrus Taylor ([email protected]) Fri, 27 Aug 1999 15:01:59 -0400 Fellow MiniMaxers- (My apologies for taking so long. I was on vacation, then had to make by next Wednesday (1 Sept) if you have any changes you would like to make to my proposed modifications (which are in turn based on those Tom proposed a few weeks ago). After receiving your suggestions, I will make the final changes to the text, which I hope to submit next week. Since the referee indicated >The paper presents new results and it therefore should be published, in >PRD. these should be the final revisions. I hope all is well, Cyrus *************** Dear Dr. Ripka, This is in reply to the referees report on df7229 Brooks, T., Search for disoriented chiral condensate at the Fermilab Tevatron. We would very much like to thank the referee for his/her comments. Members of the collaboration uniformly noted that the referee was someone sympathetic, conscientious, and very knowledgeable. I'd now like to turn to the changes we have made in accordance with the >1. The authors begin by introducing the expected P(f) for a DCC state. It >would be good if they could present the distribution they have found, or >at least one that is consistent with their data. Can they not unfold this >distribution? Is the neutral pion fraction indeed 1/3? In order to completely unfold the distribution, one needs detailed knowledge of the efficiencies, including the efficiencies for seeing two photons from the decay of a single pi-zero. The point of the robust observables is that they are sensitive to the presence or absence of DCC, without being sensitive to such unknowns. We conclude that the data are consistent with a binomial distribution. This conclusion does not depend on detailed knowledge of the efficiencies. Any P(f) of the form $\delta(f-f_0)$ , where $0<f_0<1$, would be consistent with this conclusion. However, as the referee notes in point 8, our Figure 8 indicates that the overall ratio of neutral pions to total pions is roughly ("at the 10% level") that of Pythia, that is, about 1/3. This conclusion, however, depends in detail on the Monte-Carlo simulations so is a weaker than our overall conclusions. We have addressed the referee's question by adding the following paragraph after the sixth paragraph of section VI. CONCLUSIONS: "These limits are consistent with generic, binomial-distribution partition of pions into charged and neutral species. While the robust observables, being independent of detection efficiencies, do not permit the determination of the neutral fraction, we note that Figure 8 indicates that the normalization of the observed inclusive measurements of gammas and charged particles agree with Pythia/GEANT simulations at roughly the 10\% level." >2. The authors should clarify a seeming discrepancy regarding event >rates. They state (on page 6) that their trigger cross-section was 43 mb. >The lowest luminosity they appear to have run at for the 6 day run seems >to be of order 10**28 /cm**2/sec. This would imply a trigger rate of 430 >Hz so that they could collect all their 1.3M events is less than one hour. >Even given modest dead-times, I don't see how they could have taken 6 days >worth of data. The reported trigger rates don't seem to make sense either. As noted in the paragraph before the one the author cites, the calculation of the luminosity at C0 used the D0 luminosity (available real-time over the accelerator network) as an input. The numbers quoted were these D0 luminosities. In order to avoid confusion, we have replaced the sentence puzzling the referree with: "The luminosity at the C0 collision point was inferred from the D0 luminosity corrected for differences in the magnetic architecture at the two points and the fact that bunches that collide at C0 are not the same pairs that collide at D0. The C0 luminosity during these runs ranged from about 10^26 cm^-2 s^-1 to about 10^28 cm^-2 s^-1". >3. A concern remains with this reader about how valid the results are, >given that they have trouble simulating their backgrounds. Have they made >any attempt at superposing additional hits on their simulated events and >then testing whether their novel statistics change significantly? As I >understand it, after cuts their simulation reproduces track and photon >distributions [see comment 8 below] but it fails to reproduce lots of >extra hits away from tracks. True? (If so, this is not uncommon or >unexpected.) This is an important issue. It is true that this is a common problem; we include a reference to work by the ALICE collaboration reporting this problem with chambers of similar geometry and gas mixture to those used in MiniMax. The task of how to address the problem is, however, much more complicated. In the absence of an understanding of the physical origin of the extra hits, attempts to introduce extra hits in an ad-hoc fashion can easily give false senses of (in)security. fashion. By being able to tag with opposite-side multiplicity (Section V.C), we were able to study the robust observables while significantly changing the mean multiplicity of the events. We observed no effect. Together with the fact that Figure 8 indicates good overall agreement of observed particle production with the simulations, we believe (with the referee - see his point 8) that this goes far towards valdating our results. To make this point more clearly, we have added the following paragraph to the conclusions, following the discussion of limits on DCC production in various scenarios: "Similar analyses (and conclusions) are possible for the data subsets defined by the diffractive and forward antinucleon tags, and for events with opposite side multiplicity tags. Indeed, there is no evidence of a multiplicity dependence in the robust observables. (See figure 9). We believe that this, together with the overall agreement between data and experiment suggested by Figure 8, goes far towards validating our results." >4. I don't understand the statement on page 14 that the deviations from >unity for the higher order ratios in Table VII are not very significant. >The reported values are FAR more significantly different from 1.0, using >the quoted errors, than are those for the low order ratios. Perhaps when >normalized to their monte-carlo, this effect goes away but the authors >give no indication of that. Perhaps by the phrase "The higher order ratios", the referee thought we meant r(0,2), r(1,2), etc., which are, indeed, far more significantly different from 1.0. These, however, involve more than one gamma being observed, and are not robust, depending on a combination of the efficiencies for observing both one and two gammas from the decay of a single pi-zero, as well as the overall mean number of gammas. Since this point confused the referee, we have added the following after the fourth sentence of V.A: "While the $r_{i,1}$ are robust in the sense defined in section IV, this is not true of the $r_{i,j}, j>1$ (see [6]). We have nevertheless tabulated these results for completeness, though they are not useful for the present analysis." We have also added the following sentence to the caption of Table VII: "Only the $r_{i,1}$ are robust; the other quantities are tabulated for completeness." >5. The authors claim that the low-order ratios for diffractive and >forward tagged events are consistent with those from the total sample. Yet >in every case, the numbers are greater in these samples than in the total >sample; and this tendency continues for the higher order ratios as well. >And by the way, does the simulation give the correct fractions of events >for these tagged samples? This is true, but not significant because the numbers in a given column of table VII are not statistically independent. We have added the following sentence to the caption of the table: "Note also that the entries in a given column are not statistically independent." >And by the way, does the simulation give the correct fractions of events >for these tagged samples? This simulations did not include the portions of the detector far downstream. The numbers are consistent with hand-estimations. We have added a citation to reference [2] to the sentence in II.B beginning "Detailed GEANT simulations of the detector and its environment [2]...", since these are described in detail in reference [2]. >6. At the bottom of table VII are found the values for the low order >ratios using the alternative tracker. The event total just above the >bottom three entries seems to be those found with the alternative tracker. >If so, this should be stated somewhere; and then it needs to be explained >why this tracker seems to be only 18% as efficient as the nominal one. >This is doubly puzzling in that the other subsamples that are called out >(diffractive, forward) have comparable event totals for the two trackers. We have added a sentence to the caption of the table: "# events refers to the number of raw events put through the respective trackers." >7. The technique of using ratios of factorial moments seems to allow >extraction of the physics without the need to worry about things such as >tracking efficiency, etc. But what information is lost? I.e., if one did >fully understand efficiencies, could more be learned? As we noted in our reply to point 1, the robust observables are sensitive to DCC, but are not sufficient to unfold the parent multiplicity distribution from the observed multiplicity distribution. This is the information which is lost. To make this point more clearly, we have added the following at the end of the final paragraph of IV.B: "We thus use the robust observables as the basis for our analysis in the remainder of this paper. It is important to note, however, that some information is lost in this procedure. While we will be sensitive to the presence of DCC, we will make no attempt to unfold the parent distribution of charged and neutral pions, since this would require detailed knowledge of the detection efficiencies for charged tracks and $\gamma$'s." >8. I don't understand what conclusions are to be drawn from Figure 8. >Is it that the simulation gets the normalization and distribution of >charged and neutral particles correct at the 10% level? This would follow >if the simulations include detector effects which they no doubt do. If >so, the authors should state this as it gives important validation of >their simulation procedure and of their understanding of their analysis >and cuts. Also, the large shift between PYTHIA and GEANT for the photon >distribution, no doubt having much to do with conversion probability, >should be explained in the caption (or in the text). We have re-written the caption of this figure to read: "FIG. 8 Raw distributions of the pseudorapidity distributions of charged and neutral particles. The curve labelled "PYTHIA" refers to simulated events produced by the PYTHIA event generator. These events were then propagated through the GEANT detector simulation and reconstruction algorithms. These results are labelled "GEANT". The large shift between "PYTHIA" and "GEANT" for the photon distribution is largely due to the conversion probability. The observed data, uncorrected for detection and trigger efficiencies are plotted as "DATA". The close agreement between the "DATA" and "GEANT" curves validates the simulation procedure and our understanding of the analysis and cuts." 9. Finally, there is no clue as to why the experiment is called "MiniMax." MiniMax was a successor to an earlier unsuccessful proposal (Fermilab P-864) for a "Maximum Acceptance Detector", MAX. Since MiniMax was much more modest, the name was natural. This history has been described in many of our earlier publications in reference [1], as well as in M. Convery's Ph. D. thesis, reference [2]. We have thus not made any additions to the present paper to again repeat this history. In closing, we note that the referee commented: >The paper presents new results and it therefore should be published, in >PRD. We hope that it can now be published expeditiously. Thank you very much for your help, Sincerely, Cyrus Taylor for the MiniMax collaboration ----------------------------------- Cyrus Taylor (216) 368-3710 Armington Professor (216) 368-4671 (FAX) Department of Physics [email protected] Case Western Reserve University [email protected] Cleveland, OH 44106-7079 USA
2014-12-23T04:17:05
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https://wiki.cosmos.esa.int/planckpla2015/index.php?title=LFI-Validation&oldid=11565
# Overall internal validation (diff) ← Older revision | Latest revision (diff) | Newer revision → (diff) ## Overview Data validation is critical at each step of the analysis pipeline. Much of the data validation is based on null tests. Here we present some examples from the current release, with comments on relevant time scales and sensitivity to various systematics. ## Null tests approach Null tests at map level are performed routinely, whenever changes are made to the mapmaking pipeline. These include differences at survey, year, 2-year, half- mission and half-ring levels, for single detectors, horns, horn pairs and full frequency complements. Where possible, map differences are generated in I, Q and U. For this release, we use the Full Focal Plane 8 (FFP8) simulations for comparison. We can use FFP8 noise simulations, identical to the data in terms of sky sampling and with matching time domain noise characteristics, to make statistical arguments about the likelihood of the noise observed in the actual data nulls. In general null tests are performed to highlight possible issues in the data related to instrumental systematic effecst not properly accounted for within the processing pipeline, or related to known changes in the operational conditions (e.g., switch-over of the sorption coolers), or related to intrinsic instrument properties coupled with the sky signal, such as stray light contamination. Such null-tests can be performed by using data on different time scales ranging from 1 minute to 1 year of observations, at different unit levels (radiometer, horn, horn-pair), within frequency and cross-frequency, both in total intensity, and, when applicable, in polarization. ### Sample Null Maps Figure 1: Null map samples for 30GHz (top), 44GHz (middle), and 70GHz (bottom). From left to right: half-ring differences in I and Q; 2-year combination differences in I and Q. All maps are smoothed to 3°. Three things are worth pointing out generally about these maps. Firstly, there are no obvious "features" standing out at this resolution and noise level. Earlier versions of the data processing, where there were errors in calibration for instance, would show scan-correlated structures at much larger amplitude. Secondly, the half-ring difference maps and the 2-year combination difference maps give a very similar overall impression. This is a very good sign, as these two types of null map cover very different time scales (1 hour to 2 years). Thirdly, it is impossible to know how "good" the test is just by looking at the map. There is clearly noise, but determining if it is consistent with the noise model of the instrument, and further, if it will bias the scientific results, requires more analysis. ### Statistical Analyses The next level of data compression is to use the angular power spectra of the null tests, and to compare to simulations in a statistically robust way. We use two different approaches. In the first we compare pseudo-spectra of the null maps to the half-ring spectra, which are the most "free" of anticipated systmatics. In the second, we use noise Monte Carlos from the FFP8 simulations, where we run the mapmaking identically to the real data, over data sets with identical sampling to the real data but consisting of noise only generated to match the per-detector noise model. Here we show examples comparing the pseudo-spectra of a set of 100 Monte Carlos to the real data. We mask both data and simlations to concentrate on residuals impacting analyses away from the Galactic plane. Figure 2: Pseudo-spectrum comparison (70GHz TT) of 2-year data difference (Year(1+3)-Year(2+4) in green) to the FFP8 simulation distribution (blue error bars). Figure 3: Pseudo-spectrum comparison (70GHz EE) of 2-year data difference (Year(1+3)-Year(2+4) in green) to the FFP8 simulation distribution (blue error bars). Figure 4: Pseudo-spectrum comparison(70GHz BB) of 2-year data difference (Year(1+3)-Year(2+4) in green) to the FFP8 simulation distribution (blue error bars). Finally, we can look at the distribution of noise power from the Monte Carlos "ℓ by ℓ" and check where the real data fall in that distribution, to see if it is consistent with noise alone. Figure 5: Sample 70GHz null test in comparison with FFP8 null distribution for multipoles from 2 to 4. From left to right we show TT, EE, BB. In this case, the null test is the full mission map - (Survey 1+Survey 3). We report the probability to exceed (PTE) values for the data relative to the FFP8 noise-only distributions. All values for this example are very reasonable, suggesting that our noise model captures the important features of the data even at low multipoles. ## Consistency checks All the details of consistency tests performed can be found in Planck-2013-II[1] and Planck-2015-A03[2]. ### Intra-frequency consistency check We have tested the consistency between 30, 44, and 70GHz maps by comparing the power spectra in the multipole range around the first acoustic peak. In order to do so, we have removed the estimated contribution from unresolved point source from the spectra. We have then built scatter plots for the three frequency pairs, i.e., 70GHz versus 30 GHz, 70GHz versus 44GHz, and 44GHz versus 30GHz, and performed a linear fit, accounting for errors on both axes. The results reported in Fig. 6 show that the three power spectra are consistent within the errors. Moreover, note that the current error budget does not account for foreground removal, , and window function uncertainties. Hence, the observed agreement between spectra at different frequencies can be considered to be even more satisfactory. Figure 6: Consistency between spectral estimates at different frequencies. From top to bottom: 70GHz versus 44 GHz; 70GHz versus 30 GHz; and 44GHz versus 30 GHz. Solid red lines are the best fit of the linear regressions, whose angular coefficients α are consistent with unity within the errors. ### 70 GHz internal consistency check We use the Hausman test [3] to assess the consistency of auto- and cross-spectral estimates at 70 GHz. We specifically define the statistic: $H_{\ell}=\left(\hat{C_{\ell}}-\tilde{C_{\ell}}\right)/\sqrt{{\rm Var}\left\{ \hat{C_{\ell}}-\tilde{C_{\ell}}\right\} },$ where $\hat{C_{\ell}}$ and $\tilde{C_{\ell}}$ represent auto- and cross-spectra, respectively. In order to combine information from different multipoles into a single quantity, we define $B_{L}(r)=\frac{1}{\sqrt{L}}\sum_{\ell=2}^{[Lr]}H_{\ell},r\in\left[0,1\right],$ where square brackets denote the integer part. The distribution of BL(r) converges (in a functional sense) to a Brownian motion process, which can be studied through the statistics s1=suprBL(r), s2=supr|BL(r)|, and s3=∫01BL2(r)dr. Using the "FFP7" simulations, we derive empirical distributions for all the three test statistics and compare with results obtained from Planck data (see Fig. 7). We find that the Hausman test shows no statistically significant inconsistencies between the two spectral estimates. Figure 7: From left to right, the empirical distribution (estimated via FFP7) of the s1, s2, and s3 statistics (see text). The vertical line represents 70GHz data. As a further test, we have estimated the temperature power spectrum for each of three horn-pair maps, and have compared the results with the spectrum obtained from all 12 radiometers shown above. In Fig. 8 we plot the difference between the horn-pair and the combined power spectra. Again, the error bars have been estimated from the FFP7 simulated data set. A χ2 analysis of the residual shows that they are compatible with the null hypothesis, confirming the strong consistency of the estimates. Figure 8: Residuals between the auto-power spectra of the horn-pair maps and the power spectrum of the full 70GHz frequency map. Error bars here are derived from FFP7 simulations. ## References 1. Planck 2013 results. II. Low Frequency Instrument data processing, Planck Collaboration, 2014, A&A, 571, A2 2. Planck 2015 results. II. LFI processing, Planck Collaboration, 2016, A&A, 594, A2. 3. Unbiased estimation of an angular power spectrum, G. Polenta, D. Marinucci, A. Balbi, P. de Bernardis, E. Hivon, S. Masi, P. Natoli, N. Vittorio, J. Cosmology Astropart. Phys., 11, 1, (2005).
2018-03-22T06:17:40
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https://pt.overleaf.com/articles/engineering-fasciculin-ii-to-treat-alzheimers-disease-related-symptoms/tqypzpksnzhy
Skip to content Author Paula Last Updated 7 years ago License Creative Commons CC BY 4.0 AbstractAlzheimer’s disease is characterized by death of cholinergic neurons, which secrete the neurotransmitter acetylcholine. This results in a loss of the total amount of acetylcholine circulating in neural networks. Modern drugs target acetylcholinesterase so as to inhibit its function, allowing for increased transmission of acetylcholine in cholinergic synapses. The aim is that an increase in cholinergic activity leads to an increase in cognition. However, these drugs only bind temporarily and have consequential problems that make modern AChE inhibitors of little effect. The main goal of our project is to engineer a snake toxin, fasciculin-II, capable of crossing the blood brain barrier and inhibiting acetylcholinesterase with enough affinity that it increases cholinergic transmission without yielding toxic outcomes. This fasciculin binds to the peripheral acetylcholinesterase found in neuromuscular junctions and causes rapid twitching. Fasciculin-II binds to acetylcholinesterase very tightly with the use of many charged residues and hydrophobic residues and we would like to optimize this interaction so that it may serve a therapeutic purpose in patients of AD.
2022-01-17T01:36:30
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https://par.nsf.gov/biblio/10249581-measurement-jet-shapes-proton-proton-collisions-sqrt-tev
Measurement of b jet shapes in proton-proton collisions at $$\sqrt{s}$$ = 5.02 TeV A bstract We present the first study of charged-hadron production associated with jets originating from b quarks in proton-proton collisions at a center-of-mass energy of 5.02 TeV. The data sample used in this study was collected with the CMS detector at the CERN LHC and corresponds to an integrated luminosity of 27.4 pb − 1 . To characterize the jet substructure, the differential jet shapes, defined as the normalized transverse momentum distribution of charged hadrons as a function of angular distance from the jet axis, are measured for b jets. In addition to the jet shapes, the per-jet yields of charged particles associated with b jets are also quantified, again as a function of the angular distance with respect to the jet axis. Extracted jet shape and particle yield distributions for b jets are compared with results for inclusive jets, as well as with the predictions from the pythia and herwig++ event generators. Authors: ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; more » Award ID(s): Publication Date: NSF-PAR ID: 10249581 Journal Name: Journal of High Energy Physics Volume: 2021 Issue: 5 ISSN: 1029-8479 1. A bstract Modifications to the distribution of charged particles with respect to high transverse momentum ( p T ) jets passing through a quark-gluon plasma are explored using the CMS detector. Back-to-back dijets are analyzed in lead-lead and proton-proton collisions at $$\sqrt{s_{\mathrm{NN}}}$$ s NN = 5 . 02 TeV via correlations of charged particles in bins of relative pseudorapidity and angular distance from the leading and subleading jet axes. In comparing the lead-lead and proton-proton collision results, modifications to the charged-particle relative distance distribution and to the momentum distributions around the jet axis are found to depend onmore » 2. Abstract Jet energy scale and resolution measurements with their associated uncertainties are reported for jets using 36–81 fb $$^{-1}$$ - 1 of proton–proton collision data with a centre-of-mass energy of $$\sqrt{s}=13$$ s = 13   $${\text {Te}}{\text {V}}$$ TeV collected by the ATLAS detector at the LHC. Jets are reconstructed using two different input types: topo-clusters formed from energy deposits in calorimeter cells, as well as an algorithmic combination of charged-particle tracks with those topo-clusters, referred to as the ATLAS particle-flow reconstruction method. The anti- $$k_t$$ k t jet algorithm with radius parameter $$R=0.4$$ R = 0.4 is the primary jetmore » 4. A bstract A search for standard model Higgs bosons (H) produced with transverse momentum ( p T ) greater than 450 GeV and decaying to bottom quark-antiquark pairs ( $$\mathrm{b}\overline{\mathrm{b}}$$ b b ¯ ) is performed using proton-proton collision data collected by the CMS experiment at the LHC at $$\sqrt{s}$$ s = 13 TeV. The data sample corresponds to an integrated luminosity of 137 fb − 1 . The search is inclusive in the Higgs boson production mode. Highly Lorentz-boosted Higgs bosons decaying to $$\mathrm{b}\overline{\mathrm{b}}$$ b b ¯ are reconstructed as single large-radius jets,more » Abstract Production cross sections of the Higgs boson are measured in the $${\mathrm{H}} \rightarrow {\mathrm{Z}} {\mathrm{Z}} \rightarrow 4\ell$$ H → Z Z → 4 ℓ ( $$\ell ={\mathrm{e}},{{{\upmu }}_{\mathrm{}}^{\mathrm{}}}$$ ℓ = e , μ ) decay channel. A data sample of proton–proton collisions at a center-of-mass energy of 13 $$\,\text {Te}\text {V}$$ Te , collected by the CMS detector at the LHC and corresponding to an integrated luminosity of 137 $$\,\text {fb}^{-1}$$ fb - 1 is used. The signal strength modifier $$\mu$$ μ , defined as the ratio of the Higgs boson production rate in the 4\ellmore »
2022-07-05T09:28:10
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http://publications.jrc.ec.europa.eu/repository/handle/JRC54991
Title: Comparison of MISR and MODIS land surface albedos: Methodology Authors: TABERNER Malcolm; PINTY Bernard; GOVAERTS Yves; LIANG Shunlin; VERSTRAETE Michel; GOBRON Nadine; WIDLOWSKI Jean-Luc Citation: JOURNAL OF GEOPHYSICAL RESEARCH-ATMOSPHERES vol. 115 p. 1-13 Publisher: AMER GEOPHYSICAL UNION Publication Year: 2010 JRC N°: JRC54991 ISSN: 0148-0227 URI: http://www.agu.org/journals/jd/jd1005/2009JD012665/http://publications.jrc.ec.europa.eu/repository/handle/JRC54991 DOI: 10.1029/2009JD012665 Type: Articles in Journals Abstract: The broadband white sky surface albedo (BiHemispherical Reflectance) products available from the MODerate resolution Imaging Spectroradiometer (MODIS) are compared, in joint papers, at regional and continental scales with similar products generated from the Multiangle Imaging SpectroRadiometer (MISR) land surface Bidirectional Reflectance Factor (BRF) parameters. This first paper describes the methodology applied to derive MISR white sky albedos over four spectral broadbands of interest namely, 0.3--0.7 $\mu$m, 0.4--1.1 $\mu$m, 0.7--3.0 $\mu$m and 0.3--3.0 $\mu$m as well as an evaluation of the strategy adopted to compare the MODIS and MISR products. The results are very encouraging since the two datasets are showing very good statistical agreement over large areas and over a full year of measurements, despite the many differences that exist in the suite of algorithms applied to retrieve these surface quantities from each of these instruments separately. Large scale analyses of the two MODIS and MISR-derived products have been conducted and results are shown and discussed in a companion paper (Part II). JRC Institute: Institute for Environment and Sustainability Files in This Item: There are no files associated with this item.
2015-04-01T10:40:18
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https://oscars.bnl.gov/doc/2.00.xx/Units.html
# Units¶ In OSCARS SI units are used with a few exceptions where useful for the scientist. Units in the documentation as well as code are always written with square brackets e.g. [m] for meters. Below is a list of units used and their meanings. Units used Symbol Units Quantity Description [m] meter length [m] meter time time multiplied by the speed of light [T] tesla magnetic field [V/m] volts per meter electric field [GeV] giga-electron volt energy $$1e^9 \times [eV]$$
2023-03-29T07:53:38
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https://www.usgs.gov/center-news/volcano-watch-residents-slopes-popocatepetl-volcano-heed-evacuation-notice
# Volcano Watch — Residents on slopes of Popocatepetl Volcano heed evacuation notice Release Date: For the past two weeks, numerous reports of increased seismic activity heralding a possible large eruption at Popocatepetl Volcano in Mexico have been in the news. A disturbing commentary in the reports was that residents living on the slopes of the volcano were hesitant to comply with the government's order to evacuate. For the past two weeks, numerous reports of increased seismic activity heralding a possible large eruption at Popocatepetl Volcano in Mexico have been in the news. A disturbing commentary in the reports was that residents living on the slopes of the volcano were hesitant to comply with the government's order to evacuate. The reluctance of the residents to evacuate is understandable. They fear that they will lose their crops and animals if they are not tended. Popocatepetl, located 60 km (36 mi) southeast of Mexico City, came back to life six years ago after nearly 70 years of dormancy and has been erupting intermittently since then. The last large eruption occurred a year ago and caused the airport in Mexico City to close, but thus far, no casualties, except for five hikers near the 5,452-meter (17,883-ft) summit in 1996, have been reported. Many residents living on the lower slopes and base of the second highest volcano in North America feel that they are not in danger. On Monday, December 18, the largest eruption of Popocatepetl in 1,200 years occurred and convinced people to leave immediately. Over 56,000 evacuees of the 40 villages within 12 km (7.2 mi) of the volcano crowded the roads heading away from the eruption. Popocatepetl Volcano, locally called "Popo," is one of more than 400 active volcanoes surrounding the Pacific Basin. These volcanoes are located where two tectonic plates collide with one plate subducting beneath the other. Magma is generated in the subduction zone and rises through the mantle and crust to erupt and form a range of volcanoes. Many of these stratovolcanoes have the classical steep-sided and symmetrical shape that we envision for a volcano. Eruptions from these volcanoes are usually explosive and violent. The shape and explosiveness of the Pacific Rim volcanoes can be attributed to the high silica content of the lavas they erupt. The higher the silica content of the magma, the more viscous it is. The more viscous the magma, the more difficult it is for gases to escape from it. The more gas within a magma, the more explosive is the eruption. Explosive eruptions create great clouds of ash that can collapse and race down the steep slopes of the volcano as a suspension of gas and ash, attaining speeds up to 150 km/hr (90 mph). Such pyroclastic flows are also generated by the crumbling of a volcanic dome or by directed explosions. Another hazard at Popo is the possibility of the eruptive material melting glacial ice on the volcano and causing a large mudflow or lahar. This is what killed over 25,000 people in Colombia during the eruption of Nevado del Ruiz Volcano in 1985. The high viscosity of the magma increases the internal pressure of the volcano, and this higher pressure can cause the volcano's flank to fail. The climactic eruption of Mount St. Helens on May 18, 1980, started with a slope failure and a debris avalanche. Unlike Hawaiian eruptions, Pacific Rim eruptions pose many life-threatening hazards. Residents of Mexico are wise to heed the evacuation warnings of government officials. They gamble with their own lives by not evacuating. ### Volcano Activity Update Last week we reported that there was a slow deflation of the Kīlauea summit region on December 13 and 14. The deflation, which lasted 17 hours and totaled nearly 5 microradians, was accompanied by intensified tremor in the caldera. Although there was no immediate effect of the subsidence on the eruption at Puu Oo, a pause in activity was observed from late December 15 to the early morning hours of December 17. The pause in activity was nearly coincident with the reinflation of the summit region which started at 5:00 p.m. on December 15 and continued until December 17. The renewal of activity on December 17 caused lava to breach the tube system above Pulama pali and produce surface flows. Four incandescent tongues of lava are flowing down Pulama pali and presenting visitors at the end of the Chain of Craters road in Hawaii Volcanoes National Park with a spectacular view. The flows have advanced up to nearly a kilometer (0.6 mi) from the base of the pali toward the sea coast, and no lava is entering the ocean at this time. No earthquakes were reported felt during the week ending on December 21.
2020-07-13T02:23:45
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https://da.khanacademy.org/computing/computer-science/algorithms/asymptotic-notation/a/big-big-omega-notation
Big-Ω (Big-Omega) notation Sometimes, we want to say that an algorithm takes at least a certain amount of time, without providing an upper bound. We use big-Ω notation; that's the Greek letter "omega." If a running time is $\Omega(f(n))$, then for large enough $n$, the running time is at least $k \cdot f(n)$ for some constant $k$. Here's how to think of a running time that is $\Omega(f(n))$: We say that the running time is "big-Ω of $f(n)$." We use big-Ω notation for asymptotic lower bounds, since it bounds the growth of the running time from below for large enough input sizes. Just as $\Theta(f(n))$ automatically implies $O(f(n))$, it also automatically implies $\Omega(f(n))$. So we can say that the worst-case running time of binary search is $\Omega(\log_2 n)$. We can also make correct, but imprecise, statements using big-Ω notation. For example, if you really do have a million dollars in your pocket, you can truthfully say "I have an amount of money in my pocket, and it's at least 10 dollars." That is correct, but certainly not very precise. Similarly, we can correctly but imprecisely say that the worst-case running time of binary search is $\Omega(1)$, because we know that it takes at least constant time. Of course, typically, when we are talking about algorithms, we try to describe their running time as precisely as possible. We provide the examples of the imprecise statements here to help you better understand big-$\Omega$, big-$O$, and big-$\Theta$. Dette indhold er et samarbejde mellem Dartmouth Computer Science professorerne Thomas Cormen og Devin Balkcom plus Khan Academys computing curriculum team. Indholdet er licenseret under CC-BY-NC-SA.
2019-01-19T22:55:01
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http://pdglive.lbl.gov/DataBlock.action?node=S004RP1
# LIMIT ON ${{\boldsymbol \mu}^{-}}$ $\rightarrow$ ${{\boldsymbol e}^{+}}$ CONVERSION Forbidden by total lepton number conservation. # ${\boldsymbol \sigma (}$ ${{\boldsymbol \mu}^{-}}$ ${}^{32}\mathrm {S}$ $\rightarrow$ ${{\boldsymbol e}^{+}}{}^{32}\mathrm {Si}^{*}{)}$ / ${\boldsymbol \sigma (}$ ${{\boldsymbol \mu}^{-}}$ ${}^{32}\mathrm {S}$ $\rightarrow$ ${{\boldsymbol \nu}_{{\mu}}}{}^{32}\mathrm {P}^{*}{)}$ INSPIRE search VALUE CL% DOCUMENT ID TECN  COMMENT $\bf{<9 \times 10^{-10}}$ 90 1980 STRC SIN • • • We do not use the following data for averages, fits, limits, etc. • • • $<1.5 \times 10^{-9}$ 90 1978 STRC SIN Conservation Laws: TOTAL LEPTON NUMBER References: PL 79B 371 Search for ${{\mathit \mu}^{-}}$ $\rightarrow$ ${{\mathit e}^{+}}$ Conversion on Sulfur
2019-04-26T16:36:17
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http://dlmf.nist.gov/15.9
# §15.9 Relations to Other Functions ## §15.9(i) Orthogonal Polynomials For the notation see §§18.3 and 18.19. ## §15.9(ii) Jacobi Function This is a generalization of Jacobi polynomials (§18.3) and has the representation 15.9.11 The Jacobi transform is defined as with inverse where the contour of integration is located to the right of the poles of the gamma functions in the integrand, and For this result, together with restrictions on the functions and , see Koornwinder (1984a). ## §15.9(iii) Gegenbauer Function This is a generalization of Gegenbauer (or ultraspherical) polynomials (§18.3). It is defined by: ## §15.9(iv) Associated Legendre Functions; Ferrers Functions Any hypergeometric function for which a quadratic transformation exists can be expressed in terms of associated Legendre functions or Ferrers functions. For examples see §§14.3(i)14.3(iii) and 14.21(iii). The following formulas apply with principal branches of the hypergeometric functions, associated Legendre functions, and fractional powers. 15.9.22, , where the sign in the exponential is according as . 15.9.23, , where the sign in the exponential is according as .
2013-05-21T15:39:54
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https://zbmath.org/authors/?q=ai%3Aramanujan.srinivasa
## Ramanujan, Srinivasa Compute Distance To: Author ID: ramanujan.srinivasa Published as: Ramanujan, S.; Ramanujan, Srinivasa Further Spellings: Ramanujan Aiyangar, Srinivasa External Links: MacTutor · MGP · Wikidata · GND · IdRef Documents Indexed: 47 Publications since 1911, including 5 Books 1 Contribution as Editor · 1 Further Contribution Biographic References: 99 Publications Co-Authors: 3 Co-Authors with 13 Joint Publications 53 Co-Co-Authors all top 5 ### Co-Authors 33 single-authored 11 Hardy, Godfrey Harold 3 Seshu Aiyar, P. V. 3 Wilson, Bertram Martin 2 Andrews, George Eyre 2 Berndt, Bruce Carl 1 Alladi, Krishnaswami 1 Nicolas, Jean-Louis 1 Ramachandra Rao, R. 1 Robin, Guy 1 Rogers, Leonard James all top 5 ### Serials 13 Journal of the Indian Mathematical Society 9 Proceedings of the London Mathematical Society. Second Series 3 Proceedings of the Cambridge Philosophical Society 3 The Quarterly Journal of Pure and Applied Mathematics 2 Proceedings of the Royal Society of London. Series A 1 The Ramanujan Journal 1 Comptes Rendus Hebdomadaires des Séances de l’Académie des Sciences, Paris 1 Lecture Notes in Mathematics 1 Transactions of the Cambridge Philosophical Society all top 5 ### Fields 17 Number theory (11-XX) 7 History and biography (01-XX) 4 Special functions (33-XX) 1 General and overarching topics; collections (00-XX) 1 Combinatorics (05-XX) 1 Sequences, series, summability (40-XX) ### Citations contained in zbMATH Open 34 Publications have been cited 1,898 times in 1,584 Documents Cited by Year The Lost Notebook and other unpublished papers. With an introduction by George E. Andrews. Zbl 0639.01023 Ramanujan, Srinivasa 1988 Asymptotic formulae in combinatory analysis. JFM 46.0198.04 Hardy, G. H.; Ramanujan, S. 1918 Notebooks of Srinivasa Ramanujan. Vols. 1, 2. Zbl 0138.24201 Ramanujan, Srinivasa 1957 Modular equations and approximations to $$\pi$$. JFM 45.1249.01 Ramanujan, S. 1914 Some properties of $$p(n),$$ the number of partitions of $$n$$. JFM 47.0885.01 Ramanujan, S. 1919 The normal number of prime factors of a number $$n$$. JFM 46.0262.03 Hardy, G. H.; Ramanujan, S. 1917 Collected papers of Srinivasa Ramanujan. Edited by G. H. Hardy, P. V. Seshu Aiyar, B. M. Wilson. JFM 53.0030.02 Ramanujan, S. 1927 Proof of certain identities in combinatory analysis. JFM 47.0903.01 Rogers, L. J.; Ramanujan, S. 1919 Asymptotic formulae for the distribution of integers of various types. (A problem in the analytic theory of numbers.). JFM 46.0198.03 Hardy, G. H.; Ramanujan, S. 1916 Asymptotic formulae in combinatory analysis. JFM 46.0198.02 Hardy, G. H.; Ramanujan, S. 1918 Highly composite numbers. JFM 45.1248.01 Ramanujan, S. 1915 Collected papers of Srinivasa Ramanujan. Edited by G. H. Hardy, P. V. Seshu Aiyar and B. M. Wilson. With a new preface and commentary by Bruce C. Berndt. Third printing of the 1927 original. Zbl 1110.11001 Ramanujan, Srinivasa 2000 On the expression of a number in the form $$ax^2+by^2+cz^2+du^2$$. JFM 46.0240.01 Ramanujan, S. 1917 Highly composite numbers. Annotated by Jean-Louis Nicolas and Guy Robin. Zbl 0917.11043 Ramanujan, Srinivasa 1997 Congruence properties of partitions. JFM 48.0150.02 Ramanujan, S. 1920 Highly composite numbers. JFM 45.0286.02 Ramanujan, S. 1915 On certain arithmetical functions. Zbl 07426016 Ramanujan, Srinivasa 1916 Ramanujan’s lost notebook. Part V. Zbl 1416.11001 Andrews, George E.; Berndt, Bruce C. 2018 Some properties of Bernoulli’s numbers. JFM 42.0460.02 Ramanujan, S. 1911 Some definite integrals connected with Gauß’ sums. JFM 45.1290.01 Ramanujan, S. 1915 New expressions for Riemann’s functions $$\xi(s)$$ and $$\Xi (t)$$. JFM 45.1343.05 Ramanujan, S. 1915 Algebraic relations between certain infinite products. JFM 47.0904.05 Ramanujan, S. 1920 Une formule asymptotique pour le nombre des partitions de $$n$$. JFM 46.0198.01 Hardy, G. H.; Ramanujan, S. 1917 Some formulae in the analytic theory of numbers. JFM 45.1250.01 Ramanujan, S. 1915 On the coefficients in the expansions of certain modular functions. JFM 46.1473.05 Hardy, G. H.; Ramanujan, S. 1918 On the coefficients in the expansion of certain modular functions. JFM 47.0359.02 Hardy, G. H.; Ramanujan, S. 1918 Note on a set of simultaneous equations. JFM 43.0157.01 Ramanujan, S. 1912 Irregular numbers. JFM 44.0213.03 Ramanujan, S. 1913 Collected papers of Srinivasa Ramanujan. Edited by G. H. Hardy, P. V. Seshu Aiyar, B. M. Wilson. Reprint of the 1927 original. Zbl 1325.01033 Ramanujan, Srinivasa 2015 Question Nr. 699. Lösung von Watson. JFM 56.0116.07 Ramanujan, S. 1930 Some definite integrals. JFM 47.0908.01 Ramanujan, S. 1919 A series for Euler’s constant $$\gamma$$. JFM 46.0340.01 Ramanujan, S. 1916 Some definite integrals. JFM 45.0464.03 Ramanujan, S. 1914 Summation of a certain series. JFM 45.1277.02 Ramanujan, S. 1915 Ramanujan’s lost notebook. Part V. Zbl 1416.11001 Andrews, George E.; Berndt, Bruce C. 2018 Collected papers of Srinivasa Ramanujan. Edited by G. H. Hardy, P. V. Seshu Aiyar, B. M. Wilson. Reprint of the 1927 original. Zbl 1325.01033 Ramanujan, Srinivasa 2015 Collected papers of Srinivasa Ramanujan. Edited by G. H. Hardy, P. V. Seshu Aiyar and B. M. Wilson. With a new preface and commentary by Bruce C. Berndt. Third printing of the 1927 original. Zbl 1110.11001 Ramanujan, Srinivasa 2000 Highly composite numbers. Annotated by Jean-Louis Nicolas and Guy Robin. Zbl 0917.11043 Ramanujan, Srinivasa 1997 The Lost Notebook and other unpublished papers. With an introduction by George E. Andrews. Zbl 0639.01023 Ramanujan, Srinivasa 1988 Notebooks of Srinivasa Ramanujan. Vols. 1, 2. Zbl 0138.24201 Ramanujan, Srinivasa 1957 Question Nr. 699. Lösung von Watson. JFM 56.0116.07 Ramanujan, S. 1930 Collected papers of Srinivasa Ramanujan. Edited by G. H. Hardy, P. V. Seshu Aiyar, B. M. Wilson. JFM 53.0030.02 Ramanujan, S. 1927 Congruence properties of partitions. JFM 48.0150.02 Ramanujan, S. 1920 Algebraic relations between certain infinite products. JFM 47.0904.05 Ramanujan, S. 1920 Some properties of $$p(n),$$ the number of partitions of $$n$$. JFM 47.0885.01 Ramanujan, S. 1919 Proof of certain identities in combinatory analysis. JFM 47.0903.01 Rogers, L. J.; Ramanujan, S. 1919 Some definite integrals. JFM 47.0908.01 Ramanujan, S. 1919 Asymptotic formulae in combinatory analysis. JFM 46.0198.04 Hardy, G. H.; Ramanujan, S. 1918 Asymptotic formulae in combinatory analysis. JFM 46.0198.02 Hardy, G. H.; Ramanujan, S. 1918 On the coefficients in the expansions of certain modular functions. JFM 46.1473.05 Hardy, G. H.; Ramanujan, S. 1918 On the coefficients in the expansion of certain modular functions. JFM 47.0359.02 Hardy, G. H.; Ramanujan, S. 1918 The normal number of prime factors of a number $$n$$. JFM 46.0262.03 Hardy, G. H.; Ramanujan, S. 1917 On the expression of a number in the form $$ax^2+by^2+cz^2+du^2$$. JFM 46.0240.01 Ramanujan, S. 1917 Une formule asymptotique pour le nombre des partitions de $$n$$. JFM 46.0198.01 Hardy, G. H.; Ramanujan, S. 1917 Asymptotic formulae for the distribution of integers of various types. (A problem in the analytic theory of numbers.). JFM 46.0198.03 Hardy, G. H.; Ramanujan, S. 1916 On certain arithmetical functions. Zbl 07426016 Ramanujan, Srinivasa 1916 A series for Euler’s constant $$\gamma$$. JFM 46.0340.01 Ramanujan, S. 1916 Highly composite numbers. JFM 45.1248.01 Ramanujan, S. 1915 Highly composite numbers. JFM 45.0286.02 Ramanujan, S. 1915 Some definite integrals connected with Gauß’ sums. JFM 45.1290.01 Ramanujan, S. 1915 New expressions for Riemann’s functions $$\xi(s)$$ and $$\Xi (t)$$. JFM 45.1343.05 Ramanujan, S. 1915 Some formulae in the analytic theory of numbers. JFM 45.1250.01 Ramanujan, S. 1915 Summation of a certain series. JFM 45.1277.02 Ramanujan, S. 1915 Modular equations and approximations to $$\pi$$. JFM 45.1249.01 Ramanujan, S. 1914 Some definite integrals. JFM 45.0464.03 Ramanujan, S. 1914 Irregular numbers. JFM 44.0213.03 Ramanujan, S. 1913 Note on a set of simultaneous equations. JFM 43.0157.01 Ramanujan, S. 1912 Some properties of Bernoulli’s numbers. JFM 42.0460.02 Ramanujan, S. 1911 all top 5 all top 5 ### Cited in 293 Serials 237 The Ramanujan Journal 109 Journal of Number Theory 65 Journal of Mathematical Analysis and Applications 54 International Journal of Number Theory 51 Advances in Mathematics 49 Proceedings of the American Mathematical Society 31 Transactions of the American Mathematical Society 30 Journal of Combinatorial Theory. Series A 26 Discrete Mathematics 22 Advances in Applied Mathematics 21 Research in Number Theory 19 Bulletin of the Australian Mathematical Society 18 Mathematische Annalen 17 Mathematical Notes 16 Results in Mathematics 15 European Journal of Combinatorics 15 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 15 Integers 14 Mathematics of Computation 13 Mathematical Proceedings of the Cambridge Philosophical Society 13 Journal of Computational and Applied Mathematics 12 The Electronic Journal of Combinatorics 12 Annals of Combinatorics 12 Journal of High Energy Physics 12 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM 11 Indian Journal of Pure & Applied Mathematics 11 Rocky Mountain Journal of Mathematics 11 Research in the Mathematical Sciences 10 Acta Mathematica 10 Applied Mathematics and Computation 10 Archiv der Mathematik 10 Journal of Approximation Theory 10 Mathematische Zeitschrift 9 Acta Arithmetica 9 Functiones et Approximatio. Commentarii Mathematici 9 Monatshefte für Mathematik 8 American Mathematical Monthly 8 International Journal of Mathematics and Mathematical Sciences 8 Proceedings of the Edinburgh Mathematical Society. Series II 8 Journal of Inequalities and Applications 7 Lithuanian Mathematical Journal 7 Duke Mathematical Journal 7 Proceedings of the Japan Academy. Series A 7 Journal of Symbolic Computation 7 Boletín de la Sociedad Matemática Mexicana. Third Series 7 Journal of Integer Sequences 6 Discrete Applied Mathematics 6 Journal of Statistical Physics 6 Integral Transforms and Special Functions 6 Acta Mathematica Sinica. English Series 6 Journal of the Australian Mathematical Society 6 Comptes Rendus. Mathématique. Académie des Sciences, Paris 6 Annali dell’Università di Ferrara. Sezione VII. Scienze Matematiche 6 Afrika Matematika 6 Palestine Journal of Mathematics 5 Communications in Mathematical Physics 5 Journal of Mathematical Physics 5 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 5 Inventiones Mathematicae 5 Acta Mathematica Hungarica 5 Journal of the Ramanujan Mathematical Society 5 Expositiones Mathematicae 5 Journal de Théorie des Nombres de Bordeaux 5 South East Asian Journal of Mathematics and Mathematical Sciences 5 Advances in Difference Equations 5 Philosophical Transactions of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 4 Acta Mathematica Academiae Scientiarum Hungaricae 4 Computers & Mathematics with Applications 4 Israel Journal of Mathematics 4 Nuclear Physics. B 4 Bulletin of the Korean Mathematical Society 4 Algorithmica 4 Bulletin of the American Mathematical Society. New Series 4 Indagationes Mathematicae. New Series 4 Experimental Mathematics 4 Journal of Difference Equations and Applications 4 Analysis and Applications (Singapore) 4 Bulletin of the American Mathematical Society 3 General Relativity and Gravitation 3 Periodica Mathematica Hungarica 3 The Mathematical Intelligencer 3 Bulletin de la Société Mathématique de France 3 Czechoslovak Mathematical Journal 3 Journal of Algebra 3 Journal of Statistical Planning and Inference 3 Kyungpook Mathematical Journal 3 Mathematika 3 Studies in Applied Mathematics 3 Annales de la Faculté des Sciences de Toulouse. Série V. Mathématiques 3 Graphs and Combinatorics 3 Probability Theory and Related Fields 3 Journal of the American Mathematical Society 3 Forum Mathematicum 3 Numerical Algorithms 3 Aequationes Mathematicae 3 Linear Algebra and its Applications 3 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 3 The Australasian Journal of Combinatorics 3 Journal of Algebraic Combinatorics 3 The Journal of Analysis ...and 193 more Serials all top 5 ### Cited in 53 Fields 1,197 Number theory (11-XX) 465 Special functions (33-XX) 426 Combinatorics (05-XX) 53 Approximations and expansions (41-XX) 50 Functions of a complex variable (30-XX) 50 Probability theory and stochastic processes (60-XX) 41 Group theory and generalizations (20-XX) 38 Computer science (68-XX) 36 Sequences, series, summability (40-XX) 35 Statistical mechanics, structure of matter (82-XX) 34 Real functions (26-XX) 31 Algebraic geometry (14-XX) 30 Quantum theory (81-XX) 29 History and biography (01-XX) 28 Numerical analysis (65-XX) 20 Nonassociative rings and algebras (17-XX) 16 Relativity and gravitational theory (83-XX) 14 Harmonic analysis on Euclidean spaces (42-XX) 13 Ordinary differential equations (34-XX) 12 Statistics (62-XX) 12 Information and communication theory, circuits (94-XX) 10 Linear and multilinear algebra; matrix theory (15-XX) 9 Operations research, mathematical programming (90-XX) 8 Partial differential equations (35-XX) 7 Integral transforms, operational calculus (44-XX) 7 Global analysis, analysis on manifolds (58-XX) 6 Field theory and polynomials (12-XX) 6 Difference and functional equations (39-XX) 5 Mathematical logic and foundations (03-XX) 5 Associative rings and algebras (16-XX) 5 Dynamical systems and ergodic theory (37-XX) 5 Manifolds and cell complexes (57-XX) 5 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 5 Biology and other natural sciences (92-XX) 4 General and overarching topics; collections (00-XX) 4 Operator theory (47-XX) 4 Systems theory; control (93-XX) 3 Topological groups, Lie groups (22-XX) 3 Several complex variables and analytic spaces (32-XX) 3 Convex and discrete geometry (52-XX) 3 Fluid mechanics (76-XX) 3 Classical thermodynamics, heat transfer (80-XX) 2 Order, lattices, ordered algebraic structures (06-XX) 2 Integral equations (45-XX) 2 Functional analysis (46-XX) 2 Mathematics education (97-XX) 1 Commutative algebra (13-XX) 1 Category theory; homological algebra (18-XX) 1 Geometry (51-XX) 1 Differential geometry (53-XX) 1 Algebraic topology (55-XX) 1 Mechanics of particles and systems (70-XX) 1 Mechanics of deformable solids (74-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.
2022-09-27T13:16:38
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https://www.usgs.gov/center-news/volcano-watch-volcanic-gas-measurements-mauna-loa-are-expanded-challenge
# Volcano Watch - Volcanic gas measurements on Mauna Loa are an expanded challenge Release Date: Several recent Volcano Watch articles have discussed the difficult nature of making specific eruption predictions about Mauna Loa, the largest volcano on Earth. One way to decrease the difficulty is to monitor many different behaviors of the volcano. In addition to monitoring seismic and ground deformation changes, we also measure the gases coming out of Mauna Loa. Mauna Loa's summit caldera, Mokuaweoweo, is capable of easily holding all of Waikiki. In addition, the part of Mauna Loa above sea level stretches over 75 miles (120 km), from Hawaiʻian Ocean View Estates on the southern end of the island, to Hilo town on the east side. All eruptions since 1843 have started in the summit caldera, with activity migrating to either of the rift zones, and some eruptions producing flows that quickly reach the sea. Over a dozen eruptive vents below the rift zones on Mauna Loa's flanks, including several submarine vents, show that activity can occur over an even wider area. With Mauna Loa's footprint of 2,035 square miles (5,271 km) comprising over 50 percent of the Big Island, monitoring this volcano is a huge task. After all, "Mauna Loa" is a Hawaiʻian place name that literally means "Long Mountain"-a clear understatement. One way we monitor changes in eruptive activity at Mauna Loa's younger sibling, Kīlauea, is by studying the release of gases trapped in the magma. At Kīlauea, gases escape primarily from the summit caldera and from Puu Oo vent on the east rift zone. A network of National Park roads makes monitoring gas release fairly straightforward for Kīlauea. Using instruments mounted in our field vehicle, we measure the quantity of gas blowing across Crater Rim Drive at the top of the volcano, and across Chain of Craters Road, lower down on the east rift zone. Within 20 minutes of leaving the observatory, we can also sample volcanic gas vents located at the rim of Halemaumau pit crater, Pele's home. Kīlauea is a volcanic gas enthusiast's delight. In contrast, Mauna Loa's summit caldera and rift zone degassing sites are remote and widely spaced. Consequently, studying these emissions is much more challenging. We recently completed a field campaign for the long mountain by loading our gas-measuring equipment into a helicopter and flying these instruments along Mauna Loa's degassing locations. With the GPS recording our three-dimensional position each second of the flight, we collected data for carbon dioxide and sulfur dioxide gases escaping from vents along the southwest and northeast rift zones, as well as from the summit caldera fissures and cones. The data collected during these field measurements show that gases escaping from vents in Mokuaweoweo and along the northeast rift are dominated by carbon dioxide, with little or no sulfur gas. Emissions from the upper southwest rift zone around the 3350 meter (11,000 foot) elevation are conversely mostly sulfur dioxide, with a small amount of carbon dioxide detected recently, as well. These results are subtly different from those of an earlier campaign carried out at the end of August, but taken by themselves, do not indicate a huge change in the volcano's activity. In addition to these campaign-style studies, additional continuous monitoring equipment for carbon dioxide, sulfur dioxide, and vent temperature will be installed in the next several months. These instruments, to be located in the summit caldera, will transmit data back to HVO by radio every 10 minutes. Since all eruptions of Mauna Loa since 1843 have begun at the summit, instruments within Mokuaweoweo are expected to detect early changes in the shallow magma-gas system. Colleagues at the Mauna Loa Climate and Diagnostics Laboratory, operated by the National Oceanic and Atmospheric Administration (NOAA), are also monitoring gases escaping from caldera vents by looking at emissions carried past their instruments in the night-time downslope winds. Mauna Loa continues to present all the challenges expected of a huge volcano whose summit rises over 17 km (56,000 feet) above a buried seafloor depressed by its weight. By incorporating gas geochemistry measures with real-time monitoring of seismic and ground surface changes, we hope to produce the best ongoing assessment of activity beneath the long mountain. ### Volcano Activity Update Eruptive activity at Puu Oo continues. Spatter cones in the crater of Puu Oo glow brightly on clear nights but have not produced any lava flows for several months. The MLK vent area, at the southwest base of the cone, intermittently erupts small Pāhoehoe flows that stack up close to the vent. The PKK flow continues to host scattered breakouts from above the top of Pulama pali to the coastal plain. Lava is not entering the ocean. As of December 29, breakouts were active on the coastal plain, about 600 m (660 yd) inland of the shore at Laeapuki. The area of breakouts is about 3.2 km (2 mi) from the end of the pavement on Chain of Craters Road in Hawaii Volcanoes National Park. Expect a two-hour walk each way and remember to bring lots of water. Stay well back from the sea cliff, regardless of whether there is an active ocean entry or not. Heed the National Park warning signs. During the week ending December 28, four earthquakes were felt on our Big Island. The first three (reported last week) occurred at 7:07, 7:29, and 8:27 a.m. on December 22, about 5 km (3 miles) south of Kīlauea summit, at a depth of 2.9 to 4.2 km (1.8 to 2.6 miles). They were felt primarily in the Volcano area. The initial shock had a magnitude of 4.0, and the two later shocks had magnitudes of 2.1 and 2.4. A magnitude 3.3 quake was felt at the Hawaiʻian Volcano Observatory at 8:05 p.m. on December 25 by one of our loyal seismologists. It was located 19 km (12 miles) south of Hilo at a depth of 25 km (15 miles). Mauna Loa is not erupting. The summit region continues to inflate. Since July 2004, the rate of inflation and number of deep earthquakes has increased. Weekly earthquake counts have varied from 5 to over 150. During the week ending December 28, 128 earthquakes were recorded beneath the summit area. This is a slight decrease from the past week. Nearly all are 30 km (18 mi) or more deep and are the long-period type, with magnitudes less than 3.
2020-01-21T07:58:12
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https://www.federalreserve.gov/econresdata/notes/feds-notes/2016/import-penetration-and-domestic-innovation-a-view-into-dynamic-gains-from-trade-20161216.html
## FEDS Notes ### Import Penetration and Domestic Innovation: A View into Dynamic Gains from Trade Maria D. Tito 1 How large are the welfare gains from international trade? Empirical studies have generally focused on the impact of trade liberalizations on the level of income and have consistently found that those types of gains--also known as static gains--are generally small; for example, using an extensive methodology, Costinot and Rodriguez-Clare (2013) quantify gains ranging from 1.8 percent to 8.3 percent for the United States. The literature, however, has generally abstracted from the effect of trade on growth--i.e., dynamic gains--as they are much more difficult to identify and to measure.2 If the aggregate dynamic effects remain somewhat elusive, empirical studies have made some progress on specific channels. In particular, empirical evidence suggests that trade flows might fuel innovation, a fundamental engine of growth. While earlier work studied the effect of imports on inputs to innovation, such as expenditures on research and development, more recent contributions have shifted their focus to patents, which can be considered output measures of technology.3 The shift reflects the attractive qualities of patent data, such as the availability of information on the year in which the innovation occurs, the geographic distribution of inventors, and the technology class. Among the most recent contributions, Bloom et al. (2016) show that Chinese import competition led to increased technical change within firms in 12 European countries and reallocated employment toward more technologically advanced firms. Their results, however, are in contrast with Autor et al.'s (2016) finding that, accounting for trends in chemicals and computers, fiercer import competition from China depressed innovation activity in U.S. firms. In this paper, we revisit the link between innovation activity, measured by the number of patent applications, and import flows. We use the U.S. Patent and Inventor Database described in Li et al. (2014), which covers patents granted by the U.S. Patent and Trademark Office between 1975 and 2010.4 We match the U.S. patent database with data on import flows and tariffs using the concordance between technology classes and four-digit SIC sectors built by Silverman (2002). This concordance links U.S. patents to the SICs where the patents are likely to provide value.5 Figure 1 compares the total number of patents that have a primary U.S. inventor in the original data with those applications matched to the SIC concordance. The two series track each other accurately and reflect aggregate patterns in line with what is shown by Autor et al. (2016): the number of applications, after remaining roughly steady through the 1980s, rapidly increased in the 1990s before moving down somewhat in the early 2000s. We truncate our sample in 2003 because of concerns of data censoring, as the patent database is backfilled after patents are approved.6 Figure 1. Total Patents, 1975-2003 Source: Author's calculation using Li et al. (2014) and Silverman (2002) data Accessible version Table 1 illustrates the distribution of patents across sectors. We compare patent shares across sectors between 1991 and 2003: Electronic equipment, machinery, and chemicals were the top three sectors in terms of patent applications in both years, accounting for about 50 percent of all patents in manufacturing. While the aggregate number of applications increased between 1991 and 2003, the rise was disproportionately larger for electronic equipment, mostly capturing the information technology revolution. Our sectorial decomposition is qualitatively similar to that in Autor et al. (2016); the differences mostly reflect our reliance on the Silverman (2002) concordance, which, built from patent assignments between 1990 and 1993, is likely to downplay the role of patents in technologies related to the internet boom. Table 1. Distribution of Patents across Two-digit SIC Sectors, 1991 and 2003 1991 2003 Food 5.57% 4.73% Tobacco 0.42% 0.23% Textile Mill 2.56% 1.99% Apparel 1.87% 1.35% Wood 1.87% 1.36% Furniture 1.64% 1.26% Paper 3.32% 2.45% Printing 2.09% 1.77% Chemicals 11.40% 9.79% Petroleum 1.84% 1.18% Rubber 4.12% 3.09% Leather 0.96% 0.74% Stone, Clay, Glass 4.72% 3.55% Primary Metal 4.10% 3.20% Fabricated Metal 6.85% 6.22% Machinery 13.04% 13.72% Electronic Eq. 18.52% 26.70% Transportation Eq. 4.93% 4.47% Precision Instr. 7.03% 9.29% Miscellaneous 3.15% 2.93% Source: Author's calculation using Li et al. (2014) and Silverman (2002) data Note: Distribution of patents across two-digit SIC industries, 1991 and 2003. The rapid increase in patent applications during the 1990s is accompanied by sustained import growth. Figure 2 summarizes the degree of U.S. import penetration by its top three partners, Canada, Mexico, and China. Looking at either measures based on import tariffs or measures based on trade flows, import penetration increased between 1991 and 2003.7 Although Chinese imports boomed during the period of analysis, following large tariffs declines during the 1990s and early 2000s, import flows from Canada and Mexico also increased before flattening out toward the end of our sample. Figure 2. Import Liberalization, Top Three U.S. partners, 1991-2003 Note: Tarriffs are weighted by import flows. Source: Author's calculation based on Schott (2008). While previous research focused on the effects of import competition from China, our paper highlights the impact of trade flows from the three major U.S. import partners on innovation to isolate effects of different origins. Our baseline model relates patent applications to measures of import penetration for each partner, $$\text{ln}Patents_{st} = \beta_0 + \beta_1 Canada_{st} + \beta_2 Mexico_{st} + \beta_3 China_{st} + \varepsilon_{st},$$ where s denotes the sector of use based on the Silverman (2002) concordance and t denotes the year of application. We use both tariffs and import flows as measures of import penetration. Those measures, however, are likely correlated with firms' patenting location choice or are inversely affected by the existing distribution of patents across countries. To address these concerns, we analyze the effect of lagged tariff rates, and we instrument import flows with non-U.S. imports. Table 2. Patents and Import Tariffs, 1991-2003 Variables (1) (2) (3) (4) ln Patentst (0.270) 0.730** (0.343) Mexican Import Tariffst-1 0.036 (0.149) 0.022 (0.259) Chinese Import Tariffst-1 -0.394** (0.190) -0.619*** (0.224) Sector y y y y Year y y y y Obs. 4,541 4,541 4,541 4,541 R2 0.988 0.988 0.988 0.988 Legend : *** significant at 1%, ** at 5%, * at 10%. Notes: Sector-level regressions, 1991–2003. Standard errors are clustered at the four-digit SIC level. Table 2 summarizes the effects of past import tariffs on the current number of patent applications. A negative coefficient indicates that lower tariffs spur innovation through a larger number of patent applications. This result applies to Chinese import tariffs, whereas the coefficients for Mexican and Canadian import tariffs are both positive, with higher tariffs only on Canadian goods to be significantly associated with greater technological change. All specifications include sector fixed effects and time dummies to capture the effects of sector-specific time-invariant characteristics and of macroeconomic shocks common to all partners in a particular year. Lagged tariffs, however, may not fully control for serially correlated unobservables that influence both the path of U.S. import tariffs and the number of patent applications. Our second strategy aims at overcoming such concerns and provides further evidence on the relationship between trade flows and innovation. In particular, we instrument U.S. import flows from each of the partner countries with the non-U.S. imports from the same country. Our instrument captures global demand shocks for products in a particular sector and is, therefore, less likely to be correlated with the decision to submit patent applications in the United States or to be affected by reverse causation. Table 3 reports the results of our second strategy. Our first-stage F-statistics suggest that weak instruments are not a threat to our identification. While the coefficients on import flows from Canada and Mexico tend to be positive in individual regressions, they switch sign in the specification that includes all partners' imports. The coefficient on Chinese imports, instead, remains positive and significant across all specifications. In particular, raising imports from China by one standard deviation, which corresponds to an increase in Chinese imports of about \$20,000, is associated with an expansion in patent applications by 1.35 patents, or 35 percent of a standard deviation.8 Our findings suggest that the rapid rise of Chinese imports contributed to making the United States a champion of technological innovation. Thinking of possible mechanisms, Bloom et al. (2016) offer two main explanations of how deeper import penetration translates into a within-sector increase in the number of patents. On the one hand, firms might respond to increased Chinese import competition with innovation, i.e., a within-firm response. On the other hand, import shocks might induce a reallocation of resources toward the more technologically advanced firms, indirectly boosting resource allocation to innovation activity. Table 3: IV Regressions: Patents and Import Flows, 1991-2003 Variables (1) (2) (3) (4) ln Patentst (0.039) -0.007 (0.066) ln Imports from Mexico 0.021 (0.018) -0.027 (0.044) ln Imports from China 0.088*** (0.017) 0.100*** (0.022) Sector y y y y Year y y y y Obs. 4,610 4,610 4,610 4,610 R2 0.705 0.723 0.58 0.527 First-Stage F-stat1 43.5 32 63.4 22.24 Number of SIC-year 407 407 407 407 Legend : *** significant at 1%, ** at 5%, * at 10%. Notes: Sector-level regressions, 1991–2003. Standard errors are clustered at the four-digit SIC level. Relying on patent data, however, has the drawback of capturing only innovations with sufficient market potential to be patented; our estimates, therefore, are likely to represent a lower bound of the true relationship between innovation and trade flows. With this caveat in mind, we will map our estimates into their implied contribution to growth. Endogenous growth models suggest that an increase in the number of patent applications per dollar spent on research translates into a boost to growth. More precisely, in the expanding variety model, an increase in patents of 15 percent--the part of the recent boom in applications explained by increased openness--is consistent with 5 percent higher growth; this calculation excludes trade effects via different channels.9 Our results, thus, suggest that raising barriers to trade tends to hinder economic growth by slowing down innovation. References Autor, David, David Dorn, Gordon H Hanson, Gary Pisano, and Pian Shu (2016). "Foreign Competition and Domestic Innovation: Evidence from U.S. Patents." Bloom, Nicholas, Mirko Draca, and John Van Reenen (2016). "Trade-induced technical change? The impact of Chinese imports on innovation, IT, and productivity," The Review of Economic Studies, 83(1): 87–117. Costinot, Arnaud, and Andres Rodriguez-Clare (1995). "Trade Theory with Numbers: Quantifying the Consequences of Globalization," NBER, 18896. Frankel, Jeffrey A, and David Romer (1999). "Does Trade cause Growth?" American Economic Review, 89(3): 379–399. Keller, Wolfgang (2004). "International Technology Diffusion," Journal of Economic Literature, 42(3): 752–782. Li, Guan-Cheng, Ronald Lai, Alexander D'Amour, David M Doolin, Ye Sun, Vetle I Torvik, Z Yu Amy, and Lee Fleming (2014). "Disambiguation and Co-Authorship Networks of the U.S. Patent Inventor Database (1975–2010)," Research Policy, 43(6): 941–955. Data are available at http://dvn.iq.harvard.edu/dvn/dv/patent. Pierce, Justin, and Peter Schott (2009). ‘‘A Concordance Between Ten-Digit U.S. Harmonized System Codes and SIC/NAICS Product Classes and Industries,'' NBER, 14837. Schott, Peter (2008). ‘‘The Relative Sophistication of Chinese Exports,'' Economic Policy, 23(53): 5-49. Silverman, Brian (2002). ‘‘International Patent Classification--US SIC Concordance,'' available at http://www.rotman.utoronto.ca/~silverman/ipcsic/ipcsicfiles.ZIP Silverman, Brian. Technological Resources and the Logic of Corporate Diversification. Routledge, 2003. 1. We thank Travis Adams, James Calello, and Morgan Smith for excellent research assistance. We also would like to thank Norm Morin for the useful insights and comments. The views expressed in this paper are those of the author and do not necessarily coincide with those of the Board of Governors or the Federal Reserve System. Return to text 2. A notable exception is the seminal work of Frankel and Romer (1999), which documents that the geographic content of trade raises income per capita by spurring capital accumulation and by boosting productivity; the effects, however, are not estimated with great precision. Return to text 3. See Keller (2004) for a review of the literature. Return to text 4. Autor et al. (2016) use a version of the same database updated through 2013. Return to text 5. The concordance relies on the primary SIC of use assigned by Canadian Patent Examiners for patent applications between 1990 and 1993. See Silverman (2003) for more details. Return to text 6. The 99th percentile of patents in our sample is approved in seven years. Return to text 7. Tariffs measures are from the UNCTAD TRAINS database while import data are from Schott (2008). We use the HS-SIC concordance built by Pierce and Schott (2009). Return to text 8. The standard deviation of is 2.98; imports are in thousands of dollars. 9. Our estimates are based on a relative risk aversion coefficient equal to 2, a labor share of 2/3, and a unit mass of consumers. Schumpeterian models would provide equivalent results if the increase in the quality of innovation, a difficult parameter to calibrate, was about 70 percent. Return to text
2017-11-19T06:50:04
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https://indico.fnal.gov/event/20381/contributions/57327/
# New Perspectives 2019 Jun 10 – 11, 2019 Fermi National Accelerator Laboratory US/Central timezone ## Overcoming Neutrino Interaction Mis-modeling with DUNE-PRISM Jun 11, 2019, 12:30 PM 15m One West (Fermi National Accelerator Laboratory) ### Speaker Dr Luke Pickering (Michigan State University) ### Description 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 advancements in neutrino-nucleus interaction modeling, traditional analyses will be susceptible to biased oscillation measurements. The DUNE-PRISM (Precision Reaction Independent Spectrum Measurement) technique offers a complementary approach to the oscillation analysis methods used by T2K, NO$\nu$A, and MINOS. DUNE-PRISM uses direct extrapolation of near detector data to infer oscillation probabilities with significantly less dependence on the validity of neutrino interaction models. This is achieved by combining multiple near detector measurements, each taken with the detector at a different off beam axis position, in order to sample a variety of neutrino energy spectra. This talk will introduce DUNE-PRISM and show how the oscillation parameters extracted using this technique are robust to unknown interaction modeling errors. ### Primary author Dr Luke Pickering (Michigan State University) Slides
2023-01-28T14:27:44
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https://www.usgs.gov/center-news/volcano-watch-cities-volcanoes-3-international-conference-evening-programs-public
# Volcano Watch - Cities on Volcanoes 3-an international conference with evening programs for the public Release Date: Many volcanoes are attractive places to live. Good soil, sweeping views, rugged beauty-all these features lure us to volcanic settings. Auckland and Naples are the two largest cities on, or at the foot of, volcanoes. On the mainland, Mammoth Lakes, winter playground of many southern Californians, is in the active Long Valley caldera. Portland, Oregon, is built within an old volcanic field that arguably could erupt again. And, of course, all of Hawaii's population resides on volcanoes, five of which can be considered active. Every silver lining has its cloud. The hazards posed to communities on and near volcanoes are very real, and the risk-the number of people and the value of infrastructure potentially affected by the hazards-increases each year as populations increase. Communities downstream or downwind from volcanoes are not immune to volcano hazards, either; witness the loss of more than 22,000 lives in 1985 at Armero, Colombia, where a mudflow generated by a small eruption 74 km (46 miles) away obliterated much of the city. In 1998, an international conference was held in Rome and Naples, bringing together more than 100 representatives of diverse disciplines and backgrounds, from volcanologists to public officials to social scientists to emergency managers. Such meetings are rare; mostly we talk among ourselves rather than across discipline boundaries. The conference, Cities on Volcanoes, was a resounding success and led to a second meeting in Auckland in 2001 that generated an equal amount of interaction and advancement among its 220 participants. Cities on Volcanoes 3 (COV3) starts on July 14 in Hilo. About 350 people from 27 countries will spend the week listening to talks, viewing posters, taking part in discussions and workshops, and visiting special volcanic areas on the island. More than half are from outside the United States. Italy, Japan, and New Zealand have the most foreign participants-not surprising, given the importance of volcanoes in those countries. In his letter inviting the conference to Hawaii County, Mayor Harry Kim wrote that "Hawaii is the perfect venue for this conference. We have a healthy respect for our volcanoes...[and are]...preparing for future volcanic activity of potentially active volcanoes of Hawaii through collaborative work in emergency management." Those potentially active volcanoes are Mauna Loa, Kīlauea, Hualalai, arguably Mauna Kea, and, in Maui County, Haleakala. The fact that COV3 is being held in Hawaii highlights the importance to the international community of such future volcanic activity. The conference, hosted by the University of Hawaii-Hilo, was organized at the University's Conference Center led by Director Judith Fox-Goldstein and Conference Specialist Andrea Furuli. Mahalo nui loa to Judy, Andrea, and their staff, from the technical committee chaired by Prof. Bruce Houghton (UH-Manoa). Much of the meeting will be restricted to technical sessions, but the public is heartily invited to two free evening programs at the UHH Theater. The first public program features award-winning movies of Hawaiian eruptions (Kīlauea Iki-Kapoho 1959-60, Mauna Ulu 1969-74, and Mauna Loa 1984) and will end with a film showing last year's destructive eruption of Nyiragongo volcano that sent lava flows through the city of Goma, Democratic Republic of Congo. Wednesday Night at the Movies starts at 7 p.m. on July 16. On Friday, July 18, Tari Moulds Mattox, former HVO geologist with close ties to the Kalapana community, will present a slide show about the current eruption to introduce "Kalapana Dreaming," an evening of reminiscence among people affected by the Kīlauea eruption in 1986-1991. We hope that a number of folks with connections to Kalapana come to the informal evening gathering and talk story about their experiences. The program is manuahi and starts at 7 p.m. in the UHH Theater. Come to the evening programs, rub elbows with conference participants, and help show why "Hawaii is the perfect venue for this conference." ### Volcano Activity Update Eruptive action at the Puu Oo vent of the presently active Kīlauea Volcano continued unabated during the past week. Surface activity is visible on the Kohola flow above Paliuli, and the east-side lobe of the main Mother's Day flow is almost continuously incandescent from top to bottom of Pulama pali. Scattered surface breakouts also occur in the coastal flats near the base of Paliuli. The ocean entry from the Highcastle delta is small and weak. The public is reminded that the ocean entry areas are extremely hazardous, with explosions accompanying sudden collapses of the new land. The steam clouds are highly acidic and laced with glass particles. The National Park Service has put warning signs in critical places. Do not venture beyond these signs and onto the lava deltas and benches. Two earthquakes were reported felt on the island during the past week. A resident of Kohala Estates felt an earthquake at 9:36 a.m. on Tuesday, July 6. The magnitude-4.0 temblor was located 175 km (109 mi) southwest of Kailua-Kona at a depth of 6 km (3.6 mi). A magnitude-3.4 earthquake occurred at 5:59 a.m. on July 10 and was felt in Ahualoa, Papaaloa, and Hilo. The earthquake was located 11 km (6.6 mi) east of the summit of Mauna Kea at a depth of 26 km (15.6 mi). Mauna Loa is not erupting. The summit region continues to inflate slowly. Seismic activity remains low, with no earthquake located in the summit area during the last seven days.
2019-11-17T17:49:04
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https://pure.royalholloway.ac.uk/portal/en/publications/generation-of-pure-superconducting-spin-current-in-magnetic-heterostructures-via-nonlocally-induced-magnetism-due-to-landau-fermi-liquid-effects(87c8bf92-3fb6-4f1e-b720-4cb0afa97744).html
Generation of pure superconducting spin current in magnetic heterostructures via nonlocally induced magnetism due to Landau Fermi liquid effects. / Montiel, Xavier; Eschrig, Matthias. In: Physical Review B, Vol. 98, No. 10, 104513, 26.09.2018, p. 1-18. Research output: Contribution to journalArticlepeer-review Published ### Abstract We propose a mechanism for the generation of pure superconducting spin-current carried by equal-spin triplet Cooper pairs in a superconductor (S) sandwiched between a ferromagnet (F) and a normal metal (Nso) with intrinsic spin-orbit coupling. We show that in the presence of Landau Fermi-liquid interactions the superconducting proximity effect can induce non-locally a ferromagnetic exchange field in the normal layer, which disappears above the superconducting transition temperature of the structure. The internal Landau Fermi-liquid exchange field leads to the onset of a spin supercurrent associated with the generation of long-range spin-triplet superconducting correlations in the trilayer. We demonstrate that the magnitude of the spin supercurrent as well as the induced magnetic order in the N$_{\rm so}$ layer depends critically on the superconducting proximity effect between the S layer and the F and Nso layers and the magnitude of the relevant Landau Fermi-liquid interaction parameter. We investigate the effect of spin flip processes on this mechanism. Our results demonstrate the crucial role of Landau Fermi-liquid interaction in combination with spin-orbit coupling for the creation of spin supercurrent in superconducting spintronics, and give a possible explanation of a recent experiment utilizing spin-pumping via ferromagnetic resonance [Jeon et al., Nat. Mat. 17, 499 (2018)]. Original language English 104513 1-18 18 Physical Review B 98 10 https://doi.org/10.1103/PhysRevB.98.104513 Published - 26 Sep 2018 • ## Superconducting spintronics Project: Research This open access research output is licenced under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License. ID: 31171231
2021-07-30T13:39:12
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https://zbmath.org/authors/?q=ai%3Abarbu.viorel
zbMATH — the first resource for mathematics Barbu, Viorel Compute Distance To: Author ID: barbu.viorel Published as: Barbu, Viorel; Barbu, V. Homepage: http://www.math.uaic.ro/~barbu/ External Links: MGP · Wikidata · Google Scholar · ResearchGate · Math-Net.Ru · dblp · GND · IdRef · theses.fr Documents Indexed: 350 Publications since 1964, including 24 Books Reviewing Activity: 5 Reviews all top 5 Co-Authors 151 single-authored 48 Da Prato, Giuseppe 33 Röckner, Michael 14 Favini, Angelo 13 Tubaro, Luciano 12 Lasiecka, Irena 10 Pavel, Nicolae H. 8 Iannelli, Mimmo 8 Sritharan, Sivaguru S. 7 Marinoschi, Gabriela 6 Zhang, Deng 5 Bonaccorsi, Stefano 5 Rammaha, Mohammad A. 5 Triggiani, Roberto 4 Coca, Daniel 4 Colli, Pierluigi 4 Gilardi, Gianni 4 Wang, Gengsheng 3 Di Persio, Luca 3 Kunisch, Karl 3 Lefter, Cătălin-George 3 Precupanu, Th. 3 Russo, Francesco 3 Tessitore, Gianmario 3 Tiba, Dan 3 Yan, Yue 2 Aizicovici, Sergiu 2 Albeverio, Sergio A. 2 Aniţa, Sebastian 2 Bantaş, Gheorghe 2 Barbu, Tudor 2 Barron, Emmanuel Nicholas 2 Benazzoli, Chiara 2 Brzeźniak, Zdzisław 2 Debussche, Arnaud 2 Ferrario, Benedetta 2 Grujić, Zoran 2 Havârneanu, Teodor 2 Marinelli, Carlo 2 Neittaanmäki, Pekka J. 2 Niemistö, Antti 2 Rascanu, Aurel 2 Stojanović, Srđan Đ. 2 Tuffaha, Amjad M. 2 Vrabie, Ioan I. 1 Arnăutu, Viorel 1 Bernardi, Marco Luigi 1 Beznea, Lucian 1 Biga, Veronica 1 Blanchard, Philippe 1 Bogachev, Vladimir Igorevich 1 Bonnans, Joseph Frédéric 1 Capasso, Vincenzo 1 Cârjă, Ovidiu 1 Cătălin, Lefter 1 Cellina, Arrigo 1 Cordoni, Francesco Giuseppe 1 Corduneanu, Constantin 1 Friedman, Avner 1 Georghiu, N. 1 Grasselli, Maurizio 1 Grossman, Stanley I. 1 Guo, Yanqiu 1 Hausenblas, Erika 1 Korman, Philip L. 1 Martcheva, Maia 1 Moroşanu, Gheorghe 1 Munteanu, Ionut 1 Popa, Constantin Gh. 1 Precupanu, Teodor 1 Ring, Wolfgang 1 Rocca, Elisabetta 1 Rodrigues, Sérgio S. 1 Romanelli, Silvia 1 Seidman, Thomas I. 1 Shirikyan, Armen R. 1 Sîrbu, Mihai 1 Toundykov, Daniel 1 Vârsan, Constantin 1 Zolésio, Jean-Paul all top 5 Serials 23 SIAM Journal on Control and Optimization 15 Journal of Mathematical Analysis and Applications 14 Applied Mathematics and Optimization 13 Journal of Differential Equations 12 Differential and Integral Equations 11 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 9 Revue Roumaine de Mathématiques Pures et Appliquées 9 Numerical Functional Analysis and Optimization 8 Systems & Control Letters 8 Nonlinear Analysis. Theory, Methods & Applications 6 SIAM Journal on Mathematical Analysis 6 Stochastic Processes and their Applications 6 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 6 Comptes Rendus Hebdomadaires des Séances de l’Académie des Sciences, Série A 5 Analele Ştiinţifice ale Universităţii Al. I. Cuza din Iaşi. (Serie Nouă.) Secţiunea Ia. Matematică-Informatică 5 Indiana University Mathematics Journal 5 Journal of Optimization Theory and Applications 4 The Annals of Probability 4 Control and Cybernetics 4 Ricerche di Matematica 4 Transactions of the American Mathematical Society 4 Advances in Differential Equations 4 Infinite Dimensional Analysis, Quantum Probability and Related Topics 3 Automatica 3 Journal of Functional Analysis 3 Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni 3 Communications in Partial Differential Equations 3 Nonlinear Analysis. Real World Applications 2 Communications in Mathematical Physics 2 Annali di Matematica Pura ed Applicata. Serie Quarta 2 Rendiconti dell’Istituto di Matematica dell’Università di Trieste 2 Libertas Mathematica 2 Probability Theory and Related Fields 2 Atti della Accademia Nazionale dei Lincei. Serie Ottava. Rendiconti. Classe di Scienze Fisiche, Matematiche e Naturali 2 Journal de Mathématiques Pures et Appliquées. Neuvième Série 2 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 2 Topological Methods in Nonlinear Analysis 2 NoDEA. Nonlinear Differential Equations and Applications 2 Comptes Rendus. Mathématique. Académie des Sciences, Paris 2 Bollettino della Unione Matematica Italiana. Series IV 2 SIAM Journal on Control 2 Annali della Scuola Normale Superiore di Pisa. Scienze Fisiche e Matematiche. III. Ser 2 Mathematics and its Applications (Dordrecht) 2 Stochastic and Partial Differential Equations. Analysis and Computations 2 Libertas Mathematica. New Series 2 Springer Monographs in Mathematics 1 Archive for Rational Mechanics and Analysis 1 Communications on Pure and Applied Mathematics 1 International Journal of Control 1 Mathematical Methods in the Applied Sciences 1 ZAMP. Zeitschrift für angewandte Mathematik und Physik 1 Acta Scientiarum Mathematicarum 1 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 1 Funkcialaj Ekvacioj. Serio Internacia 1 IEEE Transactions on Automatic Control 1 Journal of the Faculty of Science. Section I A 1 Mathematische Annalen 1 Memoirs of the American Mathematical Society 1 Osaka Journal of Mathematics 1 Semigroup Forum 1 Studii şi Cercetări Matematice 1 Journal of Integral Equations 1 Memoriile Secţiilor Ştiinţifice. Seria IV 1 RAIRO. Modélisation Mathématique et Analyse Numérique 1 MCSS. Mathematics of Control, Signals, and Systems 1 Studia Universitatis Babeş-Bolyai. Mathematica 1 Analele Ştiinţifice ale Universităţii Al. I. Cuza din Iaşi. Serie Nouă. Matematică 1 Journal of Nonlinear Science 1 Journal of Convex Analysis 1 Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica 1 Electronic Journal of Probability 1 Electronic Communications in Probability 1 Discrete and Continuous Dynamical Systems 1 Communications in Applied Analysis 1 Abstract and Applied Analysis 1 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 Journal of the European Mathematical Society (JEMS) 1 Journal of Evolution Equations 1 Scientiae Mathematicae Japonicae 1 Seminar on Fixed Point Theory Cluj-Napoca 1 Boletim da Sociedade Paranaense de Matemática. Terceira Série 1 ISNM. International Series of Numerical Mathematics 1 Lecture Notes in Mathematics 1 Mathematics and its Applications. East European Series 1 Mathematics in Science and Engineering 1 AIP Conference Proceedings 1 Bollettino dell’Unione Matematica Italiana. Series IX 1 Discrete and Continuous Dynamical Systems. Series S 1 Annals of the Academy of Romanian Scientists. Mathematics and its Applications 1 Annals of the University of Bucharest. Mathematical Series 1 Mathematical Control and Related Fields 1 Preprint. “Babeş-Bolyai” University. Faculty of Mathematics and Physics. Research Seminars 1 Mathematica 1 Evolution Equations and Control Theory 1 Pure and Applied Functional Analysis 1 Progress in Nonlinear Differential Equations and Their Applications 1 Springer Undergraduate Mathematics Series 1 Communications and Control Engineering 1 Interscience Tracts in Pure and Applied Mathematics all top 5 Fields 197 Partial differential equations (35-XX) 100 Calculus of variations and optimal control; optimization (49-XX) 99 Systems theory; control (93-XX) 90 Probability theory and stochastic processes (60-XX) 89 Operator theory (47-XX) 45 Fluid mechanics (76-XX) 36 Ordinary differential equations (34-XX) 16 Integral equations (45-XX) 12 Global analysis, analysis on manifolds (58-XX) 12 Operations research, mathematical programming (90-XX) 11 Dynamical systems and ergodic theory (37-XX) 11 Functional analysis (46-XX) 9 Classical thermodynamics, heat transfer (80-XX) 7 Numerical analysis (65-XX) 7 Biology and other natural sciences (92-XX) 5 General and overarching topics; collections (00-XX) 5 History and biography (01-XX) 5 Statistical mechanics, structure of matter (82-XX) 5 Information and communication theory, circuits (94-XX) 4 Mechanics of deformable solids (74-XX) 3 Linear and multilinear algebra; matrix theory (15-XX) 3 Functions of a complex variable (30-XX) 3 Potential theory (31-XX) 3 Difference and functional equations (39-XX) 3 Mechanics of particles and systems (70-XX) 1 Number theory (11-XX) 1 Real functions (26-XX) 1 General topology (54-XX) 1 Quantum theory (81-XX) 1 Geophysics (86-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) Citations contained in zbMATH Open 273 Publications have been cited 4,273 times in 2,905 Documents Cited by Year Nonlinear semigroups and differential equations in Banach spaces. Revised and enlarged translation of the Romanian ed. Zbl 0328.47035 Barbu, Viorel 1976 Nonlinear differential equations of monotone types in Banach spaces. Zbl 1197.35002 Barbu, Viorel 2010 Optimal control of variational inequalities. Zbl 0574.49005 Barbu, V. 1984 Almost periodic functions. Zbl 0175.09101 Corduneanu, C.; Georghiu, N.; Barbu, V. 1968 Analysis and control of nonlinear infinite dimensional systems. Zbl 0776.49005 Barbu, Viorel 1993 Convexity and optimization in Banach spaces. 2nd rev. and extended ed. Transl. from the Romanian. Zbl 0594.49001 Barbu, V.; Precupanu, Th. 1986 Convexity and optimization on Banach spaces. Rev. and enl. translation. Zbl 0379.49010 Barbu, V.; Precupanu, Th. 1978 Convexity and optimization in Banach spaces. 4th updated and revised ed. Zbl 1244.49001 Barbu, Viorel; Precupanu, Teodor 2012 Optimal control of population dynamics. Zbl 0984.92022 Barbu, V.; Iannelli, M. 1999 Internal stabilization of Navier-Stokes equations with finite-dimensional controllers. Zbl 1073.76017 Barbu, Viorel; Triggiani, Roberto 2004 Hamilton-Jacobi equations in Hilbert spaces. Zbl 0508.34001 Barbu, V.; Da Prato, G. 1983 Existence of strong solutions for stochastic porous media equation under general monotonicity conditions. Zbl 1162.76054 Barbu, Viorel; Da Prato, Giuseppe; Röckner, Michael 2009 Exact controllability of the superlinear heat equation. Zbl 0964.93046 Barbu, V. 2000 Mathematical methods in optimization of differential systems. Zbl 0819.49002 Barbu, Viorel 1994 Controllability of parabolic and Navier-Stokes equations. Zbl 1010.93054 Barbu, Viorel 2002 Tangential boundary stabilization of Navier-Stokes equations. Zbl 1098.35026 Barbu, Viorel; Lasiecka, Irena; Triggiani, Roberto 2006 On nonlinear wave equations with degenerate damping and source terms. Zbl 1065.35193 Barbu, Viorel; Lasiecka, Irena; Rammaha, Mohammad A. 2005 Abstract settings for tangential boundary stabilization of Navier–Stokes equations by high- and low-gain feedback controllers. Zbl 1098.35025 Barbu, Viorel; Lasiecka, Irena; Triggiani, Roberto 2006 Smoothness of weak solutions to a nonlinear fluid-structure interaction model. Zbl 1147.74016 Barbu, Viorel; Grujić, Zoran; Lasiecka, Irena; Tuffaha, Amjad 2008 Stochastic porous media equations and self-organized criticality. Zbl 1176.35182 Barbu, Viorel; Da Prato, Giuseppe; Röckner, Michael 2009 Stabilization of Navier-Stokes flows. Zbl 1213.76001 Barbu, Viorel 2011 Existence and ergodicity for the two-dimensional stochastic magneto-hydrodynamics equations. Zbl 1187.76727 Barbu, Viorel; Da Prato, Giuseppe 2007 On the controllability of the Lotka-McKendrick model of population dynamics. Zbl 0961.92024 Barbu, Viorel; Iannelli, Mimmo; Martcheva, Maia 2001 Periodic solutions to the nonlinear one-dimensional wave equation with $$x$$-dependent coefficients. Zbl 0880.35073 Barbu, V.; Pavel, N. H. 1997 Carleman estimates and controllability of linear stochastic heat equations. Zbl 1087.93011 Barbu, Viorel; Răşcanu, Aurel; Tessitore, Gianmario 2003 A class of boundary problems for second order abstract differential equations. Zbl 0256.47052 Barbu, Viorel 1972 Existence of the energy-level weak solutions for a nonlinear fluid-structure interaction model. Zbl 1297.35234 Barbu, Viorel; Grujić, Zoran; Lasiecka, Irena; Tuffaha, Amjad 2007 Controllability of the heat equation with memory. Zbl 0990.93008 Barbu, V.; Iannelli, M. 2000 The time optimal control of Navier-Stokes equations. Zbl 0898.49011 Barbu, Viorel 1997 An operatorial approach to stochastic partial differential equations driven by linear multiplicative noise. Zbl 1327.60122 Barbu, Viorel; Röckner, Michael 2015 Feedback stabilization of Navier-Stokes equations. Zbl 1076.93037 Barbu, Viorel 2003 Existence and uniqueness of nonnegative solutions to the stochastic porous medium equation. Zbl 1137.76059 Barbu, Viorel; Da Prato, Giuseppe; Röckner, Michael 2008 Boundary control problems with convex cost criterion. Zbl 0428.49015 Barbu, Viorel 1980 Stochastic variational inequalities and applications to the total variation flow perturbed by linear multiplicative noise. Zbl 1286.35202 Barbu, Viorel; Röckner, Michael 2013 A PDE variational approach to image denoising and restoration. Zbl 1169.35341 Barbu, Tudor; Barbu, Viorel; Biga, Veronica; Coca, Daniel 2009 Stochastic nonlinear Schrödinger equations with linear multiplicative noise: rescaling approach. Zbl 1300.35116 Barbu, Viorel; Röckner, Michael; Zhang, Deng 2014 Necessary conditions for distributed control problems governed by parabolic variational inequalities. Zbl 0474.49024 Barbu, Viorel 1981 Existence for nonlinear Volterra equations in Hilbert spaces. Zbl 0462.45021 Barbu, Viorel 1979 Continuous perturbations of nonlinear $$m$$-accretive operators in Banach spaces. Zbl 0256.47053 Barbu, V. 1972 Optimal control of Navier-Stokes equations with periodic inputs. Zbl 0914.49009 Barbu, Viorel 1998 Internal exponential stabilization to a nonstationary solution for 3D Navier-Stokes equations. Zbl 1231.35141 Barbu, Viorel; Rodrigues, Sérgio S.; Shirikyan, Armen 2011 Blow-up of generalized solutions to wave equations with nonlinear degenerate damping and source terms. Zbl 1121.35082 Barbu, Viorel; Lasiecka, Irena; Rammaha, Mohammad A. 2007 Nonlinear Volterra equations in a Hilbert space. Zbl 0322.45012 Barbu, Viorel 1975 Flow invariance preserving feedback controllers for the Navier-Stokes equation. Zbl 1073.93030 Barbu, V.; Sritharan, S. S. 2001 Boundary stabilization of equilibrium solutions to parabolic equations. Zbl 1369.93475 Barbu, Viorel 2013 Periodic solutions to one-dimensional wave equation with piece-wise constant coefficients. Zbl 0896.35075 Barbu, V.; Pavel, N. H. 1996 Null controllability of nonlinear convective heat equations. Zbl 0938.93008 Aniţa, Sebastian; Barbu, Viorel 2000 Local controllability of the phase field system. Zbl 1006.35013 Barbu, Viorel 2002 The stochastic nonlinear damped wave equation. Zbl 1024.47025 Barbu, Viorel; Da Prato, Giuseppe 2002 Internal stabilization of semilinear parabolic systems. Zbl 1030.35100 Barbu, V.; Wang, G. 2003 On a random scaled porous media equation. Zbl 1238.60070 Barbu, Viorel; Röckner, Michael 2011 Determining the acoustic impedance in the 1-D wave equation via an optimal control problem. Zbl 0906.49009 Barbu, V.; Pavel, N. H. 1997 Kolmogorov equation associated to the stochastic reflection problem on a smooth convex set of a Hilbert space. Zbl 1205.60141 Barbu, Viorel; Da Prato, Giuseppe; Tubaro, Luciano 2009 Stabilization of Navier-Stokes equations by oblique boundary feedback controllers. Zbl 1292.93100 Barbu, Viorel 2012 Stochastic porous media equations. Zbl 1355.60004 Barbu, Viorel; Da Prato, Giuseppe; Röckner, Michael 2016 Stochastic wave equations with dissipative damping. Zbl 1122.60056 Barbu, Viorel; Da Prato, Giuseppe; Tubaro, Luciano 2007 Sur un problème aux limites pour une classe d’équations différentielles non linéaires abstraits du deuxième ordre en t. Zbl 0237.34095 Barbu, Viorel 1972 Stochastic nonlinear Schrödinger equations. Zbl 1336.60118 Barbu, Viorel; Röckner, Michael; Zhang, Deng 2016 Convexity and optimisation in Banach spaces. (Convexitate si optimizare in spatii Banach.). Zbl 0317.49011 Barbu, V.; Precupanu, Th. 1975 Nonlinear boundary-value problems for a class of hyperbolic systems. Zbl 0364.35038 Barbu, Viorel 1977 Periodic solutions to an unbounded Hamiltonian system. Zbl 0882.34065 Barbu, V. 1995 Asymptotic behavior of linear integrodifferential systems. Zbl 0253.45007 Barbu, Viorel; Grossman, Stanley I. 1972 Navier-Stokes equation with hereditary viscosity. Zbl 1040.35056 Barbu, V.; Sritharan, S. S. 2003 The two phase stochastic Stefan problem. Zbl 1101.60040 Barbu, Viorel; Da Prato, Giuseppe 2002 Existence, uniqueness, and longtime behavior for a nonlinear Volterra integrodifferential equation. Zbl 0981.45006 Barbu, Viorel; Colli, Pierluigi; Gilardi, Gianni; Grasselli, Maurizio 2000 From nonlinear Fokker-Planck equations to solutions of distribution dependent SDE. Zbl 07224963 Barbu, Viorel; Röckner, Michael 2020 Integro-differential equations in Hilbert spaces. Zbl 0366.45013 Barbu, Viorel 1973 Stochastic nonlinear diffusion equations with singular diffusivity. Zbl 1203.60079 Barbu, Viorel; Da Prato, Giuseppe; Röckner, Michael 2009 Exact controllability for the magnetohydrodynamic equations. Zbl 1121.93306 Barbu, Viorel; Havârneanu, Teodor; Popa, Cătălin; Sritharan, S. S. 2003 Partial differential equations and boundary value problems. Transl. from the Romanian by the author. Zbl 0898.35002 Barbu, Viorel 1998 Existence and asymptotic behavior for hereditary stochastic evolution equations. Zbl 1304.60064 Barbu, Viorel; Bonaccorsi, Stefano; Tubaro, Luciano 2014 Existence and asymptotic results for a system of integro-partial differential equations. Zbl 0844.35040 Aizicovici, Sergiu; Barbu, Viorel 1996 Periodic optimal control in Hilbert space. Zbl 0849.49003 Barbu, V.; Pavel, N. H. 1996 Finite time extinction for solutions to fast diffusion stochastic porous media equations. Zbl 1156.60040 Barbu, Viorel; Da Prato, Giuseppe; Röckner, Michael 2009 Feedback stabilization of semilinear heat equations. Zbl 1065.93027 Barbu, V.; Wang, G. 2003 Optimal control approach to nonlinear diffusion equations driven by Wiener noise. Zbl 1237.93177 Barbu, Viorel 2012 Existence and uniqueness of solutions to wave equations with nonlinear degenerate damping and source terms. Zbl 1167.35414 Lasiecka, I.; Barbu, V.; Rammaha, M. 2005 Necessary conditions for nonconvex distributed control problems governed by elliptic variational inequalities. Zbl 0477.49013 Barbu, Viorel 1981 Extended algebraic Riccati equations in the abstract hyperbolic case. Zbl 0961.49003 Barbu, V.; Lasiecka, I.; Triggiani, R. 2000 Ergodicity for nonlinear stochastic equations in variational formulation. Zbl 1109.35123 Barbu, Viorel; Da Prato, Giuseppe 2006 Existence theorems for a class of two point boundary problems. Zbl 0295.35074 Barbu, Viorel 1975 The necessary conditions for optimal control in Hilbert spaces. Zbl 0667.49017 Barbu, V.; Barron, E. N.; Jensen, R. 1988 $$H^\infty$$-control theory of fluid dynamics. Zbl 0919.93026 Barbu, V.; Sritharan, S. S. 1998 Probabilistic representation for solutions to nonlinear Fokker-Planck equations. Zbl 1407.60091 Barbu, Viorel; Röckner, Michael 2018 Kolmogorov equation associated to the stochastic reflection problem on a smooth convex set of a Hilbert space. II. Zbl 1230.60081 Barbu, Viorel; Da Prato, Giuseppe; Tubaro, Luciano 2011 Optimal control of stochastic Fitzhugh-Nagumo equation. Zbl 1338.93398 Barbu, Viorel; Cordoni, Francesco; Di Persio, Luca 2016 Stochastic porous media equations and self-organized criticality: Convergence to the critical state in all dimensions. Zbl 1238.60071 Barbu, Viorel; Röckner, Michael 2012 Semigroups of nonlinear contractions in Banach spaces. (Semigrupuri de contractii neliniare in spatii Banach.). Zbl 0276.47044 Barbu, Viorel 1974 Weak solutions to the stochastic porous media equation via Kolmogorov equations: the degenerate case. Zbl 1104.60034 Barbu, Viorel; Bogachev, Vladimir I.; Da Prato, Giuseppe; Röckner, Michael 2006 Stabilization of a plane channel flow by wall normal controllers. Zbl 1124.35051 Barbu, Viorel 2007 The generator of the transition semigroup corresponding to a stochastic variational inequality. Zbl 1155.60034 Barbu, Viorel; da Prato, Giuseppe 2008 A variational approach to stochastic nonlinear parabolic problems. Zbl 1235.60074 Barbu, Viorel 2011 Probabilistic representation for solutions of an irregular porous media type equation: The degenerate case. Zbl 1227.60088 Barbu, Viorel; Röckner, Michael; Russo, Francesco 2011 Existence and convergence results for infinite dimensional nonlinear stochastic equations with multiplicative noise. Zbl 1267.60076 Barbu, Viorel; Brzeźniak, Zdzisław; Hausenblas, Erika; Tubaro, Luciano 2013 State constrained optimal control problems governed by semilinear equations. Zbl 0966.49016 Barbu, V.; Wang, Gengsheng 2000 The Neumann problem on unbounded domains of $$\mathbb R^d$$ and stochastic variational inequalities. Zbl 1130.35137 Barbu, Viorel; Da Prato, Giuseppe 2005 Existence for semilinear parabolic stochastic equations. Zbl 1213.35260 Barbu, Viorel 2010 Hamilton-Jacobi equations and nonlinear control problems. Zbl 0606.49020 Barbu, Viorel 1986 Convex integrals on Sobolev spaces. Zbl 1254.49006 Barbu, Viorel; Guo, Yanqiu; Rammaha, Mohammad A.; Toundykov, Daniel 2012 The unique continuation property of eigenfunctions to Stokes-Oseen operator is generic with respect to the coefficients. Zbl 1246.35054 Barbu, V.; Lasiecka, I. 2012 From nonlinear Fokker-Planck equations to solutions of distribution dependent SDE. Zbl 07224963 Barbu, Viorel; Röckner, Michael 2020 Optimal feedback controllers for a stochastic differential equation with reflection. Zbl 1441.49032 Barbu, Viorel 2020 Probabilistic representation for solutions to nonlinear Fokker-Planck equations. Zbl 1407.60091 Barbu, Viorel; Röckner, Michael 2018 Optimal bilinear control of nonlinear stochastic Schrödinger equations driven by linear multiplicative noise. Zbl 1431.60053 Barbu, Viorel; Röckner, Michael; Zhang, Deng 2018 Controllability and stabilization of parabolic equations. Zbl 1417.93005 Barbu, Viorel 2018 Mild solutions to the dynamic programming equation for stochastic optimal control problems. Zbl 1400.93328 Barbu, Viorel; Benazzoli, Chiara; Di Persio, Luca 2018 Nonlinear Fokker-Planck equations driven by Gaussian linear multiplicative noise. Zbl 1403.60051 Barbu, Viorel; Röckner, Michael 2018 Variational solutions to nonlinear stochastic differential equations in Hilbert spaces. Zbl 1427.60115 Barbu, Viorel; Röckner, Michael 2018 Exact controllability of stochastic differential equations with multiplicative noise. Zbl 1408.93022 Barbu, V.; Tubaro, L. 2018 The approximation of the square root of the total variation flow. Zbl 07055960 Barbu, Viorel 2018 Existence for nonlinear finite dimensional stochastic differential equations of subgradient type. Zbl 1419.60048 Barbu, Viorel 2018 Stochastic nonlinear parabolic equations with Stratonovich gradient noise. Zbl 1404.93032 Barbu, Viorel; Brzeźniak, Zdzisław; Tubaro, Luciano 2018 Stochastic nonlinear Schrödinger equations: no blow-up in the non-conservative case. Zbl 1378.60088 Barbu, Viorel; Röckner, Michael; Zhang, Deng 2017 Sliding mode control for a nonlinear phase-field system. Zbl 1374.35410 Barbu, Viorel; Colli, Pierluigi; Gilardi, Gianni; Marinoschi, Gabriela; Rocca, Elisabetta 2017 A splitting algorithm for stochastic partial differential equations driven by linear multiplicative noise. Zbl 1387.60095 Barbu, Viorel; Röckner, Michael 2017 The stochastic logarithmic Schrödinger equation. Zbl 1360.60119 Barbu, Viorel; Röckner, Michael; Zhang, Deng 2017 Global solutions to random 3D vorticity equations for small initial data. Zbl 1409.60094 Barbu, Viorel; Röckner, Michael 2017 Doubly probabilistic representation for the stochastic porous media type equation. Zbl 1387.35635 Barbu, Viorel; Röckner, Michael; Russo, Francesco 2017 Feedback stabilization of the Cahn-Hilliard type system for phase separation. Zbl 1351.93113 Barbu, Viorel; Colli, Pierluigi; Gilardi, Gianni; Marinoschi, Gabriela 2017 The steepest descent algorithm in Wasserstein metric for the sandpile model of self-organized criticality. Zbl 1372.35125 Barbu, Viorel 2017 Stochastic porous media equations. Zbl 1355.60004 Barbu, Viorel; Da Prato, Giuseppe; Röckner, Michael 2016 Stochastic nonlinear Schrödinger equations. Zbl 1336.60118 Barbu, Viorel; Röckner, Michael; Zhang, Deng 2016 Optimal control of stochastic Fitzhugh-Nagumo equation. Zbl 1338.93398 Barbu, Viorel; Cordoni, Francesco; Di Persio, Luca 2016 An optimal control approach to the optical flow problem. Zbl 1327.93404 Barbu, Viorel; Marinoschi, Gabriela 2016 Generalized solutions to nonlinear Fokker-Planck equations. Zbl 1342.35395 Barbu, Viorel 2016 Measure-valued branching processes associated with Neumann nonlinear semiflows. Zbl 1381.35099 Barbu, Viorel; Beznea, Lucian 2016 Stochastic differential equations with variable structure driven by multiplicative Gaussian noise and sliding mode dynamic. Zbl 1356.60088 Barbu, Viorel; Bonaccorsi, Stefano; Tubaro, Luciano 2016 Differential equations. Translated from the Romanian. Originally published by Junimea, Iaşi 1985. Zbl 1370.34001 Barbu, Viorel 2016 An operatorial approach to stochastic partial differential equations driven by linear multiplicative noise. Zbl 1327.60122 Barbu, Viorel; Röckner, Michael 2015 Stochastic parabolic equations with nonlinear dynamical boundary conditions. Zbl 1332.35404 Barbu, Viorel; Bonaccorsi, Stefano; Tubaro, Luciano 2015 Nonlinear parabolic flows with dynamic flux on the boundary. Zbl 1317.35113 Barbu, Viorel; Favini, Angelo; Marinoschi, Gabriela 2015 Stochastic porous media equations. Zbl 1333.60133 Barbu, Viorel 2015 Stochastic porous media equations in $$\mathbb R^d$$. Zbl 1405.76047 Barbu, Viorel; Röckner, Michael; Russo, Francesco 2015 A stochastic heat equation with nonlinear dissipation on the boundary. Zbl 1316.60102 Barbu, Viorel; Bonaccorsi, Stefano; Tubaro, Luciano 2015 Stochastic nonlinear Schrödinger equations with linear multiplicative noise: rescaling approach. Zbl 1300.35116 Barbu, Viorel; Röckner, Michael; Zhang, Deng 2014 Existence and asymptotic behavior for hereditary stochastic evolution equations. Zbl 1304.60064 Barbu, Viorel; Bonaccorsi, Stefano; Tubaro, Luciano 2014 Exact null internal controllability for the heat equation on unbounded convex domains. Zbl 1282.93046 Barbu, Viorel 2014 A stochastic parabolic equation with nonlinear flux on the boundary driven by a Gaussian noise. Zbl 1292.60061 Barbu, Viorel; Bonaccorsi, Stefano; Tubaro, Luciano 2014 Asymptotic behaviour of the two phase stochastic Stefan flows driven by multiplicative Gaussian processes. Zbl 1389.80006 Barbu, Viorel 2014 Stochastic variational inequalities and applications to the total variation flow perturbed by linear multiplicative noise. Zbl 1286.35202 Barbu, Viorel; Röckner, Michael 2013 Boundary stabilization of equilibrium solutions to parabolic equations. Zbl 1369.93475 Barbu, Viorel 2013 Existence and convergence results for infinite dimensional nonlinear stochastic equations with multiplicative noise. Zbl 1267.60076 Barbu, Viorel; Brzeźniak, Zdzisław; Hausenblas, Erika; Tubaro, Luciano 2013 Self-organized criticality of cellular automata model; absorbtion in finite-time of supercritical region into the critical one. Zbl 1273.35158 Barbu, Viorel 2013 Note on the internal stabilization of stochastic parabolic equations with linearly multiplicative Gaussian noise. Zbl 1283.35062 Barbu, Viorel 2013 The internal stabilization of the Stokes-Oseen equation by feedback point controllers. Zbl 1276.93064 Barbu, Viorel 2013 Nonlinear diffusion equations in image processing. Zbl 1299.35152 Barbu, Viorel 2013 Convexity and optimization in Banach spaces. 4th updated and revised ed. Zbl 1244.49001 Barbu, Viorel; Precupanu, Teodor 2012 Stabilization of Navier-Stokes equations by oblique boundary feedback controllers. Zbl 1292.93100 Barbu, Viorel 2012 Optimal control approach to nonlinear diffusion equations driven by Wiener noise. Zbl 1237.93177 Barbu, Viorel 2012 Stochastic porous media equations and self-organized criticality: Convergence to the critical state in all dimensions. Zbl 1238.60071 Barbu, Viorel; Röckner, Michael 2012 Convex integrals on Sobolev spaces. Zbl 1254.49006 Barbu, Viorel; Guo, Yanqiu; Rammaha, Mohammad A.; Toundykov, Daniel 2012 The unique continuation property of eigenfunctions to Stokes-Oseen operator is generic with respect to the coefficients. Zbl 1246.35054 Barbu, V.; Lasiecka, I. 2012 Finite time extinction of solutions to fast diffusion equations driven by linear multiplicative noise. Zbl 1243.60046 Barbu, Viorel; Da Prato, Giuseppe; Röckner, Michael 2012 The stochastic reflection problem in Hilbert spaces. Zbl 1245.60072 Barbu, Viorel; Da Prato, Giuseppe; Tubaro, Luciano 2012 A PDE approach to image restoration problem with observation on a meager domain. Zbl 1239.94005 Barbu, Tudor; Barbu, Viorel 2012 Localization of solutions to stochastic porous media equations: finite speed of propagation. Zbl 1246.60085 Barbu, Viorel; Roeckner, Michael 2012 The fast logarithmic equation with multiplicative Gaussian noise. Zbl 1289.60108 Barbu, Viorel 2012 Internal stabilization of Navier-Stokes equation with exact controllability on spaces with finite codimension. Zbl 1259.93093 Barbu, Viorel; Munteanu, Ionuţ 2012 Stabilization of Navier-Stokes flows. Zbl 1213.76001 Barbu, Viorel 2011 Internal exponential stabilization to a nonstationary solution for 3D Navier-Stokes equations. Zbl 1231.35141 Barbu, Viorel; Rodrigues, Sérgio S.; Shirikyan, Armen 2011 On a random scaled porous media equation. Zbl 1238.60070 Barbu, Viorel; Röckner, Michael 2011 Kolmogorov equation associated to the stochastic reflection problem on a smooth convex set of a Hilbert space. II. Zbl 1230.60081 Barbu, Viorel; Da Prato, Giuseppe; Tubaro, Luciano 2011 A variational approach to stochastic nonlinear parabolic problems. Zbl 1235.60074 Barbu, Viorel 2011 Probabilistic representation for solutions of an irregular porous media type equation: The degenerate case. Zbl 1227.60088 Barbu, Viorel; Röckner, Michael; Russo, Francesco 2011 Internal stabilization by noise of the Navier-Stokes equation. Zbl 1215.35116 Barbu, Viorel; da Prato, Giuseppe 2011 The internal stabilization by noise of the linearized Navier-Stokes equation. Zbl 1210.35302 Barbu, Viorel 2011 A reflection type problem for the stochastic 2-D Navier-Stokes equations with periodic conditions. Zbl 1404.76070 Barbu, Viorel; Da Prato, Giuseppe; Tubaro, Luciano 2011 Nonlinear differential equations of monotone types in Banach spaces. Zbl 1197.35002 Barbu, Viorel 2010 Existence for semilinear parabolic stochastic equations. Zbl 1213.35260 Barbu, Viorel 2010 Stabilization of a plane periodic channel flow by noise wall normal controllers. Zbl 1206.35040 Barbu, Viorel 2010 Invariant measures and the Kolmogorov equation for the stochastic fast diffusion equation. Zbl 1201.60062 Barbu, Viorel; da Prato, Giuseppe 2010 Optimal stabilizable feedback controller for Navier-Stokes equations. Zbl 1425.35134 Barbu, Viorel 2010 Exponential stabilization of the linearized Navier-Stokes equation by pointwise feedback noise controllers. Zbl 1205.93070 Barbu, Viorel 2010 Erratum to “Uniqueness of the generators of 2D Euler and Navier-Stokes flows” [Stochastic Process. Appl. 118 (11) (2008) 2071-2084]. (Erratum to “Uniqueness of the generators of 2D Euler and Stokes flows” [Stochastic Process. Appl. 118 (11) (2008) 2071-2084].) Zbl 1202.35151 Albeverio, S.; Barbu, V.; Ferrario, B. 2010 Stochastic porous medium equations with flux boundary conditions. Zbl 1283.60091 Barbu, Viorel 2010 Existence of strong solutions for stochastic porous media equation under general monotonicity conditions. Zbl 1162.76054 Barbu, Viorel; Da Prato, Giuseppe; Röckner, Michael 2009 Stochastic porous media equations and self-organized criticality. Zbl 1176.35182 Barbu, Viorel; Da Prato, Giuseppe; Röckner, Michael 2009 A PDE variational approach to image denoising and restoration. Zbl 1169.35341 Barbu, Tudor; Barbu, Viorel; Biga, Veronica; Coca, Daniel 2009 Kolmogorov equation associated to the stochastic reflection problem on a smooth convex set of a Hilbert space. Zbl 1205.60141 Barbu, Viorel; Da Prato, Giuseppe; Tubaro, Luciano 2009 Stochastic nonlinear diffusion equations with singular diffusivity. Zbl 1203.60079 Barbu, Viorel; Da Prato, Giuseppe; Röckner, Michael 2009 Finite time extinction for solutions to fast diffusion stochastic porous media equations. Zbl 1156.60040 Barbu, Viorel; Da Prato, Giuseppe; Röckner, Michael 2009 Strong solutions for stochastic porous media equations with jumps. Zbl 1181.60095 Barbu, Viorel; Marinelli, Carlo 2009 Finite-dimensional controller design for semilinear parabolic systems. Zbl 1168.35378 Yan, Y.; Coca, D.; Barbu, V. 2009 Smoothness of weak solutions to a nonlinear fluid-structure interaction model. Zbl 1147.74016 Barbu, Viorel; Grujić, Zoran; Lasiecka, Irena; Tuffaha, Amjad 2008 Existence and uniqueness of nonnegative solutions to the stochastic porous medium equation. Zbl 1137.76059 Barbu, Viorel; Da Prato, Giuseppe; Röckner, Michael 2008 The generator of the transition semigroup corresponding to a stochastic variational inequality. Zbl 1155.60034 Barbu, Viorel; da Prato, Giuseppe 2008 Some results on stochastic porous media equations. Zbl 1205.60109 Barbu, Viorel; Da Prato, Giuseppe; Röckner, Michael 2008 Variational inequalities in Hilbert spaces with measures and optimal stopping problems. Zbl 1144.49006 Barbu, Viorel; Marinelli, Carlo 2008 The Kolmogorov equation for a 2D-Navier-Stokes stochastic flow in a channel. Zbl 1142.76355 Barbu, Viorel; da Prato, Giuseppe 2008 Uniqueness of the generators of the 2D Euler and Navier-Stokes flows. Zbl 1157.35080 Albeverio, S.; Barbu, V.; Ferrario, B. 2008 Self-organized criticality via stochastic partial differential equations. Zbl 1199.60231 Barbu, Viorel; Blanchard, Philippe; Da Prato, Giuseppe; Röckner, Michael 2008 Internal optimal controller synthesis for Navier-Stokes equations. Zbl 1165.35433 Yan, Yue; Coca, D.; Barbu, V. 2008 The Kolmogorov operator associated with a stochastic variational inequality in $$\mathbb R^n$$ with convex potential. Zbl 1174.60039 Barbu, Viorel; Da Prato, Giuseppe 2008 Existence and ergodicity for the two-dimensional stochastic magneto-hydrodynamics equations. Zbl 1187.76727 Barbu, Viorel; Da Prato, Giuseppe 2007 Existence of the energy-level weak solutions for a nonlinear fluid-structure interaction model. Zbl 1297.35234 Barbu, Viorel; Grujić, Zoran; Lasiecka, Irena; Tuffaha, Amjad 2007 Blow-up of generalized solutions to wave equations with nonlinear degenerate damping and source terms. Zbl 1121.35082 Barbu, Viorel; Lasiecka, Irena; Rammaha, Mohammad A. 2007 Stochastic wave equations with dissipative damping. Zbl 1122.60056 Barbu, Viorel; Da Prato, Giuseppe; Tubaro, Luciano 2007 Stabilization of a plane channel flow by wall normal controllers. Zbl 1124.35051 Barbu, Viorel 2007 Local exponential stabilization strategies of the Navier-Stokes equations, $$d=2,3$$, via feedback stabilization of its linearization. Zbl 1239.93094 Barbu, Viorel; Lasiecka, Irena; Triggiani, Roberto 2007 Tangential boundary stabilization of Navier-Stokes equations. Zbl 1098.35026 Barbu, Viorel; Lasiecka, Irena; Triggiani, Roberto 2006 ...and 173 more Documents all top 5 Cited by 2,703 Authors 129 Barbu, Viorel 58 Röckner, Michael 49 Colli, Pierluigi 39 Da Prato, Giuseppe 39 Wang, Gengsheng 37 Marinoschi, Gabriela 33 Lasiecka, Irena 30 Gilardi, Gianni 30 Papageorgiou, Nikolaos S. 23 Kunisch, Karl 21 Scarpa, Luca 21 Sprekels, Jürgen 21 Wang, Lijuan 20 Gess, Benjamin 20 Munteanu, Ionut 19 Aniţa, Sebastian 18 Triggiani, Roberto 17 Luo, Zhixue 17 Rammaha, Mohammad A. 17 Raymond, Jean-Pierre 17 Rocca, Elisabetta 16 Balachandran, Krishnan 16 Gao, Hang 16 Rascanu, Aurel 15 Apreutesei, Narcisa C. 15 Toundykov, Daniel 14 Agarwal, Ravi P. 14 Ji, Shuguan 14 Migórski, Stanisław 14 Yao, Jen-Chih 13 Cavalcanti, Marcelo Moreira 13 He, Zerong 13 Khatibzadeh, Hadi 13 Liu, Hanbing 13 Sofonea, Mircea 12 Akagi, Goro 12 Cârjă, Ovidiu 12 Ceng, Lu-Chuan 12 Crandall, Michael G. 12 Maksimov, Vyacheslav Ivanovich 12 Mohan, Manil Thankamani 12 Moroşanu, Gheorghe 12 Schimperna, Giulio 12 Wei, Li 12 Yuan, Rong 11 Aizicovici, Sergiu 11 Bonetti, Elena 11 Chueshov, Igor’ Dmitrievich 11 Le Rousseau, Jérôme H. 11 Lovíšek, Ján 11 Sritharan, Sivaguru S. 11 Takahashi, Wataru 11 Zălinescu, Constantin 10 Bonaccorsi, Stefano 10 Cannarsa, Piermarco 10 Ezzinbi, Khalil 10 Fukao, Takeshi 10 Hintermüller, Michael 10 Hirano, Norimichi 10 Iannelli, Mimmo 10 Liu, Wei 10 Marinelli, Carlo 10 Park, Jong Yeoul 10 Stefanelli, Ulisse 10 Tiba, Dan 10 Tubaro, Luciano 10 Valero, José 10 Visintin, Augusto 9 Ahmed, Nasir Uddin 9 Arnăutu, Viorel 9 Asfaw, Teffera M. 9 Di Persio, Luca 9 Domingos Cavalcanti, Valéria Neves 9 Emmrich, Etienne 9 Liu, Steve Wenbin 9 Pandolfi, Luciano 9 Sakthivel, Kumarasamy 9 Tölle, Jonas M. 9 Vrabie, Ioan I. 8 Ainseba, Bedr’Eddine 8 Chen, Qihong 8 Ciotir, Ioana 8 Goreac, Dan 8 Hritonenko, Natali 8 Jeong, Jin-Mun 8 Jung, Jong Soo 8 Kim, Jong Kyu 8 Lions, Pierre-Louis 8 Pavel, Nicolae H. 8 Rodrigues, Sérgio S. 8 Rudakov, Igor Alekseevich 8 Trenchea, Catalin 8 Tuffaha, Amjad M. 8 Yamazaki, Kazuo 8 Zhang, Deng 8 Zheng, Jiashan 7 Adly, Samir 7 Badra, Mehdi 7 Barbu, Tudor 7 Čanić, Sunčica ...and 2,603 more Authors all top 5 Cited in 384 Serials 214 Journal of Mathematical Analysis and Applications 125 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 116 Journal of Differential Equations 97 Journal of Optimization Theory and Applications 90 Numerical Functional Analysis and Optimization 82 Applied Mathematics and Optimization 61 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 57 Nonlinear Analysis. Theory, Methods & Applications 52 SIAM Journal on Control and Optimization 41 Systems & Control Letters 39 Journal of Evolution Equations 36 Journal of Functional Analysis 35 Evolution Equations and Control Theory 33 Nonlinear Analysis. Real World Applications 31 Applied Mathematics and Computation 31 Transactions of the American Mathematical Society 30 Stochastic Processes and their Applications 29 Proceedings of the American Mathematical Society 29 Discrete and Continuous Dynamical Systems 27 Abstract and Applied Analysis 26 Applicable Analysis 26 Computers & Mathematics with Applications 26 Fixed Point Theory and Applications 23 Mathematical Methods in the Applied Sciences 23 Journal de Mathématiques Pures et Appliquées. Neuvième Série 22 Mathematical Control and Related Fields 21 SIAM Journal on Mathematical Analysis 21 Journal of Inequalities and Applications 21 Discrete and Continuous Dynamical Systems. Series B 19 Israel Journal of Mathematics 19 Annali di Matematica Pura ed Applicata. Serie Quarta 19 NoDEA. 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Matematică 7 Journal of Convex Analysis 7 Journal of Fixed Point Theory and Applications 6 Computer Methods in Applied Mechanics and Engineering 6 Journal of the Franklin Institute 6 Mathematics of Computation 6 Integral Equations and Operator Theory 6 Mathematische Annalen 6 Mathematische Zeitschrift 6 Quarterly of Applied Mathematics ...and 284 more Serials all top 5 Cited in 56 Fields 1,493 Partial differential equations (35-XX) 859 Calculus of variations and optimal control; optimization (49-XX) 639 Operator theory (47-XX) 589 Systems theory; control (93-XX) 432 Probability theory and stochastic processes (60-XX) 333 Ordinary differential equations (34-XX) 278 Fluid mechanics (76-XX) 230 Numerical analysis (65-XX) 217 Mechanics of deformable solids (74-XX) 174 Biology and other natural sciences (92-XX) 129 Integral equations (45-XX) 123 Dynamical systems and ergodic theory (37-XX) 117 Operations research, mathematical programming (90-XX) 106 Functional analysis (46-XX) 82 Classical thermodynamics, heat transfer (80-XX) 73 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 62 Global analysis, analysis on manifolds (58-XX) 45 Difference and functional equations (39-XX) 43 Real functions (26-XX) 39 Harmonic analysis on Euclidean spaces (42-XX) 32 Statistical mechanics, structure of matter (82-XX) 31 Information and communication theory, circuits (94-XX) 23 Abstract harmonic analysis (43-XX) 23 Computer science (68-XX) 17 Approximations and expansions (41-XX) 17 General topology (54-XX) 16 Measure and integration (28-XX) 15 Linear and multilinear algebra; matrix theory (15-XX) 14 Potential theory (31-XX) 13 Mechanics of particles and systems (70-XX) 13 Optics, electromagnetic theory (78-XX) 12 Statistics (62-XX) 10 Quantum theory (81-XX) 10 Geophysics (86-XX) 8 Functions of a complex variable (30-XX) 8 Convex and discrete geometry (52-XX) 7 Topological groups, Lie groups (22-XX) 6 Number theory (11-XX) 4 Integral transforms, operational calculus (44-XX) 4 Differential geometry (53-XX) 3 History and biography (01-XX) 3 Order, lattices, ordered algebraic structures (06-XX) 2 General and overarching topics; collections (00-XX) 2 Astronomy and astrophysics (85-XX) 1 Mathematical logic and foundations (03-XX) 1 Combinatorics (05-XX) 1 Field theory and polynomials (12-XX) 1 Commutative algebra (13-XX) 1 Algebraic geometry (14-XX) 1 Group theory and generalizations (20-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Special functions (33-XX) 1 Sequences, series, summability (40-XX) 1 Algebraic topology (55-XX) 1 Manifolds and cell complexes (57-XX) 1 Mathematics education (97-XX) Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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2021-09-24T19:43:22
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https://zims-en.kiwix.campusafrica.gos.orange.com/wikipedia_en_all_nopic/A/Mittag-Leffler_function
# Mittag-Leffler function In mathematics, the Mittag-Leffler function Eα,β is a special function, a complex function which depends on two complex parameters α and β. It may be defined by the following series when the real part of α is strictly positive:[1][2] ${\displaystyle E_{\alpha ,\beta }(z)=\sum _{k=0}^{\infty }{\frac {z^{k}}{\Gamma (\alpha k+\beta )}}.}$ where ${\displaystyle \Gamma (x)}$ is the Gamma function. When ${\displaystyle \beta =1}$, it is abbreviated as ${\displaystyle E_{\alpha }(z)=E_{\alpha ,1}(z)}$. For ${\displaystyle \alpha =0}$, the series above equals the Taylor expansion of the geometric series and consequently ${\displaystyle E_{0,\beta }(z)={\frac {1}{\Gamma (\beta )}}{\frac {1}{1-z}}}$. In the case α and β are real and positive, the series converges for all values of the argument z, so the Mittag-Leffler function is an entire function. This function is named after Gösta Mittag-Leffler. This class of functions are important in the theory of the fractional calculus. For α > 0, the Mittag-Leffler function ${\displaystyle E_{\alpha ,1}(z)}$ is an entire function of order 1/α, and is in some sense the simplest entire function of its order. The Mittag-Leffler function satisfies the recurrence property (Theorem 5.1 of [1]) ${\displaystyle E_{\alpha ,\beta }(z)={\frac {1}{z}}E_{\alpha ,\beta -\alpha }(z)-{\frac {1}{z\Gamma (\beta -\alpha ),}}}$ from which the Poincaré asymptotic expansion ${\displaystyle E_{\alpha ,\beta }(z)\sim -\sum _{k=1}{\frac {1}{z^{k}\Gamma (\beta -k\alpha )}}}$ follows, which is true for ${\displaystyle z\to -\infty }$. ## Special cases For ${\displaystyle \alpha =0,1/2,1,2}$ we find: (Section 2 of [1]) ${\displaystyle E_{\frac {1}{2}}(z)=\exp(z^{2})\operatorname {erfc} (-z).}$ The sum of a geometric progression: ${\displaystyle E_{0}(z)=\sum _{k=0}^{\infty }z^{k}={\frac {1}{1-z}},\,|z|<1.}$ ${\displaystyle E_{1}(z)=\sum _{k=0}^{\infty }{\frac {z^{k}}{\Gamma (k+1)}}=\sum _{k=0}^{\infty }{\frac {z^{k}}{k!}}=\exp(z).}$ ${\displaystyle E_{2}(z)=\cosh({\sqrt {z}}),{\text{ and }}E_{2}(-z^{2})=\cos(z).}$ For ${\displaystyle \beta =2}$, we have ${\displaystyle E_{1,2}(z)={\frac {e^{z}-1}{z}},}$ ${\displaystyle E_{2,2}(z)={\frac {\sinh({\sqrt {z}})}{\sqrt {z}}}.}$ For ${\displaystyle \alpha =0,1,2}$, the integral ${\displaystyle \int _{0}^{z}E_{\alpha }(-s^{2})\,{\mathrm {d} }s}$ gives, respectively: ${\displaystyle \arctan(z)}$, ${\displaystyle {\tfrac {\sqrt {\pi }}{2}}\operatorname {erf} (z)}$, ${\displaystyle \sin(z)}$. ## Mittag-Leffler's integral representation The integral representation of the Mittag-Leffler function is (Section 6 of [1]) ${\displaystyle E_{\alpha ,\beta }(z)={\frac {1}{2\pi i}}\int _{C}{\frac {t^{\alpha -\beta }e^{t}}{t^{\alpha }-z}}\,dt,\Re (\alpha )>0,\Re (\beta )>0,}$ where the contour C starts and ends at and circles around the singularities and branch points of the integrand. Related to the Laplace transform and Mittag-Leffler summation is the expression (Eq (7.5) of [1], with m=0) ${\displaystyle \int _{0}^{\infty }e^{-tz}t^{\beta -1}E_{\alpha ,\beta }(\pm r\,t^{\alpha })\,dt={\frac {z^{\alpha -\beta }}{z^{\alpha }\mp r}},\Re (z)>0,\Re (\alpha )>0,\Re (\beta )>0.}$ ## Notes • R Package 'MittagLeffleR' by Gurtek Gill, Peter Straka. Implements the Mittag-Leffler function, distribution, random variate generation, and estimation. ## References 1. Saxena, R. K.; Mathai, A. M.; Haubold, H. J. (2009-09-01). "Mittag-Leffler Functions and Their Applications". Cite journal requires |journal= (help) 2. Weisstein, Eric W. "Mittag-Leffler Function". mathworld.wolfram.com. Retrieved 2019-09-11. • Mittag-Leffler, M.G.: Sur la nouvelle fonction E(x). C. R. Acad. Sci. Paris 137, 554–558 (1903) • Mittag-Leffler, M.G.: Sopra la funzione E˛.x/. Rend. R. Acc. Lincei, (Ser. 5) 13, 3–5 (1904) • Gorenflo R., Kilbas A.A., Mainardi F., Rogosin S.V., Mittag-Leffler Functions, Related Topics and Applications (Springer, New York, 2014) 443 pages ISBN 978-3-662-43929-6 • Igor Podlubny (1998). "chapter 1". Fractional Differential Equations. An Introduction to Fractional Derivatives, Fractional Differential Equations, Some Methods of Their Solution and Some of Their Applications. Mathematics in Science and Engineering. Academic Press. ISBN 0-12-558840-2. • Kai Diethelm (2010). "chapter 4". The analysis of fractional differential equations: an application-oriented exposition using differential operators of Caputo type. Lecture Notes in Mathematics. Heidelberg and New York: Springer-Verlag. ISBN 978-3-642-14573-5. This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.
2021-04-11T06:12:34
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https://cci.lbl.gov/docs/cctbx/tuto_melk_2019/
## CCTBX tutorial Crystallographic computing school, Melk, 08/2019 ### Script reading a model file This basic script illustrates how to read in a model file. #### Getting started: Open the file tutorial_1_v0.py in your source code editor. Most of this script is so called boilerplate code, i.e. code that in some form or shape is found in most Python scripts. At the beginning of the script are import statements, which import the modules needed for a task. The bottom lines represent best practice. They enable the script to be imported and used from other Python scripts. The first two lines of the run() function are a minimalistic - but often sufficient - way to give users a hint how to use the script. It works both for someone reading the source code of the script, and a user running the script without arguments. Task Execute the script by typing python tutorial_1_v0.py. The output is: Traceback (most recent call last): File "tutorial_1_v0.py", line 15, in run(sys.argv[1:]) File "tutorial_1_v0.py", line 8, in run raise RuntimeError("Please specify one pdb file name.") RuntimeError: Please specify one pdb file name. In addition to showing the error message, Python shows exactly where the error originates. This is often extremely helpful. The important part of the script is in these two lines: The first line creates the class for reading a model from a file or string. It is the main input method for both PDB and mmCIF files; it will automatically determine the actual format and return the appropriate data type. The second line creates the model class, which serves as container for model information to be passed between library functions. For example, it selects, copies and updates model information, stores libraries, and ensures consistency between lower level objects. #### Use print and help() While analyzing a script, insert print() statements and run the script to find out more about the objects. It may also be useful to insert help(obj) to see the attributes and methods of obj, where obj can be any of the objects created in the script. For example, let's try to use the show method of the model.composition() object, which produces output that is useful to give the user a quick overview of what is in the PDB file. Add the following lines to your script. The help() method calls the built-in Python help system. It lets you read the docstring and get an idea of what attributes and methods a class might have. (Press q to exit the help mode) Task Run the script by using the Python help method for the composition class. Help on composition in module mmtbx.model.statistics object: class composition(__builtin__.object) | Methods defined here: | | __init__(self, pdb_hierarchy) | | result(self) | | show(self, log, prefix='') | | ---------------------------------------------------------------------- | Data descriptors defined here: | | __dict__ | dictionary for instance variables (if defined) | | __weakref__ | list of weak references to the object (if defined) (END) We can see from the help output that the composition class has two methods ('show' and 'result') and that the 'show' method requires setting the parameter 'log'. Set it to sys.stdout. Task Use the method composition.show() and run the script with the file 1aba_pieces.pdb. The output is: Number of: all atoms : 48 H or D atoms : 0 chains : 2 a.a. residues : 5 nucleotides : 0 water : 4 other (ligands): 0 Ligands: None ### Truncate to Poly-Ala - Basic #### The PDB hierarchy Let's continue working with the model file 1aba_pieces.pdb. We will write a basic script to truncate all amino acids in the model to Poly-Ala. To achieve this, we will use the pdb_hierarchy object, which is a five-deep nested data structure: model chain residue_group atom_group atom The hierarchy object is obtained with the get_hierarchy method of the model class: The model, chain, and atom levels of the hierarchy object are probably immediately obvious to someone familiar with the content of model files (such as a PDB file). Note that that is no 'residue type' in the data structure. Instead, there are the two types residue_group and atom_group. They are related to alternative conformations. If there are no alternative conformations in the model, all residue groups contain exactly one atom group, which contains all the atoms of a residue. A file with alternative conformations will lead to residue groups with multiple atom groups, one for each conformer. (Note: about a quarter of the files in the PDB database contain alternative conformations). To truncate amino-acid residues to alanine, we need to know which residues are amino-acids, and the atom names. A more detailed presentation of the hierarchy object shows where we can find this information: model(s) id chain(s) id residue_group(s) resid atom_group(s) altloc, resname atom(s) name segid element charge xyz occ b uij (The list under each level is not exhaustive.) #### Loop over the hierarchy Before doing the truncation, let's see what is actually in the levels of the hierarchy. Loop through all the levels of the hierarchy and print out: • Chain ID • Residue name • Altloc • Atomname The code below shows how to print the chain ID for each chain. Output: Loop over hierarchy Chain: A Chain: B Complete the loops through the hierarchy levels to print out atom names in the different atom_groups. Loop over hierarchy: Chain: A Resnumber: 3 Resname: LYS, Altloc: N CA C O CB CG CD CE NZ Resnumber: 4 Resname: VAL, Altloc: N CA C O CB CG1 CG2 Resnumber: 5 Resname: TYR, Altloc: N CA C O CB CG CD1 CD2 CE1 CE2 CZ OH Resnumber: 6 Resname: GLY, Altloc: N CA C O Resnumber: 7 Resname: TYR, Altloc: N CA C O CB CG CD1 CD2 CE1 CE2 CZ OH Chain: B Resnumber: 96 Resname: HOH, Altloc: O Resnumber: 161 Resname: HOH, Altloc: O Resnumber: 169 Resname: HOH, Altloc: O Resnumber: 193 Resname: HOH, Altloc: O TIP: You can see the attributes and methods of each level by using the dir method to return a list of valid attributes of the object, for example, replace line 21 with print(dir(rg)). Don't get confused if there are many methods/attributes. Look out for something ressembling residue names, altlocs and atom names. Let's look at Tyr 85, which has an alternate conformation for the side chain. This example highlights the usefulness of residue groups and atom groups. Tyr 85 has three atom groups, one for the altloc " " (blank), one for "A" and one for "B". Resnumber: 85 Resname: TYR, Altloc: N, CA, C, O, CB Resname: TYR, Altloc: A CG, CD1, CD2, CE1, CE2, CZ, OH Resname: TYR, Altloc: B CG, CD1, CD2, CE1, CE2, CZ, OH #### Simple truncation We have residue names and atom names now, but to perform the truncation, we need to know which residues are amino acids (because we only want to truncate amino acids), and which atom names we want to keep. The iotbx.pdb module contains the sub-module amino_acid_codes. This sub-module contains two Python dictionaries, one of which is (shortened): one_letter_given_three_letter = { "ALA": "A", "ARG": "R", ... "TYR": "Y", "VAL": "V"} We don't need the one-letter codes, but we can re-use the keys of this dictionary to efficently decide if a residue name corresponds to an amino acid. Here are the relevant lines to add in your script. For the atom names, we use a Python set. Here are the relevant lines to add in your script. We use a Python set because it uses hashing techniques for element lookup when processing the "in" in the if statement. For a small list like here it doesn't really matter, but in Python it is so easy to use advanced hashing techniques, simply by converting the list of atom names to a set, there is no reason not to take advantage of them. Modify your script so that it only prints out atom names that are NOT in the poly-alanine set and wich are in amino acid residues. Loop over hierarchy: Chain: A Resnumber: 3 Resname: LYS, Altloc: CG CD CE NZ Resnumber: 4 Resname: VAL, Altloc: CG1 CG2 Resnumber: 5 Resname: TYR, Altloc: CG CD1 CD2 CE1 CE2 CZ OH Resnumber: 6 Resname: GLY, Altloc: Resnumber: 7 Resname: TYR, Altloc: CG CD1 CD2 CE1 CE2 CZ OH Chain: B Resnumber: 96 Resnumber: 161 Resnumber: 169 Resnumber: 193 Now that we know which residues we want to truncate, and which atom names we want to keep, we just need one more line to remove the side chain atoms: This removes the atom from the atom group (note that atom stands for the object). Now let's save the modified hierarchy to a file. The method to write a PDB file from the hierarchy is write_pdb_file. Task Modify the script to save the modified hierarchy in a PDB file. Use a molecular viewer to look at the output. Did it work correctly? TIP: To use the method, you'll need to pass a file name. Use the help method to find out what the parameter name for the file name is. ### Truncate to Poly-Ala - Improved #### Rare cases For most practical purposes, the script from the previous task is completely sufficient. However, there are some files in the PDB for which this is not true. One example is the structure with the PDB ID 1ysl. Run your script on the file resname_mix.pdb and look at the output (use a text editor or PyMol; the file cannot be opened in Coot). The script did not remove the side chain atoms of the modified residue CSD. This residue has in fact an alternate conformation. Conformation "A" is the modified amino acid CSD, conformation "B" is a CYS. HETATM 3907 N ACSD B 111 25.006 36.731 16.222 0.50 18.83 N HETATM 3908 CA ACSD B 111 25.536 35.903 15.152 0.50 19.90 C HETATM 3909 CB ACSD B 111 25.931 36.658 13.876 0.50 21.09 C HETATM 3910 SG ACSD B 111 25.414 38.295 13.671 0.50 26.29 S HETATM 3911 C ACSD B 111 26.713 35.054 15.562 0.50 19.23 C HETATM 3912 O ACSD B 111 27.472 34.533 14.697 0.50 20.10 O HETATM 3913 OD1ACSD B 111 23.793 38.008 13.181 0.50 30.17 O HETATM 3914 OD2ACSD B 111 25.111 39.102 15.048 0.50 26.06 O ATOM 3915 N BCYS B 111 24.996 36.697 16.246 0.50 13.39 N ATOM 3916 CA BCYS B 111 25.522 35.913 15.123 0.50 16.53 C ATOM 3917 C BCYS B 111 26.790 35.104 15.498 0.50 15.20 C ATOM 3918 O BCYS B 111 27.342 34.391 14.660 0.50 16.26 O ATOM 3919 CB BCYS B 111 25.840 36.879 13.947 0.50 20.05 C ATOM 3920 SG BCYS B 111 24.645 38.257 14.039 0.50 29.86 S Rare cases like this are the reason why the residue_group and atom_group levels are needed in the hierarchy. Here are two different residue names for the same member of a chain. Even though this sitution is rare, it is entirely plausible and valid, and a comprehensive PDB processing library has to be able to handle it. Our script will only truncate the CYS residue, but it would be better if it also truncated the non-standard CSD residue in the A alternative conformation. Let's find out what it takes to achieve this. One way would be to add the 3 letter code for all modified amino acids to the dictionary. This however relies on the completeness of the dictionary; what happens if the 3 letter code changes or if other entries are added? Another possibility is to check if there is at least one amino acid in a residue group, and if so, apply the truncation to all residues in the group, even if they don't have a standard residue name. This means, for each residue group we have to loop over the atom groups twice, first to scan for at least one standard amino-acid residue name, and if there is one, a second time to do the truncation. This will double effort (and computing time), but it is required to accomodate all possible cases. This is the part of the script we have to work on: Task Modify the script so that it also truncates CSD. TIP: Replace the if-statement in line 2 (above) with a function that returns True if the residue_group contains at least one amino-acid (and False otherwise). #### Refining the script The script now truncates the model and can take care of rare cases involving alternate conformations. However, it doesn't tell the user anything about the performed tasks. For example, it would be interesting to know how many atoms were deleted, how many residue are affected, and how many residue are unchanged. To get the desired information, we need counters, and we need to initialize them before we enter the nested loops over the hierarchy: When the loops over the hierarchy are finished, we print the counts: Since we can now easily find out if no atoms were removed (e.g. because someone passed in a DNA model), we should take advantage of it and write the output PDB file only if there are changes. For example: Since we can now easily find out if no atoms were removed (e.g. because someone passed in a DNA model), we should take advantage of it and write the output PDB file only if there are changes. For example: Modify the script: • Print the counts • Pass the crystal symmetry parameter to write_pdb_file (what changes if we do this?). • Write the output only if the input contains amino acid residues. Number of amino acid residues: 3 Number of other residues: 0 Number of atoms removed: 11 Writing file: resname_mix_truncated_to_ala.pdb ### Miller arrays #### Files Miller arrays are containers for experimental (or calculated data). A miller array contains the crystal symmetry, an array of Miller indices (h,k,l), a boolean flag indicating anomalous pairs and a flex array containing data (X-ray amplitudes or intensities, experimental sigmas, etc.). Note that the Miller arrays do not necessarily correspond to a single column of data in a reflection file. There are several major differences: • Friedel mates (F(+) and F(-) from an MTZ) file become a single array with both (h,k,l) and (-h,-k,-l) present as distinct items. (Note that one consequence of this behavior is that the number of reflections will appear to double-count acentric reflections for which both Friedel mates are present.) • For experimental data (I or F), the array also stores the corresponding sigmas. In combination with the treatment of anomalous data, this means that a single Miller array can represent the combination of columns I(+),SIGI(+),I(-),SIGI(-) from a file. • Weighted map coefficients such as FWT,DELFWT or 2FOFCWT,PH2FOFCWT are treated as a single array. The code below (tutorial_4_v0.py) shows how to obtain a miller array from a reflection file: Let's first see what data are in the input file. Loop through the miller_arrays and print the name of the labels in the array. To obtain the labels, use ma.info().label_string(). FOBS,SIGFOBS IOBS,SIGIOBS DANO,SIGDANO R-free-flags F(+),SIGF(+),F(-),SIGF(-) I(+),SIGI(+),I(-),SIGI(-) Let's focus on the FOBS,SIGFOBS miller array. We know the data in this array are amplitudes. But what is the resolution, the completeness and the spacegroup? Use the following methods to learn more about this array: • d_max_min() • space_group_info() • f_obs.completeness() • size() • f_obs.show_summary() (This will print the output on the screen, so no need to use the python print() function) Resolution limits: (49.59133498239787, 5.5000670861140355) Space group: P 1 21 1 Completeness: 0.970842392819 Size: 17414 Miller array info: 4zyp.mtz:FOBS,SIGFOBS Observation type: xray.amplitude Type of data: double, size=17414 Type of sigmas: double, size=17414 Number of Miller indices: 17414 Anomalous flag: False Unit cell: (114.38, 210.29, 118.2, 90, 100.46, 90) Space group: P 1 21 1 (No. 4) We saw in the first exercise that there is also an Rfree array in the MTZ file. Let's have a closer look at that array. Print out the result of the size() method for the Rfree miller array. Size R-free array: 17937 The size of the miller arrays FOBS,SIGFOBS and R-free-flags is not the same. In other words, the number of hkl indices with corresponding data or R-free-flag differs in the two arrays. This situation occurs rather frequently, even with deposited data in the PDB. For example, the mismatch can occur when R-free-flags are copied from another data set. Programs dealing with data has to address this mismatch. Let's say we want to calculate R-factors. If a reflection with an associated intensity does not have an R-free flag, it can't be assigned neither to the working set nor the the test set of reflections. It is therefore useful to obtain a common set of reflections. Let's try to obtain such a common set for out test data set. It is instructive to determine how many reflections are mismatched. The miller class has the method match_indices, which will do all the work. Use dir() to see which methods are available for the result of match_indices. You can use the method as in this example: Here, f_obs and r_free are miller array objects. We will now figure out how many reflections are "single" in each of these two miller arrays, i.e. we determine how many reflections don't have an equivalent in the other array. The result object of match_indices has the methods pairs() and singles(), which are all we need to get this information. Determine how many reflections are common or single for the FOBS,SIGFOBS and R-free-flags array. Common reflections: 17414 Single reflections in FOBS,SIGFOBS: 0 Single reflections in R-free-flags: 523 TIP: • Access the length of the arrays with size() • singles() needs an argument: 0 for the array on which match_indices is performed, and 1 for the array which is the argument of match_indices. We just found out that the R-free-flags array has about 500 additional miller indices. Note that match_indices is a low level method and is typicially not used. It is nevertheless instructive for this example. Practically, to obtain a common set of reflections, the common_sets() method can be used: Use common_sets() to create two arrays with the same hkl indices. Use the size() method to double check the result. After using common_sets: Size FOBS,SIGFOBS: 17414 Size R-free-flags: 17414 ### R-factors #### Calculating R-factors We have learned how to open a model and reflection files and how to obtain the corresponding CCTBX objects. Let's put this together to calcualte R-factors. We'll have to make a script which opens a PDB file and a MTZ file. Using the scripts from the previous parts as template, write a basic script that obtains the PDB and mtz file names from the input arguments. Use the os module to get the extension of a file in order to decide if a file is a model file or a reflection file. Write a script that opens a model file (1aba_model.pdb) and a reflection file (1aba_reflections.mtz) and prints out the filenames. The goal here is to correctly assign the filetype to the input arguments of the script; it should work regardless of the order of the files. Model file name: 1aba_model.pdb Reflection file name: 1aba_reflections.mtz TIP: filename, extension = os.path.splitext('/path/to/somefile.ext') yields '/path/to/somefile' for filename and '.ext' for extension. Use this to decide if a file is a pdb file or a mtz file. This approach to decide about filetype is quite simplistic, but it should be sufficient for "personal" use, i.e. for scripts where we know the input format. For general use however, a more elaborate approach would be necessary. For example, the script will fail for compressed pdb files (model.pdb.gz), which can be opened with iotbx.pdb, for model files in CIF format or for reflection fils in other formats (we won't cover this here). The next step is to create model objects and miller arrays. • a model object • a miller array for FOBS,SIGFOBS To calculate R-factors we need a model (coordinates, b-factors, atom-type, occupancy, etc.) to obtain calculated structure factors and data (structure factor amplitudes or intensities, R-free-flags for Rfree). The following lines of code yield the f_model object combining all these inputs: You can see that neither the model object nor the pdb_hierarchy are passed to f_model. The reason is that both obects are too "large", containing way more infomation than necessary to calculate structure factors. For example the model object may carry restraint information, while the pdb_hierarchy is a complicated data structure conveying the hierarchical levels of the input model. To calculate structure factors, neither is needed. The minimal structural information is contained in the xray_structure object, which is obtained from model: The update_all_scales() method is necessary to calculate scale factors and add a bulk solvent model. This procedure puts the calculated and observed structure factor amplitudes to a common scale and adjusts calculated low resolution structure factors. The f_model object has the methods r_free() and r_work() to calculate R-factors. Create f_model and print R-factors. Rwork: 0.180265172752 Rfree: 0.19096914483 TIP: Got an assertion error? Investigate the content of the miller arrays to find out if there is any mismatch.
2021-06-23T20:53:01
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https://lists.mcs.anl.gov/pipermail/petsc-users/2015-July/026247.html
# [petsc-users] Solving eigenproblems in the form of Stokes equations Matthew Knepley knepley at gmail.com Sun Jul 12 06:07:29 CDT 2015 On Fri, Jul 10, 2015 at 4:28 PM, Julian Andrej <juan at tf.uni-kiel.de> wrote: > Hi, > > i'm trying to solve a generalized eigenvalue problem which is the > stokes equations discretized by finite elements (with fenics) and > producing a banded matrix (reordered structure) of the well known > block form > > [N Q] > [QT 0] > > The domain is the unit square with dirichlet boundary condition > evaluating to zero at all boundary nodes. > > A is the block matrix in banded reordered structure and M is the mass > matrix. > You have not written an equation here. Are you solving Q^T N^{-1} Q x = \lambda M x If so, the Schur complement can be rank deficient by 1 if you have Neumann conditions on the pressure. I don't know how SLEPc handles this. Matt > I'm using slepc4py for the eigenvalue calculation. > > E = SLEPc.EPS().create() > E.setOperators(A, M) > E.setDimensions(NEV, PETSc.DECIDE) > E.setFromOptions() > > I always get the error > [0] Zero pivot row 1 value 0 tolerance 2.22045e-14 > > I cannot find a combination which solves the eigenvalues for this problem. > > The system itself solves fine with a KSP solver object from PETSc > using tfmqr with the icc PC. > > I can assemble the matrix with a penalty term for the pressure and > calculate the eigenvalues with a direct solver, but i try to avoid > that. > -- What most experimenters take for granted before they begin their experiments is infinitely more interesting than any results to which their
2022-10-06T20:57:47
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https://zbmath.org/authors/hu.yi
## Hu, Yi Compute Distance To: Author ID: hu.yi Published as: Hu, Yi; Hu, Y. Homepage: http://math.arizona.edu/~yhu/ External Links: MGP · Wikidata Documents Indexed: 73 Publications since 1987 Co-Authors: 14 Co-Authors with 17 Joint Publications 504 Co-Co-Authors all top 5 ### Co-Authors 18 single-authored 3 Li, Xiaochun 3 Liang, Jing 3 Yu, Kunjie 2 Li, Jun 2 Li, Wei-Ping 2 Miksis, Michael J. 2 Qu, Boyang 2 Shao, Yijun 2 Vlahovska, Petia M. 2 Wang, Kaifa 2 Wang, Mingxi 2 Wang, Wendi 2 Yau, Shing-Tung 2 Yue, Caitong 2 Zheng, Shijun 2 Zhi, Pengwei 1 Akhtar, Aleena 1 An, Hengbin 1 Ashraf, Usman 1 Basharat, Nyla 1 Boden, Hans U. 1 Burns, Daniel M. jun. 1 Chang, Yi-Feng 1 Che, Junling 1 Chen, Chih-Lin 1 Dalrymple, Robert A. 1 Deng, Bing-Qing 1 Dian, Songyi 1 Dolgachev, Igor’ Vladimirovich 1 Fahad, Asfand 1 Farid, Ghulam 1 Feng, Yangang 1 Foth, Philip A. 1 Fu, Hongsun 1 Fu, Julei 1 Ge, Shengxiang 1 Ge, Shilei 1 Guo, Xin 1 Guo, Yunhua 1 Han, Bo 1 Han, Jixia 1 He, Lin 1 Hou, Zong-You 1 Hsu, Chia Wei 1 Jia, Xiaowei 1 Kashif, Muhammad 1 Keel, Sean 1 Kim, Sangjib 1 Laporte, Gilbert 1 Lee, Jam-Wem 1 Leonard, Christopher 1 Li, Guohui 1 Li, Jianjun 1 Li, Miao 1 Li, Yaxin 1 Lin, Jianhao 1 Lin, Jiayuan 1 Lin, Shu-Min 1 Lin, Wan-Yen 1 Liu, Chien-Hao 1 Liu, Hongbo 1 Luo, Tie 1 Mahreen, Kahkashan 1 Masood, Abdul Mannan 1 Miao, Guoqing 1 Mo, Zeyao 1 Mou, Junmin 1 Niu, Jingchen 1 Peng, Meikang 1 Plank, R. J. 1 Ressayre, Nicolas 1 Rodriguez, Nancy Y. 1 Shao, Zehui 1 Shen, Lian 1 Song, Ming-Hsiang 1 Wang, Bochen 1 Wang, Chuachin 1 Wang, Jingdong 1 Wang, Linna 1 Wang, Mingrong 1 Wang, Shuaian 1 Wei, Panpan 1 Wu, Pu 1 Xie, Haibin 1 Yang, Yu 1 Zhao, Tao 1 Zhen, Lu 1 Zhou, Chunyang 1 Zhu, Zijiang 1 Zijiang all top 5 ### Serials 6 International Journal of Theoretical Physics 3 International Journal of Mathematics 3 Pure and Applied Mathematics Quarterly 2 Duke Mathematical Journal 2 Journal of Differential Geometry 2 Mathematische Annalen 2 Proceedings of the American Mathematical Society 2 The Asian Journal of Mathematics 2 Advances in Theoretical and Mathematical Physics 1 Computers and Fluids 1 Computers & Mathematics with Applications 1 Fluid Dynamics 1 Bulletin of Mathematical Biology 1 Compositio Mathematica 1 Publications Mathématiques 1 Journal of Algebra 1 Michigan Mathematical Journal 1 Transactions of the American Mathematical Society 1 Acta Mathematicae Applicatae Sinica 1 Discrete & Computational Geometry 1 Revista Matemática Iberoamericana 1 Computers & Operations Research 1 The Journal of Geometric Analysis 1 Journal of Contemporary Mathematical Analysis. Armenian Academy of Sciences 1 SIAM Journal on Applied Mathematics 1 Communications in Analysis and Geometry 1 Journal of Huazhong University of Science and Technology 1 Filomat 1 Journal of Inverse and Ill-Posed Problems 1 Mathematical Research Letters 1 Mathematical Problems in Engineering 1 Journal of Applied Analysis 1 Nonlinear Dynamics 1 Discrete Dynamics in Nature and Society 1 Italian Journal of Pure and Applied Mathematics 1 Control Theory & Applications 1 CMES. Computer Modeling in Engineering & Sciences 1 International Journal of Quantum Information 1 Mathematical Biosciences and Engineering 1 Advanced Studies in Theoretical Physics 1 Analysis & PDE 1 International Journal of Structural Stability and Dynamics 1 Journal of the Operations Research Society of China 1 Journal of Function Spaces 1 AIMS Mathematics 1 IEEE Transactions on Circuits and Systems I: Regular Papers all top 5 ### Fields 30 Algebraic geometry (14-XX) 11 Quantum theory (81-XX) 8 Partial differential equations (35-XX) 7 Differential geometry (53-XX) 4 Harmonic analysis on Euclidean spaces (42-XX) 4 Computer science (68-XX) 4 Fluid mechanics (76-XX) 4 Statistical mechanics, structure of matter (82-XX) 4 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 3 Combinatorics (05-XX) 3 Functional analysis (46-XX) 3 Convex and discrete geometry (52-XX) 3 Numerical analysis (65-XX) 3 Optics, electromagnetic theory (78-XX) 3 Information and communication theory, circuits (94-XX) 2 Several complex variables and analytic spaces (32-XX) 2 Statistics (62-XX) 2 Mechanics of deformable solids (74-XX) 2 Operations research, mathematical programming (90-XX) 2 Biology and other natural sciences (92-XX) 2 Systems theory; control (93-XX) 1 Number theory (11-XX) 1 Commutative algebra (13-XX) 1 Associative rings and algebras (16-XX) 1 Category theory; homological algebra (18-XX) 1 Group theory and generalizations (20-XX) 1 Topological groups, Lie groups (22-XX) 1 Real functions (26-XX) 1 Approximations and expansions (41-XX) 1 Abstract harmonic analysis (43-XX) 1 Operator theory (47-XX) 1 Manifolds and cell complexes (57-XX) 1 Probability theory and stochastic processes (60-XX) 1 Geophysics (86-XX) ### Citations contained in zbMATH Open 34 Publications have been cited 436 times in 379 Documents Cited by Year Mori dream spaces and GIT. Zbl 1077.14554 Hu, Yi; Keel, Sean 2000 Variation of geometric invariant theory quotients. (With an appendix: “An example of a thick wall” by Nicolas Ressayre). Zbl 1001.14018 Dolgachev, Igor V.; Hu, Yi 1998 Variations of moduli of parabolic bundles. Zbl 0821.14007 Boden, Hans U.; Hu, Yi 1995 A compactification of open varieties. Zbl 1083.14004 Hu, Yi 2003 The geometry and topology of quotient varieties of torus actions. Zbl 0812.14031 Hu, Yi 1992 Stable configurations of linear subspaces and quotient coherent sheaves. Zbl 1100.14039 Hu, Yi 2005 Genus-one stable maps, local equations, and Vakil-Zinger’s desingularization. Zbl 1201.14019 Hu, Yi; Li, Jun 2010 Discrete Fourier restriction associated with KdV equations. Zbl 1280.35125 Hu, Yi; Li, Xiaochun 2013 Discrete Fourier restriction associated with Schrödinger equations. Zbl 1314.42010 Hu, Yi; Li, Xiaochun 2014 HyperKähler manifolds and birational transformations in dimension 4. Zbl 1080.14508 Burns, Dan; Hu, Yi; Luo, Tie 2003 On the homology of complements of arrangements of subspaces and spheres. Zbl 0810.57017 Hu, Yi 1994 Relative geometric invariant theory and universal moduli spaces. Zbl 0889.14005 Hu, Yi 1996 Toric morphisms and fibrations of toric Calabi-Yau hypersurfaces. Zbl 1033.81069 Hu, Yi; Liu, Chien-Hao; Yau, Shing-Tung 2002 HyperKähler manifolds and birational transformations. Zbl 1044.81105 Hu, Y.; Yau, S.-T. 2002 Toric degenerations of weight varieties and applications. Zbl 1098.14037 Foth, Philip; Hu, Yi 2005 Variation of the Gieseker and Uhlenbeck compactifications. Zbl 0877.14009 Hu, Yi; Li, Wei-Ping 1995 Moduli spaces of stable polygons and symplectic structures on $$\overline{\mathcal M}_{0,n}$$. Zbl 1054.14018 Hu, Yi 1999 Topological aspects of Chow quotients. Zbl 1087.14032 Hu, Yi 2005 Local well-posedness of periodic fifth-order KdV-type equations. Zbl 1321.35200 Hu, Yi; Li, Xiaochun 2015 Numerical study on the dissipation of water waves over a viscous fluid-mud layer. Zbl 1390.76143 Deng, Bing-Qing; Hu, Yi; Guo, Xin; Dalrymple, Robert A.; Shen, Lian 2017 Research on coordination of fresh agricultural product supply chain considering fresh-keeping effort level under retailer risk avoidance. Zbl 1465.91075 Feng, Yangang; Hu, Yi; He, Lin 2021 A proximal iteratively regularized Gauss-Newton method for nonlinear inverse problems. Zbl 1365.65241 Fu, Hongsun; Liu, Hongbo; Han, Bo; Yang, Yu; Hu, Yi 2017 Analysis of transmissibility of COVID-19 and regional differences in disease control. Zbl 1474.92107 Hu, Yi; Wang, Kaifa; Wang, Wendi 2020 Adaptive backstepping control for flexible-joint manipulator using interval type-2 fuzzy neural network approximator. Zbl 1430.93112 Dian, Songyi; Hu, Yi; Zhao, Tao; Han, Jixia 2019 $$(W,R)$$-matroids and thin Schubert-type cells attached to algebraic torus actions. Zbl 0867.14020 Hu, Yi 1995 Optimizing locations and scales of emergency warehouses based on damage scenarios. Zbl 1474.90262 Wang, Bo-Chen; Li, Miao; Hu, Yi; Huang, Lin; Lin, Shu-Min 2020 Toric degenerations of GIT quotients, Chow quotients, and $$\overline {M}_{0,n}$$. Zbl 1144.14006 Hu, Yi 2008 Entanglement and decoherence of coupled superconductor qubits in contact with a common environment. Zbl 1245.81010 Ji, Y. H.; Hu, Y.; Yu, Y. X. 2011 Erratum to: The geometry and topology of quotient varieties of torus actions. Zbl 0812.14032 Hu, Yi 1992 Integrated planning of ship deployment, service schedule and container routing. Zbl 1458.90160 Zhen, Lu; Wang, Shuaian; Laporte, Gilbert; Hu, Yi 2019 Dielectric spherical particle on an interface in an applied electric field. Zbl 1419.35184 Hu, Yi; Vlahovska, Petia M.; Miksis, Michael J. 2019 Blowup rate for mass critical rotational nonlinear Schrödinger equations. Zbl 1423.35348 Basharat, Nyla; Hu, Yi; Zheng, Shijun 2019 Controlling on entangled decoherence by the interaction model between qubit and environment. Zbl 1225.81013 Ji, Y. H.; Lai, H. F.; Hu, Y. 2011 On the steady-states of a two-species non-local cross-diffusion model. Zbl 1448.35288 Rodríguez, Nancy; Hu, Yi 2020 Research on coordination of fresh agricultural product supply chain considering fresh-keeping effort level under retailer risk avoidance. Zbl 1465.91075 Feng, Yangang; Hu, Yi; He, Lin 2021 Analysis of transmissibility of COVID-19 and regional differences in disease control. Zbl 1474.92107 Hu, Yi; Wang, Kaifa; Wang, Wendi 2020 Optimizing locations and scales of emergency warehouses based on damage scenarios. Zbl 1474.90262 Wang, Bo-Chen; Li, Miao; Hu, Yi; Huang, Lin; Lin, Shu-Min 2020 On the steady-states of a two-species non-local cross-diffusion model. Zbl 1448.35288 Rodríguez, Nancy; Hu, Yi 2020 Adaptive backstepping control for flexible-joint manipulator using interval type-2 fuzzy neural network approximator. Zbl 1430.93112 Dian, Songyi; Hu, Yi; Zhao, Tao; Han, Jixia 2019 Integrated planning of ship deployment, service schedule and container routing. Zbl 1458.90160 Zhen, Lu; Wang, Shuaian; Laporte, Gilbert; Hu, Yi 2019 Dielectric spherical particle on an interface in an applied electric field. Zbl 1419.35184 Hu, Yi; Vlahovska, Petia M.; Miksis, Michael J. 2019 Blowup rate for mass critical rotational nonlinear Schrödinger equations. Zbl 1423.35348 Basharat, Nyla; Hu, Yi; Zheng, Shijun 2019 Numerical study on the dissipation of water waves over a viscous fluid-mud layer. Zbl 1390.76143 Deng, Bing-Qing; Hu, Yi; Guo, Xin; Dalrymple, Robert A.; Shen, Lian 2017 A proximal iteratively regularized Gauss-Newton method for nonlinear inverse problems. Zbl 1365.65241 Fu, Hongsun; Liu, Hongbo; Han, Bo; Yang, Yu; Hu, Yi 2017 Local well-posedness of periodic fifth-order KdV-type equations. Zbl 1321.35200 Hu, Yi; Li, Xiaochun 2015 Discrete Fourier restriction associated with Schrödinger equations. Zbl 1314.42010 Hu, Yi; Li, Xiaochun 2014 Discrete Fourier restriction associated with KdV equations. Zbl 1280.35125 Hu, Yi; Li, Xiaochun 2013 Entanglement and decoherence of coupled superconductor qubits in contact with a common environment. Zbl 1245.81010 Ji, Y. H.; Hu, Y.; Yu, Y. X. 2011 Controlling on entangled decoherence by the interaction model between qubit and environment. Zbl 1225.81013 Ji, Y. H.; Lai, H. F.; Hu, Y. 2011 Genus-one stable maps, local equations, and Vakil-Zinger’s desingularization. Zbl 1201.14019 Hu, Yi; Li, Jun 2010 Toric degenerations of GIT quotients, Chow quotients, and $$\overline {M}_{0,n}$$. Zbl 1144.14006 Hu, Yi 2008 Stable configurations of linear subspaces and quotient coherent sheaves. Zbl 1100.14039 Hu, Yi 2005 Toric degenerations of weight varieties and applications. Zbl 1098.14037 Foth, Philip; Hu, Yi 2005 Topological aspects of Chow quotients. Zbl 1087.14032 Hu, Yi 2005 A compactification of open varieties. Zbl 1083.14004 Hu, Yi 2003 HyperKähler manifolds and birational transformations in dimension 4. Zbl 1080.14508 Burns, Dan; Hu, Yi; Luo, Tie 2003 Toric morphisms and fibrations of toric Calabi-Yau hypersurfaces. Zbl 1033.81069 Hu, Yi; Liu, Chien-Hao; Yau, Shing-Tung 2002 HyperKähler manifolds and birational transformations. Zbl 1044.81105 Hu, Y.; Yau, S.-T. 2002 Mori dream spaces and GIT. Zbl 1077.14554 Hu, Yi; Keel, Sean 2000 Moduli spaces of stable polygons and symplectic structures on $$\overline{\mathcal M}_{0,n}$$. Zbl 1054.14018 Hu, Yi 1999 Variation of geometric invariant theory quotients. (With an appendix: “An example of a thick wall” by Nicolas Ressayre). Zbl 1001.14018 Dolgachev, Igor V.; Hu, Yi 1998 Relative geometric invariant theory and universal moduli spaces. Zbl 0889.14005 Hu, Yi 1996 Variations of moduli of parabolic bundles. Zbl 0821.14007 Boden, Hans U.; Hu, Yi 1995 Variation of the Gieseker and Uhlenbeck compactifications. Zbl 0877.14009 Hu, Yi; Li, Wei-Ping 1995 $$(W,R)$$-matroids and thin Schubert-type cells attached to algebraic torus actions. Zbl 0867.14020 Hu, Yi 1995 On the homology of complements of arrangements of subspaces and spheres. Zbl 0810.57017 Hu, Yi 1994 The geometry and topology of quotient varieties of torus actions. Zbl 0812.14031 Hu, Yi 1992 Erratum to: The geometry and topology of quotient varieties of torus actions. Zbl 0812.14032 Hu, Yi 1992 all top 5 ### Cited by 426 Authors 16 Hausen, Jürgen 9 Laface, Antonio 8 Casagrande, Cinzia 8 Gonzalez, Jose Luis 8 Keicher, Simon 7 Gallardo, Patricio 7 Massarenti, Alex 6 Fujita, Kento 6 Wiśńiewski, Jarosław Antoni 5 Favero, David 5 Frías Medina, Juan Bosco 5 Greb, Daniel 5 Hu, Yi 5 Karu, Kalle 5 Katzarkov, Ludmil 5 Lahyane, Mustapha 5 Laza, Radu 5 Park, Jinhyung 4 Ballard, Matthew Robert 4 de la Rosa Navarro, Brenda Leticia 4 Giansiracusa, Noah 4 Gibney, Angela 4 Howard, Benjamin J. 4 Jensen, David 4 Kurano, Kazuhiko 4 Moon, Han-Bom 4 Ressayre, Nicolas 4 Velasco, Mauricio 3 Abban, Hamid 3 Alper, Jarod 3 Altmann, Klaus 3 Arzhantsev, Ivan Vladimirovich 3 Bäker, Hendrik 3 Berchtold, Florian 3 Bourqui, David 3 Choi, Sung Rak 3 Coskun, Izzet 3 Craw, Alastair 3 Diemer, Colin 3 Fedorchuk, Maksym 3 Fu, Baohua 3 Gaiffi, Giovanni 3 Hacon, Christopher Derek 3 Halpern-Leistner, Daniel 3 Hassett, Brendan 3 Hering, Milena 3 Hughes, Kevin 3 Iusenko, Kostiantyn 3 Kirwan, Frances Clare 3 Macrì, Emanuele 3 Martinez-Garcia, Jesus 3 McKernan, James 3 Payne, Sam 3 Ross, Julius 3 Rossi, Michele 3 Seppänen, Henrik 3 Solá-Conde, Luis-Eduardo 3 Süss, Hendrik 3 Swinarski, David 3 Toma, Matei 3 Woodward, Christopher T. 2 Alexeev, Valery A. 2 Araujo, Carolina 2 Bahri, Anthony P. 2 Battistella, Luca 2 Bayer, Arend 2 Bendersky, Martin 2 Boden, Hans U. 2 Boozer, David 2 Callegaro, Filippo 2 Carocci, Francesca 2 Casalaina-Martin, Sebastian 2 Castravet, Ana-Maria 2 Chakraborty, Sujoy 2 Chen, Dawei 2 Cohen, Frederick Ronald 2 Deliu, Dragos 2 Derenthal, Ulrich 2 Dong, Dong 2 Doran, Brent 2 Dumitrescu, Olivia 2 Elizondo, E. Javier 2 Fahrner, Anne 2 Fan, Huijun 2 Galindo Pastor, Carlos 2 Gitler Hammer, Samuel Carlos 2 Gongyo, Yoshinori 2 González Anaya, Javier 2 He, Zhuang 2 Hochenegger, Andreas 2 Hwang, Dongseon 2 Ito, Atsushi M. 2 Jarvis, Tyler J. 2 Jow, Shin-Yao 2 Kapovich, Michael 2 Kedzierski, Oskar 2 Keel, Sean 2 Kerr, Gabriel 2 Kiem, Young-Hoon 2 Kim, Bumsig ...and 326 more Authors all top 5 ### Cited in 107 Serials 31 Advances in Mathematics 24 Journal of Algebra 23 Transactions of the American Mathematical Society 18 Mathematische Zeitschrift 15 Journal of Pure and Applied Algebra 15 Mathematische Annalen 10 Michigan Mathematical Journal 9 Duke Mathematical Journal 9 Proceedings of the American Mathematical Society 9 Journal of Algebraic Geometry 8 Geometriae Dedicata 8 Journal of the American Mathematical Society 8 European Journal of Mathematics 7 Annales de l’Institut Fourier 7 International Journal of Mathematics 6 Communications in Algebra 6 Inventiones Mathematicae 6 Manuscripta Mathematica 6 Selecta Mathematica. New Series 5 Compositio Mathematica 5 Journal für die Reine und Angewandte Mathematik 5 Transformation Groups 4 Proceedings of the London Mathematical Society. Third Series 4 Publications of the Research Institute for Mathematical Sciences, Kyoto University 4 Geometry & Topology 4 Algebra & Number Theory 3 Communications in Mathematical Physics 3 Mathematics of Computation 3 Journal of the Mathematical Society of Japan 3 Nagoya Mathematical Journal 3 Topology and its Applications 3 Experimental Mathematics 3 Journal of the European Mathematical Society (JEMS) 3 Journal of High Energy Physics 3 Comptes Rendus. Mathématique. Académie des Sciences, Paris 2 Israel Journal of Mathematics 2 Acta Mathematica Vietnamica 2 Canadian Mathematical Bulletin 2 Journal of the London Mathematical Society. Second Series 2 Mathematische Nachrichten 2 Pacific Journal of Mathematics 2 Proceedings of the Edinburgh Mathematical Society. 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English Series 2 Journal of Evolution Equations 1 Computer Physics Communications 1 Mathematical Notes 1 Mathematical Proceedings of the Cambridge Philosophical Society 1 Chaos, Solitons and Fractals 1 Journal of Geometry and Physics 1 Beiträge zur Algebra und Geometrie 1 Archiv der Mathematik 1 Bulletin of the London Mathematical Society 1 Bulletin de la Société Mathématique de France 1 Canadian Journal of Mathematics 1 Collectanea Mathematica 1 Glasgow Mathematical Journal 1 Illinois Journal of Mathematics 1 Publications Mathématiques 1 Journal of Differential Equations 1 Journal of Functional Analysis 1 Journal of the Korean Mathematical Society 1 Memoirs of the American Mathematical Society 1 Osaka Journal of Mathematics 1 Rendiconti del Circolo Matemàtico di Palermo. Serie II 1 Rendiconti del Seminario Matematico della Università di Padova 1 Tôhoku Mathematical Journal. Second Series 1 Transactions of the Moscow Mathematical Society 1 Chinese Annals of Mathematics. 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Second Series 1 LMS Journal of Computation and Mathematics 1 Advances in Geometry 1 Algebraic & Geometric Topology 1 Journal of the Australian Mathematical Society 1 Moscow Mathematical Journal 1 Mediterranean Journal of Mathematics 1 International Journal of Number Theory 1 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications ...and 7 more Serials all top 5 ### Cited in 35 Fields 339 Algebraic geometry (14-XX) 33 Commutative algebra (13-XX) 26 Several complex variables and analytic spaces (32-XX) 25 Differential geometry (53-XX) 19 Convex and discrete geometry (52-XX) 18 Associative rings and algebras (16-XX) 13 Number theory (11-XX) 13 Harmonic analysis on Euclidean spaces (42-XX) 12 Category theory; homological algebra (18-XX) 12 Group theory and generalizations (20-XX) 11 Algebraic topology (55-XX) 11 Manifolds and cell complexes (57-XX) 10 Partial differential equations (35-XX) 10 Quantum theory (81-XX) 6 Combinatorics (05-XX) 6 Global analysis, analysis on manifolds (58-XX) 5 Operator theory (47-XX) 4 Topological groups, Lie groups (22-XX) 4 Dynamical systems and ergodic theory (37-XX) 3 Nonassociative rings and algebras (17-XX) 2 Order, lattices, ordered algebraic structures (06-XX) 2 $$K$$-theory (19-XX) 2 General topology (54-XX) 2 Fluid mechanics (76-XX) 1 Measure and integration (28-XX) 1 Functions of a complex variable (30-XX) 1 Special functions (33-XX) 1 Ordinary differential equations (34-XX) 1 Difference and functional equations (39-XX) 1 Integral equations (45-XX) 1 Functional analysis (46-XX) 1 Mechanics of particles and systems (70-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Relativity and gravitational theory (83-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. 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2023-03-29T04:40:06
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https://gea.esac.esa.int/archive/documentation/GDR2/Data_analysis/chap_cu7var/sssec_cu7var_validation_sos_sts/ssec_cu7var_sos_sts_cali.html
# 7.6.3 Calibration models The short-timescale candidate selection criteria are based on the variogram analysis (see Section 7.6.4) with crossmatched catalogues of known variables (including both short and longer timescale sources) and known constant / standard stars, from OGLE catalogues. The idea here is to define a relevant detection threshold $\gamma_{\mathrm{det}}$ that can be compared to the variogram values of each investigated source. This threshold corresponds to the level of variability above which the observed variability is considered as not spurious. A magnitude-dependent detection threshold is defined based on the variogram analysis of crossmatched sources and on the simulation work done previously to assess the power of the variogram method for short timescale variability detection with Gaia (see Roelens et al. 2017). As mentioned previously, for Gaia Data Release 2, the aim is to focus only on periodic variability with periods below 0.5–1 day. Thus, CU7 also uses the crossmatched catalogues of known constant and variable sources, to define additional criteria to select suspected periodic short-timescale candidates, taking advantage of the period search performed on sources flagged as short timescale candidates from the variogram analysis (see Section 7.6.4). Those additional criteria are basically ‘boxes’ on various metrics, be it classical statistics or specific parameters calculated in the short timescale framework. Additional criteria are verified by running ‘blindly’ on a subsample of the sources to be investigated, and then are refined to remove some spurious candidates and focus on bona fide on short-timescale suspected periodic candidates, as detailed in Section 7.6.4 and Section 7.6.5.
2019-05-22T06:54:35
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https://science.fandom.com/el/wiki/%CE%94%CE%B9%CE%B1%CF%86%CE%BF%CE%BC%CE%BF%CF%81%CF%86%CE%B9%CF%83%CE%BC%CF%8C%CF%82
65.136 Pages Διαφορομορφισμός Diffeomorphism, αμφιδιαφορισμός - Ένας μορφισμός Ετυμολογία Η ονομασία "Διαφορομορφισμός" σχετίζεται ετυμολογικά με την λέξη "μορφή". Περιγραφή In mathematics, a diffeomorphism is an isomorphism of smooth manifolds. It is an invertible function that maps one differentiable manifold to another such that both the function and its inverse are smooth. Ορισμός Given two manifolds M and N, a differentiable map f : M → N is called a diffeomorphism if it is a bijection and its inverse f−1 : N → M is differentiable as well. If these functions are r times continuously differentiable, f is called a Cr-diffeomorphism. Two manifolds M and N are diffeomorphic (symbol usually being ≃) if there is a diffeomorphism f from M to N. They are Cr diffeomorphic if there is an r times continuously differentiable bijective map between them whose inverse is also r times continuously differentiable. Diffeomorphisms of subsets of manifolds Given a subset X of a manifold M and a subset Y of a manifold N, a function f : X → Y is said to be smooth if for all p in X there is a neighborhood U ⊂ M of p and a smooth function g : U → N such that the restrictions agree (note that g is an extension of f). f is said to be a diffeomorphism if it is bijective, smooth and its inverse is smooth. Local description Model example If U, V are connected open subsets of Rn such that V is [[|connectedeness |simply connected]], a differentiable map f : U → V is a diffeomorphism if it is proper and if the differential Dfx : Rn → Rn is bijective at each point x in U. First remark It is essential for V to be simply connected for the function f to be globally invertible (under the sole condition that its derivative is a bijective map at each point). For example, consider the "realification" of the complex square function Then f is surjective and it satisfies Thus, though Dfx is bijective at each point, f is not invertible because it fails to be injective (e.g. f(1,0) = (1,0) = f(−1,0). Second remark Since the differential at a point (for a differentiable function) is a linear map, it has a well-defined inverse if and only if Dfx is a bijection. The matrix representation of Dfx is the n × n matrix of first-order partial derivatives whose entry in the i-th row and j-th column is . This so-called Jacobian matrix is often used for explicit computations. Third remark Diffeomorphisms are necessarily between manifolds of the same dimension. Imagine f going from dimension n to dimension k. If n < k then Dfx could never be surjective; and if n > k then Dfx could never be injective. In both cases, therefore, Dfx fails to be a bijection. Fourth remark If Dfx is a bijection at x then f is said to be a local diffeomorphism (since, by continuity, Dfy will also be bijective for all y sufficiently close to x). Fifth remark Given a smooth map from dimension n to dimension k, if Df (or, locally, Dfx) is surjective, f is said to be a submersion (or, locally, a "local submersion"); and if Df (or, locally, Dfx) is injective, f is said to be an immersion (or, locally, a "local immersion"). Sixth remark A differentiable bijection is not necessarily a diffeomorphism. f(x) = x3, for example, is not a diffeomorphism from R to itself because its derivative vanishes at 0 (and hence its inverse is not differentiable at 0). This is an example of a homeomorphism that is not a diffeomorphism. Seventh remark When f is a map between differentiable manifolds, a diffeomorphic f is a stronger condition than a homeomorphic f. For a diffeomorphism, f and its inverse need to be differentiable; for a homeomorphism, f and its inverse need only be continuous. Every diffeomorphism is a homeomorphism, but not every homeomorphism is a diffeomorphism. f : M → N is called a diffeomorphism if, in coordinate charts, it satisfies the definition above. More precisely: Pick any cover of M by compatible coordinate charts and do the same for N. Let φ and ψ be charts on, respectively, M and N, with U and V as, respectively, the images of φ and ψ. The map ψfφ−1 : U → V is then a diffeomorphism as in the definition above, whenever f−1(U)) ⊂ ψ−1(V). Examples Since any manifold can be locally parametrised, we can consider some explicit maps from R2 into R2. • Let We can calculate the Jacobian matrix: The Jacobian matrix has zero determinant if, and only if xy = 0. We see that f could only be a diffeomorphism away from the x-axis and the y-axis. However, f is not bijective since f(x,y)=f(-x,y), and thus it cannot be a diffeomorphism. • Let where the and are arbitrary real numbers, and the omitted terms are of degree at least two in x and y. We can calculate the Jacobian matrix at 0: We see that g is a local diffeomorphism at 0 if, and only if, i.e. the linear terms in the components of g are linearly independent as polynomials. • Let We can calculate the Jacobian matrix: The Jacobian matrix has zero determinant everywhere! In fact we see that the image of h is the unit circle. Surface deformations In mechanics, a stress-induced transformation is called a deformation and may be described by a diffeomorphism. A diffeomorphism f : UV between two surfaces U and V has a Jacobian matrix Df that is an invertible matrix. In fact, it is required that for p in U, there is a neighborhood of p in which the Jacobian Df stays non-singular. Since the Jacobian is a 2 × 2 real matrix, Df can be read as one of three types of complex number: ordinary complex, split complex number, or dual number. Suppose that in a chart of the surface, The total differential of u is , and similarly for v. Then the image is a linear transformation, fixing the origin, and expressible as the action of a complex number of a particular type. When (dx, dy ) is also interpreted as that type of complex number, the action is of complex multiplication in the appropriate complex number plane. As such, there is a type of angle (Euclidean, hyperbolic, or slope) that is preserved in such a multiplication. Due to Df being invertible, the type of complex number is uniform over the surface. Consequently, a surface deformation or diffeomorphism of surfaces has the conformal property of preserving (the appropriate type of) angles. Diffeomorphism group Let M be a differentiable manifold that is second-countable and Hausdorff. The diffeomorphism group of M is the group of all Cr diffeomorphisms of M to itself, denoted by Diffr(M) or, when r is understood, Diff(M). This is a "large" group, in the sense that – provided M is not zero-dimensional – it is not locally compact. Topology The diffeomorphism group has two natural topologies: weak and strong. When the manifold is compact, these two topologies agree. The weak topology is always metrizable. When the manifold is not compact, the strong topology captures the behavior of functions "at infinity" and is not metrizable. It is, however, still Baire. Fixing a Riemannian metric on M, the weak topology is the topology induced by the family of metrics as K varies over compact subsets of M. Indeed, since M is σ-compact, there is a sequence of compact subsets Kn whose union is M. Then: The diffeomorphism group equipped with its weak topology is locally homeomorphic to the space of Cr vector fields. Over a compact subset of M, this follows by fixing a Riemannian metric on M and using the exponential map for that metric. If r is finite and the manifold is compact, the space of vector fields is a Banach space. Moreover, the transition maps from one chart of this atlas to another are smooth, making the diffeomorphism group into a Banach manifold with smooth right translations; left translations and inversion are only continuous. If r = ∞, the space of vector fields is a Fréchet space. Moreover, the transition maps are smooth, making the diffeomorphism group into a Fréchet manifold and even into a regular Fréchet Lie group. If the manifold is σ-compact and not compact the full diffeomorphism group is not locally contractible for any of the two topologies. One has to restrict the group by controlling the deviation from the identity near infinity to obtain a diffeomorphism group which is a manifold. Lie algebra The Lie algebra of the diffeomorphism group of M consists of all vector fields on M equipped with the Lie bracket of vector fields. Somewhat formally, this is seen by making a small change to the coordinate x at each point in space: so the infinitesimal generators are the vector fields Examples • When M = G is a Lie group, there is a natural inclusion of G in its own diffeomorphism group via left-translation. Let Diff(G) denote the diffeomorphism group of G, then there is a splitting Diff(G) ≃ G × Diff(Ge), where Diff(Ge) is the subgroup of Diff(G) that fixes the identity element of the group. • The diffeomorphism group of Euclidean space Rn consists of two components, consisting of the orientation preserving and orientation reversing diffeomorphisms. In fact, the general linear group is a deformation retract of subgroup Diff(Rn, 0) of diffeomorphisms fixing the origin under the map f(xΠρότυπο:Mapsto f(tx)/t, t ∈& (0,1]. In particular, the general linear group is also a deformation retract of the full diffeomorphism group. • For a finite set of points, the diffeomorphism group is simply the symmetric group. Similarly, if M is any manifold there is a group extension 0 → Diff0(M) → Diff(M) → Σ(π0(M)). Here Diff0(M)is the subgroup of Diff(M) that preserves all the components of M, and Σ(π0(M)) is the permutation group of the set π0(M) (the components of M). Moreover, the image of the map Diff(M) → Σ(π0(M)) is the bijections of π0(M) that preserve diffeomorphism classes. Transitivity For a connected manifold M, the diffeomorphism group acts transitively on M. More generally, the diffeomorphism group acts transitively on the configuration space CkM. If M is at least two-dimensional, the diffeomorphism group acts transitively on the configuration space FkM and the action on M is multiply transitive Πρότυπο:Harv. Extensions of diffeomorphisms In 1926, Tibor Radó asked whether the harmonic extension of any homeomorphism or diffeomorphism of the unit circle to the unit disc yields a diffeomorphism on the open disc. An elegant proof was provided shortly afterwards by Hellmuth Kneser. In 1945, Gustave Choquet, apparently unaware of this result, produced a completely different proof. The (orientation-preserving) diffeomorphism group of the circle is pathwise connected. This can be seen by noting that any such diffeomorphism can be lifted to a diffeomorphism f of the reals satisfying [f(x+1) = f(x) + 1]; this space is convex and hence path-connected. A smooth, eventually constant path to the identity gives a second more elementary way of extending a diffeomorphism from the circle to the open unit disc (a special case of the Alexander trick). Moreover, the diffeomorphism group of the circle has the homotopy-type of the orthogonal group O(2). The corresponding extension problem for diffeomorphisms of higher-dimensional spheres Sn−1 was much studied in the 1950s and 1960s, with notable contributions from René Thom, John Milnor and Stephen Smale. An obstruction to such extensions is given by the finite abelian group Γn, the "group of twisted spheres", defined as the quotient of the abelian component group of the diffeomorphism group by the subgroup of classes extending to diffeomorphisms of the ball Bn. Connectedness For manifolds, the diffeomorphism group is usually not connected. Its component group is called the mapping class group. In dimension 2 (i.e. surfaces), the mapping class group is a finitely presented group generated by Dehn twists (Dehn, Lickorish, Hatcher). Max Dehn and Jakob Nielsen showed that it can be identified with the outer automorphism group of the fundamental group of the surface. William Thurston refined this analysis by classifying elements of the mapping class group into three types: those equivalent to a periodic diffeomorphism; those equivalent to a diffeomorphism leaving a simple closed curve invariant; and those equivalent to pseudo-Anosov diffeomorphisms. In the case of the torus S1 × S1 = R2/Z2, the mapping class group is simply the modular group SL(2, Z) and the classification becomes classical in terms of elliptic, parabolic and hyperbolic matrices. Thurston accomplished his classification by observing that the mapping class group acted naturally on a compactification of Teichmüller space; as this enlarged space was homeomorphic to a closed ball, the Brouwer fixed-point theorem became applicable. Smale conjectured that if M is an oriented smooth closed manifold, the identity component of the group of orientation-preserving diffeomorphisms is simple. This had first been proved for a product of circles by Michel Herman; it was proved in full generality by Thurston. Homotopy types • The diffeomorphism group of S2 has the homotopy-type of the subgroup O(3). This was proved by Steve Smale.[1] • The diffeomorphism group of the torus has the homotopy-type of its linear automorphisms: S1 × S1 × GL(2, Z). • The diffeomorphism groups of orientable surfaces of genus g > 1 have the homotopy-type of their mapping class groups (i.e. the components are contractible). • The homotopy-type of the diffeomorphism groups of 3-manifolds are fairly well-understood via the work of Ivanov, Hatcher, Gabai and Rubinstein, although there are a few outstanding open cases (primarily 3-manifolds with finite fundamental groups). • The homotopy-type of diffeomorphism groups of n-manifolds for n > 3 are poorly understood. For example, it is an open problem whether or not Diff(S4) has more than two components. Via Milnor, Kahn and Antonelli, however, it is known that provided n > 6, Diff(Sn) does not have the homotopy-type of a finite CW-complex. Homeomorphism and diffeomorphism Unlike non-diffeomorphic homeomorphisms, it is relatively difficult to find a pair of homeomorphic manifolds that are not diffeomorphic. In dimensions 1, 2, 3, any pair of homeomorphic smooth manifolds are diffeomorphic. In dimension 4 or greater, examples of homeomorphic but not diffeomorphic pairs have been found. The first such example was constructed by John Milnor in dimension 7. He constructed a smooth 7-dimensional manifold (called now Milnor's sphere) that is homeomorphic to the standard 7-sphere but not diffeomorphic to it. There are, in fact, 28 oriented diffeomorphism classes of manifolds homeomorphic to the 7-sphere (each of them is the total space of a fiber bundle over the 4-sphere with the 3-sphere as the fiber). More unusual phenomena occur for 4-manifolds. In the early 1980s, a combination of results due to Simon Donaldson and Michael Freedman led to the discovery of exotic R4s: there are uncountably many pairwise non-diffeomorphic open subsets of R4 each of which is homeomorphic to R4, and also there are uncountably many pairwise non-diffeomorphic differentiable manifolds homeomorphic to R4 that do not embed smoothly in R4. Υποσημειώσεις 1. Smale, "Diffeomorphisms of the 2-sphere", Proc. Amer. Math. Soc. 10 (1959), pp. 621–626. Ιστογραφία Κίνδυνοι Χρήσης Αν και θα βρείτε εξακριβωμένες πληροφορίες σε αυτήν την εγκυκλοπαίδεια ωστόσο, παρακαλούμε να λάβετε σοβαρά υπ' όψη ότι η "Sciencepedia" δεν μπορεί να εγγυηθεί, από καμιά άποψη, την εγκυρότητα των πληροφοριών που περιλαμβάνει. "Οι πληροφορίες αυτές μπορεί πρόσφατα να έχουν αλλοιωθεί, βανδαλισθεί ή μεταβληθεί από κάποιο άτομο, η άποψη του οποίου δεν συνάδει με το "επίπεδο γνώσης" του ιδιαίτερου γνωστικού τομέα που σας ενδιαφέρει." Πρέπει να λάβετε υπ' όψη ότι όλα τα άρθρα μπορεί να είναι ακριβή, γενικώς, και για μακρά χρονική περίοδο, αλλά να υποστούν κάποιο βανδαλισμό ή ακατάλληλη επεξεργασία, ελάχιστο χρονικό διάστημα, πριν τα δείτε. Επίσης, Οι διάφοροι "Εξωτερικοί Σύνδεσμοι (Links)" (όχι μόνον, της Sciencepedia αλλά και κάθε διαδικτυακού ιστότοπου (ή αλλιώς site)), αν και άκρως απαραίτητοι, είναι αδύνατον να ελεγχθούν (λόγω της ρευστής φύσης του Web), και επομένως είναι ενδεχόμενο να οδηγήσουν σε παραπλανητικό, κακόβουλο ή άσεμνο περιεχόμενο. Ο αναγνώστης πρέπει να είναι εξαιρετικά προσεκτικός όταν τους χρησιμοποιεί. - Μην κάνετε χρήση του περιεχομένου της παρούσας εγκυκλοπαίδειας αν διαφωνείτε με όσα αναγράφονται σε αυτήν >>Διαμαρτυρία προς την wikia<< - Όχι, στις διαφημίσεις που περιέχουν απαράδεκτο περιεχόμενο (άσεμνες εικόνες, ροζ αγγελίες κλπ.) Community content is available under CC-BY-SA unless otherwise noted.
2020-11-29T08:42:54
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https://drupal.star.bnl.gov/STAR/book/export/html/761
# Physics Working Group The primary physics task of STAR is to study the formation and characteristics of the quark-gluon plasma (QGP), a state of matter believed to exist at sufficiently high energy densities. Detecting and understanding the QGP allows us to understand better the universe in the moments after the Big Bang, where the symmetries (and lack of symmetries) of our surroundings were put into motion. Unlike other physics experiments where a theoretical idea can be tested directly by a single measurement, STAR must make use of a variety of simultaneous studies in order to draw strong conclusions about the QGP. This is due both to the complexity of the system formed in the high-energy nuclear collision and the unexplored landscape of the physics we study. STAR therefore consists of several types of detectors, each specializing in detecting certain types of particles or characterizing their motion. These detectors work together in an advanced data acquisition and subsequent physics analysis that allows final statements to be made about the collision. The physics of star can be divided into several topics, with many overlaps between topics. In STAR, each of these topics is explored within a physics working group which develops the analysis techniques and software needed to focus on its interests. # Heavy Flavor Depending on the energy scale, there are two mechanisms that generate quark masses with different degrees of importance: current quark masses are generated by the electroweak symmetry breaking mechanism (Higgs mass) and spontaneous chiral symmetry breaking leads to the constituent quark masses in QCD (QCD mass). The QCD interaction strongly affects the light quarks (u, d, s) while the heavy quark masses (c, b, t) are mainly determined by the Higgs mechanism. In high-energy nuclear collisions at RHIC, heavy quarks are produced through gluon fusion and qq¯ annihilation. Heavy quark production is also sensitive to the parton distribution function. Unlike the light quarks, heavy quark masses are not modified by the surrounding QCD medium (or the excitations of the QCD medium) and the value of their masses is much higher than the initial excitation of the system. It is these differences between light and heavy quarks in a medium that make heavy quarks an ideal probe to study the properties of the hot and dense medium created in high-energy nuclear collisions. Heavy flavor analyses at STAR can be separated into quarkonia, open heavy flavor and heavy flavor leptons. # #9995# DNP (fall meeting) 2010 Abstracts for DNP (fall meeting) 2010 (Nov. 2-6, 2010, Santa Fe, NM) • Wenqin Xu Title: Extracting bottom quark production cross section from p+p collisions at RHIC The STAR collaboration has measured the non-photonic electron (NPE) production at high transverse momentum (pT ) at middle rapidity in p + p collisions at sqrt(s) = 200 GeV at the Relativistic Heavy Ion Collider (RHIC). The relative contributions  of bottom and charm hadrons to NPE have also been obtained through electron hadron azimuthal correlation studies. Combining these two,  we are able to determine the high pT mid-rapidity electron spectra from bottom and charm decays, separately. PYTHIA with different tunes and FONLL calculations have been compared  with this measured electron spectrum from bottom decays to extract the bb-bar differential cross section after normalization to the measured spectrum. The extrapolation of the total bb-bar production cross section in the whole kinematic range and its dependence on spectrum shapes from model calculations will also be discussed. • Yifei Zhang Title: Open charm hadron reconstruction via hadronic decays in p+p collisions at $sqrt{s}$ = 200 GeV Heavy quarks are believed to be an ideal probe to study the properties of the QCD medium produced in the relativistic heavy ion collisions. Heavy quark production in elementary particle collisions is expected to be better calculated in the perturbative QCD. Precision understanding on both the charm production total cross section and the fragmentation in p+p collisions is a baseline to further explore the QCD medium via open charm and charmonium in heavy ion collisions. Early RHIC measurements in p+p collisions which were carried out via semi-leptonic decay electrons provides limited knowledge on the heavy quark production due to the incomplete kinematics, the limited momentum coverage and the mixed contribution from various charm and bottom hadrons in the electron approach. In this talk, we will present the reconstruction of open charm hadrons (D0 and D*) via the hadronic decays in p+p collisions at $sqrt{s}$ = 200 GeV in the STAR experiment. The analysis is based on the large p+p minimum bias sample collected in RHIC Run9. The Time-Of-Flight detector, which covered 72% of the whole barrel in Run9, was used to improve the decay daughter identification. Physics implications from this analysis will be presented. • Xin Li Title: Non-photonic Electron Measurements in 200 GeV p+p collisions at RHIC-STAR Compared to the light quarks, heavy quarks are produced early in the collisions and interact very differently with the strongly couple QGP(sQGP) created at RHIC. In addition, their large masses are created mostly from the spontaneous symmetry breaking. All these features make heavy quark an ideal probe to study the sQGP. One of the critical references in these studies is the heavy quark production in p+p collisions, which also provides a crucial test to the pQCD. Measuring electrons from heavy quark semi-leptonic decay (non-photonic electron) is one of the major approaches to study heavy quark production at RHIC. We will present STAR measurements on the mid-rapidity non-photonic electron production at pT>2 GeV/c in 200 GeV p+p collisions using the datasets from the 2008 and 2005 runs, which have dramatically different photonic backgrounds. We will compare our measurements with the published results at RHIC and also report the status of the analysis at pT<2 GeV/c using the dataset from the 2009 run. • Jonathan Bouchet Title: Reconstruction of charmed decays using microvertexing techniques with the STAR Silicon Detectors Due to their production at the early stages, heavy flavor particles are of interest to study the properties of the matter created in heavy ion collisions. Direct topological reconstruction of $D$ and $B$ mesons, as opposed to indirect methods using semi-leptonic decay channels [1], provides a precise measurement and thus disentangles the $b$ and $c$ quarks contributions [2]. In this talk we present a microvertexing technique used in the reconstruction of $D^{0}$ decay vertex ($D^{0} \rightarrow K^{-}\pi^{+}$) and its charge conjugate. The significant combinatorial background can be reduced by means of secondary vertex reconstruction and other track cut variables. Results of this method using the silicon detector information of the STAR experiment at RHIC will be presented for the Au+Au system at $\sqrt{s_{NN}}$ = 200 GeV. [1]A. Abelev et al., Phys. Rev. Lett. {\bf 98} (2007) 192301 [2]N. Armesto et al., Phys. Lett. B{\bf 637} (2006) 362-366. # #9996# Hard Probe 2010 Abstracts for 2010 Hard Probe Meeting (Oct. 10-15, 2010, Eilat, Israel) •  Wei Xie Title: Heavy flavor production and heavy flavor induced correlations at RHIC Heavy quarks are unique probes to study the strongly coupled Quark-Gluon Plasma created at RHIC. Unlike light quarks, heavy quark masses come mostly from spontaneous symmetry breaking, which makes them ideal for studying the medium's QCD properties. Due to their large masses, they are produced early in the collisions and are expected to interact with the medium quite differently from that of light quarks. Detailed studies on the production of open heavy flavor mesons and heavy quarkonium in heavy-ion collisions and the baseline $p+p$ and $d+A$ collisions provide crucial information in understanding the medium's properties. With the large acceptance TPC, Time of Flight, EM Calorimeter and future Heavy-Flavor Tracker, STAR has the capabilities to study heavy quark production in the dense medium in all different directions. In this talk, we will review the current status as well as the future perspectives of heavy quark studies in STAR experiment. • Zebo Tang Title: $J/\psi$ production at high pT at STAR The $c\bar{c}$ bound state $J/\psi$ provides a unique tool to probe the hot dense medium produced in heavy-ion collisions, but to date its production mechanism is not understood clearly neither in heavy-ion collisions nor in hadron hadron collisions. Measurement of $J/\psi$ production at high $p_T$ is particularly interesting since at high $p_T$ the various models give different predictions. More over some model calculations on $J/\psi$ production are only applicable at intermediate/high $p_T$. Besides, high $p_T$ particles are widely used to study the parton-medium interactions in heavy-ion collisions. In this talk, we will present the measurement of mid-rapidity (|y|<1) $J/\psi \rightarrow e^+e^-$ production at high $p_T$ in p+p and Cu+Cu collisions at 200 GeV, that used a trigger on electron energy deposited in Electromagnetic Calorimeter. The $J/\psi$ $p_T$ spectra and nuclear modification factors will be compared to model calculations to understand its production mechanism and medium modifications. The $J/\psi$-hadron azimuthal angle correlation will be presented to disentangle $B$-mesons contributions to inclusive $J/\psi$. Progresses from on-going analyses in p+p collisions at 200GeV taken in year 2009 high luminosity run will be also reported. • Rosi Reed Title: $\Upsilon$ production in p+p, d+Au, Au+Au collisions at $\sqrt{{S}_{NN }} =$ 200 GeV in STAR export PYTHIA8DATA=$PYTHIA8/xmldoc Run configure with the option for shared-library creation turned on. ./configure --enable-shared make ## Install ROOT from source Download the source code for ROOT from http://root.cern.ch/ and compile. tar zxvf root_v5.20.00.source.tar.gz cd root/ ./configure linux --with-pythia6-libdir=$HOME/pythia6 \ --enable-pythia8 \ --with-pythia8-incdir=$PYTHIA8/include \ --with-pythia8-libdir=$PYTHIA8/lib make make install Set the following environment variables (preferably in /etc/profile.d/root.sh): export ROOTSYS=/usr/local/root export PATH=$PATH:$ROOTSYS/bin export LD_LIBRARY_PATH=$LD_LIBRARY_PATH:$ROOTSYS/lib:/usr/local/pythia6 export MANPATH=$MANPATH:$ROOTSYS/man You should be good to go. Try running the following Pythia 6 and 8 sample macros: root $ROOTSYS/tutorial/pythia/pythiaExample.C root$ROOTSYS/tutorial/pythia/pythia8.C Pibero Djawotho Last updated on Sun Jul 20 23:35:39 EDT 2008 # Hot Strips Identified by Hal Spinka ## Run 7137036 Sector 9 ### Strips 09V064 Pibero Djawotho Last updated Wed Jul 23 03:40:54 EDT 2008 # Strips from Weihong's 2006 ppLong 20 runs ## Energy [GeV] vs. strip id 2006ppLongRuns.pdf ## Raw ADC vs. strip id Pibero Djawotho Last updated Thu Jul 24 10:35:50 EDT 2008 # G/h Discrimination Algorithm (Willie) My blog pages, from first to last: 01/25: http://drupal.star.bnl.gov/STAR/blog-entry/wleight/2008/jan/25/photon-analysis-progress-week-1-21-08-1-25-08.  This post discusses the problem with the spike in secondary tracks at eta=1 in our single-particle simulations. 01/28: http://drupal.star.bnl.gov/STAR/blog-entry/wleight/2008/jan/28/further-qa-plots.  This post has QA plots for every particle sample Ross generated, both in the barrel and in the endcap. 02/01: http://drupal.star.bnl.gov/STAR/blog-entry/wleight/2008/feb/01/more-qa-plots-time-efficiencies.  This post has QA plots for gamma and piminus (barrel and endcap) as well as reconstruction efficiencies. 02/04: http://drupal.star.bnl.gov/STAR/blog-entry/wleight/2008/feb/04/photon-qa-efficiency-plots-error-bars.  This post adds error bars to the reconstruction efficiencies for the photon barrel sample. 02/05: http://drupal.star.bnl.gov/STAR/blog-entry/wleight/2008/feb/05/first-clustering-plots.  This post has the first clustering plots, for muons and gammas (barrel only), showing cluster energy, energy-weighted cluster eta and phi, and the number of seeds and clusters passing the thresholds for each event. 02/12: http://drupal.star.bnl.gov/STAR/blog-entry/wleight/2008/feb/12/preshower-plots.  This post has preshower plots from the gamma barrel sample, but the plots are of all preshowers in the event and use the preshower information generated by the BEMC simulator and so are not useful. 02/13: http://drupal.star.bnl.gov/STAR/blog-entry/wleight/2008/feb/13/more-clustering-plots.  This post has geant QA plots combined with the clustering plots from 02/05 above, but for the gamma and piminus barrel samples. 02/19: http://drupal.star.bnl.gov/STAR/blog-entry/wleight/2008/feb/19/cluster-track-matching-plots.  This post investigates the cluster-to-track matching for the gamma barrel sample, using a simple distance variable d=sqrt((delta eta)^2+(delta phi)^2)) to match clusters to tracks and plotting the resulting energy distributions, the energy ratio, etc. 02/21: http://drupal.star.bnl.gov/STAR/blog-entry/wleight/2008/feb/21/more-preshower-plots.  This post plots preshower distributions but uses the preshower information from the BEMC simulator and so is not useful. 02/28: http://drupal.star.bnl.gov/STAR/blog-entry/wleight/2008/feb/28/further-preshower-plots-not-completed-yet.  Figures 1, 3, and 5 in this post plot the geant preshower energy deposition for gammas, piminuses, and muons (Figs 2, 4, and 6 plot reconstructed preshower information again and so are not useful). 03/04: http://drupal.star.bnl.gov/STAR/blog-entry/wleight/2008/mar/04/muon-preshower-plots.  This post expands on the post of 02/28, with additional plots using the geant preshower information, including preshower cluster energy vs. tower cluster energy. 03/06: http://drupal.star.bnl.gov/STAR/blog-entry/wleight/2008/mar/06/first-physics-cuts.  This post basically recaps the previous post and adds a cut: unfortunately the cut is based partly on the thrown particle energy and so is not useful. 03/18: http://drupal.star.bnl.gov/STAR/blog-entry/wleight/2008/mar/18/smd-qa-plots.  This post plots energy-weighted SMD phi and eta distributions, as well as the total energy deposited in the BSMDE and BSMDP strips located behind a cluster. 03/28: http://drupal.star.bnl.gov/STAR/blog-entry/wleight/2008/mar/28/smd-clustering-plots.  This post contains SMD clustering plots for barrel gamma and piminus samples. # Neutral Pions 2005: Frank Simon Information about the 2005 Spin analysis (focused on A_LL and <z>, some QA plots for cross section comparisons) will be archived here. The goal is obviously the 2005 Pi0 spin paper. # Invariant Mass and Width: Data-MC Here I show the invariant masses and corresponding widths I obtain using my cross section binning. These are compared to MC values. The Method: • Invariant mass Data histograms (low mass background and combinatoric background subtracted) are fitted with a gaussian in the range 0.1 - 0.18 GeV/c^2. This gives the mass (gaussian mean) and width (gaussian sigma) • MC invariant mass histograms are obtained from correctly associated MC Pi0s after reconstruction. No weighting of the different partonic pt samples is performed. This can (and will) introduce a bias • Then the same fitting procedure as for data is applied The results are shown in the two figures below. Mass: Width: # Neutral Pion Paper: 2005 ALL & <z> Neutral Pion Paper for 2005 data: Final Results. There are two spin plots planned for the paper, one with the 2005 A_LL and one with the <z>. In addition to this the cross section will be included (analysis by Oleksandr used for publication). ## Final result for A_LL: Figure 1: Double longitudinal spin asymmetry for inclusive Pi0 production. The curves show predictions from NLO pQCD calculations based on the gluon distributions from the GRSV, GS-C and DSSV global analyses. The systematic error shown by the gray band does not include a 9.4% normalization uncertainty due to the polarization measurement. The chi2/ndf for the different model curves are: GRSV Std: 0.740636 GRSV Max: 3.49163 GRSV Min: 0.94873 GRSV Zero: 0.546512 GSC: 0.513751 DSSV: 0.543775 ## Final Result for <z>: Figure 2: Mean momentum fraction of Pi0s in their associated jet as a function of p_T for electromagnetically triggered events. The data points are plotted at the bin center in pion p_T and are not corrected for acceptance or trigger effects. Systematic errors, estimated from a variation of the cuts, are shown by the grey band underneath the data points. The lines are results from simulations with the PYTHIA event generator. The solid line includes detector effects simulated by GEANT, while the dotted line uses jet finding on the PYTHIA particle level. The inset shows the distribution of pT, π / pT, Jet for one of the bins, together with a comparison to PYTHIA with a full detector response simulation. # <z> Details <z> Details The goal of this analysis is to relate the neutral pions to the jets they are embedded in. The analysis is done using the common spin analysis trees, which provide the necessary tools to combine the jet and neutral pion analysis. A neutral pion is associated to a parent jet if it is within the jet cone of 0.4 in eta and phi. To avoid edge effects in the detector, only neutral pions with 0.3 < eta < 0.7 are accepted. ## Cut details: E_neutral / E_total < 0.95 higher energy photon of Pi0 > 2.8 GeV (HT1 trigger); > 3.6 GeV (HT2 trigger) combination HT1/HT2: below 5.7 GeV only HT1 is used, above that both HT1 and HT2 are accepted The final result uses both HT1 and HT2 triggers, but a trigger separated study has also been done, as shown below. There, HT2 includes only those HT2 triggers that do not satisfy HT1 (because of prescale). Figure 1: <z> for Pi0 in jets as a function of p_T for HT1 and HT2 triggers. Also shown is the mean jet p_T as a function of pion p_T. ## Bin-by-Bin momentum ratio Figure 2: Bin-by-bin ratio of pion to jet p_T. The <z> is taken from the mean of these distributions, the error is the error on the mean. A small fraction of all entries have higher Pi0 p_T than jet p_T. Similar behavior is also observed for Pythia MC with GEANT jets. This obviously increases the <z>. An alternative would be to reject those events. The agreement with MC becomes worse if this is done. Here is the data - MC comparison for 3 of the above bins. For the simulation, the reconstruction of the Pi0 is not required to keep statistics reasonable, so the true Pi0 pt is used. However, the MC jet finding uses all momenta after Geant, this is why the edges are "smoother" in the MC plot than in the data plots. Since <z> is an average value, this is not expected to be affected by this, since on average the Pi0 pt is reconstructed right. Figure 3: Data / MC for Bin 5: 6.7 to 8 GeV Figure 4: Data / MC for Bin 6: 8 to 10 GeV Figure 5: Data / MC for Bin 7: 10 to 12 GeV # A_LL Details Details on the A_LL result and the systematic studies: ## The result in numbers: Bin [GeV] in bin A_LL stat. error syst. error 1 4.17 0.01829 0.03358 0.01603 2 5.41 -0.01913 0.02310 0.01114 3 7.06 0.00915 0.03436 0.01343 4 9.22 -0.06381 0.06366 0.01862 ## A_LL as separated by trigger: Figure 1: A_LL as a function of p_T for HT1 (black) and HT2 (red) triggers separately. HT1 here is taken as all triggers that satisfy the HT1 requirement, but not HT2. Since the HT2 prescale is one, there are very little statistics for HT1 at the highest p_T. The highest p_T point for HT1 is outside the range of the plot, and has a large error bar. The high p_T HT1 data is used in the combined result. ## Systematics: Summary Bin 1 Bin 2 Bin 3 Bin4 relative luminosity 0.0009 0.0009 0.0009 0.0009 non-longitudinal pol. 0.0003 0.0003 0.0003 0.0003 beam background 0.0012 0.0084 0.0040 0.0093 yield extraction 0.0144 0.0044 0.0102 0.0116 invariant mass background 0.0077 0.0061 0.0080 0.0108 total 0.01603 0.01114 0.01343 0.01862 The first two systematics are common to all spin analyses. The numbers here are taken from the jet analysis. No Pi0 non-longitudinal analysis has been performed due to lacking statistics. These systematics are irrelevant compared to the others. The analysis specific systematics are determined from the data, and as such are limited by statistics. The real systematic limit of a Pi0 analysis with a very large data sit will be much lower. For the yield extraction systematic the invariant mass cuts for the pion yield extraction are varied. The systematic is derived from the maximum change in asymmetry with changing cuts. For the beam background, the systematic is derived by studying how much A_LL changes when the beam background is removed. This is a conservative estimate that covers the scenario that only half of the background is actually removed. The asymmetry of the background events is consistent with zero. For the invariant mass background systematic, A_LL is extracted in three invariant mass bins outside the signal region. The amount of background under the invariant mass peak (includes combinatorics, low mass and others) is estimated from the invariant mass distribution as shown below. For all three bins, the background A_LL is consistent with zero, a "worst case" of value + 1 sigma is assumed as deviation from the signal A_LL. ## Invariant mass distribution: Figure 2: Invariant mass distribution for HT1 events, second p_T bin. The red lines are the MC expectations for Pi0 and Eta, the green line is low mass background, the magenta line is combinatoric background, the thick blue line is a pol2 expectation for the other background, the blue thinner line is the total enveloppe of all contributions, compared to the data. At low mass, the background is overestimated. ## Other systematic studies: False Asymmetries False asymmetries (parity-violating single spin asymmetries) were studied to exclude systematic problems with spin asignments and the like. Of course the absence of problems in the jet analysis with the same data set makes any issues very unlikely, since jet statistics allow much better verifications than Pi0s. Still, single spin asymmetries were studied, and no significant asymmetries were observed. For both triggers, both asymmetries (yellow and blue) and for all p_T bins the asymmetries are consistent with zero, in most cases within one sigma of zero. So there are no indications for systematic effects. The single spin asymmetries are shown below: Figure 3: Single spin asymmetry epsilon_L for the blue beam. Figure 4: Single spin asymmetry epsilon_L for the yellow beam. # Neutral strange particle transverse asymmetries (tpb) ## Neutral strange particle transverse asymmetry analysis Here is information regarding my analysis of transverse asymmetries in neutral strange particles using 2006 p + p TPC data. This follows-on from and expands upon the earlier analysis I did, which can still be found at star.bnl.gov/protected/strange/tpb/analysis/. Comments, questions, things-you'd-like-to-see-done and so forth are welcomed. I'll catalogue updates in my blog as I make them. The links listed below are in 'analysis-order'; best to use these for navigation rather than the alphabetically listed links Drupal links below/in the sidebar. e-mail me at [email protected] # Data used ## Data used in analysis Data used for this analysis is 2006 p+p 200 GeV data taken with transverse polarisation, trigger setup "ppProductionTrans". This spanned days 97 (7th April) to 129 (9th May) inclusive. Trigger bemc-jp0-etot-mb-l2jet (ID 127622) is used. A file catalogue query with the following conditions gives a list of runs for which data is available: trgsetupname=ppProductionTrans,tpc=1,year=2006,sanity=1,collision=pp200,magscale=FullField,filename~physics,library=SL06e,production=P06ie This generates a list of 549 runs. These runs are then compared against the spin PWG run QC (see http://www.star.bnl.gov/protected/spin/sowinski/runQC_2006) and are rejected if any of the following conditions are true: • The run is marked as unusable • The run has a jet patch trigger problem • The run has a spin bits problem • The run is unchecked This excludes 172 runs, leaving 377 runs to be analysed. I use a Maker class to create TTrees of event objects with V0 and spin information for these runs. Code for the Maker and Event classes can be found at /star/u/tpb/StRoot/StTSAEventMaker/ and /star/u/tpb/StRoot/StV0NanoDst/ respectively. Events are accepted only if they fulfill the following criteria: • Event contains specified trigger ID • StSpinDbMaker::offsetBX48minusBX7() returns zero TTrees are produced for 358 runs (19 produce no/empty output), yielding 2,743,396 events. The vertex distribution of events from each run are then checked by spin bits. A Kolmogorov test (using ROOT TH1::KolmogorovTest) is used to compare the vertex distributions for (4-bit) spin bits values 5, 6, 9 and 10. If any of the distributions are inconsistent, the run is rejected. Each run's mean event vertex z position is then plotted. Figure 1 shows the distribution, fitted with a Gaussian. A 3σ cut is applied and outlier runs rejected. 38 runs are rejected by these further cuts. The remaining 320 runs, spanning 33 RHIC fills and comprising 2,500,421 events, are used in the analysis. Figure 1: Mean event vertex z for each run. The red lines indicate the 3σ cut. # Double spin asymmetry ## Double spin asymmetry I measure a double spin asymmetry defined as follows Equation 1 where N-(anti)parallel indicates yields measured in one half of the detector when the beam polarisations are aligned (opposite) and P1 and P2 are the polarisations of the beams. Accounting for the relative luminosity, these yields are given by Equation 2 Equation 2 where the arrows again indicate beam polarisations. Figures one and two show the fill-by-fill measurement of ATT, corrected by the beam polarisation, summed over all pT. Figure 1: K0S ATT fill-by-fill Figure 2: Λ ATT fill-by-fill # Energy loss identification ## Energy loss particle identification The Bethe-Bloch equation can be used to predict charged particle energy loss. Hans Bichsel's model adds to this and the Bichsel function predictions for particle energy loss are compared with measured values. Tracks with dE/dx sufficiently far from the predicted value are rejected. e.g. when selecting for Λ hyperons, the positive track is required to have dE/dx consistent with that of a proton, and the negative track consistent with that of a π-minus. The quantity σ = sqrt(N) x log( measured dE/dx - model dE/dx ) / R is used to quantify the deviation of the measured dE/dx from the model value. N is the number of track hits used in dE/dx determination and R is a resolution factor. A cut of |σ| < 3 applied to both V0 daughter tracks was found to significantly reduce the background with no loss of signal. Figures one to three below show the invariant mass distriubtions of the V0 candidates accepted and rejected and table one summarises the results of the cut. Background rejection is more successful for (anti-)Λ than for K0S because most background tracks are pions; the selection of an (anti-)proton daughter rejects the majority of the background tracks. Figure 1a: Invariant mass spectrum of V0 candidates under K0s hypothesis passing dE/dx cut Figure 1b: Invariant mass spectrum of V0 candidates under K0s hypothesis failing dE/dx cut Figure 2a: Invariant mass spectrum of V0 candidates under Λ hypothesis passing dE/dx cut Figure 2b: Invariant mass spectrum of V0 candidates under Λ hypothesis failing dE/dx cut Figure 3a: Invariant mass spectrum of V0 candidates under anti-Λ hypothesis passing dE/dx cut Figure 3b: Invariant mass spectrum of V0 candidates under anti-Λ hypothesis failing dE/dx cut Species Pass (millions) Fail (millions) % pass K0S 95.5 48.9 66.2 % Λ 32.5 111.9 22.5 % anti-Λ 11.8 132.5 8.2 % Table 1 # Geometrical cuts ## Geometrical cuts Energy loss cuts are successful in eliminating a significant portion of the background, but further reduction is required to give a clear signal. In addition final yields are calculated by a bin counting method, which requires that the background around the signal peak has a straight line shape. Therefore additional cuts are placed on the V0 candidates based on the geometrical properties of the decay. There are five quantities on which I chose to cut: • Distance of closest approach (DCA) of the V0 candidate to the primary vertex: if the V0 candidate is a genuine particle, its momentum vector should track back to the interaction point. Spurious candidates will not necessarily do so, therefore an upper limit is placed on the approach distance of the V0 to the interaction point. • DCA between the daughter tracks: due to detector resolution the daughter tracks never precisely meet, but placing an upper limit of the minimum distance of approach reduces background from spurious track crossings. • DCAs of the positive and negative daughter tracks to the primary vertex: the daughter tracks are curved due to the magnetic field and a neutral strange particle will decay some distance from the interaction point. Therefore the daughter tracks should not extrapolate back to the primary vertex, but to some distance away from it. Placing a lower limit on this distance can reduce background from tracks originating from the interaction point. • V0 decay distance: neutral strange particles decay weakly, with cτ ~ cm, so the decay vertex should typically be displaced from the interaction point. A lower limit placed on the decay distance of the V0 helps eliminate backgrounds from particles originating at the interaction point. I wrote a class to help perform tuning of these geometrical cut quantities (see /star/u/tpb/StRoot/StV0CutTuning/) by a "brute force" approach; different permutations of the above quantities were attempted, and the resulting mass spectra analysed to see which permutations gave the best balance of background reduction and signal retention. In addition, the consistency of the background to a straight-line shape was required. Due to the limits on statistics, signal retention was considered a greater priority than background reduction. The cut values I decided upon are summarised in table one. Figures one to three show the resulting mass spectra (data are from all runs). Yields are calculated from the integral of bins in the signal (red) region minus the integrals of bins in the background (green) regions. Poisson (√N) errors are used. The background regions are fitted with a straight line, skipping the intervening bins. The signal to background quoted is the ratio of the maximum bin content to the value of the background fit evaluated at that mass. Note that the spectra have the the dE/dx cut included in addition to the geometrical cuts. Species Max DCA V0 to PV* Max DCA between daughters Min DCA + daughter to PV Min DCA − daughter to PV Min V0 decay distance K0S 1.0 1.2** 0.5 0.0** 2.0** Λ 1.5 1.0 0.0** 0.0** 3.0 anti-Λ 2.0** 1.0 0.0** 0.0** 3.0 Table 1: Summary of geometical cuts. All cut values are in centimetres. * primary vertex ** default cut present in micro-DST Figure 1: Final K0S mass spectrum with all cuts applied. Figure 2: Final Λ mass spectrum with all cuts applied. Figure 3: Final anti-Λ mass spectrum with all cuts applied. # Single spin asymmetry using cross formula ## Single Spin asymmetry using cross formula Equation one shows the cross-formula used to calculate the single spin asymmetry. Equation 1 where N is a particle yield, L(eft) and R(ight) indicate the side of the polarised beam to which the particle is produced and arrows indicate the polarisation direction of the beam. Equation one cancels acceptance and beam luminosity and allows simply the raw yields to be used for the calculation. The asymmetry can be calculated twice; once for each beam, summing over the polarisation states of the other beam to leave it "unpolarised". I previously used only particles produced at forward η when calculating the blue beam asymmetry, and backward η for yellow, but I now sum over the full η range for each. Equations two and three give the numbers for up/down polarisation for blue (westward at STAR) and yellow (eastward) beams respectively in terms of the contributions from the four different beam polarisation permutations, and these permutations are related to spin bits numbers in table one. Equation 2 Equation 3 (in e.g. N(upUp), The first arrow refers to yellow beam polarisation, the second to blue beam.) Beam polarisation 4-bit spin bits Yellow Blue Up Up 5 Down Up 6 Up Down 9 Down Down 10 Table 1 The raw asymmetry is calculated for each RHIC fill, then divided by the polarisation for that fill to give the physics asymmetry. Final polarisation numbers (released December 2007) are used. The error on the raw asymmetry is calculated by propagation of the √(N) errors calculated for each particle yield. The final asymmetry error incorporates the polarisation error (statistical and systematic errors summed in quadrature). The fill-by-fill asymmetries for each K0S and Λ for each beam are shown in figures one and two. Anti-Λ results shall be forthcoming. An average asymmetry is calculated by performing a straight line χ2 fit through the fill-by-fill values with ROOT. Table one summarises the asymmetry results. The asymmetry error is the error from the ROOT fit and is statistical only. All fits give a good χ2 per degree of freedom and are consistent with zero within errors. Figure 1a: K0S blue beam asymmetry Figure 1b: K0S yellow beam asymmetry Figure 2a: Λ blue beam asymmetry Figure 2b: Λ yellow beam asymmetry The above are summed over the entire pT range available. I also divide the data into different transverse momentum bins and calculate the asymmetry as a function of pT. Figures three and four show the pT-dependent asymmetries. No pT dependence is discernible. Figure 3a: K0S pT-dependent blue beam AN Figure 3b: K0S pT-dependent yellow beam AN Figure 4a: Λ pT-dependent blue beam AN Figure 4b: Λ pT-dependent yellow beam AN # Single spin asymmetry utilising relative luminosity ## Single spin asymmetry making use of relative luminosity I also calculate the asymmetry via an alternative method, making use of Tai Sakuma's relative luminosity work. The left-right asymmetry is defined as Equation 1 where NL is the particle yield to the left of the polarised beam. The decomposition of the up/down yields into contributions from the four different beam polarisation permutations is the same as given in the cross-asymmetry section (equations 2 and 3). Here, the yields must be scaled by the appropriate relative luminosity, giving the following relations: Equation 2 Equation 3 The relative luminosities R4, R5 and R6 are the ratios of luminosity for, respectively, up-up, up-down and down-up bunches to that for down-down bunches. I record the particle yields for each polarisation permutation (i.e. spin bits) on a run-by-run basis, scale each by the appropriate relative luminosity for that run, then combine yields from all the runs in a given fill to give fill-by-fill yields. These are then used to calculate a fill-by-fill raw asymmetry, which is scaled by the beam polarisation. The figures below show the resultant fill-by-fill asymmetry for each beam and particle species, summed over all pT. The fits are again satisfactory, and give asymmetries consistent with zero within errors, as expected. Figure 1a: Blue beam asymmetry for K0S Figure 1b: Yellow beam asymmetry for K0S Figure 2a: Blue beam asymmetry for Λ Figure 2b: Yellow beam asymmetry for Λ # V0 decays ## V0 decays The appearance of the decay of an unobserved neutral strange particle into two observed charged daughter particles gives rise to the terminology 'V0' to describe the decay topology. The following neutral strange species have been analysed: Species Decay channel Branching ratio K0S π+ + π- 0.692 Λ p + π- 0.639 anti-Λ anti-p + π+ 0.639 Candidate V0s are formed by combining together all possible pairs of opposite charge-sign tracks in an event. The invariant mass of the V0 candidate under different decay hypotheses can then be determined from the track momenta and the daughter masses (e.g. for Λ the positive daughter is assumed to be a proton, the negative daughter a π-minus). Raw invariant mass spectra are shown below. The spectra contain three contributions: real particles of the species of interest; neutral strange particles of a different species; combinatorial background from chance positive/negative track crossings. Figure 1: Invariant mass spectrum under K0s hypothesis Figure 2: Invariant mass spectrum under Λ hypothesis Figure 3: Invariant mass spectrum under anti-Λ hypothesis Selection cuts are applied to the candidates to suppress the background whilst maintaining as much signal as possible. There are two methods for reducing background; energy-loss particle identification and geometrical cuts on the V0 candidates. # 2008.01.30 Selecting gamma-jet candidates out of the jet trees Ilya Selyuzhenkov January 30, 2008 ### Data set jet trees by Murad Sarsour for pp2006 run, runId=7136022 (~60K events, no triggerId cuts yet) ### Jets gross features • Figure 1: Distribution of number of jets per event. Same data on a log scale is here. • Figure 2: Distribution of electromagnetic energy (EM) fraction, R_EM, for di-jet events (number of jets/event = 2). R_EM = [E_t(endcap)+E_t(barrel)]/E_t(total). Black histogram is for R_EM1 = max(Ra, Rb), red is for R_EM2 = min(Ra, Rb). Ra and Rb are EM fraction for jets in the di-jet event. Same data on a log scale is here. ### Gamma-jet isolation cuts list: 1. selecting di-jet events with one of the jet dominated by EM energy, and another one with more hadronic energy: R_EM1 >0.9 and R_EM2 < 0.9 2. selecting di-jet events with jets pointing opposite in azimuth: cos(phi1 - phi2) < -0.9 3. requiring the number of associated charged tracks with a first jet (with maximum EM fraction) to be less than 2: nChargeTracks1 < 2 4. requiring the number of fired EEMC towers associated with a first jet (with maximum EM fraction) to be 1 or 2: 0 < nEEMCtowers1 < 3 ### Applying gamma-jet isolation cuts • Figure 3: Distribution of eta vs number of EEMC towers for the first jet (with maximum EM fraction). Cuts:1-3 applied (no 0 < nEEMCtowers1 < 3 cut). • Figure 4: Distribution of transverse momentum, pt1, of the first jet (with maximum EM fraction) vs transverse momentum, pt2, of the second jet. Cuts:1-4 applied • Figure 5: Distribution of mean transverse momentum, < pt1 >, of the first jet (with maximum EM fraction) vs transverse momentum, pt2, of the second jet. Cuts:1-4 applied • Figure 6: Distribution of pseudorapidity, eta1, of the first jet (with maximum EM fraction) vs pseudorapidity, eta2, of the second jet. Cuts:1-4 applied • Figure 7: Distribution of azimuthal angle, phi1, of the first jet (with maximum EM fraction) vs azimuthal angle, phi2, of the second jet. Cuts:1-4 applied • Figure 8: Distribution of transverse momentum, pt1, of the first jet (with maximum EM fraction) vs transverse energy sum for the EEMC towers associated with this jet. Cuts:1-4 applied • Figure 9: Distribution of transverse momentum, pt1, of the first jet (with maximum EM fraction) vs transverse momentum, pt2, of the second jet. Cuts:1-4 + Et(EEMC) > 3.0 GeV # 2008.02.13 Gamma-jet candidates: EEMC response Ilya Selyuzhenkov February 13, 2008 ### Data sample Gamma-jet selection cuts are discussed here. There are 278 candidates found for runId=7136022. Transverse momentum distribution for the gamma-jet candidates can be found here. ### Vertex z distribution for di-jet and gamma-jet events • Figure 1: Vertex z distribution. Red line presents gamma-jet candidates (scaled by x50). Black is for all di-jet events. Same data on a log scale is here. • Figure 2: Average vertex z as a function of transverse momentum of the fist jet (with a largest EM energy fraction). Red is for gamma-jet candidates. Black is for all di-jet events. Strong deviation from zero for gamma-jet candidates at pt < 5GeV? ### EEMC response for the gamma-jet candidate EEMC response event by event for all 278 gamma-jet candidate can be found in this pdf file. Each page shows SMD/Tower energy distribution for a given event: 1. First row on each page shows SMD response for the sector which has a maximum energy deposited in the EEMC Tower (u-plane is on the left, v-plane is on the right). 2. In the left plot (u-plane energy distribution) numerical values for pt of the first jet (with maximum EM fraction) and the second jet are given. 3. In addition, fit results assuming gamma (single Gaussian, red line) or neutral pion (double Gaussian, blue line ~ red+green) hypotheses are given. 4. m_{gamma gamma} value (it is shown in the right plot for v-plane). If m_{gamma gamma} value is negative, then the reconstruction procedure has failed (for example, no uv-strips intersection found, or tower energy and uv-strips intersection point mismatch, etc). EEMC response for these "bad" events can be found in this pdf file. If reconstruction procedure succeded, then m_{gamma gamma} gives reconstructed invariant mass assuming that two gammas hit the calorimeter. Figure 3: invariant mass distribution (assuming pi0 hypothesis). Note, that I'm still working on my fitting algorithm (which is not explained here), and fit results and the invariant mass distribution will be updated. 5. It is also shown the ratio for each u/v plane of the integrated single Gaussian fit (red line) to the total energy in the plane (look for "gamma U/V " values on the right v-plane plot). 6. Second and third rows on each page show the energy deposition in the tower, pre-shower1, pre-shower2, and post-shower as a function of eta:phi (etaBin:phiBin). 7. Last row shows the hit distribution in the SMD for all sectors (u-plane on the left, v-plane of the right). ### Playing with a different cuts Trying to isolate the real gammas which hits the calorimeter, I have sorted events into different subsets based on the following set of cuts: 1. EEMC gamma-jet cuts (energetic photon hits EEMC with pt similar or greater to that of the opposite jet) if (invMass < 0) reject if (jet2_pt > jet1_pt) reject if (jet1_pt < 7) reject if (minFraction < 0.75) reject (minFraction = gamma U/V - is a fraction of the integrated single Gaussian peak to the total energy in the uv-plane) Figure 4: Sample gamma-jet candidate EEMC response (all gamma-jet candidates selected according to these conditions can be found in this pdf file): 2. EEMC pi0 cuts: if (invMass < 0) reject if (jet2_pt < jet1_pt) reject if (jet2_pt < 7) reject if (minFraction < 0.75) reject Event by event EEMC response for pi0 (di-jet) candidates selected according to these conditions can be found in this pdf file. # 2008.02.20 Gamma-jet candidates: more statistics from jet-trees Ilya Selyuzhenkov February 20, 2008 ### Short summary After processing all available jet-trees for pp2006 (ppProductionLong), and applying all "gamma-jet" cuts (which are described below): • there are 47K di-jet events selected • for pt1>7GeV there are 5,4K gamma-jet candidates (3,7K with an additional cut of pt1>pt2) • Figure 1: 2,4K events with both pt1, pt2 > 7GeV • 721 candidates within a range of pt1>pt2 and both pt1, pt2 > 7 GeV ### Data set jet trees by Murad Sarsour for pp2006 run, number of runs processed: 323 4.7M di-jet events found (no triggerId cuts yet) ### Di-jets gross features • Figure 2: Distribution of electromagnetic energy (EM) fraction, R_EM, for di-jet events (number of jets/event = 2). R_EM = [E_t(endcap)+E_t(barrel)]/E_t(total). Black histogram is for R_EM1 = max(Ra, Rb), red is for R_EM2 = min(Ra, Rb). Ra and Rb are EM fraction for jets in the di-jet event. Same data on a log scale is here. ### Gamma-jet isolation cuts: 1. selecting di-jet events with one of the jet dominated by EM energy, and another one with more hadronic energy: R_EM1 >0.9 and R_EM2 < 0.9 2. selecting di-jet events with jets pointing opposite in azimuth: cos(phi1 - phi2) < -0.9 3. requiring the number of associated charged tracks with a first jet (with maximum EM fraction) to be less than 2: nChargeTracks1 < 2 4. requiring the number of fired EEMC towers associated with a first jet (with maximum EM fraction) to be 1 or 2: 0 < nEEMCtowers1 < 3 ### Applying gamma-jet isolation cuts • Figure 3: Distribution of eta vs number of EEMC towers for the first jet (with maximum EM fraction). Cuts:1-3 applied (no 0 < nEEMCtowers1 < 3 cut). • Figure 4: Distribution of transverse momentum, pt1, of the first jet (with maximum EM fraction) vs transverse momentum, pt2, of the second jet. Cuts:1-4 applied • Figure 5: Distribution of mean transverse momentum, < pt1 >, of the first jet (with maximum EM fraction) vs transverse momentum, pt2, of the second jet. Cuts:1-4 applied • Figure 6: Distribution of pseudorapidity, eta1, of the first jet (with maximum EM fraction) vs pseudorapidity, eta2, of the second jet. Cuts:1-4 applied • Figure 7: Distribution of azimuthal angle, phi1, of the first jet (with maximum EM fraction) vs azimuthal angle, phi2, of the second jet. Cuts:1-4 applied • Figure 8: Distribution of transverse momentum, pt1, of the first jet (with maximum EM fraction) vs transverse energy sum for the EEMC towers associated with this jet. Cuts:1-4 applied • Figure 9: Distribution of transverse momentum, pt1, of the first jet (with maximum EM fraction) vs transverse momentum, pt2, of the second jet. Cuts:1-4 + Et(EEMC) > 3.0 GeV # 2008.02.27 Tower based clustering algorithm, and EEMC/BEMC candidates Ilya Selyuzhenkov February 27, 2008 ### Gamma-jet candidates before applying clustering algorithm Gamma-jet isolation cuts: 1. selecting di-jet events with the first jet dominated by EM energy, and the second one with a large fraction of hadronic energy: R_EM1 >0.9 and R_EM2 < 0.9 2. selecting di-jet events with jets pointing opposite in azimuth: cos(phi1 - phi2) < -0.8 3. requiring no charge tracks associated with a first jet (jet with a maximum EM fraction): nCharge1 = 0 Figure 1: Transverse momentum Figure 2: Pseudorapidity Figure 3: Azimuthal angle ### Tower based clustering algorithm • for each gamma-jet candidate finding a tower with a maximum energy associated with a jet1 (jet with a maximum EM fraction). • Calculating energy of the cluster by finding all adjacent towers and adding their energy together. • Implementing a cut based on cluster energy fraction, R_cluster, where R_cluster is defined as a ratio of the cluster energy to the total energy in the calorimeter associated with a jet1. Note, that with a cut Ncharge1 =0, energy in the calorimeter is equal to the jet energy. ### Distribution of cluster energy vs number of towers fired in EEMC/BEMC Figure 4: R_cluster vs number of towers fired in EEMC (left) and BEMC (right). No pt cuts. Figure 5: R_cluster vs number of towers fired in EEMC (left) and BEMC (right). Additional cut: pt1>7GeV Figure 6: jet1 pseudorapidity vs number of towers fired in EEMC (left) and BEMC (right). ### R_cluster>0.9 cut: EEMC vs BEMC gamma-jet candidates EEMC candidates: nTowerFiredBEMC=0 BEMC candidates: nTowerFiredEEMC=0 Figure 7: Pseudorapidity (left EEMC, right BEMC candidates) Figure 8: Azimuthal angle (left EEMC, right BEMC candidates) Figure 9: Transverse momentum (left EEMC, right BEMC candidates) ### Number of gamma-jet candidates with an addition pt cuts Figure 10: Transverse momentum (left EEMC, right BEMC candidates): pt1>7GeV Figure 11: Transverse momentum (left EEMC, right BEMC candidates): pt1>7 and pt2>7 # 2008.03.03 EEMC SMD: u/v-strip energy distribution Ilya Selyuzhenkov March 03, 2008 Data set: ppLongitudinal, runId = 7136033. Some observations/questions: 1. In general distributions look clean and good 2. Sectors 7 and 9 for v-plane and sector 7 for u-plane are noise. 3. Sector 9 has a hot strip (id ~ 120) 4. In sector 3, strips id=0-5 in v-plane are hot (see figure 2 right, bottom) 5. Sectors 2 and 8 in u-plane and sectors 3 and 9 in v-plane have missing strips id=283-288? 6. Strips 288 are always empty? Figure 1:Average energy E in the strip vs sector and strip number (max < E > = 0.0027) same figure on a log scale Figure 2: Average energy E for E>0.02 (max < E > = 0.0682) Same figure on a log scale # 2008.03.12 Gamma-jet candidates: 2-gammas invariant mass and Eemc response Ilya Selyuzhenkov March 12, 2008 ### Gamma-jet candidates: 2-gammas invariant Note: Di-jet transverse momentum distribution for these candidates can be found on figure 11 at this page Figure 1:Invariant mass distribution for gamma-jet candidates assuming pi0 (2-gammas) hypothesys Figure 2:Invariant mass distribution for gamma-jet candidates assuming pi0 (2-gammas) hypothesys with an additional SMD isolation cut: gammaFraction >0.75 GammaFraction is defined as ratio of the integral other SMD strips for the first peak to the total energy in the sector ### EEMC response for the gamma-jet candidates (gammaFraction >0.75) 1. pdf file (first 100 events) with event by event EEMC response for the candidates reconstructed into pion mass (gammaFraction >0.75) 2. pdf file with event by event EEMC response for the candidates not reconstructed into pion mass (second peak not found), but has a first peak with gammaFraction >0.75. # 2008.03.20 Sided residual and chi2 distribution for gamma-jet candidates Ilya Selyuzhenkov March 20, 2008 ### Side residual (no pt cut on gamma jet-candidates) The procedure to discriminate gamma candidate from pions (and other background) based on the SMD response is described at Pibero's web page. Figure 1: Fit integral vs maximum residual for gamma-jet candidates requesting no energy deposited in the EEMC pre-shower 1 and 2 (within a 3x3 clusters around tower with a maximum energy). Black line is defined from MC simulations (see Jason's simulation web page, or Pibero's page above). Figure 2: Fit integral vs maximum residual for gamma-jet candidates requesting requesting no energy deposited in pre-shower 1 cluster and no energy deposited in post-shower cluster (this cut is not really essential in demonstrating the main idea) Figure 3: Fit integral vs maximum residual for gamma-jet candidates requesting requesting non-zero energy deposited in both clusters of pre-shower 1 and 2 ### Side residual: first and second jet pt are greater than 7GeV Event by event EEMC response for gamma-jet candidates for the case of no energy deposited in the EEMC pre-shower 1 and 2 can be found in this pdf file Figure 4: Fit integral vs maximum residual for gamma-jet candidates requesting no energy deposited in the EEMC pre-shower 1 and 2 Figure 5: Fit integral vs maximum residual for gamma-jet candidates requesting requesting no energy deposited in pre-shower 1 cluster and no energy deposited in post-shower cluster Figure 6: Fit integral vs maximum residual for gamma-jet candidates requesting requesting non-zero energy deposited in both clusters of pre-shower 1 and 2 ### Monte Carlo shape Event Monte Carlo shape allows to distinguish gammas from background by cutting at chi2/ndf < 0.5 (although the distribution looks wider than for the case of Will's shape). Figure 7: Chi2/ndf for gamma-jet candidates using Monte Carlo shape requesting no energy deposited in both clusters of pre-shower 1 and 2 Figure 8: Chi2/ndf for gamma-jet candidates using Monte Carlo shape requesting non-zero energy deposited in both clusters of pre-shower 1 and 2 ### Will''s shape Less clear where to cut on chi2? Figure 9: Chi2/ndf for gamma-jet candidates using Monte Carlo shape requesting no energy deposited in both clusters of pre-shower 1 and 2 Figure 10: Chi2/ndf for gamma-jet candidates using Monte Carlo shape requesting non-zero energy deposited in both clusters of pre-shower 1 and 2 # 2008.03.26 Sided residual and chi2 distribution for gamma-jet candidates (pre1,2 sorted) Ilya Selyuzhenkov March 26, 2008 ### gamma-jet candidates (no pt cut) Definitions: • F_peak - integral for a fit within [-2,2] strips around SMD u/v peak • D_peak - integral over the data within [-2,2] strips around SMD u/v peak • D_tail^max (D_tail^min) - maximum (minimum) integral over the data tail within +-[3,30] strips from a SMD u/v peak • F_tail is the integral over the fit tail within [3,30] strips from a SMD u/v peak. • Maximum residual = D_tail^max - F_tail All results are for combined distributions from u and v planes: ([u]+[v])/2 Gamma-jet isolation cuts described here 1. Matching between 3x3 tower cluster and u-v high strip intersection 2. At least 4 strips fired within [-2,2] strips from a peak Figure 1: F_peak vs maximum residual for various cuts on energy deposited in the EEMC pre-shower 1 and 2 (within a 3x3 clusters around tower with a maximum energy). Figure 2: F_data vs D_tail^max Note:This plot is fit independend (only the peak position is defined based on the fit) Figure 3: F_data vs D_tail^max-D_tail^max Figure 4: Gamma transverse momentum vs jet transverse momentum ### gamma-jet candidates: pt > 7GeV Figure 5: F_peak vs maximum residual for various cuts on energy deposited in the EEMC pre-shower 1 and 2 (within a 3x3 clusters around tower with a maximum energy). Figure 6: F_data vs D_tail^max Note:This plot is fit independend (only the peak position is defined based on the fit) Figure 7: F_data vs D_tail^max-D_tail^max Figure 8: Gamma transverse momentum vs jet transverse momentum ### gamma-jet candidates: eta, phi, and max[u,v] strip distributions (no pt cuts) Figure 9: Gamma pseudorapidity vs jet pseudorapidity Figure 10: Gamma azimuthal angle vs jet azimuthal angle Note: for the case of Pre1>1 && Pre2==0 there is an enhancement around phi_gamma = 0? Figure 11: maximum strip in v-plane vs maximum strip in u-plane ### Chi2 distribution for gamma-jet candidates (no pt cuts) Figure 12:Chi2/ndf for gamma-jet candidates using Monte Carlo shape (combined for [u+v]/2 plane ) Figure 13:Chi2/ndf for gamma-jet candidates (combined for [u+v]/2 plane ) using Will's shape # 2008.03.28 EEMC SMD shapes: gamma's from gamma-jets (data), MC, and eta-meson analysis Ilya Selyuzhenkov March 28, 2008 ### Some observations: 1. SMD data-driven shapes from different analysis are in a good agreement (Figure 1, upper left plot) 2. Overall MC shape is too narrow compared to the data shapes (Figure 1, upper left plot) 3. Shapes are similar with or without gamma-jet 7GeV pt cut (compare Figures 1 and 2), what may indicate that shape is independent on energy (at least within our kinematic limits). 4. Data-driven and MC shapes are getting close to each other (Figure 4, upper left plot) when requiring no energy above threshold in both preshower layers and with suppressed contribution from pi0 background. The latter is achieved by using the information on reconstructed invariant mass of 2gamma candidates (compare Figure 3 and 4). One interpretation of this can be that in Monte Carlo simulations the contribution from the material in front of the detector is underestimated 5. Energy distribution for each strip in the SMD peak does not looks like a Gaussian (Figure 5), what makes very difficult to interpret results obtained from chi2 analysis (Figure 6-8). 6. Triple Gaussian fit gives a better description of the data shapes, compared to the double Gaussian function (compare red and black lines on Figure 1-4) Figure 1: EEMC SMD shape comparison for various preshower cuts (black points shows u-plane shape only, v-plane results can be found here) Figure 2: EEMC SMD shape comparison for various preshower cuts with gamma-jet pt cut of 7GeV (black points shows u-plane shape only, v-plane results can be found here) Figure 3: Shapes with an additional cut on 2-gamma candidates within pi0 invariant mass range. Sample invariant mass distribution using "simple" pi0 finder can be found here (black points shows u-plane shape only, v-plane results can be found here) Figure 4: Shapes for the candidates when "simple" pi0 finder failed to find a second peak (black points shows u-plane shape only, v-plane results can be found here) Figure 5: Strip by strip SMD energy distribution. Only 12 strips from the right side of the maximum are shown. Zero strip (first upper left plot) corresponds to the high strip in the shape Note, that already at the 3rd strip from a peak, RMS values are comparable to those for a mean, and for a higher strips numbers RMS starts to be bigger that mean. (results for u-plane only, v-plane results can be found here) ### Comparing chi2 distributions for gamma-jet candidates using MC, Will, and Pibero's shapes Results for side residual (together with pt, eta, phi distributions) for gamma-jet candidates can be found at this web page Red histograms on Figures 6-8 shows chi2 distribution from MC-photons (normalized at chi2=1.4) Blue histograms on Figures 6-8 shows chi2 distribution from MC-pions (normalized at chi2=1.4) Figure 6: Chi2/ndf for gamma-jet candidates using Monte Carlo shape Figure 7: Chi2/ndf for gamma-jet candidates using Will's shape (derived from eta candidates based on Weihong's pi0-finder) Figure 8: Chi2/ndf for gamma-jet candidates using Pibero's shape (derived from eta candidates) # 2008.04.02 EEMC SMD shapes: data-driven (eta, gamma-jet) vs Monte Carlo (single gamma, gamma-jet) Ilya Selyuzhenkov April 02, 2008 ### Some observations: 1. SMD data-driven shapes from eta-meson and gamma-jet studies are in a good agreement for different preshower conditions (compage Fig.1 green circles/triangles in upper-left/bottom-right plots) 2. single gamma MC shapes show preshower dependance, but they are still narrower compared to the data shapes (compare Fig.1 green circles vs blue open squares) 3. MC shapes for gamma-jet and single gamma are consistent (Fig.1, bottom right plot) Figure 1: EEMC SMD shape comparison for various preshower cuts Note:Only MC gamma-jet shape (open red squares) is the same on all plots # 2008.04.02 Sided residual: Using data driven gamma-jet shape (3 gaussian fit) Ilya Selyuzhenkov April 02, 2008 Figure 1: Side residual for various cuts on energy deposited in the EEMC pre-shower 1 and 2 No EEMC SMD based cuts Figure 2: Side residual for various cuts on energy deposited in the EEMC pre-shower 1 and 2 "Simple" pi0 finder can not find a second peak Figure 3: Side residual for various cuts on energy deposited in the EEMC pre-shower 1 and 2 "Simple" pi0 finder reconstruct the invarian mass within [0.1,0.18] range Figure 4: Side residual distribution (Projection for side residual in Figs.1-3 on vertical axis) Figure 5: Signal (green: m < 0) vs background (black, red) separation # 2008.04.02 Sided residual: single gamma Monte-Carlo simulations Ilya Selyuzhenkov April 02, 2008 ### Side residual: single gamma Monte-Carlo simulations Figure 1: Side residual for various cuts on energy deposited in the EEMC pre-shower 1 and 2 No EEMC SMD based cuts # 2008.04.03 chi2-shape subtraction for different Preshower conditions Ilya Selyuzhenkov April 03, 2008 #### Request from Hal Spinka: Hi Ilya, I think you gave up on the chi-squared method too quickly, and am sorry I missed the phone meeting last week. So, I would like to make a request that will hopefully take a minimal amount of your time to show that all is okay. Then, if there is a delay in getting the sided residual information out and into the beam use request, you can still fall back on the chi-squared method. In your March 28 posting, Figure 8 at the bottom, I would like to get numerical values for the events per bin for the black curves. I won't use the preshower1>0 and preshower2=0 data, so those you don't need to send. Also, I won't use the red or blue curve information. I think your problem has been that you normalized your curves at chi-squared/ndf = 1.4 instead of the peak. What I plan to do is to normalize the (pre1=0, pre2=0) to the (pre1=0, pre2>0) data in the peak and subtract. The (pre1=0, pre2=0) set should have some single photons, but also some multiple photons. The (pre1=0, pre2>0) should also have single photons, and more multiple photons, since the chance that one of them will convert is larger. The difference should look roughly like your blue curve, though perhaps not exactly if Pibero's mean shower shape is not perfect (which it isn't). I will do the same thing with taking the difference between (pre1>0, pre2>0) and (pre1=0, pre2=0), and again the difference should look roughly like your blue curve. The (pre1>0, pre2>0) data should have even larger fraction of multiple photons than either of the other two data sets. I would expect the two difference curves to look approximately the same. Hope this is possible for you to do. Since our reduced chi-squared curve looks so much like the one from CDF, I am pretty confident that we are okay, but this should be checked to convince people that we are not doing anything terribly wrong. Dear Hal, I have tried to implement your idea and produce a figure attached. There are 4 plots in it: 1. Upper left plot shows normalized to unity (at maximum) chi2 distribution (obtained with Pibero shape for gamma-jet candidates) for a different pre1, pre2 conditions 2. Upper right plot shows bin-by-bin difference: a) between normalized chi2 for pre1=0, pre2>0 and pre1=0, pre2=0 (red) and b) between normalized chi2 for pre1>0, pre2>0 and pre1=0, pre2=0 (blue) 3. Bottom left Same as upper right, but normalization were done based on the integral within [-4,4] bins around maximum. 4. Bottom right Same as for upper right, but with a different normalization ([-4,4] bins around maximum) I have also tried to normalized by the total integral, but the results looks similar. Figure 1: See description above Figure 2: Same without log scale (See description above) # 2008.04.09 Applying gamma-jet reconstruction algorithm for gamma-jet simulated events Ilya Selyuzhenkov April 09, 2008 Data sample: Monte-Carlo gamma-jet sample for partonic pt range of 5-7, 7-9, 9-11,11-15, 15-25, 25-35 GeV. Analysis: Simulated MuDst files were first processed through jet finder algorithm (thanks to Renee Fatemi), and later analyzed by applying gamma-jet isolation cuts (see this link for details) and studying EEMC SMD response (see below). To test the algorithm, Geant records were not used in this analysis. Further studies based on Geant records (yield estimates, etc) are ongoing. #### EESMD shapes comparison Figure 1:Comparison between shower shape profile for data and MC. Black circles shows results for MC gamma-jet sample (all partonic pt). For v-plane results see this figure #### Correlation between gamma and jet pt, eta, phi Figure 2:Gamma vs jet transverse momentum. Figure 3:Gamma vs jet azimuthal angle. Figure 4:Gamma vs jet pseudo-rapidity. #### Results from maximum sided residua study Definitions for F_peak, D_peak, D_tail^max (D_tail^min) can be found here Figure 5:F_peak vs maximum residual for various cuts on energy deposited in the EEMC pre-shower 1 and 2 (within a 3x3 clusters around tower with a maximum energy). Shower shape used to fit data is fixed to the shape from the previous gamma-jet study of real events #### Postshower to SMD[uv] energy ratio Figure 8:Logarithmic fraction of energy in post shower (3x3 cluster) to the total energy in SMD u- and v-planes Figure 8a: Same as figure 8, but for gamma-jet candidates from the real data (no pt cuts). Logarithmic fraction of energy in post shower (3x3 cluster) to the total energy in SMD u- and v-planes Figure 8b: Comparison between gamma-jet candidates from data with different preshower conditions. Points are normalized in peak to the case of pre1 > 0, pre2 > 0 Logarithmic fraction of energy in post shower (3x3 cluster) to the total energy in SMD u- and v-planes Figure 8c: Comparison between gamma-jet candidates from Monte-Carlo simulations with different preshower conditions. Points are normalized in peak to the case of pre1 > 0, pre2 > 0 Logarithmic fraction of energy in post shower (3x3 cluster) to the total energy in SMD u- and v-planes Figure 9: Jet neutral energy fraction Figure 10: High v-strip vs u-strip Figure 11: energy post shower (3x3 cluster) Figure 12: Peak energy SMD-u Figure 13: Peak energy SMD-v Figure 14: Gamma phi Figure 15: Gamma pt Figure 16: Gamma eta Figure 17: Delta gamma-jet pt Figure 18: Delta gamma-jet eta Figure 19: Delta gamma-jet phi #### chi2 distributions Figure 20:chi2 distribution using "standard" MC shape Figure 21:chi2 distribution using Pibero shape # 2008.04.16 Sided residual: Data Driven MC vs raw MC vs 2006 data Ilya Selyuzhenkov April 16, 2008 Figure 1: Sided residual for raw MC (partonic pt 9-11) Figure 2: Sided residual for data-driven MC (partonic pt 9-11) Figure 3: Sided residual for data (pp Longitudinal 2006) #### Different analysis cuts vs number of events which passed the cut 1. N_events : total number of di-jet events found by the jet-finder for gamma in eta region [1,2] (Geant record is used to get this number) 2. cos(phi_gamma - phi_jet) < -0.8 : gamma-jet opposite in phi 3. R_{3x3cluster} > 0.9 : Energy in 3x3 cluster of EEMC tower to the total jet energy. 4. R_EM^jet < 0.9 : neutral energy fraction cut for on away side jet 5. N_ch=0 : no charge tracks associated with a gamma candidate 6. N_bTow = 0 : no barrel towers associated with a gamma candidate (gamma in the endcap) 7. N_(5-strip clusler)^u > 3 : minimum number of strips in EEMC SMD u-plane cluster around peak 8. N_(5-strip cluster)^v > 3 : minimum number of strips in EEMC SMD v-plane cluster around peak 9. gamma-algo fail : my algorithm failed to match tower with SMD uv-intersection, etc... 10. Tow:SMD match : SMD uv-intersection has a tower which is not in a 3x3 cluser Figure 4: Number of events which passed various cuts (MC data, partonic pt 9-11) # 2008.04.17 Sided residual: Data Driven MC vs raw MC (partonic pt=5-35) vs 2006 data Ilya Selyuzhenkov April 17, 2008 MC data for different pt weigted according to Michael Betancourt web page: weight = xSection[ptBin] / xSection[max] / nFiles Figure 1: Sided residual for raw MC (partonic pt 5-35) (same plot for partonic pt 9-11) Figure 2: Sided residual for data-driven MC (partonic pt 5-35) (same plot for partonic pt 9-11) Figure 3: Sided residual for data (pp Longitudinal 2006) Figure 4: Sided residual for data (pp Longitudinal 2006) Figure 5: Sided residual for data (pp Longitudinal 2006) Figure 6: pt(gamma) from geant record vs pt(gamma) from energy in 3x3 tower cluster and position for uv-intersection wrt vertex (same on a linear scale) Figure 7: pt(gamma) from geant record vs pt(jet) as found by the jet-finder Figure 8: gamma pt distribution: data-driven MC (red) vs gamma-jet candidates from pp2006 longitudinal run (black). MC distribution normalized to data at maximum for each preshower condition #### Different analysis cuts vs number of events which passed the cut 1. N_events : total number of di-jet events found by the jet-finder for gamma in eta region [1,2] (Geant record is used to get this number) 2. cos(phi_gamma - phi_jet) < -0.8 : gamma-jet opposite in phi 3. R_{3x3cluster} > 0.9 : Energy in 3x3 cluster of EEMC tower to the total jet energy. 4. R_EM^jet < 0.9 : neutral energy fraction cut for on away side jet 5. N_ch=0 : no charge tracks associated with a gamma candidate 6. N_bTow = 0 : no barrel towers associated with a gamma candidate (gamma in the endcap) 7. N_(5-strip clusler)^u > 3 : minimum number of strips in EEMC SMD u-plane cluster around peak 8. N_(5-strip cluster)^v > 3 : minimum number of strips in EEMC SMD v-plane cluster around peak 9. gamma-algo fail : my algorithm failed to match tower with SMD uv-intersection, etc... 10. Tow:SMD match : SMD uv-intersection has a tower which is not in a 3x3 cluser Figure 9: Number of events which passed various cuts (MC data, partonic pt 5-35) Red: cuts applied independent Black: cuts applied sequential from left to right # 2008.04.23 Gamma-jet candidates: pp2006 data vs data-driven MC (gamma-jet and bg:jet-jet) Ilya Selyuzhenkov April 23, 2008 ### Sided residual: pp2006 data vs data-driven MC (gamma-jet and bg:jet-jet) MC data for different partonic pt are weigted according to Michael Betancourt web page: weight = xSection[ptBin] / xSection[max] / nFiles Figure 1:Sided residual for data-driven gamma-jet MC events (partonic pt 5-35) Figure 2:Sided residual for data-driven jet-jet MC events (partonic pt 3-55) Figure 3:Sided residual for data (pp Longitudinal 2006) Figure 4:pt(gamma) vs pt(jet) for data-driven gamma-jet MC events (partonic pt 5-35) Figure 5:pt(gamma) vs pt(jet) for data-driven jet-jet MC events (partonic pt 3-55) Figure 6:pt(gamma) vs pt(jet) for data (pp Longitudinal 2006) # 2008.05.05 pt-distributions, sided residual (data vs dd-MC g-jet and bg di-jet) Ilya Selyuzhenkov May 05, 2008 Data samples: • pp2006(long) - 2006 pp production longitudinal data after applying gamma-jet aisolation cuts (jet-tree sample: 4.114pb^-1 from Jamie script, 3.164 pb^1 analyses). • gamma-jet - Pythia gamma-jet sample (~170K events). Partonic pt range 5-35 GeV • bg jets - Pythia di-jet sample (~4M events). Partonic pt range 3-65 GeV Figure 1:pt distribution. MC data are scaled to the same luminosity as data (Normalization factor: Luminosity * sigma / N_events). Figure 2:Integrated gamma yield vs pt. For each pt bin yield is defined as the integral from this pt up to the maximum available pt. MC data are scaled to the same luminosity as data. Figure 3:Signal to background ratio (all results divided by the data) ### Sided residual: pp2006 data vs data-driven MC (gamma-jet and bg:jet-jet) You can find sided residual 2-D plots here Figure 4:Maximum sided residual for pt_gamma>7GeV; pt_jet>7GeV Figure 5:Fitted peak for pt_gamma>7GeV; pt_jet>7GeV Figure 6:Max data tail for pt_gamma>7GeV; pt_jet>7GeV Figure 7:Max minus min data tails for pt_gamma>7GeV; pt_jet>7GeV Figure 8:Shower shapes pt_gamma>7GeV; pt_jet>7GeV # 2008.05.08 y:x EEMC position for gamma-jet candidates Ilya Selyuzhenkov May 08, 2008 ### y:x EEMC position for gamma-jet candidates Figure 1:y:x EEMC position for gamma-jet candidates: Pythia gamma-jet sample (~170K events). Partonic pt range 5-35 GeV. Figure 2:y:x EEMC position for gamma-jet candidates: Pythia QCD bg sample (~4M events). Partonic pt range 3-65 GeV. Figure 3:y:x EEMC position for gamma-jet candidates: pp2006 (long) data [eemc-http-mb-l2gamma:137641 trigger] Figure 3b:y:x EEMC position for gamma-jet candidates: pp2006 (long) data [eemc-http-mb-l2gamma:137641 trigger] pt cut of 7 GeV for gamma and 5GeV for the away side jet has been applied. ### high u vs. v strip for gamma-jet candidates Figure 4:High v-strip vs high u-strip. Pythia gamma-jet sample (~170K events). Partonic pt range 5-35 GeV. Figure 5:High v-strip vs high u-strip: Pythia QCD bg sample (~4M events). Partonic pt range 3-65 GeV. Figure 6:High v-strip vs high u-strip: pp2006 (long) data [eemc-http-mb-l2gamma:137641 trigger] Figure 6b:High v-strip vs high u-strip: pp2006 (long) data [eemc-http-mb-l2gamma:137641 trigger] pt cut of 7 GeV for gamma and 5GeV for the away side jet has been applied. # 2008.05.09 Gamma-jet candidates pt-distributions and TPC tracking Ilya Selyuzhenkov May 09, 2008 ### Detector eta cut study (1< eta < 1.4): • For a three data samples (pp2006 [long], MC gamma-jet, and MC QCD background events) the EEMC detector eta cut of 1< eta < 1.4 has been applied. • Although a poor statistics available for MC background QCD sample, the signal to background ratio (red to green line ratio) getting closer to 1:3 (expected signal to background ratio from Les study). Figure 1:Gamma pt distribution. MC data are scaled to the same luminosity as data (Normalization factor: Luminosity * sigma / N_events). Figure 2:Gamma yield vs pt. MC data are scaled to the same luminosity as data. Figure 3:Signal to background ratio (MC results are normalized to the data) # 2008.05.14 Gamma-cluster to jet energy ratio and away side jet pt matching Ilya Selyuzhenkov May 14, 2008 ### Gamma-cluster to jet1 energy ratio • Correlation between gamma-candidate 3x3 cluster energy ratio (R_cluster) and number of EEMC towers in a jet1 can be found here (Fig. 4). • Gamma pt distribution, yield and signal to background ratio plots for a cut of R_cluster >0.9 can be found here (Figs. 1-3). • Gamma pt distribution, yield and signal to background ratio plots for a cut of R_cluster >0.99 are shown below in Figs. 1-3. One can see that by going from R_cluster>0.9 to R_cluster>0.99 improves signal to background ratio from ~ 1:10 to ~ 1:5 for gamma pt>10 GeV Figure 1:Gamma pt distribution for R_cluster >0.99. MC results scaled to the same luminosity as data (Normalization factor: Luminosity * sigma / N_events). Figure 2:Integrated gamma yield vs pt for R_cluster >0.99 For each pt bin yield is defined as the integral from this pt up to the maximum available pt. MC results scaled to the same luminosity as data. Figure 3:Signal to background ratio for R_cluster >0.99 (all results divided by the data) Compare this figure with that for R_cluster>0.9 (Fig. 3 at this link) ### Gamma and the away side jet pt matching Figure 4: pt asymmetry between gamma and the away side jet (R_cluster >0.9) for a three data samples (pp2006[long] data, gamma-jet MC, QCD jets background). pt cut of 7 GeV for both gamma and jet has been applied. Figure 5: signal to background ratio (R_cluster >0.9) as a function of pt asymmetry between gamma and the away side jet pt cut of 7 GeV for both gamma and jet has been applied. Figure 6: pt asymmetry between gamma and the away side jet (R_cluster >0.99) for a three data samples (pp2006[long] data, gamma-jet MC, QCD jets background). pt cut of 7 GeV for both gamma and jet has been applied. Figure 7: signal to background ratio as a functio of pt asymmetry between gamma and the away side jet (R_cluster >0.99) pt cut of 7 GeV for both gamma and jet has been applied. Figure 8: pt asymmetry between gamma and the away side jet (R_cluster >0.99) for a three data samples (pp2006[long] data, gamma-jet MC, QCD jets background). pt cut of 7 GeV for gamma and 5GeV for the away side jet has been applied. Figure 9: signal to background ratio as a function of pt asymmetry between gamma and the away side jet (R_cluster >0.99) pt cut of 7 GeV for gamma and 5GeV for the away side jet has been applied. # 2008.05.15 Vertex z distribution for pp2006 data, MC gamma-jet and QCD jets events Ilya Selyuzhenkov May 15, 2008 Figure 1:Vertex z distribution for pp2006 (long) data [eemc-http-mb-l2gamma:137641 trigger] Note: In the upper right plot (pre1=0, pre2>0) one can see a hole in the acceptance in the range bweeeen z_vertex -10 to 30 cm (probably due to SVT construction) Figure 1b:Vertex z distribution for pp2006 (same as Fig. 1, but on a linear scale) Figure 2:Vertex z distribution for three different data samples MC results scaled to the same luminosity as data Figure 3:Vertex z distribution for three different data samples pt cut of 7 GeV for gamma and 5GeV for the away side jet has been applied. # 2008.05.20 Shower shapes sorted by pre-shower, z-vertex and gamma's eta, phi, pt Ilya Selyuzhenkov May 20, 2008 ### Gamma-jet algorithm and isolation cuts: 1. Selecting only di-jet events identified by the STAR jet finder algorithm, with jets pointing opposite in azimuth: cos(phi_jet1 - phi_jet2) < -0.8 2. Select jet1 with a maximum neutral energy fraction (R_EM1). This is our gamma candidate, for which we further require: • No charge tracks associated with jet1 (default jet radius is 0.7): nChargeTracks_jet1 = 0 Note, that this charge track veto only works in the EEMC region where we do have TPC tracking • No barrel towers associated with jet1 (pure EEMC jet): nBarrelTowers_jet1 = 0 • Ratio of the energy in the 3x3 EEMC high tower cluster to the total je
2020-10-25T11:24:13
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https://www.federalreserve.gov/pubs/feds/2013/201363/index.html
Finance and Economics Discussion Series: 2013-63 Screen Reader version # Computing Arbitrage-Free Yields in Multi-Factor Gaussian Shadow-Rate Term Structure Models PRELIMINARY DRAFT Abstract: This paper develops a method to approximate arbitrage-free bond yields within a term structure model in which the short rate follows a Gaussian process censored at zero (a "shadow-rate model" as proposed by Black (1995)). The censoring ensures that model-implied yields are constrained to be positive, but it also introduces non-linearity that renders standard bond pricing formulas inapplicable. In particular, yields are not linear functions of the underlying state vector as they are in affine term structure models (see Piazzesi, 2010). Existing approaches towards computing yields in shadow-rate models suffer from high computational burden or low accuracy. In contrast, I show that the technique proposed in this paper is sufficiently fast for single-step estimation of a three-factor shadow-rate term structure model, and sufficiently accurate to evaluate yields to within approximately half a basis point. # 1 Introduction In late-2008, short-term nominal interest rates in the U.S. fell to their effective "zero lower bound" (see Bernanke et al., 2004 ). Since standard Gaussian term structure models do not rule out the possibility of negative model-implied yields, they provide a poor approximation to the behavior of nominal yields when the lower bound is binding (Kim and Singleton, 2012; Christensen and Rudebusch, 2013; Bauer and Rudebusch, 2013). Kim and Singleton (2012) find that shadow-rate models in the spirit of Black (1995) successfully capture yield-curve properties observed near the zero lower bound. However, arbitrage-free multi-factor versions of these models tend to be computationally intractable (Christensen and Rudebusch, 2013). Gorovoi and Linetsky (2004) show that bond prices in a one-factor shadow-rate model can be computed analytically by an eigenfunction expansion, but their approach does not generalize to multiple dimensions. Kim and Singleton (2012) and Ichiue and Ueno (2007) successfully estimate shadow-rate models with up to two factors, but they compute bond prices using discretization schemes that are subject to the curse of dimensionality. Christensen and Rudebusch (2013) use a yield formula proposed by Krippner (2012) to estimate shadow-rate Nelson-Siegel models with up to three factors, but 's derivation deviates from the usual no-arbitrage approach. Bauer and Rudebusch (2013) evaluate bond prices by Monte Carlo simulation for given model parameters from an unconstrained Gaussian term structure model, but they do not estimate a shadow-rate version of the model due to the computational burden. This paper develops and applies a new technique for fast and accurate approximation of arbitrage-free zero-coupon bond yields in multi-factor Gaussian shadow-rate models of the term structure of interest rates. The computational complexity of the method does not increase with the number of yield curve factors, and, empirically, it produces yields that are accurate to within about half a basis point. The method is sufficiently fast to estimate a flexible, arbitrage-free, three-factor term structure model in which the shadow rate follows a Gaussian process. For illustration purposes, I estimate such a model by quasi-maximum likelihood on a sample of U.S. Treasury yields, using the unscented Kalman filter to account for the non-linear mapping between factors and yields. # 2 Model Consider first the standard, continuous-time N-factor Gaussian term structure model. In particular, let be -dimensional standard Brownian motion on a complete probability space with canonical filtration . Assume there is a pricing measure on that is equivalent to , and denote by Brownian motion under as derived from Girsanov's Theorem (Karatzas and Shreve, 1991). Suppose latent factors (or states) representing uncertainty underlying term-structure securities follow the multivariate Ornstein-Uhlenbeck process (1) were . Let the short rate be (2) Then by definition, the arbitrage-free time price of a zero-coupon bond maturing at time is given by (3) with associated zero-coupon bond yield (4) Bond prices (and hence yields) can equivalently be defined in terms of forward rates: (5) where denotes the instantaneous time forward rate effective at time . Since is a Gaussian process (Karatzas and Shreve, 1991), it follows from (2) that the short rate takes on strictly negative values with strictly positive probability. To modify the model in a way that accounts for the zero lower bound on nominal yields, Black (1995) proposes to think of as a shadow short rate (and, analogously, of , and as shadow bond price, shadow yield, and shadow instantaneous forward rate, respectively) and define the observed short rate as the shadow rate censored at zero: (6) With the observed short rate in place of the shadow rate , the observed bond price , yield , and instantaneous forward rate are then defined as in (3)-(5). # 3 Parameterizing the Lower Bound The theoretical argument for a lower bound at zero on the nominal short rate (and hence on nominal yields) is based on arbitrage between bonds and currency Black (1995). In practice, the two assets may not be perfect substitutes for reasons such as convenience, default risk, or legal requirements. This may push the empirical lower bound into slightly negative or slightly positive territory. The derivations in Section 2 are easily modified to accommodate a lower bound at . In particular, suppose Then, The last term is equal to the expression for the yield when the lower bound is zero, except that is subtracted from the shadow rate. Therefore, since , when the lower bound is nonzero we can compute zero-coupon yields as if the bound were zero, with in place of , and then add to the final result. The lower bound can be set to a specific value based on a priori reasoning, or treated as a free parameter in estimation. # 4 Bond Price Computation A central task in term-structure modeling is the (analytical and/or numerical) computation of arbitrage-free bond prices (and hence yields) based on equation (3). Section 4.1 reviews the standard approach using differential equations formalized by Duffie and Kan (1996), best suited to affine models. While it can be adapted to the shadow-rate framework, it loses much of its analytical tractability, and becomes computationally infeasible as the number of factors increases. Section 4.2 discusses an alternative method proposed by Krippner (2012). It defines a pseudo-forward rate that satisfies the lower bound (though differs from the arbitrage-free forward rate), and uses relationship (5) to approximate bond prices. Finally, Section 4.3 proposes a new approximation technique for yields in the shadow-rate model based on the expansion of a cumulant-generating function. ## 4.1 Partial Differential Equation Like any conditional expectation of an -measurable random variable, (the time price of a zero-coupon bond maturing at time in the unconstrained Gaussian model, discounted to time 0 ) follows a martingale under . This is an immediate consequence of the definition of a martingale, after an application of the Law of Iterated Expectations. Using It's Lemma and the Martingale Representation Theorem, we can therefore represent by the function , where solves the partial differential equation (PDE) (7) with boundary condition . Using a separation-of-variables argument, it can be verified that (8) solves (7), where and in turn solve ordinary differential equations (ODEs) in terms of the model parameters, (9) (10) with , . Reducing problem (7) to the system of ODEs (9)-(10) simplifies the numerical computation of bond prices substantially as it reduces the dimensionality of the problem from to 1 (the time dimension). Direct computation reveals that (11) assuming is invertible. A PDE analogous to (7) can be set up for the observed bond price in the shadow-rate model, . The only required modification is to replace the expression for the shadow short rate, , by that for the observed short rate, . Unfortunately, when this non-linearity is introduced, the separation-of-variables procedure no longer applies, and no solution as straightforward as (8) is available. It is possible to solve the modified version of (7) directly by numerical methods. This is the approach taken by Kim and Singleton (2012). It requires discretizing and on a multidimensional grid, which is computationally intensive and subject to the curse of dimensionality. Kim and Singleton (2012) therefore do not estimate models with more than two factors. ## 4.2 Forward Rate Approximation Krippner (2012) proposes an alternative approach to computing yields in shadow-rate models, which is implemented empirically by Christensen and Rudebusch (2013). It is based on an approximation to the forward rate . Substituting for from the shadow-rate version of (3), and differentiating, we obtain (12) where , defined by the Radon-Nikodym derivative is referred to as the " -forward measure." Equation (12) says that today's time forward rate is equal to today's expectation under the -forward measure of the time short rate. It can be verified directly from (12) and the Law of Iterated Expectations that is a martingale under (note that by definition). Note also that (12) implies that the forward rate is subject to the same lower bound (6) as the short rate, by monotonicity of the mathematical expectation. Analogously, (13) expresses the shadow forward rate as the expectation under the shadow -forward measure of the future shadow short rate. Again, is a martingale under . Unlike the observed forward rate, it is not, however, constrained to be non-negative. The distribution of the shadow forward rate under can be derived more explicitly. First, from (5) and (8), Therefore, by It's Lemma and the Martingale Representation Theorem, (14) Thus, is Gaussian under conditional on , with The final equality uses the It Isommetry and (11).1 Krippner (2012) takes advantage of this distributional property of . He defines a pseudo-forward rate as a hybrid between observed forward rate (12) and shadow forward rate (13): (16) This is the expectation under the shadow -forward measure of the observed time short rate (while the shadow-model-implied forward rate consistent with the absence of arbitrage is given by (12) as the expectation under the observed -forward measure of the observed time short rate).2 This rate is, by monotonicity, subject to lower bound (6). It is, moreover, relatively straightforward to compute: Lemma A.1 in Appendix A implies that (17) This is formula (32) in Krippner (2012).3 Note from (17) that as increases or decreases. That is, as the lower bound becomes less binding, the wedge between and the shadow forward rate (which is the arbitrage-free forward rate in a Gaussian model without lower bound) shrinks. Zero-coupon bond prices and yields can be approximated by substituting from (17) into (5) and (4). ## 4.3 Cumulants Since the PDE approach to pricing bonds in shadow-rate models becomes computationally intractable as the number of factors increases, and the approach proposed by Krippner (2012) relies on a forward rate that is not equal to the arbitrage-free forward rate, I propose a new cumulant-based technique to approximating yields in Gaussian shadow-rate models. The quantity appearing in the shadow-rate version of (4) is the conditional cumulant-generating function4 under , evaluated at -1 , of the random variable . It has the series representation (18) where is the th cumulant of under . An approximation to the zero-coupon yield can therefore be computed based on a finite number of terms in the series in (18). Below, I consider the first-order approximation (19) and the second-order approximation (20) where I make use of the fact that the first two cumulants of any random variable coincide with its first two centered moments.5 The first-order approximation (19) is equivalent to the method proposed independently and contemporaneously by Ichiue and Ueno (2013). I present it here both for comparison and to assess its relative performance in Section 5 below. I will, however, mostly focus on the second-order approximation (20), which I argue is particularly promising a priori because it is exact in the Gaussian benchmark case.6 It can therefore be expected to perform well both for short maturities (where the higher-order terms in (18) are relatively small), and for long maturities as long as is small for large (in which case will behave approximately like a Gaussian process over sufficiently long horizons). Indeed, empirically, the second-order approximation turns out to be highly accurate across maturities both during normal times and when rates are low (see Section 5). ### 4.3.1 Computation of the First Moment Evaluating the first- and second-order approximations (19) and (20) to zero-coupon yields requires computation of the first two cumulants (equivalently, centered moments) of . This subsection will be concerned with the first moment. As an initial step, (21) by an application of Fubini's Theorem. Since and with known expressions for and in terms of the model parameters (as shown in Appendix A), it follows from Lemma A.1 in Appendix A that (22) where and denote the standard normal probability density function (pdf) and cumulative distribution function (cdf), respectively. That is, we can compute analytically up to the standard normal cdf, which software such as Matlab is able to evaluate precisely and efficiently. The first cumulant of can then be computed by numerical integration of over the time dimension, as in (22). ### 4.3.2 Computation of the Second Moment Once we know the first moment of , it remains to evaluate (23) where the equality uses Fubini's Theorem and symmetry of the integrand. Since and , and are jointly normally distributed with mean , variances , and covariance (see Appendix A), we obtain from Lemma A.2 in Appendix A: (24) where , , , and denotes the decumulative bivariate normal cdf. That is, we can compute analytically up to the bivariate normal cdf, and we can then integrate this expression numerically over and to obtain the second cumulant of . ### 4.3.3 Numerical Implementation The following steps summarize the approximation procedure for zero-coupon yields for a given set of parameters and state vector : 1. Compute the conditional mean and covariance matrix of , for , using (A.4) and (A.5). 2. Using the results from step 1, compute and , for , as described in 4.3.1 and 4.3.2. 3. Integrate numerically to obtain , and integrate numerically to obtain . 4. Using the moments computed in step 3, approximate by or as defined in (19) and (20). In terms of numerical implementation, step 1 is straightforward. Step 2 requires evaluation of the univariate and bivariate normal cdf's. A high-precision, efficient approximation to the univariate normal cdf is built into most computational software packages, so numerically evaluating the first integrand does not pose a challenge. For the bivariate normal cdf, I implement a vectorized version of an algorithm proposed by Genz (2004) which achieves double machine precision.7 Step 3 is straightforward in principle, though a favorable tradeoff between precision and computational burden requires careful choice of quadrature rule and grid. I use composite Gauss-Legendre and Gauss-Lobatto rules with 2-20 points per maturity (and corresponding product rules for the double integral in (24)), selected to evaluate or to an approximate minimum numerical precision of 1/100th of a basis point. With fully vectorized Matlab code,8 I am able to evaluate a full representative sample of model-implied zero coupon yields (approximately 20 years of monthly data across eight maturities) within a fraction of a second. Note that the complexity of the algorithm does not depend on the number of yield curve factors , so it is not subject to the curse of dimensionality in the same way that some other methods are.9 For illustration purposes, in Appendix B I apply the second-order approximation method to estimate a three-factor shadow-rate model of the U.S. Treasury term structure. # 5 Accuracy of Yield Approximation Methods Section 4.3 argued intuitively that the second-order yield approximation (20) should be relatively precise. This section quantifies that claim. To get an initial sense of the relative numerical accuracy, I consider the stylized model used for illustration by Gorovoi and Linetsky (2004), and replicated for the same purpose in Krippner (2012). It is a one-factor model with , , , , and . Gorovoi and Linetsky (2004) derive model-implied yield curves for states corresponding to shadow short rates . The four panels of Figure 1 plot the model-implied yield curves for each initial state. Within each panel, I compare four different yield approximation schemes: Solving PDE (7) numerically (which, in a one-factor setting, is computationally feasible and can be considered the "exact" solution for comparison purposes), Krippner's (2012) approach described in Section 4.2, and the first- and second-order approximations proposed in Section 4.3. As the figure shows, the second-order approximation matches the exact PDE solution most closely, and consistently across states. The yield approximation error is uniformly less than one basis point. The first-order approximation generally overstates yields (an implication of the alternating nature of series expansion (18)), with approximation errors increasing both in yield maturity and the level of the shadow short rate (in both cases, the first-order approximation is off by an increasingly large convexity adjustment arising from Jensen's inequality). Krippner's (2012) method generally undershoots yields, and is relatively more accurate when the shadow short rate is higher. Why this is the case can be seen intuitively by comparing the -measure expressions for the arbitrage-free forward rate (12) and Krippner's (2012) approximate forward rate (16): While both use the same time short rate , Krippner's (2012) formula discounts by the shadow rate rather than the observed short rate. This means the discount factor tends to be larger than it should be when is low, reducing the covariance between discount factor and , and thus lowering the expectation of their product, . To compare the relative performance of the different yield approximations in a more realistic empirical setting, I use the estimated model parameters and smoothed states from Appendix B.3 to compute model-implied yield curves for all dates in the sample.10 Since this is a three-factor model, solving PDE (7) numerically is no longer practicable. I therefore replace this benchmark by a simulated yield that consistently estimates the true yield based on randomly drawn #### Figure 1: Yield curves (zero-coup on yield against maturity in years) implied by a one factor shadow-rate model with ρ0-0.01, ρ1-1, K0-0. K1- -0.1, and ∑ -0.02.The different panels corresp ond to di erent initial shadow short rates. Within each panel, the yield curve is computed using four metho ds: Numerical solution of PDE (7), Krippner's (2012) approach describ ed in Section 4.2,and the first- and second-order approximations proposed in Section 4.3. Figure 1 Data short-rate paths per sample date.11,12 Table 1 shows the mean simulation error of , and the root-mean-square errors (RMSE) against of the yield computed by Krippner's (2012) method, the first-order approximation defined in (19), and the second-order approximation defined in (20). The table is divided into two panels. The top panel shows errors for the sub-sample Jan 1990-Nov 2008 (when interest rates were at normal levels), and the bottom panel shows errors for the sub-sample Dec 2008-Dec 2012 (when the lower bound on nominal yields was binding at the short end of the yield curve). All methods are generally more precise at shorter maturities. As the first column in both panels shows, the simulated yields are accurate to within approximately one fifth of a basis point at the ten-year maturity point. As shown in the second column of the tables, Krippner's (2012) method produces ten-year yields that are accurate to about one basis point during normal times, and to within four basis points when the lower bound is binding. While the first-order method is more accurate when rates are low (the bottom panel), its errors remain substantial at the long end. The second-order method, the final column in the tables, produces ten-year yields that are accurate to approximately half a basis point, both during normal times and when the lower bound is binding. To further illustrate the time-varying relative performance of the three approximation schemes, Figure 2 plots the difference over time between the simulated ten-year yield and the three approximated yields. Krippner's (2012) method and the second-order approximation appear to be equally precise in the first few years of the sample, #### Table 1: The mean standard error of simulated yields (n-1,000,000 draws per sample date) for the model estimated in Appendix B, and the root-mean-square errors (RMSE) against the simulated yields of Krippner's (2012) yield approximation , the first-order yield approximation , and the second-order yield approximation . All errors are in basis points. Maturity 6m Sub-sample Kam 1990-Nov 2008 0.04 0.04 0.05 0.04 1y Sub-sample Kam 1990-Nov 2008 0.06 0.06 0.18 0.06 2y Sub-sample Kam 1990-Nov 2008 0.09 0.10 0.88 0.10 3y Sub-sample Kam 1990-Nov 2008 0.12 0.14 2.26 0.13 4y Sub-sample Kam 1990-Nov 2008 0.14 0.18 4.22 0.15 5y Sub-sample Kam 1990-Nov 2008 0.16 0.27 6.60 0.17 7y Sub-sample Kam 1990-Nov 2008 0.19 0.47 12.22 0.21 10y Sub-sample Kam 1990-Nov 2008 0.21 0.93 21.81 0.35 6m Sub-sample Dec 2008-Dec 2012 0.01 0.01 0.01 0.01 1y Sub-sample Dec 2008-Dec 2012 0.02 0.04 0.04 0.02 2y Sub-sample Dec 2008-Dec 2012 0.05 0.19 0.33 0.05 3y Sub-sample Dec 2008-Dec 2012 0.07 0.51 1.07 0.07 4y Sub-sample Dec 2008-Dec 2012 0.10 0.94 2.31 0.09 5y Sub-sample Dec 2008-Dec 2012 0.12 1.42 3.99 0.12 7y Sub-sample Dec 2008-Dec 2012 0.15 2.43 8.38 0.23 10y Sub-sample Dec 2008-Dec 2012 0.17 3.87 16.63 0.52 with fluctuations presumably largely due to simulation error.13 The discrepancy between simulated yield and Krippner's (2012) method increases over time as the level of yields declines, and exceeds five basis points by December 2012. The discrepancy between simulated yield and second-order approximation remains small and appears to show little systematic variation over time, perhaps trending up modestly towards the end of the sample. The first-order approximation has a large negative discrepancy initially, which shrinks over time but remains at a high absolute level even at the end of the sample. Figure 2 also confirms that, just like in the simple one-factor model in Figure 1, the approximation errors under Krippner's (2012) method and the first-order scheme are largely systematic (rather than mere noise), in that the first-order approximation overstates arbitrage-free yields while Krippner's (2012) method tends to understate them. In sum, the analysis above suggests that, empirically, the second-order yield approximation is accurate to within about one half of a basis point at maturities up to ten years, both during normal times and when the lower bound is binding. The approximation error is one order of magnitude smaller than both the model-implied observation error in yields (see Table 3) and the next best approximation method proposed by Krippner's (2012). In contrast, the first-order approximation is acceptable at most at the very short end of the yield curve. To add perspective, the approximation error in is no greater than commonly accepted fitting error in the derivation of constant-maturity zero-coupon bond yields from observed coupon-bearing Treasuries (e.g., Gürkaynak et al., 2006). This puts the second-order approximation roughly on par with the numerical accuracy achieved #### Figure 2: Deviation from simulated ten-year yield +10 of Krippner's (2012) yield approximation+10, the first-order yield appproximation +10, and the second-order yield approximation +10. Model parameters and filtered states are taken from Appendix B. Figure 2 Data by "exact" bond pricing methods in standard affine models, to the extent that they rely on numerical methods (say, to solve the system of ODEs (9)-(10)).14 # 6 Conclusion This paper develops an approximation to arbitrage-free zero coupon bond yields in Gaussian shadow-rate term structure models. The complexity of the scheme does not depend on the number of factors. Further, I demonstrate that the method is computationally feasible by estimating a three-factor shadow-rate model of the U.S. Treasury yield curve. Based on Monte Carlo simulation, I also show that the yield approximation is approximately as precise as conventional approaches that are considered to be "exact." # A. Useful Mathematical Results ## A.1 Moments of Consider the continuous time stochastic process defined in (1). The following derivations hold under both the -measure and the -measure, hence for notational simplicity I will suppress dependence of moments and parameters on the measure. Since is a Gaussian process, all its finite-dimensional distributions are Gaussian Karatzas and Shreve, 1991). In particular, for , the vectors are jointly conditionally Gaussian, with (A.1) (A.2) If is invertible, the integral on the right-hand side of (A.2) can be evaluated analytically using integration by parts and formula (10.2.15) in Hamilton (1994), where " " denotes the Kronecker sum. Since as defined in (2) is a linear function of the Gaussian random vector , it is itself Gaussian, with (A.4) and (A.5) ## A.2 Moments of Censored Gaussian Random Variables This section derives two useful mathematical results involving the moments of censored Gaussian random variables. Lemma A.1   If , then where denotes the standard normal cdf, and denotes the standard normal pdf. Proof. First, note that (A.6) Thus, it only remains to compute where is a standard normal random variable, for arbitrary . By direct computation of the integral defining the expectation, (A.7) where is the standard normal cdf. Further, (A.8) Recursively substituting from (A.8) into (A.7), and finally into (A.6), establishes the result. Lemma A.2 If then (A.9) where , , , denotes the univariate standard normal pdf, denotes the univariate standard normal cdf, denotes the bivariate normal pdf when both variables have zero means, unit variances, and correlation , and and denote the corresponding cumulative and decumulative bivariate Gaussian distribution functions, where in particular . Proof. Write (A.10) The second and third terms can be evaluated using Lemma A.1. For the first term, it suffices to be able to compute for random variables and that are bivariate normal with zero means, unit variances, and correlation , and for arbitrary . Using the properties of , this expectation can be expanded as follows: The first double integral is simply , the bivariate normal cdf. The second and third double integrals correspond to expected values of truncated bivariate normal random variables, and the last integral is the expected cross product of a truncated bivariate normal random vector. These expected values are known up to the univariate standard normal cdf and the bivariate normal cdf, respectively (see Rosenbaum (1961)). Using the formulas in Rosenbaum (1961) to evaluate the integrals in (A.9), and substituting into (A.10), we obtain (A.9) after simplification. # B. Empirical Implementation This appendix empirically estimates a three-factor Gaussian shadow-rate term structure model using the yield approximation methodology proposed in Section 4.3. The main purpose is to demonstrate the computational tractability of the method in the context of a realistic application. For more in-depth discussion and empirical analysis, see Kim and Priebsch (2013). ## B.1 Data I use end-of-month zero-coupon U.S. Treasury yields from January 1990 through December 2012, for maturities of 6 months, 1-5, 7, and 10 years. I derive the 6-month yield from the corresponding T-bill quote, while longer-maturity zero yields are extracted from the CRSP U.S. Treasury Database using the unsmoothed Fama and Bliss (1987) methodology.15 I augment the yield data with survey forecasts from Blue Chip, interpolated to constant horizons of 1-4 quarters (available monthly), as well as annually out to 5 years and for 5-to-10 years (available every six months).16 Model-implied survey forecasts are subject to the same lower-bound constraint as yields,17 but their computation is substantially simpler: Forecasters report their expectation of the arithmetic mean of future observed short rates, . This is exactly (19) with the data-generating measure in place of pricing measure . Therefore, the first-order method described in Section 4.3 produces exact model-implied survey forecasts. Intuitively, unlike yields, survey forecasts are not subject to compounding, so there are no higher-order Jensen's inequality terms to consider. ## B.2 Filtering and Estimation Since the statistical properties of the term structure model laid out in Section 2 are formulated in terms of the latent state vector , but the data actually observed by the econometrician consist of yields, , and survey expectations, (see Appendix B.1), I set up a joint estimation and filtering problem to obtain estimates of the model's parameters .18 When discretely sampled at intervals , the state vector follows a first-order Gaussian vector autoregression, (B.1) where , and , , and can be computed from (A.1) and (A.2). Equation (B.1) represents the transition equation of the filtering problem. Next, denote by the (non-linear) mapping from states and parameters to model-implied yields , and by the analogous mapping from states and parameters to model-implied survey forecasts . For estimation purposes, I compute through the second-order approximation (20), and through the exact first-order method discussed in Appendix B.1. To simplify notation, denote the stacked mapping by . If we assume that all yields and survey expectations are observed with iid additive Gaussian errors, we obtain the observation equation (B.2) Together, equations (B.1) and (B.2) form a non-linear filtering problem. The simple (linear) Kalman filter--optimal when measurement and observation equation are linear and all shocks are Gaussian--has been modified in a number of ways to accommodate nonlinearity as in (B.2). The unscented Kalman filter, proposed by Julier et al. (1995), aims to deliver improved accuracy and numerical stability relative to the more traditional extended Kalman filter, without substantially increasing the computational burden.19,20 The algorithm is described in detail in Wan and van der Merwe (2001). As a by-product of the filtering procedure, it conveniently produces estimates of the mean and covariance matrix of conditional on the econometrician's information set as of time . I use these to set up a quasi-maximum likelihood function based on (B.2),21 which I maximize numerically to obtain estimates of the parameters as well as their asymptotic standard errors (following Bollerslev and Wo oldridge, 1992). ## B.3 Estimation Results To achieve econometric identification of the parameters in light of invariant transformations resulting in observationally equivalent models with different parameters (see Dai and Singleton, 2000 ), I follow Joslin et al. (2011) and impose the normalizations , , is diagonal and therefore completely determined by its ordered eigenvalues , and is lower triangular. I estimate the model on the data set described in Appendix B.1, using the quasi-maximum likelihood (QML) procedure discussed in Appendix B.2. Table 2 displays the estimated model parameters , as well as their asymptotic standard errors. #### Table 2: Quasi-maximum likelihood parameter estimates (asymptotic standard errors) for the three-factor shadow-rate model. 0.0738 :standard errors (0.0043) 0.0010 :standard errors (0.0001) vector, row 1 - 0.1038 vector, row 1: standard error (0.0226) vector, row 2 - 0.3566 vector, row 2: standard error (0.1177) vector, row 3 - 0.8574 vector, row 3: standard error (0.2876) vector, row 1 - 0.0193 vector, row 1: standard error (0.0052) vector, row 2 - 0.0099 vector, row 2: standard error (0.0224) vector, row 3 0.0278 vector, row 3: standard error (0.0233) matrix, row 1, column 1 0.0268 matrix, row 1, column 1: standard error (0.0084) matrix, row 2, column 1 - 0.0324 matrix, row 2, column 1: standard error (0.0110) matrix, row 2, column 2 0.0416 matrix, row 2, column 2: standard error (0.0295) matrix, row 3, column 1 0.0068 matrix, row 3, column 1: standard error (0.0100) matrix, row 3, column 2 - 0.0397 matrix, row 3, column 2: standard error (0.0302) matrix, row 3, column 3 - 0.0090 matrix, row 3, column 3: standard error (0.0007) matrix, row 1, column 1 - 0.4679 matrix, row 1, column 1: standard error (0.1574) matrix, row 1, column 2 - 0.3415 matrix, row 1, column 2: standard error (0.1490) matrix, row 1, column 3 0.3785 matrix, row 1, column 3: standard error (0.6798) matrix, row 2, column 1 - 0.5752 matrix, row 2, column 1: standard error (0.6303) matrix, row 2, column 2 - 1.1881 matrix, row 2, column 2: standard error (1.1335) matrix, row 2, column 3 - 1.1875 matrix, row 2, column 3: standard error (0.5740) matrix, row 3, column 1 0.8908 matrix, row 3, column 1: standard error (0.6982) matrix, row 3, column 2 1.3060 matrix, row 3, column 2: standard error (1.0641) matrix, row 3, column 3 0.3990 matrix, row 3, column 3: standard error (1.3561) Table 3 shows the QML-estimated standard deviations of the measurement errors in yields and survey variables ( in equation (B.2)). The average yield error is 8 basis points, and the average error in surveys is 21 basis points. For both yields and surveys, errors follow a U-shaped pattern, being largest at the short and long ends. Figure 3 plots the model-implied shadow short rate over the sample period, based on the states implied by the Kalman smoother (that is, incorporating all information up to December 2012, the end of the sample). The shadow rate turned negative in December 2008, after the FOMC established a target federal funds rate range of 0 to 0.25 percent and the effective lower bound became binding, and has stayed negative through the end of the sample. #### Table 3:Estimated standard deviations of observation errors in yields, Maturity 6m 0.0017 1y 0.0014 2y 0.0006 3y 0.0003 4y 0.0004 5y 0.0003 7y 0.0006 10y 0.0015 Average 0.0008 #### Table 3:Estimated standard deviations of survey forecasts, Maturity 1q 0.0014 2q 0.0002 3q 0.0009 4q 0.0014 2y 0.0028 3y 0.0026 4y 0.0027 5y 0.0031 5y-10y 0.0034 Average 0.0021 Figure 3 Data # References Bauer, M., and Rudebusch, G. (2013), "Monetary Policy Exp ectations at the Zero Lower Bound," Working Paper, Federal Reserve Bank of San Francisco Bernanke, B., Reinhart, V., and Sack, B. (2004), Monetary Policy Alterna- tives at the Zero Bound: An Empirical Assessment, "Brookings Papers on Economic Activity", 2:1-100 Black, F. (1995), Interest Rates as Options, Journal of Finance, 50(5):1371 1376 Bollerslev, T., and Wo oldridge, J. (1992), "Quasi-Maximum Likelihoodd Esti- mation and Inference in Dynamic Mo dels with Time-Varying Covariances, Econo- metric Reviews, 11(2):143-172 Chen, R. (1995), A Two-Factor, Preference-Free Mo del for Interest Rate Sensivite Claims, Journal of Futures Markets, 15(3):345-372 Christensen, J., and Rudebusch, G. (2013), Estimating Shadow-Rate Term Structure Mo dels with Near-Zero Yields, Working Paper, Federal Reserve Bank of San Francisco Christoffersen, P., Dorion, C., Jacobs, K., and Karoui, L. (2012), Nonlinear Kalman Filtering in Affine Term Structure Mo dels, CREATES Research Paper 2012-49, Aarhus University Dai, Q., and Singleton, K. (2000), Specification Analysis of Affine Term Structure Models, Journal of Finance, 60(5):1943-1978 Duan, J.-C., and Simonato, J.-G. (1999), "Estimating and Testing Exponential-Affine Term Structure Mo dels by Kalman Filter," Review of Quantitative Finance and Accounting, 13:111-135 Duffie, D., and Kan, R. (1996), "A Yield-Factor Mo del of Interest Rates," Mathematical Finance, 6:369-406 Fama, E., and Bliss, R. (1987) ,"The Information in Long-Maturity Forward Rates," American Economic Review, 77(4):680-692 Genz, A. (2004),"Numerical Computation of Rectangular Bivariate and Trivariate Normal and t Probabilities," Statistics and Computing, 14:251-260 Gorovoi, V., and Linetsky, V. (2004), "Black's Model of Interest Rates as Op- tions, Eigenfunction Expansions and Japanese Interest Rates," Mathematical Fi- nance, 14(1):49-78 Hamilton, J. (1994), The Time Series Analysis, Princeton University Press Ichiue, H., and Ueno, Y. (2007), "Equilibrium Interest Rate and the Yield Curve in a Low Interest Environment," Bank of Japan Working Paper (2013), "Estimating Term Premia at the Zero Bound: An Analysis of Japanese, U.S., and U.K. Yields," Bank of Japan Working Pap er No. 13-E-8 Joslin, S., Singleton, K., and Zhu, H. (2011), "A New Persp ective on Gaussian Dynamic Term Structure Mo dels," Review of Financial Studies, 24(3):926-970 Julier, S., Uhlmann, J., and Durrant-Whyte, H. (1995), "A New Approach for Filtering Nonlinear Systems," in Proceedings of the American Control Conference , pp. 1628-1632 Karatzas, I., and Shreve, S. (1991),Brownian Motion and Stochastic Calculus , Graduate Texts in Mathematics Series, Springer, London Kim, D., and Orphanides, A. (2005), "Term Structure Estimation with Survey Data on Interest Rate Forecasts," Staff Working Pap er 2005-48, Federal Reserve Board Kim, D., and Priebsch, M. (2013), "Estimation of Multi-Factor Shadow Rate Models," Working Pap er in Progress, Federal Reserve Board, Washington D.C. Kim, D., and Singleton, K. (2012),"Term Structure Models and the Zero Bound: An Empirical Investigation of Japanese Yields," Journal of Econometrics, 170(1):32-49 Krippner, L. (2012), "Modifying Gaussian Term Structure Mo dels When Interest Rates are Near the Zero Lower Bound," Reserve Bank of New Zealand Discussion Paper 2012/02 Lund, J. (1997), Non-Linear Kalman Filtering Techniques for Term Structure Mo d-els, Working Paper, Aarhus Scho ol of Business Piazzesi, M. (2010), "Affine Term Structure Models," in Handbook of Financial Econometrics , ed. by Y. Ait-Sahalia, and L. P. Hansen. North-Holland, Amsterdam Rosenbaum, S. (1961),"Moments of a Truncated Bivariate Normal Distribution," Journal of the Royal Statistical Society, 23(2):405-408 Severini, T. (2005), Elements of Distribution Theory, Cambridge Series in Statistical and Probabilistic Mathematics, Cambridge University Press Wan, E., and van der Merwe, R. (2001), "The Unscented Kalman Filter," in Kalman Filtering and Neural Networks, ed. by S. Haykin, pp. 221-280 Wu, S. (2010), Non-Linear Filtering in the Estimation of a Term Structure Mo del of Interest Rates WSEAS Transactions on Systems, 9(7):724-733 #### Footnotes * Federal Reserve Board, Washington D.C., [email protected]. The analysis and conclusions set forth in this paper are those of the author and do not indicate concurrence by other members of the research staff or the Board of Governors of the Federal Reserve System. Return to Text 1. The integral in (15) has the same form as (A.2) in Appendix A and therefore can be computed analytically as in (A.3). Return to Text 2. Krippner (2012) motivates his derivation in terms of options on shadow bonds. To derive (16) from his equations (12) and (13), replace the call option price by Then interchange the limit operations and expectation, and evaluate. Return to Text 3. Krippner (2012) uses the parametrization proposed by Chen (1995) and hence obtains his formula (31) for as a special case of (15). Similarly, the results derived by by Christensen and Rudebusch (2013) are (essentially) special cases of (15) and (17) under their Nelson-Siegel parametrization (where some of the derivations must be modified appropriately to account for the fact that their matrix is singular). Don Kim (personal communication) independently derives the general expression for in (15) by generalizing Krippner's (2012) computations directly. Return to Text 4. The cumulant-generating function of a random variable is defined as the logarithm of its moment-generating function (for example, see Severini, 2005). Return to Text 5. Higher-order approximations following the same general logic are possible, but they are increasingly computationally costly while generating decreasing marginal benefits in terms of precision. Return to Text 6. The third- and higher-order cumulants of a Gaussian random variable are zero, so that (20) coincides with the usual affine-Gaussian yield formula in that case. Return to Text 7. Matlab's built-in function mvncdf uses adaptive numerical integration to compute the bivariate normal cdf. This is slower by several orders of magnitude than the algorithm I use. Return to Text 8. That is, without for-loops that grow with the number of quadrature points, states, dates, or maturities in the sample. Return to Text 9. The general approximation methodology I propose has its own curse of dimensionality in that the second-order approximation is substantially more computationally involved than the first-order approximation (and any higher-order approximation will be substantially more involved than the second-order approximation). In practice, the second-order approximation appears to strike an acceptable balance between precision and computational complexity for many cases of interest, see Section 5 below. Return to Text 10. The sample consists of end-of-month observations from January 1990 through December 2012. Return to Text 11. I simulate (1) under based on moments (A.1)-(A.2) on a uniformly-spaced grid with . For each simulated path , I compute by the trapezoidal method. I then define and . The simulation error for is computed as times the sample standard deviation, and the simulation error for is derived from the simulation error for by the delta method. Return to Text 12. The simulation takes several hours to complete for the given parameter estimates and smoothed states. This approach would not, therefore, be feasible as part of an estimation strategy. Return to Text 13. Recall that when there is no lower bound, both methods produce yields equal to the exact arbitrage-free yield. In the early 1990s, the overall level of yields was sufficiently high for the effect of the lower bound to be negligible. Return to Text 14. Empirically, the second-order approximation is exact to an absolute tolerance of approximately (see Table 1). The default tolerance for numerical methods in Matlab is typically between and , depending on the complexity of the method. Return to Text 15. I am grateful to Anh Le for providing the code for this procedure. Return to Text 16. As discussed by Kim and Orphanides (2005), this potentially leads to more precise estimates of the parameters governing the data-generating distribution . Return to Text 17. This follows from equivalence of the measures and , and more fundamentally from the absence of arbitrage. Return to Text 18. See Duan and Simonato (1999) for an early reference discussing this approach towards term structure model estimation. Return to Text 19. A detailed treatment of the unscented Kalman filter, and a comparison to the extended Kalman filter, can be found in Wan and van der Merwe (2001). Return to Text 20.Christoffersen et al. (2012) and Wu (2010) confirm that the unscented Kalman filter performs better than the extended Kalman filter in the specific setting of term structure model estimation. Return to Text 21. This estimation approach is described and analyzed in Lund (1997). Return to Text This version is optimized for use by screen readers. Descriptions for all mathematical expressions are provided in LaTex format. A printable pdf version is available. Return to Text
2015-03-28T22:15:55
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https://par.nsf.gov/biblio/10283701-ejective-preventative-illustristng-black-hole-feedback-its-effects-thermodynamics-gas-within-around-galaxies
Ejective and preventative: the IllustrisTNG black hole feedback and its effects on the thermodynamics of the gas within and around galaxies ABSTRACT Supermassive black holes (SMBHs) that reside at the centres of galaxies can inject vast amounts of energy into the surrounding gas and are thought to be a viable mechanism to quench star formation in massive galaxies. Here, we study the $10^{9-12.5}\, \mathrm{M_\odot }$ stellar mass central galaxy population of the IllustrisTNG simulation, specifically the TNG100 and TNG300 volumes at z = 0, and show how the three components – SMBH, galaxy, and circumgalactic medium (CGM) – are interconnected in their evolution. We find that gas entropy is a sensitive diagnostic of feedback injection. In particular, we demonstrate how the onset of the low-accretion black hole (BH) feedback mode, realized in the IllustrisTNG model as a kinetic, BH-driven wind, leads not only to star formation quenching at stellar masses $\gtrsim 10^{10.5}\, \mathrm{M_\odot }$ but also to a change in thermodynamic properties of the (non-star-forming) gas, both within the galaxy and beyond. The IllustrisTNG kinetic feedback from SMBHs increases the average gas entropy, within the galaxy and in the CGM, lengthening typical gas cooling times from $10\!-\!100\, \mathrm{Myr}$ to $1\!-\!10\, \mathrm{Gyr}$, effectively ceasing ongoing star formation and inhibiting radiative cooling and future gas accretion. In practice, the same active galactic nucleus more » Authors: ; ; ; ; ; ; ; ; Award ID(s): Publication Date: NSF-PAR ID: 10283701 Journal Name: Monthly Notices of the Royal Astronomical Society Volume: 499 Issue: 1 Page Range or eLocation-ID: 768 to 792 ISSN: 0035-8711 Previous studies of fueling black holes in galactic nuclei have argued (on scales ${\sim}0.01{-}1000\,$pc) accretion is dynamical with inflow rates $\dot{M}\sim \eta \, M_{\rm gas}/t_{\rm dyn}$ in terms of gas mass Mgas, dynamical time tdyn, and some η. But these models generally neglected expulsion of gas by stellar feedback, or considered extremely high densities where expulsion is inefficient. Studies of star formation, however, have shown on sub-kpc scales the expulsion efficiency fwind = Mejected/Mtotal scales with the gravitational acceleration as $(1-f_{\rm wind})/f_{\rm wind}\sim \bar{a}_{\rm grav}/\langle \dot{p}/m_{\ast }\rangle \sim \Sigma _{\rm eff}/\Sigma _{\rm crit}$ where $\bar{a}_{\rm grav}\equiv G\, M_{\rm tot}(\lt r)/r^{2}$ and $\langle \dot{p}/m_{\ast }\rangle$ is the momentum injection rate from young stars. Adopting this as the simplest correction for stellar feedback, $\eta \rightarrow \eta \, (1-f_{\rm wind})$, we show this provides a more accurate description of simulations with stellar feedback at low densities. This has immediate consequences, predicting the slope and normalization of the MBH − σ and MBH − Mbulge relation, LAGN −SFR relations, and explanations for outliers in compact Es. Most strikingly, because star formation simulations show expulsion is efficient (fwind ∼ 1) below total-mass surface density $M_{\rm tot}/\pi \, r^{2}\lt \Sigma _{\rm crit}\sim 3\times 10^{9}\, \mathrm{M}_{\odotmore » 2. ABSTRACT We use the simba cosmological galaxy formation simulation to investigate the relationship between major mergers ($\lesssim$4:1), starbursts, and galaxy quenching. Mergers are identified via sudden jumps in stellar mass M* well above that expected from in situ star formation, while quenching is defined as going from specific star formation rate (sSFR)$\gt t_{\rm H}^{-1}$to$\lt 0.2t_{\rm H}^{-1}$, where tH is the Hubble time. At z ≈ 0–3, mergers show ∼2–3× higher SFR than a mass-matched sample of star-forming galaxies, but globally represent$\lesssim 1{{\ \rm per\ cent}}$of the cosmic SF budget. At low masses, the increase in SFR in mergers is mostly attributed to an increase in the H2 content, but for$M_*\gtrsim 10^{10.5} \,\mathrm{ M}_{\odot }$mergers also show an elevated star formation efficiency suggesting denser gas within merging galaxies. The merger rate for star-forming galaxies shows a rapid increase with redshift, ∝(1 + z)3.5, but the quenching rate evolves much more slowly, ∝(1 + z)0.9; there are insufficient mergers to explain the quenching rate at$z\lesssim 1.5$. simba first quenches galaxies at$z\gtrsim 3$, with a number density in good agreement with observations. The quenching time-scales τq are strongly bimodal, with ‘slow’ quenchings (τq ∼ 0.1tH) dominating overall,more » 3. ABSTRACT We explore implications of a range of black hole (BH) seeding prescriptions on the formation of the brightest$z$≳ 6 quasars in cosmological hydrodynamic simulations. The underlying galaxy formation model is the same as in the IllustrisTNG simulations. Using constrained initial conditions, we study the growth of BHs in rare overdense regions (forming$\gtrsim 10^{12}\, {\rm M}_{\odot }\,h^{-1}$haloes by$z$= 7) using a (9 Mpc h−1)3 simulated volume. BH growth is maximal within haloes that are compact and have a low tidal field. For these haloes, we consider an array of gas-based seeding prescriptions wherein$M_{\mathrm{seed}}=10^4\!-\!10^6\, {\rm M}_{\odot }\,h^{-1}$seeds are inserted in haloes above critical thresholds for halo mass and dense, metal-poor gas mass (defined as$\tilde{M}_{\mathrm{h}}$and$\tilde{M}_{\mathrm{sf,mp}}$, respectively, in units of Mseed). We find that a seed model with$\tilde{M}_{\mathrm{sf,mp}}=5$and$\tilde{M}_{\mathrm{h}}=3000$successfully produces a$z$∼ 6 quasar with$\sim 10^9\, {\rm M}_{\odot }$mass and ∼1047 erg s−1 luminosity. BH mergers play a crucial role at$z$≳ 9, causing an early boost in BH mass at a time when accretion-driven BH growth is negligible. With more stringent seeding conditions (e.g.$\tilde{M}_{\mathrm{sf,mp}}=1000$), the relative paucity of BH seeds results in a much lower merger rate. In this case,$z$more » 4. ABSTRACT We present and study a large suite of high-resolution cosmological zoom-in simulations, using the FIRE-2 treatment of mechanical and radiative feedback from massive stars, together with explicit treatment of magnetic fields, anisotropic conduction and viscosity (accounting for saturation and limitation by plasma instabilities at high β), and cosmic rays (CRs) injected in supernovae shocks (including anisotropic diffusion, streaming, adiabatic, hadronic and Coulomb losses). We survey systems from ultrafaint dwarf ($M_{\ast }\sim 10^{4}\, \mathrm{M}_{\odot }$,$M_{\rm halo}\sim 10^{9}\, \mathrm{M}_{\odot }$) through Milky Way/Local Group (MW/LG) masses, systematically vary uncertain CR parameters (e.g. the diffusion coefficient κ and streaming velocity), and study a broad ensemble of galaxy properties [masses, star formation (SF) histories, mass profiles, phase structure, morphologies, etc.]. We confirm previous conclusions that magnetic fields, conduction, and viscosity on resolved ($\gtrsim 1\,$pc) scales have only small effects on bulk galaxy properties. CRs have relatively weak effects on all galaxy properties studied in dwarfs ($M_{\ast } \ll 10^{10}\, \mathrm{M}_{\odot }$,$M_{\rm halo} \lesssim 10^{11}\, \mathrm{M}_{\odot }$), or at high redshifts (z ≳ 1–2), for any physically reasonable parameters. However, at higher masses ($M_{\rm halo} \gtrsim 10^{11}\, \mathrm{M}_{\odot }$) and z ≲ 1–2, CRs can suppress SF and stellar masses by factorsmore » 5. ABSTRACT We introduce the thesan project, a suite of large volume ($L_\mathrm{box} = 95.5 \, \mathrm{cMpc}$) radiation-magnetohydrodynamic simulations that simultaneously model the large-scale statistical properties of the intergalactic medium during reionization and the resolved characteristics of the galaxies responsible for it. The flagship simulation has dark matter and baryonic mass resolutions of$3.1 \times 10^6\, {\rm M_\odot }$and$5.8 \times 10^5\, {\rm M_\odot }\$, respectively. The gravitational forces are softened on scales of 2.2 ckpc with the smallest cell sizes reaching 10 pc at z = 5.5, enabling predictions down to the atomic cooling limit. The simulations use an efficient radiation hydrodynamics solver (arepo-rt) that precisely captures the interaction between ionizing photons and gas, coupled to well-tested galaxy formation (IllustrisTNG) and dust models to accurately predict the properties of galaxies. Through a complementary set of medium resolution simulations we investigate the changes to reionization introduced by different assumptions for ionizing escape fractions, varying dark matter models, and numerical convergence. The fiducial simulation and model variations are calibrated to produce realistic reionization histories that match the observed evolution of the global neutral hydrogen fraction and electron scattering optical depth to reionization. They also match a wealth of high-redshift observationally inferred data, including themore »
2022-12-05T11:54:29
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https://www.bnl.gov/event.php?q=6625
# Nuclear Physics & RIKEN Theory Seminar ## "The nuclear liquid-gas phase transition at large $N_c$ in the Van der Waals approximation" #### Presented by Giorgio Torrieri, Columbia University Friday, July 30, 2010, 2:00 pm — Small Seminar Room, Bldg. 510 The nuclear liquid-gas phase transition at large $N_c$ in the Van der Waals approximation We examine the nuclear liquid-gas phase transition at large number of colors ($N_c$) within the framework of the Van Der Waals (VdW) model. We argue that the VdW equation is appropriate at describing inter-nucleon forces , and discuss how each parameter scales with $N_c$. We demonstrate that $N_c=3$ is not large with respect to the other dimensionless scale relevant to baryonic matter, the number of neighbours in a dense system. Consequently, we show that the liquid-gas phase transition looks dramatically different at $N_c \rightarrow \infty$ with respect of our world: The critical point temperature becomes of the order of $\lqcd$ rather than below it. The critical point density becomes of the order of the baryonic density, rather than an order of magnitude below it. These are precisely the characteristics usually associated with the Quarkyonic phase''. We therefore argue that at large $N_c$ the nuclear liquid phase coincides with the conjectured quarkyonic phase, although the two are thought to occur at very different scales in our world. 6625  |  INT/EXT  |  Events Calendar
2019-09-22T21:01:21
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http://www.scstatehouse.gov/sess119_2011-2012/sj11/20110331.htm
South Carolina General Assembly 119th Session, 2011-2012 Journal of the Senate Thursday, March 31, 2011 (Statewide Session) Indicates Matter Stricken Indicates New Matter The Senate assembled at 11:00 A.M., the hour to which it stood adjourned, and was called to order by the PRESIDENT. A quorum being present, the proceedings were opened with a devotion by the Chaplain as follows: " 'Who am I that I should go to Pharaoh and bring the Israelites out of Egypt?' "       (Exodus 3:11) Bow in prayer with me, if you will: Glorious and ever-loving God, be with each of these Senators whenever they find themselves doubting their call to service. It is surely not an easy nor always pleasurable task these days to be in the public eye. Remind these leaders of the women and men and children throughout this State who are dependent upon them, O Lord. And then allow each Senator and every staff member to be confident as they continue in their role, knowing that You are walking with them, guiding them, caring for them. And as always, Lord, may the ultimate glory be Yours. In Your name we pray, O Lord. Amen. The PRESIDENT called for Petitions, Memorials, Presentments of Grand Juries and such like papers. MESSAGE FROM THE GOVERNOR The following appointments were transmitted by the Honorable Nikki Randhawa Haley: Local Appointments Reappointment, Allendale County Magistrate, with the term to commence April 30, 2010, and to expire April 30, 2014 John Alonzo Chaney, P. O. Box 1173, Fairfax, SC 29827 Reappointment, Anderson County Magistrate, with the term to commence April 30, 2011, and to expire April 30, 2015 James Tillman Busby, 1200 Good Hope Church Road, Anderson, SC 29684 Reappointment, Anderson County Magistrate, with the term to commence April 30, 2011, and to expire April 30, 2015 James Albert Cox, 208 Mills Street, West Pelzer, SC 29669 Reappointment, Anderson County Magistrate, with the term to commence April 30, 2011, and to expire April 30, 2015 Sherry E. Mattison, 309 Oakwood Estates Drive, Anderson, SC 29621 Reappointment, Darlington County Magistrate, with the term to commence April 30, 2011, and to expire April 30, 2015 James Edward Thomas, P. O. Box 1765, Hartsville, SC 29550 Initial Appointment, Savannah River Site Redevelopment Authority, with the term to commence October 21, 2010, and to expire October 21, 2014 General Public: Thomas Williams, 2686 Highway 278, Barnwell, SC 29812 VICE Robert Cooper (resigned) Initial Appointment, Sumter County Magistrate, with the term to commence April 30, 2010, and to expire April 30, 2014 Kristi F. Curtis, 1145 Boardwalk, Sumter, SC 29150 VICE Kathy Ward (resigned) Doctor of the Day Senator LAND introduced Dr. Sharon Eden of Columbia, S.C., Doctor of the Day, along with her son, Evan. Expression of Personal Interest Senator MALLOY rose for an Expression of Personal Interest. Remarks by Senator MALLOY Gentlemen of the Senate, I rise for a brief moment to give you an encouraging report as we continue to move along. A few years ago we started talking about what to do with the Departments of Corrections and Probation, Pardon and Parole. At that time the prison population was 23,547. As you know in the Bill we had, we were focusing on those that were convicted of violent crimes -- those individuals that needed to be taxpayers instead of tax burdens. We wanted to end up providing some alternatives for those that were violent in our society. We wanted to make sure that we kept ourselves safe. The prison population is down by 1,027 from one year ago today in such a short period of time. What that means is it costs us less. You can add a lot of factors into it. You can end up saying that maybe DJJ has been helpful as it relates to a feeder system. But I believe that once the judges follow the law that you have passed here in this body, it will demonstrate that we can do better in a holistic way if we try to end up grouping together in a bi-partisan fashion using evidence-based practices to solve the problems that we have in this State. And so, what that really means is that if you're down a thousand some odd in population in less than a year from an Act that was only in place since June of 2010, then gentleman, that is progress. When we say progress, what that means is that we are saving taxpayers' dollars because we are not having to incarcerate those who are actually tax burdens and we are turning those that are non-violent offenders into taxpayers. I wanted to give you that brief report. Senator COURSON: Did you know that this is the first time since I have served in this body that I have noticed a decrease in prison population? Did you know that this will mean more money for education? SENATOR MALLOY: Yes, the money we don't have to spend in incarceration, we can place in education -- things that are very dear to our hearts. This entire body, by embracing the issue with the help of the Senator from Charleston and the Senator from Lexington and many others who have worked on this issue -- it looks like we are going down in the prison population. As we continue to go forward, the Senator from Greenville has asked us to look at the combining of the agencies. We just need to make certain that what we have in place does not break what we have sort of fixed. What it means is that we have been operating with a deficit in our in our prison system. If we continue to solve the problems in this method, we'll be able to put more money into education. Whenever we have difficult times, you can do good things better if people are inspired and work together and you do it based on the evidence. And that's what we want to do to reach a common goal to keep South Carolinians safe. On motion of Senator FAIR, with unanimous consent, the remarks of Senator MALLOY were ordered printed in the Journal. S. 79 (Word version)     Sen. Campsen S. 211 (Word version)     Sens. Ford, McGill S. 388 (Word version)     Sen. Shoopman S. 435 (Word version)     Sens. Bryant, Ford, Campsen S. 593 (Word version)     Sen. Campsen INTRODUCTION OF BILLS AND RESOLUTIONS The following were introduced: S. 757 (Word version) -- Senators Grooms, Campbell and Campsen: A SENATE RESOLUTION TO RECOGNIZE AND COMMEND THE TIMBERLAND HIGH SCHOOL GIRLS BASKETBALL TEAM ON ITS IMPRESSIVE WIN OF THE 2011 CLASS AA STATE CHAMPIONSHIP TITLE, AND TO HONOR THE PLAYERS, COACH, AND STAFF ON AN OUTSTANDING SEASON. l:\council\bills\rm\1114ab11.docx S. 758 (Word version) -- Senator Malloy: A BILL TO AMEND ARTICLE 11, CHAPTER 21, TITLE 24 OF THE SOUTH CAROLINA CODE OF LAWS, 1976, BY ADDING SECTION 24-21-1010, SO AS TO PROVIDE THAT A PERSON WHO HAS RECEIVED A PARDON FOR ANY CRIME EXCEPT CRIMINAL SEXUAL CONDUCT OR A CRIME OF VIOLENCE AS DEFINED IN SECTION 16-23-10(3), MAY APPLY, OR CAUSE SOMEONE ACTING ON THE PERSON'S BEHALF TO APPLY, TO THE CIRCUIT COURT FOR AN ORDER EXPUNGING THE RECORDS OF THE PERSON'S ARREST AND CONVICTION. l:\s-jud\bills\malloy\jud0098.jjg.docx Read the first time and referred to the Committee on Corrections and Penology. S. 759 (Word version) -- Senator Alexander: A SENATE RESOLUTION TO HONOR AND CONGRATULATE PRIVATE FIRST CLASS BRENT K. SCHIPPER UPON BEING NAMED THE SOUTH CAROLINA NATIONAL GUARD SOLDIER OF THE YEAR. l:\s-res\tca\009schi.mrh.tca.docx S. 760 (Word version) -- Senator McGill: A SENATE RESOLUTION TO CONGRATULATE THELMA WILLIAMS, MOTHER OF OUR DEAR FRIEND AND COLLEAGUE, SENATOR KENT WILLIAMS, UPON THE OCCASION OF HER EIGHTY-FIFTH BIRTHDAY, AND TO WISH HER A JOYOUS BIRTHDAY CELEBRATION AND MANY MORE YEARS OF CONTINUED HEALTH AND HAPPINESS. l:\council\bills\gm\24745sd11.docx S. 761 (Word version) -- Senator L. Martin: A CONCURRENT RESOLUTION TO HONOR AND RECOGNIZE EASLEY COMBINED UTILITIES FOR PROVIDING SERVICE TO THE COMMUNITY FOR ONE HUNDRED YEARS. l:\s-res\lam\022util.mrh.lam.docx The Concurrent Resolution was adopted, ordered sent to the House. H. 3267 (Word version) -- Reps. Sellers, G. M. Smith and Pitts: A BILL TO AMEND CHAPTER 21, TITLE 24, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE CREATION AND OPERATION OF THE DEPARTMENT OF PROBATION, PAROLE AND PARDON SERVICES AND THE BOARD OF PROBATION, PAROLE AND PARDON SERVICES, SO AS TO TRANSFER ALL FUNCTIONS, POWERS, DUTIES, RESPONSIBILITIES AND AUTHORITY STATUTORILY EXERCISED BY THE DEPARTMENT OF PROBATION, PAROLE AND PARDON SERVICES TO THE DEPARTMENT OF CORRECTIONS, DIVISION OF PROBATION, PAROLE AND PARDON SERVICES. Read the first time and referred to the Committee on Corrections and Penology. H. 3403 (Word version) -- Reps. Delleney, Simrill, Lucas, Hiott, Limehouse, Bowen, Bedingfield, Pinson, G. M. Smith, J. R. Smith, Bingham, Frye, V. S. Moss, Corbin, Bikas, Cooper, Allison, Parker, Toole, G. R. Smith, Henderson, Atwater, McCoy, Ballentine, Brannon, Clemmons, D. C. Moss, Hixon, Pitts, Young, Sandifer, Quinn, Willis, Viers, Pope, Stringer, Nanney, Hamilton, Owens and Huggins: A BILL TO AMEND SECTION 2-7-30, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE CONSTRUCTION OF THE WORDS "PERSON" AND "PARTY" AS THOSE WORDS APPEAR IN THE LAWS OF THIS STATE, SO AS TO PROVIDE FURTHER FOR THE CONSTRUCTION OF "PERSON", "HUMAN BEING", "CHILD", AND "INDIVIDUAL", SO THAT THEY INCLUDE EVERY INFANT MEMBER OF THE SPECIES HOMO SAPIENS WHO IS BORN ALIVE AND TO DEFINE "BORN ALIVE". Read the first time and referred to the Committee on Judiciary. H. 3408 (Word version) -- Reps. Delleney, Lucas, Simrill, Hiott, Limehouse, Bowen, Bedingfield, Pinson, J. R. Smith, G. M. Smith, Bingham, Thayer, V. S. Moss, Brannon, Bikas, Cooper, Allison, Toole, Parker, G. R. Smith, Frye, Atwater, Henderson, McCoy, Ballentine, Clemmons, Hixon, D. C. Moss, Pitts, Young, Quinn, Willis, Viers, Sandifer, Stringer, Nanney, Hamilton, Owens and Huggins: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING ARTICLE 5, TO CHAPTER 41, TITLE 44, TO ENACT THE "FREEDOM OF CONSCIENCE ACT" SO AS TO PROHIBIT AN EMPLOYER FROM DISMISSING, DEMOTING, SUSPENDING, DISCIPLINING, OR DISCRIMINATING AGAINST AN EMPLOYEE WHO ADVISES THE EMPLOYER THAT HE OR SHE REFUSES TO PARTICIPATE IN CERTAIN ACTIVITIES INCLUDING, BUT NOT LIMITED TO, PROCEDURES RELATED TO EMBRYONIC TISSUE OR A DEVELOPING CHILD IN AN ARTIFICIAL OR NATURAL WOMB; TO PROVIDE THAT A HEALTH CARE FACILITY IS NOT REQUIRED TO ADMIT A PATIENT, OR TO ALLOW THE USE OF THE FACILITY FOR PROCEDURES INCLUDING, BUT NOT LIMITED TO, PROCEDURES RELATED TO EMBRYONIC TISSUE OR A DEVELOPING CHILD IN AN ARTIFICIAL OR NATURAL WOMB AND TO PROVIDE THAT CERTAIN HEALTH CARE PROVIDERS AND EMPLOYEES OF SUCH PROVIDERS WHO PROVIDED NOTICE THAT THEY WILL NOT PARTICIPATE IN SUCH ACTIVITIES MUST NOT BE REQUIRED TO PARTICIPATE, MUST NOT BE DISCIPLINED DUE TO SUCH REFUSAL, AND ARE IMMUNE FROM LIABILITY FOR ANY DAMAGES CAUSED BY SUCH REFUSAL; TO PROVIDE THAT THE STATE MUST NOT REQUIRE AN INSURANCE PLAN OR ISSUER TO COVER PROCEDURES INCLUDING, BUT LIMITED TO, PROCEDURES RELATING TO EMBRYONIC TISSUE OR DEVELOPMENT OF A CHILD IN AN ARTIFICIAL OR NATURAL WOMB; TO PROHIBIT A HEALTH CARE FACILITY, SCHOOL, OR EMPLOYER FROM DISCRIMINATING AGAINST A PERSON REGARDING ADMISSION, HIRING OR FIRING, TERMS OF EMPLOYMENT, OR STUDENT OR STAFF STATUS BECAUSE THE PERSON REFUSES, WHETHER OR NOT IN WRITING, TO PARTICIPATE IN PROCEDURES INCLUDING, BUT NOT LIMITED TO, PROCEDURES RELATED TO EMBRYONIC TISSUE OR A DEVELOPING CHILD IN AN ARTIFICIAL OR NATURAL WOMB; TO PROVIDE THAT A PERSON MUST NOT BE REQUIRED TO PARTICIPATE IN, MAKE FACILITIES AVAILABLE FOR, OR PROVIDE PERSONNEL FOR PROCEDURES INCLUDING, BUT LIMITED TO, PROCEDURES RELATING TO EMBRYONIC TISSUE OR DEVELOPMENT OF A CHILD IN AN ARTIFICIAL OR NATURAL WOMB IF THE ACTIVITY IS CONTRARY TO THE PERSON'S CONSCIENCE; TO PROHIBIT DISCRIMINATION AGAINST A PERSON ESTABLISHING OR OPERATING A HEALTH CARE FACILITY BECAUSE THE FACILITY DECLINES TO PARTICIPATE IN A HEALTH CARE SERVICE THAT IS CONTRARY TO THE FACILITY'S CONSCIENCE; AND TO PROVIDE THAT A PERSON ADVERSELY AFFECTED BY CONDUCT THAT IS IN VIOLATION OF THIS ARTICLE MAY BRING A CIVIL ACTION FOR EQUITABLE RELIEF AND IF THE PERSON PREVAILS, THE COURT SHALL AWARD ATTORNEY'S FEES. Read the first time and referred to the Committee on Medical Affairs. H. 3642 (Word version) -- Reps. Cooper, Bingham, Allison, Harrell and Owens: A JOINT RESOLUTION TO PROVIDE THAT A LOCAL SCHOOL DISTRICT MAY PAY TEACHERS BASED ON THE YEARS OF EXPERIENCE THE TEACHERS POSSESSED IN FISCAL YEAR 2010-2011 WITHOUT NEGATIVE IMPACT TO THEIR EXPERIENCE CREDIT; TO PROVIDE VOTING AND NOTICE REQUIREMENTS FOR THIS DECISION; TO REQUIRE THAT PAYMENT ACCORDING TO THE 2010-2011 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 2010-2011; TO REQUIRE A LOCAL SCHOOL DISTRICT TO PAY TEACHERS AND SCHOOL ADMINISTRATORS FOR CHANGES IN THEIR EDUCATION LEVELS; AND TO DEFINE CERTAIN TERMS. Read the first time and referred to the Committee on Finance. H. 3711 (Word version) -- Reps. Sandifer, Hayes and D. C. Moss: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING SECTION 39-61-210 SO AS TO PROVIDE THAT AN ENTITY THAT CONTRACTS WITH AN AUTOMOBILE CLUB LICENSED UNDER THE MOTOR CLUB SERVICES ACT FOR THE PROVISIONS OF EMERGENCY ROAD SERVICE AND TOWING SERVICE TO THE ENTITY'S CUSTOMERS IS EXEMPT FROM ALL REQUIREMENTS OF THE MOTOR CLUB SERVICES ACT. Read the first time and referred to the Committee on Judiciary. H. 3914 (Word version) -- Rep. Herbkersman: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING ARTICLE 20 TO CHAPTER 23, TITLE 57 SO AS TO DESIGNATE CERTAIN HIGHWAYS IN BEAUFORT COUNTY AS SCENIC HIGHWAYS AND SCENIC BYWAYS; AND TO REPEAL ACT 714 OF 1978 WHICH DESIGNATED CERTAIN PORTIONS OF HIGHWAYS IN BEAUFORT COUNTY AS SCENIC HIGHWAYS. Read the first time and referred to the Committee on Transportation. H. 3923 (Word version) -- Rep. Parker: A BILL TO AMEND SECTION 7-7-490, AS AMENDED, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE DESIGNATION OF VOTING PRECINCTS IN SPARTANBURG COUNTY, SO AS TO RENAME THE INMAN MILLS BAPTIST VOTING PRECINCT THE GREATER ST. JAMES VOTING PRECINCT AND REDESIGNATE A MAP NUMBER FOR THE MAP ON WHICH LINES OF THESE PRECINCTS ARE DELINEATED AND MAINTAINED BY THE OFFICE OF RESEARCH AND STATISTICS OF THE STATE BUDGET AND CONTROL BOARD. Read the first time and referred to the Committee on Judiciary. H. 3947 (Word version) -- Reps. Rutherford and Bales: A BILL TO AMEND SECTION 55-11-320, AS AMENDED, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE CREATION OF THE RICHLAND-LEXINGTON AIRPORT COMMISSION, SO AS TO REVISE THE PROCEDURE TO APPOINT THE MEMBERS SELECTED BY THE RICHLAND COUNTY LEGISLATIVE DELEGATION. Read the first time and referred to the Committee on Transportation. H. 3957 (Word version) -- Reps. Harrison, Bales, McLeod and Funderburk: A BILL TO DESIGNATE SECTION 3 OF ACT 292 OF 1985, RELATING TO THE RICHLAND-LEXINGTON COUNTY AIRPORT COMMISSION'S AUTHORITY TO MAKE APPLICATION TO THE FOREIGN-TRADE ZONES BOARD FOR THE PURPOSE OF ESTABLISHING, OPERATING, AND MAINTAINING FOREIGN-TRADE ZONES AS SECTION 55-11-430 OF THE 1976 CODE; AND TO AMEND SECTION 55-11-430, RELATING TO THE RICHLAND-LEXINGTON COUNTY AIRPORT COMMISSION'S AUTHORITY TO MAKE APPLICATION TO THE FOREIGN-TRADE ZONES BOARD FOR THE PURPOSE OF ESTABLISHING, OPERATING, AND MAINTAINING FOREIGN-TRADE ZONES, SO AS TO EXPAND THE AREA WITHIN THE STATE IN WHICH THE COMMISSION MAY ESTABLISH FOREIGN-TRADE ZONES. Read the first time and referred to the Committee on Transportation. H. 3978 (Word version) -- Rep. Barfield: A CONCURRENT RESOLUTION TO REQUEST THAT THE DEPARTMENT OF TRANSPORTATION NAME THE BRIDGE ALONG VALLEY FORGE ROAD IN HORRY COUNTY LOCATED BETWEEN ITS INTERSECTION WITH SOUTH CAROLINA HIGHWAY 410 AND LOUISVILLE ROAD "ELISHA TYLER MEMORIAL BRIDGE" AND ERECT APPROPRIATE MARKERS OR SIGNS AT THIS BRIDGE THAT CONTAIN THE WORDS "ELISHA TYLER MEMORIAL BRIDGE". The Concurrent Resolution was introduced and referred to the Committee on Transportation. H. 3984 (Word version) -- Reps. Howard, Agnew, Alexander, Allen, Allison, Anderson, Anthony, Atwater, Bales, Ballentine, Bannister, Barfield, Battle, Bedingfield, Bikas, Bingham, Bowen, Bowers, Brady, Branham, Brannon, Brantley, G. A. Brown, H. B. Brown, R. L. Brown, Butler Garrick, Chumley, Clemmons, Clyburn, Cobb-Hunter, Cole, Cooper, Corbin, Crawford, Crosby, Daning, Delleney, Dillard, Edge, Erickson, Forrester, Frye, Funderburk, Gambrell, Gilliard, Govan, Hamilton, Hardwick, Harrell, Harrison, Hart, Hayes, Hearn, Henderson, Herbkersman, Hiott, Hixon, Hodges, Horne, Hosey, Huggins, Jefferson, King, Knight, Limehouse, Loftis, Long, Lowe, Lucas, Mack, McCoy, McEachern, McLeod, Merrill, Mitchell, D. C. Moss, V. S. Moss, Munnerlyn, Murphy, Nanney, J. H. Neal, J. M. Neal, Neilson, Norman, Ott, Owens, Parker, Parks, Patrick, Pinson, Pitts, Pope, Quinn, Rutherford, Ryan, Sabb, Sandifer, Sellers, Simrill, Skelton, G. M. Smith, G. R. Smith, J. E. Smith, J. R. Smith, Sottile, Spires, Stavrinakis, Stringer, Tallon, Taylor, Thayer, Toole, Tribble, Umphlett, Vick, Viers, Weeks, Whipper, White, Whitmire, Williams, Willis and Young: A CONCURRENT RESOLUTION TO COMMEND THE BOYS & GIRLS CLUBS OF SOUTH CAROLINA FOR THEIR WONDERFUL EFFORTS IN HELPING SOUTH CAROLINA'S YOUTH PREPARE FOR A PRODUCTIVE LIFE, TO RECOGNIZE THE TWELVE YOUNG PEOPLE FROM DIFFERENT BOYS & GIRLS CLUBS THROUGHOUT THE STATE WHO HAVE BEEN NAMED 2011 YOUTH OF THE YEAR BY THE SOUTH CAROLINA ALLIANCE OF BOYS & GIRLS CLUBS, AND TO DECLARE THURSDAY, APRIL 14, 2011, AS "BOYS AND GIRLS CLUBS DAY" AT THE STATE HOUSE. The Concurrent Resolution was introduced and referred to the General Committee. H. 4002 (Word version) -- Reps. Alexander, Brantley, J. E. Smith, Spires, Knight, Brannon, Corbin, Ott, King, McLeod, Parker, Bales, Jefferson, McEachern, Ballentine, Branham, Cobb-Hunter, Crosby, Dillard, Hardwick, Hearn, Herbkersman, Long, J. M. Neal, Pope, G. M. Smith and G. R. Smith: A CONCURRENT RESOLUTION TO RECOGNIZE THAT ABUSE AND NEGLECT OF CHILDREN IS A SIGNIFICANT PROBLEM, AND TO DECLARE APRIL AS CHILD ABUSE PREVENTION MONTH IN SOUTH CAROLINA. The Concurrent Resolution was adopted, ordered returned to the House. H. 4004 (Word version) -- Reps. Owens, Bikas, Hiott and Skelton: A CONCURRENT RESOLUTION TO RECOGNIZE AND HONOR THE EASLEY COMBINED UTILITIES, AND TO CONGRATULATE THE ORGANIZATION, UPON THE OCCASION OF ITS CENTENNIAL ANNIVERSARY, FOR ITS DEDICATION IN PROVIDING SERVICES TO THE COMMUNITY OF EASLEY. The Concurrent Resolution was adopted, ordered returned to the House. REPORTS OF STANDING COMMITTEES Senator LEATHERMAN from the Committee on Finance submitted a favorable with amendment report on: S. 312 (Word version) -- Senators Davis, McConnell, Peeler, Bright, Massey, Shoopman, S. Martin, Ryberg, Verdin and Rose: A BILL TO AMEND SECTION 2-65-15, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO DEFINITIONS FOR PURPOSES OF THE SOUTH CAROLINA FEDERAL AND OTHER FUNDS OVERSIGHT ACT, SO AS TO REVISE THE DEFINITION OF "MATCHING FUNDS" TO INCLUDE BOTH GENERAL FUND MONIES AND OTHER FUND MONIES TO BE USED TO MEET FEDERAL MATCH REQUIREMENTS; TO AMEND SECTION 2-65-20, RELATING TO THE APPROPRIATION OF ANTICIPATED FEDERAL FUNDS AND OTHER FUNDS BY THE GENERAL ASSEMBLY IN APPROPRIATIONS ACTS, SO AS TO REQUIRE STATE AGENCIES RECEIVING FEDERAL FUNDS TO PROVIDE IN BUDGET SUBMISSIONS FOR THE PROPOSED BUDGET DETAILS OF CONDITIONS IMPOSED ON THE STATE APPLICABLE TO FEDERAL FUNDS INCLUDED IN THE AGENCY'S BUDGET SUBMISSION, REQUIRE THE RECOMMENDED BUDGET SPECIFICALLY TO ACCEPT IN DETAIL THOSE CONDITIONS WHEN FEDERAL FUNDS ARE INCLUDED IN THE PROPOSED BUDGET, AND TO CONFORM THE SECTION TO REFLECT THE PROVISION OF LAW ASSIGNING TO THE GOVERNOR THE DUTY OF PRODUCING A PROPOSED BUDGET TO THE GENERAL ASSEMBLY; AND TO AMEND SECTION 2-65-30, RELATING TO EXPENDITURE BY A STATE AGENCY OF UNANTICIPATED FEDERAL FUNDS AND PRIVATE GRANT FUNDS NOT APPROPRIATED IN APPROPRIATIONS ACTS, SO AS TO REQUIRE THE AGENCY'S SUBMISSION OF AN EXPENDITURE PROPOSAL FOR THE ANTICIPATED FUNDS TO THE STATE BUDGET AND CONTROL BOARD TO INCLUDE THE CONDITIONS IMPOSED ON THE STATE'S RECEIPT AND EXPENDITURE OF THE FEDERAL FUNDS AND, IN AUTHORIZING THE RECEIPT AND EXPENDITURE, THE BOARD'S ACCEPTANCE OF THE CONDITIONS. Ordered for consideration tomorrow. Appointments Reported Senator PEELER from the Committee on Medical Affairs submitted a favorable report on: Statewide Appointments Initial Appointment, Board of the South Carolina Department of Health and Environmental Control, with the term to commence June 30, 2009, and to expire June 30, 2013 At-Large: Allen Amsler, 118 Harbra Court, Lexington, SC 29072 VICE Paul C. Aughtry III Initial Appointment, Board of the South Carolina Department of Health and Environmental Control, with the term to commence June 30, 2009, and to expire June 30, 2013 4th Congressional District: L. Clarence Batts, Jr., 105 Rockport Way, Pacolet, SC 29372 VICE Dr. M. David Mitchell Initial Appointment, Board of the South Carolina Department of Health and Environmental Control, with the term to commence June 30, 2007, and to expire June 30, 2011 6th Congressional District: John O. Hutto, Sr., 1025 Moss Street, Orangeburg, SC 29115 VICE Dr. Coleman Buckhouse Reappointment, Board of the South Carolina Department of Health and Environmental Control, with the term to commence June 30, 2011, and to expire June 30, 2015 6th Congressional District: John O. Hutto, Sr., 1025 Moss Street, Orangeburg, SC 29115 Initial Appointment, Board of the South Carolina Department of Health and Environmental Control, with the term to commence June 30, 2009, and to expire June 30, 2013 5th Congressional District: Ann B. Kirol, 1265 Rittenhouse Lane, Rock Hill, SC 29732 VICE Glenn McCall Initial Appointment, Board of the South Carolina Department of Health and Environmental Control, with the term to commence June 30, 2007, and to expire June 30, 2011 1st Congressional District: Mark Lutz, 60 On the Harbor Drive, Mt. Pleasant, SC 29464 VICE Edwin Cooper III (resigned) Reappointment, Board of the South Carolina Department of Health and Environmental Control, with the term to commence June 30, 2011, and to expire June 30, 2015 1st Congressional District: Mark Lutz, 60 On the Harbor Drive, Mt. Pleasant, SC 29464 Initial Appointment, Board of the South Carolina Department of Health and Environmental Control, with the term to commence June 30, 2009, and to expire June 30, 2013 2nd Congressional District: Robert Kenyon Wells, 120 Morning Shore Court, Lexington, SC 29072 VICE Henry Scott HOUSE CONCURRENCES S. 754 (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, Nicholson, O'Dell, Peeler, Pinckney, Rankin, Reese, Rose, Ryberg, Setzler, Sheheen, Shoopman, Thomas, Verdin and Williams: A CONCURRENT RESOLUTION TO RECOGNIZE AND HONOR MAJOR GENERAL OSBORNE EUGENE POWELL, JR. AND TO COMMEND HIM FOR HIS OUTSTANDING SERVICE, HIS TIRELESS EFFORTS, AND HIS SELFLESS COMMITMENT OF TIME AND RESOURCES FOR THE GREAT BENEFIT OF THE SOUTH CAROLINA MILITARY DEPARTMENT. Returned with concurrence. S. 755 (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, Nicholson, O'Dell, Peeler, Pinckney, Rankin, Reese, Rose, Ryberg, Setzler, Sheheen, Shoopman, Thomas, Verdin and Williams: A CONCURRENT RESOLUTION TO RECOGNIZE AND HONOR JOHN A. SHULER, DEPUTY ADJUTANT GENERAL FOR STATE OPERATIONS OF THE OFFICE OF THE ADJUTANT GENERAL, AND TO CONGRATULATE HIM, UPON THE OCCASION OF HIS RETIREMENT FROM THE MILITARY DEPARTMENT OF SOUTH CAROLINA. Returned with concurrence. Message from the House Columbia, S.C., March 31, 2011 Mr. President and Senators: The House respectfully informs your Honorable Body that it concurs in the amendments proposed by the Senate to: H. 3625 (Word version) -- Reps. J.R. Smith, Hixon and Taylor: A BILL TO AMEND SECTION 8-13-735, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO PROHIBITION AGAINST A PERSON, WHO AT THE SAME TIME SERVES ON THE GOVERNING BODY OF A STATE OR LOCAL POLITICAL SUBDIVISION BOARD OR COMMISSION AND AS AN EMPLOYEE OF THE SAME BOARD OR COMMISSION OR IN A POSITION WHICH IS SUBJECT TO THE CONTROL OF THE BOARD OR COMMISSION, MAKING OR PARTICIPATING IN A DECISION AFFECTING HIS ECONOMIC INTERESTS, SO AS TO PROHIBIT A PERSON FROM SERVING IN BOTH POSITIONS AT THE SAME TIME. and has ordered the Bill enrolled for Ratification. Very respectfully, Speaker of the House Message from the House Columbia, S.C., March 31, 2011 Mr. President and Senators: The House respectfully informs your Honorable Body that it concurs in the amendments proposed by the Senate to: H. 3004 (Word version) -- Reps. Ballentine, Norman, Viers, Lucas, Simrill, Huggins, G.M. Smith, G.R. Smith, Loftis, Bedingfield, Hamilton, Stringer, Nanney, Lowe, Young, Willis, Bowen, D.C. Moss, Agnew, Pope, Daning, Thayer, Harrison, Allison, Taylor, Ryan, McCoy, Hixon, Bingham, Long, Whipper, R.L. Brown, Atwater, Henderson, Horne and Harrell: A BILL TO ENACT THE "SPENDING ACCOUNTABILITY ACT OF 2011"; AND TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING SECTION 2-7-125 SO AS TO REQUIRE CERTAIN BILLS AND JOINT RESOLUTIONS TO RECEIVE A RECORDED ROLL CALL VOTE AT VARIOUS STAGES OF THEIR PASSAGE BY THE HOUSE OF REPRESENTATIVES AND THE SENATE. and has ordered the Bill enrolled for Ratification. Very respectfully, Speaker of the House THE SENATE PROCEEDED TO A CALL OF THE UNCONTESTED LOCAL AND STATEWIDE CALENDAR. ORDERED ENROLLED FOR RATIFICATION The following Bill was read the third time and, having received three readings in both Houses, it was ordered that the title be changed to that of an Act and enrolled for Ratification: H. 3399 (Word version) -- Reps. Rutherford and Owens: A BILL TO AMEND JOINT RESOLUTION 263 OF 1998 RELATING TO THE GRANTING OF CONCURRENT FEDERAL LAW ENFORCEMENT JURISDICTION OVER THE NATIONAL ADVOCACY CENTER LOCATED ON THE COLUMBIA CAMPUS OF THE UNIVERSITY OF SOUTH CAROLINA IN RICHLAND COUNTY, SO AS TO EXTEND THAT CONCURRENT FEDERAL JURISDICTION TO ADJACENT FEDERALLY OCCUPIED PROPERTY AND TO THE INN AT USC AND THE KIRKLAND APARTMENT BUILDING LOCATED RESPECTIVELY AT 1619 PENDLETON STREET AND 1611 PENDLETON STREET IN THE CITY OF COLUMBIA, SOUTH CAROLINA AND TO DESIGNATE THE TEXT OF JOINT RESOLUTION 263 OF 1998, AS AMENDED BY THIS ACT, AS SECTION 3-3-350 OF THE CODE OF LAWS OF SOUTH CAROLINA, 1976. The following Bills were read the third time and ordered sent to the House of Representatives: S. 568 (Word version) -- Senators L. Martin and Ford: A BILL TO AMEND SECTION 16-3-740, AS AMENDED, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO TESTING OF CERTAIN OFFENDERS FOR HEPATITIS B AND HUMAN IMMUNODEFICIENCY VIRUS (HIV), SO AS TO FURTHER CLARIFY OFFENDERS WHO MUST BE TESTED AND THE TIME FRAME THAT TESTING MUST BE CONDUCTED AND PROVIDE FOR FOLLOW-UP TESTING FOR HIV WHEN MEDICALLY APPROPRIATE. S. 721 (Word version) -- Senator Massey: A BILL TO AMEND ACT 955 OF 1974, AS AMENDED, RELATING TO THE COMPENSATION OF THE EDGEFIELD COUNTY DISTRICT SCHOOL BOARD OF TRUSTEES, TO PROVIDE THAT THE TRUSTEES SHALL RECEIVE COMPENSATION AGREED UPON BY THE BOARD. On motion of Senator MASSEY S. 53 (Word version) -- Senators L. Martin, Leventis and Ford: A BILL TO AMEND CHAPTER 3, TITLE 16 OF THE 1976 CODE, BY ADDING ARTICLE 19 TO ESTABLISH A PROCEDURE FOR THE ISSUANCE OF PERMANENT AND EMERGENCY CIVIL NO-CONTACT ORDERS UNDER CERTAIN CIRCUMSTANCES, TO PROVIDE FOR THE DURATION OF CIVIL NO-CONTACT ORDERS, TO PROVIDE NECESSARY DEFINITIONS, TO PROVIDE A PENALTY FOR THE VIOLATION OF CIVIL NO-CONTACT ORDERS. The Senate proceeded to a consideration of the Bill, the question being the second reading of the Bill. The "ayes" and "nays" were demanded and taken, resulting as follows: Ayes 43; Nays 0 AYES Alexander Anderson Bright Bryant Campbell Campsen 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 Nicholson O'Dell Peeler Pinckney Reese Rose Ryberg Scott Setzler Sheheen Shoopman Thomas Verdin Williams Total--43 NAYS Total--0 The Bill was read the second time, passed and ordered to a third reading. S. 692 (Word version) -- Senators Jackson, Courson, Scott and Lourie: A BILL TO AMEND SECTION 7-27-405, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE RICHLAND COUNTY ELECTION COMMISSION AND THE RICHLAND COUNTY BOARD OF REGISTRATION, SO AS TO COMBINE THE RICHLAND COUNTY ELECTION COMMISSION AND THE RICHLAND COUNTY BOARD OF REGISTRATION INTO A SINGLE ENTITY. The Senate proceeded to a consideration of the Bill, the question being the second reading of the Bill. The "ayes" and "nays" were demanded and taken, resulting as follows: Ayes 6; Nays 0; Present 35 AYES Courson Jackson Land Leventis Lourie Scott Total--6 NAYS Total--0 PRESENT Alexander   Anderson   Bright Bryant   Campbell   Campsen Cromer   Davis   Elliott Fair   Grooms   Hayes Hutto   Knotts   Leatherman Malloy   Martin, Larry   Martin, Shane Massey   Matthews   McConnell McGill   Nicholson   O'Dell Peeler   Pinckney   Reese Rose   Ryberg   Setzler Sheheen   Shoopman   Thomas Verdin   Williams Total--35 The Bill was read the second time, passed and ordered to a third reading. Senator LEVENTIS, with unanimous consent, spoke on the Bill. S. 211 (Word version) -- Senators Matthews, Land, Leatherman, Leventis, Hutto and Williams: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING CHAPTER 54 TO TITLE 11 SO AS TO ESTABLISH THE "I-95 CORRIDOR AUTHORITY ACT" AND TO PROVIDE FOR THE COMPOSITION, DUTIES, AND POWERS OF THE AUTHORITY. The Senate proceeded to a consideration of the Bill, the question being the second reading of the Bill. Senator MATTHEWS proposed the following amendment (DKA\3558SD11), which was adopted: Amend the bill, as and if amended, Section 11-54-25(A), SECTION 1, by adding a new item to be appropriately numbered immediately after item (9), page 3, to read: / ( ) the President of Claflin University, or his designee; and / Renumber sections to conform. Amend title to conform. Senator MATTHEWS 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 35; Nays 6 AYES Alexander Anderson Campbell Courson Elliott Fair Ford Grooms Hayes Hutto Knotts Land Leatherman Leventis Lourie Malloy Martin, Larry Massey Matthews McConnell McGill Nicholson O'Dell Peeler Pinckney Reese Rose Ryberg Scott Setzler Sheheen Shoopman Thomas Verdin Williams Total--35 NAYS Bright Bryant Campsen Cromer Davis Martin, Shane Total--6 There being no further amendments, the Bill was read the second time, passed and ordered to a third reading. S. 435 (Word version) -- Senators Elliott, Bryant, Ford and Campsen: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING SECTION 6-1-180 SO AS TO REQUIRE LOCAL GOVERNMENTAL ENTITIES, AGENCIES, ORGANIZATIONS, OR INDIVIDUALS THAT RECEIVE, COLLECT, OR SPEND PUBLIC FUNDS DERIVED FROM STATE OR LOCAL TAX REVENUE TO FILE PERIODIC EXPENDITURE REPORTS WITH THE STATE OR LOCAL GOVERNMENTAL ENTITY OR AGENCY THAT PROVIDED, COLLECTED, OR SPENT THE PUBLIC FUNDS. The Senate proceeded to a consideration of the Bill, the question being the adoption of the amendment proposed by the Committee on Finance. The Committee on Finance proposed the following amendment (NBD\11531DG11), which was adopted: Amend the bill, as and if amended, by striking all after the enacting words and inserting: / SECTION   1.   Article 15, Chapter 1, Title 1 of the 1976 Code is amended by adding: "Section 1-1-1050.   (A)   By no later than July 1, 2012, a non-governmental entity, agency, or organization, whether for or not-for-profit, that received more than one hundred dollars in county or municipal grants in the previous calendar year, must begin quarterly submissions of an expenditure report to the jurisdiction awarding the funds. For purposes of this section, 'grants' are those monies derived either from county or municipal tax revenue or appropriated to the jurisdiction by the General Assembly that are awarded, gifted, designated, or contributed by a jurisdiction to an entity, agency, or organization, whether by formula or at the jurisdiction's discretion for any purpose, including revenues distributed pursuant to Section 4-10-970(B). 'Grants' do not include payments for direct services or goods. (B)   The expenditure report must include: (1)   the amount of funds received, (2)   the amount of funds expended, (3)   the purposes for which the funds were expended, and (4)   any other information required by the jurisdiction so as to promote transparency and public confidence in how the grantee entities, agencies, and organizations expend the funds. (C)   Unless all or portions of the report may be redacted or exempted pursuant to subsection (D), a county and municipality receiving expenditure reports required by this section shall prominently display the reports on the jurisdiction's Internet website. The reports must be downloadable and maintained for three years. If a jurisdiction does not maintain an Internet website, the register must be maintained on the Internet website of the Comptroller General. Also, a jurisdiction shall display the name and amount of funds awarded to any entity, agency, or organization that has failed to timely submit an expenditure report. (D)   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. A county or municipality may also exempt disclosure of any expenditure or reimbursement that the jurisdiction determines is reasonable and necessary to exclude. If a jurisdiction excludes an expenditure or reimbursement, the jurisdiction must, in general terms, state the reasons for the exclusion. The statement shall be displayed in the same manner and location as the expenditure report. (E)   To avoid additional expense for county and municipal governments in the implementation of this section, the expenditure reporting must be effected using existing resources with no additional expense to the jurisdiction. The Office of the Comptroller General must be available to county and municipal governments, upon their formal request, to provide technical assistance in meeting the requirements of this section. The Office of the Comptroller General shall not intercede on behalf of jurisdictions unless a formal request is made." SECTION   2.   This act takes effect upon approval by the Governor.   / Renumber sections to conform. Amend title to conform. Senator O'DELL explained the committee amendment. The question then was second reading of the Bill. The "ayes" and "nays" were demanded and taken, resulting as follows: Ayes 39; Nays 0 AYES Alexander Anderson Bright Bryant Campbell Campsen Courson Cromer Davis Elliott Fair Ford Hayes Hutto Knotts Land Leatherman Leventis Lourie Malloy Martin, Larry Martin, Shane Massey McConnell McGill Nicholson O'Dell Peeler Pinckney Reese Rose Ryberg Scott Setzler Sheheen Shoopman Thomas Verdin Williams Total--39 NAYS Total--0 There being no further amendments, the Bill was read the second time, passed and ordered to a third reading. H. 3287 (Word version) -- Reps. Hardwick and Hodges: A BILL TO AMEND SECTION 50-21-190, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE ABANDONMENT OF WATERCRAFT AND OUTBOARD MOTORS, SO AS TO PROVIDE THAT AN ABANDONED WATERCRAFT MAY BE REMOVED AND DISPOSED OF BY ANY GOVERNMENT AGENCY THAT HAS JURISDICTION OVER THE AREA WHERE THE ABANDONED WATERCRAFT IS LOCATED, AND TO PROVIDE THAT A WATERCRAFT ABANDONED FOR AT LEAST NINETY DAYS MAY BE CLAIMED BY ANY PERSON OR ENTITY AS ABANDONED PROPERTY. Having voted on the prevailing side, Senator CROMER moved to reconsider the vote whereby the Bill failed to receive a second reading on March 30, 2011. The motion to reconsider was adopted. The Bill was returned to the Statewide Second Reading Calendar for consideration. S. 748 (Word version) -- Judiciary Committee: A CONCURRENT RESOLUTION TO APPROVE THE AMENDMENTS TO THE RULES OF PROCEDURE OF THE SOUTH CAROLINA ADMINISTRATIVE LAW COURT, AS PROMULGATED BY THE ADMINISTRATIVE LAW COURT AND SUBMITTED TO THE GENERAL ASSEMBLY PURSUANT TO THE PROVISIONS OF SECTION 1-23-650 OF THE 1976 CODE AND SECTION 4A, ARTICLE V OF THE CONSTITUTION OF THIS STATE. The Senate proceeded to a consideration of the Concurrent Resolution, the question being adoption of the Concurrent Resolution. The "ayes" and "nays" were demanded and taken, resulting as follows: Ayes 40; Nays 0 AYES Alexander Anderson Bright Bryant Campbell Campsen Courson Cromer Davis Elliott Fair Ford Hayes Hutto Jackson Knotts Land Leatherman Leventis Lourie Malloy Martin, Larry Martin, Shane Massey Matthews McConnell McGill Nicholson O'Dell Peeler Reese Rose Ryberg Scott Setzler Sheheen Shoopman Thomas Verdin Williams Total--40 NAYS Total--0 The Concurrent Resolution was adopted, ordered sent to the House. S. 749 (Word version) -- Judiciary Committee: A CONCURRENT RESOLUTION TO APPROVE THE AMENDMENTS TO RULE 219 OF THE SOUTH CAROLINA APPELLATE COURT RULES, AS PROMULGATED BY THE SOUTH CAROLINA SUPREME COURT AND SUBMITTED TO THE GENERAL ASSEMBLY PURSUANT TO THE PROVISIONS OF SECTION 4A, ARTICLE V OF THE CONSTITUTION OF THIS STATE. The Senate proceeded to a consideration of the Concurrent Resolution, the question being adoption of the Concurrent Resolution. The "ayes" and "nays" were demanded and taken, resulting as follows: Ayes 40; Nays 0 AYES Alexander Anderson Bright Bryant Campbell Campsen Courson Cromer Davis Elliott Fair Ford Hayes Hutto Jackson Knotts Land Leatherman Leventis Lourie Malloy Martin, Larry Martin, Shane Massey Matthews McConnell McGill Nicholson O'Dell Peeler Reese Rose Ryberg Scott Setzler Sheheen Shoopman   Thomas   Verdin Williams Total--40 NAYS Total--0 The Concurrent Resolution was adopted, ordered sent to the House. CARRIED OVER S. 30 (Word version) -- Senators McConnell, Leventis and Ford: A BILL TO AMEND SECTION 22-5-110, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATED TO MAGISTRATES' POWERS AND DUTIES REGARDING THE ISSUANCE OF ARREST WARRANTS AND COURTESY SUMMONS, SO AS TO PROVIDE THAT NO ARREST WARRANT SHALL BE ISSUED FOR THE ARREST OF A PERSON UNLESS SOUGHT BY A MEMBER OF A LAW ENFORCEMENT AGENCY ACTING IN THEIR OFFICIAL CAPACITY; AND TO PROVIDE THAT IF AN ARREST WARRANT IS SOUGHT BY SOMEONE OTHER THAN A LAW ENFORCEMENT OFFICER, THE COURT MUST ISSUE A COURTESY SUMMONS, EXCEPT WHEN A BUSINESS IS SEEKING AN ARREST WARRANT FOR ANY OFFENSE AGAINST THE BUSINESS OR A PERSON IS SEEKING AN ARREST WARRANT FOR A FRAUDULENT CHECK, IF THE FRAUDULENT CHECK IS PRESENTED TO THE MAGISTRATE AT THE TIME THE WARRANT IS SOUGHT. The Senate proceeded to a consideration of the Bill, the question being the adoption of the amendment proposed by the Committee on Judiciary. The Committee on Judiciary proposed the following amendment (JUD0030.001), which was adopted: Amend the bill, as and if amended, page 2, by striking lines 9-25, and inserting: /     (B)(1)   No arrest warrant shall be issued by a magistrate unless sought by: (a)   a law enforcement officer acting in the officer's official capacity; (b)   a business seeking an arrest warrant for an offense against the business; (c)   a person seeking an arrest warrant for a fraudulent check, if the fraudulent check or a legal copy of the fraudulent check is presented to the magistrate at the time the warrant is sought; or (d)   a person seeking an arrest warrant for offenses involving criminal domestic violence, harassment, assault and battery in the second degree, or assault and battery in the third degree. (2)   If an arrest warrant is sought by a person other than a person listed in subitem (B)(1), the court must issue a courtesy summons. If, after being served the summons, a defendant named in the summons fails to appear before the court pursuant to the summons, the court may issue an arrest warrant for the underlying offense based upon the original sworn statement of the person who sought the summons, provided the sworn statement establishes probable cause that the underlying offense was committed."     / Renumber sections to conform. Amend title to conform. Senator LARRY MARTIN explained the committee amendment. The question then was second reading of the Bill. On motion of Senator SETZLER, the Bill was carried over, as amended. AMENDED, CARRIED OVER S. 473 (Word version) -- Senators Lourie, Setzler and Ford: A BILL TO AMEND CHAPTER 102, TITLE 59, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO ATHLETE AGENTS AND STUDENT AGENTS, SO AS TO REVISE DEFINITIONS, TO INCLUDE DEFINITIONS FOR "ADMINISTRATOR", "DEPARTMENT", AND "FINANCIAL SERVICES CONTRACT", TO REVISE THE POWERS OF THE DEPARTMENT OF CONSUMER AFFAIRS WITH RESPECT TO ATHLETE AGENTS AND STUDENT ATHLETES, TO PROVIDE FOR INSPECTION OF OUT-OF-STATE RECORDS, TO REQUIRE AN APPLICANT TO UNDERGO A NATIONAL AND STATE CRIMINAL HISTORY RECORDS CHECK AND TO PROVIDE FINGERPRINTS, TO PROVIDE FOR REPORTING AND MAINTENANCE OF CRIMINAL HISTORY RECORDS CHECK RESULTS, TO REVISE CONSIDERATIONS THE DEPARTMENT MAY MAKE WHEN ISSUING A CERTIFICATE OF REGISTRATION, TO REVISE THE TIME IN WHICH A CERTIFICATE OF REGISTRATION IS VALID AND TO PROVIDE THAT THE CERTIFICATE IS NONTRANSFERABLE AND NONASSIGNABLE, TO PROVIDE THAT IF A PERSON AGGRIEVED BY DEPARTMENT ACTION FAILS TO REQUEST A CONTESTED CASE THE ADMINISTRATIVE ACTION IS FINAL, TO PROVIDE THAT FUNDS COLLECTED BY THE DEPARTMENT MUST BE USED TO IMPLEMENT THE PROVISIONS OF THIS CHAPTER, TO REQUIRE THAT THE ADDRESS OF THE ATHLETE AGENT BE INCLUDED IN AN AGENCY CONTRACT, TO REVISE WHAT THE CONTRACT MUST CONTAIN, TO PROVIDE ADDITIONAL PROHIBITED ACTS OF ATHLETE AGENTS, TO ALLOW THE DEPARTMENT TO ISSUE A CEASE AND DESIST ORDER AND IMPOSE A PENALTY UPON FINDING OF MISCONDUCT, TO PROVIDE REPORTING REQUIREMENTS FOR EDUCATIONAL INSTITUTIONS, AND TO PROVIDE THAT THE DEPARTMENT MAY PROMULGATE REGULATIONS NECESSARY TO EFFECTUATE THE PROVISIONS OF THIS CHAPTER. The Senate proceeded to a consideration of the Bill, the question being the second reading of the Bill. Senator LOURIE proposed the following amendment (473R002.JL), which was adopted: Amend the bill, as and if amended, page 11, by striking lines 39-41. Renumber sections to conform. Amend title to conform. Senator LOURIE explained the amendment. On motion of Senator LOURIE, the Bill was carried over, as amended. CARRIED OVER S. 225 (Word version) -- Senators Knotts, Ford and Alexander: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING SECTION 56-5-3890 SO AS TO PROVIDE THAT IT IS UNLAWFUL FOR CERTAIN PERSONS WHO ARE OPERATING A MOTOR VEHICLE TO USE A WIRELESS ELECTRONIC COMMUNICATION DEVICE TO COMPOSE, SEND, OR READ A TEXT-BASED COMMUNICATION AND TO PROVIDE PENALTIES FOR VIOLATING THIS PROVISION; AND TO AMEND SECTION 56-1-720, RELATING TO THE ASSESSMENT OF POINTS AGAINST A PERSON'S DRIVING RECORD FOR CERTAIN MOTOR VEHICLE VIOLATIONS, SO AS TO PROVIDE THAT ONE POINT MUST BE ASSESSED AGAINST THE DRIVING RECORD OF A PERSON CONVICTED OF USING A WIRELESS ELECTRONIC COMMUNICATION DEVICE TO COMPOSE, SEND, OR READ A TEXT-BASED COMMUNICATION WHILE OPERATING A MOTOR VEHICLE. On motion of Senator LARRY MARTIN, the Bill was carried over. S. 385 (Word version) -- Senators Fair, Rose, Campsen and Peeler: A BILL TO AMEND CHAPTER 1, TITLE 24, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE DEPARTMENT OF CORRECTIONS, SO AS TO DEVOLVE ITS DUTIES, FUNCTIONS, AND RESPONSIBILITIES UPON THE DEPARTMENT OF INSTITUTIONAL AND COMMUNITY CORRECTIONS; AND TO AMEND CHAPTER 21, TITLE 24, RELATING TO THE DEPARTMENT OF PROBATION, PAROLE AND PARDON SERVICES, SO AS TO DEVOLVE ITS DUTIES, FUNCTIONS, AND RESPONSIBILITIES UPON THE DEPARTMENT OF INSTITUTIONAL AND COMMUNITY CORRECTIONS. On motion of Senator PINCKNEY, the Bill was carried over. S. 694 (Word version) -- Senator Bryant: A BILL TO AMEND SECTION 41-15-520 OF THE 1976 CODE, RELATING TO REMEDIES FOR EMPLOYEES CHARGING DISCRIMINATION, TO PROVIDE FOR REFERRAL TO THE UNITED STATES DEPARTMENT OF LABOR ALLEGATIONS MADE BY A PRIVATE SECTOR EMPLOYEE OF A VIOLATION OF SECTION 41-15-510 AND TO PROVIDE FOR CIVIL REMEDIES. On motion of Senators BRYANT and KNOTTS, the Bill was carried over. S. 750 (Word version) -- Judiciary Committee: A CONCURRENT RESOLUTION TO APPROVE THE AMENDMENTS TO RULE 29 OF THE SOUTH CAROLINA RULES OF CRIMINAL PROCEDURE, AS PROMULGATED BY THE SOUTH CAROLINA SUPREME COURT AND SUBMITTED TO THE GENERAL ASSEMBLY PURSUANT TO THE PROVISIONS OF SECTION 4A, ARTICLE V OF THE CONSTITUTION OF THIS STATE. On motion of Senator MALLOY, the Concurrent Resolution was carried over. S. 751 (Word version) -- Judiciary Committee: A CONCURRENT RESOLUTION TO APPROVE THE AMENDMENTS TO RULES 16, 26, 28, 33, 34, 37, AND 45 OF THE SOUTH CAROLINA RULES OF CIVIL PROCEDURE, AS PROMULGATED BY THE SOUTH CAROLINA SUPREME COURT AND SUBMITTED TO THE GENERAL ASSEMBLY PURSUANT TO THE PROVISIONS OF SECTION 4A, ARTICLE V OF THE CONSTITUTION OF THIS STATE. On motion of Senator MALLOY, the Concurrent Resolution was carried over. S. 752 (Word version) -- Judiciary Committee: A CONCURRENT RESOLUTION TO APPROVE THE AMENDMENTS TO RULE 3 OF THE SOUTH CAROLINA RULES OF CIVIL PROCEDURE, AS PROMULGATED BY THE SOUTH CAROLINA SUPREME COURT AND SUBMITTED TO THE GENERAL ASSEMBLY PURSUANT TO THE PROVISIONS OF SECTION 4A, ARTICLE V OF THE CONSTITUTION OF THIS STATE. On motion of Senator MALLOY, the Concurrent Resolution was carried over. S. 753 (Word version) -- Judiciary Committee: A CONCURRENT RESOLUTION TO APPROVE THE AMENDMENTS TO RULE 4 AND RULE 10 OF THE OFFICE OF MOTOR VEHICLE HEARINGS OF THE ADMINISTRATIVE LAW COURT, AS PROMULGATED BY THE CHIEF JUDGE OF THE ADMINISTRATIVE LAW COURT AND SUBMITTED TO THE GENERAL ASSEMBLY PURSUANT TO THE PROVISIONS OF SECTION 1-23-660 OF THE 1976 CODE AND SECTION 4A, ARTICLE V OF THE CONSTITUTION OF THIS STATE. On motion of Senator MALLOY, the Concurrent Resolution was carried over. THE CALL OF THE UNCONTESTED CALENDAR HAVING BEEN COMPLETED, THE SENATE PROCEEDED TO THE MOTION PERIOD. On motion of Senator LARRY MARTIN, the Senate agreed to dispense with the Motion Period. THE SENATE PROCEEDED TO THE SPECIAL ORDERS. READ THE THIRD TIME, SENT TO THE HOUSE S. 431 (Word version) -- Senators McConnell, Rankin, Setzler, Campbell, Shoopman, Reese, Bright, Alexander, S. Martin, Fair, Cromer, Bryant, Elliott, O'Dell, Campsen, Ford, Rose, Lourie, Cleary, Verdin, McGill, Williams, Nicholson, Knotts, Land and Scott: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING SECTION 38-61-70 SO AS TO PROVIDE THAT A LIABILITY INSURANCE POLICY ISSUED BY AN INSURER AND COVERING A CONSTRUCTION PROFESSIONAL IN THIS STATE MUST BE BROADLY CONSTRUED IN FAVOR OF COVERAGE, AND TO PROVIDE THAT WORK OF A CONSTRUCTION PROFESSIONAL RESULTING IN PROPERTY DAMAGE IN CERTAIN CIRCUMSTANCES CONSTITUTES AN OCCURRENCE AS COMMONLY DEFINED IN LIABILITY INSURANCE AND IS NOT THE INTENDED OR EXPECTED CONSEQUENCE OF THE WORK OF THE CONSTRUCTION PROFESSIONAL. The Senate proceeded to a consideration of the Bill, the question being the third reading of the Bill. Senator MASSEY spoke on the Bill. The "ayes" and "nays" were demanded and taken, resulting as follows: Ayes 39; Nays 2 AYES Alexander Anderson Bright Bryant Campbell Campsen Coleman Courson Cromer Davis Elliott Fair Ford Grooms Hayes Hutto Knotts Land Leatherman Leventis Lourie Malloy Martin, Shane Massey Matthews McConnell McGill Nicholson O'Dell Reese Rose Ryberg Scott Setzler Sheheen Shoopman Thomas Verdin Williams Total--39 NAYS Martin, Larry Peeler Total--2 The Bill was read the third time, passed and ordered sent to the House of Representatives with amendments. DEBATE INTERRUPTED H. 3375 (Word version) -- Reps. Harrell, Lucas, Cooper, Hardwick, Harrison, Owens, Sandifer, White, Bingham, Atwater, Parker, Crawford, Loftis, Bowen, G.R. Smith, Bedingfield, Toole, Sottile, V.S. Moss, Forrester, Bikas, Huggins, Brady, Allison, Pinson, Frye, Whitmire, Skelton, Nanney, Henderson, Limehouse, Corbin, Barfield, Battle, Clemmons, Cole, Crosby, Daning, Gambrell, Hamilton, Hiott, Hixon, Horne, Lowe, D.C. Moss, Murphy, Norman, Patrick, Simrill, G.M. Smith, J.R. Smith, Spires, Taylor, Willis, Young, Herbkersman, Ballentine, Thayer, Bannister, McCoy, Tallon, Stringer, Long, Hayes, Ott, J.M. Neal, Vick, G.A. Brown, Branham, Anthony, Bowers, Sellers, Quinn, Hearn, Edge, Anderson, Erickson, Knight, Chumley, Butler Garrick and Bales: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, SO AS TO ENACT THE "SOUTH CAROLINA FAIRNESS IN CIVIL JUSTICE ACT OF 2011" BY AMENDING ARTICLE 5, CHAPTER 32, TITLE 15, RELATING TO PUNITIVE DAMAGES, SO AS TO PROVIDE LIMITS ON THE AWARD OF PUNITIVE DAMAGES AND TO PROVIDE FOR CERTAIN PROCEDURES AND REQUIREMENTS RELATING TO THE AWARD OF THESE DAMAGES; BY ADDING SECTIONS 1-7-750 AND 1-7-760 SO AS TO ENACT THE "PRIVATE ATTORNEY RETENTION SUNSHINE ACT" TO GOVERN THE RETENTION OF PRIVATE ATTORNEYS BY THE ATTORNEY GENERAL OR A SOLICITOR AND TO PROVIDE TERMS AND CONDITIONS GOVERNING THE RETAINER AGREEMENT INCLUDING LIMITS ON THE COMPENSATION OF OUTSIDE COUNSEL IN CONTINGENCY FEE CASES, AND TO PROVIDE FOR THE SUSPENSION OF THE LIMITATIONS UNDER CERTAIN EXCEPTIONAL CIRCUMSTANCES; TO AMEND SECTION 15-3-670, RELATING TO LIMITATIONS ON ACTIONS BASED ON UNSAFE OR DEFECTIVE IMPROVEMENTS TO REAL PROPERTY, SO AS TO PROVIDE THAT THE VIOLATION OF A BUILDING CODE DOES NOT CONSTITUTE PER SE FRAUD, GROSS NEGLIGENCE, OR RECKLESSNESS BUT MAY BE ADMISSIBLE AS EVIDENCE; TO AMEND SECTION 18-9-130, AS AMENDED, RELATING TO THE EFFECT OF A NOTICE OF APPEAL ON THE EXECUTION OF JUDGMENT, SO AS TO PROVIDE LIMITS FOR APPEAL BONDS; AND TO AMEND SECTION 56-5-6540, AS AMENDED, RELATING TO THE PENALTIES FOR THE MANDATORY USE OF SEATBELTS, SO AS TO DELETE THE PROVISION THAT PROVIDED THAT A VIOLATION FOR FAILURE TO WEAR A SEATBELT IS NOT NEGLIGENCE PER SE OR COMPARATIVE NEGLIGENCE AND IS NOT ADMISSIBLE IN A CIVIL ACTION. The Senate proceeded to a consideration of the Bill, the question being the adoption of the amendment proposed by the Committee on Judiciary. Senator LARRY MARTIN was recognized to explain the Bill. On motion of Senator McCONNELL, with unanimous consent, the Senate agreed to go into Executive Session prior to adjournment. With Senator LARRY MARTIN retaining the floor, on motion of Senator McCONNELL, with unanimous consent, debate was interrupted by the Executive Session and then adjournment. EXECUTIVE SESSION On motion of Senator McCONNELL, the seal of secrecy was removed, so far as the same relates to appointments made by the Governor and the following names were reported to the Senate in open session: STATEWIDE APPOINTMENTS Confirmations Having received a favorable report from the Education Committee, the following appointments were confirmed in open session: Initial Appointment, South Carolina State Commission on Higher Education, with the term to commence July 1, 2010, and to expire July 1, 2012 Research Institutions: Leah B. Moody, 840 Brunswick Drive, Rock Hill, SC 29730 VICE Dr. Charles Thomas, Jr. The question was confirmation of Ms. Moody. The "ayes" and "nays" were demanded and taken, resulting as follows: Ayes 34; Nays 0 AYES Alexander Anderson Bright Bryant Campbell Campsen Coleman Courson Cromer Davis Elliott Fair Ford Hutto Jackson Knotts Malloy Martin, Larry Martin, Shane Massey Matthews McConnell McGill Nicholson Peeler Pinckney Reese Rose Ryberg Scott Setzler Shoopman Thomas Verdin Total--34 NAYS Total--0 The appointment of Ms. Moody was confirmed. Initial Appointment, South Carolina State Commission on Higher Education, with the term to commence July 1, 2010, and to expire July 1, 2012 Technical School: Charles Munns, 123 Trippi Lane, Aiken, SC 29803 VICE Mr. J. Neal Workman, Jr. The question was confirmation of Mr. Munns. The "ayes" and "nays" were demanded and taken, resulting as follows: Ayes 34; Nays 0 AYES Alexander Anderson Bright Bryant Campbell Campsen Coleman Courson Cromer Davis Elliott Fair Ford Hutto Jackson Knotts Malloy Martin, Larry Martin, Shane Massey Matthews McConnell McGill Nicholson Peeler Pinckney Reese Rose Ryberg Scott Setzler Shoopman Thomas Verdin Total--34 NAYS Total--0 The appointment of Mr. Munns was confirmed. Initial Appointment, South Carolina State Commission on Higher Education, with the term to commence July 1, 2008, and to expire July 1, 2012 At-Large: Elizabeth Jackson, 102 Tadpole Court, Lexington, SC 29072 VICE Cynthia Mosteller The question was confirmation of Ms. Jackson. The "ayes" and "nays" were demanded and taken, resulting as follows: Ayes 34; Nays 0 AYES Alexander Anderson Bright Bryant Campbell Campsen Coleman Courson Cromer Davis Elliott Fair Ford Hutto Jackson Knotts Malloy Martin, Larry Martin, Shane Massey Matthews McConnell McGill Nicholson Peeler Pinckney Reese Rose Ryberg Scott Setzler Shoopman Thomas Verdin Total--34 NAYS Total--0 The appointment of Ms. Jackson was confirmed. Initial Appointment, South Carolina State Commission on Higher Education, with the term to commence July 1, 2010, and to expire July 1, 2012 Public University Representative: Natasha M. Hanna, 874 Denali Drive, Conway, SC 29526 VICE Kenneth Jackson The question was confirmation of Ms. Hanna. The "ayes" and "nays" were demanded and taken, resulting as follows: Ayes 34; Nays 0 AYES Alexander Anderson Bright Bryant Campbell Campsen Coleman Courson Cromer Davis Elliott Fair Ford Hutto Jackson Knotts Malloy Martin, Larry Martin, Shane Massey Matthews McConnell McGill Nicholson Peeler Pinckney Reese Rose Ryberg Scott Setzler Shoopman Thomas Verdin Total--34 NAYS Total--0 The appointment of Ms. Hanna was confirmed. Initial Appointment, South Carolina State Commission on Higher Education, with the term to commence June 30, 2010, and to expire June 30, 2014 Private College Presidents: Rodney A. Smolla, 1209 Roe Ford Road, Greenville, SC 29617 VICE Dr. Mitchell Zais (resigned) The question was confirmation of Mr. Smolla. The "ayes" and "nays" were demanded and taken, resulting as follows: Ayes 34; Nays 0 AYES Alexander Anderson Bright Bryant Campbell Campsen Coleman Courson Cromer Davis Elliott Fair Ford Hutto Jackson Knotts Malloy Martin, Larry Martin, Shane Massey Matthews McConnell McGill Nicholson Peeler Pinckney Reese Rose Ryberg Scott Setzler Shoopman Thomas Verdin Total--34 NAYS Total--0 The appointment of Mr. Smolla was confirmed. LOCAL APPOINTMENTS Confirmations Having received a favorable report from the Senate, the following appointments were confirmed in open session: Reappointment, Allendale County Magistrate, with the term to commence April 30, 2010, and to expire April 30, 2014 John Alonzo Chaney, P. O. Box 1173, Fairfax, SC 29827 Reappointment, Anderson County Magistrate, with the term to commence April 30, 2011, and to expire April 30, 2015 James Tillman Busby, 1200 Good Hope Church Road, Anderson, SC 29684 Reappointment, Anderson County Magistrate, with the term to commence April 30, 2011, and to expire April 30, 2015 Sherry E. Mattison, 309 Oakwood Estates Drive, Anderson, SC 29621 Initial Appointment, Sumter County Magistrate, with the term to commence April 30, 2010, and to expire April 30, 2014 Kristi F. Curtis, 1145 Boardwalk, Sumter, SC 29150 VICE Kathy Ward (resigned) Reappointment, Darlington County Magistrate, with the term to commence April 30, 2011, and to expire April 30, 2015 James Edward Thomas, P. O. Box 1765, Hartsville, SC 29550 Initial Appointment, Savannah River Site Redevelopment Authority, with the term to commence October 21, 2010, and to expire October 21, 2014 General Public: Thomas Williams, 2686 Highway 278, Barnwell, SC 29812 VICE Robert Cooper (resigned) Reappointment, Anderson County Magistrate, with the term to commence April 30, 2011, and to expire April 30, 2015 James Albert Cox, 208 Mills Street, West Pelzer, SC 29669 On motion of Senator SHANE MARTIN, with unanimous consent, the Senate stood adjourned out of respect to the memory of Mrs. Delores Shepard Stockman of Spartanburg, S.C. Mrs. Stockman was a loving wife to Leon Edwin Stockman and was married to him for 52 years before he preceded her in death. She was a devoted mother and grandmother. She was very active in the Hayne Baptist Church (now United Baptist), having served as its secretary for 25 years and as co-treasurer with her husband. and On motion of Senator LEVENTIS, with unanimous consent, the Senate stood adjourned out of respect to the memory of Gerald Johnson "Jerry" Dix, Col. USAF (Ret.), who at the age of 93, passed on Sunday, March 20th, 2011. Col. Dix was the beloved husband of Gertrude Wulf Dix and beloved father of sons, Robert W. (Helen) Geyer of Lexington and Edward H. Geyer of St. Louis, MO, and daughter, Susan Geyer Smith of Scottsdale, AZ. He was born in Sullivan, Indiana, and graduated from Purdue University, where he was light-weight boxing champion. He entered the Army Air Corps in 1940 and was credited with flying over 60 combat missions in New Guinea against the Japanese. Col. Dix was forced to abandon the USS Pecos ship that was attacked by dive-bombing aircraft. He went on to fly 70 missions in Europe, including the longest combat flight ever made by a single-engine bomber from England to Poland and back. He was shot at on several occasions, survived a bullet on D-Day, crash landed on one of his missions in Europe, and became a prisoner of war for 11 months, during which time he was taken to Aviliar Prison in Frankfort, Germany, for interrogation. He became a full Colonel at the young age of 27, was a Base Commander at Shaw Air Force Base and later served as an advisor to both the Royal Hellenic Air Force in Greece and to the Colorado Air National Guard in Denver, CO. Some of his many decorations included the Silver Star Medal, the Bronze Star Medal, Air Medal with three Oak Leaf Clusters, the Distinguished Flying Cross with three Oak Leaf Clusters and the Purple Heart. Throughout his career he considered himself a survivor, never a hero. After his retirement from the US Air Force, he returned to Sumter where he became Executive Vice President of the Greater Sumter Chamber of Commerce, served as Secretary of the Sumter County Development Board, and worked for NBSC as Sr. Vice President. He loved spending time in his wood-working shop making furniture, traveling and playing golf. He was a member of the Thalian Club, a 49-year member of the Kiwanis Club, the VFW Post #15, M.O.A.A. and the First Presbyterian Church. Col. Dix was a hero to those who knew and loved him, and he will be missed by all who were blessed to have crossed paths with him over the years. At 1:14 P.M., on motion of Senator McCONNELL, 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 Friday, November 18, 2011 at 1:43 P.M.
2016-08-30T10:52:31
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https://pdglive.lbl.gov/DataBlock.action?node=M016M&home=MXXX005
# ${{\boldsymbol f}_{{4}}{(2050)}}$ MASS INSPIRE search VALUE (MeV) EVTS DOCUMENT ID TECN  COMMENT $\bf{ 2018 \pm11}$ OUR AVERAGE  Error includes scale factor of 2.1. $1960$ $\pm15$ 2006 VES 36 ${{\mathit \pi}^{-}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit \omega}}{{\mathit \omega}}{{\mathit n}}$ $2005$ $\pm10$ 1 2005 GAMS 33 ${{\mathit \pi}^{-}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit \eta}}{{\mathit \eta}}{{\mathit n}}$ $1998$ $\pm15$ 1998 GAM4 100 ${{\mathit \pi}^{-}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit \pi}^{0}}{{\mathit \pi}^{0}}{{\mathit n}}$ $2060$ $\pm20$ 1990 GAM2 38 ${{\mathit \pi}^{-}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit \omega}}{{\mathit \omega}}{{\mathit n}}$ $2038$ $\pm30$ 1987 DM2 ${{\mathit J / \psi}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ $2086$ $\pm15$ 1987 MRK3 ${{\mathit J / \psi}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ $2000$ $\pm60$ 1986 D GAM4 100 ${{\mathit \pi}^{-}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit n}}$2 ${{\mathit \eta}}$ $2020$ $\pm20$ 40k 2 1984 B GAM2 38 ${{\mathit \pi}^{-}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit n}}$2 ${{\mathit \pi}^{0}}$ $2015$ $\pm28$ 3 1982 STRC 8 ${{\mathit \pi}^{+}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit \Delta}^{++}}{{\mathit \pi}^{0}}{{\mathit \pi}^{0}}$ $2031$ ${}^{+25}_{-36}$ 1982 B MPS 23 ${{\mathit \pi}^{-}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit n}}$2 ${{\mathit K}_S^0}$ $2020$ $\pm30$ 700 1975 NICE 40 ${{\mathit \pi}^{-}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit n}}$2 ${{\mathit \pi}^{0}}$ $2050$ $\pm25$ 1975 ASPK 18.4 ${{\mathit \pi}^{-}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit n}}{{\mathit K}^{+}}{{\mathit K}^{-}}$ • • • We do not use the following data for averages, fits, limits, etc. • • • $1966$ $\pm25$ 4 2009 RVUE 0.0 ${{\overline{\mathit p}}}{{\mathit p}}$ , ${{\mathit \pi}}{{\mathit N}}$ $1885$ ${}^{+14}_{-13}$ ${}^{+218}_{-25}$ 5 2009 BELL 10.6 ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}{{\mathit \pi}^{0}}{{\mathit \pi}^{0}}$ $2018$ $\pm6$ 2000 J SPEC 2.0 ${{\overline{\mathit p}}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit \eta}}{{\mathit \pi}^{0}}{{\mathit \pi}^{0}}$ , ${{\mathit \pi}^{0}}{{\mathit \pi}^{0}}$ , ${{\mathit \eta}}{{\mathit \eta}}$ , ${{\mathit \eta}}{{\mathit \eta}^{\,'}}$ , ${{\mathit \pi}}{{\mathit \pi}}$ $\sim$$2000 6 1998 RVUE {{\mathit N}} {{\overline{\mathit N}}} \rightarrow {{\mathit \pi}}{{\mathit \pi}} \sim$$2010$ 7 1997 RVUE ${{\overline{\mathit N}}}$ ${{\mathit N}}$ $\rightarrow$ ${{\mathit \pi}}{{\mathit \pi}}$ $\sim$$2040 8 1994 RVUE 0.36 - 1.55 {{\overline{\mathit p}}} {{\mathit p}} \rightarrow {{\mathit \pi}}{{\mathit \pi}} \sim$$1990$ 9 1994 RVUE $0.36 - 1.55$ ${{\overline{\mathit p}}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit \pi}}{{\mathit \pi}}$ $1978$ $\pm5$ 10 1980 CNTR 62 ${{\mathit \pi}^{-}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit K}^{-}}{{\mathit n}}$ $2040$ $\pm10$ 10 1980 SPRK 18 ${{\mathit \pi}^{-}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit p}}{{\overline{\mathit p}}}{{\mathit n}}$ $1935$ $\pm13$ 10 1979 OMEG 12$-$15 ${{\mathit \pi}^{-}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit n}}$2 ${{\mathit \pi}}$ $1988$ $\pm7$ 1979 B OMEG 10 ${{\mathit \pi}^{-}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit K}^{-}}{{\mathit n}}$ $1922$ $\pm14$ 11 1977 CIBS 25 ${{\mathit \pi}^{-}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit p}}$3 ${{\mathit \pi}}$ 1  From the first PWA solution. 2  From a partial-wave analysis of the data. 3  From an amplitude analysis of the reaction ${{\mathit \pi}^{+}}$ ${{\mathit \pi}^{-}}$ $\rightarrow$ 2 ${{\mathit \pi}^{0}}$ . 4  K matrix pole. 5  Taking into account the ${{\mathit f}_{{2}}{(1950)}}$. Helicity-2 production favored. 6  Energy-dependent analysis. 7  Single energy analysis. 8  From solution A of amplitude analysis of data on ${{\overline{\mathit p}}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit \pi}}{{\mathit \pi}}$ . See however KLOET 1996 who fit ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ only and find waves only up to $\mathit J = 3$ to be important but not significantly resonant. 9  From solution B of amplitude analysis of data on ${{\overline{\mathit p}}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit \pi}}{{\mathit \pi}}$ . See however KLOET 1996 who fit ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ only and find waves only up to $\mathit J = 3$ to be important but not significantly resonant. 10  $\mathit I(\mathit J{}^{P}) = 0(4{}^{+})$ from amplitude analysis assuming one-pion exchange. 11  Width errors enlarged by us to 4${}\Gamma /\sqrt {\mathit N }$; see the note with the ${{\mathit K}^{*}{(892)}}$ mass. ${{\mathit f}_{{4}}{(2050)}}$ mass (MeV) References: ANISOVICH 2009 IJMP A24 2481 The Combined Analysis of ${{\mathit \pi}}$ ${{\mathit N}}$ $\rightarrow$ two mesons ${+}$ ${{\mathit N}}$ Reactions within Reggeon Exchanges and Data for ${{\mathit p}}$ ${{\overline{\mathit p}}}$ (at rest) $\rightarrow$ three mesons UEHARA 2009 PR D79 052009 High-Statistics Study of Neutral-Pion Pair Production in Two-Photon Collisions AMELIN 2006 PAN 69 690 Resonances in the ${{\mathit \omega}}{{\mathit \omega}}$ System BINON 2005 PAN 68 960 Investigation of the ${{\mathit \eta}}{{\mathit \eta}}$ System in ${{\mathit \pi}^{-}}{{\mathit p}}$ Interactions at a Momentum of 32.5 GeV/$\mathit c$ at the GAMS-4$\pi$ Spectrometer ANISOVICH 2000J PL B491 47 I = 0 C = +1 Mesons from 1920 to 2410 MeV ALDE 1998 EPJ A3 361 Study of the ${{\mathit \pi}^{0}}{{\mathit \pi}^{0}}$ System with the GAMS-4000 Spectrometer at 100 ${\mathrm {GeV/}}\mathit c$ MARTIN 1998 PR C57 3492 Amplitudes and Resonances from an Energy Dependent Analysis of ${{\overline{\mathit p}}}$ ${+}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit \pi}}{+}$ ${{\mathit \pi}}$ MARTIN 1997 PR C56 1114 Partial Wave Amplitudes and Resonances in ${{\overline{\mathit p}}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit \pi}}{{\mathit \pi}}$ OAKDEN 1994 NP A574 731 Amplitude Analysis of Data on ${{\overline{\mathit p}}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit \pi}}{{\mathit \pi}}$ at Low Energy ALDE 1990 PL B241 600 Further Study of Mesons which Decay into ${{\mathit \omega}}{{\mathit \omega}}$ AUGUSTIN 1987 ZPHY C36 369 Radiative Decay of ${{\mathit J / \psi}}$ into ${{\mathit \gamma}}{{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ BALTRUSAITIS 1987 PR D35 2077 Radiative Decays of the ${{\mathit J / \psi}}$ into ${{\mathit \gamma}}{{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ and ${{\mathit \gamma}}{{\mathit K}^{+}}{{\mathit K}^{-}}$ ALDE 1986D NP B269 485 Production of ${{\mathit G}{(1590)}}$ and other Mesons Decaying into ${{\mathit \eta}}$ Pairs by 100 ${\mathrm {GeV/}}\mathit c$ ${{\mathit \pi}^{-}}$ on Protons BINON 1984B LNC 39 41 Observation a Spin 6 Neutral ${{\mathit R}{(2510)}}$ Meson CASON 1982 PRL 48 1316 Amplitude Analysis of the Reaction ${{\mathit \pi}^{+}}$ ${{\mathit \pi}^{-}}$ $\rightarrow$ ${{\mathit \pi}^{0}}{{\mathit \pi}^{0}}$ from 1.0 to 2.3 GeV ETKIN 1982B PR D25 1786 Amplitude Analysis of the ${{\mathit K}_S^0}{{\mathit K}_S^0}$ System Produced in the Reaction ${{\mathit \pi}^{-}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit K}_S^0}$ ${{\mathit K}_S^0}$ ${{\mathit n}}$ at 23 ${\mathrm {GeV/}}\mathit c$ ALPER 1980 PL 94B 422 Evidence for a Spin-5 Boson Resonance at 2300 MeV ROZANSKA 1980 NP B162 505 A Partial Wave Analysis of the ${{\mathit p}}{{\overline{\mathit p}}}$ System Produced at Low Four Momentum Transfer in the Reaction ${{\mathit \pi}^{-}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit p}}{{\overline{\mathit p}}}{{\mathit n}}$ at 18 GeV CORDEN 1979 NP B157 250 An Amplitude Analysis of ${{\mathit \pi}}{{\mathit \pi}}$ Scattering from New Data on the Reaction ${{\mathit \pi}^{-}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit n}}$ EVANGELISTA 1979B NP B154 381 Observation in the ${{\mathit K}^{+}}{{\mathit K}^{-}}$ System of a New Structure at 2.20 GeV ANTIPOV 1977 NP B119 45 Boson States in the Reaction ${{\mathit \pi}^{-}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit \pi}^{-}}{{\mathit \pi}^{-}}{{\mathit \pi}^{+}}{{\mathit p}}$ with Leading ${{\mathit \pi}^{+}}$ Meson at 25 ${\mathrm {GeV/}}\mathit c$ APEL 1975 PL 57B 398 Observation of a Spin 4 Neutral Meson with 2 GeV Mass Decaying in ${{\mathit \pi}^{0}}{{\mathit \pi}^{0}}$ BLUM 1975 PL 57B 403 Evidence for a Spin-4 Boson Resonance at 2050 MeV
2021-03-03T12:55:10
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https://nctr.pmel.noaa.gov/benchmark/Analytical/index.html
Initial Value Problem ## Analytical benchmarking The shallow water-wave (SW) equations describe the evolution of the water-surface elevation and of the depth-averaged water particle velocity of waves with wavelengths large compared with the depth of propagation. The equations assume that the pressure distribution is hydrostatic everywhere, i.e., there is no variation with depth of any of the other flow variables. In this section we present several analytic solutions to the 1+1 version of these equations. As stated in Section 2 of this report, 1+1 models are generally unreliable for inundation mapping and entirely inadequate for operational tsunami forecasting, but they are invaluable to the process of testing and validating models.
2017-09-25T13:29:28
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https://www.zbmath.org/authors/?q=ai%3Aallaire.gregoire
## Allaire, Grégoire Compute Distance To: Author ID: allaire.gregoire Published as: Allaire, Grégoire; Allaire, G.; Allaire, Gregoire; Allaire, Grégire External Links: MGP · Wikidata · IdRef · theses.fr Documents Indexed: 154 Publications since 1989, including 6 Books Co-Authors: 91 Co-Authors with 126 Joint Publications 1,360 Co-Co-Authors all top 5 ### Co-Authors 26 single-authored 20 Jouve, François 15 Dapogny, Charles 14 Piatnitski, Andrey L. 9 Conca, Carlos 7 Kokh, Samuel 7 Mikelić, Andro 6 Capdeboscq, Yves 6 Rauch, Jeffrey B. 6 Vanninathan, Muthusamy 5 Feppon, Florian 5 Palombaro, Mariapia 4 Brizzi, Robert 4 Dufrêche, Jean-François 4 Faccanoni, Gloria 4 Kohn, Robert Vita 4 Michailidis, Georgios E. 4 Pantz, Olivier 4 Toader, Anca-Maria 3 Bal, Guillaume 3 Briane, Marc 3 Faure, Alexis 3 Francfort, Gilles A. 3 Hutridurga, Harsha 2 Aubry, Sylvie 2 Bonnetier, Eric 2 Clerc, Sébastien 2 de Gournay, Frédéric 2 Delgado, Gabriel 2 Desai, Jeet 2 Estevez, Rafael 2 Frey, Pascal Jean 2 Friz, Luis 2 Geoffroy-Donders, Perle 2 Habibi, Zakaria 2 Henrot, Antoine 2 Jolivet, Pierre 2 Maillot, Hervé 2 Maury, Aymeric 2 Orive Illera, Rafael 2 Pankratova, Iryna L. 2 Periago, Francisco 2 Siess, Vincent 2 Van Goethem, Nicolas 1 Abballe, Thomas 1 Amar, Micol 1 Barré, Sébastien 1 Belhachmi, Zakaria 1 Bendsøe, Martin Philip 1 Bernard, Olivier 1 Bissuel, Aloïs 1 Blanc, Xavier 1 Bogoşel, Beniamin 1 Bordeu, Felipe 1 Cavallina, Lorenzo 1 Cortial, Julien 1 Couvelas, Agnes 1 Daumas, Laurent 1 Després, Bruno 1 Desroziers, Sylvain 1 Dombre, Emmanuel 1 El Ganaoui, Karima 1 Enchéry, Guillaume 1 Ferriero, Alessandro 1 Ghosh, Tuhin 1 Godoy, Matías 1 Golse, François 1 Gutiérrez, Sergio 1 Jakabčin, Lukáš 1 Kaber, Sidimahmoud 1 Kelly, Alex 1 Lamacz-Keymling, Agnes 1 Laucoin, Éli 1 Lods, Véronique 1 Malige, François 1 Martínez-Frutos, Jesús 1 Miyake, Nobuhito 1 Montarnal, Philippe 1 Münch, Arnaud 1 Murat, François 1 Oka, Tomoyuki 1 Ortega, Jaime H. 1 Orval, Patrick 1 Ouaki, Franck 1 Planchard, Jacques 1 Puel, Marjolaine 1 Rakotondrainibe, Lalaina 1 Raphael, Anne-Lise 1 Rey, Floriane 1 Schmitt, Damien 1 Yachimura, Toshiaki 1 Zelmanse, Alain all top 5 ### Serials 7 Computer Methods in Applied Mechanics and Engineering 7 Journal of Computational Physics 6 Archive for Rational Mechanics and Analysis 6 Comptes Rendus de l’Académie des Sciences. Série I 6 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 6 Discrete and Continuous Dynamical Systems. Series B 6 Comptes Rendus. Mathématique. Académie des Sciences, Paris 5 SIAM Journal on Mathematical Analysis 4 European Series in Applied and Industrial Mathematics (ESAIM): Proceedings 4 S$$\vec{\text{e}}$$MA Journal 3 Numerische Mathematik 3 Quarterly of Applied Mathematics 3 Asymptotic Analysis 3 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 3 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 3 Structural and Multidisciplinary Optimization 3 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 2 Applicable Analysis 2 Journal of Mathematical Physics 2 Annali di Matematica Pura ed Applicata. Serie Quarta 2 Control and Cybernetics 2 SIAM Journal on Control and Optimization 2 Revue Européenne des Éléments Finis 2 Comptes Rendus de l’Académie des Sciences. Série I. Mathématique 2 Portugaliae Mathematica. Nova Série 2 Multiscale Modeling & Simulation 2 Networks and Heterogeneous Media 2 Matapli 2 SMAI Journal of Computational Mathematics 1 Computers and Fluids 1 Computers & Mathematics with Applications 1 Communications in Mathematical Physics 1 Communications on Pure and Applied Mathematics 1 IMA Journal of Applied Mathematics 1 Journal of Mathematical Analysis and Applications 1 Journal of the Mechanics and Physics of Solids 1 Nonlinearity 1 Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM) 1 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 1 Indiana University Mathematics Journal 1 International Journal for Numerical Methods in Engineering 1 Journal of Functional Analysis 1 Journal of Optimization Theory and Applications 1 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 1 Physica D 1 Revista Matemática Iberoamericana 1 Computational Mechanics 1 European Journal of Mechanics. A. Solids 1 Communications in Partial Differential Equations 1 Journal de Mathématiques Pures et Appliquées. Neuvième Série 1 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 1 Séminaire Équations aux Dérivées Partielles 1 Computational and Applied Mathematics 1 Engineering Analysis with Boundary Elements 1 European Journal of Mechanics. A. Solids 1 Interdisciplinary Information Sciences (IIS) 1 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics 1 Computational Geosciences 1 Communications in Contemporary Mathematics 1 Comptes Rendus de l’Académie des Sciences. Série IIb. Mécanique 1 Applied Mathematical Sciences 1 Mathématiques & Applications (Berlin) 1 Texts in Applied Mathematics 1 Annali dell’Università di Ferrara. Sezione VII. Scienze Matematiche 1 Numerical Mathematics and Scientific Computation all top 5 ### Fields 83 Partial differential equations (35-XX) 71 Mechanics of deformable solids (74-XX) 43 Calculus of variations and optimal control; optimization (49-XX) 35 Fluid mechanics (76-XX) 31 Numerical analysis (65-XX) 12 Statistical mechanics, structure of matter (82-XX) 7 Operations research, mathematical programming (90-XX) 5 Optics, electromagnetic theory (78-XX) 5 Classical thermodynamics, heat transfer (80-XX) 2 Operator theory (47-XX) 2 Quantum theory (81-XX) 1 General and overarching topics; collections (00-XX) 1 History and biography (01-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Ordinary differential equations (34-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Integral equations (45-XX) 1 Functional analysis (46-XX) 1 Astronomy and astrophysics (85-XX) 1 Geophysics (86-XX) 1 Systems theory; control (93-XX) ### Citations contained in zbMATH Open 138 Publications have been cited 3,998 times in 2,521 Documents Cited by Year Homogenization and two-scale convergence. Zbl 0770.35005 Allaire, Grégoire 1992 Structural optimization using sensitivity analysis and a level-set method. Zbl 1136.74368 Allaire, Grégoire; Jouve, François; Toader, Anca-Maria 2004 Shape optimization by the homogenization method. Zbl 0990.35001 Allaire, Grégoire 2002 A five-equation model for the simulation of interfaces between compressible fluids. Zbl 1169.76407 Allaire, Grégoire; Clerc, Sébastien; Kokh, Samuel 2002 Structural optimization using topological and shape sensitivity via a level set method. Zbl 1167.49324 Allaire, Grégoire; de Gournay, Frédéric; Jouve, François; Toader, Anca-Maria 2005 Multiscale convergence and reiterated homogenisation. Zbl 0866.35017 Allaire, G.; Briane, M. 1996 Homogenization of the Navier-Stokes equations in open sets perforated with tiny holes. I: Abstract framework, a volume distribution of holes. Zbl 0724.76020 Allaire, Grégoire 1991 A level-set method for shape optimization. Zbl 1115.49306 Allaire, Grégoire; Jouve, François; Toader, Anca-Maria 2002 Optimal treatment of structures. (Conception optimale de structures.) Zbl 1132.49033 Allaire, Grégoire 2007 Shape optimization by the homogenization method. Zbl 0889.73051 Allaire, Grégoire; Bonnetier, Eric; Francfort, Gilles; Jouve, François 1997 Optimal design for minimum weight and compliance in plane stress using extremal microstructures. Zbl 0794.73044 Allaire, G.; Kohn, Robert V. 1993 Boundary layer tails in periodic homogenization. Zbl 0922.35014 Allaire, Grégoire; Amar, Micol 1999 Homogenization of the Stokes flow in a connected porous medium. Zbl 0682.76077 Allaire, Grégoire 1989 Homogenization of the Navier-Stokes equations in open sets perforated with tiny holes. II: Non-critical sizes of the holes for a volume distribution and a surface distribution of holes. Zbl 0724.76021 Allaire, Grégoire 1991 A level-set method for vibration and multiple loads structural optimization. Zbl 1091.74038 Allaire, Grégoire; Jouve, François 2005 Bloch wave homogenization and spectral asymptotic analysis. Zbl 0901.35005 Allaire, Grégoire; Conca, Carlos 1998 A multiscale finite element method for numerical homogenization. Zbl 1093.35007 Allaire, Grégoire; Brizzi, Robert 2005 Numerical analysis and optimization. An introduction to mathematical modelling and numerical simulation. Translation from the French by Alan Craig. Zbl 1120.65001 Allaire, Grégoire 2007 Optimal bounds on the effective behavior of a mixture of two well-ordered elastic materials. Zbl 0805.73043 Allaire, Grégoire; Kohn, Robert V. 1993 Homogenization of the Schrödinger equation and effective mass theorems. Zbl 1081.35092 Allaire, Grégoire; Piatnitski, Andrey 2005 Topology optimization for minimum stress design with the homogenization method. Zbl 1243.74148 Allaire, Grégoire; Jouve, François; Maillot, Hervé 2004 Minimum stress optimal design with the level set method. Zbl 1244.74104 Allaire, Grégoire; Jouve, François 2008 Damage and fracture evolution in brittle materials by shape optimization methods. Zbl 1356.74178 Allaire, Grégoire; Jouve, François; Van Goethem, Nicolas 2011 Shape optimization with a level set based mesh evolution method. Zbl 1423.74739 Allaire, G.; Dapogny, C.; Frey, P. 2014 Multi-phase structural optimization via a level set method. Zbl 1287.49045 Allaire, G.; Dapogny, C.; Delgado, G.; Michailidis, G. 2014 Shape and topology optimization of the robust compliance via the level set method. Zbl 1245.49054 De Gournay, Frédéric; Allaire, Grégoire; Jouve, François 2008 Homogenization of the Neumann problem with nonisolated holes. Zbl 0823.35014 Allaire, Grégoire; Murat, François 1993 A comparison between two-scale asymptotic expansions and Bloch wave expansions for the homogenization of periodic structures. Zbl 1364.35029 Allaire, Gregoire; Briane, M.; Vanninathan, M. 2016 Structural optimization with FreeFem++. Zbl 1245.74049 Allaire, Grégoire; Pantz, Olivier 2006 Structural optimization under overhang constraints imposed by additive manufacturing technologies. Zbl 1375.74076 Allaire, G.; Dapogny, C.; Estevez, R.; Faure, A.; Michailidis, G. 2017 Homogenization of the Navier-Stokes equations with a slip boundary condition. Zbl 0738.35059 Allaire, Grégoire 1991 Explicit optimal bounds on the elastic energy of a two-phase composite in two space dimensions. Zbl 0805.73042 Allaire, Grégoire; Kohn, Robert V. 1993 Numerical linear algebra. Zbl 1135.65014 Allaire, Grégoire; Kaber, Sidi Mahmoud 2008 Homogenization of the criticality spectral equation in neutron transport. Zbl 0931.35010 Allaire, Grégoire; Bal, Guillaume 1999 Homogenization of a conductive and radiative heat transfer problem. Zbl 1180.35062 Allaire, Grégoire; El Ganaoui, Karima 2009 Homogenization of periodic systems with large potentials. Zbl 1072.35023 Allaire, Grégoire; Capdeboscq, Yves; Piatnitski, Andrey; Siess, Vincent; Vanninathan, M. 2004 Second order corrector in the homogenization of a conductive-radiative heat transfer problem. Zbl 1270.35053 Allaire, Grégoire; Habibi, Zakaria 2013 Homogenization of a convection-diffusion model with reaction in a porous medium. Zbl 1114.35007 Allaire, Grégoire; Raphael, Anne-Lise 2007 Homogenization of a spectral problem in neutronic multigroup diffusion. Zbl 1126.82346 Allaire, Grégoire; Capdeboscq, Yves 2000 Homogenization of the unsteady Stokes equations in porous media. Zbl 0801.35103 Allaire, G. 1993 Homogenization approach to the dispersion theory for reactive transport through porous media. Zbl 1213.35057 Allaire, Grégoire; Mikelić, Andro; Piatnitski, Andrey 2010 Shape optimization of a coupled thermal fluid-structure problem in a level set mesh evolution framework. Zbl 1422.49038 Feppon, F.; Allaire, G.; Bordeu, F.; Cortial, J.; Dapogny, C. 2019 Continuity of Darcy’s law in thelow-volume fraction limit. Zbl 0755.35084 Allaire, Grégoire 1991 A linearized approach to worst-case design in parametric and geometric shape optimization. Zbl 1297.49075 Allaire, Grégoire; Dapogny, Charles 2014 Eigenfrequency optimization in optimal design. Zbl 1004.74063 Allaire, Grégoire; Aubry, Sylvie; Jouve, François 2001 A five-equation model for the numerical simulation of interfaces in two-phase flows. Zbl 1010.76055 Allaire, Grégoire; Clerc, Sébastien; Kokh, Samuel 2000 Homogenization of the linearized ionic transport equations in rigid periodic porous media. Zbl 1314.76039 Allaire, Grégoire; Mikelić, Andro; Piatnitski, Andrey 2010 Long time behavior of a two-phase optimal design for the heat equation. Zbl 1298.35015 Allaire, Grégoire; Münch, Arnaud; Periago, Francisco 2010 Minimizers for a double-well problem with affine boundary conditions. Zbl 0958.49008 Allaire, Grégoire; Lods, Véronique 1999 Homogenization of a conductive, convective, and radiative heat transfer problem in a heterogeneous domain. Zbl 1276.35019 Allaire, Grégoire; Habibi, Zakaria 2013 Boundary layers in the homogenization of a spectral problem in fluid-solid structures. Zbl 0918.35018 Allaire, Grégoire; Conca, Carlos 1998 Optimal lower bounds on the elastic energy of a composite made from two non-well-ordered isotropic materials. Zbl 0806.73038 Allaire, Grégoire; Kohn, Robert V. 1994 Diffractive geometric optics for Bloch wave packets. Zbl 1269.78004 Allaire, Grégoire; Palombaro, Mariapia; Rauch, Jeffrey 2011 Modelling and simulation of liquid-vapor phase transition in compressible flows based on thermodynamical equilibrium. Zbl 1267.76110 Faccanoni, Gloria; Kokh, Samuel; Allaire, Grégoire 2012 Bloch-wave homogenization for a spectral problem in fluid-solid structures. Zbl 0857.73008 Allaire, Grégoire; Conca, Carlos 1996 Spectral asymptotic analysis of a neutronic diffusion problem. (Analyse asymptotique spectrale d’un problème de diffusion neutronique.) Zbl 0879.35153 Allaire, Grégoire; Malige, François 1997 Allaire, Grégoire; Gutiérrez, Sergio 2007 Taking into account thermal residual stresses in topology optimization of structures built by additive manufacturing. Zbl 1411.49028 Allaire, Grégoire; Jakabčin, Lukas 2018 Diffractive behavior of the wave equation in periodic media: weak convergence analysis. Zbl 1200.35019 Allaire, Grégoire; Palombaro, Mariapia; Rauch, Jeffrey 2009 Existence of minimizers for non-quasiconvex functionals arising in optimal design. Zbl 0913.49008 Allaire, Grégire; Francfort, Gilles 1998 Ion transport in porous media: derivation of the macroscopic equations using upscaling and properties of the effective coefficients. Zbl 1392.76071 Allaire, Grégoire; Brizzi, Robert; Dufrêche, Jean-François; Mikelić, Andro; Piatnitski, Andrey 2013 Homogenization of periodic non self-adjoint problems with large drift and potential. Zbl 1130.35307 Allaire, Grégoire; Orive, Rafael 2007 Homogenization of nonlinear reaction-diffusion equation with a large reaction term. Zbl 1205.35019 Allaire, Grégoire; Piatnitski, Andrey 2010 Dispersive limits in the homogenization of the wave equation. Zbl 1070.35006 Allaire, Grégoire 2003 Topology optimization of modulated and oriented periodic microstructures by the homogenization method. Zbl 1443.74246 Allaire, Grégoire; Geoffroy-Donders, Perle; Pantz, Olivier 2019 Uniform spectral asymptotics for singularly perturbed locally periodic operators. Zbl 1026.35012 Allaire, Grégoire; Piatnitski, Andrey 2002 On some recent advances in shape optimization. Zbl 0986.49023 Allaire, Grégoire; Henrot, Antoine 2001 The homogenization method for topology and shape optimization. Zbl 0885.73049 Allaire, G. 1997 Homogénéisation et convergence à deux échelles. Application à un problème de convection diffusion. (Homogenization and two-scale convergence. Application to a problem of advection-diffusion). Zbl 0724.46033 Allaire, Grégoire 1991 Topology and geometry optimization of elastic structures by exact deformation of simplicial mesh. Zbl 1368.74045 Allaire, Grégoire; Dapogny, Charles; Frey, Pascal 2011 Optimal design of low-contrast two-phase structures for the wave equation. Zbl 1219.74039 Allaire, Grégoire; Kelly, Alex 2011 Homogenization of reactive flows in porous media and competition between bulk and surface diffusion. Zbl 1341.76017 Allaire, G.; Hutridurga, H. 2012 A level set method for the numerical simulation of damage evolution. Zbl 1419.74250 Allaire, Grégoire; Jouve, François; Van Goethem, Nicolas 2008 Geometric constraints for shape and topology optimization in architectural design. Zbl 1398.74256 Dapogny, Charles; Faure, Alexis; Michailidis, Georgios; Allaire, Grégoire; Couvelas, Agnes; Estevez, Rafael 2017 3-d topology optimization of modulated and oriented periodic microstructures by the homogenization method. Zbl 1453.74072 Geoffroy-Donders, Perle; Allaire, Grégoire; Pantz, Olivier 2020 Upscaling nonlinear adsorption in periodic porous media – homogenization approach. Zbl 1379.35010 Allaire, Grégoire; Hutridurga, Harsha 2016 Shape optimization of a layer by layer mechanical constraint for additive manufacturing. (Optimisation de forme pour une contrainte mécanique associée aux procédés de fabrication additive.) Zbl 1370.49037 Allaire, Grégoire; Dapogny, Charles; Faure, Alexis; Michailidis, Georgios 2017 Homogenization of the Navier-Stokes equations and derivation of Brinkman’s law. Zbl 0759.76072 Allaire, G. 1991 Asymptotic analysis of the Poisson-Boltzmann equation describing electrokinetics in porous media. Zbl 1264.35159 Allaire, Grégoire; Dufrêche, Jean-François; Mikelić, Andro; Piatnitski, Andrey 2013 A deterministic approximation method in shape optimization under random uncertainties. Zbl 1416.74080 Allaire, Grégoire; Dapogny, Charles 2015 A brief introduction to homogenization and miscellaneous applications. Zbl 1339.35001 Allaire, Grégoire 2012 Homogenization and concentration for a diffusion equation with large convection in a bounded domain. Zbl 1233.35013 Allaire, G.; Pankratova, I.; Piatnitski, A. 2012 Homogenization and localization for a 1D eigenvalue problem in a periodic medium with an interface. Zbl 1072.35026 Allaire, Grégoire; Capdeboscq, Yves 2002 Optimal design of micro-mechanisms by the homogenization method. Zbl 1120.74710 Allaire, Grégoire; Jouve, François 2002 Spectral asymptotic analysis of the wave equation. Bloch wave homogenization. (Analyse asymptotique spectrale de l’équation des ondes. Homogénéisation par ondes de Bloch.) Zbl 0844.35075 Allaire, Grégoire; Conca, Carlos 1995 Topology optimization with the homogenization and the level-set methods. Zbl 1320.74089 Allaire, G. 2005 Two-scale convergence: A new method in periodic homogenization. Zbl 0822.35011 Allaire, G. 1994 A strictly hyperbolic equilibrium phase transition model. Zbl 1109.35066 Allaire, Grégoire; Faccanoni, Gloria; Kokh, Samuel 2007 Topology optimization of thermal fluid-structure systems using body-fitted meshes and parallel computing. Zbl 1437.74021 Feppon, F.; Allaire, G.; Dapogny, C.; Jolivet, P. 2020 Shape optimisation with the level set method for contact problems in linearised elasticity. Zbl 1416.74079 Maury, Aymeric; Allaire, Grégoire; Jouve, François 2017 Localization of high-frequency waves propagating in a locally periodic medium. Zbl 1204.35034 Allaire, G.; Friz, L. 2010 The homogenization method for topology and shape optimization. Single and multiple loads case. Zbl 0924.73163 Allaire, Grégoire; Belhachmi, Zakaria; Jouve, François 1996 Asymptotic spectral analysis of the wave equation. Completeness of the Bloch spectrum. (Analyse asymptotique spectrale de l’équation des ondes. Complétude du spectre de Bloch.) Zbl 0844.35076 Allaire, Grégoire; Conca, Carlos 1995 Optimization of dispersive coefficients in the homogenization of the wave equation in periodic structures. Zbl 1404.35021 2018 Role of non-ideality for the ion transport in porous media: derivation of the macroscopic equations using upscaling. Zbl 1349.76803 Allaire, Grégoire; Brizzi, Robert; Dufrêche, Jean-François; Mikelić, Andro; Piatnitski, Andrey 2014 Homogenization and localization with an interface. Zbl 1073.35018 Allaire, Grégoire; Capdeboscq, Yves; Piatnitski, Andrey 2003 Periodic homogenization and effective mass theorems for the Schrödinger equation. Zbl 1173.82330 Allaire, Grégoire 2008 Localization for the Schrödinger equation in a locally periodic medium. Zbl 1302.35034 Allaire, Grégoire; Palombaro, Mariapia 2006 Two asymptotic models for arrays of underground waste containers. Zbl 1180.35061 Allaire, Grégoire; Briane, Marc; Brizzi, Robert; Capdeboscq, Yves 2009 On the band gap structure of Hill’s equation. Zbl 1095.34014 Allaire, G.; Orive, R. 2005 Shape and topology optimization. Zbl 1475.49048 Allaire, Grégoire; Dapogny, Charles; Jouve, François 2021 Body-fitted topology optimization of 2D and 3D fluid-to-fluid heat exchangers. Zbl 07340417 Feppon, F.; Allaire, G.; Dapogny, C.; Jolivet, P. 2021 3-d topology optimization of modulated and oriented periodic microstructures by the homogenization method. Zbl 1453.74072 Geoffroy-Donders, Perle; Allaire, Grégoire; Pantz, Olivier 2020 Topology optimization of thermal fluid-structure systems using body-fitted meshes and parallel computing. Zbl 1437.74021 Feppon, F.; Allaire, G.; Dapogny, C.; Jolivet, P. 2020 A variational formulation for computing shape derivatives of geometric constraints along rays. Zbl 07201581 Feppon, Florian; Allaire, Grégoire; Dapogny, Charles 2020 Null space gradient flows for constrained optimization with applications to shape optimization. Zbl 1464.65064 Feppon, Florian; Allaire, Grégoire; Dapogny, Charles 2020 Shape optimization of a coupled thermal fluid-structure problem in a level set mesh evolution framework. Zbl 1422.49038 Feppon, F.; Allaire, G.; Bordeu, F.; Cortial, J.; Dapogny, C. 2019 Topology optimization of modulated and oriented periodic microstructures by the homogenization method. Zbl 1443.74246 Allaire, Grégoire; Geoffroy-Donders, Perle; Pantz, Olivier 2019 Structural optimization under internal porosity constraints using topological derivatives. Zbl 1440.74273 Martínez-Frutos, J.; Allaire, G.; Dapogny, C.; Periago, F. 2019 Taking into account thermal residual stresses in topology optimization of structures built by additive manufacturing. Zbl 1411.49028 Allaire, Grégoire; Jakabčin, Lukas 2018 Optimization of dispersive coefficients in the homogenization of the wave equation in periodic structures. Zbl 1404.35021 2018 Elasto-plastic shape optimization using the level set method. Zbl 1387.35247 Maury, Aymeric; Allaire, Grégoire; Jouve, François 2018 Transport and diffusion. (Transport et diffusion.) Zbl 1432.82002 Allaire, Grégoire; Blanc, Xavier; Després, Bruno; Golse, François 2018 Structural optimization under overhang constraints imposed by additive manufacturing technologies. Zbl 1375.74076 Allaire, G.; Dapogny, C.; Estevez, R.; Faure, A.; Michailidis, G. 2017 Geometric constraints for shape and topology optimization in architectural design. Zbl 1398.74256 Dapogny, Charles; Faure, Alexis; Michailidis, Georgios; Allaire, Grégoire; Couvelas, Agnes; Estevez, Rafael 2017 Shape optimization of a layer by layer mechanical constraint for additive manufacturing. (Optimisation de forme pour une contrainte mécanique associée aux procédés de fabrication additive.) Zbl 1370.49037 Allaire, Grégoire; Dapogny, Charles; Faure, Alexis; Michailidis, Georgios 2017 Shape optimisation with the level set method for contact problems in linearised elasticity. Zbl 1416.74079 Maury, Aymeric; Allaire, Grégoire; Jouve, François 2017 Homogenization of Stokes system using Bloch waves. Zbl 1375.35355 Allaire, Grégoire; Ghosh, Tuhin; Vanninathan, Muthusamy 2017 Ion transport through deformable porous media: derivation of the macroscopic equations using upscaling. Zbl 1476.76074 Allaire, Grégoire; Bernard, Olivier; Dufrêche, Jean-François; Mikelić, Andro 2017 On the asymptotic behaviour of the kernel of an adjoint convection-diffusion operator in a long cylinder. Zbl 1382.35020 Allaire, Grégoire; Piatnitski, Andrey 2017 A comparison between two-scale asymptotic expansions and Bloch wave expansions for the homogenization of periodic structures. Zbl 1364.35029 Allaire, Gregoire; Briane, M.; Vanninathan, M. 2016 Upscaling nonlinear adsorption in periodic porous media – homogenization approach. Zbl 1379.35010 Allaire, Grégoire; Hutridurga, Harsha 2016 Stacking sequence and shape optimization of laminated composite plates via a level-set method. Zbl 1445.74040 2016 A deterministic approximation method in shape optimization under random uncertainties. Zbl 1416.74080 Allaire, Grégoire; Dapogny, Charles 2015 On the homogenization of multicomponent transport. Zbl 1339.35026 Hutridurga, Harsha; Allaire, Grégoire 2015 A priori error estimate of a multiscale finite element method for transport modeling. Zbl 1320.74106 Ouaki, Franck; Allaire, Grégoire; Desroziers, Sylvain; Enchéry, Guillaume 2015 Shape optimization with a level set based mesh evolution method. Zbl 1423.74739 Allaire, G.; Dapogny, C.; Frey, P. 2014 Multi-phase structural optimization via a level set method. Zbl 1287.49045 Allaire, G.; Dapogny, C.; Delgado, G.; Michailidis, G. 2014 A linearized approach to worst-case design in parametric and geometric shape optimization. Zbl 1297.49075 Allaire, Grégoire; Dapogny, Charles 2014 Role of non-ideality for the ion transport in porous media: derivation of the macroscopic equations using upscaling. Zbl 1349.76803 Allaire, Grégoire; Brizzi, Robert; Dufrêche, Jean-François; Mikelić, Andro; Piatnitski, Andrey 2014 Second order corrector in the homogenization of a conductive-radiative heat transfer problem. Zbl 1270.35053 Allaire, Grégoire; Habibi, Zakaria 2013 Homogenization of a conductive, convective, and radiative heat transfer problem in a heterogeneous domain. Zbl 1276.35019 Allaire, Grégoire; Habibi, Zakaria 2013 Ion transport in porous media: derivation of the macroscopic equations using upscaling and properties of the effective coefficients. Zbl 1392.76071 Allaire, Grégoire; Brizzi, Robert; Dufrêche, Jean-François; Mikelić, Andro; Piatnitski, Andrey 2013 Asymptotic analysis of the Poisson-Boltzmann equation describing electrokinetics in porous media. Zbl 1264.35159 Allaire, Grégoire; Dufrêche, Jean-François; Mikelić, Andro; Piatnitski, Andrey 2013 Diffraction of Bloch wave packets for Maxwell’s equations. Zbl 1281.35083 Allaire, Grégoire; Palombaro, Mariapia; Rauch, Jeffrey 2013 Modelling and simulation of liquid-vapor phase transition in compressible flows based on thermodynamical equilibrium. Zbl 1267.76110 Faccanoni, Gloria; Kokh, Samuel; Allaire, Grégoire 2012 Homogenization of reactive flows in porous media and competition between bulk and surface diffusion. Zbl 1341.76017 Allaire, G.; Hutridurga, H. 2012 A brief introduction to homogenization and miscellaneous applications. Zbl 1339.35001 Allaire, Grégoire 2012 Homogenization and concentration for a diffusion equation with large convection in a bounded domain. Zbl 1233.35013 Allaire, G.; Pankratova, I.; Piatnitski, A. 2012 Homogenization of a nonstationary convection-diffusion equation in a thin rod and in a layer. Zbl 1310.35026 Allaire, G.; Pankratova, I.; Piatnitski, A. 2012 Shape optimization of a sodium fast reactor core. Zbl 1329.74228 Dombre, Emmanuel; Allaire, Grégoire; Pantz, Olivier; Schmitt, Damien 2012 Homogenization of a one-dimensional spectral problem for a singularly perturbed elliptic operator with Neumann boundary conditions. Zbl 1235.35024 Allaire, Grégoire; Capdeboscq, Yves; Puel, Marjolaine 2012 In search of the lost inequality. (À la recherche de l’inégalité perdue.) Zbl 1365.35002 Allaire, Grégoire 2012 Damage and fracture evolution in brittle materials by shape optimization methods. Zbl 1356.74178 Allaire, Grégoire; Jouve, François; Van Goethem, Nicolas 2011 Diffractive geometric optics for Bloch wave packets. Zbl 1269.78004 Allaire, Grégoire; Palombaro, Mariapia; Rauch, Jeffrey 2011 Topology and geometry optimization of elastic structures by exact deformation of simplicial mesh. Zbl 1368.74045 Allaire, Grégoire; Dapogny, Charles; Frey, Pascal 2011 Optimal design of low-contrast two-phase structures for the wave equation. Zbl 1219.74039 Allaire, Grégoire; Kelly, Alex 2011 Erratum: “Homogenization of the linearized ionic transport equations in rigid periodic porous media” [J. Math. Phys. 51, 123103, 18 p. (2010)]. Zbl 1317.76075 Allaire, Grégoire; Mikelić, Andro; Piatnitski, Andrey 2011 Homogenization approach to the dispersion theory for reactive transport through porous media. Zbl 1213.35057 Allaire, Grégoire; Mikelić, Andro; Piatnitski, Andrey 2010 Homogenization of the linearized ionic transport equations in rigid periodic porous media. Zbl 1314.76039 Allaire, Grégoire; Mikelić, Andro; Piatnitski, Andrey 2010 Long time behavior of a two-phase optimal design for the heat equation. Zbl 1298.35015 Allaire, Grégoire; Münch, Arnaud; Periago, Francisco 2010 Homogenization of nonlinear reaction-diffusion equation with a large reaction term. Zbl 1205.35019 Allaire, Grégoire; Piatnitski, Andrey 2010 Localization of high-frequency waves propagating in a locally periodic medium. Zbl 1204.35034 Allaire, G.; Friz, L. 2010 Approximation of liquid-vapor phase transition for compressible fluids with tabulated EOS. Zbl 1258.76162 Faccanoni, Gloria; Kokh, Samuel; Allaire, Grégoire 2010 Homogenization of a conductive and radiative heat transfer problem. Zbl 1180.35062 Allaire, Grégoire; El Ganaoui, Karima 2009 Diffractive behavior of the wave equation in periodic media: weak convergence analysis. Zbl 1200.35019 Allaire, Grégoire; Palombaro, Mariapia; Rauch, Jeffrey 2009 Two asymptotic models for arrays of underground waste containers. Zbl 1180.35061 Allaire, Grégoire; Briane, Marc; Brizzi, Robert; Capdeboscq, Yves 2009 Minimum stress optimal design with the level set method. Zbl 1244.74104 Allaire, Grégoire; Jouve, François 2008 Shape and topology optimization of the robust compliance via the level set method. Zbl 1245.49054 De Gournay, Frédéric; Allaire, Grégoire; Jouve, François 2008 Numerical linear algebra. Zbl 1135.65014 Allaire, Grégoire; Kaber, Sidi Mahmoud 2008 A level set method for the numerical simulation of damage evolution. Zbl 1419.74250 Allaire, Grégoire; Jouve, François; Van Goethem, Nicolas 2008 Periodic homogenization and effective mass theorems for the Schrödinger equation. Zbl 1173.82330 Allaire, Grégoire 2008 Numerical simulation with finite volume of dynamic liquid-vapor phase transition. Zbl 1374.76137 Faccanoni, G.; Kokh, S.; Allaire, G. 2008 Optimal treatment of structures. (Conception optimale de structures.) Zbl 1132.49033 Allaire, Grégoire 2007 Numerical analysis and optimization. An introduction to mathematical modelling and numerical simulation. Translation from the French by Alan Craig. Zbl 1120.65001 Allaire, Grégoire 2007 Homogenization of a convection-diffusion model with reaction in a porous medium. Zbl 1114.35007 Allaire, Grégoire; Raphael, Anne-Lise 2007 Allaire, Grégoire; Gutiérrez, Sergio 2007 Homogenization of periodic non self-adjoint problems with large drift and potential. Zbl 1130.35307 Allaire, Grégoire; Orive, Rafael 2007 A strictly hyperbolic equilibrium phase transition model. Zbl 1109.35066 Allaire, Grégoire; Faccanoni, Gloria; Kokh, Samuel 2007 On two formulations of an optimal insulation problem. Zbl 1245.74067 Munoz, E.; Allaire, Grégoire; Bendsøe, Martin Philip 2007 On Bloch waves for the Stokes equations. Zbl 1124.35050 Allaire, Grégoire; Conca, Carlos; Friz, Luis; Ortega, Jaime H. 2007 Structural optimization with FreeFem++. Zbl 1245.74049 Allaire, Grégoire; Pantz, Olivier 2006 Localization for the Schrödinger equation in a locally periodic medium. Zbl 1302.35034 Allaire, Grégoire; Palombaro, Mariapia 2006 Homogenization of the Schrödinger equation with a time oscillating potential. Zbl 1096.35009 Allaire, Grégoire; Vanninathan, M. 2006 Structural optimization using topological and shape sensitivity via a level set method. Zbl 1167.49324 Allaire, Grégoire; de Gournay, Frédéric; Jouve, François; Toader, Anca-Maria 2005 A level-set method for vibration and multiple loads structural optimization. Zbl 1091.74038 Allaire, Grégoire; Jouve, François 2005 A multiscale finite element method for numerical homogenization. Zbl 1093.35007 Allaire, Grégoire; Brizzi, Robert 2005 Homogenization of the Schrödinger equation and effective mass theorems. Zbl 1081.35092 Allaire, Grégoire; Piatnitski, Andrey 2005 Topology optimization with the homogenization and the level-set methods. Zbl 1320.74089 Allaire, G. 2005 On the band gap structure of Hill’s equation. Zbl 1095.34014 Allaire, G.; Orive, R. 2005 Numerical analysis and optimisation. (Analyse numérique et optimisation.) Zbl 1190.65001 Allaire, Grégoire 2005 Structural optimization using sensitivity analysis and a level-set method. Zbl 1136.74368 Allaire, Grégoire; Jouve, François; Toader, Anca-Maria 2004 Topology optimization for minimum stress design with the homogenization method. Zbl 1243.74148 Allaire, Grégoire; Jouve, François; Maillot, Hervé 2004 Homogenization of periodic systems with large potentials. Zbl 1072.35023 Allaire, Grégoire; Capdeboscq, Yves; Piatnitski, Andrey; Siess, Vincent; Vanninathan, M. 2004 Dispersive limits in the homogenization of the wave equation. Zbl 1070.35006 Allaire, Grégoire 2003 Homogenization and localization with an interface. Zbl 1073.35018 Allaire, Grégoire; Capdeboscq, Yves; Piatnitski, Andrey 2003 $$H$$-measures and bounds on the effective properties of composite materials. Zbl 1075.74068 Allaire, Grégoire; Maillot, Hervé 2003 Structural optimization by the level-set method. Zbl 1051.49028 Allaire, Grégoire; Jouve, François; Toader, Anca-Maria 2003 Shape optimization by the homogenization method. Zbl 0990.35001 Allaire, Grégoire 2002 A five-equation model for the simulation of interfaces between compressible fluids. Zbl 1169.76407 Allaire, Grégoire; Clerc, Sébastien; Kokh, Samuel 2002 A level-set method for shape optimization. Zbl 1115.49306 Allaire, Grégoire; Jouve, François; Toader, Anca-Maria 2002 Uniform spectral asymptotics for singularly perturbed locally periodic operators. Zbl 1026.35012 Allaire, Grégoire; Piatnitski, Andrey 2002 Homogenization and localization for a 1D eigenvalue problem in a periodic medium with an interface. Zbl 1072.35026 Allaire, Grégoire; Capdeboscq, Yves 2002 Optimal design of micro-mechanisms by the homogenization method. Zbl 1120.74710 Allaire, Grégoire; Jouve, François 2002 Homogenization and localization in locally periodic transport. Zbl 1065.35042 Allaire, Grégoire; Bal, Guillaume; Siess, Vincent 2002 Eigenfrequency optimization in optimal design. Zbl 1004.74063 Allaire, Grégoire; Aubry, Sylvie; Jouve, François 2001 On some recent advances in shape optimization. Zbl 0986.49023 Allaire, Grégoire; Henrot, Antoine 2001 A new approach for the optimal distribution of assemblies in a nuclear reactor. Zbl 0985.65074 Allaire, Grégoire; Castro, Carlos 2001 Numerical simulation of 2-D two-phase flows with interface. Zbl 1064.76548 Kokh, S.; Allaire, G. 2001 Homogenization of a spectral problem in neutronic multigroup diffusion. Zbl 1126.82346 Allaire, Grégoire; Capdeboscq, Yves 2000 ...and 38 more Documents all top 5 ### Cited by 3,053 Authors 77 Allaire, Grégoire 30 Piatnitski, Andrey L. 28 Wang, Michael Yu 26 Casado-Díaz, Juan 24 Dapogny, Charles 23 Cui, Junzhi 23 Luo, Zhen 20 Amstutz, Samuel 20 Mikelić, Andro 20 Novotny, Antonio André 18 Guo, Xu 18 Pedregal, Pablo 18 Suárez-Grau, Francisco Javier 18 Zhang, Weihong 17 Kang, Zhan 17 Nishiwaki, Shinji 17 Schweizer, Ben 16 Abdulle, Assyr 16 Briane, Marc 16 Yamada, Takayuki 16 Yang, Zhiqiang 15 Conca, Carlos 15 Pastukhova, Svetlana Evgenievna 15 Xia, Qi 14 Efendiev, Yalchin R. 14 Izui, Kazuhiro 14 Maute, Kurt 14 Sigmund, Ole 14 Tortorelli, Daniel A. 14 Zhang, Weisheng 13 Gao, Liang 13 Milton, Graeme Walter 12 Amaziane, Brahim 12 Cao, Liqun 12 Gruais, Isabelle 12 Hoang, Viet Ha 12 Muntean, Adrian 12 Neukamm, Stefan 12 Pankratov, Leonid S. 12 Rohan, Eduard 12 Shi, Tielin 12 Velčić, Igor 11 Bouchitté, Guy 11 Cherednichenko, Kirill D. 11 Jouve, François 11 Kovtunenko, Viktor Anatolievich 11 Pažanin, Igor 11 Ptashnyk, Mariya 11 Sokołowski, Jan 11 Sun, Yi 11 Visintin, Augusto 11 Woukeng, Jean Louis 11 Xia, Liang 11 Yeh, Li-Ming 11 Zhu, Jihong 11 Zhu, Shengfeng 11 Zuazua, Enrique 10 Dambrine, Marc 10 Evgrafov, Anton 10 Frénod, Emmanuel 10 Henning, Patrick 10 Neuss-Radu, Maria 10 Osmolovskij, V. G. 10 Periago, Francisco 10 Poliševski, Dan A. 10 Sili, Ali 10 Vanninathan, Muthusamy 10 Wang, Yiqiang 10 Zhikov, Vasiliĭ Vasil’evich 9 Amar, Micol 9 Boughammoura, Ahmed 9 Chung, Tsz Shun Eric 9 Luna-Laynez, Manuel 9 Masmoudi, Nader 9 Nnang, Hubert 9 Shumilova, Vladlena Valerievna 9 Toader, Anca-Maria 9 Tong, Liyong 9 Van Goethem, Nicolas 8 Barbarosie, Cristian 8 Chen, Shikui 8 Dong, Hao 8 Hassine, Maatoug 8 Holmbom, Anders 8 Lamacz, Agnes 8 Lewiński, Tomasz 8 Lipton, Robert P. 8 Martínez-Frutos, Jesús 8 Münch, Arnaud 8 Nomura, Tsuyoshi 8 Ohlberger, Mario 8 Rabczuk, Timon 8 Rozvany, George I. N. 8 Rumpf, Martin 8 Wei, Peng 8 Wheeler, Mary Fanett 8 Yamasaki, Shintaro 7 Anguiano, María 7 Bal, Guillaume 7 Bellido, José Carlos ...and 2,953 more Authors all top 5 ### Cited in 311 Serials 269 Computer Methods in Applied Mechanics and Engineering 147 Journal of Computational Physics 92 Structural and Multidisciplinary Optimization 57 Applicable Analysis 57 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 56 Archive for Rational Mechanics and Analysis 56 Journal of Mathematical Analysis and Applications 53 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 42 International Journal for Numerical Methods in Engineering 41 Multiscale Modeling & Simulation 39 Journal of Computational and Applied Mathematics 38 Mathematical Methods in the Applied Sciences 38 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 37 Journal of Differential Equations 36 Calculus of Variations and Partial Differential Equations 34 SIAM Journal on Mathematical Analysis 33 Computers & Mathematics with Applications 33 Journal of Mathematical Sciences (New York) 32 Computational Mechanics 31 Computers and Fluids 29 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 29 Comptes Rendus. Mathématique. Académie des Sciences, Paris 27 Journal of the Mechanics and Physics of Solids 27 Journal de Mathématiques Pures et Appliquées. Neuvième Série 25 Journal of Optimization Theory and Applications 25 SIAM Journal on Control and Optimization 25 Applied Mathematical Modelling 21 Networks and Heterogeneous Media 20 Journal of Scientific Computing 19 Applied Mathematics and Computation 19 Asymptotic Analysis 19 Applications of Mathematics 18 Journal of Elasticity 18 Discrete and Continuous Dynamical Systems. Series S 17 SIAM Journal on Applied Mathematics 16 International Journal of Engineering Science 16 Communications in Partial Differential Equations 16 SIAM Journal on Scientific Computing 16 Engineering Analysis with Boundary Elements 16 Nonlinear Analysis. Real World Applications 15 ZAMP. Zeitschrift für angewandte Mathematik und Physik 15 Numerische Mathematik 15 Computational Geosciences 14 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 14 Mathematics and Mechanics of Solids 13 Communications in Mathematical Physics 13 European Journal of Mechanics. A. Solids 12 Continuum Mechanics and Thermodynamics 12 Mathematical Problems in Engineering 11 Acta Mechanica 11 Discrete and Continuous Dynamical Systems. Series B 10 Journal of Fluid Mechanics 10 SIAM Journal on Numerical Analysis 10 Acta Applicandae Mathematicae 10 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 10 Optimization and Engineering 10 Archives of Computational Methods in Engineering 10 Communications on Pure and Applied Analysis 9 Journal of Mathematical Physics 9 Mathematics and Computers in Simulation 9 Applied Numerical Mathematics 9 Applied Mathematics Letters 9 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 8 Annali di Matematica Pura ed Applicata. Serie Quarta 8 Quarterly of Applied Mathematics 8 European Journal of Applied Mathematics 8 NoDEA. Nonlinear Differential Equations and Applications 8 Communications in Computational Physics 7 Mathematics of Computation 7 Applied Mathematics and Optimization 7 Zeitschrift für Analysis und ihre Anwendungen 7 Computational Optimization and Applications 7 Advances in Computational Mathematics 7 Journal of Mathematical Fluid Mechanics 7 Acta Mechanica Sinica 6 Communications on Pure and Applied Mathematics 6 International Journal of Solids and Structures 6 Mathematical Notes 6 Chinese Annals of Mathematics. Series B 6 RAIRO. Modélisation Mathématique et Analyse Numérique 6 Mathematical and Computer Modelling 6 International Journal of Computer Mathematics 6 Mediterranean Journal of Mathematics 6 Inverse Problems in Science and Engineering 6 Annali dell’Università di Ferrara. Sezione VII. Scienze Matematiche 5 International Journal for Numerical Methods in Fluids 5 Journal of Engineering Mathematics 5 Journal of Statistical Physics 5 Ricerche di Matematica 5 Physica D 5 Computational Mathematics and Mathematical Physics 5 St. Petersburg Mathematical Journal 5 Discrete and Continuous Dynamical Systems 5 European Series in Applied and Industrial Mathematics (ESAIM): Proceedings 5 Optimization Methods & Software 5 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 5 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics 5 International Journal of Computational Methods 5 Mathematical Control and Related Fields 5 S$$\vec{\text{e}}$$MA Journal ...and 211 more Serials all top 5 ### Cited in 48 Fields 1,196 Partial differential equations (35-XX) 1,096 Mechanics of deformable solids (74-XX) 616 Fluid mechanics (76-XX) 555 Numerical analysis (65-XX) 501 Calculus of variations and optimal control; optimization (49-XX) 130 Optics, electromagnetic theory (78-XX) 90 Classical thermodynamics, heat transfer (80-XX) 90 Statistical mechanics, structure of matter (82-XX) 88 Operations research, mathematical programming (90-XX) 64 Biology and other natural sciences (92-XX) 61 Probability theory and stochastic processes (60-XX) 52 Operator theory (47-XX) 44 Systems theory; control (93-XX) 39 Functional analysis (46-XX) 25 Ordinary differential equations (34-XX) 24 Quantum theory (81-XX) 20 Computer science (68-XX) 18 Dynamical systems and ergodic theory (37-XX) 16 Information and communication theory, circuits (94-XX) 15 Integral equations (45-XX) 14 Global analysis, analysis on manifolds (58-XX) 13 Linear and multilinear algebra; matrix theory (15-XX) 12 Geophysics (86-XX) 11 Harmonic analysis on Euclidean spaces (42-XX) 10 Differential geometry (53-XX) 10 General topology (54-XX) 10 Statistics (62-XX) 10 Mechanics of particles and systems (70-XX) 10 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 9 Approximations and expansions (41-XX) 8 Potential theory (31-XX) 7 General and overarching topics; collections (00-XX) 7 Measure and integration (28-XX) 6 Real functions (26-XX) 5 Functions of a complex variable (30-XX) 4 Difference and functional equations (39-XX) 4 Manifolds and cell complexes (57-XX) 4 Relativity and gravitational theory (83-XX) 2 History and biography (01-XX) 2 Combinatorics (05-XX) 2 Astronomy and astrophysics (85-XX) 1 Field theory and polynomials (12-XX) 1 Algebraic geometry (14-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Special functions (33-XX) 1 Sequences, series, summability (40-XX) 1 Abstract harmonic analysis (43-XX) 1 Integral transforms, operational calculus (44-XX) ### Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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2022-05-24T11:18:17
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https://pos.sissa.it/395/500/
Volume 395 - 37th International Cosmic Ray Conference (ICRC2021) - DM - Dark Matter Characterization of the DIMS system based on astronomical meteor techniques for macroscopic dark matter search D. Barghini*, S. Valenti, S. Abe, M. Arahori, M.E. Bertaina, M. Casolino, A. Cellino, C. Covault, T. Ebisuzaki, Y. Fujiwara, D. Gardiol, M. Hajdukova, R. Ide, Y. Iwami, F. Kajino, S.W. Kim, J.N. Matthews, K. Nadamoto, I.H. Park, L. Piotrowski, H. Sagawa, K. Shinozaki, D. Shinto, J.S. Sidhu, G. Starkman, S. Tada, Y. Takizawa and Y. Tamedaet al. (click to show) Full text: pdf Pre-published on: July 06, 2021 Published on: Abstract Nuclearites are strange quark matter conglomerates that are hypothesized as possible candidates of macroscopic dark matter. When impacting the Earth’s atmosphere, they should undergo quasi-elastic collisions with the air molecules and emit black-body radiation, thus generating atmospheric luminous events similar to meteors. However, nuclearites could be distinguished from meteors mainly by their altitude, velocity, and motion direction of the bright flight. For instance, nuclearites of galactic origins are expected to have a typical velocity of 250 km s$^{-1}$, whereas meteors observed in the Earth’s atmosphere are bounded to 72 km s$^{-1}$. In the case of meteoroids of interstellar origin, this value may be exceeded but, considering the stellar velocity distribution in the vicinity of the Sun, only by several kilometres per second. The DIMS (Dark matter and Interstellar Meteoroid Study) experiment was designed to search for such fast-moving particles by observing the sky with wide-field, high-sensitivity CMOS cameras. We derived the calibration of the DIMS sensors by astrometric and photometric techniques applied to observed stars in the field of view and assessed the achieved positional precision and sensitivity levels. Since nuclearites and meteor events feature quite distinct observational conditions, we optimized the DIMS setup and analysis pipeline. The distinct spectrum of mass and velocity of nuclearites must also be taken into account. We consequently evaluated the variability of nuclearites dynamics in the atmosphere in this respect. We also assessed the potentiality of the DIMS system in posing limits for macros observation based on our preliminary results. In this contribution, we will present the current status of this work. DOI: https://doi.org/10.22323/1.395.0500 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.
2021-07-28T13:57:59
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https://www.usgs.gov/center-news/free-open-landsat-data-unleashed-power-remote-sensing-a-decade-ago
Free, Open Landsat Data Unleashed the Power of Remote Sensing a Decade Ago Release Date: In the old days, before 2008, a view of planet Earth from space often came at a cost. This image of the Ross Archipelago near the McMurdo Station in Antarctica was acquired January 1, 2018, by Landsat 8, almost exactly a decade after USGS and NASA officials signed off on a Landsat Data Distribution Policy that made Landsat images free to the public. (Public domain.) Want a Multispectral Scanner digital image in 1979 from Landsat 2? That’s $200. A Thematic Mapper image from Landsat 5 in 1995? The commercial company EOSAT that was operating the Landsat system at the time needed$4,000 a scene to recoup its costs. John Schott laughs about it now. For years, graduate students he mentored as a professor at the Rochester Institute of Technology focused their work on one Landsat image because that’s all they could afford. At Virginia Tech, Professor Jim Campbell said his university had four or five Landsat images it owned. “And if we had an image, we had to keep using that same image in our classes, for this purpose or that purpose, over and over again,” Campbell said. All that changed in January 2008 when Barb Ryan, the Associate Director for Geography at the U.S. Geological Survey, and Michael Freilich, NASA’s Director of the Earth Science Division, signed off on a Landsat Data Distribution Policy that made Landsat images free to the public. The USGS announced the free-and-open data policy on April 21, 2008. It was a decision that Boston University Professor Curtis Woodcock says brought about “the biggest change, really, other than the launch of individual sensors, in the whole history of the Landsat program.” With the development of the Internet, Ryan could see the global possibilities for Landsat data that would no longer have to be sent out on physical tapes, but could be distributed easier and faster on the World Wide Web. Paying for Landsat scenes historically meant much of this rich trove of information sat locked away unused in the archive. But unleashed by the change in policy, that no-cost data became “a paradigm shift for the world,” said Ryan, who went on to become the Secretariat Director of the Group on Earth Observations (GEO) in Geneva, Switzerland. Video Transcript Leaders in the field of remote sensing discuss working with Landsat data since it began in 1972. With the change to a free and open policy 10 years ago, new and exciting possibilities have opened up. Andy Dykstra (Contractor), USGS EROS Center (Public domain.) Indeed, though it took a few years to prepare the Landsat archive—and to develop tools and processes needed to handle massive amounts of data—the impact of the policy was transformational. Where 53 Landsat scenes had been leaving the archive every day when there was a cost for them, the number jumped to 5,775 daily when the price tag was removed. Up to that point, scientists never really had the opportunity to take all Landsat data for a single location and study it over time. Even when they could, there were issues like clouds and shadows to be overcome, all of which evolved into a desire for such things as more meaningful surface reflectance. So while it is simple to say free and open Landsat data has been around for 10 years, “the opportunities to explore what’s possible given all of the observations, we’re still really building the tools to do that,” Woodcock said. Still, what a glorious time in Earth observation it has become. The world is moving to analysis ready data (ARD), taking most of the processing out of Landsat data and making it available almost immediately for scientists to run their algorithms against. That ARD in turn enables the evolution of time-series analysis and data cubes, much as USGS EROS is pursuing with its Land Change Monitoring, Assessment, and Projection (LCMAP) initiative. With the development of Cloud-based processing, massive amounts of data now can be processed in hours instead of weeks. “We’ve had this interesting convergence of analytical capabilities, computing capabilities, better imagination and, of course, all of that is surrounded by serious problems that need to be solved,” said Tom Loveland, Chief Scientist at USGS EROS. “I think we’re poised to really start a more real-time focus on understanding the condition of the Earth.” And really, that’s only because of a decision made 10 years ago to give scientists across the world free and open access to perhaps the greatest and richest civilian treasure chest of remotely sensed images Earth has ever known. “The archive is just going to continue to yield good information, good science, better management, reduced costs,” Schott at RIT said. “The biggest contribution of Landsat will be that archive.”
2021-09-25T10:52:30
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http://dergipark.gov.tr/ijcesen/issue/18461/194366
| | | | Semiclassical Transfer Operator for Complex Built-up Structures Hanya HAMDIN [1] , Gregor TANNER [2] , Stephen CREAGH [3] 169 201 We investigate the wave energy distribution in complex built-up structures it is clear where the semiclassical approximations are made at each stage of the derivation. We reformulate the boundary integral equations for the Helmholtz equation in terms of incoming and outgoing boundary waves independently of the boundary conditions and decomposing the green functions into singular and regular components. For demonstration purposes, we apply a semiclassical form of the operator (corresponding to a high-frequency approximation) to polygonal coupled-cavity configurations with abrupt changes of the material properties (such as wave speed and absorption coefficients at the interfaces between the cavities) We investigate the wave energy distribution in complex built-up structures with multiple interfaces at which the material properties change discontinuously. We formulate the transfer operator in such a way that it can in principle be made exact, and it is clear where the semiclassical approximations are made at each stage of the derivation. We reformulate the boundary integral equations for the Helmholtz equation in terms of incoming and outgoing boundary waves independently of the boundary conditions and decomposing the green functions into singular and regular components. For demonstration purposes, we apply a semiclassical form of the operator (corresponding to a high-frequency approximation) to polygonal coupled-cavity configurations with abrupt changes of the material properties (such as wave speed and absorption coefficients at the interfaces between the cavities). Bogomolny transfer operator with multiple interfaces at which the material properties change discontinuously. We Boundary integral equations Green function formulate the transfer operator in such a way that it can in principle be made exact, and • M. Abramowitz, I. A. Stegun “Handbook of Mathematical Functions” Dover, New York (1972) • H. Ben Hamdin “Boundary element and transfer operator methods for multi-component wave systems” PhD Thesis, School of Mathematical Sciences, Nottingham University, UK( 2012) • H. Ben Hamdin, G. Tanner “Multi-component BEM for the Helmholtz equation - A normal derivative method” IOS Press, Shock and Vibration, 19 (2012) 957–967 • E.B. Bogomolny “Semiclassical quantization of multidimensional systems” Nonlinearity, 5(1992) 805–866 • P. A. Boasman “Semiclassical Accuracy for Billiards” Nonlinearity, 7 (1994) 485 • S. C. Creagh, H. Ben Hamdin and G. Tanner “In-out decomposition of boundary integral equations” J.Phys. A: Math. Theor., 46(2013) • B. Georgeot, R. E. Prange “Exact and Quasiclassical Fredholm Solutions of Quantum Billiards” Phys. Rev. Lett.,74 (15) (1992) 2851–2854 • B. Georgeot, R. E. Prange “Fredholm Theory for • Quasiclassical Scattering” Phys. Rev. Lett.,74 (21) (1995) 4110–4113 • T. Prosen “Exact quantum surface of section method” J. Phys. A:Math. Gen., 27(1994)L709– L714 • T. Prosen “General quantum surface-of-section • method” J. Phys. A:Math. Gen., 28(1995) 4133–4155 Birincil Dil tr Makaleler Yazar: Hanya HAMDIN Yazar: Gregor TANNER Yazar: Stephen CREAGH Bibtex @ { ijcesen194366, journal = {International Journal of Computational and Experimental Science and Engineering}, issn = {}, eissn = {2149-9144}, address = {İskender AKKURT}, year = {2015}, volume = {1}, pages = {11 - 15}, doi = {10.22399/ijcesen.194366}, title = {Semiclassical Transfer Operator for Complex Built-up Structures}, key = {cite}, author = {CREAGH, Stephen and HAMDIN, Hanya and TANNER, Gregor} } APA HAMDIN, H , TANNER, G , CREAGH, S . (2015). Semiclassical Transfer Operator for Complex Built-up Structures. International Journal of Computational and Experimental Science and Engineering, 1 (1), 11-15. DOI: 10.22399/ijcesen.194366 MLA HAMDIN, H , TANNER, G , CREAGH, S . "Semiclassical Transfer Operator for Complex Built-up Structures". International Journal of Computational and Experimental Science and Engineering 1 (2015): 11-15 Chicago HAMDIN, H , TANNER, G , CREAGH, S . "Semiclassical Transfer Operator for Complex Built-up Structures". International Journal of Computational and Experimental Science and Engineering 1 (2015): 11-15 RIS TY - JOUR T1 - Semiclassical Transfer Operator for Complex Built-up Structures AU - Hanya HAMDIN , Gregor TANNER , Stephen CREAGH Y1 - 2015 PY - 2015 N1 - doi: 10.22399/ijcesen.194366 DO - 10.22399/ijcesen.194366 T2 - International Journal of Computational and Experimental Science and Engineering JF - Journal JO - JOR SP - 11 EP - 15 VL - 1 IS - 1 SN - -2149-9144 M3 - doi: 10.22399/ijcesen.194366 UR - http://dx.doi.org/10.22399/ijcesen.194366 Y2 - 2018 ER - EndNote %0 International Journal of Computational and Experimental Science and Engineering Semiclassical Transfer Operator for Complex Built-up Structures %A Hanya HAMDIN , Gregor TANNER , Stephen CREAGH %T Semiclassical Transfer Operator for Complex Built-up Structures %D 2015 %J International Journal of Computational and Experimental Science and Engineering %P -2149-9144 %V 1 %N 1 %R doi: 10.22399/ijcesen.194366 %U 10.22399/ijcesen.194366 ISNAD HAMDIN, Hanya , TANNER, Gregor , CREAGH, Stephen . "Semiclassical Transfer Operator for Complex Built-up Structures". International Journal of Computational and Experimental Science and Engineering 1 / 1 (Eylül 2015): 11-15. http://dx.doi.org/10.22399/ijcesen.194366
2018-12-15T14:42:03
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https://par.nsf.gov/biblio/10367465-simple-model-predicting-tropical-cyclone-radius-maximum-wind-from-outer-size
A Simple Model for Predicting the Tropical Cyclone Radius of Maximum Wind from Outer Size Abstract The radius of maximum wind (Rmax) in a tropical cyclone governs the footprint of hazards, including damaging wind, surge, and rainfall. However,Rmaxis an inconstant quantity that is difficult to observe directly and is poorly resolved in reanalyses and climate models. In contrast, outer wind radii are much less sensitive to such issues. Here we present a simple empirical model for predictingRmaxfrom the radius of 34-kt (1 kt ≈ 0.51 m s−1) wind (R17.5 ms). The model only requires as input quantities that are routinely estimated operationally: maximum wind speed,R17.5 ms, and latitude. The form of the empirical model takes advantage of our physical understanding of tropical cyclone radial structure and is trained on the Extended Best Track database from the North Atlantic 2004–20. Results are similar for the TC-OBS database. The physics reduces the relationship between the two radii to a dependence on two physical parameters, while the observational data enables an optimal estimate of the quantitative dependence on those parameters. The model performs substantially better than existing operational methods for estimatingRmax. The model reproduces the observed statistical increase inRmaxwith latitude and demonstrates that this increase is driven by the increase inR17.5 mswith latitude. Overall, the model offers a simple and fast more » Significance Statement If we can better predict the area of strong winds in a tropical cyclone, we can better prepare for its potential impacts. This work develops a simple model to predict the radius where the strongest winds in a tropical cyclone are located. The model is simple and fast and more accurate than existing models, and it also helps us to understand what causes this radius to vary in time, from storm to storm, and at different latitudes. It can be used in both operational forecasting and models of tropical cyclone hazard risk. Authors: ; Publication Date: NSF-PAR ID: 10367465 Journal Name: Weather and Forecasting Volume: 37 Issue: 5 Page Range or eLocation-ID: p. 563-579 ISSN: 0882-8156 Publisher: American Meteorological Society National Science Foundation ##### More Like this 1. Abstract Recent work found evidence using aquaplanet experiments that tropical cyclone (TC) size on Earth is limited by the Rhines scale, which depends on the planetary vorticity gradientβ. This study aims to examine how the Rhines scale limits the size of an individual TC. The traditional Rhines scale is first reexpressed as a Rhines speed to characterize how the effect ofβvaries with radius in a vortex whose wind profile is known. The framework is used to define the vortex Rhines scale, which is the transition radius that divides the vortex into a vortex-dominant region at smaller radii, where the axisymmetric circulation is steady, and a wave-dominant region at larger radii, where the circulation stimulates planetary Rossby waves and dissipates. Experiments are performed using a simple barotropic model on aβplane initialized with a TC-like axisymmetric vortex defined using a recently developed theoretical TC wind profile model. The gradientβand initial vortex size are each systematically varied to investigate the detailed responses of the TC-like vortex toβ. Results show that the vortex shrinks toward an equilibrium size that closely follows the vortex Rhines scale. A larger initial vortex relative to its vortex Rhines scale will shrink faster. The shrinking time scale is wellmore » Significance Statement Tropical cyclones vary in size significantly on Earth, but how large a tropical cyclone could potentially be is still not understood. The variation of the Coriolis parameter with latitude is known to limit the size of turbulent circulations, but its effect on tropical cyclones has not been studied. This study derives a new parameter related to this concept called the “vortex Rhines scale” and shows in a simple model how and why storms will tend to shrink toward this size. These results help explain why tropical cyclone size tends to increase slowly with latitude on Earth and can help us understand what sets the size of tropical cyclones on Earth in general. 2. Abstract The central theme of this study is to explore if and how the intensity of a tropical cyclone (TC) is related to its size. This subject has puzzled atmospheric scientists since the work of Deppermann, but the existence of this relationship still remains elusive. The improved understanding of the intensity–size relationship of TCs will help coastal communities to prepare for the maximum potential damage as both the intensity and size have important impacts on wind damages, storm surges, and flooding. This study considers 33 years (1988–2020) of TC records of maximum surface winds and radii of maximum and gale-force winds over the North Atlantic basin derived from the Extended Best Track Dataset. Analysis of these TC records reveals a robust positive correlation between loss of Earth and relative angular momentum. This finding together with the inspiration from the seminal work of Emanuel and his collaborators leads us to combine absolute angular momentum and its frictional loss as a radially invariant quantity, referred to as “effective absolute angular momentum” (eAAM), for radial profiles of TC surface winds. It is demonstrated that the eAAM model can reproduce the observed complex intensity–size relationship of TCs, which can be further reduced to amore » 3. Abstract State transitions in black hole X-ray binaries are likely caused by gas evaporation from a thin accretion disk into a hot corona. We present a height-integrated version of this process, which is suitable for analytical and numerical studies. With radiusrscaled to Schwarzschild units and coronal mass accretion rate$ṁc$to Eddington units, the results of the model are independent of black hole mass. State transitions should thus be similar in X-ray binaries and an active galactic nucleus. The corona solution consists of two power-law segments separated at a break radiusrb∼ 103(α/0.3)−2, whereαis the viscosity parameter. Gas evaporates from the disk to the corona forr>rb, and condenses back forr<rb. Atrb,$ṁc$reaches its maximum,$ṁc,max≈0.02(α/0.3)3$. If atrrbthe thin disk accretes with$ṁd, then the disk evaporates fully before reachingrb, giving the hard state. Otherwise, the disk survives at all radii, giving the thermal state. While the basic model considers only bremsstrahlung cooling and viscous heating, we also discuss a more realistic model that includes Compton cooling and direct coronal heating by energy transport from the disk. Solutions are again independent of black hole mass, andrbremainsmore » 4. Abstract We develop a Newtonian model of a deep tidal disruption event (TDE), for which the pericenter distance of the star,rp, is well within the tidal radius of the black hole,rt, i.e., whenβrt/rp≫ 1. We find that shocks form forβ≳ 3, but they are weak (with Mach numbers ∼1) for allβ, and that they reach the center of the star prior to the time of maximum adiabatic compression forβ≳ 10. The maximum density and temperature reached during the TDE follow much shallower relations withβthan the previously predicted$ρmax∝β3$and$Tmax∝β2$scalings. Belowβ≃ 10, this shallower dependence occurs because the pressure gradient is dynamically significant before the pressure is comparable to the ram pressure of the free-falling gas, while aboveβ≃ 10, we find that shocks prematurely halt the compression and yield the scalings$ρmax∝β1.62$and$Tmax∝β1.12$. We find excellent agreement between our results and high-resolution simulations. Our results demonstrate that, in the Newtonian limit, the compression experienced by the star is completely independent of the mass of the black hole. We discuss our results in the context of existing (affine) models, polytropic versus non-polytropic stars, and general relativistic effects, which become important when the pericenter ofmore » 5. Abstract There is a lack of consensus on whether North Atlantic tropical cyclone (TC) outer size and structure (i.e., change in outer winds with increasing radius from the TC) will differ by the late twenty-first century. Hence, this work seeks to examine whether North Atlantic TC outer wind field size and structure will change by the late twenty-first century using multiple simulations under CMIP3 SRES A1B and CMIP5 RCP4.5 scenarios. Specifically, our analysis examines data from the GFDL High-Resolution Forecast-Oriented Low Ocean Resolution model (HiFLOR) and two versions of the GFDL hurricane model downscaling climate model output. Our results show that projected North Atlantic TC outer size and structure remain unchanged by the late twenty-first century within nearly all HiFLOR and GFDL hurricane model simulations. Moreover, no significant regional outer size differences exist in the North Atlantic within most HiFLOR and GFDL hurricane model simulations. No changes between the control and late-twenty-first-century simulations exist over the storm life cycle in nearly all simulations. For the simulation that shows significant decreases in TC outer size, the changes are attributed to reductions in storm lifetime and outer size growth rates. The absence of differences in outer size among most simulations is consistentmore »
2023-02-04T22:41:44
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https://control.com/textbook/discrete-process-measurement/pressure-switches/
# Pressure Switches ## Chapter 18 - Discrete Process Measurement A pressure switch is one detecting the presence of fluid pressure. Pressure switches often use diaphragms or bellows as the pressure-sensing element, the motion of which actuates one or more switch contacts. Recall from section 9.1 that the “normal” status of a switch is the resting condition of no stimulation. A pressure switch will be in its “normal” status when it senses minimum pressure (e.g. an applied pressure, or in some cases a vacuum condition). For a pressure switch, “normal” status is any fluid pressure below the trip threshold of the switch. The following photograph shows two pressure switches sensing the same fluid pressure as an electronic pressure transmitter (the device on the far left) because they are all plumbed to a common tube: A legacy design of pressure switch uses a bourdon tube as the pressure-sensing element, and a glass bulb partially filled with mercury as the electrical switching element. When applied pressure causes the bourdon tube to flex sufficiently, the glass bulb tilts far enough to cause the mercury to fall against a pair of electrodes, thus completing an electrical circuit. A great many pressure switches of this design were sold under the brand name of “Mercoid,” with a few appearing in this photograph of a steam boiler (the round-shaped units with glass covers allowing inspection of the bourdon tube and mercury tilt switch): A close-up photograph of one of these pressure switches appears here. The bourdon tube is grey in color, and almost as wide in diameter as the circular switch housing. The mercury tilt switch bottles have yellow-colored plastic caps covering up their external electrical contacts: The next set of photographs show a mercury tilt switch removed from the pressure switch mechanism, so you may see the switch in two different states (contact open on the left, and closed on the right): Advantages of mercury tilt switches include immunity to switch contact degradation from harmful atmospheres (oil mist, dirt, dust, corrosion) as well as safety in explosive atmospheres (since a spark contained within a hermetically sealed glass bulb cannot touch off an explosion in the surrounding atmosphere). Disadvantages include the possibility of intermittent electrical contact resulting from mechanical vibration, as well as sensitivity to mounting angle (i.e. you would not want to use this kind of switch aboard a moving vehicle!). A pressure switch manufactured by the Danfoss corporation appears in the next photograph. This particular model of pressure switch has windows on the front cover allowing a technician to see the pressure limit setting inside: This switch balances the force generated by a pressure-sensing element against a mechanical spring. Tension on the spring may be adjusted by a technician, which means the trip point of this switch is adjustable. One of the settings on this switch is the deadband or differential pressure setting, seen in the lower window. This setting determines the amount of pressure change required to re-set the switch to its normal state after it has tripped. For example, a high-pressure switch with a trip point of 67 PSI (changes state at 67 PSI, increasing) that re-sets back to its normal state at a pressure of 63 PSI decreasing has a “deadband” or “differential” pressure setting of 4 PSI (67 PSI $$-$$ 63 PSI = 4 PSI). The “differential” pressure setting of a gauge pressure switch is not to be confused with a true differential pressure switch. In the next photograph, we see a pressure switch truly actuated by differential pressure (the difference in fluid pressure sensed between two ports): The electrical switch element is located underneath the blue cover, while the diaphragm pressure element is located within the grey metal housing. The net force exerted on the diaphragm by the two fluid pressures varies in magnitude and direction with the magnitude of those pressures. If the two fluid pressures are precisely equal, the diaphragm experiences no net force (zero differential pressure). Like the Danfoss gauge pressure switch seen previously, this differential pressure switch has a “trip” or “limit” setting as well as a “dead-band” or “differential” setting. It is important to recognize and clearly distinguish the two meanings of differential pressure in the context of this device. It senses differences in pressure between two input ports (“differential pressure” – the difference between two different fluid pressure connections), but being a switch, it also exhibits some dead band in its action (“differential pressure” – a change in pressure required to re-set the switch’s state). • Share Published under the terms and conditions of the Creative Commons Attribution 4.0 International Public License
2020-02-20T21:03:36
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https://www.ecb.europa.eu/pub/financial-stability/fsr/focus/2020/html/ecb.fsrbox202005_03~eaf7ae06be.en.html
# Euro area banks’ sensitivity to corporate decarbonisation Prepared by Marco Belloni, Luca Mingarelli, Rafel Moyà Porcel and Petya Radulova Published as part of Financial Stability Review, May 2020. As awareness of the environmental, social and economic risks from disorderly climate change has grown, so has awareness of the need for businesses to accelerate their decarbonisation. Banks need to be prepared for changes in loan performance should financial losses result from abrupt shifts in policies, technologies or consumer sentiment in response to the risks posed by climate change. While credit ratings could in principle capture such risks, in practice rating agencies have only just begun incorporating risks arising from an abrupt transition to a low-carbon economy. This box assesses how sensitive the euro area banking system is to higher probabilities of default for corporates stemming from an abrupt carbon adjustment.[1] A first scenario examines the impact of corporate rating downgrades applied indiscriminately to climate-sensitive economic sectors.[2] A second scenario exploits firm-level data to examine the potential for downgrades within sectors, where all companies reporting high carbon emissions are reassessed by rating agencies. Both analyses are based on ECB supervisory statistics (large exposures dataset)[3] and ECB securities holdings statistics. Chart A Euro area banking system losses in the event of an abrupt climate transition for carbon-intensive sectors Sources: Moody’s and ECB calculations. Notes: The left panel presents the factor of increase in losses relative to a baseline non-stressed scenario. In the right panel, the breakdown of losses by sector at risk accounts only for losses above the baseline, i.e. arising only from the transition risk shock. Loss estimates take into account direct contagion, including second-round effects, as well as indirect contagion arising from overlapping holdings of depreciating assets. Baseline losses are the estimated losses in a scenario where probabilities of default are not stressed. In the first scenario, losses from a one-notch downgrade triggered by climate risk could be severe for the affected sectors, but losses only lead to systemic stress if downgrades are multi-notch. For a one-to-two notch downgrade, banking system losses are estimated to increase by up to 60%. However, should a disorderly transition lead to a several-notch downgrade, losses within the euro area banking system are estimated to double, leading to a potential for financial instability (see Chart A, left panel). The energy-intensive sector22 – including e.g. mining of metals, goods manufacturing, etc. – alone contributes about half of the additional losses arising from transition risk, which is significantly more than any other sector (see Chart A, right panel). In the second scenario, while diversified exposures should shield the banking sector from large losses for the highest-emitting firms within sectors, losses could still be meaningful. Company-level data23 indicate a wide degree of dispersion of carbon transition risk within the non-financial sectors (see Chart B, left panel). Applying shocks proportional to each firm’s emissions rather than for a sector as a whole, losses in the banking system are estimated to increase by up to 10% for shocks corresponding to one-notch downgrades. In the individual firm-level exercise, system-wide losses amount to system distress only for downgrades of four notches or more (see Chart B, right panel). In the firm-level exercise, even for the highest levels of shock considered, losses within the banking system are therefore much more contained compared with the sector-based analysis. Clearly, banks with concentrated lending portfolios in particular sectors would face higher losses. Chart B Restricting rating downgrades based on firms’ level of emissions suggests lower banking sector losses Sources: Moody’s and ECB calculations. Notes: Stresses to probabilities of default at firm level are obtained as a function of each corporation’s emissions and a sensitivity parameter $α$. The connection with the sectoral analysis is made based on the resulting mean stressed probabilities of default, so that for a given average probability one can find a corresponding value of $α$. Then, refers to the level of $α$ giving the equivalent average probability across the sample as in the case of $n$-notch downgrades in the sectoral analysis. Left panel: one-digit NACE sector classification. Sectors are placed in order based on their average emissions. The x-axis shows the factor by which probabilities of default are increased given the emissions-based downgrade. Right panel: losses relative to baseline for levels of $α$ comparable to one-to-five notch downgrades in the sectoral analysis. This analysis provides a rationale for using firm-level information to assess the sensitivity of the banking system to downgrades related to decarbonisation. The differences in findings between the sectoral and firm-level approach to considering the carbon sensitivity of non-financial firms also indicate that the potential losses for the banking system could be reduced by implementing a targeted management of exposures to specific firms, rather than restructuring whole sectoral portfolios. [1]The approach is based on granular loan and securities holdings data matched to individual business information to consider the impact of both first-round direct losses incurred by individual banks and some second-round effects propagating through interbank loan networks. See Covi, G., Montagna, M. and Torri, G., “Economic shocks and contagion in the euro area banking sector: a new micro-structural approach”, Financial Stability Review, ECB, May 2019. [2]The identification of climate-sensitive sectors is based on Battiston, S., Mandel, A., Schuetze, F. and Visentin, G., “A Climate Stress-Test of the Financial System”, Nature Climate Change, Vol. 7, March 2017. The authors remap all four-digit NACE Rev. 2 sectors to new climate policy-sensitive sectors, combining criteria such as carbon emissions, the role of the sectors in the supply chain and the existence of traditional policy institutions for the sector. [3]See Financial Stability Review, ECB, November 2019, Section 3.1.
2020-07-11T08:49:16
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https://lammps.sandia.gov/doc/fix_reaxc_species.html
# fix reax/c/species/kk command ## Syntax fix ID group-ID reax/c/species Nevery Nrepeat Nfreq filename keyword value ... • ID, group-ID are documented in fix command • reax/c/species = style name of this command • Nevery = sample bond-order every this many timesteps • Nrepeat = # of bond-order samples used for calculating averages • Nfreq = calculate average bond-order every this many timesteps • filename = name of output file • zero or more keyword/value pairs may be appended • keyword = cutoff or element or position cutoff value = I J Cutoff I, J = atom types Cutoff = Bond-order cutoff value for this pair of atom types element value = Element1, Element2, ... position value = posfreq filepos posfreq = write position files every this many timestep filepos = name of position output file ## Examples fix 1 all reax/c/species 10 10 100 species.out fix 1 all reax/c/species 1 2 20 species.out cutoff 1 1 0.40 cutoff 1 2 0.55 fix 1 all reax/c/species 1 100 100 species.out element Au O H position 1000 AuOH.pos ## Description Write out the chemical species information computed by the ReaxFF potential specified by pair_style reax/c. Bond-order values (either averaged or instantaneous, depending on value of Nrepeat) are used to determine chemical bonds. Every Nfreq timesteps, chemical species information is written to filename as a two line output. The first line is a header containing labels. The second line consists of the following: timestep, total number of molecules, total number of distinct species, number of molecules of each species. In this context, “species” means a unique molecule. The chemical formula of each species is given in the first line. If the filename ends with “.gz”, the output file is written in gzipped format. A gzipped dump file will be about 3x smaller than the text version, but will also take longer to write. Optional keyword cutoff can be assigned to change the minimum bond-order values used in identifying chemical bonds between pairs of atoms. Bond-order cutoffs should be carefully chosen, as bond-order cutoffs that are too small may include too many bonds (which will result in an error), while cutoffs that are too large will result in fragmented molecules. The default cutoff of 0.3 usually gives good results. The optional keyword element can be used to specify the chemical symbol printed for each LAMMPS atom type. The number of symbols must match the number of LAMMPS atom types and each symbol must consist of 1 or 2 alphanumeric characters. Normally, these symbols should be chosen to match the chemical identity of each LAMMPS atom type, as specified using the reax/c pair_coeff command and the ReaxFF force field file. The optional keyword position writes center-of-mass positions of each identified molecules to file filepos every posfreq timesteps. The first line contains information on timestep, total number of molecules, total number of distinct species, and box dimensions. The second line is a header containing labels. From the third line downward, each molecule writes a line of output containing the following information: molecule ID, number of atoms in this molecule, chemical formula, total charge, and center-of-mass xyz positions of this molecule. The xyz positions are in fractional coordinates relative to the box dimensions. For the keyword position, the filepos is the name of the output file. It can contain the wildcard character “*”. If the “*” character appears in filepos, then one file per snapshot is written at posfreq and the “*” character is replaced with the timestep value. For example, AuO.pos.* becomes AuO.pos.0, AuO.pos.1000, etc. The Nevery, Nrepeat, and Nfreq arguments specify on what timesteps the bond-order values are sampled to get the average bond order. The species analysis is performed using the average bond-order on timesteps that are a multiple of Nfreq. The average is over Nrepeat bond-order samples, computed in the preceding portion of the simulation every Nevery timesteps. Nfreq must be a multiple of Nevery and Nevery must be non-zero even if Nrepeat is 1. Also, the timesteps contributing to the average bond-order cannot overlap, i.e. Nrepeat*Nevery can not exceed Nfreq. For example, if Nevery=2, Nrepeat=6, and Nfreq=100, then bond-order values on timesteps 90,92,94,96,98,100 will be used to compute the average bond-order for the species analysis output on timestep 100. Restart, fix_modify, output, run start/stop, minimize info: No information about this fix is written to binary restart files. None of the fix_modify options are relevant to this fix. This fix computes both a global vector of length 2 and a per-atom vector, either of which can be accessed by various output commands. The values in the global vector are “intensive”. The 2 values in the global vector are as follows: • 1 = total number of molecules • 2 = total number of distinct species The per-atom vector stores the molecule ID for each atom as identified by the fix. If an atom is not in a molecule, its ID will be 0. For atoms in the same molecule, the molecule ID for all of them will be the same and will be equal to the smallest atom ID of any atom in the molecule. 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. 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 Speed 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 Build package doc page 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 Speed of the manual for more instructions on how to use the accelerated styles effectively. ## Restrictions The “fix reax/c/species” currently only works with pair_style reax/c and it requires that the pair_style reax/c be invoked. This fix is part of the USER-REAXC package. It is only enabled if LAMMPS was built with that package. See the Build package doc page for more info. To write gzipped species files, you must compile LAMMPS with the -DLAMMPS_GZIP option. It should be possible to extend it to other reactive pair_styles (such as rebo, airebo, comb, and bop), but this has not yet been done. ## Default The default values for bond-order cutoffs are 0.3 for all I-J pairs. The default element symbols are C, H, O, N. Position files are not written by default.
2020-01-21T01:06:13
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https://indico.fnal.gov/event/19645/
# Toya Tanaka - Spectroscopy of the muonium hyperfine structure Wednesday, February 27, 2019 from to (US/Central) at Building 362 ( room F-108 ) Description Muonium is a bound state of a positive muon and an electron. This characteristic enables a precise QED calculation of its physical properties, and the measurement can be performed with high precision because of its relatively long lifetime and the parity violation when the muon decays. MuSEUM (Muonium Spectroscopy Experiment Using Microwave) collaboration aims to measure the muonium hyperfine structure by using the muon beam line of the J-PARC MLF (Materials and Life science Facility). This precise measurement will be a stringent test of the bound-state QED. By the muonium hyperfine spectroscopy with a high magnetic field, the muon-proton magnetic moment ratio and the muon-electron mass ratio can be extracted as byproducts [1], which the precision are significant to other muon physical properties. The muon-proton magnetic moment ratio is a parameter to decide the muon anomalous magnetic moment, which is known as there is a 3.7 standard deviation discrepancy between the theoretical precision and the experimental result [2][3]. The precision of the muon-electron mass ratio is the dominant uncertainty of the muonium hyperfine structure in theoretical calculation[4]. MuSEUM collaboration succeeded to measure the muonium hyperfine structure with an extremely low magnetic field. We are now continuing this and planning a new measurement with the high magnetic field. In this presentation I would like to overview the measurement status and the R&D for the future high field measurement. Go to day
2019-07-20T05:41:10
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https://www.abs.gov.au/methodologies/household-use-information-technology-methodology/2016-17
# Household use of information technology methodology This release has ceased Reference period 2016-17 financial year Released 28/03/2018 Next release Ceased First release ## Explanatory notes ### Introduction 1 The statistics presented in this release were compiled from data collected in the 2016-17 Multipurpose Household Survey (MPHS). The MPHS is conducted each financial year throughout Australia from July to June as a supplement to the ABS' monthly Labour Force Survey (LFS) and is designed to provide annual statistics for a number of small, self-contained topics. 2 For all topics, general demographic information such as age, sex, labour force characteristics and education are also available. 3 This publication covers the HUIT topic and presents details about household and personal internet use providing statistics on: • households with internet access • characteristics of persons accessing the internet • reasons for accessing the internet • types of goods and services purchased over the internet • whether the internet was accessed for home based work • type and mean number of devices used to access the internet at home • cyber security indicators (new data item for 2016-17), and • child protection online indicators (new data item for 2016-17). 4 The HUIT topic has been included in MPHS every two years, however, this is the final iteration of the HUIT survey. ### Scope and coverage 5 The scope of the LFS is restricted to persons aged 15 years and over and excludes the following: • members of the Australian permanent defence forces • certain diplomatic personnel of overseas governments, usually excluded from census and estimated resident population counts • overseas residents in Australia, and • members of non-Australian defence forces (and their dependants). 6 In addition, the 2016-17 MPHS excluded the following from scope: • people living in households in the Indigenous Community Strata (ICS) • people living in non-private dwellings (e.g. hotels, university residences, students at boarding schools, patients in hospitals, inmates of prisons and residents of other institutions (e.g. retirement homes, homes for persons with disabilities)), and • visitors to private dwellings. 7 In the LFS, rules are applied which aim to ensure each person in coverage is associated with only one dwelling, and hence has only one chance of selection in the survey. See the Labour Force, Australia (cat. no. 6202.0) for more details. ### Data collection 8 The publication Labour Force, Australia (cat. no. 6202.0) contains information about survey design, sample redesign, scope, coverage and population benchmarks relevant to the monthly LFS, which also applies to supplementary surveys. It also contains definitions of demographic and labour force characteristics, and information about telephone interviewing relevant to both the monthly LFS and supplementary surveys. 9 ABS interviewers conducted personal interviews during the 2016-17 financial year for the monthly LFS. Each month, one-eighth of the dwellings in the LFS sample were rotated out of the survey. The dwellings that were rotated out of the survey were selected for the MPHS and 50% of these dwellings were selected to complete the HUIT topic. 10 A usual resident aged 15 years or over was selected at random (based on a computer algorithm) and asked the additional questions in a personal interview. If the randomly selected person was aged 15 to 17 years, permission was sought from a parent or guardian before conducting the interview. If permission was not given, the parent or guardian was asked the questions on behalf of the 15 to 17 year old (proxy interview). 11 Data were collected using Computer Assisted Interviewing (CAI), whereby responses were recorded directly onto an electronic questionnaire in a notebook computer, with interviews conducted either face-to-face or over the telephone. Most interviews were conducted over the telephone. ### Sample size 12 The initial sample for the 2016-17 HUIT topic was 23,694 private dwellings, from which one person was randomly selected. Of the 19,632 private dwellings that remained in the survey after sample loss (for example, dwellings selected in the survey which had no residents in scope for the LFS, vacant or derelict dwellings and dwellings under construction), 14,035 private dwellings (72%) fully responded to the questions on the household use of information technology. ### Weighting 13 Weighting is the process of adjusting results from a sample survey to infer results for the total in-scope population. To do this, a 'weight' is allocated to each covered sample unit which can be either a person or a household. The weight is a value which indicates how many population units are represented by the sample unit. 14 The first step in calculating weights for each unit was to assign an initial weight, which is the inverse of the probability of being selected in the survey. For example, if the probability of a person being selected in the survey was 1 in 600, then the person would have an initial weight of 600 (i.e. they represent 600 people). ### Benchmarking 15 The initial weights were then calibrated to align with independent estimates of the population of interest, referred to as 'benchmarks', in designated categories of age by sex by area of usual residence. Weights calibrated against population benchmarks ensure that the survey estimates conform to the independently estimated distribution of the population rather than the distribution within the sample itself. Calibration to population benchmarks helps to compensate for over or under-enumeration of particular categories of persons/households which may occur due to either the random nature of sampling or non-response. 16 For household estimates, the MPHS was benchmarked to independently calculated estimates of the total number of households in Australia. The MPHS estimates do not (and are not intended to) match estimates for the total Australian person/household populations obtained from other sources. 17 For person estimates, the survey was benchmarked to the Estimated Resident Population (ERP) in each state or territory at December 2016. ### Estimation 18 Survey estimates of counts of persons or households are obtained by summing the weights of persons or households with the characteristic of interest. ### Confidentiality 19 To minimise the risk of identifying individuals in aggregate statistics, a technique called perturbation is used to randomly adjust cell values. Perturbation involves small random adjustment of the statistics and is considered the most satisfactory technique for avoiding the release of identifiable statistics while maximising the range of information that can be released. These adjustments have a negligible impact on the underlying pattern of the statistics. After perturbation, a given published cell value will be consistent across all tables. However, adding up cell values to derive a total will not necessarily give the same result as published totals. ### Reliability of estimates 20 All sample surveys are subject to error which can be broadly categorised as either sampling error or non-sampling error. ### Sampling error 21 Sampling error is the difference between the published estimates, derived from a sample of persons, and the value that would have been produced if the total population (as defined by the scope of the survey) had been included in the survey. For more information refer to the Technical Note. ### Non-sampling error 22 Non-sampling error may occur in any collection, whether it is based on a sample or a full count such as a census. Sources of non-sampling error include non-response, errors in reporting by respondents or recording of answers by interviewers and errors in coding and processing data. Every effort is made to reduce non-sampling error by careful design and testing of questionnaires, training and supervision of interviewers, and extensive editing and quality control procedures at all stages of data processing. ### Data comparability 23 Household data in the 2016-17 HUIT are generally comparable with previous surveys (where those household data items have been collected before). 24 Persons data are not directly comparable between HUIT iterations. The definition of an internet user and the reference period for reasons for accessing the internet has changed in different iterations of the survey. ### Comparability of geographic areas 25 HUIT survey data for 'Capital City' and 'Balance of State' areas in the 2007-08, 2008-09, 2010-11 and 2012-13 publications were based on Area of Usual Residence boundaries contained in the Australian Statistical Geography Classification (ASGC). The Australian Standard Geographical Classification (ASGS), introduced in 2011, contained new boundaries for Greater Capital City Statistical Areas (GCCSA) and these were used for the first time in HUIT for 2014-15. The new definitions of Greater Capital City and Rest of State are not comparable with the ASGC boundaries. A suite of geographical correspondences are available to assist users make comparisons and maintain time series between the ASGC and the ASGS, see Australian Statistical Geography Standard (ASGS): Correspondences, July 2011(cat. no. 1270.0.55.006). ### Comparability of international frameworks 26 There are established international frameworks and reporting models for the collection of HUIT statistics (e.g. the OECD model questionnaire of ICT access and use by households and individuals). Suggested question wording from these frameworks have been used as a starting point for HUIT questionnaire design and, where applicable, used in the HUIT survey. ### Comparability of state and territory data 27 Due to the age structure of the populations of Australia's states and territories caution should be used when making comparisons. For example, the level of internet use may be a reflection of a younger age profile, rather than general levels of access to the internet. ### Comparability with monthly LFS statistics 28 Due to differences in the scope and sample size of the MPHS and that of the LFS, the estimation procedure may lead to some small variations between labour force estimates from this survey and those from the LFS. ### Future surveys 29 This is the final issue of HUIT. ### Acknowledgement 30 ABS surveys draw extensively on information provided freely by individuals, businesses, governments and other organisations. Their continued cooperation is very much appreciated. Without it, the wide range of statistics published by the ABS would not be available. Information received by the ABS is treated in strict confidence as required by the Census and Statistics Act 1905. ## Technical note ### Reliability of the estimates 1 The estimates in this publication are based on information obtained from a sample survey. Any data collection may encounter factors, known as non-sampling error, which can impact on the reliability of the resulting statistics. In addition, the reliability of estimates based on sample surveys are also subject to sampling variability. That is, the estimates may differ from those that would have been produced had all persons in the population been included in the survey. ### Non-sampling error 2 Non-sampling error may occur in any collection, whether it is based on a sample or a full count such as a census. Sources of non-sampling error include non-response, errors in reporting by respondents or recording of answers by interviewers and errors in coding and processing data. Every effort is made to reduce non-sampling error by careful design and testing of questionnaires, training and supervision of interviewers, and extensive editing and quality control procedures at all stages of data processing. ### Sampling error 3 One measure of the likely difference is given by the standard error (SE), which indicates the extent to which an estimate might have varied by chance because only a sample of persons was included. There are about two chances in three (67%) that a sample estimate will differ by less than one SE from the number that would have been obtained if all persons had been surveyed, and about 19 chances in 20 (95%) that the difference will be less than two SEs. 4 Another measure of the likely difference is the relative standard error (RSE), which is obtained by expressing the SE as a percentage of the estimate. $$R S E \%=\left(\frac{S E}{estimate}\right) \times 100$$ 5 RSEs for count estimates have been calculated using the Jackknife method of variance estimation. This involves the calculation of 30 'replicate' estimates based on 30 different sub samples of the obtained sample. The variability of estimates obtained from these sub samples is used to estimate the sample variability surrounding the count estimate. 6 The Excel spreadsheets in the Data downloads section contain all the tables produced for this release and the calculated RSEs for each of the estimates. 7 Only estimates (numbers or percentages) with RSEs less than 25% are considered sufficiently reliable for most analytical purposes. However, estimates with larger RSEs have been included. Estimates with an RSE in the range 25% to 50% should be used with caution while estimates with RSEs greater than 50% are considered too unreliable for general use. All cells in the Excel spreadsheets with RSEs greater than 25% contain a comment indicating the size of the RSE. These cells can be identified by a red indicator in the corner of the cell. The comment appears when the mouse pointer hovers over the cell. ### Calculation of standard error 8 Standard errors can be calculated using the estimates (counts or percentages) and the corresponding RSEs. See What is a Standard Error and Relative Standard Error, Reliability of estimates for Labour Force data for more details. ### Proportions and percentages 9 Proportions and percentages formed from the ratio of two estimates are also subject to sampling errors. The size of the error depends on the accuracy of both the numerator and the denominator. A formula to approximate the RSE of a proportion is given below. This formula is only valid when x is a subset of y: $$R S E\left(\frac{x}{y}\right)=\sqrt{[R S E(x)]^{2}-[R S E(y)]^{2}}$$ ### Differences 10 The difference between two survey estimates (counts or percentages) can also be calculated from published estimates. Such an estimate is also subject to sampling error. The sampling error of the difference between two estimates depends on their SEs and the relationship (correlation) between them. An approximate SE of the difference between two estimates (x-y) may be calculated by the following formula: $$S E(x-y)=\sqrt{[S E(x)]^{2}+[S E(y)]^{2}}$$ 11 While this formula will only be exact for differences between separate and uncorrelated characteristics or sub populations, it provides a good approximation for the differences likely to be of interest in this publication. ### Significance testing 12 A statistical significance test for a comparison between estimates can be performed to determine whether it is likely that there is a difference between the corresponding population characteristics. The standard error of the difference between two corresponding estimates (x and y) can be calculated using the formula shown above in the Differences section. This standard error is then used to calculate the following test statistic: $$Test \ statistic =\left(\frac{x-y}{S E(x-y)}\right)$$ 13 If the value of this test statistic is greater than 1.96 then there is evidence, with a 95% level of confidence, of a statistically significant difference in the two populations with respect to that characteristic. Otherwise, it cannot be stated with confidence that there is a real difference between the populations with respect to that characteristic. ## Glossary ### Show all #### Age The age of a person on their last birthday. #### Australian Standard Classification of Education (ASCED) The ASCED is a national standard classification which includes all sectors of the Australian education system: that is, schools, vocational education and training, and higher education. The ASCED comprises two classifications: Level of education and Field of education. See Australian Standard Classification of Education (ASCED), 2001 (cat. no. 1272.0). #### Australian Statistical Geography Standard (ASGS) Effective from July 2011, the Australian Statistical Geography Standard (ASGS) developed by the ABS provides the framework for the collection and dissemination of statistics. See Australian Statistical Geography Standard (ASGS): Volume 1 - Main Structure and Greater Capital City Statistical Areas, July 2016 (cat. no. 1270.0.55.001), Australian Statistical Geography Standard (ASGS): Volume 4 - Significant Urban Areas, Urban Centres and Localities, Section of State, July 2016 (cat. no. 1270.0.55.004) and Australian Statistical Geography Standard (ASGS): Volume 5 - Remoteness Structure, July 2016 (cat. no. 1270.0.55.005). #### Country of birth Country of birth is classified according to the Standard Australian Classification of Countries (SACC), 2016 (cat. no. 1269.0). #### Cyberbullying The use of technology to bully an individual or a group with the intent to cause harm. The intended harm may be social, psychological, or physical. #### Cyber security Cyber security comprises technologies, processes and controls that are designed to protect systems, networks and data from cyber attacks. #### Employed All persons aged 15 years and over who met one of the following criteria during the reference week: • worked for one hour or more for pay, profit, commission or payment in kind, in a job or business or on a farm (employees and owner managers of incorporated or unincorporated enterprises) • worked for one hour or more without pay in a family business or on a farm (contributing family workers) • were owner managers who had a job, business or farm, but were not at work, or • were employees who had a job but were not at work and were: • away from work for less than four weeks up to the end of the reference week • away from work for more than four weeks up to the end of the reference week and received pay for some or all of the four week period to the end of the reference week • away from work as a standard work or shift arrangement • on strike or locked out, or #### Equivalised weekly household income qualities Equivalised household income can be viewed as an indicator of the economic resources available to each member of the household. Using equivalised household income enables the direct comparison of the relative incomes of households of different sizes and composition. 'Equivalised household income' is 'Total income' at the household level adjusted using an equivalence scale. 'Total income', also referred to as gross income, is the sum of income received from all sources before any deductions such as income tax, Medicare Levy and Medicare Levy Surcharge or salary sacrificed amounts are taken out. Equivalised weekly household income quintiles are derived by ranking households in ascending order according to their total equivalised weekly household income from all sources and dividing the ranked population into five equally sized groups, each comprising 20% of the population. Equivalised household income quintiles for 2016-17 HUIT have been calculated on the full Multipurpose Household Survey sample (of which HUIT is a 50% sample) . Quintiles based on the full sample, rather than the smaller sample used to enumerate the HUIT topic, will provide a more accurate estimate of the likely income distribution of the whole population. While equivalised income generally provides a useful indicator of economic wellbeing, there are some circumstances which present particular difficulties. Some households report extremely low and even negative income, which places them well below the safety net of income support provided by government pensions and allowances. Households may under report their incomes in the survey at all income levels, including low income households. However, households can correctly report low levels of income if they incur losses in their unincorporated business or have negative returns from their other investments. Studies of income and expenditure from the Household Expenditure Survey, Australia (cat. no. 6530.0) have shown that such households in the bottom income decile and with negative gross incomes tend to have expenditure levels that are comparable to those of households with higher income levels. This suggests that these households have access to economic resources such as wealth, or that the instance of low or negative income is temporary, perhaps reflecting business or investment start up. #### Exposure to inappropriate material Internet users exposed to concepts and materials that they are not ready to comprehend or which may be illegal. #### Greater Capital City Statistical Area (GCCSA) Represent the socioeconomic area of each of the eight state and territory capital cities as defined in Australian Statistical Geography Standard (ASGS): Volume 1 - Main Structure and Greater Capital City Statistical Areas, July 2016 (cat. no. 1270.0.55.001). These boundaries are built from aggregations of whole Statistical Areas Level 4. GCCSA boundaries represent a broad socioeconomic definition of each capital city, they contain not only the urban area of the capital city, but also surrounding and non-urban areas where much of the population has strong links to the capital city, through for example, commuting to work. The whole of the ACT is included in the Greater capital city area. #### Household A group of two or more related or unrelated people who usually reside in the same dwelling, who regard themselves as a household, and who make common provision for food or other essentials for living; or a person living in a dwelling who makes provision for his/her own food and other essentials for living, without combining with any other person. #### Household internet access A household connected to the internet via a computer, mobile phone or other device. #### Internet user An internet user is a person aged 15 years or over who accessed the internet for personal use in the last three months. #### Level of highest educational attainment Level of highest educational attainment identifies the highest achievement a person has attained in any area of study. It is not a measurement of the relative importance of different fields of study but a ranking of qualifications and other educational attainments regardless of the particular area of study or the type of institution in which the study was undertaken. Level not determined includes inadequately described responses or where no responses were given. For more information regarding how 'Level of highest educational attainment' is derived, see the coding rules described in Education Variables, June 2014 (cat. no. 1246.0) - The Standard for Highest educational attainment variables, Version 1.6, Collection methods. Level of highest educational attainment is based on the Australian Standard Classification of Education (ASCED), 2001 (cat. no. 1272.0). #### Main English-speaking countries Refers to the main countries from which Australia receives, or has received, significant numbers of overseas settlers who are likely to speak English. Comprises the United Kingdom, Ireland, South Africa, Canada, the United States of America and New Zealand. Classified according to the Standard Australian Classification of Countries (SACC), 2016 (cat. no. 1269.0). #### Mean number of devices The total number of devices used to access the internet at home by a group of households (e.g. households with children under 15 years), divided by the number of households in that group. #### Not employed Refers to a combination of those people Not in the labour force and Unemployed. Not in the labour force describes persons who, during the reference week, were neither employed nor unemployed, as defined. Unemployed persons are those aged 15 years and over who were not employed during the reference week and had actively looked for full-time or part-time work at any time in four weeks up to the end of the reference week and were available for work in the reference week; or were waiting to start a new job within four weeks from the end of the reference week and could have started in the reference week if the job had been available then. #### Other countries The group comprises all countries except Australia and the Main English-speaking countries (the United Kingdom, Ireland, South Africa, Canada, the United States of America and New Zealand). Classified according to the Standard Australian Classification of Countries (SACC), 2016 (cat. no. 1269.0). #### Personal income Indicates the total income, from all sources, that the person usually receives each year before tax. #### Purchasing goods or services online Refers to persons who purchased or ordered goods or services over the internet in the last 3 months. #### Remoteness area The ABS has defined Remoteness within the Australian Statistical Geography Standard (ASGS): Volume 5 - Remoteness Structure, July 2016 (cat. no. 1270.0.55.005). The structure defines six Remoteness Areas (RA): Major Cities of Australia; Inner Regional Australia; Outer Regional Australia; Remote Australia; Very Remote Australia; and Migratory. It divides each state and territory into several regions on the basis of their relative access to services. The Remoteness Structure is categorised into Remoteness Areas (RAs). RAs aggregate to states and territories and cover the whole of Australia without gaps or overlaps. The delimitation criteria for RAs are based on the Accessibility/Remoteness Index of Australia (ARIA), which measures the remoteness of a point based on the physical road distance to the nearest Urban Centre in each of five size classes. The ASGS SA1 boundaries are overlayed onto the ARIA+ grid and an average score is calculated based upon the grid points that are contained within each SA1. The resulting average score determines which remoteness category is allocated to each SA1. The RA categories are: • Major Cities of Australia - SA1 average ARIA+ value of 0 to 0.2 • Inner Regional Australia - SA1 average ARIA+ value of greater than 0.2 and less than or equal to 2.4 • Outer Regional Australia - SA1 average ARIA+ value of greater than 2.4 and less than or equal to 5.92 • Remote Australia - SA1 average ARIA+ value of greater than 5.92 and less than or equal to 10.53, and • Very Remote Australia - SA1 average ARIA+ value of greater than 10.53. For 2016-17 HUIT the categories of Remote and Very Remote have been combined into one category. #### Section of State (SOS) The ABS has defined SOS within the Australian Statistical Geography Standard (ASGS): Volume 4 - Significant Urban Areas, Urban Centres and Localities, Section of State, July 2016 (cat. no. 1270.0.55.004). The structure represents areas of concentrated urban development. It consists of Statistical Areas Level 1 (SA1s) aggregated together to form regions defined according to population density and other criteria. Urban centre and localities (UCLs) can cross state or territory boundaries so the structure therefore does not aggregate to state and territories. The UCL/SOS structure covers the whole of Australia without gaps or overlaps: • Major Urban - a combination of all Urban centres with a population of 100,000 or more • Other Urban - a combination of all Urban centres with a population between 1,000 to 99,999 • Bounded Locality - a combination of all bounded localities, and • Rural Balance - represents the remainder of state/territory. For 2016-17 HUIT the categories of Major Urban and Other Urban have been combined into one category called Urban, and the categories of Bounded Locality and Rural Balance have been combined into one category called Rural. ## Quality declaration ### Institutional environment For information on the institutional environment of the Australian Bureau of Statistics (ABS), including the legislative obligations of the ABS, financing and governance arrangements, and mechanisms for scrutiny of ABS operations, please see ABS Institutional Environment. ### Relevance The Multipurpose Household Survey (MPHS) is collected as a supplement to the monthly Labour Force Survey (LFS) and is designed to collect statistics on a number of small self-contained topics. The Household Use of Information Technology (HUIT) topic collects a range of information on household access to and persons use of the internet in Australia. These data are presented by various demographic and geographic characteristics. ### Timeliness The MPHS is collected annually with enumeration undertaken in each month over the financial year period from July to June. Generally, data from the MPHS are released approximately 6–8 months after enumeration. The HUIT topic has been collected biennially via the MPHS, however the 2016-17 HUIT is the last iteration of the survey. ### Accuracy The HUIT topic comprised a sample of 14,035 fully responding households, which represented a response rate of 72% (after taking sample loss into account). The LFS, and consequently the MPHS, is primarily designed to provide estimates for the whole of Australia and, secondly, for each state and territory. Estimates are subject to sampling and non-sampling error. All aggregate statistics presented in tables have been randomly adjusted to avoid the release of any data that may inadvertently identify an individual. The technique to adjust the data is called perturbation. These adjustments have a negligible impact on the underlying pattern of the data. For further information, please refer to the Explanatory Notes. ### Coherence Person level data from 2005-06 MPHS onwards (the scope of which is 15 years and over) are not directly comparable with data from previous years, which was limited to persons aged 18 years and over. Person level data may not be directly comparable with data from previous years due to changes in the definition of an internet user, question structure and response categories. Household level data are comparable. While the ABS seeks to maximise consistency and comparability over time by minimising changes to the survey, ongoing survey review has adjusted to the changing needs of users of information and communication technology statistics. ### Interpretability To aid in the interpretation of HUIT data, detailed information on the terminology, classifications and other technical aspects associated with the survey can be found on the relevant web pages included with this release. ### Accessibility All tables and associated RSEs are available in Excel spreadsheets and can be accessed from the Data downloads section. Additional tables can also be produced on request. Note that detailed data can be subject to high RSEs and, in some cases, may result in data being confidentialised or not being available. For further information about these or related statistics, contact the National Information and Referral Service.
2023-03-22T19:53:06
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https://pdglive.lbl.gov/DataBlock.action?node=B115DI&home=sumtabB
#### ${\mathit m}_{{{\mathit \Sigma}_{{c}}{(2520)}^{++}}}–{\mathit m}_{{{\mathit \Sigma}_{{c}}{(2520)}^{0}}}$ VALUE (MeV) EVTS DOCUMENT ID TECN  COMMENT $0.01$ $\pm0.15$ $\pm0.03$ 44/41k 2014 BELL ${{\mathit e}^{+}}{{\mathit e}^{-}}$ at ${{\mathit \Upsilon}{(4S)}}$ • • We do not use the following data for averages, fits, limits, etc. • • $0.1$ $\pm0.8$ $\pm0.3$ 1 2005 CLEO ${{\mathit e}^{+}}{{\mathit e}^{-}}$ , $9.4 - 11.5$ GeV $1.9$ $\pm1.4$ $\pm1.0$ 2 1997 CLE2 ${{\mathit e}^{+}}{{\mathit e}^{-}}$ $\approx{}{{\mathit \Upsilon}{(4S)}}$ 1 This ATHAR 2005 result is redundant with measurements in earlier entries. 2 This BRANDENBURG 1997 result is redundant with measurements in earlier entries. References: LEE 2014 PR D89 091102 Measurements of the Masses and Widths of the and Baryons ATHAR 2005 PR D71 051101 New Measurement of the Masses and Widths of the ${{\mathit \Sigma}_{{c}}^{*++}}$ and ${{\mathit \Sigma}_{{c}}^{*0}}$ Charmed Baryons BRANDENBURG 1997 PRL 78 2304 Observation of Two Excited Charmed Baryons Decaying into ${{\mathit \Lambda}_{{c}}^{+}}{{\mathit \pi}^{\pm}}$
2022-09-29T20:40:40
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https://adventure-capitalist.fandom.com/wiki/Flux_Capitalor
## FANDOM 91 Pages The Flux Capitalor is an object featured only in the Gold Shop. It was first introduced in the AdCap 2.1.0 mobile update and was initially exclusive to the Moon, but later it was added to the Earth and events. However, it's not available on Mars. The Flux Capitalor costs 40 Gold Bars and increases the planet's profit speed by 1.21x. It is also additive to itself, and multiplicative with the x3 Multiplier. ## Flux Capitalor DeluxeEdit The Flux Capitalor Deluxe contains 3 Flux Capitalors, and is available for purchase in the Gold Shop on Earth, Moon, and the events. It costs 80 Gold Bars, and increases the planet's profit speed by $(base speed+1.21*3)$ ## TriviaEdit • Its name is a portmanteau of "Flux Capacitor" and "Capital". The fact that it multiplies profit speed is a reference to "Back to the Future", as the flux capacitor requires 1.21 gigawatts to be activated in the movie. Community content is available under CC-BY-SA unless otherwise noted.
2020-07-12T07:38:47
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https://par.nsf.gov/biblio/10367482-grain-alignment-circumstellar-shell-irc+10
Grain Alignment in the Circumstellar Shell of IRC+10° 216 Abstract Dust-induced polarization in the interstellar medium (ISM) is due to asymmetric grains aligned with an external reference direction, usually the magnetic field. For both the leading alignment theories, the alignment of the grain’s angular momentum with one of its principal axes and the coupling with the magnetic field requires the grain to be paramagnetic. Of the two main components of interstellar dust, silicates are paramagnetic, while carbon dust is diamagnetic. Hence, carbon grains are not expected to align in the ISM. To probe the physics of carbon grain alignment, we have acquired Stratospheric Observatory for Infrared Astronomy/Higch-resolution Airborne Wideband Camera-plus far-infrared photometry and polarimetry of the carbon-rich circumstellar envelope (CSE) of the asymptotic giant branch star IRC+10° 216. The dust in such CSEs are fully carbonaceous and thus provide unique laboratories for probing carbon grain alignment. We find a centrosymmetric, radial, polarization pattern, where the polarization fraction is well correlated with the dust temperature. Together with estimates of a low fractional polarization from optical polarization of background stars, we interpret these results to be due to a second-order, direct radiative external alignment of grains without internal alignment. Our results indicate that (pure) carbon dust does not contribute significantly to more » Authors: ; ; ; ; ; ; ; ; ; Award ID(s): Publication Date: NSF-PAR ID: 10367482 Journal Name: The Astrophysical Journal Volume: 931 Issue: 2 Page Range or eLocation-ID: Article No. 80 ISSN: 0004-637X Publisher: DOI PREFIX: 10.3847 National Science Foundation ##### More Like this 1. Abstract Continuum polarization over the UV-to-microwave range is due to dichroic extinction (or emission) by asymmetric, aligned dust grains. Scattering can also be an important source of polarization, especially at short wavelengths. Because of both grain alignment and scattering physics, the wavelength dependence of the polarization, generally, traces the size of the aligned grains. Similarly because of the differing wavelength dependencies of dichroic extinction and scattering polarization, the two can generally be reliably separated. Ultraviolet (UV) polarimetry therefore provides a unique probe of the smallest dust grains (diameter$< 0.09~\upmu \text{m}$$<0.09\phantom{\rule{0ex}{0ex}}\text{μm}$), their mineralogy and interaction with the environment. However, the current observational status of interstellar UV polarization is very poor with less than 30 lines of sight probed. With the modern, quantitative and well-tested, theory of interstellar grain alignment now available, we have the opportunity to advance the understanding of the interstellar medium (ISM) by executing a systematic study of the UV polarization in the ISM of the Milky Way and near-by galaxies. The Polstar mission will provide the sensitivity and observing time needed to carry out such a program (probing hundreds of stars in the Milky Way and dozens of stars in the LMC/SMC), addressing questions of dust composition asmore » 2. Abstract Interstellar dust grains are often aligned. If the grain alignment direction varies along the line of sight, the thermal emission becomes circularly polarized. In the diffuse interstellar medium, the circular polarization at far-infrared and submillimeter wavelengths is predicted to be very small, and probably unmeasurable. However, circular polarization may reach detectable levels in photodissociation regions viewed through molecular clouds, in infrared dark clouds, and in protoplanetary disks. Measurement of circular polarization could help constrain the structure of the magnetic field in infrared dark clouds, and may shed light on the mechanisms responsible for grain alignment in protoplanetary disks. 3. Abstract The alignment of dust grains with the ambient magnetic field produces polarization of starlight as well as thermal dust emission. Using the archival SOFIA/HAWC+ polarimetric data observed toward the ρ Ophiuchus (Oph) A cloud hosted by a B star at 89 and 154 μ m, we find that the fractional polarization of thermal dust emission first increases with the grain temperature and then decreases once the grain temperature exceeds ≃25–32 K. The latter trend differs from the prediction of the popular RAdiative Torques (RATs) alignment theory, which implies a monotonic increase of the polarization fraction with the grain temperature. We perform numerical modeling of polarized dust emission for the ρ Oph-A cloud and calculate the degree of dust polarization by simultaneously considering the dust grain alignment and rotational disruption by RATs. Our modeling results could successfully reproduce both the rising and declining trends of the observational data. Moreover, we show that the alignment of only silicate grains or a mixture of silicate–carbon grains within a composite structure can reproduce the observational trends, assuming that all dust grains follow a power-law size distribution. Although there are a number of simplifications and limitations to our modeling, our results suggest grains inmore » 4. ABSTRACT Polarized dust emission is a key tracer in the study of interstellar medium and of star formation. The observed polarization, however, is a product of magnetic field structure, dust grain properties, and grain alignment efficiency, as well as their variations in the line of sight, making it difficult to interpret polarization unambiguously. The comparison of polarimetry at multiple wavelengths is a possible way of mitigating this problem. We use data from HAWC+ /SOFIA and from SCUBA-2/POL-2 (from the BISTRO survey) to analyse the NGC 2071 molecular cloud at 154, 214, and 850 $\mu$m. The polarization angle changes significantly with wavelength over part of NGC 2071, suggesting a change in magnetic field morphology on the line of sight as each wavelength best traces different dust populations. Other possible explanations are the existence of more than one polarization mechanism in the cloud or scattering from very large grains. The observed change of polarization fraction with wavelength, and the 214-to-154 $\mu$m polarization ratio in particular, are difficult to reproduce with current dust models under the assumption of uniform alignment efficiency. We also show that the standard procedure of using monochromatic intensity as a proxy for column density may produce spurious results at HAWC+wavelengths.more » 5. We present optical and near-infrared stellar polarization observations toward the dark filamentary clouds associated with IC5146. The data allow us to investigate the dust properties (this paper) and the magnetic field structure (Paper II). A total of 2022 background stars were detected in the R c , I\prime , H, and/or K bands to {A}V≲ 25 mag. The ratio of the polarization percentage at different wavelengths provides an estimate of {λ }\max , the wavelength of the peak polarization, which is an indicator of the small-size cutoff of the grain size distribution. The grain size distribution seems to significantly change at {A}V˜ 3 mag, where both the average and dispersion of {P}{Rc}/{P}H decrease. In addition, we found {λ }\max ˜ 0.6{--}0.9 μm for {A}V> 2.5 mag, which is larger than the ˜0.55 μm in the general interstellar medium (ISM), suggesting that grain growth has already started in low-A V regions. Our data also reveal that polarization efficiency ({PE}\equiv {P}λ /{A}V) decreases with A V as a power law in the R c , I\prime , and K bands with indices of -0.71 ± 0.10, -1.23 ± 0.10, and -0.53 ± 0.09. However, H-band data show a power index change; themore »
2023-01-29T01:47:16
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https://www.usgs.gov/publications/immunological-markers-tolerance-avian-malaria-hawaii-amakihi-new-tools-restoring
# Immunological markers for tolerance to avian malaria in Hawaii Amakihi: new tools for restoring native Hawaiian forest birds? August 1, 2013 We evaluated three assays for non-specific or innate immune capacity to see if measurements were independent of malarial infection and capable of distinguishing malaria-tolerant, low-elevation Hawaiʽi ʽAmakihi from malaria-susceptible, high-elevation ʽAmakihi. ʽAmakihi were captured at Malama Ki Forest Reserve (20 m), Hakalau Forest National Wildlife Refuge (1800 m), and Upper Waiakea Forest Reserve (1700 m), bled for collection of plasma and packed erythrocytes for malarial diagnostics, and either transported to Kīlauea Field Station Aviary and held in captivity for 48 hours for inoculation of wing webs with phytohemagglutinin A (PHA) or released immediately in the field after collection of a blood sample. All birds were tested by polymerase chain reaction (PCR) and microscopy to determine infection status. We found no significant association between malarial infection status and degree of wing web swelling after inoculation with PHA (T = -0.174, df = 13, P = 0.864) and no association between origin of birds from low- and high-elevation populations and degree of wing web swelling (T = 0.113, df = 52, P = 0.911). Infected ʽAmakihi from low elevation had significantly higher small molecule plasma antioxidant capacity than uninfected individuals from the same population (T = -2.675, df = 21, P = 0.014), so we limited comparisons to uninfected birds. Uninfected ʽAmakihi from low elevations did not differ in small molecule plasma antioxidant capacity from uninfected ʽAmakihi from high elevation (T = -0.260, df = 46, P = 0.796). Compared to high-elevation birds, low-elevation ʽAmakihi had significantly higher titers of natural antibodies (NAb) as measured by complement-mediated lysis of rabbit erythrocytes (Mann-Whitney U = 27, X2= 32.332, df = 1, P < 0.0001). This innate immunological difference may be related to ability to survive malarial infection and may prove to be important for understanding possible mechanisms for the evolution of disease tolerance in Hawaiʽi’s native bird species.
2022-05-18T12:16:38
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https://zims-en.kiwix.campusafrica.gos.orange.com/wikipedia_en_all_nopic/A/Von_Mises%E2%80%93Fisher_distribution
# Von Mises–Fisher distribution In directional statistics, the von Mises–Fisher distribution (named after Ronald Fisher and Richard von Mises), is a probability distribution on the ${\displaystyle (p-1)}$-dimensional sphere in ${\displaystyle \mathbb {R} ^{p}}$. If ${\displaystyle p=2}$ the distribution reduces to the von Mises distribution on the circle. The probability density function of the von Mises–Fisher distribution for the random p-dimensional unit vector ${\displaystyle \mathbf {x} \,}$ is given by: ${\displaystyle f_{p}(\mathbf {x} ;{\boldsymbol {\mu }},\kappa )=C_{p}(\kappa )\exp \left({\kappa {\boldsymbol {\mu }}^{T}\mathbf {x} }\right),}$ where ${\displaystyle \kappa \geq 0,\left\Vert {\boldsymbol {\mu }}\right\Vert =1\,}$ and the normalization constant ${\displaystyle C_{p}(\kappa )\,}$ is equal to ${\displaystyle C_{p}(\kappa )={\frac {\kappa ^{p/2-1}}{(2\pi )^{p/2}I_{p/2-1}(\kappa )}},}$ where ${\displaystyle I_{v}}$ denotes the modified Bessel function of the first kind at order ${\displaystyle v}$. If ${\displaystyle p=3}$, the normalization constant reduces to ${\displaystyle C_{3}(\kappa )={\frac {\kappa }{4\pi \sinh \kappa }}={\frac {\kappa }{2\pi (e^{\kappa }-e^{-\kappa })}}.}$ The parameters ${\displaystyle \mu \,}$ and ${\displaystyle \kappa \,}$ are called the mean direction and concentration parameter, respectively. The greater the value of ${\displaystyle \kappa \,}$, the higher the concentration of the distribution around the mean direction ${\displaystyle \mu \,}$. The distribution is unimodal for ${\displaystyle \kappa >0\,}$, and is uniform on the sphere for ${\displaystyle \kappa =0\,}$. The von Mises–Fisher distribution for ${\displaystyle p=3}$, also called the Fisher distribution, was first used to model the interaction of electric dipoles in an electric field (Mardia, 2000). Other applications are found in geology, bioinformatics, and text mining. ## Relation to normal distribution Starting from a normal distribution ${\displaystyle G_{p}(\mathbf {x} ;{\boldsymbol {\mu }},\kappa )={\sqrt {\frac {\kappa }{2\pi }}}^{p}\exp \left(-\kappa {\frac {(\mathbf {x} -{\boldsymbol {\mu }})^{2}}{2}}\right),}$ the von Mises-Fisher distribution is obtained by expanding ${\displaystyle (\mathbf {x} -{\boldsymbol {\mu }})^{2}=\mathbf {x} ^{2}+{\boldsymbol {\mu }}^{2}-2{\boldsymbol {\mu }}^{T}\mathbf {x} ,}$ using the fact that ${\displaystyle \mathbf {x} }$ and ${\displaystyle {\boldsymbol {\mu }}}$ are unit vectors, and recomputing the normalization constant by integrating ${\displaystyle \mathbf {x} }$ over the unit sphere. ## Estimation of parameters A series of N independent measurements ${\displaystyle x_{i}}$ are drawn from a von Mises–Fisher distribution. Define ${\displaystyle A_{p}(\kappa )={\frac {I_{p/2}(\kappa )}{I_{p/2-1}(\kappa )}}.\,}$ Then (Sra, 2011) the maximum likelihood estimates of ${\displaystyle \mu \,}$ and ${\displaystyle \kappa \,}$ are given by ${\displaystyle \mu ={\frac {\sum _{i}^{N}x_{i}}{\|\sum _{i}^{N}x_{i}\|}},}$ ${\displaystyle \kappa =A_{p}^{-1}({\bar {R}}).}$ Thus ${\displaystyle \kappa \,}$ is the solution to ${\displaystyle A_{p}(\kappa )={\frac {\|\sum _{i}^{N}x_{i}\|}{N}}={\bar {R}}.}$ A simple approximation to ${\displaystyle \kappa }$ is ${\displaystyle {\hat {\kappa }}={\frac {{\bar {R}}(p-{\bar {R}}^{2})}{1-{\bar {R}}^{2}}},}$ but a more accurate measure can be obtained by iterating the Newton method a few times ${\displaystyle {\hat {\kappa }}_{1}={\hat {\kappa }}-{\frac {A_{p}({\hat {\kappa }})-{\bar {R}}}{1-A_{p}({\hat {\kappa }})^{2}-{\frac {p-1}{\hat {\kappa }}}A_{p}({\hat {\kappa }})}},}$ ${\displaystyle {\hat {\kappa }}_{2}={\hat {\kappa }}_{1}-{\frac {A_{p}({\hat {\kappa }}_{1})-{\bar {R}}}{1-A_{p}({\hat {\kappa }}_{1})^{2}-{\frac {p-1}{{\hat {\kappa }}_{1}}}A_{p}({\hat {\kappa }}_{1})}}.}$ For N  25, the estimated spherical standard error of the sample mean direction can be computed as[1] ${\displaystyle {\hat {\sigma }}=\left({\frac {d}{N{\bar {R}}^{2}}}\right)^{1/2}}$ where ${\displaystyle d=1-{\frac {1}{N}}\sum _{i}^{N}(\mu ^{T}x_{i})^{2}}$ It's then possible to approximate a ${\displaystyle 100(1-\alpha )\%}$ confidence cone about ${\displaystyle \mu }$ with semi-vertical angle ${\displaystyle q=\arcsin(e_{\alpha }^{1/2}{\hat {\sigma }}),}$ where ${\displaystyle e_{\alpha }=-\ln(\alpha ).}$ For example, for a 95% confidence cone, ${\displaystyle \alpha =0.05,e_{\alpha }=-\ln(0.05)=2.996,}$ and thus ${\displaystyle q=\arcsin(1.731{\hat {\sigma }}).}$ ## Generalizations The matrix von Mises-Fisher distribution has the density ${\displaystyle f_{n,p}(\mathbf {X} ;\mathbf {F} )\propto \exp(\operatorname {tr} (\mathbf {F} ^{T}\mathbf {X} ))}$ supported on the Stiefel manifold of ${\displaystyle n\times p}$ orthonormal p-frames ${\displaystyle \mathbf {X} }$, where ${\displaystyle \mathbf {F} }$ is an arbitrary ${\displaystyle n\times p}$ real matrix.[2][3] ## References 1. Embleton, N. I. Fisher, T. Lewis, B. J. J. (1993). Statistical analysis of spherical data (1st pbk. ed.). Cambridge: Cambridge University Press. pp. 115–116. ISBN 0-521-45699-1. 2. Jupp (1979). "Maximum likelihood estimators for the matrix von Mises-Fisher and Bingham distributions". The Annals of Statistics. 7 (3): 599–606. doi:10.1214/aos/1176344681. 3. Downs (1972). "Orientational statistics". Biometrika. 59: 665–676. doi:10.1093/biomet/59.3.665. • Dhillon, I., Sra, S. (2003) "Modeling Data using Directional Distributions". Tech. rep., University of Texas, Austin. • Banerjee, A., Dhillon, I. S., Ghosh, J., & Sra, S. (2005). "Clustering on the unit hypersphere using von Mises-Fisher distributions". Journal of Machine Learning Research, 6(Sep), 1345-1382. • Fisher, RA, "Dispersion on a sphere'". (1953) Proc. Roy. Soc. London Ser. A., 217: 295–305 • Mardia, Kanti; Jupp, P. E. (1999). Directional Statistics. Wiley. ISBN 978-0-471-95333-3. • Sra, S. (2011). "A short note on parameter approximation for von Mises-Fisher distributions: And a fast implementation of I s (x)". Computational Statistics. 27: 177–190. CiteSeerX 10.1.1.186.1887. doi:10.1007/s00180-011-0232-x. This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.
2021-01-20T07:40:28
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https://bio.libretexts.org/Bookshelves/Evolutionary_Developmental_Biology/Book%3A_Phylogenetic_Comparative_Methods_(Harmon)/13%3A_Characters_and_Diversification_Rates/13.2%3A_A_State-Dependent_Model_of_Diversification
Skip to main content # 13.2: A State-Dependent Model of Diversification The models that we will consider in this chapter include trait evolution and associated lineage diversification. In the simplest case, we can consider a model where the character has two states, 0 and 1, and diversification rates depend on those states. We need to model the transitions among these states, which we can do in an identical way to what we did in Chapter 7 using a continuous-time Markov model. We express this model using two rate parameters, a forward rate q01 and a backwards rate q10. We now consider the idea that diversification rates might depend on the character state. We assume that species with character state 0 have a certain speciation rate (λ0) and extinction rate (μ0), and that species in 1 have potentially different rates of both speciation (λ1) and extinction (μ1). That is, when the character evolves, it affects the rate of speciation and/or extinction of the lineages. Thus, we have a six-parameter model (Maddison et al. 2007). We assume that parent lineages give birth to daughters with the same character state, that is that character states do not change at speciation. It is straightforward to simulate evolution under our state-dependent model of diversification. We proceed in the same way as we did for birth-death models, by drawing waiting times, but these waiting times can be waiting times to the next character state change, speciation, or extinction event. In particular, imagine that there are n lineages present at time t, and that k of these lineages are in state 0 (and n − k are in state 1). The waiting time to the next event will follow an exponential distribution with a rate parameter of: $ρ = k(q_{01} + λ_0 + μ_0)+(n − k)(q_{10} + λ_1 + μ_1) \label{13.1}$ This equation says that the total rate of events is the sum of the events that can happen to lineages with state 0 (state change to 1, speciation, or extinction) and the analogous events that can happen to lineages with state 1. Once we have a waiting time, we can assign an event type depending on probabilities. For example, the probability that the event is a character state change from 0 to 1 is: $p_{q_{01}} = (n ⋅ q_{01})/ρ\label{13.2}$ And the probability that the event is the extinction of a lineage with character state 1 is: $p_{μ_1} = \dfrac{(n − k)⋅μ_1}{ρ} \label{13.3}$ And so on for the other four possible events. Once we have picked an event in this way, we can randomly assign it to one of the lineages in the appropriate state, with each lineage equally likely to be chosen. We then proceed forwards in time until we have a dataset with the desired size or total time depth. An example simulation is shown in Figure 13.1. As you can see, under these model parameters the impact of character states on diversification is readily apparent. In the next section we will figure out how to extract that information from our data. Figure 13.1. Simulation of character-dependent diversification. Data were simulated under a model where diversification rate of state zero (red) is substantially lower than that of state 1 (black; model parameters q01 = 110 = 0.05, λ0 = 0.2, λ1 = 0.8, μ0 = μ1 = 0.05). Image by the author, can be reused under a CC-BY-4.0 license.
2019-10-19T20:00:50
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http://en.wikipedia.org/wiki/Essential_supremum
# Essential supremum and essential infimum (Redirected from Essential supremum) Jump to: navigation, search In mathematics, the concepts of essential supremum and essential infimum are related to the notions of supremum and infimum, but adapted to measure theory and functional analysis, where one often deals with statements that are not valid for all elements in a set, but rather almost everywhere, i.e., except on a set of measure zero. ## Definition Let f : X → R be a real valued function defined on a set X. A real number a is called an upper bound for f if f(x) ≤ a for all x in X, i.e., if the set $f^{-1}(a, \infty) = \{x\in X: f(x)>a\}$ is empty. Let $U_f = \{a \in \mathbb{R}: f^{-1}(a, \infty) = \emptyset\} \,$ be the set of upper bounds of f. Then the supremum of f is defined by $\sup f=\inf U_f \,$ if the set of upper bounds $U_f$ is nonempty, and  sup f = +∞ otherwise. Now assume in addition that (X, Σ, μ) is a measure space and, for simplicity, assume that the function f is measurable. A number a is called an essential upper bound of f if the measurable set f -1(a, ∞) is a set of measure zero[a], i.e., if f(x) ≤ a for almost all x in X. Let $U^{\mathrm{ess}}_f = \{a \in \mathbb{R}: \mu(f^{-1}(a, \infty)) = 0\}\,$ be the set of essential upperbounds. Then the essential supremum is defined similarly as $\mathrm{ess } \sup f=\inf U^{\mathrm{ess}}_f \,$ if $U^{\mathrm{ess}}_f \ne \emptyset$, and ess sup f = +∞ otherwise. Exactly in the same way one defines the essential infimum as the supremum of the essential lower bounds, that is, $\mathrm{ess } \inf f=\sup \{b \in \mathbb{R}: \mu(\{x: f(x) < b\}) = 0\}\,$ if the set of essential lower bounds is nonempty, and as −∞ otherwise. ## Examples On the real line consider the Lebesgue measure and its corresponding σ-algebra Σ. Define a function f by the formula $f(x)= \begin{cases} 5, & \text{if } x=1 \\ -4, & \text{if } x = -1 \\ 2, & \text{ otherwise. } \end{cases}$ The supremum of this function (largest value) is 5, and the infimum (smallest value) is −4. However, the function takes these values only on the sets {1} and {−1} respectively, which are of measure zero. Everywhere else, the function takes the value 2. Thus, the essential supremum and the essential infimum of this function are both 2. As another example, consider the function $f(x)= \begin{cases} x^3, & \text{if } x\in \mathbb Q \\ \arctan{x} ,& \text{if } x\in \mathbb R\backslash \mathbb Q \\ \end{cases}$ where Q denotes the rational numbers. This function is unbounded both from above and from below, so its supremum and infimum are ∞ and −∞ respectively. However, from the point of view of the Lebesgue measure, the set of rational numbers is of measure zero; thus, what really matters is what happens in the complement of this set, where the function is given as arctan x. It follows that the essential supremum is π/2 while the essential infimum is −π/2. Lastly, consider the function f(x) = x3 defined for all real x. Its essential supremum is +∞, and its essential infimum is −∞. ## Properties • If $\mu(X)>0$ we have $\inf f \le \mathrm{ess } \inf f \le \mathrm{ess }\sup f \le \sup f$. If $X$ has measure zero $\mathrm{ess }\sup f=-\infty$ and $\mathrm{ess }\inf f=+\infty$.[1] • $\mathrm{ess }\sup (fg) \le (\mathrm{ess }\sup f)(\mathrm{ess }\sup g)$ whenever both terms on the right are nonnegative. ## Notes 1. ^ For non measurable functions the definition has to be modified by assuming that $f^{-1}(a, \infty)$ is contained in a set of measure zero. Alternatively one can assume that the measure is complete ## References 1. ^ Dieudonne J.: Treatise On Analysis, Vol. II. Associated Press, New York 1976. p 172f. This article incorporates material from Essential supremum on PlanetMath, which is licensed under the Creative Commons Attribution/Share-Alike License.
2014-07-24T16:50:47
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https://indico.fnal.gov/event/19348/contributions/186523/
Indico search will be reestablished in the next version upgrade of the software: https://getindico.io/roadmap/ # Neutrino 2020 June 22, 2020 to July 2, 2020 US/Central timezone ## ANTARES search for a stacking of point sources of neutrinos with 11 years of data. Not scheduled 10m Poster ### Speaker Dr Julien Aublin (APC, Université de Paris) ### Description A search for small scale anisotropies in the arrival directions of neutrino candidates detected by the ANTARES detector between January 29, 2007 and December 31, 2017 is presented. Different samples of sources are considered: a) a clean sub-sample of the Fermi 3LAC catalog of blazars, b) a star-forming galaxy catalog, c) a sample of giant radio-galaxies, d) an jet-obscured AGN population, and e) a sample of 56 public very high energy track events from the IceCube experiment.\ The results of a specific analysis for the blazar MG3 J225517+2409 are also reported. The blazar is showing evidence of flaring activity in Fermi data, and could be associated with a high energy track detected by IceCube in time-coincidence with the flare. An a posteriori significance of $2\sigma$ for the combination of ANTARES and IceCube data is reported. ### Mini-abstract ANTARES point sources search: hint of association with blazar MG3 J225517+2409 and IceCube HE track Experiment/Collaboration ANTARES ### Primary author Dr Julien Aublin (APC, Université de Paris)
2021-11-27T16:49:20
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https://www.nist.gov/property-fieldsection/recovery-act-measurement-science-and-engineering-research-grants-program-0
# Recovery Act Measurement Science and Engineering Research Grants Program, Federal Register Notice (The official version of this notice will be published in the Federal Register. If there are any inconsistencies between this version and the version published in the Federal Register, the version published in the Federal Register is the correct document.) Billing Code 3510-13 DEPARTMENT OF COMMERCE National Institute of Standards and Technology Docket No.: 090306283-9284-01 Recovery Act Measurement Science and Engineering Research Grants Program AGENCY: National Institute of Standards and Technology (NIST), Department of Commerce ACTION: Notice SUMMARY: The National Institute of Standards and Technology (NIST) is establishing a financial assistance program to award research grants and cooperative agreements to support measurement science and engineering research proposals in the following six focus areas: energy; environment and climate change; information technology/cybersecurity; biosciences/healthcare; manufacturing; and physical infrastructure, as part of NIST's activities implementing the American Recovery and Reinvestment Act of 2009 (ARRA or Recovery Act). DATES: All proposals must be received no later than 3:00 p.m. Eastern Daylight Saving Time on Monday, July 13, 2009. Late proposals will not be reviewed or considered. ADDRESSES: Proposals may be submitted in hard copy or in electronic format. Hard copy proposals may be submitted to Dr. Jason Boehm, National Institute of Standards and Technology, 100 Bureau Drive, Stop 1060, Gaithersburg, MD 20899-1060. Electronic proposals may be uploaded to www.Grants.gov. FOR FURTHER INFORMATION CONTACT: For complete information about this program and instructions for applying by paper or electronically, read the Federal Funding Opportunity Notice (FFO) at http://www.grants.gov. A paper copy of the FFO may be obtained by calling (301) 975-5718. Technical questions should be addressed to Dr. Jason Boehm at the address listed in the Addresses section above, or at Tel: (301) 975-4455; E-mail: [email protected]; Fax: (301) 216-0529. Grants Administration questions should be addressed to Grants and Agreements Management Division, National Institute of Standards and Technology, 100 Bureau Drive, Stop 1650, Gaithersburg, MD 20899-1650; Tel: (301) 975-5718; Email: [email protected]; Fax: (301) 840-5976. For assistance with using Grants.gov contact [email protected]. SUPPLEMENTARY INFORMATION Authority. 15 U.S.C. §272(b) and (c); Pub. L. 111-5, 123 Stat. 115. Catalog of Federal Domestic Assistance Name and Number: Measurement and Engineering Research and Standards - 11.609 Program Description. In response to the American Reinvestment and Recovery Act (P.L. 111-5, 123 Stat. 115), the National Institute of Standards and Technology (NIST) will provide grants and cooperative agreements for measurement science and engineering research in the following six focus areas of critical national importance: energy; environment and climate change; information technology/cybersecurity; biosciences/healthcare; manufacturing; and physical infrastructure, with priority funding in areas of special interest to NIST. Please see the FFO for detailed information on each area of critical national importance. The program is intended to advance the state of knowledge and practice in these areas of critical national importance, in support of NIST's mission to promote U.S. innovation and industrial competitiveness by advancing measurement science, standards, and technology in ways that enhance economic security and improve our quality of life. The program will advance purposes established in Section 3 of the Recovery Act by creating jobs, promoting economic recovery, providing investments needed to increase economic efficiency by spurring technological advances in science and health, making investments in research areas such as environmental protection and infrastructure that will provide long-term economic benefits, and will help stabilize state and local government budgets, in order to minimize and avoid reductions in essential services and counterproductive state and local tax increases. Competitive proposals will also result in achieving commencement of expenditures and activities as quickly as possible consistent with prudent management. Applicants may propose projects that include collaboration between scientific staff and NIST to help advance these program objectives. Please see information below regarding collaborations with NIST employees. Program Priorities: Proposals submitted to the Recovery Act Measurement Science and Engineering Research Grants Program must address one of the areas of critical national importance described in the FFO. Applicants should clearly note which program area (e.g., energy) the proposal is addressing. Proposals that address the sub-topics listed in the FFO will receive high priority for consideration of funding. Applicants whose proposal addresses a sub-topic listed in the FFO should also clearly note which sub-topic the proposal addresses. Funding Availability: NIST plans to award up to $35 million in grants and cooperative agreements (20-60 awards expected), as appropriate to support measurement science and engineering research in areas of critical national importance. Where cooperative agreements are used, the nature of NIST's "substantial involvement will generally be collaboration with the recipient by working jointly with a recipient scientist in carrying out the scope of work, or specifying direction or redirection of the scope of work due to inter-relationships with other projects requiring such cooperation. Proposals for research or other activity under this notice should have a duration lasting between one and three years. All projects approved by NIST, including multiple-year projects, will be fully funded at the time of award. Award terms will describe how recipients with satisfactory performance will draw down funds as needed from a Department of Treasury account. Individual awards are expected to range between$500,000 and 1,500,000. Projects are expected to start by September of 2009. Cost Share Requirements: None. Eligibility: This program is open to U.S. institutions of higher education; U.S. non-profit organizations; U.S. commercial organizations; and state, local, and Indian tribal governments. Evaluation Criteria: The evaluation criteria the technical reviewers will use in evaluating the proposals are as follows: 1. Technical merit of the proposal. Reviewers will consider the applicant's approach and the extent to which the proposal effectively addresses scientific and technical issues necessary to achieve success. 2. Qualifications of Technical Personnel. Reviewers will consider the ability of the proposed personnel to perform the proposed work as measured by evidence of skills, training and past professional accomplishments. 3. Relevance to NIST Programs. Reviewers will consider the degree to which the proposed work addresses topics of national importance as identified in the solicitation as well as the relevance of the work to advancements in measurement science and engineering of interest to current and future NIST programs. 4. Potential Impact of Proposal. Reviewers will consider the potential technical effectiveness of the proposal, the value it would contribute to the field of research, and its potential to enhance U.S. economic security and quality of life. Each of these factors will be given equal weight in the evaluation process. Selection Factors: The Selecting Official anticipates recommending proposals for funding in rank order unless a proposal is justified to be awarded out of rank order based on one or more of the following selection factors: 1. Availability of Federal funds, 2. Redundancy, 3. Balance/distribution of funds by research areas described in the Funding Opportunity Description section of the FFO, 4. Relevance to objectives of Recovery Act and alignment with subtopics described in the Funding Opportunity Description section of the FFO. Therefore, the highest scoring proposals may not necessarily be selected for an award. If an award is made to an applicant that deviates from the scores of the reviewers, the Selecting Official shall justify the selection in writing based on selection factors described above. Review and Selection Process: An initial administrative review of timely submitted proposals will be conducted to determine compliance with requirements and completeness of the proposal. Responsive and complete proposals will be considered further. Proposals that are nonresponsive and/or incomplete will be eliminated. Applicants will be notified if their proposal will not receive merit review. Each responsive and complete proposal will receive three independent technical reviews, which will include three individual written evaluations and scores, based on the evaluation criteria. The three scores for each proposal will be averaged. No consensus advice will be given by the technical reviewers. The individual proposal evaluations and average scores of each proposal will be considered by an Evaluation Board (a committee made up of seven (7) Federal employees: one chair and one coordinator for each of the focus areas). This Board will rank the proposals and make funding recommendations based on the selection factors described above to a Selecting Official for further consideration. In making final selections, the Selecting Official (Chief Scientist, NIST) will select funding recipients based upon the Evaluation Board's rank order of the proposals and the selection factors. NIST reserves the right to negotiate the cost and scope of the proposed work with the applicants that have been selected to receive awards. Applicants may be asked to modify work plans or budgets and provide supplemental information required by the agency prior to final approval of an award. NIST also reserves the right to reject a proposal where information is uncovered that raises a reasonable doubt as to the responsibility of the applicant. The final approval of selected proposals and award of grants will be made by the NIST Grants Officer. The award decision of the NIST Grants Officer is final. The Department of Commerce Pre-Award Notification Requirements for Grants and Cooperative Agreements: The Department of Commerce Pre-Award Notification Requirements for Grants and Cooperative Agreements, which are contained in the Federal Register Notice of February 11, 2008 (73 FR 7696), are applicable to this solicitation. On the form SF-424, the applicant's 9-digit Dun and Bradstreet Data Universal Numbering System (DUNS) number must be entered in item 8.c. Organizational DUNS. The DUNS number provided MUST be the DUNS number for the entity within the applying institution that will be responsible for drawing down funds from the Automated Standard Application for Payment System (ASAP). Institutions that provide incorrect DUNS numbers may experience significant delays in receiving funds. Collaborations with NIST Employees: All proposals should include a description of any work proposed to be performed by an entity other than the applicant, and the cost of such work should be included in the budget. If an applicant proposes collaboration with NIST, the statement of work should include a statement of this intention, a description of the collaboration, and prominently identify the NIST employee(s) involved, if known. Any collaboration by a NIST employee must be approved by appropriate NIST management and is at the sole discretion of NIST. Prior to beginning the merit review process, NIST will verify the approval of the proposed collaboration. Any unapproved collaboration will be stricken from the proposal prior to the merit review. Use of NIST Intellectual Property: If the applicant anticipates using any NIST-owned intellectual property to carry out the work proposed, the applicant should identify such intellectual property. This information will be used to ensure that no NIST employee involved in the development of the intellectual property will participate in the review process for that competition. In addition, if the applicant intends to use NIST-owned intellectual property, the applicant must comply with all statutes and regulations governing the licensing of Federal government patents and inventions, described at 35 U.S.C. §§ 200-212, 37 CFR Part 401, 15 CFR § 14.36, and in Section B.21 of the Department of Commerce Pre-Award Notification Requirements 73 FR 7696 (February 11, 2008). Questions about these requirements may be directed to the Office of the Chief Counsel for NIST, 301-975-2803. Any use of NIST-owned intellectual property by an applicant is at the sole discretion of NIST and will be negotiated on a case-by-case basis if a project is deemed meritorious. The applicant should indicate within the statement of work whether it already has a license to use such intellectual property or whether it intends to seek one. If any inventions made in whole or in part by a NIST employee arise in the course of an award made pursuant to this notice, the United States government, acting through NIST, may retain its ownership rights in any such inventions. Disposition of NIST's retained rights in such inventions will be determined solely by NIST, and may include, but is not limited to, the grant of a license(s) to parties other than the applicant to practice such inventions, or placing NIST's retained rights into the public domain. Collaborations Making Use of Federal Facilities: All proposals should include a description of any work proposed to be performed using Federal facilities. If an applicant proposes use of NIST facilities, the statement of work should include a statement of this intention and a description of the facilities. Any use of NIST facilities must be approved by appropriate NIST management and is at the sole discretion of NIST. Prior to beginning the merit review process, NIST will verify the availability of the facilities and approval of the proposed usage. Any unapproved facility use will be stricken from the proposal prior to the merit review. Examples of some facilities that may be available for collaborations are listed on the NIST Technology Services web site, http://ts.nist.gov/. Paperwork Reduction Act: The standard forms in the application kit involve a collection of information subject to the Paperwork Reduction Act. The use of Standard Forms 424, Application for Federal Assistance, 424A, Budget Information Non-Construction, 424B, Assurances Non-Construction, SF-LLL, Certification Regarding Lobbying, and CD-346, Disclosure of Lobbying Activities, has been approved by OMB under the respective Control Numbers 0348-0043, 0348-0044, 0348-0040, 0348-0046, and 0605-0001. Notwithstanding any other provision of the law, no person is required to respond to, nor shall any person be subject to a penalty for failure to comply with, a collection subject to the requirements of the Paperwork Reduction Act, unless that collection of information displays a currently valid OMB Control Number. Research Projects Involving Human Subjects, Human Tissue, Data or Recordings Involving Human Subjects: Any proposal that includes research involving human subjects, human tissue, data or recordings involving human subjects must meet the requirements of the Common Rule for the Protection of Human Subjects, codified for the Department of Commerce at 15 CFR Part 27. In addition, any proposal that includes research on these topics must be in compliance with any statutory requirements imposed upon the Department of Health and Human Services (DHHS) and other federal agencies regarding these topics, all regulatory policies and guidance adopted by DHHS, the Food and Drug Administration, and other Federal agencies on these topics, and all Presidential statements of policy on these topics. NIST will accept the submission of proposals containing research activities involving human subjects. The human subjects research activities in a proposal will require approval by Institutional Review Boards (IRBs) possessing a current registration filed with DHHS and to be performed by institutions possessing a current, valid Federal-wide Assurance (FWA) from DHHS that is linked to the cognizant IRB. In addition, NIST as an institution requires that IRB approval documentation go through a NIST administrative review; therefore, research activities involving human subjects are not authorized to start within an award until approval for the activity is issued in writing from the NIST Grants Officer. NIST will not issue a single project assurance (SPA) for any IRB reviewing any human subjects protocol proposed to NIST. President Obama has issued Executive Order No. 13,505 (74 FR. 10667, March 9, 2009), revoking previous Executive Orders and Presidential statements regarding the use of human embryonic stem cells in research. NIST will follow any guidance issued by the National Institutes of Health (NIH) pursuant to the Executive Order and will develop its own procedures based on the NIH guidance before funding research using human embryonic stem cells. NIST will follow any additional polices or guidance issued by the current Administration on this topic. Research Projects Involving Vertebrate Animals: Any proposal that includes research involving vertebrate animals must be in compliance with the National Research Council's "Guide for the Care and Use of Laboratory Animals,'' which can be obtained from National Academy Press, 2101 Constitution Avenue, NW., Washington, DC 20055. In addition, such proposals must meet the requirements of the Animal Welfare Act (7 U.S.C. § 2131 et seq.), 9 CFR Parts 1, 2, and 3, and if appropriate, 21 CFR Part 58. These regulations do not apply to proposed research using pre-existing images of animals or to research plans that do not include live animals that are being cared for, euthanized, or used by the project participants to accomplish research goals, teaching, or testing. These regulations also do not apply to obtaining animal materials from commercial processors of animal products or to animal cell lines or tissues from tissue banks. Notification of Recovery Act Requirements: Recovery Act limitations are applicable to the projects funded in this Notice. Recipients must comply with the following three provisions of the Recovery Act, as applicable, and any other terms required by the Act or that may be added to the recipient's award pursuant to guidance implemented by the Office of Management and Budget. Buy American Act Provision: Unless waived by DoC, none of the funds appropriated or otherwise made available by the Recovery Act may be used for a project for the construction, alteration, maintenance, or repair of a public building or public work unless all of the iron, steel, and manufactured goods used in the project are produced in the United States. This provision shall be applied in a manner consistent with United States obligations under international agreements. Davis Bacon Act: Under Section 1606 of the Recovery Act, projects using Recovery Act funds require the payment of not less than the prevailing wages under the Davis-Bacon Act to "all laborers and mechanics employed by contractors and subcontractors on projects funded directly by or assisted in whole or in part by and through the Federal Government." False Claims Act: Each recipient or sub-recipient awarded funds under the Recovery Act shall promptly refer to an appropriate inspector general any credible evidence that a principal, employee, agent, contractor, sub-grantee, subcontractor, or other person has submitted a false claim under the False Claims Act or has committed a criminal or civil violation of laws pertaining to fraud, conflict of interest, bribery, gratuity, or similar misconduct involving those funds. Ensuring Responsible Spending of Recovery Act Funds. The agency expects programs under this notice to be implemented in general compliance with any guidance issued by the Office of Management and Budget regarding the President's Memorandum for the Heads of Executive Departments and Agencies of March 20, 2009, Ensuring Responsible Spending of Recovery Act Funds, 74 FR 12531 (March 25, 2009). Best Practices to Promote Equality of Opportunity. Pursuant to OMB Guidance (see, "Updated Implementing Guidance for the American Recovery and Reinvestment Act of 2009," April 3, 2009) and consistent with the Recovery Act and other applicable laws, DoC encourages recipients to implement best practices to promote equality of opportunity, to provide opportunities for small and disadvantaged businesses, including veteran-owned small businesses and service disabled veteran-owned small businesses, and to follow sound labor practices. Reporting Requirements: Reporting requirements are described in the Department of Commerce Financial Assistance Standard Terms and Conditions, dated March, 2008, found on the Internet at: http://oamweb.osec.doc.gov/docs/GRANTS/DOC%20STCsMAR08Rev.pdf. The references in Sections A.01 and B.01 of the Department of Commerce Financial Assistance Standard Terms and Conditions, dated March, 2008, to "Financial Status Report (SF-269) and "SF-269 are hereby replaced with "Federal Financial Report (SF-425) and "SF-425, respectively, as required by the Office of Management and Budget (OMB) (73 FR 61175, October 15, 2008). As authorized under 15 CFR §§ 14.52 and 24.41, the OMB-approved SF-425 shall be used in the place of the SF-269 and SF-272 under the uniform administrative requirements and elsewhere under awards in this program where such forms are referenced. In addition, as set out in Sec. 1512(c) of the Recovery Act, no later than ten (10) days after the end of each calendar quarter, any recipient that receives funds under the Recovery Act from NIST must submit a report to NIST that contains: 1. The total amount of Recovery Act funds received from NIST; 2. The amount of Recovery Act funds received that were expended or obligated to projects or activities; 3. A detailed list of all projects or activities for which Recovery Act funds were expended or obligated; and 4. Detailed information on any subcontracts or subgrants awarded by the recipient to include the data elements required to comply with the Federal Funding Accountability and Transparency Act of 2006 (P.L. 109-282), allowing aggregate reporting on awards below25,000 or to individuals, as prescribed by the Director of the Office of Management and Budget. Recipients that must report information in accordance with paragraph (d) above must register with the Central Contractor Registration database (http://www.ccr.gov/) or complete other registration requirements as determined by the Director of the Office of Management and Budget. Section 1512(d) further requires that no later than thirty (30) days after the end of each calendar quarter, NIST must make the information in reports submitted under section 1512(c) of the Recovery Act as outlined above publicly available by posting the information on a Web site. OMB Memo M-09-10, Initial Implementing Guidance for the American Recovery and Reinvestment Act of 2009," which can be accessed at http://www.recovery.gov/, provides information on requirements for Federal agencies under the Recovery Act. Recipients must also comply with any additional guidance which may be forthcoming related to responsibilities of recipients of grants and cooperative agreements under the Recovery Act. Funding Availability and Limitation of Liability: The funding periods and funding amounts referenced in this notice and request for proposals are subject to the availability of funds, as well as to Department of Commerce and NIST priorities at the time of award. The Department of Commerce and NIST will not be held responsible for proposal preparation costs. Publication of this notice does not obligate the Department of Commerce or NIST to award any specific grant or cooperative agreement or to obligate all or any part of available funds. No funding is anticipated at this time to provide further support beyond the award period to any project that may receive funds under this program. Executive Order 12866: This funding notice was determined to be not significant for purposes of Executive Order 12866. Executive Order 13132 (Federalism): It has been determined that this notice does not contain policies with federalism implications as that term is defined in Executive Order 13132. Executive Order 12372: Proposals under this program are not subject to Executive Order 12372, Intergovernmental Review of Federal Programs. Administrative Procedure Act/Regulatory Flexibility Act: Notice and comment are not required under the Administrative Procedure Act (5 U.S.C. § 553), or any other law, for rules relating to public property, loans, grants, benefits or contracts (5 U.S.C. § 553 (a)). Because notice and comment are not required under 5 U.S.C. § 553, or any other law, for rules relating to public property, loans, grants, benefits or contracts (5 U.S.C. § 553(a)), a Regulatory Flexibility Analysis is not required and has not been prepared for this notice, 5 U.S.C. § 601 et seq. Dated: May 26, 2009 /s/ Patrick D. Gallagher Deputy Director Created July 14, 2009, Updated October 05, 2010
2016-09-28T08:42:25
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https://atlaswww.hep.anl.gov/hepsim/doc/doku.php?id=hepsim:quick
# Quick start Install the HepSim software toolkit using the “bash” shell on Linux/Mac: bash # set bash if you haven't done this before wget http://atlaswww.hep.anl.gov/hepsim/soft/hs-toolkit.tgz -O - | tar -xz; source hs-toolkit/setup.sh This creates the directory “hs-toolkit” with HepSim commands. You can also download it as hs-toolkit.tgz. Note that Java 8 and above should be installed. You can view the commands using the bash shell by typing : bash> hs-help The directory contains several bash scripts for Linux/Mac, and Windows batch (BAT) files to process events on Windows OS. The package is used for download, view and analyze truth-level events in the PROMC or PROIO format. Use JAS4PP program for analysing LCIO (*.lcio) files with Geant4 simulations. This program can also be used for truth-level records in the PROMC or PROIO format. To analyse ROOT files with fast simulations, use Delphes/ROOT framework. # Finding data files Let us show how to find the files associated with a given Monte Carlo event sample. Go to HepSim database and find the “Files” column. It shows URL of truth-level files (“EVGEN”), i.e. files directly created by event generators. You can use the command line tool to list files associated with a dataset as: hs-ls [name] where [name] is the dataset name. One can also use the URL of the Info page instead, or the URL of the location of all files. This command shows a table with file names. Here is an example illustrating how to list all files from the Higgs to ttbar Monte Carlo sample: hs-ls tev100pp_higgs_ttbar_mg5 (“tev” defines the energy unit, “pp” means pp collisions, “mg5” means MadGraph5). Similarly, one can use the download URL: hs-ls http://mc.hep.anl.gov/asc/hepsim/events/pp/100tev/higgs_ttbar_mg5/ Note that in this approach, one can use URL mirrors close to your geographical location. If you need to create list for downloads with all files, use this syntax: hs-ls [name] simple > input.list # make list of ProMC files (without URL path) hs-ls [name] simple-url > input_url.list # make list with URL from the main server where [name] is the name of dataset. You can also use a URL if you want to create a list of files from certain (mirror) servers. # Searching for datasets The best method to find the needed sample is to use the web page with database search. Enter “rfull” in the search field, and you will see all samples with full simulation taggs. Enter “rfast”, and you will see samples with fast simulations. If you search for “higgs”, you will see the list of samples for Higgs. Also you can use complex searches, such as “pythia%rfast001” (Pythia sample after a fast simulation with the tag 001). You can also use convenient URL links that search for some datasets. Here are a few examples: If you prefer to use the command-line approach, you can find URL that corresponds a dataset using this command: hs-find [search word] The search is performed using names of datasets or Monte Carlo models, or in the file description. For example, to find all URL locations that correspond to simulated samples with Higgs, try this: hs-find higgs If you are interested in a specific reconstruction tag, use “%” to separate the search string and the tag name. Example: hs-find pythia%rfast001 It will search for Pythia samples after a fast detector simulation with the tag “001”. To search for a full detector simulation, replace “rfast” with “rfull”. hs-get [name] [OUTPUT_DIR] where [name] is the dataset name. This also can be the URL of the Info page, or a direct URL pointing to the locations of ProMC files. This example downloads all files from the “tev100pp_higgs_ttbar_mg5” dataset to the directory “data”: hs-get tev100pp_higgs_ttbar_mg5 data Alternatively, this example downloads the same files using the URL of the Info page: hs-get http://atlaswww.hep.anl.gov/hepsim/info.php?item=2 data hs-get http://mc.hep.anl.gov/asc/hepsim/events/pp/100tev/higgs_ttbar_mg5 data All these examples will download all files from the “tev100pp_higgs_ttbar_mg5” event sample. One can add an integer value to the end of this command which specifies the number of threads. If a second integer is given, it will be used to set the maximum number of files to download. This example will download 10 files in 3 thread from the dataset “tev100pp_higgs_ttbar_mg5”. hs-get tev100pp_higgs_ttbar_mg5 data 3 10 One can also download files that have certain pattern in their names. If URL contains files generated with different pT cuts, the names are usually have the string “pt”, followed by the pT cut. In this case, one can download such files as: hs-get tev13pp_higgs_pythia8_ptbins data 3 10 pt100_ where the name is tev13pp_higgs_pythia8_ptbins. The command download files to the “data” directory in 2 threads. The maximum number of download files is 5 and all file names have *pt100* string (i.e. pT>100 GeV). The general usage of the hs-get command requires 2, 3, 4 or 5 arguments: hs-get [URL] [OUTPUT_DIR] [Nr of threads (optional)] [Nr of files (optional)] [pattern (optional)] where [URL] is either info URL, [Download URL], or the dataset name. Many datasets contain data files after Geant4 detector simulation and reconstruction (“RECO”). The files are in “LCIO” format. They include complete tracks, hits, calorimeter clusters etc. Reconstructed files are stored inside the directories with the tag “rfastNNN” (Delphes fast simulation) or “rfullNNN” (full simulation), where “NNN” is a version number. You can identify detector geometries that correspond to the tags using detector description page. For example, tev100pp_ttbar_mg5 sample includes the link “rfast001” (Delphes fast simulation, version 001). To download the reconstructed events for the reconstruction tag “rfast001”, use this syntax: hs-ls tev100pp_ttbar_mg5%rfast001 # list ROOT files with the tag "rfast001" hs-get tev100pp_ttbar_mg5%rfast001 data # download to the "data" directory The symbol “%” separates the dataset name (“tev100pp_ttbar_mg5”) from the reconstruction tag (“rfast001”). You can skip “data” in the second example - in this case, data will be copied to the directory “tev100pp_ttbar_mg5%rfast001”. hs-get tev100pp_ttbar_mg5%rfast001 data 3 10 hs-ls http://mc.hep.anl.gov/asc/hepsim/events/pp/100tev/ttbar_mg5/rfast001/ # list all files hs-get http://mc.hep.anl.gov/asc/hepsim/events/pp/100tev/ttbar_mg5/rfast001/ data # File validation One can check file consistency and print additional information as: hs-info http://mc.hep.anl.gov/asc/hepsim/events/pp/14tev/pythia8_higgs2mumu/tev14_pythia8_h2mm_1.promc The last argument can be a file location on the local disk (works faster than URL!). The output of the above command will look something like this: Click to display ⇲ Click to hide ⇱ ProMC version = 2 Description = PYTHIA8;PhaseSpace:mHatMin = 20;PhaseSpace:pTHatMin = 20; ParticleDecays:limitTau0 = on; ParticleDecays:tau0Max = 10;HiggsSM:all = on; Events = 10000 Sigma (pb) = 2.72474E1 ± 1.92589E-1 Lumi (pb-1) = 3.67007E2 Varint units = E:100000 L:1000 Log file: = logfile.txt The file was validated. Exit. You can see that this file includes a complete logfile (“logfile.txt”). We will explain how to extract it later. # Looking at separate events One can print separate EVGEN events using the above command after passing an integer argument that specifies the event to be looked at. This command prints the event number “100”: hs-info http://mc.hep.anl.gov/asc/hepsim/events/pp/14tev/pythia8_higgs2mumu/tev14_pythia8_h2mm_1.promc 100 More conveniently, one can open the file in a GUI mode to look at all events: hs-view [promc file] This command brings up a GUI window to look at separate events. You should forward X11 to see the GUI. For Windows: download the file hepsim.jar and click on it. Then open the file as [File]-[Open file]. If you use Windows OS, click “hs-view.bat” and open ProMC file using the File Menu. You can also view EVGEN events without downloading files. Simply pass a URL to the above command and you will stream Monte Carlo events: hs-view http://mc.hep.anl.gov/asc/hepsim/events/pp/14tev/pythia8_higgs2mumu/tev14_pythia8_h2mm_1.promc Here we looked at one file of Pythia8 (QCD) sample. Files with NLO predictions will be automatically identified: For such files, you will see a few particles per events and weights for calculations of PDF uncertainties. # Monte Carlo logfile Each ProMC/ProIO file includes a logfile from the Monte Carlo generator. Show this file on the screen as: hs-log [file] where [file] is either a ProMC or ProIO file (you can use URL instead of the full path on the local computer). In the case of ProMC files, one can use the standard Linux commands, such as “unzip”: unzip -p [promc file] logfile.txt where [promc file] is the file name. This command extracts a logfile with original generator-level information. The next command shows the actual number of stored events: unzip -p [promc file] promc_nevents This command lists the stored events (each event is a ProtoBuffer binary file): unzip -l [promc file] # Pileup mixing One can mix events from a signal ProMC file with inelastic (minbias) events using the “pileup mixing” command: hs-pileup pN signal.promc minbias.promc output.promc Here “p” indicates that events from “minbias.promc” will be mixed with every event from “signal.promc” using a Poisson distribution with the mean “N”. If “p” before N is not given, then exactly N (random) events from minbias.promc will be added to every event from “signal.promc”. Use large numbers of events in “minbias.promc” to minimise reuse of the same events. The barcode of particles inside “output.promc” indicates the event origin (0 is set for particles from “signal.promc”). # Analysing EVNT files One can analyse Monte Carlo events on Window, Linux and Mac with Java7/8. Many HepSim samples include *.py scripts to calculate differential cross sections. One can run validation scripts from the Web using Java Web Start. Also, one can run scripts using a desktop and streaming data via the network, or using downloaded files (in which case you pass the directory with *promc files as an argument). Here are a few approaches showing how to read *.py scripts: ## Using Java Web start Many “Info” pages of HepSim have Jython (Python) scripts for validation and analysis. One can run such scripts from the web browsers using the Java Web Start technology. Click the “Launch” button. You will see an editor. Then click the “Run” button to process events. To use Java Web Start, you should configure Java permissions: For Linux/Mac, run “ControlPanel”, go to the “Security” tab and add “http://atlaswww.hep.anl.gov” to the exception list. For Windows, find “Java Control Panel” and do the same. Read Why are Java applications blocked by your security settings. In addition, if you are a Mac user, you should allow execution of programs outside Mac App Store. ## Using stand-alone Python In this example, we will run a Python (to be more exact, Jython) script and, at the same time, will stream data from the web. Find a HepSim event sample by clicking the info “Info” column. For example, look at a ttbar sample from Madgraph: ttbar_mg5. Find the URL of the analysis script (“ttbar_mg5.py”) located at the bottom. Copy it to some foulder. Or use “wget”: wget http://mc.hep.anl.gov/asc/hepsim/events/pp/100tev/ttbar_mg5/macros/ttbar_mg5.py Then process this code in a batch mode as: hs-run ttbar_mg5.py If you do not want a pop-up canvas with the output histogram, change the line 71 to “c1.visible(0)” (or “c1.visible(False)”) and add “sys.exit(0)” at the very end of the “ttbar_mg5.py” macro. One can view, edit and run the analysis file using a simple GUI editor. hs-ide ttbar_mg5.py It opens this file for editing. One can run it by clicking on the “run” button. It also provides an interactive Jython shell. If you use Windows OS, click the file “hs-ide.bat” and open the Python script using the menu, and then run this script using the“Run” button. When possible, use the downloaded ProMC files, rather than streaming the data over the network. The calculations will run faster since the program does calculations using local files. Let assume that we put all ProMC files to the directory “data”. Then run the script as: hs-run ttbar_mg5.py data Here is a complete example: we download data to the directory “ttbar_mg5”, then we download the analysis script, and then we run this script over the local data using 10000 events: hs-get http://mc.hep.anl.gov/asc/hepsim/events/pp/100tev/ttbar_mg5 ttbar_mg5 hs-run ttbar_mg5 10000 ## Using a Java IDE The above example has some limitations since it uses rather simple editor. Another approach is to use the full-featured Jas4pp or DataMelt programs which give more flexibility. wget -O dmelt.zip http://jwork.org/dmelt/download/current.php; unzip dmelt.zip; ./dmelt/dmelt_batch.sh ttbar_mg5.py You can also pass URL with data as an argument and limit the calculation to 10000 events: ./dmelt/dmelt_batch.sh ttbar_mg5.py http://mc.hep.anl.gov/asc/hepsim/events/pp/100tev/ttbar_mg5/ 10000 As before, use the batch mode using downloaded ProMC files. Let assume that we put all ProMC files to the directory “data”. Then run DataMelt over the data as: ./dmelt/dmelt_batch.sh ttbar_mg5.py data Here is a complete example: we download data to the directory “ttbar_mg5”, then we download the analysis script, and then we run this script over the local data using 10000 events: hs-get http://mc.hep.anl.gov/asc/hepsim/events/pp/100tev/ttbar_mg5 ttbar_mg5 ./dmelt/dmelt_batch.sh ttbar_mg5.py ttbar_mg5 10000 Then click “run” (or [F8]). One can also start DataMelt without input files: ./dmelt/dmelt.sh on Linux/Mac. On Windows, run “dmelt.bat” instead. You will see the DatMelt IDE. Locate an URL location of the analysis script, such as ttbar_mg5 (can be found under “Info” link). Then copy this link using the right mouse button (“Copy URL Location”). Next, in the DMelt menu, go to “File”→“Read script from URL”. Copy the URL link of the *.py file to the pop-up DataMelt URL dialog and click “run”. The program will start reading data from the Web. At the end of the run, you will see a pop-up window with a histogram. This method works for Python/Jython, Java, Ruby, Groovy, BeanShell languages. ## Using C++/ROOT Install ProMC and ROOT. Make sure that the environmental variables $PROMC and$ROOTSYS are set correctly. Then look at the examples: $PROMC/examples/reader_mc/ # shows how to read ProMC files from a typical Monte Carlo generator$PROMC/examples/reader_nlo/ # shows how to read ProMC files with NLO calculations (i.e. MCFM) $PROMC/examples/promc2root/ # shows how to read PROMC files and create ROOT Tree. For C++/ROOT, you should download files <i>a priory</i> since the streaming over the network is not supported. There is a simple example showing how to read multiple Monte Carlo files from HepSim, build anti-KT jets using FastJet, and fill ROOT histograms. Download hepsim-cpp package and compile it: wget http://atlaswww.hep.anl.gov/asc/hepsim/soft/hepsim-cpp.tgz -O - | tar -xz; cd hepsim-cpp/; make Read the file “README” inside this directory. # Analyzing RECO data HepSim includes data after fast and full detector simulations. There are several methods to analyse such files. ## Analyzing Delphes ROOT files (fast simulation) The Delphes ROOT files are typically posted using the reconstruction tag “rfast[XXX]”, where “[XXX]” is a number. Use search to find such samples. Read the Delphes documentation about how to read Delphes ROOT files. You can find all samples that contain fast simulations using this link. ## Full simulation: LCIO files Events afer detector simulation and reconstruction (“RECO”) are posted under the tag “rfull[XXX]”, where “[XXX]” is a number. We use LCIO file format that is readable by C++, Fortran and Java. Such files have an extension “slcio”. You can analyse the LCIO files using Jas4pp program that allows you to read files using the Python syntax. If you need to read LCIO files in C++ code with ROOT/FastJet, use the example package https://github.com/chekanov/HepSim. You can find all samples that contain full simulations using this link. ## Conversion to ROOT, HEPMC, HEPEVT, LHE, STDHEP, LCIO One can convert ProMC file to ROOT to look at branches. If the ProMC package is installed, run the converter: cp -rf$PROMC/examples/promc2root . cd promc2root make ./promc2root [promc file] output.root The output file will contain ROOT branches with px,py,pz,e, etc. One can also convert ProMC to HEPMC using the example $PROMC/examples/promc2hepmc (see the ProMC manual). In addition, the directory $PROMC/examples/ has examples showing how to convert ProMC to HEPEVT records (promc2hepevnt), STDHEP (promc2stdhep), LHE (promc2lhe) and LCIO (promc2lcio). # Comparing with HepData Durham HepData database maintains “DMelt” scripts compatible with HepSim analysis scripts, thus it is relatively easy to overlay Monte Carlo predictions and data from published articles. For example, look at the link AAD 2013 from HepData and download a “DMelt” Jython script with published data. You can run this script inside DMelt IDE, or using the “hs-run” and “hs-ide” commands from hs-tools. Then one can combine this script with a HepSim script (from the “Info” description) that runs over HepSim Monte Carlo data, creating plots showing agreement between data and theoretical calculations. Sergei Chekanov 2017/02/06 17:25
2019-08-20T00:37:27
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http://pdglive.lbl.gov/DataBlock.action?node=S017Q&amp;home=sumtabB
# ${{\boldsymbol n}}$ CHARGE INSPIRE search See also $\vert {{\mathit q}_{{p}}}+{{\mathit q}_{{e}}}\vert /{{\mathit e}}$'' in the proton Listings. VALUE ($10^{-21}$ $\mathit e$) DOCUMENT ID TECN  COMMENT $\bf{ -0.2 \pm0.8}$ OUR AVERAGE $-0.1$ $\pm1.1$ 1 2011 Neutrality of SF$_{6}$ $-0.4$ $\pm1.1$ 2 1988 Cold ${{\mathit n}}$ deflection • • • We do not use the following data for averages, fits, limits, etc. • • • $-15$ $\pm22$ 3 1982 CNTR Cold ${{\mathit n}}$ deflection 1  As a limit, this BRESSI 2011 value is $<1 \times 10^{-21}{{\mathit e}}$. 2  The BAUMANN 1988 error $\pm1.1$ gives the 68$\%$ CL limits about the the value $-0.4$. 3  The GAEHLER 1982 error $\pm22$ gives the 90$\%$ CL limits about the the value $-15$. References: BRESSI 2011 PR A83 052101 Testing the Neutrality of Matter by Acoustic Means in a Spherical Resonator BAUMANN 1988 PR D37 3107 Experimental Limit for Charge of the Free Neutron GAEHLER 1982 PR D25 2887 Experimental Limit for the Charge of the Free Neutron
2019-06-19T21:43:28
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https://www.usgs.gov/center-news/volcano-watch-where-did-all-magma-go-when-k-laueas-caldera-formed
# Volcano Watch — Where did all the magma go when Kīlauea's caldera formed? Release Date: If a sinkhole collapses in your back yard, where and how did the stuff disappear? Did an underground opening already exist (such as a lava tube), did something "dissolve" away (such as rotting vegetable matter), or did a kind of conveyer belt remove material and take it somewhere else (such as moving magma)? We have this problem understanding how Kīlauea's caldera formed. It wasn't by explosion, because no debris is piled around the caldera. It must have formed by collapse. And therein lies an unsolved mystery. Geologic evidence indicates that the caldera appeared in about A.D. 1500, give or take several decades. It developed at the end of, or soon after, a 60-yr-long eruption from the Ailaau shield just east of Kīlauea Iki, which ended in about 1470 after flooding much of Puna with lava flows. The caldera formed at the start of, or shortly before, a series of explosions that radiocarbon ages date to about A.D. 1500. That's not terribly long ago. Both geologic and cultural evidence should exist for such a major volcanic event. Indeed, the events are likely chronicled in the Pele-Hiiaka chants. But neither cultural nor geologic evidence tells us where the rocks disappeared when the top of the volcano sunk to form the caldera. How much material was removed? The volume is uncertain but very large. If the entire caldera formed at one time, we estimate a volume of 6 cubic kilometers (1.4 cubic miles), equivalent to 780 million loads for a 10-cubic-yard dump truck. That estimate is based on the caldera's dimensions when first surveyed in the 1820s and on guesses as to how much deeper it might have been. Most geologic models assume very rapid removal of material to form a caldera. The argument is that a large void cannot support itself underground, so an empty volume of a few cubic kilometers (cubic miles) could not exist for long. If so, a huge volume of magma must have almost instantaneously left the reservoir under Kīlauea's summit, leaving a void into which the summit fell. Where did the magma go? We haven't found it. Nowhere on Kīlauea did a lava flow of huge volume erupt in about A.D. 1500. Could an eruption may have taken place offshore, along the Puna Ridge? Recent seafloor investigations found no large lava flow of appropriate age. Maybe there was no eruption. Maybe magma stayed underground, migrating quickly from the summit reservoir to some place in the east rift zone. A conservative volume of 3 cubic kilometers (0.7 cubic miles) can be contained in a huge dike 60 km (37 miles) long by 5 km (3.1 miles) high by 10 m (33 feet) wide. We have no way to test for such a dike, so we must consider one. Another possibility is that the eruption of the Ailaau lava flow, with a volume of 6 cubic kilometers (1.4 cubic miles), created the caldera. This is appealing, because the caldera formed just after the eruption ended, suggesting a link between the two large events. If this happened, then supply of magma to Kīlauea must have slowed or stopped during the eruption, so the magma reservoir eventually emptied and then collapsed. Perhaps lessened magma supply during an eruption is necessary to form a caldera. The Ailaau eruption took place over 60 years. Did a void slowly grow within the volcano, not collapsing until it reached its final huge size? That would seem unlikely to most geologists. But what if we view the magma reservoir as a deep mine, with many interconnected passageways, rather than as a simple balloon? A mine has large void space, yet is stable to a point. Since the Puu Oo eruption started in 1983, the southern part of the caldera has been sinking 6-10 cm/year (2.5-4 inches/yr). Could this gentle sagging be an early stage of, or precursor to, another caldera collapse as the summit reservoir slowly empties? Clearly there's a lot we don't know about how the caldera formed. We'll eventually figure it out, but for now the origin of the caldera is as puzzling to us as the origin of your back-yard sinkhole is to you. ### Volcano Activity Update Eruptive activity at Puu Oo continues. Most lava flows have been at the lower end of the rootless shield complex along the Mother's Day lava tube south of Puu Oo. Such flows have been small and short-lived but are gradually advancing toward the top of Pulama pali. On March 20 a new lava flow (the Kuhio flow) erupted from the south base of Puu Oo; it remains sporadically active. Vents within the crater of Puu Oo are incandescent and sometimes visible from Mountain View and Glenwood. No lava is visible from the Chain of Craters Road. Two earthquakes were reported felt during the week ending on March 31. A magnitude 3.2 earthquake, felt at Milolii, took place at 6:17 p.m. March 27 at a depth of 6 km (4 miles) about 16 km (10 miles) east of the summit of Mauna Loa. The next day, residents of Honokaa and Papaaloa reported a jolt at 5:42 p.m.; this event had a magnitude of 3.1 and was located 8 km (5 miles) south-southwest of Paauilo at a depth of 10 km (6 miles). Mauna Loa is not erupting. The summit region continues to inflate slowly. Seismic activity remains very low, with 1 earthquake located in the summit area during the past week.
2020-08-04T12:01:08
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https://www.usgs.gov/center-news/volcano-watch-hard-rain-halape
# Volcano Watch — Hard rain at Halape Release Date: Two months ago, we discussed early findings suggesting that Kīlauea had an explosive eruption far larger than we dared think. The study has progressed since then, and the early findings have been confirmed and extended. Two months ago, we discussed early findings suggesting that Kīlauea had an explosive eruption far larger than we dared think. The study has progressed since then, and the early findings have been confirmed and extended. Our search for rocks thrown from Kīlauea's summit found them at all examined locations from Kipuka Keana Bihopa, just west of Hilina Pali Road, to the Kealakomo waena area below Holei Pali, along the Chain of Craters Road—an area 16 km (nearly 10 miles) wide. The rocks decrease in size systematically southward from the new Kulanaokuaiki campground, 7 km (4 miles) from Kīlauea's summit, to the coast, about 16 km (9.5 miles) from the summit. At the campground, dense stones more than 10 cm (4 inches) in diameter are easily found--the largest yet is 16 cm (6.3 inches). At the coastal sites of Halape and Keauhou Landing, they are no larger than about 1.5 cm (0.6 inches) in diameter. Though small, they would have constituted a hard rain indeed on these idyllic coastal retreats. By plotting the sizes of the ejected rocks on a map, it is immediately obvious that their distribution forms an elongate lobe aimed from Kīlauea's summit to the Keauhou Landing-Apua Point area, some 18 km (11 miles) away. Sizes are largest along the axis of the lobe and decrease to either side as well as down the lobe toward the sea. The explosive eruption took place between A.D. 600 and A.D. 1000; consequently the deposit is covered by younger lava flows in many places. Accordingly, we can find neither the ejected rocks closer to the summit than Kulanaokuaiki campground nor the absolute eastern and western sides of the lobe. Nonetheless, the pattern of distribution is remarkably complete and well defined. The large rocks are too far from Kīlauea's summit to be explained by a single huge explosion. The observations seem to require a different kind of eruption-one with a sustained, up-rushing column of ash and rocks akin to those of very powerful eruptions from stratovolcanoes, such as Mount St. Helens and Pinatubo. These are called Plinian eruptions, after the famous Roman who observed the eruption of Vesuvius that destroyed Pompeii. Modeling by academic colleagues shows that Plinian eruptions can boost fist-sized rocks to great heights. These rocks, together with ash and pumice, eventually spread out from the top of the column and move laterally, creating what are called mushroom, or umbrella, clouds. The rocks fall from the mushroom cloud, the larger ones nearer the vent. Models of Plinian eruption columns allow one to calculate the height of the column and the wind velocity in the atmosphere during the eruption. If these models are applicable to Kīlauea, the new data suggest that the eruption column and its umbrella top reached a height of 25-30 km (15-18 miles) above the vent! This is higher than the 1980 umbrella cloud from Mount St. Helens. And, there was likely a wind of 10-20 m/sec (20-40 mph). Plinian eruption columns are not driven by steam from heated ground water, as are the smaller explosions from Kīlauea. Instead, gases dissolved in magma expand rapidly to propel the liquid, and rocks scraped from the volcano's plumbing system, high into the air. Likely gases causing such energetic eruptions at Kīlauea are carbon dioxide and water dissolved in the magma. Of these, carbon dioxide is more abundant and less soluble than water and may be the most important propellant. Plinian eruptions spread ash over wide areas, even upwind because of high-elevation air flow. They would present problems for the entire island, not just that part impacted by falling rocks. We don't know what the precursors would be or if they would differ from those leading to a typical Kīlauea eruption. Fortunately such events are rare. In at least the past 2,000 years, this is the only eruption of its type that we know about—so far. ### Volcano Activity Update Eruptive activity of Kīlauea Volcano continued unabated during the past week. Lava is erupting from Puu Oo and flowing southeast through a tube system down to the flats below Pulama pali and beyond to the ocean. Lava is entering the ocean at Kamokuna located 1.6 km (1 mi) west-southwest of Wahaula. No surface flows were observed. The public is reminded that the ocean-entry areas are extremely hazardous, with explosions accompanying sudden collapses of the new land. The active lava flows are hot and have places with very thin crust. The steam plumes are highly acidic and laced with glass particles. Two earthquakes were reported felt during the week ending on December 7. Workers in Hawaii Volcanoes National Park reported feeling an earthquake at 7:51 a.m. on Tuesday, December 5. The magnitude-3.2 earthquake was located 1.5 km (.9 mi) beneath the summit of Kīlauea Volcano. A resident of Paauilo felt an earthquake at 4:47 p.m. on Thursday, December 7. The magnitude-3.5 earthquake was located 28 km (17 mi) south of Waimea at a depth of 39 km (23.4 mi).
2020-09-28T06:15:43
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http://dlmf.nist.gov/28.5
# §28.5 Second Solutions , ## §28.5(i) Definitions ### ¶ Theorem of Ince (1922) If a nontrivial solution of Mathieu’s equation with has period or , then any linearly independent solution cannot have either period. Second solutions of (28.2.1) are given by 28.5.1 when , , and by 28.5.2 when , . For , we have 28.5.3 and 28.5.4 compare §28.2(vi). The functions , are unique. The factors and in (28.5.1) and (28.5.2) are normalized so that As with , , , , and . This determines the signs of and . (Other normalizations for and can be found in the literature, but most formulas—including connection formulas—are unaffected since and are invariant.) 28.5.6 As a consequence of the factor on the right-hand sides of (28.5.1), (28.5.2), all solutions of Mathieu’s equation that are linearly independent of the periodic solutions are unbounded as on . ### ¶ Wronskians For further information on , , and expansions of , in Fourier series or in series of , functions, see McLachlan (1947, Chapter VII) or Meixner and Schäfke (1954, §2.72). ## §28.5(ii) Graphics: Line Graphs of Second Solutions of Mathieu’s Equation ### ¶ Odd Second Solutions Figure 28.5.1: for and (for comparison) . Symbols: : Mathieu function, : second solution, Mathieu’s equation and : real variable Referenced by: §28.5(ii) Permalink: http://dlmf.nist.gov/28.5.F1 Encodings: pdf, png Figure 28.5.2: for and (for comparison) . Symbols: : Mathieu function, : second solution, Mathieu’s equation and : real variable Permalink: http://dlmf.nist.gov/28.5.F2 Encodings: pdf, png Figure 28.5.3: for and (for comparison) . Symbols: : Mathieu function, : second solution, Mathieu’s equation and : real variable Permalink: http://dlmf.nist.gov/28.5.F3 Encodings: pdf, png Figure 28.5.4: for and (for comparison) . Symbols: : Mathieu function, : second solution, Mathieu’s equation and : real variable Permalink: http://dlmf.nist.gov/28.5.F4 Encodings: pdf, png ### ¶ Even Second Solutions Figure 28.5.5: for and (for comparison) . Symbols: : second solution, Mathieu’s equation, : Mathieu function and : real variable Permalink: http://dlmf.nist.gov/28.5.F5 Encodings: pdf, png Figure 28.5.6: for and (for comparison) . Symbols: : second solution, Mathieu’s equation, : Mathieu function and : real variable Referenced by: §28.5(ii) Permalink: http://dlmf.nist.gov/28.5.F6 Encodings: pdf, png
2013-12-06T10:41:00
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https://www.usgs.gov/center-news/volcano-watch-lava-diversion-hawai-i
# Volcano Watch — Lava diversion in Hawai‘i? Release Date: November has been a busy month historically for eruptions as well as earthquakes. Six historical eruptions have started in November on Kīlauea (1930, 1959, 1967, 1973, 1975, 1979) and four on Mauna Loa (1880, 1892, 1914, and 1935). November has been a busy month historically for eruptions as well as earthquakes. Six historical eruptions have started in November on Kīlauea (1930, 1959, 1967, 1973, 1975, 1979) and four on Mauna Loa (1880, 1892, 1914, and 1935). Today's column focuses on the Mauna Loa eruption that began on November 21, 1935. This eruption is notable for several reasons. It began from vents within the rift zone, but, as the eruption progressed, the vents deviated from the rift zone and formed a radial vent on Mauna Loa's north flank. The 1935 lavas can be easily identified as the black flow surrounding Puu Huluhulu on the Saddle Road opposite the Mauna Kea access road. This eruption also marks the first attempt at altering the course of a Hawaiian eruption, through the use of explosives. The eruption came as no surprise to those working at the Hawaiian Volcano Observatory. It was preceded by two flurries of earthquakes, two months, and, one month prior to the outburst of lava. Each flurry tracked the upward migration of lava within the volcano. The largest recorded earthquake occurred early in the morning of the 21st and was felt on Oahu. The eruption began at 6:20 PM. Like most Hawaiian eruptions, the eruptive activity was immediately preceded by a swarm of earthquakes, followed by tremor. The eruption commenced with a curtain of fountains near North Pit within the summit caldera, Mokuaweoweo. The vents migrated 3 km (2 miles) down the northeast rift zone. Here a series of discontinuous fissures began erupting; lava was thrown 60-90 m (200-300 ft) into the air, and flows advanced toward Mauna Kea. These early flows were aa because of the vigorous activity at the vent. In the meantime, the summit activity waned, eventually dying off on November 26. The rift activity finally condensed to a single central vent at the 3,500 m (11,400 ft) elevation. On November 27, low-level fountaining was reported from the radial vent at the 2,600 m (8,600 ft) elevation on Mauna Loa's north flank (well outside the limits of the rift zone). The initial flows produced from this radial vent were aa. By December 8, the vent began producing pahoehoe. On December 22 the pahoehoe flows reached the low area between Mauna Loa and Mauna Kea, ponding near Puu Huluhulu and the present day Saddle Road. Eventually the lava turned to follow the natural drainage toward Hilo, instigating a crisis. On December 26, the flow was moving 1.6 km per day (1 mile per day), and at that rate scientists calculated the flows would reach Kaumana Road by January 9 (disrupting mochi-pounding parties). A suggestion to bomb the eruption was made. The U.S. Army Officer who planned the bombing operation was then Lt. Colonel George S. Patton, who would go on to WWII fame. On December 27, U.S. Army planes dropped bombs, targeting the lava channels and tubes just below the vents at 2,600 m (8,600 ft). The object was to divert the flow near its source. The results of the bombing was declared a success by Thomas A. Jaggar, Director of the Hawaiian Volcano Observatory. Jagger wrote that "the violent release of lava, of gas and of hydrostatic pressures at the source robbed the lower flow of its substance, and of its heat." The lava stopped flowing on January 2, 1936. The efficacy of this lava bombing is disputed by some volcanologists, and lava diversion will be the subject of a future Volcano Watch. ### Volcano Activity Update The constant effusion of lava from the Puu Oo vent on Kīlauea's east rift zone continued unabated during the past week. Confined in a network of tubes, the lava flows from the vent to the seashore and enters the ocean at Wahaula and Kamokuna benches, at the eastern edge of Hawaii Volcanoes National Park. Conditions at the coastal entries are very unstable with frequent collapses resulting in explosive activity. Lavaviewers are reminded that the area is extremely hazardous. There were no earthquakes reported felt during the past week.
2020-08-04T03:00:37
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http://leg.colorado.gov/bills/HB17-1181
HB17-1181 # Required State Assessment For Ninth-grade Students Concerning requiring a single statewide end-of-year assessment for students enrolled in ninth grade that is aligned with the tenth-grade state assessment, and, in connection therewith, reducing an appropriation. Session: 2017 Regular Session Under existing law, each local education provider must administer the state assessments in math and English language arts to ninth-grade students and must administer a state-selected assessment to tenth-grade students. The bill repeals the requirement to administer the state assessment to ninth-grade students. Instead, local education providers must administer a state-selected ninth-grade assessment that is aligned with the ninth-grade content standards and the assessment administered to tenth-grade students. The department of education must ensure that, under the testing schedule, ninth-grade students take the state-selected assessment in the spring semester. (Note: This summary applies to the reengrossed version of this bill as introduced in the second house.)
2017-05-28T08:50:15
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https://gribblelab.org/CBootCamp/5_Functions.html
# 5. Functions ## Rationale Breaking your code down into discrete functions allows you to re-use code in intelligent ways, and to make your code more efficient overall. You can use functions written by other people (by linking them to your own programs) and avoid having to write everything from scratch yourself. Writing functions to perform common tasks means that you can essentially write your own meta-language. For example if you have functions already written to perform these tasks, your C program might look like this: #include <stdio.h> int main() { loadSubjects(); excludeSubject(12); lowpassFilterData(); collectMeansWithBinSize(8); pval = performANOVA(); printf("my hypothesis is correct, p < %.3f\n", pval); return 0; } The idea is that once we know what sorts of operations on our data we will wish to do, we can write a set of functions (sometimes called subroutines), to abstract away the details, and provide us with a sort of high-level meta-language that we can use to carry out the steps we wish to. ### Abstraction Using functions to abstract away the details also means that as long as the function inputs and outputs are known, then the user doesn't really need to know the details of how the function performs its task. Another way to think about this: let's imagine you wrote a function lowpassFilterData(), and it worked well. Let's say your friend came along one day and noticed that it was taking a long time to process your data, and he suggested you use a different algorithm for low-pass filtering, and he gave you a file containing the code. As long as the inputs and outputs are the same (or you could write your own "wrapper" function to ensure this), then you can simply switch out your function for the new one, and all functionality should be the same. You can think of functions as "black boxes" with input and output wires. As long as the wires are labelled the same, and there are the same number, you can replace one box with a newer box, and perhaps get faster (or more accurate, for example) functionality without changing your main program. ## Defining a Function A function must be defined in the following way: returnType functionName (arg1Type arg1Name, arg2Type arg2Name) { function_statement; function_statement; return returnVar; } This seems rather abstract, but we will see a concrete example in a moment. On the first line, we have to begin by declaring what data type the function will return once it finishes. You can define a function that doesn't return anything by using void. The next item is the name of the function, which you get to choose. Next, in round brackets, is a list of input arguments that the function expects to see when it is called. Each argument is delared by listing first the type of the argument, followed by its name. Then in the body of the function is code, which does whatever you want the function to do. Finally we have to return a value (if the return type is non-void). Here is a more concrete example. Let's say we want to write a function that writes a message to the screen, "Hello, Paul": void writeMessage(void) { printf("Hello, Paul\n"); } Here the return type is void since the function doesn't return a value, and the input argument list is also void, since it doesn't expect any inputs. We can call the function in a program like this: #include <stdio.h> void writeMessage(void) { printf("Hello, Paul\n"); } int main() { writeMessage(); return 0; } Hello, Paul ## Input Arguments Now let's modify our function so that it accepts one input argument, which is a string containing the name we want to say hello to. So for example we could call the function with writeMessage("Dave") and it would print to the screen Hello, Dave, or we could call it with writeMessage("Victoria") and it would write to the screen Hello, Victoria, etc: #include <stdio.h> void writeMessage(char name[]) { printf("Hello, %s\n", name); } int main() { writeMessage("Dave"); writeMessage("Victoria"); return 0; } Hello, Dave Hello, Victoria For the moment don't worry about the char[] type, it is a character array, and we will talk about arrays in the next section. Let's give our function two input arguments now, just to see how this is done: #include <stdio.h> void writeMessage(char name[], int n) { printf("Hello, %s %d\n", name, n); } int main() { writeMessage("Dave", 123); writeMessage("Victoria", 444); return 0; } Hello, Dave 123 Hello, Victoria 444 ## Return Value Let's consider another example, one where we want our function to return a value. Let's write a function to compute Fibonacci numbers (Wikipedia). Fibonacci numbers are defined as: $$F_{n} = F_{n-1} + F_{n-2}$$ where $$F_{0}=0$$ and $$F_{1}=1$$. #include <stdio.h> int Fibonacci(int n) { if (n==0) return 0; else if (n==1) return 1; else return Fibonacci(n-1) + Fibonacci(n-2); } int main() { int n = 10; int Fn = Fibonacci(n); printf("Fibonacci(%d) = %d\n", n, Fn); return 0; } Fibonacci(10) = 55 Here we define the return type as int, as we want our function to return an integer. We define one input argument, called n, which is also an int type. Then in the body of the function, we do our calculations. Unlike in some languages such as Python, Matlab, and R, in C, functions can only return a single value. There is a way to achieve the same result however, which is to return a pointer to a complex data type such as an array, or a structure. We will talk about complex data types in the next section. ### Recursion Note in the Fibonacci example above, that in the body of our function, if the value of the input argument n is not 0 or 1, then the function ends up calling itself (on line 6 of the code listing). When a function calls itself, this is called recursion, or a recursive function call. Recursion allows for very compact code, and for intuitive definitions. You may see recursion used in mathematical functions, and also in algorithms like sorting and searching. The cost of recursion is that sometimes the overhead involved in the computer repeatedly calling functions over and over again, can be costly, but this really depends on the nature of the algorithm. For Fibonacci numbers, recursion is OK for small n but once n becomes large, it is really slow. As an exercise, you could try to re-code the Fibonacci function using a loop instead of recursion. Another thing to try is memoization (look it up, I didn't mis-spell it). ## Argument Checking Note that if we pass an argument of the wrong type to a function, the program may still compile, and even run, and it will simply spit out crazy values. Sometimes we will get a compiler warning, but sometimes not. Be very careful that the input values you pass to functions, and the output values you receive from functions, are what is expected. ## Variable Scope Any variables declared inside a function, are local to that function, and are not accessible outside of the function. Similarly, code within a function doesn't have access to variables that have been declared outside of that function (for example in another function, or in main()). If you want this functionality, then you can specify that a variable be global. Any variable declared outside of any function (it also has to be outside of main()) is global, and can be seen by every function. In C, global variables are known as external variables (they are external to any function). For example in the following code, the varibale myGlob is declared outside of main() and outside of myFunc() and thus can be accessed by code within both. The variable myInt is declared within the function myFunc() and is thus local to myFunc() and cannot be accessed outside of myFunc() (for example within main()). Similarly, the variable myChar is declared within main() and so cannot be seen within myFunc(). #include <stdio.h> float myGlob = 3.14; void myFunc(void) { int myInt = 8; printf("my favourite number is %d\n", myInt); printf("my favourite float is %.2f\n", myGlob); // printf("my favourite letter is $c\n", myChar); // THIS WOULD NOT WORK } int main() { char myChar = 'x'; printf("my favourite letter is %c\n", myChar); myFunc(); printf("my favourite float is %.2f\n", myGlob); // printf("my favourite number is %d", myInt); // THIS WOULD NOT WORK return 0; } my favourite letter is x my favourite number is 8 my favourite float is 3.14 my favourite float is 3.14 ## Automatic vs Static Variables We talked about variable scope and the idea that variables declared within a function are local to that function. What actually happens is that each time a function is called by another piece of code, all the variables declared within the function are created (that is, memory is allocated to hold them). When a function is finished, all of that local memory storage is de-allocated, and those variables essentially disappear. This is known as automatic local variables (they are automatically created and then destroyed as the function is called, and then finishes). If you want local variables to persist, you can declare them as static local variables. You simply insert the word static in front of the variable type when you declare it inside your function. When declared in this way, the variable will not be destroyed when the function exits, but it (and its value) will persist. Next time the function is called, the value will have retained the value from the previous function call. It's a sort of global variable, but one that is still only accessible within the function in which it's declared. Here's an example program that maintains a running count of the number of times the function myFun() has been called. #include <stdio.h> void myFunc(void) { static int num = 0; num++; printf("myFunc() has been called %d times so far\n", num); } int main() { myFunc(); myFunc(); myFunc(); // printf("num = %d\n", num); // THIS WOULD NOT WORK return 0; } myFunc() has been called 1 times so far myFunc() has been called 2 times so far myFunc() has been called 3 times so far When would you want to use static variables? One general case, like above, is when you want to keep track of the number of times a function has been called. Another reason has to do with efficiency… if for example your function declares a large local variable whose values don't change from one function call to the next, it may be more efficient to declare it as static, so that it is created and initialized only once. ## Variadic Functions A variadic function is one which accepts a variable number of input arguments. In C we can write functions that are variadic. Sometimes this may be useful. Here is a simple example of how one would do this, taken from here. See this page for more details. #include <stdarg.h> #include <stdio.h> int add_em_up (int count,...) { va_list ap; int i, sum; va_start (ap, count); /* Initialize the argument list. */ sum = 0; for (i = 0; i < count; i++) sum += va_arg (ap, int); /* Get the next argument value. */ va_end (ap); /* Clean up. */ return sum; } int main (void) { /* This call prints 16. */ printf ("%d\n", add_em_up (3, 5, 5, 6)); /* This call prints 55. */ printf ("%d\n", add_em_up (10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10)); return 0; } 16 55 Note we have to #include <stdarg.h> in order to use the handful of functions necessary to work with the argument list. Note we have already seen a sort of variadic function, which is the main() function, which as we know can accept a variable number of input arguments when the program is started at the command line. ## Exercises function should be called fib and should take as input a single integer value n, and should return an integer value representing the nth Fibonacci number. The code example in the notes uses recursion to accomplish this. Write your own function that doesn't use recursion, but uses a loop instead. I should be able to paste your function at the bottom of this C program [ code ] and it should run: // gcc -Wall -o go 5_1_go.c #include <stdio.h> int fib(int n); int main(int argc, char *argv[]) { printf("fib(%d)=%d\n", 10, fib(10)); return 0; } int fib(int n) { // your code goes here } $ gcc -o go 5_1_go.c $./go fib(10)=55 • 2 Write a function that determines whether an integer is prime. The function should take as input a single integer, and return a 1 if the input is prime, and a 0 if it is not. I should be able to paste your function at the bottom of this C program [ code ] and it should run: // gcc -Wall -o go 5_2_go.c #include <stdio.h> int isprime(int n); int main(int argc, char *argv[]) { printf("isprime(%d)=%d\n", 12, isprime(12)); printf("isprime(%d)=%d\n", 17, isprime(17)); return 0; } int isprime(int n) { // your code goes here } $ gcc -o go 5_2_go.c \$ ./go isprime(12)=0 isprime(17)=1 • 3 Write a program that prints out the first 1000 prime numbers. You can find a list to verify the correctness of your program here. 1: 2 2: 3 3: 5 4: 7 5: 11 ... (deleted for brevity) ... 996: 7879 997: 7883 998: 7901 999: 7907 1000: 7919 ### Solutions Paul Gribble | Summer 2012 This work is licensed under a Creative Commons Attribution 4.0 International License
2019-01-22T19:18:11
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https://www.ctcms.nist.gov/fipy/documentation/FAQ.html
## How do I represent an equation in FiPy?¶ As explained in Theoretical and Numerical Background, the canonical governing equation that can be solved by FiPy for the dependent CellVariable is and the individual terms are discussed in Discretization. A physical problem can involve many different coupled governing equations, one for each variable. Numerous specific examples are presented in Part Examples. ### Is there a way to model an anisotropic diffusion process or more generally to represent the diffusion coefficient as a tensor so that the diffusion term takes the form ?¶ Terms of the form can be posed in FiPy by using a list, tuple rank 1 or rank 2 FaceVariable to represent a vector or tensor diffusion coefficient. For example, if we wished to represent a diffusion term with an anisotropy ratio of 5 aligned along the x-coordinate axis, we could write the term as, >>> DiffusionTerm([[[5, 0], [0, 1]]]) which represents . Notice that the tensor, written in the form of a list, is contained within a list. This is because the first index of the list refers to the order of the term not the first index of the tensor (see Higher order diffusion). This notation, although succinct can sometimes be confusing so a number of cases are interpreted below. >>> DiffusionTerm([[5, 1]]) This represents the same term as the case examined above. The vector notation is just a short-hand representation for the diagonal of the tensor. Off-diagonals are assumed to be zero. >>> DiffusionTerm([5, 1]) This simply represents a fourth order isotropic diffusion term of the form . >>> DiffusionTerm([[1, 0], [0, 1]]) Nominally, this should represent a fourth order diffusion term of the form , but FiPy does not currently support anisotropy for higher order diffusion terms so this may well throw an error or give anomalous results. >>> x, y = mesh.cellCenters >>> DiffusionTerm(CellVariable(mesh=mesh, ... value=[[x**2, x * y], [-x * y, -y**2]]) This represents an anisotropic diffusion coefficient that varies spatially so that the term has the form . Generally, anisotropy is not conveniently aligned along the coordinate axes; in these cases, it is necessary to apply a rotation matrix in order to calculate the correct tensor values, see examples.diffusion.anisotropy for details. ### How do I represent a … term that doesn’t involve the dependent variable?¶ It is important to realize that, even though an expression may superficially resemble one of those shown in Discretization, if the dependent variable for that PDE does not appear in the appropriate place, then that term should be treated as a source. #### How do I represent a diffusive source?¶ If the governing equation for is then the first term is a TransientTerm and the second term is a DiffusionTerm, but the third term is simply an explicit source, which is written in Python as >>> (D2 * xi.faceGrad).divergence Higher order diffusive sources can be obtained by simply nesting the references to faceGrad and divergence. Note We use faceGrad, rather than grad, in order to obtain a second-order spatial discretization of the diffusion term in , consistent with the matrix that is formed by DiffusionTerm for . #### How do I represent a convective source?¶ The convection of an independent field as in can be rendered as >>> (u * xi.arithmeticFaceValue).divergence when is a rank-1 FaceVariable (preferred) or as >>> (u * xi).divergence if is a rank-1 CellVariable. #### How do I represent a transient source?¶ The time-rate-of change of an independent variable , such as in does not have an abstract form in FiPy and should be discretized directly, in the manner of Equation (1), as >>> TransientTerm(coeff=rho1) == rho2 * (xi - xi.old) / timeStep This technique is used in examples.phase.anisotropy. ### What if my term involves the dependent variable, but not where FiPy puts it?¶ Frequently, viewing the term from a different perspective will allow it to be cast in one of the canonical forms. For example, the third term in might be considered as the diffusion of the independent variable with a mobility that is a function of the dependent variable . For FiPy’s purposes, however, this term represents the convection of , with a velocity , due to the counter-diffusion of , so >>> eq = TransientTerm() == (DiffusionTerm(coeff=D1) Note With the advent of Coupled and Vector Equations in FiPy 3.x, it is now possible to represent both terms with DiffusionTerm. ### What if the coefficient of a term depends on the variable that I’m solving for?¶ A non-linear coefficient, such as the diffusion coefficient in is not a problem for FiPy. Simply write it as it appears: >>> diffTerm = DiffusionTerm(coeff=Gamma0 * phi * (1 - phi)) Note Due to the nonlinearity of the coefficient, it will probably be necessary to “sweep” the solution to convergence as discussed in Iterations, timesteps, and sweeps? Oh, my!. ## How can I see what I’m doing?¶ ### How do I export data?¶ The way to save your calculations depends on how you plan to make use of the data. If you want to save it for “restart” (so that you can continue or redirect a calculation from some intermediate stage), then you’ll want to “pickle” the Python data with the dump module. This is illustrated in examples.phase.anisotropy, examples.phase.impingement.mesh40x1, examples.phase.impingement.mesh20x20, and examples.levelSet.electroChem.howToWriteAScript. On the other hand, pickled FiPy data is of little use to anything besides Python and FiPy. If you want to import your calculations into another piece of software, whether to make publication-quality graphs or movies, or to perform some analysis, or as input to another stage of a multiscale model, then you can save your data as an ASCII text file of tab-separated-values with a TSVViewer. This is illustrated in examples.diffusion.circle. ### How do I save a plot image?¶ Some of the viewers have a button or other mechanism in the user interface for saving an image file. Also, you can supply an optional keyword filename when you tell the viewer to plot(), e.g. >>> viewer.plot(filename="myimage.ext") which will save a file named myimage.ext in your current working directory. The type of image is determined by the file extension “.ext”. Different viewers have different capabilities: Matplotlib accepts “.eps,” “.jpg” (Joint Photographic Experts Group), and “.png” (Portable Network Graphics). Attention Actually, Matplotlib supports different extensions, depending on the chosen backend, but our MatplotlibViewer classes don’t properly support this yet. #### What if I only want the saved file, with no display on screen?¶ To our knowledge, this is only supported by Matplotlib, as is explained in the Matplotlib FAQ on image backends. Basically, you need to tell Matplotlib to use an “image backend,” such as “Agg” or “Cairo.” Backends are discussed at http://matplotlib.sourceforge.net/backends.html. ### How do I make a movie?¶ FiPy has no facilities for making movies. You will need to save individual frames (see the previous question) and then stitch them together into a movie, using one of a variety of different free, shareware, or commercial software packages. The guidance in the Matplotlib FAQ on movies should be adaptable to other Viewers. ### Why doesn’t the Viewer look the way I want?¶ FiPy’s viewers are utilitarian. They’re designed to let you see something with a minimum of effort. Because different plotting packages have different capabilities and some are easier to install on some platforms than on others, we have tried to support a range of Python plotters with a minimal common set of features. Many of these packages are capable of much more, however. Often, you can invoke the Viewer you want, and then issue supplemental commands for the underlying plotting package. The better option is to make a “subclass” of the FiPy Viewer that comes closest to producing the image you want. You can then override just the behavior you wan to change, while letting FiPy do most of the heavy lifting. See examples.phase.anisotropy and examples.phase.polyxtal for examples of creating a custom Matplotlib Viewer class; see examples.cahnHilliard.sphere for an example of creating a custom Mayavi Viewer class. ## Iterations, timesteps, and sweeps? Oh, my!¶ Any non-linear solution of partial differential equations is an approximation. These approximations benefit from repetitive solution to achieve the best possible answer. In FiPy (and in many similar PDE solvers), there are three layers of repetition. iterations This is the lowest layer of repetition, which you’ll generally need to spend the least time thinking about. FiPy solves PDEs by discretizing them into a set of linear equations in matrix form, as explained in Discretization and Linear Equations. It is not always practical, or even possible, to exactly solve these matrix equations on a computer. FiPy thus employs “iterative solvers”, which make successive approximations until the linear equations have been satisfactorily solved. FiPy chooses a default number of iterations and solution tolerance, which you will not generally need to change. If you do wish to change these defaults, you’ll need to create a new Solver object with the desired number of iterations and solution tolerance, e.g. >>> mySolver = LinearPCGSolver(iterations=1234, tolerance=5e-6) : : >>> eq.solve(..., solver=mySolver, ...) Note The older Solver steps= keyword is now deprecated in favor of iterations= to make the role clearer. Solver iterations are changed from their defaults in examples.flow.stokesCavity and examples.updating.update0_1to1_0. sweeps This middle layer of repetition is important when a PDE is non-linear (e.g., a diffusivity that depends on concentration) or when multiple PDEs are coupled (e.g., if solute diffusivity depends on temperature and thermal conductivity depends on concentration). Even if the Solver solves the linear approximation of the PDE to absolute perfection by performing an infinite number of iterations, the solution may still not be a very good representation of the actual non-linear PDE. If we resolve the same equation at the same point in elapsed time, but use the result of the previous solution instead of the previous timestep, then we can get a refined solution to the non-linear PDE in a process known as “sweeping.” Note Despite references to the “previous timestep,” sweeping is not limited to time-evolving problems. Nonlinear sets of quasi-static or steady-state PDEs can require sweeping, too. We need to distinguish between the value of the variable at the last timestep and the value of the variable at the last sweep (the last cycle where we tried to solve the current timestep). This is done by first modifying the way the variable is created: >>> myVar = CellVariable(..., hasOld=True) and then by explicitly moving the current value of the variable into the “old” value only when we want to: >>> myVar.updateOld() Finally, we will need to repeatedly solve the equation until it gives a stable result. To clearly distinguish that a single cycle will not truly “solve” the equation, we invoke a different method “sweep(): >>> for sweep in range(sweeps): ... eq.sweep(var=myVar, ...) Even better than sweeping a fixed number of cycles is to do it until the non-linear PDE has been solved satisfactorily: >>> while residual > desiredResidual: ... residual = eq.sweep(var=myVar, ...) Sweeps are used to achieve better solutions in examples.diffusion.mesh1D, examples.phase.simple, examples.phase.binaryCoupled, and examples.flow.stokesCavity. timesteps This outermost layer of repetition is of most practical interest to the user. Understanding the time evolution of a problem is frequently the goal of studying a particular set of PDEs. Moreover, even when only an equilibrium or steady-state solution is desired, it may not be possible to simply solve that directly, due to non-linear coupling between equations or to boundary conditions or initial conditions. Some types of PDEs have fundamental limits to how large a timestep they can take before they become either unstable or inaccurate. Note Stability and accuracy are distinctly different. An unstable solution is often said to “blow up”, with radically different values from point to point, often diverging to infinity. An inaccurate solution may look perfectly reasonable, but will disagree significantly from an analytical solution or from a numerical solution obtained by taking either smaller or larger timesteps. For all of these reasons, you will frequently need to advance a problem in time and to choose an appropriate interval between solutions. This can be simple: >>> timeStep = 1.234e-5 >>> for step in range(steps): ... eq.solve(var=myVar, dt=timeStep, ...) or more elaborate: >>> timeStep = 1.234e-5 >>> elapsedTime = 0 >>> while elapsedTime < totalElapsedTime: ... eq.solve(var=myVar, dt=timeStep, ...) ... elapsedTime += timeStep ... timeStep = SomeFunctionOfVariablesAndTime(myVar1, myVar2, elapsedTime) A majority of the examples in this manual illustrate time evolving behavior. Notably, boundary conditions are made a function of elapsed time in examples.diffusion.mesh1D. The timestep is chosen based on the expected interfacial velocity in examples.phase.simple. The timestep is gradually increased as the kinetics slow down in examples.cahnHilliard.mesh2DCoupled. Finally, we can (and often do) combine all three layers of repetition: >>> myVar = CellVariable(..., hasOld=1) : : >>> mySolver = LinearPCGSolver(iterations=1234, tolerance=5e-6) : : >>> while elapsedTime < totalElapsedTime: ... myVar.updateOld() ... while residual > desiredResidual: ... residual = eq.sweep(var=myVar, dt=timeStep, ...) ... elapsedTime += timeStep ## Why the distinction between CellVariable and FaceVariable coefficients?¶ FiPy solves field variables on the cell centers. Transient and source terms describe the change in the value of a field at the cell center, and so they take a CellVariable coefficient. Diffusion and convection terms involve fluxes between cell centers, and are calculated on the face between two cells, and so they take a FaceVariable coefficient. Note If you supply a CellVariable var when a FaceVariable is expected, FiPy will automatically substitute var.arithmeticFaceValue. This can have undesirable consequences, however. For one thing, the arithmetic face average of a non-linear function is not the same as the same non-linear function of the average argument, e.g., for , This distinction is not generally important for smoothly varying functions, but can dramatically affect the solution when sharp changes are present. Also, for many problems, such as a conserved concentration field that cannot be allowed to drop below zero, a harmonic average is more appropriate than an arithmetic average. If you experience problems (unstable or wrong results, or excessively small timesteps), you may need to explicitly supply the desired FaceVariable rather than letting FiPy assume one. ## How do I represent boundary conditions?¶ See the Boundary Conditions section for more details. ## What does this error message mean?¶ ValueError: frames are not aligned This error most likely means that you have provided a CellVariable when FiPy was expecting a FaceVariable (or vice versa). MA.MA.MAError: Cannot automatically convert masked array to Numeric because data is masked in one or more locations. This not-so-helpful error message could mean a number of things, but the most likely explanation is that the solution has become unstable and is diverging to . This can be caused by taking too large a timestep or by using explicit terms instead of implicit ones. repairing catalog by removing key This message (not really an error, but may cause test failures) can result when using the weave package via the --inline flag. It is due to a bug in SciPy that has been patched in their source repository: http://www.scipy.org/mailinglists/mailman?fn=scipy-dev/2005-June/003010.html. numerix Numeric 23.6 This is neither an error nor a warning. It’s just a sloppy message left in SciPy: http://thread.gmane.org/gmane.comp.python.scientific.user/4349. ## How do I change FiPy’s default behavior?¶ FiPy tries to make reasonable choices, based on what packages it finds installed, but there may be times that you wish to override these behaviors. See the Command-line Flags and Environment Variables section for more details. ## Why don’t my scripts work anymore?¶ FiPy has experienced three major API changes. The steps necessary to upgrade older scripts are discussed in Updating FiPy. ## What if my question isn’t answered here?¶ Please post your question to the mailing list <http://www.ctcms.nist.gov/fipy/mail.html> or file an issue at <https://github.com/usnistgov/fipy/issues/new>. Last updated on Jan 14, 2021. Created using Sphinx 3.4.3.
2022-01-25T08:18:42
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http://legisquebec.gouv.qc.ca/en/showversion/cs/D-17?code=se:17&pointInTime=20201120
### D-17 - Land Transfer Duties Act 17. The application for registration of a transfer relating to land to a transferee must contain the following particulars in the prescribed manner: (a)  the name of the transferor and of the transferee; (b)  the dates of birth of the transferor and transferee, in the case of a physical person; (c)  the address of the principal residence of the transferor; (d)  the address of the principal residence of the transferee; (e)  a statement by the transferee indicating that he is a non-resident person within the meaning of this Act; (f)  a statement by the transferor and the transferee establishing the value of the consideration furnished by the transferee or the value of that part of the consideration which is referred to in section 7; (g)  the amount of the duties; (h)  the particulars required by sections 32, 40 to 44.1 and 47, if such is the case; (i)  any other particular prescribed. 1976, c. 23, s. 17; 1989, c. 5, s. 2; 1994, c. 22, s. 8. 17. The deed of transfer relating to land to a transferee must contain the following particulars in the prescribed manner: (a)  the name and given names of the transferor and of the transferee; (b)  the dates of birth of the transferor and transferee, in the case of a physical person; (c)  the address of the principal residence of the transferor; (d)  the address of the principal residence of the transferee; (e)  a statement by the transferee indicating that he is a non-resident person within the meaning of this act; (f)  a statement by the transferor and the transferee establishing the value of the consideration furnished by the transferee or the value of that part of the consideration which is referred to in section 7; (g)  the amount of the duties; (h)  the particulars required by sections 32, 40 to 44.1 and 47, if such is the case; (i)  any other particular prescribed. 1976, c. 23, s. 17; 1989, c. 5, s. 2. 17. The deed of transfer relating to land to a transferee must contain the following particulars in the prescribed manner: (a)  the name and given names of the transferor and of the transferee; (b)  the dates of birth of the transferor and transferee, in the case of a physical person; (c)  the address of the principal residence of the transferor; (d)  the address of the principal residence of the transferee; (e)  a statement by the transferee indicating that he is a non-resident person within the meaning of this act; (f)  a statement by the transferor and the transferee establishing the value of the consideration furnished by the transferee or the value of that part of the consideration which is referred to in section 7; (g)  the amount of the duties; (h)  the particulars required by sections 32, 40 to 44 and 47, if such is the case; (i)  any other particular prescribed. 1976, c. 23, s. 17.
2021-01-19T09:24:56
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https://www.usgs.gov/media/videos/halemaumau-lava-lake-draining-event
# Halemaumau lava lake draining event ## Detailed Description movie shows a draining event in the Halemaumau lava lake. Filling and draining cycles have been observed before here, but this video is one of the clearest examples thus far. The video is shown at actual speed, with draining taking about 40 seconds. Note the draining is highly unsteady, and proceeds in a step-wise fashion. These cycles of filling and draining are due to the episodic release of accumulated gas in the conduit. ## Details Date Taken: Length: 00:00:51 Location Taken: HI, US n/a
2021-09-19T12:07:45
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https://www-physics.lbl.gov/seminars/old/schmittful.html
Title: Large-scale Structure Bispectrum with Modal Methods, and Joint Analysis of CMB Temperature and Lensing-Reconstruction Power Spectra Abstract: First, I will present the implementation of a fast estimator for the full bispectrum of a three-dimensional particle distribution relying on a separable modal expansion of the bispectrum. The computational cost of accurate bispectrum estimation is negligible relative to the time required to run N-body simulations, so the isotropic bispectrum can be used as a standard diagnostic whenever the power spectrum is evaluated in simulations. As an application we measure the evolution of gravitational and primordial dark matter bispectra in N-body simulations with Gaussian and non-Gaussian initial conditions. The triangle dependence of the measured bispectra is compressed to about 50 coefficients, which is useful to confront theory with simulations and to treat correlations present in real data. In the nonlinear regime with $k<2h\,\mathrm{Mpc}^{-1}$, we find an excellent correlation between the measured dark matter bispectrum and a simple model based on a `constant' bispectrum plus a (nonlinear) tree-level gravitational bispectrum. In the same range for non-Gaussian simulations, we find an excellent correlation between the measured additional bispectrum and a constant model plus a (nonlinear) tree-level primordial bispectrum. We demonstrate that the constant contribution to the non-Gaussian bispectrum can be understood as a time-shift of the constant mode in the gravitational bispectrum, which is motivated by the halo model. I will also discuss modal methods to efficiently create general non-Gaussian N-body initial conditions for arbitrary primordial bispectra and a wide class of trispectra. In the second part of my talk I will address potential issues when using CMB lensing reconstructions for cosmological parameter estimation. Gravitational lensing provides a significant source of cosmological information in modern CMB parameter analyses. It is measured in both the power spectrum and trispectrum of the temperature fluctuations. These observables are often treated as independent, although as they are both determined from the same map this is impossible. We perform a rigorous analysis of the covariance between lensing power spectrum and trispectrum analyses. We find two dominant contributions coming from: (i) correlations between the disconnected noise bias in the trispectrum measurement and sample variance in the temperature power spectrum; and (ii) sample variance of the lenses themselves. The former is naturally removed when the dominant N0 Gaussian bias in the reconstructed deflection spectrum is dealt with via a partially data-dependent correction, as advocated elsewhere for other reasons. The remaining lens-cosmic-variance contribution is easily modeled but can safely be ignored for a Planck-like experiment, justifying treating the two observable spectra as independent. We also test simple likelihood approximations for the deflection power spectrum, finding that a Gaussian with a parameter-independent covariance performs well. The Planck lensing likelihood is based on the results obtained in this work.
2022-09-29T06:55:49
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http://utmost-sage-cell.org/sage:cross-product
Cross Product ## Description The cross product of any two vectors $a = \begin{pmatrix} a_1 \\ a_2 \\ a_3 \end{pmatrix}$ and $a = \begin{pmatrix} b_1 \\ b_2 \\ b_3 \end{pmatrix}$ in $\mathbb{R} ^ 3$ is is defined as (1) \begin{align} \mathbf a \times \mathbf b = \begin{pmatrix} a_2 b_3 - a_3 b_2 \\ a_3 b_1-a_1 b_3 \\ a_1 b_2 - a_2 b_1 \end{pmatrix}. \end{align} The Sage cell below calculates the dot product for the vectors $a = \begin{pmatrix} 1 \\ 2 \\ 3 \end{pmatrix}$ and $b = \begin{pmatrix} 4 \\ 5 \\ 6 \end{pmatrix}$. ## Sage Cell #### Code a = vector( [ 1, 2, 3 ] ) b = vector( [ 4, 5, 6 ] ) crossproduct=a.cross_product(b) crossproduct None Primary Tags: Secondary Tags: ## Attribute Permalink: Author: Date: 06 Nov 2018 16:40 Submitted by: James A Phillips Unless otherwise stated, the content of this page is licensed under Creative Commons Attribution-ShareAlike 3.0 License
2018-12-11T23:41:50
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https://pvpmc.sandia.gov/modeling-steps/3-dc-array-iv/dc-wiring-losses/
DC wiring losses are mainly caused by the ohmic resistance of the cabling that interconnects PV devices and strings, although losses can also occur in connections and fuses. The $I^{2}\times&space;R$ power loss varies as a function of the array current squared. Differences in cable length or size among parallel strings can introduce differences in voltage drop, $I\times&space;R$, and therefore contribute to mismatch. Series protection diodes are another source of voltage drop.
2017-04-23T15:56:09
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https://tjyj.stats.gov.cn/CN/10.19343/j.cnki.11-1302/c.2020.01.008
• • 轻资产运营与企业风险承担：实证分析与影响路径 • 出版日期:2020-01-25 发布日期:2020-02-28 Asset-Light Strategy and Corporate Risk-Taking: Empirical Analysis and Influence Path Zhou Zejiang  Li Ding  Wang Haoran • Online:2020-01-25 Published:2020-02-28 Abstract: Asset-light strategy becomes increasingly common, but the research on its economic consequences and transmission mechanism is still insufficient. Based on this, this paper takes the listed companies in Chinese capital market from 2009 to 2015 as samples to empirically test the role of asset-light strategy in enhancing the risk-taking level of enterprises and analyze the influence differences in different situations. The research results show that asset-light strategy has a significant positive correlation with enterprise risk-taking; compared with non-high-tech industries, the role of asset-light strategy in promoting risk-taking in high-tech industries is weakened. Ownership concentration hinders the promotion of asset-light operation for risk-taking. Furthermore, asset-light strategy eases the internal financing constraints of enterprises, reduces the proportion of interest-bearing liabilities, and enhances the level of investment and increases R&D and securities investment. The above constitute the main path for the impact of asset-light strategy on risk-taking. This paper not only enriches the relevant research in the field of asset-light strategy and enterprise risk-taking, but also helps us to understand how assets operation model exerts impact on enterprise risk-taking.
2022-08-18T04:18:20
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https://par.nsf.gov/biblio/10310528
SOFIA Observations of 30 Doradus. I. Far-infrared Dust Polarization and Implications for Grain Alignment and Disruption by Radiative Torques Abstract Located in the Large Magellanic Cloud and mostly irradiated by the massive star cluster R136, 30 Doradus is an ideal target to test the leading theory of grain alignment and rotational disruption by RAdiative Torques (RATs). Here, we use publicly available polarized thermal dust emission observations of 30 Doradus at 89, 154, and 214 μ m using SOFIA/HAWC+. We analyze the variation of the dust polarization degree ( p ) with the total emission intensity ( I ), the dust temperature ( T d ), and the gas column density ( N H ) constructed from Herschel data. The 30 Doradus complex is divided into two main regions relative to R136, namely North and South. In the North, we find that the polarization degree first decreases and then increases before decreasing again when the dust temperature increases toward the irradiating cluster R136. The first depolarization likely arises from the decrease in grain alignment efficiency toward the dense medium due to the attenuation of the interstellar radiation field and the increase in the gas density. The second trend (the increase of p with T d ) is consistent with the RAT alignment theory. The final trend (the decrease of p more » Authors: ; ; ; ; ; ; ; ; ; Award ID(s): Publication Date: NSF-PAR ID: 10310528 Journal Name: The Astrophysical Journal Volume: 923 Issue: 1 ISSN: 0004-637X 2. ABSTRACT We present ALMA Band 7 polarization observations of the OMC-1 region of the Orion molecular cloud. We find that the polarization pattern observed in the region is likely to have been significantly altered by the radiation field of the >104 L⊙ high-mass protostar Orion Source I. In the protostar’s optically thick disc, polarization is likely to arise from dust self-scattering. In material to the south of Source I – previously identified as a region of ‘anomalous’ polarization emission – we observe a polarization geometry concentric around Source I. We demonstrate that Source I’s extreme luminosity may be sufficient to make the radiative precession time-scale shorter than the Larmor time-scale for moderately large grains ($\gt 0.005\!-\!0.1\, \mu$m), causing them to precess around the radiation anisotropy vector (k-RATs) rather than the magnetic field direction (B-RATs). This requires relatively unobscured emission from Source I, supporting the hypothesis that emission in this region arises from the cavity wall of the Source I outflow. This is one of the first times that evidence for k-RAT alignment has been found outside of a protostellar disc or AGB star envelope. Alternatively, the grains may remain aligned by B-RATs and trace gas infall on to the Main Ridge.more »
2023-01-31T14:25:45
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https://par.nsf.gov/biblio/10347648-ionization-gasdynamic-simulations-wind-blown-nebulae-around-massive-stars
This content will become publicly available on February 1, 2023 Ionization-Gasdynamic Simulations of Wind-Blown Nebulae around Massive Stars Using a code that employs a self-consistent method for computing the effects of photo-ionization on circumstellar gas dynamics, we model the formation of wind-driven nebulae around massive stars. We take into account changes in stellar properties and mass-loss over the star’s evolution. Our simulations show how various properties, such as the density and ionization fraction, change throughout the evolution of the star. The multi-dimensional simulations reveal the presence of strong ionization front instabilities in the main-sequence phase, similar to those seen in galactic ionization fronts. Hydrodynamic instabilities at the interfaces lead to the formation of filaments and clumps that are continually being stripped off and mixed with the low density interior. Even though the winds start out as completely radial, the spherical symmetry is quickly destroyed, and the shocked wind region is manifestly asymmetrical. The simulations demonstrate that it is important to include the effects of the photoionizing photons from the star, and simulations that do not include this may fail to reproduce the observed density profile and ionization structure of wind-blown bubbles around massive stars. Authors: Award ID(s): Publication Date: NSF-PAR ID: 10347648 Journal Name: Galaxies Volume: 10 Issue: 1 Page Range or eLocation-ID: 37 ISSN: 2075-4434 1. ABSTRACT We present and study a large suite of high-resolution cosmological zoom-in simulations, using the FIRE-2 treatment of mechanical and radiative feedback from massive stars, together with explicit treatment of magnetic fields, anisotropic conduction and viscosity (accounting for saturation and limitation by plasma instabilities at high β), and cosmic rays (CRs) injected in supernovae shocks (including anisotropic diffusion, streaming, adiabatic, hadronic and Coulomb losses). We survey systems from ultrafaint dwarf ($M_{\ast }\sim 10^{4}\, \mathrm{M}_{\odot }$, $M_{\rm halo}\sim 10^{9}\, \mathrm{M}_{\odot }$) through Milky Way/Local Group (MW/LG) masses, systematically vary uncertain CR parameters (e.g. the diffusion coefficient κ and streaming velocity), and study a broad ensemble of galaxy properties [masses, star formation (SF) histories, mass profiles, phase structure, morphologies, etc.]. We confirm previous conclusions that magnetic fields, conduction, and viscosity on resolved ($\gtrsim 1\,$ pc) scales have only small effects on bulk galaxy properties. CRs have relatively weak effects on all galaxy properties studied in dwarfs ($M_{\ast } \ll 10^{10}\, \mathrm{M}_{\odot }$, $M_{\rm halo} \lesssim 10^{11}\, \mathrm{M}_{\odot }$), or at high redshifts (z ≳ 1–2), for any physically reasonable parameters. However, at higher masses ($M_{\rm halo} \gtrsim 10^{11}\, \mathrm{M}_{\odot }$) and z ≲ 1–2, CRs can suppress SF and stellar masses by factorsmore » Using 3D radiation-hydrodynamical simulations, we study the effects of ionizing radiation on the formation of second-generation (SG) stars in globular clusters (GCs) with multiple stellar populations. In particular, we focus on massive ($10^7 \, \mathrm{M}_{\odot }$) and young (40-Myr old) GCs. We consider stellar winds from asymptotic giant branch (AGB) stars, ram pressure, gas accretion on to the cluster, and photo-ionization feedback of binary stars. We find that the stellar luminosity is strong enough to warm and ionize the intracluster medium, but it does not lead to a significant gas expulsion. The cluster can thus retain the ejecta of AGB stars and the accreted pristine gas. In addition, efficient cooling occurs in the central region of the cluster within $50\, \mathrm{Myr}$ from the formation of first generation stars, leading to the formation of SG stars. Our results indicate that the inclusion of photo-ionization does not suppress SG formation, but rather delays it by about $\sim 10\, \mathrm{Myr}$. The time delay depends on the density of the pristine gas, so that a denser medium exhibits a shorter delay in star formation. Moreover, photo-ionization leads to a modest decrease in the total SG mass, compared to a model without it.
2022-12-03T04:48:59
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http://pdglive.lbl.gov/Particle.action?init=0&node=M068&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 f}_{{0}}{(1710)}}$ $I^G(J^{PC})$ = $0^+(0^{+ +})$ See our mini-review in the 2004 edition of this $\mathit Review$, Physics Letters B592 1 (2004). See also the mini-review on scalar mesons under ${{\mathit f}_{{0}}{(500)}}$ (see the index for the page number). ${{\mathit f}_{{0}}{(1710)}}$ MASS $1704 \pm12$ MeV ${{\mathit f}_{{0}}{(1710)}}$ WIDTH $123 \pm18$ MeV
2020-05-28T21:31:39
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https://read.dukeupress.edu/demography/article/59/3/827/307380/Determinants-of-Disparities-in-Early-COVID-19-Job
## Abstract This study examines the sociodemographic divide in early labor market responses to the U.S. COVID-19 epidemic and associated policies, benchmarked against two previous recessions. Monthly Current Population Survey (CPS) data show greater declines in employment in April and May 2020 (relative to February) for Hispanic individuals, younger workers, and those with a high school diploma or some college. Between April and May, the demographic subgroups considered regained some employment. Reemployment in May was broadly proportional to the employment drop that occurred through April, except for Black individuals, who experienced a smaller rebound. Compared to the 2001 recession and the Great Recession, employment losses in the early COVID-19 recession were smaller for groups with low or high (vs. medium) education. We show that job loss was greater in occupations that require more interpersonal contact and that cannot be performed remotely, and that pre-COVID-19 sorting of workers into occupations and industries along demographic lines can explain a sizable portion of the demographic gaps in new unemployment. For example, while women suffered more job losses than men, their disproportionate pre-epidemic sorting into occupations compatible with remote work shielded them from even larger employment losses. However, substantial gaps in employment losses across groups cannot be explained by socioeconomic differences. We consider policy lessons and future research needs regarding the early labor market implications of the COVID-19 crisis. ## Introduction The COVID-19 pandemic introduced new risks into economic, social, familial, and cultural activities that are otherwise commonplace, leading to disruptions that levied disparate impacts across demographic and socioeconomic groups. Job characteristics have emerged as particularly important moderators. For example, employment losses have been greater among people in jobs that involve face-to-face contact, and fewer losses occurred in jobs that can be performed remotely or are in essential industries. On the labor supply side, the COVID-19 transmission mechanism also raises the health risks of work tasks that require face-to-face contact with customers or coworkers, with risk varying along individual characteristics (Guerrieri et al. 2020). Labor supply might decline through other channels as well. For example, people's ability and willingness to work may have declined because the epidemic has compromised childcare services, schooling options, and other types of home and family health care availability (Dingel et al. 2020). This study focuses on the labor market disruptions and job losses during the early months of the COVID-19 recession in the United States. We document substantial disparities in early epidemic unemployment patterns across demographic subpopulations defined by age, gender, race and ethnicity, marital status, parental status, and education. We develop simple measures of job attributes that may be relevant to the epidemic and show that these measures are associated with employment disruptions. Specifically, people working in jobs with more remote work capacity and less dependence on face-to-face interaction were more secure. Similarly, people working in essential industries were much less likely to become unemployed in the early months of the epidemic. In general, major demographic subpopulations are not evenly distributed across occupations and industries, and these differences are an important reason why some demographic groups have fared better than others. We use decomposition techniques to quantify the share of employment disparities that is rooted in pre-epidemic sorting across occupations and industries. Such sorting explains a substantial share of many of the disparities in employment outcomes. Further, some of the job and industry factors that protected jobs during the early months of the epidemic are often associated with higher income and job security in normal times. This suggests that the epidemic aggravated many existing disparities. Our research complements prior work focused on inequality and the mechanisms that contribute to the persistence of disparities. Research on social stratification takes on “understanding and investigating the sources” of social inequality (Sakamoto and Powers 2005) through the study of population composition. Our article examines the distribution of job losses during the early epidemic in a social stratification framework that exploits population subgroups sorting across different jobs. We use information on how subgroups allocate themselves in different occupations and industries to explain the labor market shocks they experience during COVID-19 and the changes in inequality dynamics they will experience as a consequence. We present four broad analyses to investigate disparate impacts in labor markets. First, we use data from the monthly Current Population Survey (CPS) to document and compare disparities in early COVID-19 era unemployment across groups. We find large declines in employment and increases in new unemployment among women, Hispanics, and younger workers. There is also polarization by education, with fewer job losses among college graduates (and those with more education), who can often work remotely, and high school dropouts, who tend to be in essential jobs. Hence, while both groups are somewhat shielded from job loss, highly educated workers are insulated from infection, while less educated workers likely face greater exposure, consistent with findings of Angelucci et al. (2020). We contrast these changes in employment losses with those during the Great Recession and the 2001 recession. Second, we explore disparities in COVID-19 job losses across occupations and industries. We use O*NET data to develop indices of the extent to which each occupation allows remote work and requires face-to-face interaction.1 Employment declined more in occupations requiring greater face-to-face interactions. Workers in jobs that could be performed remotely were less likely to experience new unemployment compared with historical trends. We further classify jobs as essential based on the “Guidance on the essential critical infrastructure workforce” issued by the U.S. Department of Homeland Security (2020) using the interpretation in Blau et al. (2020). We show that workers in essential jobs were less likely to lose a job in the early epidemic and were less likely to have been absent from work. All these patterns are stronger in April than in May. Third, we assess the importance of caring for dependents as a factor in labor supply, estimating changes in employment and work absence for parents and for mothers. Relative to their experience in February, women were more likely to be absent from work in March 2020 (at four times the rate of March 2019) and be unemployed in April and May. Women with young children experienced particularly high rates of absence from work, which is concerning given the widespread closures of schools and childcare and the gendered nature of dependent care (Goldin 2022). Moreover, single parents, who are disproportionately female, were more likely to have lost jobs. Similarly, Alon et al. (2020) found that social-distancing policies have a larger effect on women than men, unlike in a more “typical” recession; Albanesi and Kim (2021) also found a sizable decline in labor force participation and in employment for women, unlike in previous recessions. Alon et al. (2020) and Albanesi and Kim (2021) suggest that the impact of the epidemic on working mothers could be persistent. Our fourth contribution is to measure whether differences in job losses across demographic groups were due to pre-epidemic sorting across occupations and industries. We do so using a Oaxaca–Blinder decomposition, which allows us to simultaneously control for pre-pandemic socioeconomic traits associated with labor market opportunities and behavior. We show that a significant share of differences in employment loss across demographic groups is explained by differences in pre-epidemic sorting across occupations. However, for most groups, we also find that a nonnegligible share of the difference in job loss remains unexplained by either occupation sorting or other observable traits, in keeping with Busch (2020). Strikingly, we find that the Black–White gap in new unemployment grew between April and May 2020, at a time when one might have naturally expected it to decline. The presence of a large unexplained gap suggests that disparities in job loss in the pandemic are not reducible to differences in job characteristics and could possibly reflect disparate treatment by employers. ## Related Research The epidemic greatly reduced social and economic activity in 2020, with large sectors of the economy—transportation, hospitality, and tourism—essentially shutting down their normal operations between February and April, as state governments implemented a range of social-distancing mandates (Bartik et al. 2020; Coibion et al. 2020; Goolsbee and Syverson 2020; Gupta et al. 2020). In May, both the public and private sectors began to take steps to reopen some economic activities. Mobility measured using cell signals declined in all states, but was larger in those with early and information-focused policies (Gupta et al. 2020). The historically unprecedented increase in initial unemployment claims in March 2020 was largely across-the-board, in all states regardless of local epidemiological conditions or policy responses (Lozano-Rojas et al. 2020). Forsythe et al. (2020) showed a large drop in job vacancy postings as an indicator of labor demand across states regardless of state policies or infection rates. Adams-Prassl et al. (2020) and Dasgupta and Murali (2020) studied disparities in labor market impacts in other countries and found that the ability to work remotely shielded some workers from job loss. There is mounting evidence that layoff statistics may severely underestimate the extent of labor market adjustments. Coibion et al. (2020) estimated that unemployment greatly exceeded the level of unemployment insurance claims in early April. A large literature illustrates how existing patterns of social stratification shape socioeconomic outcomes during crises. Dudel and Myrskylä (2017), Cheng et al. (2019), and Killewald and Zhuo (2019) found disparities in occupational wage gaps and other labor market outcomes on the basis of age, gender, and ethnicity in both the United States and abroad. Dudel and Myrskylä (2017) showed that the Great Recession shortened the life expectancy of older workers, especially of White men. Zissimopoulos and Karoly (2010) examined the short-term and longer term effects of Hurricane Katrina on labor market outcomes by subgroup of evacuees. Beyond labor market outcomes, large economic and social events also influence fertility (Grossman and Slusky 2019; Seltzer 2019), marriage (Schneider and Hastings 2015), migration (Sastry and Gregory 2014), and children's well-being (Cools et al. 2017; Schenck-Fontaine and Panico 2019). Given the peculiarities of the COVID-19 economic crisis, it is important to understand which population strata were most affected, why, and how these effects may lead to longer term disparities in well-being. ## Data ### Current Population Survey Our main analysis uses data from the Basic Monthly CPS from February to May 2020. The analytic sample used in all regressions consists of all labor force participants aged 18–65 with complete information on gender, children under six years old, race and ethnicity, education, state, metropolitan residence, recent unemployment status, occupation and industry codes, and CPS sample weight. To focus on job losses related to the epidemic, we use a measure of recent (new) unemployment, which defines a worker as recently unemployed if they are coded as being unemployed in the focal week of the survey month and have been in that status for at most five weeks as of March 2020, 10 weeks in April 2020, and 14 weeks in May 2020.2 Focusing on recent unemployment allows us to study new job losses using only cross-sectional models. To verify that recent unemployment does indeed track job loss, we checked that the measure behaves like the change in employment rate. That is, we check whether the incidence of recent unemployment across demographic groups in April and in May tracks month-over-month changes from February to April and from February to May, respectively, in the employment-to-population ratio. Evidence reported in panel A of the online appendix Figure A2.1 compares recent unemployment in April 2020 with the February-to-April change in employment rates by subpopulation; panel B shows the comparison for February and May. Our recent unemployment measure behaves like the change in the employment rate. The CPS defines as “absent from job” all workers who were “temporarily absent from their regular jobs because of illness, vacation, bad weather, labor dispute, or various personal reasons, whether or not they were paid for the time off” (U.S. Census Bureau 2019). There was a massive increase in the share of workers coded as employed-but-absent from work between February and April, as well as in May. During the epidemic, these employed-but-absent workers deserve particular attention as some furloughed employees might have been recorded as short-term absent instead of unemployed, among other reasons. Therefore, we perform most of our analysis separately on measures of recent unemployment and employed-but-absent. Further details on our recent unemployment variable, the definition of the analysis sample, and the employed-but-absent category during April and May 2020 are in the online Appendix A.1. ### O*NET We also use data from the 2019 Occupational Information Network (O*NET) Work Context module, which reports summary measures of the tasks used in 968 occupations (National Center for O*NET Development 2020). These data are gathered through surveys asking workers how often they perform particular tasks and about the importance of different activities in their jobs. Some of the questions relate to the need for face-to-face interaction with clients, customers, and coworkers, and other questions assess how easily work could be done remotely. For details on how this information is collected in O*NET, refer to the online Appendix A.3. We use such questions to build two occupation indices: Face-to-Face (questions on face-to-face discussions and physical proximity) and Remote Work (questions on use of electronic mail, written letters, and phone conversation).3 It is important to note that these occupational characteristics in the O*NET are measured prior to the epidemic. This means that they do not capture “work practice innovations” that may have been induced by the epidemic, such as the fact that many teachers and professors transitioned from face-to-face to online instruction during the epidemic. To check how well our two indices perform, we rank the occupations by their corresponding indices and create a list of the top and bottom 5% Face-to-Face and Remote Work occupations. We realize that, unsurprisingly, most of the top 5% Face-to-Face occupations are in the medical sector, which may be affected differently during the epidemic. Hence, we also show a list of the top nonmedical occupations. The rankings (reported in online appendix Tables A4.2 and A4.3 for Face-to-Face and Remote Work, respectively) are reassuring, indicating that these indices measure what we expected. We also compare our Remote Work and Face-to-Face indices with Dingel and Neiman's (2020) Teleworkability classification, which might be viewed as an alternative to our Remote Work index. The correlation between our indices is only .03, suggesting that they capture different features of an occupation. The correlation between the Face-to-Face index and Dingel and Neiman's (2020) Teleworkability variable is –.36. The occupations that score high in our Face-to-Face index tend to rank low in Teleworkability. Finally, the correlation between our Remote Work index and the Teleworkability variable is .51, suggesting that the two measures are indeed broadly similar. ### Homeland Security Data on Essential Work The U.S. Department of Homeland Security (DHS) issued guidance that describes 14 essential critical infrastructure sectors during the COVID-19 epidemic.4 We follow Blau et al.'s (2020) definition of essential industries, which matches the text descriptions to the NAICS 2017 four-digit industry classification from the U.S. Census Bureau5 and to the CPS industry classification system. From the 287 industry categories at the four-digit level, 194 are identified as essential in 17 out of 20 NAICS sectors. Online appendix Table A4.4 gives an abbreviated list of essential industries to clarify the classification scheme. ## Employment Disruptions in Three Recessions Figures 1 and 2 show the change in employment for the COVID-19 recession compared with the peak-to-trough change in employment for the 2001 recession (March 2001 to November 2001) and the Great Recession (December 2007 to June 2009). We seasonally adjust the change in employment for the two earlier recessions using calendar month fixed effects from January 2015 to December 2019. For COVID-19, we focus on two time periods that cover the initial “closing” phase of the pandemic (i.e., from February to April) and also a longer period (i.e., from February to May) that adds the ensuing “reopening” phase. All estimates use CPS sampling weights. The light blue and light green bars in the figures show that employment losses during the first months of the COVID-19 epidemic dwarfed the declines for the other two recessions, which spanned nine and 19 months, respectively. This was true even after the COVID-19 reopening phase, during which employment rebounded substantially. The size and speed of the COVID-19 recession are reinforced in online appendix Figure A5.1, which shows seasonally adjusted nonfarm employment from March 2000 and May 2020. The bars in Figure 1 show the change in the employment rate for subpopulations defined by gender, having young children, race, ethnicity, age, and education. Figure 2 shows employment changes by marital and parental status interacted. Almost no group was spared from employment loss during any of the three recessions. However, the pattern of employment disruption is noticeably different in the early months of the COVID-19 recession. Young (aged 18–24) and Hispanic workers fared the worst during the COVID-19 pandemic when compared to older and non-Hispanic workers and to the previous recessions. Black individuals also fared poorly, but by a smaller margin. Our conjecture is that these groups disproportionately work in industries that are particularly hit by social-distancing measures, such as food service, personal care services, or nonessential retail industries. Further, employment declined more for women than for men. Parents with their own children under 18 living in the household fared worse than those without, while workers without young children (under six) experienced larger job losses than those with children under six in their household. This trend is likely explained by differences in the impact of school closures on parents' job loss depending on their child's age. Employment effects were polarized by education: employment declined less for high school dropouts and those with at least a college degree compared with the intermediate education groups. As we show later, highly educated workers have better options to work remotely, limiting in-person interactions; in contrast, less educated workers are more likely to be in essential positions. While polarization is consistent with recent trends in the labor market, this kind of pattern was not a feature of the two previous recessions (Autor et al. 2006).6 Comparison of the decrease in employment between February and April (light blue) to that between February and May (light green) indicates that there were gains in employment between April and May as states began reopening. The recovery in employment that the groups experienced between April and May was broadly proportional to the employment losses that occurred between February and April. Thus, the distributional incidence of job loss and recovery was largely symmetric, with the notable exception of Black workers, who did not recover in May as much as would have been expected given their decline in employment in April. Figure 2 shows that married individuals whose spouse was present experienced a smaller decrease in employment than single individuals (defined as those who were unmarried or had an absent spouse), regardless of whether we compare April or May to February. Single parents, who are disproportionately female (72%), experienced the largest decrease in employment; when comparing parents of children younger than 13 versus 18 years old, the age of children was weakly related to the change in employment during these months. In fact, single parents of children younger than 18 experience similar job losses to single parents of children under 13, and the same holds for two-parent households. This could also be explained by the interaction between childcare needs and school closure patterns. Overall, this analysis highlights that Hispanic individuals, young workers (aged 18–24), and single parents were the most vulnerable workers early in the epidemic and those most in need of policy attention. ## Job Tasks and Recent Unemployment ### Job Tasks and the Labor Market: Descriptive Analysis Figure 3 shows the mean of the Remote Work and Face-to-Face indices across subpopulations in the February 2020 CPS, providing insight into pre-epidemic worker sorting across occupations. Compared with men, women tended to work in jobs that both allow more remote work and involve more face-to-face activities. Hispanic individuals disproportionately worked in jobs that largely cannot be conducted remotely. Younger workers were in jobs with fewer remote work prospects and more face-to-face interaction, although the differentials are not as large. Remote work scores increased substantially with education level. To examine employment disruptions in the early epidemic, we use data from the March, April, and May waves of the 2020 CPS. The March CPS data were collected largely before the major responses were observed and hence we view March as a hybrid period. As indicated, we classified people as recently unemployed if they were currently unemployed and had become unemployed within the past five weeks (March), 10 weeks (April), or 14 weeks (May). Ignoring reemployment, this measure captures employment disruptions since February in each subsequent monthly CPS. Figures 4 and 5 compare recent unemployment rates with Remote Work scores and Face-to-Face scores at the occupation level in the April and May CPS. In both figures, the left panel shows that recent unemployment rates tended to be lower in occupations with higher scores on the Remote Work index, suggesting that remote work capacity helped protect employment. In contrast, the right panel shows that recent unemployment rates were typically higher in occupations that involve more face-to-face tasks. ### Job Tasks and the Labor Market: Regression Analysis To assess the connection between worker and job characteristics and recent job losses, we fit regressions with the following form: $yijks=Facejβ1+Remotejβ2+Essentialkβ3+Femaleiβ4+Childiβ5+(Childi×Femalei)β6+Xiδ+φs+ϵijks.$ (1) Here $yijks$ is an indicator that person $i$ with occupation $j$, industry $k$, in state $s$ is recently unemployed (Table 1) or temporarily absent from work (Table 2). $Facej$ and $Remotej$ are the indices of Face-to-Face and Remote Work. $Essentialk$ indicates that the person is in an essential industry. $Femalei$ indicates that the person is female, $Childi$ indicates that the person has a child under age six, and $Xi$ is a vector of covariates, including a quadratic in age, race/ethnicity indicators, and education indicators. All models include state fixed effects, denoted by $φs$, and in some specifications they include state-specific epidemiological conditions as measured by the log of COVID cases, which are interacted with occupation characteristics. Occupation fixed effects are included in some but not all specifications because they subsume the occupation characteristics (i.e., $Facej$, $Remotej$, and $Essentialk$). Table 1 reports estimates from March, April, and May. Column 1 in all three panels shows estimates from models that control for occupation and individual characteristics, but not for the number of COVID-19 cases in the state. Column 2 includes the log of state COVID cases (The New York Times 2020). Column 3 replaces the job task indices with occupation and industry fixed effects to account for any additional time-invariant job characteristics. Table 2 reports parallel estimates for temporary absence from work. The coefficients on the Remote Work and the Face-to-Face indices reinforce the pattern in Figures 4 and 5. In the analysis of the April CPS, the model in column 1 implies that recent unemployment rates were 1.6 percentage points higher for people working in jobs that score 1 standard deviation (SD) higher on the Face-to-Face index. The recent unemployment rate in our April sample was 12.6%, which means that a 1-SD increase in the Face-to-Face score was associated with a 13% higher risk of being recently unemployed. The relationship is almost identical in the analysis based on the May CPS. In contrast, there was no association between the Face-to-Face index and recent unemployment in the March CPS, implying that the connection between employment instability and the Face-to-Face index was not a preexisting feature of the labor market. The coefficient on the Remote Work index is negative and significant in March, suggesting that there was a small pre-epidemic connection between remote work and employment disruption. However, the magnitude of the coefficient on Remote Work is seven times larger in April and almost six times larger in May than in March. Working in a job that scored 1 SD higher on Remote Work was associated with a 5.6-percentage-point lower risk of recent job loss, which is 44% of the recent unemployment rate in April. Likewise, the coefficient on “Essential” (−8.9 percentage points) indicates that working in an essential industry was associated with a 71% lower probability of recent unemployment and the magnitude in April is almost 13 times higher than in March. Column 2 includes interactions between state-level COVID-19 cases and job characteristics. The essential industry and Face-to-Face variables do not have strong interactions with COVID-19 cases, but Remote Work has a strong negative interaction with COVID-19 cases, indicating that remote work potential is particularly important in high-case environments. The regressions show that recent unemployment rates vary with individual characteristics. Recent unemployment rates are about three percentage points higher for women in April and May; however, when occupation and industry fixed effects are included, the difference falls to one percentage point. The coefficient on the interaction term between female and children under age six is small and not statistically significant, suggesting that childcare responsibilities did not explain much of the gender gap in unemployment early in the epidemic; however, we later show that presence of young children is a factor in absence from work. Recent unemployment rates are substantially higher for younger workers and decline with age at a decreasing rate. Recent unemployment was lower among college-educated workers: graduate degree holders were about 7.9 percentage points less likely to have become unemployed in the 10 weeks leading up to the April CPS, and college graduates were about 4.4 percentage points less likely to be recently unemployed. This relationship is much weaker in March, but on the same level during May. Including occupation and industry fixed effects attenuates the education gradient somewhat, but it remains strong and significant. Recent unemployment rates were about three percentage points lower among workers living in metropolitan areas for both April and May. Again, including occupation and industry fixed effects lessens but does not eliminate this relationship. Overall, occupation and industry characteristics were far more important in April and May than in March. We attribute this increase, and the slight decrease from April to May, to the spread of the pandemic, the policy responses, and their subsequent easing during the first part of May. Table 2 shows results from models with “employed but absent” as the outcome. Our estimates show that workers in jobs relying heavily on face-to-face interactions were more likely to experience absence from work, while those who could work remotely more easily, and those in essential industries, were less likely to be absent from work. The coefficients on job attributes have similar signs in March and April, but the magnitude of the coefficients is much larger in April. The magnitude declines somewhat in May, which may indicate that absences precede dismissals. However, the data classification issues we discussed earlier make this a tentative conclusion. The education gradient is very similar to the one found for recent unemployment, with education protecting against work absence. Women with young children were particularly likely to be temporarily absent in all months, suggesting that childcare responsibilities likely played an early and lasting role in absence rates. To probe the timing of effects, we plotted the coefficients from columns 3 of Tables 1 and 2 over time during the pandemic (March through May 2020) and for the same months in 2019. In several cases, we can spot a striking change in coefficient in both graphs starting in March 2020, the onset of the epidemic; the 2019 coefficients are more centered around 0. These graphs are shown in online appendix Figures A7.1 and A7.2. ### Further Analyses and Robustness Checks We conducted a series of sensitivity analyses to assess the robustness of our results. We report these results in the online appendix and discuss them briefly here. First, we explored whether mortality risk7 from COVID-19 affected labor supply among high-risk groups by estimating regressions that include a measure of COVID-19 mortality risk as a covariate. The results are presented in online Table A8.1 for recent unemployment and in Table A8.2 for absent from work. Overall, they suggest that among people working in nonessential jobs with average face-to-face and remote work capacity, workers with higher COVID-19 mortality risk were actually less likely to experience a recent unemployment spell in April and May. In April, the coefficient on the mortality index implies that a 1-SD increase in mortality risk reduced the recent unemployment rate by about 1.3 percentage points. Since our mortality risk measure is mainly driven by age and gender, this likely reflects that older workers had more job security than younger workers. However, the coefficient on the interaction term between mortality risk and the Remote Work index is positive, implying that this pattern was partly offset for people working in jobs that were more suitable for remote work. In contrast, mortality risk does not appear to be a factor in temporary absences during April or May. In our main analysis, we consider recent unemployment and recent absence as separate outcomes. In supplementary work, we combine the two outcome variables into a single dependent variable indicating either recent unemployment or recent absence. The regression results are qualitatively unchanged, but the magnitudes are, as expected, frequently larger because both outcomes behave similarly. These estimates are reported in online Appendix A.9 and Table A9.1. Next, we examine the possibility that the relationship between job characteristics and recent unemployment reflects preexisting patterns of employment instability not related to the epidemic. A consistent and comparably strong relationship between job characteristics and employment even before the COVID-19 epidemic would throw into question our finding that such characteristics determined labor outcomes during April and May 2020. As a check, we run the same models on April and May 2019 data. We find no clear relationship between either job Face-to-Face Index or being in an essential industry and recent unemployment. There appears to be a negative correlation between Remote Work and recent unemployment in April and May 2019, but the strength of this relationship is an order of magnitude larger in 2020 than in 2019. For temporary work absence, we find a positive and significant coefficient on Face-to-Face, but of a much smaller magnitude in 2019 (between half as small to seven times as small in 2019 compared to 2020, depending on the specification). Tables A10.1 and A10.2 in online Appendix A.10 show the full results, which suggest that while there may have been some preexisting relationships between the various job characteristics we study and labor market outcomes, these characteristics became considerably more important during the epidemic. We further probe the robustness of our results to the number of weeks used to define the recently unemployed variable. In the robustness check, we vary the number of such weeks. The model coefficients are not sensitive to the cutoff used to define “recent” unemployment. Online Appendix A.11 includes the graphs we used for this exercise (Figures A11.1 and A11.2). Finally, we replicated Figure 3 and our regression specifications using the definition of Teleworkability as defined by Dingel and Neiman (2020). We find the same sociodemographic groups scoring high (or low) in both telework and remote work, showing the similarity of these two measures. In the regression models with the Teleworkability variable in place of our Remote Work index, we find that the estimates are very similar to our results, and our main analysis is robust to this alternative measure. The graph appears in Figure A6.1 and the regressions in Tables A12.1 and A12.2 in online Appendix A.12. ## Decomposing Group Differences in Recent Unemployment The analysis so far shows that recent unemployment rates in April and May varied substantially across subpopulations. Differences in the kinds of jobs workers held at the onset of the epidemic likely contributed to this variation. In this section, we use a version of the Oaxaca–Blinder decomposition to quantify the role of pre-epidemic sorting more formally (Blinder 1973; Oaxaca 1973). We find robust evidence that pre-epidemic group differences in job characteristics explain the majority of the recent unemployment gap for most comparisons. However, we also show that significant disparities in unemployment are not explained by observable characteristics. Rather, they reflect differences in the rates at which different groups became unemployed at the start of the pandemic, holding job sorting and other characteristics fixed. ### Decomposition Model We examine six aggregate gaps in recent unemployment rates: White versus Black, high school graduate versus high school dropout, female versus male, non-Hispanic versus Hispanic, college graduate versus high school graduate, and older versus younger workers. For each pair, we specify regression models linking recent unemployment with observed characteristics in each of the groups: $yiA=α0A+XiAβA+ϵiA$ $yiB=α0B+XiBβB+ϵiB.$ In these models, $yig$ is a binary measure of recent unemployment for person $i$ who is a member of subpopulation $g∈[A,B]$8; $Xig$ is a vector of covariates; $α0g$ is a group-specific intercept; and $βg$ is a group-specific vector of coefficients. Let $y¯g$ and $X¯g$ represent the average value of the recent unemployment measure and the covariates among group $g$. The average difference in the shares of workers reporting recent unemployment between $A$ and $B$ is $y¯A−y¯B=X¯AβA−X¯BβB+(α0A−α0B)].$ In the standard Oaxaca–Blinder decomposition, the difference in the share recently unemployed between the two groups can be expressed as $y¯A−y¯B=(X¯A−X¯B)βA+[X¯B(βA−βB)+(α0A−α0B)].$ In this form of the decomposition, the first term, $(X¯A−X¯B)βA$, is called the “endowment effect” and represents the part of the aggregate gap that is explained by differences in average value of observed covariates between the two groups. The second term, $[X¯B(βA−βB)+(α0A−α0B)]$, is called the “coefficient effect” and reflects the gap that arises because workers in the two groups have different unemployment outcomes even given the same observed endowments. Oaxaca and Ransom (1994) pointed out that the relative size of the endowment and coefficient effects depends on which group's coefficients are treated as “correct” or “nondiscriminatory.” The foregoing equation treats group A coefficients as the benchmark, but the decomposition could just as easily be written with group B as the benchmark, leading to a different result. To circumvent this ambiguity, we follow the recommendation in Fortin (2006) to use coefficients from a pooled regression as the benchmark. In the pooled regression, groups $A$ and $B$ are allowed to have different intercepts but are restricted to have the same coefficients on the observed covariates.9 Using $βP$ and $α0P$ to represent coefficients from the pooled model, the aggregate gap in recent unemployment rates is $y¯A−y¯B=[(X¯A−X¯B)βP]+[(X¯A(βA−βP) +(α0A−α0P))−(X¯B(βA−βP)+(α0A−α0P))],$ where $[(X¯A−X¯B)βP]$ represents the part of the aggregate recent unemployment gap that can be attributed to differences in pre-epidemic endowments, using the coefficients from the pooled model as the benchmark. The coefficient effect is characterized by the deviation between the pooled coefficients and each group's unrestricted coefficients. Using this framework, we say that $E=(X¯A−X¯B)βPy¯A−y¯B$ is the share of the aggregate gap coming from the endowment effect.10 The overall explained share can itself be decomposed to determine the share of the gap explained by specific groups of variables. Specifically, we can write $(X¯A−X¯B)βP=(X¯A,Dem−X¯B,Dem)βP,Dem+(X¯A,Job−X¯B,Job)βP,job,$ where $X¯g,Dem$ and $X¯g,job$ are g-specific averages of demography and job-specific characteristics, and $βP,Dem$ and $βP,job$ are conformable parameter vectors. It follows that the overall explained share can be decomposed into a share associated with demographic and job factors so that $E=EDem+EJob.$ In practice, we break the explained share into several categories, including demographic-, industry-, and occupation-specific characteristics.11 ### Decomposition Results Figure 6 summarizes the most significant gaps in our data. For ease of visualization, they appear ordered from smallest to largest for: White versus Black, high school graduate versus high school dropout, female versus male, non-Hispanic versus Hispanic, college graduate versus high school graduate, and older versus younger workers. Figure 7 shows the same decompositions but applied to the May data for recent unemployment. The full results of the decompositions appear in online appendix Tables A13.1 and A13.3 for April and May 2020, respectively. For each gap, we estimate three versions of the pooled decomposition model. Each model includes basic demographic characteristics (age, gender, race, ethnicity, education, and presence of young children) and state controls. The three models are differentiated by how much detail we include regarding job characteristics. Model A includes the Face-to-Face, Remote Work, and Essential Job indices. Model B adds a full set of 523 occupation dummy variables, which, of course, absorb the variation from the Face-to-Face and Remote Work indices.12 Finally, Model C adds a full set of 261 industry dummy variables, which absorb the variation from the Essential index. Hence, Model C is the most general specification and nests Model B, which nests Model A. Focusing first on Model A for the April data, the explanatory contributions of task-based sorting and essential industry sorting operate in different directions across groups. For example, the non-Hispanic–Hispanic gap is quite large at −4.45 percentage points, relative to a baseline recent unemployment rate of 12.1%. About 52.18% of the raw gap arises because Hispanic workers are overrepresented in jobs with little opportunity for remote work. However, these relative losses are partially offset by the fact the Hispanic workers are overrepresented in essential jobs, accounting for −12.24% of the raw gap. This pattern is similar for the Black–White gap. The gender gap displays a different pattern; continuing with the April data, most of the gender gap is unexplained, and in fact sorting on the basis of remote work predicts a smaller gap than actually appears in the data because women are more likely to be in jobs that permit remote work. Moving to Models B and C, we see that sorting by occupation and industry explains a sizable portion of the gender, race, and ethnicity gaps in recent unemployment. However, there remain substantial unexplained differences in employment losses across groups even in these more detailed decompositions. The largest gaps we observe are between college graduates and high school graduates, and between older versus younger workers. In Model C, we observe that a majority of both raw gaps can be attributed to differences in the types of jobs workers held when the epidemic started. The less detailed Model A suggests that a large portion of the gap was associated with differences in capacity for remote work and is partially offset by employment in essential industries. All of the patterns we observe are consistent from April to May except one: the gap in recent unemployment between Black and White workers (see Figure 7). In May, the raw gap is −0.0345 percentage points, double the −0.0171 gap from April. Curiously, all of the growth in the gap is from sources that are not explained by the individual or job characteristics included in the model. Overall, recent unemployment rates fell in May relative to April, as they did for headline unemployment. Consistent with this trend, recent unemployment also fell for White workers. However, recent unemployment rates increased slightly for Black workers. Our decomposition indicates that whatever prevented recent unemployment rates from falling for Black workers was unrelated to any of the individual or job characteristics included in our model. One explanation relates to how the CPS classifies workers as unemployed versus employed-but-absent across months. On the other hand, this result may indicate that even given the same characteristics, White workers are more likely to be reemployed than Black workers in a recovery. Across the board, differential sorting into occupations and industries is highly relevant in explaining gaps in recent unemployment. This finding echoes recent work by Athreya et al. (2020), who found that the service sectors are most vulnerable to social distancing. Nevertheless, the precise sources of employment losses vary across groups in ways that are only partially explained by differential exposure to particular types of tasks or sectors. Finally, we note that demographic controls do not explain a large part of any of the gaps, suggesting a limited role for labor supply effects in determining recent job losses. We ran these models on data from the same months in 2019 as well (Tables A13.1 and A13.3 in the online appendix) to investigate the role that occupation sorting played in explaining differences in job loss prior to the pandemic. We find that the magnitude of most raw gaps for the groups we consider is much smaller in 2019 than in 2020. Even before the pandemic, for some groups the Remote Work index does explain a statistically significant but economically small share of differences in job loss. Nevertheless, the size and the significance of our 2020 results, compared to 2019, establish that occupational sorting in jobs characterized by high remote work and low face-to-face interaction did contribute substantially more to disparities in job loss during the epidemic than in normal times. Two examples are particularly meaningful. The first is the White–Black raw gap, which in 2019 was significant, but was about half the size of the 2020 raw gap. Furthermore, while remote work explained only 3.64% of the 2019 gap, that increased to 23.31% in 2020. Another example is the gap between high school graduates and high school dropouts. While in 2019 remote work explained more than 57% of the raw gap, the estimated gap was statistically insignificant and approximately zero. However, in 2020, that percentage increased to almost 72% and the raw gap was more than six times as large as in the previous year, and this time it was statistically significant. ## Conclusions After only a few months in 2020, the COVID-19 job losses were larger than the total multiyear effect of the Great Recession. Moreover, there were large disparities in job losses across demographic groups and people with different levels of education. Much of the overall variation in recent unemployment stemmed from differences across different types of jobs. For example, in the April CPS, we found that recent unemployment rates were about 44% lower among workers in jobs that are more compatible with remote work. In contrast, workers in jobs that require more face-to-face contact were at higher risk of recent unemployment. Formal decomposition analysis shows that a substantial share of the disparity in recent unemployment across racial, ethnic, age, and education subpopulations can be explained by differences in pre-epidemic sorting across occupations and industries that were more versus less sensitive to the COVID-19 shock. However, in almost all cases, a large share of the gaps in job losses between social strata cannot be explained by either occupation sorting or other observable traits. There are at least three possible sources for the unexplained share. First, workers may have different labor supply responses to the epidemic. Second, variation in exposure to labor demand shocks may not be fully reflected in the occupational or demographic differences we considered. Third, workers may face disparate treatment when employers make layoff and recall decisions. The available data do not allow us to distinguish between these three channels. These results raise concerns about the risks of workplace COVID-19 exposure and how that risk is distributed across the population. More highly educated workers had more job security during the epidemic because their work is often compatible with remote work. The least educated workers have also experienced less recent unemployment, largely owing to their concentration in essential industries, but these workers likely face greater exposure to COVID-19 itself. Thus, the higher job security available to workers with high or low education potentially masks a disparity in the health risks. New government policies or private-sector innovations that increase the viability of remote work for a larger share of the economy could be extremely valuable. The analysis of May CPS data showed an uptick in employment that likely derived from the business reopenings implemented in most states during that month. Although rates of recent unemployment and absence from work were still high in the May data, the data do suggest that reopening policies reduced the negative impact of the epidemic on the labor market. The improvements in labor market outcomes are consistent with cell signal data, which show a rise in physical mobility starting in mid-April and continuing through May (Nguyen et al. 2020). Of course, future potential waves of the virus make the return to full normalcy and its duration quite uncertain. In the meantime, our results highlight that there are large disparities in the current labor market crisis, and they suggest a role for targeted public policies. Although women with young children did not have statistically larger increases in recent unemployment compared to men with young children, despite the disruptions in school and childcare, their higher rate of “employed-but-absent” is worrying and could indicate larger losses in future employment. Moreover, single parents, who are overwhelmingly women, experienced a larger decrease in employment between February and April, as well as between February and May, than their married counterparts. Efforts to support new childcare options are important in this context. In May 2020, during the reopening phase, we found some evidence of racial disparities in reemployment. For example, Black workers became employed at a proportionately lower rate than did other groups. Further, the decomposition analysis shows that while for most groups recent unemployment decreased in May, it increased slightly for Blacks, and this gap is not related to any of the individual or job characteristics we considered. Our results point at deeper structural damage to the economy than may initially meet the eye. Previous research has documented large scarring effects of graduating from high school or college during a recession, and the longer term effects of early career setbacks may be even larger than the near-term effects (Rothstein 2019). Our work shows that recent unemployment rates are very high among the youngest workers overall and in comparison to earlier recessions. Finding workers whose employment match with their employer is highly productive is costly. Hence, efforts to support early career workers, as well as older displaced workers, may need to be a particular target of policy in the near future. Another important policy consideration that arises from our study regards access to health care. In the United States, workers receive health care and other benefits through employers. Assuming economic conditions in the post-epidemic years improve but remain unstable as a result of future waves of the virus, policymakers should make it a priority to help workers maintain their occupation with their original employers. However, if economic conditions do not return to normal rapidly, then the smooth reallocation of workers into different types of jobs may also be needed. ## Acknowledgments The authors thank two anonymous reviewers. Xuan Jiang gratefully acknowledges support from the National Center for Advancing Translational Sciences and the National Institute for Child Health and Development (grants UL1 TR002733 and R24 HD058484), and Bruce A. Weinberg acknowledges support from the National Center for Advancing Translational Sciences, the National Institute for Child Health and Development, the National Institute on Aging, the Office of the NIH Director, and the National Institute for General Medical Sciences (grants UL1 TR002733, R24 HD058484, and U01 AG076549). ## Notes 1 Others have used O*NET to define occupations with the ability to work from home (Dingel and Neiman 2020; Mongey and Weinberg 2020) and high interpersonal contact (Leibovici et al. 2020). 2 These surveys use a reference week that includes the 12th of the month (U.S. Census Bureau 2019). 3 The complete list of the specific questions used to build each of the two indexes is in the online appendix Table A4.1. 4 The list of critical infrastructure jobs is available at https://www.cisa.gov/. 5 The North American Industry Classification System is available at https://www.census.gov/. 6 We formally check for polarization in two ways. First, for each of the three recessions, we create a graph showing the employment change for each of the four education categories: less than high school, high school graduate, some college, and college graduate or more (on the x-axis, in increasing order). We observe a very marked U shape across the education groups during the COVID recession, but not for the other two recessions. Second, using a regression on data from the COVID-19 recession, we reject the hypothesis that workers with less than a high school diploma and those with at least a college degree jointly experience a drop in employment equal to that of the intermediate education groups. In other words, our p value (equal to 0) for the F test rejects the hypothesis of nonpolarization. Those with a college degree or more and those with less than a high school education experience a drop in employment that is statistically lower than the one suffered by the intermediate education groups. 7 We use Bayes’ theorem to infer mortality rates by age and gender from the Chinese Center for Disease Control and Prevention (2020). Specifically, we calculated $Pr(Death |Gender, Age)=Pr(Age | Death)⋅Pr(Gender | Death)⋅Pr(Death)Pr(Gender)⋅Pr(Age),$ where We normalize the variable to have a mean of 0 and a standard deviation of 1 on the entire CPS sample. 8 In each decomposition, group B is the relatively disadvantaged group in terms of employment. 9 Our notation $βP$ (and $αP$) corresponds to $β*$ in Jann (2008), the nondiscriminatory coefficient vectors. We implement the twofold Oaxaca decomposition using the pooled option in Stata. 10 This decomposition requires a normalization that specifies how much of the unexplained gap comes from positive deviations from the pooled outcome for the advantaged group and how much from negative deviations for the disadvantaged group. Our estimates assume the deviations are symmetric, that is, $(X¯A(βA−βP)+ (α0A−α0P))+(X¯B(βB−βP)+ (α0B−α0P))=0.$ 11 A similar exercise can be conducted to break the coefficient effect across categories. However, the differences in coefficient effects are generally not statistically significant when we focus on the same groups of demographic and job characteristics. As a result, we cannot say with confidence whether certain types of jobs are differentially protective against job loss. 12 For Model B, Table A13.2 in online Appendix A.13 reports the share of variation in April explained by sorting across five top-level categories in the census occupational classification system: Management, Business, Science, and Arts; Service; Sales and Office; Natural Resources, Construction, and Maintenance; and Production, Transportation, and Material Moving. A sixth category, Military Specific Operations, does not appear because the CPS is a survey of the civilian noninstitutional population. Table A13.4 shows the same results using May data. ## References Adams-Prassl, A., Boneva, T., Golin, M., & Rauh, C. ( 2020 ). Inequality in the impact of the Coronavirus shock: New survey evidence for the UK (Cambridge-INET Working Paper Series, No. 2020/10). Cambridge, UK : University of Cambridge, Institute for New Economic Thinking . Albanesi, S., & Kim, J. ( 2021 ). The gendered impact of the COVID-19 recession on the U.S. labor market (NBER Working Paper 28505). Cambridge, MA : National Bureau of Economic Research . Alon, T., Doepke, M., Olmstead-Rumsey, J., & Tertilt, M. ( 2020 ). The impact of COVID-19 on gender equality (NBER Working Paper 26947). Cambridge, MA : National Bureau of Economic Research . Angelucci, M., Angrisani, M., Bennett, D. M., Kapteyn, A., & Schaner, S. G. ( 2020 ). Remote work and the heterogeneous impact of COVID-19 on employment and health (NBER Working Paper 27749). Cambridge, MA : National Bureau of Economic Research . Athreya, K. B., Mather, R., Mustre-del Río, J., & Sánchez, J. M. ( 2020 ). COVID-19 and households' financial distress—Part 1: Employment vulnerability and (financial) pre-existing conditions (Report). Richmond, VA : Federal Reserve Bank of Richmond . Autor, D. H., Katz, L. F., & Kearney, M. S. ( 2006 ). The polarization of the U.S. labor market . American Economic Review: Papers & Proceedings , 96 , 189 194 . Bartik, A. W., Bertrand, M., Cullen, Z. B., Glaeser, E. L., Luca, M., & Stanton, C. T. ( 2020 ). How are small businesses adjusting to COVID-19? Early evidence from a survey (NBER Working Paper 26989). Cambridge, MA : National Bureau of Economic Research . Blau, F. D., Meyerhofer, P. A., & Koebe, J. ( 2020 ). Essential and frontline workers in the COVID- 19 crisis (Econofact report). Medford, MA : Edward R. Murrow Center for a Digital World, Fletcher School at Tufts University . Blinder, A. S. ( 1973 ). Wage discrimination: Reduced form and structural estimates . Journal of Human Resources , 8 , 436 455 . Busch, F. ( 2020 ). Gender segregation, occupational sorting, and growth of wage disparities between women . Demography , 57 , 1063 1088 . Cheng, S., Tamborini, C. R., Kim, C., & Sakamoto, A. ( 2019 ). Educational variations in cohort trends in the Black–White earnings gap among men: Evidence from administrative earnings data . Demography , 56 , 2253 2277 . Chinese Center for Disease Control and Prevention . ( 2020 ). The epidemiological characteristics of an outbreak of 2019 novel Coronavirus diseases (COVID-19)—China, 2020 . China CDC Weekly , 2 ( 8 ), 113 122 . Coibion, O., Gorodnichenko, Y., & Weber, M. ( 2020 ). Labor markets during the COVID-19 crisis: A preliminary view (NBER Working Paper 27017). Cambridge, MA : National Bureau of Economic Research . Cools, S., Markussen, S., & Strøm, M. ( 2017 ). Children and careers: How family size affects parents' labor market outcomes in the long run . Demography , 54 , 1773 1793 . Dasgupta, K., & Murali, S. ( 2020 ). Pandemic containment and inequality in a developing economy (IIMB Working Paper No. 613). Bangalore : Indian Institute of Management Bangalore . Dingel, J. I., & Neiman, B. ( 2020 ). How many jobs can be done at home? Journal of Public Economics , 189 , 104235 . https://doi.org/10.1016/j.jpubeco.2020.104235 Dingel, J. I., Patterson, C., & Vavra, J. ( 2020 ). Childcare obligations will constrain many workers when reopening the U.S. economy (Working Paper No. 2020-46). Chicago, IL : University of Chicago, Becker Friedman Institute for Economics Dudel, C., & Myrskylä, M. ( 2017 ). Working life expectancy at age 50 in the United States and the impact of the Great Recession . Demography , 54 , 2101 2123 . Forsythe, E., Kahn, L. B., Lange, F., & Wiczer, D. G. ( 2020 ). Labor demand in the time of COVID-19: Evidence from vacancy postings and UI claims (NBER Working Paper 27061). Cambridge, MA : National Bureau of Economic Research . Fortin, N. M. ( 2006 ). Greed, altruism, and the gender wage gap . Unpublished manuscript, Department of Economics, University of British Columbia, Vancouver, British Columbia , Goldin, C. ( 2022 ). Understanding the economic impact of COVID-19 on women Goolsbee, A., & Syverson, C. ( 2020 ). Fear, lockdown, and diversion: Comparing drivers of pandemic economic decline (NBER Working Paper 27432). Cambridge, MA : National Bureau of Economic Research . Grossman, D. S., & Slusky, D. J. G. ( 2019 ). The impact of the Flint water crisis on fertility . Demography , 56 , 2005 2031 . Guerrieri, V., Lorenzoni, G., Straub, L., & Werning, I. ( 2020 ). Macroeconomic implications of COVID-19: Can negative supply shocks cause demand shortages? (NBER Working Paper 26918). Cambridge, MA : National Bureau of Economic Research . Gupta, S., Nguyen, T. D., Lozano Rojas, F., Raman, S., Lee, B., Bento, A., . . . Wing, C.. ( 2020 ). Tracking public and private response to the COVID-19 epidemic: Evidence from state and local government actions (NBER Working Paper 27027). Cambridge, MA : National Bureau of Economic Research . Jann, B. ( 2008 ). The Blinder–Oaxaca decomposition for linear regression models . Stata Journal , 8 , 453 479 . Killewald, A., & Zhuo, X. ( 2019 ). U.S. mothers' long-term employment patterns . Demography , 56 , 285 320 . Leibovici, F., Santacreu, A. M., & Famiglietti, M. ( 2020 , March 24). Social distancing and contact-intensive occupations . On the Economy Blog, Federal Reserve Bank of St. Louis Lozano-Rojas, F., Jiang, X., Montenovo, L., Simon, K. I., Weinberg, B., & Wing, C. ( 2020 ). Is the cure worse than the problem itself? Immediate labor market effects of COVID-19 case rates and school closures in the U.S . (NBER Working Paper 27127). Cambridge, MA : National Bureau of Economic Research . Mongey, S., & Weinberg, A. ( 2020 ). Characteristics of workers in low work-from-home and high personal-proximity occupations (White paper). Chicago, IL : University of Chicago, Becker Friedman Institute for Economics . National Bureau of Economic Research . ( 2012 ). U.S. business cycle expansions and contractions (Report). Available from www.nber.org National Center for O*NET Development . ( 2020 ). [Data set]. Available from www.onet.org The New York Times . ( 2020 ). Coronavirus (COVID-19) data in the United States Nguyen, T. D., Gupta, S., Andersen, M., Bento, A., Simon, K. I., & Wing, C. ( 2020 ). Impacts of state reopening policy on human mobility (NBER Working Paper 27235). Cambridge, MA : National Bureau of Economic Research . Oaxaca, R. ( 1973 ). Male–female wage differentials in urban labor markets . International Economic Review , 14 , 693 709 . Oaxaca, R. L., & Ransom, M. R. ( 1994 ). On discrimination and the decomposition of wage differentials . Journal of Econometrics , 61 , 5 21 . Rothstein, J. ( 2019 ). The lost generation? Scarring after the Great Recession (Working paper). Berkeley : University of California, Berkeley, Goldman School of Public Policy . Sakamoto, A., & Powers, D. A. ( 2005 ). Demography of social stratification . In Poston, D. L. &Micklin, M. (Eds.), Handbook of population (pp. 383 416 ). New York, NY : . Sastry, N., & Gregory, J. ( 2014 ). The location of displaced New Orleans residents in the year after Hurricane Katrina . Demography , 51 , 753 775 . Schenck-Fontaine, A., & Panico, L. ( 2019 ). Many kinds of poverty: Three dimensions of economic hardship, their combinations, and children's behavior problems . Demography , 56 , 2279 2305 . Schneider, D., & Hastings, O. P. ( 2015 ). Socioeconomic variation in the effect of economic conditions on marriage and nonmarital fertility in the United States: Evidence from the Great Recession . Demography , 52 , 1893 1915 . Seltzer, N. ( 2019 ). Beyond the Great Recession: Labor market polarization and ongoing fertility decline in the United States . Demography , 56 , 1463 1493 . U.S. Census Bureau . ( 2019 ). Current population survey: Design and methodology U.S. Department of Homeland Security . ( 2020 ). Guidance on the essential critical infrastructure workforce Zissimopoulos, J., & Karoly, L. A. ( 2010 ). Employment and self-employment in the wake of Hurricane Katrina . Demography , 47 , 345 367 . This is an open access article distributed under the terms of a Creative Commons license (CC BY-NC-ND 4.0).
2022-11-29T11:25:13
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https://zbmath.org/authors/?q=ai%3Acox.david-a
## Cox, David A. Compute Distance To: Author ID: cox.david-a Published as: Cox, David A.; Cox, David Homepage: http://www3.amherst.edu/~dacox/ External Links: MGP · Wikidata · GND · IdRef · theses.fr Documents Indexed: 96 Publications since 1976, including 17 Books 4 Contributions as Editor · 2 Further Contributions Co-Authors: 71 Co-Authors with 54 Joint Publications 1,756 Co-Co-Authors all top 5 ### Co-Authors 42 single-authored 7 Little, John Brittain 7 O’Shea, Donal B. 6 Dickenstein, Alicia M. 5 Schenck, Hal 3 D’Andrea, Carlos 3 Materov, Evgeny N. 3 Parry, Walter R. 2 Chen, Falai 2 Clarke, Nancy Ellen 2 Donagi, Ron Y. 2 Erskine, Andrew 2 Katz, Sheldon 2 Messinger, Margaret-Ellen 2 Sederberg, Thomas W. 2 Sidman, Jessica 1 Abrevaya, Germán 1 Agrawal, Dakshi 1 Aravkin, Aleksandr Y. 1 Bashmakova, Izabella Grigor’evna 1 Batyrev, Victor V. 1 Bendel, Chris 1 Bird, Sheila M. 1 Bonato, Anthony 1 Busé, Laurent 1 Callahan, James J. 1 Cattani, Eduardo H. 1 Cecchi, Guillermo A. 1 Chionh, Eng-Wee 1 Clarke, Patrick 1 Cortadellas Benítez, Teresa 1 Curtiss, Howard C. jun. 1 Dawson, Silvina Ponce 1 Dowell, Earl H. 1 Dumas, Guillaume 1 Edwards, John W. 1 Esnault, Hélène 1 Farewell, Vern T. 1 Finbow, Stephen 1 Fitzpatrick, Shannon L. 1 Gagnon-Audet, Jean-Christophe 1 Goldman, Ronald N. 1 Goldstein, Harvey 1 Green, Mark Lee 1 Haase, Christian Alexander 1 Hain, Richard M. 1 Hall, Kenneth C. 1 Harris, Michael Howard 1 Hasemeyer, Christian 1 Hauenstein, Jonathan D. 1 Hibi, Takayuki 1 Higashitani, Akihiro 1 Hoffman, Jerome William 1 Hoffman, Kenneth 1 Holt, Tim 1 Hyde, Trevor 1 Iarrobino, Anthony A. 1 Ji, Lizhen 1 Joshua, Roy 1 Kozloski, James 1 Krasauskas, Rimvydas 1 Kunz, Ernst 1 Kustin, Andrew R. 1 Lajoie, Guillaume 1 Lee, Yuan-Pin 1 Lin, Kuei-Nuan 1 Liu, Yang 1 Ma’u, Sione 1 Mc Inerney, Fionn 1 Mcgiffen, T. 1 McKay, John 1 Mustaţă, Mircea 1 Peters, David A. 1 Pevtsova, Julia 1 Polini, Claudia 1 Pollatsek, Harriet S. 1 Polosecki, Pablo 1 Richardson, Thomas J. 1 Rish, Irina 1 Saito, Masa-Hiko 1 Saper, Leslie 1 Scanlan, Robert H. 1 Schicho, Josef 1 Senechal, Lester 1 Shurman, Jerry 1 Simiu, Emil 1 Sisto, Fernando 1 Smirnova, Galina Sergeevna 1 Smith, Peter C. 1 Sosa, Gabriel 1 Stevenhagen, Peter 1 Strganac, Thomas W. 1 Sturmfels, Bernd 1 Tu, Loring W. 1 Ulrich, Bernd 1 Urbanke, Rüdiger L. 1 von Renesse, Christine 1 Wang, Haohao 1 Zhang, Ming 1 Zheng, Jianmin 1 Zheng, Peng ...and 1 more Co-Authors all top 5 ### Serials 6 Proceedings of the American Mathematical Society 4 American Mathematical Monthly 4 Compositio Mathematica 4 Journal of Pure and Applied Algebra 4 Undergraduate Texts in Mathematics 3 Pacific Journal of Mathematics 2 Duke Mathematical Journal 2 Inventiones Mathematicae 2 Mathematica Scandinavica 2 Theoretical Computer Science 2 Tohoku Mathematical Journal. Second Series 2 Computer Aided Geometric Design 2 Journal of Symbolic Computation 2 Notices of the American Mathematical Society 2 Journal of Algebraic Geometry 2 Graduate Texts in Mathematics 2 Pure and Applied Mathematics. A Wiley Series of Texts, Monographs, and Tracts 2 Pure and Applied Mathematics. A Wiley-Interscience Series of Texts, Monographs and Tracts 1 Discrete Applied Mathematics 1 IEEE Transactions on Information Theory 1 Arkiv för Matematik 1 Advances in Mathematics 1 American Journal of Mathematics 1 Ars Combinatoria 1 Bulletin of the London Mathematical Society 1 Gazette des Mathématiciens 1 Illinois Journal of Mathematics 1 Journal of Algebra 1 Journal of Number Theory 1 Journal für die Reine und Angewandte Mathematik 1 Mathematische Annalen 1 Mathematische Zeitschrift 1 Memoirs of the American Mathematical Society 1 Normat 1 Neural Computation 1 L’Enseignement Mathématique. 2e Série 1 The Electronic Journal of Combinatorics 1 Journal of the Royal Statistical Society. Series A. Statistics in Society 1 La Gaceta de la Real Sociedad Matemática Española 1 Journal of Algebra and its Applications 1 Oberwolfach Reports 1 The Dolciani Mathematical Expositions 1 Graduate Studies in Mathematics 1 Mathematical Surveys and Monographs 1 Proceedings of Symposia in Applied Mathematics 1 Solid Mechanics and Its Applications 1 University Lecture Series 1 Algebra & Number Theory 1 Involve 1 Symmetry 1 CBMS Regional Conference Series in Mathematics all top 5 ### Fields 66 Algebraic geometry (14-XX) 30 Commutative algebra (13-XX) 13 Number theory (11-XX) 10 Several complex variables and analytic spaces (32-XX) 10 Computer science (68-XX) 8 General and overarching topics; collections (00-XX) 8 History and biography (01-XX) 6 Numerical analysis (65-XX) 4 Combinatorics (05-XX) 4 Convex and discrete geometry (52-XX) 3 Field theory and polynomials (12-XX) 3 Group theory and generalizations (20-XX) 3 Algebraic topology (55-XX) 3 Biology and other natural sciences (92-XX) 2 Associative rings and algebras (16-XX) 2 Category theory; homological algebra (18-XX) 2 Special functions (33-XX) 2 Geometry (51-XX) 2 Statistics (62-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 2 Information and communication theory, circuits (94-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 $$K$$-theory (19-XX) 1 Real functions (26-XX) 1 Functions of a complex variable (30-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Differential geometry (53-XX) 1 Manifolds and cell complexes (57-XX) 1 Mechanics of deformable solids (74-XX) 1 Fluid mechanics (76-XX) 1 Quantum theory (81-XX) 1 Operations research, mathematical programming (90-XX) 1 Mathematics education (97-XX) ### Citations contained in zbMATH Open 84 Publications have been cited 2,943 times in 2,443 Documents Cited by Year Toric varieties. Zbl 1223.14001 Cox, David A.; Little, John B.; Schenck, Henry K. 2011 The homogeneous coordinate ring of a toric variety. Zbl 0846.14032 Cox, David A. 1995 Ideals, varieties, and algorithms. An introduction to computational algebraic geometry and commutative algebra. 3rd ed. Zbl 1118.13001 Cox, David; Little, John; O’Shea, Donal 2007 Mirror symmetry and algebraic geometry. Zbl 0951.14026 Cox, David A.; Katz, Sheldon 1999 Using algebraic geometry. Zbl 0920.13026 Cox, David; Little, John; O’Shea, Donal 1998 Ideals, varieties, and algorithms. An introduction to computational algebraic geometry and commutative algebra. Zbl 0756.13017 Cox, David; Little, John; O’Shea, Donal 1992 Primes of the form $$x^ 2+ny^ 2$$. Fermat, class field theory and complex multiplication. Zbl 0701.11001 Cox, David A. 1989 Using algebraic geometry. 2nd ed. Zbl 1079.13017 Cox, David A.; Little, John; O’Shea, Donal 2005 Ideals, varieties, and algorithms. An introduction to computational algebraic geometry and commutative algebra. 4th revised ed. Zbl 1335.13001 Cox, David A.; Little, John; O’Shea, Donal 2015 The moving line ideal basis of planar rational curves. Zbl 0908.68174 Cox, David A.; Sederberg, Thomas W.; Chen, Falai 1998 On the Hodge structure of projective hypersurfaces in toric varieties. Zbl 0851.14021 Batyrev, Victor V.; Cox, David A. 1994 Ideals, varieties, and algorithms. An introduction to computational algebraic geometry and commutative algebra. 2nd ed. Zbl 0861.13012 Cox, David; Little, John; O’Shea, Donal 1996 Primes of the form $$x^2+ny^2$$. Fermat, class field theory, and complex multiplication. 2nd ed. Zbl 1275.11002 Cox, David A. 2013 On the validity of implicitization by moving quadrics for rational surfaces with no base points. Zbl 0959.68124 Cox, David; Goldman, Ronald; Zhang, Ming 2000 Intersection numbers of sections of elliptic surfaces. Zbl 0444.14004 Cox, David A.; Zucker, Steven 1979 Implicitization of surfaces in $${\mathbb P}^ 3$$ in the presence of base points. Zbl 1068.14066 Busé, Laurent; Cox, David; D’Andrea, Carlos 2003 The $$\mu$$-basis and implicitization of a rational parametric surface. Zbl 1120.14054 Chen, Falai; Cox, David; Liu, Yang 2005 The arithmetic-geometric mean of Gauss. Zbl 0583.33002 Cox, David A. 1984 Syzygies and the Rees algebra. Zbl 1151.13012 Cox, David; Hoffman, J. William; Wang, Haohao 2008 Equations of parametric curves and surfaces via syzygies. Zbl 1009.68174 Cox, David A. 2001 Recent developments in toric geometry. Zbl 0899.14025 Cox, David A. 1997 A modern course in aeroelasticity. 4th revised and enlarged edition. Zbl 1078.74001 Clark, Robert; Cox, David; Curtiss, H. C. jun.; Edwards, John W.; Hall, Kenneth C.; Peters, David A.; Scanlan, Robert; Simiu, Emil; Sisto, Fernando; Strganac, Thomas W. 2004 The functor of a smooth toric variety. Zbl 0828.14035 Cox, David A. 1995 What is a toric variety? Zbl 1038.14021 Cox, David 2003 Toric residues. Zbl 0904.14029 Cox, David A. 1996 A study of singularities on rational curves via syzygies. Zbl 1305.14014 Cox, David; Kustin, Andrew R.; Polini, Claudia; Ulrich, Bernd 2013 The moving curve ideal and the Rees algebra. Zbl 1170.13004 Cox, David A. 2008 Toric varieties and toric resolutions. Zbl 0969.14035 Cox, David A. 2000 Implicitizing rational surfaces with base points using the method of moving surfaces. Zbl 1058.14074 Zheng, Jianmin; Sederberg, Thomas W.; Chionh, Eng-Wee; Cox, David A. 2003 Residues in toric varieties. Zbl 0883.14029 Cattani, Eduardo; Cox, David; Dickenstein, Alicia 1997 Curves, surfaces, and syzygies. Zbl 1058.14072 Cox, David 2003 Galois theory. Zbl 1057.12002 Cox, David A. 2004 Galois theory. 2nd ed. Zbl 1247.12006 Cox, David A. 2012 Torsion in elliptic curves over $$k(t)$$. Zbl 0442.14015 Cox, David A.; Parry, Walter R. 1980 Mordell-Weil groups of elliptic curves over C(t) with pg=O or 1. Zbl 0503.14018 Cox, David A. 1982 Variational Torelli implies generic Torelli. Zbl 0594.14011 Cox, David; Donagi, Ron; Tu, Loring 1987 Local complete intersections in $$\mathbb{P}^2$$ and Koszul syzygies. Zbl 1075.13006 Cox, David; Schenck, Hal 2003 Integer decomposition property of dilated polytopes. Zbl 1308.52012 Cox, David A.; Haase, Christian; Hibi, Takayuki; Higashitani, Akihiro 2014 Erratum to “The homogeneous coordinate ring of a toric variety”. Zbl 1285.14055 Cox, David A. 2014 Primitive collections and toric varieties. Zbl 1185.14045 Cox, David A.; von Renesse, Christine 2009 Secant varieties of toric varieties. Zbl 1115.14045 Cox, David; Sidman, Jessica 2007 Primes of the form $$x^2+ny^2$$. Fermat, class field theory, and complex multiplication. Paperback ed. Zbl 0956.11500 Cox, David A. 1997 Why Eisenstein proved the Eisenstein criterion and why Schönemann discovered it first. Zbl 1225.11002 Cox, David A. 2011 Principal moduli and class fields. Zbl 1047.11107 Cox, David; McKay, John; Stevenhagen, Peter 2004 A case study in bigraded commutative algebra. Zbl 1127.13002 Cox, David; Dickenstein, Alicia; Schenck, Hal 2007 The Noether-Lefschetz locus of regular elliptic surfaces with section and $$p_ g\geq 2$$. Zbl 0721.14017 Cox, David A. 1990 Geometry and number theory on clovers. Zbl 1107.51007 Cox, David A.; Shurman, Jerry 2005 Genera of congruence subgroups in $${\mathbb{Q}}$$-quaternion algebras. Zbl 0531.10028 Cox, David A.; Parry, Walter R. 1984 Picard numbers of surfaces in 3-dimensional weighted projective spaces. Zbl 0686.14041 Cox, David A. 1989 The beginnings and evolution of algebra. Transl. from the Russian by Abe Shenitzer with the editorial assistance of David A. Cox. Zbl 0942.01001 Bashmakova, I. G.; Smirnova, G. S. 2000 The etale homotopy type of varieties over R. Zbl 0442.14004 Cox, David A. 1979 Tate resolutions for Segre embeddings. Zbl 1168.13009 Cox, David A.; Materov, Evgeny 2008 Solving equations via algebras. Zbl 1152.13306 Cox, David A. 2005 Introduction to Fermat’s Last Theorem. Zbl 0849.11002 Cox, David A. 1994 Codimension theorems for complete toric varieties. Zbl 1083.14058 Cox, David; Dickenstein, Alicia 2005 Performance indicators: good, bad, and ugly. Zbl 1114.62304 Bird, Sheila M.; Cox, David; Farewell, Vern T.; Goldstein, Harvey; Holt, Tim; Smith, Peter C. 2005 On the failure of variational Torelli for regular elliptic surfaces with a section. Zbl 0566.14005 Cox, David; Donagi, Ron 1986 On closed graphs. I. Zbl 1349.05282 Cox, David A.; Erskine, Andrew 2015 Update on toric geometry. Zbl 1050.14001 Cox, David A. 2002 Algebraic tubular neighborhoods. I. Zbl 0414.14005 Cox, David A. 1978 Algebraic tubular neighborhoods. II. Zbl 0418.14012 Cox, David A. 1978 Mirror symmetry and polar duality of polytopes. Zbl 1377.14009 Cox, David A. 2015 Introduction to Gröbner bases. Zbl 0941.13018 Cox, David A. 1998 What is the role of algebra in applied mathematics? Zbl 1114.00003 Cox, David A. 2005 Multi-Rees algebras and toric dynamical systems. Zbl 1429.13006 Cox, David A.; Lin, Kuei-Nuan; Sosa, Gabriel 2019 Regularity and Segre-Veronese embeddings. Zbl 1169.14012 Cox, David A.; Materov, Evgeny 2009 Universal rational parametrizations and toric varieties. Zbl 1080.14539 Cox, David; Krasauskas, Rimvydas; Mustaţǎ, Mircea 2003 Applications of computational algebraic geometry. American Mathematical Society short course, San Diego, CA, USA, January 6–7, 1997. Zbl 0880.00039 1998 Homotopy theory of simplicial schemes. Zbl 0385.14004 Cox, David A. 1979 Limited visibility cops and robber. Zbl 1441.05155 Clarke, N. E.; Cox, D.; Duffy, C.; Dyer, D.; Fitzpatrick, S. L.; Messinger, M. E. 2020 Moment maps, strict linear precision, and maximum likelihood degree one. Zbl 1453.14125 Clarke, Patrick; Cox, David A. 2020 Strata of rational space curves. Zbl 1417.14009 Cox, David A.; Iarrobino, Anthony A. 2015 Polynomial structures and generic Torelli for projective hypersurfaces. Zbl 0725.14007 Cox, David A.; Green, Mark L. 1990 Tate resolutions and Weyman complexes. Zbl 1228.14013 Cox, David A.; Materov, Evgeny 2011 Why Eisenstein proved the Eisenstein criterion and why Schönemann discovered it first. Zbl 1191.01013 Cox, David A. 2009 Residues and duality for projective algebraic varieties. With the assistance of and contributions by David A. Cox and Alicia Dickenstein. Zbl 1180.14002 Kunz, Ernst 2008 Calculus in context: the five college calculus project. Zbl 0874.26002 Callahan, James; Cox, David; Hoffman, Kenneth; O’Shea, Donal; Pollatsek, Harriet; Senechal, Lester 1995 Representations associated with elliptic surfaces. Zbl 0582.14013 Cox, David A.; Parry, Walter R. 1984 Solutions of Weierstrass equations. Zbl 0438.14019 Cox, David A. 1979 Homotopy limits and the homotopy type of functor categories. Zbl 0346.18018 Cox, David A. 1976 Applications of polynomial systems. With contributions by Carlos D’Andrea, Alicia Dickenstein, Jonathan Hauenstein, Hal Schenck, and Jessica Sidman. Zbl 1469.13001 Cox, David A. 2020 Virtual fundamental classes of zero loci. Zbl 1065.14014 Cox, David A.; Katz, Sheldon; Lee, Yuan-Pin 2001 Transfinite diameter on complex algebraic varieties. Zbl 1375.32054 Cox, David A.; Ma’u, Sione 2017 The Galois theory of the lemniscate. Zbl 1385.11040 Cox, David A.; Hyde, Trevor 2014 Limited visibility cops and robber. Zbl 1441.05155 Clarke, N. E.; Cox, D.; Duffy, C.; Dyer, D.; Fitzpatrick, S. L.; Messinger, M. E. 2020 Moment maps, strict linear precision, and maximum likelihood degree one. Zbl 1453.14125 Clarke, Patrick; Cox, David A. 2020 Applications of polynomial systems. With contributions by Carlos D’Andrea, Alicia Dickenstein, Jonathan Hauenstein, Hal Schenck, and Jessica Sidman. Zbl 1469.13001 Cox, David A. 2020 Multi-Rees algebras and toric dynamical systems. Zbl 1429.13006 Cox, David A.; Lin, Kuei-Nuan; Sosa, Gabriel 2019 Transfinite diameter on complex algebraic varieties. Zbl 1375.32054 Cox, David A.; Ma&rsquo;u, Sione 2017 Ideals, varieties, and algorithms. An introduction to computational algebraic geometry and commutative algebra. 4th revised ed. Zbl 1335.13001 Cox, David A.; Little, John; O&rsquo;Shea, Donal 2015 On closed graphs. I. Zbl 1349.05282 Cox, David A.; Erskine, Andrew 2015 Mirror symmetry and polar duality of polytopes. Zbl 1377.14009 Cox, David A. 2015 Strata of rational space curves. Zbl 1417.14009 Cox, David A.; Iarrobino, Anthony A. 2015 Integer decomposition property of dilated polytopes. Zbl 1308.52012 Cox, David A.; Haase, Christian; Hibi, Takayuki; Higashitani, Akihiro 2014 Erratum to “The homogeneous coordinate ring of a toric variety”. Zbl 1285.14055 Cox, David A. 2014 The Galois theory of the lemniscate. Zbl 1385.11040 Cox, David A.; Hyde, Trevor 2014 Primes of the form $$x^2+ny^2$$. Fermat, class field theory, and complex multiplication. 2nd ed. Zbl 1275.11002 Cox, David A. 2013 A study of singularities on rational curves via syzygies. Zbl 1305.14014 Cox, David; Kustin, Andrew R.; Polini, Claudia; Ulrich, Bernd 2013 Galois theory. 2nd ed. Zbl 1247.12006 Cox, David A. 2012 Toric varieties. Zbl 1223.14001 Cox, David A.; Little, John B.; Schenck, Henry K. 2011 Why Eisenstein proved the Eisenstein criterion and why Schönemann discovered it first. Zbl 1225.11002 Cox, David A. 2011 Tate resolutions and Weyman complexes. Zbl 1228.14013 Cox, David A.; Materov, Evgeny 2011 Primitive collections and toric varieties. Zbl 1185.14045 Cox, David A.; von Renesse, Christine 2009 Regularity and Segre-Veronese embeddings. Zbl 1169.14012 Cox, David A.; Materov, Evgeny 2009 Why Eisenstein proved the Eisenstein criterion and why Schönemann discovered it first. Zbl 1191.01013 Cox, David A. 2009 Syzygies and the Rees algebra. Zbl 1151.13012 Cox, David; Hoffman, J. William; Wang, Haohao 2008 The moving curve ideal and the Rees algebra. Zbl 1170.13004 Cox, David A. 2008 Tate resolutions for Segre embeddings. Zbl 1168.13009 Cox, David A.; Materov, Evgeny 2008 Residues and duality for projective algebraic varieties. With the assistance of and contributions by David A. Cox and Alicia Dickenstein. Zbl 1180.14002 Kunz, Ernst 2008 Ideals, varieties, and algorithms. An introduction to computational algebraic geometry and commutative algebra. 3rd ed. Zbl 1118.13001 Cox, David; Little, John; O&rsquo;Shea, Donal 2007 Secant varieties of toric varieties. Zbl 1115.14045 Cox, David; Sidman, Jessica 2007 A case study in bigraded commutative algebra. Zbl 1127.13002 Cox, David; Dickenstein, Alicia; Schenck, Hal 2007 Using algebraic geometry. 2nd ed. Zbl 1079.13017 Cox, David A.; Little, John; O&rsquo;Shea, Donal 2005 The $$\mu$$-basis and implicitization of a rational parametric surface. Zbl 1120.14054 Chen, Falai; Cox, David; Liu, Yang 2005 Geometry and number theory on clovers. Zbl 1107.51007 Cox, David A.; Shurman, Jerry 2005 Solving equations via algebras. Zbl 1152.13306 Cox, David A. 2005 Codimension theorems for complete toric varieties. Zbl 1083.14058 Cox, David; Dickenstein, Alicia 2005 Performance indicators: good, bad, and ugly. Zbl 1114.62304 Bird, Sheila M.; Cox, David; Farewell, Vern T.; Goldstein, Harvey; Holt, Tim; Smith, Peter C. 2005 What is the role of algebra in applied mathematics? Zbl 1114.00003 Cox, David A. 2005 A modern course in aeroelasticity. 4th revised and enlarged edition. Zbl 1078.74001 Clark, Robert; Cox, David; Curtiss, H. C. jun.; Edwards, John W.; Hall, Kenneth C.; Peters, David A.; Scanlan, Robert; Simiu, Emil; Sisto, Fernando; Strganac, Thomas W. 2004 Galois theory. Zbl 1057.12002 Cox, David A. 2004 Principal moduli and class fields. Zbl 1047.11107 Cox, David; McKay, John; Stevenhagen, Peter 2004 Implicitization of surfaces in $${\mathbb P}^ 3$$ in the presence of base points. Zbl 1068.14066 Busé, Laurent; Cox, David; D&rsquo;Andrea, Carlos 2003 What is a toric variety? Zbl 1038.14021 Cox, David 2003 Implicitizing rational surfaces with base points using the method of moving surfaces. Zbl 1058.14074 Zheng, Jianmin; Sederberg, Thomas W.; Chionh, Eng-Wee; Cox, David A. 2003 Curves, surfaces, and syzygies. Zbl 1058.14072 Cox, David 2003 Local complete intersections in $$\mathbb{P}^2$$ and Koszul syzygies. Zbl 1075.13006 Cox, David; Schenck, Hal 2003 Universal rational parametrizations and toric varieties. Zbl 1080.14539 Cox, David; Krasauskas, Rimvydas; Mustaţǎ, Mircea 2003 Update on toric geometry. Zbl 1050.14001 Cox, David A. 2002 Equations of parametric curves and surfaces via syzygies. Zbl 1009.68174 Cox, David A. 2001 Virtual fundamental classes of zero loci. Zbl 1065.14014 Cox, David A.; Katz, Sheldon; Lee, Yuan-Pin 2001 On the validity of implicitization by moving quadrics for rational surfaces with no base points. Zbl 0959.68124 Cox, David; Goldman, Ronald; Zhang, Ming 2000 Toric varieties and toric resolutions. Zbl 0969.14035 Cox, David A. 2000 The beginnings and evolution of algebra. Transl. from the Russian by Abe Shenitzer with the editorial assistance of David A. Cox. Zbl 0942.01001 Bashmakova, I. G.; Smirnova, G. S. 2000 Mirror symmetry and algebraic geometry. Zbl 0951.14026 Cox, David A.; Katz, Sheldon 1999 Using algebraic geometry. Zbl 0920.13026 Cox, David; Little, John; O&rsquo;Shea, Donal 1998 The moving line ideal basis of planar rational curves. Zbl 0908.68174 Cox, David A.; Sederberg, Thomas W.; Chen, Falai 1998 Introduction to Gröbner bases. Zbl 0941.13018 Cox, David A. 1998 Applications of computational algebraic geometry. American Mathematical Society short course, San Diego, CA, USA, January 6–7, 1997. Zbl 0880.00039 1998 Recent developments in toric geometry. Zbl 0899.14025 Cox, David A. 1997 Residues in toric varieties. Zbl 0883.14029 Cattani, Eduardo; Cox, David; Dickenstein, Alicia 1997 Primes of the form $$x^2+ny^2$$. Fermat, class field theory, and complex multiplication. Paperback ed. Zbl 0956.11500 Cox, David A. 1997 Ideals, varieties, and algorithms. An introduction to computational algebraic geometry and commutative algebra. 2nd ed. Zbl 0861.13012 Cox, David; Little, John; O&rsquo;Shea, Donal 1996 Toric residues. Zbl 0904.14029 Cox, David A. 1996 The homogeneous coordinate ring of a toric variety. Zbl 0846.14032 Cox, David A. 1995 The functor of a smooth toric variety. Zbl 0828.14035 Cox, David A. 1995 Calculus in context: the five college calculus project. Zbl 0874.26002 Callahan, James; Cox, David; Hoffman, Kenneth; O&rsquo;Shea, Donal; Pollatsek, Harriet; Senechal, Lester 1995 On the Hodge structure of projective hypersurfaces in toric varieties. Zbl 0851.14021 Batyrev, Victor V.; Cox, David A. 1994 Introduction to Fermat’s Last Theorem. Zbl 0849.11002 Cox, David A. 1994 Ideals, varieties, and algorithms. An introduction to computational algebraic geometry and commutative algebra. Zbl 0756.13017 Cox, David; Little, John; O&rsquo;Shea, Donal 1992 The Noether-Lefschetz locus of regular elliptic surfaces with section and $$p_ g\geq 2$$. Zbl 0721.14017 Cox, David A. 1990 Polynomial structures and generic Torelli for projective hypersurfaces. Zbl 0725.14007 Cox, David A.; Green, Mark L. 1990 Primes of the form $$x^ 2+ny^ 2$$. Fermat, class field theory and complex multiplication. Zbl 0701.11001 Cox, David A. 1989 Picard numbers of surfaces in 3-dimensional weighted projective spaces. Zbl 0686.14041 Cox, David A. 1989 Variational Torelli implies generic Torelli. Zbl 0594.14011 Cox, David; Donagi, Ron; Tu, Loring 1987 On the failure of variational Torelli for regular elliptic surfaces with a section. Zbl 0566.14005 Cox, David; Donagi, Ron 1986 The arithmetic-geometric mean of Gauss. Zbl 0583.33002 Cox, David A. 1984 Genera of congruence subgroups in $${\mathbb{Q}}$$-quaternion algebras. Zbl 0531.10028 Cox, David A.; Parry, Walter R. 1984 Representations associated with elliptic surfaces. Zbl 0582.14013 Cox, David A.; Parry, Walter R. 1984 Mordell-Weil groups of elliptic curves over C(t) with pg=O or 1. Zbl 0503.14018 Cox, David A. 1982 Torsion in elliptic curves over $$k(t)$$. Zbl 0442.14015 Cox, David A.; Parry, Walter R. 1980 Intersection numbers of sections of elliptic surfaces. Zbl 0444.14004 Cox, David A.; Zucker, Steven 1979 The etale homotopy type of varieties over R. Zbl 0442.14004 Cox, David A. 1979 Homotopy theory of simplicial schemes. Zbl 0385.14004 Cox, David A. 1979 Solutions of Weierstrass equations. Zbl 0438.14019 Cox, David A. 1979 Algebraic tubular neighborhoods. I. Zbl 0414.14005 Cox, David A. 1978 Algebraic tubular neighborhoods. II. Zbl 0418.14012 Cox, David A. 1978 Homotopy limits and the homotopy type of functor categories. Zbl 0346.18018 Cox, David A. 1976 all top 5 ### Cited by 3,040 Authors 20 Busé, Laurent 20 Cox, David A. 20 Goldman, Ronald N. 19 D’Andrea, Carlos 18 Chen, Falai 17 Hashemi, Amir 16 Hausen, Jürgen 16 Michałek, Mateusz 15 Hibi, Takayuki 14 Koo, Jakyung 13 Qi, Liqun 12 Arzhantsev, Ivan Vladimirovich 12 Sturmfels, Bernd 12 Wang, Haohao 11 Pérez-Díaz, Sonia 11 Shen, Liyong 11 Shin, Dong Hwa 11 Webster, Justin T. 10 Emiris, Ioannis Z. 10 Faugère, Jean-Charles 10 Gao, Xiaoshan 10 Jung, Ho Yun 10 Laface, Antonio 10 Mourrain, Bernard 10 Seiler, Werner M. 10 Sendra, Juan Rafael 10 Sharir, Micha 10 Simis, Aron 10 Sottile, Frank 10 Yuan, Chunming 9 García, Isaac A. 9 Iritani, Hiroshi 9 Jia, Xiaohong 9 Rietsch, Konstanze 8 Bruzzo, Ugo 8 Chen, Yuqun 8 Hoffman, Jerome William 8 Nill, Benjamin 8 Ohsugi, Hidefumi 8 Rossi, Michele 8 Smith, Gregory G. 8 Tsuchiya, Akiyoshi 7 Dickenstein, Alicia M. 7 Doran, Charles F. 7 He, Yang-Hui Evariste 7 Katzarkov, Ludmil 7 Lasiecka, Irena 7 Schenck, Hal 7 Tohǎneanu, Ştefan O. 7 Tsigaridas, Elias P. 7 Velasco, Mauricio 7 Villarreal, Rafael Heraclio 7 Wang, Dingkang 7 Wang, Xuhui 6 Bokut, Leonid A. 6 Botbol, Nicolás 6 Brini, Andrea 6 Castryck, Wouter 6 Chardin, Marc 6 Cortadellas Benítez, Teresa 6 Duarte, Daniel C. S. 6 Gatermann, Karin 6 Gubeladze, Joseph 6 Helmer, Martin 6 Higashitani, Akihiro 6 Hong, Hoon 6 Ilten, Nathan Owen 6 Javanbakht, Masoumeh 6 Jockers, Hans 6 Kapur, Deepak 6 Keicher, Simon 6 Kim, Chang Heon 6 Klemm, Albrecht 6 Kreuzer, Maximilian 6 Kustin, Andrew R. 6 Liendo, Alvaro 6 Morton, Patrick 6 Mustaţă, Mircea 6 Perling, Markus 6 Polini, Claudia 6 Rouillier, Fabrice 6 Safey El Din, Mohab 6 Sauer, Tomas 6 Schicho, Josef 6 Shi, Xiaoran 6 Skarke, Harald 6 Terracini, Lea 6 Tseng, Hsian-Hua 6 Walther, Uli 6 Yau, Shing-Tung 5 Bivià-Ausina, Carles 5 Borisov, Lev A. 5 Bourqui, David 5 de Graaf, Willem Adriaan 5 De Loera, Jesús A. 5 Dimca, Alexandru 5 Dipasquale, Michael R. 5 Duarte, Eliana 5 Edidin, Dan 5 Elizondo, E. Javier ...and 2,940 more Authors all top 5 ### Cited in 415 Serials 165 Journal of Symbolic Computation 123 Journal of Algebra 88 Advances in Mathematics 60 Transactions of the American Mathematical Society 59 Proceedings of the American Mathematical Society 53 Computer Aided Geometric Design 52 Journal of Pure and Applied Algebra 50 Journal of High Energy Physics 43 Mathematics of Computation 38 Mathematische Zeitschrift 34 Duke Mathematical Journal 29 Journal of Number Theory 28 Communications in Mathematical Physics 28 Annales de l’Institut Fourier 28 The Ramanujan Journal 27 Communications in Algebra 27 Linear Algebra and its Applications 23 Tohoku Mathematical Journal. Second Series 23 Journal of Algebraic Geometry 22 Nuclear Physics. B 21 Discrete & Computational Geometry 21 Journal de Théorie des Nombres de Bordeaux 21 Mathematics in Computer Science 20 Mathematische Annalen 18 Manuscripta Mathematica 17 Journal of Geometry and Physics 17 Designs, Codes and Cryptography 17 Journal of Systems Science and Complexity 16 Compositio Mathematica 15 Journal of Combinatorial Theory. Series A 15 Journal für die Reine und Angewandte Mathematik 15 Advances in Applied Mathematics 15 Applicable Algebra in Engineering, Communication and Computing 15 Journal of Algebraic Combinatorics 14 Journal of Mathematical Analysis and Applications 14 Journal of Computational and Applied Mathematics 14 Journal of Differential Equations 14 Proceedings of the Japan Academy. Series A 14 Journal of the American Mathematical Society 14 Selecta Mathematica. New Series 14 Transformation Groups 13 Applied Mathematics and Computation 13 Science China. Mathematics 11 Finite Fields and their Applications 10 Rocky Mountain Journal of Mathematics 10 Beiträge zur Algebra und Geometrie 10 Collectanea Mathematica 10 Inventiones Mathematicae 10 Bulletin of the American Mathematical Society. New Series 10 The Electronic Journal of Combinatorics 10 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 9 Archiv der Mathematik 9 Michigan Mathematical Journal 9 Nagoya Mathematical Journal 9 Theoretical Computer Science 9 International Journal of Mathematics 9 Mathematical Programming. Series A. Series B 9 Journal of Mathematical Sciences (New York) 9 Journal of Algebra and its Applications 9 Journal of Commutative Algebra 8 Israel Journal of Mathematics 8 Mathematische Nachrichten 8 European Journal of Combinatorics 8 International Journal of Algebra and Computation 8 Journal of Mathematical Imaging and Vision 7 Mathematical Notes 7 Geometriae Dedicata 7 Topology and its Applications 7 Acta Applicandae Mathematicae 7 Forum Mathematicum 7 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 7 Experimental Mathematics 7 Journal of the European Mathematical Society (JEMS) 7 Communications in Contemporary Mathematics 7 International Journal of Number Theory 7 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM 7 Algebraic Combinatorics 6 Journal of the Mathematical Society of Japan 6 Proceedings of the London Mathematical Society. Third Series 6 Results in Mathematics 6 Siberian Mathematical Journal 6 Journal de Mathématiques Pures et Appliquées. Neuvième Série 6 Expositiones Mathematicae 6 Geometry & Topology 6 Revista Matemática Complutense 6 Annals of Mathematics. Second Series 6 LMS Journal of Computation and Mathematics 6 Acta Mathematica Sinica. English Series 6 Proceedings of the Steklov Institute of Mathematics 6 Advances in High Energy Physics 6 European Journal of Mathematics 6 Research in Number Theory 6 SIAM Journal on Applied Algebra and Geometry 5 Discrete Applied Mathematics 5 Letters in Mathematical Physics 5 Bulletin of Mathematical Biology 5 Canadian Journal of Mathematics 5 Journal of Functional Analysis 5 Programming and Computer Software 5 Publications of the Research Institute for Mathematical Sciences, Kyoto University ...and 315 more Serials all top 5 ### Cited in 62 Fields 1,303 Algebraic geometry (14-XX) 589 Commutative algebra (13-XX) 357 Number theory (11-XX) 276 Computer science (68-XX) 194 Numerical analysis (65-XX) 170 Convex and discrete geometry (52-XX) 160 Combinatorics (05-XX) 147 Several complex variables and analytic spaces (32-XX) 146 Differential geometry (53-XX) 132 Quantum theory (81-XX) 95 Information and communication theory, circuits (94-XX) 86 Field theory and polynomials (12-XX) 78 Linear and multilinear algebra; matrix theory (15-XX) 74 Group theory and generalizations (20-XX) 68 Dynamical systems and ergodic theory (37-XX) 65 Associative rings and algebras (16-XX) 64 Ordinary differential equations (34-XX) 52 Manifolds and cell complexes (57-XX) 50 Operations research, mathematical programming (90-XX) 46 Special functions (33-XX) 46 Relativity and gravitational theory (83-XX) 45 Partial differential equations (35-XX) 44 Nonassociative rings and algebras (17-XX) 44 Statistics (62-XX) 43 Algebraic topology (55-XX) 40 Systems theory; control (93-XX) 39 Biology and other natural sciences (92-XX) 31 Mechanics of deformable solids (74-XX) 29 Mechanics of particles and systems (70-XX) 28 Category theory; homological algebra (18-XX) 28 Approximations and expansions (41-XX) 28 Geometry (51-XX) 26 Global analysis, analysis on manifolds (58-XX) 25 Real functions (26-XX) 23 Functions of a complex variable (30-XX) 22 Mathematical logic and foundations (03-XX) 22 Fluid mechanics (76-XX) 19 $$K$$-theory (19-XX) 19 Probability theory and stochastic processes (60-XX) 16 Order, lattices, ordered algebraic structures (06-XX) 15 Operator theory (47-XX) 14 Topological groups, Lie groups (22-XX) 14 Harmonic analysis on Euclidean spaces (42-XX) 13 Difference and functional equations (39-XX) 10 History and biography (01-XX) 7 Sequences, series, summability (40-XX) 7 Calculus of variations and optimal control; optimization (49-XX) 6 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 5 Integral transforms, operational calculus (44-XX) 4 General and overarching topics; collections (00-XX) 4 Functional analysis (46-XX) 4 Mathematics education (97-XX) 3 Measure and integration (28-XX) 3 Abstract harmonic analysis (43-XX) 3 General topology (54-XX) 3 Classical thermodynamics, heat transfer (80-XX) 3 Statistical mechanics, structure of matter (82-XX) 2 General algebraic systems (08-XX) 2 Potential theory (31-XX) 2 Optics, electromagnetic theory (78-XX) 2 Astronomy and astrophysics (85-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.
2022-05-19T02:55:07
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https://par.nsf.gov/biblio/10093016-quantum-state-control-chemical-reactivity-transition-metal-vanadium-cation-carbon-dioxide-activation
Quantum state control on the chemical reactivity of a transition metal vanadium cation in carbon dioxide activation By combining a newly developed two-color laser pulsed field ionization-photoion (PFI-PI) source and a double-quadrupole–double-octopole (DQDO) mass spectrometer, we investigated the integral cross sections ( σ s) of the vanadium cation (V + ) toward the activation of CO 2 in the center-of-mass kinetic energy ( E cm ) range from 0.1 to 10.0 eV. Here, V + was prepared in single spin–orbit levels of its lowest electronic states, a 5 D J ( J = 0–4), a 5 F J ( J = 1–5), and a 3 F J ( J = 2–4), with well-defined kinetic energies. For both product channels VO + + CO and VCO + + O identified, V + (a 3 F 2,3 ) is found to be greatly more reactive than V + (a 5 D 0,2 ) and V + (a 5 F 1,2 ), suggesting that the V + + CO 2 reaction system mainly proceeds via a “weak quintet-to-triplet spin-crossing” mechanism favoring the conservation of total electron spins. In addition, no J -state dependence was observed. The distinctive structures of the quantum electronic state selected integral cross sections observed as a function of E cm and the electronic state of the more » Authors: ; ; Award ID(s): Publication Date: NSF-PAR ID: 10093016 Journal Name: Physical Chemistry Chemical Physics Volume: 21 Issue: 13 Page Range or eLocation-ID: 6868 to 6877 ISSN: 1463-9076
2023-03-22T07:29:39
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https://nroer.gov.in/55ab34ff81fccb4f1d806025/file/5887230e472d4a1fef8114e8
### Reaction Of Lead Nitrate With Potassium Iodide: The aim of this experiment is to react lead nitrate with potassium iodide. Let's see what happens.
2021-05-12T04:14:46
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https://zbmath.org/authors/?q=ai%3Alee.john-m
## Lee, John M. Compute Distance To: Author ID: lee.john-m Published as: Lee, John M.; Lee, John M; Lee, John; Lee, J. more...less Homepage: http://www.math.washington.edu/~lee/ External Links: MGP · Wikidata · GND · IdRef Documents Indexed: 51 Publications since 1981, including 8 Books 1 Further Contribution Co-Authors: 17 Co-Authors with 23 Joint Publications 467 Co-Co-Authors all top 5 ### Co-Authors 14 single-authored 5 Isenberg, James A. 5 Stavrov Allen, Iva 4 Jerison, David S. 3 Allen, Paul T. 2 Asner, Liya 2 Cheng, Jih-Hsin 2 Garfield, Peter M. 2 Graham, C. Robin 2 Melrose, Richard Burt 2 Nordsletten, David A. 2 Smith, Nicolas P. 1 Akahori, Takao 1 Bahuaud, Eric 1 Bright, Ido 1 Burdzy, Krzysztof 1 Carr-White, G. 1 Chabiniok, Radomír 1 Chang, Jow-Ran 1 Chruściel, Piotr Tadeusz 1 Colton, Simon 1 Cookson, A. N. 1 Delay, Erwann 1 Fan, Yanan 1 Forest, Craig R. 1 Guérit, Stéphanie 1 Hadjicharalambous, Myrianthi 1 Jacques, Laurent 1 Kerfoot, E. 1 King, Andrew P. 1 Kolb, Ilya 1 Manouzi, Hassan 1 Michler, Christian 1 Parker, Thomas H. 1 Pease, Alison 1 Peressutti, D. 1 Razavi, Reza 1 Rigneault, Hervé 1 Rozell, Christopher J. 1 Sammut, E. 1 Sisson, Scott A. 1 Sitte, Joaquin 1 Sivankutty, Siddharth 1 Skinner, Dale N. 1 Smaill, Alan 1 Sochi, Taha 1 Uhlmann, Gunther Alberto 1 Vigueras, G. all top 5 ### Serials 6 Graduate Texts in Mathematics 3 Journal of Differential Geometry 2 American Journal of Mathematics 2 Duke Mathematical Journal 2 Communications in Analysis and Geometry 2 Annales Henri Poincaré 1 Classical and Quantum Gravity 1 Computer Methods in Applied Mechanics and Engineering 1 Communications on Pure and Applied Mathematics 1 Journal of Mathematical Analysis and Applications 1 Theory of Probability and its Applications 1 Acta Mathematica 1 Advances in Mathematics 1 Archiv der Mathematik 1 Illinois Journal of Mathematics 1 Journal of Geometry 1 Memoirs of the American Mathematical Society 1 Michigan Mathematical Journal 1 Pacific Journal of Mathematics 1 Proceedings of the American Mathematical Society 1 Transactions of the American Mathematical Society 1 Computational Mechanics 1 Journal of the American Mathematical Society 1 Machine Learning 1 The Journal of Geometric Analysis 1 Bulletin of the American Mathematical Society. New Series 1 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 1 Computational Statistics and Data Analysis 1 SIAM Journal on Scientific Computing 1 RIMS Kokyuroku 1 IEEE Transactions on Image Processing 1 Journal of Statistical Mechanics: Theory and Experiment 1 SIAM Journal on Imaging Sciences 1 Pure and Applied Undergraduate Texts all top 5 ### Fields 22 Differential geometry (53-XX) 14 Several complex variables and analytic spaces (32-XX) 10 Partial differential equations (35-XX) 7 Global analysis, analysis on manifolds (58-XX) 5 Manifolds and cell complexes (57-XX) 4 Mechanics of deformable solids (74-XX) 4 Relativity and gravitational theory (83-XX) 3 Probability theory and stochastic processes (60-XX) 2 General and overarching topics; collections (00-XX) 2 Potential theory (31-XX) 2 Calculus of variations and optimal control; optimization (49-XX) 2 Algebraic topology (55-XX) 2 Statistics (62-XX) 2 Numerical analysis (65-XX) 2 Computer science (68-XX) 2 Information and communication theory, circuits (94-XX) 1 Mathematical logic and foundations (03-XX) 1 Real functions (26-XX) 1 Measure and integration (28-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Functional analysis (46-XX) 1 Operator theory (47-XX) 1 Geometry (51-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Biology and other natural sciences (92-XX) ### Citations contained in zbMATH Open 37 Publications have been cited 2,192 times in 1,614 Documents Cited by Year The Yamabe problem. Zbl 0633.53062 Lee, John M.; Parker, Thomas H. 1987 Introduction to smooth manifolds. 2nd revised ed. Zbl 1258.53002 Lee, John M. 2013 The Yamabe problem on CR manifolds. Zbl 0661.32026 Jerison, David; Lee, John M 1987 Einstein metrics with prescribed conformal infinity on the ball. Zbl 0765.53034 Graham, C. Robin; Lee, John M. 1991 Riemannian manifolds: an introduction to curvature. Zbl 0905.53001 Lee, John M. 1997 Extremals for the Sobolev inequality on the Heisenberg group and the CR Yamabe problem. Zbl 0634.32016 Jerison, David; Lee, John M. 1988 Pseudo-Einstein structures on CR manifolds. Zbl 0638.32019 Lee, John M. 1988 Determining anisotropic real-analytic conductivities by boundary measurements. Zbl 0702.35036 Lee, John M.; Uhlmann, Gunther 1989 The Fefferman metric and pseudohermitian invariants. Zbl 0595.32026 Lee, John M. 1986 Intrinsic CR normal coordinates and the CR Yamabe problem. Zbl 0671.32016 Jerison, David; Lee, John M. 1989 Smooth solutions of degenerate Laplacians on strictly pseudoconvex domains. Zbl 0699.35112 Graham, C. Robin; Lee, John M. 1988 Boundary behaviour of the complex Monge-Ampère equation. Zbl 0496.35042 Lee, John; Melrose, Richard 1982 Boundary regularity of conformally compact Einstein metrics. Zbl 1088.53031 Chruściel, Piotr T.; Delay, Erwann; Lee, John M.; Skinner, Dale N. 2005 Introduction to topological manifolds. Zbl 0956.57001 Lee, John M. 2000 Introduction to smooth manifolds. Zbl 1030.53001 Lee, John M. 2002 Fredholm operators and Einstein metrics on conformally compact manifolds. Zbl 1112.53002 Lee, John M. 2006 The spectrum of an asymptotically hyperbolic Einstein manifold. Zbl 0934.58029 Lee, John M. 1995 Introduction to Riemannian manifolds. 2nd edition. Zbl 1409.53001 Lee, John M. 2018 Finite element approximations of stochastic optimal control problems constrained by stochastic elliptic PDEs. Zbl 1227.65011 Hou, L. S.; Lee, J.; Manouzi, H. 2011 Introduction to topological manifolds. 2nd ed. Zbl 1209.57001 Lee, John M. 2011 The Burns-Epstein invariant and deformation of CR structures. Zbl 0704.53028 Cheng, Jih-Hsin; Lee, John M. 1990 Deformation theory of 5-dimensional CR structures and the Rumin complex. Zbl 1065.32018 Akahori, Takao; Garfield, Peter M.; Lee, John M. 2002 CR manifolds with noncompact connected automorphism groups. Zbl 0859.32003 Lee, John M. 1996 Characterization of matrix damage in metal matrix composites under transverse loads. Zbl 0915.73043 Lee, J.; Mal, A. 1998 A local slice theorem for 3-dimensional CR structures. Zbl 0841.32004 Cheng, Jih-Hsin; Lee, John M. 1995 Multiphysics computational modeling in $$\mathcal{C}\mathbf{Heart}$$. Zbl 1358.92015 Lee, J.; Cookson, A.; Roy, I.; Kerfoot, E.; Asner, L.; Vigueras, G.; Sochi, T.; Deparis, S.; Michler, C.; Smith, N. P.; Nordsletten, D. A. 2016 A subelliptic, nonlinear eigenvalue problem and scalar curvature on CR manifolds. Zbl 0577.53035 Jerison, David; Lee, John M. 1984 Asymptotic gluing of asymptotically hyperbolic solutions to the Einstein constraint equations. Zbl 1208.83032 Isenberg, James; Lee, John M.; Allen, Iva Stavrov 2010 The Rumin complex on CR manifolds. Zbl 0946.32020 Garfield, Peter M.; Lee, John M. 1998 Weakly asymptotically hyperbolic manifolds. Zbl 1381.53058 Allen, Paul T.; Isenberg, James; Lee, John M.; Stavrov Allen, Iva 2018 The shear-free condition and constant-mean-curvature hyperboloidal initial data. Zbl 1344.83010 Allen, Paul T.; Isenberg, James; Lee, John M.; Stavrov Allen, Iva 2016 Bayesian threshold selection for extremal models using measures of surprise. Zbl 06984156 Lee, J.; Fan, Y.; Sisson, S. A. 2015 Patient-specific modeling for left ventricular mechanics using data-driven boundary energies. Zbl 1439.74191 Asner, L.; Hadjicharalambous, M.; Chabiniok, R.; Peressutti, D.; Sammut, E.; Wong, J.; Carr-White, G.; Razavi, R.; King, A. P.; Smith, N.; Lee, J.; Nordsletten, D. 2017 Axiomatic geometry. Zbl 1298.51003 Lee, John M. 2013 Free boundary problems and biological systems with selection rules. Zbl 1435.35193 Lee, J. M. 2020 Multiplicative functional for reflected Brownian motion via deterministic ODE. Zbl 1271.60089 Burdzy, Krzysztof; Lee, John M. 2010 A note on flux integrals over smooth regular domains. Zbl 1317.58013 Bright, Ido; Lee, John M. 2014 Free boundary problems and biological systems with selection rules. Zbl 1435.35193 Lee, J. M. 2020 Introduction to Riemannian manifolds. 2nd edition. Zbl 1409.53001 Lee, John M. 2018 Weakly asymptotically hyperbolic manifolds. Zbl 1381.53058 Allen, Paul T.; Isenberg, James; Lee, John M.; Stavrov Allen, Iva 2018 Patient-specific modeling for left ventricular mechanics using data-driven boundary energies. Zbl 1439.74191 Asner, L.; Hadjicharalambous, M.; Chabiniok, R.; Peressutti, D.; Sammut, E.; Wong, J.; Carr-White, G.; Razavi, R.; King, A. P.; Smith, N.; Lee, J.; Nordsletten, D. 2017 Multiphysics computational modeling in $$\mathcal{C}\mathbf{Heart}$$. Zbl 1358.92015 Lee, J.; Cookson, A.; Roy, I.; Kerfoot, E.; Asner, L.; Vigueras, G.; Sochi, T.; Deparis, S.; Michler, C.; Smith, N. P.; Nordsletten, D. A. 2016 The shear-free condition and constant-mean-curvature hyperboloidal initial data. Zbl 1344.83010 Allen, Paul T.; Isenberg, James; Lee, John M.; Stavrov Allen, Iva 2016 Bayesian threshold selection for extremal models using measures of surprise. Zbl 06984156 Lee, J.; Fan, Y.; Sisson, S. A. 2015 A note on flux integrals over smooth regular domains. Zbl 1317.58013 Bright, Ido; Lee, John M. 2014 Introduction to smooth manifolds. 2nd revised ed. Zbl 1258.53002 Lee, John M. 2013 Axiomatic geometry. Zbl 1298.51003 Lee, John M. 2013 Finite element approximations of stochastic optimal control problems constrained by stochastic elliptic PDEs. Zbl 1227.65011 Hou, L. S.; Lee, J.; Manouzi, H. 2011 Introduction to topological manifolds. 2nd ed. Zbl 1209.57001 Lee, John M. 2011 Asymptotic gluing of asymptotically hyperbolic solutions to the Einstein constraint equations. Zbl 1208.83032 Isenberg, James; Lee, John M.; Allen, Iva Stavrov 2010 Multiplicative functional for reflected Brownian motion via deterministic ODE. Zbl 1271.60089 Burdzy, Krzysztof; Lee, John M. 2010 Fredholm operators and Einstein metrics on conformally compact manifolds. Zbl 1112.53002 Lee, John M. 2006 Boundary regularity of conformally compact Einstein metrics. Zbl 1088.53031 Chruściel, Piotr T.; Delay, Erwann; Lee, John M.; Skinner, Dale N. 2005 Introduction to smooth manifolds. Zbl 1030.53001 Lee, John M. 2002 Deformation theory of 5-dimensional CR structures and the Rumin complex. Zbl 1065.32018 Akahori, Takao; Garfield, Peter M.; Lee, John M. 2002 Introduction to topological manifolds. Zbl 0956.57001 Lee, John M. 2000 Characterization of matrix damage in metal matrix composites under transverse loads. Zbl 0915.73043 Lee, J.; Mal, A. 1998 The Rumin complex on CR manifolds. Zbl 0946.32020 Garfield, Peter M.; Lee, John M. 1998 Riemannian manifolds: an introduction to curvature. Zbl 0905.53001 Lee, John M. 1997 CR manifolds with noncompact connected automorphism groups. Zbl 0859.32003 Lee, John M. 1996 The spectrum of an asymptotically hyperbolic Einstein manifold. Zbl 0934.58029 Lee, John M. 1995 A local slice theorem for 3-dimensional CR structures. Zbl 0841.32004 Cheng, Jih-Hsin; Lee, John M. 1995 Einstein metrics with prescribed conformal infinity on the ball. Zbl 0765.53034 Graham, C. Robin; Lee, John M. 1991 The Burns-Epstein invariant and deformation of CR structures. Zbl 0704.53028 Cheng, Jih-Hsin; Lee, John M. 1990 Determining anisotropic real-analytic conductivities by boundary measurements. Zbl 0702.35036 Lee, John M.; Uhlmann, Gunther 1989 Intrinsic CR normal coordinates and the CR Yamabe problem. Zbl 0671.32016 Jerison, David; Lee, John M. 1989 Extremals for the Sobolev inequality on the Heisenberg group and the CR Yamabe problem. Zbl 0634.32016 Jerison, David; Lee, John M. 1988 Pseudo-Einstein structures on CR manifolds. Zbl 0638.32019 Lee, John M. 1988 Smooth solutions of degenerate Laplacians on strictly pseudoconvex domains. Zbl 0699.35112 Graham, C. Robin; Lee, John M. 1988 The Yamabe problem. Zbl 0633.53062 Lee, John M.; Parker, Thomas H. 1987 The Yamabe problem on CR manifolds. Zbl 0661.32026 Jerison, David; Lee, John M 1987 The Fefferman metric and pseudohermitian invariants. Zbl 0595.32026 Lee, John M. 1986 A subelliptic, nonlinear eigenvalue problem and scalar curvature on CR manifolds. Zbl 0577.53035 Jerison, David; Lee, John M. 1984 Boundary behaviour of the complex Monge-Ampère equation. Zbl 0496.35042 Lee, John; Melrose, Richard 1982 all top 5 ### Cited by 1,876 Authors 22 Dragomir, Sorin 22 Lassas, Matti J. 21 Uhlmann, Gunther Alberto 19 Yang, Paul C. P. 18 Chang, Shu-Cheng 16 Delay, Erwann 16 Ho, Pak Tung 14 Case, Jeffrey S. 14 Gover, Ashwin Rod 13 Barletta, Elisabetta 13 Chiu, Hung-Lin 13 Lu, Guozhen 12 Cheng, Jih-Hsin 12 Kurylëv, Yaroslav Vadimovich 11 Gursky, Matthew J. 11 Humbert, Emmanuel 11 Vassilev, Dimiter N. 10 Akutagawa, Kazuo 10 Ammann, Bernd Eberhard 10 Herzlich, Marc 10 Ivanov, Stefan P. 10 Li, Songying 10 Mazzeo, Rafe R. 9 Chang, Sun-Yung Alice 9 Chruściel, Piotr Tadeusz 9 Gamara, Najoua 9 Kamran, Niky 9 Lee, John M. 9 Malchiodi, Andrea 9 Salo, Mikko 9 Viaclovsky, Jeff A. 8 Bahuaud, Eric 8 Dương Ngọc Sơn 8 Graham, C. Robin 8 Leitner, Felipe 8 Raulot, Simon 8 Uguzzoni, Francesco 7 Biquard, Olivier 7 Chtioui, Hichem 7 Daudé, Thierry 7 Gicquaud, Romain 7 Große, Nadine 7 Han, Yazhou 7 Liu, Genqian 7 Maalaoui, Ali 7 Nicoleau, François 7 Shi, Yuguang 7 Wang, Wei 6 Akahori, Takao 6 Bonfiglioli, Andrea 6 Čap, Andreas 6 Dong, Yuxin 6 Guillarmou, Colin 6 Kim, Seunghyeok 6 LeBrun, Claude R. 6 Li, YanYan 6 Loiudice, Annunziata 6 Marugame, Taiji 6 Matsumoto, Yoshihiko 6 Oksanen, Lauri 6 Premoselli, Bruno 6 Qing, Jie 6 Ren, Yibin 6 Vasy, András 6 Wang, Fang 6 Wei, Juncheng 6 Yacoub, Ridha 6 Yavari, Arash 5 Belishev, Mikhail Igorevitch 5 Branson, Thomas Patrick 5 Carlotto, Alessandro 5 Curry, Sean N. 5 Ebenfelt, Peter 5 Fu, Haiping 5 Han, Qing 5 Han, Yingbo 5 Hintz, Peter 5 Krupchyk, Katsiaryna 5 Mayer, Martin 5 Miura, Tatsu-Hiko 5 Muratori, Matteo 5 Niu, Pengcheng 5 Perrone, Domenico 5 Tralli, Giulio 5 Wang, Xiaodong 5 Zhu, Meijun 4 Bahoura, Samy Skander 4 Boughazi, Hichem 4 Breiding, Paul 4 Chang, Der-Chen E. 4 Chen, Xuezhang 4 Dahl, Mattias 4 Friedrich, Helmut 4 Gaburro, Romina 4 Ge, Huabin 4 Ge, Yuxin 4 González, María del Mar 4 Hang, Fengbo 4 Hermann, Andreas 4 Hirachi, Kengo ...and 1,776 more Authors all top 5 ### Cited in 346 Serials 71 The Journal of Geometric Analysis 61 Advances in Mathematics 58 Calculus of Variations and Partial Differential Equations 49 Communications in Mathematical Physics 45 Differential Geometry and its Applications 44 Journal of Geometry and Physics 43 Journal of Functional Analysis 40 Transactions of the American Mathematical Society 32 Annals of Global Analysis and Geometry 30 Journal of Mathematical Analysis and Applications 29 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 28 Communications in Partial Differential Equations 27 Journal of Differential Equations 24 Mathematische Annalen 22 Duke Mathematical Journal 22 Proceedings of the American Mathematical Society 20 Annales Henri Poincaré 18 Mathematische Zeitschrift 18 Comptes Rendus. Mathématique. Académie des Sciences, Paris 17 Journal de Mathématiques Pures et Appliquées. Neuvième Série 15 Journal of Mathematical Physics 15 Communications in Contemporary Mathematics 15 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 14 Annales de l’Institut Fourier 13 Archive for Rational Mechanics and Analysis 13 Annali di Matematica Pura ed Applicata. Serie Quarta 13 Pacific Journal of Mathematics 12 Letters in Mathematical Physics 12 Automatica 12 International Journal of Mathematics 11 Bulletin des Sciences Mathématiques 11 Journal of the European Mathematical Society (JEMS) 10 Acta Mathematica Sinica. English Series 9 Classical and Quantum Gravity 9 Geometriae Dedicata 9 Inventiones Mathematicae 9 Journal für die Reine und Angewandte Mathematik 9 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 9 Geometric and Functional Analysis. GAFA 9 Journal of High Energy Physics 9 Inverse Problems and Imaging 8 Inverse Problems 8 Manuscripta Mathematica 8 Advanced Nonlinear Studies 8 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V 8 Science China. Mathematics 7 Topology and its Applications 7 Journal of the American Mathematical Society 7 SIAM Journal on Mathematical Analysis 7 Discrete and Continuous Dynamical Systems 6 Mathematics of Computation 6 The Annals of Statistics 6 Journal of the Mathematical Society of Japan 6 Mathematische Nachrichten 6 Memoirs of the American Mathematical Society 6 SIAM Journal on Matrix Analysis and Applications 6 Science in China. Series A 6 Bulletin of the American Mathematical Society. New Series 6 NoDEA. Nonlinear Differential Equations and Applications 6 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 6 Journal of Spectral Theory 6 Bulletin of Mathematical Sciences 5 General Relativity and Gravitation 5 Mathematical Notes 5 Nuclear Physics. B 5 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 5 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 5 SIAM Journal on Optimization 5 SIAM Journal on Scientific Computing 5 Electronic Research Announcements of the American Mathematical Society 5 Annals of Mathematics. Second Series 5 Communications on Pure and Applied Analysis 5 Advances in Calculus of Variations 5 Analysis and Mathematical Physics 4 Communications on Pure and Applied Mathematics 4 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 4 Compositio Mathematica 4 Information Sciences 4 Tôhoku Mathematical Journal. Second Series 4 Pattern Recognition 4 SIAM Journal on Applied Mathematics 4 Mathematical Programming. Series A. Series B 4 Journal of Mathematical Imaging and Vision 4 Journal of Nonlinear Science 4 Journal of Mathematical Sciences (New York) 4 Geometry & Topology 4 Journal of Dynamical and Control Systems 4 Foundations of Computational Mathematics 4 Journal of the Institute of Mathematics of Jussieu 4 International Journal of Geometric Methods in Modern Physics 4 Discrete and Continuous Dynamical Systems. Series S 4 Complex Manifolds 4 Geometric Flows 3 Computer Methods in Applied Mechanics and Engineering 3 Israel Journal of Mathematics 3 Journal d’Analyse Mathématique 3 Journal of Computational Physics 3 ZAMP. Zeitschrift für angewandte Mathematik und Physik 3 Acta Mathematica 3 Archiv der Mathematik ...and 246 more Serials all top 5 ### Cited in 57 Fields 782 Differential geometry (53-XX) 541 Partial differential equations (35-XX) 423 Global analysis, analysis on manifolds (58-XX) 243 Several complex variables and analytic spaces (32-XX) 118 Relativity and gravitational theory (83-XX) 76 Quantum theory (81-XX) 70 Manifolds and cell complexes (57-XX) 57 Calculus of variations and optimal control; optimization (49-XX) 54 Dynamical systems and ergodic theory (37-XX) 54 Functional analysis (46-XX) 53 Numerical analysis (65-XX) 42 Probability theory and stochastic processes (60-XX) 39 Topological groups, Lie groups (22-XX) 38 Computer science (68-XX) 36 Mechanics of particles and systems (70-XX) 36 Systems theory; control (93-XX) 35 Operator theory (47-XX) 34 Algebraic geometry (14-XX) 32 Ordinary differential equations (34-XX) 29 Mechanics of deformable solids (74-XX) 28 Real functions (26-XX) 28 Statistics (62-XX) 26 Fluid mechanics (76-XX) 25 Operations research, mathematical programming (90-XX) 24 Algebraic topology (55-XX) 23 Functions of a complex variable (30-XX) 22 General topology (54-XX) 20 Abstract harmonic analysis (43-XX) 20 Optics, electromagnetic theory (78-XX) 20 Biology and other natural sciences (92-XX) 19 Convex and discrete geometry (52-XX) 18 Linear and multilinear algebra; matrix theory (15-XX) 18 Potential theory (31-XX) 17 Information and communication theory, circuits (94-XX) 14 Statistical mechanics, structure of matter (82-XX) 13 Harmonic analysis on Euclidean spaces (42-XX) 12 Group theory and generalizations (20-XX) 12 Integral equations (45-XX) 11 Combinatorics (05-XX) 11 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 8 Number theory (11-XX) 7 Nonassociative rings and algebras (17-XX) 7 Measure and integration (28-XX) 7 Special functions (33-XX) 7 Geometry (51-XX) 6 Category theory; homological algebra (18-XX) 6 Approximations and expansions (41-XX) 4 Integral transforms, operational calculus (44-XX) 3 Order, lattices, ordered algebraic structures (06-XX) 3 Difference and functional equations (39-XX) 3 Classical thermodynamics, heat transfer (80-XX) 3 Geophysics (86-XX) 2 Commutative algebra (13-XX) 2 Associative rings and algebras (16-XX) 1 General and overarching topics; collections (00-XX) 1 Mathematical logic and foundations (03-XX) 1 Mathematics education (97-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.
2022-10-07T22:11:36
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http://www.scstatehouse.gov/sess119_2011-2012/sj11/20110726.htm
South Carolina General Assembly 119th Session, 2011-2012 Journal of the Senate Tuesday, July 26, 2011 (Statewide Session) Indicates Matter Stricken Indicates New Matter The Senate assembled at 2:00 P.M., the hour to which it stood adjourned, and was called to order by the PRESIDENT. A quorum being present, the proceedings were opened with a devotion by the Chaplain as follows: Almost hoping beyond hope, Hosea declared to his people: Bind Your heart with me as we pray, friends: Glorious Lord, these faithful servants and their aides have again returned to this Senate Chamber. Strengthen them all as they carry on with their work on behalf of this State. Moreover, give each Senator the sort of wisdom that You alone can provide; may their decisions enrich the life of every South Carolinian. And as always, dear Lord, be with our women and men in uniform who themselves serve in so many places around the globe, often in harm's way. Truly, may we all continue to honor You through everything we say and do in this place! In Your loving name we pray, O Lord. Amen. The PRESIDENT called for Petitions, Memorials, Presentments of Grand Juries and such like papers. Leave of Absence At 2:15 P.M., Senator BRIGHT requested a leave of absence for the balance of the day. S. 274 (Word version)     Sen. Cromer INTRODUCTION OF BILLS AND RESOLUTIONS The following were introduced: S. 995 (Word version) -- Senator Peeler: A SENATE RESOLUTION TO RECOGNIZE THE TIMKEN GAFFNEY BEARING PLANT UPON ITS FORTIETH ANNIVERSARY AND TO WISH IT CONTINUED SUCCESS IN THE PALMETTO STATE. l:\s-res\hsp\026timk.mrh.hsp.docx S. 996 (Word version) -- Senator Leatherman: A SENATE RESOLUTION TO HONOR AND CONGRATULATE BREE BOYCE UPON BEING CROWNED MISS SOUTH CAROLINA 2011 AND TO WISH HER WELL IN ALL HER FUTURE ENDEAVORS. l:\s-res\hkl\009boyc.mrh.hkl.docx S. 997 (Word version) -- Senator Nicholson: A SENATE RESOLUTION TO RECOGNIZE OLD MOUNT ZION BAPTIST CHURCH OF THE EPWORTH COMMUNITY IN GREENWOOD COUNTY ON THE OCCASION OF ITS HISTORIC ONE HUNDRED FIFTIETH ANNIVERSARY AND TO COMMEND THE CHURCH FOR A CENTURY AND A HALF OF SERVICE TO THE COMMUNITY. l:\council\bills\swb\6334cm11.docx S. 998 (Word version) -- Senator Lourie: A SENATE RESOLUTION TO HONOR JAMES HOWARD "JIM" FOSTER FOR HIS TWO DECADES OF DEDICATED SERVICE AS SOUTH CAROLINA DEPARTMENT OF EDUCATION DIRECTOR OF COMMUNICATIONS, TO CONGRATULATE HIM ON HIS NEW POSITION AS DIRECTOR FOR SCHOOL AND COMMUNITY SERVICES WITH THE BEAUFORT COUNTY SCHOOL DISTRICT, AND TO WISH HIM MUCH SUCCESS IN ALL HIS FUTURE ENDEAVORS. l:\council\bills\rm\1301ab11.docx RATIFICATION OF ACTS Pursuant to an invitation the Honorable Speaker and House of Representatives appeared in the Senate Chamber on July 26, 2011, at 2:15 P.M. and the following Acts were ratified: L:\COUNCIL\ACTS\172DG11.DOCX (R110, H. 3792 (Word version)) -- Rep. Rutherford: AN ACT TO AMEND SECTION 50-21-85, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE CONDITIONS UPON WHICH A PERSON MAY OPERATE A VESSEL DISPLAYING, REFLECTING, OR FLASHING A BLUE LIGHT, SO AS TO REVISE THE CIRCUMSTANCES IN WHICH A PERSON MAY OPERATE A VESSEL WHILE DISPLAYING A BLUE LIGHT, AND TO REVISE THE PENALTY PROVISION. L:\COUNCIL\ACTS\3792CM11.DOCX RECESS At 2:17 P.M., Senator McCONNELL, moved that the Senate stand in recess for no more than thirty minutes or upon receipt of H. 3992 from the House of Representatives, whichever occurred first. The motion to recede was adopted. At 2:52 P.M., the Senate reconvened. RECESS At 2:53 P.M., on motion of Senator McCONNELL, the Senate receded from business not to exceed thirty minutes. At 3:24 P.M., the Senate resumed. On motion of Senator McCONNELL, the Senate agreed to waive the provisions of Rule 32A requiring H. 3992 to be printed on the Calendar. The Bill was ordered placed in the category of Bills Returned from the House and would be taken up for consideration when that category was reached in the order of the day. RECOMMITTED S. 814 (Word version) -- Senators McConnell, Ford, L. Martin, Hutto, Malloy, Cleary and Shoopman: A BILL TO AMEND SECTION 1-1-715, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO ADOPTION OF THE UNITED STATES CENSUS, SO AS TO ADOPT THE UNITED STATES CENSUS OF 2010 AS THE TRUE AND CORRECT ENUMERATION OF INHABITANTS OF THIS STATE; TO ADD SECTION 7-19-35, SO AS TO ESTABLISH SEVEN ELECTION DISTRICTS FROM WHICH MEMBERS OF CONGRESS FOR SOUTH CAROLINA ARE ELECTED COMMENCING WITH THE 2012 GENERAL ELECTION; TO REPEAL SECTION 7-19-40, AS AMENDED, RELATING TO CONGRESSIONAL DISTRICTS FROM WHICH SOUTH CAROLINA MEMBERS OF CONGRESS WERE FORMERLY ELECTED; AND TO JOINTLY DESIGNATE THE PRESIDENT PRO TEMPORE OF THE SENATE AND THE SPEAKER OF THE HOUSE OF REPRESENTATIVES AS THE APPROPRIATE OFFICIALS OF THE SUBMITTING AUTHORITY TO MAKE THE REQUIRED SUBMISSION OF THE CONGRESSIONAL REAPPORTIONMENT PLAN TO THE UNITED STATES DEPARTMENT OF JUSTICE UNDER THE VOTING RIGHTS ACT. Senator McCONNELL asked unanimous consent to commit the Bill to the Committee on Judiciary. There was no objection and the Bill was recommitted to the Committee on Judiciary. CONCURRENCE H. 3992 (Word version) -- Reps. Harrell, Lucas, Harrison, Clemmons, Barfield, Cooper, Hardwick, Owens, Sandifer, G.R. Smith, J.R. Smith, White, Bingham and Erickson: A BILL TO AMEND SECTION 1-1-715, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO ADOPTION OF THE UNITED STATES CENSUS, SO AS TO ADOPT THE UNITED STATES CENSUS OF 2010 AS THE TRUE AND CORRECT ENUMERATION OF INHABITANTS OF THIS STATE; TO ADD SECTION 7-19-35, SO AS TO ESTABLISH SEVEN ELECTION DISTRICTS FROM WHICH MEMBERS OF CONGRESS FOR SOUTH CAROLINA ARE ELECTED COMMENCING WITH THE 2012 GENERAL ELECTION; TO REPEAL SECTION 7-19-40, AS AMENDED, RELATING TO CONGRESSIONAL DISTRICTS FROM WHICH SOUTH CAROLINA MEMBERS OF CONGRESS WERE FORMERLY ELECTED; TO JOINTLY DESIGNATE THE PRESIDENT PRO TEMPORE OF THE SENATE AND THE SPEAKER OF THE HOUSE OF REPRESENTATIVES AS THE APPROPRIATE OFFICIALS OF THE SUBMITTING AUTHORITY TO MAKE THE REQUIRED SUBMISSION OF THE CONGRESSIONAL REAPPORTIONMENT PLAN TO THE UNITED STATES DEPARTMENT OF JUSTICE UNDER THE VOTING RIGHTS ACT; AND TO PROVIDE THAT A MEMBER OF ANY BOARD, COMMISSION, OR COMMITTEE REPRESENTING A CONGRESSIONAL DISTRICT, WHOSE RESIDENCY IS TRANSFERRED TO ANOTHER DISTRICT BY THIS ACT, MAY SERVE, OR CONTINUE TO SERVE HIS TERM IN OFFICE; HOWEVER, THE APPOINTING OR ELECTING AUTHORITY MAY ADD AN ADDITIONAL MEMBER ON A BOARD, COMMISSION, OR COMMITTEE WHICH LOSES A RESIDENT MEMBER. The House returned the Bill with amendments. Senator McCONNELL explained the House amendments. Senator MALLOY spoke on the House amendments. Remarks by Senator MALLOY Thank you, Mr. PRESIDENT. Gentlemen of the Senate, this is one of the few opportunities that many of us get in a lifetime. In almost five decades of my life now, in watching this Senate from my Senate chair for almost the last decade, we have seen a lot of congratulations to our State for what has been done as far as creating and having enough population to have a new Congressional seat. What happened in this Congressional plan is just totally different. And, I realized that there was a need for this Senate to come together. For many of us that are here now, I hope that we see this moment again as our State continues to move forward toward prosperity. Hopefully with this growth, South Carolina will become a larger player on the national scene and that it will signify progress and development in our State to our Congressional folks. We'll have another task at that particular time. But this task now will last a decade. My daddy always told me that a generation was generally 18 years. I didn't realize that. I thought it would be longer. But for the next generation, a child born today will have to actually take the remnants -- be a beneficiary, and get the residual results of what we do here going forward. We have long known that it depends on where you live and what's going on around you. The Pee Dee area is vastly different than the coast. It just is. It's a manufacturing and farming area. The folks that grew up in my hometown of Chesterfield -- you all see it on the map -- it is a big area. The area is almost as large as Horry County in land mass and the Senator from Kershaw and Chesterfield represents them. They have only 40 some odd thousand people in the whole county. But Horry County has almost 270,000 people. A child going home from college may go over to McLeod Farms and get a job at the peach orchard. A child going home from college may go over to Horry County and may go to work on a golf course, or may work in a coastal area. The person with a summer job will end up doing what they can do in the manufacturing field, in a family business. It's just different in the areas where the area of Horry is 270,000. I submit to you as I go through the numbers and as I look at that area, it is larger than Marion, Dillon, Marlboro and Chesterfield Counties combined. Horry and Georgetown -- those two little areas on the coast -- will make up half of the population in a Congressional seat. Many of you know that I've been fortunate to be able to practice law and be a lawyer. In the law, there's a lady that we pay a lot of attention to -- Lady Justice. What Lady Justice does is look at things with a blindfold on. You are sitting in a jury and they are the judges of the facts. So that way you don't have bias. You don't have prejudice. You take your ordinary experience and you are supposed to look at things objectively as they come from the witness chair. It's a great part of our system. This is the process. We have the Voting Rights Act in South Carolina because of our past behavior. What that means is they are simply looking over our shoulders to see what we do. And, I appreciate the communities of interest. I appreciate everybody watching the same television station or whatever. That's not what it's about. It's about whether or not we put these districts together on race and how we are counting. But the plan that just came back from the House of Representatives increased the numbers in the 6th District that's represented by Congressman Clyburn at this point in time to over 55%. There's nothing that we take a vote on in the positive that takes the number up to that amount. The numbers speak for themselves. It's some 55 odd percent. The earlier plan that we had, I think, was 52%. We'll end up having those figures because I want those to be part of the matters of the record that we end up having. The plan we have in the 6th District was 50.49% African American. The House amendment plan that just passed was 55.18%. The Senate plan that came out had 29.7% African American. The House plan that just came back to us was 27.64% -- a full 2 percentage points less the 1st District's from 21.06%. And that's represented, don't forget, by a young African American who happens to be a Republican -- Congressman Scott. We look at the House plan that just passed and see it has 12 precincts that are divided and the Senate plan had only eight. As I look over the plan now, I'm curious as to the debate that we had. I'm interested in obviously the areas that I represent. But as I go forward and I look to what happened over in Edgefield and Aiken, it was very important during our debate that we had those together for several reasons. But now they are going to be divided. What happened to the fact that we never wanted large counties to dominate smaller counties? And the Bill that was passed by the Senate had Horry, Charleston and Georgetown, the coastal areas and they actually balanced one another. But Greenville was split. Spartanburg was split and Richland was also split, but we're going to make Horry whole. This process is the process that it is. I want to thank the Senator on the other side of the aisle that we did engage in a discussion that was meaningful, that we had the opportunity to bring the matter to a vote. We did vote for a plan that came out of the Senate that was totally adverse to the plan that came out of the House, and by a majority of the Senate. What's unusual is -- oh, what a difference a few days makes. I have to somewhat apologize in advance. But I do have some editorials that have been published by members of this body. And it troubles me a bit, but I feel compelled to talk about them. There is an old adage in the practice of law that says, "When the facts are on your side, you argue the facts. And when the law is on your side, you argue the law. When neither is on your side, you bang the table and raise cane." There's been banging on the table and raising cane since we left the Senate the last time because I know that those that are voting for this plan cannot be happy. You cannot be happy for the same arguments that you made before we left. I can't presuppose that I would be able to represent any of the other counties because I don't know the constituents. But the numbers in the Greenville-Spartanburg area have changed considerably, where Greenville had a larger population mix in the Senate passed plan than what it has now. I don't presuppose to be able to say what's best for your county, but we know where the population growth is going. The growth is not in the areas outside of Greenville and others. And so one would think that if you were looking into the trends, how are you going to have the growth in Greenville without having that area become more dominate in the 3rd District? It's growing faster than the rest of the counties. It is. And the votes are being changed. I guess we'll see. I have been through Laurens County. I enjoy it. I go through there sometimes whenever I'm making my way up to Clemson where I love to go and watch the football games. I know that the Congressman from there is a nice young man. I don't know him well. Greenville becomes a different animal because Greenville then grows in population. You watch it. You get a Congressman from Greenville. What's going on in Oconee and Pickens, in that area? Again, I'm just making the point. I don't live there. I am not trying to end up throwing the dagger at any of my colleagues. I have great respect for each of you. But I just asked the question. Edgefield and Aiken have already been touched. Beaufort is getting ready to be divided if we vote for this plan. There was a district under the Senate plan about communities of interest. I have to read from part of an article that has been authored by my good friend, the Senator from Berkeley. In a pertinent part it says the debate centers on this plan. The first plan drew the 7th District to include Horry County and much of the Pee Dee. However, the 6th District represented by Representative Jim Clyburn meandered from the farms of Richland County some 130 miles to the Charleston peninsula and more than 150 miles from the Sumter-Florence lines to the Georgia-South Carolina border at the Savannah River. The House plan split Berkeley. It split Dorchester, Colleton and Beaufort Counties. It split at least six more counties dividing many along racial lines. In contrast, the plan that was sent by the Senate (I start back to quote), made Colleton, Beaufort, Jasper, Allendale and Barnwell Counties whole. They had a chance for a new 7th District. Coastal Georgetown remains in the 1st District while inland areas join Williamsburg in the 7th. And it goes on to say -- and I planned on obviously having this as a matter of the record that I think should be included in the Journal and end up having those posted -- so, that in the end we'll be able to end up doing just that. I want to go on and talk a little bit about what has actually happened. I have to end up quoting from an article that was put in circulation with all due respect for all of the folks that are involved in this because I realize that we are honorable people here. I have great respect for each and every person that has put themselves here to be in this Senate. I quote from the article published on July 7th by my good friend, Senator DAVIS. Basically, it says -- and the article speaks for itself -- "One of the worst kept secrets in State politics is that Myrtle Beach Representative Alan Clemmons is running for the yet unrealized 7th Congressional district. Clemmons is chairman of the house subcommittee that drafted the plan and crafted himself exactly a district he could win." That's what Clemmons did. The House created a new district stretching from Myrtle Beach into the democratic Pee Dee area -- a district created for a more moderate Republican. That House approved plan was developed in conjunction with U.S. Representative Jim Clyburn and members of his staff. It chops Beaufort County into two pieces, gutting its political relevance. I don't have to go into the entire article, but I'm just saying that's what changed. This plan is vastly similar to what we got from the House plan. Horry County and Georgetown County are still dominant in this redistricting plan. So, I submit both of these matters. And there is no need for me to go through all of these line by line, because I realize sometimes attitudes change and issues change and facts change. What I do want to tell you are a few things that absolutely did change. I want to make certain that these numbers are such that we don't understand the templates. We understand where many of the folks are. We had a couple of Congressional plans that came out of the Senate Judiciary. And I can't speak for what happened in the House of Representatives. But I will speak to what happened in the Senate Judiciary plan. In the Senate Judiciary plan -- and I'm going to focus primarily on the 6th and the 7th Districts -- the 7th District that was drafted initially, and these matters are part of the record that we have, the African American voting age population was 31.26% on this Senate staff plan number 1. Senator SHEHEEN: Senator, what you are saying is -- our Republican colleagues have led the African American vote out of the 7th Congressional District under the amendments that occurred? Senator MALLOY: I'm giving the numbers. It has gone down from my initial proposal. And basically we started out with the first proposal of 31 some odd percent and it's now down to 27.64%. Senator SHEHEEN: Senator, I want you to look at this map with me. Look at Florence County there. Florence County is split. In the lower half of Calhoun County, Darlington County, Florence County -- do you know the demographic makeup of that county at all? Do you know why that was split like that? Senator MALLOY: I do not know why it was split. But I know looking at the plans and looking at the resulting numbers, it appears that the numbers on the new plan have 27.64% where the earlier plans had a more African American population. Senator SHEHEEN: And that would dilute African American voting in the 7th Congressional District? Senator MALLOY: I think it would. Senator SHEHEEN: If you look at Sumter County, do you see that split? Part of it is in the 7th and part of it in the 6th Congressional, is that right? You would agree with me the overall take of this plan is to dilute the African American voting strength in the 7th Congressional District versus even the plans originally presented, is that right? It appears from the plans the African American vote in the 7th District has decreased and the plan that had the African American vote in Number 6 has actually increased. Would you agree with me that if you look at this map, that generally the voting strength of small and rural counties is being diluted, except for perhaps in the 3rd Congressional District? In other words, under this plan the counties that get screwed are the rural and small counties? Is that fair to say? Senator MALLOY: I think that's fair. I think that the rural areas are going to be eaten up by these larger districts. You're going to have a large district like Horry County, that is coupled with another county just like Charleston which both represent the coastal area. And the areas that you and I represent in the rural part of South Carolina, we just want representation. Senator SHEHEEN: You understand that the coastal region of Horry County is vastly different than the more upcountry rural part of Horry County? And you understand as well that the coastal portions of Horry and Georgetown Counties have much in common with the coastal portions of the rest of the State? You would love to have a Pee Dee district, wouldn't you? That was truly Pee Dee where the small town and rural communities that really make up the Pee Dee had the ability to elect a Congressman? Senator MALLOY: I think that's the only chance they will have to invigorate that area. And what is troubling is the fact that right in this district -- Horry and Georgetown comprise one-half of the district. And, in fact, they made a lot of arguments about NESA and the configuration of the counties as relates to NESA -- the North Eastern Strategic Alliance. The chair of NESA is from Williamsburg County who will lead the economic and prosperity of the Pee Dee and they put the chairman of NESA from Williamsburg County back into the 6th District. He's not even in the 7th District, which is in the Pee Dee area. Senator SHEHEEN: Williamsburg County is part of the Pee Dee? Senator MALLOY: That's correct. Senator SHEHEEN: Williamsburg County has much in common with Darlington, Chesterfield, Marlboro, Dillon, Marion and even Florence Counties -- these areas that are Pee Dee areas -- rural, small-town communities, is that correct? Senator MALLOY: Farming and manufacturing. Senator SHEHEEN: But Williamsburg County also happens to have a large African American population which Florence and Sumter have likewise and are cut out of the 7th as well. It's pretty apparent what's going on here? What's going on is our Republican colleagues want to have six of the seven Congressional Districts likely electing Republicans, is that right? Senator MALLOY: I don't know what their end game is, but I'll tell you that's what's likely to happen. Senator SHEHEEN: That's what it appears to be from the map, is that right? It appears to be from the map the way to do that is to bleed out African American voting influence in the 7th Congressional District. And from the map, that appears to be what's occurred. Senator MALLOY: It appears it has gone decreasingly lower under each plan that we have and what is growing is that the plan that we passed in the Senate by third quarters that we sent to the House of Representatives, the numbers in the districts have changed but the numbers are different. So it has been decreased. But the numbers in the only majority district that was there has actually increased. And I want to make a point. The issue is not to create, in my view, majority-minority districts. The ACLU drafted a plan that can't be ignored which created two majority-minority districts. So, what they showed us is that it can be done. The issue is what happens with what we're talking about -- these communities of interest. If you look at the landscape in South Carolina, and we look at what has happened to the electorate in South Carolina. With two Congressional seats, the Democratic vote is well over 40% in this State. And so if you are well over 40%, why would a Congressional district then only yield one Democratic candidate that will win? That would have to be a majority district. One of the highlights I had in my life was whenever I ran for the Senate. The people in my area -- which was not a majority district -- proclaimed it differently. They elected a person like me from that district that was not a majority. They showed us that it could be done, which is critical in our situation because the Justice Department and the courts and others don't know what retrogressing is. But whenever it's seen as though we should be trying to have the fairness of "one person, one vote," and we met the criteria -- even at the 50% level or slightly above that -- was in the Senate plan. Now we go from 50.49% in the plan that we passed in the Senate up to 55.18%, another 5 percentage points. I want to be careful when I tell you what 5 percentage points mean. It's well over 30-some odd thousand people. And so each percentage point, when you do the deviation down to a seat plus one, you're talking over 30-some odd thousand people with 5.5%. I mean it is almost a 5% deviation of 660,000 people. And so, that's what happened whenever you put those folks in a district that dilutes the voting strength in the adjoining district. I think that's the issue that we have to address. I want to make one point on this other district. In the Senate plan that we had -- Number Two -- the Senate Staff Judiciary Plan which we passed in District Number 4, the population at that time was 28.84% in the 7th District. That was in the other proposal. I have asked for the amendment that we had -- that we passed here that the Senator from Florence ended putting up because I wanted to see the African American population in that one. But we went from 28.84% under this plan to now 27.64%. Does it make a difference? You are talking about 1.2%. You are talking well over 7,000 people when that happens. That's what's happened. We have gradually gotten down to a lower African American population in the final vote that we are about to end up taking. My thanks to Mr. Terreni who has worked with us on this. I have known him 20 years and I appreciate his diligence in giving us the information. The plan that we had that we passed through an amendment was 28.12% African American in the 7th District. Now that plan has gone down to 27.64%. Again, the pattern is a decrease, diluting the voting strength in the population mix. Senator McCONNELL: In the plans that we have adopted under that plan the population, the voting population in District 6, that's 27,000 new voters? Senator MALLOY: I think it will be more than that. In the population it is probably a greater number. I'm not certain how many of the voting age, but I know that the population is at least right at 5%. Senator McCONNELL: Tell me, is it also true that you and I served on the Senate Reapportionment Subcommittee? Senator MALLOY: Yes. Senator McCONNELL: During the testimony, for example, let's say in York County, in Spartanburg County, and even in Beaufort County, isn't it true that those residents of those counties thought that the new 7th District should be in their county and should be the flagship for the new Congressional district just like the people in Horry County thought it should be in Horry? Isn't it true we had least four counties bidding to have the new flagship district in their counties? Senator MALLOY: Yes. We went through all of the hearings and it was a task, and they obviously wanted to end up having the anchor district in their home counties. But here is what we have in South Carolina, Senator. We have certain areas that are growing at the disproportionate rate as it compares to other areas. I'm very concerned about the rural areas. The rural areas in South Carolina are where we're losing the population. Do you know why? We don't have the development there. I have great concerns that in the area where I live, if it stays the way that it is now, we will have over half of the district being a part of the coastal county. That's 330,000 people. Senator McCONNELL: I don't know whether or not you watched the news today but did you know that in the past two years, the African American wealth has gone down from 52%? In other words, the household wealth of the average African American household in South Carolina is $5,000 compared with our white counterpart which is$89,000. The average income in Horry County is about $115,000. You are a trained lawyer -- a real astute lawyer. Can you tell me what would they have in common in Horry County with an$115,000 average income with Darlington, Chesterfield, Marlboro, and parts of Dillon and Marion Counties and let's say about one-third of Florence County where the average income is no more than \$5,000? Senator MALLOY: I've said it and over and over again -- the commonality in the areas of the Pee Dee is just not the same. I understand the arguments on the communities of interests, but with all due respect, it's what the courts said in 2000. In 2000, those communities were basically the same then and when the courts drew a plan which was in 2002, they drew Horry, Georgetown, and went up in Charleston, similar to the way that they came up into the Berkeley County area. But Horry and Georgetown Counties were there. What is odd is that that is a great contrast in the change that we have from that point in time until now. And so the Horry area then comes up so that they can dominate the Pee Dee as opposed to having competing areas in Charleston. With the Congressional seat from the 1st District now in Horry and Georgetown, well over 300,000 people are displaced from one district to another. And the question is -- is that politically expedient? I think that's the question that we have to end up posing. You know, last time that we were in Session, the Senate did work. And I realize that there was some discussion as to where we should go, how we should end up dividing this district and how much time that it was going to end up taking us to do it. Basically, I begged then to please not to vote cloture on this matter because we need a chance to end up continuing debate. What happened then was there was a Bill and the Senate spoke at that point in time, which was a majority of the Senate that was present and voting. They voted for a plan that decreased the African American population in the 7th District, albeit in a different location. But they increased tremendously the vote in the protected district, which is a majority 6th District, and it went up 5 percentage points. So, that is the question that is presented to us. And, that is the question as to how well we wear it in our conscience? Are we actually voting like we would if we were Lady Justice and having blinders on and making certain that we were trying to be fair and making certain that we were trying to represent one party, one vote and making certain that we were not packing districts and making certain that we were not lightening districts? Are we going to end up voting with political expediency? The question is only what we answer in our own hearts. Senator HUTTO: First of all, let me thank you for your efforts and what you have been doing on reapportionment. Back when we did this before, there were a couple of terms that we used that were relevant today to those efforts. We called those bleaching and stacking. So when you look at this plan, would you define it as a bleaching of districts, which means removing African Americans from it and then stacking them in certain districts? Senator MALLOY: The point I have been laboriously going through is that from every proposal that we have termed as a 7th District has gotten progressively lesser in African American voting strength. We have culminated today to having at least 2 percentage points down from the 7th District as it was from the plan that we had passed. But even equally as important with the plans that have been reported out and the plans that we have looked at here in this body from the proposals that came out of Senate Judiciary to the amendment that was passed on the floor, the only one that was really passed, that actually got a majority vote and maybe one or two others, but the District 7, Congressional Seat 7 has gotten a progressively lesser African American vote. You would call that bleaching. Senator HUTTO: It has increased in every one of those proposals and on the vote on the amendment. The increase is because of your good friend, my good friend, Congressman Clyburn, the one who represents what we called the 6th District, which is a protected district where the African American population has increased to the point that it was 55.18%. And that is almost 5 percentage points higher than the plan that we passed from the Senate. That's five percentage points -- over 30,000 thousand people. Would you not agree also under the Voting Rights Act, the African American community is the only protected class? Would you say they are better off under this plan or worse off? Senator MALLOY: I think that's the ultimate question that we have to say overwhelmingly -- they are worse off under the plan that has just passed back from the House of Representatives than they were under the Senate plan that we had passed, and under every proposal that we had that would have reached a vote here in this body, particularly with the two proposals and the one amendment that we had, that we passed -- that came from the Senator from Florence. Senator HUTTO: The other point I want to make is when you look at these districts, you look at retrogression. You look at African American majority districts. You also look at influential districts. When you look at this drawing, versus the current situation, the current 5th District was about what percentage under the current existing plan that Congressmen now get elected from? That's somewhere around 31 or 32%. Senator MALLOY: Under the current court plan, the numbers that I have for voting age population is 29.41%. That's voting age population. Senator HUTTO: So, if you take that as an influential district, are there any other districts that meet the criteria with 29% under this plan? Senator MALLOY: There are not. Under the first plan -- and I think they are looking at voting age population in the 1st, it is 18.18%. Under the second plan it is 21.48%. That's the 2nd District. 3rd District is 17.93%. The 4th District is 18.23%. The 5th District is 24.46%. The 6th District is 55% in that protected district. And the 7th District is 27.64%. Nothing comes close to that number. Senator HUTTO: So, in most of those districts there has been retrogression except we stacked the 6th Congressional District? In essence, if you were a minority in this State, from a political point of view, under this plan you would be worse off? Senator MALLOY: It would be my view they are worse off under the plan that just came back from the House of Representatives than they were under the previous court-ordered plan and under the plans that we have previously passed in the Senate. So all we have to compare are the court-ordered plan we have from 2002 and the plan we have now. Numbers in the plan we have now are progressively less in African American population. I think the voting strength has been diluted. There has been an increase from the numbers that we have for every proposal as it relates to the 6th District, which is our protected district. Senator HUTTO: Another thing on retrogression from a rural perspective, would you agree that the rural communities under this proposal are worse off than they were under the current proposal? Senator MALLOY: I think certainly the rural district is losing the impact -- the voting strength -- particularly under the scenario that's been passed back from the House. I think that the rural interest for the one person has been diluted to end up for them to have a fair vote. They are worse off. Senator HUTTO: Would you agree that if you wanted to diminish rural interest, you take all the small rural counties and put them where there is a predominantly Republican county? You really dilute their influence as a rural community? Senator MALLOY: I think what we are seeing is that we are only growing in certain portions of the State. Let's take a look at the map that we have up there. Let's suppose that a Congressman comes out of Horry County. You look at one on the coast from Horry, one on the coast in Charleston, one up at the very top of the map almost into North Carolina, in the York County area. Then you come to the Richland and Lexington area where there are two. Then you go into the Laurens area where there is one. And then you would go right there in the Spartanburg area where there is another. So you could draw a line up there by the interstate with York and draw it all the way down, and you would get half of the State where you would not have a representative that will live there, but for the fact that there could be one from Horry County drawn around it. So, you have that area that would come in from Chesterfield, Kershaw, the Fairfield area, Lee County, Sumter, Williamsburg, and Dorchester -- all of that area with no representation. Suppose you have to live in a top part of Chesterfield or Marlboro County, where would you drive to see a Congressman? You have to go all the way down to the Horry area. Senator, the thing that's troublesome is simply this -- we are all in the political world. Let's suppose you have a Rotary meeting in one county with 250 people there, and you have a cattleman's association or a farm association where there are eight or ten people that want to come and talk to you. Which meeting will common sense and human behavior tell you to go to? You will go to the one with 200 or 300 people there. What happens is you are diluting their representation because those individuals will not be able to reach their Congressmen. Their Congressman is going to go to where those people are and that's the most people that get the most bang for the buck. That's how it's going to be. This is a sad day for rural South Carolina. Senator HUTTO: It is very sad because if you are running for Congress, you can just campaign in Horry and Georgetown and forget the rest of it and still be elected? The influence factor when you take these small counties and lump them with the big county, then you negate any opportunity for them to have real influence in that district? All they are doing is making the numbers? So, in essence, we are moving backwards in terms of rural influence and backwards as far as minority influence under this plan? I think so. That's what makes it difficult for those who represent some rural interests, some poverty interests and some educational interests where they may not have those kinds of interests. Our voice will not be heard. Senator MALLOY: I think we are going to have a very difficult time of our voices being heard, particularly in the rural areas in South Carolina. Because the population mix is just going to spill itself out. That's what's going to happen. I didn't hear these comments that were coming out during the last census, during the last time we had a court-ordered plan. All of a sudden we want to put the Pee Dee together. I grew up in the Pee Dee. I am from the Pee Dee. My parents are from the Pee Dee. My grandparents and every ancestor that I have ever heard about are from the Pee Dee area. Not once in my life did I end up understanding the joining of that area included the coastline down in Horry and Georgetown. I have a lot of respect for those individuals. They have done a good job and masterful job saying let's keep the Pee Dee together. But I will tell you, that is not the Pee Dee, and I grew up in the Pee Dee. It is simply not the Pee Dee. What I am having a hard time with is that it seems to be a time of convenience. A time of convenience is to lump it together because the big guys will swallow up the small guys once again. That's what's going to happen. Senator HUTTO: Senator, you think this plan has national implications rather than in it being in the best interests of the citizens of this State? Senator MALLOY: I am hesitant to speak to that. I can tell you it is not in the best interest for those in rural South Carolina; however, they have the motivation and whatever the cause was or what instigated it, they were not part of the Pee Dee. In the court-ordered plan in 2002, I didn't see the same arguments being made to keep the Pee Dee together and put us back in the 6th District where other guys came out. I wasn't serving then. I didn't hear that argument, but I hear it now. So that's what I have an issue with. Senator HUTTO: Would you say it's not the argument of convenience, and it does not reflect what the facts are because this is really not a Pee Dee district, it is a coastal district? Senator MALLOY: The 7th District is a coastal district? Senator HUTTO: It is going to be. That's what the population mix says. The numbers spell it out. There is in Horry County. There are over 60,000 in Georgetown. Added together that's 330,000. The median number is 660,000. So the 330,000 is half of it. You have two counties that will have more population or equal population, at least, to Florence, Marion, Dillon, Darlington, Chesterfield, and Marlboro Counties all combined? Senator MALLOY: That's just not right. When the children that are born today who are from the Pee Dee area -- I don't think we are doing them a service because what we have done is we have worked hard in this body to promote tourism. What we have done is that we have sent dollars there to try to create and promote tourism in this State. That's what happened with the growth. I heard arguments made that we have been in a bit of recession -- my goodness, wait until we come out. And so those numbers that we have now. Look at the Senate districts of the Senator from Marion, Senator WILLIAMS, who was 11,000 down in population, and any Senate district that is almost 18,000 in population, where the other areas over there are losing in population, the area that's growing is the Horry-Georgetown coast. They will continue to increase, which will continue to dilute the strength. That was the wisdom apparently in 2002, when the court came in and said they were going to put the coastal region together, which will be Horry, Georgetown and Charleston Counties. So they will be able to end up growing. That coastal area will be able to end up having the areas to bounce off of one another. That's the issue. But now what happens is that Horry comes in and they are able to end up being the largest county there. They are not divided. Greenville is divided. Richland is divided. It looks like Charleston has a bit of a division as well. So the largest counties in our State are divided. And the one that's growing as fast as any of the other ones is not. How are we going to address the large double digit unemployment issues in Marion County? How are we going to end up creating an economic engine over in those areas so that those folks will be able to have a working and living wage and make certain that they are educating their children? We know how the money comes in these districts. We know what happens to our educational system. We know what you have worked on many years for the I-95 Corridor. I-95 comes directly through the Pee Dee. What are we going to do? We don't want to be a depository for I-73. I support I-73, but, whenever you bring in an interstate there without doing the infrastructure and those matters in the corresponding areas, then you will have lack of development, and we are going to end up initiating and putting some gunpowder on the unemployment aspects in that area. It will continue to grow because their Congressman from that area is from the largest area. How often is he going to sit down with the mom and pop shops to say we want to make you grow, we want to make it better for you? The votes are just simply not there. Senator HUTTO: I want to make two points and then I will be through. I think you addressed one of them. The first one is that Horry and Georgetown now make up 50% of that proposed district based on current population. But based on projected growth, they will dominate that district substantially in the next two to three to five years. Do you know what the growth rate in Horry and Georgetown has been over the last ten years? Senator MALLOY: I do not know it, but I know it surpasses the other rural counties we have in that area. Senator HUTTO: If you look at the population of Marion County today versus what it was ten years ago, Marion lost population. So, its influence in this district will continue to go down as it proportionately goes down as the population is to the total district? Their future is not nearly as good. Let me ask you two more questions. Does this plan kind of remind you of the Voting Rights Act of the Voter ID Bill we just passed? You know, they didn't say you couldn't vote. They just shave off some points. They just make it more difficult for a senior to get an ID. They make it more difficult for a person if you are in college. They make it more difficult for working mothers. So, it is just shaving off points. Senator MALLOY: I think that this plan is going to be exactly what we think it is. I think that it actually is a very opportunistic plan. The plan will not be reflective of the political landscape of the African American voting population in this State. It has gotten progressively higher in the 6th District, progressively lower in the new 7th. I think what we are doing now is it becomes more of a political plan. Our voting strength has been diluted. I think we are worse off as far as an African American voter. Senator HUTTO: Let's talk about the 6th District a little bit in the same manner. One of the big things I see to get elected is the cost to get elected. If you look at the 6th Congressional District under this proposal versus the proposal we passed out in the Senate, a compact plan that reduced the number of counties, but it also did two unique things, under this proposed plan. There are about four different media markets you have to run in. And really, that's where your costs come out. You have to run in the Pee Dee market, Charleston, Columbia and Savannah. So it's the most expensive district out of all the districts. Who do you think more likely gets the opportunity to run -- an African American or a Caucasian? Senator MALLOY: I will tell you what I understand about that point. I think that it is unfortunately expensive to end up running a race. I think that what we have is the attempt obviously to comply with the Voting Rights Act. I think we have gone further than what we needed to put more of the African American population in the plan that just came back from the House of Representatives than was necessary for compliance under the Voting Rights Act. The increased amount, which is 5 percentage points from what we passed in the Senate, represents the fact that there are more African Americans placed in the 6th District now than what we had under the Senate plan and the question I have is -- if we are opposed to vote for that, then what we are voting for? This body is voting to increase the African American population in the 6th District. That isn't the total issue because what it does is dilute the voting strength of African Americans' political value in the rest of the districts. Senator HUTTO: So, if you are under 21 or 22%, really they ignore you. They can ignore the African American community in all these Congressional districts probably, except the 5th. The plan that has just come back, I don't think that it is as helpful as those that we had passed previously. Senator MALLOY: Thank you. One of the things my friend, Senator McCONNELL, taught me was the Rules, and I've been a great admirer of his. During the process I know he has a Rule book back in his drawer and he has the precedents that are already set forth. And I understand the Rule as it relates to a reapportionment discussion. We have particular Rules, and I realize, gentlemen of the Senate, as you all may not think this is an important time. I speak to a half empty Chamber as to how critical this issue is. We know that even under the Rules generally that we would not be able to bring this matter to a close until we have two legislative days of discussion. I do not know if we are making our points, I'm not certain the folks are listening. So I'm going to talk for a while until I make certain that my colleagues pay the respect that we have for this plan. Because of the importance of what is going to happen over the next decade. So really two days to end up making the folks understand that what we're doing here is changing the district in a way that they are increasing the African American population in the 6th District. As I went home after the fourth, after the last vote that we took, a family member asked me, "What are you doing as it relates to the Pee Dee under the plan that you have voted for?" And I tell you what -- it's a difficult question. It's perplexing. But I submit to you that even under that plan, that those in the Pee Dee get a chance to have more contact with their Congressman than they will under the plan with the 7th District. In every race that we have in the next five years, it's going to be very difficult for anyone outside of the Horry County area to become a Congressman. And that's sad. And under the plan that came out you had three or four Congressional seats that would reach into it, but how dare you make the argument as to when you are better off or why you are not. I was always told a piece of something is better than all of nothing. You are getting all of nothing because that person has to reach down deep in their hearts whenever they are part of a big fish in a small pond. They are the biggest guy on the block, the biggest person on the playground. Will then they be a bully or will they cease and make peace with the children if they are on the playground if you are the biggest guy there? That's what's going to happen. So we get an opportunity to make a difference here and operate as if we have blinders on and to see what we would do. We are not Lady Justice, but we have an opportunity to fix it now as opposed to going into the hearts of man and then saying you may get a good person that will lead the Grand Strand and come up to Shiloh Community and Cash Community -- these little areas that you probably have never heard of in Chesterfield County and others. I know you all travel some, but what's going to make them come up there and see the people? There's nothing that's going to make them come. You've got a ready-made audience with convention centers and conferences. That's not what happens in the Pee Dee. NESA is working for development in the Pee Dee, but Williamsburg County is not in it. That's not the goal. If we're talking about economic and communities of interest, tell me what the communities of interest are in the coastline and Horry County? Oh, they watch the same television stations. That's not a community of interest. It's just simply not. As I labor here and they go back and forth. Since I've been elected here, I can say that there are good times. I tell you this is a noble place and we have an awesome, awesome responsibility. I think this plan will eventually pass that came back from the House of Representatives. I think it's going to pass largely on party lines. I just ask you to search your hearts. Is it political expediency? Are we really doing what's right for South Carolina? Are we positioning ourselves so that we can end up making a run and we don't want to have the backlash of our party? Are we doing what's right for South Carolina? A chain is no stronger than the weakest link. We've got a weak link in the Pee Dee. We need jobs. We need representation. We need someone to hear our voice. And does this plan do that? I don't think that it does. What happened to the arguments that were being made last week? In the Greenville area I'm surprised, almost shocked, that the arguments that came from this floor, arguing over percentage points as to what you would do with Greenville and Spartanburg and all of a sudden it's changed. The Greenville population is decreased, Spartanburg increased, and now where are we? We get those numbers right. I don't want to step down from here and say we are butchering the numbers. I want to be a bit specific. When we passed the Bill, it was 61.6% in Greenville and 38.04% in Spartanburg. Now it's 59.97% and 40.2%. Greenville, you lost under this plan. The population from the 3rd District, the Greenville population increased to 54,952 from 41,827, a full 13,000 people. In Spartanburg, you now have only 19,814 in the 5th, when under the earlier plan you had 32,938. The question is what changed? Will someone from Greenville soon represent a Congressional seat in Anderson, Pickens and Oconee? It was an issue a few weeks ago, but it's not an issue now. And I make the point because I can't look inside your heart. I can just only look at the numbers and see what they say and it appears that it's just politically expedient. And so I look around and I think that, maybe you did not feel our passion. And again, I can't speak into the hearts of men and women, but I do know that something changed. And something changed from a few weeks ago because what I anticipate the vote to be at this point in time seems to be contrary to not what I believe you said as what I've seen on this Senate floor. Part of what I wish could happen is that we could reach into the hearts of men and tell them more about Lady Justice so that they then will try and respond and see if they will look into the eyes of the children and the eyes of the future in South Carolina and say this is what's going to happen and this is what's better for my State, not necessarily what's better for my party. What the question becomes is -- if we can continue to talk to you and educate you on this issue for the next couple of days. Certainly you can. The Rules allow it. Gentlemen, I've got news for you today. With everything that we've said here -- and I realize that we may have stepped on some toes -- but it had to be done. It's not right. And only you can know whether or not it's just politics or whether it's something that you think is genuinely right for South Carolina. My father always told me that "two wrongs don't make a right." It doesn't make a right. And so you can hold that body hostage for not just today but tomorrow, and come back on Thursday and we can get a vote. But as I stand here before you, a little bit disappointed at the response that it seems that we've given this debate and the cavalier approach that I believe that we are taking whenever we have some serious allegations that are being made as to what the numbers represent and we've got a cavalier approach, I want to see how we respond because the population did increase for African Americans in the 6th District and they did decrease for African Americans in the 7th District. The influential district is different than it was under the court's plan. I realize the arguments can be made -- but then speaking from a little old country boy from the Pee Dee area -- you would be surprised to know that, Senator, even though I always love to talk to the Senator from Cherokee because he and I are both friends and we both like to fight. You know, the fight in me says to raise cane because I fundamentally disagree with it. It's going to surprise some of you because I have too much respect for this body and this State that's already struggling to have to bring us back day after day to come in and take what will be the same vote. But I want you to hear what I'm saying because I think we made a mistake. I heard the chatter in the room from somebody who gave me credit for talking 11½ hours not too long ago. My wife tells me I talk too much anyway and everybody says I do talk a lot, but most of the time I'm pretty quiet, and I think I should, but I am going to, believe it or not, sit down and give us a chance to vote today. I made the decision since I've been up here even though there have been some serious allegations being made, serious reasons that we are under the Voting Rights Act to have the United States government looking over our shoulders as to how we do things. It has been what I believe that something is on the increase. Does it meet a legal definition? I guess we don't know. I believe it does. And when the Bill comes back here, that however you cut it, the numbers will spell it out. And I submit to you that the only person that can really answer it is what's in your heart. But I also say that those that actually made the arguments last week for your district, the changes that were made, the diluting of the counties, the change in the population mix, the percentages of divided county, and that we're dividing some larger counties and not dividing others, and the fact that we have continued to digress in the African American population in the 7th District to I think was at the lowest point as the plan is now if you vote for concurrence. When you cast your vote, if you are doing it for political expediency, I wouldn't care if one of my Republican friends from a rural area in a community of interest represented me. I really don't have any problem with that. I see the people in my area suffering. They can't find jobs. One of my friends asked me why when they had the catastrophe in New Orleans and some people didn't leave because they said they couldn't. Where were these folks going to go? They also had bus loads of people that they packed up to send down to Horry County from various counties to work in hotels as maids and stuff. I've seen it before. When will it ever happen that we will pack up and move to these rural areas and work there? If we don't envision that happening in our lifetime, then we're giving up hope on our area. And the rural areas are going to continue to suffer. I had a few matters I needed to put in the record. As much as it pains me, I have to let this matter come to a close. I think we erred, folks. The only problem is that we may not get this opportunity at another time in our history as to whether we grow at a rate large enough in a ten-year census that will allow us to expand our Congressional seat. So we get that one opportunity in history, and the question is will we blow it? So I would urge you, and I anticipate if one will stand up and say because my arguments that I made last week, they are with me this week and I'm going to stay with my arguments. I hope that you all will say that the Senator from Darlington told us the first day that what he was opposed to was having a large county like Horry be a dominant area in the Pee Dee. I submit to you that we are consistent. But I don't see the consistency therein, and so I ask you to search into your hearts and see if one person will stand up and say, "No, no, we're going to nonconcur. We're going to put this thing into conference and give it an opportunity and see if the Senate position can be upheld." This is going to sound like a bit of a sour grapes thing, but the House has done it to you again. It beat us up. We had no cards going over there and they came in and gave us what they wanted us to have, and now they are bringing it down and shoving it down our throats once again. So, when are we going to tell them, "No?" And as I stand here now, the House of Representatives -- you know where they are? They are gone. They left a few hours ago. And I saw on the television that they will reconvene at the Call of the Speaker. They dumped it in your lap, and they said, "If one of you comes up and upsets the apple cart, woe be unto you. We are going to win the public relations game. And it's going to be your fault." That's right. They dare any of you that have to depend on them to say we're going to nonconcur. You can't stand it in the political world because they don't know what goes on generally in your heart in your local area because you are the king there. But they are daring you. You know, when we were children, I used to hate it when somebody said, "I dare you to cross that line." Senator from Cherokee, I would jump across it. They would draw a line with me and I would jump across it. But the House has dared us again. They have dared us again because they are sending it to us. I came up to one Senator earlier and I joked, "You know you guys are my friends. We work together. We just have some difference of opinions from time to time, but most of the time we work those out. Do you remember when you were young and your mom or whatever used to give you medicine and she told you to hold your nose, it won't taste so bad?" How many folks are going to have to hold their nose whenever they vote for this because they know it's not what they wanted and they know that it's not good, but it may be like that little child that may say, "But, maybe it's good for me." Well, here's the difference. You are not that little child now. You represent 80,000-90,000 people. Under our new areas we're going to have over 100,000 people. That's who you are representing. All of those children that come in that district that will grow up and be voters and all those that are there now will have to live with this for a period of time. So, what is politically expedient to do what is right? I wish I could tell all of you to be like Lady Justice, to put your blinders on and look strictly at the facts and look strictly at the law and then say, "If all is well, then cast your vote then, as opposed to -- what's going to happen during the next time I get ready to run? Who is going to come after me because I went against what the House has said that we should end up doing?" So with that, my leaders, I told all three of you all three weeks ago whenever we had this conversation, that I was on my heels, I knew you would be successful. Anticipating the vote, I want to congratulate you. You all did it. I don't think it is right, but I knew this day was going to happen. I don't think it's good for South Carolina, and I hope that I'm wrong. On motion of Senator ANDERSON, with unanimous consent, the remarks of Senator MALLOY were ordered printed in the Journal. On motion of Senator MALLOY, with unanimous consent, the following two articles regarding redistricting were ordered reprinted in the Journal: Redistricting Plan Strikes Fair Balance by Senator GROOMS July 8, 2011 The General Assembly recessed last week, the Senate ending its deliberations on the once-per-decade question of redistricting. South Carolina's population growth means that we gain a new, seventh congressional seat. The debate centered on two plans. The first plan drew the 7th District to include Horry County and much of the Pee Dee. However, the 6th District, represented by Rep. Jim Clyburn, meandered from the farms of Blythewood in northern Richland County some 130 miles to the Charleston peninsula, and more than 150 miles from the Sumter-Florence line to the Georgia-South Carolina border at the Savannah River. That plan split Charleston County. It split Berkeley. It split Dorchester, Colleton and Beaufort. It split at least six more counties, dividing many along racial lines. In contrast, the plan I presented keeps all of Berkeley, Dorchester, Colleton, Beaufort, Jasper, Hampton, Allendale and Barnwell counties whole, within the 7th. Charleston and Horry remain anchors of the 1st District and are not split. Coastal Georgetown remains in the 1st while its inland areas join Williamsburg in the 7th. Daniel Island, Goose Creek, Moncks Corner, Summerville, Walterboro, Ridgeville, St. Stephen, St. George -- these towns are growing. They can emerge from Charleston's shadow and have their own representative in Congress. Beaufort's sizeable population will have significant influence. And because of the size and significance of the Charleston metro area, which extends into Berkeley and Dorchester, Charleston effectively could have two voices in Congress. Communities of interest -- where people live, work, shop, worship -- are kept whole wherever possible. County and city boundaries are generally protected. Racial gerrymandering is avoided, while we are careful not to dilute minority voting strength. Common geography, transportation, and communication are accounted for to ensure more compact districts. Statewide just eight counties are split. Sadly, the plan has been rebuked by some in my own party who seem to prefer racially fractured counties. Some even insinuate that the plan is part of a conspiracy designed to aid Democrats. Why would I do that? I am one of the most consistently conservative Republicans in the General Assembly. What it is, is a conservative, common-sense plan. It was carefully drawn, in part by a well-respected, nationally known Republican demographer. Democrats knew this, and initially balked at supporting it. However, with a few changes, we were able to craft a plan that both sides could support. The plan has such broad support that not only did Democrats and Republicans back it, Senators from 44 of our 46 county delegations voted for it. It's revealing that, with one or two exceptions, those who voted against the plan are moderate and liberal Republicans. They fought our common-sense plan because it brought to light the flaws in their gerrymandered, parochial plan. These Senators, and many in the South Carolina House, will continue to fight our plan and hope to change it later this summer. They say that their plan stands a better chance in any court challenge. The truth is the map we passed on June 29 is the better one. It needs only a vote of the House to become law. A quick glance at the maps shows that ours is the common-sense plan. It recognizes communities of interest, avoids racial gerrymandering, minimizes county splits, and has broad, bipartisan support. Senate Congressional Plan Best for State, Beaufort County by Senator DAVIS July 7, 2011 Recently, a new congressional plan for South Carolina, pushed by the Myrtle Beach business community in general and by a Myrtle Beach state representative in particular, unraveled in the Senate. Much to their dismay, as reported by The (Columbia) State newspaper, "the state Senate approved a redistricting plan that creates a new 7th District that is centered in Beaufort County." South Carolina once had a 7th Congressional District, but the 1930 census took it away. The 2010 census, however, showed our state's population had grown at a rate of 15.3 percent, greater than the country as a whole at 9.7 percent. So our state's 7th District was restored. Wesley Donehue, director of the state Senate Republican Caucus, summarized what happened next: "One of the worst kept secrets in state politics is that (Myrtle Beach) Rep. Alan Clemmons is running for the yet-unrealized 7th Congressional District. Clemmons, as chairman of the House) subcommittee drafting the plan, had the ability to craft himself a district that he could win." And that's exactly what Clemmons did. The House adopted his plan to create a new district stretching from Myrtle Beach "into the Democratic Pee Dee area ... a district created for a more moderate Republican." (That House-approved plan was developed in conjunction with U.S. Rep. Jim Clyburn and members of his staff, and it chops Beaufort County into two pieces, gutting its political relevance; more on that later.) Clemmons is an honorable man; however, drawing a new district to suit the desire of a particular politician is horrible public policy. The Senate Republican Caucus agreed, so it hired John Morgan, one of America's leading electoral demographers, to draw a congressional plan that reflected South Carolina's communities of interest, avoided gerrymandering and had the strongest chance of surviving the inevitable legal challenges in federal court. Morgan objectively reviewed the data, applied federal Justice Department criteria and drew a plan that, among other things, happened to anchor the new 7th District in Beaufort County. That plan became the state Senate Republican Caucus plan, and attorneys specializing in redistricting law formally recommended it to the Senate's special redistricting subcommittee. That subcommittee then held a meeting to consider it, and that's when power politics reared its head again. Unhappy that the new district might not be anchored in Myrtle Beach and include the Pee Dee, hundreds of people from that area went to the subcommittee meeting and demanded adoption of the Clemmons plan passed by the House. The subcommittee had no such plan -- none resembling it had even been recommended -- but one was hurriedly prepared that evening and quickly approved. That hasty action was subsequently corrected by the full Senate, which voted 25 to 15 to approve the Senate Republican Caucus plan. Senators from all parts of the State -- except those from Myrtle Beach and the Pee Dee -- voted for the plan, for the same reason I did: It is the most logical plan for the State, the least gerrymandered and the one with the least number of county splits. I also supported the Senate-passed plan because it recognizes Beaufort County's growing prominence. There is finally a chance for our county and its surrounding economic region (the counties of Jasper, Hampton and Colleton) to be the heart of a congressional district, rather than the forgotten tail-end appendages of metropolitan-dominated districts to the north (Lexington-Columbia) or the northeast (Charleston). I did not support that plan for personal reasons. During the congressional redistricting debate, I publicly stated that if the new district ended up centered in Beaufort County, I would not run for the seat. I am making progress as a state senator on things important to me and my constituents, and right now, I can make more of a difference in Columbia than in Washington. The General Assembly will reconvene July 26 to decide which chamber's plan will prevail. I am convinced the one approved by the House, based on the gerrymandering of raw politics, would be successfully challenged in federal court and result in judge-drawn district boundaries, a nightmare scenario that must be avoided. I will do everything in my power to keep that from happening * * * The question then was concurrence with the House amendments. The "ayes" and "nays" were demanded and taken, resulting as follows: Ayes 24; Nays 16 AYES Alexander Bryant Campbell Campsen Cleary Courson Cromer Davis Elliott Fair Gregory Grooms Knotts Leatherman Martin, Larry Martin, Shane McConnell McGill O'Dell Peeler Rankin Rose Shoopman Verdin Total--24 NAYS Anderson Coleman Ford Hutto Jackson Leventis Lourie Malloy Massey Matthews Nicholson Reese Scott Setzler Sheheen Thomas Total--16 The Senate concurred in the House amendments and a message was sent to the House accordingly. Ordered that the title be changed to that of an Act and the Act enrolled for Ratification. Expression of Personal Interest Senator FORD rose for an Expression of Personal Interest. RATIFICATION OF AN ACT Pursuant to an invitation the Honorable Speaker and House of Representatives appeared in the Senate Chamber on July 26, 2011, at 5:30 P.M. and the following Act was ratified: (R111, H. 3992 (Word version)) -- Reps. Harrell, Lucas, Harrison, Clemmons, Barfield, Cooper, Hardwick, Owens, Sandifer, G.R. Smith, J.R. Smith, White, Bingham and Erickson: AN ACT TO AMEND SECTION 1-1-715, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO ADOPTION OF THE UNITED STATES CENSUS, SO AS TO ADOPT THE UNITED STATES CENSUS OF 2010 AS THE TRUE AND CORRECT ENUMERATION OF INHABITANTS OF THIS STATE; BY ADDING SECTION 7-19-35 SO AS TO ESTABLISH SEVEN ELECTION DISTRICTS FROM WHICH MEMBERS OF CONGRESS FOR SOUTH CAROLINA ARE ELECTED COMMENCING WITH THE 2012 GENERAL ELECTION; TO REPEAL SECTION 7-19-40 RELATING TO CONGRESSIONAL DISTRICTS FROM WHICH SOUTH CAROLINA MEMBERS OF CONGRESS WERE FORMERLY ELECTED; TO JOINTLY DESIGNATE THE PRESIDENT PRO TEMPORE OF THE SENATE AND THE SPEAKER OF THE HOUSE OF REPRESENTATIVES AS THE APPROPRIATE OFFICIALS OF THE SUBMITTING AUTHORITY WHO ARE RESPONSIBLE FOR OBTAINING PRECLEARANCE OF THE CONGRESSIONAL REAPPORTIONMENT PLAN UNDER THE VOTING RIGHTS ACT; AND TO PROVIDE THAT A MEMBER OF ANY BOARD, COMMISSION, OR COMMITTEE REPRESENTING A CONGRESSIONAL DISTRICT WHOSE RESIDENCY IS TRANSFERRED TO ANOTHER DISTRICT BY THIS ACT MAY CONTINUE TO SERVE HIS TERM IN OFFICE; HOWEVER, THE APPOINTING OR ELECTING AUTHORITY MAY ADD AN ADDITIONAL MEMBER ON A BOARD, COMMISSION, OR COMMITTEE WHICH LOSES A RESIDENT MEMBER. L:\COUNCIL\ACTS\3992AHB11.DOCX On motion of Senator ROSE, with unanimous consent, the Senate stood adjourned out of respect to the memory of Mrs. Emily Myers Millhouse of Summerville, S.C., beloved wife of Tillman Millhouse, Jr. and devoted mother of four. and On motion of Senators KNOTTS and SETZLER, with unanimous consent, the Senate stood adjourned out of respect to the memory of Mrs. Ruth J. Buzhardt of Cayce, S.C. and On motion of Senators MATTHEWS, PINCKNEY and GROOMS, with unanimous consent, the Senate stood adjourned out of respect to the memory of Mr. Floyd Buckner of Colleton, S.C., Colleton County Councilman. and
2014-07-31T15:43:10
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https://par.nsf.gov/biblio/10047591-measurement-differential-total-cross-sections-dk0-reaction-within-resonance-region
Measurement of the differential and total cross sections of the $\gamma d\to {K}^{0}\mathrm{\Lambda }\left(p\right)$ reaction within the resonance region Authors: ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; more » Award ID(s): Publication Date: NSF-PAR ID: 10047591 Journal Name: Physical Review C Volume: 96 Issue: 6 ISSN: 2469-9985 Publisher: American Physical Society
2022-08-12T16:14:10
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http://dlmf.nist.gov/22.14
# §22.14 Integrals ## §22.14(i) Indefinite Integrals of Jacobian Elliptic Functions Lastly, with , For alternative, and symmetric, formulations of the results in this subsection see Carlson (2006a). ## §22.14(ii) Indefinite Integrals of Powers of Jacobian Elliptic Functions See §22.16(ii). The indefinite integral of the 3rd power of a Jacobian function can be expressed as an elementary function of Jacobian functions and a product of Jacobian functions. The indefinite integral of a 4th power can be expressed as a complete elliptic integral, a polynomial in Jacobian functions, and the integration variable. See Lawden (1989, pp. 87–88). See also Gradshteyn and Ryzhik (2000, pp. 618–619) and Carlson (2006a). For indefinite integrals of squares and products of even powers of Jacobian functions in terms of symmetric elliptic integrals, see Carlson (2006b). ## §22.14(iv) Definite Integrals Corresponding results for the subsidiary functions follow by subtraction; compare (22.2.10).
2013-05-23T23:17:21
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http://pdglive.lbl.gov/Particle.action?init=0&node=M065&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 \rho}{(1700)}}$ $I^G(J^{PC})$ = $1^+(1^{- -})$ See related review: ${{\mathit \rho}{(1450)}}$ and ${{\mathit \rho}{(1700)}}$ ${{\boldsymbol \rho}{(1700)}}$ MASS ${{\mathit \eta}}{{\mathit \rho}^{0}}$ AND ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ MODES $1720 \pm20$ MeV ${{\mathit \eta}}{{\mathit \rho}^{0}}$ MODE ${{\mathit \pi}}{{\mathit \pi}}$ MODE ${{\mathit \pi}}{{\mathit \omega}}$ MODE ${{\mathit K}}{{\overline{\mathit K}}}$ MODE 2 ( ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ ) MODE ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}{{\mathit \pi}^{0}}$ MODE 3( ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ ) AND 2( ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}$ ) MODES ${\mathit m}_{{{\mathit \rho}{(1700)}^{0}}}$ $−$ ${\mathit m}_{{{\mathit \rho}{(1700)}^{\pm}}}$ ${{\boldsymbol \rho}{(1700)}}$ WIDTH ${{\mathit \eta}}{{\mathit \rho}^{0}}$ AND ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ MODES $250 \pm100$ MeV ${{\mathit \eta}}{{\mathit \rho}^{0}}$ MODE ${{\mathit \pi}}{{\mathit \pi}}$ MODE ${{\mathit K}}{{\overline{\mathit K}}}$ MODE 2 ( ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ ) MODE ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}{{\mathit \pi}^{0}}$ MODE ${{\mathit \omega}}{{\mathit \pi}^{0}}$ MODE 3( ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ ) AND 2( ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}$ ) MODES ${\Gamma}_{{\mathit \rho}{(1700)}^{0}}$ $−$ ${\Gamma}_{{\mathit \rho}{(1700)}^{\pm}}$
2019-12-14T06:07:23
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https://www.usgs.gov/center-news/volcano-watch-whats-scientists-role-planning-volcanoes-quakes
Volcano Watch — What's scientists' role in planning for volcanoes, quakes? Release Date: The Center for the Study of Active Volcanoes at the University of Hawaii in Hilo and the U.S. Geological Survey's Hawaiian Volcano Observatory sponsored a public symposium on the prediction and mitigation of volcanic eruptions and earthquakes about a month ago. One of the topics mentioned at the symposium was the role of scientists and of other public officials. The Center for the Study of Active Volcanoes at the University of Hawaii in Hilo and the U.S. Geological Survey's Hawaiian Volcano Observatory sponsored a public symposium on the prediction and mitigation of volcanic eruptions and earthquakes about a month ago. One of the topics mentioned at the symposium was the role of scientists and of other public officials. The discussion focused on the recent hearings at the Hawaii County Council about adoption of the 1991 Unified Building Code (UBC). It was argued that the Council needed the input of scientists in order to evaluate the merits of adopting the UBC and that, because none of the scientists testified at the hearings, they were not responsible to the public. The discussion reflects a widely held but, in my view, incorrect, perception of the role of scientists' in society. In the issue at hand - that of adoption of the Unified Building Code - the scientists' role is to establish what the seismic hazard is in Hawaii. Four earthquake hazard zones have been defined, with hazard zone 4 reflecting the most severe earthquake hazard and hazard zone 0 with the least severe hazard. The subdividing of the Hawaiian Islands into different zones was done in 1970, based on the best data available at that time. It resulted in classifying Hawaii in earthquake hazard zone 3, Maui in earthquake zone 2, Oahu in earthquake hazard zone 1, and Kauai in earthquake hazard zone 0. Since then, several modifications have been made; hence, zonation in 1988 was changed so that Hawaii is still in earthquake zone 3, Maui in earthquake zone 2B, Oahu in earthquake zone 2A, and Kauai in earthquake zone 1. Dr. Carl Johnson of the University of Hawaii at Hilo presented data at the symposium, indicating that Hawaii County has a larger seismic hazard than was previously recognized and that, therefore, the appropriate earthquake hazard zone is zone 4. The idea that new data can cause a reevaluation of the assigned earthquake zonation does not mean that the scientists were withholding information or were indifferent to the concerns of the public or to public officials. It simply means that observations and data available presently, but not known or recognized when the previous evaluation was made, have changed our interpretation of the seismic hazard on Hawaii. These ideas will now be discussed and argued amongst the scientists until a consensus is reached that the seismic risk is indeed higher than thought. At that point, the International Conference of Building Officials, on the recommendation of the Hawaii Structural Engineers Association, will consider upgrading Hawaii to zone 4. The County Council can also simply enact an ordinance to the effect that the County will be considered to be in earthquake zone 4. This was done by the Oahu Board of Supervisors in 1956. The scientists' formal responsibility ends once they have reached a consensus on the level of hazard and have communicated that consensus to the public and to public officials. To go beyond that would be overstepping their bounds. The fact that the scientists sponsor these annual hazard symposia reflects our desire and sense of responsibility in informing the public about natural hazards. Another example of our desire to convey information to the public involves lava flow hazards. U.S. Geological Survey scientists have synthesized data on lava coverage on the island and created a lava flow hazard map. This map establishes the state of current knowledge on the hazard posed to different areas by lava flows. Once the map is available to policy makers, scientists would be trespassing on the role of other professionals if they went beyond updating the lava flow hazard map if, and when, new and pertinent data become available. Their credibility as scientists would be compromised if the information they presented was perceived to be biased. It is for a very good reason that the U.S. Geological Survey has strict guidelines restricting our active role in partisan issues. The next stage, after scientists reach a consensus on the hazards posed by lava flows and communicate that information to the public and to policy-makers, is for policy-makers to define administrative boundaries that can then be used for planning purposes by the county, by home purchasers, by mortgages lenders, or by insurance companies. By administrative boundaries I mean workable boundaries that may not exactly follow the geological boundaries, because geological boundaries are gradational. For example, slightly shifting a boundary to include an entire subdivision may make the administrative map more workable. The Hazards Symposia sponsored by the Center for the Study of Active Volcanoes and the Hawaiian Volcano Observatory offer the public a chance to question scientists about natural hazards and policymakers about the application of scientific knowledge to issues that affect our everyday lives. For those of you who missed this year's symposium but wish you had come, Jones Space Link will give you another opportunity to see each of the four panel presentations and the discussion that followed. Mark your calendar for 7:30 p.m. on October 10, 11, 13, and 16 if you are interested.
2021-09-19T15:30:09
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https://ihsgrp.com/2t4r141q/left-inverse-function-684573
In our next example we will test inverse relationships algebraically. If $f\left(x\right)=x^2-3$, for $x\ge0$ and $g\left(x\right)=\sqrt{x+3}$, is g the inverse of f? A function must be a one-to-one relation if its inverse is to be a function. If the function is one-to-one, there will be a unique inverse. Often is a map of a specific type, such as a linear map between vector spaces, or a continuous map between topological spaces, and in each such case, one often requires a right inverse to be of the same type as that of . inverse f ( x) = 1 x2. has no right inverse and that if it has two distinct right inverses it has no left inverse." The inverse function theorem allows us to compute derivatives of inverse functions without using the limit definition of the derivative. The outputs of the function $f$ are the inputs to ${f}^{-1}$, so the range of $f$ is also the domain of ${f}^{-1}$. The inverse function reverses the input and output quantities, so if. If you're seeing this message, it means we're having trouble loading external resources on our website. Inverses can be verified using tabular data as well as algebraically. A function is injective if, for all and , whenever, we have . Generally speaking, the inverse of a function is not the same as its reciprocal. inverse f ( x) = ln ( x − 5) $inverse\:f\left (x\right)=\frac {1} {x^2}$. It is the notation for indicating the inverse of a function. So if you’re asked to graph a function and its inverse, all you have to do is graph the function and then switch all x and y values in each point to graph the inverse. denotes composition).. l is a left inverse of f if l . More formally, if $$f$$ is a function with domain $$X$$, then $${f}^{-1}$$ is its inverse function if and only if $${f}^{-1}\left(f\left(x\right)\right)=x$$ for every $$x \in X$$. What does left inverse mean? We will think a bit about when such an inverse function exists. In our last example we will define the domain and range of a function’s inverse using a table of values, and evaluate the inverse at a specific value. So, to have an inverse, the function must be injective. For example, we could evaluate $T\left(5\right)$ to determine the average daily temperature on the $5$th day of the year. If a function is not one-to-one, it can be possible to restrict it’s domain to make it so. {eq}f\left( x \right) = y \Leftrightarrow g\left( y \right) = x{/eq}. $\endgroup$ – Asaf Karagila ♦ Apr 7 '13 at 14:18 $inverse\:y=\frac {x} {x^2-6x+8}$. Thanks in advance. An inverse function is the "reversal" of another function; specifically, the inverse will swap input and output with the original function. If $f(x)$ and  $g(x)$ are inverses, then  $f(x)=g^{-1}(x)$ and $g(x)=f^{-1}(x)$. $\endgroup$ – Inceptio Apr 7 '13 at 14:12 $\begingroup$ @Inceptio: I suppose this is why the exercise is somewhat tricky. United States. Thus, we can evaluate the cost function at the temperature $T\left(d\right)$. Formula for the derivative of the inverse Under the assumptions above we have the formula $$\label{e:derivative_inverse} (f^{-1})' (y) = \frac{1}{f'(f^{-1}(y))}$$ for the derivative of the inverse. Left and right inverses; pseudoinverse Although pseudoinverses will not appear on the exam, this lecture will help us to prepare. Some functions have a two-sided inverse map, another function that is the inverse of the first, both from the left and from the right.For instance, the map given by → ↦ ⋅ → has the two-sided inverse → ↦ (/) ⋅ →.In this subsection we will focus on two-sided inverses. If the function is one-to-one, there will be a unique inverse. This is often called soft inverse function theorem, since it can be proved using essentially the same techniques as those in the finite-dimensional version. Consider the function that converts degrees Fahrenheit to degrees Celsius: $$C(x)=\frac{5}{9}(x-32)$$. Two sided inverse A 2-sided inverse of a matrix A is a matrix A−1 for which AA−1 = I = A−1 A. Figure 2. Yes, this is a homework assignment that my friend has been working on for over a week. 1. Then solve for $y$ as a function of $x$. Learn how to find the formula of the inverse function of a given function. The transpose of the left inverse of A is the right inverse A right −1 = (A left −1) T.Similarly, the transpose of the right inverse of A is the left inverse A left −1 = (A right −1) T.. 2. This article will show you how to find the inverse of a function. So, the inverse of f (x) = 2x+3 is written: f-1(y) = (y-3)/2. For example, find the inverse of f(x)=3x+2. $f\left(g(x)\right)=x$, Substitute $f(x)$ into $g(x)$. ''[/latex] This naturally leads to the output of the original function becoming the input of the inverse function. Alternatively, if we want to name the inverse function $g$, then $g\left(4\right)=2$ and $g\left(12\right)=5$. Substitute $g(x)=\sqrt{x+3}$ into $f(x)$, this means the new variable in $f(x)$ is $\sqrt{x+3}$ so you will substitute that expression where you see x. ${f}^{-1}\left(x\right)\ne \frac{1}{f\left(x\right)}$, $\begin{array}{c}f\left(2\right)=4,\text{ then }{f}^{-1}\left(4\right)=2;\\ f\left(5\right)=12,{\text{ then f}}^{-1}\left(12\right)=5.\end{array}$, Domain and Range of the Original Function, http://cnx.org/contents/[email protected], Use compositions of functions to verify inverses algebraically, Identify the domain and range of inverse functions with tables, Substitute $g(x)$ into $f(x)$. Suppose we want to calculate how much it costs to heat a house on a particular day of the year. If for a particular one-to-one function $f\left(2\right)=4$ and $f\left(5\right)=12$, what are the corresponding input and output values for the inverse function? inverse y = x x2 − 6x + 8. Important: for $${f}^{-1}$$, the superscript $$-\text{1}$$ is not an exponent. 2. Embedded videos, simulations and presentations from external sources are not necessarily covered Here, he is abusing the naming a little, because the function combine does not take as input the pair of lists, but is curried into taking each separately.. functions inverse. To find the inverse of a function $y=f\left(x\right)$, switch the variables $x$ and $y$. And the reason we introduced composite functions is because you can verify, algebraically, whether two functions are inverses of each other by using a composition. The range of a function will become the domain of it’s inverse. Left-cancellative; Loop (algebra), an algebraic structure with identity element where every element has a unique left and right inverse A left inverse element with respect to a binary operation on a set; A left inverse function for a mapping between sets; A kind of generalized inverse; See also. The inverse of a function can be defined for one-to-one functions. Create a random matrix A of order 500 that is constructed so that its condition number, cond(A), is 1e10, and its norm, norm(A), is 1.The exact solution x is a random vector of length 500, and the right side is b = A*x. So, to have an inverse, the function must be injective. Here is the graph of the function and inverse from the first two examples. It is well known that a real-valued, continuous, and strictly monotone function of a single variable possesses an inverse on its range. Be careful not to confuse the inverse of a function and the reciprocal of a function: All Siyavula textbook content made available on this site is released under the terms of a Learn how to find the formula of the inverse function of a given function. r is a right inverse of f if f . Any point on the line $$y = x$$ has $$x$$- and $$y$$-coordinates with the same numerical value, for example $$(-3;-3)$$ and $$\left( \frac{4}{5}; \frac{4}{5} \right)$$. We would write $C\left(T\left(5\right)\right)$. $g={f}^{-1}$, for $x\ge0$. In the following video we show an example of finding corresponding input and output values given two ordered pairs from functions that are inverses. We will show one more example of how to verify whether you have an inverse algebraically. Using parentheses helps keep track of things. See the lecture notesfor the relevant definitions. By combining these two relationships into one function, we have performed function composition. The cost to heat a house will depend on the average daily temperature, and in turn, the average daily temperature depends on the particular day of the year. For any one-to-one function $f\left(x\right)=y$, a function ${f}^{-1}\left(x\right)$ is an inverse function of $f$ if ${f}^{-1}\left(y\right)=x$. $\begin{array}g\left(f\left(x\right)\right)=3-\left(2x+1\right)\hfill \\ \text{ }=3 - 2x - 1\hfill \\ \text{ }=-2x+2\hfill \end{array}$. by this license. Left inverse $g\left(f(x)\right)=x$. If a function $$f$$ has an inverse function $$f^{-1}$$, then $$f$$ is said to be invertible. In this section we define one-to-one and inverse functions. In fact, if a function has a left inverse and a right inverse, they are both the same two-sided inverse, so it can be called the inverse. In this case, the converse relation $${f^{-1}}$$ is also not a function. 3Blue1Brown series S1 • E7 Inverse matrices, column space and null space | Essence of linear algebra, chapter 7 - Duration: 12:09. Figure 2. Inverse function definition by Duane Q. Nykamp is licensed under a Creative Commons Attribution-Noncommercial-ShareAlike 4.0 License. We can use the inverse function theorem to develop differentiation formulas for the inverse trigonometric functions. Just as zero does not have a reciprocal, some functions do not have inverses. We write the inverse as $$y = \pm \sqrt{\frac{1}{3}x}$$ and conclude that $$f$$ is not invertible. One is obvious, but as my answer points out -- that obvious inverse is not well-defined. An inverse function is a function for which the input of the original function becomes the output of the inverse function.This naturally leads to the output of the original function becoming the input of the inverse function. In our first example we will identify an inverse function from ordered pairs. Replace y by \color{blue}{f^{ - 1}}\left( x \right) to get the inverse function. For example, the inverse of $$f(x) = 3x^2$$ cannot be written as $$f^{-1}(x) = \pm \sqrt{\frac{1}{3}x}$$ as it is not a function. It is also known that one can $inverse\:f\left (x\right)=\sqrt {x+3}$. In many cases, if a function is not one-to-one, we can still restrict the function to a part of its domain on which it is one-to-one. Substitute $g(x)=\frac{1}{x}-2$ into $f(x)$, this means the new variable in $f(x)$ is $\frac{1}{x}-2$ so you will substitute that expression where you see x. The inverse of a function is denoted by f^-1(x), and it's visually represented as the original function reflected over the line y=x. An important generalization of this fact to functions of several variables is the Inverse function theorem, Theorem 2 below. In … Now we can substitute $f\left(x\right)$ into $g\left(x\right)$. This algebra 2 and precalculus video tutorial explains how to find the inverse of a function using a very simple process. Glossary inverse function A foundational part of learning algebra is learning how to find the inverse of a function, or f(x). The Inverse Function goes the other way: So the inverse of: 2x+3 is: (y-3)/2. In this case, the converse relation $${f^{-1}}$$ is also not a function. It is not an exponent; it does not imply a power of $-1$ . If a function $$f$$ is not surjective, not all elements in the codomain have a preimage in the domain. A function function f(x) is said to have an inverse if there exists another function g(x) such that g(f(x)) = x for all x in the domain of f(x). Show Instructions. Meaning of left inverse. Learn how to find the formula of the inverse function of a given function. The calculator will find the inverse of the given function, with steps shown. If is a left inverse and a right inverse of , for all ∈, () = ((()) = (). Ex 2: Determine if Two Functions Are Inverses. We read the left-hand side as $f$ composed with $g$ at $x,''$ and the right-hand side as $f$ of $g$ of $x. In this case, g(x) is called the inverse of f(x), and is often written as f-1 (x). The function [latex]T\left(d\right)$ gives the average daily temperature on day $d$ of the year. $\begin{array}{c} f\left(\frac{1}{x}-2\right)=\frac{1}{\left(\frac{1}{x}-2\right)+2}\hfill\\=\frac{1}{\frac{1}{x}}\hfill\\={ x }\hfill \end{array}$. Using the functions provided, find $f\left(g\left(x\right)\right)$ and $g\left(f\left(x\right)\right)$. An inverse function is a function which does the “reverse” of a given function. Left inverse Left Inverse Given a map between sets and , the map is called a left inverse to provided that , that is, composing with from the left gives the identity on . The notation ${f}^{-1}$ is read $\text{}f$ inverse.” Like any other function, we can use any variable name as the input for ${f}^{-1}$, so we will often write ${f}^{-1}\left(x\right)$, which we read as $f$ inverse of $x. An inverse function is a function which does the “reverse” of a given function. There is an interesting relationship between the graph of a function and its inverse. Key Steps in Finding the Inverse Function of a Rational Function. [latex]g={f}^{-1}?$. Notice that if we show the coordinate pairs in a table form, the input and output are clearly reversed. A left inverse in mathematics may refer to: . You appear to be on a device with a "narrow" screen width (i.e. inverse f ( x) = cos ( 2x + 5) Define the domain and range of the function and it’s inverse. What follows is a proof of the following easier result: If $$MA = I$$ and $$AN = I$$, then $$M = N$$. Similarly, we find the range of the inverse function by observing the horizontal extent of the graph of the original function, as this is the vertical extent of the inverse function. An example will be really helpful. In general, you can skip the multiplication sign, so 5x is equivalent to 5*x. How can both of these conditions be valid simultaneously without being equal ? Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share … If we represent the function $$f$$ and the inverse function $${f}^{-1}$$ graphically, the two graphs are reflected about the line $$y=x$$. Two sided inverse A 2-sided inverse of a matrix A is a matrix A−1 for which AA−1 = I = A−1 A. In general, you can skip the multiplication sign, so 5x is equivalent to 5*x. This holds for all $x$ in the domain of $f$. We think you are located in Therefore interchanging the $$x$$- and $$y$$-values makes no difference. I usually wouldn't do this but it's due tomorrow and I don't want her to fail. If we want to evaluate an inverse function, we find its input within its domain, which is all or part of the vertical axis of the original function’s graph. Definition of left inverse in the Definitions.net dictionary. If we want to evaluate an inverse function, we find its input within its domain, which is all or part of the vertical axis of the original function’s graph. For example, we can make a restricted version of the square function $f\left(x\right)={x}^{2}$ with its range limited to $\left[0,\infty \right)$, which is a one-to-one function (it passes the horizontal line test) and which has an inverse (the square-root function). An inverse function is a function for which the input of the original function becomes the output of the inverse function. The result must be x. More formally, if $$f$$ is a function with domain $$X$$, then $${f}^{-1}$$ is its inverse function if and only if $${f}^{-1}\left(f\left(x\right)\right)=x$$ for every $$x \in X$$. We can use the inverse function theorem to develop … Left function in excel is a type of text function in excel which is used to give the number of characters from the start from the string which is from left to right, for example if we use this function as =LEFT ( “ANAND”,2) this will give us AN as the result, from the example we can see that this function … inverse f ( x) = √x + 3. Find and interpret ${f}^{-1}\left(70\right)$. Informally, this means that inverse functions “undo” each other. First, replace f(x) with y. A function accepts values, performs particular operations on these values and generates an output. Inverse Function Calculator. Switch the roles of \color{red}x and \color{red}y, in other words, interchange x and y in the equation. Keep in mind that. When a function has no inverse function, it is possible to create a new function where that new function on a limited domain does have an inverse function. $$f(x)$$ and $$f^{-1}(x)$$ symmetrical about $$y=x$$, Example: $$\qquad \qquad \qquad \qquad \qquad \qquad$$, Example: $$\qquad \qquad \qquad \qquad \qquad$$, $$g(x) = 5x \therefore g^{-1}(x)= \frac{x}{5}$$, $$g(x) = 5x \therefore \frac{1}{g(x)} = \frac{1}{5x}$$. (An example of a function with no inverse on either side is the zero transformation on .) This is what we’ve called the inverse of A. Really clear math lessons (pre-algebra, algebra, precalculus), cool math games, online graphing calculators, geometry art, fractals, polyhedra, parents and teachers areas too. f is an identity function.. The inverse function theorem allows us to compute derivatives of inverse functions without using the limit definition of the derivative. $\begin{array}{c}f\left(\sqrt{x+3}\right)={(\sqrt{x+3})}^2-3\hfill\\=x+3-3\\=x\hfill \end{array}$. 5. the composition of two injective functions is injective 6. the composition of two surjective functions is surjective 7. the composition of two bijections is bijective It is also important to understand the order of operations in evaluating a composite function. I see only one inverse function here. This translates to putting in a number of miles and getting out how long it took to drive that far in minutes. We use this information to present the correct curriculum and In the following video we use algebra to determine if two functions are inverses. In classical mathematics, every injective function f with a nonempty domain necessarily has a left inverse; however, this may fail in constructive mathematics. However, just as zero does not have a reciprocal, some functions do not have inverses.. So in the expression ${f}^{-1}\left(70\right)$, $70$ is an output value of the original function, representing $70$ miles. Show Instructions. $\begin{array}f\left(g\left(x\right)\right)=2\left(3-x\right)+1\hfill \\ \text{ }=6 - 2x+1\hfill \\ \text{ }=7 - 2x\hfill \end{array}$ Notice how we have just defined two relationships: The cost depends on the temperature, and the temperature depends on the day. The inverse is usually shown by putting a little "-1" after the function name, like this: f-1(y) We say "f inverse of y". Given a function $f\left(x\right)$, we represent its inverse as ${f}^{-1}\left(x\right)$, read as $f$ inverse of $x.\text{}$ The raised $-1$ is part of the notation. interchanging $$x$$ and $$y$$ in the equation; making $$y$$ the subject of the equation; expressing the new equation in function notation. Function from ordered pairs from functions that are inverses by starting with the innermost first... Good way of thinking about Injectivity is that the domain Creative Commons Attribution-Noncommercial-ShareAlike License... This lecture will help us to compute derivatives of inverse functions and reciprocal functions comes down to operations... Can skip the multiplication sign, so if and output are clearly reversed more example of to. If you have a preimage in the codomain have a preimage in the video. Although pseudoinverses will not appear on the day combining these two relationships the! { x } { x^2-6x+8 } $our next example we will show one more of... Also important to understand the order of operations in evaluating a composite function seeing this message, it means 're! Y\ ) -values makes no difference denotes composition ).. l is a function case, the relation! Will not appear on the exam, this is what we ’ ve called composition. About when such an inverse algebraically show an example of how to the! The converse relation \ ( f\ ) is also not a function \ ( { f^ { - 1 }! Which AA−1 = I = A−1 a equation have the time to do to an element of the.! If f left inverse function definition of the function is one-to-one, there will a. 12.2.1 ) – define a composite function domain and range of a function with no inverse on either side the... Creative Commons Attribution-Noncommercial-ShareAlike 4.0 License { x } { f^ { -1 } } \ ) also. This information to present the correct curriculum and to personalise content to meet. That means that has no freedom in what it chooses to do to an element of the function and functions. Turns out that left inverses are also right inverses ; pseudoinverse Although pseudoinverses will not appear on the.! If anyone can help awesome with no inverse on either side is notation... Degrees Celsius as follows two examples here is the zero transformation on. this License in next. In maths are the key to your success and future plans become domain! Equivalent to 5 * x of two functions are inverses the of. Output values given two ordered pairs and inverse functions “ undo ” other., not all elements in the following video we use this information to the. Functions comes down to understanding operations, identities, and then working to the.... Converse relation \ ( { f^ { -1 } } \ ) is not surjective not! Quickly before we leave this section quantities, so if inverse is not surjective, not all in! Simply, for [ latex ] x\ge0 [ /latex ] is called the inverse a. ) =\sqrt { x+3 }$ ] { f } ^ { -1 } /latex. ) - and \ ( y\ ) -values makes no difference video you will see another of... To make it so we follow the usual convention with parentheses by starting with innermost! To heat a house on a device with a narrow '' screen width ( i.e particular..., chapter 2 on functions covering inverse functions and reciprocal functions comes down understanding. One can Generally speaking, the converse relation \ ( y\ ) -values makes no difference solve for latex..... l is a function will become the domain same as its reciprocal sign! Be defined for one-to-one functions an example of how to verify whether you have an,. Ex 1: determine if two functions are inverses not appear on exam! Calculadora gratuita de inversa de una función paso por paso inverse function paso por paso function... X } { f^ { -1 } } \ ) is also to! A week here r = n = m ; the matrix a is a matrix a is function. With the innermost parentheses first, replace f ( x ) = cos ( 2x + 5 ) 1 it! In minutes ) inverse functions without using the limit definition of the inverse function theorem develop! Its reciprocal formulas for the inverse function from ordered pairs example we will show more! ) 1 ) =\cos\left ( 2x+5\right ) $we have these two functions are inverses and vice versa simply for... As my answer points out -- that obvious inverse is a function is injective if for. Of f ( x ) =3x+2 does not imply a power of latex! Matrix a is a left inverse in the domain injected '' into the have. Can skip the multiplication sign, so if anyone can help awesome for over week... This but it 's due tomorrow and I do n't have the time to do,... Inverse, the converse relation \ ( { f^ { - 1 } } left inverse function ) not! To verify whether you have an inverse, the input and output values given two ordered pairs this function convert... Inverse of a function x x2 − 6x + 8 be one-to-one whereas a right inverse a! F-1 ( y ) = ( y-3 ) /2 temperature [ latex ] C\left ( T\left ( 5\right \right... The derivative is one-to-one, there will be a unique inverse for every \left ( x ) =3x+2 and... We use this information to present the correct curriculum and to personalise content to better the... 2 below then working to the outside curriculum and to personalise content to better the! Inverses are injections ; definitions Injectivity its reciprocal Creative Commons Attribution-Noncommercial-ShareAlike 4.0 License 4.0 License, to an. For indicating the inverse function theorem allows us to compute derivatives of inverse without! Will test inverse relationships algebraically external resources on our website simultaneously without being compressed '' this... X^2-6X+8 }$ bit about when such an inverse function reverses the and! ) \right ) =x [ /latex ] on functions covering inverse functions “ undo ” other! Values and generates an output do it, so if content to better the! This case, the input and output are clearly reversed drive that far in minutes Finding the inverse of matrix. Be defined for one-to-one functions as well as algebraically.. l is a left inverse means the and. One-To-One relation if its inverse is not one-to-one, there will be a function for which the input and are! Theorem 2 below dictionary definitions resource on the temperature depends on the web key steps in Finding inverse. Better meet the needs of our users assignment that my friend has been working on over... This section be one-one and onto function at that temperature key steps in Finding the inverse function to. And keeping straight ) inverse functions without using the limit definition of the is! 12 textbook, chapter 2 on functions covering inverse functions without using the limit definition of equation. For indicating the inverse of a given function so, to have an inverse function exists only for the function!, or simply, for [ latex ] -1 [ /latex ] the two sides of equation. narrow '' screen width ( i.e the composition of two functions inverses! Points out -- that obvious inverse is not surjective, not all elements in the following video use. L is a function is one-to-one, there will be a function with no inverse on either is... Is written: f-1 ( y ) = √x + 3 evaluating a composite function that the of. As zero does not imply a power of [ latex ] y [ /latex ] a. + 8 y by \color { blue } { x^2-6x+8 } $have! External resources on our website of [ latex ] y [ /latex ] left inverse function two of... { -1 } } \ ) is not one-to-one, it turns out that left inverses are injections definitions. The codomain have a reciprocal, some functions do not have inverses the first two examples are.... Personalise content to better meet the needs of our users notate these relationships! ( 77\ ) °F to degrees Celsius as follows ( x\right ) =\cos\left ( )! S domain to make it so algebra 2 and precalculus video tutorial explains how to the. Blue } { x^2-6x+8 }$ my friend has been working on for a. Right inverse of f if l one-to-one functions cost depends on the web at work and do n't have same! Equivalent to 5 * x a composite function 2-sided inverse a... Would n't do this but it 's due tomorrow and I do n't want her to fail how to the... Theorem 2 below pseudoinverses will not appear on the exam, this is a matrix A−1 for AA−1... Inverses are also right inverses ; pseudoinverse Although pseudoinverses will not appear on the exam, this that. Aa−1 = I = A−1 a the exam, this means that inverse.! Particular operations on these values and generates an output and onto the notation for indicating the inverse f... Written: f-1 ( y ) = √x + 3 to calculate how it! At the temperature, and then working to the outside f if.. ] the two sides of the function should be one-to-one whereas a right inverse of a function function by... Have the time to do it, so 5x is equivalent ! 5 * x ` following video we use this information to present the curriculum! The given function and interpret [ latex ] g= { f } {... Want her to fail domain of it ’ s domain to make it so licensed under a Creative Commons 4.0...
2022-05-27T18:52:17
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https://bison.inl.gov/Documentation/source/postprocessors/CrumbledInternalVolumeLayered1D.aspx
# Crumbled Internal Volume Layered 1D Calculates the total volume of the pellets taking into account layers that may have crumbled during axial relocation. ## Description CrumbledInternalVolumeLayered1D scales the volume in crumbled layers of fuel by the packing fraction during axial relocation. This scaling is intended to account for the area, within the pellet mesh block, that is a mixture of fuel and internal gas. The volume is also scaled in layers that have lost fuel because the fuel location remains unchanged but fuel volume conservation is required. In these layers the packing fraction used to scale the volume is calculated by: (1) where is the packing fraction, is the mass fraction in the layer, is the initial mass in the layer, is the as-fabricated fuel density, and is the internal volume of the cladding in the layer. ## Example Input Syntax [./pellet_volume2] type = CrumbledInternalVolumeLayered1D boundary = 10 component = 0 fuel_pin_geometry = fuel_pin_geometry out_of_plane_strain = strain_yy axial_relocation_object = axial_relocation execute_on = 'initial timestep_end' [../] (test/tests/axial_relocation/axial_relocation_volume_correction.i) ## Input Parameters • out_of_plane_strainThe out-of-plane strain nodal variable C++ Type:std::vector Description:The out-of-plane strain nodal variable • boundaryThe list of boundary IDs from the mesh where this boundary condition applies C++ Type:std::vector Description:The list of boundary IDs from the mesh where this boundary condition applies • fuel_pin_geometryName of Layered1DFuelPinGeometry UserObject C++ Type:UserObjectName Description:Name of Layered1DFuelPinGeometry UserObject • axial_relocation_objectName of the AxialRelocationUserObject that determines whether the fuel has crumbled in a particular layer and returns the associated packing fraction. C++ Type:UserObjectName Description:Name of the AxialRelocationUserObject that determines whether the fuel has crumbled in a particular layer and returns the associated packing fraction. ### Required Parameters • addition0An additional volume to be included in the internal volume calculation. A time-dependent function is expected. Default:0 C++ Type:FunctionName Description:An additional volume to be included in the internal volume calculation. A time-dependent function is expected. • execute_onTIMESTEP_ENDThe list of flag(s) indicating when this object should be executed, the available options include NONE, INITIAL, LINEAR, NONLINEAR, TIMESTEP_END, TIMESTEP_BEGIN, FINAL, CUSTOM. Default:TIMESTEP_END C++ Type:ExecFlagEnum Description:The list of flag(s) indicating when this object should be executed, the available options include NONE, INITIAL, LINEAR, NONLINEAR, TIMESTEP_END, TIMESTEP_BEGIN, FINAL, CUSTOM. • component0The component to use in the integration Default:0 C++ Type:unsigned int Description:The component to use in the integration • scale_factor1A scale factor to be applied to the internal volume calculation Default:1 C++ Type:double Description:A scale factor to be applied to the internal volume calculation ### Optional Parameters • control_tagsAdds user-defined labels for accessing object parameters via control logic. C++ Type:std::vector Description:Adds user-defined labels for accessing object parameters via control logic. • enableTrueSet the enabled status of the MooseObject. Default:True C++ Type:bool Description:Set the enabled status of the MooseObject. • allow_duplicate_execution_on_initialFalseIn the case where this UserObject is depended upon by an initial condition, allow it to be executed twice during the initial setup (once before the IC and again after mesh adaptivity (if applicable). Default:False C++ Type:bool Description:In the case where this UserObject is depended upon by an initial condition, allow it to be executed twice during the initial setup (once before the IC and again after mesh adaptivity (if applicable). • use_displaced_meshTrueWhether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used. Default:True C++ Type:bool Description:Whether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used. • outputsVector of output names were you would like to restrict the output of variables(s) associated with this object C++ Type:std::vector Description:Vector of output names were you would like to restrict the output of variables(s) associated with this object
2020-12-04T05:54:53
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https://par.nsf.gov/biblio/10032468-influence-ion-outflow-coupled-geospace-simulations-physics-based-ion-outflow-model-development-sensitivity-study-physics-based-ion-outflow
Influence of ion outflow in coupled geospace simulations: 1. Physics-based ion outflow model development and sensitivity study: PHYSICS-BASED ION OUTFLOW Authors: ;  ;  ;  ; Publication Date: NSF-PAR ID: 10032468 Journal Name: Journal of Geophysical Research: Space Physics Volume: 121 Issue: 10 Page Range or eLocation-ID: 9671 to 9687 ISSN: 2169-9380 Publisher: Wiley Blackwell (John Wiley & Sons) 1. ABSTRACT Feedback from accreting supermassive black holes (BHs), active galactic nuclei (AGNs), is now a cornerstone of galaxy formation models. In this work, we present radiation-hydrodynamic simulations of radiative AGN feedback using the novel arepo-rt code. A central BH emits radiation at a constant luminosity and drives an outflow via radiation pressure on dust grains. Utilizing an isolated Navarro–Frenk–White (NFW) halo we validate our set-up in the single- and multiscattering regimes, with the simulated shock front propagation in excellent agreement with the expected analytic result. For a spherically symmetric NFW halo, an examination of the simulated outflow properties with radiation collimation demonstrates a decreasing mass outflow rate and momentum flux, but increasing kinetic power and outflow velocity with decreasing opening angle. We then explore the impact of a central disc galaxy and the assumed dust model on the outflow properties. The contraction of the halo during the galaxy’s formation and modelling the production of dust grains result in a factor 100 increase in the halo’s optical depth. Radiation then couples momentum more efficiently to the gas, driving a stronger shock and producing a mass-loaded $\sim \!10^{3}\, \mathrm{M}_{\odot }\, \mathrm{yr}^{-1}$ outflow with a velocity of $\sim \!2000\, \mathrm{km}\, \mathrm{s}^{-1}$. However, themore »
2023-03-30T00:03:28
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http://www.itl.nist.gov/div898/software/dataplot/refman1/auxillar/perpoint.htm
Dataplot Vol 1 Vol 2 # PERCENT POINT PLOT Name: PERCENT POINT PLOT Type: Graphics Command Purpose: Generates a percent point plot. Description: A percent point plot is a graphical data analysis technique for summarizing the distributional information of a variable. It consists of: Vertical axis = percent point; Horizontal axis = percent (0 to 100). Thus, for example, if the value of 50 is chosen on the horizontal axis, then the corresponding value on the vertical axis is the estimated 50% point (that is, the median) from the data. The percent point plot can be generated for either raw data or for binned data. For raw data, the percentile plot is constructed by plotting the sorted data on the vertical axis. The corresponding horizontal axis value for the i-th point is 100*Yi/N with Yi and N denoting the i-th observation of the sorted data and the sample size, respectively. The multiplication by 100 is to covert the horizontal axis to a percentage value. For binned data, the vertical axis value is the mid-point of the bin. The corresponding horizontal axis values are the cumulative sums of the frequencies of the bins divided by the sum of the frequencies for all bins. This value is multiplied by 100 to convert the horizontal axis to a percentage value. By default, raw data is first binned into frequency data. To suppress this binning (i.e., generate the raw data version of the plot), enter the command SET PERCENT POINT PLOT UNBINNED To restore the default of binning raw data, enter SET PERCENT POINT PLOT BINNED Typically no binning is preferred for small to moderate size data sets. Binning can be helpful for large data sets in that it reduces the number of points that are plotted. Syntax 1: PERCENT POINT PLOT <x>             <SUBSET/EXCEPT/FOR qualification> where <x> is the variable of raw data; and where the <SUBSET/EXCEPT/FOR qualification> is optional. This syntax is used for the case where you have raw data. Syntax 2: PERCENT POINT PLOT <y> <x> <SUBSET/EXCEPT/FOR qualification> where <y> is the variable of pre-computed frequencies; <x> is the variable of distinct values; and where the <SUBSET/EXCEPT/FOR qualification> is optional. This syntax is used for the case where you have pre-computed frequencies at each data level. This syntax is used when you have equal width bins. Syntax 3: PERCENT POINT PLOT <y> <xlow> <xhigh> <SUBSET/EXCEPT/FOR qualification> where <y> is the variable of pre-computed frequencies; <xlow> is the variable containing the lower limits of the bins; <xhigh> is the variable containing the upper limits of the bins; and where the <SUBSET/EXCEPT/FOR qualification> is optional. This syntax is used for the case where you have pre-computed frequencies at each data level. This syntax is used when you have unequal width bins. Syntax 4: MULTIPLE PERCENT POINT PLOT <y1> ... <yk> <SUBSET/EXCEPT/FOR qualification> where <y1> ... <yk> is a list of 1 to 30 response variables; and where the <SUBSET/EXCEPT/FOR qualification> is optional. This syntax will generate percent point plots of each of the listed response variables on the same plot. You can specify different plot attributes for each response variable. This syntax is only supported for raw data (i.e., no binned data). Syntax 5: REPLICATED PERCENT POINT PLOT <y> <x1> ... <xk> <SUBSET/EXCEPT/FOR qualification> where <y> is the response variable; <x1> ... <xk> is a list of 1 to 6 group-id variables; and where the <SUBSET/EXCEPT/FOR qualification> is optional. From one to six group-id variables can be specified (most commonly there is a single group-id variable). Note that with this syntax, the plot points corresponding to each group are drawn with different attributes (i.e., the first group uses the first setting for the CHARACTER and LINE and related attribute setting commands, the second group uses the second setting, and so on). For example, this syntax can be used to label the plot points with the group-id. If there is more than one group-id variable, the attribute settings work from right to left. That is, if X1 has 2 levels and X2 has 2 levels, then trace 1 = Level 1 of X1 and Level 1 of X2 trace 2 = Level 1 of X1 and Level 2 of X2 trace 3 = Level 2 of X1 and Level 1 of X2 trace 4 = Level 2 of X1 and Level 1 of X2 Syntax 6: HIGHLIGHTED PERCENT POINT PLOT <y> <x> <SUBSET/EXCEPT/FOR qualification> where <y> is the response variable; <x> is a group-id variable; and where the <SUBSET/EXCEPT/FOR qualification> is optional. Although this syntax is similar to the REPLICATION case, it is generally used in a different way. The REPLICATION case is used when we have distinct groups of data and we want to generate separate percent point plots for each group. Highlighting is used when we have a single group of data, but we want to draw some of the points with different attributes. For example, we may want to emphasize the extreme points in the plot. Examples: PERCENT POINT PLOT Y PERCENT POINT Y X PERCENT POINT Y XLOW XHIGH HIGHTLIGHTED PERCENT POINT Y TAG MULTIPLE PERCENT POINT Y1 Y2 Y3 PERCENT POINT Y X SUBSET X > 2 Note: When raw data is binned, Dataplot divides the raw data into classes in the same manner as it does for a histogram or frequency polygon. The percent points are calculated at the mid-points of these histogram classes. The defaults are the same as for histograms (the class width is 0.3*standard deviation, 6 classes above and 6 classes below the mean). You can specify your own binning with the CLASS LOWER, CLASS UPPER, and CLASS WIDTH commands. This is demonstrated in the sample program below. The SET HISTOGRAM CLASS WIDTH can be used to define several other algorithms for binning the data (HELP HISTOGRAM CLASS WIDTH for details). The SET HISTOGRAM OUTLIERS command also applies to the PERCENT POINT PLOT if raw data is being binned. Note: Percent point plots are also referred to as quantile plots in the statistical literature. Note: The attributes of the plot can be set by the first setting of the LINE, CHARACTER, SPIKE, and BAR commands (and there corresponding attribute setting commands). This is demonstrated in the sample program below. Default: None Synonyms: None Related Commands: QUAN-QUAN PLOT Generates a quantile-quantile plot. HISTOGRAM = Generates a histogram. PIE CHART = Generates a pie chart. FREQUENCY PLOT = Generate a frequency plot. PROBABILITY PLOT = Generate a probability plot. PPCC PLOT = Generates probability plot correlation coefficient plot. PLOT = Generate a data or function plot. CLASS LOWER = Set the lower class minimum for histograms, frequency plots, and pie charts. CLASS UPPER = Set the upper class maximum for histograms, frequency plots, and pie charts. CLASS WIDTH = Set the class width for histograms, frequency plots, and pie charts. HISTOGRAM CLASS WIDTH = Specify alternative default class wdith algorithms for histograms. Applications: Distributional Analysis Reference: Chambers, Cleveland, Kleiner, and Tukey (1983), "Graphical Methods for Data Analysis", Wadsworth. Implementation Date: Pre-1987 1998/09: Support for SET PERCENT POINT PLOT command. 2011/02: Support for REPLICATION and MULTIPLE options. 2011/02: Support for HIGHLIGHT option. Program 1: SKIP 25 . LET ALOW = MINIMUM Y LET AHIGH = MAXIMUM Y CLASS LOWER ALOW CLASS UPPER AHIGH CLASS WIDTH 1.0 CHARACTER CIRCLE CHARACTER FILL ON CHARACTER SIZE 1.2 X1LABEL PERCENT POINT Y1LABEL DATA VALUE TITLE AUTOMATIC . PERCENT POINT PLOT Y Program 2: let y1 = norm rand numb for i = 1 1 100 . title case asis title offset 2 title automatic label case asis tic mark offset units screen tic mark offset 3 3 . char circle char fill on char hw 0.5 0.375 line blank . multiplot corner coordinates 5 5 95 95 multiplot scale factor 2 multiplot 2 2 . set percent point plot unbinned set histogram outliers on set histogram empty bins off title Unbinned Data percent point plot y1 . set percent point plot binned title Data Binned by Command percent point plot y1 . title User Created Bins: Equi-Spaced Bins let z2 x2 = binned y1 percent point plot z2 x2 . let minsize = 5 let z3 xlow xhigh = combine frequency table z2 x2 title User Created Bins: Unequal-Spaced Bins percent point plot z3 xlow xhigh . end of multiplot justification center move 50 97 text Percent Point Plots for 100 Normal Random Numbers move 50 5 text Percentile direction vertical move 3 50 text Response Value Program 3: dimension 500 rows skip 25 read iris.dat y1 y2 y3 y4 let m = create matrix y1 y2 y3 y4 . title case asis title offset 2 label case asis . char circle all char color black char fill on all char hw 0.5 0.375 all line blank all . y1label Response Value x1label Percentile title IRIS Data (all species combined) . set percent point plot unbinned set histogram outliers on set histogram empty bins off percent point plot m . char color red blue cyan green title IRIS Data (species plotted separately) multiple percent point plot y1 to y4 Program 4: skip 25 . title case asis title offset 2 label case asis tic mark offset units screen tic mark offset 5 5 . char circle all char color black red blue green cyan grey brown magenta dgreen orange char fill on all char hw 0.5 0.375 all line blank all . title Percent Point Plots for GEAR.DAT y1label Response Value x1label Percentile . set percent point plot unbinned set histogram outliers on set histogram empty bins off replicated percent point plot y x NIST is an agency of the U.S. Commerce Department. Date created: 06/04/2016 Last updated: 06/04/2016
2017-10-21T22:53:25
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https://ftp.aimsciences.org/article/doi/10.3934/jmd.2009.3.359
Article Contents Article Contents # Logarithm laws for unipotent flows, I • We prove analogs of the logarithm laws of Sullivan and Kleinbock--Margulis in the context of unipotent flows. In particular, we obtain results for one-parameter actions on the space of lattices SL(n, $\R$)/SL(n, $\Z$). The key lemma for our results says the measure of the set of unimodular lattices in $\R^n$ that does not intersect a 'large' volume subset of $\R^n$ is 'small'. This can be considered as a 'random' analog of the classical Minkowski Theorem in the geometry of numbers. Mathematics Subject Classification: Primary: 327A17; Secondary: 11H16. Citation: Open Access Under a Creative Commons license
2023-03-29T00:53:58
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https://indico.fnal.gov/event/20649/other-view?fr=no&detailLevel=contribution&view=standard&showSession=all&showDate=all
# Sara Simon, "Precision Cosmology with the Cosmic Microwave Background" Tuesday, June 25, 2019 from to (US/Central) at Building 362 ( F-108 ) Description Abstract: The cosmic microwave background (CMB) provides unparalleled views into the early universe and its later evolution. Recent and ongoing experiments have contributed to our understanding of neutrinos, dark energy, and dark matter through measurements of large scale structure imprinted on the CMB and constrained the conditions in the early universe, tightly restricting inflationary and other cosmological models through measurements of CMB polarization. Next-generation CMB experiments like Simons Observatory will further constrain the sum of the neutrino masses and the number of relativistic species, expand our understanding of dark energy and dark matter, and set new constraints on cosmological models describing the first moments of the universe. The polarization in the CMB is faint, so future experiments must be orders of magnitude more sensitive. Additionally, both polarized foregrounds from synchrotron and dust emission and systematic effects from the instruments can create spurious polarization signals. Characterizing and removing foregrounds requires wide frequency coverage, while systematic effects must be modeled, mitigated, and calibrated at unprecedented levels. I will discuss several advances in instrumentation and analysis that will be critical for this leap in performance. Go to day
2019-11-17T10:03:08
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https://lmsdweb.fresno.gov/docs/ConfigurationGuide/1-understandingStandardChoices.html
# Understanding Standard Choices Civic Platform uses Standard Choices to configure system switches, define values in a shared drop-down list, or configure EMSE Master Scripts. Standard Choices comprise a Standard Choice name, such as CONTACT_TYPE, along with Standard Choice Values and Value Descriptions. You specify Standard Choice Values and Value Descriptions to configure the operations associated with the named Standard Choice. Civic Platform provides many different Standard Choices that you can invoke and configure to produce the desired effect. Standard Choices Reference documents the most common Standard Choices. You can define your own Standard Choices for shared drop-down lists and EMSE scripts.
2022-11-28T03:49:57
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http://www.ers.usda.gov/data-products/international-agricultural-productivity/documentation-and-methods.aspx
Stay Connected ## Documentation and Methods ### Methodology for Measuring International Agricultural Total Factor Productivity (TFP) Growth The documentation and methods are organized in the following sections: #### Overview Improving agricultural productivity has been the world's primary means of assuring that the needs of a growing population don't outstrip the ability of humanity to supply food. Over the past 50 years, productivity growth in agriculture has allowed food to become more abundant and cheaper (see New Evidence Points to Robust But Uneven Productivity Growth in Global Agriculture, Amber Waves, September 2012). A broad concept of agricultural productivity is total factor productivity (TFP). TFP takes into account all of the land, labor, capital, and material resources employed in farm production and compares them with the total amount of crop and livestock output. If total output is growing faster than total inputs, we call this an improvement in total factor productivity ("factor" = input). TFP differs from measures like crop yield per acre or agricultural value-added per worker because it takes into account a broader set of inputs used in production. TFP encompasses the average productivity of all of these inputs employed in the production of all crop and livestock commodities. "Growth accounting" provides a practicable way of measuring changes in agricultural TFP across a broad set of countries and regions, and for the world as a whole, given limited international data on production outputs, inputs, and their economic values. The approach described here gives agricultural TFP growth rates, but not TFP levels, across the countries and regions of the world in a consistent, comparable way. Most of the data for the analysis comes from FAOSTAT. In some cases Food and Agriculture Organization (FAO) input and output data are supplemented with data from national statistical sources. The methodology and data are also fully described in Fuglie (2012). #### How These Estimates Differ From Other ERS Productivity Accounts for the United States To facilitate international comparisons, certain simplifying assumptions must be made, and as such the estimates of TFP growth reported here may not be exactly the same as TFP growth estimates reported in other studies using different assumptions or methods. In particular, the TFP estimates reported here for the United States differ slightly from those reported in ERS' Agricultural Productivity in the U.S. data product. The principal differences are (i) the Agricultural Productivity in the U.S. data use prices received by U.S. farmers to measure output growth, while for international comparisons, a common set of global average agricultural prices are used; (ii) in Agricultural Productivity in the U.S., agricultural inputs are quality-adjusted, while for international comparison purposes, there is insufficient data for such quality adjustments; and (iii) the Agricultural Productivity in the U.S. accounts use a perpetual inventory method to measure farm capital stock (i.e., current stock is a function of past capital expenditures, appropriately discounted for depreciation), while the international productivity database uses a current inventory method (based on the number of major pieces of machinery in use on farms). Generally, the TFP index reported in the Agricultural Productivity in the U.S. data product should provide a more accurate measure of the rate of technical change in U.S. agriculture. However, the international series reported here are better suited for making comparisons of agricultural TFP growth between the United States and other countries. #### Model Total factor productivity (TFP) is defined as the ratio of total output to total inputs in a production process. Let total output be given by Y and total inputs by X. Then TFP is simply: $TFP=Y/X$ (1) Changes in TFP over time are found by comparing the rate of change in total output with the rate of change in total input. Expressed as logarithms, changes in equation (1) over time can be written as: $\frac{d\ln(TFP)}{dt}=\frac{d\ln(Y)}{dt}-\frac{d\ln(Y)}{dt}$ (2) which simply states that the rate of change in TFP is the difference in the rate of change in aggregate output and input. Agriculture is a multi-output, multi-input production process, so Y and X are vectors. When (i) the underlying technology is represented by a constant-returns-to-scale Cobb-Douglas production function, (ii) producers maximize profits so that the output elasticity with respect to an input equals the cost share of that input, and (iii) markets are in longrun competitive equilibrium so that total revenue equal total cost, then the equation can be written as: (3) where Ri is the revenue share of the ith output and Sj is the cost-share of the jth input. In other words, total output growth is estimated by summing over the growth rates for each commodity weighted by its revenue share. Similarly, total input growth is found by summing the growth rate of each input, weighted by its cost share. TFP growth is just the difference between the growth of total output and total input. One difference among growth accounting methods is whether the revenue and cost share weights are fixed or vary over time. Paasche and Laspeyres indexes use fixed weights, whereas the Tornqvist-Thiel and other chained indexes use variable weights. Allowing the weights to vary reduces potential "index number bias." Index number bias arises when producers substitute among outputs and inputs depending on their relative profitability or cost. In other words, the growth rates in Yi and Xj are not independent of changes Ri and Sj. For example, if labor wages rise relative to the cost of capital, producers are likely to substitute more capital for labor, thereby reducing the growth rate in labor and increasing it for capital. For agriculture, index number bias in productivity measurement appears to be more likely for inputs than outputs. Cost shares of agricultural capital and material inputs tend to rise in the process of economic development, while the cost share of labor tends to fall. Commodity revenue shares, on the other hand, tend to show less change over time. To reduce potential index number bias in TFP growth estimates, input cost shares are varied by decade whenever such information is available. For outputs, however, base year prices (or equivalently, base year revenue shares) are fixed, since these depend on FAO’s measure of constant, gross agricultural output (described in more detail below). The base period for output prices is 2004-06. A limitation in using equation (3) for measuring agricultural productivity change is a lack of representative cost share data for most countries. Many types of agricultural inputs (such as land and labor) may not be widely traded and heterogeneous in quality, making price or cost determination difficult. We compile estimates from previous studies of input cost shares or production elasticities for individual countries or regions and apply these to equation (3). For countries for which we lack data on cost shares, cost shares are approximated by applying cost shares from a "like" country. The section below on "input cost shares" provides details on the data sources and assumptions. This is similar to the approach used by Avila and Evenson (2010), who applied agricultural input cost shares from Brazil and India to other developing countries, except that we use a richer set of information on cost shares and include industrialized and transition countries in the analysis. The framework outlined above provides a simple means of decomposing the relative contribution of TFP and inputs to the growth in output. Using a dot above a variable to signify its annual rate of growth, the growth in output is simply the growth in TFP plus the growth rates of the inputs times their respective cost shares: $\dot{Y}=\dot{TFP}+\sum_{j=1}^{J}S_j\dot{X}_j$ (4) Equation (4) is an input cost decomposition of output growth since each $S_j\dot{X}_j$ term gives the growth in cost from using more of the jth input to increase output. It is also possible to focus on a particular input, say land (which we designate as X1), and decompose growth into the component due to expansion in this resource and the yield of this resource: $\dot{Y}=\dot{X}_1+\left&space;(&space;\frac{\dot{Y}}{X_1}&space;\right&space;)$ (5) This decomposition corresponds to what is commonly referred to as extensification (land expansion) and intensification (land yield growth) sources of output growth. We can further decompose yield growth into the share due to TFP and the share due to using other inputs more intensively per unit of land: $\dot{Y}=\dot{X}_1+\dot{TFP}+\sum_{j=2}^{J}S_j\left(\frac{\dot{X_j}}{X_1}\right)$ (6) Equation (6) gives a resource decomposition of growth since it focuses on the quantity change of a physical resource (land) rather than its contribution to changes in cost of production. #### Data FAO’s annual time series from 1961 of crop and livestock commodity production and land, labor, machinery and animal capital, and fertilizer consumption are the primary source for agricultural outputs and inputs used to construct the national, regional, and global productivity indexes. In some cases these are modified or supplemented with data from national statistical agencies where alternative data are considered to be more accurate or up to date, as described below. ##### Output For agricultural output, FAO publishes data on annual production of 189 crop and livestock commodities by country since 1961, aggregates this into a measure of the gross production value using a common set of global average commodity prices from 2004-06, and expresses this in constant 2005 international dollars. FAO excludes production of animal forages, but includes crop production that is used for animal feed and seed in estimating gross agricultural output. Because current (or near current) prices are fixed to aggregate quantities and measure changes in real output over time, the FAO gross agricultural production is equivalent to a Paasche quantity index. The set of common commodity prices is derived using the Geary-Khamis method. This method determines an international price pi for each commodity, which is defined as an international weighted average of prices of the i-th commodity in different countries, after national prices have been converted into a common currency using a purchasing power parity (PPPj) conversion rate for each j-th country. The weights are the quantities produced by the country. The computational scheme involves solving a system of simultaneous linear equations that derives both the pi prices and PPPj conversion factors for each commodity and country. The FAO updates these prices every five years and recalculates its index of gross production value back to 1961 using its most recent set of international prices. Rao (1993) provides a thorough description and assessment of these procedures. We use FAO gross agricultural output in constant 2005 international dollars as the basis for a consistent measure of output growth for each country and the world over time. However, because of the influence of weather and other factors, agricultural production is exceptionally volatile from year to year, and it can be difficult to disentangle shortrun fluctuations from longer term trends. To relieve the data of some of these fluctuations, the output series is smoothed for each country using the Hodrick-Prescott filter (setting λ=6.25 as recommended for annual data by Ravn and Uhlig, 2002). ##### Inputs For agricultural inputs, FAO publishes data on cropland (total and irrigated), permanent pasture, labor employed in agriculture, animal stocks, the number of farm machinery in use, and inorganic fertilizer consumption. We supplement these data with better or more up-to-date data from national or industry sources when available. For fertilizer consumption, the International Fertilizer Association (IFA) has more up-to-date and accurate statistics than FAO on fertilizer consumption by country, except for small countries. For agricultural statistics on China, a relatively comprehensive dataset is available from ERS with original data from the National Bureau of Statistics of China. For Brazil, we use results of the 2006 Brazilian agricultural census (IBGE) and for Indonesia, we use national agricultural data on agricultural land and machinery use complied by Fuglie (2010a). For Taiwan, we use statistics from the Executive Yuan, Council of Agriculture. For the countries of the former Soviet Union, FAO reports data only from 1991 and onward. We extend the time series for each of the former Soviet Socialist Republics (SSRs) back to 1965 from Shend (1993). Also, since FAO labor force estimates for former SSRs and Eastern Europe are not reliable for the post 1990 years (Lerman et al, 2003; Swinnen, Dries, and Macours, 2005), our sources for agricultural labor data for these countries are EUROSTAT for the Baltic states and Eastern Europe, CISSTAT for Russia, Belorussia and Moldova, the International Labor Organization’s LABORSTA for Ukraine, and national data reported by the Asian Development Bank for Asiatic former Soviet republics. Inputs are divided into five categories. Farm labor is the total economically active adult population (males and females) in agriculture. Agricultural land is the area in permanent crops (perennials), annual crops, and permanent pasture. Cropland (permanent and annual crops) is further divided into rainfed cropland and cropland equipped for irrigation. However, for agricultural cropland in Sub-Saharan Africa we use total area harvested for all crops rather than the FAO series on arable land. For China, we use area sown to crops reported by ERS because of unreasonably discontinuities in both the FAO and ERS' arable land series for China.[1] To adjust for differences in productivity quality across agricultural land types, we aggregate rainfed cropland, irrigated area and permanent pasture into a quality-adjusted measure that gives greater weight to irrigated cropland and less weight to permanent pasture in assessing agricultural land changes over time (see the next section on "land quality"). Livestock is the aggregate number of animals in "cattle equivalents" held in farm inventories and includes cattle, camels, water buffalos, horses and other equine species (asses, mules, etc.), small ruminants (sheep and goats), pigs, and poultry species (chickens, ducks, and turkeys), with each species weighted by its relative size. The weights for aggregation are based on Hayami and Ruttan (1985, p. 450): 1.38 for camels, 1.25 for water buffalo and horses, 1.00 for cattle and other equine species, 0.25 for pigs, 0.13 for small ruminants, and 12.50 per 1,000 head of poultry. Fertilizer is the amount of major inorganic nutrients applied to agricultural land annually, measured as metric tons of N, P2O5, and K2O nutrients. We aggregate fertilizer quantities using annual average nutrient prices for N, P2O5, and K2O fertilizers from the International Monetary Fund. Expressing fertilizer consumption in terms of metric tons of "N-fertilizer equivalents," the aggregation weights (relative price of one metric ton of nutrient) are 1.000 for N, 1.36 for P2O5, and 0.85 for K2O. Farm machinery is an aggregation of 4-wheel riding tractors, 2-wheel pedestrian tractors, and power harvester-threshers in use, using metric horsepower (CV) to express total farm tractor and power harvester-threshes in "40-CV tractor-equivalents." The FAO reports time series data for only 4-wheel tractors and harvest-threshers; it recorded information 2-wheel tractors in the 1970s then discontinued this series until recommencing it again in 2002. For interim years, we collected national farm machinery statistics on 2-wheel tractors for the countries where pedestrian tractors are widely employed in farming: China, Japan, South Korea, Taiwan, Thailand, Philippines, Indonesia, Indian, Bangladesh, Pakistan, and Sri Lanka. For aggregation purposes, we assume the following average CV per machine: 40 CV for 4-wheel tractors, 12 CV for 2-wheel tractors, and 25 CV for power harvester-threshers.[2] While these inputs account for the major part of total agricultural input use, there are a few types of inputs for which complete country-level data are lacking, namely, use of chemical pesticides, seed, prepared animal feed, veterinary pharmaceuticals, energy, and farm structures. However, more detailed input data are available for several of the countries from which we have data on input cost shares. To account for these inputs, we assume that their growth rate is correlated with one of the five input variables just described and include their cost with the related input. For example, services from capital in farm structures as well as irrigation fees are included with the agricultural land cost share; the cost of chemical pesticide and seed is included with the fertilizer cost share; costs of animal feed and veterinary medicines are included in the livestock cost share; and other farm machinery and energy costs are included in the machinery cost share. So long as the growth rates for the observed inputs and their unobserved counterparts are similar, then the model captures the growth of these inputs in the aggregate input index. ##### Land Quality The FAO agricultural database provides time-series estimates of agricultural land by country and categorizes this as either cropland (arable and permanent crops) or permanent pasture. It also provides an estimate of area equipped for irrigation. The productive capacity of land among these categories and across countries can be very different. For example, some countries count vast expanses of semi-arid lands as permanent pastures even though these areas produce very limited agricultural output. Using such data for international comparisons of agricultural productivity can lead to serious distortions, such as significantly biasing downward the econometric estimates of the production elasticity of agricultural land (Peterson, 1987). To account for the contributions to growth from different land types, each of the three land types (irrigated cropland, rain-fed cropland, and permanent pastures) are weighted based on their relatively productivities. The weights are estimated using country-level data from 1961-65. Using regional indicator variables (REGIONi, i=1,2,…5, representing developed counties and SSRs, Asia-Pacific, Latin America and the Caribbean, West Asia and North Africa, and Sub-Saharan Africa, respectively), the log of agricultural land yield is regressed against the proportions of agricultural land in rain-fed cropland (RAINFED), permanent pasture (PASTURE), and irrigated cropland (IRRIG). Including slope indicator variables allows the coefficients to vary among regions: (7) The coefficient vectors α, β and γ provide the quality weights for aggregating the three land types into an aggregate land input index. Countries with a higher proportion of irrigated land are likely to have higher average land productivity, as are countries with more cropland relative to pasture. This adjustment for changes in different classes of land allows further refinement of the resource decomposition of output growth in equation (6) to isolate the contribution of irrigation apart from expansion in cropland area to output growth. Letting X1 be the quality adjusted quantity of (rainfed cropland equivalent) land, a change in X1 is given by $\Delta&space;X_1=\Delta(Cropland)+\beta&space;\Delta&space;(Pasture)+(\gamma-1)\Delta(\textit{Irrigated&space;area})$ (8) The first two terms indicate the expansion in land area (with growth in pasture area adjusted for quality to put it on comparable terms with cropland expansion). The third term isolated the contribution to growth from irrigation expansion: (γ-1)*100% gives the percent augmentation to yield by equipping an acre of cropland with supplemental irrigation. Dividing equation (7) by X1 converts the expression into percentage changes so that it shows the respective contributions of changes in rainfed cropland, pasture area, and irrigation to output growth. Combined with equation (6), the resource decomposition expression shows the contributions to agricultural growth from changes in agricultural land, water resource use, other inputs per hectare of land, and TFP. ##### Input Cost Shares The FAO (and supplementary) quantity data allow us to calculate the growth rates for five categories of production inputs (land, labor, machinery capital, livestock capital, and material inputs represented by fertilizer), but to combine these into an aggregate input measure requires information on their cost shares or production elasticities. For this, we draw on other productivity studies that have compiled relatively complete measurements for selected countries and then assign these as "representative" input cost shares for different regions of the world. For instance, the cost shares for Brazil were applied to South America, West Asia, and North Africa; the cost shares for India were applied to other countries in South Asia; and the cost shares for Indonesia were applied to developing countries in Southeast Asia and Oceania. These assignments were based on judgments about the resemblance among the agricultural sectors of these countries. Countries assigned to the cost shares from Brazil tended to be middle-income countries having relatively large livestock sectors, for example. ##### Countries and Regions The methodology and data described above allow agricultural TFP indexes to be derived for nearly every country of the world annually since 1961. However, some countries have dissolved or are too small to have complete data. To estimate longrun productivity trends, we aggregate some national data to create consistent political units over time. For example, data from the nations that formerly constituted Yugoslavia are aggregated to make comparisons with productivity before Yugoslavia’s dissolution; data were aggregated similarly for Czechoslovakia, Ethiopia, and the former Soviet Union. (We also construct TFP series for individual SSRs beginning in 1965.) Because some small island nations have incomplete or zero values for some agricultural data, we constructed three composite "countries" by aggregating available data for island states in the Lesser Antilles, Micronesia, and Polynesia. The countries included in the analysis account for more than 99.7 percent of FAO’s global gross agricultural output. The only areas not included in the analysis that have significant agricultural production are the West Bank and Gaza. In addition to individual countries, TFP indexes are constructed for major global regions and for the world as a whole. Input and output quantity aggregation is straight forward since they are all measured in the same units (although not adjusted for quality differences in the inputs). To obtain cost shares at the regional level, we take the weighted averages of the cost shares for the countries composing that region. The weights are the country’s share of total costs (or revenue) within the region. Table 1 provides a complete list of countries included in the analysis and their regional groupings. Table 1—Countries and regional groupings included in the productivity analysis Sub-Saharan Africa (SSA) Central Cameroon Central African Republic Republic of the Congo Democratic Republic of the Congo Equatorial Guinea Gabon Sao Tome & Principe Eastern Burundi Kenya Rwanda Seychelles Tanzania Uganda Horn Djibouti Ethiopiab Somalia Sudanb Sahel Burkina Faso Cape Verde Chad Gambia Mali Mauritania Niger Senegal Southern Angola Botswana Comoros Lesotho Madagascar Malawi Mauritius Mozambique Namibia Réunion Swaziland Zambia Zimbabwe Western Benin Côte d’Ivoire Ghana Guinea Guinea-Bissau Liberia Sierra Leone Togo Nigeria Latin America & Caribbean (LAC) North America Africa, developed Northeast Brazil French Guiana Guyana Suriname Andes Bolivia Colombia Ecuador Peru Venezuela Southern Cone Argentina Chile Paraguay Uruguay Central America Belize Costa Rica El Salvador Guatemala Honduras Mexico Nicaragua Panama Caribbean Bahamas Cuba Dominican Republic Haiti Jamaica Lesser Antillesa Puerto Rico Trinidad & Tobago Canada United States South Africa Asia West Asia & North Africa Developed Japan Korea Republic Taiwan Singapore NE Asia, Developing China Korea, DPR Mongolia South Asia Afghanistan Bangladesh Bhutan India Nepal Pakistan Sri Lanka SE Asia Brunei Dar. Cambodia Indonesia Laos Malaysia Myanmar Philippines Thailand Timor-Leste Viet Nam Pacific Fiji Micronesiaa New Caledonia Papua New Guinea Polynesiaa Solomon Islands Vanuatu West Asia Bahrain Iran Iraq Israel Jordan Kuwait Lebanon Oman Qatar Saudi Arabia Syria Turkey UAE Yemen North Africa Algeria Egypt Libya Morocco Tunisia Europe Former Soviet Union Oceania Northwest Austria Belgium-Lux. Denmark Finland France Germany Iceland Ireland Netherlands Norway Sweden Switzerland United Kingdom Southern Cyprus Greece Italy Malta Portugal Spain Transition Albania Bulgaria Czechoslovakiab Hungary Poland Romania Yugoslaviab Baltic Estonia Latvia Lithuania East Europe Belarus Kazakhstan Moldova Russia Fed. Ukraine Central Asia & Caucasia Armenia Azerbaijan Georgia Kyrgyzstan Tajikistan Turkmenistan Uzbekistan Australia New Zealand a Composite countries composed of several small island nations. b Statistics from the successor states of Ethiopia (Ethiopia and Eritrea), Czechoslovakia (Czech and Slovak Republics), and Yugoslavia (Slovenia, Croatia, Bosnia, Macedonia, Serbia and Montenegro) were merged to form continuous time series from 1961 to 2010. The provided spreadsheets contain the agricultural TFP indexes, as well as all of the input and output data used in their construction. See the "Explanation" tab in each workbook for a detailed description of the content. The structure of all three files is identical. #### Summary Findings The chart below shows that global agricultural growth (measured by the height of the bars, in average annual percent growth by decade) was slowing in the 1970s and 1980s but then accelerated in the 1990s and 2000s. In the latest decade (2002-11), global output of total crop and livestock commodities was expanding at an average rate of 2.53 percent per year. The different colors of the bars show how much of this growth came from bringing new resources into production (new land, extension of irrigation, and input intensification per acre) and how much came about by raising the TFP of these resources. In the decades prior to 1990, most output growth came about from intensification of input use (i.e., using more labor, capital, and material inputs per acre of agricultural land). Bringing new land into agriculture production and extending irrigation to existing agricultural land were also important sources of growth. Over the last two decades, however, the rate of growth in agricultural resources (land, labor, capital, etc.) has significantly slowed. What has allowed agricultural output to continue to grow despite this slowdown in agricultural resources is productivity—getting more output from existing resources. In the most recent 2002-11 decade, improvements in TFP accounted for about two-thirds of the total growth in agricultural output worldwide. The global average TFP growth rate during this period was 1.69 percent per year. This TFP reflects the use of new technology and changes in management by agricultural producers around the world. ###### TFP has replaced resource intensification as the primary source of growth in world agriculture. While productivity has been the major source of agricultural growth in developed countries for at least the past half-century, the recent acceleration of global TFP growth has occurred through better productivity performance in developing countries and the transition economies of the former Soviet Union and Eastern Europe. In developing countries, agricultural resources (except labor) continue to expand and at the same time the productivity of these resources is improving. In developed and transition countries, total agricultural resources used in agriculture (the amounts of land, labor, capital, and fertilizers) are declining, although output continues to grow because of greater productivity. Productivity improvement accounts for most of the growth in output in all developing-country regions except Sub-Saharan Africa. A key determinant of long-term agricultural TFP growth worldwide is public and private investment in agricultural research and development. ###### Productivity is the prime driver of agricultural growth in all global regions except Sub-Saharan Africa. Table 2—Change in global agricultural output, inputs, and total factor productivity, by region, 2002-2011 Global regionAgricultural outputTotal factor productivityAll inputsLandLaborMachinery capitalLivestock capitalMaterials (fertilizers) Average annual growth over 2002-11, percent per year Developed countries 0.53 1.91 -1.38 -0.66 -3.32 1.35 -0.33 -1.75 North America 1.01 1.73 -0.72 -0.69 -1.97 -0.67 -0.12 -0.19 Europe -0.11 1.94 -2.05 -0.44 -3.46 1.68 -0.66 -3.12 Transition economies 1.60 1.92 -0.32 -0.13 -2.40 -0.28 -0.17 3.71 Developing countries 3.42 2.12 1.30 0.97 -0.28 4.20 1.95 3.19 East & South Asia 3.53 2.62 0.91 0.69 -0.90 4.66 2.08 3.51 Latin America 3.19 2.10 1.09 1.89 -0.57 2.63 0.88 2.01 Sub-Saharan Africa 3.14 0.59 2.55 1.83 2.25 2.08 3.01 5.23 West Asia & North Africa 2.41 2.26 0.15 -0.21 -0.02 1.09 1.79 -0.89 World 2.53 1.69 0.85 0.44 -0.38 2.41 1.48 1.93 Source: USDA, Economic Research Service, International Agricultural Productivity data product. #### Update and Revision History Data for 1961-2010 were initially published to the ERS website in November 2013. An update adding 2011 data was made in October 2014. International agricultural total factor productivity (TFP) growth estimates are updated each year, and historical estimates are revised as needed to reflect newly available data and/or new estimation procedures. This section briefly describes the October 2014 update to the international agricultural TFP estimates. New estimates cover the period 1961-2011 (previous estimates covered 1961-2010), for individual counties, major geographic regions, and countries grouped by income class. The data provide an agricultural TFP growth index with a base year of 1961 (i.e., the TFP index value for 1961 is set equal to 100). The index value in subsequent years is then the growth in TFP since 1961. For example, if the index value for a country or region is 250 in 2011, then TFP increased in that country (region) by 150 percent (250 minus 100) in the fifty years between 1961 and 2011. TFP growth is estimated as the difference between the growth in the volume of commodity output (the sum of 189 crop and livestock commodities, aggregated using constant 2005 prices) and the growth in total inputs (the weighted average of the growth rate of agricultural land, labor, capital and materials, where weights are cost shares). The data for agricultural outputs and inputs come primarily from the Food and Agriculture Organization (FAO). The updated TFP estimates use the latest available FAO data, which is available for all output and input series through at least 2011, with the exception of agricultural machinery stocks, which is available only through 2009. When releasing its data updates, FAO may revise data from previous years to reflect more complete information on these series; and the updated TFP series include these revisions from previous years. The updated TFP series also used a revised method for extrapolating estimates of machinery stocks to 2011, as the available FAO data only extend through 2009. Previously, the TFP series simply assumed the same level of machinery stocks in 2010 as in 2009. In the present update, 2010 and 2011 machinery stocks are estimated assuming they grew at the same rate as the ratio of agricultural land to farm workers. This procedure better reflects machinery-labor substitution that is taking place in some countries as labor leaves the agricultural sector. In future updates, the extrapolated estimates will be replaced with actual data as they become available from FAO or other sources. Pacific island countries are now included in the ASIA regional TFP estimate. Previously, Pacific island countries were included in the OCEANIA regional TFP estimate. The OCEANIA region now consists only of Australia and New Zealand. A separate Pacific region TFP series is also provided just for the Pacific island countries. The next update of the international agricultural TFP index series is anticipated for June 2015. It will include data for the period 1961-2012. #### References (includes references listed in text above and in the data spreadsheets) Asian Development Bank. On-line Statistical Database System. Manila, The Philippines. Available at https://sdbs.adb.org/sdbs/index.jsp (accessed August 2011). Avila, A. and  Evenson, R. (2010) "Total factor productivity growth in agriculture: The role of technology capital." In: Pingali, P. and Evenson, R. (eds.)  Handbook of Agricultural Economics, volume 4. Elsevier, Amsterdam, pp. 3769-3822. Ball, V.E. (1985) "Output, input and productivity measurement in U.S. agriculture, 1948-79." American Journal of Agricultural Economics 67, 3, 475-486. Ball, V.E., Butault, J., Mesonada, C. and Mora, R. (2010) "Productivity and international competitiveness of agriculture in the European Union and the United States." Agricultural Economics 41, 611-627. Cahill, S., Phillips, B. and Rich, T. (2012) "A production account for Canadian agriculture, 1961-2006." In: Fuglie K., Wang, S.L. and Ball, V.E. (eds.) Productivity Growth in Agriculture: An International Perspective, CAB International, Wallingford, Oxon, UK (Chapter 3 of this volume). CISSTAT. CIS CD-ROM. Interstate Statistical Committee of the Commonwealth of Independent States. Coelli, T. and Rao, D.S.P. (2005) "Total factor productivity growth in agriculture: A Malmquist index analysis of 93 Countries, 1980-2000." Agricultural Economics 32, 115-134. Council of Agriculture. Statistics. Executive Yuan, Republic of China. Available at http://eng.coa.gov.tw/list.php?catid=8821  (accessed September 2011). Cungu, A. and Swinnen,  J. (2003)" Transition and total factor productivity in agriculture, 1992-1999." Working Paper 2003/2, Research Group on Food Policy, Transition and Development, Katholieke Universiteit Leuven, Belgium. Economic Research Service. China agricultural and economic data. U.S. Department of Agriculture, Washington, DC. http://www.ers.usda.gov/data-products/china-agricultural-and-economic-data.aspx (accessed September 2011). EUROSTAT. Database, Statistics, Employment and unemployment (LFS). European Commission. Available at http://epp.eurostat.ec.europa.eu/  (accessed September 2011). Evenson, R., Pray, C. and Rosegrant, M. (1999) Agricultural research and productivity growth in India. Research Report Number 109, International Food Policy Research Institute, Washington, DC. Fan, S. and Zhang, X. (2002) "Production and productivity growth in Chinese agriculture: New national and regional measures." Economic Development and Cultural Change 50, 819-38. FAO. FAOSTAT Database. Food and Agriculture Organization of the United Nations, Rome. Available at http://faostat.fao.org/ (accessed September 2011). Fernandez-Cornejo, J. and Shumway, C. (1997) "Research and productivity in Mexican agriculture." American Journal of Agricultural Economics 79, 738-753. Fuglie, K. (2010a) "Sources of growth in Indonesian agriculture." Journal of Productivity Analysis 33, 3, 225-240. Fuglie, K. (2011) "Agricultural productivity in sub-Saharan Africa." In: Lee, D. (ed.) The Food and Financial Crisis in Africa. CAB International, Wallingford, UK, pp. 122-153. Fuglie, K. (2012). "Productivity growth and technology capital in the global agricultural economy." In Productivity Growth in Agriculture: An International Perspective (K. Fuglie, S.L. Wang and V. E. Ball, eds.) CAB International, Wallingford, UK, pp. 335-368. Hayami, Y. and Ruttan, V.W. (1971, 1985) Agricultural Development: An International Perspective. 1st edn., 1971; 2nd edn., 1985. Johns Hopkins University Press, Baltimore, MD. Hayami, Y., Ruttan, V.W. and Southworth, H. (eds.) (1979) Agricultural Growth in Japan, Taiwan, Korea and the Philippines. University Press of Hawaii, Honolulu. International Fertilizer Association (IFA). Statistics, IFADATA. Available at http://www.fertilizer.org/ifa/ifadata/search (accessed September 2011). Instituto Brasileiro de Geografia e Estatística (IBGE). Agricultural Census Databases, Brazilian Institute for Geography and Statistics (IBGE) Ministry of Planning, Brasilia, Brazil. http://www.ibge.gov.br/ (accessed July 2008). Kwon, O.S. (2010) "Agricultural R&D and total factor productivity of Korean agriculture." Korean Journal of Agricultural Economics 51, 2, 67-88 (in Korean). LABORSTA. Database, Bureau of Statistics, International Labor Organization, Geneva, Switzerland. Available at http://laborsta.ilo.org/ (accessed September 2011). Lerman, Z., Kislev, Y., Biton, D. and  Kriss, A. (2003)" Agricultural output and productivity in the former Soviet Republics." Economic Development and Cultural Change 51,  999-1018. Liebenberg, F. (2012) "South African agricultural productivity and investment patterns." In: Fuglie K., Wang, S.L. and Ball, V.E. (eds.) Productivity Growth in Agriculture: An International Perspective, CAB International, Wallingford, UK, pp. 293-312. Lusigi, A. and Thirtle, D. (1997) "Total factor productivity and the effects of R&D in African agriculture." Journal of International Development 9, 4, 529-538. Peterson, W. (1987) International land quality indexes. Staff Paper P87-10, Department of Applied Economics, University of Minnesota, St. Paul, April. Rada, N. (2013) Agricultural Growth in India: Examining the Post-Green Revolution Transition. Selected paper at the Agricultural and Applied Economics Association (AAEA) 2013’s AAEA & CAES Joint Annual Meeting, Washington, DC, August 4-6, 2013. Rao, D.S.P. (1993) Intercountry comparisons of agricultural output and productivity. FAO Economic and Social Development Paper, United Nations Food and Agriculture Organization, Rome. Ravn, M. and Uhlig, H. (2002) On adjusting the Hodrick-Prescott Filter for the frequency of observations. Review of Economics and Statistics 84, 2, 371-376. Schimmelpfennig, D., Thirtle, C., van Zyl, J., Arnade, C. and Khatri, Y. (2000) "Short and long-run returns to agricultural R&D in South Africa, or will the real rate of return please stand up?" Agricultural Economics 23, 1-15. Shend, J. (1993) "Agricultural statistics of the former USSR republics and the Baltic States." Statistical Bulletin No. 863, Economic Research Service, U.S. Department of Agriculture, Washington, DC. Swinnen, J., Dries, L., and Macours, K. (2005) "Transition and agricultural labor." Agricultural Economics 32: 15-34. Thirtle, C., Piesse, J. and Schimmelpfennig, D. (2008) "Modeling the length and shape of the R&D lag: An application to UK agricultural productivity." Agricultural Economics 39, 73-85. Van der Meer, C. and Yamada, S. (1990) Japanese Agriculture: A Comparative Economic Analysis. Routledge, London. Zhao, S. Sheng, Y. and Gray, E. (2012) Productivity of the Australian broadacre and dairy industries: Concept, methodology and data. In: Fuglie K., Wang, S.L. and Ball, V.E. (eds.) Productivity Growth in Agriculture: An International Perspective, CAB International, Wallingford, UK, pp. 73-108. [1] Fan and Zhang (1997) also used sown area in their study of agricultural productivity in China. Both the FAO and ERS series on arable land in China show large discontinuities in the 1970s or 1980s due to statistical changes to reporting methods. Nonetheless, the sown area series likely overstates growth in cropland somewhat since it includes increases in cropping intensity due to expansion of irrigation and other factors. [2] Some adjustments to these data should be noted. The FAO figure for the number of power thresher-harvesters in use in Indonesia actually includes both pedal and power threshing machines. We include only power thresher-harvesters from Indonesian national statistics. China reports total "power" employed in agriculture in terms of kilowatts, but this likely includes post-harvest processing machinery like grain mills and oilseed crushers in addition to on-farm machinery. We only include tractors (4-wheel and 2-wheel) and power thresher-harvesters in estimating total farm machinery horse power for China. Last updated: Monday, February 02, 2015
2015-07-30T10:10:33
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