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http://lammps.sandia.gov/doc/fix_shardlow.html
|
# fix shardlow command
## Syntax
fix ID group-ID shardlow
• ID, group-ID are documented in fix command
• shardlow = style name of this fix command
## Examples
fix 1 all shardlow
## Description
Specifies that the Shardlow splitting algorithm (SSA) is to be used to integrate the DPD equations of motion. The SSA splits the integration into a stochastic and deterministic integration step. The fix shardlow performs the stochastic integration step and must be used in conjunction with a deterministic integrator (e.g. fix nve or fix nph). The stochastic integration of the dissipative and random forces is performed prior to the deterministic integration of the conservative force. Further details regarding the method are provided in (Lisal) and (Larentzos1).
The fix shardlow must be used with the pair_style dpd/fdt or pair_style dpd/fdt/energy command to properly initialize the fluctuation-dissipation theorem parameter(s) sigma (and kappa, if necessary).
Note that numerous variants of DPD can be specified by choosing an appropriate combination of the integrator and pair_style dpd/fdt command. DPD under isothermal conditions can be specified by using fix shardlow, fix nve and pair_style dpd/fdt. DPD under isoenergetic conditions can be specified by using fix shardlow, fix nve and pair_style dpd/fdt/energy. DPD under isobaric conditions can be specified by using fix shardlow, fix nph and pair_style dpd/fdt. DPD under isoenthalpic conditions can be specified by using fix shardlow, fix nph and pair_style dpd/fdt/energy. Examples of each DPD variant are provided in the examples/USER/dpd directory.
## Restrictions
This command is part of the USER-DPD package. It is only enabled if LAMMPS was built with that package. See the Making LAMMPS section for more info.
This fix is currently limited to orthogonal simulation cell geometries.
This fix must be used with an additional fix that specifies time integration, e.g. fix nve or fix nph.
The Shardlow splitting algorithm requires the sizes of the sub-domain lengths to be larger than twice the cutoff+skin. Generally, the domain decomposition is dependent on the number of processors requested.
| 2017-03-25T05:45:15 |
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|
https://ftp.mcs.anl.gov/pub/fathom/moab-docs/classmoab_1_1EdgeSizeSimpleImplicit.html
|
MOAB: Mesh Oriented datABase (version 5.4.0)
moab::EdgeSizeSimpleImplicit Class Reference
#include <EdgeSizeSimpleImplicit.hpp>
Inheritance diagram for moab::EdgeSizeSimpleImplicit:
Collaboration diagram for moab::EdgeSizeSimpleImplicit:
## Public Member Functions
EdgeSizeSimpleImplicit ()
Construct an evaluator.
virtual ~EdgeSizeSimpleImplicit ()
Destruction is virtual so subclasses may clean up after refinement.
virtual bool evaluate_edge (const double *p0, const void *t0, double *p1, void *t1, const double *p2, const void *t2)
Given an edge of length L, true when edge midpoint is within $^2$ of $({2f(x,y,z)}{L})^2$.
virtual void set_implicit_function (double *coeffs)
void get_implicit_function (double *&coeffs)
virtual void set_ratio (double r)
Set the threshold ratio of function value to half-edge length that triggers subdivision.
double get_ratio ()
Get the threshold ratio of function value to half-edge length that triggers subdivision.
## Protected Attributes
double coeffA [6]
double coeffB [3]
double coeffC
double ratio
## Detailed Description
This is an simple example edge evaluator tha subdivides edges based on their midpoint's distance to a simple, fixed-form implicit surface written as $$x^T A x + B x + C$$ where $$x$$ is a column vector of holding the edge midpoint coordinates, $$A$$ is a symmetric 3x3 matrix, $$B$$ is a 1x3 row vector, and $$C$$ is a scalar. Whenever the implicit function divided by half of the edge length is smaller than some minimum ratio (which defaults to 1), the edge is marked for subdivision.
Date:
19 November 2007
Definition at line 38 of file EdgeSizeSimpleImplicit.hpp.
## Constructor & Destructor Documentation
moab::EdgeSizeSimpleImplicit::EdgeSizeSimpleImplicit ( )
Construct an evaluator.
Definition at line 6 of file EdgeSizeSimpleImplicit.cpp.
References coeffA, coeffB, coeffC, and ratio.
{
int i;
// Default to the plane: x = 0.
this->coeffC = 0.;
for( i = 0; i < 3; ++i )
{
this->coeffB[i] = this->coeffA[i] = this->coeffA[i + 3] = 0.;
}
this->coeffB[0] = 1.;
// Default to a scaling ratio of 1.
this->ratio = 1.;
}
moab::EdgeSizeSimpleImplicit::~EdgeSizeSimpleImplicit ( ) [virtual]
Destruction is virtual so subclasses may clean up after refinement.
Definition at line 20 of file EdgeSizeSimpleImplicit.cpp.
{}
## Member Function Documentation
bool moab::EdgeSizeSimpleImplicit::evaluate_edge ( const double * p0, const void * t0, double * p1, void * t1, const double * p2, const void * t2 ) [virtual]
Given an edge of length L, true when edge midpoint is within $^2$ of $({2f(x,y,z)}{L})^2$.
Implements moab::EdgeSizeEvaluator.
Definition at line 22 of file EdgeSizeSimpleImplicit.cpp.
References coeffA, coeffB, coeffC, ratio, and z.
{
(void)t0;
(void)t1;
(void)t2;
double L2 = 0.;
double delta;
int i;
for( i = 0; i < 3; ++i )
{
delta = p2[i + 3] - p0[i + 3];
L2 += delta * delta;
}
// parametric coords in p1[{0,1,2}]
double x = p1[3];
double y = p1[4];
double z = p1[5];
double F2 = this->coeffA[0] * x * x + 2. * this->coeffA[1] * x * y + 2. * this->coeffA[2] * x * z +
this->coeffA[3] * y * y + 2. * this->coeffA[4] * y * z + this->coeffA[5] * z * z + this->coeffB[0] * x +
this->coeffB[1] * y + this->coeffB[2] * z + this->coeffC;
F2 = F2 * F2; // square it
double r2 = this->ratio * this->ratio;
if( 4. * F2 / L2 < r2 ) return true; // Midpoint is close to surface => split edge
return false; // Don't split edge
}
void moab::EdgeSizeSimpleImplicit::get_implicit_function ( double *& coeffs )
Get the 10 coefficients of the implicit function. The vector contains the entries of A, followed by B, followed by C.
Definition at line 67 of file EdgeSizeSimpleImplicit.cpp.
References coeffA, coeffB, and coeffC.
{
int i;
// Default to the plane: x = 0.
for( i = 0; i < 3; ++i )
{
coeffs[i] = this->coeffA[i];
coeffs[i + 3] = this->coeffA[i + 3];
coeffs[i + 6] = this->coeffB[i];
}
coeffs[9] = this->coeffC;
}
double moab::EdgeSizeSimpleImplicit::get_ratio ( ) [inline]
Get the threshold ratio of function value to half-edge length that triggers subdivision.
Definition at line 69 of file EdgeSizeSimpleImplicit.hpp.
References ratio.
{
return this->ratio;
}
void moab::EdgeSizeSimpleImplicit::set_implicit_function ( double * coeffs ) [virtual]
Set the 10 coefficients of the implicit function. The vector contains the entries of A, followed by B, followed by C.
Definition at line 54 of file EdgeSizeSimpleImplicit.cpp.
References coeffA, coeffB, and coeffC.
{
int i;
// Default to the plane: x = 0.
for( i = 0; i < 3; ++i )
{
this->coeffA[i] = coeffs[i];
this->coeffA[i + 3] = coeffs[i + 3];
this->coeffB[i] = coeffs[i + 6];
}
this->coeffC = coeffs[9];
}
virtual void moab::EdgeSizeSimpleImplicit::set_ratio ( double r ) [inline, virtual]
Set the threshold ratio of function value to half-edge length that triggers subdivision.
Definition at line 64 of file EdgeSizeSimpleImplicit.hpp.
References ratio.
Referenced by TestMeshRefiner().
{
this->ratio = r;
}
## Member Data Documentation
double moab::EdgeSizeSimpleImplicit::coeffA[6] [protected]
Definition at line 75 of file EdgeSizeSimpleImplicit.hpp.
double moab::EdgeSizeSimpleImplicit::coeffB[3] [protected]
Definition at line 76 of file EdgeSizeSimpleImplicit.hpp.
double moab::EdgeSizeSimpleImplicit::coeffC [protected]
Definition at line 77 of file EdgeSizeSimpleImplicit.hpp.
double moab::EdgeSizeSimpleImplicit::ratio [protected]
List of all members.
The documentation for this class was generated from the following files:
| 2022-10-02T18:30:22 |
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|
http://ocw.usu.edu/Electrical_and_Computer_Engineering/Information_Theory/lecture2_5.htm
|
##### Personal tools
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You are here: Home Definitions and Basic Facts
# Definitions and Basic Facts
##### Document Actions
Entropy Function :: Joint Entropy :: Relative Entropy :: Multivariable :: Convexity
## Convexity and Jensen's inequality
A large part of information theory consists in finding bounds on certain performance measures. The analytical idea behind a bound is to substitute a complicated expression for something simpler but not exactly equal, known to be either greater or smaller than the thing it replaces. This gives rise to simpler statements (and hence gain some insight), but usually at the expense of precision. Knowing when to use a bound to get a useful results generally requires a fair amount of mathematical maturity and experience.
One of the more important inequalities we will use throughout information theory is Jensen's inequality. Before introducing it, you need to know about convex and concave functions.
To understand the definition, recall that is simply a line segment connecting x 1 and x 2 (in the x direction) and is a line segment connecting f ( x 1 ) and f ( x 2 ). Pictorially, the function is convex if the function lies below the straight line segment connecting two points , for any two points in the interval.
You will need to keep reminding me of which is which, since when I learned this, the nomenclature was "convex '' and "convex ''.
One reason why we are interested in convex functions is that it is known that over the interval of convexity there is only one minimum . This can strengthen many of the results we might want.
We now introduce Jensen's inequality .
The theorem allows us (more or less) to pull a function outside of a summation in some circumstances.
There is another inequality that got considerable use (in many of the same ways as Jensen's inequality) way back in the dark ages when I took information theory. I may refer to it simply as the information inequality .
This can also be generalized by taking the line at different points along the function.
With these simple inequalities we can now prove some facts about some of the information measures we defined so far.
Let be the set of values that the random variable X takes on and let denote the number of elements in the set. For discrete random variables, the uniform distribution over the range has the maximum entropy .
Note how easily this optimizing value drops in our lap by means of an inequality. There is an important principle of engineering design here: if you can show that some performance criterion is upper-bounded by some function, then show how to achieve that upper bound, you have got an optimum design. No calculus required!
The more we know, the less uncertainty there is:
Copyright 2008, by the Contributing Authors. Cite/attribute Resource . admin. (2006, May 17). Definitions and Basic Facts. Retrieved January 07, 2011, from Free Online Course Materials — USU OpenCourseWare Web site: http://ocw.usu.edu/Electrical_and_Computer_Engineering/Information_Theory/lecture2_5.htm. This work is licensed under a Creative Commons License
| 2017-12-14T02:35:42 |
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|
https://indico.fnal.gov/event/13745/timetable/?view=standard
|
The Indico system will be unavailable due to system upgrades on August 30th from 6 - 9PM CST. Please email Indico support with any questions or concerns.
# New Perspectives 2017
US/Central
One West (Fermilab, Wilson Hall)
### One West
#### Fermilab, Wilson Hall
, , , , ,
Description
New Perspectives is a conference for, and by, young researchers in the Fermilab community. It provides a forum for graduate students, postdocs, visiting researchers, and all other young persons that contribute to the scientific program at Fermilab to present their work to an audience of peers.
New Perspectives has a rich history of providing the Fermilab community with a venue for young researchers to present their work. Oftentimes, the content of these talks wouldn't appear at typical HEP conferences, because of its work-in-progress status or because its part of work that will never be published. However, it is exactly this type of work, frequently performed by the youngest members of our community, that forms the backbone of the research programme at Fermilab. The New Perspectives Organizing Committee is deeply committed to presenting to the community a programme that accurately reflects the breadth and depth of research being done by young researchers at Fermilab.
New Perspectives is organized by the Fermilab Student and Postdoc Association (FSPA) and serves as a preamble to the Fermilab Users Annual Meeting. Please direct any questions, concerns, and comments to [email protected]
Participants
• Alec Tewsley-Booth
• Aleena Rafique
• Alejandro Diaz
• Andres Alba
• Andrew Long
• Andrew Mogan
• Andrés Abreu
• Aristeidis Tsaris
• Ashley Back
• Axel Gross
• Barbara Yaeggy
• Benjamin Schlitzer
• Bing Guo
• Biswaranjan Behera
• Bobby Butler
• Bogdan Dobrescu
• Christopher Hilgenberg
• Cindy Joe
• Colton Hill
• Cory Rude
• Cristina Ana Mantilla Suarez
• Daisy Daisy Kalra
• Daniel Baxter
• Daniil Frolov
• David Caratelli
• David Flay
• David Martinez Caicedo
• David Sweigart
• David Tarazona
• Diego Gutierrez Coronel
• Dipsikha Debnath
• Dongwi Handiipondola Dongwi
• Elena Gramellini
• Emrah Tiras
• Erika Catano Mur
• Esra Barlas Yucel
• Fang Han
• Felipe Garcia Ken Kamiya
• Gleb Lukicov
• Gonzalo Díaz Bautista
• Gray Yarbrough
• Gregorio Bernardi
• Hector Perez
• Ivan Lepetic
• Jacob Colston
• Jamie Santucci
• Jean Somalwar
• Jessica Esquivel
• Jorge Martinez Armas
• JOSE SEPULVEDA-QUIROZ
• Joseph Lykken
• Joshua Eby
• Joshua Feldman
• Julie Hogan
• Justin Vasel
• Jyoti Tripathi
• Kanika Sachdev
• Katherine Woodruff
• Kim Siang Khaw
• Lauren Yates
• Leonard Apanasevich
• Manolis Kargiantoulakis
• Marcos Vinicius dos Santos
• Marianette Wospakrik
• Mateus Carneiro
• Matthew Judah
• Mehreen Sultana
• Mete Yücel
• Michael Krohn
• Monica Nunes
• Nicola McConkey
• Nitish Nayak
• Norman Martinez
• Ohkyung Kwon
• Oleg Samoylov
• Orgho Neogi
• Polina Abratenko
• Prakash Thapa
• Pranava Teja Surukuchi
• Prasanth Shyamsundar
• Qing Yang Tang
• Rachel Osofsky
• Rachitha Mendis
• Ran Hong
• Reddy Pratap Gandrajula
• Rijeesh Keloth
• Rimal Dipak
• Ritoban Basu Thakur
• Rob Fine
• Robert Murrells
• Roger Rodrigo Galindo Orjuela
• Ross Cawthon
• Rui An
• RuthAnn Gregory
• Ryan Murphy
• Samantha Young
• Scarlet Norberg
• Shiqi Yu
• Shivesh Mandalia
• Sijith Edayath
• Stephen Mrenna
• Steve Dennis
• Sudeshna Ganguly
• Tanaz Angelina Mohayai
• Teppei Katori
• Teresa Lackey
• Thomas Carroll
• Ting Li
• Tyler Alion
• Varuna Crishan Meddage
• Vassili Papavassiliou
• Victor Genty
• Vijay Iyer
• Vinay Hegde
• Wanwei Wu
• Wes Gohn
• XIANYI ZHANG
• Yangyang Cheng
• Yuanyuan Zhang
• Zaki Rowan
• Zhen Liu
• Monday, June 5
• 8:30 AM 10:35 AM
Short Baseline Neutrino Program One West
### One West
#### Fermilab, Wilson Hall
• 8:30 AM
Welcome to New Perspectives 2017 from FSPA 15m
• 8:45 AM
A Summary of Machine Learning Applications at Fermilab 15m
A premier challenge of HEP analysis is the interpretation of highly multivariate data. The efforts to extract the strongest measurements from the available data combined with access to large-scale computing resources allow researchers to take advantage of and contribute to the development of cutting-edge machine learning tools. Recent applications have shown that some techniques, especially deep learning, significantly improve the physics reach of running neutrino experiments. A variety of applications are under development using these tools not only for analysis but for reconstruction and even simulation. The Fermilab Machine Learning Working Group brings together a community of scientists from across the laboratory with an interest in machine learning. This presentation will summarize the most prominent machine learning applications in use in Fermilab experiments and introduce the activities of the Working Group.
Speaker: Ms Fernanda Psihas (Indiana University)
• 9:00 AM
MicroBooNE in Ten minutes 15m
MicroBooNE is a Liquid Argon Time Projection Chamber (LArTPC) that has been operating for the past 18 months on the Booster Neutrino Beamline at Fermilab. MicroBooNE’s physics goals include studying the excess of low energy electromagnetic events observed by the MiniBooNE experiment as well as performing the first set of neutrino-argon cross-section measurements in the 1 GeV energy range. MicroBooNE is also making significant contributions to LArTPC R&D that is informing the Short Baseline Neutrino (SBN) program and DUNE. This talk will give an overview and cover recent developments of the MicroBooNE experiment.
Speaker: Ms Jessica Esquivel (Syracuse University)
• 9:15 AM
Measurement of Reconstructed Charged Particle Multiplicities of Neutrino Interactions in MicroBooNE 15m
In this talk, we present a comparison of the observed charged particle multiplicity distributions in the MicroBooNE liquid argon time projection chamber from neutrino interactions in a restricted final state phase space to predictions of this distribution from several GENIE models. The measurement uses a data sample consisting of neutrino interactions with a final state muon candidate fully contained within the MicroBooNE detector. These data were collected in 2015-2016 with the Fermilab Booster Neutrino Beam (BNB), which has an average neutrino energy of 800 MeV, using an exposure corresponding to 5e19 protons-on-target. The analysis employs fully automatic event selection and charged particle track reconstruction and uses a data-driven technique to determine the contribution to each multiplicity bin from neutrino interactions and cosmic-induced backgrounds. The restricted phase space employed makes the measurement most sensitive to the higher-energy charged particles expected from primary neutrino-argon collisions and less sensitive to lower energy protons expected to be produced in final state interactions of collision products with the target argon nucleus.
Speaker: Ms Aleena Rafique (Kansas State University)
• 9:30 AM
Low energy single-photon search in MicroBooNE 15m
MicroBooNE, an 89 ton (active volume) liquid argon time projection chamber (TPC), began studying neutrino interactions in the Fermilab Booster Neutrino Beamline (BNB) in October 2015. One of its primary physics goals is to investigate the MiniBooNE electromagnetic "Low Energy Excess". A leading interpretation of this excess is single photon production in neutrino neutral current (NC) interactions with nuclei. I will discuss the reconstruction and event selection scheme developed and optimized for the MicroBooNE single-photon search, which aims to investigate the MiniBooNE excess under the single photon interpretation. The ongoing studies of the selected single photon signal and backgrounds that will dictate MicroBooNE’s sensitivity to such an excess will also be presented.
Speaker: Mr Robert Murrells (University of Manchester)
• 9:45 AM
Electron Neutrino Events in MicroBooNE originating from the NuMI Beamline 15m
MicroBooNE is a liquid argon neutrino detector at the Fermi National Accelerator Laboratory with the unique feature to simultaneously receive neutrinos from both Fermilab neutrino beams. The electron neutrino search from the lower-energy on-axis BNB will address MicroBooNE’s signature analysis investigating the low-energy electromagnetic event excess previously observed by the MiniBooNE experiment. The higher-energy neutrinos from the NuMI beam reaching the MicroBooNE detector off-axis, will be primarily used for a comprehensive understanding of electron neutrino interactions and a νe cross section measurement on Liquid Argon. These measurements using the NuMI neutrinos will be crucial for reducing cross section systematics for current and future oscillation measurements at short and long baselines. We will present ongoing simulation studies of the signal and backgrounds leading towards a measurement of the νe cross section on argon.
Speaker: Colton Hill (The University of Manchester)
• 10:00 AM
Electron Neutrino Reconstruction in MicroBooNE Using Deep Learning Technique 15m
MicroBooNE employs the first large scale (> 100 ton) Liquid Argon Time Projection Chamber (LArTPC) in the U.S. to detect electron and muon neutrinos produced from the Fermilab Booster Neutrino Beamline (BNB). The primary goal of the experiment is to perform a definitive study of the observed electron neutrino event excess at low energy by the MiniBooNE experiment, which could indicate the presence of sterile neutrinos. The current challenge of the experiment is efficient and effective event reconstruction to identify any possible event excess above background. In this talk, I describe the use of the machine learning technique called Deep Learning to these problems in MicroBooNE, in particular for electron neutrino event reconstruction and analysis. Deep Learning is making revolutionary advancements in the field of artificial intelligence and computer vision and is also making an impact on neutrino experiments such as NOvA. We demonstrate that Convolutional Neural Networks (CNNs), a type of Deep Learning algorithm, can also be used for event reconstruction using LArTPC data. I will discuss the current status of the application of this technique for electron neutrino event reconstruction in MicroBooNE.
Speaker: Mr Victor Genty (Columbia University, Nevis Labs)
• 10:15 AM
ANNIE: Present and Future 20m
The Accelerator Neutrino Neutron Interaction Experiment (ANNIE) is located at SciBooNE Hall along the Booster Neutrino Beam at Fermilab. It consists of a 23-ton water Cherenkov detector loaded with gadolinium, muon range detector and a veto wall. The main goal of the experiment is to measure the final state neutron multiplicity from charged current neutrino-nucleus interactions within the gadolinium-loaded water. Currently, ANNIE is running in Phase-I and it will be upgraded to Phase-II in the summer, by installing Large Area Picosecond Photodetectors (LAPPDs) in the detector. LAPPDs are a novel photodetector technology with single photoelectron time resolutions less than 100 picoseconds, and spatial imaging capabilities to within a single centimeter. They will play a crucial role to separate events of charged-current quasi-elastic (CCQE) interactions and inelastic multi-track charged current interactions. In this talk, we discuss the current status and future plans of the experiment.
Speaker: Mr Emrah Tiras (University of Iowa- High Energy Physics)
• 10:35 AM 11:00 AM
Coffee Break One West
### One West
#### Fermilab, Wilson Hall
• 11:00 AM 12:30 PM
Short Baseline Neutrino Program One West
### One West
#### Fermilab, Wilson Hall
• 11:00 AM
LArIAT in 10 Minutes 15m
The LArIAT (Liquid Argon in a Test Beam) experiment in Fermilab's Test Beam Facility exposes a liquid argon time projection chamber (LArTPC) to a test beam in order to study LArTPC responses to a variety of charged particles. Event identification and reconstruction techniques as well as cross section measurements from LArIAT will provide critical input to existing liquid argon neutrino experiments such as MicroBooNE, SBND, and ICARUS, and will also help to improve future precision neutrino oscillation measurements in the Deep Underground Neutrino Experiment (DUNE). The work presented here will give an overview of the experiment and highlight several recent results.
Speaker: Johnny Ho (University of Chicago)
• 11:15 AM
SBND in 10 minutes 15m
SBND is the Short Baseline Near Detector, which is a 112 ton liquid argon time projection chamber (TPC) that will be located 110m from the target of the Fermilab Booster Neutrino Beam. SBND, together with MicroBooNE and ICARUS-T600 detectors at 470m and 600m, respectively, make up the Fermilab Short Baseline Program (SBN). SBN will search for new physics in the neutrino sector by testing the sterile neutrino hypothesis in the 1 eV^2 mass-squared region with unrivaled sensitivity. SBND will measure the un-oscillated beam flavor composition to enable precision searches for neutrino oscillations via both electron neutrino appearance and muon neutrino disappearance in the far detectors. With a data sample of millions of neutrino interactions (both electron and muon neutrinos), SBND will also perform detailed studies of the physics of neutrino-argon interactions, even in rare channels. In addition, SBND plays an important role in an on-going R&D effort within neutrino physics to develop the LArTPC technology toward many-kiloton-scale detectors for next generation long-baseline neutrino oscillation experiments The SBND detector is currently under construction; this talk will give an overview of the current experimental efforts and future outlook, putting this in the context of the current neutrino landscape.
Speaker: Dr Nicola McConkey (University of Sheffield)
• 11:30 AM
Testing, Installation, Integration and Performance Studies of a Cosmic Ray Tagging System for the Short Baseline Neutrino Program Far Detector (ICARUS) 15m
The ICARUS T600 liquid argon time-projection chamber will be the far detector for the Short Baseline Neutrino Program. The detector will operate at shallow depth and therefore be exposed to the full surface flux of cosmic rays. Application of overburden attenuates most of this background expected for muons. However, the remaining background is problematic since a photon produced by a muon passing in close proximity to the T600 active volume can be mistaken for a neutrino event. In principle, a large fraction of these events can be removed from the data through application of selection cuts as suggested by Monte Carlo studies. However, this method of background rejection reduces fiducial target mass and renders analysis of the systematics difficult. A straightforward way to remove the cosmic muon background more thoroughly is to utilize a detector external to the liquid argon active volume capable of tagging thoroughgoing cosmic muons with high efficiency (e.g. > 95%). Ideally, this external cosmic ray tagger (CRT) would provide full geometric coverage of the T600. During the past 18 months at Colorado State University (CSU), we performed Monte Carlo studies of the tagging efficiencies of the system and conducted an extensive research and development program of such a system based on extruded organic scintillator, wavelength-shifting fibers, and silicon photomultipliers. Subsequently, it was decided that our European colleagues would design and construct the top portion of the CRT while the US groups would provide the side (~400 m^2) and bottom (~215 m^2) portions using salvaged MINOS veto shield modules on the sides and Double Chooz veto modules on the bottom. These two systems will need to be tested for basic functionality and to have their detailed response characterized in order to optimize the system configuration as well as prepare for future analysis tasks and integration with the other detector sub-systems.
Speaker: Mr Christopher Hilgenberg (Colorado State University)
• 11:45 AM
Search For Sterile Neutrinos At The NOvA Near Detector 15m
Anomalous results from past neutrino experiments have been interpreted as potential evidence for an additional sterile neutrino with a mass on order of 1 eV, but this evidence remains inconclusive. The NOvA Near Detector is a 300 ton almost fully-active fine-grained liquid scintillator detector, that was designed for electron-neutrino identification. The detector is placed along the Fermilab NuMI beam line 1 km from the target and 14.6 mrad off-axis. At this off-axis angle, the detector is exposed to a narrow band beam peaked at 2 GeV. Therefore the NOvA Near Detector will see neutrinos with an L/E range that is sensitive to oscillations between active neutrinos and light sterile neutrinos. In this talk I discuss NOvA sensitivity from the joint electron-neutrino appearance and muon-neutrino disappearance analysis search for short-baseline sterile neutrino mixing.
• 12:00 PM
NOvA Short-Baseline Tau-Neutrino Appearance Search 15m
Three-flavor neutrino oscillations have successfully explained a wide range of neutrino oscillation experiment results. However, anomalous results, such as the electron-antineutrino appearance excesses seen by LSND and MiniBooNE, do not fit the three-flavor paradigm and can be explained by the addition of a sterile neutrino at a larger mass scale than the existing three flavor mass states. The NOvA experiment consists of two finely segmented, liquid scintillator detectors operating 14.6 mrad off-axis from the NuMI muon-neutrino beam. The Near Detector is located on the Fermilab campus, 1 km from the NuMI target, while the Far Detector is located at Ash River, MN, 810 km from the NuMI target. The NOvA experiment is primarily designed to measure electron-neutrino appearance at the Far Detector using the Near Detector to control systematic uncertainties. However, the Near Detector is well suited for searching for anomalous short-baseline oscillations. I will present a novel method for selecting tau neutrino interactions with high purity at the Near Detector using a convolutional neural network. Further, I will discuss the sensitivity to anomalous short-baseline tau-neutrino appearance due to sterile neutrino oscillations determined using this method.
Speaker: Mr Rijeesh Keloth (Cochin University of Science and Technology)
• 12:15 PM
Sterile Neutrinos: A Possible Explanation for Oscillation Excesses 15m
Neutrino oscillations have provided proof of the existence of massive neutrino states. The standard model currently accepts the existence of three different neutrinos, but oscillation experiments such as LSND and MiniBooNE have detected an excess of neutrinos above that expected from a standard 3 neutrino model. We will discuss this excess, and explain how an explanation could lie in the existence of additional, sterile (non-interacting), neutrino states. We will then present the latest results in our constraints for the parameters space of sterile neutrinos given the global data on oscillations.
Speaker: Mr Alejandro Diaz (Graduate Student (MIT))
• 12:30 PM 1:30 PM
Lunch
• 1:30 PM 3:30 PM
Dark Matter and Astrophysics One West
### One West
#### Fermilab, Wilson Hall
• 1:30 PM
Probing Nuclear Recoils in Liquid Argon with the ARIS Experiment 15m
One of the unique challenges facing direct dark matter searches is the signal characterization of the dark matter particle with the detector medium. The goal of the Argon Recoil Ionization and Scintillation (ARIS) experiment is to characterize the response of nuclear recoils in liquid argon (as expected from WIMPs) by measuring the energy scale of nuclear recoils with respect to electron recoils, the ion recombination probability as a function of electric field, and the scintillation time response of nuclear recoils at various energies. A scintillation chamber with an active mass of ~0.5 kg was constructed with a tunable cathode to provide a varying electric field within the active volume. This detector was exposed to a highly collimated inverse kinematic neutron beam at the Institut de physique nucléaire d'Orsay in France. Events coincident with one of an array of 8 neutron detectors allowed a scan of nuclear recoil energies. The present status of the experimental analysis will be presented.
Speaker: Mr Benjamin Schlitzer (UC Davis)
• 1:45 PM
Constraining the Nature of Dark Matter with the Milky Way Satellite Galaxies 15m
The census of Milky Way satellite galaxies provides crucial tests of both galaxy formation models and the broader Cold Dark Matter paradigm. A total of 27 new Milky Way satellite candidates have been discovered in the last two years, primarily in data from the Dark Energy Survey. These discoveries may represent a 100% increase in the number of known Milky Way satellite galaxies, leading a huge advance in solving the missing satellite problem, if spectroscopic follow-up observations confirm the majority of these systems are dark matter dominated dwarf galaxies. Furthermore, many of these newly discovered dwarf galaxies are excellent targets for providing constraints on WIMP dark matter cross section and MACHO dark matter abundance with the spectroscopic follow-up analysis. In this talk, I will present the initial results from a spectroscopic campaign on the newly discovered dwarf galaxy candidates using 4-8 meter class telescopes in the southern hemisphere.
Speaker: Ting Li (Fermilab)
• 2:00 PM
AstroEncoder: Applications of Deep Learning to Cosmological Data 15m
Current and future cosmology surveys will provide data sets unprecedented in size and precision with which to measure dark energy, dark matter and the early universe through probes like strong gravitational lensing, supernovae, and the cosmic microwave background. First, we’ll discuss the challenges posed by astronomically big and complex data, and the potential for machine learning. Then, I will present a variety of successful applications of deep learning techniques to astrophysical and cosmological data, including classification, measurement, and simulation.
Speaker: Dr Brian Nord (Fermilab)
• 2:15 PM
Calibration of Photometric Redshifts from Clustering in the Dark Energy Survey 15m
Redshift estimation is among the most significant issues in photometric cosmological surveys. Undetected biases in photometric redshift estimation can be found using clustering redshifts. In this presentation, we describe our clustering redshift estimates for weak lensing source galaxies, and redMaGiC galaxies in the Dark Energy Survey year 1 data. We also describe our methodology of applying corrections to photometric redshifts based on the clustering measurements as tested in simulations.
Speaker: Ross Cawthon (University of Chicago)
• 2:30 PM
Fabrication of antenna-coupled KID array for Cosmic Microwave Background detection 15m
Microwave Kinetic Inductance Detectors (MKIDs) have become an attractive alternative to traditional Transition Edge Sensor (TES) bolometers in the sub-mm and mm observing community due to its innate frequency multiplexing capabilities and simple lithographic processes. These advantages make MKIDs a viable option for the O(100,000) detectors needed for the upcoming Cosmic Microwave Background - Stage 4 (CMB-S4) experiment. We have fabricated dual polarization antenna-coupled MKID array in the ~100GHz band optimized for CMB detection. The Al KIDs are made from evaporating Al on a high resistivity silicon substrate. The microstrip coupling the antenna and KID consists of growing Si3N4 between two layers of evaporated Nb. In addition, we present the preliminary characterization of these devices with a cryogenic blackbody load.
Speaker: Ms Qing Yang Tang (University of Chicago)
• 2:45 PM
Deep Learning for Hidden Signals—Enabling Real-time Multimessenger Astrophysics 15m
We developed a new method for end-to-end time-series signal processing, based on deep convolutional neural networks, which can rapidly identify and extract signals much weaker than the background noise. We applied this method for analyzing gravitational waves from mergers of black holes and demonstrated that it significantly outperforms conventional machine learning techniques, is far more efficient than matched-filtering allowing real-time processing of raw big data with minimal resources, and extends the range of gravitational waves that can be detected by advanced LIGO. This initiates a new paradigm for scientific research which uses massively-parallel numerical simulations to train artificial intelligence algorithms that exploit emerging hardware architectures. Our approach offers a unique framework to enable coincident detection campaigns of gravitational wave sources and their multimessenger counterparts.
Speaker: Mr Daniel George (University of Illinois at Urbana Champaign)
• 3:00 PM
Measurement and characterization of low-energy ionization signals from Compton scattering with a Silicon CCD 15m
We report results of low-energy Compton scattering calibration studies in Silicon undertaken under the umbrella of the DAMIC (Dark Matter in CCDs) experiment. We expose a calibration detector at the University of Chicago to Co-57 and Am-241 gamma-ray sources and measure and characterize the resultant spectrum. We identify several theoretically motivated, but heretofore unobserved in the literature, structural features of these spectra and validate these results with an MCNP simulation. We further report an energy detection threshold of 60 eVee. These studies provide relevant information on low-energy ionization signals from electrons Compton scattered by radiogenic gamma-rays, often a dominant background for low-mass WIMP (Weakly Interacting Massive Particle) searches.
Speaker: Mr Karthik Ramanathan (University of Chicago)
• 3:15 PM
The physical origin of long gas depletion times in galaxies 15m
[https://arxiv.org/abs/1704.04239] We present a physical model that elucidates why gas depletion times in galaxies are long compared to the time scales of the processes driving the evolution of the interstellar medium. We show that global depletion times are not set by any "bottleneck" in the process of gas evolution towards the star-forming state. Instead, depletion times are long because star-forming gas converts only a small fraction of its mass into stars before it is dispersed by dynamical and feedback processes. Thus, complete depletion requires that gas transitions between star-forming and non-star-forming states multiple times. Our model does not rely on the assumption of equilibrium and can be used to interpret trends of depletion times with the properties of observed galaxies and the parameters of star formation and feedback recipes in galaxy simulations. In particular, the model explains the mechanism by which feedback self-regulates star formation rate in simulations and makes it insensitive to the local star formation efficiency. We illustrate our model using the results of an isolated $L_*$-sized disk galaxy simulation that reproduces the observed Kennicutt-Schmidt relation for both molecular and atomic gas. Interestingly, the relation for molecular gas is close to linear on kiloparsec scales, even though a non-linear relation is adopted in simulation cells. This difference is due to stellar feedback, which breaks the self-similar scaling of the gas density PDF with the average gas surface density.
Speaker: Mr Vadim Semenov (The University of Chicago)
• 3:30 PM 4:00 PM
Coffee Break One West
### One West
#### Fermilab, Wilson Hall
• 3:40 PM 6:15 PM
Neutrino Interaction Physics One West
### One West
#### Fermilab, Wilson Hall
• 4:00 PM
MINERvA in 10 Minutes 15m
The MINERvA experiment is a dedicated neutrino scattering experiment located on the NuMI beamline in Fermilab. It aims to make high precision measurement of neutrino interaction cross sections in the 1-to 10-GeV energy range, to support the current and future oscillation experiments as well as to provide information about the structure of nuclei, protons and neutrons and the strong force dynamics that affect neutrino-nucleus interactions. The MINERvA detector is comprised of a fine-grained scintillator with electromagnetic and hadronic calorimetry regions. Various nuclear targets are located inside and in front of the detector for studying nuclear medium effects in neutrino-induced interactions. This talk presents a summary of the MINERvA experiment.
Speaker: Marianette Wospakrik (University of Florida)
• 4:15 PM
Low Energy CCQE Results from MINERvA 15m
MINERvA is a neutrino scattering experiment designed for high precision measurements of cross sections and studies of nuclear effects. Charged-current quasielastic (CCQE) scattering events are a significant contribution to the signal of many oscillation experiments. It is the dominant reaction near 1 GeV, a critical energy region for long baseline oscillation experiments. MINERvA has conducted many CCQE studies in the low energy NuMI beam. In this talk, I will present an overview of the Minerva detector and summarize the low energy quasi-elastic scattering results.
Speaker: Ms Mehreen Sultana (University of Rochester)
• 4:30 PM
Minerva CCQE in the 'Medium Energy' Era 15m
Charged-current quasielastic (CCQE) scattering events are one of the most numerous and most important categories of neutrino interactions available to us today to study neutrino cross sections and oscillations. This presentation will cover the progress of the Minerva collaboration towards fully leveraging the awesome statistics that the NuMI 'Medium Energy' exposure has to offer. Data collected during this run allow for unprecedented access to as-yet-unstudied regions of phase space, in an energy range that is of particular relevance to future long-baseline oscillation experiments.
Speaker: Rob Fine (University of Rochester)
• 4:45 PM
Single neutral pion production on MINERvA using ME beam 15m
MINERvA is a neutrino scattering experiment that uses the NuMI beamline with the goal of measuring neutrino-nucleus cross sections on targets of different materials with high precision, as well as studying the internal structure of the nuclei of those materials. Among the different kinds of neutrino interactions that could occur in the detector, charged and neutral pion production are significant since they represent a large fraction of the events that can be detected. In particular, the study of single neutral pion production in multiple targets acquires relevance since not only will it provide constraints to the systematic errors of appearance and disappearance oscillation results in the range of energies of NOvA and DUNE, but also it will help to understand and compare the underlying structure of these nuclei. A previous result on this topic using a Low Energy antineutrino beam of 3.6 GeV in plastic scintillator has been published in 2015 by the MINERvA experiment. This time, I will present the current status of the single neutral pion production in C, Fe and Pb targets using a 6 GeV neutrino beam; and the future steps in order to get a precise cross section measurement on these materials.
Speaker: Mr Gonzalo Diaz Bautista (University of Rochester)
• 5:00 PM
Neutral Pion Reconstruction for NuMI at ME in MINER$\nu$A 15m
Many analyses in neutrino experiments require the reconstruction of neutral pions, particularly neutrino oscillation experiments measuring $\nu_{e}$ appearance, where $pi^0$ production is a background. Neutral pions are identified in the MINER$\nu$A detector by identifying the gammas that result from the neutral pion decay. The gamma candidates are energy depositions which are not associated with charged pions, protons or muons. The reconstruction that was developed in the simpler environment of the NuMI Low Energy beam is not satisfactory for the more complicated environment of the Medium Energy beam. By changing the MINER$\nu$A neutral pion reconstruction to consider only energy depositions with a well reconstructed direction and position and a set of cuts on energy, distance to the interaction vertex and dEdX, we have significantly improved the neutral pion reconstruction in the Medium Energy dataset.
Speaker: Mr Roger Rodrigo Galindo Orjuela (Universidad Tecnica Federico Santa Maria)
• 5:15 PM
CC coherent/diffractive Pion Production at MINERvA in the NuMI ME era 15m
Charged Current Coherent pion production is a rare neutrino reaction producing a forward muon and a forward charged pion while leaving the target nucleus in its initial state. On its own, it provides a way to study the weak axial vector current, by testing theories such as PCAC and related models. After the discovery of neutrino oscillations, coherent pion production has become an important reaction, helping to reduce systematic uncertainties in both the signal and background of oscillation studies. MINERvA, a neutrino scattering experiment, has already published an analysis of coherent pion production in plastic scintillator (CH) using the NuMI low energy neutrino and anti-neutrino beams at Fermilab. The current NOvA era, with a more energetic and intense NuMI beam, allows an improved charged current coherent analysis, which is at the first stages. Here we present the highlights of both analyses.
• 5:30 PM
Progress of the Inclusive Muon Neutrino Charged-current Cross Section Measurement in the NOvA Near Detector 15m
NOvA is a long-baseline (810 km) neutrino oscillation experiment. It uses a NuMI neutrino beam from Fermilab and two mostly active, segmented, liquid scintillator off-axis detectors that offer a remarkable capability in event identification. The 293 ton Near Detector at Fermilab is to measure the unoscillated neutrino energy spectrum, which can be used to predict the neutrino energy spectrum at the 14 kton Far Detector at Ash River, MN. It provides an excellent opportunity to measure cross sections with high statistics. Improved understanding of neutrino- nucleus interactions will benefit current and future long-baseline neu- trino oscillation experiments. In this talk we present an update to the progress of the measurement of the inclusive $\nu_{\mu}$ CC cross section in the NOvA Near Detector.
Speaker: Mr Biswaranjan Behera (IIT Hyderabad/Fermilab)
• 5:45 PM
Progress of the Measurement of the Electron Neutrino Charged-current Inclusive Cross Section in NOvA 15m
We present an update to the progress of the measurement of the electron neutrino charged-current inclusive cross section per nucleon with data collected from November 2014 to February 2017 in the NOvA near detector. The NOvA near detector, located at Fermilab 800m from the primary target, provides an excellent platform to measure and study neutrino interactions and cross sections. We are measuring the cross section in four energy bins from 1-3 GeV. This energy range is of particular importance since it corresponds to the expected region of interest for electron neutrino appearance in future neutrino oscillation experiments.
Speaker: Matthew Judah (Colorado State University)
• 6:00 PM
Progress of the Charged Pion Semi-Inclusive Neutrino Charged-Current Cross Section in NOvA 15m
The NOvA experiment is a long-baseline neutrino oscillation experiment designed to measure the rates of electron neutrino appearance and muon neutrino disappearance. The NOvA near detector is located at Fermilab, 800~m from the primary target and provides an excellent platform to measure and study neutrino interaction and cross sections. We present the status of the measurement of the double differential cross section with at least one charged pion in the final state, $\nu_\mu + N \rightarrow N + \mu^{\pm} \pi^\mp X$. A convolutional neural network based approach is presented for the identification of neutrino interactions with the specific final state topology. This method of event classification has been used successfully to identify charged current electron neutrinos interactions in the NOvA oscillations measurements. The approach is nearly ideal for semi-inclusive cross section measurements as it does not require detailed a priori particle by particle reconstruction of the sub-leading tracks to classify the signal events. In this talk we present event classification efficiency studies using this event identification and classification methodology, along with background estimates and prospects for the measurement.
Speakers: Aristeidis Tsaris (Fermilab), Ms Jyoti Tripathi (Panjab University)
• 6:15 PM 10:00 PM
FSPA Barbecue Kuhn Barn (Fermilab Village)
### Kuhn Barn
#### Fermilab Village
• Tuesday, June 6
• 9:00 AM 10:35 AM
Long Baseline Neutrino Program One West
### One West
#### Fermilab, Wilson Hall
• 9:00 AM
NOvA in 10 min 15m
NOνA is a second generation, long-baseline, neutrino oscillation experiment that uses the NuMI beam, the world’s most powerful neutrino beam, from Fermilab. It consists of two functionally similar, finely segmented, liquid scintillator calorimeter detectors that operate 809 km apart, 14 mrad off-axis from the beam. NOνA’s main physics goals include measuring electron (anti)neutrino appearance and muon (anti)neutrino disappearance. These measurements can provide constraints on the $\sin^2{\theta_{23}}$ octant, the mass hierarchy, and the CP violating phase, along with precision measurements of $\sin^2{\theta_{23}}$ and $\Delta m^{2}_{32}$ . In this talk, an overview of NOνA's experimental effort will be presented.
Speaker: Ryan Murphy (Indiana University)
• 9:15 AM
Data Monitoring and Performance of the NOvA Detectors 15m
NOvA consists of two detectors, one at Fermilab, and the second 810km away in northern Minnesota. The experiment uses Fermilab's NuMI beam to measure the νμ to νe oscillation probability in order to learn more about the neutrino mass hierarchy, mixing angles, and CP violation in the neutrino sector. As with any large experiment, there are many components that need to operate smoothly to maximize uninterrupted data-taking and ensure the recorded data is of high quality. If any component fails it is essential know as soon as possible what failed, and why it failed, so the problem can be promptly resolved. In order to do this, NOvA has a multitude of monitoring tools and procedures to continuously monitor various aspects of the experiment. In this talk, I will discuss these tools and procedures and how they enable the high quality physics results produced by NOvA.
Speaker: Teresa Lackey (Indiana University)
• 9:30 AM
Increased Neutrino Yield with the new NOvA Target Design: Simulation Study 15m
NOvA (NuMI Off-axis νe Appearance) is a long baseline neutrino oscillation experiment designed to search for both νe appearance and νμ disappearance. Fermilab NuMI (Neutrinos at Main Injector) facility produces an intense neutrino beam (narrow band νμ beam peaked at 2 GeV in energy) colliding 120 GeV protons from the Main Injector into a long target with a set of two magnetic horns (Horn1 and Horn2) to focus the pions produced at the target. We studied different target designs and Horn2 configuration. Here, we present the New Target design which increases the νμ (anti-νμ) yield at the NOvA Near and Far detectors by about 17% (20%) compared to the event yield with the current NuMI target.
Speaker: Ms Daisy Daisy Kalra (Panjab University)
• 9:45 AM
Calorimetric Energy Scale in the NOvA Detectors 15m
NOvA is a long-baseline neutrino oscillation experiment consisting of a near and far detector, both comprising layers of orthogonal scintillator-filled PVC extrusions. Reconstructing hits along the orthogonal views provides 3D tracks, and scintillation light provides calorimetry important for determining the visible hadronic energy of an interaction. Selecting muon tracks which stop inside the detector and choosing hits inside a sufficiently flat region around it's point of minimum ionization isolates a constant energy in the detectors. This energy is scaled by the path length of each hit, so additional quality cuts must be imposed to ensure accurate path lengths. Care must also be taken to avoid bias from electronic thresholds, which are meant to suppress noise hits but can also suppress low-energy muon hits far from the readout. After removing reconstruction and threshold biases, cosmic muon data provides a standard candle scintillation, while well-understood Monte Carlo simulation provides a standard candle energy, equipping NOvA analyses with a precise scale factor between observed light and desired energy measurements.
Speaker: Mr Tyler Alion (University of Sussex)
• 10:00 AM
Decomposition Methods for the $\nu_{e}$ Appearance analysis in the NOvA Near Detector 15m
NOvA is a long-baseline neutrino oscillation experiment that is designed to probe the neutrino mass hierarchy and mixing structure. It uses two functionally identical liquid scintillator detectors 14mrad off-axis from the NuMI beamline at Fermilab, allowing a tightly focused neutrino flux peaked at around 2 GeV. The Near Detector is located 100 m underground and is used to characterize the neutrino beam before oscillations. Since the beam components are affected differently by oscillations, the data collected at the Near Detector needs to be broken down into these components. This enables a precise prediction to be made of the beam-induced backgrounds to the $\nu_{e}$ appearance signal at the Far Detector, 810 km from the neutrino source. Various data-driven techniques are employed for this purpose, in particular by constraining the flux yields and correcting for observed neutrino interaction characteristics. In this talk, I will present an overview of the methodology used to decompose the Near Detector data and predict the FD spectrum in the latest $\nu_{e}$ appearance analysis, utilizing an accumulated exposure of $6.05\times10^{20}$ protons-on-target.
Speaker: Mr Nitish Nayak (University of California-Irvine)
• 10:15 AM
Exploring the $\nu_{\mu}$ charged-current uncontained sample at the NOvA Far Detector 15m
NOvA is a long-baseline neutrino oscillation experiment based at Fermilab that uses two highly active liquid scintillator detectors located off-axis of the NuMI beam. Latest results have excluded maximal mixing at $2.6\sigma$ via the muon-neutrino disappearance channel, which use fully contained interactions of the type $\nu_{\mu} + X \to \mu + X'$. We explore potential improvement of the neutrino oscillation parameters $\sin^{2}{2\theta_{23}}$ and $\Delta m^{2}_{32}$ by including uncontained events where the muon is the only final-state particle exiting the detector. Two main problems arise with this sample. First, the signal now mimics the cosmic ray induced background. Second, the reconstructed energy resolution decreases due to the escaping muon. To address these questions, we explore the use of multivariate analysis techniques.
Speaker: JOSE SEPULVEDA-QUIROZ (IOWA STATE UNIVERSITY)
• 10:30 AM
INSS Announcement 5m
Announcement about the International Neutrino Summer School being help at Fermilab in Summer of 2017.
Speaker: Anne Schukraft (Fermilab)
• 10:35 AM 11:00 AM
Coffee Break One West
### One West
#### Fermilab, Wilson Hall
• 11:00 AM 12:30 PM
Long Baseline Neutrino Program One West
### One West
#### Fermilab, Wilson Hall
• 11:00 AM
Results From the Joint Fit to $\nu_e$ Appearance and $\nu_{\mu}$ Disappearance in NOvA 15m
NOvA is a long baseline neutrino oscillation experiment at Fermilab. It uses two detectors, the Near Detector at Fermilab and the Far Detector at a distance of 810 km at Ash River, Minnesota.These two functionally identical liquid scintillator calorimeters are 14 mrad off-axis from the beam, providing a neutrino flux narrowly peaked at around 2 GeV. NOvA measures the rate of $\nu_{e}$ appearance and $\nu_{\mu}$ disappearance at the Far Detector in the $\nu_{\mu}$ beam produced by the NuMI facility at Fermilab. In this talk,I will present the latest NOvA results from a joint fit to $\nu_{\mu}$ disappearance and $\nu_e$ appearance. This talk will focus on the $\nu_e$ appearance analysis. The latest data set had $6.05\times10^{20}$ protons-on-target and we observed 33 $\nu_e$ candidate events over 8.2 predicted background events in our Far Detector. I will describe the fit to the FD data and discuss constraints on $\delta_{CP}$ , mass-hierarchy and the octant of the $\theta_{23}$ mixing angle.
Speaker: Ms Shiqi Yu (IIT/ANL)
• 11:15 AM
Sterile neutrino search in the NOvA Far Detector. 15m
The majority of neutrino oscillation experiments have obtained evidence for neutrino oscillations that are compatible with the three-flavor model. Explaining the apparent neutrino flavor change observed in short-baseline experiments such as LSND and MiniBooNE in terms of neutrino oscillations requires the existence of sterile neutrinos. The search for sterile neutrino mixing conducted in NOvA is unique that it uses a long base-line of 810 km between Near Detector at Fermilab and Far Detector at Minnesota, with a well-defined neutrino beam peaked at an energy of 2 GeV. The tell-tale signal for sterile neutrino oscillations in NOvA is a deficit of neutral-current neutrino interaction at the Far Detector with respect to the Near Detector prediction. The neutral-current rate is insensitive to three-flavor oscillations, so such a deficit would indicate some of the beam muon neutrinos oscillated into non-interacting sterile neutrinos. I will present the first results of this search which demonstrate NOvA's ability to look for sterile neutrinos, and will discuss the improvements being readied for future analyses. These improvements include a shape fit of the Far Detector energy spectrum, enabled by improved modeling of the detector response and of neutrino interactions, and a joint fit of the Far and Near detectors, extending the range of sterile mass-squared splittings NOvA can probe to larger values.
Speaker: Mr Sijith Edayath (Cochin University of science and Technology, India)
• 11:30 AM
Muon Neutrino Disappearance at MINOS+ 15m
The MINOS experiment ran from 2003 until 2012 and produced some of the best precision measurements of the atmospheric neutrino oscillation parameters $\Delta m^2_{32}$ and $\theta_{23}$ using muon neutrino disappearance of beam and atmospheric neutrinos and electron neutrino appearance of beam neutrinos. The MINOS+ experiment succeeded MINOS in September 2013. For almost three years MINOS+ collected data from the Medium Energy NuMI neutrino beam at Fermilab. We will describe the MINOS+ muon neutrino disappearance measurement and present the results of this analysis. These results will be compared to and combined with the MINOS measurement.
Speaker: Thomas Carroll (University of Texas at Austin)
• 11:45 AM
Non-Standard Interaction Effects in the Neutrino Propagation in DUNE 15m
Based on the premise that the neutrino beam used in DUNE traverses the Earth’s crust on its journey from being produced until detection, we propose a non-standard interaction (NSI) between the neutrinos and the matter of the Earth’s crust. Such NSI can cause the change of the flavor and change the energy of the neutrinos. The phenomenon of the flavor oscillations that we know can produce changes that may be measurable from the analysis of the oscillation parameters. In this work we study how the proposed NSI can change the sensitivity of the DUNE in measuring the values of the parameters δCP, θ13, and θ23. NSI also affect the determination of the hierarchy of the neutrino masses. For this study we performed simulations using the General Long Baseline Experiment Simulator (GLoBES). We determined optimal values for the oscillation parameters from the literature and tested some values for δCP. We used a method of χ² to test different values of δCP, θ13, and θ23. This way we were able to determine regions of sensitivity. We chose nine distinct forms of mass density distribution in the baseline and determined how the oscillation parameters change for each of them. When we compared the various sensitivity curves we elaborated a relative χ² for the purpose of determining the influence of the distribution of matter. Finally, we determined which values the parameters describing the NSI εαβ should be in order to be similar to the interactions we know. With these studies, we conclude that the matter density distribution does not significantly change the sensitivity of the DUNE in measuring the parameters δCP, θ13, and θ23, however, the presence of the NSI causes sufficiently large changes in the sensitivity of the DUNE. NSI is also affected by mass hierarchy and, in this way, it can help to determine it. After an accurate study of NSI on the propagation, we intend to study NSI in the interaction, and how it may affect the events in LArTPCs.
Speaker: Mr Felipe Garcia Ken Kamiya (Universidade Federal do ABC)
• 12:00 PM
Re-optimization of the LBNF Neutrino Beam 15m
The Long Baseline Neutrino Facility (LBNF) will use high energy protons impinging on a graphite target to produce kaons and pions, which will be focused by a set of magnetized focusing horns and directed into a decay pipe where they will decay, producing an intense neutrino beam. The neutrino energy spectrum can be tuned by changing a variety of parameters in the beamline such as horn and target shapes. Recent advances in computing power coupled with the development of complex optimization algorithms enable identification of parameters that are precisely tuned to optimize physics parameter sensitivity. An optimization of the LBNF beam parameters for sensitivity to CP violation has been performed. The resulting beam design and its physics performance will be discussed, as well as engineering modifications to that design and re-optimization incorporating these engineering constraints. For instance, the horn positions have been revisited and fine tuned, and the amount of material in the downstream target support carefully reviewed.
Speaker: Mr Rowan Zaki (Radboud University Nijmegen)
• 12:15 PM
Multi-channel analyses for future neutrino oscillation experiments. 15m
Neutrino physics is entering the liquid argon era, and these experiments offer large statistics with excellent reconstruction abilities. The wealth of information available opens new opportunities to break degenaracies between different sources of systematic uncertainty by simultaneously fitting samples selected for different final state topologies. At near detectors, use of many such samples can pin down specific interaction model and flux uncertainties, while for far detectors smaller numbers of fitted topologies can be used to separate event types with better and worse neutrino energy resolution, optimising oscillation sensitivity.Neutrino physics is entering the liquid argon era, and these experiments offer large statistics with excellent reconstruction abilities. The wealth of information available opens new opportunities to break degenaracies between different sources of systematic uncertainty by simultaneously fitting samples selected for different final state topologies. At near detectors, use of many such samples can pin down specific interaction model and flux uncertainties, while for far detectors smaller numbers of fitted topologies can be used to separate event types with better and worse neutrino energy resolution, optimising oscillation sensitivity.
Speaker: Dr Dennis Steve (University of Liverpool)
• 12:30 PM 1:30 PM
Lunch
• 1:30 PM 3:30 PM
Collider Physics One West
### One West
#### Fermilab, Wilson Hall
• 1:30 PM
CMS in 10 Minutes 15m
The Large Hadron Collider is one of the most powerful machines in the world, accelerating protons to 99.9999990% of the speed of light to provide 40 million collisions per second at particle detectors such as CMS. The CMS detector is highly versatile, featuring a 4 Tesla solenoid magnet (the largest superconducting magnet ever built!) and over 100 million detection elements in trackers, calorimeters, and muon detectors. CMS physicists were instrumental in the discovery of the Higgs boson in 2012 and are now searching for evidence of many new physics theories such as dark matter, supersymmetry, and extended Higgs sectors.
Speaker: Julie Hogan (Brown University)
• 1:45 PM
Search for low-mass pair-produced dijet resonances using jet substructure techniques in proton-proton collisions at $\sqrt{s}=13$\TeV 15m
We present a search for low mass paired dijet resonances using jet substructure techniques. This search uses data from proton-proton collisions at a center-of-mass energy of 13~TeV, recorded by the CMS detector at the LHC. Limits at 95% confidence level are set on the production of top squarks decaying to two quarks in the framework of R-parity violating supersymmetry.
Speaker: Ms Jean Somalwar (Rutgers University)
• 2:00 PM
Search for Heavy Resonancs Decaying to diHiggs Pairs in pp Collisions at sqrt(s) = 13 TeV 15m
A search for heavy resonances decaying into pairs of standard model Higgs bosons is performed using 35.9 $\text{fb}^{-1}$ of data collected by the CMS experiment during 2016 at a center of mass energy of 13 TeV. The final state consists of both Higgs bosons decaying to b quark-antiquark pairs. Results are consistent with the Standard Model expectations and are interpreted as upper limits on the production cross sections of narrow bulk gravitons and scalar radions in warped extradimensional models.
Speaker: Michael Krohn (University of Colorado Boulder)
• 2:15 PM
Search for light vector resonances decaying to quarks produced in association with a jet in pp collisions 15m
A search for narrow vector resonances decaying to quarks is presented using events collected in sqrt(s) = 13 TeV proton-proton collisions with the CMS detector at the LHC. The data sample, collected in 2016, corresponds to an integrated luminosity of 35.9 fb−1. The hypothetical resonance is produced with high transverse momentum such that the decay products of the resonance are merged into a single jet. The resulting experimental signature is an enhancement over background processes in the distribution of the invariant mass of the jet. No evidence for resonant particles are observed within the targeted mass range from 50-300 GeV. Upper limits at a 95% con- fidence level are set on the production cross-section of leptophobic vector resonances. Results are presented in a mass-coupling phase space and are the most sensitive to date, extending previous limits below 100 GeV. The limits are also presented as functions of dark matter mass, in a simplified model of interactions between quarks and dark matter with a vector mediator.
Speaker: Cristina Ana Mantilla Suarez (Fermilab)
• 2:30 PM
Supersymmetry searches in all-hadronic channel 15m
Presenting on searchs for the direct production of top squarks in events with multiple jets and large missing transverse energy, using 35.9 fb−1 of data collected by the CMS detector in 2016 at a center-of-mass energy of 13 TeV. Events are categorized into exclusive search regions optimized for different signal topologies. Discussing analysis that use multi variant techniques to identify tops and w’s. Exclusion limits are set in the context of simplified models of top squark pair production under different decay hypotheses.
Speaker: Dr Scarlet Norberg (university of puerto rico mayaguez)
• 2:45 PM
Detecting kinematic boundary surfaces in phase space and particle mass measurements 15m
We critically examine the classic endpoint method for particle mass determination, focusing on difficult corners of parameter space, where some of the measurements are not independent, while others are adversely aected by the experimental resolution.In such scenarios, mass dierences can be measured relatively well, but the overall mass scale remains poorly constrained. Using the example of a standard SUSY decay chain we demonstrate that sensitivity to the remaining mass scale parameter can be recovered by measuring the two-dimensional kinematical boundary in the relevant three-dimensional phase space of invariant masses squared. We develop an algorithm for detecting this boundary, which uses the geometric properties of the Voronoi tessellation of the data, and in particular, the relative standard deviation (RSD) of the volumes of the neighbors for each Voronoi cell in the tessellation. We propose a new observable, which is the average RSD per unit area, calculated over the hypothesized boundary. We show that the location of the function maximum correlates very well with the true values of the new particle masses. Our approach represents the natural extension of the one-dimensional kinematic endpoint method to the relevant three dimensions of invariant mass phase space.
Speaker: Ms Dipsikha Debnath (University of Florida)
• 3:00 PM
PROSPECT - A Precision Oscillation and Spectrum Experiment 15m
PROSPECT, the PRecision Oscillation and SPECTrum Experiment, is a multi-phased short baseline reactor antineutrino experiment that aims to precisely measure the U-235 antineutrino spectrum and prob for oscillation effects involving a possible ∆m^2 ∼ 1 eV^2 scale sterile neutrino. In PROSPECT Phase-I, an optically segmented Li-6 loaded liquid scintillator detector will be deployed at at the baseline of 7-12m from the High Flux Isotope Reactor at the Oak Ridge National Laboratory. PROSPECT will measure the spectrum of U-235 to aid in resolving the unexplained inconsistency between predictive spectral models and recent experimental measurements using LEU cores, while the oscillation measurement will probe the best fit region suggested by global fitting studies within 1-year data taking. This talk will introduce the design of PROSPECT Phase-I, the discovery potential of the experiment, and the progress the collaboration has made toward realizing PROSPECT Phase-I.
Speaker: Mr XIANYI ZHANG (ILLINOIS INSTITUTE OF TECHNOLOGY)
• 3:15 PM
Sterile Neutrino Search with the PROSPECT Experiment 15m
PROSPECT is a short-baseline reactor antineutrino experiment with primary goals of performing a search for sterile neutrinos and making a precise measurement of 235U reactor antineutrino spectrum from the High Flux Isotope Reactor at Oak Ridge National Labo- ratory. PROSPECT will provide a model-independent oscillation measurement of electron antineutrinos by comparing the observed antineutrino spectrum at several baselines. By covering the baselines of 7-12 m, the PROSPECT experiment will be able to address the current eV-scale sterile neutrino oscillation best-fit region within a single year of data-taking and covers a major portion of suggested parameter space within 3 years. In this talk, we describe the PROSPECT oscillation fitting framework and expected detector sensitivity to the oscillations arising from eV-scale sterile neutrinos.
Speaker: Mr Pranava Teja Surukuchi (Illinois Institute of Technology)
• 3:30 PM 4:00 PM
Coffee Break One West
### One West
#### Fermilab, Wilson Hall
• 4:00 PM 6:00 PM
Muon Physics etc One West
### One West
#### Fermilab, Wilson Hall
• 4:00 PM
The Muon g-2 experiment at Fermilab 15m
Precise measurements of the anomalous magnetic moment, a = (g - 2)/2, of the muon provide strong tests of the Standard Model, and are more sensitive to physics beyond the Standard Model than measurements of the electron anomalous magnetic moment. The most recent measurement of the muon magnetic moment at Brookhaven E821 has hinted at new physics, with its result differing from theoretical calculations by over three standard deviations, with an uncertainty of 540 ppb. The new Fermilab E989 experiment seeks to improve on both the statistical and systematic errors of the measurement with a projected uncertainty of 140 ppb, which represents a four-fold improvement on the Brookhaven result. The experiment will use the high intensity muon beam at the new Fermilab muon campus, and store polarized muons in a magnetic storage ring. The magnetic field with be monitored by an array of calibrated NMR probes; calorimeters will measure muon decays as they travel around the ring, which indicates the spin direction. The combined measurements of the magnetic field and muon precession rate can be used to calculate the anomalous magnetic moment. A general overview of the theoretical motivation, experimental techniques, and possible implications of the experiment will be presented.
Speaker: Mr Alec Tewsley-Booth (University of Michigan, Ann Arbor)
• 4:15 PM
Muon g-2 Electrostatic Quadrupole System Plate Alignment 15m
The Muon g-2 experiment uses electrostatic quadrupoles for vertical focusing in the muon storage ring, where higher-order electric field multipoles produce non linearities in the restoring forces. Top/bottom quadrupole plates are aligned to 0.5 mm and side plates are aligned to 0.75 mm over long length scales to limit the higher-order multipoles. Plate alignment techniques and an electric field map generated with OPERA 3D software are presented in this poster.
Speaker: Cristina Schlesier (University of Illinois)
• 4:30 PM
The Muon g-2 experiment uses electrostatic quadrupoles for vertical focusing in the muon storage ring. High voltage (HV) feedthroughs provide electrical contact across the vacuum-air interface. Trapped electrons drift in the direction of the cross product between the electric and magnetic fields. These electrons drift along the quadrupole HV leads and eventually damage the HV feedthrough insulators on the vacuum side. Damaging these insulators increases the likelihood of sparking in the Quadrupole System. HV feedthrough extensions are used to position the HV feedthroughs in a low magnetic field region, thereby eliminating the trapped electrons that cause damage. The design and installation of the HV feedthrough extensions are presented in this poster.
Speaker: Ms Esra B. Yucel (ISTANBUL TECHNICAL UNIVERSITY)
• 4:45 PM
Precision Magnetic Field Calibration for the Muon $g-2$ Experiment at Fermilab 15m
The Muon $g-2$ Experiment at Fermilab (E989) has been designed to determine the muon anomalous magnetic moment to a precision of 140 parts per billion (ppb), a four-fold improvement over the Brookhaven E821 measurement. Key to this precision goal is the determination of the magnetic field of the experiment's muon storage ring to better than 100 ppb. The magnetic field will be measured and monitored by nuclear magnetic resonance (NMR) probes, which are mounted on a trolley and pulled through the muon storage region when muons are not being stored. These trolley probes will be calibrated in terms of the free-proton Larmor precession frequency $\omega_{p}$ by a specially-constructed NMR calibration probe. In E821, the uncertainty in the field measurement was 170 ppb, of which 50 ppb was due to the calibration probe. In E989, these uncertainties will be reduced to 70 ppb and 35 ppb, respectively. To meet these stringent requirements, a new specially-designed probe called the plunging probe'' has been built which will be used to calibrate the trolley probes. This talk will present the design, fabrication, and testing of the plunging probe, along with the calibration procedure to be conducted during the experiment.
Speaker: Dr David Flay (University of Massachusetts, Amherst)
• 5:00 PM
Mu2e in 10 Minutes 15m
This talk will give a concise, graduate-student-level overview of the Mu2e experiment. It will describe the goal of the Mu2e experiment (to search for neutrino-less muon-electron conversion), and why this process would indicate physics beyond the Standard Model. It will further detail the implementation and design of the experiment: (1) a brief description of how the low-energy, high-intensity muon beam is produced using Fermilab’s accelerator system, (2) a small discussion on the three solenoids of the Mu2e experiment and their function, and (3) a layout of the detector system with descriptions of the primary detector components.
Speaker: Jacob Colston (Mu2e)
• 5:15 PM
Design of the Mu2e Straw Tracker Detector 15m
The Mu2e experiment in Fermilab will search for the coherent neutrinoless conversion of a muon into an electron in the field of an aluminum nucleus, improving sensitivity by 4 orders of magnitude over existing limits and indirectly probing new physics beyond the reach of current or planned high energy colliders. To achieve a single conversion event sensitivity better than 3e-17, the experiment requires a high precision measurement of the ~105 MeV/c electron momentum while reducing to negligible all background contributions in the signal window. The primary detector element is a low-mass straw tracker chamber, comprising ~21,000 thin straw drift tubes of 5 mm diameter, arranged in a 3 m long cylinder of radius 700 mm, and operated in a magnetic field of 1 T and in vacuum. The tracker is designed to reconstruct the momentum of conversion electrons with a resolution of <180 keV/c. The distance of an electron track from the straw sense wire must be extracted within 200 μm from a TDC timing measurement, while time division yields the hit position along the straw within 3 cm. The straws are also instrumented with an ADC for dE/dx capability to separate electrons from highly ionizing protons. We will present the status and design of the tracker and the scheme for its front-end electronics, which handles amplification, shaping, digitization and readout of the straw signals.
Speaker: Manolis Kargiantoulakis (Fermilab)
• 5:30 PM
Novel Implementation of Density Estimation in Muon Cooling 15m
The international Muon Ionization Cooling Experiment (MICE) is a high energy physics experiment located at Rutherford Appleton Laboratory in U.K. The aim of MICE is to demonstrate muon beam cooling for the first time. The process of reducing beam phase-space volume is known as beam cooling and this process is necessary for a beam of muons because of the large phase-space volume that they occupy upon production. Cooled muon beams are essential for future muon-based facilities such as neutrino factory or muon collider. Several beam cooling techniques exist, but the ionization cooling is the only technique fast enough for muons within their short lifetime. In MICE, commonly used figures of merit for cooling are the beam emittance reduction, the phase-space volume reduction, and the phase-space density increase. Given the precision with which MICE aims to demonstrate beam cooling, it is necessary to work around any beam effects which may lead to inaccurate cooling measurements. Non-linear effects in beam optics is an example of such effects which can result in beam heating. The Density Estimation, DE techniques are analysis tools which are insensitive to these non-linear effects and measure the muon beam phase-space density and volume. This talk will give an overview of the recent MICE results and the novel application of the DE techniques, in specific the kernel density estimation, KDE technique in MICE.
Speaker: Tanaz Angelina Mohayai (Illinois Institute of Technology)
• 5:45 PM
New Physics Search with Experiment TREK/E36 at J-PARC 15m
We are potentially standing at the precipice in the quest for discovery of New Physics (NP) beyond the Standard Model (SM) by performing a precision test of lepton universality. Experiment E36 conducted at J- PARC in Japan is testing lepton universality in the RK = Γ(Ke2)/Γ(Kμ2) ratio. In the SM, the ratio of leptonic K+ decays is highly precise with an uncertainty of δRK /RK = 4 · 10−4. Any observed deviation from the SM prediction would break the universality of the lepton couplings and provide a clear indication of NP beyond the SM. The E36 detector apparatus allows sensitivity to search for sterile neutrinos and light U(1) gauge bosons below 300 MeV/c2, which could be associated with dark matter or explain established muon-related anomalies such as the muon g − 2 value, and perhaps the proton radius puzzle. E36 data taking was completed in 2015. A scintillating fiber target was used to stop a beam of up to 1.2 Million K+ per spill. The K+ decay products were detected with a large-acceptance toroidal spectrometer capable of tracking charged particles with high resolution, combined with a CsI(Tl) photon calorimeter with large solid angle covering about 75% of 4π and particle identification systems. The status of the data analysis will be presented. This work has been supported by DOE Early Career Award DE-SC0003884 and DOE DE-SC0013941.
Speaker: Mr Dongwi Handiipondola Dongwi (Hampton University)
| 2022-08-14T10:34:44 |
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|
https://par.nsf.gov/biblio/10237287-radio-galaxy-population-simba-simulations
|
The radio galaxy population in the simba simulations
ABSTRACT We examine the 1.4 GHz radio luminosities of galaxies arising from star formation and active galactic nuclei (AGNs) within the state-of-the-art cosmological hydrodynamic simulation Simba. Simba grows black holes via gravitational torque limited accretion from cold gas and Bondi accretion from hot gas, and employs AGN feedback including jets at low Eddington ratios. We define a population of radio loud AGNs (RLAGNs) based on the presence of ongoing jet feedback. Within RLAGN, we define high and low excitation radio galaxies (HERGs and LERGs) based on their dominant mode of black hole accretion: torque limited accretion representing feeding from a cold disc, or Bondi representing advection-dominated accretion from a hot medium. Simba predicts good agreement with the observed radio luminosity function (RLF) and its evolution, overall as well as separately for HERGs and LERGs. Quiescent galaxies with AGN-dominated radio flux dominate the RLF at $\gtrsim 10^{22-23}$ W Hz−1, while star formation dominates at lower radio powers. Overall, RLAGNs have higher black hole accretion rates and lower star formation rates than non-RLAGN at a given stellar mass or velocity dispersion, but have similar black hole masses. Simba predicts an LERG number density of 8.53 Mpc−3, ∼10× higher than for HERGs, broadly as observed. While LERGs dominate among more »
Authors:
; ; ;
Award ID(s):
Publication Date:
NSF-PAR ID:
10237287
Journal Name:
Monthly Notices of the Royal Astronomical Society
Volume:
503
Issue:
3
Page Range or eLocation-ID:
3492 to 3509
ISSN:
0035-8711
1. ABSTRACT The sensitivity of X-ray facilities and our ability to detect fainter active galactic nuclei (AGNs) will increase with the upcoming Athena mission and the AXIS and Lynx concept missions, thus improving our understanding of supermassive black holes (BHs) in a luminosity regime that can be dominated by X-ray binaries. We analyse the population of faint AGNs ($L_{\rm x, 2{-}10 \, keV}\leqslant 10^{42}\, \rm erg\,s^{ -1}$) in the Illustris, TNG100, EAGLE, and SIMBA cosmological simulations, and find that the properties of their host galaxies vary from one simulation to another. In Illustris and EAGLE, faint AGNs are powered by low-massmore »
2. 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 themore »
| 2022-09-25T08:57:22 |
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|
https://www.scstatehouse.gov/sess122_2017-2018/sj18/20180123.htm
|
South Carolina General Assembly
122nd Session, 2017-2018
Journal of the Senate
NO. 9
JOURNAL
OF THE
SENATE
OF THE
STATE OF SOUTH CAROLINA
REGULAR SESSION BEGINNING TUESDAY, JANUARY 9, 2018
_________
TUESDAY, JANUARY 23, 2018
Tuesday, January 23, 2018
(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:
Psalm 111: 10
In Psalms we read that: "the fear of the Lord is the beginning of wisdom: all who follow his precepts have good understanding. To him belongs eternal praise."
Let us pray. Gracious God, it is so apparent that we are blessed with an abundance of talent at the staff level and in our elected Senators.
In addition, we are so fortunate to have a strong constitution with an open system of government that has checks and balances. As we move into 2018, we boldly pray for Your presence in this Chamber that guides and directs the hearts and minds of our leaders. Grant to each of our Senators a wise and discerning spirit that glorifies You in every decision that is made. We offer this prayer in Your holy name, Amen
The PRESIDENT called for Petitions, Memorials, Presentments of Grand Juries and such like papers.
Point of Quorum
At 2;02 P.M., Senator LEATHERMAN made the point that a quorum was not present. It was ascertained that a quorum was not present.
Call of the Senate
Senator LEATHERMAN moved that a Call of the Senate be made. The following Senators answered the Call:
Alexander Allen Cash
Climer Corbin Cromer
Davis Gambrell Goldfinch
Hembree Hutto Kimpson
Leatherman Malloy Martin
Massey Matthews, John Nicholson
Peeler Rice Sabb
Scott Setzler Shealy
Sheheen Talley Turner
Williams Young
A quorum being present, the Senate resumed.
MESSAGE FROM THE GOVERNOR
The following appointments were transmitted by the Honorable Henry Dargan McMaster:
Statewide Appointments
Initial Appointment, Governing Board of Department of Natural Resources, with the term to commence July 1, 2018, and to expire July 1, 2022
3rd Congressional District:
Jake Rasor, Jr., 103 Calvert Avenue, Clinton, SC 29325 VICE Larry L. Yonce
Referred to the Committee on Fish, Game and Forestry.
Reappointment, South Carolina Workers' Compensation Commission, with the term to commence June 30, 2018, and to expire June 30, 2024
At-Large:
Henry Gene McCaskill, 604 Kirkwood Circle, Camden, SC 29020
Referred to the Committee on Judiciary.
Reappointment, South Carolina Workers' Compensation Commission Chairman, with the term to commence June 30, 2018, and to expire June 30, 2024
Chairman:
Thomas Scott Beck, 422 Gold Nugget Point, Prosperity, SC 29127
Referred to the Committee on Judiciary.
Reappointment, South Carolina Workers' Compensation Commission, with the term to commence June 30, 2018, and to expire June 30, 2024
At-Large:
Richard M. Campbell II, 131 High Knoll Rd., Columbia, SC 29223
Referred to the Committee on Judiciary.
Initial Appointment, Board of the South Carolina Department of Health and Environmental Control, with the term to commence June 30, 2015, and to expire June 30, 2019
1st Congressional District:
Rick Toomey, 3 Lucy Creek Drive, Beaufort, SC 29907-2222 VICE Mark Lutz
Referred to the Committee on Medical Affairs.
Initial Appointment, Director of Department of Health and Human Services, with term coterminous with Governor
Director:
Joshua Baker, 141 Montrose Drive, Lexington, SC 29072-6908 VICE Deirdra Singleton
Referred to the Committee on Medical Affairs.
Initial Appointment, South Carolina Department of Highways and Public Transportation, with the term to commence February 16, 2017, and to expire February 15, 2021
7th Congressional District:
Tony K. Cox, 817 Saint Charles Road, North Myrtle Beach, SC 29582
Referred to the Committee on Transportation.
COMMUNICATION FROM THE CLERK
Chapter 2, Title 2 of the 1976 Code, as added by the South Carolina Restructuring Act of 2014, provides a framework for systematic oversight of government agencies by the General Assembly. The President Pro Tempore, after consulting with the Standing Committee Chairmen and the Clerk of the Senate pursuant to Section 2-2-30 of the 1976 Code, determined that the Senate will schedule the following state agencies for Oversight Review during 2018:
Arts Commission
SC Ethics Commission
First Steps
Department of Health and Environmental Control - environmental
State Housing Finance and Development Authority
John de la Howe School
Law Enforcement Training Council
Department of Motor Vehicles
State Board for Technical and Comprehensive Education
Sea Grant Consortium
Vocational Rehabilitation Department
Agencies scheduled for review are encouraged to review the provisions contained in Chapter 2, Title 2 so that they may prepare for the oversight process. Final reports issued for the 2017 Oversight Reviews can be found on the individual committee pages of the General Assembly's website.
Doctor of the Day
Senator CAMPSEN introduced Dr. Alexander Ramsay of Charleston, S.C., Doctor of the Day.
Leave of Absence
On motion of Senator HEMBREE, at 3:10 P.M., Senator GREGORY was granted a leave of absence for the balance of the week.
Leave of Absence
On motion of Senator HEMBREE, at 3:10 P.M., Senator BENNETT was granted a leave of absence for the balance of the day.
Leave of Absence
On motion of Senator KIMPSON, at 3:10 P.M., Senator M.B. MATTHEWS was granted a leave of absence for the balance of the day.
Expression of Personal Interest
Senator CLIMER rose for an Expression of Personal Interest.
Remarks to be Printed
On motion of Senator SETZLER, with unanimous consent, the remarks of Senator CLIMER, when reduced to writing and made available to the Desk, would be printed in the Journal.
Expression of Personal Interest
Senator PEELER rose for an Expression of Personal Interest.
Remarks to be Printed
On motion of Senator DAVIS, with unanimous consent, the remarks of Senator PEELER, when reduced to writing and made available to the Desk, would be printed in the Journal.
S. 878 (Word version) Sens. Turner, Campbell, Verdin
RECALLED
H. 4268 (Word version) -- Rep. Crawford: A BILL TO AMEND SECTION 7-7-320, AS AMENDED, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE DESIGNATION OF VOTING PRECINCTS IN HORRY COUNTY, SO AS TO REDESIGNATE VARIOUS PRECINCTS AND REDESIGNATE THE MAP NUMBER ON WHICH THE NAMES OF THESE PRECINCTS MAY BE FOUND AND MAINTAINED BY THE REVENUE AND FISCAL AFFAIRS OFFICE.
Senator GOLDFINCH asked unanimous consent to make a motion to recall the Bill from the Committee on Judiciary.
The Bill was recalled from the Committee on Judiciary and ordered placed on the Calendar for consideration tomorrow.
Expression of Personal Interest
Senator CAMPSEN rose for an Expression of Personal Interest.
INTRODUCTION OF BILLS AND RESOLUTIONS
The following were introduced:
S. 897 (Word version) -- Senators Setzler, Massey and Young: A SENATE RESOLUTION TO EXPRESS THE PROFOUND SORROW OF THE MEMBERS OF THE SOUTH CAROLINA SENATE UPON THE PASSING OF ALLEAN COLEMAN HAMMOND, AND TO EXTEND THEIR DEEPEST SYMPATHY TO HER FAMILY AND MANY FRIENDS.
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S. 898 (Word version) -- Senator Malloy: A SENATE RESOLUTION TO EXPRESS THE PROFOUND SORROW OF THE MEMBERS OF THE SOUTH CAROLINA SENATE UPON THE PASSING OF DR. LUNS C. RICHARDSON, AND TO EXTEND THEIR DEEPEST SYMPATHY TO HIS FAMILY AND MANY FRIENDS.
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S. 899 (Word version) -- Senator Johnson: A SENATE RESOLUTION TO EXPRESS THE PROFOUND SORROW OF THE MEMBERS OF THE SOUTH CAROLINA SENATE UPON THE PASSING OF HAYES F. SAMUELS, JR., AND TO EXTEND THEIR DEEPEST SYMPATHY TO HIS FAMILY AND MANY FRIENDS.
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S. 900 (Word version) -- Senator Setzler: A SENATE RESOLUTION TO CONGRATULATE MIKE GRAY UPON THE OCCASION OF HIS RETIREMENT AS SENIOR VICE PRESIDENT OF RESOURCE DEVELOPMENT FOR UNITED WAY OF THE MIDLANDS, TO COMMEND HIM FOR HIS THIRTY-FIVE YEARS OF SERVICE TO THE ORGANIZATION, AND TO WISH HIM CONTINUED SUCCESS IN ALL HIS FUTURE ENDEAVORS.
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S. 901 (Word version) -- Senator Shealy: A SENATE RESOLUTION TO CONGRATULATE UNIVERSITY OF SOUTH CAROLINA DANCE MARATHON UPON THE OCCASION OF ITS TWENTIETH ANNIVERSARY AND TO RECOGNIZE AND HONOR THE ORGANIZATION FOR ITS MANY YEARS OF SERVICE TO THE COMMUNITY.
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S. 902 (Word version) -- Senator Sheheen: A CONCURRENT RESOLUTION TO CONGRATULATE ST. PAUL UNITED METHODIST CHURCH UPON THE OCCASION OF ITS ONE HUNDRED FIFTIETH ANNIVERSARY, TO RECOGNIZE AND HONOR THE CHURCH FOR ITS DEEP HERITAGE IN CAMDEN, AND TO COMMEND ITS LEADERSHIP AND CONGREGATION FOR THEIR MANY YEARS OF SERVICE TO THE COMMUNITY.
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The Concurrent Resolution was adopted, ordered sent to the House.
S. 903 (Word version) -- Senator Hembree: A SENATE RESOLUTION TO RECOGNIZE THE WEEK OF JANUARY 21 THROUGH JANUARY 27, 2018 AS "NATIONAL SCHOOL CHOICE WEEK IN SOUTH CAROLINA" AND TO HONOR STUDENTS, PARENTS, TEACHERS, AND SCHOOL LEADERS FROM K-12 EDUCATIONAL ENVIRONMENTS OF ALL VARIETIES FOR THEIR PERSISTENCE, ACHIEVEMENTS, DEDICATION, AND CONTRIBUTIONS TO THEIR COMMUNITIES IN SOUTH CAROLINA.
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S. 904 (Word version) -- Senator Peeler: A CONCURRENT RESOLUTION TO CONGRATULATE THE LIMESTONE COLLEGE MEN'S LACROSSE TEAM AND COACHES FOR AN EXTRAORDINARY SEASON AND FOR WINNING THE 2017 NCAA DIVISION II NATIONAL CHAMPIONSHIP TITLE.
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The Concurrent Resolution was adopted, ordered sent to the House.
S. 905 (Word version) -- Senator J. Matthews: A CONCURRENT RESOLUTION TO REMEMBER AND CELEBRATE THE LIFE OF DR. BENJAMIN FRANKLIN PAYTON AND TO HONOR HIS SIGNIFICANT CONTRIBUTIONS TO ACADEMIA.
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The Concurrent Resolution was adopted, ordered sent to the House.
S. 906 (Word version) -- Senator J. Matthews: A SENATE RESOLUTION TO RECOGNIZE AND HONOR LOW COUNTRY HEALTHY START (LCHS) FOR TWENTY YEARS OF DEDICATED SERVICE IN REDUCING DISPARITIES IN INFANT MORTALITY AND TO EXTEND BEST WISHES TO THE ORGANIZATION FOR CONTINUED SUCCESS IN ITS WORTHY ENDEAVORS.
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S. 907 (Word version) -- Senator Shealy: A BILL TO AMEND ARTICLE 31, CHAPTER 5, TITLE 56 OF THE 1976 CODE, RELATING TO MISCELLANEOUS TRAFFIC RULES, TO PROVIDE THAT A VEHICLE IN A FUNERAL PROCESSION HAS THE RIGHT OF WAY AT AN INTERSECTION AND MAY PROCEED THROUGH THE INTERSECTION IF THE PROCESSION IS LED BY AN ESCORT VEHICLE DISPLAYING FLASHING AMBER OR PURPLE LIGHTS, VISIBLE IN ALL DIRECTIONS FOR A DISTANCE OF FIVE HUNDRED FEET IN NORMAL SUNLIGHT AND ATTACHED SO AS TO BE CLEARLY VISIBLE TO APPROACHING TRAFFIC; TO PROVIDE FOR EXCEPTIONS; AND TO DEFINE NECESSARY TERMS.
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Read the first time and referred to the Committee on Transportation.
S. 908 (Word version) -- Senator Shealy: A BILL TO AMEND SECTION 56-1-2080 OF THE 1976 CODE, RELATING TO QUALIFICATIONS FOR A COMMERCIAL DRIVER'S LICENSE, TO PROVIDE THAT A PERSON MAY NOT BE ISSUED A COMMERCIAL DRIVER'S LICENSE UNLESS THAT PERSON COMPLETES AN IN-PERSON OR ONLINE HUMAN TRAFFICKING AWARENESS COURSE AND TO PROVIDE THAT THE PERSON MUST PROVIDE EVIDENCE OF COMPLETION TO THE DEPARTMENT WITH HIS APPLICATION FOR A COMMERCIAL DRIVER'S LICENSE.
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Read the first time and referred to the Committee on Transportation.
S. 909 (Word version) -- Senators Davis and Fanning: A BILL TO AMEND SECTION 58-31-200 OF THE 1976 CODE, RELATING TO JOINT OWNERSHIP OF THE NUCLEAR ELECTRIC GENERATING STATION IN FAIRFIELD COUNTY, TO PROVIDE THAT THE PUBLIC SERVICE AUTHORITY IS JOINTLY RESPONSIBLE FOR PRESERVING ANY PARTIALLY CONSTRUCTED NUCLEAR ELECTRIC GENERATION UNITS ON THE SITE AT OR NEAR PARR SHOALS IN FAIRFIELD COUNTY; TO PROVIDE THAT A PRIVATELY OWNED ELECTRIC UTILITY PROVIDING POWER TO RATEPAYERS PURSUANT TO SECTION 58-27-620 THAT IS A JOINT OWNER WITH THE PUBLIC SERVICE AUTHORITY OF A PARTIALLY CONSTRUCTED NUCLEAR ELECTRIC PLANT SHALL BE RESPONSIBLE FOR PRESERVING THE PARTIALLY CONSTRUCTED SITE AS A CONDITION OF BEING APPROVED TO DO BUSINESS IN THIS STATE; TO PROVIDE FOR COST RECOVERY; AND TO PROVIDE CONDITIONS FOR PRESERVATION; AND TO DEFINE NECESSARY TERMS.
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Senator DAVIS spoke on the Bill.
Read the first time and referred to the Committee on Judiciary.
S. 910 (Word version) -- Senator Malloy: A BILL TO AMEND SECTION 14-1-200 OF THE 1976 CODE, RELATING TO THE SALARIES OF SUPREME COURT JUSTICES AND COURT OF APPEALS, CIRCUIT COURT, AND FAMILY COURT JUDGES, TO PROVIDE FOR A SALARY SCHEDULE FOR THOSE JUDGES; TO AMEND SECTION 1-7-325 OF THE 1976 CODE, RELATING TO SOLICITOR COMPENSATION, TO PROVIDE THAT EACH FULL-TIME CIRCUIT SOLICITOR SHALL EARN A SALARY NOT LESS THAN THE SALARY PAID TO A CIRCUIT COURT JUDGE FOR THE 2016-2017 FISCAL YEAR; TO AMEND SECTION 14-11-30 OF THE 1976 CODE, RELATING TO MASTER-IN-EQUITY COMPENSATION, TO PROVIDE FOR A PAY SCHEDULE BASED ON THE SALARY PAID TO A CIRCUIT COURT JUDGE FOR THE 2016-2017 FISCAL YEAR; TO AMEND SECTION 17-3-510(C) OF THE 1976 CODE, RELATING TO CIRCUIT PUBLIC DEFENDERS, TO PROVIDE THAT THE CIRCUIT PUBLIC DEFENDER FOR EACH JUDICIAL CIRCUIT MUST EARN A SALARY NOT LESS THAN THE SALARY PAID TO A CIRCUIT COURT JUDGE FOR THE 2016-2017 FISCAL YEAR; TO AMEND SECTIONS 22-8-40(B)(2) AND (3) OF THE 1976 CODE, RELATING TO FULL-TIME AND PART-TIME MAGISTRATE SALARIES, TO PROVIDE FOR A PAY SCHEDULE BASED ON THE SALARY PAID TO A CIRCUIT COURT JUDGE FOR THE 2016-2017 FISCAL YEAR; TO AMEND SECTION 42-3-40 OF THE 1976 CODE, RELATING TO SALARIES OF WORKERS' COMPENSATION COMMISSIONERS, TO PROVIDE THAT THE ANNUAL SALARY FOR EACH COMMISSIONER SHALL BE EIGHTY-FIVE PERCENT OF THE SALARY PAID TO A CIRCUIT COURT JUDGE FOR THE 2016-2017 FISCAL YEAR;
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Senator MALLOY spoke on the Bill.
Read the first time and referred to the Committee on Judiciary.
Objection
Senator MALLOY asked unanimous consent that S. 910 be placed on the calendar without reference.
Senator PEELER objected.
S. 911 (Word version) -- Senator Alexander: A BILL TO AMEND SECTION 12-39-360 OF THE 1976 CODE, RELATING TO A COUNTY'S AUTHORITY TO EXTEND THE PAYMENT OF PROPERTY TAXES FOR SERVICE MEMBERS IN OR NEAR A HAZARD DUTY ZONE, TO REQUIRE EACH COUNTY TO ALLOW FOR A DEFERMENT, TO PROVIDE THAT THE DEFERMENT BEGINS ON THE TAX DUE DATE AND ENDS NINETY DAYS AFTER THE LAST DATE OF DEPLOYMENT, AND TO PROVIDE THAT NO INTEREST MAY BE CHARGED DURING THE DEPLOYMENT UNLESS THE TAX IS NOT PAID WITHIN THE NINETY-DAY GRACE PERIOD.
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Read the first time and referred to the Committee on Finance.
S. 912 (Word version) -- Senators Jackson, Allen, Reese, Shealy, Talley, Johnson, Campbell, Sabb, Gambrell, Nicholson and Rankin: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING SECTION 40-18-75 SO AS TO PROHIBIT A PRIVATE INVESTIGATION BUSINESS FROM KNOWINGLY REPRESENTING MULTIPLE PARTIES WITH OPPOSING INTERESTS IN CIVIL OR CRIMINAL MATTERS AND TO PROVIDE PENALTIES.
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Read the first time and referred to the Committee on Labor, Commerce and Industry.
S. 913 (Word version) -- Senator Campsen: A BILL TO AMEND SECTION 50-9-740(B) OF THE 1976 CODE, RELATING TO YOUTH HUNTING DAYS, TO PROVIDE THAT A LICENSE OR TAG REQUIRED PURSUANT TO CHAPTER 9, TITLE 50 IS WAIVED FOR A YOUTH HUNTER ON A YOUTH HUNTING DAY.
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Read the first time and referred to the Committee on Fish, Game and Forestry.
S. 914 (Word version) -- Senators Shealy and Massey: A BILL TO AMEND SECTION 61-4-730 OF THE 1976 CODE, RELATING TO SALES BY PERMITTED WINERIES, TO PROVIDE THAT PERMITTED WINERIES MAY APPLY FOR A RETAIL ON-PREMISES PERMIT FOR THE SALE OF WINE PRODUCED BY THE LICENSEE FOR SALE IN A SEPARATE LOCATION FROM ITS LICENSED PREMISES, TO PROVIDE THAT PERMITTED WINERIES MAY APPLY FOR UP TO FIFTY SPECIAL EVENT PERMITS PER YEAR FROM THE DEPARTMENT OF REVENUE FOR LOCATIONS THAT ARE NOT A WINERY'S LICENSED PREMISES, AND TO PROVIDE FOR QUALIFICATIONS FOR ON-PREMISES PERMITS.
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Read the first time and referred to the Committee on Judiciary.
S. 915 (Word version) -- Senator Timmons: A BILL TO AMEND SECTION 8-13-1312 OF THE 1976 CODE, RELATING TO CAMPAIGN BANK ACCOUNTS, TO PROVIDE THAT ALL CONTRIBUTIONS RECEIVED BY CANDIDATES SHALL BE DEPOSITED INTO AN INTEREST ON CAMPAIGN ACCOUNT KNOWN AS AN "IOCA," TO PROVIDE THAT AN IOCA BENEFITS THE STATE ETHICS COMMISSION, TO PROVIDE THAT AN IOCA SHALL BE ESTABLISHED WITH AN ELIGIBLE INSTITUTION THAT VOLUNTARILY CHOOSES TO PARTICIPATE, TO PROVIDE FOR THE RATE OF INTEREST OR DIVIDENDS PAYABLE ON ANY IOCA, TO PROVIDE THAT ONE PERCENT OF ALL CONTRIBUTIONS DEPOSITED INTO AN IOCA SHALL BE REMITTED TO BENEFIT THE COMMISSION, AND TO PROVIDE THAT THE FUNDS REMITTED TO THE COMMISSION PURSUANT TO THIS SECTION SHALL BE USED BY THE COMMISSION TO CREATE A POSITION OR POSITIONS WITHIN ITS EMPLOY TO CHECK AND CONFIRM THE COMPLETENESS OF CANDIDATE FILINGS; TO AMEND SECTION 8-13-320 OF THE 1976 CODE, RELATING TO THE DUTIES AND POWERS OF THE STATE ETHICS COMMISSION, TO PROVIDE THAT THOSE DUTIES AND RESPONSIBILITIES INCLUDE RECEIVING, ADMINISTERING, INVESTING, DISBURSING, AND SEPARATELY ACCOUNTING FOR FUNDS REMITTED TO IT PURSUANT TO SECTION 8-13-1312; TO AMEND SECTION 8-13-340 OF THE 1976 CODE, RELATING TO THE ANNUAL REPORT OF THE STATE ETHICS COMMISSION, TO PROVIDE THAT THE STATE ETHICS COMMISSION AT THE CLOSE OF EACH FISCAL YEAR SHALL REPORT TO THE GENERAL ASSEMBLY AND THE GOVERNOR CONCERNING THE ACTION IT HAS TAKEN, THE NAMES, SALARIES, AND DUTIES OF ALL PERSONS IN ITS EMPLOY, THE MONEY IT HAS DISBURSED, AND THE AMOUNT OF FUNDS IT HAS RECEIVED FROM IOCAS AND THAT THE COMMISSION SHALL ALSO MAKE OTHER REPORTS ON MATTERS WITHIN ITS JURISDICTION AND RECOMMENDATIONS FOR FURTHER LEGISLATION AS MAY APPEAR DESIRABLE; TO AMEND ARTICLE 3, CHAPTER 13, TITLE 8 OF THE 1976 CODE, RELATING TO THE STATE ETHICS COMMISSION, BY ADDING SECTION 8-13-367, TO PROVIDE THAT THE COMMISSION SHALL BE GRANTED ACCESS TO A CANDIDATE'S INCOME TAX RETURNS ON FILE WITH THE SOUTH CAROLINA DEPARTMENT OF REVENUE IF THE COMMISSION, BY A TWO-THIRDS VOTE DURING A PENDING INVESTIGATION OR OPEN COMPLAINT, DECIDES A CANDIDATE'S INCOME TAX RETURN IS RELEVANT TO A PENDING INVESTIGATION OR OPEN COMPLAINT; TO AMEND ARTICLE 3, CHAPTER 4, TITLE 12 OF THE 1976 CODE, RELATING TO THE GENERAL POWERS AND DUTIES OF THE SOUTH CAROLINA DEPARTMENT OF REVENUE, BY ADDING SECTION 12-4-365, TO PROVIDE THAT THE DEPARTMENT, WHEN REQUESTED BY THE STATE ETHICS COMMISSION IN ACCORDANCE WITH SECTION 8-13-367, SHALL PROVIDE INFORMATION CONTAINED ON THE INDIVIDUAL INCOME TAX RETURNS OF A CANDIDATE, AS DEFINED IN SECTION 8-13-1300(4), TO THE STATE ETHICS COMMISSION; AND TO DEFINE NECESSARY TERMS.
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Read the first time and referred to the Committee on Judiciary.
S. 916 (Word version) -- Senator Cromer: A BILL TO AMEND SECTION 48-52-870, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE ENERGY EFFICIENT MANUFACTURED HOMES INCENTIVE PROGRAM, SO AS TO EXTEND THE PROGRAM TEN ADDITIONAL YEARS.
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Read the first time and referred to the Committee on Agriculture and Natural Resources.
S. 917 (Word version) -- Senator Kimpson: A BILL TO AMEND SECTIONS 6-1-530, 6-1-730, AND 6-4-10, ALL AS AMENDED, CODE OF LAWS OF SOUTH CAROLINA, 1976, ALL RELATING TO THE EXPENDITURE OF THE STATE ACCOMMODATIONS TAX, LOCAL HOSPITALITY TAX, AND LOCAL ACCOMMODATIONS TAX, RESPECTIVELY, SO AS TO ALLOW THE REVENUE TO BE EXPENDED FOR THE CONTROL AND REPAIR OF FLOODING AND DRAINAGE AT TOURISM-RELATED LANDS OR AREAS.
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Read the first time and referred to the Committee on Finance.
S. 918 (Word version) -- Senators Peeler, Malloy and Hembree: A BILL TO AMEND SECTION 44-53-110, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO TERMS DEFINED IN THE "NARCOTICS AND CONTROLLED SUBSTANCES ACT", SO AS TO ADD A DEFINITION FOR "TARGETED CONTROLLED SUBSTANCE"; TO AMEND SECTION 44-53-360, RELATING TO PRESCRIPTIONS, SO AS TO REQUIRE THE USE OF ELECTRONIC PRESCRIPTIONS WHEN PRESCRIBING NARCOTIC DRUGS, WITH EXCEPTIONS, AND TO ESTABLISH CERTAIN PRESCRIBING LIMITATIONS; BY ADDING SECTION 44-53-1655 SO AS TO REQUIRE THE DEPARTMENT OF HEALTH AND ENVIRONMENTAL CONTROL TO PROVIDE PRESCRIPTION REPORTS TO PRACTITIONERS AND TO CONDUCT AUDITS OF THE PRESCRIPTION MONITORING PROGRAM, AND SECTION 44-53-1665 SO AS TO ESTABLISH REPORTING REQUIREMENTS OF THE DEPARTMENT; TO AMEND SECTIONS 44-53-1630, AS AMENDED, 44-53-1640, AS AMENDED, 44-53-1645, 44-53-1650, AND 44-53-1680, AS AMENDED, ALL RELATING TO THE PRESCRIPTION MONITORING PROGRAM, SO AS TO ADD A DEFINITION FOR "TARGETED CONTROLLED SUBSTANCE", TO REQUIRE DISPENSERS TO SUBMIT ADDITIONAL INFORMATION TO THE PROGRAM AND TO REVIEW PROGRAM DATA BEFORE DISPENSING IN CERTAIN CIRCUMSTANCES, TO CHANGE THE REQUIREMENTS FOR PRACTITIONERS TO REVIEW PRESCRIPTION HISTORY BEFORE PRESCRIBING SELECT CONTROLLED SUBSTANCES, TO ALLOW PRACTITIONERS TO OBTAIN PRESCRIPTION REPORTS, AND TO MAKE CONFORMING CHANGES, RESPECTIVELY; AND TO AMEND SECTIONS 40-47-965 AND 40-33-34, BOTH AS AMENDED, RELATING TO PRESCRIPTIVE AUTHORITY OF PHYSICIANS ASSISTANTS AND NURSES, RESPECTIVELY, SO AS TO ADDRESS THE AUTHORITY TO PRESCRIBE NARCOTICS TO CERTAIN PATIENTS.
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Read the first time and referred to the Committee on Medical Affairs.
S. 919 (Word version) -- Senators Turner and Hembree: A BILL TO AMEND CHAPTER 5, TITLE 43 OF THE 1976 CODE, RELATING TO PUBLIC AID, ASSISTANCE AND RELIEF, GENERALLY, BY ADDING ARTICLE 13, TO REQUIRE THE DEPARTMENT OF HEALTH AND HUMAN SERVICES TO ESTABLISH A COMPUTERIZED INCOME, ASSET, AND IDENTITY ELIGIBILITY VERIFICATION SERVICE TO VERIFY A PERSON'S IDENTITY AND ELIGIBILITY FOR PUBLIC ASSISTANCE, TO REQUIRE THE DEPARTMENT AND THE DEPARTMENT OF SOCIAL SERVICES TO USE THE SERVICE AS PART OF DETERMINING WHETHER TO AWARD AN APPLICANT OR RECIPIENT PUBLIC ASSISTANCE, TO ENABLE OTHER DEPARTMENTS PROVIDING PUBLIC ASSISTANCE TO USE THE SERVICE, TO REQUIRE CERTAIN REPORTING TO THE ATTORNEY GENERAL AND THE OFFICE OF INSPECTOR GENERAL FOR CASES OF SUSPECTED FRAUD, TO REQUIRE THE DEPARTMENT OF HEALTH AND HUMAN SERVICES AND THE DEPARTMENT OF SOCIAL SERVICES TO SUBMIT REPORTS TO THE GOVERNOR AND OTHER PUBLIC OFFICIALS, AND FOR OTHER PURPOSES.
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Read the first time and referred to the General Committee.
S. 920 (Word version) -- Senators Turner and Hembree: A BILL TO AMEND ARTICLE 1, CHAPTER 5, TITLE 43 OF THE 1976 CODE, RELATING TO PUBLIC AID AND ASSISTANCE, BY ADDING SECTION 43-5-260, TO PROHIBIT THE DEPARTMENT OF SOCIAL SERVICES FROM APPLYING FOR, SEEKING, ACCEPTING, OR RENEWING A WAIVER OF WORK REQUIREMENTS FOR A PERSON APPLYING FOR OR RECEIVING SUPPLEMENTAL NUTRITION ASSISTANCE PROGRAM BENEFITS.
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Read the first time and referred to the General Committee.
S. 921 (Word version) -- Senator Turner: A BILL TO AMEND ARTICLE 1, CHAPTER 5, TITLE 43 OF THE 1976 CODE, RELATING TO PUBLIC AID AND ASSISTANCE, BY ADDING SECTION 43-5-250, TO REQUIRE AN INDIVIDUAL APPLYING OR REAPPLYING FOR BENEFITS THROUGH THE SUPPLEMENTAL NUTRITION ASSISTANCE PROGRAM TO COOPERATE WITH THE DEPARTMENT OF SOCIAL SERVICES' DIVISION OF CHILD SUPPORT SERVICES AS A CONDITION OF ELIGIBILITY FOR THOSE BENEFITS.
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Read the first time and referred to the General Committee.
S. 922 (Word version) -- Senators Turner and Hembree: A BILL TO AMEND ARTICLE 1, CHAPTER 5, TITLE 43 OF THE 1976 CODE, RELATING TO PUBLIC AID AND ASSISTANCE, BY ADDING SECTION 43-5-255, TO PROHIBIT THE DEPARTMENT OF SOCIAL SERVICES FROM ESTABLISHING FINANCIAL RESOURCE LIMITS APPLICABLE TO DETERMINING ELIGIBILITY FOR THE SUPPLEMENTAL NUTRITION ASSISTANCE PROGRAM THAT EXCEED FEDERAL LIMITS OR EXEMPTING HOUSEHOLDS FROM THE RESOURCE LIMITS.
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Read the first time and referred to the General Committee.
S. 923 (Word version) -- Senator Goldfinch: A CONCURRENT RESOLUTION TO DECLARE JANUARY 31, 2018, AS OMPHALOCELE AWARENESS DAY IN SOUTH CAROLINA AND TO ENCOURAGE ALL SOUTH CAROLINIANS TO LEARN MORE ABOUT OMPHALOCELE AND MORE ABOUT HOW THEY CAN SUPPORT OMPHALOCELE PATIENTS AND THEIR FAMILIES.
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The Concurrent Resolution was introduced and referred to the Committee on Medical Affairs.
S. 924 (Word version) -- Senator Gambrell: A SENATE RESOLUTION TO RECOGNIZE AND COMMEND THE HONORABLE JAMES P. "SONNY" DAVIS ON THE OCCASION OF HIS RETIREMENT FROM HONEA PATH TOWN COUNCIL AND TO THANK HIM FOR HIS DEDICATED SERVICE TO THE PEOPLE OF THE TOWN OF HONEA PATH.
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H. 4631 (Word version) -- Rep. Lucas: A CONCURRENT RESOLUTION INVITING HIS EXCELLENCY, HENRY DARGAN MCMASTER, GOVERNOR OF THE STATE OF SOUTH CAROLINA, TO ADDRESS THE GENERAL ASSEMBLY IN JOINT SESSION AT 7:00 P.M. ON WEDNESDAY, JANUARY 24, 2018, IN THE CHAMBER OF THE SOUTH CAROLINA HOUSE OF REPRESENTATIVES.
The Concurrent Resolution was adopted, ordered returned to the House.
H. 4646 (Word version) -- Reps. Bryant, Pope, Simrill, Delleney, Felder, King, D. C. Moss, V. S. Moss and B. Newton: A CONCURRENT RESOLUTION TO HONOR AND REMEMBER THE SUPREME SACRIFICE MADE BY DETECTIVE MICHAEL R. DOTY OF THE YORK COUNTY SHERIFF'S OFFICE IN THE LINE OF DUTY AND TO EXPRESS TO HIS FAMILY THE DEEPEST SYMPATHY AND APPRECIATION OF A GRATEFUL STATE FOR HIS LIFE, SACRIFICE, AND SERVICE.
The Concurrent Resolution was adopted, ordered returned to the House.
Message from the House
Columbia, S.C., January 9, 2018
Mr. President and Senators:
The House respectfully informs your Honorable Body that it has overridden the veto by the Governor on R.127, S. 662 by a vote of 86 to 3:
(R127, S662 (Word version)) -- Senators J. Matthews and Hutto: AN ACT TO CONSOLIDATE THE SCHOOL DISTRICTS IN ORANGEBURG COUNTY INTO ONE SCHOOL DISTRICT TO BE KNOWN AS THE ORANGEBURG COUNTY SCHOOL DISTRICT; TO PROVIDE FOR THE ORDERLY TRANSITION TO A SINGLE SCHOOL DISTRICT; TO PROVIDE FOR THE MEMBERSHIP OF THE BOARD OF TRUSTEES, ITS ELECTION, POWERS, AND DUTIES; TO PROVIDE THAT A DISTRICT SUPERINTENDENT IS THE CHIEF OPERATING OFFICER OF THE DISTRICT AND IS RESPONSIBLE TO THE BOARD FOR THE PROPER ADMINISTRATION OF ALL AFFAIRS OF THE DISTRICT AND SUBJECT TO ALL OTHER PROVISIONS OF LAW RELATING TO HIS DUTIES.
Very respectfully,
Speaker of the House
Expression of Personal Interest
Senator MALLOY rose for an Expression of Personal Interest.
THE SENATE PROCEEDED TO A CALL OF THE UNCONTESTED LOCAL AND STATEWIDE CALENDAR.
SENT TO THE HOUSE
The following Bill was read the third time and ordered sent to the House of Representatives:
S. 882 (Word version) -- Senator Rankin: A BILL TO ADOPT REVISED CODE VOLUMES 15A AND 18 OF THE CODE OF LAWS OF SOUTH CAROLINA, 1976, TO THE EXTENT OF THEIR CONTENTS, AS THE ONLY GENERAL PERMANENT STATUTORY LAW OF THE STATE; AND TO ADOPT THE 2017 CUMULATIVE SUPPLEMENTS TO THE CODE OF LAWS AS PART OF THE CODE AND PROVIDE THAT THESE SUPPLEMENTS, VOLUMES AS SUPPLEMENTED BY THEM, AND THE REPLACEMENT VOLUMES CONSTITUTE THE ONLY GENERAL PERMANENT STATUTORY LAWS OF THE STATE AS OF JANUARY 1, 2018.
CARRIED OVER
H. 3929 (Word version) -- Reps. Hiott, Pitts, Kirby, Forrest, Yow, Sandifer, Atkinson, Hayes, Hixon, V.S. Moss, S. Rivers, Magnuson, Long, Chumley, Burns, Loftis and Gagnon: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING SECTION 44-1-65 SO AS TO ESTABLISH SPECIFIC REQUIREMENTS FOR THE REVIEW AND APPEAL OF DECISIONS BY THE SOUTH CAROLINA DEPARTMENT OF HEALTH AND ENVIRONMENTAL CONTROL (DHEC) REGARDING THE PERMITTING OF CERTAIN AGRICULTURAL ANIMAL FACILITIES; TO AMEND SECTION 44-1-60, AS AMENDED, RELATING TO APPEALS FROM DHEC DECISIONS GIVING RISE TO CONTESTED CASES, SO AS TO REVISE AND CLARIFY PROCEDURES FOR REVIEWING PERMITS FOR CERTAIN AGRICULTURAL ANIMAL FACILITIES; TO AMEND SECTION 46-45-60, RELATING TO APPLICABILITY OR LOCAL ORDINANCES TO AGRICULTURAL OPERATIONS, SO AS TO CHANGE CERTAIN EXCEPTIONS; AND TO AMEND SECTION 46-45-80, RELATING TO SETBACK DISTANCES FOR CERTAIN AGRICULTURAL ANIMAL FACILITIES, SO AS TO PROHIBIT DHEC FROM REQUIRING ADDITIONAL SETBACK DISTANCES IF ESTABLISHED DISTANCES ARE ACHIEVED, TO PROHIBIT THE WAIVER OR REDUCTION OF SETBACK DISTANCES IF THEY ARE ACHIEVED, WITH EXCEPTIONS, WITHOUT WRITTEN CONSENT OF ADJOINING PROPERTY OWNERS, AND TO ALLOW DHEC TO REQUIRE CERTAIN BUFFERS.
On motion of Senator VERDIN, the Bill was carried over.
AMENDED, CARRIED OVER
S. 841 (Word version) -- Agriculture and Natural Resources Committee: A BILL TO AMEND SECTION 22-1-17(A) OF THE 1976 CODE, RELATING TO CONTINUING EDUCATION FOR MAGISTRATES, TO PROVIDE THAT CONTINUING EDUCATION FOR MAGISTRATES MUST REQUIRE TWO HOURS OF EDUCATION IN THE AREA OF ANIMAL CRUELTY; TO AMEND CHAPTER 1, TITLE 47 OF THE 1976 CODE, RELATING TO CRUELTY TO ANIMALS, BY ADDING ARTICLE 2, TO PROVIDE THAT A PERSON WHO CRUELLY TETHERS A DOG IS GUILTY OF A MISDEMEANOR AND, UPON CONVICTION, MUST BE PUNISHED BY IMPRISONMENT NOT EXCEEDING NINETY DAYS OR BY A FINE OF NOT LESS THAN ONE HUNDRED DOLLARS NOR MORE THAN ONE THOUSAND DOLLARS, OR BOTH, FOR A FIRST OFFENSE, OR BY IMPRISONMENT NOT EXCEEDING TWO YEARS OR BY A FINE NOT EXCEEDING TWO THOUSAND DOLLARS, OR BOTH, FOR A SECOND OR SUBSEQUENT OFFENSE; TO AMEND SECTION 47-3-60 OF THE 1976 CODE, RELATING TO THE DISPOSITION OF QUARANTINED OR IMPOUNDED ANIMALS, TO PROVIDE THAT, UNDER CERTAIN CIRCUMSTANCES, A LITTER OF UNIDENTIFIABLE DOGS OR CATS FOUR MONTHS OF AGE OR YOUNGER MAY BE TURNED OVER TO AN ORGANIZATION, AND TO PROVIDE THAT ALL HEALTHY, UNIDENTIFIABLE CATS FOUND OR PICKED UP FROM AN OUTSIDE AREA AND CONSIDERED STRAY MAY BE STERILIZED WITHIN TWENTY-FOUR HOURS AND THEN RETURNED TO THE AREA IN WHICH THEY WERE FOUND TWENTY-FOUR HOURS AFTER SURGERY; TO AMEND CHAPTER 1, TITLE 47 OF THE 1976 CODE, RELATING TO CRUELTY TO ANIMALS, BY ADDING SECTION 47-1-145, TO PROVIDE THAT ANY PERSON, ORGANIZATION, OR OTHER ENTITY THAT IS AWARDED CUSTODY OF AN ANIMAL UNDER THE PROVISIONS OF SECTION 47-1-150 AND THAT PROVIDES SERVICES TO AN ANIMAL WITHOUT COMPENSATION MAY FILE A PETITION WITH THE COURT REQUESTING THAT THE DEFENDANT, IF FOUND GUILTY, BE ORDERED TO DEPOSIT FUNDS IN AN AMOUNT SUFFICIENT TO SECURE PAYMENT OF ALL THE REASONABLE EXPENSES INCURRED BY THE CUSTODIAN; TO AMEND SECTION 56-3-9600(B) OF THE 1976 CODE, RELATING TO THE SPECIAL FUND TO SUPPORT LOCAL ANIMAL SPAYING AND NEUTERING PROGRAMS, TO PROVIDE THAT AN AGENCY MAY APPLY FOR UP TO TWO THOUSAND DOLLARS PER GRANT APPLICATION AT THE BEGINNING OF EACH FISCAL YEAR AND MAY APPLY FOR MULTIPLE GRANTS DURING A FISCAL YEAR, TO PROVIDE THAT GRANTS MUST BE FULFILLED WITHIN SIX MONTHS OF RECEIVING FUNDS, AND TO PROVIDE THAT THE DEPARTMENT OF AGRICULTURE SHALL ENCOURAGE TIER 3 AND TIER 4 COUNTIES TO PARTICIPATE IN THE GRANT PROGRAM; TO AMEND SECTION 40-69-30 OF THE 1976 CODE, RELATING TO LICENSING REQUIREMENTS TO PRACTICE VETERINARY MEDICINE, TO PROVIDE THAT, SUBJECT TO THE JURISDICTION OF THIS STATE, DURING AN EMERGENCY OR NATURAL DISASTER, A VETERINARIAN OR VETERINARY TECHNICIAN WHO IS NOT LICENSED IN THIS STATE, BUT IS LICENSED AND IN GOOD STANDING IN ANOTHER JURISDICTION, MAY PRACTICE VETERINARY MEDICINE RELATED TO THE RESPONSE EFFORTS IN LOCATIONS IN THIS STATE IF AN OFFICIAL DECLARATION OF A STATE OF EMERGENCY HAS BEEN MADE BY THE GOVERNOR AND AN OFFICIAL INVITATION HAS BEEN EXTENDED TO THE VETERINARIAN OR VETERINARY TECHNICIAN FOR A SPECIFIED TIME BY THE GOVERNOR WITHIN OR OUTSIDE THE EMERGENCY MANAGEMENT ASSISTANCE COMPACT; TO AMEND SECTION 47-3-470(3), SECTION 47-3-480, AND SECTION 47-3-490 OF THE 1976 CODE, ALL RELATING TO THE STERILIZATION OF DOGS AND CATS, TO REPLACE THE TERM "ANIMAL REFUGE" WITH "RESCUE ORGANIZATION"; TO AMEND CHAPTER 3, TITLE 47 OF THE 1976 CODE, RELATING TO DOGS AND OTHER DOMESTIC PETS, BY ADDING ARTICLE 16, TO PROVIDE FOR SHELTERING STANDARDS AND TO PROVIDE THAT ANIMAL CONTROL OFFICERS SHALL HAVE THE DUTY TO ENFORCE SHELTER STANDARDS, INCLUDING THE INVESTIGATION OF COMPLAINTS AGAINST, AND THE INSPECTION OF, ANIMAL SHELTERING FACILITIES; AND TO DEFINE NECESSARY TERMS.
The Senate proceeded to a consideration of the Bill.
Senators HUTTO, SHEHEEN, RANKIN, and VERDIN proposed the following amendment (JUD0841.001), which was adopted:
Amend the bill, as and if amended, page 1, by striking lines 11 through 16, and inserting therein the following:
/ TO AMEND CHAPTER 1, TITLE 47 OF THE 1976 CODE, RELATING TO CRUELTY TO ANIMALS, BY ADDING SECTION 47-1-225, SO AS TO PROVIDE THAT, EVERY FOUR YEARS, AT THEIR MANDATORY CONTINUING LEGAL EDUCATION PROGRAMS, MAGISTRATES AND MUNICIPAL COURT JUDGES MUST RECEIVE AT LEAST TWO HOURS OF INSTRUCTION ON ISSUES CONCERNING ANIMAL CRUELTY; TO AMEND CHAPTER 1, TITLE 47 OF THE 1976 /
Amend the bill further, as and if amended, page 3, lines 10 through 22, by striking SECTION 1 in its entirety and inserting therein the following:
/ SECTION 1. Chapter 1, Title 47 of the 1976 Code is amended by adding:
"Section 47-1-225. Every four years, at their mandatory continuing legal education programs, magistrates and municipal court judges must receive at least two hours of instruction on issues concerning animal cruelty. The content of the continuing legal education must be determined by the South Carolina Court Administration at the direction of the Chief Justice of the South Carolina Supreme Court." /
Renumber sections to conform.
Amend title to conform.
Senator SHEHEEN explained the amendment.
On motion of Senator VERDIN, the Bill was carried over.
THE CALL OF THE UNCONTESTED CALENDAR HAVING BEEN COMPLETED, THE SENATE PROCEEDED TO THE MOTION PERIOD.
At 4:01 P.M., on motion of Senator MASSEY, the Senate agreed to dispense with the balance of the Motion Period.
THE SENATE PROCEEDED TO A CONSIDERATION OF THE VETOES.
Message from the House
Columbia, S.C., January 9, 2018
Mr. President and Senators:
The House respectfully informs your Honorable Body that it has overridden Veto 13 by the Governor on R128, H. 3720 (Word version) by a vote of 81 to 22:
R128, H. 3720--GENERAL APPROPRIATIONS ACT
Veto 13 Part lB, Page 405, Section 81, Department of Labor, Licensing and Regulation - Proviso 81.13, LLR: Amusement Park Rides
Respectfully submitted,
Speaker of the House
VETO 13 OVERRIDDEN
R128, H. 3720--GENERAL APPROPRIATIONS ACT
Veto 13 Part lB, Page 405, Section 81, Department of Labor, Licensing and Regulation - Proviso 81.13, LLR: Amusement Park Rides
Senator SETZLER moved that the veto be taken up for immediate consideration.
Senator SHEHEEN spoke on the veto.
The question was put, "Shall the Act become law, the veto of the Governor to the contrary notwithstanding?"
The "ayes" and "nays" were demanded and taken, resulting as follows:
Ayes 39; Nays 1; Abstain 1
AYES
Alexander Allen Campbell
Campsen Cash Climer
Corbin Cromer Davis
Fanning Gambrell Goldfinch
Grooms Hembree Hutto
Jackson Johnson Kimpson
Leatherman Malloy Martin
McElveen McLeod Nicholson
Peeler Rankin Reese
Rice Sabb Scott
Senn Setzler Shealy
Sheheen Talley Timmons
Turner Verdin Williams
Total--39
NAYS
Massey
Total--1
ABSTAIN
Young
Total--1
The necessary two-thirds vote having been received, the veto of the Governor was overridden, and a message was sent to the House accordingly.
Message from the House
Columbia, S.C., January 9, 2018
Mr. President and Senators:
The House respectfully informs your Honorable Body that it has overridden Veto 28 by the Governor on R128, H. 3720 (Word version) by a vote of 86 to 24:
R128, H. 3720--GENERAL APPROPRIATIONS ACT
Veto 28 Part lB, Page 356, Section 34, Department of Health and Environmental Control - Proviso 34.59, DHEC: Alida Street Project
Respectfully submitted,
Speaker of the House
SUSTAINED
RECONSIDERED AND OVERRIDDEN
R128, H. 3720--GENERAL APPROPRIATIONS ACT
Veto 28 Part lB, Page 356, Section 34, Department of Health and Environmental Control - Proviso 34.59, DHEC: Alida Street Project
Senator SETZLER asked unanimous consent to take up Veto 28.
On motion of Senator SETZLER, the vote whereby Veto 28 was sustained was reconsidered.
Senator ALEXANDER spoke on the veto.
The question was put, "Shall the Act become law, the veto of the Governor to the contrary notwithstanding?"
The "ayes" and "nays" were demanded and taken, resulting as follows:
Ayes 39; Nays 2
AYES
Alexander Allen Campbell
Campsen Climer Corbin
Cromer Davis Fanning
Gambrell Goldfinch Grooms
Hembree Hutto Jackson
Johnson Kimpson Leatherman
Malloy Martin Massey
McElveen McLeod Nicholson
Peeler Rankin Reese
Sabb Scott Senn
Setzler Shealy Sheheen
Talley Timmons Turner
Verdin Williams Young
Total--39
NAYS
Cash Rice
Total--2
The necessary two-thirds vote having been received, the veto of the Governor was overridden, and a message was sent to the House accordingly.
Message from the House
Columbia, S.C., January 9, 2018
Mr. President and Senators:
The House respectfully informs your Honorable Body that it has overridden Veto 29 by the Governor on R128, H. 3720 (Word version) by a vote of 86 to 22:
R128, H. 3720--GENERAL APPROPRIATIONS ACT
Veto 29 Part lB, Page 374, Section 49, Department of Parks, Recreation and Tourism - Proviso 49.18, PRT: Horry County Museum
Respectfully submitted,
Speaker of the House
SUSTAINED
RECONSIDERED AND OVERRIDDEN
R128, H. 3720--GENERAL APPROPRIATIONS ACT
Veto 29 Part lB, Page 374, Section 49, Department of Parks, Recreation and Tourism - Proviso 49.18, PRT: Horry County Museum
On motion of Senator SETZLER, the vote whereby Veto 29 was sustained was reconsidered.
Senator SETZLER spoke on the veto.
The question was put, "Shall the Act become law, the veto of the Governor to the contrary notwithstanding?"
The "ayes" and "nays" were demanded and taken, resulting as follows:
Ayes 26; Nays 15
AYES
Alexander Allen Campbell
Campsen Cromer Fanning
Gambrell Goldfinch Grooms
Hembree Hutto Jackson
Johnson Kimpson Leatherman
McElveen McLeod Nicholson
Rankin Reese Sabb
Scott Setzler Sheheen
Williams Young
Total--26
NAYS
Cash Climer Corbin
Davis Malloy Martin
Massey Peeler Rice
Senn Shealy Talley
Timmons Turner Verdin
Total--15
Having failed to receive the necessary two-thirds vote, the veto of the Governor was sustained, and a message was sent to the House accordingly.
On motion of Senator MALLOY, the vote whereby Veto 29 was sustained was reconsidered.
Senator MALLOY spoke on the veto.
The question was put, "Shall the Act become law, the veto of the Governor to the contrary notwithstanding?"
The "ayes" and "nays" were demanded and taken, resulting as follows:
Ayes 29; Nays 9
AYES
Alexander Allen Campbell
Campsen Cromer Davis
Fanning Gambrell Goldfinch
Grooms Hembree Hutto
Jackson Johnson Kimpson
Leatherman Malloy McElveen
McLeod Nicholson Rankin
Reese Sabb Scott
Setzler Sheheen Turner
Williams Young
Total--29
NAYS
Cash Climer Corbin
Martin Massey Peeler
Rice Talley Timmons
Total--9
The necessary two-thirds vote having been received, the veto of the Governor was overridden, and a message was sent to the House accordingly.
Senator SETZLER moved to carry over all further vetoes on H. 3720.
THE SENATE PROCEEDED TO A CONSIDERATION OF BILLS AND RESOLUTIONS RETURNED FROM THE HOUSE.
RECOMMITTED
H. 3789 (Word version) -- Reps. Govan, Yow, Henegan, J.E. Smith, Thigpen, Hart, Clemmons, Whipper and Brown: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, SO AS TO ENACT THE "SOUTH CAROLINA YOUTH CHALLENGE ACADEMY AND SOUTH CAROLINA JOBS CHALLENGE PROGRAM EXPUNGEMENT ACT"; BY ADDING ARTICLE 10 TO CHAPTER 22, TITLE 17 SO AS TO PROVIDE THAT PERSONS ELIGIBLE FOR EXPUNGEMENT OF A CRIMINAL RECORD PURSUANT TO SECTION 17-22-910 WHO SUCCESSFULLY GRADUATE AND COMPLETE THE SOUTH CAROLINA YOUTH CHALLENGE ACADEMY AND SOUTH CAROLINA JOBS CHALLENGE PROGRAM ADMINISTERED BY THE SOUTH CAROLINA ARMY NATIONAL GUARD MAY APPLY TO HAVE THEIR RECORD EXPUNGED UPON SUCCESSFUL GRADUATION AND COMPLETION OF THE PROGRAMS UNDER CERTAIN DELINEATED CIRCUMSTANCES; AND TO AMEND SECTION 17-22-940, AS AMENDED, RELATING TO THE EXPUNGEMENT PROCESS, SO AS TO INCLUDE A REFERENCE TO THE DIRECTOR OF THE SOUTH CAROLINA YOUTH CHALLENGE ACADEMY ATTESTING TO THE ELIGIBILITY OF THE CHARGE FOR EXPUNGEMENT ON AN EXPUNGEMENT APPLICATION.
The Senate proceeded to the consideration of the Bill.
Senator HUTTO moved to recommit the Bill to the Committee on Judiciary.
THE SENATE PROCEEDED TO THE SPECIAL ORDERS.
DEBATE INTERRUPTED
H. 3653 (Word version) -- Reps. Forrester, Yow, Loftis, Henegan, Spires, Anderson, Burns, V.S. Moss, Crawford, Hamilton, Felder, Norman, Anthony, Chumley, Erickson, Gagnon, Hayes, Henderson, Hosey, Jefferson, S. Rivers, Ryhal, Sandifer, Thayer, Willis, Atkinson, Alexander, West, Hixon, Murphy, Arrington, Bennett and Crosby: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING CHAPTER 24 TO TITLE 31 SO AS TO PROVIDE THE OPERATIONS OR EXPANSIONS OF MANUFACTURING AND INDUSTRIAL FACILITIES MAY NOT BE CONSIDERED PUBLIC OR PRIVATE NUISANCES IN CERTAIN CIRCUMSTANCES, TO PROVIDE RELATED FINDINGS, TO EXPLICITLY PROHIBIT LOCAL GOVERNMENTS FROM ENACTING ORDINANCES TO THE CONTRARY, TO DEFINE NECESSARY TERMINOLOGY, TO PROVIDE THAT THE PROVISIONS OF THIS ACT MAY NOT BE CONSTRUED TO MODIFY STATUTORY EMINENT DOMAIN LAWS OR ENVIRONMENTAL LAWS, AND TO PROVIDE THE PROVISIONS OF THIS ACT DO NOT APPLY TO NUISANCE ACTIONS COMMENCED WITHIN ONE YEAR OF THE EFFECTIVE DATE OF THIS CHAPTER.
The Senate proceeded to a consideration of the Bill, the question being the second reading of the Bill.
Senator MASSEY spoke on the Bill.
On motion of Senator LEATHERMAN, the Senate agreed to stand adjourned.
| 2018-02-26T03:44:46 |
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|
https://vinatom.gov.vn/en/development-of-a-neutron-detector-for-the-ambient-dose-equivalent-measurement/
|
# Development of a neutron detector for the ambient dose equivalent measurement
651
In recent years, Vietnam has experienced an increase in the use of radioactive sources, especially the applications of neutrons in industry, medicine and thus radiation protection monitoring has been of wide interest. Besides the main sources of neutrons detected in sealed radio-isotopic sources, nuclear reactors and neutron generators, neutrons are also encountered in high energy particle accelerator systems. The radiation field outside the shielding of accelerators is frequently dominated by the neutron component, which has complex and non-uniform energy distributions. Exposure to free neutrons can be hazardous since the interaction of neutrons with molecules in the human body can lead to chromosome damage and adversely affect human health. According to the recommendations of the International Commission on Radiological Protection (ICRP) for area monitoring, the ambient dose equivalent, H*(10), is used as an approximation of the protection quantity in radiation measurements of external exposure. The ambient dose equivalent measurement will provide necessary information for controlling the radiation at workplaces and defining restricted or prohibited areas. However, the precise measurement and assessment of neutron dose remains difficult due to the intrinsic characteristics of neutron radiation, for example, no-charge, continuous neutron fluence spectrum, etc.
Based on the results of the project entitled: “Optimization of the energy response function of a neutron survey meter using a Helium proportional counter”, a team of researchers of the Institute for Nuclear Science and Technology (INST) have developed a neutron detector for measuring the ambient dose equivalent H*(10) rate in the energy range from thermal to 15 MeV with high sensitivity and fully compliant with the recommendations of the international standard IEC 61005-2014 for neutron survey meters.
The developed instrument consists of a 3He proportional counter embedded in a multi-layer moderator made of high-density polyethylene (HDPE) and Cadmium (Cd). It is designed with the outer dimensions of 20.5 cm in diameter and 24.5 cm in length, and about 6 kg in weight. The sensitivity, the linearity as well as the performance of the instrument in the workplace was measured at the neutron calibration laboratory of the INST using a standard neutron field of 241Am-Be and several simulated workplace neutron fields.
• DETECTOR CONFIGURATION
The layout of the experiment at the neutron calibration laboratory of the INST
• SPECIFICATIONS
Mai Văn Diện, INST
| 2022-08-14T08:36:51 |
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|
https://da.overleaf.com/articles/a-rigorous-introduction-to-the-reals/vsdhhjtydwjr
|
Skip to content
Forfatter
Gaurav Goel
Last Updated
4 years ago
License
Creative Commons CC BY 4.0
ResuméA rigorous construction of the field of real numbers: the unique (up to isomorphism) completely ordered field with the least upper bound property; along with various formulations of completeness and with a postlude on the measure of sets.
| 2023-03-21T02:03:57 |
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https://aacrjournals.org/cancerrescommun/article/2/5/380/698987/Delineation-of-Cancer-Service-Areas-Anchored-by
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Defining a reliable geographic unit pertaining to cancer care is essential in its assessment, planning, and management. This study aims to delineate and characterize the cancer service areas (CSA) accounting for the presence of major cancer centers in the United States. We used the Medicare enrollment and claims from January 1, 2014 to September 30, 2015 to build a spatial network from patients with cancer to cancer care facilities that provided inpatient and outpatient care of cancer-directed surgery, chemotherapy, and radiation. After excluding those without clinical care or outside of the United States, we identified 94 NCI-designated and other academic cancer centers from the members of the Association of American Cancer Institutes. By explicitly incorporating existing specialized cancer referral centers, we refined the spatially constrained Leiden method that accounted for spatial adjacency and other constraints to delineate coherent CSAs within which the service volumes were maximal but minimal between them. The derived 110 CSAs had a high mean localization index (LI; 0.83) with a narrow variability (SD = 0.10). The variation of LI across the CSAs was positively associated with population, median household income, and area size, and negatively with travel time. Averagely, patients traveled less and were more likely to receive cancer care within the CSAs anchored by cancer centers than their counterparts without cancer centers. We concluded that CSAs are effective in capturing the local cancer care markets in the United States. They can be used as reliable units for studying cancer care and informing more evidence-based policy.
Significance:
Using the most refined network community detection method, we can delineate CSAs in a more robust, systematic, and empirical manner that incorporates existing specialized cancer referral centers. The CSAs can be used as a reliable unit for studying cancer care and informing more evidence-based policy in the United States. The cross-walk tabulation of ZIP code areas, CSAs, and related programs for CSAs delineation are disseminated for public access.
Cancer care assessment, planning, and management require a standardized system of geographic units on which reliable analyses can be conducted to address many challenges of the U.S. cancer care system (1). Since 2012, the NCI has mandated its designated cancer centers to identify and describe their catchment areas (CA) to address the cancer burden, risk factors, incidence, morbidity, mortality, and inequities within the CAs (2). In response, many centers either treated surrounding counties or an entire state as their CAs or combined the two (3). However, the rationale for defining the boundary was unknown and the self-declared CAs were not suitable for consistent comparisons at the national scale. Prior studies have concretized geographic unit for health care markets into various terms, such as hospital service areas (HSA; ref. 4), hospital referral regions (HRR; ref. 4), and primary care service areas (ref. 5). These units either lacked timely updates to meet the challenges of the ever-changing health care market or were not suitable for the highly specialized cancer care. More importantly, they were defined by the plurality rule that only emphasized the greatest interaction between patients and providers and lacked a systematic perspective of how to resolve uncertainties in the method to define them and standardize the delineation process (6). These concerns were addressed in recent studies (6–8) that developed novel data-driven and scale-flexible methods to define cancer service areas (CSA), within which cancer care utilizations among underlying populations were tightly tied to the service providers (7, 9, 10). A pilot study refined a recently developed effective network community detection method by accounting for spatial adjacency and other desirable constraints, termed “spatially constrained Leiden (ScLeiden) method,” and proved to be highly effective and efficient in delineating CSAs at various scales in the Northeast United States (7). However, the question remains as to what the appropriate number of CSAs is when extending the analysis to a national scope, and whether the presence of major cancer centers needs to be considered. This study addresses these two important aspects of delineating CSAs.
Cancer centers form the backbone of the cancer care system in the United States. The current 71 NCI-designated Cancer Centers (NCI-CC) in 36 states and the District of Columbia are dedicated to advancing cancer research and treatment and promoting community outreach and engagement. Their reputation for achieving better outcomes attracts more than 250,000 patients diagnosed or treated on average at an NCI-CC each year (around 16 million patients for all NCI-CCs that provide clinical care; ref. 11). The 71 NCI-CCs and 32 other cancer centers form the 103 members of the Association of American Cancer Institutes (AACI), and are premier academic and freestanding cancer centers which serve as major hubs of cancer research and care in the United States and Canada. These AACI-CCs are simply referred to as CCs hereafter. Prior studies found that the utilization of these centers was associated with proximity (12) and varied across regions and populations (13, 14). However, without defining their service areas, within which they draw most of their patients, reliable analysis of variabilities across their CSAs, as well as between the CSAs with and without any CC, is not feasible.
This study aimed to use the ScLeiden method, automated in a Geographic Information Systems (GIS) tool (6), to delineate a set of scientifically sound and reliable CSAs that best captured the local cancer care markets in the United States. The study differs from previous research as it made use of the scale flexibility of the ScLeiden method twice by accounting for the presence of the CCs. Special efforts were made to ensure that the CCs, banning close proximity, had their distinctive CSAs, and the remaining areas formed other CSAs with no anchoring CCs inside. The derived CSAs were assessed by indices such as population and area sizes, geometric shape, urbanicity, median income of residents, and average travel time, localization index (LI), and market share index (MSI) of service utilization.
### Data Sources and Processing
The cancer care utilization data were extracted from the Medicare enrollment and claims from January 1, 2014 to September 30, 2015 provided by the Centers for Medicare & Medicaid Services (CMS) with an approved Data Use Agreement and Institutional Review Board protocol. The ending date was cut off because of the transition of new codes of International Classification of Disease (ICD; ref. 15). Medicare beneficiaries were ascertained from the Medicare beneficiary denominator file by identifying those who were ages 65–99 years old, continuously enrolled in fee-for-service, enrolled in both Medicare Parts A and B, and with no missing ZIP codes in 50 states and the District of Columbia. Then cancer care services (utilizations) that were defined as cancer-directed surgery, chemotherapy, and radiotherapy were identified from Medicare Provider Analysis and Review (MedPAR), outpatient, and carrier files using ICD-9-CM procedure (16), Current Procedure Terminology (CPT-4), and Healthcare Common Procedure Coding System codes. The cancer care providers that included hospitals, ambulatory surgical centers, and outpatient facilities were extracted from the Provider of Services files provided by CMS. By linking the Medicare beneficiaries as the origins and cancer care providers as the destinations to the Medicare claims of cancer care utilization, an initial spatial network was created from the locations of patients with cancer to the locations of cancer care providers with the total claims as the service volumes between them.
Considering ZIP code was the most granular feasible unit in Medicare data, the locations of cancer patients’ residences and cancer care providers were geocoded at the ZIP code level. Point ZIP codes (typically associated with large business entities) were aggregated to the ZIP code areas that enclosed those points. The ZIP code areas were extracted from the 2015 ZIP Code Tabulation Areas. Each ZIP code area had the point location represented by its population weighted centroid calibrated from the 2010 census block population data for achieving better accuracy in the rural or suburban areas with uneven populations (17). Thus, the initial spatial network can be represented by the ZIP code centroids of patients with cancer as origin nodes and ZIP code centroids of cancer care providers as the destination nodes, and the total service volumes (or claims) as the edge weights between each other.
However, the majority (70.15%) of flows had volumes < 11 and were suppressed based on the CMS data use agreement. To define reliable and meaningful CSAs, we interpolated these flows using the strategy proposed by Wang and colleagues (6, 9). We first estimated the travel time between ZIP code areas from a national drive time matrix that accounted for the hierarchical structure of road network and real-time traffic (18). We then used a spatial interaction model to derive the best-fitting distance decay function from the remaining flows (29.85%) with volumes ≥ 11 and interpolated the suppressed ones. As a result, our estimated flow accounted for 16.6% of the total service volumes in the spatial network. We also created a spatial adjacency matrix based on the contiguity of ZIP code areas that accounted for the availability of transport modes (6).
The cancer center data were downloaded and geocoded from the member directory of AACI, comprised of 103 leading cancer centers in North America (19). This study excluded 11 (two in Canada, one in Puerto Rico, and seven basic laboratories and the St. Jude Children's Research Hospital in the United States) and unfolded Louisiana Cancer Research Consortium of New Orleans at Stanley S. Scott Cancer Center and Tulane Cancer Center. A total of 94 CCs were identified.
### GIS Automated ScLeiden Method
In network science literature, there are many network community detection methods including hierarchical agglomeration (20), simulated annealing (21), Infomap (22), Louvain (23), Leiden algorithms (24), and their variants (7). Among them, the ScLeiden method has been demonstrated to outperform other well-known methods in defining high-quality service areas with high efficiency and effectiveness (6–8). Because of the recent advances in GIS, the ScLeiden method has been automated in a GIS tool, and used in this study to delineate CSAs in the United States (6).
In a brief, given the spatial network of cancer care utilization from the ZIP codes of patients with cancer to the ZIP codes of cancer care providers in our case, the ScLeiden method optimized modularity to group a set of densely connected and spatially contiguous ZIP codes in terms of the utilizations between into preliminary CSAs and continue to group densely connected preliminary CSAs into larger CSAs until no further improvement of modularity can be made and each CSA reached minimal region size. Thus, the service volumes (or utilizations) were maximal between each derived CSAs and minimal between CSAs. This study chose a threshold population of 120,000 as the minimal region size that was used to define HRRs because CSAs were similar but more specific to referral cancer care. The modularity, a quality measure to guide the process of delineating CSAs, was defined to capture the difference between the fraction of the total service volumes within CSAs and the fraction of the total service volumes between CSAs. Mathematically, it was formulat-ed as:
where Q represented the modularity value that summed over each CSA c ∈ C, m was the total number of service volumes in the spatial network, was the total number of service volumes between all ZIP codes within the CSA was the sum of the service volumes between ZIP codes in the CSA c and ZIP codes in other CSAs. The constant γ > 0 was the resolution parameter. One may increase its value to define a series of spatially contiguous CSAs at different scales, thus enabled the ScLeiden method being scale flexible.
### Delineating CSAs Using ScLeiden Method
The whole processing of delineating CSAs in this study contained three steps. We first used the scale flexibility of the ScLeiden method to delineate as many CSAs as the CCs. For each of the initial CSAs that contained multiple CCs, our second step was to extract flows within it to form a new subnetwork and then use the scale flexibility of the ScLeiden method again to further divide such a CSA into two or more sub-CSAs so that no two CCs were > 30 minutes apart and each sub-CSA had local utilization rate (LUR) ≥ 0.5. The 30-minute travel time was selected as a criterion following the prior studies (12, 25, 26) although it was open to debate. The travel time between CCs was estimated via Google Maps. Similar to LI, LUR referred to the proportion of service volumes within a sub-CSA out of total service volumes originated from the same sub-CSA and ended at any CSAs within the subnetwork. In other words, LUR was calculated for the sub-CSAs based on the service flow volumes within a subnetwork, thus it was a local indicator. LI was calculated for the CSAs based on all service volumes within the entire network, thus it was a global indicator. The 50% of LUR was used in other service area delineations (27). In our third step, we combined the initial CSAs without the need of further division from the first step and sub-CSAs from the second step to form the final set of CSAs, within which the service volumes were maximal but minimal between.
### Statistical Analysis
The main outcome measures were LI and MSI that were commonly used to measure the characteristics of health care service areas (28–30). LI was defined as the ratio of total service volumes within a CSA divided by the total service volumes originated from the same CSA and ended at any CSAs. As a population-based index, a higher LI was more favorable as it indicated a higher degree of utilization of local care, and a CSA therefore more effectively captured its cancer care market. MSI referred to the proportion of incoming service volumes from outside of a CSA over the total service volumes originated from any CSAs and ended at the same CSA. As a hospital-based index, a lower MSI implied that the hospitals in a CSA were less attractive to patients outside the CSA, and thus a more favorable CSA delineation. Prior studies also used net patient flow to capture the patient movement across regions (28–30). Because it can be inferred from LI and MSI, we omitted its discussion here.
A systematic literature review also suggested population, urbanicity, travel time, area, and income affected health behaviors and outcomes (5, 10, 29). We selected seven independent variables: population, population density, urbanization ratio, average travel time, area size, area compactness, and median household income to characterize the CSAs. Note that population, population density, and median household income were calculated on the basis of all age population. Average travel time was the weighted average travel time for patients with cancer originated from the CSA to any CSAs. Mathematically, it was defined as the sum of the actual travel time of patients with cancer multiplied by the associated service volume divided by the sum of service volumes originated from the same CSA to any CSAs.
To assess possible differences between CSAs anchored by CCs and those without CCs, we compiled descriptive statistics of all variables for the two groups, and compared their values using a t test. For all CSAs, the global Moran I value of LI or MSI indicated no significant spatial autocorrelation, and therefore a correlation analysis was used to examine the association between either of them and each of the independent variables, and a stepwise regression was further used to examine the collective effect of independent variables on LI or MSI. All analyses were performed in ArcGIS Pro and R software. All statistical tests were two tailed.
### Data Availability
The data generated in this study are publicly available via https://faculty.lsu.edu/fahui/news/2022/usa-110csa.php.
The spatial network was composed of 32,989 nodes with total population of 308,774,408 and 520,960 edges (or flows) with a total service volume of 13,581,725. The 94 CCs included 50 NCI comprehensive cancer centers, 13 NCI cancer centers, and 31 academic cancer centers (Fig. 1). They were in 42 states with the most (N = 10) in California or New York, second most (N = 6) in Texas, and third most (N = 5) in Illinois or Pennsylvania. Nine states (Alaska, Nevada, Idaho, Montana, Wyoming, North Dakota, South Dakota, Delaware, and Maine) did not contain any CCs. Many hub-and-spoke subnetworks with large flow volumes were anchored by a stand-alone CC except those in Los Angeles, Chicago, Boston, New York, and Philadelphia that contained multiple CCs. Some subnetworks were intertwined in highly urbanized areas, such as those in northeast coast states, Florida, Texas, and southern California. Many service flows crossed state borders.
FIGURE 1
Spatial network of major cancer care service flows (volumes ≥ 30 and travel time ≤ 12 hours) overlaid with 94 CCs. Blue lines represented edges with widths proportional to service flow volumes between ZIP code areas of patients with cancer and ZIP code areas of cancer care providers at the two ends. Colored dots were locations of CCs.
FIGURE 1
Spatial network of major cancer care service flows (volumes ≥ 30 and travel time ≤ 12 hours) overlaid with 94 CCs. Blue lines represented edges with widths proportional to service flow volumes between ZIP code areas of patients with cancer and ZIP code areas of cancer care providers at the two ends. Colored dots were locations of CCs.
Close modal
The ScLeiden method first delineated 94 CSAs as there were 94 CCs, among which 32 CSAs had no CCs, 45 CSAs contained one CC each, and 17 CSAs contained multiple (≥2) CCs each. The ScLeiden method was used again to delineate each of the 17 multi-CC CSAs into a series of sub-CSAs using resolution values ranging from 0.1 to 2 with an increment of 0.1 to assess whether it was feasible to derive a distinctive CSA for each CC. A higher resolution value corresponded to a larger number of sub-CSAs. In other words, each of the 17 CSAs, treated as a study area, was divided into a number of sub-CSAs that could not be further divided (i.e., CCs in each sub-CSA in close proximity, a threshold value 0.5 for LUR, and a minimum population of 120,000). As a result, eight CSAs stayed intact, and nine other CSAs were further divided. For the latter scenario, the nine initial CSAs were segmented into 25 sub-CSAs.
Here the CSA containing six CCs in Los Angeles was selected to illustrate the process (Fig. 2A). No sub-CSAs were formed until resolution = 0.3 that yielded all three sub-CSAs (Fig. 2B): two sub-CSAs contained one CC each, and one large sub-CSA (in blue) had four CCs, some of which were > 30 minutes apart. When resolution = 0.5, 4 sub-CSAs were formed (Fig. 2C): the large sub-CSA from the previous round was split into two, such that no sub-CSA could be further divided (each with either one CC or multiple CCs ≤ 30 minutes apart, each with LUR > 0.5). If one proceeded to resolution = 0.6 to generate five sub-CSAs (Fig. 2C), one small sub-CSA (at the northwest corner) would have population < 120,000 and no CC. Therefore, four sub-CSAs with resolution = 0.5 were retained.
FIGURE 2
Delineating the CSA containing six CCs in Los Angeles into sub-CSAs. One initial CSA (blue color) in Los Angeles (A), three colored sub-CSAs with resolution = 0.3 or 0.4 (B), four colored sub-CSAs with resolution = 0.5 (C), and five colored sub-CSAs with resolution = 0.6 (D). Each CSA or sub-CSA was overlaid with service flow volumes ≥ 30 and six CCs. (Dot sizes were proportional to service volumes at CC hospitals, line width represented service volumes, and service flows between CSAs were negligible. The white areas represented large water bodies or large unpopulated land areas.)
FIGURE 2
Delineating the CSA containing six CCs in Los Angeles into sub-CSAs. One initial CSA (blue color) in Los Angeles (A), three colored sub-CSAs with resolution = 0.3 or 0.4 (B), four colored sub-CSAs with resolution = 0.5 (C), and five colored sub-CSAs with resolution = 0.6 (D). Each CSA or sub-CSA was overlaid with service flow volumes ≥ 30 and six CCs. (Dot sizes were proportional to service volumes at CC hospitals, line width represented service volumes, and service flows between CSAs were negligible. The white areas represented large water bodies or large unpopulated land areas.)
Close modal
To recap, among the 94 initial CSAs, 85 initial CSAs stayed intact (32 without CCs, 45 with one CC in each, and 8 with multiple CCs in each but indivisible), and 25 sub-CSAs (5 without CCs, 16 with one CC in each, and four with multiple CCs in each) were “spin-offs” from nine initial CSAs. The 85 initial CSAs and 25 sub-CSAs were derived by the same algorithm but with different resolutions and criteria in setting parameters. Together these 110 final CSAs were simply referred to as CSAs, and they varied in demographic and geographic characteristics. The mean LI was 0.83 (median = 0.86, range = 0.37–0.94) with a SD of 0.1, and the mean MSI was 0.14 (median = 0.11, range = 0.04–0.56) with a SD of 0.10. Their population size ranged from the smallest Ozona CSA of Texas (154,639) to the largest Dallas CSA (10,435,733) with mean = 2,807,040 and median = 2,309,342. Patients averagely travelled 112 minutes (median = 91 minutes, range = 57–515) to seek cancer care with a high variability (SD = 63 minutes).
Figure 3 depicted the spatial distribution of LI among 110 CSAs in the United States. Three CSAs in Crestview-Freeport of Florida, McAllen-Harlingen of Texas, and Gainesville-Ocala of Florida, accounting for 1% U.S. population, had the lowest LI (0.37–0.51), suggesting that most or nearly most patients traveled beyond their CSAs to seek cancer care (Fig. 1). Among the remaining 107 CSAs with LI > 0.51, the 34 CSAs with LI values in the highest category (0.89–0.94) had 44.5% population and were in large cities, such as Seattle, San Diego, Phoenix, Tucson, Denver, Oklahoma, Dallas, Houston, New Orleans, Atlanta, and Pittsburgh. The Kansas City CSA, anchored by the University of Kansas Cancer Center, had the highest LI = 0.94 and a population of 2,811,731.
FIGURE 3
LI of 110 CSAs classified by natural breaks overlaid with 94 CCs. (Nine CSAs in black boundaries were divided into multiple sub-CSAs in gray boundaries, and the small wad at the east corner of Alaska (inset) was part of the Seattle CSA in the main map. The fragmental white patches represented large water bodies or large unpopulated land areas.)
FIGURE 3
LI of 110 CSAs classified by natural breaks overlaid with 94 CCs. (Nine CSAs in black boundaries were divided into multiple sub-CSAs in gray boundaries, and the small wad at the east corner of Alaska (inset) was part of the Seattle CSA in the main map. The fragmental white patches represented large water bodies or large unpopulated land areas.)
Close modal
In terms of presence of CCs, the 73 CSAs with at least one CC included population more than five times that in the 37 CSAs without CCs. Among these 73 CSAs, 61 CSAs had one CC, seven CSAs had two CCs in each, three CSAs in Houston, Washington DC, and Philadelphia (the left inset in Fig. 3) had three CCs in each, and the Chicago CSA with a population of 8,701,735 had four CCs and the New York City CSA with a population of 7,610,200 had six CCs (the middle and right insets in Fig. 3).
Figure 4 plotted the characteristics of 37 CSAs without CCs and 73 CSAs with CCs. Both the mean and median values of each variable indicated the 73 CSAs with CCs had higher values in LI, population, population density, urbanization ratio, and median household income, and lower values in average travel time, area size, and compactness than the 37 CSAs without CCs. The differences in their means were statistically significant at 0.001 level for LI, population, and median household income, significant at 0.01 level for urbanization ratio and average travel time, and significant at 0.05 level for population density.
FIGURE 4
Boxplots of nine variables in across two groups: 37 CSAs without CCs and 73 CSAs with CCs. LI (A), MSI (B), population (in 100,000; C), population density (persons/km2; D), urbanization ratio (E), average travel time (minutes; F), area size (in 1,000 km2; G), area compactness (H), and median household income (in $100,000; I). The Df at the bottom of each boxplot referred to the difference of the mean value of the variable between two groups. *, **, *** significant at 0.05, 0.01, 0.001. (Red dash line and black solid line in the box referred to the mean and median values of each variable across the group.) FIGURE 4 Boxplots of nine variables in across two groups: 37 CSAs without CCs and 73 CSAs with CCs. LI (A), MSI (B), population (in 100,000; C), population density (persons/km2; D), urbanization ratio (E), average travel time (minutes; F), area size (in 1,000 km2; G), area compactness (H), and median household income (in$100,000; I). The Df at the bottom of each boxplot referred to the difference of the mean value of the variable between two groups. *, **, *** significant at 0.05, 0.01, 0.001. (Red dash line and black solid line in the box referred to the mean and median values of each variable across the group.)
Close modal
Correlation analysis on the 110 CSAs indicted that LI was positively correlated with population, area size, or median household income, especially when the latter three variables were in logarithmic scale but negatively correlated with average travel time (Fig. 5). In a multivariate regression on LI, we first eliminated median household income as it was highly correlated with other variables. The stepwise regression further eliminated other variables (population density, urbanization ratio, and compactness) that were not significant in explaining the variability of LI. The combination of population, average travel time, and area size explained 51% of the variation of LI, and all were statistically significant at 0.001 level. Their variation inflation factors indicated no significant collinearity between them.
FIGURE 5
Correlation coefficient matrices of nine variables across 110 CSAs. Note that population, area size, and median household income were in logarithmic scales.
FIGURE 5
Correlation coefficient matrices of nine variables across 110 CSAs. Note that population, area size, and median household income were in logarithmic scales.
Close modal
MSI was positively correlated with population density or urbanization ratio in a linear scale but negatively correlated with population, area size, or median household income in a logarithmic scale (Fig. 5). The stepwise regression eliminated other variables (population, urbanization ratio, average travel time, and compactness) that were not statistically significant. The combination of population density, area size, and median household income, with no collinearity between them, explained 37% of the variation of MSI, and each was statistically significant (population density and area size at 0.05, and median household income at 0.001).
This study delineated 110 CSAs in the Unites States by a refined network community detection method while accounting for the presence of major cancer centers. The method maximized the service volumes within the units and minimized the volumes between them, and thus ensured that the CSAs reflected cancer-specific health care markets. The quality of CSAs was evidenced by high LI values with a small SD. About 99% of the U.S. population resided in CSAs for which more than 51% of utilization occurred in the same CSAs, and 76.7% of population were in CSAs above 82% of local utilization. A large majority (84%) of population were in CSAs anchored by leading cancer centers that were members of AACI. This is consistent with the purpose of cancer centers defining CAs to serve a predominance of the populations within them (2). In addition, it highlights that a significant portion (16%) of residents, mostly rural, were not readily within reach of these prominent centers.
The presence of cancer centers significantly affected the characteristics of CSAs. Patients living in CSAs with major cancer centers were most likely to utilize cancer care services provided by these cancer centers or their affiliated hospitals. These patients also experienced shorter average travel time in relatively higher density and smaller areas where cancer centers were located.
The cancer care utilization pattern captured by LI and MSI varied across CSAs. Patients living in populous CSAs were more likely to stay local for cancer care. This pattern is similar to a study by Kilaru and colleagues in which they characterized patient movement across boundaries defining health services areas and found that the large majority of urban patients sought inpatient care in the HSA in which they resided (29). Reported in the same study, more urbanized HSAs also tended to have higher LI and higher MSI (29); however, only the latter pattern was observed in this study. Larger CSAs in terms of population and areal size were associated with higher LI but lower MSI, so were the CSAs with higher median household income and shorter average travel time. One likely explanation was that such CSAs were able to support large hospitals of higher quality and better reputation and thus attracted more patients to seek cancer care within, simultaneously, the competition may create barriers to draw patients outside. Together, they (population, area, and travel time) explained more than half of the LI variation across the 110 CSAs. The combination of population density, area, and income only explained 37% of the MSI variation.
The value of the 110 derived CSAs and the scale-flexible method lies in the ability of many stakeholders to use this approach to evaluate cancer-specific care both nationally and within smaller areas. Cancer care costs in the United States are staggering and continue to rise; the national cost of cancer-related care was estimated at $185 billion in 2015 and is expected to rise to$245 billion by 2030. At the same time, notable gains in survival are being made for some cancers, due largely to new agents, such as immunotherapy (31). Given that cancer is the second leading cause of death in the United States (32), care utilization, costs, and outcomes are critical to be able to assess nationally, robustly, reproducibly, and readily. The utility of CSAs for stakeholders, such as the CMS, private insurers, health systems, cancer centers, and researchers will be high if used to understand cancer care delivery to improve efficient care and outcomes. For example, federal agencies can apply CSAs to conduct standardized comparative analyses of cancer care resources across the whole country and in different time ranges to identify regions with overuse or underuse of effective care. There are myriad examples of utilization-based service areas derived for evaluative and comparative purposes (33). For example, the Dartmouth Atlas of Healthcare derived HRRs in the United States and measured unwarranted variation (i.e., overuse or underuse not related to underlying population characteristics) in hospital-based services, costs, and outcomes (34). Similarly, in England, the National Health Service measured unwarranted variation across its service districts and sought to reduce that variation; that is—improve care delivery in regions identified as outliers (35).
CSAs will further facilitate cancer-relevant policy targeting specific regions to improve access and outcomes with affordable cost. Also, health systems and cancer centers can apply CSAs to their CAs for understanding which cancer populations are truly underlying their regional scope of cancer control and prevention efforts. Recent studies both complement this work and highlight its importance. One study examined geographic and population coverage of 102 AACI cancer centers and found that 15% of U.S. counties (∼25 million people) do not fall within an AACI cancer center's CA (36). This corresponds closely with our finding that 16% of the population lives in a CA that is not anchored by an AACI cancer center. Yet individuals in these areas with cancer will receive cancer care, including at local/regional hospitals that are not represented in the 102 AACI cancer centers. Our CSAs capture the full geographic extent and population denominator. Thus, unlike self-defined CAs, defining geographic units based on where cancer patients receive care allows for systematic and actionable comparisons and underscores the utility of the full geographic and population coverage for the United States as has been evidenced by the Dartmouth Atlas of HealthCare's HRRs.
Another recent study mapped the CAs of the 63 NCI-CCs that provide patient care nationally and found that 88% of the U.S. population resides within an NCI-CC CA (37). However, given that only about 12% of individuals with a cancer diagnosis attend an NCI-CC, the unit of “catchment area” is not the best comparative unit for care received. While CAs of NCI-CCs may serve to benchmark measure of cancer care and outcomes, they are not geographic units that capture population-based patterns of cancer care utilization (i.e., “cancer care markets”). In that recent study, cancer mortality rates were compared across the geographic regions of the 63 CAs and found a wide range of variation. While this analysis was informative, it would be even more informative if we could compare range of cancer mortality rates across 100% of cancer care delivered, not just the approximately 12% which occurs at NCI-CCs (37). This is the utility of the CSAs.
Finally, health care professionals and researchers may use the CSAs to study the geographic variation of cancer care access, utilizations, outcomes, and spending to identify effective therapies across heterogeneous populations and better care delivery models for specific populations and geographic areas. Thus, more evidence-based policies can be implemented to optimize cancer care delivery, maximize resource utilization, reduce extant disparities, and identify intervention targets. All potential users are able to use the scale-flexible method automated in a GIS tool to define CSAs in other study areas, update CSAs to meet the challenges of market changes and population movement or delineate other type of service areas (i.e., the newly defined HSAs and HRRs in very recent studies (6)) to fit their needs.
There were some limitations in this study. Medicare data were used as the basis for cancer care utilization to delineate the CSAs because it is fully population-based for individuals age 65 and older; however, nearly half of all cancer occur in younger age groups (38). Future studies will test the generalizability of CSAs to younger populations when related data are available at a population level. Also, we only included fee-for-service Medicare claims to ascertain cancer care utilization since beneficiaries enrolled in Medicare Advantage do not have claims or bills submitted for each service. To protect the privacy of patients with cancer, some Medicare data with volumes less than 11 were suppressed. Future studies may consider adding more years of data to lessen this issue. For the same reason, Medicare data were aggregated at the ZIP code level to delineate CSAs, during which several criteria including 30-minute travel time, 50% of the local utilization rate, and minimal population of 120,000 were used, these may invoke the modified area unit problem (MAUP), leading to different number of CSAs being defined. Therefore, their selection calls for consensus among health care professionals and researchers. The number of cancer centers may change with more cancer centers joining the membership of AACI. This would cause changes in the number and boundaries of CSAs. Nevertheless, AACI has rigorous membership criteria, the number of leading cancer centers may not change significantly in a few years. Also, the scale-flexible method can easily redelineate a comparable number of CSAs or allow a new number of CSAs to be set based on new major cancer centers. This study used a simple and clean set of cancer centers as a baseline to define CSAs, other satellite cancer centers or large hospitals not in the list also played important roles in cancer diagnosis and treatment (see dense flows ending at locations without cancer centers in Fig. 1). However, the providers aggregated at ZIP code level cannot be identified because of the privacy issues.
From this study, we conclude that by using the most refined network community detection method, we can delineate CSAs in a more robust, systematic, and empirical manner that incorporates existing specialized cancer referral centers. The CSAs can be used as a reliable unit for studying cancer care and informing more evidence-based cancer care policy in the United States. The cross-walk tabulation of ZIP code areas and CSAs and related programs for CSA delineation are disseminated for public access.
F. Wang reports grants from NCI during the conduct of the study. T. Onega reports grants from NIH during the conduct of the study. No other disclosures were reported.
C. Wang: Conceptualization, data curation, software, formal analysis, validation, investigation, visualization, methodology, writing-original draft, writing-review and editing. F. Wang: Conceptualization, resources, supervision, funding acquisition, validation, methodology, writing-review and editing. T. Onega: Conceptualization, resources, supervision, funding acquisition, validation, methodology, writing-review and editing.
This work receives financial support from the NCI (R21CA212687, T. Onega, F. Wang) is gratefully acknowledged. Points of view or opinions in this article are those of the authors, and do not necessarily represent the official position or policies of NCI. We thank anonymous reviewers for their constructive comments to make our final version greatly improved.
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This open access article is distributed under the Creative Commons Attribution License 4.0 International (CC BY).
| 2022-08-13T00:20:03 |
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https://verse-and-dimensions.fandom.com/wiki/Pentagram
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## FANDOM
1,109 Pages
The pentagram is a star polygon with five edges, with every second vertex missed by the edges going around it. The Bowers acronym for the pentagram is star. It is topologically the same as a pentagon.
## Structure and Sections
### Subfaces
$\{1\}$ $\{2\}$ $\{3\}$ $\{4\}$ $\{5\}$ $\{\frac{5}{2}\}$ $\{6\}$ $\{7\}$ $\{\frac{7}{2}\}$ $\{\frac{7}{3}\}$ $\{8\}$ $\{\frac{8}{3}\}$ $\{9\}$ $\{\frac{9}{2}\}$ $\{\frac{9}{4}\}$ $\{10\}$ $\{\frac{10}{3}\}$ $\{11\}$ $\{\frac{11}{2}\}$ $\{\frac{11}{3}\}$ $\{\frac{11}{4}\}$ $\{\frac{11}{5}\}$ $\{12\}$ $\{\frac{12}{5}\}$ $\{13\}$ $\{\frac{13}{2}\}$ $\{\frac{13}{3}\}$ $\{\frac{13}{4}\}$ $\{\frac{13}{5}\}$ $\{\frac{13}{6}\}$ $\{14\}$ $\{\frac{14}{3}\}$ $\{\frac{14}{5}\}$ $\{15\}$ $\{\frac{15}{2}\}$ $\{\frac{15}{4}\}$ $\{\frac{15}{7}\}$ $\{16\}$ $\{\frac{16}{3}\}$ $\{\frac{16}{5}\}$ $\{\frac{16}{7}\}$ ... $\{\infty\}$ $\{x\}$ $\{\frac{\pi i}{\lambda}\}$
Monogon Digon Triangle Square Pentagon Pentagram Hexagon Heptagon Heptagram Great heptagram Octagon Octagram Enneagon Enneagram Great enneagram Decagon Decagram Hendecagon Small hendecagram Hendecagram Great hendecagram Grand hendecagram Dodecagon Dodecagram Tridecagon Small tridecagram Tridecagram Medial tridecagram Great tridecagram Grand tridecagram Tetradecagon Tetradecagram Great tetradecagram Pentadecagon Small pentadecagram Pentadecagram Great pentadecagram Hexadecagon Small hexadecagram Hexadecagram Great hexadecagram ... Apeirogon Failed star polygon ($x$-gon) Pseudogon ($\frac{\pi i}{\lambda}$-gon)
Regular
$t_0 \{\frac{5}{2} \}$
Rectified
$t_1 \{\frac{5}{2} \}$
Truncated
$t_{0,1} \{\frac{5}{2} \}$
Pentagram Pentagram Pentagon
Regular
$t_0 \{\frac{5}{3} \}$
Rectified
$t_1 \{\frac{5}{3} \}$
Truncated
$t_{0,1} \{\frac{5}{3} \}$
Pentagram Pentagram Decagram
Community content is available under CC-BY-SA unless otherwise noted.
| 2020-07-14T11:13:54 |
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https://math.wikia.org/wiki/Proof:The_Decimal_0.999..._is_Equivalent_to_1
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## FANDOM
1,168 Pages
There are many proofs that the repeating decimal 0.999... is equivalent to the number one, some more rigorous than others. Also with counter-proofs.
## Prerequisites
• The notion that 0.999... represents an infinitely repeating decimal—that is, the digit 9 repeats itself without end to the right of the decimal place.
## Proof
### Sum/product of fractions
$\frac13=0.333\ldots$
Therefore:
$\frac13+\frac13+\frac13=0.333\ldots+0.333\ldots+0.333\ldots$
$\frac13=1=0.999\ldots$
Likewise:
$\frac19=0.111\ldots$
$9\cdot\frac19=9\cdot0.111\ldots$
Multiplying each side by 9 we obtain:
$1=0.999\ldots$
QED
The only refutation this example proof has is that which questions whether or not $\frac13=0.333\ldots$ . Both one-third as an infinitely repeating set of three's and one as an infinitely repeating set of nine's are equally exact, and both must be taken on a little bit of faith. 1/3 being equivalent to a repeating threes rarely ever questioned, but is the same reasoning phenomenon - the same paradox. If one-third and one-ninth in decimal form are taken without question to be equal to their fractional counterparts, then why cant one as a decimal of nines?
### Conversion to fraction
$n=0.999\ldots$
Multiply by a factor of 10:
$10n=9.999\ldots$
Subtract:
$10n-n=9.999\ldots-0.999\ldots$
$9n=9.000\ldots=9$
$n=1$
QED
The only refutation this example has is as follows. One might argue that when multiplying by ten, the right hand side shifts to the left a decimal place, leaving a terminating zero at the end of the infinite string of 9's ($10n=9.999\ldots9990$). And, therefore, when subtracting $10n-n=9n=8.999\ldots991$ (with a one after the last of infinite nines). But it is important to realize the meaning of infinite. There is no terminating 9 and therefore no placeholder after it. There will always be another 9.
### Infinite geometric series
$0.999\ldots=0.9+0.09+0.009\cdots$
$0.999\ldots=9\cdot0.1+9\cdot0.01+9\cdot0.001+\cdots$
$0.999\ldots=9\cdot10^{-1}+9\cdot10^{-2}+9\cdot10^{-3}+\cdots$
$0.999\ldots=9\cdot(10^{-1}+10^{-2}+10^{-3}+\cdots)$
$0.999\ldots=9\cdot\sum_{n=1}^\infty 10^{-n}$
$0.999\ldots=9\cdot\sum_{n=1}^\infty\left(\frac{1}{10}\right)^n$
Evaluating infinite geometric series is easy when utilizing the theorem:
$\sum_{n=1}^\infty r^n=\frac{r}{1-r}$
Therefore:
$0.999\ldots=9\cdot\sum_{n=1}^\infty\left(\frac{1}{10}\right)^n=9\cdot\frac{\frac{1}{10}}{\left(1-\frac{1}{10}\right)}$
$0.999\ldots=9\cdot\frac{\frac{1}{10}}{\frac{9}{10}}$
$0.999\ldots=9\cdot\frac19=1$
QED
### Argument from averages
The average $A$ of two numbers $m,n$ is found by adding them and dividing by two.
$A=\frac{m+n}{2}$
The average is larger than the smaller number $m$ , but smaller than the larger number $n$ .
$m<A<n$
If $m=n$ , then $A=m=n$
Assuming that 0.999... is less than 1, the average between the two is:
$A=\frac{0.999\ldots+1}{2}$
$A=\frac{1.999\ldots}{2}$
$A=0.999\ldots$
Since $A=m$ , then so does $A=n$ , thus $m=n$ : $0.999\ldots=1$
QED
### Argument from philosophy
The definition of the real numbers as a continuum:
If two numbers $x,z$ exist, such $x\ne z$ and $x<z$ ;
there must exist a third number $y$ in between such that $x<y<z$
This is saying that if two numbers are not equal, there is a third number that is also unequal and that can fit in between them on the number line. Regardless of the type of real number or the difficulty in computing its value or representing its value, from a purely abstract perspective, there does exist a number that is larger than one but smaller than the other. It is impossible to find a "next higher" number that is both larger to a given value but couldnt have been smaller (see argument from averages).
If $0.999\ne1$ , then what number $y$ could exist in between them such that $0.999\ldots<y< 1$ ?
Since there is no conceivable number that can exist in between the two, they must be equal according to the definition of the real numbers as a continuum.
$0.999\ldots=1$
QED
There could also be numbers between 0.99999999..9...... and 1: like 0.9.....................91 (the dots represent infinite "9" repeating after each other.)
### Arithmetic proof
Evaluate the difference between 1 and 0.9999...
$1-0.999\ldots=0.000\ldots$
One might argue that after the infinitely many zeros, there is going to be a 1 ($0.000\ldots0001$). But it is important to grasp what "infinite" means. The 9's are infinite, there is no terminating number at the end. The zeros are also infinite, there is no 1 at the end. There is no "end", there will also be another 9 or another 0.
An infinite string of zeros past the decimal is still just 0:
$1-0.9999\ldots=0$
Since any number subtracted from an equal value is zero: $m-m=0$
Algebraic rearranging:
$1=0.999\ldots$
QED
It is not a law in Mathematics that there could not be an end to the result of $=0.999\Idots$
Community content is available under CC-BY-SA unless otherwise noted.
| 2019-12-14T23:12:37 |
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|
https://phys.libretexts.org/TextBooks_and_TextMaps/College_Physics/Book%3A_College_Physics_(OpenStax)/08._Linear_Momentum_and_Collisions/8.7%3A_Introduction_to_Rocket_Propulsion
|
$$\require{cancel}$$
# 8.7: Introduction to Rocket Propulsion
Rockets range in size from fireworks so small that ordinary people use them to immense Saturn Vs that once propelled massive payloads toward the Moon. The propulsion of all rockets, jet engines, deflating balloons, and even squids and octopuses is explained by the same physical principle—Newton’s third law of motion. Matter is forcefully ejected from a system, producing an equal and opposite reaction on what remains. Another common example is the recoil of a gun. The gun exerts a force on a bullet to accelerate it and consequently experiences an equal and opposite force, causing the gun’s recoil or kick.
Making Connections: Take-Home Experiment —Propulsion of a Balloon
• Hold a balloon and fill it with air. Then, let the balloon go. In which direction does the air come out of the balloon and in which direction does the balloon get propelled? If you fill the balloon with water and then let the balloon go, does the balloon’s direction change? Explain your answer.
Figure shows a rocket accelerating straight up. In part (a), the rocket has a mass $$m$$ and a velocity $$v$$ relative to Earth, and hence a momentum $$mv$$ In part (b), a time $$\Delta t$$ has elapsed in which the rocket has ejected a mass $$\Delta m$$ of hot gas at a velocity $$v_e$$ relative to the rocket. The remainder of the mass $$(m - \Delta m)$$ now has a greater velocity $$(v + \Delta v)$$. The momentum of the entire system (rocket plus expelled gas) has actually decreased because the force of gravity has acted for a time $$\Delta t$$, producing a negative impulse $$\Delta p = -mg\Delta t$$. (Remember that impulse is the net external force on a system multiplied by the time it acts, and it equals the change in momentum of the system.) So, the center of mass of the system is in free fall but, by rapidly expelling mass, part of the system can accelerate upward. It is a commonly held misconception that the rocket exhaust pushes on the ground. If we consider thrust; that is, the force exerted on the rocket by the exhaust gases, then a rocket’s thrust is greater in outer space than in the atmosphere or on the launch pad. In fact, gases are easier to expel into a vacuum.By calculating the change in momentum for the entire system over $$\Delta t$$, and equating this change to the impulse, the following expression can be shown to be a good approximation for the acceleration of the rocket.
$a = \dfrac{v_e}{m} \dfrac{\Delta m}{\Delta t} - g,$
where $$a$$ is the acceleration of the rocket, $$v_e$$ is the escape velocity, $$m$$ is the mass of the rocket, $$\ Delta m$$ is the mass of the ejected gas, and $$\Delta t$$ is the time in which the gas is ejected.
Figure $$\PageIndex{1}$$: (a) This rocket has a mass $$m$$ and an upward velocity $$v$$. The net external force on the system is $$-mg$$, if air resistance is neglected. (b) A time $$\Delta t$$ later the system has two main parts, the ejected gas and the remainder of the rocket. The reaction force on the rocket is what overcomes the gravitational force and accelerates it upward.
A rocket’s acceleration depends on three major factors, consistent with the equation for acceleration of a rocket . First, the greater the exhaust velocity of the gases relative to the rocket, $$v_e$$, the greater the acceleration is. The practical limit for $$v_e$$ is about $$2.5 \times 10^3 \space m/s$$ for conventional (non-nuclear) hot-gas propulsion systems. The second factor is the rate at which mass is ejected from the rocket. This is the factor $$(\Delta m/\Delta t)v_e$$, with units of newtons, is called "thrust.” The faster the rocket burns its fuel, the greater its thrust, and the greater its acceleration. The third factor is the mass $$m$$ of the rocket. The smaller the mass is (all other factors being the same), the greater the acceleration. The rocket mass $$m$$ decreases dramatically during flight because most of the rocket is fuel to begin with, so that acceleration increases continuously, reaching a maximum just before the fuel is exhausted.
Factors Affecting a Rocket’s Acceleration
• The greater the exhaust velocity $$v_e$$ of the gases relative to the rocket, the greater the acceleration.
• The faster the rocket burns its fuel, the greater its acceleration.
• The smaller the rocket’s mass (all other factors being the same), the greater the acceleration.
Example $$\PageIndex{1}$$: Calculating Acceleration: Initial Acceleration of a Moon Launch
A Saturn V’s mass at liftoff was $$2.80 \times 10^6 \space kg$$, its fuel-burn rate was $$1.40 \times 10^4 \times kg/s$$, and the exhaust velocity was $$2.40 \times 10^3 m/s$$. Calculate its initial acceleration.
Strategy
This problem is a straightforward application of the expression for acceleration because a is the unknown and all of the terms on the right side of the equation are given.
Solution
Substituting the given values into the equation for acceleration yields
$a = \dfrac{v_e}{m} \dfrac{\Delta m}{\delta t} - g$
$= \dfrac{2.40 \times 10^3 \space m/s}{2.80 \times 10^6 \space kg}(1.40 \times 10^4 \space kg/s) - 9.8 \space m/s^2$
$= 2.20 \space m/s^2.$
Discussion
This value is fairly small, even for an initial acceleration. The acceleration does increase steadily as the rocket burns fuel, because $$m$$ decreases while $$v_e$$ and $$\frac{\Delta m}{\Delta t}$$ remain constant. Knowing this acceleration and the mass of the rocket, you can show that the thrust of the engines was $$3.36 \times 10^7 \space N.$$
To achieve the high speeds needed to hop continents, obtain orbit, or escape Earth’s gravity altogether, the mass of the rocket other than fuel must be as small as possible. It can be shown that, in the absence of air resistance and neglecting gravity, the final velocity of a one-stage rocket initially at rest is
$v = v_e \space ln \dfrac{m_0}{m_r},$
where $$ln (m_0/m_r)$$ is the natural logarithm of the ratio of the initial mass of the rocket $$(m_0)$$ to what is left $$(m_r)$$ after all of the fuel is exhausted. (Note that $$v$$ is actually the change in velocity, so the equation can be used for any segment of the flight. If we start from rest, the change in velocity equals the final velocity.) For example, let us calculate the mass ratio needed to escape Earth’s gravity starting from rest, given that the escape velocity from Earth is about $$11.2 \times 10^3 \space m/s$$, and assuming an exhaust velocity $$v_e = 2.5 \times 10^3 \space m/s.$$ $ln \dfrac{m_0}{m_r} = \dfrac{v}{v_e} = \dfrac{11.2 \times 10^3 \space m/s}{2.5 \times 10^3 \space m/s} = 4.48$ Solving for $$m_0/m_r$$ gives $\dfrac{m_0}{m_r} = e^{4.48} = 88.$
Thus, the mass of the rocket is $m_r = \dfrac{m_0}{88}.$
This result means that only $$1/88$$ of the mass is left when the fuel is burnt, and $$87/88$$ of the initial mass was fuel. Expressed as percentages, 98.9% of the rocket is fuel, while payload, engines, fuel tanks, and other components make up only 1.10%. Taking air resistance and gravitational force into account, the mass $$m_r$$ remaining can only be about $$m_0/180$$. It is difficult to build a rocket in which the fuel has a mass 180 times everything else. The solution is multistage rockets. Each stage only needs to achieve part of the final velocity and is discarded after it burns its fuel. The result is that each successive stage can have smaller engines and more payload relative to its fuel. Once out of the atmosphere, the ratio of payload to fuel becomes more favorable, too.The space shuttle was an attempt at an economical vehicle with some reusable parts, such as the solid fuel boosters and the craft itself. (See Figure) The shuttle’s need to be operated by humans, however, made it at least as costly for launching satellites as expendable, unmanned rockets. Ideally, the shuttle would only have been used when human activities were required for the success of a mission, such as the repair of the Hubble space telescope. Rockets with satellites can also be launched from airplanes. Using airplanes has the double advantage that the initial velocity is significantly above zero and a rocket can avoid most of the atmosphere’s resistance.
Figure $$\PageIndex{2}$$:The space shuttle had a number of reusable parts. Solid fuel boosters on either side were recovered and refueled after each flight, and the entire orbiter returned to Earth for use in subsequent flights. The large liquid fuel tank was expended. The space shuttle was a complex assemblage of technologies, employing both solid and liquid fuel and pioneering ceramic tiles as reentry heat shields. As a result, it permitted multiple launches as opposed to single-use rockets. (credit: NASA)
Phet Explorations: Lunar Lander
Can you avoid the boulder field and land safely, just before your fuel runs out, as Neil Armstrong did in 1969? Our version of this classic video game accurately simulates the real motion of the lunar lander with the correct mass, thrust, fuel consumption rate, and lunar gravity. The real lunar lander is very hard to control.
Phet Explorations: Lunar Lander
Can you avoid the boulder field and land safely, just before your fuel runs out, as Neil Armstrong did in 1969? Our version of this classic video game accurately simulates the real motion of the lunar lander with the correct mass, thrust, fuel consumption rate, and lunar gravity. The real lunar lander is very hard to control.
Figure $$\PageIndex{3}$$: Lunar Lander
# Summary
• Newton’s third law of motion states that to every action, there is an equal and opposite reaction.
• Acceleration of a rocket is $$a = \frac{v_e}{m} \frac{\Delta m}{\Delta t} - g.$$
• A rocket’s acceleration depends on three main factors. They are
1. The greater the exhaust velocity of the gases, the greater the acceleration.
2. The faster the rocket burns its fuel, the greater its acceleration.
3. The smaller the rocket's mass, the greater the acceleration.
## Contributors
Paul Peter Urone (Professor Emeritus at California State University, Sacramento) and Roger Hinrichs (State University of New York, College at Oswego) with Contributing Authors: Kim Dirks (University of Auckland) and Manjula Sharma (University of Sydney). This work is licensed by OpenStax University Physics under a Creative Commons Attribution License (by 4.0).
| 2018-12-18T15:39:41 |
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|
https://www.usgs.gov/natural-hazards/earthquake-hazards/science/loma-prieta-earthquake-professional-papers
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# Loma Prieta Earthquake Professional Papers
## Science Center Objects
The four Loma Prieta Earthquake Professional Papers, which were published as multiple chapters, comprehensively document the magnitude 6.9 earthquake in California that shook the San Francisco and Monterey Bay regions on October 17, 1989. They contain almost 3000 pages written by 401 investigators of the earthquake. The investigations were funded by a special Congressional appropriation to the U.S. Geological Survey and National Science Foundation after the earthquake to improve understanding of both the complexity of earthquakes and how society can reduce losses in future earthquakes. PDF’s of individual chapters can be downloaded by clicking on the appropriate professional paper below. Paper copies can be purchased at https://store.usgs.gov.
### Professional Paper 1550 – Earthquake Occurrence
William H. Bakun and William H. Prescott, editors
Cover image for Professional Paper 1550. (Public domain.)
Professional Paper 1550 seeks to understand the M6.9 Loma Prieta earthquake itself. It examines how the fault that generated the earthquake ruptured, searches for and evaluates precursors that may have indicated an earthquake was coming, reviews forecasts of the earthquake, and describes the geology of the earthquake area and the crustal forces that affect this geology. Some significant findings were:
• Slip during the earthquake occurred on 35 km of fault at depths ranging from 7 to 20 km. Maximum slip was approximately 2.3 m. The earthquake may not have released all of the strain stored in rocks next to the fault and indicates a potential for another damaging earthquake in the Santa Cruz Mountains in the near future may still exist.
• The earthquake involved a large amount of uplift on a dipping fault plane. Pre-earthquake conventional wisdom was that large earthquakes in the Bay area occurred as horizontal displacements on predominantly vertical faults.
• The fault segment that ruptured approximately coincided with a fault segment identified in 1988 as having a 30% probability of generating a M7 earthquake in the next 30 years. This was one of more than 20 relevant earthquake forecasts made in the 83 years before the earthquake.
• Calculations show that the Loma Prieta earthquake changed stresses on nearby faults in the Bay area. In particular, the earthquake reduced stresses on the Hayward Fault which decreased the frequency of small earthquakes on it.
• Geological and geophysical mapping indicate that, although the San Andreas Fault can be mapped as a through going fault in the epicentral region, the southwest dipping Loma Prieta rupture surface is a separate fault strand and one of several along this part of the San Andreas that may be capable of generating earthquakes.
### Professional Paper 1551 - Strong ground motion and ground failure
Thomas L. Holzer, editor
Cover image for Professional Paper 1551. (Public domain.)
Professional Paper 1551 describes the effects at the land surface caused by the Loma Prieta earthquake. These effects: include the pattern and characteristics of strong ground shaking, liquefaction of both floodplain deposits along the Pajaro and Salinas Rivers in the Monterey Bay region and sandy artificial fills along the margins of San Francisco Bay, landslides in the epicentral region, and increased stream flow. Some significant findings and their impacts were:
• Strong shaking that was amplified by a factor of about two by soft soils caused damage at up to 100 kilometers (60 miles) from the epicenter. Instrumental recordings of this ground shaking have been used to improve how building codes consider site amplification effects from soft soils.
• Liquefaction at 134 locations caused $99.2 million of the total earthquake loss of$5.9 billion. Liquefaction of floodplain deposits and sandy artificial fills was similar in nature to that which occurred in the 1906 San Francisco earthquake and indicated that many areas remain susceptible to liquefaction damage in the San Francisco and Monterey Bay regions.
• Landslides caused $30 million in earthquake losses, damaging at least 200 residences. Many landslides showed evidence of movement in previous earthquakes. • Recognition of the similarities between liquefaction and landslides in 1906 and 1989 and research in intervening years that established methodologies to map liquefaction and landslide hazards prompted the California legislature to pass in 1990 the Seismic Hazards Mapping Act that required the California Geological Survey to delineate areas potentially susceptible to these hazards and communities to regulate development in these zones. • The earthquake caused the flow of many streams in the epicentral region to increase. Effects were noted up to 88 km from the epicenter. • Post-earthquake studies of the Marina District of San Francisco provide one of the most comprehensive case histories of earthquake effects at a specific site. Soft soils beneath the Marina amplified ground shaking to damaging levels and caused liquefaction of sandy artificial fills. Liquefaction required 123 repairs of pipelines in the Municipal Water Supply System, more than three times the number of repairs elsewhere in the system. Approximately 13.6 km of gas-distribution lines were replaced, and more than 20% of the wastewater collection lines were repaired or replaced. ### Professional Paper 1552 – Performance of the Built Environment Thomas L. Holzer, editor Cover image for Professional Paper 1552. (Public domain.) Professional Paper 1552 focuses on the response of buildings, lifelines, highway systems, and earth structures to the earthquake. Losses to these systems totaled approximated$5.9 billion. The earthquake displaced many residents from their homes and severely disrupted transportation systems. Some significant findings were:
• Approximately 16,000 housing units were uninhabitable after the earthquake including 13,000 in the San Francisco Bay region. Another 30,000-35,000 units were moderately damaged in the earthquake. Renters and low-income residents were particularly hard hit.
| 2019-10-17T14:02:57 |
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https://zbmath.org/authors/?s=0&q=Voevodsky%2C+Vladimir
|
## Voevodskiĭ, Vladimir Aleksandrovich
Compute Distance To:
Author ID: voevodsky.vladimir-aleksandrovich Published as: Voevodsky, Vladimir; Voevodskij, V. A.; Voevodsky, V.; Voevodsky, V. A. more...less Further Spellings: Воеводский Владимир Александрович Homepage: https://www.math.ias.edu/vladimir/home External Links: MacTutor · MGP · ORCID · Wikidata · ResearchGate · Math-Net.Ru · dblp · GND · IdRef Awards: Fields Medal (2002)
Documents Indexed: 54 Publications since 1989, including 3 Books 1 Contribution as Editor · 1 Further Contribution Biographic References: 11 Publications Co-Authors: 21 Co-Authors with 24 Joint Publications 420 Co-Co-Authors
all top 5
### Co-Authors
30 single-authored 6 Kapranov, Mikhail M. 5 Suslin, Andreĭ Aleksandrovich 3 Ahrens, Benedikt 3 Friedlander, Eric Mark 3 Lumsdaine, Peter LeFanu 2 Awodey, Steve 2 Garner, Richard 2 Martin-Löf, Per 2 Pelayo, Alvaro 2 Warren, Michael Alton 2 Weibel, Charles A. 1 Aczel, Peter 1 Altenkirch, Thorsten 1 Angiuli, Carlo 1 Avigad, Jeremy 1 Barras, Bruno 1 Bauer, Andrej 1 Bertot, Yves 1 Bezem, Marc 1 Bordg, Anthony 1 Brunerie, Guillaume 1 Cohen, Cyril 1 Constable, Robert Lee 1 Coquand, Thierry 1 Curien, Pierre-Louis 1 Dundas, Bjørn Ian 1 Dybjer, Peter 1 Finster, Eric 1 Fiore, Marcelo P. 1 Gambino, Nicola 1 Gonthier, Georges 1 Grayson, Daniel Richard 1 Hales, Thomas Callister 1 Harper, Robert 1 Herbelin, Hugo 1 Hofmann, Martin 1 Hofstra, Pieter J. W. 1 Hötzel Escardó, Martín 1 Hou (Favonia), Kuen-Bang 1 Joyal, André 1 Kapulkin, Chris 1 Kapulkin, Krzysztof 1 Kock, Joachim 1 Kraus, Nicolai 1 Levine, Marc Noel 1 Li, Nuo 1 Licata, Dan 1 Luo, Zhaohui 1 Mahboubi, Assia 1 Mazza, Carlo 1 Melikhov, Sergey Aleksandrovich 1 Morel, Fabien 1 Nahas, Michael 1 Orlov, Dmitri O. 1 Østvær, Paul Arne 1 Palmgren, Erik 1 Polonsky, Andrew 1 Riehl, Emily 1 Rijke, Egbert 1 Röndigs, Oliver 1 Scott, Dana Stewart 1 Scott, Philip J. 1 Shulman, Michael A. 1 Sojakova, Kristina 1 Solov’ëv, Sergeĭ Vladimirovich 1 Sozeau, Matthieu 1 Spitters, Bas 1 1 Van den Berg, Benno 1 Vishik, A. S. 1 Zeilberger, Noam
all top 5
### Serials
4 Publications Mathématiques 4 Theory and Applications of Categories 3 Journal of Pure and Applied Algebra 2 Russian Mathematical Surveys 2 Cahiers de Topologie et Géométrie Différentielle Catégoriques 2 Mathematics of the USSR. Izvestiya 2 MSCS. Mathematical Structures in Computer Science 2 IMRN. International Mathematics Research Notices 2 Documenta Mathematica 2 Annals of Mathematics. Second Series 2 Journal of $$K$$-Theory 1 Uspekhi Matematicheskikh Nauk [N. S.] 1 Functional Analysis and its Applications 1 Inventiones Mathematicae 1 Proceedings of the American Mathematical Society 1 Soviet Mathematics. Doklady 1 Selecta Mathematica. New Series 1 Oberwolfach Reports 1 Annals of Mathematics Studies 1 Clay Mathematics Monographs 1 Logical Methods in Computer Science 1 Journal of Topology 1 Universitext
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### Fields
32 Algebraic geometry (14-XX) 23 Category theory; homological algebra (18-XX) 20 Algebraic topology (55-XX) 15 $$K$$-theory (19-XX) 14 Mathematical logic and foundations (03-XX) 6 Computer science (68-XX) 3 Convex and discrete geometry (52-XX) 2 Number theory (11-XX) 2 Field theory and polynomials (12-XX) 2 Group theory and generalizations (20-XX) 2 Manifolds and cell complexes (57-XX) 1 General and overarching topics; collections (00-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 General algebraic systems (08-XX) 1 Commutative algebra (13-XX) 1 Nonassociative rings and algebras (17-XX) 1 Functions of a complex variable (30-XX) 1 Several complex variables and analytic spaces (32-XX) 1 General topology (54-XX) 1 Quantum theory (81-XX) 1 Relativity and gravitational theory (83-XX)
### Citations contained in zbMATH Open
55 Publications have been cited 2,228 times in 1,074 Documents Cited by Year
$$\mathbb{A}^1$$-homotopy theory of schemes. Zbl 0983.14007
Morel, Fabien; Voevodsky, Vladimir
1999
Motivic cohomology with $$\mathbb Z/2$$-coefficients. Zbl 1057.14028
2003
Triangulated categories of motives over a field. Zbl 1019.14009
2000
Lecture notes on motivic cohomology. Zbl 1115.14010
Mazza, Carlo; Voevodsky, Vladimir; Weibel, Charles
2006
On motivic cohomology with $$\mathbb{Z}/l$$-coefficients. Zbl 1236.14026
2011
Bloch-Kato conjecture and motivic cohomology with finite coefficients. Zbl 1005.19001
Suslin, Andrei; Voevodsky, Vladimir
2000
2-categories and Zamolodchikov tetrahedra equations. Zbl 0809.18006
Kapranov, M. M.; Voevodsky, V. A.
1994
Reduced power operations in motivic cohomology. Zbl 1057.14027
2003
$$\mathbb{A}^1$$-homotopy theory. Zbl 0907.19002
1998
Singular homology of abstract algebraic varieties. Zbl 0896.55002
Suslin, Andrei; Voevodsky, Vladimir
1996
Cycles, transfers, and motivic homology theories. Zbl 1021.14006
Voevodsky, Vladimir; Suslin, Andrei; Friedlander, Eric M.
2000
An exact sequence for $$K^M_*/2$$ with applications to quadratic forms. Zbl 1124.14017
Orlov, D.; Vishik, A.; Voevodsky, V.
2007
Homotopy type theory. Univalent foundations of mathematics. Zbl 1298.03002
The Univalent Foundations Program
2013
Homology of schemes. Zbl 0871.14016
Voevodsky, V.
1996
Motivic cohomology groups are isomorphic to higher Chow groups in any characteristic. Zbl 1057.14026
2002
Cohomological theory of presheaves with transfers. Zbl 1019.14010
2000
A nilpotence theorem for cycles algebraically equivalent to zero. Zbl 0861.14006
Voevodsky, V.
1995
Relative cycles and Chow sheaves. Zbl 1019.14004
Suslin, Andrei; Voevodsky, Vladimir
2000
Bivariant cycle cohomology. Zbl 1019.14011
Friedlander, Eric M.; Voevodsky, Vladimir
2000
Homotopy theory of simplicial sheaves in completely decomposable topologies. Zbl 1194.55020
2010
Open problems in the motivic stable homotopy theory. I. Zbl 1047.14012
2002
Drawing curves over number fields. Zbl 0790.14026
Shabat, G. B.; Voevodskij, V. A.
1990
Motivic Eilenberg-MacLane spaces. Zbl 1227.14025
2010
Braided monoidal 2-categories and Manin-Schechtman higher braid groups. Zbl 0791.18010
Kapranov, M.; Voevodsky, V.
1994
Unstable motivic homotopy categories in Nisnevich and cdh-topologies. Zbl 1187.14025
2010
Cancellation theorem. Zbl 1202.14022
2010
Combinatorial-geometric aspects of polycategory theory: Pasting schemes and higher Bruhat orders (list of results). Zbl 0748.18010
Kapranov, M. M.; Voevodskij, V. A.
1991
Free $$n$$-category generated by a cube, oriented matroids, and higher Bruhat orders. Zbl 0766.20005
Voevodskij, V. A.; Kapranov, M. M.
1991
An experimental library of formalized mathematics based on the univalent foundations. Zbl 1361.68192
2015
On the zero slice of the sphere spectrum. Zbl 1182.14012
Voevodsky, V.
2004
Motives over simplicial schemes. Zbl 1194.14029
2010
A possible new approach to the motivic spectral sequence for algebraic $$K$$-theory. Zbl 1009.19003
2002
A C-system defined by a universe category. Zbl 1436.03311
2015
Equilateral triangulations of Riemann surfaces, and curves over algebraic number fields. Zbl 0697.14017
Voevodskij, V. A.; Shabat, G. B.
1989
Subsystems and regular quotients of C-systems. Zbl 1452.03040
2016
$$\infty$$-groupoids and homotopy types. Zbl 0754.18008
Kapranov, M. M.; Voevodskij, V. A.
1991
Voevodsky’s Seattle lectures: $$K$$-theory and motivic cohomology. (Notes by C. Weibel). Zbl 0941.19001
Voevodsky, V.
1999
Simplicial radditive functors. Zbl 1194.55021
2010
Products of families of types and $$(\Pi,\lambda)$$-structures on C-systems. Zbl 1380.03072
2016
Motivic homotopy theory. Lectures at a summer school in Nordfjordeid, Norway, August 2002. Zbl 1118.14001
Dundas, Bjørn Ian; Levine, Marc; Østvær, Paul Arne; Röndigs, Oliver; Voevodsky, V.
2007
C-systems defined by universe categories: presheaves. Zbl 1453.03067
2017
The $$(\Pi,\lambda)$$-structures on the C-systems defined by universe categories. Zbl 1383.03056
2017
Categorical structures for type theory in univalent foundations. Zbl 06943957
Ahrens, Benedikt; Lumsdaine, Peter Lefanu; Voevodsky, Vladimir
2018
Galois representations connected with hyperbolic curves. Zbl 0770.14016
Voevodskij, V. A.
1991
Univalent foundations of mathematics. Zbl 1371.03097
2011
A univalent formalization of the $$p$$-adic numbers. Zbl 1361.68190
Pelayo, Álvaro; Voevodsky, Vladimir; Warren, Michael A.
2015
A cubical approach to straightening. Zbl 1470.18028
Kapulkin, Krzysztof; Voevodsky, Vladimir
2020
$$\infty$$-groupoids as a model for a homotopy category. Zbl 0721.55015
Voevodskij, V. A.; Kapranov, M. M.
1990
Mini-workshop: The homotopy interpretation of constructive type theory. Abstracts from the mini-workshop held February 27th-March 05th, 2011. Zbl 1242.00037
2011
Introduction. Zbl 1019.14008
Friedlander, Eric M.; Suslin, A.; Voevodsky, V.
2000
Étale topologies of schemes over fields of finite type over $$\mathbb{Q}$$. Zbl 0759.14012
Voevodskij, V. A.
1990
On Galois groups of function fields over fields of finite type over $$\mathbb{Q}$$. Zbl 0786.12004
Voevodskij, V. A.
1991
Univalent semantics of constructive type theories. Zbl 1250.03121
2011
Lawvere theories and C-systems. Zbl 1451.18013
Fiore, Marcelo; Voevodsky, Vladimir
2020
Categorical structures for type theory in univalent foundations. Zbl 07204300
Ahrens, Benedikt; Lumsdaine, Peter LeFanu; Voevodsky, Vladimir
2017
A cubical approach to straightening. Zbl 1470.18028
Kapulkin, Krzysztof; Voevodsky, Vladimir
2020
Lawvere theories and C-systems. Zbl 1451.18013
Fiore, Marcelo; Voevodsky, Vladimir
2020
Categorical structures for type theory in univalent foundations. Zbl 06943957
Ahrens, Benedikt; Lumsdaine, Peter Lefanu; Voevodsky, Vladimir
2018
C-systems defined by universe categories: presheaves. Zbl 1453.03067
2017
The $$(\Pi,\lambda)$$-structures on the C-systems defined by universe categories. Zbl 1383.03056
2017
Categorical structures for type theory in univalent foundations. Zbl 07204300
Ahrens, Benedikt; Lumsdaine, Peter LeFanu; Voevodsky, Vladimir
2017
Subsystems and regular quotients of C-systems. Zbl 1452.03040
2016
Products of families of types and $$(\Pi,\lambda)$$-structures on C-systems. Zbl 1380.03072
2016
An experimental library of formalized mathematics based on the univalent foundations. Zbl 1361.68192
2015
A C-system defined by a universe category. Zbl 1436.03311
2015
A univalent formalization of the $$p$$-adic numbers. Zbl 1361.68190
Pelayo, Álvaro; Voevodsky, Vladimir; Warren, Michael A.
2015
Homotopy type theory. Univalent foundations of mathematics. Zbl 1298.03002
The Univalent Foundations Program
2013
On motivic cohomology with $$\mathbb{Z}/l$$-coefficients. Zbl 1236.14026
2011
Univalent foundations of mathematics. Zbl 1371.03097
2011
Mini-workshop: The homotopy interpretation of constructive type theory. Abstracts from the mini-workshop held February 27th-March 05th, 2011. Zbl 1242.00037
2011
Univalent semantics of constructive type theories. Zbl 1250.03121
2011
Homotopy theory of simplicial sheaves in completely decomposable topologies. Zbl 1194.55020
2010
Motivic Eilenberg-MacLane spaces. Zbl 1227.14025
2010
Unstable motivic homotopy categories in Nisnevich and cdh-topologies. Zbl 1187.14025
2010
Cancellation theorem. Zbl 1202.14022
2010
Motives over simplicial schemes. Zbl 1194.14029
2010
Simplicial radditive functors. Zbl 1194.55021
2010
An exact sequence for $$K^M_*/2$$ with applications to quadratic forms. Zbl 1124.14017
Orlov, D.; Vishik, A.; Voevodsky, V.
2007
Motivic homotopy theory. Lectures at a summer school in Nordfjordeid, Norway, August 2002. Zbl 1118.14001
Dundas, Bjørn Ian; Levine, Marc; Østvær, Paul Arne; Röndigs, Oliver; Voevodsky, V.
2007
Lecture notes on motivic cohomology. Zbl 1115.14010
Mazza, Carlo; Voevodsky, Vladimir; Weibel, Charles
2006
On the zero slice of the sphere spectrum. Zbl 1182.14012
Voevodsky, V.
2004
Motivic cohomology with $$\mathbb Z/2$$-coefficients. Zbl 1057.14028
2003
Reduced power operations in motivic cohomology. Zbl 1057.14027
2003
Motivic cohomology groups are isomorphic to higher Chow groups in any characteristic. Zbl 1057.14026
2002
Open problems in the motivic stable homotopy theory. I. Zbl 1047.14012
2002
A possible new approach to the motivic spectral sequence for algebraic $$K$$-theory. Zbl 1009.19003
2002
Triangulated categories of motives over a field. Zbl 1019.14009
2000
Bloch-Kato conjecture and motivic cohomology with finite coefficients. Zbl 1005.19001
Suslin, Andrei; Voevodsky, Vladimir
2000
Cycles, transfers, and motivic homology theories. Zbl 1021.14006
Voevodsky, Vladimir; Suslin, Andrei; Friedlander, Eric M.
2000
Cohomological theory of presheaves with transfers. Zbl 1019.14010
2000
Relative cycles and Chow sheaves. Zbl 1019.14004
Suslin, Andrei; Voevodsky, Vladimir
2000
Bivariant cycle cohomology. Zbl 1019.14011
Friedlander, Eric M.; Voevodsky, Vladimir
2000
Introduction. Zbl 1019.14008
Friedlander, Eric M.; Suslin, A.; Voevodsky, V.
2000
$$\mathbb{A}^1$$-homotopy theory of schemes. Zbl 0983.14007
Morel, Fabien; Voevodsky, Vladimir
1999
Voevodsky’s Seattle lectures: $$K$$-theory and motivic cohomology. (Notes by C. Weibel). Zbl 0941.19001
Voevodsky, V.
1999
$$\mathbb{A}^1$$-homotopy theory. Zbl 0907.19002
1998
Singular homology of abstract algebraic varieties. Zbl 0896.55002
Suslin, Andrei; Voevodsky, Vladimir
1996
Homology of schemes. Zbl 0871.14016
Voevodsky, V.
1996
A nilpotence theorem for cycles algebraically equivalent to zero. Zbl 0861.14006
Voevodsky, V.
1995
2-categories and Zamolodchikov tetrahedra equations. Zbl 0809.18006
Kapranov, M. M.; Voevodsky, V. A.
1994
Braided monoidal 2-categories and Manin-Schechtman higher braid groups. Zbl 0791.18010
Kapranov, M.; Voevodsky, V.
1994
Combinatorial-geometric aspects of polycategory theory: Pasting schemes and higher Bruhat orders (list of results). Zbl 0748.18010
Kapranov, M. M.; Voevodskij, V. A.
1991
Free $$n$$-category generated by a cube, oriented matroids, and higher Bruhat orders. Zbl 0766.20005
Voevodskij, V. A.; Kapranov, M. M.
1991
$$\infty$$-groupoids and homotopy types. Zbl 0754.18008
Kapranov, M. M.; Voevodskij, V. A.
1991
Galois representations connected with hyperbolic curves. Zbl 0770.14016
Voevodskij, V. A.
1991
On Galois groups of function fields over fields of finite type over $$\mathbb{Q}$$. Zbl 0786.12004
Voevodskij, V. A.
1991
Drawing curves over number fields. Zbl 0790.14026
Shabat, G. B.; Voevodskij, V. A.
1990
$$\infty$$-groupoids as a model for a homotopy category. Zbl 0721.55015
Voevodskij, V. A.; Kapranov, M. M.
1990
Étale topologies of schemes over fields of finite type over $$\mathbb{Q}$$. Zbl 0759.14012
Voevodskij, V. A.
1990
Equilateral triangulations of Riemann surfaces, and curves over algebraic number fields. Zbl 0697.14017
Voevodskij, V. A.; Shabat, G. B.
1989
all top 5
### Cited by 830 Authors
29 Østvær, Paul Arne 21 Panin, Ivan A. 17 Asok, Aravind 17 Levine, Marc Noel 15 Tabuada, Gonçalo 15 Voevodskiĭ, Vladimir Aleksandrovich 14 Isaksen, Daniel C. 14 Kahn, Bruno 14 Mináč, Ján 14 Weibel, Charles A. 14 Yagita, Nobuaki 13 Fasel, Jean 13 Laterveer, Robert 12 Déglise, Frédéric 12 Krishna, Amalendu 11 Bondarko, Mikhail Vladimirovich 11 Kelly, Shane P. 10 Ayoub, Joseph 10 Binda, Federico 10 Garkusha, Grigory 10 Ormsby, Kyle M. 10 Röndigs, Oliver 10 Walker, Mark E. 10 Wickelgren, Kirsten G. 9 Friedlander, Eric Mark 9 Gille, Stefan G. 9 Hasemeyer, Christian 9 Heller, Jeremiah 9 Voisin, Claire 8 Ananyevskiy, Alexey 8 Bachmann, Tom 8 Dugger, Daniel 8 Geisser, Thomas H. 8 Hoyois, Marc 8 Marcolli, Matilde 8 Quadrelli, Claudio 8 Saito, Shuji 8 Yamazaki, Takao 7 Coquand, Thierry 7 Ivorra, Florian 7 Nguyêñ Duy Tân 7 Rosenschon, Andreas 7 Rülling, Kay 7 Wendt, Matthias 6 Ahrens, Benedikt 6 Barbieri Viale, Luca 6 Hornbostel, Jens 6 Kerz, Moritz C. 6 Kuniba, Atsuo 6 Pelaez, Pablo 6 Schmidt, Alexander 6 Spitzweck, Markus 6 Vezzani, Alberto 6 Vishik, Alexander 6 Williams, Ben 5 Becher, Karim Johannes 5 Choudhury, Utsav 5 Cisinski, Denis-Charles 5 Cortiñas, Guillermo H. 5 Druzhinin, Andreĭ É. 5 Elgueta, Josep 5 Gallauer, Martin 5 Guletskiǐ, Vladimir 5 Hopkins, Michael Jerome 5 Huber-Klawitter, Annette 5 Kapranov, Mikhail M. 5 Merkur’ev, Aleksandr Sergeevich 5 Morel, Fabien 5 Positselski, Leonid Efimovich 5 Scholbach, Jakob 5 Suslin, Andreĭ Aleksandrovich 5 Vezzosi, Gabriele 4 Baez, John C. 4 Cegarra, Antonio Martínez 4 Crane, Louis 4 Crans, Sjoerd E. 4 Fu, Lie 4 Guillou, Bertrand J. 4 Hill, Michael A. 4 Hutchinson, Kevin 4 Itzykson, Claude 4 Jin, Fangzhou 4 Joshua, Roy 4 Karoubi, Max 4 Karpenko, Nikita Aleksandrovich 4 Khan, Adeel A. 4 Kondo, Satoshi 4 Kříž, Igor 4 Lumsdaine, Peter LeFanu 4 Matzri, Eliyahu 4 Neshitov, Alexander 4 Okado, Masato 4 Park, Jinhyun 4 Quick, Gereon 4 Quigley, James D. 4 Sato, Kanetomo 4 Sivatski, Alexander S. 4 Smirnov, Aleksandr Leonidovich 4 Sosnilo, Vladimir Aleksandrovich 4 Szabo, Richard J. ...and 730 more Authors
all top 5
### Cited in 182 Serials
93 Advances in Mathematics 74 Journal of Pure and Applied Algebra 37 Journal of Algebra 34 Transactions of the American Mathematical Society 32 Journal of $$K$$-Theory 30 Compositio Mathematica 29 Documenta Mathematica 25 Mathematische Annalen 22 Mathematische Zeitschrift 19 Journal of Number Theory 18 Algebraic & Geometric Topology 18 Journal of the Institute of Mathematics of Jussieu 17 Duke Mathematical Journal 17 Inventiones Mathematicae 17 Comptes Rendus. Mathématique. Académie des Sciences, Paris 16 Manuscripta Mathematica 15 Communications in Mathematical Physics 15 Proceedings of the American Mathematical Society 15 Journal of Mathematical Sciences (New York) 14 Journal of Algebraic Geometry 14 Selecta Mathematica. New Series 14 Geometry & Topology 13 $$K$$-Theory 13 Applied Categorical Structures 13 St. Petersburg Mathematical Journal 13 Forum of Mathematics, Sigma 11 Annals of Mathematics. Second Series 11 Journal of the European Mathematical Society (JEMS) 11 Journal of Homotopy and Related Structures 9 Topology and its Applications 8 Publications Mathématiques 8 Rendiconti del Seminario Matematico della Università di Padova 8 Journal of the American Mathematical Society 7 Journal of Mathematical Physics 7 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 7 Journal für die Reine und Angewandte Mathematik 7 Bulletin of the American Mathematical Society. New Series 6 Communications in Algebra 6 Annales de l’Institut Fourier 6 Research in the Mathematical Sciences 5 Theoretical and Mathematical Physics 5 Annali di Matematica Pura ed Applicata. Serie Quarta 5 Cahiers de Topologie et Géométrie Différentielle Catégoriques 5 MSCS. Mathematical Structures in Computer Science 5 Journal of High Energy Physics 5 International Journal of Number Theory 5 Logical Methods in Computer Science 5 Journal of Topology 5 Annals of $$K$$-Theory 4 Discrete Mathematics 4 Letters in Mathematical Physics 4 Bulletin of the London Mathematical Society 4 Functional Analysis and its Applications 4 Journal of Combinatorial Theory. Series A 4 Journal of the Mathematical Society of Japan 4 Nagoya Mathematical Journal 4 Tôhoku Mathematical Journal. Second Series 4 International Journal of Mathematics 4 Indagationes Mathematicae. New Series 4 Journal of Knot Theory and its Ramifications 4 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 4 Theory and Applications of Categories 4 Transformation Groups 3 Mathematical Proceedings of the Cambridge Philosophical Society 3 Canadian Journal of Mathematics 3 Canadian Mathematical Bulletin 3 Journal of the Ramanujan Mathematical Society 3 Journal de Mathématiques Pures et Appliquées. Neuvième Série 3 Expositiones Mathematicae 3 Journal of Algebraic Combinatorics 3 The New York Journal of Mathematics 3 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V 3 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 3 Algebra & Number Theory 3 Japanese Journal of Mathematics. 3rd Series 3 Journal de l’École Polytechnique – Mathématiques 3 Higher Structures 2 Mathematical Notes 2 Nuclear Physics. B 2 Russian Mathematical Surveys 2 Beiträge zur Algebra und Geometrie 2 Collectanea Mathematica 2 Commentarii Mathematici Helvetici 2 Geometriae Dedicata 2 International Journal of Mathematics and Mathematical Sciences 2 Kodai Mathematical Journal 2 Mathematische Nachrichten 2 Memoirs of the American Mathematical Society 2 Michigan Mathematical Journal 2 Pacific Journal of Mathematics 2 Tokyo Journal of Mathematics 2 European Journal of Combinatorics 2 Forum Mathematicum 2 Sugaku Expositions 2 Proceedings of the National Academy of Sciences of the United States of America 2 Vestnik St. Petersburg University. Mathematics 2 Annales Mathématiques Blaise Pascal 2 Sbornik: Mathematics 2 Izvestiya: Mathematics 2 Journal of Group Theory ...and 82 more Serials
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### Cited in 42 Fields
688 Algebraic geometry (14-XX) 315 $$K$$-theory (19-XX) 236 Algebraic topology (55-XX) 235 Category theory; homological algebra (18-XX) 170 Number theory (11-XX) 92 Group theory and generalizations (20-XX) 63 Associative rings and algebras (16-XX) 58 Manifolds and cell complexes (57-XX) 53 Field theory and polynomials (12-XX) 49 Quantum theory (81-XX) 45 Commutative algebra (13-XX) 37 Mathematical logic and foundations (03-XX) 28 Nonassociative rings and algebras (17-XX) 28 Several complex variables and analytic spaces (32-XX) 27 Combinatorics (05-XX) 20 Convex and discrete geometry (52-XX) 19 Computer science (68-XX) 13 Dynamical systems and ergodic theory (37-XX) 13 Differential geometry (53-XX) 12 Global analysis, analysis on manifolds (58-XX) 8 Order, lattices, ordered algebraic structures (06-XX) 8 Topological groups, Lie groups (22-XX) 8 Functions of a complex variable (30-XX) 6 General and overarching topics; collections (00-XX) 6 History and biography (01-XX) 6 Relativity and gravitational theory (83-XX) 5 Partial differential equations (35-XX) 5 Functional analysis (46-XX) 4 Special functions (33-XX) 4 Statistical mechanics, structure of matter (82-XX) 3 Linear and multilinear algebra; matrix theory (15-XX) 3 Measure and integration (28-XX) 3 Geometry (51-XX) 3 General topology (54-XX) 2 General algebraic systems (08-XX) 2 Difference and functional equations (39-XX) 2 Probability theory and stochastic processes (60-XX) 1 Ordinary differential equations (34-XX) 1 Approximations and expansions (41-XX) 1 Mechanics of particles and systems (70-XX) 1 Biology and other natural sciences (92-XX) 1 Information and communication theory, circuits (94-XX)
### Wikidata Timeline
The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata.
| 2022-09-25T04:58:08 |
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https://codereview.meta.stackexchange.com/questions/9162/should-a-question-poster-include-the-boost-software-license
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# Should a question poster include the Boost Software License?
In an edit to this question the poster added the Boost Software License text. I think the code subject to the license is in the poster's GitHub repo and not included in the question (it is only referenced via #include statements).
Is it necessary or desirable to include this license text? Or is this a case where the code subject to the license (which would only be part of the question in this particular case) is off topic as it was not written by the OP?
• "Is it necessary or desirable to include this license text?" I'm not sure the community can answer this. It's a legal question, and the community is not equipped to handle those. That's Community Moderator (SE empolyees, not our usual moderators) territory, IMO. – Mast May 11 '19 at 18:52
I am not a lawyer, blah blah blah....
There is no problem, per se, in including the details of the Boost Software License in the post. Note that if the Boost folk feel there's been a copyright violation, they can use DMCA takedown processes to have the post removed, and that's the established procedure if things are copied inappropriately by a poster on Code Review.
Also, note that the post, just by being a post, on Stack Exchange, also licenses the specific code under the Creative Commons license (CC-BY-SA). There is no legal issue (from the perspective of Code Review) with using multiple licenses to publish under.
So, there is no reason to prohibit adding the text of the Boost Software License.
Now, from an armchair/layman analysis perspective, and reading the OP's post, and assuming they are correct in their assumptions, it appears that the Boost code on a file-by-file basis are each individually in the public domain:
// pem-rd.cpp - PEM read routines. Written and placed in the public domain by Jeffrey Walton
// Copyright assigned to the Crypto++ project.
//
// Modified for selective standalone use by Mako Bates
//
// Crypto++ Library is copyrighted as a compilation and (as of version 5.6.2) licensed
// under the Boost Software License 1.0, while the individual files in the compilation
// are all public domain.
but the library as a whole is licensed under the Boost license. If this is the case, then as far as I can tell, there is no reason to believe the Boost license is needed to publish this code here... although it is polite, and probably is a reasonable CYA thing.
If you're looking for a TL;DR - there's nothing wrong with including that text, but including it, in my assessment, does not change anything in terms of licensing the code in this post (it's CC-BY-CA - and perhaps also licensed under Boost)
| 2020-02-22T01:02:41 |
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|
https://phys.libretexts.org/Courses/Joliet_Junior_College/Physics_201_-_Fall_2019/Book%3A_Physics_(Boundless)/03%3A_Vectors/3.04%3A__Coordinate_Systems_and_Components_of_a_Vector_(Part_1)
|
$$\require{cancel}$$
# 3.4: Coordinate Systems and Components of a Vector (Part 1)
$$\begin{cases} A_{x} = A \cos \theta_{A} \\ A_{y} = A \sin \theta_{A} \ldotp \end{cases} \label{2.17}$$
When calculating vector components with Equation 2.17, care must be taken with the angle. The direction angle $$\theta$$A of a vector is the angle measured counterclockwise from the positive direction on the x-axis to the vector. The clockwise measurement gives a negative angle.
Example $$\PageIndex{3}$$: Components of Displacement Vectors
A rescue party for a missing child follows a search dog named Trooper. Trooper wanders a lot and makes many trial sniffs along many different paths. Trooper eventually finds the child and the story has a happy ending, but his displacements on various legs seem to be truly convoluted. On one of the legs he walks 200.0 m southeast, then he runs north some 300.0 m. On the third leg, he examines the scents carefully for 50.0 m in the direction 30° west of north. On the fourth leg, Trooper goes directly south for 80.0 m, picks up a fresh scent and turns 23° west of south for 150.0 m. Find the scalar components of Trooper’s displacement vectors and his displacement vectors in vector component form for each leg.
Strategy
Let’s adopt a rectangular coordinate system with the positive x-axis in the direction of geographic east, with the positive y-direction pointed to geographic north. Explicitly, the unit vector $$\hat{i}$$ of the x-axis points east and the unit vector $$\hat{j}$$ of the y-axis points north. Trooper makes five legs, so there are five displacement vectors. We start by identifying their magnitudes and direction angles, then we use Equation 2.17 to find the scalar components of the displacements and Equation 2.12 for the displacement vectors.
Solution
On the first leg, the displacement magnitude is L1 = 200.0 m and the direction is southeast. For direction angle $$\theta_{1}$$ we can take either 45° measured clockwise from the east direction or 45° + 270° measured counterclockwise from the east direction. With the first choice, $$\theta_{1}$$ = −45°. With the second choice, $$\theta_{1}$$ = + 315°. We can use either one of these two angles. The components are
$$L_{1x} = L_{1} \cos \theta_{1} = (200.0\; m) \cos 315^{o} = 141.4\; m,$$
$$L_{1y} = L_{1} \sin\theta_{1} = (200.0\; m) \sin 315^{o} = -141.4\; m,$$
The displacement vector of the first leg is
$$\vec{L}_{1} = L_{1x}\; \hat{i} + L_{1y}\; \hat{j} = (14.4\; \hat{i} - 141.4\; \hat{j})\; m \ldotp$$
On the second leg of Trooper’s wanderings, the magnitude of the displacement is L2 = 300.0 m and the direction is north. The direction angle is $$\theta_{2}$$ = + 90°. We obtain the following results:
$$L_{2x} = L_{2} \cos \theta_{2} = (300.0\; m) \cos 90^{o} = 0.0,$$
$$L_{2y} = L_{2} \sin \theta_{2} = (300.0\; m) \sin 90^{o} = 300.0\; m,$$
$$\vec{L}_{2} = L_{2x}\; \hat{i} + L_{2y}\; \hat{j} = (300.0\; m)\; \hat{j} \ldotp$$
On the third leg, the displacement magnitude is L3 = 50.0 m and the direction is 30° west of north. The direction angle measured counterclockwise from the eastern direction is $$\theta$$3 = 30° + 90° = + 120°. This gives the following answers:
$$L_{3x} = L_{3} \cos \theta_{3} = (50.0\; m) \cos 120^{o} = -25.0\; m,$$
$$L_{3y} = L_{3} \sin \theta_{3} = (50.0\; m) \sin 120^{o} = + 43.3\; m,$$
$$\vec{L}_{3} = L_{3x}\; \hat{i} + L_{3y}\; \hat{j} = (-25.0\; \hat{i} + 43.3\; \hat{j})\; m \ldotp$$
On the fourth leg of the excursion, the displacement magnitude is L4 = 80.0 m and the direction is south. The direction angle can be taken as either $$\theta_{4}$$ = −90° or $$\theta_{4} = + 270°. We obtain L_{4x} = L_{4} \cos \theta_{4} = (80.0\; m) \cos (-90^{o}) = 0, L_{4y} = L_{4} \sin \theta_{4} = (80.0\; m) \sin (-90^{o}) = -80.0\; m, \vec{L}_{4} = L_{4x}\; \hat{i} + L_{4y}\; \hat{j} = (-80.0\; m)\; \hat{j} \ldotp On the last leg, the magnitude is L5 = 150.0 m and the angle is \(\theta_{5}$$ = −23° + 270° = + 247° (23° west of south), which gives
$$L_{5x} = L_{5} \cos \theta_{5} = (150.0\; m) \cos 247^{o} = -58.6\; m,$$
$$L_{5y} = L_{5} \sin \theta_{5} = (150.0\; m) \sin 247^{o} = -138.1\; m,$$
$$\vec{L}_{5} = L_{5x}\; \hat{i} + L_{5y}\; \hat{j} = (-58.6\; \hat{i} - 138.1\; \hat{j})\; m \ldotp$$
Exercise 2.6
If Trooper runs 20 m west before taking a rest, what is his displacement vector?
# Contributors
• Samuel J. Ling (Truman State University), Jeff Sanny (Loyola Marymount University), and Bill Moebs with many contributing authors. This work is licensed by OpenStax University Physics under a Creative Commons Attribution License (by 4.0).
| 2020-01-25T00:06:15 |
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https://www.federalreserve.gov/econresdata/notes/feds-notes/2016/corporate-bond-issuers-swap-exposure-to-rising-interest-rates-20160526.html
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## FEDS Notes
### Corporate Bond Issuers' Swap Exposure to Rising Interest Rates
Richard Ogden, Francisco Palomino, Nitish Sinha, and Youngsuk Yook 1
United States corporate bond issuance has been elevated in recent years relative to historical standards (figure 1), reflecting in part accommodative financing conditions at historically low rates. This development may increase the debt rollover risk of U.S. corporations in an environment of rising interest rates.2 In particular, the rollover risk can be high if issuance has been concentrated in short-term or floating-rate bonds. The average maturity of corporate bonds has increased consistently since the Great Recession, and floating-rate bonds have remained a small fraction of the total corporate bonds outstanding, as shown in figure 2. This evidence, however, can be misleading if firms actively use interest-rate swaps to convert fixed-rate obligations to floating-rate ones. In this note, we analyze the exposure to interest-rate swaps of U.S. nonfinancial firms that recently issued corporate bonds. In summary, we find that:
• Only 13 percent of our sample of bond issuers have swaps contracts.
• Speculative grade firms with swaps have weaker balance sheets than their peers without swaps, making them more vulnerable to a deterioration in external financing conditions.
• However, only 10 percent of speculative grade firms use swaps, and their swap exposure is fairly small relative to their total debt.
• The results should be taken with caution since the analysis excludes possible swap exposure of firms obtaining external financing only through loans.
Figure 1: Gross Issuance of Nonfinancial Corporate Bonds
Note: Bonds are categorized by Moody's, Standard & Poor's and Fitch.
Source: Mergent, Fixed Income Securities Database (FISD).
Accessible version
Figure 2: Fraction of Non-financial Corporate Floating Rate Notes
Source: Mergent, Fixed Income Securities Database (FISD): Shown as fraction of total amount outstanding.
Accessible version
Analysis of Interest Rate Swap Usage
We examined the 322 nonfinancial firms that issued bonds between July 1, 2015, and November 30, 2015, according to the Mergent Fixed Income Securities Database. To estimate the exposure of these firms to interest-rate swaps, we searched through their Form 10-Qs in the Securities and Exchange Commission (SEC) Edgar database. Publicly traded corporations are required to file this form quarterly with the SEC. They typically disclose their use of derivatives in a section dedicated to address their exposure to various risks, including interest rate risk. We searched 10-Qs filed between September and December 2015 using the keywords "interest rate swap" and "interest-rate swap." 3 We read the 10-Qs of all firms containing these keywords to check whether they have outstanding swaps positions and to obtain the type and notional amounts of these swaps.
Of the 322 bond-issuing firms, only 43 (13 percent) reported having outstanding swaps contracts. These firms used receive-fixed pay-floating swaps (generally referred to as fair value hedges), receive-floating pay-fixed swaps (generally referred to as cash flow hedges), or both. Most firms reported that they mainly used swaps for hedging purposes: They noted they used swaps contracts to maintain a desired mix of fixed- and floating-rate debt, or to mitigate earnings and cash flow fluctuations that may result from interest rate volatility. In addition, some firms linked their fair value hedges to particular fixed-rate bond issues. This purpose is also supported by evidence in Covitz and Sharpe (2005), who find that differences in debt structure across firms and time tend to be counterbalanced by differences in their derivatives positions.
We cannot rule out, however, the possibility that receive-fixed pay-floating swaps are also used to speculate on future interest rate changes. For example, some firms noted that lowering overall borrowing costs was one of the objectives of using swaps, in line with the findings of Faulkender (2005). These firms could be especially vulnerable to possible rate increases.
Table 1 summarizes the swap exposure of the 43 firms. Of particular interest are 19 firms reporting fixed-to-floating swaps. Ten of these firms have only fixed-to-floating swaps while the other nine also have receive-floating pay-fixed swaps. The average reported notional amount of fixed-to-floating swaps is $1,840 million, substantially larger than the$373 million average receive-floating pay-fixed swaps position. Unfortunately, 9 firms do not specify whether these contracts are fixed-to-floating or floating-to-fix swaps.
Table 1: Swaps by Contract Type
Fixed to Floating Only Floating to Fixed Only Both Unspecified Total 10 (10) 12 (15) 9 (9) 8 (9) 39 (43) 1,839.60 373 2,016.90 1,332.60 1,325.20
Source: SEC Edgar database; the number of firms inside parentheses includes firms with swaps that do not report nominal values of swaps contracts. Return to text.
To better understand differences between firms with and without swap exposure, we obtained financial information from the Compustat quarterly database, and Standard & Poor's credit ratings from the Capital IQ credit ratings database. We found financial and ratings information for 243 firms of 322, including 42 with swaps contracts.4 Table 2 summarizes the characteristics of these firms.
Table 2: Firm Characteristics
Number of Firms Assets ($millions) Debt ($ millions) Leverage Ratio Cash/Assets Swap/Debt 42 27,220.46 9,526.54 0.39 0.07 0.15 201 19,670.37 6,195.43 0.38 0.12 -- 30 34,452.64 11,395.35 0.35 0.08 0.15 93 35,137.92 10,193.91 0.32 0.08 -- 12 9,139.99 4,854.50 0.48 0.03 0.17 108 6,226.61 2,560.50 0.43 0.15 --
Source: Standard & Poor's Financial Services LLC ("S&P"), Compustat Unrestated Quarterly Data, 2016. All rights reserved. For intended recipient only. No further distribution and or reproduction permitted. Accessed via Wharton Research Data Services (WRDS); Capital IQ credit ratings database; SEC Edgar database.
Panel A shows that firms with swaps contracts tend to be larger in assets and debt, relative to firms with no exposure to swaps. The firms with swaps contracts also hold less cash relative to their assets. These differences are concentrated among firms with low credit ratings, as shown in panel B. This panel reports characteristics of these firms sorted by their credit ratings. Speculative grade firms with swaps are much larger than their peers without swaps, with their assets and debt 1.5 and 2 times as large, respectively. These firms also have higher leverage ratios (debt/assets) and hold less cash (only about 3 percent of their assets), making them more vulnerable to a deterioration in external financing conditions. Nevertheless, the number of speculative-grade firms with swaps constitutes a small fraction of the universe: Only 12 firms with swaps are rated speculative grade. Also, the size of their swap positions is small relative to their total debt: On average, speculative-grade firms have \$1.1 billion worth of swaps contracts, or about 17 percent of their total debt. Finally, only 2 of the speculative-grade firms specify that they use fixed-to-floating swaps.
There are two caveats in our analysis. First, our analysis may not capture all bond issuers with outstanding interest rate swaps contracts. Firms might not use the words "interest rate swaps" when disclosing their derivatives usage in Form 10-Q.5 Second, our exercise is limited to firms issuing bonds and does not cover the exposure of firms to the corporate loan market. Expanding the analysis to include this market would provide a broader view of the exposure to rising interest rates in the nonfinancial corporate sector, as loans tend to be linked to floating rates. Ippolito, Perez and Ozdagli (2015) offer some insights into this market. They find that firms with bank loans are twice as likely as firms with n0n-bank debt to use floating-to-fixed swaps, but their remaining exposure to floating rates is still significant.
References
Covitz, D. and Sharpe, S.A. (2005). "Do Nonfinancial Firms Use Interest Rate Derivatives to Hedge? (PDF)" Finance and Economics Discussion Series, 2005-39. Washington: Board of Governors of the Federal Reserve System.
Faulkender, M. (2005). "Hedging or Market Timing? Selecting the Interest Rate Exposure of Corporate Debt," Journal of Finance, 60.
Ippolito, I., Ozdagli, A. K., and Perez, A. (2015). "The Transmission of Monetary Policy through Bank Lending: The Floating Rate Channel," CEPR Working Paper No. 9696.
1. All four authors are at the Board of Governors of the Federal Reserve System. The views expressed in this note do not necessarily reflect those of the Board of Governors, or its staff. We thank Daniel Covitz and Steven Sharpe for their helpful comments. Return to text
2. See Covitz and Sharpe (2005) for an analysis of interest rate derivative contracts in a period characterized by a steep decline in interest rates. Return to text
3. This time window excludes firms filing the form late. Some risky firms or those under distress are likely to be in this category. Return to text
4. Some firms were not matched because they were private or subsidiary firms. Return to text
5. For example, they can use phrases such as "interest-rate lock" or "derivatives." Return to text
| 2023-03-21T17:37:28 |
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https://www.aofm.gov.au/publications/annual-reports/part-2-performance-and-outcomes
|
# Part 2: Performance and Outcomes
## Introduction
This part of the annual report is presented in two sections: Section 1 comprises the PGPA Act Annual Performance Statement requirement; and Section 2 gives context to outcomes achieved through the AOFM’s operations in support of its principal functions. Section 2 includes discussion of the relevant market environment in which the AOFM operates.
## Section 1: Annual Performance Statement
The 2020-21 Annual Performance Statement of the Australian Office of Financial Management (AOFM) is presented as required under paragraph 39(1)(a) of the Public Governance, Performance and Accountability Act 2013 (PGPA Act).
In my opinion as accountable authority of the AOFM the statement accurately reflects the performance of the Australian Office of Financial Management, is based on properly maintained records, and complies with subsection 39(2) of the PGPA Act.
Rob Nicholl
Chief Executive Officer
25 October 2021
### Purpose
The AOFM’s purpose is to fully meet the Government’s debt financing and cash needs and achieve its policy objectives to support the domestic lending market. The AOFM will take account of the potential for its operations to impact Australian financial markets.
The following key functions underpin the AOFM’s role:
• issuing AGS to meet the Government’s financing task and in accordance with government policy objectives (such as facilitating sovereign bond market liquidity);
• settlement and payment of Government financial obligations on AGS;
• managing the cash account to meet the Government’s commitments at all times;
• undertaking cost effective management of the debt and asset portfolios;
• where appropriate, supporting efficient operation of the Australian financial system; and
• managing the ABSF and SFSF investment portfolios consistent with related policy objectives.
The AOFM balances cost and risk considerations but its overriding aim is to ensure financing requirements of the Government are met at all times. The AOFM has minimal appetite for failure in any function associated with debt issuance, settlement and payment obligations, and cash management. The design and conduct of core business processes (including business continuity arrangements) reflects this low-risk appetite.
The AOFM monitors its performance against the indicators presented in Table1, which are sourced from the AOFM’s Corporate Plan 2020-21 and Portfolio Budget Statements 2020-21. Sections 2 and 3 of this part of this report provide detail on a range of outcomes towards the AOFM’s annual and longer‑term aims. This detail is provided separately to the Performance Statement because it is aimed at financial market participants as the relevant audience.
Table 1: Performance Information 2020-21
Target
Zero
Result
Target met
### Objective 2: Facilitate the Government’s cash outlay requirements as and when they fall due
Indicator 4
Use of overdraft facility: Number of instances the RBA overdraft facility was utilised to the extent that it required Ministerial approval during the assessment period
Target
Zero
Result
Target met
The RBA overdraft facility was not utilised in 2020-21.
#### How AOFM achieves this objective
This objective is achieved through appropriate management of the cash portfolio, with the AOFM using information from the ATO and spending agencies to forecast daily revenue collections and expenditure outlays. Throughout the year there are time of significant mismatches between expenditure needs and revenue collected. The AOFM uses short term funding (through Treasury Notes) and cash portfolio assets to manage these mismatches.
### Objective 3: Be a credible custodian of the Australian Government Securities (AGS) market and other portfolio responsibilities, including the Australian Business Securitisation Fund (ABSF) and Structured Finance Support Fund (SFSF).
Indicator 5
A liquid and efficient secondary market: Annual turnover in the secondary market for Treasury Bonds and Treasury Indexed Bonds
Target
Greater than previous year
Result
Target met
AGS liquidity remained strong in 2020‑21. Turnover of Treasury Bonds totalled $2.1 trillion (a 36 per cent increase from the previous year). Annual Treasury Indexed Bond turnover increased by 19 per cent, to$58 billion. Strong secondary market liquidity is a key consideration for most investors because it reflects an ability to transact (either through buying or selling AGS) in a timely manner and in volumes to meet their needs, without market prices being materially moved by those transactions. It reflects a range of factors. including: regular AOFM issuance that, among other factors, takes account of prevailing market conditions; the presence of a range of active ‘price makers’ in AGS; good access to interest rate risk hedging; and a diverse (and active) investor base. The AOFM also plans issuance with the aim of supporting (ASX) Treasury Bond futures (risk hedging) contracts.
The AOFM also supports liquidity through: restricting the number of individual bond lines so each can have greater volume outstanding including consideration of RBA holdings; clear communication about and transparency regarding AOFM issuance; and a long‑standing focus on maintaining a functional and resilient AGS market.
High levels of secondary market turnover and feedback from investors attesting to their capacity to buy and sell large parcels of AGS at acceptable prices are strong indicators of liquidity for 2020‑21.
Indicator 6
Market commitments: Number of times the AOFM failed to take actions consistent with public announcements
Target
Zero
Result
Target met
The AOFM’s actions remained consistent with its public announcements throughout the year.
This included announcements in July and December 2020, and at Budget in May 2021. These announcements progressively updated planned AGS issuance, including for new lines and weekly issuance rates. At all times issuance remained consistent with the most recent public guidance. The unusual frequency in changes to public (market) guidance was driven by updates to the Government’s COVID-19 response package and uncertainty surrounding the potential impact on the underlying Budget position following initial lockdowns that commenced during 2020.
The AOFM considers the above actions were consistent with public announcements, but notes revisions were necessarily made multiple times throughout the year (a departure from the preferred and traditional approach of only updating guidance at official Budget updates). Market feedback indicates the AOFM’s adopted approach of regular issuance updates, given the circumstances, was a welcome departure from established practice.
#### How AOFM achieves this objective
The AOFM is judged by financial markets to be a credible and predictable major participant in the AGS market and uses its operational flexibility responsibly. It is important to note the AOFM does not have any regulatory or statutory authority - any influence it has is by virtue of its guidance and issuance operations (although it recognises the potential for this influence to be significant).
Indicator 7
ABSF rate of return Accrual earnings (net of losses) divided by average drawn (invested) amount.
Target
Greater than or equal to the investment mandate benchmark(Bloomberg AusBond Treasury 0-1 year index)
Result
Target met
The ABSF achieved a return on average drawn funds of 1.63 per cent for the financial year ending 30 June 2021, versus a benchmark return of 0.18percent.
Indicator 8
SME loan level data template in use for securitisation sector SME loan level data template was: agreed to by the industry body; and populated by sponsor of ABSF investment.
Target
1. Agreement by 31March 2021;
2. data collection commenced by 30 June 2021.
Result
Target not met
Progress toward agreement on the template was suspended due to the onset of the pandemic. Work recommenced in the second half of the year culminating in agreement of a draft template published by the ASF in August 2021.
#### How AOFM achieves this objective
Central to the AOFM’s strategy for developing the SME lending sector of the securitisation market is coalescence around a standardised data template, so investment performance can be readily assessed by ratings agencies and investors. The AOFM sought and received assistance from the ASF to sponsor a working group of industry participants (including AOFM staff) to design the template. Publication of the template represents a key milestone for the ABSF program. The AOFM can now use ABSF investment to support adoption of this reporting standard by SME lenders.
A key driver of the ABSF’s financial outperformance was the yield on short term debt instruments, which fell sharply in 2020 as a direct consequence of the RBA’s monetary policy response to the pandemic. The initial investment made by the ABSF had a return commensurate with the risk of the investment. No subsidy was provided on this investment as the originator could not adopt the (as then unfinished) standardised SME loan level data template.
Indicator 9
SFSF warehouse proposals processed. Number of warehouse proposals recommended to the delegate
Target
Up to 20 per quarter while there are, at any time, outstanding proposals with AOFM for consideration
Result
Target met
A total of 32 warehouse applications from lenders were considered by the SFSF delegate during the 2020-21 financial year. Q1 was the period of peak activity (and thus when the target for the performance indicator was most relevant) in which 22 applications were considered by the delegate (of which 15 were approved). As market conditions improved, calls for assistance abated, and seven proposals were considered in Q2 (four of which were approved), one in Q3 and two in Q4.
Indicator 10
SFSF leverage ratio Private sector investment in primary transactions of small lenders, in which AOFM was engaged, divided by SFSF monies applied to public (primary + secondary) investments.
Target
> Four in the year overall
Result
Target met
In Q1, the multiplier was over 40, as only a very small volume of SFSF investment was required to support primary market activity. In subsequent quarters the multiplier was either infinite or not applicable because no SFSF investment was required due to further improvements in market conditions. While contingent support was sought by issuers in Q2 that was ultimately not called on, no requests for this kind of support were received in the second half of 2020-21.
#### How AOFM achieves this objective
The AOFM’s objective for implementing the SFSF has been to fill gaps in the market created by liquidity and other constraints arising from the pandemic induced market disruption as well as supporting lenders granting loan forbearance through establishment of the Forbearance Special Purpose Vehicle.
By seeking to limit its investment to the minimum required to allow transactions to occur, and thus maintain the flow of finance to eligible lenders, the AOFM has avoided crowding out private sector investment, while maintaining confidence that additional capital can be deployed if required.
As market conditions improved the AOFM was able to step back from the market while maintaining the SFSF apparatus.
## Section 2: Outcomes
### Debt issuance
#### Aims
The AOFM currently issues three debt instruments: Treasury Bonds; Treasury Indexed Bonds (TIBs) and Treasury Notes. The primary objectives of issuance are to cost‑effectively meet the Government’s budget funding task (including both deficit financing and repayment of maturing debt obligations) and to assist managing interest rate, liquidity, and debt refinancing risks.
Treasury Bonds are used as the primary funding tool to meet the budget funding task. TIBs issuance is used primarily to support the inflation‑linked market. Treasury Notes are typically issued for within‑year financing purposes.
Through its operations the AOFM is aware that:
• AGS and the (ASX) Treasury Bond futures act as key reference points for the pricing of other capital market instruments and to manage interest rate risk; and
• active and efficient sovereign debt markets (both physical and futures markets) are important for the resilience of the broader financial system to economic and financial market shocks.
A key element of market efficiency important to issuers, intermediaries and investors is market liquidity. Liquidity is broadly taken to mean the ability to trade bonds at short notice and low cost without materially moving prices. Strong liquidity is attractive to investors and reflects favourably on a sovereign bond market but will vary across maturities along the yield curve. There is no single measure of liquidity because it is an assessment by individuals (and institutions) based on several considerations, including, but not restricted to the following indicators: turnover in secondary markets; frequency of primary market activity; bid‑offer spreads; and the time it takes to execute ‘large’ transactions.
#### Approach to achieving these aims and market influences
The AOFM uses competitive tenders and syndications for debt issuance (with tenders the mainstay of issuance operations). In 2020-21 there were 75Treasury Bond tenders, 18 TIB tenders and 47Treasury Note tenders. Five new Treasury Bond lines were launched by syndication and there was one syndicated tap of an existing bond line.
The Government’s funding requirements were considerably higher than last year due to COVID‑19 associated fiscal response packages. However, due to an improvement in Australia’s economic performance against initial forecasts, budget outcomes were better than expected and the financing task was lower than initially forecast.
In the second half of 2020-21 global financial markets reflected an emergence of rising inflation expectations due to accommodative monetary and fiscal policies. Rising inflationary expectations were reflected in a sharp sell-off in bond markets in which yields on 10‑year Treasury Bonds increased rapidly, particularly through the third quarter of the financial year. The result was yields rising to around 90 basis points above the trading range observed through the first half of the year. With the RBA’s yield curve control operations anchored yields on short term bonds at around 10basis points, the AGS yield curve steepened considerably as a result.
#### Outcomes
The financing task for 2020-21 was fully met through a combination of Treasury Bond and TIB issuance. There was a reduced reliance on Treasury Notes with outstandings decreased (by $31.5billion) to a level around$27billion compared with 2019-20. The improved underlying Budget position throughout the year allowed for lower issuance than planned at the (delayed) 2020-21 Budget release. At that time an issuance task of around $240 billion had been forecast for the year. ##### Treasury Bonds Gross Treasury Bond issuance for the year totalled$207.3 billion, a significant increase from the $128.2 billion issued in 2019-20. New bond lines maturing in November 2025, September 2026, November 2031, November 2032, and June 2051 were established. Around 60 per cent of total Treasury Bond issuance for the year was into these new bond lines. In selecting the bond lines to issue each week, the AOFM takes account of prevailing market conditions, liaison with financial market contacts, relative value considerations, and liquidity of outstanding bond lines. The AOFM refrained from issuing into any bond lines forming part of the RBA’s yield curve control operation and continued suspension of the regular (short) bond buyback program. Between July 2020 and June 2021, up to three tenders were held each week. Issuance via tender continued to be concentrated into bonds in the 10-year futures basket and shorter, which is consistently the most liquid part of the AGS market and therefore, best able to absorb larger issuance volumes. At the end of the year, there were 29 Treasury Bond lines: 14 having over$30billion on issue and a further 6 having over $20 billion on issue. Chart 1 shows Treasury Bonds outstanding as at 30June2021 and the allocation of issuance across bond lines during 2020-21. Chart 1: Treasury Bonds outstanding at 30 June 2021 and issuance in 2020-21 Table 2 summarises results of Treasury Bond tenders conducted during the year. These are averages for each half‑year and grouped by maturity dates of the bonds offered. Table 2: Summary of Treasury Bond tender results Period Maturity Face value amount allocated ($m) Weighted average issue yield (%) Average spread to secondary market yield (basis points) Average times covered July - December 2020 Up to 2028 32,000 0.4106 -0.82 5.17 2029 - 2033 36,200 0.9152 -0.49 4.18 2034 - 2051 1,300 1.3348 -1.02 2.91 January - June 2021 Up to 2028 12,800 0.5399 -0.85 4.69 2029- 2033 26,300 1.5583 -0.45 3.66 2034 - 2051 700 2.2115 -0.58 3.19
The average tender coverage ratio for Treasury Bond tenders in 2020-21 was 4.29, an increase from 3.67 in 2019-20. The average tender size of $1.46 billion was higher than in 2019‑20 ($1.2 billion). A total of 75 tenders were held in 2020-21, compared with 79 in 2019-20.
Shorter‑dated bond tenders generally received higher than average coverage ratios, which reflected core investor interest and a greater willingness, and ability of, intermediaries to warehouse the risk associated with shorter dated bonds.
The strength of bidding at tenders was also reflected in issue yield spreads relative to secondary market yields. At most Treasury Bond tenders the weighted average issue yields were below prevailing secondary market yields (a better price outcome than at mid-market).
##### Treasury Notes
Treasury Notes on issue decreased by $31.5 billion in 2020-21. A total of 47 Treasury Note tenders were conducted. Treasury Notes were primarily used for within‑year financing throughout 2020-21. Issuance tenors were focused around 3 and 6 month maturities. The volume of Treasury Notes outstanding gradually declined throughout the financial year as those issued between March and June 2020 (to fund the initial increase in Government COVID-19 related expenditure) matured. Treasury Notes totalling$94.5billion were issued in 2020-21 (in face value terms), an increase of $4.6 billion on 2019-20. Chart 2: Treasury Notes outstanding (by maturity) at 30 June 2021 and issuance in 2020-21 Table 3 summarises Treasury Note tender results during the year. Averages for each half‑year and grouped by tenor. Issuance was met with strong demand as accommodative monetary policy created substantially increased banking system liquidity. The average coverage ratio at tenders was above 6, an increase from 3.96 in 2019-20. Yields were on average 1 basis point higher than Overnight Indexed Swap (OIS) rates for corresponding tenors (compared to around 20 basis points higher than OIS rates in 2019-20). This reflected lower spreads across Australian short‑dated funding rates. Table 3: Summary of Treasury Note tender results Period Maturity Face value amount allocated ($m) Weighted average issue yield (%) Average spread to Overnight Indexed Swap (basis points) Average times covered July - December 2020 Up to 120 days 32,500 0.1150 1.56 5.05 121 days to 210 days 15,500 0.1079 3.04 5.41 Longer than 210 days 15,000 0.1508 5.17 5.81 January - June 2021 Up to 120 days 18,450 0.0140 -1.83 6.77 121 days to 210 days 13,050 0.0196 -1.58 6.83 Longer than 210 days - - 0.00 -
TIB issuance for the year totalled $2.50 billion over 18 tenders. Feedback from market participants and prevailing market conditions were considered in issuance decisions. Chart 4 shows the amount outstanding in each of the 8 TIB lines at 30 June 2021, and allocation of issuance during the 2020-21 year. Chart 3: Treasury Indexed Bonds outstanding at 30 June 2021 and issuance in 2020-21 TIBs comprise around five per cent of the long-term debt portfolio (in face value terms). The capital value of TIBs are adjusted with changes to the CPI; they typically attract a different (and predominantly domestic) class of investor compared to Treasury Bonds. While the Indexed Bond portfolio has declined as a share of long-term funding overtime, the total stock outstanding of indexed bonds has continued to grow broadly in line with the past issuance trend. Tender coverage ratios were slightly lower in 2020-21 (4.52 compared with 4.70 in 2019-20). This is in part a function of the higher overall issuance volume in 2020-21. In 2019-20 the decision was taken to reduce tender sizes in response to deteriorating market conditions arising from market disruption associated with the onset of the pandemic (the average tender size was$138 million in 2020-21 compared with $118 million in 2019‑20). However, the weighted average issue yield was below prevailing secondary market yields at most tenders (a reflection of the AOFM restricting tender volumes). ##### AGS market liquidity and efficiency Market liquidity was generally good in 2020-21 with efficient price discovery and tight bid‑offer spreads available through most of the year. Turnover of Treasury Bonds was 36 per cent higher than the 2019-20 level. Annual turnover reported in AOFM’s survey was$2.1 trillion for 2020-21. This was influenced by the large increase in AOFM primary issuance in 2020-21.
Chart 4: Annual Treasury Bond Turnover
TIB turnover in 2020-21 was around $58 billion, an increase of 19 per cent from the 2019-20 volume. Chart 5: Annual Treasury Indexed Bond Turnover ##### Treasury Bond Futures turnover Turnover in the (ASX) Treasury Bond futures market is significantly higher than in underlying Treasury Bonds. The 3 and 10‑year futures contracts are highly liquid: over 45 million 3‑year contracts (representing$4.5 trillion face value of bonds) and over 65 million 10‑year contracts ($6.5 trillion face value of bonds) were traded in 2020-21. A new 5‑year contract was launched in 2020‑21 with over 1 million contracts ($100 billion face value of bonds) traded. Turnover in the 20‑year contract is considerably lower with around 200,000 contracts (or just over $13.0 billion face value of bonds) traded. Turnover in 3‑year futures was lower than previous years. One factor driving this was the RBA including some bonds from the 3 year futures basket in its yield curve control policy; this reduced usefulness of the contract as a hedging instrument. ##### Securities Lending Facility The AOFM Securities Lending Facility allows market participants to borrow Treasury Bonds and TIBs for short periods when they can’t be obtained in the secondary market. Lending bond lines enhances efficiency of the market by improving capacity of intermediaries to continuously make two‑way prices, reduces settlement risk, and can supports market liquidity. The facility was used 123 times for overnight borrowing in 2020-21, compared with 163times during 2019-20. Volumes borrowed were higher than in 2019-20, with the total face value lent in 2020-21 of$6.02 billion, an increase of $3.37 billion. The April 2023 and April 2024 Treasury Bonds were the most heavily borrowed (by volume). TIBs generally exhibit lower liquidity and have less stock available for trading in the secondary market, which accounts for regular borrowing of these securities. During 2020-21, the RBA implemented its own lending facility. It has accumulated large volumes of some Treasury Bond lines and made these available to facilitate market lending related transactions. This contributed to reduced usage of the AOFM Securities Lending Facility. ### Cost across AOFM portfolios Debt portfolio cost outcomes are presented in this Section. #### Aim The AOFM is tasked with meeting the Budget financing task while managing trade‑offs between cost and risks for the cash and long-term debt portfolios, this being over the medium to long-term. Funds in the investment portfolios earn returns, described later in this section. #### Approach to achieving the aims The AOFM cost and risk measures reflect considerations faced by sovereign debt managers generally. The primary cost measure is historic accrual debt servicing cost. This includes: interest payments made on AGS; realised market value gains and losses on repurchases; capital indexation of TIBs; and amortisation of issuance premiums and discounts. The effective yield of the portfolio is the total accrual debt servicing cost expressed as a percentage of debt outstanding. Historic accrual debt service cost excludes unrealised market value gains and losses. An alternative measure of cost is ‘fair value’, which takes account of unrealised gains and losses from movements in market value. Debt service cost outcomes are also presented in the AOFM’s financial statements on this basis. Fair value facilitates an assessment of: financial risk exposures and changes in those exposures from year-to-year; the value of transactions managed; and the economic consequences of alternative strategies. However, this measure is most useful in the context of ‘trading for profit making’ purposes (which does not relate to the AOFM’s core operations). ### Outcomes The net debt servicing cost[1] of the portfolio managed by the AOFM in2020‑21 was$16.8 billion on an average book volume of $748.8 billion; this represents a net cost of funds of 2.24 per cent. Table 4 provides details of the cost outcomes for the portfolio of debt and assets administered by the AOFM, broken down by instrument and portfolio for 2020‑21 and 2019‑20. Table 4: Commonwealth debt and assets administered by the AOFM Debt servicing cost Book volume Effective yield 2019-20 2020-21 2019-20 2020-21 2019-20 2020-21$ million $million per cent per annum Contribution by instrument Treasury Bonds (15,538) (15,984) (530,342) (725,243) 2.93 2.20 Treasury Indexed Bonds (1,468) (977) (45,360) (45,130) 3.24 2.16 Treasury Notes (136) (81) (19,963) (49,920) 0.68 0.16 Gross AGS (17,142) (17,042) (595,665) (820,293) 2.88 2.08 Deposits with the RBA 170 104 24,598 67,836 0.69 0.15 ABSF investments - 1 0 47 0.00 1.63 SFSF investments1 (2) 59 142 2,063 -1.41 2.87 State housing advances (50) 88 1,604 1,498 -3.10 5.86 Gross assets 118 252 26,344 71,443 0.45 0.35 Net portfolio (17,024) (16,790) (569,321) (748,850) 2.99 2.24 Contribution by portfolio Long Term Debt Portfolio (17,006) (16,961) (575,702) (770,373) 2.95 2.20 Cash Management Portfolio 34 23 4,635 17,916 0.73 0.13 Investments for Policy Purposes Portfolio1 (52) 148 1,746 3,607 -2.96 4.10 Total debt and assets (17,024) (16,790) (569,321) (748,850) 2.99 2.24 1SFSF investment income is before allowances for expected credit losses ($3 million in 2020-21 and $2 million in 2019-20) Note: Sub totals and totals are actual sum results, rounded to the nearest million dollars. Effective yields are based on actual results before rounding to two decimal places. Book volume is a through the year average. (a) Re‑measurements refer to unrealised gains and losses from changes in the market valuation of financial assets and liabilities. The cost for AGS was slightly lower than the previous year, despite the average volume of debt on issue increasing by$224.6 billion. The funding cost of gross debt declined by 80 basis points to 2.08 per cent. This result was driven by the issuance of new bonds at yields below the average issuance yield of existing bonds, and increased use of Treasury Notes at very low (occasionally negative) yields.
Return on gross assets for the period was $252 million, an increase of$134 million. Extremely low short-dated interest rates resulted in interest income from cash deposits falling despite an average level of asset balances over $40 billion higher. Income on state housing advances was positive following a loss in 2019-20 related to the waiver of Tasmanian housing loan advances (a policy decision taken by the Australian Government). There was$59 million of income from the SFSF, which was established towards the end of 2019-20. In percentage terms the return on gross assets decreased from 0.45 per cent to 0.35 per cent.
### Long‑Term Debt Portfolio management
#### Aims
In managing the Long-Term Debt Portfolio (LTDP) and meeting the Government’s financing requirements, the AOFM aims to minimise debt servicing costs over the medium to long-term while effectively managing interest rate and refinancing risk. It also seeks to support efficient operation of the AGS market through debt issuance.
#### Approach to achieving the aims
The AOFM influences the cost and risk profile of the LTDP through the maturity structure of securities issued (and to a lesser extent, the mix between nominal and inflation‑linked securities). Issuing longer‑term securities will typically involve paying higher debt servicing costs, compensated by a reduced risk of variability in future interest cost outcomes and lower exposure to annual refinancing risk.[2]Shorter‑term borrowing will typically incur lower interest costs but result in higher variability in cost outcomes through time and a greater debt refinancing task each year. Striking the right balance between these cost and risk considerations, while not adversely impacting market functioning through issuance operations, requires constant judgement.
Developing a medium‑to‑long term view on appropriate portfolio management and then translating that into annual issuance strategies is informed by ongoing research. This explores the cost and risk characteristics of alternative portfolio structures and issuance strategies under a range of scenarios; the program considers prevailing fiscal and economic conditions, as well as an assessment of broader market trends. A range of complementary thresholds limits and targets in support of the annual issuance strategy is put to the Secretary to the Treasury for endorsement.
Weekly issuance decisions focus on volume and maturities. These decisions are influenced by prevailing market conditions, progress toward achieving the annual issuance strategy, relative value considerations, and feedback from intermediaries.
#### Long‑Term Debt Portfolio issuance strategy
When formulating the Treasury Bond issuance strategy for 2020‑21 the AOFM aimed to maintain a long-dated issuance bias. Low yields, the unknown impact of the pandemic and a deteriorating fiscal outlook provided strong support for the long-dated issuance bias. At the time the strategy was set, the unprecedented size of the annual financing task and limits to investor appetite for duration risk were viewed as possible constraints to achieving a weighted average maturity to match previous years.
The AOFM avoided issuing bonds subject to the RBA’s yield target operations because it did not want to appear to be acting in conflict with the RBA’s monetary policy aims.
#### Outcomes
Debt cost outcomes are driven in large part by the level of bond yields, which remained near historic lows during 2020‑21, and the volume of issuance. Yields out to three years were anchored by the RBA’s yield target regime. Longer-dated rates rose across developed economies at the beginning of calendar 2021 as part of a ‘reflation trade’, before remaining steady for the rest of the year (Chart 6).
Chart 6: Evolution of Treasury Bond benchmark yields
The weighted average maturity of Treasury Bond issuance in 2020‑21 was considerably longer than in 2019-20. Last year large volumes of shorter-dated bonds were issued to assist with the sudden and massive increase in the funding requirement upon the onset of the pandemic; there was also several months of market recovery during which the AOFM found it difficult to issue long dated maturities. The average issuance yield remained below 1 per cent (Chart7).
Chart 7: Treasury Bond issuance — average yield and maturity
Chart 8 shows the funding cost profile of the LTDP and the net cost outcome (incorporating short term assets and liabilities) over the past decade. These profiles are compared to the cash rate and 10‑year moving average of the 10‑year bond yield. Interest rates on the LTDP and for the net cost outcome have declined significantly over the decade. Given the largely fixed cost structure of the LTDP and net cost outcome, changes in funding cost rates lag changes in the cash rate (changing only when debt securities or assets mature or new securities are issued/investments made).
Chart 8: LTDP and net portfolio cost of funds analysis
The structure and effective yield on the Treasury Bond portfolio are a product of issuance undertaken since 2009‑10 because most current outstanding debt has been issued since then. Furthermore, around 45 per cent of the current portfolio was issued in the last two financial years at average yields significantly below the portfolio average of 2.07 per cent (Chart 9).
Chart 9: Treasury Bond portfolio — composition and average yield by issuance year, at 30 June 2021
#### Long‑Term Debt Portfolio risk outcomes
The average maturity of the Treasury Bond portfolio lengthened by 0.28 years to 7.67 years over 2020‑21. Duration was higher by 0.08 years (finishing at 6.74 years). The low level of issuance yields meant Treasury Bond portfolio lengthening was achieved with a lower cost of funds (Chart 10).[3]
Chart 10: Treasury Bond portfolio — modified duration, average maturity and cost of funds
Changes to portfolio risk over time in terms of funding, refinancing and interest rate risk are represented in Chart 11. The chart reflects a steady decline in the three- and five-year Treasury Bond refinancing tasks measured as a proportion of the stock of Treasury Bonds on issue, but higher absolute refinancing tasks over time as the stock of Treasury Bonds on issue has increased.
Chart 11: Treasury Bond portfolio — maturity profile
More than half of all outstanding Treasury Bonds were issued with an original maturity between nine and 12 years. Around three quarters of the portfolio was issued with an original term to maturity of nine years or longer (Chart 12). The predominance of longer-term bonds reflects long‑dated issuance biases over the past decade. This has contributed to investor diversity and reduced funding risk and the potential for high volatility in future interest cost outcomes.
Chart 12: Treasury Bond portfolio — composition and average yield by original term to maturity, at 30 June 2021
#### Inflation exposure outcomes
Managing the indexed bond portfolio centres on sufficient supply to meet demand while supporting liquidity and continuing development of the TIB market (for which the focus is largely on understanding domestic investor mandates). Issuance of TIBs in 2020‑21 totalled $2.5 billion (compared with$207billion of nominal Treasury Bonds).
The effective yield on TIBs fell noticeably compared to the previous year. This was driven by low inflation outcomes and issuance of TIBs at historically low yields. Real yields were negative for most tenors throughout 2020-21. TIBs were only issued at positive real yields twice during the year, on each occasion this was a tender for ultra-long TIBs.
Break‑even inflation (essentially the difference between nominal and real yields), rose as the outlook for inflation improved. 10‑year break‑even inflation ended the year at 2.1 per cent, double the level at the beginning of the year.
Chart 13: Evolution of Treasury Indexed Bond benchmark break‑even inflation
TIBs comprised around 6 per cent of total term debt (nominal and indexed bonds) on issue at the end of 2020-21 (in book value terms). This proportion has declined as annual TIB issuance has been relatively steady while Treasury Bond programs have increased significantly to meet the increased Budget requirements. The TIB market does not offer sufficient depth, liquidity, or demand to support large and sudden uplifts in AOFM issuance, which is why Budget funding is focused on Treasury Bond issuance.
## Cash management
### Aims
The AOFM manages the Australian Government’s daily cash balances in the OPA[4]. This ensures the Government can meet its financial obligations at all times. Other objectives include minimising the costs of funding and holding cash balances to avoid using the overdraft facility provided by the RBA.[5]
### Approach to achieving the aims
Achieving the cash management objective involves formulating, monitoring and regularly revising forecasts of Government cash flows (revenue and outlays) and developing and implementing appropriate strategies for short term investments and debt issuance.
A precautionary asset balance is maintained to manage the forecasting risk associated with potentially large, unexpected cash requirements (or shortfalls in revenue collections) and the funding risk associated with sudden and severe market constraints.
Until November 2020, cash balances not required at short notice were invested in term deposits at the RBA, with their magnitudes and tenors determined by the AOFM. Maturity dates were selected to efficiently finance net outflows. Term deposit rates reflect rates earned by the RBA in open market operations.
In November 2020, the Cash Management Account (CMA) was created, with entire cash balances, less an overnight buffer, automatically swept to the CMA at the end of each day. This removes overnight forecasting risk. The CMA interest rate is similar to the rate earned by term deposits and again reflects rates earned by the RBA in open market operations.
The volume of Treasury Notes on issue during 2020-21 ranged from a low of $27 billion to a peak of$77 billion, representing a continued upscaling in usage compared to prior years (up to $63 billion in 2019-20). The AOFM relied heavily on Treasury Notes early in the COVID-19 pandemic both for budget financing and re-building liquidity in the cash portfolio. The volume of Treasury Notes on issue decreased through 2020-21 as earlier issuance matured and Treasury Bond issuance was increased. Chart 14: Short‑term financial asset holdings and Treasury Notes on issue 2020-21 ### Outcomes The task of meeting the Government’s financial obligations was met in full. During 2020-21, 154 term deposits were placed with the RBA. No term deposits have been placed since November 2020. The stock of AOFM’s short term assets (Term Deposits and the CMA) fluctuated over the year to maintain sufficient liquidity at all times. The average yield obtained on term deposits and the CMA during 2020-21 was 0.16 percent, compared with 0.85 percent in 2019-20; the decrease reflects the lower average level of short‑dated interest rates that prevailed during 2020-21. The movement in total short term financial assets managed by the AOFM (OPA cash balance plus term deposits with the RBA and the CMA), together with the volume of Treasury Notes on issue during 2020–21 are shown in Chart 14. Chart 15: Short‑term financial asset holdings net of Treasury Notes on issue in 2020-21 ### Market Engagement #### Aims Consistent and regular market engagement assists the AOFM in achieving its core goals. To meet those goals the AOFM maintains a comprehensive understanding of market related issues. Issues include: changing global circumstances; major government announcements and policies; influences on global flow of capital; changing investor preferences; and performance of intermediaries — particularly in the primary AGS market. The AOFM investor and intermediary engagement continues to place strong emphasis on maintaining regular lines of communication with stakeholders. This is done directly with bank intermediaries and investors, and indirectly, with investors through feedback from banks and via the AOFM website. Ongoing engagement assists greatly in understanding how investors are viewing the market, how demand for AGS might be changing, and how intermediaries interact with investors. Frequent liaison provides the AOFM with up‑to‑date assessments that can be used to contribute to weekly operational decisions. #### Approach to achieving the aims The AOFM investor engagement program is year specific and underpinned by a strategy reviewed annually in response to changes in market conditions, investor activity, notable changes to the investor base, and the AOFM’s issuance responsibilities and strategy. The Investor Relations strategy has three themes: • collecting and analysing market intelligence; • managing and maintaining updates to planned AOFM operations, and • focusing on engagement with new or potentially new investors. #### Outcomes Investor engagements were conducted during 2020-21 in a similar manner to those undertaken in the latter part of 2019-20. Conveying Budget and issuance updates and receiving investors’ views via feedback through one-on-one engagement remained key to the investor program. The AOFM has not been travelling to meet investors since the onset of the pandemic and has relied on the use of video and teleconferencing, and webinars (some arranged and hosted by banks and other market organisations). The annual Business Economists (ABE) speech, together with updates and releases on the AOFM website, remain useful conduits for information dissemination. Two ABE speeches were given by the CEO during the year. The first, in late July 2020, was an important opportunity to provide guidance on the planned approach by AOFM to a range of operational issues, particularly the substantial increase in funding for the year ahead, operational flexibility and increased use of Treasury Notes, and a concentrated schedule of syndications to achieve the large issuance task. This was at a time of widespread uncertainty in anticipation of Australia’s response to the previously announced fiscal and monetary policy measures, and how the underlying Budget position would be impacted. Although updates had much shorter application than in previous years, the increased frequency was received well by intermediaries and investors. In a second ABE speech on 8 June 2021 the AOFM provided guidance on learning from the previous year, as well as issuance plans for the six months ahead. Investors are increasingly interested in discussing topics relating to green bond issuance or Environmental, Social and Governance (ESG) related issues. In mid-September the AOFM undertook several meetings with investors on this topic. These included smaller domestic Authorised Deposit-taking Institutions and a couple of larger fund managers. Increasingly through the year investors approached the AOFM regarding the Government’s commitments and policies towards climate change, carbon emission reductions, and renewable energy development and implementation. Several organisations with specific green or sustainable fund mandates requested meetings, along with ESG units of some larger mainstream funds. It is clear from these discussions that financial markets will continue extending analysis and consideration of climate change related policies to guide investment decisions. In October, the AOFM conducted a campaign to provide a 2020-21 Budget update to investors. This included a four-week program of one-on-one investor calls beginning in mid-October with 58 offshore primary investors. The meetings covered a range of investor types and included all the major global regions - Asia, the Americas, Europe, the UK and Japan. The campaign also included a 10-minute webinar posted on the AOFM website; and release of a comprehensive investor chart pack (for the first time also translated into Japanese, reflecting the importance of this investor group). A second program of investor calls was conducted in February 2021 following the MYEFO and a market guidance update released early in the new year. This campaign focused on 25 major domestic investors. Given the suspension of many regular global market conferences, there were limited opportunities to present or speak to larger audiences in the first half of the year. Some opportunities opened in the second half of 2020-21. The AOFM presented at a bank ‘virtual investor’ seminar (to approximately 200 investors) in March. Two roundtable forums were also conducted; the first in January 2020 was a virtual event (usually held annually face-to-face) that included the AOFM with state Government borrowing authorities. The second roundtable was a further update later in the year in Sydney. Table 5: Summary of investor relations activities in 2020-21 Activity Details Investor Calls: Primary Investor Campaigns: Video/Teleconferencing Investor Calls: One off Tele/ Video Offshore 58 meetings Domestic 25 meetings Offshore/Domestic 17 meetings Presentations: large engagements 3 presentations (ABE speeches, ANZ virtual Investor Tour) Roundtables 2 Kanganews AOFM staff participating in investor relation activities CEO, Head of Investor Relations, Head Funding & Liquidity, Head Portfolio Strategy & Research, Senior Analyst - Investor Relations, Communications Manager Hosting banks: Investor roadshows, conferences, roundtable discussions ANZ, Commonwealth Bank of Australia, JP Morgan, Toronto Dominion, UBS ### Establishing the Structured Finance Support Fund (SFSF) #### Aim The SFSF was established in March 2020 to enable eligible smaller lenders to access finance via investments in structured finance products, such as residential and commercial mortgage‑backed securities (RMBS, CMBS), asset backed securities (ABS), and securities issued by revolving warehouse finance facilities. This section sets out how the AOFM has approached the task of utilising the SFSF as a vehicle to achieve the Government’s objective of maintaining access to finance for eligible lenders, namely Non‑ADI lenders and ADIs unable to access the RBA’s Term Funding Facility (TFF). #### Approach to achieving the Aim The legislation, rules and directions set out the eligibility requirements and provide guidance to the delegate (CEO of the AOFM) on investment prioritisation. Importantly, the delegate must aim to receive a positive return on investments after expected credit losses. In addition, the directions require the delegate to place a high priority on investments that catalyse rather than displace private sector investment. The AOFM identified three distinct priorities for the SFSF: • maintaining access to primary (term) securitisation markets for Non‑ADI lenders across all collateral types (RMBS, CMBS and ABS); • maintaining eligible smaller lenders’ access to finance via supporting revolving warehouse facilities; and • supporting the establishment of a mechanism that will assist eligible smaller lenders to provide forbearance to their client base. Maintaining access to primary funding markets provided confidence to eligible lenders that they could continue to originate new loans and to warehouse financiers that a natural exit strategy to their investments remained open. A dual approach was taken to keeping primary markets open: (1) direct investment in term transactions to fill gaps as required; and (2) providing third party investors with capacity to ‘switch’ out of existing investments to recycle proceeds into primary market transactions. During 2020 the warehouse finance market experienced significant disruption, with some senior financiers restricting lending to existing clients and in some cases seeking additional credit enhancement at a time when mezzanine financiers[6]had been unwilling or unable to increase their commitments; some had been exercising their option to withdraw finance at the earliest opportunity. Consistent with the Directions, the SFSF investments have been used to fill gaps in these facilities, typically but not exclusively within mezzanine tranches, consistent with the objective of maximising the extent to which private sector investment is retained. In addition the AOFM worked with industry via the Australian Securitisation Forum (ASF) to establish a ‘forbearance special purpose vehicle’ (fSPV). This allowed participating lenders to maintain an income stream from loans granted a payment holiday due to COVID‑19 related hardship. The fSPV was designed to mitigate yield strain, buffer returns on securitisation trusts, and to support participating originators’ income flows. Support was provided retrospectively from 1 March 2020 and concluded on 31 March 2021. The arrangement advanced up to 90 per cent of missed interest payments on loans in COVID‑19 hardship. Since April 2021 participating originators have been required to start repaying drawn amounts from excess spread. Consistent with SFSF Rules the SFSF is the senior financier and does not hold the ‘first loss’ securities issued by the fSPV. #### Outcomes Australian securitisation market conditions improved considerably during 2020‑21. Despite improvements in conditions, eligible lenders gained additional confidence from the AOFM’s preparedness to fill gaps in their primary market book-building processes. This resulted in continued inquiries for support of issuance throughout the first half of the year. Further improvements in market conditions in early 2021 meant that no requests for AOFM public market support were received in the second half of the financial year. From inception 16 eligible lenders benefited from SFSF support in public markets bringing 31 term securitisation transactions to market with a total issuance volume of$16.69billion.[7]Of these 31 transactions the SFSF was called on to invest either directly in the primary market transaction, the secondary market, or both, in 11 instances, with total investments of $1.35billion. Of these, just two transactions were supported (in July 2020) with associated secondary market investments of$0.17 billion. At 30 June 2021, public market investments held by the SFSF had reduced to $0.95 billion; a result of amortisation and exercising call options. The SFSF continued to receive warehouse proposals in 2020-21, predominantly in the first half of the year. Peak SFSF warehouse commitments reached$2.34billion, reflecting investments in 45 warehouses from 34 eligible lenders.[8]The improvement in market conditions assisted replacement of the SFSF by private sector investment, particularly in the second half of the financial year. By 30 June the SFSF had been fully replaced in 10 warehouses and partially replaced in a further three. At this time the SFSF had active investments in 26 warehouses across 21 eligible lenders. The approved SFSF limits within these facilities totalled $1.1 billion and the total drawn amount across these facilities stood at around$770 million.
Arrangements for the fSPV were finalised early in the financial year. Total limits of $101.6 million for eight participating eligible lenders were approved by the SFSF delegate. Of these, six eligible lenders called on the facility. The availability period ceased on 31 March 2021 as planned, and the fSPV moved into amortisation on 1 April 2021. One participating eligible lender repaid its loans in full in the last quarter of the year and the total drawn amount of the facility stood at circa$39 million on 30 June 2021.
Across the three SFSF components 41 eligible lenders had received at least one form of support by 30 June 2021. The call on SFSF investments ranged from in‑principle support for a public deal in which the SFSF was ultimately not required to invest (in two cases), through to the full suite of support across public transactions (in primary and/or secondary markets), warehouses and the fSPV (in five cases).
Through 2020-21 the SFSF held a weighted average investment of $2.06billion and earned gross accrual revenue of$59.3 million, implying a gross yield of 2.87 per cent on the average invested amount held across all investment types.[9]To date there have been no credit losses on SFSF investments.
### Establishing the Australian Business Securitisation Fund (ABSF)
#### Aim
In November 2018, the Government announced plans to establish the ABSF to increase competition within the small and medium enterprise (SME) lending market by improving access to securitisation for smaller SME lenders.
The ABSF enabling legislation was enacted in April 2019. The first investment tranche of $250 million (of a total$2 billion) was credited to the ABSF’s special account on 1 July 2019. A second tranche of $500 million was credited on 1July 2020. This section sets out how the AOFM has approached the task of establishing the ABSF as a vehicle to achieve the Government’s objective of opening securitisation markets to SME lenders. #### Approach to achieving the Aim Following announcement of the ABSF, the AOFM and Treasury undertook extensive market engagement to gain insights into SME lending. This included detailed assessment of barriers to investment activity that might explain the under-representation of SME loans within collateral pools supporting Australian securitisation products. One potential barrier was lack of standardisation in arrangements supporting securitisation of SME loans. Examples included absences of standard documentation of revolving warehouse finance facilities, and a standardised SME loan performance reporting template. Other contributing factors are seen as the lack of homogeneity in lending products offered to SMEs and a lack of scale within specialist lenders (constraining their ability to price loans at close to the marginal risk‑adjusted cost of delivery). The AOFM’s efforts have focused on establishment of a track record for various types of SME lending that would be available to investors. In time, it is expected this will support rating agency and investor assessments, attract new capital, and facilitate expansion of existing collateral types underpinning the Australian asset backed securities (ABS) market to include new types of SME lending. The Australian Securitisation Forum (ASF) has supported the data template initiative by establishing a working group to undertake its development. The working group comprised industry‑wide representation including trustees, data analytics firms, rating agencies, originators, and investors. In parallel, the AOFM will seek to use ABSF investments to subsidise the costs for participating lenders in updating their systems to adequately capture loan level data for the reporting template. #### Outcomes The ASF working group expects finalisation toward the end of the year of a live SME receivables reporting template.[10] Following the pandemic driven pause in ABSF activities, improved market conditions enabled the AOFM to issue a second‑round call for proposals in January 2021, which closed in late March 2021 and attracted 16 proposals. Assessments were in progress at 30 June 2021. The sole investment of the ABSF continues to be in securities issued by a warehouse sponsored by Judo Bank, with a limit of$250 million. At 30June2021 ABSF investment stood at $102.2million. Gross earnings of the ABSF in 2020-21 were$0.76 million, on an average through-the-year drawn investment of \$46.6 million, implying a gross yield of 1.63 per cent. This compares favourably with the ABSF’s benchmark return of 0.18 per cent.[11]
[1] Debt servicing cost includes net interest expense (measured on an accruals basis and includes realised gains and losses on the disposal of assets or liabilities) plus foreign exchange revaluation gains and losses (now minimal). Unrealised changes in the market valuation of domestic debt and assets are not part of this measure.
[2] Refinancing risk, also referred to as rollover risk or re‑pricing risk, is the risk that borrowing to replace maturing debt occurs on unfavourable terms (or is not possible at all).
[3] These are point-in-time measures at 30 June each year, in contrast to debt servicing cost incurred throughout the year captured in Table 3. Figures are calculated by weighting Treasury Bond issuance yields by book volume.
[4] The OPA is the collective term for the core bank accounts maintained at the RBA for Australian Government cash balance management.
[5] The overdraft facility is more costly than equivalent short term borrowing (for example, issuance of Treasury Notes). The terms of the facility provide it is to cover only temporary shortfalls of cash and is to be used infrequently and, only to cover unexpected events.
[6] Mezzanine financiers are typically specialist credit investors who provide additional credit enhancement between the ‘skin in the game’ or ‘first loss’ equity investment retained by the (eligible lender) originator and the senior note held by the warehouse provider (typically a bank).
[7] The maximum number of public market transactions for which an individual originator received support was five.
[8] This includes warehouse proposals subsequently withdrawn or that lapsed, or were yet to be finalised by 30 June 2021.
[9] These numbers exclude provisions for expected credit losses and mark-to-market gains on public transactions.
[10] The template was published by the ASF in August 2021 and will be subject to periodic review.
[11] The benchmark is designed to approximate the Government’s borrowing costs on short term liabilities, given the floating rate instruments held by the ABSF, and is constructed from Australian Government Bonds with less than one year to maturity.
| 2022-05-27T21:34:04 |
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http://popflock.com/learn?s=Reactance_(electronics)
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Reactance (electronics)
Get Reactance Electronics essential facts below. View Videos or join the Reactance Electronics discussion. Add Reactance Electronics to your PopFlock.com topic list for future reference or share this resource on social media.
Reactance Electronics
In electric and electronic systems, reactance is the opposition of a circuit element to the flow of current due to that element's inductance or capacitance. Greater reactance leads to smaller currents for the same voltage applied. Reactance is similar to electric resistance in this respect, but differs in that reactance does not lead to dissipation of electrical energy as heat. Instead, energy is stored in the reactance, and later returned to the circuit whereas a resistance continuously loses energy.
Reactance is used to compute amplitude and phase changes of sinusoidal alternating current (AC) going through a circuit element. It is denoted by the symbol ${\displaystyle \scriptstyle {X}}$. An ideal resistor has zero reactance, whereas ideal inductors and capacitors have zero resistance – that is, respond to current only by reactance. As frequency increases, inductive reactance also increases and capacitive reactance decreases.
## Comparison to resistance
Reactance is similar to resistance in that larger reactance leads to smaller currents for the same applied voltage. Further, a circuit made entirely of elements that have only reactance (and no resistance) can be treated the same way as a circuit made entirely of elements with no reactance (pure resistance). These same techniques can also be used to combine elements with reactance with elements with resistance but complex numbers are typically needed. This is treated below in the section on impedance.
There are several important differences between reactance and resistance, though. First, reactance changes the phase so that the current through the element is shifted by a quarter of a cycle relative to the voltage applied across the element. Second, power is not dissipated in a purely reactive element but is stored instead. Third, reactances can be negative so that they can 'cancel' each other out. Finally, the main circuit elements that have reactance (capacitors and inductors) have a frequency dependent reactance, unlike resistors which typically have the same resistance for all frequencies.
The term reactance was first suggested by French engineer M. Hospitalier in L'Industrie Electrique on 10 May 1893. It was officially adopted by the American Institute of Electrical Engineers in May 1894.[1]
## Capacitive reactance
A capacitor consists of two conductors separated by an insulator, also known as a dielectric.
Capacitive reactance is an opposition to the change of voltage across an element. Capacitive reactance ${\displaystyle \scriptstyle {X_{C}}}$ is inversely proportional to the signal frequency ${\displaystyle \scriptstyle {f}}$ (or angular frequency ?) and the capacitance ${\displaystyle \scriptstyle {C}}$.[2]
There are two choices in the literature for defining reactance for a capacitor. One is to use a uniform notion of reactance as the imaginary part of impedance, in which case the reactance of a capacitor is the negative number,[2][3][4]
${\displaystyle X_{C}=-{\frac {1}{\omega C}}=-{\frac {1}{2\pi fC}}}$.
Another choice is to define capacitive reactance as a positive number,[5][6][7]
${\displaystyle X_{C}={\frac {1}{\omega C}}={\frac {1}{2\pi fC}}}$
In this case however one needs to remember to add a negative sign for the impedance of a capacitor, i.e. ${\displaystyle Z_{c}=-jX_{c}}$.
At low frequencies a capacitor is an open circuit so no current flows in the dielectric.
A DC voltage applied across a capacitor causes positive charge to accumulate on one side and negative charge to accumulate on the other side; the electric field due to the accumulated charge is the source of the opposition to the current. When the potential associated with the charge exactly balances the applied voltage, the current goes to zero.
Driven by an AC supply (ideal AC current source), a capacitor will only accumulate a limited amount of charge before the potential difference changes polarity and the charge is returned to the source. The higher the frequency, the less charge will accumulate and the smaller the opposition to the current.
## Inductive reactance
Inductive reactance is a property exhibited by an inductor, and inductive reactance exists based on the fact that an electric current produces a magnetic field around it. In the context of an AC circuit (although this concept applies any time current is changing), this magnetic field is constantly changing as a result of current that oscillates back and forth. It is this change in magnetic field that induces another electric current to flow in the same wire (counter-EMF), in a direction such as to oppose the flow of the current originally responsible for producing the magnetic field (known as Lenz's Law). Hence, inductive reactance is an opposition to the change of current through an element.
For an ideal inductor in an AC circuit, the inhibitive effect on change in current flow results in a delay, or a phase shift, of the alternating current with respect to alternating voltage. Specifically, an ideal inductor (with no resistance) will cause the current to lag the voltage by a quarter cycle, or 90°.
In electric power systems, inductive reactance (and capacitive reactance, however inductive reactance is more common) can limit the power capacity of an AC transmission line, because power is not completely transferred when voltage and current are out-of-phase (detailed above). That is, current will flow for an out-of-phase system, however real power at certain times will not be transferred, because there will be points during which instantaneous current is positive while instantaneous voltage is negative, or vice versa, implying negative power transfer. Hence, real work is not performed when power transfer is "negative". However, current still flows even when a system is out-of-phase, which causes transmission lines to heat up due to current flow. Consequently, transmission lines can only heat up so much (or else they would physically sag too much, due to the heat expanding the metal transmission lines), so transmission line operators have a "ceiling" on the amount of current that can flow through a given line, and excessive inductive reactance can limit the power capacity of a line. Power providers utilize capacitors to shift the phase and minimize the losses, based on usage patterns.
Inductive reactance ${\displaystyle \scriptstyle {X_{L}}}$ is proportional to the sinusoidal signal frequency ${\displaystyle \scriptstyle {f}}$ and the inductance ${\displaystyle \scriptstyle {L}}$, which depends on the physical shape of the inductor.
${\displaystyle X_{L}=\omega L=2\pi fL}$
The average current flowing through an inductance ${\displaystyle \scriptstyle {L}}$ in series with a sinusoidal AC voltage source of RMS amplitude ${\displaystyle \scriptstyle {A}}$ and frequency ${\displaystyle \scriptstyle {f}}$ is equal to:
${\displaystyle I_{L}={A \over \omega L}={A \over 2\pi fL}.}$
Because a square wave has multiple amplitudes at sinusoidal harmonics, the average current flowing through an inductance ${\displaystyle \scriptstyle {L}}$ in series with a square wave AC voltage source of RMS amplitude ${\displaystyle \scriptstyle {A}}$ and frequency ${\displaystyle \scriptstyle {f}}$ is equal to:
${\displaystyle I_{L}={A\pi ^{2} \over 8\omega L}={A\pi \over 16fL}}$
making it appear as if the inductive reactance to a square wave was about 19% smaller ${\displaystyle X_{L}={16 \over \pi }fL}$ than the reactance to the AC sine wave:
Any conductor of finite dimensions has inductance; the inductance is made larger by the multiple turns in an electromagnetic coil. Faraday's law of electromagnetic induction gives the counter-emf ${\displaystyle \scriptstyle {\mathcal {E}}}$ (voltage opposing current) due to a rate-of-change of magnetic flux density ${\displaystyle \scriptstyle {B}}$ through a current loop.
${\displaystyle {\mathcal {E}}=-{{d\Phi _{B}} \over dt}}$
For an inductor consisting of a coil with ${\displaystyle \scriptstyle N}$ loops this gives.
${\displaystyle {\mathcal {E}}=-N{d\Phi _{B} \over dt}}$
The counter-emf is the source of the opposition to current flow. A constant direct current has a zero rate-of-change, and sees an inductor as a short-circuit (it is typically made from a material with a low resistivity). An alternating current has a time-averaged rate-of-change that is proportional to frequency, this causes the increase in inductive reactance with frequency.
## Impedance
Both reactance ${\displaystyle {X}}$ and resistance ${\displaystyle {R}}$ are components of impedance ${\displaystyle {\mathbf {Z} }}$.
${\displaystyle \mathbf {Z} =R+\mathbf {j} X}$
where:
• ${\displaystyle \mathbf {Z} }$ is the complex impedance, measured in ohms;
• ${\displaystyle R}$ is the resistance, measured in ohms. It is the real part of the impedance: ${\displaystyle {R={\text{Re}}{(\mathbf {Z} )}}}$
• ${\displaystyle X}$ is the reactance, measured in ohms. It is the imaginary part of the impedance: ${\displaystyle {X={\text{Im}}{(\mathbf {Z} )}}}$
• ${\displaystyle \mathbf {j} }$ is the square root of minus one, usually represented by ${\displaystyle \mathbf {i} }$ in non-electrical formulas. ${\displaystyle \mathbf {j} }$ is used so as not to confuse the imaginary unit with current, commonly represented by ${\displaystyle \mathbf {i} }$.
When both a capacitor and an inductor are placed in series in a circuit, their contributions to the total circuit impedance are opposite. Capacitive reactance ${\displaystyle \scriptstyle {X_{C}}}$ and inductive reactance ${\displaystyle \scriptstyle {X_{L}}}$ contribute to the total reactance ${\displaystyle \scriptstyle {X}}$ as follows.
${\displaystyle {X=X_{L}+X_{C}=\omega L-{\frac {1}{\omega C}}}}$
where:
• ${\displaystyle \scriptstyle {X_{L}}}$ is the inductive reactance, measured in ohms;
• ${\displaystyle \scriptstyle {X_{C}}}$ is the capacitive reactance, measured in ohms;
• ${\displaystyle \omega }$ is the angular frequency, ${\displaystyle 2\pi }$ times the frequency in Hz.
Hence:[4]
• if ${\displaystyle \scriptstyle X>0}$, the total reactance is said to be inductive;
• if ${\displaystyle \scriptstyle X=0}$, then the impedance is purely resistive;
• if ${\displaystyle \scriptstyle X<0}$, the total reactance is said to be capacitive.
Note however that if ${\displaystyle \scriptstyle {X_{L}}}$ and ${\displaystyle \scriptstyle {X_{C}}}$ are assumed both positive by definition, then the intermediary formula changes to a difference:[6]
${\displaystyle {X=X_{L}-X_{C}=\omega L-{\frac {1}{\omega C}}}}$
but the ultimate value is the same.
### Phase relationship
The phase of the voltage across a purely reactive device (i.e. with zero parasitic resistance) lags the current by ${\displaystyle {\frac {\pi }{2}}}$ radians for a capacitive reactance and leads the current by ${\displaystyle {\frac {\pi }{2}}}$ radians for an inductive reactance. Without knowledge of both the resistance and reactance the relationship between voltage and current cannot be determined.
The origin of the different signs for capacitive and inductive reactance is the phase factor ${\displaystyle e^{\pm \mathbf {j} {\frac {\pi }{2}}}}$ in the impedance.
{\displaystyle {\begin{aligned}\mathbf {Z} _{C}&={1 \over \omega C}e^{-\mathbf {j} {\pi \over 2}}=\mathbf {j} \left({-{\frac {1}{\omega C}}}\right)=\mathbf {j} X_{C}\\\mathbf {Z} _{L}&=\omega Le^{\mathbf {j} {\pi \over 2}}=\mathbf {j} \omega L=\mathbf {j} X_{L}\quad \end{aligned}}}
For a reactive component the sinusoidal voltage across the component is in quadrature (a ${\displaystyle {\frac {\pi }{2}}}$ phase difference) with the sinusoidal current through the component. The component alternately absorbs energy from the circuit and then returns energy to the circuit, thus a pure reactance does not dissipate power.
## References
• Shamieh C. and McComb G., Electronics for Dummies, John Wiley & Sons, 2011.
• Meade R., Foundations of Electronics, Cengage Learning, 2002.
• Young, Hugh D.; Roger A. Freedman; A. Lewis Ford (2004) [1949]. Sears and Zemansky's University Physics (11 ed.). San Francisco: Addison Wesley. ISBN 0-8053-9179-7.
1. ^ Charles Proteus Steinmetz, Frederick Bedell, "Reactance", Transactions of the American Institute of Electrical Engineers, vol. 11, pp. 640-648, January-December 1894.
2. ^ a b Irwin, D. (2002). Basic Engineering Circuit Analysis, page 274. New York: John Wiley & Sons, Inc.
3. ^ Hayt, W.H., Kimmerly J.E. (2007). Engineering Circuit Analysis, 7th ed., McGraw-Hill, p. 388
4. ^ a b Glisson, T.H. (2011). Introduction to Circuit Analysis and Design, Springer, p. 408
5. ^ Horowitz P., Hill W. (2015). The Art of Electronics, 3rd ed., p. 42
6. ^ a b Hughes E., Hiley J., Brown K., Smith I.McK., (2012). Hughes Electrical and Electronic Technology, 11th edition, Pearson, pp. 237-241
7. ^ Robbins, A.H., Miller W. (2012). Circuit Analysis: Theory and Practice, 5th ed., Cengage Learning, pp. 554-558
This article uses material from the Wikipedia page available here. It is released under the Creative Commons Attribution-Share-Alike License 3.0.
| 2020-10-29T02:10:30 |
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https://math.libretexts.org/Bookshelves/Combinatorics_and_Discrete_Mathematics/Book%3A_Elementary_Number_Theory_(Raji)/02%3A_Prime_Numbers/2.01%3A_The_Sieve_of_Eratosthenes
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# 2.1: The Sieve of Eratosthenes
A prime is an integer greater than 1 that is only divisible by 1 and itself. The integers 2, 3, 5, 7, 11 are prime integers. Note that any integer greater than 1 that is not prime is said to be a composite number.
## The Sieve of Eratosthenes
The Sieve of Eratosthenes is an ancient method of finding prime numbers up to a specified integer. This method was invented by the ancient Greek mathematician Eratosthenes. There are several other methods used to determine whether a number is prime or composite. We first present a lemma that will be needed in the proof of several theorems.
Every integer greater than one has a prime divisor.
We present the proof of this Lemma by contradiction. Suppose that there is an integer greater than one that has no prime divisors. Since the set of integers with elements greater than one with no prime divisors is nonempty, then by the well ordering principle there is a least positive integer $$n$$ greater than one that has no prime divisors. Thus $$n$$ is composite since $$n$$ divides $$n$$. Hence $n=ab \mbox{with} \ \ 1<a<n \mbox{and} \ \ 1<b<n.$ Notice that $$a<n$$ and as a result since $$n$$ is minimal, $$a$$ must have a prime divisor which will also be a divisor of $$n$$.
If $$n$$ is a composite integer, then n has a prime factor not exceeding $$\sqrt{n}$$.
Since $$n$$ is composite, then $$n=ab$$, where $$a$$ and $$b$$ are integers with $$1<a\leq b<n$$. Suppose now that $$a>\sqrt{n}$$, then
$\sqrt{n}<a \leq b$
and as a result
$ab>\sqrt{n}\sqrt{n}=n.$
Therefore $$a\leq \sqrt{n}$$. Also, by Lemma 3, $$a$$ must have a prime divisor $$a_1$$ which is also a prime divisor of $$n$$ and thus this divisor is less than $$a_1 \leq a\leq \sqrt{n}$$.
We now present the algorithm of the Sieve of Eratosthenes that is used to determine prime numbers up to a given integer.
The Algorithm of the Sieve of Eratosthenes
1. Write a list of numbers from 2 to the largest number $$n$$ you want to test. Note that every composite integer less than $$n$$ must have a prime factor less than $$\sqrt{n}$$. Hence you need to strike off the multiples of the primes that are less than $$\sqrt{n}$$
2. Strike off all multiples of 2 greater than 2 from the list . The first remaining number in the list is a prime number.
3. Strike off all multiples of this number from the list.
4. Repeat the above steps until no more multiples are found of the prime integers that are less than $$\sqrt{n}$$
Exercises
1. Use the Sieve of Eratosthenes to find all primes less than 100.
2. Use the Sieve of Eratosthenes to find all primes less than 200.
3. Show that no integer of the form $$a^3+1$$ is a prime except for $$2=1^3+1$$.
4. Show that if $$2^n-1$$ is prime, then $$n$$ is prime.
Hint: Use the identity $$(a^{kl}-1)=(a^{k}-1)(a^{k(l-1)}+a^{k(l-2)}+...+a^k+1)$$.
## Contributors
• Dr. Wissam Raji, Ph.D., of the American University in Beirut. His work was selected by the Saylor Foundation’s Open Textbook Challenge for public release under a Creative Commons Attribution (CC BY) license.
| 2020-05-28T08:23:21 |
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https://indico.fnal.gov/event/15949/contributions/34806/
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# 36th Annual International Symposium on Lattice Field Theory
Jul 22 – 28, 2018
Kellogg Hotel and Conference Center
EST timezone
## Charmed (and heavier) meson decay constants and heavy neutral meson mixing in the continuum limit using 2+1f of domain wall fermions
Jul 26, 2018, 9:30 AM
20m
103 (Kellogg Hotel and Conference Center)
### 103
#### Kellogg Hotel and Conference Center
219 S Harrison Rd, East Lansing, MI 48824
Weak Decays and Matrix Elements
### Speaker
Dr J Tobias Tsang (University of Edinburgh)
### Description
I will present a status update of RBC/UKQCD's charm (to bottom) physics program based on ensembles with $N_f=2+1$ flavours of domain wall fermions featuring physical pion masses. After a brief review of our program, the main focus will be on mesonic decay constants and neutral meson mixing in the charm and bottom sector, where results for the bottom sector are obtained from an extrapolation from the (heavier than) charm-quark mass region to the physical $b$-quark mass. In particular, I will focus on the ratio of the pseudo-scalar decay constants $f_{D_s}/f_{D}$ and on the extrapolation of the ratio $\xi$ to the $b$-quark mass.
### Primary author
Dr J Tobias Tsang (University of Edinburgh)
### Co-authors
Dr Andreas Juettner (University of Southampton) Prof. Luigi Del Debbio (University of Edinburgh) Dr Nicolas Garron (University of Liverpool) Oliver Witzel Witzel (University of Colorado Boulder) Prof. Peter Boyle (University of Edinburgh)
Slides
| 2022-12-05T06:57:09 |
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https://par.nsf.gov/biblio/10363233
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The K2 Galactic Archaeology Program Data Release 3: Age-abundance Patterns in C1–C8 and C10–C18
Abstract
We present the third and final data release of the K2 Galactic Archaeology Program (K2 GAP) for Campaigns C1–C8 and C10–C18. We provide asteroseismic radius and mass coefficients,κRandκM, for ∼19,000 red giant stars, which translate directly to radius and mass given a temperature. As such, K2 GAP DR3 represents the largest asteroseismic sample in the literature to date. K2 GAP DR3 stellar parameters are calibrated to be on an absolute parallactic scale based on Gaia DR2, with red giant branch and red clump evolutionary state classifications provided via a machine-learning approach. Combining these stellar parameters with GALAH DR3 spectroscopy, we determine asteroseismic ages with precisions of ∼20%–30% and compare age-abundance relations to Galactic chemical evolution models among both low- and high-αpopulations forα, light, iron-peak, and neutron-capture elements. We confirm recent indications in the literature of both increased Ba production at late Galactic times as well as significant contributions tor-process enrichment from prompt sources associated with, e.g., core-collapse supernovae. With an eye toward other Galactic archeology applications, we characterize K2 GAP DR3 uncertainties and completeness using injection tests, suggesting that K2 GAP DR3 is largely unbiased in mass/age, with uncertainties of 2.9% (stat.) ± 0.1% (syst.) and 6.7% (stat.) ± more »
Authors:
; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; more »
Award ID(s):
Publication Date:
NSF-PAR ID:
10363233
Journal Name:
The Astrophysical Journal
Volume:
926
Issue:
2
Page Range or eLocation-ID:
Article No. 191
ISSN:
0004-637X
Publisher:
DOI PREFIX: 10.3847
National Science Foundation
##### More Like this
1. ABSTRACT
Analyses of data from spectroscopic and astrometric surveys have led to conflicting results concerning the vertical characteristics of the Milky Way. Ages are often used to provide clarity, but typical uncertainties of >40 per cent from photometry restrict the validity of the inferences made. Using the Kepler APOKASC sample for context, we explore the global population trends of two K2 campaign fields (3 and 6), which extend further vertically out of the Galactic plane than APOKASC. We analyse the properties of red giant stars utilizing three asteroseismic data analysis methods to cross-check and validate detections. The Bayesian inference tool PARAM is used to determine the stellar masses, radii, and ages. Evidence of a pronounced red giant branch bump and an [α/Fe] dependence on the position of the red clump is observed from the K2 fields radius distribution. Two peaks in the age distribution centred at ∼5 and ∼12 Gyr are found using a sample with σage < 35 per cent. In comparison with Kepler, we find the older peak to be more prominent for K2. This age bimodality is also observed based on a chemical selection of low-[α/Fe] (≤0.1) and high-[α/Fe] (>0.1) stars. As a function of vertical distance from the Galactic mid-plane (|Z|),more »
2. Abstract Large-scale surveys open the possibility to investigate Galactic evolution both chemically and kinematically; however, reliable stellar ages remain a major challenge. Detailed chemical information provided by high-resolution spectroscopic surveys of the stars in clusters can be used as a means to calibrate recently developed chemical tools for age-dating field stars. Using data from the Open Cluster Abundances and Mapping survey, based on the Sloan Digital Sky Survey/Apache Point Observatory Galactic Evolution Experiment 2 survey, we derive a new empirical relationship between open cluster stellar ages and the carbon-to-nitrogen ([C/N]) abundance ratios for evolved stars, primarily those on the red giant branch. With this calibration, [C/N] can be used as a chemical clock for evolved field stars to investigate the formation and evolution of different parts of our Galaxy. We explore how mixing effects at different stellar evolutionary phases, like the red clump, affect the derived calibration. We have established the [C/N]–age calibration for APOGEE Data Release 17 (DR17) giant star abundances to be log [ Age ( yr ) ] DR 17 = 10.14 ( ± 0.08 ) + 2.23 ( ± 0.19 ) [ C / N ] , usable for 8.62 ≤ log ( Age [ yrmore »
3. ABSTRACT
We present a detailed near-infrared chemical abundance analysis of 10 red giant members of the Galactic open cluster NGC 752. High-resolution (R ≃ 45000) near-infrared spectral data were gathered with the Immersion Grating Infrared Spectrograph, providing simultaneous coverage of the complete H and K bands. We derived the abundances of H-burning (C, N, O), α (Mg, Si, S, Ca), light odd-Z (Na, Al, P, K), Fe-group (Sc, Ti, Cr, Fe, Co, Ni), and neutron-capture (Ce, Nd, Yb) elements. We report the abundances of S, P, K, Ce, and Yb in NGC 752 for the first time. Our analysis yields solar-metallicity and solar abundance ratios for almost all of the elements heavier than the CNO group in NGC 752. O and N abundances were measured from a number of OH and CN features in the H band, and C abundances were determined mainly from CO molecular lines in the K band. High-excitation $\rm{C\,\small {I}}$ lines present in both near-infrared and optical spectra were also included in the C abundance determinations. Carbon isotopic ratios were derived from the R-branch band heads of first overtone (2−0) and (3−1) 12CO and (2−0) 13CO lines near 23 440 Å and (3−1) 13CO lines at about 23 730 Å. The CNOmore »
4. Abstract
We analyze existing measurements of [Fe/H] and [α/Fe] for individual red giant branch (RGB) stars in the Giant Stellar Stream (GSS) of M31 to determine whether spatial abundance gradients are present. These measurements were obtained from low- (R∼ 3000) and moderate- (R∼ 6000) resolution Keck/DEIMOS spectroscopy using spectral synthesis techniques as part of the Elemental Abundances in M31 survey. From a sample of 62 RGB stars spanning the GSS at 17, 22, and 33 projected kpc, we measure a [Fe/H] gradient of −0.018 ± 0.003 dex kpc−1and negligible [α/Fe] gradient with M31-centric radius. We investigate GSS abundance patterns in the outer halo using additional [Fe/H] and [α/Fe] measurements for six RGB stars located along the stream at 45 and 58 projected kpc. These abundances provide tentative evidence that the trends in [Fe/H] and [α/Fe] beyond 40 kpc in the GSS are consistent with those within 33 kpc. We also compare the GSS abundances to 65 RGB stars located along the possibly related Southeast (SE) shelf substructure at 12 and 18 projected kpc. The abundances of the GSS and SE shelf are consistent, supporting a common origin hypothesis, although this interpretation may be complicated by the presence of [Fe/H] gradientsmore »
5. Context. With the advent of space-based asteroseismology, determining accurate properties of red-giant stars using their observed oscillations has become the focus of many investigations due to their implications in a variety of fields in astrophysics. Stellar models are fundamental in predicting quantities such as stellar age, and their reliability critically depends on the numerical implementation of the physics at play in this evolutionary phase. Aims. We introduce the Aarhus red giants challenge, a series of detailed comparisons between widely used stellar evolution and oscillation codes that aim to establish the minimum level of uncertainties in properties of red giants arising solely from numerical implementations. We present the first set of results focusing on stellar evolution tracks and structures in the red-giant-branch (RGB) phase. Methods. Using nine state-of-the-art stellar evolution codes, we defined a set of input physics and physical constants for our calculations and calibrated the convective efficiency to a specific point on the main sequence. We produced evolutionary tracks and stellar structure models at a fixed radius along the red-giant branch for masses of 1.0 M ⊙ , 1.5 M ⊙ , 2.0 M ⊙ , and 2.5 M ⊙ , and compared the predicted stellar properties. Results. Oncemore »
| 2022-11-30T14:27:34 |
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https://pos.sissa.it/307/027/
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Volume 307 - XVII International Workshop on Neutrino Telescopes (NEUTEL2017) - Session vii - convener: flavio gatti – double beta decays (1)
KamLAND-Zen
J. Shirai* on behalf of the KamLAND-Zen Collaboration
Full text: pdf
Pre-published on: March 28, 2018
Published on: April 05, 2018
Abstract
KamLAND-Zen is a high sensitivity experiment searching for neutrinoless double beta decay ($0¥nu¥beta¥beta$) of $^{136}$Xe nucleus by using a large volume ultralow-radioactivity environment of KamLAND detector. In this talk results of the KamLAND-Zen experiment using up to 380kg of enriched xenon (KamLAND-Zen 400) is presented together with the current status of the new phase, KamLAND-Zen 800, with 750kg enriched Xe aiming at a search in the inverted mass hierarchy (IH) region, and the planned experiment of KamLAND2-Zen.
DOI: https://doi.org/10.22323/1.307.0027
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.
| 2022-06-25T20:28:51 |
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https://ec.europa.eu/eurostat/statistics-explained/index.php?title=Glossary:Lead
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Lead refers to a difference in time between an observation and a future observation. Thus $y_{t-k}$ leads $y_{t}$ by k periods.
| 2020-11-25T05:50:48 |
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https://www.zbmath.org/authors/?q=ai%3Agreenbaum.anne
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# zbMATH — the first resource for mathematics
## Greenbaum, Anne
Compute Distance To:
Author ID: greenbaum.anne Published as: Greenbaum, A.; Greenbaum, Anne External Links: MGP · Wikidata
Documents Indexed: 61 Publications since 1979, including 7 Books
all top 5
#### Co-Authors
19 single-authored 5 Mayo, Anita A. 5 Strakoš, Zdeněk 3 Choi, Daeshik 3 Overton, Michael L. 2 Anderson, Edward 2 Ashby, Steve 2 Bai, Zhaojun 2 Bischof, Christian H. 2 Caldwell, Trevor 2 Chao, Han Zheng 2 Demmel, James Weldon 2 Dongarra, Jack J. 2 Du Croz, Jeremy J. 2 Elman, Howard C. 2 Freund, Roland W. 2 Greengard, Leslie F. 2 Gurvits, Leonid 2 Hammarling, Sven J. 2 Knizhnerman, L. A. 2 Li, Congming 2 Li, Kenan 2 McKenney, Alan 2 Parter, Seymour V. 2 Rodrigue, Garry H. 2 Rozlozník, Miroslav 2 Saylor, Paul E. 2 Sorensen, Danny C. 2 Walker, Homer F. 2 Widlund, Olof B. 1 Blackford, S. 1 Burke, James V. 1 Chang, Britton 1 Chartier, Timothy P. 1 Chen, Menghuo 1 Crouzeix, Michel 1 Cullum, Jane K. 1 Drkošová, Jitka 1 Drushkin, V. L. 1 Druskin, V. L. 1 Dubois, Paul F. 1 Faber, Vance 1 Ferguson, Jake M. 1 Golub, Gene Howard 1 Kyanfar, Faranges 1 Lewis, Adrian S. 1 Li, Rencang 1 Luskin, Mitchell 1 Machorro, Eric A. 1 Marshall, Donald E. 1 McFadden, Geoffrey Bey 1 Ostrouchov, Susan 1 Pták, Vlastimil 1 Salemi, Abbas 1 Sonnad, Vijay 1 Trefethen, Lloyd Nicholas
all top 5
#### Serials
10 SIAM Journal on Matrix Analysis and Applications 9 Linear Algebra and its Applications 5 SIAM Journal on Scientific Computing 4 Journal of Computational Physics 3 BIT 3 SIAM Review 2 Numerische Mathematik 2 Numerical Linear Algebra with Applications 1 Computer Physics Communications 1 Applied Mathematics and Computation 1 Computing 1 SIAM Journal on Numerical Analysis 1 SIAM Journal on Scientific and Statistical Computing 1 Physica D 1 Parallel Computing 1 Computational Mathematics and Mathematical Physics 1 Mathematical Programming. Series A. Series B 1 ETNA. Electronic Transactions on Numerical Analysis 1 Frontiers in Applied Mathematics 1 The IMA Volumes in Mathematics and its Applications 1 Software - Environments - Tools
all top 5
#### Fields
51 Numerical analysis (65-XX) 20 Linear and multilinear algebra; matrix theory (15-XX) 9 Partial differential equations (35-XX) 6 General and overarching topics; collections (00-XX) 5 Operator theory (47-XX) 4 Computer science (68-XX) 3 Potential theory (31-XX) 2 Integral equations (45-XX) 1 Functions of a complex variable (30-XX) 1 Special functions (33-XX) 1 Approximations and expansions (41-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Probability theory and stochastic processes (60-XX) 1 Statistical mechanics, structure of matter (82-XX)
#### Citations contained in zbMATH
48 Publications have been cited 1,484 times in 1,284 Documents Cited by Year
LAPACK user’s guide. This work is dedicated to Jim Wilkinson. 3rd ed. Zbl 0934.65030
Anderson, E.; Bai, Z.; Bischof, C.; Blackford, S.; Demmel, J.; Dongarra, J.; Du Croz, J.; Greenbaum, A.; Hammarling, S.; McKenney, A.; Sorensen, D.
1999
Iterative methods for solving linear systems. Zbl 0883.65022
Greenbaum, Anne
1997
LAPACK user’s guide. 2nd ed. Zbl 0843.65018
Anderson, E.; Bai, Z.; Bischof, C.; Demmel, J.; Dongarra, J.; Du Croz, J.; Greenbaum, A.; Hammarling, S.; McKenney, A.; Ostrouchov, S.; Sorensen, D.
1995
Any nonincreasing convergence curve is possible for GMRES. Zbl 0857.65029
Greenbaum, Anne; Pták, Vlastimil; Strakoš, Zdeněk
1996
Laplace’s equation and the Dirichlet-Neumann map in multiply connected domains. Zbl 0769.65085
Greenbaum, A.; Greengard, L.; McFadden, G. B.
1993
Approximating the inverse of a matrix for use in iterative algorithms on vector processors. Zbl 0438.65037
Dubois, P. F.; Greenbaum, A.; Rodrigue, Garry H.
1979
Behavior of slightly perturbed Lanczos and conjugate-gradient recurrences. Zbl 0662.65032
Greenbaum, A.
1989
Predicting the behavior of finite precision Lanczos and conjugate gradient computations. Zbl 0755.65037
Greenbaum, A.; Strakos, Z.
1992
Fast parallel iterative solution of Poisson’s and the biharmonic equations on irregular regions. Zbl 0752.65080
Mayo, A.; Greenbaum, A.
1992
On the numerical solution of the biharmonic equation in the plane. Zbl 0824.65117
Greenbaum, Anne; Greengard, Leslie; Mayo, Anita
1992
Generalizations of the field of values useful in the study of polynomial functions of a matrix. Zbl 1004.15027
Greenbaum, Anne
2002
Relations between Galerkin and norm-minimizing iterative methods for solving linear systems. Zbl 0855.65021
Cullum, Jane; Greenbaum, Anne
1996
Estimating the attainable accuracy of recursively computed residual methods. Zbl 0873.65027
Greenbaum, Anne
1997
Matrices that generate the same Krylov residual spaces. Zbl 0803.65029
Greenbaum, Anne; Strakos, Zdenek
1994
GMRES/CR and Arnoldi/Lanczos as matrix approximation problems. Zbl 0806.65031
Greenbaum, Anne; Trefethen, Lloyd N.
1994
Using nonorthogonal Lanczos vectors in the computation of matrix functions. Zbl 0912.65021
Druskin, V.; Greenbaum, A.; Knizhnerman, L.
1998
Numerical stability of GMRES. Zbl 0837.65040
Drkošová, J.; Greenbaum, A.; Rozložník, M.; Strakoš, Z.
1995
Numerical behaviour of the modified Gram-Schmidt GMRES implementation. Zbl 0891.65031
Greenbaum, A.; Rozložník, M.; Strakoš, Z.
1997
Comparison of splittings used with the conjugate gradient algorithm. Zbl 0394.65011
Greenbaum, A.
1979
The polynomial numerical hulls of Jordan blocks and related matrices. Zbl 1044.15019
Faber, Vance; Greenbaum, Anne; Marshall, Donald E.
2003
Analysis of a multigrid method as an iterative technique for solving linear systems. Zbl 0539.65011
Greenbaum, Anne
1984
Fourth order accurate evaluation of integrals in potential theory on exterior 3D regions. Zbl 1109.65028
Mayo, Anita; Greenbaum, Anne
2007
Crouzeix’s conjecture and perturbed Jordan blocks. Zbl 1390.15074
Greenbaum, Anne; Choi, Daeshik
2012
Parallelizing preconditioned conjugate gradient algorithms. Zbl 0798.65040
Greenbaum, Anne; Li, Congming; Chao, Han Zheng
1989
A multigrid method for multiprocessors. Zbl 0616.65094
Greenbaum, A.
1986
Diagonal scalings of the Laplacian as preconditioners for other elliptic differential operators. Zbl 0754.65042
Greenbaum, A.
1992
Some extensions of the Crouzeix-Palencia result. Zbl 1392.15029
Caldwell, Trevor; Greenbaum, Anne; Li, Kenan
2018
Rapid parallel evaluation of integrals in potential theory on general three-dimensional regions. Zbl 0911.65016
Greenbaum, A.; Mayo, A.
1998
Optimal preconditioners of a given sparsity pattern. Zbl 0689.65014
Greenbaum, A.; Rodrigue, G. H.
1989
A Petrov-Galerkin finite element method for solving the neutron transport equation. Zbl 0589.65090
Greenbaum, A.; Ferguson, J. M.
1986
Roots of matrices in the study of GMRES convergence and Crouzeix’s conjecture. Zbl 1314.15015
Choi, Daeshik; Greenbaum, Anne
2015
Upper and lower bounds on norms of functions of matrices. Zbl 1155.15032
Greenbaum, Anne
2009
Characterizations of the polynomial numerical hull of degree $$k$$. Zbl 1106.15018
Burke, James V.; Greenbaum, Anne
2006
Card shuffling and the polynomial numerical hull of degree $$k$$. Zbl 1047.15013
Greenbaum, Anne
2003
Max-min properties of matrix factor norms. Zbl 0799.15014
Greenbaum, A.; Gurvits, L.
1994
Analysis of an aggregation-based algebraic two-grid method for a rotated anisotropic diffusion problem. Zbl 1363.65213
Chen, Meng-Huo; Greenbaum, Anne
2015
Some theoretical results derived from polynomial numerical hulls of Jordan blocks. Zbl 1068.15039
Greenbaum, Anne
2004
Accuracy of computed solutions from conjugate-gradient-like methods. Zbl 0811.65026
Greenbaum, Anne
1994
Variational analysis of the Crouzeix ratio. Zbl 1376.15015
Greenbaum, Anne; Lewis, Adrian S.; Overton, Michael L.
2017
Near normal dilations of nonnormal matrices and linear operators. Zbl 1388.15019
Greenbaum, Anne; Caldwell, Trevor; Li, Kenan
2016
Numerical methods. Design, analysis, and computer implementation of algorithms. Zbl 1247.65001
Greenbaum, Anne; Chartier, Timothy P.
2012
First-order perturbation theory for eigenvalues and eigenvectors. Zbl 07207347
Greenbaum, Anne; Li, Ren-Cang; Overton, Michael L.
2020
Spectral sets: numerical range and beyond. Zbl 07122453
Crouzeix, Michel; Greenbaum, Anne
2019
Numerical investigation of Crouzeix’s conjecture. Zbl 1415.15021
Greenbaum, Anne; Overton, Michael L.
2018
An algorithm for finding a 2-similarity transformation from a numerical contraction to a contraction. Zbl 1323.65040
Choi, Daeshik; Greenbaum, Anne
2015
On solving indefinite symmetric linear systems by means of the Lanczos method. Zbl 0970.65040
Greenbaum, A.; Drushkin, V. L.; Knizhnerman, L. A.
1999
On the role of the left starting vector in the two-sided Lanczos algorithm and nonsymmetric linear system solvers. Zbl 0902.65011
Greenbaum, A.
1998
The Lanczos and conjugate gradient algorithms in finite precision arithmetic. Zbl 1260.65026
Greenbaum, Anne
1994
First-order perturbation theory for eigenvalues and eigenvectors. Zbl 07207347
Greenbaum, Anne; Li, Ren-Cang; Overton, Michael L.
2020
Spectral sets: numerical range and beyond. Zbl 07122453
Crouzeix, Michel; Greenbaum, Anne
2019
Some extensions of the Crouzeix-Palencia result. Zbl 1392.15029
Caldwell, Trevor; Greenbaum, Anne; Li, Kenan
2018
Numerical investigation of Crouzeix’s conjecture. Zbl 1415.15021
Greenbaum, Anne; Overton, Michael L.
2018
Variational analysis of the Crouzeix ratio. Zbl 1376.15015
Greenbaum, Anne; Lewis, Adrian S.; Overton, Michael L.
2017
Near normal dilations of nonnormal matrices and linear operators. Zbl 1388.15019
Greenbaum, Anne; Caldwell, Trevor; Li, Kenan
2016
Roots of matrices in the study of GMRES convergence and Crouzeix’s conjecture. Zbl 1314.15015
Choi, Daeshik; Greenbaum, Anne
2015
Analysis of an aggregation-based algebraic two-grid method for a rotated anisotropic diffusion problem. Zbl 1363.65213
Chen, Meng-Huo; Greenbaum, Anne
2015
An algorithm for finding a 2-similarity transformation from a numerical contraction to a contraction. Zbl 1323.65040
Choi, Daeshik; Greenbaum, Anne
2015
Crouzeix’s conjecture and perturbed Jordan blocks. Zbl 1390.15074
Greenbaum, Anne; Choi, Daeshik
2012
Numerical methods. Design, analysis, and computer implementation of algorithms. Zbl 1247.65001
Greenbaum, Anne; Chartier, Timothy P.
2012
Upper and lower bounds on norms of functions of matrices. Zbl 1155.15032
Greenbaum, Anne
2009
Fourth order accurate evaluation of integrals in potential theory on exterior 3D regions. Zbl 1109.65028
Mayo, Anita; Greenbaum, Anne
2007
Characterizations of the polynomial numerical hull of degree $$k$$. Zbl 1106.15018
Burke, James V.; Greenbaum, Anne
2006
Some theoretical results derived from polynomial numerical hulls of Jordan blocks. Zbl 1068.15039
Greenbaum, Anne
2004
The polynomial numerical hulls of Jordan blocks and related matrices. Zbl 1044.15019
Faber, Vance; Greenbaum, Anne; Marshall, Donald E.
2003
Card shuffling and the polynomial numerical hull of degree $$k$$. Zbl 1047.15013
Greenbaum, Anne
2003
Generalizations of the field of values useful in the study of polynomial functions of a matrix. Zbl 1004.15027
Greenbaum, Anne
2002
LAPACK user’s guide. This work is dedicated to Jim Wilkinson. 3rd ed. Zbl 0934.65030
Anderson, E.; Bai, Z.; Bischof, C.; Blackford, S.; Demmel, J.; Dongarra, J.; Du Croz, J.; Greenbaum, A.; Hammarling, S.; McKenney, A.; Sorensen, D.
1999
On solving indefinite symmetric linear systems by means of the Lanczos method. Zbl 0970.65040
Greenbaum, A.; Drushkin, V. L.; Knizhnerman, L. A.
1999
Using nonorthogonal Lanczos vectors in the computation of matrix functions. Zbl 0912.65021
Druskin, V.; Greenbaum, A.; Knizhnerman, L.
1998
Rapid parallel evaluation of integrals in potential theory on general three-dimensional regions. Zbl 0911.65016
Greenbaum, A.; Mayo, A.
1998
On the role of the left starting vector in the two-sided Lanczos algorithm and nonsymmetric linear system solvers. Zbl 0902.65011
Greenbaum, A.
1998
Iterative methods for solving linear systems. Zbl 0883.65022
Greenbaum, Anne
1997
Estimating the attainable accuracy of recursively computed residual methods. Zbl 0873.65027
Greenbaum, Anne
1997
Numerical behaviour of the modified Gram-Schmidt GMRES implementation. Zbl 0891.65031
Greenbaum, A.; Rozložník, M.; Strakoš, Z.
1997
Any nonincreasing convergence curve is possible for GMRES. Zbl 0857.65029
Greenbaum, Anne; Pták, Vlastimil; Strakoš, Zdeněk
1996
Relations between Galerkin and norm-minimizing iterative methods for solving linear systems. Zbl 0855.65021
Cullum, Jane; Greenbaum, Anne
1996
LAPACK user’s guide. 2nd ed. Zbl 0843.65018
Anderson, E.; Bai, Z.; Bischof, C.; Demmel, J.; Dongarra, J.; Du Croz, J.; Greenbaum, A.; Hammarling, S.; McKenney, A.; Ostrouchov, S.; Sorensen, D.
1995
Numerical stability of GMRES. Zbl 0837.65040
Drkošová, J.; Greenbaum, A.; Rozložník, M.; Strakoš, Z.
1995
Matrices that generate the same Krylov residual spaces. Zbl 0803.65029
Greenbaum, Anne; Strakos, Zdenek
1994
GMRES/CR and Arnoldi/Lanczos as matrix approximation problems. Zbl 0806.65031
Greenbaum, Anne; Trefethen, Lloyd N.
1994
Max-min properties of matrix factor norms. Zbl 0799.15014
Greenbaum, A.; Gurvits, L.
1994
Accuracy of computed solutions from conjugate-gradient-like methods. Zbl 0811.65026
Greenbaum, Anne
1994
The Lanczos and conjugate gradient algorithms in finite precision arithmetic. Zbl 1260.65026
Greenbaum, Anne
1994
Laplace’s equation and the Dirichlet-Neumann map in multiply connected domains. Zbl 0769.65085
Greenbaum, A.; Greengard, L.; McFadden, G. B.
1993
Predicting the behavior of finite precision Lanczos and conjugate gradient computations. Zbl 0755.65037
Greenbaum, A.; Strakos, Z.
1992
Fast parallel iterative solution of Poisson’s and the biharmonic equations on irregular regions. Zbl 0752.65080
Mayo, A.; Greenbaum, A.
1992
On the numerical solution of the biharmonic equation in the plane. Zbl 0824.65117
Greenbaum, Anne; Greengard, Leslie; Mayo, Anita
1992
Diagonal scalings of the Laplacian as preconditioners for other elliptic differential operators. Zbl 0754.65042
Greenbaum, A.
1992
Behavior of slightly perturbed Lanczos and conjugate-gradient recurrences. Zbl 0662.65032
Greenbaum, A.
1989
Parallelizing preconditioned conjugate gradient algorithms. Zbl 0798.65040
Greenbaum, Anne; Li, Congming; Chao, Han Zheng
1989
Optimal preconditioners of a given sparsity pattern. Zbl 0689.65014
Greenbaum, A.; Rodrigue, G. H.
1989
A multigrid method for multiprocessors. Zbl 0616.65094
Greenbaum, A.
1986
A Petrov-Galerkin finite element method for solving the neutron transport equation. Zbl 0589.65090
Greenbaum, A.; Ferguson, J. M.
1986
Analysis of a multigrid method as an iterative technique for solving linear systems. Zbl 0539.65011
Greenbaum, Anne
1984
Approximating the inverse of a matrix for use in iterative algorithms on vector processors. Zbl 0438.65037
Dubois, P. F.; Greenbaum, A.; Rodrigue, Garry H.
1979
Comparison of splittings used with the conjugate gradient algorithm. Zbl 0394.65011
Greenbaum, A.
1979
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#### Cited by 2,183 Authors
20 Greenbaum, Anne 15 Axelsson, Axel Owe Holger 15 Benner, Peter 14 Strakoš, Zdeněk 13 Dongarra, Jack J. 12 Quintana-Ortí, Enrique S. 12 Serra-Capizzano, Stefano 11 Helsing, Johan 11 Li, Rencang 11 Meurant, Gérard A. 11 Rozlozník, Miroslav 11 Zlatev, Zahari 10 Simoncini, Valeria 9 Salemi, Abbas 8 Bai, Zhongzhi 8 Demmel, James Weldon 8 Golub, Gene Howard 7 Faragó, István 7 Kropinski, Mary Catherine A. 7 Li, Zhilin 7 Lowengrub, John Samuel 7 Quintana-Ortí, Gregorio 7 Van der Vorst, Henk Albertus 6 Aishima, Kensuke 6 Carson, Erin Claire 6 Duintjer Tebbens, Jurjen 6 Higham, Nicholas J. 6 Kressner, Daniel 6 Lin, Wen-Wei 6 Pan, Victor Yakovlevich 6 Pestana, Jennifer 6 Szyld, Daniel B. 6 van de Geijn, Robert Alexander 6 Wathen, Andrew John 5 Aghamollaei, Gholamreza 5 Bai, Zhaojun 5 Bhaya, Amit 5 Bientinesi, Paolo 5 Chen, Jinhai 5 Ding, Chao 5 Drmač, Zlatko 5 Ferronato, Massimiliano 5 Giraud, Luc 5 Gravvanis, George A. 5 Greengard, Leslie F. 5 Gutknecht, Martin H. 5 Karátson, János 5 Keyes, David Elliot 5 Langou, Julien 5 Lin, Lin 5 Lipitakis, Elias A. 5 Lu, Linzhang 5 Morgan, Ronald B. 5 O’Leary, Dianne P. 5 Paprzycki, Marcin 5 Quaife, Bryan D. 5 Saad, Yousef 5 Sherwin, Spencer J. 5 Sleijpen, Gerard L. G. 5 Sun, Defeng 5 Tichý, Petr 5 Toh, Kimchuan 5 Vecharynski, Eugene 5 Walker, David W. 5 Ward, Michael J. 5 Yang, Chao 5 Ying, Wenjun 4 Bosner, Nela 4 Botchev, Mikhail A. 4 Carpentieri, Bruno 4 Diao, Huaian 4 Du, Kui 4 Fasano, Giovanni 4 Güttel, Stefan 4 Hadjidimos, Apostolos 4 Haidar, Azzam 4 Havasi, Ágnes 4 Huang, Ting-Zhu 4 Kågström, Bo 4 Kamiya, Norio 4 Kita, Eisuke 4 Koev, Plamen 4 Kolokolnikov, Theodore 4 Kontoghiorghes, Erricos John 4 Liesen, Jörg 4 Mach, Thomas 4 Manteuffel, Thomas A. 4 Matsuo, Takayasu 4 Mehrmann, Volker 4 Murota, Kazuo 4 Nasser, Mohamed M. S. 4 Neytcheva, Maya G. 4 Novati, Paolo 4 Overton, Michael L. 4 Parlett, Beresford Neill 4 Reichel, Lothar 4 Stoll, Martin 4 Tomov, Stanimire Z. 4 Vuik, Cornelis 4 Wei, Juncheng ...and 2,083 more Authors
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#### Cited in 199 Serials
126 Journal of Computational Physics 107 Linear Algebra and its Applications 89 Journal of Computational and Applied Mathematics 52 Numerical Linear Algebra with Applications 46 SIAM Journal on Scientific Computing 40 Computers & Mathematics with Applications 40 Applied Mathematics and Computation 40 BIT 35 Computer Physics Communications 34 Numerical Algorithms 33 Computer Methods in Applied Mechanics and Engineering 32 Applied Numerical Mathematics 25 Engineering Analysis with Boundary Elements 24 SIAM Journal on Matrix Analysis and Applications 23 International Journal for Numerical Methods in Engineering 23 Journal of Scientific Computing 22 Numerische Mathematik 19 Computers and Fluids 16 Optimization Methods & Software 13 Journal of Fluid Mechanics 12 Mathematics of Computation 12 Journal of Optimization Theory and Applications 12 Computational Optimization and Applications 12 Advances in Computational Mathematics 10 ACM Transactions on Mathematical Software 10 International Journal of Computer Mathematics 9 Mathematics and Computers in Simulation 9 Japan Journal of Industrial and Applied Mathematics 9 Computational Statistics and Data Analysis 9 Mathematical Programming. Series A. Series B 8 SIAM Journal on Optimization 7 Computing 7 Physica D 6 Parallel Computing 6 Applied Mathematics Letters 6 European Journal of Operational Research 5 International Journal for Numerical Methods in Fluids 5 Journal of Mathematical Physics 5 Calcolo 5 Physics of Fluids 5 Computational and Applied Mathematics 5 Acta Numerica 4 Acta Mechanica 4 Journal of the Mechanics and Physics of Solids 4 Linear and Multilinear Algebra 4 SIAM Journal on Numerical Analysis 4 Mathematical and Computer Modelling 4 Journal of Nonlinear Science 4 Communications in Numerical Methods in Engineering 4 Mathematical Problems in Engineering 4 Archives of Computational Methods in Engineering 4 JSIAM Letters 4 SIAM/ASA Journal on Uncertainty Quantification 3 International Journal of Solids and Structures 3 Wave Motion 3 Automatica 3 Theoretical Computer Science 3 Systems & Control Letters 3 Computer Aided Geometric Design 3 Computational Mechanics 3 Numerical Methods for Partial Differential Equations 3 SIAM Review 3 Computing and Visualization in Science 3 Mathematical and Computer Modelling of Dynamical Systems 3 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics 3 International Journal of Modern Physics C 3 Concurrency and Computation: Practice & Experience 3 Journal of Numerical Mathematics 3 Journal of Applied Mathematics and Computing 3 Multiscale Modeling & Simulation 2 Applicable Analysis 2 International Journal of Control 2 International Journal of Heat and Mass Transfer 2 International Journal for Numerical and Analytical Methods in Geomechanics 2 Mathematical Biosciences 2 Journal of Soviet Mathematics 2 Numerical Functional Analysis and Optimization 2 Studies in Applied Mathematics 2 Journal of Symbolic Computation 2 Computers & Operations Research 2 Neural Networks 2 Annals of Operations Research 2 Journal of Global Optimization 2 Annals of Physics 2 Applied Mathematical Modelling 2 Russian Journal of Numerical Analysis and Mathematical Modelling 2 Journal of Geodesy 2 Parallel Algorithms and Applications 2 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 2 International Journal of Numerical Modelling 2 European Journal of Mechanics. B. Fluids 2 International Journal of Applied Mathematics and Computer Science 2 Combustion Theory and Modelling 2 Journal of Applied Mathematics 2 Journal of Industrial and Management Optimization 2 The Journal of Prime Research in Mathematics 2 SIAM Journal on Imaging Sciences 2 Mathematical Programming Computation 2 Statistics and Computing 1 Astrophysics and Space Science ...and 99 more Serials
all top 5
#### Cited in 48 Fields
945 Numerical analysis (65-XX) 193 Partial differential equations (35-XX) 174 Fluid mechanics (76-XX) 154 Linear and multilinear algebra; matrix theory (15-XX) 85 Mechanics of deformable solids (74-XX) 82 Operations research, mathematical programming (90-XX) 69 Computer science (68-XX) 41 Quantum theory (81-XX) 39 Optics, electromagnetic theory (78-XX) 38 Statistics (62-XX) 37 Ordinary differential equations (34-XX) 33 Calculus of variations and optimal control; optimization (49-XX) 33 Statistical mechanics, structure of matter (82-XX) 29 Biology and other natural sciences (92-XX) 26 Operator theory (47-XX) 25 Systems theory; control (93-XX) 23 Probability theory and stochastic processes (60-XX) 19 Classical thermodynamics, heat transfer (80-XX) 15 Approximations and expansions (41-XX) 15 Integral equations (45-XX) 14 Potential theory (31-XX) 14 Dynamical systems and ergodic theory (37-XX) 12 Geophysics (86-XX) 10 Information and communication theory, circuits (94-XX) 8 Functions of a complex variable (30-XX) 8 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 7 Combinatorics (05-XX) 5 Field theory and polynomials (12-XX) 5 Special functions (33-XX) 5 Mechanics of particles and systems (70-XX) 5 Astronomy and astrophysics (85-XX) 4 History and biography (01-XX) 4 Harmonic analysis on Euclidean spaces (42-XX) 4 Global analysis, analysis on manifolds (58-XX) 3 Sequences, series, summability (40-XX) 2 Algebraic geometry (14-XX) 2 Real functions (26-XX) 2 Difference and functional equations (39-XX) 2 Mathematics education (97-XX) 1 General and overarching topics; collections (00-XX) 1 Commutative algebra (13-XX) 1 Group theory and generalizations (20-XX) 1 Integral transforms, operational calculus (44-XX) 1 Geometry (51-XX) 1 Convex and discrete geometry (52-XX) 1 Differential geometry (53-XX) 1 General topology (54-XX) 1
#### Wikidata Timeline
The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata.
| 2021-01-24T07:04:31 |
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|
http://pdglive.lbl.gov/Particle.action?init=0&node=B023&home=BXXX025
|
${{\boldsymbol \Sigma}}$ BARYONS($\boldsymbol S$ = $-1$, $\boldsymbol I$ = 1) ${{\mathit \Sigma}^{+}}$ = ${\mathit {\mathit u}}$ ${\mathit {\mathit u}}$ ${\mathit {\mathit s}}$, ${{\mathit \Sigma}^{0}}$ = ${\mathit {\mathit u}}$ ${\mathit {\mathit d}}$ ${\mathit {\mathit s}}$, ${{\mathit \Sigma}^{-}}$ = ${\mathit {\mathit d}}$ ${\mathit {\mathit d}}$ ${\mathit {\mathit s}}$ INSPIRE search
# ${{\boldsymbol \Sigma}{(1480)}}$ Bumps $I(J^P)$ = $1(?^{?})$
These are peaks seen in ${{\mathit \Lambda}}{{\mathit \pi}}$ and ${{\mathit \Sigma}}{{\mathit \pi}}$ spectra in the reaction ${{\mathit \pi}^{+}}$ ${{\mathit p}}$ $\rightarrow$ ( ${{\mathit Y}}{{\mathit \pi}}$ ) ${{\mathit K}^{+}}$ at 1.7 ${\mathrm {GeV/}}\mathit c$. Also, the ${{\mathit Y}}$ polarization oscillates in the same region. MILLER 1970 suggests a possible alternate explanation in terms of a reflection of ${{\mathit N}{(1675)}}$ $\rightarrow$ ${{\mathit \Lambda}}{{\mathit K}}$ decay. However, such an explanation for the ( ${{\mathit \Sigma}^{+}}{{\mathit \pi}^{0}}$ ) ${{\mathit K}^{+}}$ channel in terms of ${{\mathit \Delta}{(1650)}}$ $\rightarrow$ ${{\mathit \Sigma}}{{\mathit K}}$ decay seems unlikely (see PAN 1970 ). In addition such reflections would also have to account for the oscillation of the ${{\mathit Y}}$ polarization in the 1480 MeV region. HANSON 1971 , with less data than PAN 1970 , can neither confirm nor deny the existence of this state. MAST 1975 sees no structure in this region in ${{\mathit K}^{-}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit \Lambda}}{{\mathit \pi}^{0}}$ . ENGELEN 1980 performs a multichannel analysis of ${{\mathit K}^{-}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit p}}{{\overline{\mathit K}}^{0}}{{\mathit \pi}^{-}}$ at 4.2 ${\mathrm {GeV/}}\mathit c$. They observe a 3.5 standard-deviation signal at 1480 MeV in ${{\mathit p}}{{\overline{\mathit K}}^{0}}$ which cannot be explained as a reflection of any competing channel. PRAKHOV 2004 sees no evidence for this or other light ${{\mathit \Sigma}}$ resonances, aside from the ${{\mathit \Sigma}{(1385)}}$, in ${{\mathit K}^{-}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit \Lambda}}{{\mathit \pi}^{0}}{{\mathit \pi}^{0}}$ . ZYCHOR 2006 finds peaks in ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit p}}{{\mathit K}^{+}}$ ( ${{\mathit \pi}^{\pm}}{{\mathit X}^{\mp}}$ ) at $\mathit p_{{\mathrm {beam}}}$ = 3.65$~$GeV/c.
${{\mathit \Sigma}{(1480)}}$ MASS (PRODUCTION EXPERIMENTS) $\approx1480$ MeV
${{\mathit \Sigma}{(1480)}}$ WIDTH (PRODUCTION EXPERIMENTS)
$\Gamma_{1}$ ${{\mathit N}}{{\overline{\mathit K}}}$ 178
$\Gamma_{2}$ ${{\mathit \Lambda}}{{\mathit \pi}}$ 296
$\Gamma_{3}$ ${{\mathit \Sigma}}{{\mathit \pi}}$ 232
| 2019-08-24T16:18:45 |
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https://zbmath.org/authors/?q=ai%3Aharish-chandra.
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## Harish-Chandra
Compute Distance To:
Author ID: harish-chandra. Published as: Harish-Chandra Further Spellings: Хариш-Чандра External Links: MacTutor · MGP · Wikidata · Math-Net.Ru · GND · IdRef
Documents Indexed: 77 Publications since 1944, including 6 Books Biographic References: 16 Publications Co-Authors: 1 Co-Author with 2 Joint Publications 64 Co-Co-Authors
all top 5
### Co-Authors
71 single-authored 2 Borel, Armand 2 Varadarajan, Veeravalli S. 1 DeBacker, Stephen 1 Gangolli, Ramesh 1 Graev, Mark Iosifovich 1 Kolk, Johan A. C. 1 Sally, Paul J. jun.
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### Serials
13 Proceedings of the National Academy of Sciences of the United States of America 10 American Journal of Mathematics 7 Annals of Mathematics. Second Series 6 Transactions of the American Mathematical Society 4 Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences 4 Bulletin of the American Mathematical Society 3 Proceedings of the Indian Academy of Sciences 2 Acta Mathematica 2 Proceedings of the American Mathematical Society 2 Physical Review, II. Series 2 Lecture Notes in Mathematics 1 Publications Mathématiques 1 Inventiones Mathematicae 1 Journal of Functional Analysis 1 Journal de Mathématiques Pures et Appliquées. Neuvième Série 1 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 1 Proceedings of the Cambridge Philosophical Society 1 University Lecture Series 1 Springer Collected Works in Mathematics
all top 5
### Fields
18 Topological groups, Lie groups (22-XX) 8 Abstract harmonic analysis (43-XX) 4 Group theory and generalizations (20-XX) 3 Number theory (11-XX) 2 History and biography (01-XX) 2 Algebraic geometry (14-XX) 2 Nonassociative rings and algebras (17-XX) 2 Functional analysis (46-XX)
### Citations contained in zbMATH Open
71 Publications have been cited 2,601 times in 1,691 Documents Cited by Year
Arithmetic subgroups of algebraic groups. Zbl 0107.14804
Borel, Armand; Harish-Chandra
1962
Spherical functions on a semisimple Lie group. I, II. Zbl 0093.12801
Harish-Chandra
1958
Discrete series for semisimple Lie groups. II: Explicit determination of the characters. Zbl 0199.20102
Harish-Chandra
1966
Differential operators on a semisimple Lie algebra. Zbl 0072.01901
Harish-Chandra
1957
Harmonic analysis on real reductive groups. I: The theory of the constant term. Zbl 0315.43002
Harish-Chandra
1975
Harmonic analysis on real reductive groups. III: The Maass-Selberg relations and the plancherel formula. Zbl 0331.22007
Harish-Chandra
1976
Harmonic analysis on reductive p-adic groups. Notes by G van Dijk. Zbl 0202.41101
Harish-Chandra
1970
Representations of a semisimple Lie group on a Banach space. I. Zbl 0051.34002
Harish-Chandra
1953
Automorphic forms on semisimple Lie groups. Notes by J. G. M. Mars. Zbl 0186.04702
Harish-Chandra
1968
Representations of semisimple Lie groups VI. Integrable and square- integrable representations. Zbl 0072.01702
Harish-Chandra
1956
Representations of semisimple Lie groups. II, III. Zbl 0055.34002
Harish-Chandra
1954
Representations of semisimple Lie groups. IV. Zbl 0066.35603
Harish-Chandra
1955
Discrete series for semisimple Lie groups. I: Construction of invariant eigendistributions. Zbl 0152.13402
Harish-Chandra
1965
Invariant eigendistributions on a semisimple Lie group. Zbl 0199.46402
Harish-Chandra
1965
On some applications of the universal envelopping algebra of a semisimple Lie algebra. Zbl 0042.12701
Harish-Chandra
1951
The characters of semisimple Lie groups. Zbl 0072.01801
Harish-Chandra
1956
Representations of semisimple Lie groups. V. Zbl 0070.11602
Harish-Chandra
1956
Harmonic analysis on real reductive groups. II: Wave-packets in the Schwartz space. Zbl 0341.43010
Harish-Chandra
1976
The Plancherel formula for complex semisimple Lie groups. Zbl 0055.34003
Harish-Chandra
1954
Invariant differential operators and distributions on a semisimple Lie algebra. Zbl 0161.33804
Harish-Chandra
1964
Two theorems on semi-simple Lie groups. Zbl 0199.46403
Harish-Chandra
1966
Harmonic analysis on reductive p-adic groups. Zbl 0289.22018
Harish-Chandra
1973
Admissible invariant distributions on reductive $$p$$-adic groups. Notes by Stephen DeBacker and Paul J. Sally jun. Zbl 0928.22017
Harish-Chandra
1999
On representations of Lie algebras. Zbl 0035.01901
Harish-Chandra
1949
Fourier transforms on a semisimple Lie algebra. I. Zbl 0077.25205
Harish-Chandra
1957
A formula for semisimple Lie groups. Zbl 0080.10201
Harish-Chandra
1957
Invariant distributions on Lie algebras. Zbl 0131.33302
Harish-Chandra
1964
Harmonic analysis on semi-simple Lie groups. Zbl 0212.15101
Harish-Chandra
1970
Eisenstein series over finite fields. Zbl 0226.20049
Harish-Chandra
1970
Harish-Chandra
1978
Invariant eigendistributions on semisimple Lie groups. Zbl 0115.10801
Harish-Chandra
1963
On the equations of motion of point particles. Zbl 0063.01931
Harish-Chandra
1946
Plancherel formula for the $$2\times 2$$ real unimodular group. Zbl 0049.15703
Harish-Chandra
1952
Invariant eigendistributions on a semisimple Lie algebra. Zbl 0199.46401
Harish-Chandra
1965
A submersion principle and its applications. Zbl 0512.22010
Harish-Chandra
1981
The correspondence between the particle and the wave aspects of the meson and the photon. Zbl 0060.45308
Harish-Chandra
1946
On relativistic wave equations. Zbl 0032.37202
Harish-Chandra
1947
Representations of semisimple Lie groups on a Banach space. Zbl 0042.12602
Harish-Chandra
1951
Some results on an invariant integral on a semi-simple Lie algebra. Zbl 0152.13401
Harish-Chandra
1964
Lie algebras and the Tannaka duality theorem. Zbl 0036.15701
Harish-Chandra
1950
Supertempered distributions on real reductive groups. Zbl 0512.22005
Harish-Chandra
1983
Invariant differential operators on a semisimple Lie algebra. Zbl 0072.02001
Harish-Chandra
1956
On the theory of the Eisenstein integral. Zbl 0245.22019
Harish-Chandra
1972
On the radical of a Lie algebra. Zbl 0036.29804
Harish-Chandra
1950
Representations of semisimple Lie groups. II, III, IV. Zbl 0045.38602
Harish-Chandra
1951
Some results on differential equations and their applications. Zbl 0161.33803
Harish-Chandra
1959
On a lemma of F. Bruhat. Zbl 0070.26004
Harish-Chandra
1956
On the characters of a semisimple Lie group. Zbl 0065.35002
Harish-Chandra
1955
Plancherel formula for complex semisimple Lie groups. Zbl 0044.32801
Harish-Chandra
1951
Automorphic forms on a semisimple Lie group. Zbl 0085.10401
Harish-Chandra
1959
The characters of reductive p-adic groups. Zbl 0365.22016
Harish-Chandra
1977
Fourier transforms on a semisimple Lie algebra II. Zbl 0079.32901
Harish-Chandra
1957
Arithmetic subgroups of algebraic groups. Zbl 0119.37001
Borel, Armand; Harish-Chandra
1961
Motion of an electron in the field of a magnetic pole. Zbl 0032.09602
Harish-Chandra
1948
Representations of semisimple Lie groups. Zbl 0080.10202
Harish-Chandra
1957
Collected papers. Volume I (1944–1954). Volume II (1955–1958). Volume III (1959–1968). Volume IV (1970–1983). Edited by V. S. Varadarajan. Reprint of the 1984 edition. Zbl 1325.01031
Harish-Chandra
2014
On the Plancherel formula for the right-invariant functions on a semisimple Lie group. Zbl 0055.10303
Harish-Chandra
1954
On the algebra of the meson matrices. Zbl 0029.09606
Harish-Chandra
1947
Some applications of the Schwartz space of a semisimple Lie group. Zbl 0212.15102
Harish-Chandra
1970
Relativistic equations for elementary particles. Zbl 0031.14201
Harish-Chandra
1948
Faithful representation of Lie algebras. Zbl 0032.25201
Harish-Chandra
1949
On faithful representations of Lie groups. Zbl 0039.02004
Harish-Chandra
1950
Spherical functions on a semisimple Lie group. Zbl 0077.25204
Harish-Chandra
1957
Harmonic analysis on semisimple Lie groups. Zbl 0201.46002
Harish-Chandra
1968
Automorphic forms on semisimple Lie groups. (Avtomorfnye formy na poluprostyh gruppah Li.) Übersetzung aus dem Englischen von D. A. Kazhdan. Herausgegeben von M. I. Graev. Zbl 0223.22011
Harish-Chandra
1971
Representations of semisimple Lie groups. V. Zbl 0056.25901
Harish-Chandra
1954
On the removal of the infinite self-energies of point-particles. Zbl 0063.01930
Harish-Chandra
1944
A submersion principle and its applications. Zbl 0485.22023
Harish-Chandra
1981
A formula for semisimple Lie groups. Zbl 0072.02002
Harish-Chandra
1956
Collected papers V (posthumous). Harmonic analysis in real semisimple groups. Edited by Ramesh Gangolli and V. S. Varadarajan. With assistance from Johan Kolk. Zbl 1390.22003
Harish-Chandra
2018
Representations of semisimple Lie groups. VI. Zbl 0056.25902
Harish-Chandra
1954
Collected papers V (posthumous). Harmonic analysis in real semisimple groups. Edited by Ramesh Gangolli and V. S. Varadarajan. With assistance from Johan Kolk. Zbl 1390.22003
Harish-Chandra
2018
Collected papers. Volume I (1944–1954). Volume II (1955–1958). Volume III (1959–1968). Volume IV (1970–1983). Edited by V. S. Varadarajan. Reprint of the 1984 edition. Zbl 1325.01031
Harish-Chandra
2014
Admissible invariant distributions on reductive $$p$$-adic groups. Notes by Stephen DeBacker and Paul J. Sally jun. Zbl 0928.22017
Harish-Chandra
1999
Supertempered distributions on real reductive groups. Zbl 0512.22005
Harish-Chandra
1983
A submersion principle and its applications. Zbl 0512.22010
Harish-Chandra
1981
A submersion principle and its applications. Zbl 0485.22023
Harish-Chandra
1981
Harish-Chandra
1978
The characters of reductive p-adic groups. Zbl 0365.22016
Harish-Chandra
1977
Harmonic analysis on real reductive groups. III: The Maass-Selberg relations and the plancherel formula. Zbl 0331.22007
Harish-Chandra
1976
Harmonic analysis on real reductive groups. II: Wave-packets in the Schwartz space. Zbl 0341.43010
Harish-Chandra
1976
Harmonic analysis on real reductive groups. I: The theory of the constant term. Zbl 0315.43002
Harish-Chandra
1975
Harmonic analysis on reductive p-adic groups. Zbl 0289.22018
Harish-Chandra
1973
On the theory of the Eisenstein integral. Zbl 0245.22019
Harish-Chandra
1972
Automorphic forms on semisimple Lie groups. (Avtomorfnye formy na poluprostyh gruppah Li.) Übersetzung aus dem Englischen von D. A. Kazhdan. Herausgegeben von M. I. Graev. Zbl 0223.22011
Harish-Chandra
1971
Harmonic analysis on reductive p-adic groups. Notes by G van Dijk. Zbl 0202.41101
Harish-Chandra
1970
Harmonic analysis on semi-simple Lie groups. Zbl 0212.15101
Harish-Chandra
1970
Eisenstein series over finite fields. Zbl 0226.20049
Harish-Chandra
1970
Some applications of the Schwartz space of a semisimple Lie group. Zbl 0212.15102
Harish-Chandra
1970
Automorphic forms on semisimple Lie groups. Notes by J. G. M. Mars. Zbl 0186.04702
Harish-Chandra
1968
Harmonic analysis on semisimple Lie groups. Zbl 0201.46002
Harish-Chandra
1968
Discrete series for semisimple Lie groups. II: Explicit determination of the characters. Zbl 0199.20102
Harish-Chandra
1966
Two theorems on semi-simple Lie groups. Zbl 0199.46403
Harish-Chandra
1966
Discrete series for semisimple Lie groups. I: Construction of invariant eigendistributions. Zbl 0152.13402
Harish-Chandra
1965
Invariant eigendistributions on a semisimple Lie group. Zbl 0199.46402
Harish-Chandra
1965
Invariant eigendistributions on a semisimple Lie algebra. Zbl 0199.46401
Harish-Chandra
1965
Invariant differential operators and distributions on a semisimple Lie algebra. Zbl 0161.33804
Harish-Chandra
1964
Invariant distributions on Lie algebras. Zbl 0131.33302
Harish-Chandra
1964
Some results on an invariant integral on a semi-simple Lie algebra. Zbl 0152.13401
Harish-Chandra
1964
Invariant eigendistributions on semisimple Lie groups. Zbl 0115.10801
Harish-Chandra
1963
Arithmetic subgroups of algebraic groups. Zbl 0107.14804
Borel, Armand; Harish-Chandra
1962
Arithmetic subgroups of algebraic groups. Zbl 0119.37001
Borel, Armand; Harish-Chandra
1961
Some results on differential equations and their applications. Zbl 0161.33803
Harish-Chandra
1959
Automorphic forms on a semisimple Lie group. Zbl 0085.10401
Harish-Chandra
1959
Spherical functions on a semisimple Lie group. I, II. Zbl 0093.12801
Harish-Chandra
1958
Differential operators on a semisimple Lie algebra. Zbl 0072.01901
Harish-Chandra
1957
Fourier transforms on a semisimple Lie algebra. I. Zbl 0077.25205
Harish-Chandra
1957
A formula for semisimple Lie groups. Zbl 0080.10201
Harish-Chandra
1957
Fourier transforms on a semisimple Lie algebra II. Zbl 0079.32901
Harish-Chandra
1957
Representations of semisimple Lie groups. Zbl 0080.10202
Harish-Chandra
1957
Spherical functions on a semisimple Lie group. Zbl 0077.25204
Harish-Chandra
1957
Representations of semisimple Lie groups VI. Integrable and square- integrable representations. Zbl 0072.01702
Harish-Chandra
1956
The characters of semisimple Lie groups. Zbl 0072.01801
Harish-Chandra
1956
Representations of semisimple Lie groups. V. Zbl 0070.11602
Harish-Chandra
1956
Invariant differential operators on a semisimple Lie algebra. Zbl 0072.02001
Harish-Chandra
1956
On a lemma of F. Bruhat. Zbl 0070.26004
Harish-Chandra
1956
A formula for semisimple Lie groups. Zbl 0072.02002
Harish-Chandra
1956
Representations of semisimple Lie groups. IV. Zbl 0066.35603
Harish-Chandra
1955
On the characters of a semisimple Lie group. Zbl 0065.35002
Harish-Chandra
1955
Representations of semisimple Lie groups. II, III. Zbl 0055.34002
Harish-Chandra
1954
The Plancherel formula for complex semisimple Lie groups. Zbl 0055.34003
Harish-Chandra
1954
On the Plancherel formula for the right-invariant functions on a semisimple Lie group. Zbl 0055.10303
Harish-Chandra
1954
Representations of semisimple Lie groups. V. Zbl 0056.25901
Harish-Chandra
1954
Representations of semisimple Lie groups. VI. Zbl 0056.25902
Harish-Chandra
1954
Representations of a semisimple Lie group on a Banach space. I. Zbl 0051.34002
Harish-Chandra
1953
Plancherel formula for the $$2\times 2$$ real unimodular group. Zbl 0049.15703
Harish-Chandra
1952
On some applications of the universal envelopping algebra of a semisimple Lie algebra. Zbl 0042.12701
Harish-Chandra
1951
Representations of semisimple Lie groups on a Banach space. Zbl 0042.12602
Harish-Chandra
1951
Representations of semisimple Lie groups. II, III, IV. Zbl 0045.38602
Harish-Chandra
1951
Plancherel formula for complex semisimple Lie groups. Zbl 0044.32801
Harish-Chandra
1951
Lie algebras and the Tannaka duality theorem. Zbl 0036.15701
Harish-Chandra
1950
On the radical of a Lie algebra. Zbl 0036.29804
Harish-Chandra
1950
On faithful representations of Lie groups. Zbl 0039.02004
Harish-Chandra
1950
On representations of Lie algebras. Zbl 0035.01901
Harish-Chandra
1949
Faithful representation of Lie algebras. Zbl 0032.25201
Harish-Chandra
1949
Motion of an electron in the field of a magnetic pole. Zbl 0032.09602
Harish-Chandra
1948
Relativistic equations for elementary particles. Zbl 0031.14201
Harish-Chandra
1948
On relativistic wave equations. Zbl 0032.37202
Harish-Chandra
1947
On the algebra of the meson matrices. Zbl 0029.09606
Harish-Chandra
1947
On the equations of motion of point particles. Zbl 0063.01931
Harish-Chandra
1946
The correspondence between the particle and the wave aspects of the meson and the photon. Zbl 0060.45308
Harish-Chandra
1946
On the removal of the infinite self-energies of point-particles. Zbl 0063.01930
Harish-Chandra
1944
all top 5
### Cited by 1,460 Authors
20 Helgason, Sigurdur 20 Herb, Rebecca A. 16 Schlichtkrull, Henrik 16 Wallach, Nolan Russell 15 Delorme, Patrick 14 Arthur, James Greig 14 Harish-Chandra 13 Knapp, Anthony William 12 Havas, Peter 12 Schwermer, Joachim 12 Van den Ban, Erik Peter 11 Kazhdan, David A. 11 Kieburg, Mario 11 Kobayashi, Toshiyuki 11 Ólafsson, Gestur 11 Schmid, Wilfried 11 Wolf, Joseph Albert 10 Johnson, Kenneth D. 10 Opdam, Eric Marcus 10 Varadarajan, Veeravalli S. 10 Vergne, Michèle 9 Barbasch, Dan M. 9 Chuah, Meng-Kiat 9 Eguchi, Masaaki 9 Flicker, Yuval Z. 9 Przebinda, Tomasz 9 van Dijk, Gerrit 9 Vogan, David Alexander jun. 8 Clozel, Laurent 8 Deitmar, Anton 8 Huang, Jing-Song 8 Muić, Goran 8 Ørsted, Bent 8 Williams, Floyd L. 7 Borel, Armand 7 Duflo, Michel 7 Fioresi, Rita 7 Guhr, Thomas 7 Heckman, Gert 7 Krötz, Bernhard J. 7 Lepowsky, James 7 Moy, Allen 7 Paulin, Frédéric 7 Shahidi, Freydoon 7 Speh, Birgit 7 Stein, Elias Menachem 7 Torasso, Pierre 6 Casselman, William A. 6 Curtis, Charles W. 6 Dixmier, Jacques 6 Harris, Benjamin 6 Hecht, Henryk 6 Henniart, Guy M. 6 Hochs, Peter 6 Howe, Roger Evans 6 Jakobsen, Hans Plesner 6 Lemaire, Bertrand 6 Neeb, Karl-Hermann 6 Nevo, Amos 6 Oda, Takayuki 6 Okamoto, Kiyosato 6 Rallis, Stephen James 6 Sarnak, Peter Clive 6 Stanton, Robert J. 6 Vargas, Jorge Antonio 5 Aizenbud, Avraham 5 Bergeron, Nicolas 5 DeBacker, Stephen 5 Gel’fand, Israil’ Moiseevich 5 Goldberg, David 5 Gorodnik, Alexander 5 Gourevitch, Dmitry 5 Gross, Benedict Hyman 5 Harnad, John 5 Jespers, Eric 5 Kuit, Job J. 5 Lohoué, Noël 5 Morozov, Alexei Yurievich 5 Müller, Werner 5 Oh, Hee 5 Parkkonen, Jouni 5 Rowe, David J. 5 Sally, Paul J. jun. 5 Sekiguchi, Jiro 5 Šijački, Djordje 5 Strahov, Eugene 5 Warner, Garth 4 Adams, Jeffrey David 4 Akemann, Gernot 4 Barchini, Leticia 4 Ben Saïd, Salem 4 Beuzart-Plessis, Raphaël 4 Blattner, Robert J. 4 Bouaziz, Abderrazak 4 Crisp, Tyrone 4 Duncan, Tyrone E. 4 Flensted-Jensen, Mogens 4 Forrester, Peter J. 4 Gelbart, Stephen S. 4 Gruber, Bruno J. ...and 1,360 more Authors
all top 5
### Cited in 215 Serials
124 Journal of Functional Analysis 109 Transactions of the American Mathematical Society 85 Inventiones Mathematicae 75 Duke Mathematical Journal 67 Mathematische Annalen 60 Journal of Mathematical Physics 56 Compositio Mathematica 47 Advances in Mathematics 43 Journal of Algebra 38 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 38 Bulletin of the American Mathematical Society 34 Communications in Mathematical Physics 32 Mathematische Zeitschrift 30 Proceedings of the American Mathematical Society 27 Physical Review, II. Series 23 Acta Mathematica 23 Representation Theory 22 Functional Analysis and its Applications 22 Journal of Number Theory 21 Proceedings of the Japan Academy. Series A 21 Journal of High Energy Physics 19 Israel Journal of Mathematics 19 Annales de l’Institut Fourier 18 Proceedings of the Japan Academy 17 Journal für die Reine und Angewandte Mathematik 17 Bulletin of the American Mathematical Society. New Series 16 Publications Mathématiques 14 Geometriae Dedicata 14 Manuscripta Mathematica 14 Journal of the American Mathematical Society 13 Letters in Mathematical Physics 12 Bulletin de la Société Mathématique de France 12 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 12 Transformation Groups 11 Journal of Geometry and Physics 11 Geometric and Functional Analysis. GAFA 10 Tohoku Mathematical Journal. Second Series 10 Mémoires de la Société Mathématique de France. Nouvelle Série 10 Indagationes Mathematicae. New Series 10 Selecta Mathematica. New Series 9 Journal of Statistical Physics 9 Nagoya Mathematical Journal 8 Arkiv för Matematik 8 Journal of Pure and Applied Algebra 8 Journal of Soviet Mathematics 8 Monatshefte für Mathematik 8 Publications of the Research Institute for Mathematical Sciences, Kyoto University 8 Journal of the Institute of Mathematics of Jussieu 7 Annals of Global Analysis and Geometry 7 Forum Mathematicum 7 International Journal of Mathematics 7 Journal of Mathematical Sciences (New York) 7 Annals of Mathematics. Second Series 6 Communications in Algebra 6 Annales de l’Institut Henri Poincaré. Nouvelle Série. Section A. Physique Théorique 6 Archiv der Mathematik 6 Memoirs of the American Mathematical Society 6 The Journal of Geometric Analysis 6 Comptes Rendus. Mathématique. Académie des Sciences, Paris 5 International Journal of Modern Physics A 5 Journal of Mathematical Analysis and Applications 5 Nuclear Physics. B 5 Theoretical and Mathematical Physics 5 Acta Applicandae Mathematicae 5 Journal of Lie Theory 5 Groups, Geometry, and Dynamics 5 Random Matrices: Theory and Applications 4 Mathematical Proceedings of the Cambridge Philosophical Society 4 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 4 The Journal of Fourier Analysis and Applications 4 Algebras and Representation Theory 4 Journal of the European Mathematical Society (JEMS) 4 Algebraic & Geometric Topology 4 Central European Journal of Mathematics 4 Journal of Statistical Mechanics: Theory and Experiment 4 Science China. Mathematics 4 Journal de l’École Polytechnique – Mathématiques 3 International Journal of Theoretical Physics 3 Journal d’Analyse Mathématique 3 Mathematical Notes 3 Reviews of Modern Physics 3 Reviews in Mathematical Physics 3 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 3 Commentarii Mathematici Helvetici 3 Glasgow Mathematical Journal 3 Journal of the Mathematical Society of Japan 3 Mathematische Nachrichten 3 Mathematika 3 Differential Geometry and its Applications 3 Linear Algebra and its Applications 3 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 3 Annales de l’Institut Henri Poincaré. Physique Théorique 3 Electronic Research Announcements of the American Mathematical Society 3 Documenta Mathematica 3 Annales Henri Poincaré 3 International Journal of Geometric Methods in Modern Physics 3 International Journal of Number Theory 3 Journal of Modern Dynamics 2 Linear and Multilinear Algebra 2 Physics Letters. B ...and 115 more Serials
all top 5
### Cited in 54 Fields
917 Topological groups, Lie groups (22-XX) 326 Number theory (11-XX) 260 Abstract harmonic analysis (43-XX) 214 Group theory and generalizations (20-XX) 185 Nonassociative rings and algebras (17-XX) 146 Differential geometry (53-XX) 131 Algebraic geometry (14-XX) 115 Quantum theory (81-XX) 103 Several complex variables and analytic spaces (32-XX) 98 Global analysis, analysis on manifolds (58-XX) 77 Manifolds and cell complexes (57-XX) 60 Functional analysis (46-XX) 56 Associative rings and algebras (16-XX) 55 Linear and multilinear algebra; matrix theory (15-XX) 52 Special functions (33-XX) 51 Dynamical systems and ergodic theory (37-XX) 43 Partial differential equations (35-XX) 35 Probability theory and stochastic processes (60-XX) 30 Harmonic analysis on Euclidean spaces (42-XX) 24 Relativity and gravitational theory (83-XX) 23 Operator theory (47-XX) 23 Statistical mechanics, structure of matter (82-XX) 19 Combinatorics (05-XX) 17 Algebraic topology (55-XX) 15 Measure and integration (28-XX) 14 Integral transforms, operational calculus (44-XX) 9 $$K$$-theory (19-XX) 9 Functions of a complex variable (30-XX) 9 Statistics (62-XX) 8 Commutative algebra (13-XX) 8 Mechanics of particles and systems (70-XX) 7 Geometry (51-XX) 6 History and biography (01-XX) 6 Category theory; homological algebra (18-XX) 6 Potential theory (31-XX) 5 Mathematical logic and foundations (03-XX) 5 Ordinary differential equations (34-XX) 5 Convex and discrete geometry (52-XX) 5 Numerical analysis (65-XX) 5 Information and communication theory, circuits (94-XX) 4 Optics, electromagnetic theory (78-XX) 3 General and overarching topics; collections (00-XX) 3 Approximations and expansions (41-XX) 3 General topology (54-XX) 2 Field theory and polynomials (12-XX) 2 Difference and functional equations (39-XX) 2 Sequences, series, summability (40-XX) 2 Calculus of variations and optimal control; optimization (49-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 2 Biology and other natural sciences (92-XX) 2 Systems theory; control (93-XX) 1 Real functions (26-XX) 1 Computer science (68-XX) 1 Fluid mechanics (76-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.
| 2022-07-07T09:48:33 |
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|
http://physics.nist.gov/PhysRefData/MolSpec/Diatomic/Html/sec3.html
|
3. 3Σ-Ground State Molecules
The O2 and SO molecules are the only diatomic molecules in this compilation which possess a 3Σ electronic ground state. Since the energy level calculations differ quite markedly from those in section 2, a detailed description of the calculations will be given here. Although a number of authors have treated this problem in slightly different manners than that discussed below, for uniformity we have chosen the formulation which corresponds closest to that employed in the previous section.
In order to describe the rotational spectra of this class, Hund's coupling case (b) was chosen as the starting point. The rotational levels are characterized by the rotational angular momentum quantum number, N, and the resultant angular momentum quantum number, J, which includes the total electron spin angular momentum. If the molecule has nuclei with non-zero nuclear spin, I, these are coupled to J to form the total angular momentum quantum number F, whereby coupling case (bβJ) is assumed here. For pure case (bβJ) the electric dipole transitions occur with the selection rules: ΔN = ± 1, ΔF = 0, ± 1, and ΔJ = 0, ± 1, in the absence of external fields. Since an intermediate coupling case is actually observed, transitions are allowed for ΔN = ± 3. The magnetic dipole transitions occur with the selection rules: ΔN = 0, ± 2 and ΔJ = 0, ± 1.
a. Molecular Parameters and Energy Level Formulation
The rotational energy levels may be described with the Hamiltonian [8]: = 2/3 λ(3Sz2 - S2) + γ(N · S) + BN2 whereby a molecule fixed cartesian coordinate system is employed with the z-axis along the molecular axis. The first term describes the spin-spin interaction, the second term refers to the spin-rotation interaction and the last term describes the rotational kinetic energy. Since the coefficients λ, γ and B are functions of the internuclear distance, r, centrifugal distortion and vibration-rotation interactions arise. If we define the coefficients as follows:
(eq10)
where , the vibrational state dependence of the molecular parameters is given by:
(eq11)
where the Dunham coefficients, Ylj , are defined in section 2 and
(eq12)
(eq13)
The centrifugal distortion terms are defined as:
(eq14)
(eq15) and (eq16)
With these definitions, the rotational energy levels are given in the form [9]:
(eq17)
(eq18)
The sextic terms, Hυ, of the rotational energy are neglected because they cannot be determined from the data presently available for the spectral observations on 3Σ electronic ground state molecules. The energy equations are utilized with the selection rules stated above to allow the determination of the molecular constants Bυ, λυ, γυ, Dυ, ρυ, and δυ, for vibrational state υ. Combining the data available for various vibrational states allows the derivation of potential coefficients, ai, and the expansion parameters of λ and γ.
Magnetic hyperfine structure has been described by Frosch and Foley [10] in terms of the determinable parameters, b and c. The nuclear electric quadrupole hyperfine structure is described by Amano, et al. [11] and results in determination of the constant, eQqυ, as defined in the discussion of 1Σ ground electronic state molecules.
b. List of Symbols
Symbols (See section 2b for additional definitions.)
ai Dunham potential coefficients.
λυ Spin-spin coupling parameter in the υth vibrational state (MHz).
αλ Spin-spin vibrational constant (MHz).
γυ Spin-rotation coupling parameter in the υth vibrational state (MHz).
αγ Coefficient in the power series expansion of γυ.
ρυ Centrifugal distortion correction to λυ (MHz).
δυ Centrifugal distortion correction to γυ (MHz) .
λeλ(1)λ(2) Expansion coefficients of λ in a power series of ξ.
γe, γ(1) Expansion coefficients of γ in a power series of ξ.
b, c Magnetic hyperfine coupling constants:
(eq19a) (eq19b) where µB is the Bohr magneton, µN the nuclear magneton and gN, the nuclear g-valve.
| 2015-05-28T15:59:47 |
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|
http://xxx.lanl.gov/abs/0710.3590
|
astro-ph
(what is this?)
# Title: Protoplanetary disk fragmentation with varying radiative physics, initial conditions and numerical techniques
Authors: Lucio Mayer (University of Zurich and ETH Zurich), Artur Gawryszczak (Max Planck Institute fuer Astronomie, Heidelberg, and Copernicus Astronomical Center, Warsaw)
Abstract: We review recent results of SPH simulations of gravitational instability in gaseous protoplanetary disks,emphasizing the role of thermodynamics in both isolated and binary systems. Contradictory results appeared in the literature regarding disk fragmentation at tens of AU from the central star are likely due to the different treatment of radiation physics as well as reflecting different initial conditions. Further progress on the subject requires extensive comparisons between different codes with the requirement that the same initial conditions are adopted. It is discussed how the local conditions of the disks undergoing fragmentation at $R < 25$ AU in recent SPH simulations are in rough agreement with the prediction of analytical models, with small differences being likely related to the inability of analytical models to account for the dynamics and thermodynamics of three-dimensional spiral shocks. We report that radically different adaptive hydrodynamical codes, SPH and adaptive mesh refinement (AMR), yield very similar results on disk fragmentation at comparable resolution in the simple case of an isothermal equation of state. A high number of refinements in AMR codes is necessary but not sufficient to correctly follow fragmentation, rather an initial resolution of the grid high enough to capture the wavelength of the strongest spiral modes when they are still barely nonlinear is essential. These tests represent a useful benchmark and a starting point for a forthcoming code comparison with realistic radiation physics.
Comments: 13 pages, 4 figures, invited review, proceedings of the Conference "Extreme Solar Systems", Santorini, Greece, June 25-29, 2007, slightly extended version with bigger figures Subjects: Astrophysics (astro-ph) Cite as: arXiv:0710.3590 [astro-ph] (or arXiv:0710.3590v1 [astro-ph] for this version)
## Submission history
From: Lucio Mayer [view email]
[v1] Fri, 19 Oct 2007 17:58:05 GMT (344kb)
| 2014-04-24T00:22:59 |
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|
https://lammps.sandia.gov/doc/compute_edpd_temp_atom.html
|
# compute edpd/temp/atom command
## Syntax
compute ID group-ID edpd/temp/atom
• ID, group-ID are documented in compute command
• edpd/temp/atom = style name of this compute command
## Examples
compute 1 all edpd/temp/atom
## Description
Define a computation that calculates the per-atom temperature for each eDPD particle in a group.
The temperature is a local temperature derived from the internal energy of each eDPD particle based on the local equilibrium hypothesis. For more details please see (Espanol1997) and (Li2014).
## Output info
This compute calculates a per-atom vector, which can be accessed by any command that uses per-atom values from a compute as input. See the Howto output doc page for an overview of LAMMPS output options.
The per-atom vector values will be in temperature units.
## Restrictions
This compute is part of the USER-MESODPD package. It is only enabled if LAMMPS was built with that package. See the Build package doc page for more info.
## Default
none
(Espanol1997) Espanol, Europhys Lett, 40(6): 631-636 (1997). DOI: 10.1209/epl/i1997-00515-8
(Li2014) Li, Tang, Lei, Caswell, Karniadakis, J Comput Phys, 265: 113-127 (2014). DOI: 10.1016/j.jcp.2014.02.003.
| 2020-09-20T04:29:29 |
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|
https://ftp.aimsciences.org/article/doi/10.3934/proc.2011.2011.475
|
Article Contents
Article Contents
# Comparing the efficiency of numerical techniques for the integration of variational equations
• We present a comparison of different numerical techniques for the integration of variational equations. The methods presented can be applied to any autonomous Hamiltonian system whose kinetic energy is quadratic in the generalized momenta, and whose potential is a function of the generalized positions. We apply the various techniques to the well-known H´enon-Heiles system, and use the Smaller Alignment Index (SALI) method of chaos detection to evaluate the percentage of its chaotic orbits. The accuracy and the speed of the integration schemes in evaluating this percentage are used to investigate the numerical efficiency of the various techniques.
Mathematics Subject Classification: Primary: 37M25, 65P10; Secondary: 70H07, 37J99, 65P20.
Citation:
Open Access Under a Creative Commons license
| 2023-03-22T02:18:22 |
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|
https://de.overleaf.com/articles/involutory-property-of-the-discrete-hartley-transform/mspfrqwxmtmr
|
Zum Inhalt springen
Autor
Frank the Bunny
Letzte Aktualisierung
7 years ago
Lizenz
Creative Commons CC BY 4.0
AbstraktDiscret Hartley Transform is a unitary transform although its proof is hard to find in the Web. This short note explains that the Discrete Hartley Transform is an involution, which implies that this transform is unitary indeed.
| 2023-03-29T01:20:57 |
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# Volume 3, Number 3
o - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - o
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- May 16, 1996 -
- O P - S F N E T Volume 3, Number 3 -
- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ -
- Editors: -
- Tom H. Koornwinder [email protected] -
- Martin Muldoon [email protected] -
- -
- The Electronic News Net of the SIAM Activity Group -
- on Orthogonal Polynomials and Special Functions -
- -
- Please send contributions to: [email protected] -
- & address changes to: [email protected] -
- -
o - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - o
Today's Topics:
1. Minisymposium on Modern Topics in Orthogonal System
2. Errata and additions to earlier issues of OP-SF Net
3. International Memorial Conference D.S. Mitrinovic
4. Symmetries and Integrability of Difference Equations, Canterbury
5. MSRI program on Combinatorics
6. Workshop on Special Functions & Differential Equations, Madras
7. Waleed Al-Salam 1926-1996
8. Contents of Delft Proceedings
9. Foata Festschrift
10. New book on integral transforms
12. Revising the 1991 Mathematics Subject Classification
15. ftp site for papers in Orthogonal Polynomials and
Special Functions
16. Obtaining back issues of OP-SF Net and submitting contributions
Calendar of events: see issue/topic:
1996
May 13-26: CRM Workshop on the Theory of Special Functions 3.1 #8
May 22-24: Special Functions session at International Joint
Mathematics Meeting (Antwerp) 3.2 #6
June 20-22: International Memorial Conference D.S. Mitrinovic 3.3 #4
June 23-27: Joint summer research conference on Random Matrices,
Statistical Mechanics, and Painleve Transcendents 2.6 #8
June 24-26: International Workshop on Orthogonal Polynomials in
July 1-5: Meeting in Canterbury on Symmetries and Integrability of
Difference Equations 2.4 #6 and 3.3 #4
July 1-7: XVth Workshop on Geometric Methods in Physics, Poland 3.1 #10
July 15-20: International Colloquium on Group Theoretical Methods in
Physics, Goslar, Germany 3.1 #11
July 21-26: ICCAM 96, Leuven, Belgium 3.1 #12
July 22-26: SIAM Annual Meeting in Kansas City 3.2 #3
July 23 and 26: Minisymposium on Modern Topics in Orthogonal Systems
at SIAM Annual Meeting in Kansas City 3.3 #1
August 23-30: Workshop Transform Methods & Special Functions 2.6 #10
(Varna, Bulgaria)
September 1 - October 25: MSRI program on
Enumeration and partially ordered sets 3.3 #5
September 23-28: III International Conference on Functional Analysis
and Approximation Theory (Italy) 3.1 #13
1997
January 13-24: Workshop on Special Functions & Differential Equations,
March 17 - May 30: MSRI program on
Symmetric functions and representation theory 3.3 #5
June 24-28: Continued Fractions and Geometric Function Theory 3.2 #8
(Trondheim, Norway)
Topic #1 ----------------- OP-SF NET ------------------ May 16, 1996
From: Willard Miller, Jr. <[email protected]>
Subject: Minisymposium on Modern Topics in Orthogonal Systems
Minisymposium on Modern Topics in Orthogonal Systems
SIAG/OS is sponsoring this minisymposium at the 1996 SIAM Annual Meeting
which will be held July 22-26, 1996 at the Hyatt Regency Crown Center,
Kansas City, Missouri. The minisymposium will be devoted to two modern
extensions of the classical theory of orthogonal systems of special
functions in one real variable. The first topic is Wavelets, organized by
Gilbert G. Walter. Talks by Walter, P. R. Massopust, and T. Q. Nguyen will
be given at the first meeting of the minisymposium, 8:30-10:30 on Tuesday
morning, July 23, and there will be a talk by A. Ron at the second
meeting, 8:30-10:30, Friday, July 26. The second topic, also treated at
the Friday session, is Multivariate Orthogonal Polynomials That Generalize
Jacobi Polynomials with Robert Gustafson as the speaker. Both topics are
of importance in the approximation of functions and representation of
data. Wavelets, in particular, have applications in signal processing,
medicine and biology. The titles and abstracts follow.
Improving wavelet approximations
Gilbert G. Walter
University of Wisconsin-Milwaukee
Abstract: Discrete wavelets are orthogonal systems on the real line (or in
n-space) which generally have superior convergence properties compared to
classical systems. However, they share a shortcoming - Gibbs' phenomenon
- which causes errors at the edge of a truncated signal or image. It was
shown by Shim and Volkmer that this always happens for orthogonal
approximations for all continuous wavelets with sufficient decay. It also
occurs for some interpolating approximations. Ways of avoiding this for
both types of approximations will be presented.
Multiwavelets, Multiresolution Schemes, and Hyperbolic Conservation
Laws
Peter R. Massopust
Sam Houston State University, Huntsville, TX
Abstract: Multiresolution schemes based on multiwavelets are presented.
These schemes employ a combination of interpolation and direct evaluation
and are a generalization of earlier work by A. Harten. It is shown how
such multiresolution schemes can be used to obtain accurate and
computationally efficient numerical weak solutions of partial differential
equations arising in computational fluid dynamics. The emphasis is on
one-dimensional problems but extensions to higher dimensions will be
indicated. Numerical experiments are given.
Image Coding Using Shift-Invariant Dyadic Wavelet Transform
Y.Hui, University of Wisconsin - Madison
C.W.Kok, University of Wisconsin - Madison
T.Q.Nguyen, University of Wisconsin - Madison
Abstract: A new class of wavelet filters, shift-invariant wavelet filters,
is proposed for the purpose of image compression. The existing approaches
obtain the shift-invariant wavelet transform by finding the path in the
decomposition tree that minimizes shift-variance with respect to the given
cost function. This procedure is signal dependent and is inefficient for
image compression, since the subband decomposition has to be performed for
all shifts of input signal during processing time. The proposed
shift-invariant wavelet transform has better shift-invariant property
compared with the conventional dyadic wavelet transform without changing
the structure of it. Two bit allocation schemes, which are suitable for
the proposed shift-invariant wavelet transform coding, are proposed and
evaluated. Experimental results show that the shift-invariant wavelet
transform has better energy compaction property in image coding compared
to the conventional wavelet transform.
Multivariate symmetric orthogonal polynomials generalizing Jacobi
polynomials and interpolation on symmetric lattices in $R^n$
Robert A. Gustafson
Texas A&M University, College Station, TX
Abstract: We discuss a family of multivariate symmetric orthogonal
polynomials which have expansion formulas (as multivariate hypergeometric
series) and properties similar to classical Jacobi polynomials. We also
discuss discrete analogs of these polynomials. In the construction of
these orthogonal polynomials, we use a new family of inhomogeneous
symmetric polynomials, generalizing the classical symmetric functions
(Schur functions). These new symmetric polynomials can be used in
interpolation problems for symmetric functions on multidimensional
symmetric lattices.
Wavelet frames - a new approach
Amos Ron, University of Wisconsin - Madison
Zuowei Shen, National University of Singapore
Abstract: We unravel the structure of wavelet system with the aid of two
new notions: the affine product, and a quasi-affine system. This leads
to a characterization of affine frames; the induced characterization of
tight affine frames is in terms of exact orthogonality relations. A
general oversampling theorem trivially follow from these characterizations.
Most importantly, the affine product can be factored during a
multiresolution analysis construction, and this leads to a very simple
sufficient condition for constructing tight frames from multiresolution.
Of particular importance are the facts that the underlying scaling
function does not need to satisfy any a-priori conditions, and that the
freedom offered by redundancy can be fully exploited in these
constructions.
Topic #2 ----------------- OP-SF NET ------------------ May 16, 1996
From: OP-SF Net editor <[email protected]>
Subject: errata and additions to earlier issues of OP-SF Net
Re: OP-SF Net 3.1, Topic #10 (XVth Workshop on Geometric Methods in
Physics, Bialowieza, Poland)
This meeting does not take place in 1997 but in 1996:
XVth Workshop on Geometric Methods in Physics
Quantizations, deformations and coherent states
Bialowieza, Poland, July 1-7, 1996
Re: OP-SF Net 3.2, Topic #6 (Special Functions session at International
Joint Mathematics Meeting, Antwerp, Belgium)
The title of H. Bavinck's lecture has changed to
"A new result for Laguerre, Charlier, and Meixner polynomials"
Topic #3 ----------------- OP-SF NET ------------------ May 16, 1996
Subject: International Memorial Conference D.S. Mitrinovic
Editors' note: the following was adapted from the first and second
announcements of the conference.
***********************************************************
* "International Memorial Conference D.S. Mitrinovic" *
* June 20-22, 1996 *
* Nis, Serbia, Yugoslavia *
***********************************************************
The following institutions:
- Faculty of Electrical Engineering, Belgrade,
- Faculty of Electronic Engineering, Nis,
- Institute of Mathematics SANU, Belgrade,
organize an International conference devoted to memory of the outstanding
mathematician
Professor Dragoslav S. Mitrinovic
(1908-1995)
and his scientific work. The Conference will be held in Nis, Serbia,
Yugoslavia from June 20-22, 1996. The location is the Faculty of
The topics of the conference are:
- Approximation Theory
- Complex Analysis
- Differential, Integral and Functional Equations
- General Inequalities
- Orthogonal Polynomials and Special Functions
- Possible other relevant topics
The accepted papers will be published in three volumes dedicated to
Professor Mitrinovic. The titles of volumes will be as follows:
1) RECENT PROGRESS IN INEQUALITIES;
3) TOPICS IN MATHEMATICS WITH APPLICATIONS.
The approximate number of pages per volume will be 400. The appearance of
the first volume is expected ahead of the conference, whereas the other
two will appear later. All volumes will be comprised of survey and
contribution papers. Survey papers, due to their length, content and
scientific value may be considered as book chapters, and therefore, could
be of great interest to the wide range of mathematicians. Also, the
authors are well-known and have made significant contributions to the
relevant topics. All interested mathematicians who wish to attend
the conference are welcomed and could send their applications to the
Organizing Committee until April 30, 1996.
On behalf of the Organizing Committee
Faculty of Electronic Engineering
Department of Mathematics
18000 Nis, Yugoslavia.
e-mail: [email protected] and/or
Topic #4 ----------------- OP-SF NET ------------------ May 16, 1996
From: OP-SF Net editor <[email protected]>
Subject: Symmetries and Integrability of Difference Equations, Canterbury
The Conference on Symmetries and Integrability of Difference Equations,
University of Kent, Canterbury, July 1st-5th 1996 was announced in
OP-SF Net 2.4, Topic #6. A second announcement, with a preliminary list
of speakers and information about registration is now available at WWW:
http://stork.ukc.ac.uk/IMS/maths/SIDE96/
Topic #5 ----------------- OP-SF NET ------------------ May 16, 1996
From: OP-SF Net editor <[email protected]>
Subject: MSRI program on Combinatorics
The MSRI, Berkeley organizes during 1996-97 a full-year program on
Combinatorics. The program focuses on four main areas of approximately
half a semester each. During each of these four periods there will be a
one-week workshop. See WWW: http://www.msri.org/application/comb.html
Two of the areas may have some relevance for readers of OP-SF Net:
Enumeration and partially ordered sets: September 1 - October 25, 1996.
Workshop: October 14-18.
Combinatorial identities (especially computer proofs); conjectures on
monotone triangles and plane partitions; enumeration and classification of
tilings; combinatorial problems arising from statistical mechanics and
knot theory; combinatorial properties of Kazhdan-Lusztig polynomials;
q-analogues and quantum groups.
The workshop is being organized by Lynne Butler, Ira Gessel, Rodica Simion
(chair), and Michelle Wachs. The program of the workshop revolves around
enumerative and order-theoretic aspects in the study of combinatorial
structures. Included among the workshop topics are:
q-series
Partitions
Plane partitions
Alternating sign matrices
Enumerative aspects of group algebras and symmetric functions
Combinatorics of orthogonal polynomials
Computer algebra
Combinatorial, topological, and algebraic aspects of the theory of
partially ordered sets
WWW: http://www.msri.org/sched/CombPosets.html
email: [email protected]
Symmetric functions and representation theory: March 17 - May 30, 1997.
Workshop: April 14-18
Macdonald's two-parameter symmetric functions and the corresponding two
variable Kostka polynomial; immanent conjectures of Lieb, Goulden-Jackson,
Stembridge, et al.; constant term identities and their connection with
nilpotent Lie algebras and cyclic homology; random walks on groups and
shuffling problems; internal products of symmetric functions; invariant
theory.
The workshop is being organized by Curtis Greene (Chair), Sergey Fomin,
Phil Hanlon, and Sheila Sundaram.
Scope: In recent years there have been many exciting developments in areas
that link combinatorics (especially the theory of symmetric functions)
with representation theory and algebraic geometry. This workshop will
focus on current problems in these areas, emphasizing the interplay
between algebraic and combinatorial methods. The program will include the
following topics, as well as others:
Schur functions and their generalizations
Combinatorics and representations of finite Coxeter groups
Quantum groups and Hecke algebras
Centralizer algebras
Homology representations
WWW: http://www.msri.org/sched/CombSymfns.html
email: [email protected]
Topic #6 ----------------- OP-SF NET ------------------ May 16, 1996
From: K. Srinivasa Rao <[email protected]>
Subject: Workshop on Special Functions & Differential Equations, Madras
(shortened by OP-SF Net editor)
Workshop on Special Functions & Differential Equations, Madras
January 13-24, 1997
This is a Workshop in the field of Special Functions, Differential
Equations and closely related topics, to be held at the Institute of
Mathematical Sciences (I.M.Sc.), Madras during Jan. 13-24, 1997.
Mini-series of lectures by experts will introduce the recent trends and
developments in the topics listed. The objective of the Workshop is to
bring together experts and active research students, to help strengthening
of research activities at the universities and research institutions in
this ever green-area.
Topics include:
Special Functions
Differential Equations
Orthogonal Polynomials (One/Several Variables)
Group Theory and Special Functions
Difference Equations
q-Special Functions
Quantum Groups and Special Functions
Numerical Methods
Algebraic/Symbolic Computer Packages
Plenary speakers include (* means: to be confirmed):
R.P. Agarwal (India)
B C. Berndt (U.S.A) *
F. Calogero (Italy)
H.D. Doebner (Germany)*
R.F. Gustafson (U.S.A.)*
E. Kalnins (New Zealand)
T.H. Koornwinder (Netherlands)
M. Lakshmanan (India)
H.L. Manocha (India)
S.C. Milne (U.S.A.) *
M. Lohe (Australia)
T.D. Palev (Bulgaria)
C. Quesne (Belgium)
A. Ronveaux (Belgium)
T.S. Santhanam (U.S.A.)
W. Van Assche (Belgium)*
G. Vanden Berghe (Belgium)
J. Van der Jeugt (Belgium)
A. Verma (India)
M. Waldschmidt (France)
There is an international Advisory Committee and a local Organizing
Committee.
Participation Participants should be active research scientists, students,
in the field of Special Functions, Differential Equations and related
topics. Interested candidates should send by e-mail (or on plain paper)
details giving their name, address, age, qualifications, present position
and a resume of research work done. (Maximum number of participants:
Financial
Financial support for train travel, board and lodging will be
provided to some of the participants. Registration Fee: US$100 (Rs.200 for Indian participants) Last date for receiving application: October 14, 1996 Further information: WWW: http://www.imsc.ernet.in/~wssf97/ or by sending a message to: Prof. K. Srinivasa Rao Convener, Workshop on Special Functions & Differential Equations The Institute of Mathematical Sciences (I.M.Sc.) CIT Campus, Tharamani Madras 600113, India email: [email protected] fax: +91-44-235 0586 Topic #7 ----------------- OP-SF NET ------------------ May 16, 1996 From: Martin Muldoon <[email protected]> Subject: Waleed Al-Salam 1926-1996 Friends and colleagues are saddened by news of the passing, a few months short of his 70th birthday, of Waleed Al-Salam, Professor Emeritus of Mathematics at the University of Alberta. Born on July 15, 1926 in Baghdad, Iraq, he died on April 14, 1996 in Edmonton, Alberta, Canada. Waleed studied at the University of California, Berkeley, earning a Bachelor's degree in Engineering Physics in 1950 and a M.A. in Mathematics in 1951. He returned to Baghdad as an Instructor at the College of Science for a few years, before enrolling for the Ph.D. at Duke University. He completed the degree in 1958 with a thesis "On the Bessel Polynomials" written under the supervision of Leonard Carlitz. By this time he was already a regular contributor to the periodical literature with some 20 published articles on a variety of topics in orthogonal polynomials and special functions. After completing his Ph.D., Waleed returned to the College of Science in Baghdad as Associate Professor. Coming back to North America in 1962, he eventually (1966) took a position at the University of Alberta, where he was Professor of Mathematics from 1967 until his retirement in 1992. Waleed continued to contribute to several areas related to orthogonal polynomials; his CV lists over 80 articles. Areas covered by his work include characterization theorems (see his survey article in pp. 1-24 of P. Nevai, ed., Orthogonal Polynomials: Theory and Practice, Kluwer, 1990), Turan expressions, generating functions, summation formulas, q-analogs, and fractional operators. He and his collaborators did much work on various special and generalized systems of orthogonal polynomials. The Al-Salam-Carlitz polynomials (1965) are still frequently cited; see, e.g., the papers of R. Askey and S. K. Suslov in Lett. Math. Phys. 29 (1993), 123-132 and J. Phys. A 20 (1993), L693-L698. The Al-Salam-Chihara polynomials (1976) play an important role in the Askey-Wilson scheme of basic hypergeometric orthogonal polynomials. Waleed supervised the Ph.D work of Bill Allaway (1972) and Mourad Ismail (1974), and conducted joint work with a variety of people at Alberta and elsewhere. In later years, these included Ted Chihara, A. Verma, Mourad Ismail and Waleed's wife, Nadhla Al-Salam, also on the faculty at Alberta, and a member of this Activity Group. On his retirement in 1992, Waleed decided to put his expertise and energy at the disposal of the orthogonal polynomials community by starting and maintaining an ftp site for papers in the area. This effort prospered and he continued to oversee it until last year when his failing health made it necessary to pass the task to Hans Haubold at the UN Office in Vienna. Waleed had been diagnosed with leukemia in 1993 and this was to reduce his active participation in conferences in subsequent years. Nevertheless, with Nadhla's constant support, he still managed to travel and old and new friends were able to benefit from his knowledge and enjoy his optimistic and humorous personality. Topic #8 ----------------- OP-SF NET ------------------ May 16, 1996 From: Martin Muldoon <[email protected]> Subject: Contents of Delft Proceedings The Proceedings of the International Conference on "Orthogonality, Moment Problems and Continued Fractions" (dedicated to Thomas Jan Stieltjes Jr.) and held October 31--November 4, 1994 at Delft University of Technology, The Netherlands, have now appeared, in Journal of Computational and Applied Mathematics, Volume 65, December 1995. We thank the volume editor, Marcel G. de Bruin, for supplying us with a LaTeX version of the table of contents, from which the text below has been prepared. CONTENTS M. G. de Bruin, Preface, p.1 R. \'Alvarez-Nodarse, A.G. Garc\'ia, and F. Marcell\'an, On the properties for modifications of classical orthogonal polynomials of discrete variables, p.3 H. Bavinck, The zeros of a certain linear combination of Chebyshev polynomials, p.19 C. Berg, Indeterminate moment problems and the theory of entire functions, p.27 A. Bultheel, p. Gonz\'alez-Vera and R. Orive, On the convergence of general two-point Pad\'e approximants to Stieltjes functions. Part I. Algebraic aspects, p.57 W. C. Connett and A.L. Schwartz, Subsets of R which support hypergroups with polynomial characters, p.73 H. Dette, On the minimum of the Christoffel function, p. 85 K. Diethelm, Gaussian quadrature formulae of the third kind for Cauchy principal value integrals: Basic properties and error estimates, p. 97 J. Dombrowski and S. Pedersen, Orthogonal polynomials, spectral measures and absolute continuity, p. 115 K.A. Driver, Nondiagonal quadratic Hermite-Pad\'e approximation to the exponential function, p. 125 S. Ehrlich, Asymptotic behaviour of Stieltjes polynomials for ultraspherical weight functions, p. 135 D. Fasino, Spectral properties of Hankel matrices and numerical solutions of finite moment problems, p. 145 D.P. Gupta and D.R. Masson, Contiguous relations, continued fractions and orthogonality: an _8\phi_7 model, p. 157 E.K. Ifantis and P.D. Siafarikas, An alternative proof of a theorem of Stieltjes and related results, p. 165 I.H. Jung, K.H. Kwon, D.W. Lee and L.L. Littlejohn, Differential equations and Sobolev orthogonality, p. 173 V.A. Kaliaguine, The operator moment problem, vector continued fractions and an explicit form of the Favard theorem for vector orthogonal polynomials, p. 181 M. Kijima and E.A. van Doorn, Weighted sums of orthogonal polynomials with positive zeros, p. 195 A.B.J. Kuijlaars, Chebyshev quadrature for measures with a strong singularity, p. 207 S. Lewanowicz, Results on the associated classical orthogonal polynomials, p. 215 L. Lorentzen, A convergence question inspired by Stieltjes and by value sets in continued fraction theory, p. 233 A.P. Magnus, Special non uniform lattice (snul) orthogonal polynomials on discrete sets of points, p. 253 F. Marcell\'an, J.C. Petronilho, T.E. P\'erez and M.A. Pi\~nar, What is beyond coherent pairs of orthogonal polynomials?, p. 267 G. Mastroianni, Some weighted polynomial inequalities, p. 279 D.M. Matjila, Bounds for weighted Lebesgue functions for Freud weights on a larger interval, p. 293 M.E. Muldoon, Electrostatics and zeros of Bessel functions, p. 299 O. Nj\aa stad, Extremal solutions of the strong Stieltjes moment problem, p. 309 F. Peherstorfer, Stieltjes polynomials and functions of the second kind, p. 319 F. Peherstorfer and R. Steinbauer, Characterization of orthogonal polynomials with respect to a functional, p. 339 M. R\"osler, Trigonometric convolution structures on Z derived from Jacobi polynomials, p. 357 A. Sinap, Gaussian quadrature for matrix valued functions on the real line, p. 369 F.H. Szafraniec, A method of localizing the spectra of sequences of orthogonal polynomials, p. 387 N.M. Temme, Uniform asymptotic expansions of integrals: a selection of problems, p. 395 G. Valent and W. Van Assche, The impact of Stieltjes' work on orthogonal polynomials: additional material, p. 419 M. Voit, Limit theorems for random walks on the double coset spaces U(n)/U(n-1) for n \to \infty, p. 449 List of talks presented at the conference, p. 461 List of registered participants, p. 464 Author Index, p. 469 Topic #9 ----------------- OP-SF NET ------------------ May 16, 1996 From: Tom H. Koornwinder <[email protected]> Subject: Foata Festschrift A special issue of The Electronic Journal of Combinatorics appeared which is dedicated to Dominique Foata on the occasion of his 60th birthday. It is Volume 3 (2) (1996), WWW: http://ejc.math.gatech.edu:8080/Journal/Volume_3/festschrift.html It contains 25 contributions, some of which are in the field of orthogonal polynomials or relevant for this field. I mention a few and I recommend the reader to inspect the contents for other titles: R1: Daniel Barsky and Michel Carpentier, Polynomes de Jacobi generalises et integrales de Selberg (33pp) R13: Doron Zeilberger, Proof of the alternating sign matrix conjecture (84pp) (see also the comments file) R16: Shalosh B. Ekhad and J. E. Majewicz, A short WZ-style proof of Abel's identity (1 p) R17: Dominique Dumont and Armand Ramamonjisoa, Grammaire de Ramanujan et arbres de Cayley (18pp) R19: Marko Petkov\vsek and Herbert S. Wilf, A high-tech proof of the Mills-Robbins-Rumsey determinant formula (3 pp.) R20: Alun Morris and A. A. Abdel-Aziz, Schur Q-functions and spin characters of symmetric groups I (14pp) R21: George E. Andrews, Pfaff's method (III): Comparison with the WZ method (18pp) R24: A. M. Garsia and M. Haiman, Some natural bigraded S_n-modules (60pp) (related to Macdonald polynomials) Topic #10 ----------------- OP-SF NET ------------------ May 16, 1996 From: S.B. Yakubovich <[email protected]> Subject: New book on integral transforms The following book has appeared: S.B. Yakubovich, Index Transforms, World Scientific, Singapore. London. Hong Kong, 1996. 264 pp. "This book deals with the theory and some applications of integral transforms that involve integration with respect to an index or parameter of special functions of hypergeometric type as the kernel (index transforms). The basic index transforms are considered, such as the Kontorovich-Lebedev transform, the Mehler-Fock transform, the Olevskii transform, the Lebedev-Skalskaya transforms. The Lp theory of index transforms is discussed and new index transforms and convolution constructions are demonstrated. For the first time, the essentially multidimensional Kontorovich-Lebedev transform is announced. The book is self-contained, and includes a list of symbols with definitions, author and subject indices, and an up-to-date bibliography". Topic #11 ----------------- OP-SF NET ------------------ May 16, 1996 From: Tom Koornwinder <[email protected]> Subject: Askey-Wilson computer algebra mini-project As described in OP-SF Net 3.1, Topic #16, Rene Swarttouw is working during the period January-June 1996 at RIACA, Eindhoven, The Netherlands on a project "A computer implementation of the Askey-Wilson scheme". The purpose of the project is to make a start with bringing the report R. Koekoek and R.F. Swarttouw, The Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue, Report 94-05, Delft University of Technology, Faculty TWI, 1994. to the form of an interactive book, with facilities for symbolic manipulation of formulas. Further information about this project is now available from WWW: http://www.can.nl/~renes/index.html -From there you can also download a preliminary version of the electronic -book version. It is a dvi file named AW.dvi, which is equipped with -hyperlinks. This file can be read by using the program xhdvi. Consult also -the above WWW site for the way to obtain xhdvi. There is another version -available which can be read via Netscape. It uses a dvi viewer created by -Garth Dickie. Swarttouw is also working on a package for calculating formulas for orthogonal polynomials belonging to the Askey-scheme by Maple. At the mentioned WWW site there is an online facility to do some of these computations, for which you do not need to have Maple on your own computer. The present demos use Maple procedures written by Wolfram Koepf. Topic #12 ----------------- OP-SF NET ------------------ May 16, 1996 From: OP-SF Net editor <[email protected]> Subject: Revising the 1991 Mathematics Subject Classification Editor's note (THK): The following was taken from Notices AMS, December 1995, p.1547, see also WWW: http://www.ams.org/committee/publications/msc-2000-let.html I suggest that you send suggestions for revision of numbers 33 (Special functions), 42Cxx (Nontrigonometric Fourier analysis) and 44 (Integral transforms, operational calculus) also to the editors of OP-SF Net, in order that a summary of suggestions for this subject can be listed, and maybe discussed here. Note from Notices AMS: Mathematics Subject Classification Scheme Revision To the Mathematical Community: The editors of Mathematical Reviews and Zentralblatt f|r Mathematik have initiated the process of revising the 1991 Mathematics Subject Classification, which is used by both journals as their classification system. The editors do not plan a radical revision of the present 1991 system, but it is clear that some changes will be needed in order to accommodate recent developments in mathematical research. It will be necessary to have this revision completed by the end of 1998 so that it can begin to be used in Current Mathematical Publications in mid 1999, and in Mathematical Reviews and Zentralblatt f|r Mathematik beginning in 2000. We hereby solicit comments and suggestions from the mathematical community to be considered in this revision process. These should be submitted by June, 1997. The preferred method of communication is by e-mail: [email protected] or [email protected] (Comments and suggestions may also be sent to either one of us at the addresses given below.) We are eager that research mathematicians and scholars have input in this revision process as soon as possible. R. Keith Dennis Bernd Wegner Executive Editor Chefredakteur Mathematical Reviews Zentralblatt f|r Mathematik Topic #13 ----------------- OP-SF NET ------------------ May 16, 1996 From: OP-SF Net editor <[email protected]> Subject: WWW and ftp addresses A more comprehensive list of ftp and WWW addresses relevant for our field is available at the home page of the Activity Group WWW: http://www.math.yorku.ca/Who/Faculty/Muldoon/siamopsf/ under "Links to WWW pages of interest to members" This list will be regularly updated, and the changes will be mentioned in OP-SF Net. Please mail corrections and additions for this list to Martin Muldoon <[email protected]> Between March 5 and May 12, 1996 the following addresses in this list were changed or added: Organizations: Center of Hypergeometric Systems, Kobe, Japan: http://www.math.s.kobe-u.ac.jp/rchs/ Other information: Askey-Wilson computer algebra mini-project: WWW: http://www.can.nl/~renes/index.html Individuals: David Bressoud: WWW: http://www.math.macalstr.edu/~bressoud/ Mathijs Dijkhuizen: WWW: http://www.math.s.kobe-u.ac.jp/HOME/dijkhuizen/index.html Paul Floris: WWW: http://www.math.s.kobe-u.ac.jp/HOME/floris/index.html Erik Koelink: WWW: http://turing.fwi.uva.nl/~koelink/ Tom Koornwinder: WWW: http://turing.fwi.uva.nl/~thk/ Katsuhisa Mimachi WWW: http://www.math.s.kobe-u.ac.jp/HOME/mimachi/index.html Masatoshi Noumi WWW: http://www.math.s.kobe-u.ac.jp/HOME/noumi/index.html Toshio Oshima WWW: http://akagi.ms.u-tokyo.ac.jp/~oshima/ Nico Temme: WWW: http://www.cwi.nl/~nicot/ Walter Van Assche: http://www.wis.kuleuven.ac.be/wis/walter.html Topic #14 ----------------- OP-SF NET ------------------ May 16, 1996 From: OP-SF Net editor <[email protected]> Subject: Changes of address Jan Felipe van Diejen has moved in April 1996 from Tokyo to Montreal: Centre de Recherches Mathematiques Universite de Montreal C.P. 6128, Succursale Centre-ville Montreal (Quebec) H3C 3J7 Canada Phone : +1-514-343-6111 ext. 4068 Fax : +1-514-343-2254 E-mail: [email protected] Topic #15 ----------------- OP-SF NET ------------------ May 16, 1996 From: OP-SF Net editor <[email protected]> Subject: ftp site for papers in Orthogonal Polynomials and Special Functions Hans Haubold's ftp archive for preprints in the area of Orthogonal Polynomials and Special functions is the continuation of Waleed Al-Salam's preprint archive. One can approach the archive by anonymous ftp to unvie6.un.or.at, directory siam, or at the WWW address ftp://unvie6.un.or.at/siam . See the file 00contents.ftpsite in the submissions directory for the contents (titles, authors, filenames) of the directories opsf and abstracts. This list of contents is in chronological order of submission. The most recent contributions will just reside as files in the submissions directory, and are not yet documented in the list of contents. Hans Haubold is sending regular info about new submissions to a large mailing list. Please contact him <[email protected]> if you want to be added to this mailing list or if your email address on the list is no longer correct. Between 27 February and 10 April 1996, the following papers were submitted: W. Koepf and D. Schmersau, On the De Branges theorem. (siam/opsf/koepf/deBranges.ps, deBranges.tex) W. Koepf and D. Schmersau, Weinstein's functions and the Askey-Gasper identity. (siam/opsf/koepf/weinstein.ps, weinstein.tex) W. Koepf, The algebra of holonomic equations. (siam/opsf/koepf/holonomic.ps, holonomic.tex) N.M. Temme, Uniform asymptotics for the incomplete gamma functions starting from negative values of the parameters. (siam/opsf/temme.ps) J.F. van Diejen, Properties of some families of hypergeometric polynomials in several variables. (siam/opsf/diejen2.tex) Topic #16 ----------------- OP-SF NET ------------------ May 16, 1996 From: OP-SF Net editor <[email protected]> Subject: Obtaining back issues of OP-SF Net and submitting contributions to OP-SF Net and Newsletter Back issues of OP-SF Net can be obtained from ftp: ftp.fwi.uva.nl, in directory pub/mathematics/reports/Analysis/koornwinder/opsfnet.dir or WWW: ftp://ftp.fwi.uva.nl/pub/mathematics/reports/Analysis/koornwinder/opsfnet.dir or WWW: http://www.math.ohio-state.edu/JAT/DATA/OPSFNET/opsfnet.html Contributions to the OP-SF Net 3.4 should reach the email address [email protected] before July 1, 1996. The Activity Group also sponsors a Newsletter edited by Wolfram Koepf. Deadline for submissions to be included in the June 1996 issue is May 15, 1996. Please send your Newsletter contributions directly to the Editor: Wolfram Koepf Konrad-Zuse-Zentrum Heilbronner Str. 10, D-10711 Berlin, Germany tel.: +49-30-896 04-216 fax: +49-30-896 04-125, email: [email protected] preferably by email, and in latex format. Other formats are also acceptable and can be submitted by email, regular mail or fax. Please note that submissions to the Newsletter (if not containing mathematics symbols or pictures) are automatically considered for publication in OP-SF Net, and vice versa, unless the writer requests otherwise. Previous issues of the Newsletter, but not the most recent one, can be obtained as dvi or PostScript files from Wolfram Koepf's WWW homepage: http://www.zib-berlin.de/~bzfkoepf/ or by anonymous ftp at ftp.zib-berlin.de in directory pub/UserHome/Koepf/SIAM In order to join the SIAM Activity Group on Orthogonal Polynomials and Special Functions, and thereby receive the Newsletter, you have to become a member of SIAM. The annual dues are$93 for
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Date Index | Thread Index | Problems or questions? Contact [email protected]
| 2015-05-27T17:41:59 |
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|
http://nasb.gov.by/eng/publications/npcs/npcs99_2.php
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Bel · Eng · Rus | Text only |
# Nonlinear Phenomena in Complex Systems, 1999, Vol.2, No.2
/ Publications / Scientific Journals
Nonlinear Phenomena in Complex Systems, 1999, Vol.2, No.2
NONLINEAR PHENOMENA IN COMPLEX SYSTEMS An Interdisciplinary Journal Published by The "Education and Upbringing" Publishing Company, Minsk, Republic of Belarus
## CONTENTS
Srinivas Jammalamadaka, Jцrg Main, Gьnter Wunner
The Effect of Scars on the Statistics of Transition Probabilities of Classically Chaotic Quantum Systems. pp. 1--5
Summary: We study the statistical properties of generalized intensities (squared matrix elements of Hermitian operators) for the hydrogen atom in strong magnetic fields in a range of parameters where the classical analogue of the system exhibits completely chaotic dynamics. In this way we extend previous work by Prosen and Robnik on the statistics of generalized intensities in billiard systems in the transition region with mixed classical dynamics. We observe deviations from the statistics found in that work, and demonstrate that these are due to the effect of scarring of wave functions by unstable periodic orbits.
V.P. Gribkovskii, S.V. Voitikov, M.I. Kramar, G.I. Ryabtsev, and R. Kragler
Amplified Luminescence as a Source of Nonlinearity in Laser Diodes. pp. 6--10
Summary: Nonlinear properties of amplified luminescence in semiconductor bulk and quantum-well (QW) lasers have been investigated and modeled. Amplified luminescence depends strictly on carrier concentration and temperature representing by itself an additional relatively powerful source of nonlinearity that can make laser dynamics much more complicated. In general, the rate of amplified luminescence still keeps its quadratic character as that of spontaneous recombination. In QW lasers, in the vicinities of laser mode hopping the amplified luminescence exhibits local peak-like carrier dependence and may affects abruptly on a bifurcation of mode hopping with the injection level increasing.
H.V. Grushevskaya
Chaos in Near-Hamiltonian Systems with Singular Perturbation: Applications to Oscillatory Model of Hodgkin--Huxley Neuron. pp. 11--24
Summary: Neuron's oscillatory model is transformed to the form of near-Hamiltonian system with singular coefficients. We demonstratethat singular coefficients can be considered as a perturbation of the system by virtue of discrete sequence of kicks. The linearization of the perturbation in the vicinity of periodical solution for a given kick allows us to rewrite the system as a matrix Schrцdinger equation for two-level quantum system in a resonant quasi-monochromatic field. As a result, the original system demonstrates chaotic behavior through the cascade of period doubling bifurcations. The bifurcations in this case correspond to the series of quantum nutation of nutations.
Global Attractors, Attracting Regions and Regions of Visiting for Dynamical Systems. pp. 25--30
Summary: The phase space of an autonomous dissipative nonlinear dynamical system is investigated. It is proved that under certain conditions such a system has an attracting region A with a basin of attraction around it, i.e. any trajectory starting somewhere inside this basin reaches the region A after a finite time interval and never leaves A. In certain cases, the region A turns into a global attractor of the system when the basin of attraction coincides with the whole remaining part of the phase space and all attractors of the system lie inside the region A. Another theorem yields sufficient conditions under which a system has a region of visiting G in the phase space, i.e. any trajectory starting outside G reaches this region after a finite time interval (and further can leave G in contrast to the case of an attracting region). Several examples are considered.
V.A. Gaisyonok, G.G. Krylov
On the Green Function for the Restricted Rotational Diffusion Model. pp. 31--34
Summary: The explicit expression for the Green function of the restricted rotational diffusion equation has been constructed based on singular perturbations approach to boundary problems.
Alexander Rauh
Remarks on Perturbation Theory for Hamiltonian Systems. pp. 35--43
Summary: A comparative discussion of the normal form and action angle variable method is presented in a tutorial way. Normal forms are introduced by Lie series which avoid mixed variable canonical transformations. The main interest is focused on establishing a third integral of motion for the transformed Hamiltonian truncated at finite order of the perturbation parameter. In particular, for the case of the action angle variable scheme, the proper canonical transformations are worked out which reveal the third integral in consistency with the normal form. Details are discussed exemplarily for the Hйnon--Heiles Hamiltonian. The main conclusions are generalized to the case of n perturbed harmonic oscillators.
H. Rehfeld, H. Alt, C. Dembowski, H.-D. Grдf, R. Hofferbert, H. Lengeler, A. Richter
Wave Dynamical Chaos in Superconducting Microwave Billiards. pp. 44--48
Summary: During the last few years we have studied the chaotic behavior of special formed Euclidian geometries, so-called billiards, from the quantum or in more general sense "wave dynamical'' point of view. Due to the equivalence between the stationary Schrцodinger equation and the classical Helmholtz equation in the two-dimensional case (plain billiards), it is possible to simulate "quantum chaos'' with the help of macroscopic, superconducting microwave cavities. Using this technique we investigated spectra of three billiards of the family of Pascal's Snails (Robnik--Billiards) with a different chaoticity in each case in order to test predictions of standard stochastical models for classical chaotic systems.
Marko Robnik, Luca Salasnich and Marko Vranicar
WKB Corrections to the Energy Splitting in Double Well Potentials. pp. 49--62
Summary: By using the WKB quantization we deduce an analytical formula for the energy splitting in a double-well potential which is the usual Landau formula with additional quantum corrections. Then we analyze the accuracy of our formula for the double square well potential, the inverted harmonic oscillator and the quartic potential.
Vassilios M. Rothos and Tassos C. Bountis
Non-Integrability and Infinite Branching of Solutions of 2DOF Hamiltonian Systems in Complex Plane of Time. pp.63--71
Summary: It has been proved by S.L. Ziglin, for a large class of 2-degree-of-freedom (d.o.f) Hamiltonian systems, that transverse intersections of the invariant manifolds of saddle fixed points imply infinite branching of solutions in the complex time plane and the non-existence of a second analytic integral of the motion. Here, we review in detail our recent results, following a similar approach to show the existence of infinitely-sheeted solutions for 2 d.o.f. Hamiltonians which exhibit, upon perturbation, subharmonic bifurcations of resonant tori around an elliptic fixed point. Moreover, as shown recently, these Hamiltonian systems are non--integrable if their resonant tori form a dense set. These results can be extended to the case where the periodic perturbation is not Hamiltonian.
Aneta Stefanovska, Saso Strle, Maja Bracic and Hermann Haken
Model Synthesis of the Coupled Oscillators Which Regulate Human Blood Flow Dynamics. pp.72--87
Summary: A model synthesis for the system that regulates blood flow is presented. The model consists of coupled oscillators which present subsystems involved in the regulation of one passage of blood through the cardiovascular system. It is based on a priori physiological knowledge and observations of the system's functions by measurements and linear and nonlinear analysis of measured time series. Furthermore, the blood flow through the system of closed tubes consisting of blood vessels is described by wave equations.
V.V. Belov, G.S. Bokun, V.S. Vikhrenko
Many-body Correlations in Equilibrium Lattice Systems. pp. 88--92
Summary: The procedure of successive approximations beyond the quasichemical one for lattice gas systems of arbitrary density is suggested. Even at the lowest order approximation the calculation results for the phase diagram of the system of particles with attractive nearest neighbor interaction are in good agreement with Monte Carlo simulation.
E.A. Nikiforov and R.M. Yulmetyev
First Experimental Observation of Memory Effects in Biological Complex System by NMR Method. pp. 93--95
Summary: Direct registration of memory effects in biological complex system (plant tissue) has been carried out for the first time. Measurements of temperature dependence of the proton spin-lattice relaxation time in rotation frame allow to observe quasi-Markovian scenario of NMR spin relaxation in biological system.
Lissajous Solutions of the Satellite Oscillation Equation: Stability and Bifurcations via Higher Order Averaging. pp.96--100
Summary: The equation of plane oscillations of a satellite is a Hamiltonian system with one degree of freedom and 2p-periodic dependence on time and on x1. It contains two parameters $e\eps$ and e, one of which ($\eps$) is small. The unperturbed system is linear. Solutions that correspond to cycles of the Poincar\'e map on a cylinder $(x1\mpi,\,x2)$ are called Lissajous solutions. Their stability and bifurcations with parameter e changing are studied by the averaging method. It is shown how degenerate cases, where calculation of higher order terms is needed, arise in a natural way. Sufficient truncations of the normal form for those cases are described.
Andreas Ruffing
Discretized Schroedinger Eigenfunctions and q-Hypergeometric Series on Deforming Geometric Progressions. pp.101--116
Summary: Discretizations of the Schroedinger equation are introduced on geometric progressions $\R_{q} := \{+q^{n}, -q^{n} \vert n \in \Z\}, q > 1$. The symmetries of the geometric progressions are elaborated. We investigate the influence of this discretization to q-deformations of Hermite polynomials. The limits $q \rightarrow 1$ and $q \rightarrow \infty$ as deformations of $\R_{q}$ are considered. The first limit, $q \rightarrow 1$, is related to an approximation theoretical problem for step functions in ${\cal{L}}^{2}(\R)$. The second limit, $q \rightarrow \infty$, is related to the theory of topological deformations on compact Riemann surfaces. Both limits are related to each other. Proceeding into this direction, one obtains the fascinating fact that quantum group structures can be related to topological degeneration effects. The results finally contribute to a better mathema-tical understanding of quantum models with dilatative supersymmetry.
Designed and maintained by Dr. Nikolai N. Kostyukovich. Last updated: October 31, 1999
Created with assistance of Dr. Leonid F. Babichev
| 2018-04-23T02:10:41 |
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https://www.itl.nist.gov/div898/handbook/prc/section4/prc46.htm
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7. Product and Process Comparisons
7.4. Comparisons based on data from more than two processes
## Do all the processes have the same proportion of defectives?
The contingency table approach
Testing for homogeneity of proportions using the chi-square distribution via contingency tables When we have samples from $$n$$ populations (i.e., lots, vendors, production runs, etc.), we can test whether there are significant differences in the proportion defectives for these populations using a contingency table approach. The contingency table we construct has two rows and $$n$$ columns.
To test the null hypothesis of no difference in the proportions among the $$n$$ populations
$$\mbox{H}_0: \,\,\, p_1 = p_2 = \cdots = p_n$$
against the alternative that not all $$n$$ population proportions are equal
$$\mbox{H}_a: \,\,\, \mbox{Not all } p_i \mbox{ are equal } (i = 1, \, 2, \, \ldots, \, n) \, ,$$
The chi-square test statistic we use the following test statistic: $$\chi^2 = \sum_{\mbox{all cells}} \frac{(f_o - f_c)^2}{f_c} \, ,$$ where $$f_o$$ is the observed frequency in a given cell of a $$2 \times n$$ contingency table, and $$f_c$$ is the theoretical count or expected frequency in a given cell if the null hypothesis were true.
The critical value The critical value is obtained from the $$\chi^2$$ distribution table with degrees of freedom $$(2-1)(n-1) = n-1$$, at a given level of significance.
An illustrative example
Data for the example Diodes used on a printed circuit board are produced in lots of size 4000. To study the homogeneity of lots with respect to a demanding specification, we take random samples of size 300 from 5 consecutive lots and test the diodes. The results are:
Lot Results 1 2 3 4 5 Totals Nonconforming 36 46 42 63 38 225 Conforming 264 254 258 237 262 1275 Totals 300 300 300 300 300 1500
Computation of the overall proportion of nonconforming units Assuming the null hypothesis is true, we can estimate the single overall proportion of nonconforming diodes by pooling the results of all the samples as $$\bar{p} = \frac{36 + 46 + 42 + 63 + 38}{5(300)} = \frac{225}{1500} = 0.15 \, .$$
Computation of the overall proportion of conforming units We estimate the proportion of conforming ("good") diodes by the complement 1 - 0.15 = 0.85. Multiplying these two proportions by the sample sizes used for each lot results in the expected frequencies of nonconforming and conforming diodes. These are presented below:
Table of expected frequencies
Lot Results 1 2 3 4 5 Totals Nonconforming 45 45 45 45 45 225 Conforming 255 255 255 255 255 1275 Totals 300 300 300 300 300 1500
Null and alternate hypotheses To test the null hypothesis of homogeneity or equality of proportions
$$\mbox{H}_0: \,\,\, p_1 = p_2 = \cdots = p_5$$
against the alternative that not all 5 population proportions are equal
$$\mbox{H}_a: \,\,\, \mbox{Not all } p_i \mbox{ are equal } (i = 1, \, 2, \, \ldots, \, 5) \, ,$$
Table for computing the test statistic we use the observed and expected values from the tables above to compute the $$\chi^2$$ test statistic. The calculations are presented below:
$$f_o$$ $$f_c$$ $$(f_o - f_c)$$ $$(f_o - f_c)^2$$ $$(f_o - f_c)^2 / f_c$$ 36 45 -9 81 1.800 46 45 1 1 0.022 42 45 -3 9 0.200 63 45 18 324 7.200 38 45 -7 49 1.089 264 225 9 81 0.318 254 255 -1 1 0.004 258 255 3 9 0.035 237 255 -18 324 1.271 262 255 7 49 0.192 12.131
Conclusions If we choose a 0.05 level of significance, the critical value of $$\chi^2$$ with 4 degrees of freedom is 9.488 (see the chi square distribution table in Chapter 1). Since the test statistic (12.131) exceeds this critical value, we reject the null hypothesis.
| 2021-10-21T06:34:40 |
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https://www.usgs.gov/center-news/volcano-watch-lava-meets-sea-enjoy-park-don
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# Volcano Watch — Lava meets the sea—Enjoy the park but don
Release Date:
Lava flowing from Kīlauea's ongoing eruption finally made its way to the ocean once again a couple of weeks ago. And for the first time in nearly a year, everyone—;from curious park visitors and staff, to intent photographers, to nerdy (and intent) volcanologists—have been treated to the enrapturing experience of seeing liquid rock encounter liquid ocean.
While making observations at the coastal entry, those of us in the last group of observers are reminded of the unusual hazards posed by the interaction of hot lava and cool seawater. Nearly a half dozen people have died at the coastal entry in the past 10 years and scores more injured. Being prepared for the hazards can help us all to avoid becoming "statistics." The U.S. Geological Survey, in cooperation with the National Park Service, has prepared a useful Fact Sheet on viewing Hawaii's lava safely, #152-00, available at the Kīlauea Visitor Center in the park.
There are two types of hazards discussed in the Fact Sheet that are especially important to consider right now as the new coastal entry evolves: collapse of the lava delta or "bench" and hazardous conditions associated with the coastal entry steam plume.
New land begins to form when molten (2,120°F, 1,160°C) lava encounters the comparatively cool seawater and disintegrates into rubble. The rubble piles up at the edge of the sea eventually gets plated over with more lava, and forms a delta. The actively growing part of the delta is a bench. And although this "bench" is located in a park, it is definitely not one you want to sit on—;or go near for that matter! In a cyclic process, part of the unstable bench collapses through ocean-wave erosion and then is rebuilt and extended a bit by the successive addition of fresh lava, thus continuing the build-erode-rebuild cycle. Eventually the active bench may substantially extend the size of the coastal entry delta.
A poignant hazard associated with new land formation involves being on, or near a delta when a bench collapse occurs. These collapses happen without warning and sometimes result in several acres of new land catastrophically breaking off into the sea in a matter of seconds. Literally all hell breaks loose. As the land slides into the ocean, the ocean responds by sending huge waves up over the shoreline that encounter, among other things, molten lava. Depending upon whether the lava is on the surface or in lava tubes, this interaction can produce anything from superheated steam clouds at ground level to explosions that hurl hundred pound rocks tens of meters (yards). Coastal entry visitors are implored to stay inland of the national park's guard rope perimeter. Stay alert, stay off the new delta, and, if you hear unusual sounds, move inland quickly.
A subtler hazard posed by molten lava entering the ocean involves the evaporation of seawater to dryness and the associated series of chemical reactions that produce a dense white "laze" plume comprised of a suspended mixture of hydrochloric acid, concentrated seawater steam, and volcanic glass fragments. Hydrochloric acid (HCl) is toxic and extremely corrosive. It causes skin and eye irritation and can also cause breathing difficulties, as well. The mixture of tiny glass fragments, HCl, and seawater raining out of laze plumes has the stinging and corrosive properties of dilute battery acid.
Several years ago, a pair of visitors who ventured too near the coastal entry was found dead, apparently burned by acid-laced steam on the lava bench. Other people have been severely scalded by being near rogue waves washing over molten lava. Avoid being under, or close to, the coastal entry plume. Wear long pants and shirts, and bring plenty of water and a flashlight for each person. Watch for wind shifts, and if you're caught off guard, put on a hat and raingear and rinse off any precipitation that gets on you as soon as possible.
While the foregoing advice may seem like overkill, it is important for all of us to remember that the coastal part of the park is certainly a wonderland but IS NOT Disneyland. With the right precautions taken, we can all witness this most amazing process of the formation of new land. It is enthralling to see it again for the first time!
### Volcano Activity Update
Eruptive activity at Puu Oo continues. The Banana flow, which breaks out of the Mother's Day lava tube a short distance above Pulama pali, is entering the ocean in two areas off the 2002 Wilipea lava delta. In addition, lava has been visible between Pulama pali and Paliuli for the past week. The national park has marked a trail to within a short distance of the end of the flow, and thousands have been enjoying the show. Eruptive activity in Puu Oo's crater is weak, with sporadic minor spattering and small flows. The upper part of the PKK (Kuhio) flow south of Puu Oo has also been active and creating bright glow most nights.
Four earthquakes were reported felt on the island during the week ending June 9. A magnitude 3.2 earthquake was felt at Hale Pohaku and Keaau at 2:19 p.m. June 3; it was located 6 km (4 miles) south-southwest of Puu Oo at a depth of 10 km (6 miles). Two earthquakes within 22 seconds of one another were felt at HVO and Volcano Village at 12:33 p.m. June 4. The first had a magnitude of 3.2 and occurred 5 km (3 miles) south of Volcano at a depth of 3 km (2 miles). The second, of magnitude 3.4 took place 4 km (2 miles)southeast of Kīlauea's summit at the same depth. The last felt earthquake was the largest of the week, a magnitude 3.6 at 2:06 June 4 located 15 km (10 miles) southeast of Pahala at a depth of 35 km (22 miles); it was felt in Hawaiian Ocean View Estates, Honaunau, and Kona Paradise.
Mauna Loa is not erupting. The summit region continues to inflate slowly. Seismic activity remains low, with only 4 earthquakes located in the summit area during the past week.
### Volcano Activity Update
Eruptive activity at Puu Oo continues. The Banana flow, which breaks out of the Mother's Day lava tube a short distance above Pulama pali, is entering the ocean in two areas off the 2002 Wilipea lava delta. In addition, lava has been visible between Pulama pali and Paliuli for the past week. The national park has marked a trail to within a short distance of the end of the flow, and thousands have been enjoying the show. Eruptive activity in Puu Oo's crater is weak, with sporadic minor spattering and small flows. The upper part of the PKK (Kuhio) flow south of Puu Oo has also been active and creating bright glow most nights.
Four earthquakes were reported felt on the island during the week ending June 9. A magnitude 3.2 earthquake was felt at Hale Pohaku and Keaau at 2:19 p.m. June 3; it was located 6 km (4 miles) south-southwest of Puu O`o at a depth of 10 km (6 miles). Two earthquakes within 22 seconds of one another were felt at HVO and Volcano Village at 12:33 p.m. June 4. The first had a magnitude of 3.2 and occurred 5 km (3 miles) south of Volcano at a depth of 3 km (2 miles). The second, of magnitude 3.4 took place 4 km (2 miles)southeast of Kīlauea's summit at the same depth. The last felt earthquake was the largest of the week, a magnitude 3.6 at 2:06 June 4 located 15 km (10 miles) southeast of Pahala at a depth of 35 km (22 miles); it was felt in Hawaiian Ocean View Estates, Honaunau, and Kona Paradise.
Mauna Loa is not erupting. The summit region continues to inflate slowly. Seismic activity remains low, with only 4 earthquakes located in the summit area during the past week.
| 2020-10-22T16:23:40 |
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|
https://modeltheory.fandom.com/wiki/DLO
|
## FANDOM
78 Pages
DLO is the theory of dense linear orders (without endpoints). A model of DLO is a linearly ordered set $(M,<)$ satisfying the following additional conditions:
$\forall x \forall y : x < y \rightarrow \exists z : x < z < y$
$\forall x \exists y : x < y$
$\forall x \exists y : y < x.$
For example, $(\mathbb{Q},<)$ and $(\mathbb{R},<)$ are models, but $(\mathbb{Z},<)$ is not, and neither is the extended real line, or the interval $[0,1]$.
DLO is o-minimal, countably categorical, and NIP, but not uncountably categorical, stable, or simple. It has quantifier elimination in the language with the ordering. It has elimination of imaginaries in the weak sense that every element of $M^{eq}$ is interdefinable with an element of the home sort (right?), but there are quotients that cannot be eliminated. In particular, after naming two elements, DLO has elimination of imaginaries in every sense of the word.
DLO is the model companion of totally ordered sets, and can be seen as a Fraïsse limit of finite total orderings.
Community content is available under CC-BY-SA unless otherwise noted.
| 2020-07-12T13:18:18 |
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https://www.pnnl.gov/news-media/balancing-act-pnnl-study-featured-bulk-power-systems-book
|
September 12, 2017
Web Feature
## Balancing Act: PNNL Study Featured in Bulk Power Systems Book
Consolidation of balancing authorities could result in economic and regulatory efficiencies
A recent study by PNNL researchers is part of a new book about integrating renewable energy in bulk power systems.
The study, “Balancing Authority Cooperation Concepts to Reduce Variable Generation Integration Costs in the Western Interconnection: Consolidating Balancing Authorities and Sharing Balancing Reserves,” was published as Chapter 6 in the book Integration of Large-Scale Renewable Energy into Bulk Storage Systems.
## Avoiding the Dark
Solar and wind power is affordable and infinite, but also intermittent. As these renewable energy sources increasingly penetrate the power grid, grid operators must be continuously nimble in adjusting operating parameters, as an imbalance of electricity demand (load) and supply (generation) can have repercussions such as widespread blackouts.
This challenge is pervasive especially in large interconnected power systems, such as the Western Interconnection, which stretches from western Canada to Baja California in Mexico and reaches eastward to the Great Plains. Such systems are typically operated by a network of individual balancing authorities who are tasked to make sure that electricity generation, transmission, and distribution systems work reliably within their regions. But, at times balancing authorities find their energy resources limited due to variability of renewable energy. This forces the balancing authority to seek more expensive energy resources to maintain balance of load and generation, or even run out of resources.
## Making the Case for Consolidation
The Western Electricity Coordinating Council—responsible for bulk electric system reliability—has been exploring issues surrounding integration of variable generation resources such as wind and solar into the Western Interconnection. PNNL has supported WECC’s effort by developing and deploying a detailed model and methodology to demonstrate the benefits of consolidating balancing authorities—which would result in the ability for neighboring balancing authorities to access and use spare energy resources to manage variations in power. In particular, the team investigated savings in both energy production costs and balancing reserve requirements within the WECC system.
The study assumed two different scenarios of variable generation penetration: 11 percent (8 percent wind and 3 percent solar), and 33 percent (24 percent wind and 9 percent solar) of WECC projected energy demand in 2020. The team used projections from a WECC Transmission Expansion Planning Policy Committee 2020 case to obtain load, wind and solar data as well as hydropower plant, thermal generation, and transmission modeling data and applied that data to three simulated scenarios:
• Scenario 1: today’s balancing authority structure;
• Scenario 2: full balancing authority consolidation with the transmission system having infinite capability; and
• Scenario 3: full balancing authority consolidation with transmission system constraints, such as thermal and security constraints.
Results of the study indicate that diversity of electricity load and renewable generation over a wide area, versus with individual balancing authorities, can result in significant savings as well as smaller reserve requirements, widespread use of inexpensive power resources, and fewer load and renewable resource forecasting errors.
In the 11 percent variable generation penetration case, the study found that annual production cost savings by consolidating balancing authorities (Scenario 3) ranges from $440 million and$610 million, depending on the balancing authority simulation scenario. In addition, Scenario 2 results in an extra savings of $240 million per year. In the 33 percent case, annual production cost savings by consolidating balancing authorities range from$442 million to $636 million (Scenario 3), with another$980 million in savings achieved in Scenario 2 due to lower curtailment of renewable generation.
The results from the study also show evidence that consolidation can achieve significant savings in regulation and load-following requirements, such as increased ramping—the ability to start and stop energy output on demand—and duration of ramping. Outcomes in this study represent an upper bound of potential benefits of balancing authority cooperation and provide the evidence needed to motivate cooperation to enable higher levels of renewable penetration without significant costs due to integration. Partial benefits can be achieved by other forms of balancing authority cooperation, such as the implementation of an Energy Imbalance Market—a real-time energy supply market that offers electricity generation and transmission services.
This research is based on work funded by the DOE Office of Energy Efficiency and Renewable Energy Wind Program and the DOE Office of Electricity Delivery and Energy Reliability Advanced Grid Modeling Program.
The book is available for purchase on the Springer website.
## Key Capabilities
Published: September 12, 2017
### PNNL Research Team
Nader Samaan, Yuri Makarov, Tony Nguyen, and Ruisheng Diao
| 2020-09-21T19:27:07 |
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https://www.detailedpedia.com/wiki-Moon
|
# Moon
Moon
The near side of the Moon (north at top) as seen from Earth
Designations
Designation
Earth I
Orbital characteristics
Epoch J2000
Perigee362600 km
(356400370400 km)
Apogee405400 km
(404000406700 km)
384399 km (1.28 ls, 0.00257 AU)
Eccentricity0.0549
27.321661 d
(27 d 7 h 43 min 11.5 s)
29.530589 d
(29 d 12 h 44 min 2.9 s)
1.022 km/s
Inclination5.145° to the ecliptic
Regressing by one revolution in 18.61 years
Progressing by one
revolution in 8.85 years
Satellite ofEarth
Physical characteristics
1737.4 km
(0.2727 of Earth's)
1738.1 km
(0.2725 of Earth's)
1736.0 km
(0.2731 of Earth's)
Flattening0.0012
Circumference10921 km
3.793×107 km2
(0.074 of Earth's)
Volume2.1958×1010 km3
(0.02 of Earth's)
Mass7.342×1022 kg
(0.0123 of Earth's)
Mean density
3.344 g/cm3
0.606 × Earth
1.622 m/s2 (0.1654 g; 5.318 ft/s2)
0.3929±0.0009
2.38 km/s
(8600 km/h; 5300 mph)
29.530589 d
(29 d 12 h 44 min 2.9 s; synodic; solar day) (spin-orbit locked)
27.321661 d (spin-orbit locked)
Equatorial rotation velocity
4.627 m/s
North pole right ascension
• 17h 47m 26s
• 266.86°
North pole declination
65.64°
Albedo0.136
Surface temp. min mean max
Equator 100 K 250 K 390 K
85°N 150 K 230 K
Surface absorbed dose rate13.2 μGy/h
Surface equivalent dose rate57.0 μSv/h
• −2.5 to −12.9
• −12.74 (mean full moon)
29.3 to 34.1 arcminutes
Atmosphere
Surface pressure
• 10−7 Pa (1 picobar) (day)
• 10−10 Pa (1 femtobar)
(night)
Composition by volume
The Moon is Earth's only natural satellite. It is the fifth largest satellite in the Solar System and the largest and most massive relative to its parent planet, with a diameter about one-quarter that of Earth (comparable to the width of Australia). The Moon is a planetary-mass object with a differentiated rocky body, making it a satellite planet under the geophysical definitions of the term and larger than all known dwarf planets of the Solar System. It lacks any significant atmosphere, hydrosphere, or magnetic field. Its surface gravity is about one-sixth of Earth's at 0.1654 g, with Jupiter's moon Io being the only satellite in the Solar System known to have a higher surface gravity and density.
Orbiting Earth at an average distance of 384,400 km (238,900 mi), or about 30 times Earth's diameter, its gravitational influence very slowly lengthens Earth's day and is the main driver of Earth's tides. The Moon's orbit around Earth has a sidereal period of 27.3 days. During each synodic period of 29.5 days, the amount of visible surface illuminated by the Sun varies from none up to 100%, resulting in lunar phases that form the basis for the months of a lunar calendar. The Moon is tidally locked to Earth, which means that the length of a full rotation of the Moon on its own axis causes its same side (the near side) to always face Earth, and the somewhat longer lunar day is the same as the synodic period. However, 59% of the total lunar surface can be seen from Earth through shifts in perspective due to libration.
The most widely accepted origin explanation posits that the Moon formed 4.51 billion years ago, not long after Earth, out of the debris from a giant impact between the planet and a hypothesized Mars-sized body called Theia. It then receded to a wider orbit because of tidal interaction with the Earth. The near side of the Moon is marked by dark volcanic maria ("seas"), which fill the spaces between bright ancient crustal highlands and prominent impact craters. Most of the large impact basins and mare surfaces were in place by the end of the Imbrian period, some three billion years ago. The lunar surface is relatively non-reflective, with a reflectance just slightly brighter than that of worn asphalt. However, because it has a large angular diameter, the full moon is the brightest celestial object in the night sky. The Moon's apparent size is nearly the same as that of the Sun, allowing it to cover the Sun almost completely during a total solar eclipse.
Both the Moon's prominence in Earth's sky and its regular cycle of phases have provided cultural references and influences for human societies throughout history. Such influences can be found in language, calendar systems, art, and mythology. The first artificial object to reach the Moon was the Soviet Union's Luna 2 uncrewed spacecraft in 1959; this was followed by the first successful soft landing by Luna 9 in 1966. The only human lunar missions to date have been those of the United States' Apollo program, which landed twelve men on the surface between 1969 and 1972. These and later uncrewed missions returned lunar rocks that have been used to develop a detailed geological understanding of the Moon's origins, internal structure, and subsequent history.
## Names and etymology
The usual English proper name for Earth's natural satellite is simply Moon, with a capital M. The noun moon is derived from Old English mōna, which (like all its Germanic cognates) stems from Proto-Germanic *mēnōn, which in turn comes from Proto-Indo-European *mēnsis "month" (from earlier *mēnōt, genitive *mēneses) which may be related to the verb "measure" (of time).
Occasionally, the name Luna /ˈluːnə/ is used in scientific writing and especially in science fiction to distinguish the Earth's moon from others, while in poetry "Luna" has been used to denote personification of the Moon. Cynthia /ˈsɪnθiə/ is another poetic name, though rare, for the Moon personified as a goddess, while Selene /səˈliːniː/ (literally "Moon") is the Greek goddess of the Moon.
The usual English adjective pertaining to the Moon is "lunar", derived from the Latin word for the Moon, lūna. The adjective selenian /səliːniən/, derived from the Greek word for the Moon, σελήνη selēnē, and used to describe the Moon as a world rather than as an object in the sky, is rare, while its cognate selenic was originally a rare synonym but now nearly always refers to the chemical element selenium. The Greek word for the Moon does however provide us with the prefix seleno-, as in selenography, the study of the physical features of the Moon, as well as the element name selenium.
The Greek goddess of the wilderness and the hunt, Artemis, equated with the Roman Diana, one of whose symbols was the Moon and who was often regarded as the goddess of the Moon, was also called Cynthia, from her legendary birthplace on Mount Cynthus. These names – Luna, Cynthia and Selene – are reflected in technical terms for lunar orbits such as apolune, pericynthion and selenocentric.
The astronomical symbol for the Moon is a crescent, , for example in M 'lunar mass' (also ML).
## Natural history
### Lunar geologic timescale
Millions of years before present
Geologic map of the Moon with general features are colored in by age, except in the case of maria (in blue), KREEP (red) and other special features. Oldest to youngest: Aitkenian (pink), Nectarian (brown), Imbrian (greens/turquoise), Eratosthenian (light orange) and Copernican (yellow).
### Formation
Isotope dating of lunar samples suggests the Moon formed around 50 million years after the origin of the Solar System. Historically, several formation mechanisms have been proposed, but none satisfactorily explains the features of the Earth–Moon system. A fission of the Moon from Earth's crust through centrifugal force would require too great an initial rotation rate of Earth. Gravitational capture of a pre-formed Moon depends on an unfeasibly extended atmosphere of Earth to dissipate the energy of the passing Moon. A co-formation of Earth and the Moon together in the primordial accretion disk does not explain the depletion of metals in the Moon. None of these hypotheses can account for the high angular momentum of the Earth–Moon system.
Earth–Moon system from Mars orbit
The prevailing theory is that the Earth–Moon system formed after a giant impact of a Mars-sized body (named Theia) with the proto-Earth. The impact blasted material into orbit about the Earth and the material accreted and formed the Moon just beyond the Earth's Roche limit of ~2.56 R🜨.
Giant impacts are thought to have been common in the early Solar System. Computer simulations of giant impacts have produced results that are consistent with the mass of the lunar core and the angular momentum of the Earth–Moon system. These simulations show that most of the Moon derived from the impactor, rather than the proto-Earth. However, more recent simulations suggest a larger fraction of the Moon derived from the proto-Earth. Other bodies of the inner Solar System such as Mars and Vesta have, according to meteorites from them, very different oxygen and tungsten isotopic compositions compared to Earth. However, Earth and the Moon have nearly identical isotopic compositions. The isotopic equalization of the Earth-Moon system might be explained by the post-impact mixing of the vaporized material that formed the two, although this is debated.
The impact would have released enough energy to liquefy both the ejecta and the Earth's crust, forming a magma ocean. The liquefied ejecta could have then re-accreted into the Earth–Moon system. Similarly, the newly formed Moon would have had its own lunar magma ocean; its depth is estimated from about 500 km (300 miles) to 1,737 km (1,079 miles).
While the giant-impact theory explains many lines of evidence, some questions are still unresolved, most of which involve the Moon's composition.[example needed]Above a high resolution threshold for simulations, a study published in 2022 finds that giant impacts can immediately place a satellite with similar mass and iron content to the Moon into orbit far outside Earth's Roche limit. Even satellites that initially pass within the Roche limit can reliably and predictably survive, by being partially stripped and then torqued onto wider, stable orbits.
### Natural development
Artist's impression of the Moon as it might have appeared in Earth's sky after the Late Heavy Bombardment around 4 billion years ago. At that time the Moon orbited Earth much closer, appearing much larger.
After the Moon's formation the Moon settled in orbit around Earth much closer than today, making both bodies appear much larger in each's sky and causing on both more frequent and stronger eclipses and tidal effects. Since then, due to tidal acceleration, the Moon's orbit around Earth has become significantly larger as well as longer, tidally locking the so-called lunar near side, always facing Earth with this same side.
The post formation cooled lunar surface has been shaped by large and many small impact events, retaining a broadly cratered landscape of all ages, as well as by volcanic activity, producing the prominent lunar maria. Volcanically active until 1.2 billion years ago, most of the Moon's mare basalts erupted during the Imbrian period, 3.3–3.7 billion years ago, though some being as young as 1.2 billion years and some as old as 4.2 billion years. The causes for the eruption of mare basalts, particularly their uneven occurrence on mainly the near-side, like the lunar highlands on the far side, has been an unresolved issue due to differing explanations. One explanation suggests that large meteorites were hitting the Moon in its early history leaving large craters which then were filled with lava. Other explanations suggest processes of lunar volcanism.
## Physical characteristics
The Moon is a very slightly scalene ellipsoid due to tidal stretching, with its long axis displaced 30° from facing the Earth, due to gravitational anomalies from impact basins. Its shape is more elongated than current tidal forces can account for. This 'fossil bulge' indicates that the Moon solidified when it orbited at half its current distance to the Earth, and that it is now too cold for its shape to adjust to its orbit.
### Size and mass
Size comparison of the main moons of the Solar System with Earth to scale. Nineteen moons are large enough to be round, several having subsurface oceans and one, Titan, having a considerable atmosphere.
The Moon is by size and mass the fifth largest natural satellite of the Solar System, categorizeable as one of its planetary-mass moons, making it a satellite planet under the geophysical definitions of the term. It is smaller than Mercury and considerably larger than the largest dwarf planet of the Solar System, Pluto. While the minor-planet moon Charon of the Pluto-Charon system is larger relative to Pluto, the Moon is the largest natural satellite of the Solar System relative to their primary planets.
The Moon's diameter is about 3,500 km, more than a quarter of Earth's, with the face of the Moon comparable to the width of Australia. The whole surface area of the Moon is about 38 million square kilometers, slightly less than the area of the Americas (North and South America).
The Moon's mass is 1/81 of Earth's, being the second densest among the planetary moons, and having the second highest surface gravity, after Io, at 0.1654 g and an escape velocity of 2.38 km/s (8600 km/h; 5300 mph).
### Structure
Moon's internal structure
The Moon is a differentiated body that was initially in hydrostatic equilibrium but has since departed from this condition. It has a geochemically distinct crust, mantle, and core. The Moon has a solid iron-rich inner core with a radius possibly as small as 240 kilometres (150 mi) and a fluid outer core primarily made of liquid iron with a radius of roughly 300 kilometres (190 mi). Around the core is a partially molten boundary layer with a radius of about 500 kilometres (310 mi). This structure is thought to have developed through the fractional crystallization of a global magma ocean shortly after the Moon's formation 4.5 billion years ago.
Crystallization of this magma ocean would have created a mafic mantle from the precipitation and sinking of the minerals olivine, clinopyroxene, and orthopyroxene; after about three-quarters of the magma ocean had crystallized, lower-density plagioclase minerals could form and float into a crust atop. The final liquids to crystallize would have been initially sandwiched between the crust and mantle, with a high abundance of incompatible and heat-producing elements. Consistent with this perspective, geochemical mapping made from orbit suggests a crust of mostly anorthosite. The Moon rock samples of the flood lavas that erupted onto the surface from partial melting in the mantle confirm the mafic mantle composition, which is more iron-rich than that of Earth. The crust is on average about 50 kilometres (31 mi) thick.
The Moon is the second-densest satellite in the Solar System, after Io. However, the inner core of the Moon is small, with a radius of about 350 kilometres (220 mi) or less, around 20% of the radius of the Moon. Its composition is not well understood, but is probably metallic iron alloyed with a small amount of sulfur and nickel; analyses of the Moon's time-variable rotation suggest that it is at least partly molten. The pressure at the lunar core is estimated to be 5 GPa (49,000 atm).
#### Magnetic and gravitational fields
The Moon has an external magnetic field of less than 0.2 nanoteslas, or less than one hundred thousandth that of Earth. The Moon does not currently have a global dipolar magnetic field and only has crustal magnetization likely acquired early in its history when a dynamo was still operating. However, early in its history, 4 billion years ago, its magnetic field strength was likely close to that of Earth today. This early dynamo field apparently expired by about one billion years ago, after the lunar core had completely crystallized. Theoretically, some of the remnant magnetization may originate from transient magnetic fields generated during large impacts through the expansion of plasma clouds. These clouds are generated during large impacts in an ambient magnetic field. This is supported by the location of the largest crustal magnetizations situated near the antipodes of the giant impact basins.
The Moon's gravitational field is not uniform. The details of the gravitational field have been measured through tracking the Doppler shift of radio signals emitted by orbiting spacecraft. The main lunar gravity features are mascons, large positive gravitational anomalies associated with some of the giant impact basins, partly caused by the dense mare basaltic lava flows that fill those basins. The anomalies greatly influence the orbit of spacecraft about the Moon. There are some puzzles: lava flows by themselves cannot explain all of the gravitational signature, and some mascons exist that are not linked to mare volcanism.
### Surface conditions
On average the Moon's surface gravity is 1.62 m/s2 (0.1654 g; 5.318 ft/s2), about half of the surface gravity of Mars and about a sixth of Earth's. The surface of the Moon, having a surface pressure of 10−10 Pa, lacks any significant atmosphere to moderate the extreme conditions of the surface.
Ionizing radiation from cosmic rays, the Sun and the resulting neutron radiation produce radiation levels on average of 1,369 microsieverts per day, which is about 2-3 times more than on the International Space Station at about 400 km above Earth in orbit, 5-10 times more than during a trans-Atlantic flight, 200 times more than on Earth's surface. For further comparison radiation on a flight to Mars is about 1.84 millisieverts per day and on Mars 0.64 millisieverts per day.
The Moon's axial tilt with respect to the ecliptic is only 1.5427°, much less than the 23.44° of Earth. Because of this small tilt, the Moon's solar illumination varies much less with season than on Earth and it allows for the existence of some peaks of eternal light at the Moon's north pole, at the rim of the crater Peary.
The surface is exposed to drastic temperature differences ranging from 140 °C to −171 °C depending on the solar irradiance. Because of the lack of atmosphere, temperatures of different areas vary particularly upon whether they are in sunlight or shadow, making topographical details play a decisive role on local surface temperatures. Parts of many craters, particularly the bottoms of many polar craters, are permanently shadowed, these "craters of eternal darkness" have extremely low temperatures. The Lunar Reconnaissance Orbiter measured the lowest summer temperatures in craters at the southern pole at 35 K (−238 °C; −397 °F) and just 26 K (−247 °C; −413 °F) close to the winter solstice in the north polar crater Hermite. This is the coldest temperature in the Solar System ever measured by a spacecraft, colder even than the surface of Pluto.
These extreme conditions for example are considered making it unlikely for spacecrafts to harbor bacterial spores at the Moon longer than just one lunar orbit.
### Atmosphere
The thin lunar atmosphere is visible on the Moon's surface at sunrise and sunset with the Lunar Horizon Glow and lunar twilight rays, like Earth's crepuscular rays. This Apollo 17 sketch depicts the glow and rays among the general zodiacal light.
The Moon has an atmosphere so tenuous as to be nearly vacuum, with a total mass of less than 10 tonnes (9.8 long tons; 11 short tons). The surface pressure of this small mass is around 3 × 10−15 atm (0.3 nPa); it varies with the lunar day. Its sources include outgassing and sputtering, a product of the bombardment of lunar soil by solar wind ions. Elements that have been detected include sodium and potassium, produced by sputtering (also found in the atmospheres of Mercury and Io); helium-4 and neon from the solar wind; and argon-40, radon-222, and polonium-210, outgassed after their creation by radioactive decay within the crust and mantle. The absence of such neutral species (atoms or molecules) as oxygen, nitrogen, carbon, hydrogen and magnesium, which are present in the regolith, is not understood. Water vapor has been detected by Chandrayaan-1 and found to vary with latitude, with a maximum at ~60–70 degrees; it is possibly generated from the sublimation of water ice in the regolith. These gases either return into the regolith because of the Moon's gravity or are lost to space, either through solar radiation pressure or, if they are ionized, by being swept away by the solar wind's magnetic field.
Studies of Moon magma samples retrieved by the Apollo missions demonstrate that the Moon had once possessed a relatively thick atmosphere for a period of 70 million years between 3 and 4 billion years ago. This atmosphere, sourced from gases ejected from lunar volcanic eruptions, was twice the thickness of that of present-day Mars. The ancient lunar atmosphere was eventually stripped away by solar winds and dissipated into space.
A permanent Moon dust cloud exists around the Moon, generated by small particles from comets. Estimates are 5 tons of comet particles strike the Moon's surface every 24 hours, resulting in the ejection of dust particles. The dust stays above the Moon approximately 10 minutes, taking 5 minutes to rise, and 5 minutes to fall. On average, 120 kilograms of dust are present above the Moon, rising up to 100 kilometers above the surface. Dust counts made by LADEE's Lunar Dust EXperiment (LDEX) found particle counts peaked during the Geminid, Quadrantid, Northern Taurid, and Omicron Centaurid meteor showers, when the Earth, and Moon pass through comet debris. The lunar dust cloud is asymmetric, being more dense near the boundary between the Moon's dayside and nightside.
### Surface features
Topography of the Moon
The topography of the Moon has been measured with laser altimetry and stereo image analysis. Its most extensive topographic feature is the giant far-side South Pole–Aitken basin, some 2,240 km (1,390 mi) in diameter, the largest crater on the Moon and the second-largest confirmed impact crater in the Solar System. At 13 km (8.1 mi) deep, its floor is the lowest point on the surface of the Moon. The highest elevations of the Moon's surface are located directly to the northeast, which might have been thickened by the oblique formation impact of the South Pole–Aitken basin. Other large impact basins such as Imbrium, Serenitatis, Crisium, Smythii, and Orientale possess regionally low elevations and elevated rims. The far side of the lunar surface is on average about 1.9 km (1.2 mi) higher than that of the near side.
The discovery of fault scarp cliffs suggest that the Moon has shrunk by about 90 metres (300 ft) within the past billion years. Similar shrinkage features exist on Mercury. Mare Frigoris, a basin near the north pole long assumed to be geologically dead, has cracked and shifted. Since the Moon doesn't have tectonic plates, its tectonic activity is slow and cracks develop as it loses heat.
#### Volcanic features
The largest mare, the main dark region of the near side, is Oceanus Procellarum, with smaller mare, such as Imbrium and Serenitatis, that sit within its ring. Left of the centerline is Procellarum proper.
The main features visible from Earth by the naked eye are dark and relatively featureless lunar plains called maria (singular mare; Latin for "seas", as they were once believed to be filled with water) are vast solidified pools of ancient basaltic lava. Although similar to terrestrial basalts, lunar basalts have more iron and no minerals altered by water. The majority of these lava deposits erupted or flowed into the depressions associated with impact basins. Several geologic provinces containing shield volcanoes and volcanic domes are found within the near side "maria".
Almost all maria are on the near side of the Moon, and cover 31% of the surface of the near side compared with 2% of the far side. This is likely due to a concentration of heat-producing elements under the crust on the near side, which would have caused the underlying mantle to heat up, partially melt, rise to the surface and erupt. Most of the Moon's mare basalts erupted during the Imbrian period, 3.3–3.7 billion years ago, though some being as young as 1.2 billion years and as old as 4.2 billion years.
In 2006, a study of Ina, a tiny depression in Lacus Felicitatis, found jagged, relatively dust-free features that, because of the lack of erosion by infalling debris, appeared to be only 2 million years old. Moonquakes and releases of gas indicate continued lunar activity. Evidence of recent lunar volcanism has been identified at 70 irregular mare patches, some less than 50 million years old. This raises the possibility of a much warmer lunar mantle than previously believed, at least on the near side where the deep crust is substantially warmer because of the greater concentration of radioactive elements. Evidence has been found for 2–10 million years old basaltic volcanism within the crater Lowell, inside the Orientale basin. Some combination of an initially hotter mantle and local enrichment of heat-producing elements in the mantle could be responsible for prolonged activities on the far side in the Orientale basin.
The lighter-colored regions of the Moon are called terrae, or more commonly highlands, because they are higher than most maria. They have been radiometrically dated to having formed 4.4 billion years ago, and may represent plagioclase cumulates of the lunar magma ocean. In contrast to Earth, no major lunar mountains are believed to have formed as a result of tectonic events.
The concentration of maria on the near side likely reflects the substantially thicker crust of the highlands of the Far Side, which may have formed in a slow-velocity impact of a second moon of Earth a few tens of millions of years after the Moon's formation. Alternatively, it may be a consequence of asymmetrical tidal heating when the Moon was much closer to the Earth.
#### Impact craters
Lunar crater Daedalus on the Moon's far side
A major geologic process that has affected the Moon's surface is impact cratering, with craters formed when asteroids and comets collide with the lunar surface. There are estimated to be roughly 300,000 craters wider than 1 km (0.6 mi) on the Moon's near side. The lunar geologic timescale is based on the most prominent impact events, including Nectaris, Imbrium, and Orientale; structures characterized by multiple rings of uplifted material, between hundreds and thousands of kilometers in diameter and associated with a broad apron of ejecta deposits that form a regional stratigraphic horizon. The lack of an atmosphere, weather, and recent geological processes mean that many of these craters are well-preserved. Although only a few multi-ring basins have been definitively dated, they are useful for assigning relative ages. Because impact craters accumulate at a nearly constant rate, counting the number of craters per unit area can be used to estimate the age of the surface. The radiometric ages of impact-melted rocks collected during the Apollo missions cluster between 3.8 and 4.1 billion years old: this has been used to propose a Late Heavy Bombardment period of increased impacts.
High-resolution images from the Lunar Reconnaissance Orbiter in the 2010s show a contemporary crater-production rate significantly higher than was previously estimated. A secondary cratering process caused by distal ejecta is thought to churn the top two centimeters of regolith on a timescale of 81,000 years. This rate is 100 times faster than the rate computed from models based solely on direct micrometeorite impacts.
#### Lunar swirls
Lunar Reconnaissance Orbiter Wide Angle Camera image of the lunar swirl Reiner Gamma
Lunar swirls are enigmatic features found across the Moon's surface. They are characterized by a high albedo, appear optically immature (i.e. the optical characteristics of a relatively young regolith), and often have a sinuous shape. Their shape is often accentuated by low albedo regions that wind between the bright swirls. They are located in places with enhanced surface magnetic fields and many are located at the antipodal point of major impacts. Well known swirls include the Reiner Gamma feature and Mare Ingenii. They are hypothesized to be areas that have been partially shielded from the solar wind, resulting in slower space weathering.
### Surface composition
Relative elemental composition of the lunar soil
Blanketed on top of the Moon's crust is a highly comminuted (broken into ever smaller particles) and impact gardened mostly gray surface layer called regolith, formed by impact processes. The finer regolith, the lunar soil of silicon dioxide glass, has a texture resembling snow and a scent resembling spent gunpowder. The regolith of older surfaces is generally thicker than for younger surfaces: it varies in thickness from 10–15 m (33–49 ft) in the highlands and 4–5 m (13–16 ft) in the maria.
Beneath the finely comminuted regolith layer is the megaregolith, a layer of highly fractured bedrock many kilometers thick.
#### Presence of water
Liquid water cannot persist on the lunar surface. When exposed to solar radiation, water quickly decomposes through a process known as photodissociation and is lost to space. However, since the 1960s, scientists have hypothesized that water ice may be deposited by impacting comets or possibly produced by the reaction of oxygen-rich lunar rocks, and hydrogen from solar wind, leaving traces of water which could possibly persist in cold, permanently shadowed craters at either pole on the Moon. Computer simulations suggest that up to 14,000 km2 (5,400 sq mi) of the surface may be in permanent shadow. The presence of usable quantities of water on the Moon is an important factor in rendering lunar habitation as a cost-effective plan; the alternative of transporting water from Earth would be prohibitively expensive.
In years since, signatures of water have been found to exist on the lunar surface. In 1994, the bistatic radar experiment located on the Clementine spacecraft, indicated the existence of small, frozen pockets of water close to the surface. However, later radar observations by Arecibo, suggest these findings may rather be rocks ejected from young impact craters. In 1998, the neutron spectrometer on the Lunar Prospector spacecraft showed that high concentrations of hydrogen are present in the first meter of depth in the regolith near the polar regions. Volcanic lava beads, brought back to Earth aboard Apollo 15, showed small amounts of water in their interior.
The 2008 Chandrayaan-1 spacecraft has since confirmed the existence of surface water ice, using the on-board Moon Mineralogy Mapper. The spectrometer observed absorption lines common to hydroxyl, in reflected sunlight, providing evidence of large quantities of water ice, on the lunar surface. The spacecraft showed that concentrations may possibly be as high as 1,000 ppm. Using the mapper's reflectance spectra, indirect lighting of areas in shadow confirmed water ice within 20° latitude of both poles in 2018. In 2009, LCROSS sent a 2,300 kg (5,100 lb) impactor into a permanently shadowed polar crater, and detected at least 100 kg (220 lb) of water in a plume of ejected material. Another examination of the LCROSS data showed the amount of detected water to be closer to 155 ± 12 kg (342 ± 26 lb).
In May 2011, 615–1410 ppm water in melt inclusions in lunar sample 74220 was reported, the famous high-titanium "orange glass soil" of volcanic origin collected during the Apollo 17 mission in 1972. The inclusions were formed during explosive eruptions on the Moon approximately 3.7 billion years ago. This concentration is comparable with that of magma in Earth's upper mantle. Although of considerable selenological interest, this insight does not mean that water is easily available since the sample originated many kilometers below the surface, and the inclusions are so difficult to access that it took 39 years to find them with a state-of-the-art ion microprobe instrument.
Analysis of the findings of the Moon Mineralogy Mapper (M3) revealed in August 2018 for the first time "definitive evidence" for water-ice on the lunar surface. The data revealed the distinct reflective signatures of water-ice, as opposed to dust and other reflective substances. The ice deposits were found on the North and South poles, although it is more abundant in the South, where water is trapped in permanently shadowed craters and crevices, allowing it to persist as ice on the surface since they are shielded from the sun.
In October 2020, astronomers reported detecting molecular water on the sunlit surface of the Moon by several independent spacecraft, including the Stratospheric Observatory for Infrared Astronomy (SOFIA).
## Earth–Moon system
### Orbit
DSCOVR satellite sees the Moon passing in front of Earth
The Earth and the Moon form the Earth-Moon satellite system with a shared center of mass, or barycenter. This barycenter stays located at all times 1,700 km (1,100 mi) (about a quarter of Earth's radius) beneath the Earth's surface, making the Moon seemingly orbit the Earth.
Earth and Moon
(Orion; 28 Nov 2022)
The orbital eccentricity, giving ovalness of the orbit, is 0.055. The Lunar distance, or the semi-major axis of the geocentric lunar orbit, is approximately 400,000 km, which is a quarter of a million miles or 1.28 light-seconds, and a unit of measure in astronomy. This is not to be confused with the instantaneous Earth–Moon distance, or distance to the Moon, the momentanous distance from the center of Earth to the center of the Moon.
The Moon makes a complete orbit around Earth with respect to the fixed stars, its sidereal period, about once every 27.3 days,. However, because the Earth-Moon system moves at the same time in its orbit around the Sun, it takes slightly longer, 29.5 days;, to return at the same lunar phase, completing a full cycle, as seen from Earth. This synodic period or synodic month is commonly known as the lunar month and is equal to the length of the solar day on the Moon.
Due to tidal locking, the Moon has a 1:1 spin–orbit resonance. This rotationorbit ratio makes the Moon's orbital periods around Earth equal to its corresponding rotation periods. This is the reason for only one side of the Moon, its so-called near side, being visible from Earth. That said, while the movement of the Moon is in resonance, it still is not without nuances such as libration, resulting in slightly changing perspectives, making over time and location on Earth about 59% of the Moon's surface visible from Earth.
Unlike most satellites of other planets, the Moon's orbital plane is closer to the ecliptic plane than to the planet's equatorial plane. The Moon's orbit is subtly perturbed by the Sun and Earth in many small, complex and interacting ways. For example, the plane of the Moon's orbit gradually rotates once every 18.61years, which affects other aspects of lunar motion. These follow-on effects are mathematically described by Cassini's laws.
Minimum, mean and maximum distances of the Moon from Earth with its angular diameter as seen from Earth's surface, to scale.
### Tidal effects
Simplified diagram of the Moon's gravity tidal effect on the Earth
The gravitational attraction that Earth and the Moon (as well as the Sun) exert on each other manifests in a slightly greater attraction on the sides of closest to each other, resulting in tidal forces. Ocean tides are the most widely experienced result of this, but tidal forces considerably affect also other mechanics of Earth, as well as the Moon and their system.
The lunar solid crust experiences tides of around 10 cm (4 in) amplitude over 27 days, with three components: a fixed one due to Earth, because they are in synchronous rotation, a variable tide due to orbital eccentricity and inclination, and a small varying component from the Sun. The Earth-induced variable component arises from changing distance and libration, a result of the Moon's orbital eccentricity and inclination (if the Moon's orbit were perfectly circular and un-inclined, there would only be solar tides). According to recent research, scientists suggest that the Moon's influence on the Earth may contribute to maintaining Earth's magnetic field.
The cumulative effects of stress built up by these tidal forces produces moonquakes. Moonquakes are much less common and weaker than are earthquakes, although moonquakes can last for up to an hour – significantly longer than terrestrial quakes – because of scattering of the seismic vibrations in the dry fragmented upper crust. The existence of moonquakes was an unexpected discovery from seismometers placed on the Moon by Apollo astronauts from 1969 through 1972.
The most commonly known effect of tidal forces are elevated sea levels called ocean tides. While the Moon exerts most of the tidal forces, the Sun also exerts tidal forces and therefore contributes to the tides as much as 40% of the Moon's tidal force; producing in interplay the spring and neap tides.
The tides are two bulges in the Earth's oceans, one on the side facing the Moon and the other on the side opposite. As the Earth rotates on its axis, one of the ocean bulges (high tide) is held in place "under" the Moon, while another such tide is opposite. As a result, there are two high tides, and two low tides in about 24 hours. Since the Moon is orbiting the Earth in the same direction of the Earth's rotation, the high tides occur about every 12 hours and 25 minutes; the 25 minutes is due to the Moon's time to orbit the Earth.
If the Earth were a water world (one with no continents) it would produce a tide of only one meter, and that tide would be very predictable, but the ocean tides are greatly modified by other effects:
• the frictional coupling of water to Earth's rotation through the ocean floors
• the inertia of water's movement
• ocean basins that grow shallower near land
• the sloshing of water between different ocean basins
As a result, the timing of the tides at most points on the Earth is a product of observations that are explained, incidentally, by theory.
Delays in the tidal peaks of both ocean and solid-body tides cause torque in opposition to the Earth's rotation. This "drains" angular momentum and rotational kinetic energy from Earth's rotation, slowing the Earth's rotation. That angular momentum, lost from the Earth, is transferred to the Moon in a process known as tidal acceleration, which lifts the Moon into a higher orbit while lowering orbital speed around the Earth.
Thus the distance between Earth and Moon is increasing, and the Earth's rotation is slowing in reaction. Measurements from laser reflectors left during the Apollo missions (lunar ranging experiments) have found that the Moon's distance increases by 38 mm (1.5 in) per year (roughly the rate at which human fingernails grow). Atomic clocks show that Earth's day lengthens by about 17 microseconds every year, slowly increasing the rate at which UTC is adjusted by leap seconds.
This tidal drag makes the rotation of Earth and the orbital period of the Moon very slowly match. This matching first results in tidally locking the lighter body of the orbital system, as already the case with the Moon. Eventually, after 50 billion years, also the Earth would be made to always face the Moon with the same side. This would complete the mutual tidal locking of Earth and the Moon, matching the length of Earth's day to the then also significantly increased lunar month and the Moon's day, and suspending the Moon over one meridian (comparable to the Pluto-Charon system). However, the Sun will become a red giant engulfing the Earth-Moon system long before the latter occurs.
## Position and appearance
### Rotation
Comparison between the Moon on the left, rotating tidally locked (correct), and with the Moon on the right, without rotation (incorrect).
The tidally locked synchronous rotation of the Moon as it orbits the Earth results in it always keeping nearly the same face turned towards the planet. The side of the Moon that faces Earth is called the near side, and the opposite the far side. The far side is often inaccurately called the "dark side", but it is in fact illuminated as often as the near side: once every 29.5 Earth days. During dark moon to new moon, the near side is dark.
The Moon originally rotated at a faster rate, but early in its history its rotation slowed and became tidally locked in this orientation as a result of frictional effects associated with tidal deformations caused by Earth. With time, the energy of rotation of the Moon on its axis was dissipated as heat, until there was no rotation of the Moon relative to Earth. In 2016, planetary scientists using data collected on the 1998-99 NASA Lunar Prospector mission, found two hydrogen-rich areas (most likely former water ice) on opposite sides of the Moon. It is speculated that these patches were the poles of the Moon billions of years ago before it was tidally locked to Earth.
### View from Earth
Libration, the slight variation in the Moon's apparent size and viewing angle over a single lunar month as viewed from Earth's north.
The Moon's highest altitude at culmination varies by its lunar phase, or more correctly its orbital position, and time of the year, or more correctly the position of the Earth's axis. The full moon is highest in the sky during winter and lowest during summer (for each hemisphere respectively), with its altitude changing towards dark moon to the opposite.
At the North and South Poles the Moon is 24 hours above the horizon for two weeks every tropical month (about 27.3 days), comparable to the polar day of the tropical year. Zooplankton in the Arctic use moonlight when the Sun is below the horizon for months on end.
The apparent orientation of the Moon depends on its position in the sky and the hemisphere of the Earth from which it is being viewed. In the northern hemisphere it is seen upside down compared to the view in the southern hemisphere. Sometimes the "horns" of a crescent moon appear to be pointing more upwards than sideways. This phenomenon is called a wet moon and occurs more frequently in the tropics.
The distance between the Moon and Earth varies from around 356,400 km (221,500 mi) to 406,700 km (252,700 mi) at perigee (closest) and apogee (farthest), respectively, making the Moon's apparent size fluctuate. On sverage the Moon's angular diameter is about 0.52° (on average) in the sky, roughly the same apparent size as the Sun (see § Eclipses). Additionally when close to the horizon a purely psychological effect, known as the Moon illusion, makes the Moon appear larger.
Despite the Moon's tidal locking, the effect of libration makes about 59% of the Moon's surface visible from Earth over the course of one month.
### Albedo and color
The changing apparent color of the Moon, filtered by Earth's atmosphere.
The Moon has an exceptionally low albedo, giving it a reflectance that is slightly brighter than that of worn asphalt. Despite this, it is the brightest object in the sky after the Sun. This is due partly to the brightness enhancement of the opposition surge; the Moon at quarter phase is only one-tenth as bright, rather than half as bright, as at full moon. Additionally, color constancy in the visual system recalibrates the relations between the colors of an object and its surroundings, and because the surrounding sky is comparatively dark, the sunlit Moon is perceived as a bright object. The edges of the full moon seem as bright as the center, without limb darkening, because of the reflective properties of lunar soil, which retroreflects light more towards the Sun than in other directions. The Moon's color depends on the light the Moon reflects, which in turn depends on the Moon's surface and its features, having for example large darker regions. In general the lunar surface reflects a brown-tinged gray light.
Viewed from Earth the air filters the reflected light, at times giving it a red color depending on the angle of the Moon in the sky and thickness of the atmosphere, or a blue tinge depending on the particles in the air, as in cases of volcanic particles. The terms blood moon and blue moon do not necessarily refer to circumstances of red or blue moonlight, but are rather particular cultural references such as particular full moons of a year.
There has been historical controversy over whether observed features on the Moon's surface change over time. Today, many of these claims are thought to be illusory, resulting from observation under different lighting conditions, poor astronomical seeing, or inadequate drawings. However, outgassing does occasionally occur and could be responsible for a minor percentage of the reported lunar transient phenomena. Recently, it has been suggested that a roughly 3 km (1.9 mi) diameter region of the lunar surface was modified by a gas release event about a million years ago.
### Illumination and phases
Day moon, the moon is visible during daylight almost every day.
Half of the Moon's surface is always illuminated by the Sun (except during a lunar eclipse). Earth also reflects light onto the Moon, observable at times as Earthlight when it is again reflected back to Earth from areas of the near side of the Moon that are not illuminated by the Sun.
With the different positions of the Moon, different areas of it are illuminated by the Sun. This illumination of different lunar areas, as viewed from Earth, produces the different lunar phases during the synodic month. A phase is equal to the area of the visible lunar sphere that is illuminated by the Sun. This area or degree of illumination is given by ${\displaystyle (1-\cos e)/2=\sin ^{2}(e/2)}$, where ${\displaystyle e}$ is the elongation (i.e., the angle between Moon, the observer on Earth, and the Sun).
The monthly changes in the angle between the direction of sunlight and view from Earth, and the phases of the Moon that result, as viewed from the Northern Hemisphere. The Earth–Moon distance is not to scale.
On 14 November 2016, the Moon was at full phase closer to Earth than it had been since 1948. It was 14% closer and larger than its farthest position in apogee. This closest point coincided within an hour of a full moon, and it was 30% more luminous than when at its greatest distance because of its increased apparent diameter, which made it a particularly notable example of a "supermoon".
At lower levels, the human perception of reduced brightness as a percentage is provided by the following formula:
${\displaystyle {\text{perceived reduction}}\%=100\times {\sqrt {{\text{actual reduction}}\% \over 100}}}$
When the actual reduction is 1.00 / 1.30, or about 0.770, the perceived reduction is about 0.877, or 1.00 / 1.14. This gives a maximum perceived increase of 14% between apogee and perigee moons of the same phase.
### Eclipses
A solar eclipse cause the Sun to be covered, revealing the white corona
The Moon, tinted reddish, during a lunar eclipse
Eclipses only occur when the Sun, Earth, and Moon are all in a straight line (termed "syzygy"). Solar eclipses occur at new moon, when the Moon is between the Sun and Earth. In contrast, lunar eclipses occur at full moon, when Earth is between the Sun and Moon. The apparent size of the Moon is roughly the same as that of the Sun, with both being viewed at close to one-half a degree wide. The Sun is much larger than the Moon but it is the vastly greater distance that gives it the same apparent size as the much closer and much smaller Moon from the perspective of Earth. The variations in apparent size, due to the non-circular orbits, are nearly the same as well, though occurring in different cycles. This makes possible both total (with the Moon appearing larger than the Sun) and annular (with the Moon appearing smaller than the Sun) solar eclipses. In a total eclipse, the Moon completely covers the disc of the Sun and the solar corona becomes visible to the naked eye. Because the distance between the Moon and Earth is very slowly increasing over time, the angular diameter of the Moon is decreasing. As it evolves toward becoming a red giant, the size of the Sun, and its apparent diameter in the sky, are slowly increasing. The combination of these two changes means that hundreds of millions of years ago, the Moon would always completely cover the Sun on solar eclipses, and no annular eclipses were possible. Likewise, hundreds of millions of years in the future, the Moon will no longer cover the Sun completely, and total solar eclipses will not occur.
Because the Moon's orbit around Earth is inclined by about 5.145° (5° 9') to the orbit of Earth around the Sun, eclipses do not occur at every full and new moon. For an eclipse to occur, the Moon must be near the intersection of the two orbital planes. The periodicity and recurrence of eclipses of the Sun by the Moon, and of the Moon by Earth, is described by the saros, which has a period of approximately 18 years.
Because the Moon continuously blocks the view of a half-degree-wide circular area of the sky, the related phenomenon of occultation occurs when a bright star or planet passes behind the Moon and is occulted: hidden from view. In this way, a solar eclipse is an occultation of the Sun. Because the Moon is comparatively close to Earth, occultations of individual stars are not visible everywhere on the planet, nor at the same time. Because of the precession of the lunar orbit, each year different stars are occulted.
## History of exploration and human presence
### Pre-telescopic observation (before 1609)
It is believed by some that 20–30,000 year old tally sticks, were used to observe the phases of the Moon, keeping time using the waxing and waning of the Moon's phases. One of the earliest-discovered possible depictions of the Moon is a 5000-year-old rock carving Orthostat 47 at Knowth, Ireland.
The ancient Greek philosopher Anaxagoras (d. 428 BC) reasoned that the Sun and Moon were both giant spherical rocks, and that the latter reflected the light of the former.: 227 Elsewhere in the 5th century BC to 4th century BC, Babylonian astronomers had recorded the 18-year Saros cycle of lunar eclipses, and Indian astronomers had described the Moon's monthly elongation. The Chinese astronomer Shi Shen (fl. 4th century BC) gave instructions for predicting solar and lunar eclipses.: 411
In Aristotle's (384–322 BC) description of the universe, the Moon marked the boundary between the spheres of the mutable elements (earth, water, air and fire), and the imperishable stars of aether, an influential philosophy that would dominate for centuries. Archimedes (287–212 BC) designed a planetarium that could calculate the motions of the Moon and other objects in the Solar System. In the 2nd century BC, Seleucus of Seleucia correctly theorized that tides were due to the attraction of the Moon, and that their height depends on the Moon's position relative to the Sun. In the same century, Aristarchus computed the size and distance of the Moon from Earth, obtaining a value of about twenty times the radius of Earth for the distance.
Although the Chinese of the Han Dynasty believed the Moon to be energy equated to qi, their 'radiating influence' theory recognized that the light of the Moon was merely a reflection of the Sun, and Jing Fang (78–37 BC) noted the sphericity of the Moon.: 413–414 Ptolemy (90–168 AD) greatly improved on the numbers of Aristarchus, calculating the values of a mean distance of 59 times Earth's radius and a diameter of 0.292 Earth diameters were close to the correct values of about 60 and 0.273 respectively. In the 2nd century AD, Lucian wrote the novel A True Story, in which the heroes travel to the Moon and meet its inhabitants. In 499 AD, the Indian astronomer Aryabhata mentioned in his Aryabhatiya that reflected sunlight is the cause of the shining of the Moon. The astronomer and physicist Alhazen (965–1039) found that sunlight was not reflected from the Moon like a mirror, but that light was emitted from every part of the Moon's sunlit surface in all directions. Shen Kuo (1031–1095) of the Song dynasty created an allegory equating the waxing and waning of the Moon to a round ball of reflective silver that, when doused with white powder and viewed from the side, would appear to be a crescent.: 415–416
During the Middle Ages, before the invention of the telescope, the Moon was increasingly recognised as a sphere, though many believed that it was "perfectly smooth".
### Telescopic exploration (1609-1959)
Galileo's sketches of the Moon from the ground-breaking Sidereus Nuncius, publishing among other findings the first descriptions of the Moons topography.
In 1609, Galileo Galilei used an early telescope to make drawings of the Moon for his book Sidereus Nuncius, and deduced that it was not smooth but had mountains and craters. Thomas Harriot had made, but not published such drawings a few months earlier.
Telescopic mapping of the Moon followed: later in the 17th century, the efforts of Giovanni Battista Riccioli and Francesco Maria Grimaldi led to the system of naming of lunar features in use today. The more exact 1834–1836 Mappa Selenographica of Wilhelm Beer and Johann Heinrich Mädler, and their associated 1837 book Der Mond, the first trigonometrically accurate study of lunar features, included the heights of more than a thousand mountains, and introduced the study of the Moon at accuracies possible in earthly geography. Lunar craters, first noted by Galileo, were thought to be volcanic until the 1870s proposal of Richard Proctor that they were formed by collisions. This view gained support in 1892 from the experimentation of geologist Grove Karl Gilbert, and from comparative studies from 1920 to the 1940s, leading to the development of lunar stratigraphy, which by the 1950s was becoming a new and growing branch of astrogeology.
### First missions to the Moon (1959–1990)
After World War II the first launch systems were developed and by the end of the 1950s they reached capabilities that allowed the Soviet Union and the United States to launch spacecrafts into space. The Cold War fueled a closely followed development of launch systems by the two states, resulting in the so-called Space Race and its later phase the Moon Race, accelerating efforts and interest in exploration of the Moon.
First view in history of the far side of the Moon, taken by Luna 3, 7 October 1959
After the first spaceflight of Sputnik 1 in 1957 during International Geophysical Year the spacecrafts of the Soviet Union's Luna program were the first to accomplish a number of goals. Following three unnamed failed missions in 1958, the first human-made object Luna 1 escaped Earth's gravity and passed near the Moon in 1959. Later that year the first human-made object Luna 2 reached the Moon's surface by intentionally impacting. By the end of the year Luna 3 reached as the first human-made object the normally occluded far side of the Moon, taking the first photographs of it. The first spacecraft to perform a successful lunar soft landing was Luna 9 and the first vehicle to orbit the Moon was Luna 10, both in 1966.
Earthrise, the first color image of Earth taken by a human from the Moon, during Apollo 8 (1968) the first time a crewed spacecraft left Earth orbit and reached another astronomical body.
Following President John F. Kennedy's 1961 commitment to a manned Moon landing before the end of the decade, the United States, under NASA leadership, launched a series of uncrewed probes to develop an understanding of the lunar surface in preparation for human missions: the Jet Propulsion Laboratory's Ranger program, the Lunar Orbiter program and the Surveyor program. The crewed Apollo program was developed in parallel; after a series of uncrewed and crewed tests of the Apollo spacecraft in Earth orbit, and spurred on by a potential Soviet lunar human landing, in 1968 Apollo 8 made the first human mission to lunar orbit. The subsequent landing of the first humans on the Moon in 1969 is seen by many as the culmination of the Space Race.
Neil Armstrong, the first human on the Moon, working at the Lunar Module Eagle, a first lunar base, during Apollo 11 (1969), the first Moon landing
Neil Armstrong became the first person to walk on the Moon as the commander of the American mission Apollo 11 by first setting foot on the Moon at 02:56 UTC on 21 July 1969. An estimated 500 million people worldwide watched the transmission by the Apollo TV camera, the largest television audience for a live broadcast at that time. The Apollo missions 11 to 17 (except Apollo 13, which aborted its planned lunar landing) removed 380.05 kilograms (837.87 lb) of lunar rock and soil in 2,196 separate samples.
Scientific instrument packages were installed on the lunar surface during all the Apollo landings. Long-lived instrument stations, including heat flow probes, seismometers, and magnetometers, were installed at the Apollo 12, 14, 15, 16, and 17 landing sites. Direct transmission of data to Earth concluded in late 1977 because of budgetary considerations, but as the stations' lunar laser ranging corner-cube retroreflector arrays are passive instruments, they are still being used. Apollo 17 in 1972 remains the last crewed mission to the Moon. Explorer 49 in 1973 was the last dedicated U.S. probe to the Moon until the 1990s.
A replica of Lunokhod 1, which reached the Moon becoming the first remote controlled rover on an extraterrestrial surface (1970)
The Soviet Union continued sending robotic missions to the Moon until 1976, deploying in 1970 with Luna 17 the first remote controlled rover Lunokhod 1 on an extraterrestrial surface, and collecting and returning 0.3 kg of rock and soil samples with three Luna sample return missions (Luna 16 in 1970, Luna 20 in 1972, and Luna 24 in 1976).
### Moon Treaty and explorational absence (1976–1990)
A near lunar quietude of fourteen years followed the last Soviet mission to the Moon of 1976. Astronautics had shifted its focus towards the exploration of the inner (e.g. Venera program) and outer (e.g. Pioneer 10, 1972) Solar System planets, but also towards Earth orbit, developing and continuously operating, beside communication satellites, Earth observation satellites (e.g. Landsat program, 1972) space telescopes and particularly space stations (e.g. Salyut program, 1971).
The until 1979 negotiated Moon treaty, with its ratification in 1984 by its few signatories was about the only major activity regarding the Moon until 1990.
### Renewed exploration (1990-present)
In 1990 Hiten-Hagoromo, the first dedicated lunar mission since 1976, reached the Moon. Sent by Japan, it became the first mission that was not a Soviet Union or U.S. mission to the Moon.
In 1994, the U.S. dedicated a mission to fly a spacecraft (Clementine) to the Moon again for the first time since 1973. This mission obtained the first near-global topographic map of the Moon, and the first global multispectral images of the lunar surface. In 1998 this was followed by the Lunar Prospector mission, whose instruments indicated the presence of excess hydrogen at the lunar poles, which is likely to have been caused by the presence of water ice in the upper few meters of the regolith within permanently shadowed craters.
The next years saw a row of first missions to the Moon by a new group of states actively exploring the Moon. Between 2004 and 2006 the first spacecraft by the European Space Agency (ESA) (SMART-1) reached the Moon, recording the first detailed survey of chemical elements on the lunar surface. The Chinese Lunar Exploration Program began with Chang'e 1 between 2007 and 2009, obtaining a full image map of the Moon. India reached the Moon in 2008 for the first time with its Chandrayaan-1, creating a high-resolution chemical, mineralogical and photo-geological map of the lunar surface, and confirming the presence of water molecules in lunar soil.
NASA's Moon Mineralogy Mapper equipment on India's Chandrayaan-1 for the first time discovered in 2008 water-rich minerals (light blue), shown in blue around a small crater from which it was ejected.
The U.S. launched the Lunar Reconnaissance Orbiter (LRO) and the LCROSS impactor on 18 June 2009. LCROSS completed its mission by making a planned and widely observed impact in the crater Cabeus on 9 October 2009, whereas LRO is currently in operation, obtaining precise lunar altimetry and high-resolution imagery.
China continued its lunar program in 2010 with Chang'e 2, mapping the surface at a higher resolution over an eight-month period, and in 2013 with Chang'e 3, a lunar lander along with a lunar rover named Yutu (Chinese: 玉兔; literally "Jade Rabbit"). This was the first lunar rover mission since Lunokhod 2 in 1973 and the first lunar soft landing since Luna 24 in 1976.
In 2014 the first privately funded probe, the Manfred Memorial Moon Mission, reached the Moon.
Another Chinese rover mission, Chang'e 4, achieved the first landing on the Moon's far side in early 2019.
Also in 2019, India successfully sent its second probe, Chandrayaan-2 to the Moon.
In 2020, China carried out its first robotic sample return mission (Chang'e 5), bringing back 1,731 grams of lunar material to Earth.
With the signing of the U.S.-led Artemis Accords in 2020, the Artemis program aims to return in the astronauts to the Moon in the 2020s. The Accords have been joined by a growing number of countries. The introduction of the Artemis Accords has fueled a renewed discussion about the international framework and cooperation of lunar activity, building on the Moon Treaty and the ESA-led Moon Village concept. The U.S. developed plans for returning to the Moon beginning in 2004, which resulted in several programs. The Artemis program has advanced the farthest, and includes plans to send the first woman to the Moon as well as build an international lunar space station called Lunar Gateway.
### Future
Symbol of the Artemis program
Upcoming lunar missions include the Artemis program missions and Russia's first lunar mission, Luna-Glob: an uncrewed lander with a set of seismometers, and an orbiter based on its failed Martian Fobos-Grunt mission.
China has announced in 2021 the plan to develop and construct with Russia an International Lunar Research Station towards and into the 2030s. India in 2006 had among others expressed its hope to send people to the Moon by 2020.
## Human presence
Map of all soft landing sites on the near side of the Moon.
Humans have been active around and on the Moon for more than half a century, having send a wide range of missions to the Moon, having stayed robotically and with people, leaving many traces and having set up temporary moonbases. The Moon remains a challenging and particular environment.
### Human impact
While the Moon has the lowest planetary protection target-categorization, its degradation as a pristine body and scientific place has been discussed. If there is astronomy performed from the Moon, it will need to be free from any physical and radio pollution. While the Moon has no significant atmosphere, traffic and impacts on the Moon causes clouds of dust that can spread far and possibly contaminate the original state of the Moon and its special scientific content. Scholar Alice Gorman asserts that, although the Moon is inhospitable, it is not dead, and that sustainable human activity would require treating the Moon's ecology as a co-participant.
The so-called "Tardigrade affair" of the 2019 crashed Beresheet lander and its carrying of tardigrades has been discussed as an example for lacking measures and lacking international regulation for planetary protection.
Space debris beyond Earth around the Moon has been considered as a future challenge with increasing numbers of missions to the Moon, particularly as a danger for such missions. As such lunar waste management has been raised as an issue which future lunar missions, particularly on the surface, need to tackle.
Beside the remains of human activity on the Moon, there have been some intended permanent installations like the Moon Museum art piece, Apollo 11 goodwill messages, six lunar plaques, the Fallen Astronaut memorial, and other artifacts.
Longterm missions continuing to be active are some orbiters such as the 2009-launched Lunar Reconnaissance Orbiter surveilling the Moon for future missions, as well as some Landers such as the 2013-launched Chang'e 3 with its Lunar Ultraviolet Telescope still operational. Five retroreflectors have been installed on the Moon since the 1970s and since used for accurate measurements of the physical librations through laser ranging to the Moon.
There are several missions by different agencies and companies planned to establish a longterm human presence on the Moon, with the Lunar Gateway as the currently most advanced project as part of the Artemis program.
### Astronomy from the Moon
For many years, the Moon has been recognized as an excellent site for telescopes. It is relatively nearby; astronomical seeing is not a concern; certain craters near the poles are permanently dark and cold, and thus especially useful for infrared telescopes; and radio telescopes on the far side would be shielded from the radio chatter of Earth. The lunar soil, although it poses a problem for any moving parts of telescopes, can be mixed with carbon nanotubes and epoxies and employed in the construction of mirrors up to 50 meters in diameter. A lunar zenith telescope can be made cheaply with an ionic liquid.
In April 1972, the Apollo 16 mission recorded various astronomical photos and spectra in ultraviolet with the Far Ultraviolet Camera/Spectrograph.
The Moon has been also a sight of Earth observation, particularly culturally as in the imagery called Earthrise.
### Living on the Moon
The only instances of humans living on the Moon have taken place in an Apollo Lunar Module for several days at a time (for example, during the Apollo 17 mission). One challenge to astronauts during their stay on the surface is that lunar dust sticks to their suits and is carried into their quarters. Astronauts could taste and smell the dust, calling it the "Apollo aroma". This fine lunar dust can cause health issues.
In 2019 at least one plant seed sprouted in an experiment on the Chang'e 4 lander. It was carried from Earth along with other small life in its Lunar Micro Ecosystem.
## Legal status
Although Luna landers scattered pennants of the Soviet Union on the Moon, and U.S. flags were symbolically planted at their landing sites by the Apollo astronauts, no nation claims ownership of any part of the Moon's surface. Likewise no private ownership of parts of the Moon, or as a whole, is considered credible.
The 1967 Outer Space Treaty defines the Moon and all outer space as the "province of all mankind". It restricts the use of the Moon to peaceful purposes, explicitly banning military installations and weapons of mass destruction. A majority of countries are parties of this treaty. The 1979 Moon Agreement was created to elaborate, and restrict the exploitation of the Moon's resources by any single nation, leaving it to a yet unspecified international regulatory regime. As of January 2020, it has been signed and ratified by 18 nations, none of which have human spaceflight capabilities.
Since 2020 countries have joined the U.S. in their Artemis Accords, which are challenging the treaty. The U.S. has furthermore emphasized in an presidential executive order ("Encouraging International Support for the Recovery and Use of Space Resources.") that "the United States does not view outer space as a 'global commons'" and calls the Moon Agreement "a failed attempt at constraining free enterprise."
With Australia signing and ratifying both the Moon Treaty in 1986 as well as the Artemis Accords in 2020, there has been a discussion if they can be harmonized. In this light an Implementation Agreement for the Moon Treaty has been advocated for, as a way to compensate for the shortcomings of the Moon Treaty and to harmonize it with other laws, allowing it to be more widely accepted.
In the face of such increasing commercial and national interest, particularly prospecting territories, U.S. lawmakers have introduced in late 2020 specific regulation for the conservation of historic landing sites and interest groups have argued for making such sites World Heritage Sites and zones of scientific value protected zones, all of which add to the legal availability and territorialization of the Moon.
In 2021 the Declaration of the Rights of the Moon was created by a group of "lawyers, space archaeologists and concerned citizens", drawing on precedents in the Rights of Nature movement and the concept of legal personality for non-human entities in space.
### Coordination
In light of future development on the Moon some international and multi-space agency organizations have been created:
## In culture and life
### Calendar
The Venus of Laussel (c. 25,000 BP) holding a crescent shaped horn, the 13 notches on the horn may symbolize the number of days from menstruation to ovulation, or of menstrual cycles or moons per year.
Since pre-historic times people have taken note of the Moon's phases, its waxing and waning, and used it to keep record of time. Tally sticks, notched bones dating as far back as 20–30,000 years ago, are believed by some to mark the phases of the Moon. The counting of the days between the Moon's phases gave eventually rise to generalized time periods of the full lunar cycle as months, and possibly of its phases as weeks.
The words for the month in a range of different languages carry this relation between the period of the month and the Moon etymologically. The English month as well as moon, and its cognates in other Indo-European languages (e.g. the Latin mensis and Ancient Greek μείς (meis) or μήν (mēn), meaning "month") stem from the Proto-Indo-European (PIE) root of moon, *méh1nōt, derived from the PIE verbal root *meh1-, "to measure", "indicat[ing] a functional conception of the Moon, i.e. marker of the month" (cf. the English words measure and menstrual). To give another example from a different language family, the Chinese language uses the same word () for moon as well as for month, which furthermore can be found in the symbols for the word week (星期).
This lunar timekeeping gave rise to the historically dominant, but varied, lunisolar calendars. The 7th-century Islamic calendar is an example of a purely lunar calendar, where months are traditionally determined by the visual sighting of the hilal, or earliest crescent moon, over the horizon.
Of particular significance has been the occasion of full moon, highlighted and celebrated in a range of calenders and cultures. Around autumnal equinox, the Full Moon is called the Harvest Moon and is celebrated with festivities such as the Harvest Moon Festival of the Chinese Lunar Calendar, its second most important celebration after Chinese New Year.
Furthermore, association of time with the Moon can also be found in religion, such as the ancient Egyptian temporal and lunar deity Khonsu.
### Cultural representation
From top: examples of lunar deities featuring around the world recurring aspects, like the crescent (Nanna/Sîn, c. 2100 BC), crescent headgear and chariot (Luna, 2nd–5th century), as well as the Moon rabbit (Mayan moon goddess, 6th–9th century).
Since prehistoric and ancient times humans have depicted and interpreted the Moon, particularly for astrology and religion, as lunar deity.
For the representation of the Moon, especially its lunar phases, the crescent symbol (🌙) has been particularly used by many cultures. In writing systems such as Chinese the crescent has developed into the symbol , the word for Moon, and in ancient Egyptian it was the symbol 𓇹, which is spelled like the ancient Egyptian lunar deity Iah, meaning Moon.
Iconographically the crescent was used in Mesopotamia as the primary symbol of Nanna/Sîn, the ancient Sumerian lunar deity, who was the father of Innana/Ishtar, the goddess of the planet Venus (symbolized as the eight pointed Star of Ishtar), and Utu/Shamash, the god of the Sun (symbolized as a disc, optionally with eight rays), all three often depicted next to each other. Nanna was later known as Sîn, and was particularly associated with magic and sorcery.
The crescent was further used as an element of lunar deities wearing headgears or crowns in an arrangement reminiscent of horns, as in the case of the ancient Greek Selene or the ancient Egyptian Khonsu. Selene is associated with Artemis and paralleled by the Roman Luna, which both are occasionally depicted driving a chariot, like the Hindu lunar deity Chandra. The different or sharing aspects of deities within pantheons has been observed in many cultures, especially by later or contemporary culture, particularly forming triple deities. The Moon in Roman mythology for example has been associated with Juno and Diana, while Luna being identified as their byname and as part of a triplet (diva triformis) with Diana and Proserpina, Hecate being identified as their binding manifestation as trimorphos.
The star and crescent (☪️) arrangement goes back to the Bronze Age, representing either the Sun and Moon, or the Moon and planet Venus, in combination. It came to represent the goddess Artemis or Hecate, and via the patronage of Hecate came to be used as a symbol of Byzantium, possibly influencing the development of the Ottoman flag, specifically the combination of the Turkish crescent with a star. Since then the heraldric use of the star and crescent proliferated becoming a popular symbol for Islam (as the hilal of the Islamic calendar) and for a range of nations.
In Roman Catholic Marian veneration, the Virgin Mary (Queen of Heaven) has been depicted since the late middle ages on a crescent and adorned with stars. In Islam Muhammad is particularly attributed with the Moon through the so-called splitting of the Moon (Arabic: انشقاق القمر) miracle.
The contrast between the brighter highlands and the darker maria have been seen by different cultures forming abstract shapes, which are among others the Man in the Moon or the Moon Rabbit (e.g. the Chinese Tu'er Ye or in Indigenous American mythologies, as with the aspect of the Mayan Moon goddess).
In Western alchemy silver is associated with the Moon, and gold with the Sun.
### Modern culture representation
The perception of the Moon in modern times has been informed by telescope enabled modern astronomy and later by spaceflight enabled actual human activity at the Moon, particularly the culturally impactful lunar landings. These new insights inspired cultural references, connecting romantic reflections about the Moon and speculative fiction such as science-fiction dealing with the Moon.
Contemporarily the Moon has been seen as a place for economic expansion into space, with missions prospecting for lunar resources. This has been accompanied with renewed public and critical reflection on humanity's cultural and legal relation to the celestial body, especially regarding colonialism, as in the 1970 poem "Whitey on the Moon". In this light the Moon's nature has been invoked, particularly for lunar conservation and as a common.
The Moon is prominently featured in Vincent van Gogh's 1889 painting, The Starry Night (left). An iconic image of the Man in the Moon from the first science-fiction film set in space, A Trip to the Moon (1902), inspired by a history of literature about going to the Moon (right).
### Lunar effect
The lunar effect is a purported unproven correlation between specific stages of the roughly 29.5-day lunar cycle and behavior and physiological changes in living beings on Earth, including humans. The Moon has long been associated with insanity and irrationality; the words lunacy and lunatic are derived from the Latin name for the Moon, Luna. Philosophers Aristotle and Pliny the Elder argued that the full moon induced insanity in susceptible individuals, believing that the brain, which is mostly water, must be affected by the Moon and its power over the tides, but the Moon's gravity is too slight to affect any single person. Even today, people who believe in a lunar effect claim that admissions to psychiatric hospitals, traffic accidents, homicides or suicides increase during a full moon, but dozens of studies invalidate these claims.
## Explanatory notes
1. ^ Between 18.29° and 28.58° to Earth's equator.
2. ^ There are a number of near-Earth asteroids, including 3753 Cruithne, that are co-orbital with Earth: their orbits bring them close to Earth for periods of time but then alter in the long term (Morais et al, 2002). These are quasi-satellites – they are not moons as they do not orbit Earth. For more information, see Other moons of Earth.
3. ^ The maximum value is given based on scaling of the brightness from the value of −12.74 given for an equator to Moon-centre distance of 378 000 km in the NASA factsheet reference to the minimum Earth–Moon distance given there, after the latter is corrected for Earth's equatorial radius of 6 378 km, giving 350 600 km. The minimum value (for a distant new moon) is based on a similar scaling using the maximum Earth–Moon distance of 407 000 km (given in the factsheet) and by calculating the brightness of the earthshine onto such a new moon. The brightness of the earthshine is [ Earth albedo × Radius of Moon's orbit)2 ] relative to the direct solar illumination that occurs for a full moon. (Earth albedo = 0.367; Earth radius = (polar radius × equatorial radius)½ = 6 367 km.)
4. ^ The range of angular size values given are based on simple scaling of the following values given in the fact sheet reference: at an Earth-equator to Moon-centre distance of 378 000 km, the angular size is 1896 arcseconds. The same fact sheet gives extreme Earth–Moon distances of 407 000 km and 357 000 km. For the maximum angular size, the minimum distance has to be corrected for Earth's equatorial radius of 6 378 km, giving 350 600 km.
5. ^ Lucey et al. (2006) give 107 particles cm−3 by day and 105 particles cm−3 by night. Along with equatorial surface temperatures of 390 K by day and 100 K by night, the ideal gas law yields the pressures given in the infobox (rounded to the nearest order of magnitude): 10−7 Pa by day and 10−10 Pa by night.
6. ^ a b With 27% the diameter and 60% the density of Earth, the Moon has 1.23% of the mass of Earth. The moon Charon is larger relative to its primary Pluto, but Earth and the Moon are different since Pluto is considered a dwarf planet and not a planet, unlike Earth.
7. ^ There is no strong correlation between the sizes of planets and the sizes of their satellites. Larger planets tend to have more satellites, both large and small, than smaller planets.
8. ^ More accurately, the Moon's mean sidereal period (fixed star to fixed star) is 27.321661 days (27 d 07 h 43 min 11.5 s), and its mean tropical orbital period (from equinox to equinox) is 27.321582 days (27 d 07 h 43 min 04.7 s) (Explanatory Supplement to the Astronomical Ephemeris, 1961, at p.107).
9. ^ More accurately, the Moon's mean synodic period (between mean solar conjunctions) is 29.530589 days (29 d 12 h 44 min 02.9 s) (Explanatory Supplement to the Astronomical Ephemeris, 1961, at p.107).
10. ^ The Sun's apparent magnitude is −26.7, while the full moon's apparent magnitude is −12.7.
11. ^ See graph in Sun#Life phases. At present, the diameter of the Sun is increasing at a rate of about five percent per billion years. This is very similar to the rate at which the apparent angular diameter of the Moon is decreasing as it recedes from Earth.
12. ^ On average, the Moon covers an area of 0.21078 square degrees on the night sky.
This page was last updated at 2022-12-02 04:23 UTC. . View original page.
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# Linking different sectoral risk weight policies to capital buffer and leverage ratio policies
Prepared by Jan Hannes Lang and Marek Rusnák
In recent years different macroprudential sectoral risk weight policies have been used in EU countries to address systemic risk in residential real estate markets. For example, sectoral risk weight floors for domestic internal ratings-based (IRB) mortgage loans were adopted in Estonia, Finland and Sweden, while sectoral risk weight add-ons and multipliers were implemented in Belgium.[1] The use of different sectoral risk weight policy designs raises the question of how they link to policies that would change sectoral capital or leverage ratio requirements.[2]
It can be demonstrated that sectoral risk weight floors, add-ons and multipliers are similar to different sectoral capital and leverage ratio requirement policies. This conceptual similarity between different policy instruments occurs because they bring about similar changes in the minimum required capital for a given bank.[3] To illustrate this, we consider two banks that have an initial sectoral capital requirement of 10%, and no sectoral leverage ratio requirement. The two banks differ only in terms of their average sectoral risk weight, which is 10% for bank 1 and 12.5% for bank 2. The minimum capital requirement and the average risk weight together implicitly set a minimum sectoral leverage ratio (required CET1 capital/sectoral exposure) of 1% for bank 1 and 1.25% for bank 2. We then consider three different risk weight policies: a risk weight floor of 15%, a risk weight add-on of 5 percentage points, and a risk weight multiplier of 33%.
A sectoral risk weight floor is similar to imposing a common sectoral leverage ratio requirement for all banks, in addition to the risk-based capital requirement. For the example above, we consider a sectoral risk weight floor of 15%. As both banks had initial sectoral risk weights of less than 15%, the floor will be binding for the calculation of minimum capital requirements. The risk weight floor will thus give rise to an implicit minimum sectoral leverage ratio of 1.5% for both banks. Therefore, the sectoral risk weight floor acts like a minimum sectoral leverage ratio imposed on both banks, along with the sectoral risk-based capital requirement. Such a policy would be warranted if systemic risk could result in minimum unexpected losses for all sectoral exposures.
A sectoral risk weight add-on is similar to a common increase in the sectoral leverage ratio for all banks. We go on to consider that a sectoral risk weight add-on of 5 percentage points is imposed, which raises average risk weights to 15% and 17.5% for banks 1 and 2 in the example. The implicit minimum sectoral leverage ratios will now be 1.5% and 1.75%, respectively, which represents an increase of 0.5 percentage points for both banks (Chart A, panel b) and. Hence, the common risk weight add-on acts like a common increase in the implicit sectoral leverage ratio for both banks. Such a policy would be warranted if systemic risk could increase unexpected losses for all sectoral exposures by the same amount.
A sectoral risk weight multiplier is similar to a common increase in a sectoral risk-based capital requirement for all banks, akin to a sectoral systemic risk buffer (SyRB). Finally, we consider the application of a 1.33 risk weight multiplier. As the capital requirement remains unchanged at 10% but risk weights (and risk-weighted assets) increase by 33%, both banks in the example will face a 33% increase in required CET1 capital. In an alternative policy scenario where risk weights (and risk-weighted assets) remain at their initial levels, it is intuitive that the capital requirement of both banks would need to increase by 33% to achieve the same increase in required CET1 capital as the risk weight policy. Given the initial capital requirement of 10%, this could be considered analogous to imposing a common increase in a risk-based capital requirement of 3.3 percentage points for both banks (Chart A, panel a). If systemic risk could increase unexpected losses in proportion to the underlying (microprudential) riskiness of the exposure, then a risk weight multiplier would be appropriate.
The flexibility of risk weight policies provides a rich set of policy tools that are useful for making macroprudential policy effective and targeted to different types of underlying systemic risk. Therefore, even if the sectoral SyRB is now available under the Capital Requirements Directive (CRD) V legislative package, the flexibility provided by sectoral risk weight policies under Article 458 of the Capital Requirements Regulation (CRR), which allows a targeted approach to underlying systemic risk, is still likely to be useful for macroprudential authorities in certain situations.[4]
1. See European Systemic Risk Board (2019), “Use of national flexibility measures under Article 458 of the CRR”, A Review of Macroprudential Policy in the EU in 2018, April.
2. The term “sectoral leverage ratio” is used to refer to the ratio of required CET1 capital that a bank needs to hold relative to total sectoral exposures. While such a sectoral leverage ratio is currently not part of the EU capital requirements framework, linking risk weight floors and add-ons to conceptually similar leverage ratio policies helps to better understand their impact on banks.
3. This similarity in the capital impact will hold as long as initial capital requirements are similar across banks. The close link between risk weights ($RW$), minimum required CET1 capital ($CET1-$), capital requirements ($R$) and the implicit leverage ratio ($LR$) is shown in the equation: $R=CET1-RW∙A→LR=R∙RW=CET1-A$.
4. For example, the Netherlands introduced an Article 458 measure in the form of an LTV-dependent risk weight floor for domestic mortgage loan portfolios, which entered into force on 1 January 2022.
| 2023-02-02T02:53:10 |
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|
https://www.anl.gov/topic/novel-nanocarbon-materials
|
# Novel Nanocarbon Materials
## Filter Results
• ### Novel Nanocarbon Materials
Ultrananocrystalline Diamond and Graphene Films
• ### Slippery when dry
Anyone who has ever taken their car in for an oil change recognizes the importance of reducing the friction that arises when steel touches steel.
• ### Direct Synthesis of Reduced Graphene Oxide Films on Dielectric Substrates (ANL-IN-14-110)
A method for coating a dielectric substrate with a R-GO film includes positioning the dielectric substrate in a chamber which is purged with a first gas to adjust a pressure of the chamber to a first pressure
• ### Superlubricating Graphene and Graphene Oxide Films (ANL-IN-11-056)
A system and method for forming at least one of graphene and graphene oxide on a substrate and an opposed wear member.
• ### Nanotechnology moves from the clean room to the classroom
For years, scientists have been creating and tweaking extremely tiny materials atom by atom in special clean rooms scrubbed of debris. Students needed a Ph.D. to join the club and study those tiny materials in a field known as nanoscience.
• ### Argonne-developed technology for producing graphene wins TechConnect National Innovation Award
A method that significantly cuts the time and cost needed to grow graphene has won a 2017 TechConnect National Innovation Award.
• ### Diamond proves useful material for growing graphene
Graphene is the stuff of the future.
• ### Argonne-developed technology for achieving superlubricity wins 2016 TechConnect National Innovation Award
Friction is the enemy of efficiency, and since the days of the Egyptian pharaohs, people have sought ways to get rid of it.
• ### Slip sliding away: Graphene and diamonds prove a slippery combination
Scientists at the U.S. Department of Energy’s Argonne National Laboratory have found a way to use tiny diamonds and graphene to give friction the slip, creating a new material combination that demonstrates the rare phenomenon of superlubricity.”
| 2019-07-23T19:59:08 |
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|
https://par.nsf.gov/biblio/10181473-combined-subsampling-analytical-integration-efficient-large-scale-gw-calculations-systems
|
Combined subsampling and analytical integration for efficient large-scale GW calculations for 2D systems
Abstract
Accurate and efficient predictions of the quasiparticle properties of complex materials remain a major challenge due to the convergence issue and the unfavorable scaling of the computational cost with respect to the system size. QuasiparticleGWcalculations for two-dimensional (2D) materials are especially difficult. The unusual analytical behaviors of the dielectric screening and the electron self-energy of 2D materials make the conventional Brillouin zone (BZ) integration approach rather inefficient and require an extremely densek-grid to properly converge the calculated quasiparticle energies. In this work, we present a combined nonuniform subsampling and analytical integration method that can drastically improve the efficiency of the BZ integration in 2DGWcalculations. Our work is distinguished from previous work in that, instead of focusing on the intricate dielectric matrix or the screened Coulomb interaction matrix, we exploit the analytical behavior of various terms of the convolved self-energy Σ(q) in the smallqlimit. This method, when combined with another acceleratedGWmethod that we developed recently, can drastically speed up (by over three orders of magnitude)GWcalculations for 2D materials. Our method allows fully convergedGWcalculations for complex 2D systems at a fraction of computational cost, facilitating future high throughput screening of the quasiparticle properties of 2D semiconductors for various applications. To demonstrate more »
Authors:
; ; ; ; ; ;
Publication Date:
NSF-PAR ID:
10181473
Journal Name:
npj Computational Materials
Volume:
6
Issue:
1
ISSN:
2057-3960
Publisher:
Nature Publishing Group
National Science Foundation
##### More Like this
1. Abstract
The discovery of high-dielectric materials is crucial to increasing the efficiency of electronic devices and batteries. Here, we report three previously unexplored materials with very high dielectric constants (69 < ϵ < 101) and large band gaps (2.9 < Eg(eV) < 5.5) obtained by screening materials databases using statistical optimization algorithms aided by artificial neural networks (ANN). Two of these new dielectrics are mixed-anion compounds (Eu5SiCl6O4and HoClO) and are shown to be thermodynamically stable against common semiconductors via phase diagram analysis. We also uncovered four other materials with relatively large dielectric constants (20 < ϵ < 40) and band gaps (2.3 < Eg(eV) < 2.7). While the ANN training-data are obtained from the Materials Project, the search-space consists of materials from the Open Quantum Materials Database (OQMD)—demonstrating a successful implementation of cross-database materials design. Overall, we report the dielectric properties of 17 materials calculated using ab initio calculations, that were selected in our design workflow. The dielectric materials with high-dielectric properties predicted in this work open up further experimental research opportunities.
2. Abstract
Complete theoretical understanding of the most complex superconductors requires a detailed knowledge of the symmetry of the superconducting energy-gap$${\mathrm{{\Delta}}}_{\mathbf{k}}^\alpha$$${\Delta }_{k}^{\alpha }$, for all momentakon the Fermi surface of every bandα. While there are a variety of techniques for determining$$|{\mathrm{{\Delta}}}_{\mathbf{k}}^\alpha |$$$\mid {\Delta }_{k}^{\alpha }\mid$, no general method existed to measure the signed values of$${\mathrm{{\Delta}}}_{\mathbf{k}}^\alpha$$${\Delta }_{k}^{\alpha }$. Recently, however, a technique based on phase-resolved visualization of superconducting quasiparticle interference (QPI) patterns, centered on a single non-magnetic impurity atom, was introduced. In principle, energy-resolved and phase-resolved Fourier analysis of these images identifies wavevectors connecting allk-space regions where$${\mathrm{{\Delta}}}_{\mathbf{k}}^\alpha$$${\Delta }_{k}^{\alpha }$has the same or opposite sign. But use of a single isolated impurity atom, from whose precise location the spatial phase of the scattering interference pattern must be measured, is technically difficult. Here we introduce a generalization of this approach for use with multiple impurity atoms, and demonstrate its validity by comparing the$${\mathrm{{\Delta}}}_{\mathbf{k}}^\alpha$$${\Delta }_{k}^{\alpha }$it generates to the$${\mathrm{{\Delta}}}_{\mathbf{k}}^\alpha$$${\Delta }_{k}^{\alpha }$determined from single-atom scattering in FeSe where s±energy-gap symmetry is established. Finally, to exemplify utility, we use the multi-atom technique on LiFeAs and find scattering interference between the hole-like and electron-like pockets as predicted for$${\mathrm{{\Delta}}}_{\mathbf{k}}^\alpha$$${\Delta }_{k}^{\alpha }$of opposite sign.
3. Abstract
For more than three decades, nearly free-electron elemental metals have been a topic of debate because the computed bandwidths are significantly wider in the local density approximation to density-functional theory (DFT) than indicated by angle-resolved photoemission (ARPES) experiments. Here, we systematically investigate this using first principles calculations for alkali and alkaline-earth metals using DFT and various beyond-DFT methods such as meta-GGA, G0W0, hybrid functionals (YS-PBE0, B3LYP), and LDA + eDMFT. We find that the static non-local exchange, as partly included in the hybrid functionals, significantly increase the bandwidths even compared to LDA, while the G0W0bands are only slightly narrower than in LDA. The agreement with the ARPES is best when the local approximation to the self-energy is used in the LDA + eDMFT method. We infer that even moderately correlated systems with partially occupiedsorbitals, which were assumed to approximate the uniform electron gas, are very well described in terms of short-range dynamical correlations that are only local to an atom.
4. Discovering new materials with desired properties has been a dominant and crucial topic of interest in the field of materials science in the past few decades. In this work, novel carbon allotropes and ternary B–C–N structures were generated using the state-of-the-art RG 2 code. All structures were fully optimized using density functional theory with first-principles calculations. Several hundred carbon allotropes and ternary B–C–N structures were identified to be superhard materials. The thermodynamic stability of some randomly selected superhard materials was confirmed by evaluating the full phonon dispersions in the Brillouin zone. The new carbon allotropes and ternary B–C–N structures possess a wide range of mechanical properties generally and Vickers hardness specifically. Through 2D Pearson's correlation map, we first reproduced the well-accepted explanation and relationship of the Vickers hardness of the generated structures with other mechanical properties such as shear modulus, bulk modulus, Pugh's ratio, universal anisotropy, and Poisson's ratio. We then propose two fundamentally new descriptors from the electronic level, namely local potential and electron localization function averaged over a unit cell, both of which exhibit a strong correlation with Vickers hardness. More importantly, these descriptors are easy to access from first-principles calculations (at least two orders of magnitude fastermore »
5. Abstract
Increasing demand for self-powered wearable sensors has spurred an urgent need to develop energy harvesting systems that can reliably and sufficiently power these devices. Within the last decade, reverse electrowetting-on-dielectric (REWOD)-based mechanical motion energy harvesting has been developed, where an electrolyte is modulated (repeatedly squeezed) between two dissimilar electrodes under an externally applied mechanical force to generate an AC current. In this work, we explored various combinations of electrolyte concentrations, dielectrics, and dielectric thicknesses to generate maximum output power employing REWOD energy harvester. With the objective of implementing a fully self-powered wearable sensor, a “zero applied-bias-voltage” approach was adopted. Three different concentrations of sodium chloride aqueous solutions (NaCl-0.1 M, NaCl-0.5 M, and NaCl-1.0 M) were used as electrolytes. Likewise, electrodes were fabricated with three different dielectric thicknesses (100 nm, 150 nm, and 200 nm) of Al2O3and SiO2with an additional layer of CYTOP for surface hydrophobicity. The REWOD energy harvester and its electrode–electrolyte layers were modeled using lumped components that include a resistor, a capacitor, and a current source representing the harvester. Without using any external bias voltage, AC current generation with a power density of 53.3 nW/cm2was demonstrated at an external excitation frequency of 3 Hz with an optimal external load. The experimental results were analytically verifiedmore »
| 2023-02-07T08:12:16 |
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|
https://www.pnnl.gov/news-media/steel-mill-doe-laboratory-arun-devaraj-seeks-perfection
|
April 6, 2022
Feature
## From Steel Mill to DOE Laboratory, Arun Devaraj Seeks Perfection
Studying imperfections in materials at the new Energy Sciences Center could help perfect energy transport
PNNL materials scientist Arun Devaraj is exploring how hydrogen, combined with stress and oxidation, leads to catastrophic failures of high-strength steels.
(Photo by Andrea Starr | Pacific Northwest National Laboratory)
Through sparks, dust, and a primordial roar, a fiery world took shape outside Arun Devaraj’s office.
Three giant electric arc furnaces transformed steel scrap and hot briquetted iron made from iron ore into steel. Every day, Devaraj would venture onto the floor of the cavernous Essar steel factory in Surat, a city in the western Indian state of Gujarat. He’d feel a heat blast from the 1,600-degree molten metal inside a giant cauldron while checking for the quality of the steel chemistry. He’d walk as close as 10 feet from the glowing, sloshing mass. Giant cranes groaned overhead, carrying tons of finished steel slabs toward the rolling mill.
He worked as a quality control and assurance engineer for about two years after graduating in 2005 with a Bachelor of Technology degree in metallurgical engineering and material science from Malaviya National Institute of Technology in Jaipur, India.
It was his first job out of college and Surat was a long way from his hometown in Kannur, Kerala, in southern India. But he was where he wanted to be. He could see, hear, and smell what he’d only read about in books. The son of N. C. Devarajan, a mechanical engineer, and M. Poonchola Devi, a schoolteacher, was at the front lines of an industry that traced its origins to India.
“It was hot, and dusty, and intense,” said Devaraj, now a Pacific Northwest National Laboratory (PNNL) senior research scientist in material science. “I saw steel born out of what used to be dirt. It was fun.”
The mill churned out hundreds of tons of coiled steel an hour. Flawed product occasionally made it to market. And it was Devaraj’s job, when customers complained, to examine the imperfect steel part under a scanning electron microscope, find the defect, determine its cause and origin in the steel making process, then venture into the mill to talk with steel workers to make sure it didn’t happen again.
At PNNL, Devaraj remains committed to improving the quality and performance of metals. He is in the midst of an ambitious project to explore how hydrogen, combined with stress and oxidation, leads to catastrophic failures of high-strength steels that are widely used in the nuclear and automotive industries.
He often publishes research on the topic. In 2020, for example, he contributed to two articles published in Nature that explored the atomic causes of materials degradation. One of the studies examined the degradation of zirconium alloys, a material used most commonly as nuclear reactor fuel cladding in pressurized water reactors. Devaraj also was co-author of a study that looked at a lightweight aluminum silicon alloy widely used in the defense, aerospace, and automotive industries.
His research will have important implications for carbon-free energy sources and their storage. And his research will unfold at PNNL’s Energy Sciences Center, a recently dedicated $90 million facility on the Richland, Washington, campus. ## Science over commerce Devaraj could have stayed at the mill in India and perhaps pursued a lucrative career within a massive corporation. But that mill experience unleashed a deeper interest. Two influential professors as well as an undergraduate internship at the Bhabha Atomic Research Centre near Mumbai also offered a glimpse at the appealing menagerie that is the atomic structure of metallic alloys. A steel mill laboratory colleague helped guide him through the thicket of overseas graduate school applications. An undergraduate research project mentor pointed Devaraj toward the University of North Texas and its materials science program. There, Devaraj worked for the first time with atom probe tomography (APT), the instrument that has been at the center of his PNNL work. “You can see atoms in materials in 3D!” Devaraj said, describing the instrument’s specialty. “Basically, it shows atomic arrangement in solids. It’s a powerful instrument to help reveal how atoms get rearranged in materials when we process them differently.” Devaraj credits a former University of North Texas professor for alerting him in 2010 to a potential PNNL job. At the time, PNNL was adding atom probe tomography instruments at the Environmental Molecular Sciences Laboratory (EMSL) in the first steps to establishing PNNL as a global leader with the instrument. ## Three skilled APT practitioners arrive at PNNL Devaraj, having earned a PhD in materials science and engineering, applied for a PNNL postdoctoral research position. Suntharampillai Thevuthasan, a PNNL materials scientist who was then a technical group manager, was looking for someone with experience working in atom probe tomography and who was ideally familiar with titanium. Devaraj had both qualifications and began work in May 2011. “He was fantastic,” said Thevuthasan, now a project manager whose duties have included overseeing development of the Energy Sciences Center. “He knew atom probe tomography and he knew what he was doing.” “Arun makes things happen,” Thevuthasan added. “When I first talked to him, on the phone, I saw a motivated early career researcher who liked to push capabilities to the limit. That was really important to me at the time, because we were pushing the capabilities of atom probe tomography at EMSL.” When Devaraj first interviewed to be a full-time scientist in EMSL, however, he didn’t get the job. Instead, PNNL selected Daniel Perea, then a postdoctoral researcher at Los Alamos National Laboratory who’d earned his PhD in materials science and engineering at Northwestern University. But Devaraj was persistent and memorable to the hiring team. It wasn’t long before he was hired as a full-time staff scientist at EMSL. The hirings of Perea and Devaraj were part of PNNL’s fledgling advances in APT. Since their hiring, PNNL has added about 25 more APT-skilled scientists, a number rivaled by few other laboratories worldwide. “When we were hired, Dan Schreiber was already doing APT work in the Energy and Environment Directorate,” said Perea, a materials scientist whose work focuses on using atom probe tomography to map the three-dimensional atomic-scale composition of materials. “Over the past 10 years, Arun, Dan, and myself set the foundation for APT growth at PNNL.” Devaraj and Perea were co-authors of a review article, “Three-dimensional nanoscale characterisation of materials by atom probe tomography,” published in 2017 in the journal International Materials, that looked at the evolving and improving techniques for use of APT. ## Pursuing Early Career award Devaraj is pushing the boundaries of that science. The Department of Energy (DOE) in June 2020 bestowed him with an Early Career Research Program award. The competitive annual award comes with five years of research support totaling about$2.5 million.
Shortly before the award was made, Devaraj published two journal studies that offered a glimpse of his focus on materials performance as well as the importance of APT in his research. In 2015, he was lead author of a study in Nature that detailed the use of APT to examine the durability of advanced lithium-ion battery cathodes. In 2016, he was lead author of a study, also published in Nature, that suggested a nanostructured titanium alloy could offer carmakers a lightweight, strong metal that could make autos lighter and thus consume less energy.
Devaraj’s program research combines a broad range of techniques available at PNNL and DOE facilities to understand how events at the atomic level result in microscopic cracks and eventually large-scale degradation. To understand this stress corrosion cracking, Devaraj and team members are studying individual diffusion and oxidation events by using advanced microscopy methods such as cryogenic-transfer atom probe tomography, in situ electron microscopy, synchrotron X-ray methods, and simulations. The goal of the work will be to develop scientific strategies for designing metal alloys capable of withstanding extreme environments of corrosion, stress, and high temperature, which has applications in many industrial-relevant materials for use in nuclear reactors and energy storage, particularly for transportation.
Preparing the application was among the hardest tasks he’s ever completed, Devaraj said, essentially working two jobs at the same time: the day job as a PNNL scientist, then the nighttime push to submit the Early Career application. The proposal process was the culmination of three years of preparatory work that included seeking and receiving a PNNL Laboratory Directed Research and Development Award to get ready for the application. He also consulted with Perea, Schreiber, and PNNL materials scientists Peter Sushko and Karen Kruska.
The proposal process itself lasted four months. But it was not only at night. He also had to negotiate a compromise during a planned vacation on a tiny Caribbean island with his wife. “I had her OK to devote four hours a day to the application,” he said. It may have helped that his wife, Priya Thekkumparambath Mana, is a PNNL power system research engineer who is pursuing a PhD in electrical engineering at Georgia Tech.
## Oh, happy day
Then one day, a DOE official sent an email with the good news. Devaraj had been selected as one of 76 recipients nationwide to receive a 2020 Early Career Research Program award.
“I told my wife and then I cried,” Devaraj said. “It was the happiest moment of my career.”
He called Perea. “Because it was right at the start of Covid,” Perea said, “we didn’t have an opportunity to properly celebrate. But I told him I was very happy for him.”
Devaraj is in the first year of the five-year program.
“In the first year, we established several capabilities that can probe how hydrogen is distributed in materials at an atomic scale and how we can map it in 3-D using atom probe tomography,” Devaraj said. “We are looking at individual pieces: mechanisms of deformation, oxidation, and hydrogen embrittlement.
“Now, in the second year of the award, and in future years, we will be examining the coupled effect of these three individual pieces together as a whole for understanding the mechanisms of stress corrosion cracking of steels in real world environments.”
## Life away from the lab
Perea said he has been impressed with Devaraj’s energy at work as well as away from work. “He’s extremely adventurous,” Perea said.
Ah, yes. Devaraj the action figure. There he is now, driving up to North Cascades National Park for a weekend of hiking with his wife. But wait, he’s now leading younger PNNL colleagues to the top of Mount Adams. Mount Hood? Done that. What’s that background during the video interview? A photo he shot of tents arrayed at Camp Muir, launching pad for a Mount Rainier summit. He will climb Washington’s tallest mountain one day, count on it. He’ll find the time to train between martial arts practice and instruction.
“We live through him vicariously,” Perea said, “when we see his social media posts on top of mountains.”
## Preparing for move to new Energy Sciences Center home
At EMSL, Devaraj walks around an atom probe tomography instrument in a laboratory, explaining its capabilities.
“In this analysis chamber, we’re evaporating one atom at a time from the tip of the APT needle sample,” he said, pointing at a stainless steel chamber on the complex instrument. “The sample is very cold, about 40 Kelvin. That’s more than 350 degrees below zero Fahrenheit. This way, we slow the atoms as much as possible and freeze them in place.
“Then we apply a laser and a really high electric field. We’re essentially ripping away atoms, one by one. Those detached atoms from the sample hit a detector, which records the type of atom and where it came from. We collect information on millions of ions,” Devaraj said. The data will be used to create a three-dimensional image of the arrangement of atoms in that material.
Devaraj has anticipated the day he and his team and crucial instrumentation move into the Energy Sciences Center.
He will be searching for material failure due to corrosion. He seeks a refined understanding of how to prevent corrosion and improve materials. Solutions will be found to store hydrogen and transfer the gas across long distances—essential strides in sustainable energy—and he wants to be part of it.
In essence, he is performing the same task as he did inside the steel mill.
“One big difference; three, actually,” Devaraj said. “I don’t miss the heat, the noise, and the dust.”
Published: April 6, 2022
| 2022-05-19T14:49:22 |
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|
http://www-spires.fnal.gov/spires/find/books/www?keyword=Gas+detectors
|
Fermilab Core Computing Division
Library Home | Ask a Librarian [email protected] | Book Catalog | Library Journals | Requests | SPIRES | Fermilab Documents |
Fermilab Library
SPIRES-BOOKS: FIND KEYWORD GAS DETECTORS *END*INIT* use /tmp/qspiwww.webspi1/10587.273 QRY 131.225.70.96 . find keyword gas detectors ( in books using www
Call number: 3527405976:ONLINE Show nearby items on shelf Title: Noble Gas Detectors Author(s): Aprile Date: 2006 Publisher: Wiley-VCH Size: 1 online resource (363 p.) ISBN: 9783527405978 Series: eBooks Series: Wiley Online Library Series: Wiley 2016 package purchase Keywords: Physics Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE
Call number: SPRINGER-1985-9781468449679:ONLINE Show nearby items on shelf Title: Fundamental Interactions in Low-Energy Systems Author(s): Date: 1985 Size: 1 online resource (501 p.) Note: 10.1007/978-1-4684-4967-9 Contents: I The Electro-Weak Force at Low Energy -- Weak Interactions at Low Energy -- Determination of the Muon Decay Parameters -- Measurement of the ?-Parameter in ?-Decay -- Muon Capture in Hydrogen -- Muon Capture in Deuterium -- Parity Violation in Atoms -- Neutral Currents in Muonic Atoms -- Rare Muon Decays and Lepton-family Number Conservation -- Neutrino Masses and Mixing from Neutrino Oscillations -- Searches for Mixed Heavy Neutrinos in Meson Decays and in Muon Capture -- II Strong Interactions -- The Exotic Atoms of QCD: Glueballs, Hybrids and Baryonia -- Quarkonium Spectroscopy -- The LEAR Physics Programme -- Electron-positron Pair Production in $$p\bar p$$ annihilation at LEAR -- $$p\bar p$$ Annihilations at Rest in Hydrogen Gas: Report on Preliminary Results of the Asterix Experiment at LEAR -- First Physics Results from Experiment PS172 at LEAR -- Antiproton-proton Reactions in the Momentum Range from 250 to 600 MeV/c -- X-rays from Protonium — PS 174 Progress Report -- Antiproton X-ray Spectroscopy in the Cyclotron Trap: Preliminary Results -- PS184: A Study of Antiproton-nucleus Interactions at LEAR -- Perspectives of Antineutron Physics -- III Search for Hypothetical Particles and Interactions -- Weakly Charged Exotic Particles -- Search for Muon-hadron Interactions from Muonic X-rays -- Experimental Search for Strong van der Waals Forces -- Photon-photon Interaction Detection via the Vacuum Birefringence Induced by a Magnetic Field: Status of the Experiment -- IV Perspectives of Superconducting Junctions in Nuclear and Particle Physics -- Potential of Superconducting Tunnel Junctions as Detectors in Nuclear and Particle Physics -- Development of a High Resolution Superconducting Detector for keV Radiation at SIN -- New Detectors and Neutrino Mass -- V Some Aspects of the Physics of Muonic Atoms and Molecules -- Different Facets of Muonic Molecules -- New Experimental Results on Muon Catalyzed Fusion in Low Density Deuterium-tritium gas -- Progress in Muon Catalyzed Fusion at JINR in Dubna (USSR) -- Triplet State Lifetimes and Muon Capture in Gaseous Hydrogen -- Formation of the Lightest Muonic Atoms and the 2S-lifetime of the (??4He)+-ion ISBN: 9781468449679 Series: eBooks Series: SpringerLink (Online service) Series: Springer eBooks Series: Ettore Majorana International Science Series : 23 Keywords: Physics , Physics , Physics, general Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE
| 2019-03-27T01:34:54 |
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|
https://xgc.pppl.gov/html/kernels_and_tests.html
|
# Kernels and Tests¶
XGC’s major components can be run independently from the full code to aid in testing and development. The kernels can be run in test mode for verification. There is also a unit test suite, UnitTests-cpu (currently CPU only) which tests individual functions throughout the code; as such, there is no corresponding kernel.
## Compiling¶
The kernels are built by default if you are building XGC (see cmake_build_instructions.rst). However, this can be inconvenient since the kernels require only a subset of the XGC dependencies. If you only want the kernels and tests, use the following instructions instead.
All kernels/tests require Kokkos and Cabana. The Collisions kernel requires LAPACK. Tests will only configure if GTest is found. For instructions on installing these dependencies, see 3rd Party Software Installations.
Once Kokkos, Cabana, and optionally GTest are installed, you can configure and build with:
mkdir build; cd build
cmake \
-DBUILD_FULL_XGC=Off \
-DKokkos_ROOT=<path to Kokkos> \
-DCabana_ROOT=<path to Cabana> \
-DLAPACK_ROOT=<path to LAPACK> \
-DGTEST_ROOT=<path to GTest> \
..
make -j
The executables have the form {component}Kernel-{cpu,gpu}, for example: collisionsKernel-gpu. Commonly used components:
• collisions
• electron_push
• electron_scatter
## Running¶
All component kernels require input files. If security settings permit it, running
ctest
in the build directory will download the directory containing these files from the Kitware website, then run all CPU tests. However, this automatic download fails in many systems. In that case, you must download the data manually, taking the most recent* tarball from here. The tarball contains a directory called SmallExample.
Run the executables from the directory that contains SmallExample. (i.e. the executables expect to find files of the form ./SmallExample/example.txt)
To test the kernels, use “–test”, e.g.:
./electron_pushKernel-cpu --test
This mode will run a small, predefined example and compares against expected results. For collisions, it is the same calculation as -n_nodes 3. For the other kernels, it is the same calculation as -n_ptl 37. GoogleTest (GTest) is used to confirm correctness of results.
Outside of test mode, results are not verified. The kernel scale must be user-specified via a command-line input, e.g.:
./electron_pushKernel-cpu -n_ptl 50000
will run with 50000 particles. “-n_ptl” is the input for all kernels except the collision kernel, since the collision kernel does not involve particles. In that kernel, scaling is done by adding mesh nodes. The syntax is:
./collisionsKernel-cpu -n_nodes 3000
If further customization of the collision kernel inputs is desired, one can supply a file in Fortran namelist format, specifiying its location with “-file”.
Currently, all kernels and tests are single-process (i.e. no MPI).
* More robustly, use the tarball with the sha512 found in your repo’s version of utils/regression_tests/SmallExample.tar.gz.sha512
| 2021-06-24T23:45:10 |
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|
https://zbmath.org/authors/?q=ai%3Amardesic.sibe
|
# zbMATH — the first resource for mathematics
## Mardešić, Sibe
Compute Distance To:
Author ID: mardesic.sibe Published as: Mardesic, S.; Mardesic, Sibe; Mardesić, Sibe; Mardešić, S.; Mardešić, Sibe; Mardéšic, Sibe External Links: MGP · Math-Net.Ru · Wikidata · GND
Documents Indexed: 170 Publications since 1951, including 7 Books Reviewing Activity: 1 Review Biographic References: 6 Publications
all top 5
#### Co-Authors
101 single-authored 15 Segal, Jack 8 Lisitsa, Yurij T. 6 Uglešić, Nikica 5 Papić, Pavle 4 Gordh, George R. jun. 4 Rubin, Leonard Roy 3 Rushing, T. Benny 3 Šostak, Alexander P. 3 Watanabe, Tadashi 2 Horvatic, Kreso 2 Matijević, Vlasta 2 Prasolov, Andrei V. 1 Anderson, Richard D. 1 Antonian, Sergej A. 1 Betković, D. 1 Bilinski, Stanko 1 Comfort, William Wistar 1 Coram, Donald S. 1 Delinić, Krešimir 1 Dydak, Jerzy 1 Fleissner, Bill 1 Gruenhage, Gary F. 1 Hart, Joan E. 1 Henriksen, Melvin 1 Juhász, István 1 Keesling, James Edgar 1 Koyama, Akira 1 Kraljevic, Hrvoje 1 Lisica, Juriǐ 1 Lončar, Ivan 1 Miminoshvili, Zaza 1 Nagata, Jun-iti 1 Nyikos, Peter J. 1 Ostaszweski, Adam 1 Rudin, Mary Ellen 1 Shekutkovskiĭ, Nikita 1 Smirnov, Yuriĭ Mikhaĭlovich 1 Tall, Frank 1 Toruńczyk, Henryk 1 Ungar, Sime 1 van Mill, Jan 1 Vaughan, Jerry E. 1 Yamazaki, Kaori
all top 5
#### Serials
25 Topology and its Applications 21 Glasnik Matematički. Serija III 11 Fundamenta Mathematicae 8 Bulletin de l’Académie Polonaise des Sciences, Série des Sciences Mathématiques, Astronomiques et Physiques 8 Periodicum Mathematico-Physicum et Astronomicum 6 Transactions of the American Mathematical Society 5 Societas Scientiarum Naturalium Croatica. Periodicum Mathematico-Physicum et Astronomicum, II. Serie 4 Pacific Journal of Mathematics 4 Tsukuba Journal of Mathematics 4 Comptes Rendus Hebdomadaires des Séances de l’Académie des Sciences, Paris 3 Michigan Mathematical Journal 3 Proceedings of the American Mathematical Society 3 Bulletin of the Polish Academy of Sciences, Mathematics 3 Mathematical Communications 3 General Topology and its Applications 2 Rad Hrvatske Akademije Znanosti i Umjetnosti. Matematičke Znanosti 2 Topology Proceedings 2 Lecture Notes in Mathematics 1 Houston Journal of Mathematics 1 Rocky Mountain Journal of Mathematics 1 Russian Mathematical Surveys 1 Colloquium Mathematicum 1 Commentationes Mathematicae Universitatis Carolinae 1 Duke Mathematical Journal 1 Illinois Journal of Mathematics 1 Mathematica Japonica 1 Publications de l’Institut Mathématique. Nouvelle Série 1 Publicationes Mathematicae 1 Rendiconti dell’Istituto di Matematica dell’Università di Trieste 1 Soviet Mathematics. Doklady 1 Topology 1 Rendiconti del Seminario Matematico 1 Bulletin of the American Mathematical Society. New Series 1 Bulletin de l’Académie Polonaise des Sciences. Série des Sciences Mathématiques 1 Matematichki Bilten 1 Georgian Mathematical Journal 1 Mediterranean Journal of Mathematics 1 Bulletin de la Société des Mathématiciens et Physiciens de la R. P. de Serbie 1 North-Holland Mathematical Library 1 Supplemento ai Rendiconti del Circolo Matemàtico di Palermo. Serie II 1 Springer Monographs in Mathematics
all top 5
#### Fields
107 General topology (54-XX) 84 Algebraic topology (55-XX) 14 Manifolds and cell complexes (57-XX) 10 History and biography (01-XX) 7 Category theory; homological algebra (18-XX) 2 General and overarching topics; collections (00-XX) 2 Topological groups, Lie groups (22-XX) 2 Real functions (26-XX) 1 Group theory and generalizations (20-XX) 1 Measure and integration (28-XX) 1 Geometry (51-XX) 1 Convex and discrete geometry (52-XX)
#### Citations contained in zbMATH Open
111 Publications have been cited 951 times in 529 Documents Cited by Year
Shape theory. The inverse system approach. Zbl 0495.55001
Mardešić, S.; Segal, J.
1982
On covering dimension and inverse limits of compact spaces. Zbl 0094.16902
Mardešić, Sibe
1960
Shapes of compacta and ANR-systems. Zbl 0222.55017
Mardešić, Sibe; Segal, Jack
1971
Strong shape and homology. Zbl 0939.55007
Mardešić, Sibe
2000
History of shape theory and its application to general topology. Zbl 0996.54002
Mardešić, Sibe; Segal, Jack
2001
Approximate polyhedra, resolutions of maps and shape fibrations. Zbl 0411.54019
Mardesic, Sibe
1981
Shapes for topological spaces. Zbl 0269.55008
Mardesic, Sibe
1973
$$\varepsilon$$-mappings onto polyhedra. Zbl 0118.39001
Mardešić, Sibe; Segal, Jack
1963
Coherent prohomotopy and strong shape theory. Zbl 0553.55009
Lisitsa, Yu. T.; Mardešić, S.
1984
Sur les espaces dont toute transformation réelle continue est bornée. Zbl 0066.40903
Mardešić, Sibe; Papić, Pavle
1955
Approximate resolutions of spaces and mappings. Zbl 0715.54009
Mardešić, S.; Watanabe, T.
1989
Approximate inverse systems of compacta and covering dimension. Zbl 0631.54006
Mardešić, Sibe; Rubin, Leonard R.
1989
Equivalence of the Borsuk and the ANR-system approach to shapes. Zbl 0222.55018
Mardešić, Sibe; Segal, Jack
1971
Classifying overlay structures of topological spaces. Zbl 0989.57002
Mardešić, Sibe; Matijević, Vlasta
2001
Shape fibrations I. Zbl 0398.55011
Mardesic, Sibe; Rushing, T. B.
1978
Movable compacta and ANR-systems. Zbl 0201.55502
Mardešić, S.; Segal, J.
1970
Strong homology is not additive. Zbl 0648.55007
Mardešić, S.; Prasolov, A. V.
1988
Strong homology of inverse systems of spaces. I; II. Zbl 0559.55008
Lisitsa, Yurij T.; Mardešić, Sibe
1985
Images of ordered compacta are locally peripherally metric. Zbl 0161.19903
Mardešić, Sibe
1967
Cell-like mappings and nonmetrizable compacta of finite cohomological dimension. Zbl 0698.54027
Mardešić, Sibe; Rubin, Leonard R.
1989
Steenrod-Sitnikov homology for arbitrary spaces. Zbl 0532.55003
Lisica, Ju. T.; Mardešić, S.
1983
A locally connected continuum which contains no proper locally connected subcontinuum. Zbl 0173.25302
Mardešić, Sibe
1967
Continuous images of ordered compacta, the Suslin property and dyadic compacta. Zbl 0119.17906
Mardešić, S.; Papić, P.
1963
Equivariant shape. Zbl 0644.55009
Antonian, S. A.; Mardešić, S.
1987
Shape fibrations. II. Zbl 0448.55006
Mardesic, Sibe; Rushing, T. B.
1979
Compact subsets of R$$^n$$ and dimension of their projections. Zbl 0272.54030
Mardesic, Sibe
1973
On the Hahn-Mazurkiewicz theorem in nonmetric spaces. Zbl 0100.19003
Mardešić, Sibe
1961
A shape fibration with fibers of different shape. Zbl 0436.55010
Keesling, J.; Mardesic, S.
1979
Retracts in shape theory. Zbl 0221.55014
Mardešić, Sibe
1971
$$\epsilon$$-mappings and generalized manifolds. Zbl 0152.21704
Mardesic, S.; Segal, J.
1967
Continuous images of ordered continua. Zbl 0097.15804
Mardešić, Sibe; Papić, Pavle
1960
Comparison of singular and Čech homology in locally connected spaces. Zbl 0088.38503
Mardešić, Sibe
1959
Strong homology of inverse systems. III. Zbl 0574.55005
Lisica, Juriǐ; Mardešić, Sibe
1985
On approximate inverse systems and resolutions. Zbl 0810.54013
Mardešić, S.
1993
Stability of almost commutative inverse systems of compacta. Zbl 0668.54007
Mardešić, Sibe; Segal, Jack
1989
$${\mathcal P}$$-like continua and approximate inverse limits. Zbl 0668.54008
Mardešić, Sibe; Segal, Jack
1988
n-shape fibrations. Zbl 0415.55012
Mardesic, Sibe; Rushing, T. B.
1979
On the Whitehead theorem in shape theory. II. Zbl 0327.55016
Mardesic, Sibe
1976
On the Whitehead theorem in shape theory. I. Zbl 0323.55020
Mardesic, Sibe
1976
The relative Hurewicz theorem in shape theory. Zbl 0298.55004
Mardesic, Sibe; Ungar, Sime
1974
Equivalence of singular and Čech homology for ANR-s application to unicoherence. Zbl 0085.37303
Mardešić, S.
1958
Continuous images of linearly ordered continua and compacta. Zbl 1327.54005
Mardešić, Sibe
2015
Strong expansions of products and products in strong shape. Zbl 1052.54018
Mardešić, Sibe
2004
Nonvanishing derived limits in shape theory. Zbl 0857.55007
Mardešić, Sibe
1996
Geometric topology and shape theory. Proceedings of a Conference held in Dubrovnik, Yugoslavia, September 29 - October 10, 1986. Zbl 0619.00017
Mardešić, S. (ed.); Segal, J. (ed.)
1987
Characterizing local connectedness in inverse limits. Zbl 0272.54008
Gordh, G. R. jun.; Mardesic, Sibe
1975
A note on inverse sequences of ANR’s. Zbl 0157.53701
Lončar, Ivan; Mardešić, Sibe
1968
A note on polyhedra embeddable in the plane. Zbl 0168.21602
Mardesic, S.; Segal, J.
1966
A category whose isomorphisms induce an equivalence relation coarser than shape. Zbl 1082.54012
Mardešić, Sibe; Uglešić, Nikica
2005
A resolution for the product of a compactum with a polyhedron. Zbl 1037.54010
Mardešić, Sibe
2003
The relative homeomorphism and wedge axioms for strong homology. Zbl 0794.55004
Mardešić, S.; Miminoshvili, Z.
1990
Factorization theorems for cohomological dimension. Zbl 0659.55001
Mardešić, Sibe
1988
Steenrod homology. Zbl 0646.55003
Lisitsa, Yu. T.; Mardešić, S.
1986
Coherent prohomotopy and strong shape for pairs. Zbl 0593.55009
Lisitsa, Yu. T.; Mardešić, S.
1985
Comparing fibres in a shape fibration. Zbl 0403.55012
Mardesic, Sibe
1978
Pairs of compacta and trivial shape. Zbl 0284.55017
Mardesic, Sibe
1974
Chainable continua and inverse limits. Zbl 0089.17701
Mardešić, Sibe
1959
On inverse limits of compact spaces. Zbl 0100.19102
Mardešić, Sibe
1958
Functoriality of the standard resolution of the Cartesian product of a compactum and a polyhedron. Zbl 1139.54011
Mardešić, Sibe
2007
A counterexample concerning products in the shape category. Zbl 1086.54012
Dydak, J.; Mardešić, S.
2005
Products of compacta with polyhedra and topological spaces in the shape category. Zbl 1072.54015
Mardešić, Sibe
2004
Absolute neighborhood retracts and shape theory. Zbl 0973.54002
Mardešić, Sibe
1999
Strong homology does not have compact supports. Zbl 0845.55009
Mardešić, Sibe
1996
A note on approximate systems of metric compacta. Zbl 0855.54015
Mardešić, S.; Rubin, L.; Uglešić, N.
1994
On resolutions for pairs of spaces. Zbl 0579.54011
Mardešić, Sibe
1984
The Hurewicz and Whitehead theorems in shape theory. Zbl 0317.55009
Mardesic, Sibe
1975
On Borsuk’s shape theory for compact pairs. Zbl 0269.55010
Mardesic, S.
1973
Decreasing sequences of cubes and compacta of trivial shape. Zbl 0232.55026
Mardešić, Sibe
1972
A non-movable compactum with movable suspension. Zbl 0222.55016
Mardešić, S.
1971
Mappings of inverse systems. Zbl 0126.18404
Mardešić, S.
1963
A note on extension theory and direct limits. Zbl 1212.54038
Mardešić, Sibe; Rubin, Leonard R.
2009
Approximating topological spaces by polyhedra. Zbl 1195.54001
Mardešić, S.
2005
Extension dimension of inverse limits. Zbl 0971.54009
Mardešić, Sibe
2000
On strong homology of compact spaces. Zbl 0897.55002
Mardešić, Sibe; Prasolov, Andrei V.
1998
$$\mathcal P$$-like spaces are limits of approximate $$\mathcal P$$-resolutions. Zbl 0755.54004
Mardešić, Sibe; Matijević, Vlasta
1992
Strong expansions and strong shape theory. Zbl 0715.55008
Mardešić, Sibe
1991
Strong expansions and strong shape for pairs of spaces. Zbl 0790.54019
Mardešić, Sibe
1991
Mapping approximate inverse systems of compacta. Zbl 0707.54011
Mardešić, Sibe; Segal, Jack
1990
Strong homology and dimension. Zbl 0648.55006
Mardešić, S.; Watanabe, T.
1988
Images of ANR’s under shape fibrations. Zbl 0592.55016
Coram, Donald S.; Mardešić, Sibe; Toruńczyk, Henryk
1985
Coherent prohomotopy and strong shape of metric compacta. Zbl 0592.55007
Lisitsa, Yu. T.; Mardešić, S.
1985
Coherent prohomotopy and a strong shape category of topological spaces. Zbl 0553.55008
Lisitsa, Yu. T.; Mardešić, S.
1984
On the shape of movable Hausdorff curves. Zbl 0314.55015
Gordh, G. R. jun.; Mardesic, S.
1975
Equivalence of two notions of shape for metric spaces. Zbl 0269.55009
Mardesic, S.
1973
On the shape of the quotient space $$S^ n/A$$. Zbl 0231.55017
Mardešić, S.
1971
Mapping products of ordered compacta onto products of more factors. Zbl 0195.52301
Mardešić, Sibe
1970
$$\epsilon$$-mappings and generalized manifolds. II. Zbl 0161.42601
Mardesic, S.; Segal, J.
1967
On the Hahan-Mazurkiewicz problem in non-metric spaces. Zbl 0159.52802
Mardesic, S.
1967
Continuous images of ordered compacta and a new dimension which neglects metric subcontinua. Zbl 0151.30303
Mardešić, Sibe
1966
Some problems concerning mappings of ordered compacta. Zbl 0163.17303
Mardesic, S.; Papic, P.
1963
$$\epsilon$$-mappings and inverse limits. Zbl 0144.21902
Mardesic, S.
1963
Not every metrizable compactum is the limit of an inverse sequence with simplicial bonding maps. Zbl 1388.54011
Mardešić, Sibe
2018
There are no essential phantom mappings from 1-dimensional CW-complexes. Zbl 1286.55007
Mardešić, Sibe
2013
An existence theorem concerning ordinary shape of Cartesian products. Zbl 1299.54036
Mardešić, Sibe
2011
The Cartesian product of a compactum and a space is a bifunctor in shape. Zbl 1183.54007
Mardešić, Sibe
2009
Functoriality of the standard resolution of the Cartesian product of a compactum and a polyhedron. II. Zbl 1157.55008
Mardešić, Sibe
2008
There are no phantom pairs of mappings to 1-dimensional CW-complexes. Zbl 1139.55013
Mardešić, Sibe
2007
On rectangular inverse systems of topological spaces. Zbl 1054.54009
Mardešić, Sibe
2004
Coherent and strong expansions of spaces coincide. Zbl 0912.55007
Mardešić, Sibe
1998
Thirty years of shape theory. Zbl 0886.55010
Mardešić, Sibe
1997
Not every metrizable compactum is the limit of an inverse sequence with simplicial bonding maps. Zbl 1388.54011
Mardešić, Sibe
2018
Continuous images of linearly ordered continua and compacta. Zbl 1327.54005
Mardešić, Sibe
2015
There are no essential phantom mappings from 1-dimensional CW-complexes. Zbl 1286.55007
Mardešić, Sibe
2013
An existence theorem concerning ordinary shape of Cartesian products. Zbl 1299.54036
Mardešić, Sibe
2011
A note on extension theory and direct limits. Zbl 1212.54038
Mardešić, Sibe; Rubin, Leonard R.
2009
The Cartesian product of a compactum and a space is a bifunctor in shape. Zbl 1183.54007
Mardešić, Sibe
2009
Functoriality of the standard resolution of the Cartesian product of a compactum and a polyhedron. II. Zbl 1157.55008
Mardešić, Sibe
2008
Functoriality of the standard resolution of the Cartesian product of a compactum and a polyhedron. Zbl 1139.54011
Mardešić, Sibe
2007
There are no phantom pairs of mappings to 1-dimensional CW-complexes. Zbl 1139.55013
Mardešić, Sibe
2007
A category whose isomorphisms induce an equivalence relation coarser than shape. Zbl 1082.54012
Mardešić, Sibe; Uglešić, Nikica
2005
A counterexample concerning products in the shape category. Zbl 1086.54012
Dydak, J.; Mardešić, S.
2005
Approximating topological spaces by polyhedra. Zbl 1195.54001
Mardešić, S.
2005
Strong expansions of products and products in strong shape. Zbl 1052.54018
Mardešić, Sibe
2004
Products of compacta with polyhedra and topological spaces in the shape category. Zbl 1072.54015
Mardešić, Sibe
2004
On rectangular inverse systems of topological spaces. Zbl 1054.54009
Mardešić, Sibe
2004
A resolution for the product of a compactum with a polyhedron. Zbl 1037.54010
Mardešić, Sibe
2003
History of shape theory and its application to general topology. Zbl 0996.54002
Mardešić, Sibe; Segal, Jack
2001
Classifying overlay structures of topological spaces. Zbl 0989.57002
Mardešić, Sibe; Matijević, Vlasta
2001
Strong shape and homology. Zbl 0939.55007
Mardešić, Sibe
2000
Extension dimension of inverse limits. Zbl 0971.54009
Mardešić, Sibe
2000
Absolute neighborhood retracts and shape theory. Zbl 0973.54002
Mardešić, Sibe
1999
On strong homology of compact spaces. Zbl 0897.55002
Mardešić, Sibe; Prasolov, Andrei V.
1998
Coherent and strong expansions of spaces coincide. Zbl 0912.55007
Mardešić, Sibe
1998
Thirty years of shape theory. Zbl 0886.55010
Mardešić, Sibe
1997
Nonvanishing derived limits in shape theory. Zbl 0857.55007
Mardešić, Sibe
1996
Strong homology does not have compact supports. Zbl 0845.55009
Mardešić, Sibe
1996
On irreducible mappings into polyhedra. Zbl 0827.57010
Mardešić, Sibe; Uglešić, Nikica
1995
A note on approximate systems of metric compacta. Zbl 0855.54015
Mardešić, S.; Rubin, L.; Uglešić, N.
1994
Approximate inverse systems which admit meshes. Zbl 0828.54010
Mardešić, S.; Uglešić, N.
1994
On approximate inverse systems and resolutions. Zbl 0810.54013
Mardešić, S.
1993
$$\mathcal P$$-like spaces are limits of approximate $$\mathcal P$$-resolutions. Zbl 0755.54004
Mardešić, Sibe; Matijević, Vlasta
1992
Strong shape of the Stone-Čech compactification. Zbl 0783.54017
Mardešić, Sibe
1992
Strong expansions and strong shape theory. Zbl 0715.55008
Mardešić, Sibe
1991
Strong expansions and strong shape for pairs of spaces. Zbl 0790.54019
Mardešić, Sibe
1991
The relative homeomorphism and wedge axioms for strong homology. Zbl 0794.55004
Mardešić, S.; Miminoshvili, Z.
1990
Mapping approximate inverse systems of compacta. Zbl 0707.54011
Mardešić, Sibe; Segal, Jack
1990
Approximate resolutions of spaces and mappings. Zbl 0715.54009
Mardešić, S.; Watanabe, T.
1989
Approximate inverse systems of compacta and covering dimension. Zbl 0631.54006
Mardešić, Sibe; Rubin, Leonard R.
1989
Cell-like mappings and nonmetrizable compacta of finite cohomological dimension. Zbl 0698.54027
Mardešić, Sibe; Rubin, Leonard R.
1989
Stability of almost commutative inverse systems of compacta. Zbl 0668.54007
Mardešić, Sibe; Segal, Jack
1989
Strong homology is not additive. Zbl 0648.55007
Mardešić, S.; Prasolov, A. V.
1988
$${\mathcal P}$$-like continua and approximate inverse limits. Zbl 0668.54008
Mardešić, Sibe; Segal, Jack
1988
Factorization theorems for cohomological dimension. Zbl 0659.55001
Mardešić, Sibe
1988
Strong homology and dimension. Zbl 0648.55006
Mardešić, S.; Watanabe, T.
1988
Equivariant shape. Zbl 0644.55009
Antonian, S. A.; Mardešić, S.
1987
Geometric topology and shape theory. Proceedings of a Conference held in Dubrovnik, Yugoslavia, September 29 - October 10, 1986. Zbl 0619.00017
Mardešić, S. (ed.); Segal, J. (ed.)
1987
A note on strong homology of inverse systems. Zbl 0627.55006
Mardešić, Sibe
1987
Steenrod homology. Zbl 0646.55003
Lisitsa, Yu. T.; Mardešić, S.
1986
Strong homology of inverse systems of spaces. I; II. Zbl 0559.55008
Lisitsa, Yurij T.; Mardešić, Sibe
1985
Strong homology of inverse systems. III. Zbl 0574.55005
Lisica, Juriǐ; Mardešić, Sibe
1985
Coherent prohomotopy and strong shape for pairs. Zbl 0593.55009
Lisitsa, Yu. T.; Mardešić, S.
1985
Images of ANR’s under shape fibrations. Zbl 0592.55016
Coram, Donald S.; Mardešić, Sibe; Toruńczyk, Henryk
1985
Coherent prohomotopy and strong shape of metric compacta. Zbl 0592.55007
Lisitsa, Yu. T.; Mardešić, S.
1985
Coherent prohomotopy and strong shape theory. Zbl 0553.55009
Lisitsa, Yu. T.; Mardešić, S.
1984
On resolutions for pairs of spaces. Zbl 0579.54011
Mardešić, Sibe
1984
Coherent prohomotopy and a strong shape category of topological spaces. Zbl 0553.55008
Lisitsa, Yu. T.; Mardešić, S.
1984
Mardešić, Sibe
1984
Steenrod-Sitnikov homology for arbitrary spaces. Zbl 0532.55003
Lisica, Ju. T.; Mardešić, S.
1983
Shape theory. The inverse system approach. Zbl 0495.55001
Mardešić, S.; Segal, J.
1982
Approximate polyhedra, resolutions of maps and shape fibrations. Zbl 0411.54019
Mardesic, Sibe
1981
Approximate fibrations and shape fibrations. Zbl 0505.55019
Mardesic, Sibe
1980
Shape fibrations. II. Zbl 0448.55006
Mardesic, Sibe; Rushing, T. B.
1979
A shape fibration with fibers of different shape. Zbl 0436.55010
Keesling, J.; Mardesic, S.
1979
n-shape fibrations. Zbl 0415.55012
Mardesic, Sibe; Rushing, T. B.
1979
Shape fibrations I. Zbl 0398.55011
Mardesic, Sibe; Rushing, T. B.
1978
Comparing fibres in a shape fibration. Zbl 0403.55012
Mardesic, Sibe
1978
On the Whitehead theorem in shape theory. II. Zbl 0327.55016
Mardesic, Sibe
1976
On the Whitehead theorem in shape theory. I. Zbl 0323.55020
Mardesic, Sibe
1976
Characterizing local connectedness in inverse limits. Zbl 0272.54008
Gordh, G. R. jun.; Mardesic, Sibe
1975
The Hurewicz and Whitehead theorems in shape theory. Zbl 0317.55009
Mardesic, Sibe
1975
On the shape of movable Hausdorff curves. Zbl 0314.55015
Gordh, G. R. jun.; Mardesic, S.
1975
The relative Hurewicz theorem in shape theory. Zbl 0298.55004
Mardesic, Sibe; Ungar, Sime
1974
Pairs of compacta and trivial shape. Zbl 0284.55017
Mardesic, Sibe
1974
Shapes for topological spaces. Zbl 0269.55008
Mardesic, Sibe
1973
Compact subsets of R$$^n$$ and dimension of their projections. Zbl 0272.54030
Mardesic, Sibe
1973
On Borsuk’s shape theory for compact pairs. Zbl 0269.55010
Mardesic, S.
1973
Equivalence of two notions of shape for metric spaces. Zbl 0269.55009
Mardesic, S.
1973
Decreasing sequences of cubes and compacta of trivial shape. Zbl 0232.55026
Mardešić, Sibe
1972
Shapes of compacta and ANR-systems. Zbl 0222.55017
Mardešić, Sibe; Segal, Jack
1971
Equivalence of the Borsuk and the ANR-system approach to shapes. Zbl 0222.55018
Mardešić, Sibe; Segal, Jack
1971
Retracts in shape theory. Zbl 0221.55014
Mardešić, Sibe
1971
A non-movable compactum with movable suspension. Zbl 0222.55016
Mardešić, S.
1971
On the shape of the quotient space $$S^ n/A$$. Zbl 0231.55017
Mardešić, S.
1971
n-dimensional $$LC^{n-1}$$ compacta are movable. Zbl 0216.19401
Mardešić, S.
1971
Movable compacta and ANR-systems. Zbl 0201.55502
Mardešić, S.; Segal, J.
1970
Mapping products of ordered compacta onto products of more factors. Zbl 0195.52301
Mardešić, Sibe
1970
A note on inverse sequences of ANR’s. Zbl 0157.53701
Lončar, Ivan; Mardešić, Sibe
1968
Images of ordered compacta are locally peripherally metric. Zbl 0161.19903
Mardešić, Sibe
1967
A locally connected continuum which contains no proper locally connected subcontinuum. Zbl 0173.25302
Mardešić, Sibe
1967
$$\epsilon$$-mappings and generalized manifolds. Zbl 0152.21704
Mardesic, S.; Segal, J.
1967
$$\epsilon$$-mappings and generalized manifolds. II. Zbl 0161.42601
Mardesic, S.; Segal, J.
1967
On the Hahan-Mazurkiewicz problem in non-metric spaces. Zbl 0159.52802
Mardesic, S.
1967
A note on polyhedra embeddable in the plane. Zbl 0168.21602
Mardesic, S.; Segal, J.
1966
Continuous images of ordered compacta and a new dimension which neglects metric subcontinua. Zbl 0151.30303
Mardešić, Sibe
1966
$$\varepsilon$$-mappings onto polyhedra. Zbl 0118.39001
Mardešić, Sibe; Segal, Jack
1963
Continuous images of ordered compacta, the Suslin property and dyadic compacta. Zbl 0119.17906
Mardešić, S.; Papić, P.
1963
Mappings of inverse systems. Zbl 0126.18404
Mardešić, S.
1963
Some problems concerning mappings of ordered compacta. Zbl 0163.17303
Mardesic, S.; Papic, P.
1963
$$\epsilon$$-mappings and inverse limits. Zbl 0144.21902
Mardesic, S.
1963
The method of inverse limits in topology. Zbl 0121.17603
Mardešić, Sibe
1962
...and 11 more Documents
all top 5
#### Cited by 407 Authors
24 Mardešić, Sibe 22 Dydak, Jerzy 22 Sanjurjo, José M. R. 16 Rubin, Leonard Roy 12 Moron, Manuel Alonso 12 Segal, Jack 11 Kołodziejczyk, Danuta 10 Giraldo, Antonio 10 Miyata, Takahisa 10 Stramaccia, Luciano 10 Watanabe, Tadashi 9 Matijević, Vlasta 9 Ruiz del Portal, Francisco Romero 8 Geoghegan, Ross 8 Hernández Paricio, Luis Javier 8 Repovš, Dušan D. 8 Uglešić, Nikica 8 Venema, Gerard A. 7 Barge Yáñez, Héctor 7 Iseki, Kiyoshi 7 Keesling, James Edgar 7 Nikiel, Jacek 7 Porter, Timothy 7 Quintero, Antonio 7 Spiez, Stanislaw 6 Eda, Katsuya 6 Ferry, Steven C. 6 Kato, Hisao 6 Lin, Huaxin 6 Lisitsa, Yurij T. 6 Treybig, L. B. 5 Antonyan, Sergey A. 5 Bykov, Alexander I. 5 Cárdenas, Manuel 5 Clark, Alex 5 Dimov, Georgi D. 5 Koyama, Akira 5 Mashayekhy, Behrooz 5 Prasolov, Andrei V. 5 Sánchez-Gabites, Jaime J. 5 Smrekar, Jaka 5 Tymchatyn, Edward D. 4 Baladze, Vladimer 4 Cordier, Jean-Marc 4 Dranishnikov, Alexander Nikolaevich 4 Gevorgyan, Pavel S. 4 Hurder, Steven E. 4 Jiménez Benitez, Rolando 4 Kawamura, Kazuhiro 4 Koceić Bilan, Nikola 4 Lasheras, Francisco F. 4 Mirebrahimi, Hanieh 4 Mrozik, Peter Alexander 4 Nasri, Tayyebe 4 Prajs, Janusz R. 4 Shekutkovskiĭ, Nikita 4 Tuncali, H. Murat 4 Virk, Žiga 3 Anaya, José G. 3 Batanin, Mikhail A. 3 Bogatyĭ, Semeon Antonovich 3 Bonzio, Stefano 3 Čerin, Zvonko Tomislav 3 Chigogidze, Alex 3 Edwards, David A. 3 Fedorchuk, Vitaly Vitalievich 3 Ghanei, Fateme 3 Günther, Bernd 3 Hastings, Harold M. 3 Kalinin, V. A. 3 Keremedis, Kyriakos 3 Laguna, Víctor F. 3 Liem, Vo-Thanh 3 Marciszewski, Witold 3 Morita, Kiiti 3 Nowak, Sławomir 3 Plebanek, Grzegorz 3 Schapiro, Philip J. 3 Skopenkov, Arkadiĭ Borisovich 3 Sternfeld, Yaki 3 Watanabe, Tadashi 2 Ageev, Sergei M. 2 Ball, Billy Joe 2 Banič, Iztok 2 Bauer, Friedrich-Wilhelm 2 Bennett, Ralph 2 Beridze, Anzor 2 Betti, Renato 2 Boroński, Jan P. 2 Brady, Noel 2 Brodsky, N. B. 2 Brudnyi, Alexander 2 Bryant, John Logan 2 Buzyakova, Raushan Z. 2 Castañeda Alvarado, Enrique 2 Cathey, Frederick W. 2 Cencelj, Matija 2 Charalambous, Michael George 2 Charatonik, Janusz Jerzy 2 Chinen, Naotsugu ...and 307 more Authors
all top 5
#### Cited in 88 Serials
245 Topology and its Applications 50 Proceedings of the American Mathematical Society 31 Transactions of the American Mathematical Society 16 Journal of Pure and Applied Algebra 14 Cahiers de Topologie et Géométrie Différentielle Catégoriques 14 Proceedings of the Japan Academy 7 Compositio Mathematica 7 Bulletin of the American Mathematical Society 6 Journal of Mathematical Sciences (New York) 6 Mediterranean Journal of Mathematics 5 Mathematical Notes 5 Siberian Mathematical Journal 4 Israel Journal of Mathematics 4 Rocky Mountain Journal of Mathematics 4 Advances in Mathematics 4 Annali di Matematica Pura ed Applicata. Serie Quarta 4 Journal of Differential Equations 4 Journal of Soviet Mathematics 4 Quaestiones Mathematicae 3 Commentationes Mathematicae Universitatis Carolinae 3 Czechoslovak Mathematical Journal 3 Acta Mathematica Hungarica 2 Bulletin of the Australian Mathematical Society 2 Archiv der Mathematik 2 Duke Mathematical Journal 2 Geometriae Dedicata 2 Inventiones Mathematicae 2 Journal of Functional Analysis 2 Manuscripta Mathematica 2 Mathematische Annalen 2 Mathematische Zeitschrift 2 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 2 Proceedings of the Japan Academy. Series A 2 Physica D 2 Revista Matemática Iberoamericana 2 Discrete and Continuous Dynamical Systems 2 Acta Mathematica Sinica. English Series 2 Algebraic & Geometric Topology 2 Cahiers de Topologie et Géométrie Différentielle Catégoriques 2 Journal of Topology and Analysis 2 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM 1 Communications in Algebra 1 Discrete Applied Mathematics 1 Journal of Mathematical Analysis and Applications 1 Mathematical Proceedings of the Cambridge Philosophical Society 1 Studia Mathematica 1 Journal of Geometry and Physics 1 The Mathematical Intelligencer 1 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 1 Algebra Universalis 1 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 1 Fuzzy Sets and Systems 1 Journal of Algebra 1 Mathematics and Computers in Simulation 1 Memoirs of the American Mathematical Society 1 Monatshefte für Mathematik 1 Publications of the Research Institute for Mathematical Sciences, Kyoto University 1 Rendiconti del Seminario Matematico della Università di Padova 1 Semigroup Forum 1 Studia Logica 1 Tohoku Mathematical Journal. Second Series 1 Discrete & Computational Geometry 1 $$K$$-Theory 1 Glasnik Matematički. Serija III 1 Pattern Recognition 1 Bulletin of the American Mathematical Society. New Series 1 Bulletin of the Polish Academy of Sciences, Mathematics 1 Indagationes Mathematicae. New Series 1 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 1 Topology Proceedings 1 St. Petersburg Mathematical Journal 1 Geometry & Topology 1 Annals of Mathematics. Second Series 1 Journal of the European Mathematical Society (JEMS) 1 Foundations of Science 1 Lobachevskii Journal of Mathematics 1 Foundations of Computational Mathematics 1 Central European Journal of Mathematics 1 Journal of Function Spaces and Applications 1 Journal of Fixed Point Theory and Applications 1 Logica Universalis 1 Journal of Noncommutative Geometry 1 Journal of Homotopy and Related Structures 1 Advances in Calculus of Variations 1 Applied General Topology 1 Nonlinear Analysis. Theory, Methods & Applications 1 European Journal of Mathematics 1 Vestnik Samarskogo Universiteta. Estestvennonauchnaya Seriya
all top 5
#### Cited in 38 Fields
337 General topology (54-XX) 276 Algebraic topology (55-XX) 92 Manifolds and cell complexes (57-XX) 54 Category theory; homological algebra (18-XX) 35 Dynamical systems and ergodic theory (37-XX) 22 Functional analysis (46-XX) 19 Group theory and generalizations (20-XX) 19 Topological groups, Lie groups (22-XX) 11 Mathematical logic and foundations (03-XX) 9 Order, lattices, ordered algebraic structures (06-XX) 6 History and biography (01-XX) 6 Differential geometry (53-XX) 6 Global analysis, analysis on manifolds (58-XX) 4 Combinatorics (05-XX) 4 General algebraic systems (08-XX) 4 Associative rings and algebras (16-XX) 3 Algebraic geometry (14-XX) 3 Measure and integration (28-XX) 3 Computer science (68-XX) 2 General and overarching topics; collections (00-XX) 2 Functions of a complex variable (30-XX) 2 Ordinary differential equations (34-XX) 2 Operator theory (47-XX) 2 Calculus of variations and optimal control; optimization (49-XX) 2 Geometry (51-XX) 2 Numerical analysis (65-XX) 1 Number theory (11-XX) 1 Nonassociative rings and algebras (17-XX) 1 $$K$$-theory (19-XX) 1 Real functions (26-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Partial differential equations (35-XX) 1 Approximations and expansions (41-XX) 1 Convex and discrete geometry (52-XX) 1 Quantum theory (81-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Biology and other natural sciences (92-XX) 1 Systems theory; control (93-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.
| 2021-06-23T23:39:42 |
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|
https://www.usgs.gov/center-news/photo-and-video-chronology-k-lauea-june-5-1998
|
# Photo and Video Chronology - Kīlauea - June 5, 1998
Release Date:
Lava Continues to Erupt from Puu Oo and Flow Into the Sea
This update current as of June 5, 1998. Eruption updates are posted monthly; more frequent updates will accompany drastic changes in activity or increased threat to residential areas.
### Overview
Episode 55 of Kīlauea's east rift zone eruption continues. On most days lava issues quietly from vents on the SW flank of Puu Oo and travels about 12 km through lava tubes to the coast. Several vents within Puu Oo crater are intermittently active. For example, over a several-hour period, lava will emerge from one or more of these vents, sometimes reaching to within 10-30 m of the crater rim, then suddenly drain back into one or more of the vents (activity occurring within Puu Oo is documented by the remote video-telemetry system; see images below recorded on June 4). Such lava fill and drain cycles occur irregularly. This activity, however, does not appear to affect the steady flow of lava through the tube system into the ocean. Between 300,000 to 600,000 m3 of lava continues to enter the ocean at two entry points -- Wahaula and Kamokuna.
1) Crater between fill & drain cycle, 2) Crater during peak fill cycle, 3) Crater during drain cycle (Public domain.)
### Lava Intermittently Visible in Puu Oo Cinder-and-Spatter Cone
Puu Oo crater has a major vent at its west end, a feature we call the crater vent. Several smaller pits have formed elsewhere across the crater floor; a new one developed at the base of the east crater wall on May 7. Such pits form by undermining as magma beneath the crater floor erodes parts of the solidified crust. Where the crust becomes thin, the floor collapses to form a pit, which may become a new vent or a place where lava can drain back into the main magma conduit system beneath the cone. These pits periodically overflow and spill small lava flows across the crater floor. All these flows remain contained within the crater of Puu Oo. The most recent crater overflow occurred in January 18, 1998.
### Pause on May 19-20 Leads to Lava Breakouts
A temporary pause in the supply of magma to Puu Oo on May 19-20 permitted lava within the tube system to drain completely so that lava ceased flowing into the ocean at the Wahaula and Kamokuna entry points. After lava began re-entering the tube system during the evening of May 20, several breakouts occurred along the length of the tube. The most voluminous breakouts began early in the morning of May 21 on the steep slope of the pali between 2,000 and 1,100 feet.
During a pause, the roof and walls of the drained tubes are prone to collapse. When lava reoccupies the tube system, blockages or irregularities in the tube cause the lava to back up and escape through skylights or other weak points. A prolonged period of surface flow activity inevitably results in lateral expansion of the lava-flow field, because the middle of the field is usually higher than the sides and new surface flows are diverted to the edges. During this most recent pause, however, the tube system quickly accommodated nearly all of the lava. The Kamokuna entry point resumed abruptly at about 1240 on May 21. Sixteen similar pauses have occurred since episode 55 began in March 1997.
May 21, 1998. Aerial view SW across one of the lava breakouts that occurred when magma was resupplied to Puu Oo and the tube system. The lava channel spreading from the tube's skylight is feeding an aa flow that is moving down the pali (left) out of view (Public domain.)
May 21, 1998. Aerial view to SW above a breakout from the lava tube on the steep pali about 6 km from Puu Oo. The breakout is feeding an aa lava flow that reached the base of the pali. This breakout ceased within a few hours after this image was taken as the tube system accomodated more of the erupting lava.
(Public domain.)
May 21, 1998. Lava breakout moves through a forested kipuka. (Public domain.)
May 21, 1998. Close view of lava cascading down a steep slope within a lava tube as lava re-occupies the tube system. The cascade is about 2 m high, but the entire cascade is hidden from view by the roof of the tube, which is estimated to be about 6 m high. (Public domain.)
June 4, 1998. Aerial view to NW shows the underground path of the lava tube that leads from Puu Oo (6 km in distance) over the steep pali (foreground) and to the sea. The tube's path is marked by the blue-colored fume that rises from skylights and several other weak points in the roof of the tube. (Public domain.)
### Lava Entry Points Remain Hazardous
At the coast, the tube system continues to discharge lava into the ocean at two sites, Wahaula and Kamokuna. Most of the lava enters the ocean at the Kamokuna entry point, where new land collapses into the ocean without warning, and various types of littoral explosions occur frequently. Following a collapse of the Kamokuna bench sometime between May 1 and 4, a new bench about 90 m wide was built by June 2. Numerous breakouts have been occurring along the entire bench area, and prominent cracks have formed immediately behind a new littoral cone that is forming on the seaward edge of the new bench. This bench is susceptible to collapse, which is likely to trigger vigorous explosions and scalding waves that can endanger people who venture too close to the entry point.
May 7, 1998. View is SW across the Kamokuna entry a few days after new land (lava bench) seaward of the littoral cone collapsed into the ocean. The cone is about 10 m tall. By June 2, a new bench about 90 m wide had formed. (Public domain.)
June 4, 1998. Aerial view to SW shows the Wahaula (bottom) and Kamokuna (upper) lava entry points on the south coastline of Kīlauea Volcano. The three small but distinct plumes rising from the Wahaula entry point indicate that lava is entering the sea at three different points. In the past few weeks, most lava poured into the sea at the Kamokuna entry. (Public domain.)
May 25, 1998. View is SW across a new bench forming at the Wahaula entry point. Following the brief pause on May 19-20, many small breakouts from the lava tube feeding this entry point poured over the 3-to 4-m-tall cliff onto the bench. The cliff was created when an older bench collapsed into the ocean. (Public domain.)
As the lava enters the sea it builds new land along the ocean edge. This land proves unstable, owing to the steep submarine slope along the south coast of the Big Island. The lava builds a low shelf known as a bench, but periodically the bench and its underpinnings slide seaward, a process called bench collapse. These collapses are life endangering; the land itself is destroyed and numerous explosions ensue as the hot lava reacts violently with the ocean water. For more information about this activity and the associated hazards, see:
• Collapse of new land into the sea
• Explosions at lava entry points
• Waves send scalding water onto new land
Eruption-viewing opportunities change constantly, so those readers planning a visit to the volcano should contact Hawaii Volcanoes National Park for the most current eruption information (ph. 808-985-6000). Additional photographs and descriptions of east rift eruptive activity may be found on the University of Hawaii's web site.
Flow-field map showing lava emplaced during the Puu Oo - Kupaianaha eruption since 1983. Note the new lava flows that were emplaced on the Pulama pali and at the Kamokuna and Waha`ula entry points following the brief pause May 19-20. This map was compiled on June 5, 1998 (Public domain.)
| 2021-09-25T11:01:50 |
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|
http://blog.metagenomics.anl.gov/howto/mg-rast-analysis-tools/
|
## MG-RAST analysis tools
### This page is being retired and its content has been transferred to the MG-RAST user manual.
[URL: ftp://ftp.metagenomics.anl.gov/data/manual/mg-rast-manual.pdf]
MGRAST version 3 provides a variety of tools to visualize data, perform statistical analyses, and visualize data with respect to analysis outputs. Here we provide some pointers to consider when using any of the visualization and/or statistical analysis tools.
What are abundance counts?
An abundance count is an integer (0 or positive) based count of the number of items under consideration. MGRAST produces several outputs that can be classified as abundance counts. Chief among these are counts of taxon (each abundance represents the number of times a particular taxon is detected, e.g. the number of a particular species that have been detected) or function (each count represents the number of times a particular functional role is detected, e.g. the number of a particular functional role that have been detected). Abundance counts provide the bases for several MGRAST analysis tools, particularly the heatmap-dendrogram and PCA.
Data normalization: a brief overview
A key question to ask with respect to visualization and/or analysis of abundance count data, is if the data should be preprocessed before they are used in visualizations, comparative analyses, and/or statistical tests. First, it is important that the user understands the purpose and benefits of normalizing the data. One of the most concise and jargon-free definitions of normalization can be found on Wikipedia (excerpted from http://en.wikipedia.org/wiki/Normalization_(statistics)):
… normalization refers to the division of multiple sets of data by a common variable in order to negate that variable’s effect on the data, thus allowing underlying characteristics of the data sets to be compared: this allows data on different scales to be compared, by bringing them to a common scale.
When comparisons are made between/among metagenomic sequencing samples it is critical to negate the effect of variables that introduce variation/bias but are not under experimental control.
Common examples include:
– experimental methods to extract and prepare genetic material
– the use of different sequencing technologies
– source, size, and quality of sampled genetic material
– personnel conducting the experiment(s) and procedure(s)
– selection and implementation of computational analysis tools (signal to code)
All of these variables (as well as many others; this list is by no means exhaustive) can contribute to variation in observed abundance values, and could obscure observations made with respect to experimentally controlled variables. Unless some effort has been taken to remove (or at least suppress) trends in abundance count values that are attributable to variables not under experimental control, it is impossible to determine if observed similarities/differences are the product of interpretable experimental quantities, or uncontrolled, non-experimental variables.
Normalization is used as a means to mitigate the contribution of non-experimental variables, such that their contribution to observed trends (similarities and differences in abundance values) is minimized. Specifically, differences in the distribution (normal versus non-normal), scale (difference between minimum and maximum observed abundance values), and location (essentially, the sample mean) of the abundance counts observed in each samples are treated to remove effect’s that are likely to be the product of variables that are not under experimental control.
Normalization is also a means to transform data with a non-normal distribution to one that achieves, or is much closer to, normal (Gaussian or bell-curve). Why is this important? Several statistical tests (t-test and ANOVA for example) and other tools (PCA, clustering based on parametric metrics) expect that data are normally distributed; if the distribution of the data is unknown, or exhibit a non-normal distribution, it is necessary to use non-parametric tests/metrics (those that make no assumption about data distributions, examples include the Mann-Whitney and Kruskal-Wallis tests) to determine meaningful significance values. In some cases, the use of non-parametric methods can be an advantage; principally, there is no need to explore distribution characteristics of the data. It can also be a disadvantage; non-parametric tests typically exhibit a lower statistical power than their parametric equivalents. A larger number of observations is required to achieve an equivalent level of statistical fidelity.
Normalization provides the the user with a measure of control with respect to the bias that is introduced by non-experimental variables. Unless the user has good (and statistically defensible) reason to suspect that raw values and/or non-parametric tests would be more suitable for their particular needs, we recommend use of data that have been normalized.
Data normalization: MGRAST V3 Normalization
In version 3.0, normalization refers to the specific procedure implemented to produce “normalized” abundance count values. The procedure is based on similar ones that have been used to control for non-experimental variation in microarrays and other informatics scale studies [Speed]. The procedure includes two steps that are applied, independently, to each metagenomic sample , transformation and standardization. A third step, multiple sample scaling, is applied to all considered data (i.e. is applied simultaneously to all samples under consideration). Briefly, the three steps include:
(1) Data normalization: MGRAST V3 Normalization: Transformation
We attempt to normalize abundance counts with a log based transformation:
$y_{s,i} = log_{2} (x_{s,i} + 1)$
Where $x_{s,i}$ represents an abundance measure ($i$) in sample ($s$).
Log transformation of the data is essential if they are to be considered with a parametric test (t-test, ANOVA, Pearson correlation etc.). These tests require data under consideration to be normally distributed. Raw abundance count data are rarely (if ever) distributed normally; however, log transformed abundance counts frequently do follow a normal distribution.
After this procedure most (but not all) samples will exhibit a distribution of values that is a much closer approximation of the normal distribution (bell-curve or gaussian distribution). The boxplots (see Boxplots below) provide a means to quickly visualize the distribution of abundance counts, for every sample under consideration.
(2) Data normalization: MGRAST V3 Normalization: Standardization
Also referred to as “data centering”, standardization of log transformed counts from a given sample. is achieved as follows:
$z_{s,i} = \left ( \frac{y_{s,i} - \bar{y_{s}}}{\sigma_{s}} \right )$
Where $z_{s,i}$ is the standardized abundance of an individual measure $y_{s,i}$ that has already undergone log transformation (see step 1 above). From each log transformed measure ($i$) of sample ($s$), the arithmetic mean of all transformed values ($\bar{y_{s}}$) is subtracted; the difference is divided by the standard deviation ($\sigma_{s}$) of all log transformed values for the given sample.
After this procedure, the abundance profiles for all samples will exhibit a mean of 0 and a standard deviation of 1.
NOTE:
Values that have been transformed (1) and standardized (2) as described above are used as “normalized” values in several MGRAST analysis tools. Occasionally, values undergo one additional scaling procedure. This procedure (Multiple sample scaling, see 3 below) is applied after analyses have been performed (PCA, Heatmap/dendrogram, p-value estimation).
(3) Data normalization: MGRAST V3 Normalization: Multiple sample scaling
After each sample has undergone transformation (1) and standardization (2), the values for all considered samples are scaled from 0 (the minimum value of all considered samples) to 1 (the maximum value of all considered samples). This is a uniform scaling that does not affect the relative differences of values within a single sample or between/among 2 or more samples.
This procedure places all values on a scale from 0 to 1, and is used to produce figures where the entire abundance range (for all samples under consideration) is expressed on a scale from 0 to 1. This eliminates negative abundance values (a byproduct of the log transformation), presenting all abundance counts in a more intuitive scale.
p-value tool: overview
The p-value tool allows the user to perform automated statistical tests to determine if there is a “significant” difference in the abundance of a given category across the specified grouping of samples. The tool selects the most appropriate test for a given data set, and reports a p-value (all tests utilize R based functions that are implemented in a high throughout automated pipeline). P-values are not adjusted, i.e. no adjustment has been to account for multiple testing.
p-value tool: Sample Grouping
In order to perform statistical tests to determine the category(ies) that may exhibit significant levels of differential abundance, it is necessary to segregate samples into two or more groups. In the current implementation, group selection can only be performed from the PCA analysis tool. Groupings selected in the PCA tool do not have to be informed by the PCA output. The user can specify any grouping of the samples. You can use the output of the PCA and/or the heatmap/dendrogram and/or any other selection criteria to determine your groups. The production of p-values requires at least two groups to be selected; at least one of the two groups has to have 2 or more samples in it. Once these two conditions have been met, you can choose any number of groups, and add as many samples to them as you wish. A sample may be included in only one group. This video will show you how to perform grouping:
p-value tool: Test Selection
In future releases, users will be able to choose from a variety of tests to determine the significance (expressed as a p-value) of differences that exist in abundance profile categories
for the selected groupings. Currently, the tool automatically chooses the “best” of 4 statistical tests to analyze the selected sample grouping. Tests are selected based on two criteria, data type (raw or normalized) and number of groups (2 or more than 2). The table below summarizes test selection:
p-value tool: Performing the p test
In the current implementation, p-values are calculated through the bar-chart tool, after a grouping has been specified (see Sample Grouping). This video will show you how to perform p-value analyses:
Boxplots
Boxplots are a simple means to visualize multiple data distributions at the same time. MGRAST uses a traditional box-and-whisker plot representing the 5 number summary (minimum, first quartile, median, third quartile, and maximum) of each sample. MGRAST automatically produces sample boxplots when the PCA or heatmap/dendrogram tools are used. By default, MGRAST displays two boxplots for each series of samples. One (top) is produced from the raw abundance counts; the second (lower) is produced from data that have undergone MGRAST-based normalization. A cursory examination of the boxplots is usually sufficient to determine (1) if the distribution of abundance counts among the selected samples is similar enough to allow for meaningful comparisons (2) the normality/non-normality of the abundance distributions.
Generally, the distributions of raw abundance values vary considerably among samples; distributions of normalized abundance values tend to be more similar, close enough to allow for meaningful comparisons. However, it is possible for raw abundance values to exhibit distributions that are similar enough for direct comparison. Similarly, even after normalization, samples can exhibit differences in their abundance profiles sufficient to preclude meaningful comparative analyses. It is always good practise to check the boxplots for a given group of samples to ensure that comparisons are not obscured by obvious differences in the sample abundance distributions, and/or to see the extent to which normalization was able to reduce the amount of variation among the sample abundance distributions. Boxplots are produced whenever you use the PCA or heatmap/dendrogram tools. Click on these links to see demonstration videos for the PCA and heatmap/dendrogram tools.
PCA
PCA (principal component analysis) is a well known method for dimensionality reduction of large data sets. Dimensionality reduction is a process that allows the complex variation found in a large data set (e.g. the abundance values of thousands of functional roles across dozens of metagenomic samples) to be reduced to a much smaller number of variables, fit for human interpretation. In the context of MGRAST, PCA allows for samples that exhibit similar abundance profiles (taxonomic or functional) to be grouped together. Separate methods (like the p-value tool) can then be used to explore the content of clustered groups in order to determine the individual categories that define PCA observed similarities/ differences. This video shows how to produce PCAs of the taxonomic and functional content of a selected group of metagenomic samples:
Heatmap/Dendrogram
The heatmap/dendrogram is a tool that allows an enormous amount of information (e.g. the abundance values of thousands of functional roles across dozens of metagenomic samples) to be presented in a visual form that is amenable to human interpretation. Dendrograms are trees that indicate how similar/dissimilar a group of vectors (list of values, like the abundance counts from a single metagenome) are to each other. Vectors in a dendrogram are usually ordered with respect to their level of similarity: similar vectors are placed next to each other, more distantly related vectors are placed further apart. The MGRAST heatmap/dendrogram has two dendrograms, one indicating the similarity/dissimilarity among metagenomic samples (x axis dendrogram) and another to indicate the similarity/dissimilarity among categories (e.g., functional roles; the y-axis dendrogram. A distance metric (euclidean distance is the only metric available to the current version of MGRAST – future versions will contain a much larger selection of distance metrics to choose from) is used to determine the similarity/dissimilarity between every possible pair of sample abundance profiles. The resulting distance matrix is used with a clustering algorithm (ward-based clustering in the current version – future versions will include a wide selection of clustering methods) to produce the dendrogram trees. Each square in the heatmap dendrogram represents the abundance level (as raw or MGRAST normalized values) of a single category in a single sample. Values used to generate the heatmap/dendrogram figure can be downloaded as a table by clicking on the “download” button. This video will show you how to use the heatmap tool:
references
Statistical analysis of gene expression microarray data / edited by Terry Speed.
Boca Raton, FL : Chapman & Hall/CRC, c2003.
| 2016-10-24T10:32:38 |
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|
https://theory.pppl.gov/news/seminars.php?scid=9&n=heliophysics-seminars
|
# Heliophysics Seminars
The Heliophysics seminars are intended to:
• allow guests and local members of the plasma physics community to present heliophysics related research and foster collaborations
• facilitate development of theoretical tools for understanding fundamental physical processes such as reconnection, turbulence, waves, and transport that control the dynamics in the context of the heliosphere
• provide a forum to facilitate cross-fertilization between laboratory plasma physics, astrophysics, and heliospheric science
Heliophysics seminars are usually held Thursdays, @3 PM, in the Theory Conference Room, T169.
### Past
• Mercury‘s Dynamic Magnetosphere
Prof. James Slavin, University of Michigan, abstract, slides
[#s743, 06 Dec 2018]
MESSENGER’s exploration of Mercury has led to many important discoveries and a global perspective on its magnetosphere, exosphere, and interior as a coupled system. Mercury’s proximity to the Sun, weak planetary magnetic field, electrically conducting core, and sodium-dominated exosphere give rise to a highly dynamic magnetosphere unlike that of any other planet. The strong interplanetary magnetic fields so close to the Sun result in a high rate of energy transfer from the solar wind into Mercury’s magnetosphere. Surprisingly, direct solar wind impact on the surface during coronal mass ejection impact has been found to be infrequent. Electric currents induced in Mercury’s highly conducting interior buttress the weak planetary magnetic field against direct impact for all but the strongest solar events. Kinetic effects associated with the large orbits of planetary ions about the magnetic field and the small dimensions of the magnetosphere are observed to significantly affect some fluid instabilities such as Kelvin-Helmholtz waves along the magnetopause. As at Earth, magnetic reconnection, dipolarization fronts, and plasmoid ejection are closely associated with substorms in Mercury’s magnetosphere, and MESSENGER frequently observed energetic electrons with energies of tens to several hundred thousand electron volts. However, no “Van Allen” radiation belts with durable trapping are present.
• The lunar plasma wake and electron phase-space holes
Prof. Ian Hutchinson, MIT, abstract, slides
[#s926, 30 Nov 2018]
Wakes of plasma flowing past unmagnetized bodies like probes, moons, or large particles are usually unsteady. Detailed theory and simulations show instabilities excited by the velocity distribution distortions give rise to electron holes (soliton-like BGK modes). We have recently discovered from spacecraft observations that the solar wind wake of the moon is full of electron holes, in agreement with predictions. Transverse instability of these holes determines their evolution and persistence and how they eventually merge into the background plasma.
2 related papers:
"Prediction and Observation of Electron Instabilities and Phase Space Holes Concentrated in the Lunar Plasma Wake", Ian H. Hutchinson, David M. Malaspina, Geophysical Res. Lett. 2018
"Transverse instability of electron phase-space holes in multi-dimensional Maxwellian plasmas", I. H. Hutchinson J. Plasma Phys. 2018
• On the role of magnetic reconnection in kinetic-range turbulence and the existence of cascades in the entire phase space from hybrid-Vlasov-Maxwell simulations
Silvio Cerri, Princeton University , abstract, slides
[#s735, 30 May 2018]
Understanding the properties of turbulent fluctuations and how turbulent energy is dissipated in weakly collisional plasmas is a fundamental step towards understanding how turbulence feeds back on the evolution of several astrophysical systems. In this context, space plasmas are probably the best laboratory for the study of plasma turbulence in a weakly collisional regime, as the Earth’s environment has become accessible to increasingly accurate direct measurements. In situ observations of the solar wind and the terrestrial magnetosheath have indeed provided relevant constraints on the turbulent energy spectra, determining the typical values of their slopes and revealing the presence of breaks in the electromagnetic fluctuation cascade at kinetic scales. A first break in the turbulent spectrum is indeed encountered at the proton kinetic scales and separates the so-called “MHD inertial range” spectrum from the kinetic spectrum that arises at scales smaller than the proton gyroradius (also referred to as the “dissipation” or “dispersion” range). Such transition is a clear evidence of a change in the physics underlying the cascade process, and its understanding is today a matter of a strong debate. Very high resolution measurements by MMS have also recently pointed out the presence of structures in the particle (electron) distribution function that can be interpreted as a cascade in velocity space.
In this talk I will present some recent developments in the investigation of the properties of kinetic-range turbulence via high-resolution hybrid-kinetic (fully-kinetic ions and fluid electrons) simulations both in 2D and 3D. In particular, I will show the first numerical evidence that has led to the suggestion of a link between magnetic reconnection, ion break and turbulent energy transfer in the sub-ion-gyroradius cascade[1,2] (also known as “reconnection-mediated scenario” for plasma turbulence). Finally, I will show the first evidence for a six-dimensional (“dual”) phase-space cascade of ion-entropy fluctuations in a 3D3V simulation of electromagnetic turbulence: such phase-space cascade is shown to be anisotropic with respect to the background magnetic fleld in both real and velocity space and suggests that both linear and non-linear phase mixing are simultanously at work[3].
[1] S. S. Cerri & F. Califano, New J. Phys. 19, 025007 (2017)
[2] Luca Franci, Silvio Sergio Cerri et al., Astrophys. J. Lett. 850, L16 (2017)
[3] S. S. Cerri, M. W. Kunz & F. Califano, Astrophys. J. Lett. 856, L13 (2018)
• Magnetic Reconnection during Turbulence and the Role it Plays in Dissipation and Heating
Mike Shay, U. Delaware , abstract, slides
[#s707, 09 May 2018]
Turbulence plays an important role in many plasmas, including those in accretion disks, in the heliosphere, and in the laboratory. In plasmas with low collisionality, such as those in the heliosphere, exactly how this turbulent energy damps away is an open question, with ramifications for the heating of the solar corona and the solar wind. Magnetic reconnection, where magnetic field lines break and reform in a plasma, is one possible mechanism for damping this turbulent energy and heating the plasma, but the role it may play is uncertain. Recently, however, significant progress has been made in understanding plasma heating in isolated reconnection sites. Can this new knowledge shed light on the properties of plasma heating during turbulence?
In this talk, after reviewing our understanding of heating due to reconnection, I will lay out a framework for applying reconnection heating predictions to turbulent systems, and show initial results for testing this framework using fully kinetic PIC simulations. In addition, I will discuss recent MMS observations of reconnection in Earth's turbulent magnetosheath. I will then explore the statistics of magnetic reconnection in kinetic simulations of turbulence. By statistics, I mean the number of x-lines, the spread of reconnection rates, and how these quantities vary in time. How these statistics vary in different turbulence regimes and its impact on reconnection heating will be discussed.
• Collisionless damping of slow magnetosonic waves (and related compressional fluctuations)
Bill Dorland, University of Maryland , abstract
[#s663, 30 Mar 2018]
Compressional perturbations are observed in the solar wind even when the collision time is much longer than an inferred wave period. This is puzzling. Lithwick & Goldreich argued that the parallel wavenumbers of the slow modes would be inherited from the Alfvén cascade, which would itself be well-described as being in critical balance. For most parameters, this argument favors rapid damping of compressional fluctuations, $\gamma \sim k_\parallel v_A \sim k_\perp v_\perp$. Schekochihin et al. argued instead that the compressional perturbations would evolve in Lagrangian fashion, maintaining their original (possibly very long) wavelengths along the magnetic field, even as the field itself developed ever-shorter parallel wavelengths. Although compressional waves would still experience Landau and/or Barnes damping in this picture, the rate could be very small. Kanekar et al. observed that stochastic echoes could “fluidize” the compressional fluctuations, allowing them to evade collisionless damping altogether. It remains unclear which mechanism is dominant, if any. I will present recent work on this problem by R. Meyrand, A. Kanekar, A. Schekochihin, and myself.
• Magnetic Reconnection in MHD and Kinetic Turbulence
Nuno Loureiro, MIT , abstract
[#s631, 21 Feb 2018]
Recent works have revisited the current understanding of Alfvénic turbulence to account for the role of magnetic reconnection [1-3]. Theoretical arguments suggest that reconnection inevitably becomes important in the inertial range, at the scale where it becomes faster than the eddy turn over time. This leads to a transition to a new sub-inertial interval, suggesting a route to energy dissipation that is fundamentally different from that envisioned in the usual Kolmogorov-like phenomenology.
These concepts can be extended to weakly collisional plasmas, where reconnection is enabled by electron inertia rather than resistivity [4,5]. Although several different cases must then be considered (whether the eddies themselves are on MHD or kinetic scales, whether the plasma beta is large or small, etc.), a common result to all of them is that the energy spectrum exhibits a scaling with the perpendicular wave number that scales between $k_\perp^{−8/3}$ and $k_\perp^{−3}$, in favourable agreement with many numerical results and observations.
This talk aims to review these results, and discuss their implications.
[1] Nuno F. Loureiro & Stanislav Boldyrev, Phys. Rev. Lett. 118, 245101 (2017)
[2] A. Mallet, A. A. Schekochihin & B.D.G. Chandran, Mon. Not. R. Astron. Soc. 468, 4862 (2017)
[3] Stanislav Boldyrev & Nuno F. Loureiro, Astrophys. J. 844, 125 (2017)
[4] Nuno F. Loureiro & Stanislav Boldyrev, Astrophys. J. 850, 182 (2017)
[5] Alexander A. Schekochihin & Benjamin D. G. Chandran, J. Plasma Phys. 83, 905830609 (2017)
| 2018-12-17T16:50:21 |
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|
https://pos.sissa.it/345/003/
|
Hard Probes Results from the ATLAS Experiment
A. Milov* on behalf of the ATLAS collaboration
*corresponding author
Full text: pdf
Pre-published on: 2019 January 12
Published on:
Abstract
The ATLAS experiment at the LHC has a diverse research program exploring the physics of the heavy ion collisions at the LHC energies. The strength of the ATLAS detector is in the measuring the hard probes that play the crucial role in understanding various physics phenomena helping to unveil the physics nature of the system created in ion collisions. The results of the ATLAS effort over the last year are reviewed in this proceeding that includes the last measurement done with the electroweak probes, a very broad spectrum of measurements performed with jets, the first results on bound and open heavy quark states and results from the ultra-peripheral collisions. The measurements performed by ATLAS span all the collision systems available at the LHC, from small $pp$ and $p+$Pb to intermediate and large Xe+Xe and Pb+Pb
Open Access
Copyright owned by the author(s) under the term of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
| 2019-04-18T20:59:20 |
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|
https://lammps.sandia.gov/doc/pair_spin_dmi.html
|
# pair_style spin/dmi command
## Syntax
pair_style spin/dmi cutoff
• cutoff = global cutoff pair (distance in metal units)
## Examples
pair_style spin/dmi 4.0
pair_coeff * * dmi 2.6 0.001 1.0 0.0 0.0
pair_coeff 1 2 dmi 4.0 0.00109 0.0 0.0 1.0
## Description
Style spin/dmi computes the Dzyaloshinskii-Moriya (DM) interaction between pairs of magnetic spins:
where si and sj are two neighboring magnetic spins of two particles, eij = (ri - rj)/|ri-rj| is the normalized separation vector between the two particles, and D is the DM vector defining the intensity and the sign of the interaction.
| 2018-07-19T09:33:09 |
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https://nethack.fandom.com/wiki/Crysknife
|
FANDOM
2,034 Pages
)
Name crysknife
Appearance crysknife
Damage vs. small 1d10
Damage vs. large 1d10
To-hit bonus +3
Weapon skill knife
Size one-handed
Cost 100 zm
(+10/positive
enchant)
Weight 20
Material mineral
A crysknife is a weapon that can only be produced by enchanting a worm tooth. It has a +3 to-hit bonus and does d10 damage against both small and large monsters, making it a nice choice for #twoweaponing. However, if it leaves your possession, it reverts back into a worm tooth (when fixed, this only happens 10% of the time). It can safely be put in a container without reverting, as long as that container remains in your possession.
Crysknives count as throwing weapons, so they get a to-hit bonus when thrown. Because of their reversion property, throwing them is typically not a good idea.
Slash'EMEdit
Slash'EM changes the damage for crysknives to 1d20 against small and 1d30 against large. The Ice Mage, Flame Mage and Necromancer roles can gain Skilled in knife, Healer can gain Expert, and Yeomen can gain Basic. A healer can benefit seriously from the Crysknife, since they have little weapon choice other than darts, but still can achieve expert in knives, this can be the most lethal weapon (see below) for a healer in Slash'EM.
GenerationEdit
See: Worm tooth
Crysknifes are not normally generated, but instead created by the player through enchanting a worm tooth.
Average damage calculationEdit
NetHackEdit
We assume the player has expert skill in knife, which gives a +2 damage bonus. A blessed weapon deals 1d4 extra damage against demons and undead. The worst case scenario is against a non-undead, non-demon monster. The best case scenario is against a undead/demon monster. Further, this damage calculation is based per 3.4.3, and not SLASH'EM.
Weapon Against regular small monsters Against regular large monsters Worst case scenario Best case scenario
Blessed crysknife +0 $\frac{1+10}{2}+2=\bold{7.5}$ $\frac{1+10}{2}+2=\bold{7.5}$ $\frac{1+10}{2}+2=\bold{7.5}$ $\frac{1+10}{2}+\frac{1+4}{2}+2=\bold{10}$
Blessed crysknife +7 $\frac{1+10}{2}+2+7=\bold{14.5}$ $\frac{1+10}{2}+2+7=\bold{14.5}$ $\frac{1+10}{2}+2+7=\bold{14.5}$ $\frac{1+10}{2}+\frac{1+4}{2}+2+7=\bold{17}$
Blessed crysknife +9 $\frac{1+10}{2}+2+9=\bold{16.5}$ $\frac{1+10}{2}+2+9=\bold{16.5}$ $\frac{1+10}{2}+2+9=\bold{16.5}$ $\frac{1+10}{2}+\frac{1+4}{2}+2+9=\bold{19}$
SLASH'EMEdit
We assume the player has expert skill in knife, which gives a +2 damage bonus. A blessed weapon deals 1d4 extra damage against demons and undead. The worst case scenario is against a non-undead, non-demon small monster. The best case scenario is against a undead/demon large monster.
Weapon Against regular small monsters Against regular large monsters Worst case scenario Best case scenario
Blessed crysknife +0 $\frac{1+20}{2}+2=\bold{12.5}$ $\frac{1+30}{2}+2=\bold{17.5}$ $\frac{1+20}{2}+2=\bold{12.5}$ $\frac{1+30}{2}+\frac{1+4}{2}+2=\bold{20}$
Blessed crysknife +7 $\frac{1+20}{2}+2+7=\bold{17.5}$ $\frac{1+30}{2}+2+7=\bold{22.5}$ $\frac{1+20}{2}+2+7=\bold{17.5}$ $\frac{1+30}{2}+\frac{1+4}{2}+2+7=\bold{25}$
Blessed crysknife +9 $\frac{1+20}{2}+2+9=\bold{19.5}$ $\frac{1+30}{2}+2+9=\bold{24.5}$ $\frac{1+20}{2}+2+9=\bold{19.5}$ $\frac{1+30}{2}+\frac{1+4}{2}+2+9=\bold{27}$
Because of this increase in damage, the SLASH'EM crysknife compares favorably even to artifacts such as Excalibur. Against large monsters, it actually does more damage than the similarly enchanted Excalibur.
ThrowingEdit
At d10, the highest of any projectile weapon (above even the shuriken and boomerang), it begs to be used as such. However, this usually isn't worth the trouble. Even when a crysknife in question is fixed—throwing is best reserved for sheer desperation or complete and utter stupidity. The simple reason for this is that they do not stack—meaning only one may ever be thrown at a time, and it'll take far more enchant weapon scrolls than is worth that small upgrade. Consider that even 3d3 has a higher average (three unenchanted knives, thrown at once) than the 1d10 of a crysknife. Further, when enchantment is considered, 3d3+21 (average of 27) is far larger than 1d10+7 (average of 9). Furthermore, Your strength modifier makes multi-shot thrown weapons even better.
In nethack 3.6, crysknives stack, which changes things significantly (though they still have a chance to become worm teeth when thrown).
MythologyEdit
The crysknife and the concept of worm teeth are from Frank Herbert's science fiction novel Dune.
Encyclopedia entryEdit
[The crysknife] is manufactured in two forms from teeth taken
from dead sandworms. The two forms are "fixed" and "unfixed".
An unfixed knife requires proximity to a human body's
electrical field to prevent disintegration. Fixed knives
are treated for storage. All are about 20 centimeters long.
[ Dune, by Frank Herbert ]
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| 2019-12-13T10:26:20 |
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https://publications.drdo.gov.in/ojs/index.php/dsj/article/download/1086/4756
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Design/Development of Mini/Micro Air Vehicles through Modelling and Simulation: Case of an Autonomous Quadrotor
Design and development of an autonomous quadrotor micro aerial vehicle is undertaken following a systematic approach. A fairly detailed model was constructed and simulations were then carried out with the purpose of refining the baseline design, building a controller, and testing the flying qualities of the vehicle on a ground-based flight simulator. Following this, a smooth transition to rig and flight testing has been enabled in a cost- and time-effective manner, meeting all the design requirements.
Keywords: Modelling, simulation, micro air vehicle, quadrotor
A Rotation matrix Ap Area of rotor B Body-fixed frame D Drag moment DOFs Degrees of freedom FwI Forces due to translational velocity and wind G Gear ratio h Altitude of vehicle I Inertial frame Ixx,Iyy,Izz Quadrotor moments of inertia about body x, y, z axes, respectively Ict Inertial counter torque J Moment of inertia matrix Jp Moment of inertia of single rotor kd Aerodynamic drag moment coefficient ki Current constant of motor kr Friction coefficients due to rotational velocities ks, ku Friction coefficients due to translational velocities kt Aerodynamic thrust coefficient kv Speed constant of motor L Distance of centre of rotor from origin M Matrix relating Euler time derivatives with body angular rates Mf Friction torque Mg Gyroscopic moments m Mass of quadrotor vehicle assembly P Pitch of rotor blade R Resistance of motor Rp Radius of rotor T Thrust force V Voltage applied to motor w Wind velocity ${\stackrel{˙}{X}}_{i}^{\text{'}}$ , ${\stackrel{˙}{Y}}_{i}^{\text{'}}$ Forward and sideward velocities in the horizontal plane Ẋi, Ẏi Velocities in inertial frame α Angular speed of rotor φ, θ, ψ Euler angles φb, θb Commanded base Euler angles τ Torque τt Disturbance torque τm Motor torque ω Angular rates of quadrotor in body frame Subscripts 1, 2, 3, 4 Rotor numbers b Coordinate in body frame c Commanded value d Desired value i Coordinate in inertial frame o Obtained value
There has been an explosion of interest in micro and mini aerial vehicles over the last decade and what was once perhaps a hobby for the aviation enthusiast is now a full-fledged area of research and development1,2. The interest has been fuelled by the prospect of their use in various civilian forums3 in addition to the usual military applications. With the availability of low-cost and commercial off-the-shelf components, building and flying mini and micro air vehicles has become an integral part of capstone design courses in aerospace engineering programmeme in many universities. In fact, universities have been a significant source of research advancement in this area as new concepts can be tested within the resources available from standard research grants using graduate students as manpower. Many small business houses have been attracted to developing mini/micro air vehicles as products, though much of the market at present appears to be for the larger mini-sized vehicles than the smaller micro ones.
Like other aerospace systems, micro/mini aerial vehicle development is a multidisciplinary endeavour requiring skills in several areas of engineering science and technology, and hence, must necessarily be a team effort. On the other hand, due to the apparent ease and simplicity of their development cycle, and the usual lack of programme management skills in academia and small businesses, a systematic approach to engineering design and development is often not followed. Inevitably, this leads to cost- and time-over-runs, and eventual discord between members of the various participating teams. In case of a collaborative development venture between two or more entities, the need for precise planning and timely implementation is even more critical.
modelling and simulation technologies for aerospace systems have today advanced to the level where much of the uncertainty in the development process can be ironed out during ground-based simulations, thus obviating the need for repeated trials and modifications4. Integrated modelling and simulation of all systems and sub-systems is a key milestone in any aerospace vehicle design and development programme5. Multidisciplinary design optimisation methods may also be employed6, provided appropriate-fidelity tools for each disciplinary analysis suitable for micro air vehicles are available. However, the use of modelling and simulation for mini/micro air vehicle development does not seem to be the norm except to a limited extent for control system design and evaluation7.
An interesting exercise in which a quadrotor micro aerial vehicle was designed and developed following a systematic approach under severe time and cost constraints is reported. Beginning with a baseline configuration, based on the existing components and components readily available in the market, all sub-systems were modelled and integrated into a single system model. This was used to test the performance of the vehicle, its stability and response to external disturbances and control inputs. The model was validated against an existing quadrotor system for which data was available. In parallel with the modelling and simulation exercise, components were procured and the quadrotor assembled.
The model was then used to design a controller which was implemented in software and integrated with the model. Simulations of the closed-loop system were then carried out to verify its stability and response characteristics. Where necessary, design modifications were made, such as adjusting the vertical location of the centre of mass, and the exercise was repeated. The digital simulation was then integrated with a joystick and an open-source flight simulator to evaluate the vehicle flying qualities before being cleared. Multidisciplinary design optimisation was not employed due to lack of time and non-availability of the requisite tools.
The control law was embedded into an autopilot board and integrated with the vehicle air frame. The quadrotor was then mounted on a 3-DOFs roll-pitch-yaw test rig specially built for this purpose. The test rig was used to assess the stabilisability and controllability of the vehicle in roll, pitch, and yaw, and tune the controller PID gains, and also to correct for thrust asymmetry between the four rotors. Once the rig tests were satisfactory, the vehicle was test flown indoors, first manually, and then in autonomous mode. Some adjustment of the PID controller gains were necessary as the pivot point on the test rig does not coincide with the vehicle center of mass. Finally, flight tests were conducted outdoors in an open ground and in a built-up area.
Due to unforeseen reasons, a pressure altitude sensor could not be placed on board the autopilot, so thrust command to control the altitude was provided manually in all flights. But for this, the entire programme went as planned with no significant disruptions. In all, a little under than half the scheduled programme time was spent on the modelling and simulation task, which, the authors believe, was worthwhile as it helped cut down the time spent on costly redesigns, controller gain tuning and flight testing. The flight simulator was immensely helpful to the test pilot whose previous experience had mostly been on fixed-wing aircraft. Based on this experience, the use of modelling and simulation tools during design and development of micro/mini aerial vehicles, especially to academia and small businesses is strongly recommend.
Control of the quadrotor is achieved by commanding different speeds to different rotors, which in turn produce differential aerodynamic forces and moments. For hovering, all the four rotors have to rotate at the same speed; for vertical motion, the speed of all the four rotors has to be increased or decreased by the same amount, simultaneously. To pitch and move laterally in that direction, speeds of rotors 1 and 3 have to be changed conversely. Similarly, for producing roll and corresponding lateral motion, speed of rotors 2 and 4 is changed conversely. To produce yaw, the speed of one pair of two oppositely-placed rotors has to be increased while the speed of the other pair has to be decreased by the same amount. In this way, overall thrust produced is the same, but the differential drag moment creates yawing motion.
The quadrotor has been designed using X-UFO (commercially available model) as the baseline. The brushed motors have been replaced by brushless motors, and 3-cell lithium-polymer battery has been used to improve the lifting capability and endurance of the vehicle. Further, to reduce the weight, the rotor shrouds and other non-critical structural components have been removed. The electronics has been replaced by custom autopilot hardware (including brushless motor controllers). A snapshot of the completed vehicle is shown in Fig. 2.
The autopilot used is a product developed in-house by Coral Digital Technologies (P) Ltd., Bengaluru, India. The autopilot uses a single 16-bit 24HJ series PIC microcontroller for all the computations, communication, and switching between manual and automodes.
The navigation algorithm used three gyros and two accelerometers to estimate orientation. Altitude and velocity were estimated using pressure sensors, and position was obtained using the GPS. A Zigbee modem was used for communication with the ground control station (GCS) during flight. The GCS receives data from the autopilot to monitor vehicle trajectory and other key parameters during flight, and is capable of updating way-points and PID gains during flight. An onboard SD card recorded several parameters at 50 Hz during flight for post-flight analysis of flight data. The autopilot hardware along with key interfaces and communication protocols used is illustrated in Fig. 3.
The final vehicle, capable of lifting autopilot and suitable battery pack, weighs 320 g (including battery, autopilot) and has an additional 40 g payload capability. The horizontal dimensions of this prototype are 65 cm each way, and the vertical dimension is ~ 15 cm.
In Fig. 1, I is the inertial frame (subscript “i”) and B is the body-fixed frame (subscript “b”). The dynamic model was derived under the following assumptions7,10, and is briefly presented below:
• Structure is rigid and has roll-pitch symmetry.
• Centre of mass of the vehicle and the origin of B axis system coincide.
• The rotors are rigid in plane.
3.1 Kinematics
Using Euler angle parameterisation, the orientation of the vehicle in space is given by rotation matrix A from frame B to I:
$A\text{\hspace{0.17em}}=\text{\hspace{0.17em}}\left(\begin{array}{l}C\text{ψ}C\text{θ}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}C\text{ψ}S\text{θ}S\varphi \text{\hspace{0.17em}}-\text{\hspace{0.17em}}S\text{ψ}C\varphi \text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}C\text{ψ}S\text{θ}C\varphi \text{\hspace{0.17em}}+\text{\hspace{0.17em}}S\text{ψ}S\varphi \\ S\text{ψ}C\text{θ}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}S\text{ψ}S\text{θ}S\varphi \text{\hspace{0.17em}}+\text{\hspace{0.17em}}C\text{ψ}C\varphi \text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}S\text{ψ}S\text{θ}C\text{θ}\text{\hspace{0.17em}}\text{\hspace{0.17em}}-\text{\hspace{0.17em}}C\text{ψ}S\varphi \\ -S\theta \text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}C\text{θ}S\varphi \text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}C\text{θ}C\varphi \end{array}\right)$
where, Cθ, Sϕ etc. are cos ϕ, sin ϕ, etc.
Euler time derivatives are related to body angular rate as
$\begin{array}{l}{\left[\stackrel{˙}{\varphi }\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{θ˙}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\stackrel{˙}{\text{ψ}}\right]}^{T}\text{\hspace{0.17em}}=\text{\hspace{0.17em}}{M}^{-1}{\left[{\text{ω}}_{xi}\text{\hspace{0.17em}}\text{\hspace{0.17em}}{\text{ω}}_{yi}\text{\hspace{0.17em}}\text{\hspace{0.17em}}{\text{ω}}_{zi}\right]}^{T}\\ =\text{\hspace{0.17em}}{M}^{-1}A{\left[{\text{ω}}_{xb}\text{\hspace{0.17em}}\text{\hspace{0.17em}}{\text{ω}}_{yb}\text{\hspace{0.17em}}\text{\hspace{0.17em}}{\text{ω}}_{zb}\right]}^{T}\end{array}$ (1)
where, $M\text{\hspace{0.17em}}=\text{\hspace{0.17em}}\left(\begin{array}{ccc}\frac{C\text{ψ}}{C\text{θ}}& \frac{S\text{ψ}}{C\text{θ}}& 0\\ -\text{\hspace{0.17em}}S\text{ψ}& C\text{ψ}& 0\\ 0& 0& 1\end{array}\right)$
Since the concern is only about the velocity of centre of mass located at origin of B, one can directly get body frame velocities from inertial frame velocities, using the transformation matrix as
${\left[\stackrel{˙}{x}b\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\stackrel{˙}{y}b\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\stackrel{˙}{z}b\right]}^{T}\text{\hspace{0.17em}}=\text{\hspace{0.17em}}{A}^{-1}{\left[\stackrel{˙}{x}i\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\stackrel{˙}{y}i\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\stackrel{˙}{z}i\right]}^{T}$ (2)
3.2 Force Equations
Aerodynamic force (thrust) of a rotor can be shown proportional to square of its rotational speed, and square of its radius, using momentum theory11. It is modelled as
${T}_{i}\text{\hspace{0.17em}}=\text{\hspace{0.17em}}{C}_{1}\left(\frac{1\text{\hspace{0.17em}}-\text{\hspace{0.17em}}2\text{π}LCS}{P{\text{α}}_{i}}\text{\hspace{0.17em}}+\text{\hspace{0.17em}}2\text{π}\frac{{\stackrel{˙}{z}}_{b}\text{\hspace{0.17em}}-\text{\hspace{0.17em}}{w}_{{z}_{b}}}{P{\text{α}}_{i}}\right)$ (3)
where, ${C}_{1}\text{\hspace{0.17em}}=\text{\hspace{0.17em}}{\text{κ}}_{t\text{ρ}}{A}_{p}{\text{α}}_{i}^{2}{R}_{p}^{2}$ C = 1 if i = 1 or 4, or C = –1 if i = 2 or 3, and S = ωyb if i = 1 or 3, or S = ωxb if i = 2 or 4.
Forces due to translational velocity of quadrotor and wind disturbances are modelled as
${F}_{wI}\text{\hspace{0.17em}}=\text{\hspace{0.17em}}A{\left[{k}_{s}\left({w}_{xb}\text{\hspace{0.17em}}-\text{\hspace{0.17em}}{\stackrel{˙}{x}}_{b}\right)\text{\hspace{0.17em}}{k}_{s}\left({w}_{yb}\text{\hspace{0.17em}}-\text{\hspace{0.17em}}{\stackrel{˙}{y}}_{b}\right)\text{\hspace{0.17em}}{k}_{u}\left({w}_{zb}\text{\hspace{0.17em}}-\text{\hspace{0.17em}}{\stackrel{˙}{z}}_{b}\right)\right]}^{T}$ (4)
Hence, linear momentum balance in inertial frame gives
$\begin{array}{l}\left[\begin{array}{l}{\stackrel{¨}{x}}_{i}\\ {\stackrel{¨}{y}}_{i}\\ {\stackrel{¨}{z}}_{i}\end{array}\right]\text{\hspace{0.17em}}=\text{\hspace{0.17em}}-\text{\hspace{0.17em}}\left[\begin{array}{l}{\text{ω}}_{xb}\\ {\text{ω}}_{yb}\\ {\text{ω}}_{zb}\end{array}\right]\text{\hspace{0.17em}}\text{\hspace{0.17em}}×\text{\hspace{0.17em}}\text{\hspace{0.17em}}\left[\begin{array}{l}{\stackrel{˙}{x}}_{i}\\ {\stackrel{˙}{y}}_{i}\\ {\stackrel{˙}{z}}_{i}\end{array}\right]\text{\hspace{0.17em}}\text{\hspace{0.17em}}+\text{\hspace{0.17em}}g\left[\begin{array}{l}0\\ 0\\ 1\end{array}\right]\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}+\text{\hspace{0.17em}}\frac{{F}_{wI}}{m}\text{\hspace{0.17em}}-\text{\hspace{0.17em}}\frac{{T}_{1}\text{\hspace{0.17em}}+\text{\hspace{0.17em}}{T}_{2}\text{\hspace{0.17em}}+\text{\hspace{0.17em}}{T}_{3}\text{\hspace{0.17em}}+\text{\hspace{0.17em}}{T}_{4}}{m}\text{\hspace{0.17em}}A\text{\hspace{0.17em}}\left[\begin{array}{l}0\\ 0\\ 1\end{array}\right]\end{array}$ (5)
3.3 Moment Equations
Aerodynamic drag moment of a rotor can be shown to be proportional to square of its rotational speed, and cube of its radius, using momentum theory11. It is modelled as
${D}_{i}\text{\hspace{0.17em}}=\text{\hspace{0.17em}}{C}_{2}\left(1-\frac{2\text{π}LCS}{P{\text{α}}_{i}}\text{\hspace{0.17em}}+\text{\hspace{0.17em}}2\text{π}\frac{{\stackrel{˙}{z}}_{b}\text{\hspace{0.17em}}-\text{\hspace{0.17em}}{w}_{{z}_{b}}}{P{\text{α}}_{i}}\right)$ (6)
where, ${C}_{2}\text{\hspace{0.17em}}{C}_{2}\text{\hspace{0.17em}}=\text{\hspace{0.17em}}{k}_{d\text{ρ}}{A}_{p}{\text{α}}_{i}^{2}{R}_{p}^{3}$
Inertial counter torque, which is the reaction torque produced by a change in rotational speed of rotors, is modelled as
${I}_{ct}\text{\hspace{0.17em}}=\text{\hspace{0.17em}}{J}_{p}\left(-{\stackrel{˙}{\text{α}}}_{1}\text{\hspace{0.17em}}+\text{\hspace{0.17em}}{\stackrel{˙}{\text{α}}}_{2}\text{\hspace{0.17em}}-\text{\hspace{0.17em}}{\stackrel{˙}{\text{α}}}_{3}\text{\hspace{0.17em}}+\text{\hspace{0.17em}}{\stackrel{˙}{\text{α}}}_{4}\right)$ (7)
Friction torque due to rotational motion is modelled as12
${M}_{f}\text{\hspace{0.17em}}=\text{\hspace{0.17em}}{k}_{r}{\left[\stackrel{˙}{\varphi }\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{θ˙}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\stackrel{˙}{\text{ψ}}\right]}^{T}$ (8)
Disturbance torque due to uncontrollable factors (wind etc.) is modelled as
${\text{τ}}_{d}\text{\hspace{0.17em}}=\text{\hspace{0.17em}}{\left[{\text{τ}}_{xb}\text{\hspace{0.17em}}\text{\hspace{0.17em}}{\text{τ}}_{yb}\text{\hspace{0.17em}}\text{\hspace{0.17em}}{\text{τ}}_{zb}\right]}^{T}$ (9)
Gyroscopic moments, caused by combination of rotations of four rotors and vehicle frame, are modelled as
${M}_{g}\text{\hspace{0.17em}}=\text{\hspace{0.17em}}{J}_{p}{\left[\stackrel{˙}{\varphi }\text{α}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\stackrel{˙}{\text{θ}}\text{α}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}0\right]}^{T}$ (10)
where, α = – α1 + α2 – α3 + α4
Hence, angular momentum balance in body frame gives
$\begin{array}{l}\left[\begin{array}{l}{\stackrel{˙}{\text{ω}}}_{xb}\\ {\stackrel{˙}{\text{ω}}}_{yb}\\ {\stackrel{˙}{\text{ω}}}_{zb}\end{array}\right]\text{\hspace{0.17em}}\text{\hspace{0.17em}}=\text{\hspace{0.17em}}-\text{\hspace{0.17em}}{J}^{-1}\text{ω}\text{\hspace{0.17em}}×\text{\hspace{0.17em}}J\text{\hspace{0.17em}}\left[\begin{array}{l}{\text{ω}}_{xb}\\ {\text{ω}}_{yb}\\ {\text{ω}}_{zb}\end{array}\right]\text{\hspace{0.17em}}-\text{\hspace{0.17em}}{J}^{-1}\left({M}_{f}\text{\hspace{0.17em}}+\text{\hspace{0.17em}}{\text{τ}}_{d}\text{\hspace{0.17em}}+\text{\hspace{0.17em}}{M}_{g}\right)\\ +\text{\hspace{0.17em}}{J}^{-1}\left[\begin{array}{l}L\left({T}_{4}\text{\hspace{0.17em}}-\text{\hspace{0.17em}}{T}_{2}\right)\\ L\left({T}_{1}\text{\hspace{0.17em}}-\text{\hspace{0.17em}}{T}_{3}\right)\\ {D}_{1}\text{\hspace{0.17em}}-\text{\hspace{0.17em}}{D}_{2}\text{\hspace{0.17em}}+\text{\hspace{0.17em}}{D}_{4}\text{\hspace{0.17em}}+\text{\hspace{0.17em}}{I}_{ct}\end{array}\right]\text{\hspace{0.17em}}\end{array}$ (11)
where, $\text{ω}\text{\hspace{0.17em}}×\text{\hspace{0.17em}}\text{=}\text{\hspace{0.17em}}\left[\begin{array}{ccc}0& -\text{\hspace{0.17em}}{\text{ω}}_{zb}& {\text{ω}}_{yb}\\ {\text{ω}}_{zb}& 0& -\text{\hspace{0.17em}}{\text{ω}}_{xb}\\ -\text{\hspace{0.17em}}{\text{ω}}_{yb}& {\text{ω}}_{xb}& 0\end{array}\right]$
3.4 Motor Dynamics
A standard dc motor with negligible inductance is modelled as
${\text{τ}}_{{m}_{i}}\text{\hspace{0.17em}}=\text{\hspace{0.17em}}{k}_{i}\left({v}_{i}\text{\hspace{0.17em}}-\text{\hspace{0.17em}}\frac{{k}_{v}{\text{α}}_{i}}{G}\right)\text{\hspace{0.17em}}/\text{\hspace{0.17em}}R\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}{\stackrel{˙}{\text{α}}}_{i}\text{\hspace{0.17em}}=\text{\hspace{0.17em}}\frac{G{\text{τ}}_{{m}_{i}}\text{\hspace{0.17em}}-\text{\hspace{0.17em}}{D}_{i}}{{J}_{p}}$ (12)
The dynamic model was coded in Matlab® and a verification exercise was carried out using data from Nice13, reproduced in Table 1.
In spite of having four independent actuators, the quadrotor is still an underactuated system. Hence, the controller design uses a two-loop structure: an inner and an outer. This is depicted in Fig. 4. In the inner loop, four parameters: θ, φ, ψ, and h – are independently controlled by suitably adjusting the speed of the four rotors. As already described, speeds of rotors 1 and 3 need to be adjusted for controlling θ, 2 and 4 for controlling φ, and all four rotors for controlling ψ and h. In the outer loop, forward and sideward velocities ${\stackrel{˙}{X}}_{i}^{\text{'}}$ and ${\stackrel{˙}{Y}}_{i}^{\text{'}}$ are controlled. These are velocities in a frame which are obtained by rotating the inertial frame by ψ, as shown below:
$\begin{array}{l}{\stackrel{˙}{X}}_{i}^{\text{'}}=\text{\hspace{0.17em}}{\stackrel{˙}{X}}_{i}\mathrm{cos}\text{\hspace{0.17em}}\text{ψ}\text{\hspace{0.17em}}\text{+}\text{\hspace{0.17em}}{\stackrel{˙}{Y}}_{i}\text{\hspace{0.17em}}\mathrm{sin}\text{\hspace{0.17em}}\text{ψ}\\ {\stackrel{˙}{Y}}_{i}^{\text{'}}\text{\hspace{0.17em}}=\text{\hspace{0.17em}}-\text{\hspace{0.17em}}{\stackrel{˙}{X}}_{i}\text{\hspace{0.17em}}\mathrm{sin}\text{\hspace{0.17em}}\text{ψ}\text{\hspace{0.17em}}\text{+}\text{\hspace{0.17em}}{\stackrel{˙}{Y}}_{i}\text{\hspace{0.17em}}\mathrm{cos}\text{\hspace{0.17em}}\text{ψ}\end{array}$ (13)
This choice is helpful when using ajoystick to navigate the quadrotor on a simulator screen. In addition, actuator saturation and rate limits are also modelled. One of the objectives of the controller design is to avoid hitting these limits. Many control design methodologies have been described in the literature for controlling the motion of the quadrotor14-17. However, from a practical viewpoint, PID controllers are the simplest and can be designed quickly. Also, standard procedures for tuning the PID gains are available and are well known18. Hence, four separate PID blocks are built corresponding to each variable to be controlled in the inner loop. Based on the error signals between the commanded and measured values of a variable, the inner loop PIDs command differential voltages to reach the set point.
For the outer loop, based on trim calculations or simulation results, look-up tables are formulated, to find base θ and φ required to fly at a particular velocity. These base angles (θb and φb) act as set points for the inner loop θ and φ controllers. The outer loop PIDs command additional pitch (Δθ) and roll (Δφ) angles based on error velocities, so that the desired set point is maintained. This is shown in Fig. 4.
The PID gains are first tuned using the Ziegler-Nichols method and then tuned manually based on the desired simulation response. Some typical outputs from the simulation exercise are presented. Figure 5 shows the simulation response used to tune the inner loop parameters. The task of the controller was to stabilise the orientation angles at zero and attain a height of 45 m starting from an initial condition of h = 30 m, φ = θ =Ψ = 18°, w = τ = ω = 0.
After the performance of inner loop controller was found satisfactory, simulations were carried out to tune the parameters of outer loop controller. In the simulation response shown in Fig. 6, the task of the controller is to obtain a forward velocity ${\stackrel{˙}{X}}_{i}^{\text{'}}=\text{\hspace{0.17em}}10\text{\hspace{0.17em}}\text{m/s}$ and h = 50 m. Initial altitude and rotor parameters were the same as above, but initial Euler angles were kept at zero. Due to symmetry, identical control parameters may be used for sideward velocity $\left({\stackrel{˙}{Y}}_{i}^{\text{'}}\right)$ . The PID gains finally selected are presented in Table 2. Interestingly, despite best efforts, altitude control remained sluggish, as seen from the h vs time subplots (please note the different time scale on this subplot) of Figs 5 and 6.
The simulation model was implemented in real-time on Simulink®. For 3-D visualisation, Flightgear (http://www.flightgear.org, accessed Dec 3, 2009), an open source flight simulator under GNU license was used. Interfacing Flightgear with Matlab essentially requires sending the output vector from Matlab/Simulink to Flightgear, as seen in Fig. 4. A pre-configured interface block with Aerospace Blockset of Matlab was used for this purpose. For visualisation, the inertial frame coordinates were converted into latitude, longitude and height at that location, and orientation is specified by passing on the three Euler angles. The inbuilt model of a helicopter, Eurocopter Bo105, was used for 3-D visualisation due to lack of a quadrotor model in Flightgear. The leftmost block in Fig. 4 represents joystick interface. A standard force feedback joystick was used for setting the desired values of ${\stackrel{˙}{X}}_{i}^{\text{'}}$ , ${\stackrel{˙}{Y}}_{i}^{\text{'}}$ , ψ and h. In this manner, a real-time simulator was set up which could be flown with a joystick and the quadrotor flight could be observed on the Flightgear screen. A small snapshot of the simulator screen is shown in Fig. 7 with the model at h = 1000 m. For better speed and performance, Matlab and Flightgear were run on separate PCs.
Following the simulator studies, the control law was loaded on to the autopilot, which was then integrated with the quadrotor air frame as described earlier. The autopilot design incorporates a switching logic between auto and manual models for safety during testing. The flow diagram of the autopilot in manual and auto modes is shown in Fig. 8. Note that in either case, the rate feedback loop is part of the vehicle dynamics, i.e., even in the manual mode, the rate feedback controller continues to work. Due to its inherent instability, it would be impossible to fly any quadrotor manually if such a rate feedback is not provided to assist the pilot. The architecture also allows one to selectively assign any of the inputs to manual or auto modes. The outputs of the autopilot correspond to pitch, roll, yaw and thrust commands, which are converted into motor rpm commands by the channel-splitting block.
6.1 Rig Tests
The first set of experiments was conducted on a 3-DOFs test rig, allowing only rotations, to test the attitude stabilisation and orientation control of the vehicle. The test rig also allows the PID gains to be further fine-tuned. The vehicle with autopilot was mounted on the 3-DOFs test rig, as shown in Fig. 9. The autopilot (mounted on the vehicle) was connected to the PC to monitor attitudes and control actions in real-time. Sample results from the test rig for checking system stability in pitch and roll are shown in Fig. 10. In Fig. 10, starting with autopilot in manual mode, the switch to auto mode was made at t = 19 s. During the entire experiment, the desired roll and pitch angles were kept at zero, and a constant thrust was maintained. The spikes in Fig. 10 are the manual disturbances imparted to the system to test the controller robustness. The controller was observed to perform well and reject disturbances suitably both in pitch and roll.
6.2 Flight Tests
Following the rig tests, the controller was qualified to be flown in free-flight. The free-flight experiments were conducted first with the aim of achieving autonomous hover (attitude stabilisation and control), and later for up- and away-flights. As stated earlier, only the thrust was controlled in manual mode by the pilot. Sample results for attitude stabilisation and control are shown in Fig. 11. The dotted lines represent the commanded value and the solid lines represent the measured attitude of the vehicle. Satisfactory attitude stabilisation was achieved in the presence of disturbances. It was observed that the vehicle was able to keep itself afloat in hover with no active pilot inputs. However, a slow drift in position was observed because an outermost navigation loop was not yet implemented.
An elaborate modelling and simulation exercise for a micro quadrotor, which was then built and successfully test flown, has been described. In addition to its use for control law design, the model formed an integral part of a ground-based simulation system. For this, the model was integrated with a joystick and a flight simulator and was run in real-time to make the experience quite realistic. It is believed that the modelling and simulation exercise helped cut down development time and cost by avoiding intermediate design changes and also by reducing the time taken for flight tests.
The vehicle integration, rig, and flight testing was carried out at Coral Digital Technologies (P) Ltd, Bengaluru. The authors would like to acknowledge the contribution by Cdr VS Renganathan and Mr Srikanth towards development of autopilot hardware; Mr SM Shah for the controller development, and Mr Shyam for helping with the flight tests. The autopilot used was an in-house product developed by Coral Digital Technologies (P) Ltd, Bengaluru.
1. Mueller, T.J.; Kellogg, J.C.; Ifju, P.G. & Shkarayev, S.V. Introduction to the design of fixed-wing micro air vehicles–Including three case studies. In AIAA Education Series, January 2007.
2. Mueller, T.J. On the birth of micro air vehicles. Int. J. Micro Air Veh., 2009, 1(1), 1-12.
3. Nonami, K. Prospect and recent research and development for civil use autonomous unmanned aircraft as UAV and MAV. J. Syst. Des.Dyn., 2007, 1(2), 120-28.
4. Reed, J.A.; Follen, G.J. & Afjeh, A.A. Improving the aircraft design process using web-based modelling and simulation. ACM Trans. Model. Comp. Simul., 2000, 10(1), 58-83.
5. Kumar, P.B.C.; Gupta, N.K.; Ananthkrishnan, N.; Renganathan, V.S.; Park, I.S. & Yoon, H.G. modelling, dynamic simulation, and controller design for an air-breathing combustion system. In the 47th AIAA Aerospace Sciences Meeting, 5-8 Jan 2009, Orlando, Florida. AIAA Paper No. AIAA 2009-708.
6. Rohani, M.R. & Hicks, G.R. Multidisciplinary design and prototype development of a micro air vehicle, Journal of Aircraft, 1999, 36(1), 227-34.
7. Castillo, P.; Lozano, R. & Dzul, A.E. In Modelling and control of mini-flying machines. Springer-Verlag, New York, 2005. pp. 39-60.
8. Bouabdallah, S.; Murrieri, P. & Siegwart, R. Design and control of an indoor micro quadrotor. International Conference on Robotics and Automation, New Orleans, USA, 2004.
9. Roberts, J.F.; Stirling, T.S.; Zufferey, J.C. & Floreano, D. Quadrotor using minimal sensing for autonomous indoor flight. In 3rd US-European Competition and Workshop on Micro Air Vehicle Systems (MAV07) & European Micro Air Vehicle Conference and Flight Competition (EMAV2007), 17-21 September 2007, Toulouse, France.
10. Hamel, T.; Mahony, R.; Lozano, R. & Ostrowski, J. Dynamic modelling and configuration stabilisation for an X4-Flyer. In 15th Triennial World Congress of International Federation of Automatic Control, Barcelona, Spain, 2002.
11. Bramwell, A.R.S.; Done, G. & Balmford, D. Bramwell’s Helicopter dynamics. Ed. 2. Butterworth Heinemann, Oxford, UK, 2001.
12. Mahony, R.; Altug, E. & Ostrowski, J.P. Control of a Quadrotor helicopter using visual feedback. In Proceedings of 2002 IEEE Conference on Robotics and Automation, Washington DC, 2002. pp. 72-77.
13. Nice, E.B. Design of a four rotor hovering vehicle. Cornell University, 2004. MS thesis.
14. Tomlin, C.J.; Jang, J.S.; Waslander, S.L. & Hoffmann, G.M. Multi-agent quadrotor testbed control design: Integral sliding mode vs. reinforcement learning. In IEEE International Conference on Intelligent Robots and Systems, Alberta, Canada, 2005. pp. 468-73.
15. Tayebi, A. & McGilvray, S. Attitude stabilisation of a VTOL quadrotor aircraft. IEEE Trans. Cont. Syst. Technol., 2006, 14, 562-71.
16. Kendoul, F.; Lara, D.; Coichot, I.F. & Lozano, R. Real-time nonlinear embedded control for an autonomous quadrotor helicopter. J. Guid. Cont. Dyn., 2007, 30(4), 1049-061.
17. Das, A.; Lewis, F. & Subbarao, K. Backstepping approach for controlling a quadrotor using lagrange form dynamics. J. Intell. Robotic Syst., 2009, 56(1-2), 127-51.
18. Wang, Q.G.; Lee, T.H.; Fung, H.W.; Bi, Q. & Zhang, Y. PID tuning for improved performance. IEEE Trans. Cont. Syst. Technol., 1999, 7(4), 457-65.
Shri Nitin Kumar Gupta obtained BTech(Aerospace Engg.) and MTech (Aerospace Engg.) from IIT Bombay, Mumbai and MS from University of Maryland. He is currently Director and CEO at IDeA Research, Pune. His research interests include: Modelling, dynamics, simulation, control systems, automation, embedded systems and image processing. Shri Rahul Goel received his Masters degree in Aeronautics and Astronautics from MIT. He is currently working with EADS Astrium in Germany. He is interested in space systems engineering, and specifically in the human-related aspects of space flight, like crew performance, space physiology, and human factors. Dr Narayan Ananthkrishnan has served on the faculty at IIT Bombay, Mumbai, and CalTech, USA. Presently, he is a member of the Board of Directors at IDeA Research. His research interests include: Nonlinear dynamics, aerodynamics, control systems, and systems design.
| 2021-10-27T22:02:21 |
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|
https://par.nsf.gov/biblio/10093378-first-data-release-cosmos-lya-mapping-tomography-observations-lya-forest-tomography
|
First Data Release of the COSMOS LyA Mapping and Tomography Observations: 3D LyA Forest Tomography at 2.05
Faint star-forming galaxies at z∼2–3 can be used as alternative background sources to probe the Lyα forest in addition to quasars, yielding high sightline densities that enable 3D tomographic reconstruction of the foreground absorption field. Here, we present the first data release from the COSMOS Lyα Mapping And Tomography Observations (CLAMATO) Survey, which was conducted with the LRIS spectrograph on the Keck I telescope. Over an observational footprint of 0.157 deg2 within the COSMOS field, we used 240 galaxies and quasars at 2.17<z<3.00, with a mean comoving transverse separation of 2.37 h-1 Mpc, as background sources probing the foreground Lyα forest absorption at 2.05<z<2.55. The Lyα forest data was then used to create a Wiener- filtered tomographic reconstruction over a comoving volume of 3.15 ́ 105 h-3 Mpc3 with an effective smoothing scale of 2.5 h-1 Mpc. In addition to traditional figures, this map is also presented as a virtual-reality visualization and manipulable interactive figure. We see large overdensities and underdensities that visually agree with the distribution of coeval galaxies from spectroscopic redshift surveys in the same field, including overdensities associated with several recently discovered galaxy protoclusters in the volume. Quantitatively, the map signal-to- noise is S Nwiener » 3.4 more »
Authors:
; ; ; ; ;
Award ID(s):
Publication Date:
NSF-PAR ID:
10093378
Journal Name:
Astrophysical journal. Supplement series
Volume:
237
Page Range or eLocation-ID:
31
ISSN:
1538-4365
We present the large-scale structure over a more than 50 comoving Mpc scale at $z \sim 0.9$ where the CL1604 supercluster, which is one of the largest structures ever known at high redshifts, is embedded. The wide-field deep imaging survey by the Subaru Strategic Program with the Hyper Suprime-Cam reveals that the already-known CL1604 supercluster is a mere part of larger-scale structure extending to both the north and the south. We confirm that there are galaxy clusters at three slightly different redshifts in the northern and southern sides of the supercluster by determining the redshifts of 55 red-sequence galaxiesmore »
| 2022-09-25T18:01:33 |
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|
https://hq2006.bnl.gov/abstracts/JaroslavBielcik.html
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## Suppression of high $p_{T}$ non-photonic electrons in Au+Au collisions at $\sqrt{s_{NN}}=200$ GeV at RHIC.
### Jaroslav Bielcik
Strong suppression of high $p_{T}$ hadrons observed at RHIC has led to the interpretation that the energetic partons lose their energy via induced gluon radiation in the hot and dense matter before fragmenting into hadrons. The study of heavy quark production can extend our understanding of this scenario. Due to the dead cone effect, the suppression of heavy quark mesons at high $p_{T}$ is expected to be smaller than that observed for charged hadrons at the same energy. The measurement of non-photonic single electrons up to high $p_{T}$ provides information on charm and beauty production. The semi-leptonic decays of D and B mesons are the dominant contribution to the non-photonic electron spectra. The preliminary spectra from p+p, d+Au and Au+Au collisions at $\sqrt{s_{NN}}=200$ GeV have been extracted for mid-rapidity non-photonic electrons in the range $1.5 < p_{T}$ (GeV/c) $< 10$. The corresponding nuclear modification factors ($R_{AA}$) are presented and show a large suppression in central Au+Au collisions, indicating an unexpectedly large energy loss for heavy quarks in the hot and dense matter created at RHIC. This observed suppression is compared to recent theoretical models.
| 2018-12-10T11:22:41 |
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https://pos.sissa.it/390/421/
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Volume 390 - 40th International Conference on High Energy physics (ICHEP2020) - Parallel: Quark and Lepton Flavour Physics
$\tau-\mu$ lepton flavor universality in $\Upsilon(3S)$ decays at the $BABAR$ experiment
A. Sibidanov
Full text: Not available
How to cite
Metadata are provided both in "article" format (very similar to INSPIRE) as this helps creating very compact bibliographies which can be beneficial to authors and readers, and in "proceeding" format which is more detailed and complete.
Open Access
Copyright owned by the author(s) under the term of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
| 2020-12-04T21:17:31 |
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https://firas.moosvi.com/oer/physics_bank/content/public/019.Magnetism/Electromagnetic%20Induction/OSUPv2p13_56/OSUPv2p13_56.html
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# Square Coil#
## Question Text#
A flat, square coil of 10 turns that has sides of length 30 $$\rm\ {cm}$$ is rotating in a magnetic field of strength 0.060 $$\rm\ {T}$$. If the maximum emf produced in the coil is 25 $$\textrm{ mV}$$, what is the angular velocity of the coil?
### pl-answer-panel#
$$\omega=$$ $$\rm\ {rad/s}$$
## Attribution#
Problem is from the OpenStax University Physics Volume 2 textbook, licensed under the CC-BY 4.0 license.
| 2022-09-28T10:21:00 |
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http://www.engr.mun.ca/~theo/Courses/AlgCoCo/recursionWonderland/Factorial.html
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Copyright (c) Theodore Norvell 2017. Licence: Creative Commons Noncommercial Attribution International 4.0.
This is a Jupyter notebook. See How to use these notes.
# Factorial¶
## The problem¶
Five friends go to the movie theatre. They grab five seats in a row. First the sit in alphabetical order: Alice, Bill, Cat, Dinah, Edith. Then Alice switches with Edith because she doesn't want to sit next to Bill. But Dinah wants to sit next to Edith, so Cat switches with Edith.
They wonder how many ways they can sit in the five seats. Alice says any of us could sit in the first seat. Then there are 4 of us left. So we just need to know how many ways the four people can sit in the four remaining seats. Then we can multiply that number by 5.
### A generalization¶
Alice's observation invites a generalization of the original problem. We are now interested in how many ways $n$ people can sit in $n$ seats. Here $n$ should be a positive integer. (Later we will consider the problem of putting $0$ people in $0$ seats, but for now $n$ will be 1 or 2 or 3, ... .) Let's call that number $permCount(n)$.
Aside I call it $permCount(n)$ since a permutation of a set is an ordering of all members of the set with no repetitions. The number of permutations of a set depends only on its size, not on its contents. End of Aside
### A contract¶
We write a contract for the $permCount$ function.
Aside A contract specifies the following things
• The name of the function.
• The parameter list
• Any constraints on the function's inputs. This is called the function'ss precondition. It is the responsibility of the coder who writes calls (the caller) to the function to ensure that the precondition is true.
• The relationship between the inputs and the outputs of the function. This is called the function's postcondition. It is the responsibility of the coder who implements the function (the implementor) to ensure that the postcondition is respected by the implementation in every case in which the precondition was respect by the caller. For most of our examples the only output is the function's result, which I will call result in postconditions
End of Aside
In the case of the permCount function the contract is
def permCount( n ):
"""Pre: n is an integer greater than 0
Post: result == the number of permutations of a set of n things
"""
## Problem analysis¶
### Alice's observation¶
Generalizing Alice's observation, we can see that that the number of ways $n$ people can sit in $n$ seats is $n$ times $permCount(n-1)$, provided $n>1$.
### We need a base case¶
Alice's observation is no help when n is 1, since permCount(0) isn't (yet) clearly defined. Luckly this problem is easy. There is obviously only one way that one person can sit in one seat. permcount must obey the following two properties
• $permcount(1) = 1$
• $permcount(n) = n \times permcount(n-1)$ when $n$ is an integer greater than $1$.
### Is this a definition¶
The two properties above are properties that we expect permCount to have. But they are more than that. They completely define the function, at least for arguments greater than or equal to 1. You convince yourself of this by doing a simple inductive proof that these two properties uniquely define permCount.
### Some tests¶
Based on the contract, here are some tests
• permCount(1) should have a result of 1
• permCount(2) should have a result of 2
• permCount(3) should have a result of 6
• permCount(4) should have a result of 24
• permCount(5) should have a result of 120
• permCount( 100 ) should have a result of 93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000
• permCount( 500 ) should have a result of 1220136825991110068701238785423046926253574342803192842192413588385845373153881997605496447502203281863013616477148203584163378722078177200480785205159329285477907571939330603772960859086270429174547882424912726344305670173270769461062802310452644218878789465754777149863494367781037644274033827365397471386477878495438489595537537990423241061271326984327745715546309977202781014561081188373709531016356324432987029563896628911658974769572087926928871281780070265174507768410719624390394322536422605234945850129918571501248706961568141625359056693423813008856249246891564126775654481886506593847951775360894005745238940335798476363944905313062323749066445048824665075946735862074637925184200459369692981022263971952597190945217823331756934581508552332820762820023402626907898342451712006207714640979456116127629145951237229913340169552363850942885592018727433795173014586357570828355780158735432768888680120399882384702151467605445407663535984174430480128938313896881639487469658817504506926365338175055478128640000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## Design¶
Based on the problem analysis, we can write a design in pseudocode. In this case the pseudocode will look a lot like Python, so you can take this step if you want or skip it if you don't.
## Analyze design¶
Before coding, you should check that your design will work. Here is a checklist
• Is every case allowed by the precondition covered?
• Does the code do the right thing (i.e. return a result allowed by the postcondition) in each case?
• Is every recursive call smaller in some sense than its parent call?
## Code¶
Complete the following function
In [2]:
def permCount( n ) :
"""Pre: n is an integer greater than 0
Post: result == the number of permutations of a set of n things
"""
if n == 1: return 1
else: return permCount(n-1) * n
## Analyze code¶
If you wrote pseudocode, check that your design is consistant with the pseudocode. If you didn't write pseudocode, use the checklist above to check your code.
## Test¶
Below are some tests. After you define the function, you can run these tests and compare the answers with expected answers above.
In [3]:
permCount(1) # Expect 1
Out[3]:
1
In [4]:
permCount(2) # Expect 2
Out[4]:
2
In [5]:
permCount(3) # Expect 6
Out[5]:
6
In [6]:
permCount(4) # Expect 24
Out[6]:
24
In [7]:
permCount(5) # Expect 120
Out[7]:
120
In [8]:
permCount(100) # Expect 933262154...00000000
Out[8]:
93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000
In [9]:
permCount(500) # Expect 1220136...00000000000000
Out[9]:
1220136825991110068701238785423046926253574342803192842192413588385845373153881997605496447502203281863013616477148203584163378722078177200480785205159329285477907571939330603772960859086270429174547882424912726344305670173270769461062802310452644218878789465754777149863494367781037644274033827365397471386477878495438489595537537990423241061271326984327745715546309977202781014561081188373709531016356324432987029563896628911658974769572087926928871281780070265174507768410719624390394322536422605234945850129918571501248706961568141625359056693423813008856249246891564126775654481886506593847951775360894005745238940335798476363944905313062323749066445048824665075946735862074637925184200459369692981022263971952597190945217823331756934581508552332820762820023402626907898342451712006207714640979456116127629145951237229913340169552363850942885592018727433795173014586357570828355780158735432768888680120399882384702151467605445407663535984174430480128938313896881639487469658817504506926365338175055478128640000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
# My Solution¶
## Design¶
Here is pseudo code
function $permCount( n : int )$
pre $n$ is an integer greater than 0
post result = the number of permutations of a set of $n$ things
if $n = 1$ then 1
| $n > 1$ then $n \times permCount( n-1 )$
end if
## Code¶
In [2]:
def permCountMine( n ) :
"""Pre: n is an integer greater than 0
Post: result == the number of permutations of a set of n things
"""
assert isinstance(n, int) and n > 0
if n==1 :
return 1
else:
return n * permCountMine( n-1 )
## Test¶
In [3]:
permCountMine(1)
Out[3]:
1
In [4]:
permCountMine(2)
Out[4]:
2
In [5]:
permCountMine(3)
Out[5]:
6
In [6]:
permCountMine(4)
Out[6]:
24
In [7]:
permCountMine(5)
Out[7]:
120
In [8]:
permCountMine(100)
Out[8]:
93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000
In [9]:
permCountMine(500)
Out[9]:
1220136825991110068701238785423046926253574342803192842192413588385845373153881997605496447502203281863013616477148203584163378722078177200480785205159329285477907571939330603772960859086270429174547882424912726344305670173270769461062802310452644218878789465754777149863494367781037644274033827365397471386477878495438489595537537990423241061271326984327745715546309977202781014561081188373709531016356324432987029563896628911658974769572087926928871281780070265174507768410719624390394322536422605234945850129918571501248706961568141625359056693423813008856249246891564126775654481886506593847951775360894005745238940335798476363944905313062323749066445048824665075946735862074637925184200459369692981022263971952597190945217823331756934581508552332820762820023402626907898342451712006207714640979456116127629145951237229913340169552363850942885592018727433795173014586357570828355780158735432768888680120399882384702151467605445407663535984174430480128938313896881639487469658817504506926365338175055478128640000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
# Going further¶
As you likely know, the permCount function is normally called the factorial function and it has lots of uses.
We can extend the function to 0 as follows. How many permutations are there of a set of size 0? The only set of size 0 is the empty set $\emptyset$ and there is only one sequence we can make that contains only elements of this set. That is the empty sequence. Also the empty sequence contains every element of the set and there are no repetitions. So the set of all permutations of $\emptyset$ is $\{ [\,] \}$; this set has size 1, so the factorial of 0 should be 1. Note that Alice's law now holds for n equal to 1.
The new contract and code is
In [16]:
def factorial( n ) :
"""Pre: n is an integer greater than or equal to 0
Post: result == the factorial of n
"""
assert isinstance(n, int) and n >= 0
if n == 0 :
return 1
else:
return n * factorial( n-1 )
## Testing¶
In [17]:
factorial(0)
Out[17]:
1
In [18]:
factorial(1)
Out[18]:
1
In [19]:
factorial(2)
Out[19]:
2
In [20]:
factorial(3)
Out[20]:
6
In [21]:
factorial(4)
Out[21]:
24
In [22]:
factorial(5)
Out[22]:
120
In [23]:
factorial(100)
Out[23]:
93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000
In [24]:
factorial(500)
Out[24]:
1220136825991110068701238785423046926253574342803192842192413588385845373153881997605496447502203281863013616477148203584163378722078177200480785205159329285477907571939330603772960859086270429174547882424912726344305670173270769461062802310452644218878789465754777149863494367781037644274033827365397471386477878495438489595537537990423241061271326984327745715546309977202781014561081188373709531016356324432987029563896628911658974769572087926928871281780070265174507768410719624390394322536422605234945850129918571501248706961568141625359056693423813008856249246891564126775654481886506593847951775360894005745238940335798476363944905313062323749066445048824665075946735862074637925184200459369692981022263971952597190945217823331756934581508552332820762820023402626907898342451712006207714640979456116127629145951237229913340169552363850942885592018727433795173014586357570828355780158735432768888680120399882384702151467605445407663535984174430480128938313896881639487469658817504506926365338175055478128640000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
Another approach to factorial is to use an accumulator. An accumulator is an extra parameter that we use to record a partial result. We use two functions: factorialWithAccumulator and factorialWithAccumulatorHelper. The helper function has the accumulator.
In [25]:
def factorialWithAccumulator( n ) :
"""Pre: n is an integer greater than or equal to 0
Post: result == the factorial of n
"""
assert isinstance(n, int) and n >= 0
return factorialWithAccumulatorHelper( n, 1 )
def factorialWithAccumulatorHelper( n, accumulator ) :
"""Pre: n is an integer greater than or equal to 0 and accumulator is an integer.
Post: result == the product of accumulator * the factorial of n
"""
if n == 0 :
# accumulator * 0! = accumulator * 1 = accumulator
return accumulator
else :
# accumulator * n! = accumulator * n * (n-1)! = (n*accumulator) * (n-1)!
return factorialWithAccumulatorHelper( n-1, n*accumulator )
In [26]:
factorialWithAccumulator( 0 )
Out[26]:
1
In [27]:
factorialWithAccumulator( 5 )
Out[27]:
120
In [28]:
factorialWithAccumulator( 500 )
Out[28]:
1220136825991110068701238785423046926253574342803192842192413588385845373153881997605496447502203281863013616477148203584163378722078177200480785205159329285477907571939330603772960859086270429174547882424912726344305670173270769461062802310452644218878789465754777149863494367781037644274033827365397471386477878495438489595537537990423241061271326984327745715546309977202781014561081188373709531016356324432987029563896628911658974769572087926928871281780070265174507768410719624390394322536422605234945850129918571501248706961568141625359056693423813008856249246891564126775654481886506593847951775360894005745238940335798476363944905313062323749066445048824665075946735862074637925184200459369692981022263971952597190945217823331756934581508552332820762820023402626907898342451712006207714640979456116127629145951237229913340169552363850942885592018727433795173014586357570828355780158735432768888680120399882384702151467605445407663535984174430480128938313896881639487469658817504506926365338175055478128640000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
We can apply tail recursion optimization and inlining to the last pair of functions to get an slightly more efficient implementation. I won't explain these concepts here in detail. But carefully compare this version with the previous. There will be more examples later.
In [29]:
def iterativeFactorial( n ) :
"""Pre: n is an integer greater than or equal to 0
Post: result == the factorial of n
"""
assert isinstance(n, int) and n >= 0
accumulator = 1
while n > 0 :
accumulator = n*accumulator
n = n-1
return accumulator
In [30]:
iterativeFactorial(0)
Out[30]:
1
In [31]:
iterativeFactorial(5)
Out[31]:
120
In [32]:
iterativeFactorial(500)
Out[32]:
1220136825991110068701238785423046926253574342803192842192413588385845373153881997605496447502203281863013616477148203584163378722078177200480785205159329285477907571939330603772960859086270429174547882424912726344305670173270769461062802310452644218878789465754777149863494367781037644274033827365397471386477878495438489595537537990423241061271326984327745715546309977202781014561081188373709531016356324432987029563896628911658974769572087926928871281780070265174507768410719624390394322536422605234945850129918571501248706961568141625359056693423813008856249246891564126775654481886506593847951775360894005745238940335798476363944905313062323749066445048824665075946735862074637925184200459369692981022263971952597190945217823331756934581508552332820762820023402626907898342451712006207714640979456116127629145951237229913340169552363850942885592018727433795173014586357570828355780158735432768888680120399882384702151467605445407663535984174430480128938313896881639487469658817504506926365338175055478128640000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
One advantage of the nonrecursive version is that it have handle larger inputs. Try any of the recusive versions with an input of 5000 and I suspect that you won't get an anwswer.
In [33]:
iterativeFactorial(5000)
Out[33]:
42285779266055435222010642002335844053907866746266467488497824021813580527081082006908990478717063875370847466573006854458784860666838127363372108937727876312793903630584621606439044789869822398719297088962116126529683217755003992421968370314690726447287878979040475488416221522667192841096923691044956597173635294840022384038112064482023085767110450230617489475542830976178172404080532480992780932878405548619936454829121187625824880218917397790005021321259804363924462646077051135884659510867547058583392465522558903547443598834738317898803463300845863151020909150993565382001093304796574255674193091705517280520023607508599119763522875590790204336974312350691683121192449597155626740752146219898623308862599830285986485757874944596311528697088671004626842364817898990545469086139161321834417414880718623444811483120949036119654687276775561788682872026910481409245641034183597560427645816151317857590166107178254415698088335937272999560337137120047104943765629114248860533529949964230069997220491812010081905943914067505326500477553385089909794510155109148690700440711957233602624336813233021870928769919680665656975279042225826784156108337642578103262920268721107027468139435112860150232619064995917189736417637843649121970910984094451489535895910380417694195665783482207174910551275263914838117205260482696516264271009491939333266103010436053045911701455720958471435372194824668679346737590487226813341020786090365710880637661624974950741310707740168218058594552644517140927746923006269751134604417456794673582878226162958424867515737917294272417878310542985824511757551188450657442482757466080023858837849239624736876150701576772589832112863229553704490251638792512759084179174464046691353104734798446499615459554201399631735747630174003679619291994219076289544565626176704179953816113338731282351153415258130908791588363835166479722591294427065355714251173732380723263295812179791667969232968709692390100325557478905509980748706104723064619598495523965761220867386651417169930755769189790267515734207586479634533844683508596549072732632191050406428971309622450516206466946809886991712212740450402068492326624176013291022786668727030528470945252682549661777249964520669983692591069089408263740104349837159112645582228060636139411534431677176993435366428492829443641476961588199366138825557748770993700459475390784514903443452117456059403991626844469766182138747070532555957793319646099666214537756493547416970856238921477322286550718249043001618614219276045230767062114296176727470412361610722000974375864749275366514953216478084907514633007101669131342066288256261828386583698363210876071042751607334834778841479673242708041086076184128188830711509898213533840661065214708704687476099542747367350945155359976904036735338555105257168265031768240574399341486239233198143257918219332189894045086501361099809838399311099635598132800104973158859631213185380120504678764291066936560043730563343198487904899852470129330078934453286815667976288049553284638602013348026527983694639338499567504999370781474656154343893043138423787898184780288600997108869563298834771186312238278596365311513237793137364739742936941149902875197222799954518261548829895115192668211245135531847220999043535594988729992203506203981601108637623653978217238023784665067362451063503442318731533830821204380471099941922782103974755271741604389016972396130554937184483611980356589606202500909366439936017200738361335440509432907247651890950250772467584198941222465939216311635203814736247952853973208930953342191063570280557662972015655651076778080593345363112182956179288767300280245093212277885296841820826177847695564498038569127578737267804095915871173397110316523267806079812760924617350412018266687426280538527584397916760900774338074842075118511910292196033937628098675366508521286925532153678793252188257410186613705432897373586272537017855880663985135038694403960492825882018041917807364969388580259775839889201438974716546597351085260570623440206963706566012953573404358296147342727580563083951066737534925965951857564693972321827578000325059389530382053969755887051154307392082742244051629970873959976846120624662909811236801257989128480250509402891695976507939543719131137931442740513559963037564221452729434179724618759796407423914783899354156583471615685849903677305661135383336708754890041309198167633074904151033759730724688583924694171554829573075061850588158195952899266022562690343957331345066697295211523066869622792094777997433657447267347140892807141128388808269337737807729310411076751363947620061085804059601963905801576100233746386935222838580143495717812558144586293004247940406573685986200791460459025541392995008804471038475899032654809733816694050008545272371357139490246382030866854180283831752766806427848956100575585999171896678644915406357001449719424987892085973125427556751457520639911815073639748310249079384172565342189427676911659815343008463708776951029541513655173467505401523970604257174600108996844049884598547797790503163256848915655723100649972649872148080018177035770150298300887948724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| 2017-11-19T14:04:08 |
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|
http://jde27.uk/blog/hea-course.html
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# HEA course for new maths lecturers
[2012-09-18 Tue]
Last week I had the pleasure of attending a course for new maths lecturers run by the Maths, Stats and Operations Research discipline of the Higher Education Academy (HEA/MSOR). I was pleased that it dispelled several myths for me, in particular the myth that these courses never cater for mathematicians' needs. All the talks were given by experienced mathematics lecturers or people who have spent a considerable amount of time undertaking educational research specific to university-level maths. With such good quality input, and with the high level of engagement discussion amongst the participants, I learned a lot. Here are a couple of ideas I took away (not necessarily maths-specific!).
• It's important to let people figure things out by themselves. Maybe this advice sounds obvious, but I realised during the course that my natural inclination when I see someone struggling with a problem for more than about a minute is to jump in and suggest or hint at the next step. (e.g. "If you don't believe the statement, maybe you should just try and write down a counterexample?") If someone figures out the answer with my help, that's not as valuable to them as figuring out for themselves how to even approach the question in the first place. So in future I will try and sit back and listen and let my students shine.
• Get students to construct examples. I liked this extremely practical piece of advice. Instead of giving them a list of examples and saying "Check which ones have certain properties," you can instead ask them to get their hands dirty and construct examples. You can even do this during a lecture to give them time to absorb the definitions you've just told them (or to realise that they didn't understand something). Much like a radio or an atomic bomb, when you construct a mathematical object for yourself you understand it much better than if it's handed to you with a set of how-to-use instructions.
• There's a distinction between problems and exercises, and students need both to thrive. Problems being problematic and involving thought, exercises being repetitive (even if hard). The point was also made that exercises can conceivably be automated and that there is software (STACK, due to Chris Sangwin) which interacts with Moodle (a popular "virtual learning environment") which allows students to respond in mathematics which is then parsed by a computer algebra system and the answer is checked. For example, the student is asked "Give an example of an odd function", they input $$sin(x)$$ and the computer checks that they got it right. This has the advantage that they can do many exercise and get immediate feedback on how they're doing. By contrast, imagine having to mark a student's answers to an indeterminate number of randomly generated integrals... isn't there something better you could be doing with your time? You might argue that university level maths involves more thought and proof than mindless computation, and maybe this automation is more useful for pre-university students. That's probably true, but my Methods course this term will involve plenty of computation, mindless or otherwise.
• New lecturers are overambitious with content. Having lectured two graduate-level courses and struggled to say what I wanted to say in the time I had to say it, I can testify to this. But can I put this observation to use when lecturing this year? My second years had better hope so...
A useful piece of software I encountered was GeoGebra (for producing geometric diagrams, etc.). While it's true that the same results (and many more) could be obtained with Maple or Sage, it's also true that GeoGebra is free and intuitive, and it's extremely quick to produce diagrams of the sort it's good at (not as code-heavy as Maple). I'm told there's a 3d version and this would have been useful for producing these diagrams.
I can highly recommend this HEA course for new maths/stats lecturers.
Comments, corrections and contributions are very welcome; please drop me an email at j.d.evans at lancaster.ac.uk if you have something to share.
CC-BY-SA 4.0 Jonny Evans.
| 2020-09-19T15:59:50 |
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|
https://par.nsf.gov/biblio/10326700-coresets-classification-simplified-strengthened
|
Coresets for Classification - Simplified and Strengthened
We give relative error coresets for training linear classifiers with a broad class of loss functions, including the logistic loss and hinge loss. Our construction achieves $(1\pm \epsilon)$ relative error with $\tilde O(d \cdot \mu_y(X)^2/\epsilon^2)$ points, where $\mu_y(X)$ is a natural complexity measure of the data matrix $X \in \mathbb{R}^{n \times d}$ and label vector $y \in \{-1,1\}^n$, introduced in Munteanu et al. 2018. Our result is based on subsampling data points with probabilities proportional to their \textit{$\ell_1$ Lewis weights}. It significantly improves on existing theoretical bounds and performs well in practice, outperforming uniform subsampling along with other importance sampling methods. Our sampling distribution does not depend on the labels, so can be used for active learning. It also does not depend on the specific loss function, so a single coreset can be used in multiple training scenarios.
Authors:
; ;
Award ID(s):
Publication Date:
NSF-PAR ID:
10326700
Journal Name:
Advances in neural information processing systems
ISSN:
1049-5258
2. Abstract Kernelized Gram matrix $W$ constructed from data points $\{x_i\}_{i=1}^N$ as $W_{ij}= k_0( \frac{ \| x_i - x_j \|^2} {\sigma ^2} )$ is widely used in graph-based geometric data analysis and unsupervised learning. An important question is how to choose the kernel bandwidth $\sigma$, and a common practice called self-tuned kernel adaptively sets a $\sigma _i$ at each point $x_i$ by the $k$-nearest neighbor (kNN) distance. When $x_i$s are sampled from a $d$-dimensional manifold embedded in a possibly high-dimensional space, unlike with fixed-bandwidth kernels, theoretical results of graph Laplacian convergence with self-tuned kernels have been incomplete. This paper proves the convergence of graph Laplacian operator $L_N$ to manifold (weighted-)Laplacian for a new family of kNN self-tuned kernels $W^{(\alpha )}_{ij} = k_0( \frac{ \| x_i - x_j \|^2}{ \epsilon \hat{\rho }(x_i) \hat{\rho }(x_j)})/\hat{\rho }(x_i)^\alpha \hat{\rho }(x_j)^\alpha$, where $\hat{\rho }$ is the estimated bandwidth function by kNN and the limiting operator is also parametrized by $\alpha$. When $\alpha = 1$, the limiting operator is the weighted manifold Laplacian $\varDelta _p$. Specifically, we prove the point-wise convergence of $L_N f$ and convergence of the graph Dirichlet form with rates. Our analysis is based on first establishing a $C^0$more »
4. We study the $\ell_p$ regression problem, which requires finding $\mathbf{x}\in\mathbb R^{d}$ that minimizes $\|\mathbf{A}\mathbf{x}-\mathbf{b}\|_p$ for a matrix $\mathbf{A}\in\mathbb R^{n \times d}$ and response vector $\mathbf{b}\in\mathbb R^{n}$. There has been recent interest in developing subsampling methods for this problem that can outperform standard techniques when $n$ is very large. However, all known subsampling approaches have run time that depends exponentially on $p$, typically, $d^{\mathcal{O}(p)}$, which can be prohibitively expensive. We improve on this work by showing that for a large class of common \emph{structured matrices}, such as combinations of low-rank matrices, sparse matrices, and Vandermonde matrices, there are subsampling based methods for $\ell_p$ regression that depend polynomially on $p$. For example, we give an algorithm for $\ell_p$ regression on Vandermonde matrices that runs in time $\mathcal{O}(n\log^3 n+(dp^2)^{0.5+\omega}\cdot\text{polylog}\,n)$, where $\omega$ is the exponent of matrix multiplication. The polynomial dependence on $p$ crucially allows our algorithms to extend naturally to efficient algorithms for $\ell_\infty$ regression, via approximation of $\ell_\infty$ by $\ell_{\mathcal{O}(\log n)}$. Of practical interest, we also develop a new subsampling algorithm for $\ell_p$ regression for arbitrary matrices, which is simpler than previous approaches for $p \ge 4$.
| 2023-03-29T12:48:43 |
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|
https://tjyj.stats.gov.cn/CN/Y2021/V38/I8/111
|
• •
### 城市网络位置与疫情风险
• 出版日期:2021-08-25 发布日期:2021-08-25
### City’s Network Position and Epidemic Risk
Zhang Cui Fu Hang
• Online:2021-08-25 Published:2021-08-25
Abstract: As a major public health emergency, the risk of an epidemic is a new but important research topic. From a new network topological perspective, this paper constructs an inter-city epidemic connection network due to the mobility of infected people based on COVID-19 and empirically examines the impacts of a city’s network position on its epidemic risk. We find that the inter-city epidemic is highly interconnected. A city’s network centrality has a positive and significant effect on epidemic risk. Further analysis shows that a city’s network centrality can amplify the epidemic spread risk. Hubei’s lockdown reduces the effects of a city’ s network centrality on epidemic risk.
| 2022-08-14T21:06:52 |
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|
https://nroer.gov.in/55ab34ff81fccb4f1d806025/file/57cfeed016b51c6b39a80809
|
### Nernst equation, Gibbs Energy and Conductance:
Episode 03 of the video lectures of chapter 03 of the Chemistry textbook for class 12; covers Nernst equation, Gibbs energy and conductance
| 2021-04-21T03:04:57 |
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|
https://nroer.gov.in/55ab34ff81fccb4f1d806025/file/55ccae5e81fccb0f71de69da
|
Metals and Non Metals:
Next
Chapter 03 of the Science textbook for class 10
License:[Source NCERT ] May 24, 2016, 10:14 p.m.
| 2020-02-28T15:49:01 |
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|
https://fermi.gsfc.nasa.gov/ssc/data/analysis/gbm/gbm_data_tools/gdt-docs/notebooks/SpectralFitting.html
|
# Analysis Workflow: Spectral Fitting¶
The GBM Data Tools has a module designed for spectral fitting. As discussed, GBM data can be prepared and exported for use in XSPEC and other fitting packages. To provide a full experience with GBM data, we also provide a way to fit GBM data by extending and wrapping standard optimizers provided in scipy. In fact, we can pretty easily leverage complicated optimization algorithms that can use imposed bounds and constraints on parameters, and we allow the user to decide if they want to use a more or less complex fitting procedure (of course we have suggestions!). The spectral fitting class can be extended to use various likelihoods, and can even be extended to perform a Bayesian analysis and posterior sampling (although we haven’t directly implemented it yet). We don’t want to get too much into the weeds here, but we’ll briefly mention areas of note as we go along.
The previous section on export for use in XSPEC was a bit simplified in that we only looked at a single detector for analysis, and typically we’ll want to jointly fit multiple detectors that have good viewing of the source. This means that for each detector you’re using, you need to multiply all your steps in the previous section by the number of detectors. What a slog! So to help reduce the amount of repetitive work we have to do, we can use the GbmDetectorCollection class. If we add our data to this “collection,” then we can easily perform operations on all items in the collection. There are great benefits to doing this as we will find out shortly.
Let’s look at CSPEC data this time:
[1]:
from gbm import test_data_dir
from gbm.data import Cspec, GbmDetectorCollection
# Load some CSPEC files for a GRB
n0 = Cspec.open(test_data_dir+'/160509374/glg_cspec_n0_bn160509374_v01.pha')
n1 = Cspec.open(test_data_dir+'/160509374/glg_cspec_n1_bn160509374_v01.pha')
b0 = Cspec.open(test_data_dir+'/160509374/glg_cspec_b0_bn160509374_v01.pha')
# create a collection from the list of our files
cspecs = GbmDetectorCollection.from_list([n0, n1, b0])
Now that you know the general process of fitting the background, selecting the time and energy ranges, and plotting, we’ll go ahead and define these ranges here. One thing to note is that we are using both NaI and BGO detectors. That means we need to be using the appropriate energy ranges for the detectors.
[2]:
# define some time and energy ranges
view_range = (-33.0, 102.0) # zoom in to this time range
bkgd_range = [(-550., -300.), (675., 1000.)] # the background fit ranges
src_range = (14.0, 17.0) # our time selection
erange_nai = (8.0, 900.0) # in keV
erange_bgo = (325, 35000.0)
Let’s perform our background fits. Second-order polynomials for all of them, unless we decide they need to be adjusted:
[3]:
from gbm.background import BackgroundFitter
from gbm.background.binned import Polynomial
# initialize the fitters and add to collection, making sure the collection knows which background
# goes with which detector
backfitters = [BackgroundFitter.from_phaii(cspec, Polynomial, time_ranges=bkgd_range) for cspec in cspecs]
backfitters = GbmDetectorCollection.from_list(backfitters, dets=cspecs.detector())
# do the fit
backfitters.fit(order=2)
# interpolate/extrapolate and store in a collection
bkgds = backfitters.interpolate_bins(cspecs.data()[0].tstart, cspecs.data()[0].tstop)
bkgds = GbmDetectorCollection.from_list(bkgds, dets=cspecs.detector())
Ok, we actually just did a lot on a few lines, so let’s recap and explain. We created a background fitter for each detector’s data and added the fitters to their own collection. We also made sure that we tagged the background fitters to correspond to the correct detectors. This will be vitally important in a minute. So, instead of having to call backfitter.fit() for each backfitter, we can call that method on the collection, and it performs the operation on every item in the collection. Cool. This works if you have the same arguments to be applied to each item. What if for one detector, you want to fit a 1st-order polynomial? We’d suggest a list comprehension, similar to:
[backfitter.fit(order=poly_order) for backfitter, poly_order in zip(backfitters, poly_orders)]
So you can definitely iterate over the collection like a list, but there is a lot of convenience for easily performing the same operation on a collection of data objects.
After performing the fit, we interpolate each backfitter over an array of times. The array of times we use is actually just the bin times from the first CSPEC file we added to the collection. This is fine because all our data are binned to the same bin edges. Then we add these interpolated backgrounds to their own collection.
Now we need to apply our selections, especially if we want to make a few plots and not go blindly into dark:
[4]:
# the lightcurves
data_lcs = cspecs.to_lightcurve(nai_kwargs={'energy_range':erange_nai}, bgo_kwargs={'energy_range':erange_bgo})
# the energy-integrated background
bkgd_lcs = bkgds.integrate_energy(nai_args=erange_nai, bgo_args=erange_bgo)
# the source time selection
src_lcs = cspecs.to_lightcurve(time_range=src_range, nai_kwargs={'energy_range':erange_nai}, bgo_kwargs={'energy_range':erange_bgo})
# the count spectrum
data_specs = cspecs.to_spectrum(time_range=src_range)
# the time-integrated background
bkgd_specs = bkgds.integrate_time(*src_range)
# the energy selection
src_specs = cspecs.to_spectrum(time_range=src_range, nai_kwargs={'energy_range':erange_nai}, bgo_kwargs={'energy_range':erange_bgo})
We just massively leveraged the collections to avoid having to write loops or list comprehensions. And we were able to treat the NaI and BGO energy selections all in one line for each set of lightcurves or spectra. Notice the nai_args, nai_kwargs, and the corresponding bgo arguments? Those allow us to specify arguments and keywords to be passed to either NaI or BGO detectors. Something like the time_range is the same for both detector types, so we pass it like a normal keyword as the object method expects, but energy_range is detector-type-dependent, since we usually want different energy ranges for the different types of detectors. Can you implement this in a loop over the separate objects instead? Sure, but your code will be at least 2x as long and harder to follow.
Whew. Now time to plot:
[5]:
%matplotlib inline
from gbm.plot import Lightcurve, Spectrum
# Plot the lightcurves with the selections and background fit
lcplots = [Lightcurve(data=data_lc, background=bkgd_lc) for data_lc, bkgd_lc in zip(data_lcs, bkgd_lcs)]
_ = [lcplot.add_selection(src_lc) for lcplot, src_lc in zip(lcplots, src_lcs)]
# zoom in
for lcplot in lcplots:
lcplot.xlim = view_range
# Plot the spectra with the selections and background fit
specplots = [Spectrum(data=data_spec, background=bkgd_spec) for data_spec, bkgd_spec in zip(data_specs, bkgd_specs)]
_ = [specplot.add_selection(src_spec) for specplot, src_spec in zip(specplots, src_specs)]
What you see are the three lightcurves of the three data files, and the three corresponding count spectra. We need to create PHAs and responses similar to the previous workflow. Let’s choose to interpolate the responses.
[6]:
from gbm.data import RSP
phas = cspecs.to_pha(time_ranges=src_range, nai_kwargs={'energy_range':erange_nai}, bgo_kwargs={'energy_range':erange_bgo})
# open responses
rsp1 = RSP.open(test_data_dir+'/160509374/glg_cspec_n0_bn160509374_v00.rsp2')
rsp2 = RSP.open(test_data_dir+'/160509374/glg_cspec_n1_bn160509374_v00.rsp2')
rsp3 = RSP.open(test_data_dir+'/160509374/glg_cspec_b0_bn160509374_v00.rsp2')
rsps = GbmDetectorCollection.from_list([rsp1, rsp2, rsp3])
# and interpolate response files to get DRMs at center of the source window
rsps_interp = [rsp.interpolate(pha.tcent) for rsp, pha in zip(rsps, phas)]
Everything we’ve done so far is only slightly more complicated than the previous workflow, but we got the chance to demo working with collections of detectors. If you haven’t had fun yet, you will now.
As mentioned, the spectral fitting class (SpectralFitter) is built on top of scipy’s optimization algorithms, and therefore you can directly specify which algorithm you want to use and the various arguments/settings that go along with it. Additionally, there are various derived classes of SpectralFitter that implement a specific likelihood function. For GBM data, you will most likely want to use pgstat (Profile-Gaussian likelihood), and therefore you would use the SpectralFitterPgstat fitter. There are other likelihoods avaliable, like chi-squared, and of course you can make your own.
[7]:
from gbm.spectra.fitting import SpectralFitterPgstat
# we initialize with our PHAs, backgrounds, and responses:
specfitter = SpectralFitterPgstat(phas, bkgds.to_list(), rsps.to_list(), method='TNC')
You’ll notice the ‘TNC’ method defined. This is the Truncated Newton algorithm, which performs optimization considering the boundaries and constraints on your parameters.
Now you need to select a function to fit. A whole tutorial could probably be devoted to the functionality of the functions, but let’s make this as simple as possible. The gbm.spectra.functions module contains a listing of functions with a variety of metadata attached to them. Essentially for each parameter of a function, you can set basic defaults (like in XSPEC), such as the starting guess values for parameters, their min/max bounds, and if they are fixed or free to be fit. This allows them to be used with the more complex algorithms like TNC. What’s cool is that you can easily make one of your own functions that inherit all this functionality (pun intended). But let’s worry about that later, and import a few standard functions:
[8]:
# a power law, cut-off power law, and a Band function
from gbm.spectra.functions import PowerLaw, Comptonized, Band
# instantiate a Band function
band = Band()
You can easily see what the parameter listing is for your function:
[9]:
band.param_list
[9]:
[('A', 'ph/s/cm^2/keV', 'Amplitude'),
('Epeak', 'keV', 'SED Peak'),
('alpha', '', 'Low-Energy Photon index'),
('beta', '', 'High-Energy Photon index'),
('Epiv', 'keV', 'Pivot energy')]
And similarly, the default values, minimum/maximum allowable values, etc.:
[10]:
print(band.default_values)
print(band.min_values)
print(band.max_values)
[0.01, 500.0, -0.5, -2.5, 100.0]
[1e-10, 0.01, -1.9, -10.0, 0.01]
[inf, inf, 20.0, -2.0001, inf]
That was painless. Now let’s fit it. Remember that you can use any of the options and settings for the scipy optimizer you chose. We can also print out some relevant info to make sure the fit succeeded, and if it did, we can quickly access things like the best-fit parameters and parameter uncertainties at the xx% confidence level.
[11]:
print('Band Fit:')
specfitter.fit(band, options={'maxiter': 1000})
# After the fit has converged, we can query the fitter for lots of info, including the parameters that
# satisfy the maximum likelihood as well as the parameter uncertainties resulting from -2(Delta)LogLike
print(specfitter.message)
print('Parameters: {}'.format(specfitter.parameters))
print('90% Asymm. Errors:\n {}'.format(specfitter.asymmetric_errors(cl=0.9)))
print('Pgstat/DoF: {}/{}'.format(specfitter.statistic, specfitter.dof))
Band Fit:
Converged (|f_n-f_(n-1)| ~= 0)
Parameters: [ 3.06953043e-01 3.13978720e+02 -7.60642875e-01 -2.19161093e+00]
90% Asymm. Errors:
[[3.71213297e-03 3.74687465e-03]
[5.52273992e+00 5.66382428e+00]
[1.53509429e-02 1.57720638e-02]
[5.00633717e-02 4.59141731e-02]]
Pgstat/DoF: 277.3252207934582/358
Hey hey! We’ve successfully completed our first fit! It converged, and we printed out (in ugly print) the maximum likelihood parameter values and 90% confidence uncertainties, which are calculated from the shape of the likelihood surface. We also output the fit statistic and the fit degrees of freedom.
This is nice, but as always, a plot is worth a 1000 words. We can use the ModelFit class from the gbm.plot module to view the fit:
[12]:
from gbm.plot import ModelFit
# initialize with your spectral fitter once the fit is done
modelplot = ModelFit(fitter=specfitter)
The default view of the model plot shows the fit of the Band function to the count spectrum. The data are converted to upper limits based on the model variances, and that seems to largely happen above a few hundred keV. The residual plot shows significant deviation around the Iodine K-edge, which usually only rears its ugly head for very bright spectra. If you’re concerned about how the K-edge affects the fit, you can always select energy ranges that omit ~30-40 keV.
If you’re feeling good about your fit, you can also switch views to plot the resulting photon, energy, or $$\nu F_\nu$$ spectrum:
[13]:
modelplot = ModelFit(fitter=specfitter, view='nufnu')
modelplot.ax.grid(which='both')
/Users/amgoldst/Desktop/gbm-data-tools/gbm/spectra/fitting.py:601: RuntimeWarning: covariance is not positive-semidefinite.
**kwargs)
The model plot samples from the covariance matrix to produce a density plot of the spectrum. A word of caution here: you don’t always have a valid covariance matrix that is symmetric and positive semi-definite (and will be alerted if this is the case), so you should investigate the parameter posteriors further, perhaps with MCMC or nested sampling.
You can quickly get the flux for the best-fit parameters using band.integrate() or produce samples (again using the covariance matrix) using specfitter.sample_flux():
[14]:
# flux over 10-1000 keV
photon_flux = band.integrate(specfitter.parameters, (10.0, 1000.0)) # photons/s/cm^2
energy_flux = band.integrate(specfitter.parameters, (10.0, 1000.0), energy=True) # erg/s/cm^2
photon_flux, energy_flux
[14]:
(73.03416490430172, 1.4720268196516327e-05)
You can always rerun the fit with a different function if you want. Let’s have a little fun and perform a multi-component fit. Another feature of the functions are that you can elegantly add or multiply components into a single model.
[15]:
# we've defined a new model that is the sum of a Comptonized function and a power law
comp_pl = Comptonized() + PowerLaw()
# rerun the fit
print('Comp+PL Fit:')
specfitter.fit(comp_pl, options= {'maxiter': 1000})
print(specfitter.message)
print('Parameters: {}'.format(specfitter.parameters))
print('Pgstat/DoF: {}/{}'.format(specfitter.statistic, specfitter.dof))
Comp+PL Fit:
Converged (|f_n-f_(n-1)| ~= 0)
Parameters: [ 2.54578195e-01 3.79044937e+02 -8.10083989e-01 1.30777519e-02
-1.36467487e+00]
Pgstat/DoF: 352.50370024792556/357
Cool, that fit converged as well. What does the fit look like?
[16]:
modelplot = ModelFit(fitter=specfitter)
You can tell the residuals at < 30 keV are a little worse than for the Band function (and the PG-stat is higher), but at least it let us demo the multi-component functionality. To round it out, let’s just take a look at the $$\nu F_\nu$$ spectrum.
[17]:
modelplot = ModelFit(fitter=specfitter)
# plot 1000 samples instead of the default 100
modelplot.nufnu_spectrum(num_samples=1000)
modelplot.ylim = (0.1, 10000.0)
modelplot.ax.grid(which='both')
/Users/amgoldst/Desktop/gbm-data-tools/gbm/spectra/fitting.py:601: RuntimeWarning: covariance is not positive-semidefinite.
**kwargs)
And finally, to finish up the workflow, we can save the entire state of the fitter and fit results for later:
specfitter.save('./my_second_fit.npz')
This will save everything to a compressed numpy file, which can be loaded at any time with
restored_specfitter = SpectralFitterPgstat.load('./my_second_fit.npz')
This concludes the workflow example for spectral fitting. Continue on for a brief tutorial on the interface to the GBM Spectral Catalog files
| 2023-03-23T15:31:29 |
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|
https://par.nsf.gov/biblio/10391738-light-dark-searching-electromagnetic-counterparts-black-holeblack-hole-mergers-ligo-virgo-o3-zwicky-transient-facility
|
A Light in the Dark: Searching for Electromagnetic Counterparts to Black Hole–Black Hole Mergers in LIGO/Virgo O3 with the Zwicky Transient Facility
Abstract
The accretion disks of active galactic nuclei (AGNs) are promising locations for the merger of compact objects detected by gravitational wave (GW) observatories. Embedded within a baryon-rich, high-density environment, mergers within AGNs are the only GW channel where an electromagnetic (EM) counterpart must occur (whether detectable or not). Considering AGNs with unusual flaring activity observed by the Zwicky Transient Facility (ZTF), we describe a search for candidate EM counterparts to binary black hole (BBH) mergers detected by LIGO/Virgo in O3. After removing probable false positives, we find nine candidate counterparts to BBH mergers during O3 (seven in O3a, two in O3b) with ap-value of 0.0019. Based on ZTF sky coverage, AGN geometry, and merger geometry, we expect ≈3(NBBH/83)(fAGN/0.5) potentially detectable EM counterparts from O3, whereNBBHis the total number of observed BBH mergers andfAGNis the fraction originating in AGNs. Further modeling of breakout and flaring phenomena in AGN disks is required to reduce our false-positive rate. Two of the events are also associated with mergers with total masses >100M, which is the expected rate for O3 if hierarchical (large-mass) mergers occur in the AGN channel. Candidate EM counterparts in future GW observing runs can be better constrained by coverage of more »
Authors:
; ; ; ; ; ; ; ; ; ; ; ; ;
Publication Date:
NSF-PAR ID:
10391738
Journal Name:
The Astrophysical Journal
Volume:
942
Issue:
2
Page Range or eLocation-ID:
Article No. 99
ISSN:
0004-637X
Publisher:
DOI PREFIX: 10.3847
1. ABSTRACT Advanced LIGO and Advanced Virgo are detecting a large number of binary stellar origin black hole (BH) mergers. A promising channel for accelerated BH merger lies in active galactic nucleus (AGN) discs of gas around supermasssive BHs. Here, we investigate the relative number of compact object (CO) mergers in AGN disc models, including BH, neutron stars (NS), and white dwarfs, via Monte Carlo simulations. We find the number of all merger types in the bulk disc grows ∝ t1/3 which is driven by the Hill sphere of the more massive merger component. Median mass ratios of NS–BH mergers in AGN discs are $\tilde{q}=0.07\pm 0.06(0.14\pm 0.07)$ for mass functions (MF) M−1(− 2). If a fraction fAGN of the observed rate of BH–BH mergers (RBH–BH) come from AGN, the rate of NS–BH (NS–NS) mergers in the AGN channel is ${R}_{\mathrm{ BH}\!-\!\mathrm{ NS}} \sim f_{\mathrm{ AGN}}[10,300]\, \rm {Gpc}^{-3}\, \rm {yr}^{-1},({\mathit{ R}}_{NS\!-\!NS} \le \mathit{ f}_{AGN}400\, \rm {Gpc}^{-3}\, \rm {yr}^{-1}$). Given the ratio of NS–NS/BH–BH LIGO search volumes, from preliminary O3 results the AGN channel is not the dominant contribution to observed NS–NS mergers. The number of lower mass gap events expected is a strong function of the nuclear MF and mass segregation efficiency. CO merger ratiosmore »
Galactic nuclei are promising sites for stellar origin black hole (BH) mergers, as part of merger hierarchies in deep potential wells. We show that binary black hole (BBH) merger rates in active galactic nuclei (AGNs) should always exceed merger rates in quiescent galactic nuclei (nuclear star clusters, NSCs) around supermassive black holes (SMBHs) without accretion discs. This is primarily due to average binary lifetimes in AGNs that are significantly shorter than those in NSCs. The lifetime difference comes from rapid hardening of BBHs in AGNs, such that their semimajor axes are smaller than the hard–soft boundary of their parent NSC; this contrasts with the large average lifetime to merger for BBHs in NSCs around SMBHs, due to binary ionization mechanisms. Secondarily, merger rates in AGNs are enhanced by gas-driven binary formation mechanisms. Formation of new BHs in AGN discs is a minor contributor to the rate differences. With the gravitational wave detection of several BBHs with at least one progenitor in the upper mass gap, and signatures of dynamical formation channels in the χeff distribution, we argue that AGNs could contribute $\sim 25{\!-\!}80{{\ \rm per\ cent}}$ of the LIGO–Virgo measured rate of $\sim 24\, \rm {Gpc}^{-3} \rm {yr}^{-1}$.
| 2023-03-26T16:16:51 |
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|
https://gea.esac.esa.int/archive/documentation/GEDR3/Catalogue_consolidation/chap_cu9val/sec_cu9val_943/ssec_cu9val_943_colour.html
|
7.3.5 Colour distributions
The median of the $G_{\rm BP}-G_{\rm RP}$ colour is computed in each healpix bin and presented in Figure 7.18 in three range of magnitudes. We also consider the average colour per magnitude bin, for Gaia EDR3 and GOG20 in Figure 7.19 for three ranges of latitudes. At intermediate and faint magnitudes, the differences can be large in the Galactic plane and are clearly linked to the extinction. At higher latitudes, the model is in agreement with the data at the level of 0.1 mag. However at bright magnitudes ($G<$9 at intermediate latitudes and towards the pole, $G<$12 in the plane), the data deviates from the values predicted by the model, showing a problem in the colour determination for those bright stars, although this discrepancy is slightly reduced compared to Gaia DR2.
Summary of the results:
• At high latitudes, model and data are in agreement at the level of 0.1 mag.
• The differences between data and model can be large in the Galactic plane and are clearly linked to the extinction.
• The colour determination of relatively stars ($G<9$) seems problematic, although this discrepancy is reduced compared to Gaia DR2.
| 2021-02-28T10:46:00 |
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|
https://control.com/textbook/dc-electricity/electrical-sources-and-loads/
|
# Electrical Sources and Electronic Load
## Chapter 4 - Basic Direct Current (DC) Theory
By definition, a source is a device delivering energy into a system, while a load is a device extracting energy from a system. Examples of typical electrical sources include generators, photovoltaic cells, thermopiles, and primary-cell batteries. These devices create electrical voltage, which in turn motivates electrical current to flow in a circuit. Examples of typical electrical loads include resistors, lamps, and electric motors. These devices resist the flow of electrical current through them, creating a voltage drop as a result.
In a working circuit, electrical sources and loads may be easily distinguished by comparison of their current directions and voltage polarities. An electrical source always manifests a voltage polarity in a direction aiding the direction of charge flow; i.e. a source is “pushing” the current along. An electrical load always manifests a voltage polarity in a direction opposing the direction of charge flow; i.e. a load “resists” the current.
The way in which we designate the direction of current (charge flow) becomes very important here. Since there are two commonly accepted notations – electron flow and “conventional” flow, exactly opposite of each other – it is easy to become confused.
First we see a diagram showing a source and a load, using electron flow notation. Electrons, being negatively charged particles, are repelled by the negative ($$-$$) poles of both source and load, and attracted to the positive (+) poles of both source and load. The difference between source and load is that the source device motivates the flow of electrons while the load device resists the flow of electrons:
In the case of the source (battery), the polarity of the voltage works for the direction of charge motion. In the case of the load (resistor), the polarity of the voltage drop works against the direction of charge motion.
Next we see a diagram showing the same source and load, this time using “conventional” flow notation to designate the direction of current. Here we must imagine positively-charged carriers moving through the wires instead of electrons. These positive charge carriers are repelled by any positive (+) pole and attracted to any negative ($$-$$) pole. Viewed in this light, we see the exact same principle at work: the source device is seen to motivate the flow of these positive charge carriers while the load device resists the flow:
Despite using a different notation for charge motion, the concept of source and load remains the same. In the case of the source (battery), the polarity of the voltage works for the direction of charge motion. In the case of the load (resistor), the polarity of the voltage drop works against the direction of charge motion.
An alternative notation for voltage (other than using “+” and “$$-$$” symbols) that many students find particularly illustrative is the use of curved arrows, where the tip of the curved arrow is the positive pole and the tail of the curved arrow is the negative pole. This notation is intended to be used when the direction of current (using “straight” or “angular” arrows) is shown using conventional flow notation:
Using arrows to represent voltage polarity in addition to using arrows to represent current direction is highly intuitive. It shows which way each component in the DC circuit is “pushing” in relation to the flow of charge carriers. Note how the source’s voltage arrow points in the same direction as the current: this means the source is motivating the current, causing charge carriers to flow in this circuit. Note how the resistor’s voltage arrow points opposite to the direction of current: this means the resistor is opposing the current, in a sense “fighting against” the flow of charge carriers. This comparison of voltage-arrow versus current-arrow direction makes the distinction between sources and loads rather obvious: sources push in the direction of current while loads push against the direction of current.
I personally lament the obscurity of this “curved-arrow” notation for voltage, as it greatly aids comprehension of this critically important distinction between sources and loads. When the voltage and current arrows point in the same direction, it means the component in question is motivating charge carriers along and therefore imparts energy to the circuit. When voltage and current arrows point in opposite directions, it means the component in question opposes charge carrier motion and therefore acts to extract energy from the circuit.
This directly relates to the fundamental physics concept of work, specifically in relation to the mathematical sign of work being a function of the relative angle between force and displacement. When a force acts in the same direction as motion, the work done is positive; when a force acts in the opposite direction as motion, the work done is negative:
Positive work represents an infusion of energy into a system (source), while negative work represents an extraction of energy from that system (load).
If we examine a hydraulic system, where a pump pushes fluid around a pipe loop and an orifice (called a “restrictor”) restricts the flow of this fluid, we see this same concept in action: the pump’s pressures at its discharge and suction ports work for the direction of fluid flow, while the pressures at the upstream and downstream ports of the restrictor work against the direction of fluid flow. The pump acts as a power source in this hydraulic “circuit” (infusing energy into the system) while the restrictor acts as a power load (extracting energy from the system):
We may even see this concept revealed in a simple mechanical system where work is being done. Examine the case of a crane lifting a heavy weight into the air, shown below. As the crane lifts the weight upward, the crane’s upward force on the weight is clearly working for the direction of motion, while the weight’s downward force against the crane is clearly working against the direction of motion:
Thus, the crane is doing positive work (acting as a source, infusing potential energy into the weight) while the weight is doing negative work (acting as a load, absorbing potential energy from the crane). A mathematically rigorous way to demonstrate this is to calculate the work done by each using the formula $$W = \vec{F} \cdot \vec{x}$$ or $$W = F x \cos \theta$$. Since the crane’s force and motion vectors both point in the same direction, $$\theta = 0$$ and work is a positive quantity $$Fx$$. The weight’s force vector, however, points 180$$^{o}$$ away from the motion vector, and so its work calculation is $$Fx \cos (180^o)$$ or $$-Fx$$.
Some electric components have the ability to act as sources and loads at different times. Both capacitors and inductors have the ability to temporarily contribute to and extract energy from electrical circuits, both having the ability to act as energy storage devices. One of the key concepts necessary to grasp the energy-storing abilities of capacitors and inductors is being able to recognize sources and loads at a glance based on the relationship between voltage polarity and charge motion. A set of three schematic diagrams shows how a capacitor is able to play the role of either source or load depending on what other component it is connected to:
Rechargeable batteries (called “secondary-cell” batteries as opposed to “primary-cell” batteries which cannot be recharged) may also behave as either sources or loads depending on external conditions. If a secondary-cell battery is connected to a resistor, the battery will discharge its energy (i.e. act as a source) while the resistor will dissipate that energy (i.e. act as a load). If a depleted secondary-cell battery is connected to an electrical generator of greater voltage, the generator will source energy to the battery while the re-charging battery will load down the generator (i.e. conventional flow entering the battery’s positive terminal and exiting the negative terminal).
Another practical benefit of clearly comprehending the distinction between electrical sources and electrical loads is being able to understand and troubleshoot 4-20 mA signal “loop” circuits used extensively in industrial instrumentation, especially circuits containing 2-wire (“loop-powered”) process transmitters. A “2-wire transmitter” is a device designed to regulate the amount of electrical current through it to a value determined by some physical variable such as a sensed pressure, temperature, or flow rate. The purpose of such a device is to represent that physical measurement in the form of an electric current that may be carried far distances through wires. What makes this device so troublesome for people to understand is that despite its function to set the value of current in the circuit, it is actually an electrical load and not an electrical source as one might assume. That is, a 2-wire transmitter relies wholly on some other source of electrical power in the circuit to function, although the transmitter solely defines how much current will flow in the circuit by virtue of its function as a regulator. For more information on this subject, refer to the section starting on the page.
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Published under the terms and conditions of the Creative Commons Attribution 4.0 International Public License
| 2020-02-17T01:10:03 |
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|
http://math.lanl.gov/Research/Publications/bergner-2003-step.shtml
|
T-5 HomeResearchPublications › bergner-2003-step
### Cite Details
Yoav Bergner and Luis M. A. Bettencourt, "A step beyond the bounce: Bubble dynamics in quantum phase transitions", Physical Review D, vol. 68, pp. 025014, 2003
### Abstract
We study the dynamical evolution of a phase interface or bubble in the context of a $\lambda~\phi^4+g~\phi^6$ scalar quantum field theory. We use a self-consistent mean-field approximation derived from a 2PI effective action to construct an initial value problem for the expectation value of the quantum field and two-point function. We solve the equations of motion numerically in 1+1 dimensions and compare the results to the purely classical evolution. We find that the quantum fluctuations dress the classical profile, affecting both the early time expansion of the bubble and the behavior upon collision with a neighboring interface.
### BibTeX Entry
@article{bergner-2003-step,
author = {Yoav Bergner and Luis M. A. Bettencourt},
title = {A step beyond the bounce: Bubble dynamics in quantum phase transitions},
year = {2003},
journal = {Physical Review D},
volume = {68},
pages = {025014}
}
| 2017-07-20T20:36:37 |
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|
http://dlmf.nist.gov/13.24
|
# §13.24(i) Expansions in Series of Whittaker Functions
For expansions of arbitrary functions in series of $\mathop{M_{\kappa,\mu}\/}\nolimits\!\left(z\right)$ functions see Schäfke (1961b).
# §13.24(ii) Expansions in Series of Bessel Functions
For $z\in\Complex$, and again with the notation of §§10.2(ii) and 10.25(ii),
13.24.1 $\mathop{M_{\kappa,\mu}\/}\nolimits\!\left(z\right)=\mathop{\Gamma\/}\nolimits% \!\left(\kappa+\mu\right)2^{2\kappa+2\mu}z^{\frac{1}{2}-\kappa}\*\sum_{s=0}^{% \infty}(-1)^{s}\frac{\left(2\kappa+2\mu\right)_{s}\left(2\kappa\right)_{s}}{% \left(1+2\mu\right)_{s}s!}\*\left(\kappa+\mu+s\right)\mathop{I_{\kappa+\mu+s}% \/}\nolimits\!\left(\tfrac{1}{2}z\right),$ $2\mu,\kappa+\mu\neq-1,-2,-3,\dots$,
and
13.24.2 $\frac{1}{\mathop{\Gamma\/}\nolimits\!\left(1+2\mu\right)}\mathop{M_{\kappa,\mu% }\/}\nolimits\!\left(z\right)=2^{2\mu}z^{\mu+\frac{1}{2}}\sum_{s=0}^{\infty}p_% {s}^{(\mu)}(z)\left(2\sqrt{\kappa z}\right)^{-2\mu-s}\mathop{J_{2\mu+s}\/}% \nolimits\!\left(2\sqrt{\kappa z}\right),$
where $p_{0}^{(\mu)}(z)=1$, $p_{1}^{(\mu)}(z)=\frac{1}{6}z^{2}$, and higher polynomials $p_{s}^{(\mu)}(z)$ are defined by
13.24.3 $\mathop{\exp\/}\nolimits\!\left(-\tfrac{1}{2}z\left(\mathop{\coth\/}\nolimits t% -\frac{1}{t}\right)\right)\left(\frac{t}{\mathop{\sinh\/}\nolimits t}\right)^{% 1-2\mu}=\sum_{s=0}^{\infty}p_{s}^{(\mu)}(z)\left(-\frac{t}{z}\right)^{s}.$
(13.18.8) is a special case of (13.24.1).
| 2014-07-29T00:33:00 |
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|
https://www.zbmath.org/authors/?q=ai%3Aholmes.philip-j
|
# zbMATH — the first resource for mathematics
## Holmes, Philip J.
Compute Distance To:
Author ID: holmes.philip-j Published as: Holmes, P.; Holmes, P. J.; Holmes, Philip; Holmes, Philip J. Homepage: https://www.princeton.edu/mae/people/faculty/holmes/ External Links: MGP · Math-Net.Ru · Wikidata · dblp · GND
Documents Indexed: 209 Publications since 1976, including 9 Books
all top 5
#### Co-Authors
35 single-authored 15 Lumley, John Leask 14 Berkooz, Gal 11 Domokos, Gábor 11 Marsden, Jerrold Eldon 7 Elezgaray, Juan 7 Schmitt, John M. 6 Ghigliazza, R. M. 6 Moehlis, Jeff 5 Guckenheimer, John M. 5 Smith, Troy R. 4 Brown, Eric N. 4 Cohen, Jonathan D. 4 Coller, B. D. 4 Doelman, Arjen 4 Duan, Jinqiao 4 Ghrist, Robert W. 4 Proctor, Joshua L. 4 Stone, Emily F. 4 Wong-Lin, Kongfatt 3 Aubry, Nadine 3 Bogacz, Rafal 3 Full, Robert J. 3 Goodman, Roy H. 3 Hek, Geertje 3 Hockett, Kevin G. 3 Koditschek, Dan 3 Kukillaya, Raghavendra P. 3 Mielke, Alexander 3 Rand, David A. 3 Simen, Patrick 3 Swart, Pieter J. 3 Weinstein, Michael I. 3 Whitley, David L. 3 Wiggins, Stephen 3 Wittenberg, Ralf W. 2 Altendorfer, Richard 2 Aminzare, Zahra 2 Armbruster, Dieter 2 Campbell, Sue Ann 2 Cisternas, Jaime E. 2 Cohen, Avis H. 2 Dankowicz, Harry J. 2 Gao, Juan 2 Kutz, J. Nathan 2 Liu, Yuan Sophie 2 Moon, Francis C. 2 O’Reilly, Oliver Mary 2 Poje, Andrew C. 2 Rand, Richard H. 2 Royce, B. 2 Seipel, Justin E. 2 Shaw, Steven W. 2 Szeri, Andrew J. 2 Titi, Edriss Saleh 2 Veerman, Peter 1 Ball, John M. 1 Ball, Rowena 1 Bélair, Jacques 1 Broderick, Tamara 1 Brunsden, V. 1 Clarkson, B. L. 1 Coleman, Michael J. 1 Cortell, J. 1 Cusumano, Joseph P. 1 Diacu, Florin Nicolae 1 Eckhoff, Philip 1 Faisst, Holger 1 Garcia, Mark Anthony 1 Gilzenrat, Mark S. 1 Greenspan, B. D. 1 Greenspan, Bernie 1 Hammond, Joseph K. 1 Hanßmann, Heinz 1 Harris-Warrick, Ronald M. 1 Hoffman, Kathleen A. 1 Holmes, Catherine A. 1 Ilyashenko, Yulij Sergeevich 1 James, Richard D. 1 Jenkins, Jeffrey 1 Kalies, William D. 1 Kevrekidis, Ioannis George 1 Khibnik, Alexander I. 1 Kiemel, Tim 1 Kistner, A. 1 Lángi, Zsolt 1 Leibovich, Sidney 1 Leonard, Naomi Ehrich 1 Lewis, Donald C. 1 Lin, Yue-Kuhn 1 Mattingly, Jonathan C. 1 McMillan, Thomas 1 McMillen, Tyler 1 Medvedev, Georgi S. 1 Myers, Mark H. 1 Newton, Paul K. 1 Ono, Kinya 1 Pego, Robert L. 1 Razo, R. C. 1 Rowley, Clarence W. 1 Scheurle, Jürgen ...and 23 more Co-Authors
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#### Serials
24 Physica D 8 Biological Cybernetics 8 Journal of Sound and Vibration 8 Journal of Nonlinear Science 7 International Journal of Non-Linear Mechanics 7 SIAM Journal on Applied Dynamical Systems 6 Neural Computation 5 Archive for Rational Mechanics and Analysis 5 Nonlinearity 5 SIAM Journal on Applied Mathematics 4 Journal of Applied Mechanics 4 Journal of Fluid Mechanics 4 Journal of Mathematical Psychology 4 SIAM Journal on Mathematical Analysis 4 Regular and Chaotic Dynamics 3 Journal of Mathematical Biology 3 Philosophical Transactions of the Royal Society of London. Ser. A 3 Quarterly of Applied Mathematics 3 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 3 Physics of Fluids 3 Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 2 Theoretical and Computational Fluid Dynamics 2 Automatica 2 Journal of Differential Equations 2 SIAM Review 2 Nonlinear Dynamics 2 Journal of Theoretical Biology 1 Applied Scientific Research 1 Communications in Mathematical Physics 1 Computer Methods in Applied Mechanics and Engineering 1 IMA Journal of Applied Mathematics 1 Journal of Mathematical Physics 1 Mathematical Proceedings of the Cambridge Philosophical Society 1 Physics of Fluids 1 Quarterly Journal of Mechanics and Applied Mathematics 1 Rocky Mountain Journal of Mathematics 1 ZAMP. Zeitschrift für angewandte Mathematik und Physik 1 Indiana University Mathematics Journal 1 Proceedings of the American Mathematical Society 1 Proceedings of the Edinburgh Mathematical Society. Series II 1 Studies in Applied Mathematics 1 Ergodic Theory and Dynamical Systems 1 IMA Journal of Mathematics Applied in Medicine and Biology 1 Mathematical and Computer Modelling 1 Dynamics and Stability of Systems 1 Neural Networks 1 European Journal of Applied Mathematics 1 Applied Mathematical Modelling 1 Journal of Dynamic Systems, Measurement and Control 1 Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences 1 Journal of Dynamics and Differential Equations 1 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 Moscow Mathematical Journal 1 Stochastics and Dynamics 1 AMRX. Applied Mathematics Research eXpress 1 Applied Mathematical Sciences 1 Lecture Notes in Mathematics 1 Nonlinear Analysis. Theory, Methods & Applications 1 Cambridge Monographs on Mechanics
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#### Fields
95 Dynamical systems and ergodic theory (37-XX) 62 Ordinary differential equations (34-XX) 41 Mechanics of particles and systems (70-XX) 37 Biology and other natural sciences (92-XX) 36 Fluid mechanics (76-XX) 30 Partial differential equations (35-XX) 27 Mechanics of deformable solids (74-XX) 11 Systems theory; control (93-XX) 8 Probability theory and stochastic processes (60-XX) 8 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 6 General and overarching topics; collections (00-XX) 5 Manifolds and cell complexes (57-XX) 5 Global analysis, analysis on manifolds (58-XX) 4 Numerical analysis (65-XX) 4 Computer science (68-XX) 3 History and biography (01-XX) 3 Differential geometry (53-XX) 3 Optics, electromagnetic theory (78-XX) 2 Approximations and expansions (41-XX) 2 General topology (54-XX) 2 Statistical mechanics, structure of matter (82-XX) 1 Topological groups, Lie groups (22-XX) 1 Real functions (26-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Functional analysis (46-XX) 1 Convex and discrete geometry (52-XX) 1 Statistics (62-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Information and communication theory, circuits (94-XX)
#### Citations contained in zbMATH
182 Publications have been cited 7,513 times in 6,010 Documents Cited by Year
Nonlinear oscillations, dynamical systems, and bifurcations of vector fields. Zbl 0515.34001
Guckenheimer, John; Holmes, Philip
1983
Turbulence, coherent structures, dynamical systems and symmetry. Zbl 0890.76001
Holmes, Philip; Lumley, John L.; Berkooz, Gal
1996
The dynamics of coherent structures in the wall region of a turbulent layer. Zbl 0643.76066
Aubry, Nadine; Holmes, Philip; Lumley, John L.; Stone, Emily
1988
A periodically forced piecewise linear oscillator. Zbl 0561.70022
Shaw, S. W.; Holmes, P. J.
1983
A nonlinear oscillator with a strange attractor. Zbl 0423.34049
Holmes, P.
1979
Turbulence, coherent structures, dynamical systems and symmetry. 2nd ed. Zbl 1251.76001
Holmes, Philip; Lumley, John L.; Berkooz, Gahl; Rowley, Clarence W.
2012
On the phase reduction and response dynamics of neural oscillator population. Zbl 1054.92006
Brown, Eric; Moehlis, Jeff; Holmes, Philip
2004
Heteroclinic cycles and modulated travelling waves in systems with 0(2) symmetry. Zbl 0634.34027
Armbruster, Dieter; Guckenheimer, John; Holmes, Philip
1988
A partial differential equation with infinitely many periodic orbits: Chaotic oscillations of a forced beam. Zbl 0507.58031
Holmes, Philip; Marsden, Jerrold
1981
Structurally stable heteroclinic cycles. Zbl 0645.58022
Guckenheimer, John; Holmes, Philip
1988
Horseshoes in perturbations of Hamiltonian systems with two degrees of freedom. Zbl 0489.58013
Holmes, Philip J.; Marsden, Jerrold E.
1982
Turbulence, coherent structures, dynamical systems and symmetry. Zbl 0923.76002
Holmes, Philip; Lumley, John L.; Berkooz, Gal
1998
Melnikov’s method and Arnold diffusion for perturbations of integrable Hamiltonian systems. Zbl 0497.70025
Holmes, Philip J.; Marsden, Jerrold E.
1982
A magnetoelastic strange attractor. Zbl 0405.73082
Moon, F. C.; Holmes, P. J.
1979
On the relation between low-dimensional models and the dynamics of coherent structures in the turbulent wall layer. Zbl 0782.76048
Berkooz, Gal; Holmes, Philip; Lumley, J. L.
1993
The dynamics of repeated impacts with a sinusoidally vibrating table. Zbl 0518.73015
Holmes, P. J.
1982
Horseshoes and Arnold diffusion for Hamiltonian systems and Lie groups. Zbl 0488.70006
Holmes, Philip J.; Marsden, Jerrold E.
1983
The nature of the coupling between segmental oscillators of the lamprey spinal generator for locomotion: a mathematical model. Zbl 0476.92003
Cohen, Avis H.; Holmes, Philip J.; Rand, Richard H.
1982
Knots and links in three-dimensional flows. Zbl 0869.58044
Ghrist, Robert W.; Holmes, Philip J.; Sullivan, Michael C.
1997
Cascades of homoclinic orbits to, and chaos near, a Hamiltonian saddle- center. Zbl 0749.58022
Mielke, A.; Holmes, P.; O’Reilly, O.
1992
Random perturbations of heteroclinic attractors. Zbl 0702.58038
Stone, Emily; Holmes, Philip
1990
Kuramoto-Sivashinsky dynamics on the center-unstable manifold. Zbl 0687.34036
Armbruster, Dieter; Guckenheimer, John; Holmes, Philip
1989
Averaging and chaotic motions in forced oscillations. Zbl 0472.70024
Holmes, Philip J.
1980
Bifurcations to divergence and flutter in flow-induced oscillations: a finite dimensional analysis. Zbl 0363.73059
Holmes, P. J.
1977
Strong NLS soliton-defect interactions. Zbl 1061.35132
Goodman, Roy H.; Holmes, Philip J.; Weinstein, Michael I.
2004
The dynamics of legged locomotion: Models, analyses, and challenges. Zbl 1100.34002
Holmes, Philip; Full, Robert J.; Koditschek, Dan; Guckenheimer, John
2006
Global existence theory for a generalized Ginzburg-Landau equation. Zbl 0783.35070
Duan, Jinqiao; Holmes, Philip; Titi, Edriss S.
1992
Phase portraits and bifurcations of the non-linear oscillator: $$x''+(\alpha+\gamma x^ 2)x'+\beta x+\delta x^ 3=0$$. Zbl 0453.70015
Holmes, P.; Rand, D.
1980
Bifurcation of periodic motions in two weakly coupled van der Pol oscillators. Zbl 0447.70028
Rand, R. H.; Holmes, P. J.
1980
On the dynamics of fine structure. Zbl 0791.35030
Ball, J. M.; Holmes, P. J.; James, R. D.; Pego, R. L.; Swart, P. J.
1991
Regularity, approximation and asymptotic dynamics for a generalized Ginzburg-Landau equation. Zbl 0808.35133
Duan, Jinqiao; Titi, Edriss S.; Holmes, Philip
1993
Exponentially small splittings of separatrices with applications of KAM theory and degenerate bifurcations. Zbl 0685.70017
Holmes, Philip; Marsden, Jerrold; Scheurle, Jürgen
1988
Energy minimization and the formation of microstructure in dynamic anti- plane shear. Zbl 0786.73066
Swart, Pieter J.; Holmes, Philip J.
1992
Bifurcation to divergence and flutter in flow-induced oscillations: An infinite dimensional analysis. Zbl 0385.93028
Holmes, Philip; Marsden, Jerrold
1978
On the Cauchy problem of a generalized Ginzburg-Landau equation. Zbl 0833.35067
Duan, Jinqiao; Holmes, Philip
1994
Bifurcations of one- and two-dimensional maps. Zbl 0556.58023
Holmes, P.; Whitley, D.
1984
Nonlinear propagation of light in one-dimensional periodic structures. Zbl 1005.78011
Goodman, R. H.; Weinstein, M. I.; Holmes, P. J.
2001
Homoclinic orbits, subharmonics and global bifurcations in forced oscillations. Zbl 0532.58019
Greenspan, B. D.; Holmes, P. J.
1983
Knotted periodic orbits in suspensions of Smale’s horseshoe: torus knots and bifurcation sequences. Zbl 0593.58027
Holmes, Philip; Williams, R. F.
1985
Second order averaging and bifurcations to subharmonics in Duffing’s equation. Zbl 0478.73028
Holmes, C.; Holmes, P.
1981
A periodically forced impact oscillator with large dissipation. Zbl 0539.70032
Shaw, S. W.; Holmes, P. J.
1983
Interaction of sine-Gordon kinks with defects: Phase space transport in a two-mode model. Zbl 0985.35074
Goodman, Roy H.; Holmes, Philip J.; Weinstein, Michael I.
2002
Spatially complex equilibria of buckled rods. Zbl 0655.73029
Mielke, Alexander; Holmes, Philip
1988
Spatial structure of time-periodic solutions of the Ginzburg-Landau equation. Zbl 0618.35003
Holmes, Philip
1986
The dynamics of choice among multiple alternatives. Zbl 1139.91028
McMillen, Tyler; Holmes, Philip
2006
Periodic orbits in slowly varying oscillators. Zbl 0619.34041
Wiggins, Stephen; Holmes, Philip
1987
Repeated resonance and homoclinic bifurcation in a periodically forced family of oscillators. Zbl 0547.34028
Greenspan, Bernie; Holmes, Philip
1984
Homoclinic orbits in slowly varying oscillators. Zbl 0622.34041
Wiggins, Stephen; Holmes, Philip
1987
Celestial encounters. The origins of chaos and stability. Zbl 0944.37001
Diacu, Florin; Holmes, Philip
1996
Low-dimensional modelling of turbulence using the proper orthogonal decomposition: A tutorial. Zbl 1094.76024
Smith, Troy R.; Moehlis, Jeff; Holmes, Philip
2005
Constrained Euler buckling: An interplay of computation and analysis. Zbl 0949.74023
Holmes, Philip; Domokos, Gábor; Schmitt, John; Szeberényi, Imre
1999
Bifurcations of the forced van der Pol oscillator. Zbl 0375.34031
Holmes, P. J.; Rand, D. A.
1978
Chaotic motions in a weakly nonlinear model for surface waves. Zbl 0602.76015
Holmes, Philip
1986
Globally coupled oscillator networks. Zbl 1132.92316
Brown, Eric; Holmes, Philip; Moehlis, Jeff
2003
Constrained Euler buckling. Zbl 0876.34047
Domokos, G.; Holmes, P.; Royce, B.
1997
Fronts, domain walls and pulses in a generalized Ginzburg-Landau equation. Zbl 0820.58053
Duan, Jinqiao; Holmes, Philip
1995
Nonlinear stability of axisymmetric swirling flows. Zbl 0658.76044
Szeri, A.; Holmes, P.
1988
Mechanical models for insect locomotion: Dynamics and stability in the horizontal plane. I: Theory. Zbl 1033.92005
Schmitt, John; Holmes, Philip
2000
Dynamics of the Kirchhoff equations. I: Coincident centers of gravity and buoyancy. Zbl 1194.70009
Holmes, Philip; Jenkins, Jeffrey; Leonard, Naomi Ehrich
1998
The existence of transverse homoclinic points in the Sitnikov problem. Zbl 0815.34032
Dankowicz, Harry; Holmes, Philip
1995
On a Painlevé-type boundary-value problem. Zbl 0552.34023
Holmes, Philip; Spence, David
1984
The bifurcations of Duffing’s equation: An application of catastrophe theory. Zbl 0337.34049
Holmes, P. J.; Rand, D. A.
1976
Simple neural networks that optimize decisions. Zbl 1069.92004
Brown, Eric; Gao, Juan; Holmes, Philip; Bogacz, Rafal; Gilzenrat, Mark; Cohen, Jonathan D.
2005
On the attracting set for Duffing’s equation. II: A geometrical model for moderate force and damping. Zbl 0574.58024
Holmes, Philip; Whitley, David
1983
Minimal models of bursting neurons: How multiple currents, conductances, and timescales affect bifurcation diagrams. Zbl 1090.34039
Ghigliazza, R. M.; Holmes, P.
2004
Some remarks on chaotic particle paths in time-periodic, three- dimensional swirling flows. Zbl 0521.76049
Holmes, Philip
1984
A simply stabilized running model. Zbl 1088.34517
Ghigliazza, R. M.; Altendorfer, R.; Holmes, P.; Koditschek, D.
2003
The limited effectiveness of normal forms: A critical review and extension of local bifurcation studies of the Brusselator PDE. Zbl 0893.34027
Wittenberg, Ralf W.; Holmes, Philip
1997
Knotted periodic orbits in suspensions of Smale’s horseshoe: period multiplying and cabled knots. Zbl 0623.58014
Holmes, Philip
1986
Rapid decision threshold modulation by reward rate in a neural network. Zbl 1103.68726
Simen, Patrick; Cohen, Jonathan D.; Holmes, Philip
2006
Intermittent dynamics in simple models of the turbulent wall layer. Zbl 0729.76040
Berkooz, Gal; Holmes, Philip; Lumley, J. L.
1991
Bifurcation from $$O(2)$$ symmetric heteroclinic cycles with three interacting modes. Zbl 0737.58038
Campbell, Sue Ann; Holmes, Philip
1991
Noise induced intermittency in a model of a turbulent boundary layer. Zbl 0687.76055
Stone, Emily; Holmes, Philip
1989
Center manifolds, normal forms and bifurcations of vector fields with application to coupling between periodic and steady motions. Zbl 1194.37075
Holmes, Philip J.
1981
A hexapedal jointed-leg model for insect locomotion in the horizontal plane. Zbl 1248.92003
Kukillaya, Raghavendra P.; Holmes, Philip J.
2007
Low-dimensional models for turbulent plane Couette flow in a minimal flow unit. Zbl 1108.76031
Smith, T. R.; Moehlis, J.; Holmes, P.
2005
Mechanical models for insect locomotion: Dynamics and stability in the horizontal plane. II: Application. Zbl 1039.92006
Schmitt, John; Holmes, Philip
2000
Josephson’s junction, annulus maps, Birkhoff attractors, horseshoes and rotation sets. Zbl 0582.58020
Hockett, Kevin; Holmes, Philip
1986
The existence of arbitrarily many distinct periodic orbits in a two degree of freedom Hamiltonian system. Zbl 0595.58036
Veerman, Peter; Holmes, Philip
1985
A phase-reduced neuro-mechanical model for insect locomotion: feed-forward stability and proprioceptive feedback. Zbl 1211.93099
Proctor, J.; Kukillaya, R. P.; Holmes, P.
2010
Dynamics and stability of insect locomotion: a hexapedal model for horizontal plane motions. Zbl 1082.92010
Seipel, Justin E.; Holmes, Philip J.; Full, Robert J.
2004
An ODE whose solutions contain all knots and links. Zbl 0878.34038
Ghrist, Robert W.; Holmes, Philip J.
1996
An elastic rod model for anguilliform swimming. Zbl 1113.92005
McMillan, T.; Holmes, P.
2006
A minimal model of a central pattern generator and motoneurons for insect locomotion. Zbl 1090.34040
Ghigliazza, R. M.; Holmes, P.
2004
Dynamics and stability of legged locomotion in the horizontal plane: a test case using insects. Zbl 1068.92004
Schmitt, J.; Garcia, M.; Razo, R. C.; Holmes, P.; Full, R. J.
2002
Unfolding a degenerate nonlinear oscillator: A codimension two bifurcation. Zbl 0506.34034
Holmes, Philip
1980
A simple model for clock-actuated legged locomotion. Zbl 1229.70028
Seipel, J.; Holmes, P.
2007
Models for turbulent plane Couette flow using the proper orthogonal decomposition. Zbl 1185.76261
Moehlis, J.; Smith, T. R.; Holmes, P.; Faisst, H.
2002
Modeling a simple choice task: Stochastic dynamics of mutually inhibitory neural groups. Zbl 1060.92019
Brown, Eric; Holmes, Philip
2001
Homoclinic explosions and implosions. Zbl 0881.58044
Doelman, Arjen; Holmes, Philip
1996
Euler’s problem, Euler’s method, and the standard map; or, the discrete charm of buckling. Zbl 0797.34041
Domokos, G.; Holmes, P.
1993
Proof of non-integrability for the Hénon-Heiles Hamiltonian near an exceptional integrable case. Zbl 1194.37128
Holmes, Philip
1982
A strange family of three-dimensional vector fields near a degenerate singularity. Zbl 0421.58016
Holmes, Philip J.
1980
Pipes supported at both ends cannot flutter. Zbl 0386.73056
Holmes, P. J.
1978
Mechanical models for insect locomotion: Stability and parameter studies. Zbl 1059.70006
Schmitt, John; Holmes, Philip
2001
Heteroclinic cycles and modulated travelling waves in a system with $$D_ 4$$ symmetry. Zbl 0774.34031
Campbell, Sue Ann; Holmes, Philip
1992
The effect of modeled drag reduction on the wall region. Zbl 0708.76072
Aubry, N.; Lumley, J. L.; Holmes, P.
1990
Ninety plus thirty years of nonlinear dynamics: less is more and more is different. Zbl 1092.37500
Holmes, Philip
2005
Euler buckling in a potential field. Zbl 1139.74415
Holmes, P.; Domokos, G.; Hek, G.
2000
Simple models for excitable and oscillatory neural networks. Zbl 0908.92013
Taylor, David; Holmes, Philip
1998
Heterogeneous inputs to central pattern generators can shape insect gaits. Zbl 1425.92036
Aminzare, Zahra; Holmes, Philip
2019
Gait transitions in a phase oscillator model of an insect central pattern generator. Zbl 1385.92007
Aminzare, Zahra; Srivastava, Vaibhav; Holmes, Philip
2018
Explicit moments of decision times for single- and double-threshold drift-diffusion processes. Zbl 1396.91627
Srivastava, V.; Holmes, P.; Simen, P.
2016
A genealogy of convex solids via local and global bifurcations of gradient vector fields. Zbl 1359.52005
Domokos, Gábor; Holmes, Philip; Lángi, Zsolt
2016
Some joys and trials of mathematical neuroscience. Zbl 1293.92006
Holmes, Philip
2014
Turbulence, coherent structures, dynamical systems and symmetry. 2nd ed. Zbl 1251.76001
Holmes, Philip; Lumley, John L.; Berkooz, Gahl; Rowley, Clarence W.
2012
Neural dynamics, bifurcations, and firing rates in a quadratic integrate-and-fire model with a recovery variable. I: Deterministic behavior. Zbl 1311.92051
Shlizerman, Eli; Holmes, Philip
2012
Dimension reduction and dynamics of a spiking neural network model for decision making under neuromodulation. Zbl 1217.34079
Eckhoff, Philip; Wong-Lin, Kongfatt; Holmes, Philip
2011
A phase-reduced neuro-mechanical model for insect locomotion: feed-forward stability and proprioceptive feedback. Zbl 1211.93099
Proctor, J.; Kukillaya, R. P.; Holmes, P.
2010
Reflexes and preflexes: on the role of sensory feedback on rhythmic patterns in insect locomotion. Zbl 1266.92037
Proctor, J.; Holmes, P.
2010
Robust versus optimal strategies for two-alternative forced choice tasks. Zbl 1204.91043
Zacksenhouse, M.; Bogacz, R.; Holmes, P.
2010
A model for insect locomotion in the horizontal plane: feedforward activation of fast muscles, stability, and robustness. Zbl 1403.92015
Kukillaya, Raghavendra P.; Holmes, Philip
2009
A comparison of bounded diffusion models for choice in time controlled tasks. Zbl 1176.60075
Zhang, Jiaxiang; Bogacz, Rafal; Holmes, Philip
2009
Sequential effects in two-choice reaction time tasks: decomposition and synthesis of mechanisms. Zbl 1402.92086
Gao, Juan; Wong-Lin, KongFatt; Holmes, Philip; Simen, Patrick; Cohen, Jonathan D.
2009
Dynamical analysis of Bayesian inference models for the Eriksen task. Zbl 1183.68487
Liu, Yuan Sophie; Yu, Angela; Holmes, Philip
2009
Closed-form approximations of first-passage distributions for a stochastic decision-making model. Zbl 1186.91061
Broderick, Tamara; Wong-Lin, Kong Fatt; Holmes, Philip
2009
Time-varying perturbations can distinguish among integrate-to-threshold models for perceptual decision making in reaction time tasks. Zbl 1168.91515
Zhou, Xiang; Wong-Lin, Kongfatt; Holmes, Philip
2009
How well can spring-mass-like telescoping leg models fit multi-pedal sagittal-plane locomotion data? Zbl 1400.92052
Srinivasan, Manoj; Holmes, Philip
2008
A neural network model of the Eriksen task: reduction, analysis, and data fitting. Zbl 1146.68421
Liu, Yuan Sophie; Holmes, Philip; Cohen, Jonathan D.
2008
Steering by transient destabilization in piecewise-holonomic models of legged locomotion. Zbl 1229.70018
Proctor, J.; Holmes, P.
2008
On synchronization and traveling waves in chains of relaxation oscillators with an application to Lamprey CPG. Zbl 1167.34347
Várkonyi, Péter L.; Holmes, Philip
2008
A hexapedal jointed-leg model for insect locomotion in the horizontal plane. Zbl 1248.92003
Kukillaya, Raghavendra P.; Holmes, Philip J.
2007
A simple model for clock-actuated legged locomotion. Zbl 1229.70028
Seipel, J.; Holmes, P.
2007
The dynamics of legged locomotion: Models, analyses, and challenges. Zbl 1100.34002
Holmes, Philip; Full, Robert J.; Koditschek, Dan; Guckenheimer, John
2006
The dynamics of choice among multiple alternatives. Zbl 1139.91028
McMillen, Tyler; Holmes, Philip
2006
Rapid decision threshold modulation by reward rate in a neural network. Zbl 1103.68726
Simen, Patrick; Cohen, Jonathan D.; Holmes, Philip
2006
An elastic rod model for anguilliform swimming. Zbl 1113.92005
McMillan, T.; Holmes, P.
2006
Low-dimensional modelling of turbulence using the proper orthogonal decomposition: A tutorial. Zbl 1094.76024
Smith, Troy R.; Moehlis, Jeff; Holmes, Philip
2005
Simple neural networks that optimize decisions. Zbl 1069.92004
Brown, Eric; Gao, Juan; Holmes, Philip; Bogacz, Rafal; Gilzenrat, Mark; Cohen, Jonathan D.
2005
Low-dimensional models for turbulent plane Couette flow in a minimal flow unit. Zbl 1108.76031
Smith, T. R.; Moehlis, J.; Holmes, P.
2005
Ninety plus thirty years of nonlinear dynamics: less is more and more is different. Zbl 1092.37500
Holmes, Philip
2005
Towards a neuromechanical model for insect locomotion: hybrid dynamical systems. Zbl 1084.34050
Ghigliazza, R. M.; Holmes, P.
2005
Heteroclinic cycles and periodic orbits for the O(2)-equivariant 0:1:2 mode interaction. Zbl 1099.37044
Smith, T. R.; Moehlis, J.; Holmes, P.
2005
A simply stabilized running model. Zbl 1074.70005
Ghigliazza, R. M.; Altendorfer, R.; Holmes, P.; Koditschek, D.
2005
On the phase reduction and response dynamics of neural oscillator population. Zbl 1054.92006
Brown, Eric; Moehlis, Jeff; Holmes, Philip
2004
Strong NLS soliton-defect interactions. Zbl 1061.35132
Goodman, Roy H.; Holmes, Philip J.; Weinstein, Michael I.
2004
Minimal models of bursting neurons: How multiple currents, conductances, and timescales affect bifurcation diagrams. Zbl 1090.34039
Ghigliazza, R. M.; Holmes, P.
2004
Dynamics and stability of insect locomotion: a hexapedal model for horizontal plane motions. Zbl 1082.92010
Seipel, Justin E.; Holmes, Philip J.; Full, Robert J.
2004
A minimal model of a central pattern generator and motoneurons for insect locomotion. Zbl 1090.34040
Ghigliazza, R. M.; Holmes, P.
2004
Globally coupled oscillator networks. Zbl 1132.92316
Brown, Eric; Holmes, Philip; Moehlis, Jeff
2003
A simply stabilized running model. Zbl 1088.34517
Ghigliazza, R. M.; Altendorfer, R.; Holmes, P.; Koditschek, D.
2003
On nonlinear boundary-value problems: Ghosts, parasites and discretizations. Zbl 1069.34020
Domokos, G.; Holmes, P.
2003
Travelling wave solutions of the degenerate Kolmogorov-Petrovski-Piskunov equation. Zbl 1060.35052
Medvedev, G. S.; Ono, K.; Holmes, P. J.
2003
Mechanical models for insect locomotion: active muscles and energy losses. Zbl 1105.92307
Schmitt, John; Holmes, Philip
2003
Buckling in response to applied heat sources. Zbl 1083.74021
Cisternas, Jaime; Holmes, Philip; Kevrekidis, Ioannis G.
2003
Interaction of sine-Gordon kinks with defects: Phase space transport in a two-mode model. Zbl 0985.35074
Goodman, Roy H.; Holmes, Philip J.; Weinstein, Michael I.
2002
Dynamics and stability of legged locomotion in the horizontal plane: a test case using insects. Zbl 1068.92004
Schmitt, J.; Garcia, M.; Razo, R. C.; Holmes, P.; Full, R. J.
2002
Models for turbulent plane Couette flow using the proper orthogonal decomposition. Zbl 1185.76261
Moehlis, J.; Smith, T. R.; Holmes, P.; Faisst, H.
2002
On the dynamics of cranes, or spherical pendula with moving supports. Zbl 1346.37069
Ghigliazza, R. M.; Holmes, P.
2002
Buckling of extensible thermoelastic rods. Zbl 1027.74025
Cisternas, J.; Holmes, P.
2002
Nonlinear propagation of light in one-dimensional periodic structures. Zbl 1005.78011
Goodman, R. H.; Weinstein, M. I.; Holmes, P. J.
2001
Modeling a simple choice task: Stochastic dynamics of mutually inhibitory neural groups. Zbl 1060.92019
Brown, Eric; Holmes, Philip
2001
Mechanical models for insect locomotion: Stability and parameter studies. Zbl 1059.70006
Schmitt, John; Holmes, Philip
2001
Homoclinic orbits and chaos in three- and four-dimensional flows. Zbl 1004.37013
Holmes, Philip; Doelman, Arjen; Hek, Geertje; Domokos, Gábor
2001
Low-dimensional models of turbulence or, the dynamics of coherent structures. Zbl 1007.35059
Holmes, P. J.; Mattingly, J. C.; Wittenberg, R. W.
2001
On the global dynamics of Kirchhoff’s equations: Rigid body models for underwater vehicles. Zbl 1015.37043
Hanßmann, Heinz; Holmes, Philip
2001
Low-dimensional models with varying parameters: A model problem and flow through a diffuser with variable angle. Zbl 1020.76041
Smith, Troy; Holmes, Philip
2001
Mechanical models for insect locomotion: Dynamics and stability in the horizontal plane. I: Theory. Zbl 1033.92005
Schmitt, John; Holmes, Philip
2000
Mechanical models for insect locomotion: Dynamics and stability in the horizontal plane. II: Application. Zbl 1039.92006
Schmitt, John; Holmes, Philip
2000
Euler buckling in a potential field. Zbl 1139.74415
Holmes, P.; Domokos, G.; Hek, G.
2000
Constrained Euler buckling: An interplay of computation and analysis. Zbl 0949.74023
Holmes, Philip; Domokos, Gábor; Schmitt, John; Szeberényi, Imre
1999
Motions and stability of a piecewise holonomic system: The discrete Chaplygin sleigh. Zbl 1020.70007
Coleman, M. J.; Holmes, P.
1999
Constrained Euler buckling: Line contact solutions. Zbl 0983.74024
Holmes, Philip; Schmitt, John; Domokos, Gabor
1999
Turbulence, coherent structures, dynamical systems and symmetry. Zbl 0923.76002
Holmes, Philip; Lumley, John L.; Berkooz, Gal
1998
Dynamics of the Kirchhoff equations. I: Coincident centers of gravity and buoyancy. Zbl 1194.70009
Holmes, Philip; Jenkins, Jeffrey; Leonard, Naomi Ehrich
1998
Simple models for excitable and oscillatory neural networks. Zbl 0908.92013
Taylor, David; Holmes, Philip
1998
Homoclinic saddle-node bifurcations and subshifts in a three-dimensional flow. Zbl 0930.37026
Hek, Geertje; Doelman, Arjen; Holmes, Philip
1998
Global existence and uniqueness for an optical fibre laser model. Zbl 0913.35018
Mielke, Alexander; Holmes, Philip; Kutz, J. Nathan
1998
Knots and links in three-dimensional flows. Zbl 0869.58044
Ghrist, Robert W.; Holmes, Philip J.; Sullivan, Michael C.
1997
Constrained Euler buckling. Zbl 0876.34047
Domokos, G.; Holmes, P.; Royce, B.
1997
The limited effectiveness of normal forms: A critical review and extension of local bifurcation studies of the Brusselator PDE. Zbl 0893.34027
Wittenberg, Ralf W.; Holmes, Philip
1997
Suppression of bursting. Zbl 0868.93057
Coller, B. D.; Holmes, Philip
1997
Erratum: ”Interaction of adjacent bursts in the wall region” [Phys. Fluids 6 (1994), no. 2, part 2, 954–961]. Zbl 1185.76746
Coller, B. D.; Holmes, P.; Lumley, John
1997
Turbulence, coherent structures, dynamical systems and symmetry. Zbl 0890.76001
Holmes, Philip; Lumley, John L.; Berkooz, Gal
1996
Celestial encounters. The origins of chaos and stability. Zbl 0944.37001
Diacu, Florin; Holmes, Philip
1996
An ODE whose solutions contain all knots and links. Zbl 0878.34038
Ghrist, Robert W.; Holmes, Philip J.
1996
Homoclinic explosions and implosions. Zbl 0881.58044
Doelman, Arjen; Holmes, Philip
1996
On a dynamical model for phase transformation in nonlinear elasticity. Zbl 0876.73015
Kalies, W. D.; Holmes, P. J.
1996
Local models of spatio-temporally complex fields. Zbl 0885.35115
Dankowicz, Harry; Holmes, Philip; Berkooz, Gal; Elezgaray, Juan
1996
Fronts, domain walls and pulses in a generalized Ginzburg-Landau equation. Zbl 0820.58053
Duan, Jinqiao; Holmes, Philip
1995
The existence of transverse homoclinic points in the Sitnikov problem. Zbl 0815.34032
Dankowicz, Harry; Holmes, Philip
1995
Wavelet projections of the Kuramoto-Sivashinsky equation. I: Heteroclinic cycles and modulated traveling waves for short systems. Zbl 0890.58086
Myers, Mark; Holmes, Philip; Elezgaray, Juan; Berkooz, Gal
1995
On the Cauchy problem of a generalized Ginzburg-Landau equation. Zbl 0833.35067
Duan, Jinqiao; Holmes, Philip
1994
Control of noisy heteroclinic cycles. Zbl 0816.76037
Coller, B. D.; Holmes, Philip; Lumley, John L.
1994
Knotting within the gluing bifurcation. Zbl 0864.58045
Holmes, P.; Ghrist, R.
1994
Interaction of adjacent bursts in the wall region. Zbl 0830.76040
Coller, B. D.; Holmes, P.; Lumley, J. L.
1994
The proper orthogonal decomposition, wavelets and modal approaches to the dynamics of coherent structures. Zbl 0823.76036
Berkooz, Gal; Elezgaray, Juan; Holmes, Philip; Lumley, John; Poje, Andrew
1994
On the relation between low-dimensional models and the dynamics of coherent structures in the turbulent wall layer. Zbl 0782.76048
Berkooz, Gal; Holmes, Philip; Lumley, J. L.
1993
Regularity, approximation and asymptotic dynamics for a generalized Ginzburg-Landau equation. Zbl 0808.35133
Duan, Jinqiao; Titi, Edriss S.; Holmes, Philip
1993
Euler’s problem, Euler’s method, and the standard map; or, the discrete charm of buckling. Zbl 0797.34041
Domokos, G.; Holmes, P.
1993
Wavelet analysis of the motion of coherent structures. Zbl 0899.76236
Elezgaray, J.; Berkooz, G.; Holmes, P.
1993
Knots and orbit genealogies in three dimensional flows. Zbl 0803.58047
Ghrist, Robert; Holmes, Philip
1993
Reduction, stability, instability and bifurcation in rotationally symmetric Hamiltonian systems. Zbl 0782.70015
Zombro, Brett; Holmes, Philip
1993
On non-inflectional solutions of non-uniform elasticae. Zbl 0793.73036
Domokos, Gábor; Holmes, Philip
1993
Symmetries, heteroclinic cycles and intermittency in fluid flow. Zbl 0788.76008
Holmes, Philip
1993
Cascades of homoclinic orbits to, and chaos near, a Hamiltonian saddle- center. Zbl 0749.58022
Mielke, A.; Holmes, P.; O’Reilly, O.
1992
Global existence theory for a generalized Ginzburg-Landau equation. Zbl 0783.35070
Duan, Jinqiao; Holmes, Philip; Titi, Edriss S.
1992
Energy minimization and the formation of microstructure in dynamic anti- plane shear. Zbl 0786.73066
Swart, Pieter J.; Holmes, Philip J.
1992
Heteroclinic cycles and modulated travelling waves in a system with $$D_ 4$$ symmetry. Zbl 0774.34031
Campbell, Sue Ann; Holmes, Philip
1992
Nonlinear, nonplanar and nonperiodic vibrations of a string. Zbl 0924.73127
O’Reilly, O.; Holmes, P. J.
1992
...and 82 more Documents
all top 5
#### Cited by 7,877 Authors
77 Holmes, Philip J. 55 Li, Jibin 48 Llibre, Jaume 43 Luo, Zhendong 37 Yu, Pei 34 Jing, Zhujun 33 Zhang, Weinian 29 Ashwin, Peter 27 Marsden, Jerrold Eldon 26 Chen, Guanrong 26 Knobloch, Edgar 25 Xu, Wei 24 Moehlis, Jeff 24 Rodríguez-Luis, Alejandro J. 23 Algaba, Antonio 23 Yagasaki, Kazuyuki 21 Haller, George 21 Rand, Richard H. 20 Fečkan, Michal 20 Han, Maoan 20 Luo, Albert C. J. 20 Volkwein, Stefan 20 Zhang, Wei 19 Champneys, Alan R. 19 Feichtinger, Gustav 19 Jiang, Weihua 18 Balasuriya, Sanjeeva 18 Kevrekidis, Ioannis George 18 Yang, Qigui 17 Guo, Boling 17 Lu, Qishao 17 Noack, Bernd R. 17 Stewart, Ian Nicholas 16 Golubitsky, Martin A. 16 Guckenheimer, John M. 16 Iliescu, Traian 16 M-Seara, Tere 16 Shen, Jianwei 16 Wiggins, Stephen 15 Aubry, Nadine 15 Buonomo, Bruno 15 Kühn, Christian 15 Kutz, J. Nathan 14 Broer, Henk W. 14 Brunton, Steven L. 14 Gardini, Laura 14 Krauskopf, Bernd 14 Kuznetsov, Yuri Alexandrovich 14 Rega, Giuseppe 14 Xie, Jianhua 14 Yorke, James Alan 13 Doelman, Arjen 13 Duan, Jinqiao 13 Guo, Shangjiang 13 Lacitignola, Deborah 13 Leung, Andrew Yee-Tak 13 Liu, Qian 13 Liu, Zhengrong 13 Lumley, John Leask 13 Wiercigroch, Marian 13 Wilson, Dan D. 12 Akhmet, Marat Ubaydulla 12 Awrejcewicz, Jan 12 Campbell, Sue Ann 12 Cao, Hongjun 12 Freire Macías, Emilio 12 Grebogi, Celso 12 Huseyin, Koncay 12 Kooi, Bob W. 12 Merino, Manuel 12 Navon, Ionel Michael 12 Piqueira, José Roberto Castilho 12 Rom-Kedar, Vered 12 Rowley, Clarence W. 12 Sapsis, Themistoklis P. 12 Xu, Jian 11 Battelli, Flaviano 11 Bi, Qinsheng 11 Bishop, Steven R. 11 Cao, Qingjie 11 Chen, Yushu 11 Gamero, Estanislao 11 Gao, Hongjun 11 Labouriau, Isabel S. 11 Lenci, Stefano 11 Mezić, Igor 11 Osinga, Hinke Maria 11 Proctor, Joshua L. 11 Rinaldi, Sergio 11 Teixeira, Marco Antonio 11 Vakakis, Alexander F. 11 Wirl, Franz 11 Zgliczyński, Piotr 10 Aihara, Kazuyuki 10 Blackmore, Denis L. 10 Bountis, Tassos C. 10 Chossat, Pascal 10 Govaerts, Willy J. F. 10 Jiang, Guirong 10 Kaper, Tasso J. ...and 7,777 more Authors
all top 5
#### Cited in 462 Serials
605 Physica D 389 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 328 Chaos, Solitons and Fractals 230 Nonlinear Dynamics 160 Journal of Differential Equations 155 Chaos 144 Journal of Fluid Mechanics 143 Applied Mathematics and Computation 119 Communications in Nonlinear Science and Numerical Simulation 92 Journal of Mathematical Analysis and Applications 88 Journal of Computational Physics 85 Physics Letters. A 85 Physics of Fluids 84 Journal of Nonlinear Science 61 SIAM Journal on Applied Dynamical Systems 60 Journal of Mathematical Biology 59 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 59 Applied Mathematics and Mechanics. (English Edition) 56 Journal of Computational and Applied Mathematics 54 Journal of Dynamics and Differential Equations 54 Nonlinear Analysis. Real World Applications 51 Computer Methods in Applied Mechanics and Engineering 49 Dynamics and Stability of Systems 48 Journal of Statistical Physics 44 Automatica 43 Mathematical and Computer Modelling 42 Biological Cybernetics 42 Communications in Mathematical Physics 40 Applied Mathematical Modelling 40 Nonlinear Analysis. Theory, Methods & Applications 39 Mathematical Biosciences 39 Journal of Economic Dynamics & Control 38 ZAMP. Zeitschrift für angewandte Mathematik und Physik 38 Journal of Theoretical Biology 37 Computers and Fluids 36 Journal of Mathematical Physics 35 Neural Computation 34 Computers & Mathematics with Applications 34 Mathematical Problems in Engineering 32 Bulletin of Mathematical Biology 31 Discrete and Continuous Dynamical Systems. Series B 31 Advances in Difference Equations 30 Regular and Chaotic Dynamics 29 Acta Mechanica 28 Systems & Control Letters 27 Archive for Rational Mechanics and Analysis 27 Journal of Computational Neuroscience 27 Discrete Dynamics in Nature and Society 25 Physica A 25 Acta Mathematicae Applicatae Sinica. English Series 25 Dynamical Systems 24 Transactions of the American Mathematical Society 23 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 22 Mathematics and Computers in Simulation 22 Meccanica 20 International Journal of Engineering Science 20 Mathematical Methods in the Applied Sciences 20 Theoretical and Computational Fluid Dynamics 20 Applied Mathematics Letters 19 Journal of Vibration and Control 18 Journal of the Franklin Institute 18 Nonlinearity 18 Studies in Applied Mathematics 18 Theoretical Population Biology 18 Acta Applicandae Mathematicae 17 International Journal for Numerical Methods in Fluids 17 Journal of Mathematical Psychology 17 Applied Numerical Mathematics 17 Abstract and Applied Analysis 16 International Journal for Numerical Methods in Engineering 16 European Journal of Mechanics. A. Solids 15 International Journal of Control 15 International Journal of Circuit Theory and Applications 15 Topology and its Applications 15 Ergodic Theory and Dynamical Systems 15 Journal of Difference Equations and Applications 15 European Journal of Mechanics. B. Fluids 15 Qualitative Theory of Dynamical Systems 13 Journal of the Mechanics and Physics of Solids 13 Physics Reports 13 Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM) 13 Celestial Mechanics and Dynamical Astronomy 12 International Journal of Theoretical Physics 12 Reports on Mathematical Physics 12 Journal of Economic Theory 12 Journal of Optimization Theory and Applications 12 The Journal of Mathematical Neuroscience 11 International Journal of Modern Physics B 11 Journal of Economics 11 International Journal of Robust and Nonlinear Control 11 SIAM Journal on Scientific Computing 11 Journal of Biological Dynamics 10 Wave Motion 10 Proceedings of the American Mathematical Society 10 Numerical Methods for Partial Differential Equations 10 Advances in Computational Mathematics 10 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 10 Acta Mechanica Sinica 10 Journal of Applied Analysis and Computation 9 Applicable Analysis ...and 362 more Serials
all top 5
#### Cited in 58 Fields
2,490 Dynamical systems and ergodic theory (37-XX) 2,002 Ordinary differential equations (34-XX) 898 Biology and other natural sciences (92-XX) 871 Fluid mechanics (76-XX) 829 Partial differential equations (35-XX) 801 Mechanics of particles and systems (70-XX) 548 Numerical analysis (65-XX) 436 Systems theory; control (93-XX) 390 Mechanics of deformable solids (74-XX) 242 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 136 Probability theory and stochastic processes (60-XX) 122 Computer science (68-XX) 121 Statistical mechanics, structure of matter (82-XX) 107 Calculus of variations and optimal control; optimization (49-XX) 100 Difference and functional equations (39-XX) 84 Information and communication theory, circuits (94-XX) 74 Optics, electromagnetic theory (78-XX) 74 Classical thermodynamics, heat transfer (80-XX) 74 Quantum theory (81-XX) 69 Global analysis, analysis on manifolds (58-XX) 66 Geophysics (86-XX) 63 Manifolds and cell complexes (57-XX) 57 Statistics (62-XX) 55 Operations research, mathematical programming (90-XX) 44 Operator theory (47-XX) 29 Differential geometry (53-XX) 27 General topology (54-XX) 23 Relativity and gravitational theory (83-XX) 21 Measure and integration (28-XX) 17 History and biography (01-XX) 17 Integral equations (45-XX) 12 Linear and multilinear algebra; matrix theory (15-XX) 12 Real functions (26-XX) 12 Approximations and expansions (41-XX) 11 Functional analysis (46-XX) 9 General and overarching topics; collections (00-XX) 9 Harmonic analysis on Euclidean spaces (42-XX) 9 Astronomy and astrophysics (85-XX) 7 Combinatorics (05-XX) 6 Topological groups, Lie groups (22-XX) 5 Mathematical logic and foundations (03-XX) 5 Number theory (11-XX) 5 Algebraic geometry (14-XX) 5 Sequences, series, summability (40-XX) 5 Algebraic topology (55-XX) 3 Field theory and polynomials (12-XX) 3 Commutative algebra (13-XX) 3 Functions of a complex variable (30-XX) 3 Several complex variables and analytic spaces (32-XX) 3 Special functions (33-XX) 3 Integral transforms, operational calculus (44-XX) 3 Mathematics education (97-XX) 2 Order, lattices, ordered algebraic structures (06-XX) 2 Category theory; homological algebra (18-XX) 2 Group theory and generalizations (20-XX) 2 Geometry (51-XX) 2 Convex and discrete geometry (52-XX) 1 Nonassociative rings and algebras (17-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.
| 2021-04-15T02:26:45 |
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5961035490036011, "perplexity": 11785.999818072407}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618038082988.39/warc/CC-MAIN-20210415005811-20210415035811-00142.warc.gz"}
|
https://par.nsf.gov/biblio/10335627-erratum-flux-based-modeling-heat-mass-transfer-multicomponent-systems-phys-fluids
|
This content will become publicly available on May 1, 2023
Erratum: “Flux-based modeling of heat and mass transfer in multicomponent systems” [Phys. Fluids 34 , 033113 (2022)]
Authors:
; ;
Award ID(s):
Publication Date:
NSF-PAR ID:
10335627
Journal Name:
Physics of Fluids
Volume:
34
Issue:
5
Page Range or eLocation-ID:
059905
ISSN:
1070-6631
1. Abstract We show that for some even $k\leqslant 3570$ and all $k$ with $442720643463713815200|k$, the equation $\phi (n)=\phi (n+k)$ has infinitely many solutions $n$, where $\phi$ is Euler’s totient function. We also show that for a positive proportion of all $k$, the equation $\sigma (n)=\sigma (n+k)$ has infinitely many solutions $n$. The proofs rely on recent progress on the prime $k$-tuples conjecture by Zhang, Maynard, Tao, and PolyMath.
2. A bstract We report the first measurement of the exclusive cross sections e + e − → $$B\overline{B}$$ B B ¯ , e + e − → $$B{\overline{B}}^{\ast }$$ B B ¯ ∗ , and e + e − → $${B}^{\ast }{\overline{B}}^{\ast }$$ B ∗ B ¯ ∗ in the energy range from 10 . 63 GeV to 11 . 02 GeV. The B mesons are fully reconstructed in a large number of hadronic final states and the three channels are identified using a beam-constrained-mass variable. The shapes of the exclusive cross sections showmore »
| 2022-08-17T23:30:44 |
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 5, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8403118252754211, "perplexity": 886.2862187830308}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882573118.26/warc/CC-MAIN-20220817213446-20220818003446-00522.warc.gz"}
|
https://par.nsf.gov/biblio/10309322-dart-adaptive-accept-reject-algorithm-non-linear-combinatorial-bandits
|
DART: Adaptive Accept Reject Algorithm for Non-Linear Combinatorial Bandits
We consider the bandit problem of selecting K out of N arms at each time step. The joint reward can be a non-linear function of the rewards of the selected individual arms. The direct use of a multi-armed bandit algorithm requires choosing among all possible combinations, making the action space large. To simplify the problem, existing works on combinatorial bandits typically assume feedback as a linear function of individual rewards. In this paper, we prove the lower bound for top-K subset selection with bandit feedback with possibly correlated rewards. We present a novel algorithm for the combinatorial setting without using individual arm feedback or requiring linearity of the reward function. Additionally, our algorithm works on correlated rewards of individual arms. Our algorithm, aDaptive Accept RejecT (DART), sequentially finds good arms and eliminates bad arms based on confidence bounds. DART is computationally efficient and uses storage linear in N. Further, DART achieves a regret bound of Õ(K√KNT) for a time horizon T, which matches the lower bound in bandit feedback up to a factor of √log 2NT. When applied to the problem of cross-selling optimization and maximizing the mean of individual rewards, the performance of the proposed algorithm surpasses that of more »
Authors:
; ; ;
Award ID(s):
Publication Date:
NSF-PAR ID:
10309322
Journal Name:
Proceedings of the AAAI Conference on Artificial Intelligence
ISSN:
2159-5399
Many real-world problems like Social Influence Maximization face the dilemma of choosing the best $K$ out of $N$ options at a given time instant. This setup can be modeled as a combinatorial bandit which chooses $K$ out of $N$ arms at each time, with an aim to achieve an efficient trade-off between exploration and exploitation. This is the first work for combinatorial bandits where the feedback received can be a non-linear function of the chosen $K$ arms. The direct use of multi-armed bandit requires choosing among $N$-choose-$K$ options making the state space large. In this paper, we present a novelmore »
| 2022-08-15T15:41:23 |
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|
http://legisquebec.gouv.qc.ca/en/showversion/cr/M-22.1,%20r.%202?code=se:3&pointInTime=20200217
|
M-22.1, r. 2 - Regulation respecting the signing of certain documents of the Ministère des Affaires municipales, des Régions et de l’Occupation du territoire
3. Subparagraphs b and c of paragraph 2.1 of section 2 do not have the effect of authorizing the signatory to exercise the powers mentioned in the third paragraph of subsection 3 of section 28 and in the third paragraph of section 29.3 of the Cities and Towns Act (chapter C-19) nor the powers mentioned in the third paragraph of section 9 and in the second paragraph of section 14.1 of the Municipal Code of Québec (chapter C-27.1).
O.C. 589-2000, s. 3; O.C. 1129-2000, s. 2; O.C. 796-2006, s. 2.
| 2020-04-07T06:24:53 |
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|
https://mooseframework.inl.gov/source/userobjects/PorousFlowCapillaryPressureVG.html
|
# PorousFlowCapillaryPressureVG
van Genuchten capillary pressure
van Genuchten's capillary-pressure relationship (Genuchten, 1980)
(1) or (2)
The effective saturation has been denoted by and is the porepressure, which is the negative of the capillary pressure: . Here and are user-defined parameters. The parameter must satisfy (3)
By default, a logarithmic extension for low liquid phase saturations is implemented. This can be disabled by setting log_extension = false.
## Input Parameters
• alphavan Genuchten parameter alpha. Must be positive
C++ Type:double
Options:
Description:van Genuchten parameter alpha. Must be positive
• mvan Genuchten exponent m. Must be between 0 and 1, and optimally should be set to >0.5
C++ Type:double
Options:
Description:van Genuchten exponent m. Must be between 0 and 1, and optimally should be set to >0.5
### Required Parameters
• pc_max1e+09Maximum capillary pressure (Pa). Must be > 0. Default is 1e9
Default:1e+09
C++ Type:double
Options:
Description:Maximum capillary pressure (Pa). Must be > 0. Default is 1e9
• sat_lr0Liquid residual saturation. Must be between 0 and 1. Default is 0
Default:0
C++ Type:double
Options:
Description:Liquid residual saturation. Must be between 0 and 1. Default is 0
• log_extensionTrueUse a logarithmic extension for low saturation to avoid capillary pressure going to infinity. Default is true. Set to false if your capillary pressure depends on spatially-dependent variables other than saturation, as the log-extension C++ code for this case has yet to be implemented
Default:True
C++ Type:bool
Options:
Description:Use a logarithmic extension for low saturation to avoid capillary pressure going to infinity. Default is true. Set to false if your capillary pressure depends on spatially-dependent variables other than saturation, as the log-extension C++ code for this case has yet to be implemented
• blockThe list of block ids (SubdomainID) that this object will be applied
C++ Type:std::vector
Options:
Description:The list of block ids (SubdomainID) that this object will be applied
• s_scale1CapillaryPressure = f(Seff * s_scale) - f(s_scale), where f is the van Genuchten expression. Setting s_scale<1 is unusual but sometimes helps fully saturated, 2-phase PP simulations converge as the zero derivative (1/f'(S=1)=0) is removed
Default:1
C++ Type:double
Options:
Description:CapillaryPressure = f(Seff * s_scale) - f(s_scale), where f is the van Genuchten expression. Setting s_scale<1 is unusual but sometimes helps fully saturated, 2-phase PP simulations converge as the zero derivative (1/f'(S=1)=0) is removed
### Optional Parameters
• enableTrueSet the enabled status of the MooseObject.
Default:True
C++ Type:bool
Options:
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
Options:
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_meshFalseWhether 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:False
C++ Type:bool
Options:
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Description:Adds user-defined labels for accessing object parameters via control logic.
• seed0The seed for the master random number generator
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Description:The seed for the master random number generator
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| 2019-04-24T14:44:06 |
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http://dlmf.nist.gov/9.11
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§9.11 Products
§9.11(i) Differential Equation
9.11.1 $\frac{{\mathrm{d}}^{3}w}{{\mathrm{d}z}^{3}}-4z\frac{\mathrm{d}w}{\mathrm{d}z}-% 2w=0,$ $w=w_{1}w_{2}$,
where $w_{1}$ and $w_{2}$ are any solutions of (9.2.1). For example, $w={\mathrm{Ai}^{2}}\left(z\right)$, $\mathrm{Ai}\left(z\right)\mathrm{Bi}\left(z\right)$, $\mathrm{Ai}\left(z\right)\mathrm{Ai}\left(ze^{\mp 2\pi i/3}\right)$, ${M^{2}}\left(z\right)$. Numerically satisfactory triads of solutions can be constructed where needed on $\mathbb{R}$ or $\mathbb{C}$ by inspection of the asymptotic expansions supplied in §9.7.
§9.11(ii) Wronskian
9.11.2 $\mathscr{W}\left\{{\mathrm{Ai}^{2}}\left(z\right),\mathrm{Ai}\left(z\right)% \mathrm{Bi}\left(z\right),{\mathrm{Bi}^{2}}\left(z\right)\right\}=2\pi^{-3}.$
§9.11(iii) Integral Representations
9.11.3 ${\mathrm{Ai}^{2}}\left(x\right)=\frac{1}{4\pi\sqrt{3}}\int_{0}^{\infty}J_{0}% \left(\tfrac{1}{12}t^{3}+xt\right)t\mathrm{d}t,$ $x\geq 0$, ⓘ Symbols: $\mathrm{Ai}\left(\NVar{z}\right)$: Airy function, $J_{\NVar{\nu}}\left(\NVar{z}\right)$: Bessel function of the first kind, $\pi$: the ratio of the circumference of a circle to its diameter, $\mathrm{d}\NVar{x}$: differential of $x$, $\int$: integral and $x$: real variable Source: Lebedev (1965, Problem 22, p. 142) Referenced by: §9.5(i) Permalink: http://dlmf.nist.gov/9.11.E3 Encodings: TeX, pMML, png See also: Annotations for 9.11(iii), 9.11 and 9
where $J_{0}$ is the Bessel function (§10.2(ii)).
9.11.4 ${\mathrm{Ai}^{2}}\left(z\right)+{\mathrm{Bi}^{2}}\left(z\right)=\frac{1}{\pi^{% 3/2}}\int_{0}^{\infty}\exp\left(zt-\tfrac{1}{12}t^{3}\right)t^{-1/2}\mathrm{d}t.$ ⓘ Symbols: $\mathrm{Ai}\left(\NVar{z}\right)$: Airy function, $\mathrm{Bi}\left(\NVar{z}\right)$: Airy function, $\pi$: the ratio of the circumference of a circle to its diameter, $\mathrm{d}\NVar{x}$: differential of $x$, $\exp\NVar{z}$: exponential function, $\int$: integral and $z$: complex variable Source: Muldoon (1977, p. 32, extended to complex $z$ by analytic continuation) Referenced by: §9.5(ii) Permalink: http://dlmf.nist.gov/9.11.E4 Encodings: TeX, pMML, png See also: Annotations for 9.11(iii), 9.11 and 9
For an integral representation of the Dirac delta involving a product of two $\mathrm{Ai}$ functions see §1.17(ii).
For further integral representations see Reid (1995, 1997a, 1997b).
§9.11(iv) Indefinite Integrals
Let $w_{1},w_{2}$ be any solutions of (9.2.1), not necessarily distinct. Then
9.11.5 $\int w_{1}w_{2}\mathrm{d}z=-w^{\prime}_{1}w^{\prime}_{2}+zw_{1}w_{2},$ ⓘ Symbols: $\mathrm{d}\NVar{x}$: differential of $x$, $\int$: integral, $z$: complex variable and $w$: function Source: Albright (1977, (A.16)) Permalink: http://dlmf.nist.gov/9.11.E5 Encodings: TeX, pMML, png See also: Annotations for 9.11(iv), 9.11 and 9
9.11.6 $\int w_{1}w^{\prime}_{2}\mathrm{d}z=\tfrac{1}{2}\left(w_{1}w_{2}+z\mathscr{W}% \left\{w_{1},w_{2}\right\}\right),$ ⓘ Symbols: $\mathscr{W}$: Wronskian, $\mathrm{d}\NVar{x}$: differential of $x$, $\int$: integral, $z$: complex variable and $w$: function Source: Albright (1977, (A.17)) Permalink: http://dlmf.nist.gov/9.11.E6 Encodings: TeX, pMML, png See also: Annotations for 9.11(iv), 9.11 and 9
9.11.7 $\int w^{\prime}_{1}w^{\prime}_{2}\mathrm{d}z=\tfrac{1}{3}(w_{1}w^{\prime}_{2}+% w^{\prime}_{1}w_{2}+zw^{\prime}_{1}w^{\prime}_{2}-z^{2}w_{1}w_{2}),$ ⓘ Symbols: $\mathrm{d}\NVar{x}$: differential of $x$, $\int$: integral, $z$: complex variable and $w$: function Source: Albright (1977, (A.18)) Permalink: http://dlmf.nist.gov/9.11.E7 Encodings: TeX, pMML, png See also: Annotations for 9.11(iv), 9.11 and 9
9.11.8 $\int zw_{1}w_{2}\mathrm{d}z=\tfrac{1}{6}(w_{1}w^{\prime}_{2}+w^{\prime}_{1}w_{% 2})-\tfrac{1}{3}(zw^{\prime}_{1}w^{\prime}_{2}-z^{2}w_{1}w_{2}),$ ⓘ Symbols: $\mathrm{d}\NVar{x}$: differential of $x$, $\int$: integral, $z$: complex variable and $w$: function Source: Albright (1977, (A.19)) Permalink: http://dlmf.nist.gov/9.11.E8 Encodings: TeX, pMML, png See also: Annotations for 9.11(iv), 9.11 and 9
9.11.9 $\int zw_{1}w^{\prime}_{2}\mathrm{d}z=\tfrac{1}{2}w^{\prime}_{1}w^{\prime}_{2}+% \tfrac{1}{4}z^{2}\mathscr{W}\left\{w_{1},w_{2}\right\},$ ⓘ Symbols: $\mathscr{W}$: Wronskian, $\mathrm{d}\NVar{x}$: differential of $x$, $\int$: integral, $z$: complex variable and $w$: function Source: Albright (1977, (A.20)) Permalink: http://dlmf.nist.gov/9.11.E9 Encodings: TeX, pMML, png See also: Annotations for 9.11(iv), 9.11 and 9
9.11.10 $\int zw^{\prime}_{1}w^{\prime}_{2}\mathrm{d}z=\tfrac{3}{10}(-w_{1}w_{2}+zw_{1}% w^{\prime}_{2}+zw^{\prime}_{1}w_{2})+\tfrac{1}{5}(z^{2}w^{\prime}_{1}w^{\prime% }_{2}-z^{3}w_{1}w_{2}).$ ⓘ Symbols: $\mathrm{d}\NVar{x}$: differential of $x$, $\int$: integral, $z$: complex variable and $w$: function Source: Albright (1977, (A.21)) Permalink: http://dlmf.nist.gov/9.11.E10 Encodings: TeX, pMML, png See also: Annotations for 9.11(iv), 9.11 and 9
For $\int z^{n}w_{1}w_{2}\mathrm{d}z$, $\int z^{n}w_{1}w^{\prime}_{2}\mathrm{d}z$, $\int z^{n}w^{\prime}_{1}w^{\prime}_{2}\mathrm{d}z$, where $n$ is any positive integer, see Albright (1977). For related integrals see Gordon (1969, Appendix B).
For any continuously-differentiable function $f$
9.11.11 $\int\frac{1}{w_{1}^{2}}f^{\prime}\!\left(\frac{w_{2}}{w_{1}}\right)\mathrm{d}z% =\frac{1}{\mathscr{W}\left\{w_{1},w_{2}\right\}}f\!\left(\frac{w_{2}}{w_{1}}% \right).$ ⓘ Symbols: $\mathscr{W}$: Wronskian, $\mathrm{d}\NVar{x}$: differential of $x$, $\int$: integral, $z$: complex variable, $w$: function and $f$: function Source: Albright and Gavathas (1986, p. 2664) Permalink: http://dlmf.nist.gov/9.11.E11 Encodings: TeX, pMML, png See also: Annotations for 9.11(iv), 9.11 and 9
Examples
9.11.12 $\displaystyle\int\frac{\mathrm{d}z}{{\mathrm{Ai}^{2}}\left(z\right)}$ $\displaystyle=\pi\frac{\mathrm{Bi}\left(z\right)}{\mathrm{Ai}\left(z\right)},$ 9.11.13 $\displaystyle\int\frac{\mathrm{d}z}{\mathrm{Ai}\left(z\right)\mathrm{Bi}\left(% z\right)}$ $\displaystyle=\pi\ln\left(\frac{\mathrm{Bi}\left(z\right)}{\mathrm{Ai}\left(z% \right)}\right),$ 9.11.14 $\displaystyle\int\frac{\mathrm{Ai}\left(z\right)\mathrm{Bi}\left(z\right)}{% \left({\mathrm{Ai}^{2}}\left(z\right)+{\mathrm{Bi}^{2}}\left(z\right)\right)^{% 2}}\mathrm{d}z$ $\displaystyle=\frac{\pi}{2}\frac{{\mathrm{Bi}^{2}}\left(z\right)}{{\mathrm{Ai}% ^{2}}\left(z\right)+{\mathrm{Bi}^{2}}\left(z\right)}.$
§9.11(v) Definite Integrals
9.11.15 $\int_{0}^{\infty}t^{\alpha-1}{\mathrm{Ai}^{2}}\left(t\right)\mathrm{d}t=\frac{% 2\Gamma\left(\alpha\right)}{\pi^{1/2}12^{(2\alpha+5)/6}\Gamma\left(\frac{1}{3}% \alpha+\frac{5}{6}\right)},$ $\Re\alpha>0$.
9.11.16 $\displaystyle\int_{-\infty}^{\infty}{\mathrm{Ai}^{3}}\left(t\right)\mathrm{d}t$ $\displaystyle=\frac{{\Gamma^{2}}\left(\frac{1}{3}\right)}{4\pi^{2}},$ 9.11.17 $\displaystyle\int_{-\infty}^{\infty}{\mathrm{Ai}^{2}}\left(t\right)\mathrm{Bi}% \left(t\right)\mathrm{d}t$ $\displaystyle=\frac{{\Gamma^{2}}\left(\frac{1}{3}\right)}{4\sqrt{3}\pi^{2}}.$ 9.11.18 $\displaystyle\int_{0}^{\infty}{\mathrm{Ai}^{4}}\left(t\right)\mathrm{d}t$ $\displaystyle=\frac{\ln 3}{24\pi^{2}}.$
9.11.19 $\int_{0}^{\infty}\frac{\mathrm{d}t}{{\mathrm{Ai}^{2}}\left(t\right)+{\mathrm{% Bi}^{2}}\left(t\right)}=\int_{0}^{\infty}\frac{t\mathrm{d}t}{{\mathrm{Ai}'^{2}% }\left(t\right)+{\mathrm{Bi}'^{2}}\left(t\right)}=\frac{\pi^{2}}{6}.$ ⓘ Symbols: $\mathrm{Ai}\left(\NVar{z}\right)$: Airy function, $\mathrm{Bi}\left(\NVar{z}\right)$: Airy function, $\pi$: the ratio of the circumference of a circle to its diameter, $\mathrm{d}\NVar{x}$: differential of $x$, $\int$: integral, $M\left(\NVar{z}\right)$: Airy modulus function, $N\left(\NVar{z}\right)$: Airy modulus function, $\phi\left(\NVar{z}\right)$: Airy phase function, $\theta\left(\NVar{z}\right)$: Airy phase function and $x$: real variable Source: Extend the definitions of §9.8(i) to positive values of $x$, obtain the indefinite integrals of $1/{M^{2}}\left(x\right)$ and $x/{N^{2}}\left(x\right)$ via the first two of (9.8.14), then combine the values of $\theta\left(0\right)$ and $\phi\left(0\right)$ given in §9.8(i) with $\theta\left(+\infty\right)=\phi\left(+\infty\right)=0$ obtained from (9.8.4), (9.8.8), and §9.7(ii). (Communicated by M.E. Muldoon.) Permalink: http://dlmf.nist.gov/9.11.E19 Encodings: TeX, pMML, png See also: Annotations for 9.11(v), 9.11 and 9
For further definite integrals see Prudnikov et al. (1990, §1.8.2), Laurenzi (1993), Reid (1995, 1997a, 1997b), and Vallée and Soares (2010, Chapters 3, 4).
| 2018-01-21T14:37:52 |
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http://xxx.lanl.gov/abs/astro-ph/9807091
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astro-ph
(what is this?)
# Title: Investigating the Dark Matter Distribution with NGST
Authors: Peter Schneider (MPA, Garching), Jean-Paul Kneib (OMP, Toulouse)
Abstract: The developments summarized with the name weak gravitational lensing'' have led to exciting possibilities to study the (statistical properties of the) dark matter distribution in the Universe. Concentrating on those aspects which require deep wide-field imaging surveys, we describe the basic principles of weak lensing and discuss its future applications in view of NGST (a) to determine the statistical properties of the dark matter halos of individual galaxies, (b) to determine the mass and the mass profile of very low-mass clusters and groups at medium redshift and/or of more massive clusters at very high redshift, and (c) to measure the power spectrum of the matter distribution in the Universe in the non-linear regime, thereby also obtaining a mass-selected sample of halos and providing a means to investigate the scale- and redshift dependence of the bias `factor'.
Comments: To appear in ESA conference Proceedings of the "Workshop on the Next Generation of Space Telescope: Science Drivers & Technical Challenges" Liege, Belgium June 15-18, 1998 Subjects: Astrophysics (astro-ph) Cite as: arXiv:astro-ph/9807091 (or arXiv:astro-ph/9807091v1 for this version)
## Submission history
From: Kneib Jean-Paul [view email]
[v1] Thu, 9 Jul 1998 10:14:21 GMT (428kb)
| 2014-04-24T00:22:30 |
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https://zbmath.org/authors/?q=ai%3Ahochbaum.dorit-s
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# zbMATH — the first resource for mathematics
## Hochbaum, Dorit S.
Compute Distance To:
Author ID: hochbaum.dorit-s Published as: Hochbaum, D. S.; Hochbaum, Dorit; Hochbaum, Dorit S. External Links: MGP · Wikidata · GND
Documents Indexed: 121 Publications since 1980, including 2 Books
all top 5
#### Co-Authors
29 single-authored 10 Levin, Asaf 8 Shmoys, David B. 7 Goldschmidt, Olivier 5 Shamir, Ron 4 Ahuja, Ravindra K. 4 Orlin, James B. 4 Pathria, Anu 3 Landy, Dan 3 Maass, Wolfgang 3 Moreno-Centeno, Erick 3 Naor, Joseph Seffi 3 Rao, Xu 3 Velednitsky, Mark 2 Chang, Minjun 2 Chudak, Fabián A. 2 Cosares, Steven 2 Fisher, Marshall L. 2 Garg, Naveen Kumar 2 Hall, Nicholas G. 2 Hong, Sung-Pil 2 Lu, Cheng 2 Lyu, Cheng 2 Olinick, Eli V. 2 Queyranne, Maurice 2 Shanthikumar, Jeyaveerasingam George 2 Spaen, Quico 2 Yu, Gang 1 Adams, Joseph Brian 1 Alon, Noga M. 1 Atamtürk, Alper 1 Baumann, Pierre 1 Bertelli, Erik 1 Catena, Rodolfo A. 1 Chandran, Bala G. 1 Cui, Tingting 1 Feo, Thomas A. 1 Fishbain, Barak 1 Goemans, Michel X. 1 Hurkens, Cor A. J. 1 Jansen, Klaus 1 Liu, Sheng 1 Megiddo, Nimrod 1 Nishizeki, Takao 1 Ordóñez, Fernando 1 Qranfal, Joe 1 Rolim, José D. P. 1 Segev, Arie 1 Seshadri, Sridhar 1 Sinclair, Alistair 1 Steele, J. Michael 1 Tamir, Arie 1 Tanoh, Germain 1 Tucker, Paul A. 1 Wagner, Michael R. 1 Wigderson, Edna 1 Williamson, David P. 1 Woeginger, Gerhard Johannes 1 Yang, Yatao 1 Yelland, Phillip
all top 5
#### Serials
13 Operations Research 10 Networks 9 Discrete Applied Mathematics 8 Operations Research Letters 7 European Journal of Operational Research 5 Mathematics of Operations Research 4 Journal of Algorithms 4 SIAM Journal on Discrete Mathematics 4 SIAM Journal on Optimization 3 Information Processing Letters 3 Journal of the Association for Computing Machinery 3 SIAM Journal on Computing 3 SIAM Journal on Algebraic and Discrete Methods 3 Annals of Operations Research 3 Mathematical Programming. Series A. Series B 2 Management Science 2 Algorithmica 1 Acta Informatica 1 Advances in Applied Probability 1 Mathematical Programming 1 Naval Research Logistics 1 Theoretical Computer Science 1 Linear Algebra and its Applications 1 INFORMS Journal on Computing 1 Theory of Computing Systems 1 Optimization Methods & Software 1 Journal of the ACM 1 4OR 1 Discrete Optimization 1 Lecture Notes in Computer Science 1 Algorithmic Operations Research 1 Optimization Letters 1 Numerical Mathematics: Theory, Methods and Applications 1 ACM Transactions on Algorithms 1 EURO Journal on Computational Optimization
all top 5
#### Fields
91 Operations research, mathematical programming (90-XX) 53 Computer science (68-XX) 26 Combinatorics (05-XX) 6 Numerical analysis (65-XX) 5 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 4 Statistics (62-XX) 3 Convex and discrete geometry (52-XX) 3 Biology and other natural sciences (92-XX) 3 Information and communication theory, circuits (94-XX) 2 General and overarching topics; collections (00-XX) 1 Number theory (11-XX) 1 Probability theory and stochastic processes (60-XX)
#### Citations contained in zbMATH Open
96 Publications have been cited 1,665 times in 1,388 Documents Cited by Year
Approximation algorithms for NP-hard problems. Zbl 1368.68010
Hochbaum, Dorit S. (ed.)
1996
Approximation schemes for covering and packing problems in image processing and VLSI. Zbl 0633.68027
Hochbaum, Dorit S.; Maass, Wolfgang
1985
Approximation algorithms for the set covering and vertex cover problems. Zbl 0486.68067
Hochbaum, Dorit S.
1982
A best possible heuristic for the k-center problem. Zbl 0565.90015
Hochbaum, Dorit S.; Shmoys, David B.
1985
A polynomial approximation scheme for scheduling on uniform processors: Using the dual approximation approach. Zbl 0647.68040
Hochbaum, Dorit S.; Shmoys, David B.
1988
Convex separable optimization is not much harder than linear optimization. Zbl 0721.90060
Hochbaum, Dorit S.; Shanthikumar, J. George
1990
Efficient bounds for the stable set, vertex cover and set packing problems. Zbl 0523.05055
Hochbaum, Dorit S.
1983
A polynomial algorithm for the $$k$$-cut problem for fixed $$k$$. Zbl 0809.90125
Goldschmidt, Olivier; Hochbaum, Dorit S.
1994
Scheduling semiconductor burn-in operations to minimize total flowtime. Zbl 0895.90116
Hochbaum, Dorit S.; Landy, Dan
1997
Simple and fast algorithms for linear and integer programs with two variables per inequality. Zbl 0831.90089
Hochbaum, Dorit S.; Naor, Joseph
1994
Heuristics for the fixed cost median problem. Zbl 0473.90029
Hochbaum, Dorit S.
1982
Lower and upper bounds for the allocation problem and other nonlinear optimization problems. Zbl 0820.90082
Hochbaum, Dorit S.
1994
Tight bounds and 2-approximation algorithms for integer programs with two variables per inequality. Zbl 0802.90080
Hochbaum, Dorit S.; Megiddo, Nimrod; Naor, Joseph; Tamir, Arie
1993
A nonlinear knapsack problem. Zbl 0838.90092
Hochbaum, Dorit S.
1995
About strongly polynomial time algorithms for quadratic optimization over submodular constraints. Zbl 0844.90061
Hochbaum, Dorit S.; Hong, Sung-Pil
1995
Strongly polynomial algorithms for the high multiplicity scheduling problem. Zbl 0736.90043
Hochbaum, Dorit S.; Shamir, Ron
1991
A primal-dual interpretation of two 2-approximation algorithms for the feedback vertex set problem in undirected graphs. Zbl 0920.90137
Chudak, Fabián A.; Goemans, Michel X.; Hochbaum, Dorit S.; Williamson, David P.
1998
A fast approximation algorithm for the multicovering problem. Zbl 0602.90110
Hall, Nicholas G.; Hochbaum, Dorit S.
1986
An efficient algorithm for image segmentation, Markov random fields and related problems. Zbl 1127.68474
Hochbaum, Dorit S.
2001
Approximating clique and biclique problems. Zbl 0919.68056
Hochbaum, Dorit S.
1998
The pseudoflow algorithm: A new algorithm for the maximum-flow problem. Zbl 1167.90394
Hochbaum, Dorit S.
2008
Scheduling with batching: Minimizing the weighted number of tardy jobs. Zbl 0820.90052
Hochbaum, Dorit S.; Landy, Dan
1994
Database location in computer networks. Zbl 0445.68071
Fisher, Marshall L.; Hochbaum, Dorit S.
1980
Solving the convex cost integer dual network flow problem. Zbl 1232.90317
Ahuja, Ravindra K.; Hochbaum, Dorit S.; Orlin, James B.
2003
Efficient algorithms for the inverse spanning-tree problem. Zbl 1165.90658
Hochbaum, Dorit S.
2003
Capacity acquisition, subcontracting, and lot sizing. Zbl 1232.90008
Atamtürk, Alper; Hochbaum, Dorit S.
2001
Analysis of the greedy approach in problems of maximum $$k$$-coverage. Zbl 0938.90026
Hochbaum, Dorit S.; Pathria, Anu
1998
Analysis of a flow problem with fixed charges. Zbl 0673.90035
Hochbaum, Dorit S.; Segev, Arie
1989
Minimizing the number of tardy job units under release time constraints. Zbl 0707.90049
Hochbaum, Dorit S.; Shamir, Ron
1990
An algorithm for the detection and construction of Monge sequences. Zbl 0666.65044
Alon, Noga; Cosares, Steven; Hochbaum, Dorit S.; Shamir, Ron
1989
The SONET edge-partition problem. Zbl 1026.90076
Goldschmidt, Olivier; Hochbaum, Dorit S.; Levin, Asaf; Olinick, Eli V.
2003
A half-integral linear programming relaxation for scheduling precedence-constrained jobs on a single machine. Zbl 0958.90042
Chudak, Fabián A.; Hochbaum, Dorit S.
1999
Strongly polynomial algorithms for the quadratic transportation problem with a fixed number of sources. Zbl 0802.90073
Cosares, Steven; Hochbaum, Dorit S.
1994
Minimizing a convex Cost closure set. Zbl 1041.68070
Hochbaum, Dorit S.; Queyranne, Maurice
2003
Solving integer programs over monotone inequalities in three variables: A framework for half integrality and good approximations. Zbl 1001.90050
Hochbaum, Dorit S.
2002
Complexity and algorithms for nonlinear optimization problems. Zbl 1159.90485
Hochbaum, Dorit S.
2007
Cyclical scheduling and multi-shift scheduling: complexity and approximation algorithms. Zbl 1112.90023
Hochbaum, Dorit S.; Levin, Asaf
2006
Fast approximation algorithms for a nonconvex covering problem. Zbl 0636.68082
Hochbaum, Dorit S.; Maass, Wolfgang
1987
Probabilistic analysis of the planar K-median problem. Zbl 0435.90057
Fisher, M. L.; Hochbaum, D. S.
1980
A polynomial algorithm for an integer quadratic non-separable transportation problem. Zbl 0761.90061
Hochbaum, Dorit S.; Shamir, Ron; Shanthikumar, J. George
1992
The $$t$$-vertex cover problem: Extending the half integrality framework with budget constraints. Zbl 0908.90213
Hochbaum, Dorit S.
1998
A modified greedy heuristic for the set covering problem with improved worst case bound. Zbl 0811.68099
Goldschmidt, Olivier; Hochbaum, Dorit S.; Yu, Gang
1993
A computational study of the pseudoflow and push-relabel algorithms for the maximum flow problem. Zbl 1181.90271
Chandran, Bala G.; Hochbaum, Dorit S.
2009
Complexity and algorithms for convex network optimization and other nonlinear problems. Zbl 1099.90059
Hochbaum, Dorit S.
2005
$$k$$-edge subgraph problems. Zbl 0870.68111
Goldschmidt, Olivier; Hochbaum, Dorit S.
1997
A better than ”best possible” algorithm to edge color multigraphs. Zbl 0594.68041
Hochbaum, Dorit S.; Nishizeki, Takao; Shmoys, David B.
1986
An O$$(\log k)$$-approximation algorithm for the $$k$$ minimum spanning tree problem in the plane. Zbl 0866.68076
Garg, N.; Hochbaum, D. S.
1997
A new-old algorithm for minimum-cut and maximum-flow in closure graphs. Zbl 1044.90083
Hochbaum, Dorit S.
2001
An $$O(n \log^ 2\,n)$$ algorithm for the maximum weighted tardiness problem. Zbl 0672.68011
Hochbaum, Dorit S.; Shamir, Ron
1989
Optimizing over consecutive 1’s and circular 1’s constraints. Zbl 1165.90607
Hochbaum, Dorit S.; Levin, Asaf
2006
A cut-based algorithm for the nonlinear dual of the minimum cost network flow problem. Zbl 1134.90512
Ahuja, Ravindra K.; Hochbaum, Dorit S.; Orlin, James B.
2004
Monotonizing linear programs with up to two nonzeroes per column. Zbl 1056.90105
Hochbaum, Dorit S.
2004
Generalized $$p$$-center problems: Complexity results and approximation algorithms. Zbl 0918.90098
Hochbaum, Dorit S.; Pathria, Anu
1997
Solving linear cost dynamic lot-sizing problems in $$O(n \log n)$$ time. Zbl 1167.90307
Ahuja, Ravindra K.; Hochbaum, Dorit S.
2008
Solving the convex cost integer dual network flow problem. Zbl 0948.90116
Ahuja, Ravindra K.; Hochbaum, Dorit S.; Orlin, James B.
1999
Approximation algorithms for the $$k$$-clique covering problem. Zbl 0857.05086
Goldschmidt, Olivier; Hochbaum, Dorit S.; Hurkens, Cor; Yu, Gang
1996
Steinhaus’s geometric location problem for random samples in the plane. Zbl 0501.60040
Hochbaum, Dorit; Steele, J. Michael
1982
A polynomial time algorithm for Rayleigh ratio on discrete variables: replacing spectral techniques for expander ratio, normalized cut, and Cheeger constant. Zbl 1267.90149
Hochbaum, Dorit S.
2013
Instant recognition of half integrality and 2-approximations. Zbl 0911.90261
Hochbaum, Dorit S.
1998
Why should biconnected components be identified first. Zbl 0789.90084
Hochbaum, Dorit S.
1993
An $$O(| V| ^ 2)$$ algorithm for the planar 3-cut problem. Zbl 0572.05040
Hochbaum, Dorit S.; Shmoys, David B.
1985
On the fractional solution to the set covering problem. Zbl 0518.90055
Hochbaum, Dorit S.
1983
Security routing games with multivehicle Chinese postman problem. Zbl 1390.90167
Hochbaum, Dorit S.; Lyu, Cheng; Ordóñez, Fernando
2014
Nuclear threat detection with mobile distributed sensor networks. Zbl 1225.90016
Hochbaum, Dorit S.; Fishbain, Barak
2011
Complexity of some inverse shortest path lengths problems. Zbl 1208.05141
Cui, Tingting; Hochbaum, Dorit S.
2010
The bounded cycle-cover problem. Zbl 1238.90131
Hochbaum, Dorit S.; Olinick, Eli V.
2001
A linear-time algorithm for the bottleneck transportation problem with a fixed number of sources. Zbl 0956.90019
Hochbaum, Dorit S.; Woeginger, Gerhard J.
1999
The bottleneck graph partition problem. Zbl 0873.90102
Hochbaum, Dorit S.; Pathria, Anu
1996
On the complexity of the production-transportation problem. Zbl 0845.90087
Hochbaum, Dorit S.; Hong, Sung-Pil
1996
An $$O(\log k)$$ approximation algorithm for the $$k$$ minimum spanning tree problem in the plane. Zbl 1344.68285
Garg, Naveen; Hochbaum, Dorit S.
1994
A polynomial approximation scheme for machine scheduling on uniform processors: Using the dual approximation approach. Zbl 0623.68033
Hochbaum, Dorit S.; Shmoys, David B.
1986
Easy solutions for the K-center problem or the dominating set problem on random graphs. Zbl 0562.68029
Hochbaum, Dorit S.
1985
Evaluating performance of image segmentation criteria and techniques. Zbl 1307.90006
Hochbaum, Dorit S.; Lyu, Cheng; Bertelli, Erik
2013
Multi-label Markov random fields as an efficient and effective tool for image segmentation, total variations and regularization. Zbl 1289.68201
Hochbaum, Dorit S.
2013
The pseudoflow algorithm and the pseudoflow-based simplex for the maximum flow problem. Zbl 0911.90154
Hochbaum, Dorit S.
1998
Scheduling with batching: Two job types. Zbl 0873.90050
Hochbaum, Dorit S.; Landy, Dan
1997
The multicovering problem. Zbl 0759.90072
Hall, Nicholas G.; Hochbaum, Dorit S.
1992
Best possible heuristics for the bottleneck wandering salesperson and bottleneck vehicle routing problem. Zbl 0596.90093
Hochbaum, Dorit S.; Shmoys, David B.
1986
When are NP-hard location problems easy? Zbl 0671.90019
Hochbaum, Dorit S.
1984
Approximation schemes for covering and packing problems in robotics and VLSI. Zbl 0557.68035
Hochbaum, Dorit S.; Maass, Wolfgang
1984
The replenishment schedule to minimize peak storage problem: the gap between the continuous and discrete versions of the problem. Zbl 1444.90014
Hochbaum, Dorit S.; Rao, Xu
2019
Algorithms and complexity of range clustering. Zbl 1416.62341
Hochbaum, Dorit S.
2019
A comparative study of the leading machine learning techniques and two new optimization algorithms. Zbl 1403.90560
Baumann, P.; Hochbaum, D. S.; Yang, Y. T.
2019
A faster algorithm solving a generalization of isotonic median regression and a class of fused Lasso problems. Zbl 1383.90009
Hochbaum, Dorit S.; Lu, Cheng
2017
Approximation algorithms for a minimization variant of the order-preserving submatrices and for biclustering problems. Zbl 1301.68273
Hochbaum, Dorit S.; Levin, Asaf
2013
Simplifications and speedups of the pseudoflow algorithm. Zbl 1269.90129
Hochbaum, Dorit S.; Orlin, James B.
2013
Rating customers according to their promptness to adopt new products. Zbl 1233.90204
Hochbaum, Dorit S.; Moreno-Centeno, Erick; Yelland, Phillip; Catena, Rodolfo A.
2011
How to allocate review tasks for robust ranking. Zbl 1210.90166
Hochbaum, Dorit S.; Levin, Asaf
2010
Covering the edges of bipartite graphs using $$K_{2,2}$$ graphs. Zbl 1187.68343
Hochbaum, Dorit S.; Levin, Asaf
2010
Country credit-risk rating aggregation via the separation-deviation model. Zbl 1154.90335
Hochbaum, Dorit S.; Moreno-Centeno, Erick
2008
Covering the edges of bipartite graphs using $$K _{2,2}$$ graphs. Zbl 1130.90409
Hochbaum, Dorit S.; Levin, Asaf
2008
Minimax problems with bitonic matrices. Zbl 1020.90046
Hochbaum, Dorit S.; Tucker, Paul A.
2002
Minimizing a convex cost closure set. Zbl 0974.90016
Hochbaum, Dorit S.; Queyranne, Maurice
2000
Approximating a generalization of MAX 2SAT and MIN 2SAT. Zbl 0971.68070
Hochbaum, Dorit S.; Pathria, Anu
2000
The empirical performance of a polynomial algorithm for constrained nonlinear optimization. Zbl 0786.90066
1993
A fast perfect-matching algorithm in random graphs. Zbl 0733.05072
Goldschmidt, Oliver; Hochbaum, Dorit S.
1990
The replenishment schedule to minimize peak storage problem: the gap between the continuous and discrete versions of the problem. Zbl 1444.90014
Hochbaum, Dorit S.; Rao, Xu
2019
Algorithms and complexity of range clustering. Zbl 1416.62341
Hochbaum, Dorit S.
2019
A comparative study of the leading machine learning techniques and two new optimization algorithms. Zbl 1403.90560
Baumann, P.; Hochbaum, D. S.; Yang, Y. T.
2019
A faster algorithm solving a generalization of isotonic median regression and a class of fused Lasso problems. Zbl 1383.90009
Hochbaum, Dorit S.; Lu, Cheng
2017
Security routing games with multivehicle Chinese postman problem. Zbl 1390.90167
Hochbaum, Dorit S.; Lyu, Cheng; Ordóñez, Fernando
2014
A polynomial time algorithm for Rayleigh ratio on discrete variables: replacing spectral techniques for expander ratio, normalized cut, and Cheeger constant. Zbl 1267.90149
Hochbaum, Dorit S.
2013
Evaluating performance of image segmentation criteria and techniques. Zbl 1307.90006
Hochbaum, Dorit S.; Lyu, Cheng; Bertelli, Erik
2013
Multi-label Markov random fields as an efficient and effective tool for image segmentation, total variations and regularization. Zbl 1289.68201
Hochbaum, Dorit S.
2013
Approximation algorithms for a minimization variant of the order-preserving submatrices and for biclustering problems. Zbl 1301.68273
Hochbaum, Dorit S.; Levin, Asaf
2013
Simplifications and speedups of the pseudoflow algorithm. Zbl 1269.90129
Hochbaum, Dorit S.; Orlin, James B.
2013
Nuclear threat detection with mobile distributed sensor networks. Zbl 1225.90016
Hochbaum, Dorit S.; Fishbain, Barak
2011
Rating customers according to their promptness to adopt new products. Zbl 1233.90204
Hochbaum, Dorit S.; Moreno-Centeno, Erick; Yelland, Phillip; Catena, Rodolfo A.
2011
Complexity of some inverse shortest path lengths problems. Zbl 1208.05141
Cui, Tingting; Hochbaum, Dorit S.
2010
How to allocate review tasks for robust ranking. Zbl 1210.90166
Hochbaum, Dorit S.; Levin, Asaf
2010
Covering the edges of bipartite graphs using $$K_{2,2}$$ graphs. Zbl 1187.68343
Hochbaum, Dorit S.; Levin, Asaf
2010
A computational study of the pseudoflow and push-relabel algorithms for the maximum flow problem. Zbl 1181.90271
Chandran, Bala G.; Hochbaum, Dorit S.
2009
The pseudoflow algorithm: A new algorithm for the maximum-flow problem. Zbl 1167.90394
Hochbaum, Dorit S.
2008
Solving linear cost dynamic lot-sizing problems in $$O(n \log n)$$ time. Zbl 1167.90307
Ahuja, Ravindra K.; Hochbaum, Dorit S.
2008
Country credit-risk rating aggregation via the separation-deviation model. Zbl 1154.90335
Hochbaum, Dorit S.; Moreno-Centeno, Erick
2008
Covering the edges of bipartite graphs using $$K _{2,2}$$ graphs. Zbl 1130.90409
Hochbaum, Dorit S.; Levin, Asaf
2008
Complexity and algorithms for nonlinear optimization problems. Zbl 1159.90485
Hochbaum, Dorit S.
2007
Cyclical scheduling and multi-shift scheduling: complexity and approximation algorithms. Zbl 1112.90023
Hochbaum, Dorit S.; Levin, Asaf
2006
Optimizing over consecutive 1’s and circular 1’s constraints. Zbl 1165.90607
Hochbaum, Dorit S.; Levin, Asaf
2006
Complexity and algorithms for convex network optimization and other nonlinear problems. Zbl 1099.90059
Hochbaum, Dorit S.
2005
A cut-based algorithm for the nonlinear dual of the minimum cost network flow problem. Zbl 1134.90512
Ahuja, Ravindra K.; Hochbaum, Dorit S.; Orlin, James B.
2004
Monotonizing linear programs with up to two nonzeroes per column. Zbl 1056.90105
Hochbaum, Dorit S.
2004
Solving the convex cost integer dual network flow problem. Zbl 1232.90317
Ahuja, Ravindra K.; Hochbaum, Dorit S.; Orlin, James B.
2003
Efficient algorithms for the inverse spanning-tree problem. Zbl 1165.90658
Hochbaum, Dorit S.
2003
The SONET edge-partition problem. Zbl 1026.90076
Goldschmidt, Olivier; Hochbaum, Dorit S.; Levin, Asaf; Olinick, Eli V.
2003
Minimizing a convex Cost closure set. Zbl 1041.68070
Hochbaum, Dorit S.; Queyranne, Maurice
2003
Solving integer programs over monotone inequalities in three variables: A framework for half integrality and good approximations. Zbl 1001.90050
Hochbaum, Dorit S.
2002
Minimax problems with bitonic matrices. Zbl 1020.90046
Hochbaum, Dorit S.; Tucker, Paul A.
2002
An efficient algorithm for image segmentation, Markov random fields and related problems. Zbl 1127.68474
Hochbaum, Dorit S.
2001
Capacity acquisition, subcontracting, and lot sizing. Zbl 1232.90008
Atamtürk, Alper; Hochbaum, Dorit S.
2001
A new-old algorithm for minimum-cut and maximum-flow in closure graphs. Zbl 1044.90083
Hochbaum, Dorit S.
2001
The bounded cycle-cover problem. Zbl 1238.90131
Hochbaum, Dorit S.; Olinick, Eli V.
2001
Minimizing a convex cost closure set. Zbl 0974.90016
Hochbaum, Dorit S.; Queyranne, Maurice
2000
Approximating a generalization of MAX 2SAT and MIN 2SAT. Zbl 0971.68070
Hochbaum, Dorit S.; Pathria, Anu
2000
A half-integral linear programming relaxation for scheduling precedence-constrained jobs on a single machine. Zbl 0958.90042
Chudak, Fabián A.; Hochbaum, Dorit S.
1999
Solving the convex cost integer dual network flow problem. Zbl 0948.90116
Ahuja, Ravindra K.; Hochbaum, Dorit S.; Orlin, James B.
1999
A linear-time algorithm for the bottleneck transportation problem with a fixed number of sources. Zbl 0956.90019
Hochbaum, Dorit S.; Woeginger, Gerhard J.
1999
A primal-dual interpretation of two 2-approximation algorithms for the feedback vertex set problem in undirected graphs. Zbl 0920.90137
Chudak, Fabián A.; Goemans, Michel X.; Hochbaum, Dorit S.; Williamson, David P.
1998
Approximating clique and biclique problems. Zbl 0919.68056
Hochbaum, Dorit S.
1998
Analysis of the greedy approach in problems of maximum $$k$$-coverage. Zbl 0938.90026
Hochbaum, Dorit S.; Pathria, Anu
1998
The $$t$$-vertex cover problem: Extending the half integrality framework with budget constraints. Zbl 0908.90213
Hochbaum, Dorit S.
1998
Instant recognition of half integrality and 2-approximations. Zbl 0911.90261
Hochbaum, Dorit S.
1998
The pseudoflow algorithm and the pseudoflow-based simplex for the maximum flow problem. Zbl 0911.90154
Hochbaum, Dorit S.
1998
Scheduling semiconductor burn-in operations to minimize total flowtime. Zbl 0895.90116
Hochbaum, Dorit S.; Landy, Dan
1997
$$k$$-edge subgraph problems. Zbl 0870.68111
Goldschmidt, Olivier; Hochbaum, Dorit S.
1997
An O$$(\log k)$$-approximation algorithm for the $$k$$ minimum spanning tree problem in the plane. Zbl 0866.68076
Garg, N.; Hochbaum, D. S.
1997
Generalized $$p$$-center problems: Complexity results and approximation algorithms. Zbl 0918.90098
Hochbaum, Dorit S.; Pathria, Anu
1997
Scheduling with batching: Two job types. Zbl 0873.90050
Hochbaum, Dorit S.; Landy, Dan
1997
Approximation algorithms for NP-hard problems. Zbl 1368.68010
Hochbaum, Dorit S. (ed.)
1996
Approximation algorithms for the $$k$$-clique covering problem. Zbl 0857.05086
Goldschmidt, Olivier; Hochbaum, Dorit S.; Hurkens, Cor; Yu, Gang
1996
The bottleneck graph partition problem. Zbl 0873.90102
Hochbaum, Dorit S.; Pathria, Anu
1996
On the complexity of the production-transportation problem. Zbl 0845.90087
Hochbaum, Dorit S.; Hong, Sung-Pil
1996
A nonlinear knapsack problem. Zbl 0838.90092
Hochbaum, Dorit S.
1995
About strongly polynomial time algorithms for quadratic optimization over submodular constraints. Zbl 0844.90061
Hochbaum, Dorit S.; Hong, Sung-Pil
1995
A polynomial algorithm for the $$k$$-cut problem for fixed $$k$$. Zbl 0809.90125
Goldschmidt, Olivier; Hochbaum, Dorit S.
1994
Simple and fast algorithms for linear and integer programs with two variables per inequality. Zbl 0831.90089
Hochbaum, Dorit S.; Naor, Joseph
1994
Lower and upper bounds for the allocation problem and other nonlinear optimization problems. Zbl 0820.90082
Hochbaum, Dorit S.
1994
Scheduling with batching: Minimizing the weighted number of tardy jobs. Zbl 0820.90052
Hochbaum, Dorit S.; Landy, Dan
1994
Strongly polynomial algorithms for the quadratic transportation problem with a fixed number of sources. Zbl 0802.90073
Cosares, Steven; Hochbaum, Dorit S.
1994
An $$O(\log k)$$ approximation algorithm for the $$k$$ minimum spanning tree problem in the plane. Zbl 1344.68285
Garg, Naveen; Hochbaum, Dorit S.
1994
Tight bounds and 2-approximation algorithms for integer programs with two variables per inequality. Zbl 0802.90080
Hochbaum, Dorit S.; Megiddo, Nimrod; Naor, Joseph; Tamir, Arie
1993
A modified greedy heuristic for the set covering problem with improved worst case bound. Zbl 0811.68099
Goldschmidt, Olivier; Hochbaum, Dorit S.; Yu, Gang
1993
Why should biconnected components be identified first. Zbl 0789.90084
Hochbaum, Dorit S.
1993
The empirical performance of a polynomial algorithm for constrained nonlinear optimization. Zbl 0786.90066
1993
A polynomial algorithm for an integer quadratic non-separable transportation problem. Zbl 0761.90061
Hochbaum, Dorit S.; Shamir, Ron; Shanthikumar, J. George
1992
The multicovering problem. Zbl 0759.90072
Hall, Nicholas G.; Hochbaum, Dorit S.
1992
Strongly polynomial algorithms for the high multiplicity scheduling problem. Zbl 0736.90043
Hochbaum, Dorit S.; Shamir, Ron
1991
Convex separable optimization is not much harder than linear optimization. Zbl 0721.90060
Hochbaum, Dorit S.; Shanthikumar, J. George
1990
Minimizing the number of tardy job units under release time constraints. Zbl 0707.90049
Hochbaum, Dorit S.; Shamir, Ron
1990
A fast perfect-matching algorithm in random graphs. Zbl 0733.05072
Goldschmidt, Oliver; Hochbaum, Dorit S.
1990
Analysis of a flow problem with fixed charges. Zbl 0673.90035
Hochbaum, Dorit S.; Segev, Arie
1989
An algorithm for the detection and construction of Monge sequences. Zbl 0666.65044
Alon, Noga; Cosares, Steven; Hochbaum, Dorit S.; Shamir, Ron
1989
An $$O(n \log^ 2\,n)$$ algorithm for the maximum weighted tardiness problem. Zbl 0672.68011
Hochbaum, Dorit S.; Shamir, Ron
1989
A polynomial approximation scheme for scheduling on uniform processors: Using the dual approximation approach. Zbl 0647.68040
Hochbaum, Dorit S.; Shmoys, David B.
1988
Fast approximation algorithms for a nonconvex covering problem. Zbl 0636.68082
Hochbaum, Dorit S.; Maass, Wolfgang
1987
A fast approximation algorithm for the multicovering problem. Zbl 0602.90110
Hall, Nicholas G.; Hochbaum, Dorit S.
1986
A better than ”best possible” algorithm to edge color multigraphs. Zbl 0594.68041
Hochbaum, Dorit S.; Nishizeki, Takao; Shmoys, David B.
1986
A polynomial approximation scheme for machine scheduling on uniform processors: Using the dual approximation approach. Zbl 0623.68033
Hochbaum, Dorit S.; Shmoys, David B.
1986
Best possible heuristics for the bottleneck wandering salesperson and bottleneck vehicle routing problem. Zbl 0596.90093
Hochbaum, Dorit S.; Shmoys, David B.
1986
Approximation schemes for covering and packing problems in image processing and VLSI. Zbl 0633.68027
Hochbaum, Dorit S.; Maass, Wolfgang
1985
A best possible heuristic for the k-center problem. Zbl 0565.90015
Hochbaum, Dorit S.; Shmoys, David B.
1985
An $$O(| V| ^ 2)$$ algorithm for the planar 3-cut problem. Zbl 0572.05040
Hochbaum, Dorit S.; Shmoys, David B.
1985
Easy solutions for the K-center problem or the dominating set problem on random graphs. Zbl 0562.68029
Hochbaum, Dorit S.
1985
When are NP-hard location problems easy? Zbl 0671.90019
Hochbaum, Dorit S.
1984
Approximation schemes for covering and packing problems in robotics and VLSI. Zbl 0557.68035
Hochbaum, Dorit S.; Maass, Wolfgang
1984
Efficient bounds for the stable set, vertex cover and set packing problems. Zbl 0523.05055
Hochbaum, Dorit S.
1983
On the fractional solution to the set covering problem. Zbl 0518.90055
Hochbaum, Dorit S.
1983
Approximation algorithms for the set covering and vertex cover problems. Zbl 0486.68067
Hochbaum, Dorit S.
1982
Heuristics for the fixed cost median problem. Zbl 0473.90029
Hochbaum, Dorit S.
1982
Steinhaus’s geometric location problem for random samples in the plane. Zbl 0501.60040
Hochbaum, Dorit; Steele, J. Michael
1982
Database location in computer networks. Zbl 0445.68071
Fisher, Marshall L.; Hochbaum, Dorit S.
1980
Probabilistic analysis of the planar K-median problem. Zbl 0435.90057
Fisher, M. L.; Hochbaum, D. S.
1980
all top 5
#### Cited by 2,325 Authors
36 Hochbaum, Dorit S. 15 Levin, Asaf 14 Subramani, Krishnan 14 Zhang, Zhao 13 Cheng, Tai-Chiu Edwin 13 Das, Gautam Kumar 13 Paschos, Vangelis Th. 11 Xu, Dachuan 10 Du, Ding-Zhu 10 Wu, Weili 9 Chan, Timothy Moon-Yew 9 Hassin, Refael 9 Jansen, Klaus 9 Kovalyov, Mikhail Yakovlevich 9 Nandy, Subhas Chandra 9 Pardalos, Panos M. 9 Shioura, Akiyoshi 9 Strusevich, Vitaly A. 9 Woeginger, Gerhard Johannes 8 Chen, Jian-er 8 Shakhlevich, Natalia V. 8 Tamir, Arie 8 Trystram, Denis R. 8 Xu, Chao 7 Brauner, Nadia 7 Epstein, Leah 7 Guan, Xiucui 7 Ibaraki, Toshihide 7 Rawitz, Dror 7 Ray, Saurabh 7 Sun, Xiaoling 7 Wang, Jianxin 7 Wu, Chenchen 6 Crama, Yves 6 Du, Donglei 6 Escoffier, Bruno 6 Fujito, Toshihiro 6 Hermelin, Danny 6 Huang, Wenqi 6 Jallu, Ramesh K. 6 Kakimura, Naonori 6 Kellerer, Johann 6 Krumke, Sven Oliver 6 Li, Duan 6 Marathe, Madhav V. 6 Murota, Kazuo 6 Mustafa, Nabil Hassan 6 Razzazi, Mohammadreza 6 Rudolf, Rudiger 6 Segev, Danny 6 Shachnai, Hadas 6 Steiner, George 6 Tu, Jianhua 6 Vohra, Rakesh V. 6 Wang, Lusheng 6 Zhang, Jianzhong 6 Zhang, Jiawei 5 Atamtürk, Alper 5 Burkard, Rainer E. 5 Chambolle, Antonin 5 Chekuri, Chandra S. 5 Demange, Marc 5 El Ouali, Mourad 5 Fellows, Michael Ralph 5 Fiorini, Samuel 5 Goldreich, Oded 5 Grigoriev, Alexander 5 Ito, Takehiro 5 Klasing, Ralf 5 Kortsarz, Guy 5 Leung, Joseph Y.-T. 5 Li, Guojun 5 Lingas, Andrzej 5 Mastrolilli, Monaldo 5 Milis, Ioannis 5 Monnot, Jérôme 5 Ng, Chi To 5 Parekh, Ojas 5 Peleg, David 5 Shamir, Ron 5 Shetty, Bala 5 Srivastav, Anand 5 Sung, Chang Sup 5 Teo, Chungpiaw 5 Wang, Wei 5 Xiao, Mingyu 5 Yagiura, Mutsunori 5 Yuan, Jinjiang 5 Zissimopoulos, Vassilis 4 Agnetis, Alessandro 4 Bar-Yehuda, Reuven 4 Basappa, Manjanna 4 Bertsimas, Dimitris John 4 Bretthauer, Kurt M. 4 Bus, Norbert 4 Carmi, Paz 4 Chen, Zhizhong 4 Damaschke, Peter 4 Darbon, Jerome 4 Detti, Paolo ...and 2,225 more Authors
all top 5
#### Cited in 176 Serials
123 European Journal of Operational Research 121 Theoretical Computer Science 88 Discrete Applied Mathematics 75 Algorithmica 57 Information Processing Letters 54 Journal of Combinatorial Optimization 47 Mathematical Programming. Series A. Series B 46 Computers & Operations Research 44 Operations Research Letters 36 Discrete Optimization 34 Annals of Operations Research 32 Journal of Scheduling 28 Journal of Computer and System Sciences 23 Computational Geometry 19 International Journal of Foundations of Computer Science 18 Networks 18 Journal of Global Optimization 17 Theory of Computing Systems 14 Journal of Discrete Algorithms 12 Discrete Mathematics 12 Mathematics of Operations Research 12 Optimization Letters 11 International Journal of Computational Geometry & Applications 10 SIAM Journal on Computing 10 RAIRO. Operations Research 9 Operations Research 8 Discrete & Computational Geometry 8 SIAM Journal on Optimization 7 International Journal of Production Research 7 Computational Optimization and Applications 7 Top 7 INFORMS Journal on Computing 6 Information Sciences 6 Naval Research Logistics 6 SIAM Journal on Discrete Mathematics 5 Artificial Intelligence 5 Applied Mathematics and Computation 5 Optimization 5 Games and Economic Behavior 5 Linear Algebra and its Applications 5 Journal of Heuristics 5 OR Spectrum 5 SIAM Journal on Imaging Sciences 5 Discrete Mathematics, Algorithms and Applications 4 Journal of Optimization Theory and Applications 4 Information and Computation 4 Journal of Parallel and Distributed Computing 4 Applied Mathematical Modelling 4 4OR 4 Journal of Industrial and Management Optimization 4 Computer Science Review 3 BIT 3 Computing 3 Journal of Combinatorial Theory. Series B 3 Journal of Computational and Applied Mathematics 3 Advances in Applied Mathematics 3 Combinatorica 3 Journal of Computer Science and Technology 3 Asia-Pacific Journal of Operational Research 3 Formal Aspects of Computing 3 Random Structures & Algorithms 3 International Journal of Computer Mathematics 3 Distributed Computing 3 International Journal of Computer Vision 3 Optimization Methods & Software 3 Mathematical Methods of Operations Research 3 Data Mining and Knowledge Discovery 3 Mathematical Programming Computation 3 Journal of the Operations Research Society of China 2 Acta Informatica 2 Journal of Mathematical Physics 2 Chaos, Solitons and Fractals 2 Mathematica Slovaca 2 Statistica Neerlandica 2 European Journal of Combinatorics 2 OR Spektrum 2 SIAM Journal on Algebraic and Discrete Methods 2 Acta Mathematicae Applicatae Sinica. English Series 2 Graphs and Combinatorics 2 Mathematical and Computer Modelling 2 Queueing Systems 2 Real-Time Systems 2 The Annals of Applied Probability 2 Discrete Event Dynamic Systems 2 Computational Statistics and Data Analysis 2 Applied Mathematics. Series B (English Edition) 2 Combinatorics, Probability and Computing 2 Annals of Mathematics and Artificial Intelligence 2 Wuhan University Journal of Natural Sciences (WUJNS) 2 International Journal of Applied Mathematics and Computer Science 2 RAIRO. Theoretical Informatics and Applications 2 Trudy Instituta Matematiki 2 Sādhanā 2 JMMA. Journal of Mathematical Modelling and Algorithms 2 Acta Numerica 2 Computational Management Science 2 The Annals of Applied Statistics 2 Algorithms 1 Applicable Analysis 1 Computers & Mathematics with Applications ...and 76 more Serials
all top 5
#### Cited in 27 Fields
878 Operations research, mathematical programming (90-XX) 652 Computer science (68-XX) 326 Combinatorics (05-XX) 60 Numerical analysis (65-XX) 58 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 31 Statistics (62-XX) 29 Convex and discrete geometry (52-XX) 14 Biology and other natural sciences (92-XX) 13 Calculus of variations and optimal control; optimization (49-XX) 13 Probability theory and stochastic processes (60-XX) 13 Information and communication theory, circuits (94-XX) 7 Systems theory; control (93-XX) 6 Linear and multilinear algebra; matrix theory (15-XX) 6 Partial differential equations (35-XX) 5 General and overarching topics; collections (00-XX) 4 Mathematical logic and foundations (03-XX) 4 Statistical mechanics, structure of matter (82-XX) 3 Number theory (11-XX) 2 Order, lattices, ordered algebraic structures (06-XX) 2 Differential geometry (53-XX) 2 General topology (54-XX) 2 Geophysics (86-XX) 1 Algebraic geometry (14-XX) 1 Functional analysis (46-XX) 1 Operator theory (47-XX) 1 Manifolds and cell complexes (57-XX) 1 Mechanics of particles and systems (70-XX)
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The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata.
| 2021-06-12T17:07:42 |
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|
https://wiki.cosmos.esa.int/planck-legacy-archive/index.php?title=Help:Contents&oldid=416
|
# Help:Contents
## Organisation of the Explanatory Supplement
The explanatory supplement is organised in terms of what MediaWiki calls Categories. Using categories provides an automatic mechanism for Index and Table of Contents generation that would otherwise be time consuming and error prone. On top of that, there are a number of extensions based on the category concept, providing a useful set of features for the development, maintenance and use of this Wiki.
Each of the entries in the table of contents in the Main Page is a category. Categories are pages (and for the ES one expects them to be reasonably self contained for the subject they cover) and can independently be added to a Collection. A typical example can be found in the Mission Products Section: a user interested in frequency maps may or may not be interested in timelines as well but will certainly be interested in understanding the formats the maps are stored, the naming conventions, the size of the maps and will most likely also look for the details of the map making process possibly in the form of papers explaining algorithms. It will therefore make sense for the frequency maps page to contain sections on format, naming conventions, size and references to the map making process. On the other hand, the description of the timelines will most naturally appear under a different page. In order not to end up with a huge number of separate pages, instead of creating a page for frequency maps only we grouped all the map products under a single maps page which is also a category. After all, it is not entirely unexpected that a user interested in frequency maps may also be interested in other types of maps.
### Guidelines for development
In order to keep the development of the wiki under control we would like to ask all contributors to follow a set of very simple guidelines.
• Each topic on the table of contents is assigned to particular contributors (look here for the current list). This does not mean the others can not make minor changes or corrections but in general it would be advisable that contributors not assigned to a specific topic refrain from making major corrections on that topic's pages;
• A very concise help with some recipes for common editing actions can be found below. For a more detailed User Guide please refer to the MediaWiki User's Guide;
• Concerning pages mostly contributed to by other contributors try to keep in mind the following:
• Fixing typos or performing minor corrections is encouraged. If you find one of those please go ahead and fix it;
• If what you have in mind is a major rewriting or you would like to propose extensive changes we ask you not to do so before discussing it with all those concerned. For each page there is a discussions page associated which can be accessed through one of the tabs at the top of the page (see Fig. below). Please use it to circulate more widely the changes you would like to propose.
• If you would like to add a new page bear in mind the discussion above. If you are still convinced the new page is necessary, make your intention know in the discussion page associated with the root page of your new page. If your proposal is approved follow the procedure for the creation of a new page
Note that as all contributors have access to the entire wiki the enforcement of these simple rules depends on self-discipline and it is absolutely essential you stick to them.
## Use of the available extensions
### MathJax
The MathJax extension allows the use of MathJax, a display engine for mathematics providing high quality mathematics fonts. The main interest for the ES lies in its ability to produce high quality display of latex formulae with no need for any extra tags. Equations may simply be written in Latex and MathJax will recognize the Latex Tags.
Simple mathematical expressions can be easily written inline. The following
$x^2 + y^2 +z^2 = 1$
will be displayed by MathJax as $x^2 + y^2 +z^2 = 1$.
We can write complex equations and even make use of \newcommand as illustrated by the following lines.
\begin{align}
\label{def:Wns}
W_n (s)
&:=
\int_{[0, 1]^n}
\left| \sum_{k = 1}^n \mathrm{e}^{2 \pi \mathrm{i} \, x_k} \right|^s \mathrm{d}\boldsymbol{x}
\end{align}
\begin{align}
\label{eq:W3k}
W_3(k) &= \Re \, \pFq32{\frac12, -\frac k2, -\frac k2}{1, 1}{4}.
\end{align}
\label{def:Wns}
W_n (s)
&:=
\int_{[0, 1]^n}
\left| \sum_{k = 1}^n \mathrm{e}^{2 \pi \mathrm{i} \, x_k} \right|^s \mathrm{d}\boldsymbol{x}
\end{align}
\begin{align}
\label{eq:W3k}
W_3(k) &= \Re \, \pFq32{\frac12, -\frac k2, -\frac k2}{1, 1}{4}.
\end{align}
We can also refer to equations with a valid \label using the latex \eqref command. The second of the two eqautions above can be referred to with
\eqref{eq:W3k}
resulting in a correct reference to equation \eqref{eq:W3k} above. Note the reference works as a link. Clicking it you will be taken to the equation referred to.
### Collection
The Collection extension allows a user to organise a set of pages as a book that can be converted to pdf. This comes handy for a user that is interested in a few sections of the ES but would rather print only the contents of the sections of interested than the entire ES. The user adds each section of interest to a book using a button on the toolbar. When the selection is complete the generate pdf button is pressed and a pdf version of the selected section, including a table of contents, is generated.
This section is still incomplete waiting for the extension to be installed.
### Linking to other pages in the ES
#### New section in an existing page
In this case the syntax is the following:
==New Section==
===New Subsection===
====New SubSubSection====
More details can be found in the MediaWiki User's Guide.
#### New section as new page
Should the new section appear as a new page (see the guidelines above on the addition of new pages) the Category syntax should be used:
Assuming a new page with the title New Page is to be added to the ES, add the line
[[:Category:New Page|New Page]]
to the Main Page. This will create a link to the (yet non existing) page New Page. Note the slightly different link syntax: the : after the [[ is required otherwise the tag would be interpreted not as a link but as a Category hierarchy definitios (see step 2 below).
When the Category link above is added to the Main Page make sure it appears in the correct location as the Main Page is basically a table of contents for the ES.
1. Create the page (and Category)
Clicking on the link just created on step 1 (which will be displayed in red as the page still does not exist) will take you to an empty page displaying the warning You have followed a link to a page that does not exist yet. Enter the content of the new page as you would for any other page. Since we want this page to be part of the category tree enter the line
[[Category:TopCategory]]
where TopCategory is the existing category under which the new category will appear in the Category Tree. If this last step step is missed the new page will not be part of the Category Tree and you will therefore not be able to take advantage of the Category Tree features. The line above can be entered anywhere on the page but the structure of the page results easier to understand if it appears consistently at the end. For example, in the maps section under mission products, the following line appears at the end of the page
[[Category:Mission products]]
This guarantees the maps section will correctely appear in the Category Tree
Explanatory Supplement
| 2022-05-16T15:24:55 |
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|
http://www.itl.nist.gov/div898/software/dataplot/refman2/auxillar/diffbilo.htm
|
Dataplot Vol 2 Vol 1
# DIFFERENCE OF BIWEIGHT LOCATION
Name:
DIFFERENCE OF BIWEIGHT LOCATION (LET)
Type:
Let Subcommand
Purpose:
Compute the difference between the biweight locations for two response variables.
Description:
The biweight location estimate is defined as:
$$y* = \frac{\sum_{i=1}^{n}{w_{i}y_{i}}} {\sum_{i=1}^{n}{w_{i}}}$$
where
$$w_{i} = (1 - (\frac{y_{i} - y*}{cS})^{2})^{2} \hspace{0.5in} \mbox{for } (\frac{y_{i} - y*}{cS})^{2} < 1$$
$$w_{i} = 0 \hspace{0.5in} \mbox{otherwise}$$
and
$$S = \mbox{median}\{|y_{i} - y*|\}$$
c = 6 (using 6 means that residuals up to approximately $$4 \sigma$$ are included)
Note that this is an iterative estimate since y* depends on wi and wi depends on y*.
Dataplot will compute up to 10 iterations (computation is terminated if the biweight location estimate does not change in value by more than 0.000001).
For the differeence of biweight locations, the biweight location is computed for each of two samples then their difference is taken.
Syntax:
LET <par> = DIFFERENCE OF BIWEIGHT LOCATION
<y1> <y2> <SUBSET/EXCEPT/FOR qualification>
where <y1> is the first response variable;
<y2> is the first response variable;
<par> is a parameter where the computed difference of the biweight locations is stored;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.
Examples:
LET A = DIFFERENCE OF BIWEIGHT LOCATION Y1 Y2
LET A = DIFFERENCE OF BIWEIGHT LOCATION Y1 Y2 SUBSET X > 1
Note:
Dataplot statistics can be used in a number of commands. For details, enter
Default:
None
Synonyms:
None
Related Commands:
BIWEIGHT LOCATION = Compute the biweight location. DIFFERENCE OF MEDIAN = Compute the difference of medians. DIFFERENCE OF TRIMMED MEAN = Compute the difference of trimmed means. DIFFERENCE OF MIDMEAN = Computes the difference of midmeans. DIFFERENCE OF MEAN = Compute the difference of means. BIWEIGHT SCALE = Compute a biweight scale estimate of a variable. BIWEIGHT CONFIDENCE LIMITS = Compute a biweight based confidence interval.
Applications:
Data Analysis
Implementation Date:
3/2003
Program:
SKIP 25
READ IRIS.DAT Y1 TO Y4 X
.
LET A = DIFFERENCE OF BIWEIGHT LOCATION Y1 Y2
TABULATE DIFFERENCE OF BIWEIGHT LOCATION Y1 Y2 X
.
XTIC OFFSET 0.2 0.2
X1LABEL GROUP ID
Y1LABEL DIFFERENCE OF BIWEIGHT LOCATIONS
CHAR X
LINE BLANK
DIFFERENCE OF BIWEIGHT LOCATION PLOT Y1 Y2 X
CHAR X ALL
LINE BLANK ALL
BOOTSTRAP DIFFERENCE OF BIWEIGHT LOCATION PLOT Y1 Y2 X
The following output is generated.
*****************************************************
** LET A = DIFFERENCE OF BIWEIGHT LOCATION Y1 Y2 **
*****************************************************
THE COMPUTED VALUE OF THE CONSTANT A = 0.27841682E+01
********************************************************
** TABULATE DIFFERENCE OF BIWEIGHT LOCATION Y1 Y2 X **
********************************************************
* Y1 AND Y2
X * DIFFERENCE OF BIWEIGHT LOCATION
**********************************************
1.00000 * 1.57608
2.00000 * 3.14232
3.00000 * 3.60915
GROUP-ID AND STATISTIC WRITTEN TO FILE DPST1F.DAT
NIST is an agency of the U.S. Commerce Department.
Date created: 03/21/2003
Last updated: 11/03/2015
| 2017-10-24T02:27:47 |
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|
https://pdglive.lbl.gov/DataBlock.action?node=S013D&home=sumtabM
|
#### ${\boldsymbol m}_{{{\boldsymbol K}_L^0} }–{\boldsymbol m}_{{{\boldsymbol K}_S^0} }$
For earlier measurements, beginning with GOOD 1961 and FITCH 1961 , see our 1986 edition, Physics Letters 170B 132 (1986).
OUR FIT is described in the note on “$\mathit CP$ violation in ${{\mathit K}_{{L}}}$ decays” in the ${{\mathit K}_L^0}$ Particle Listings. The result labeled “OUR FIT Assuming $\mathit CPT$” [“OUR FIT Not assuming $\mathit CPT$”] includes all measurements except those with the comment “Not assuming $\mathit CPT$” [“Assuming $\mathit CPT”$]. Measurements with neither comment do not assume $\mathit CPT$ and enter both fits.
VALUE ($10^{10}$ $\hbar{}$ s${}^{-1}$) DOCUMENT ID TECN COMMENT
$\bf{ 0.5289 \pm0.0010}$ OUR FIT Not assuming $\mathit CPT$
$\bf{ 0.5293 \pm0.0009}$ OUR FIT Error includes scale factor of 1.3. Assuming $\mathit CPT$
$0.52797$ $\pm0.00195$ 1, 2
2011
KTEV Not assuming $\mathit CPT$
$0.52699$ $\pm0.00123$ 1, 3
2011
KTEV Assuming $\mathit CPT$
$0.5240$ $\pm0.0044$ $\pm0.0033$
1999 C
CPLR ${{\mathit K}^{0}}-{{\overline{\mathit K}}^{0}}$ to ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$
$0.5297$ $\pm0.0030$ $\pm0.0022$ 4
1995
E773 $20 - 160$ GeV ${{\mathit K}}$ beams
$0.5286$ $\pm0.0028$ 5
1993
E731 Assuming $\mathit CPT$
$0.5257$ $\pm0.0049$ $\pm0.0021$ 4
1993 C
E731 Not assuming $\mathit CPT$
$0.5340$ $\pm0.00255$ $\pm0.0015$ 6
1974 C
SPEC Gap method
$0.5334$ $\pm0.0040$ $\pm0.0015$ 6, 7
1974
SPEC Assuming $\mathit CPT$
• • We do not use the following data for averages, fits, limits, etc. • •
$0.5261$ $\pm0.0015$ 8
2003
KTEV Assuming $\mathit CPT$
$0.5288$ $\pm0.0043$ 9
2003
KTEV Not assuming $\mathit CPT$
$0.5343$ $\pm0.0063$ $\pm0.0025$ 10
2001
CPLR
$0.5295$ $\pm0.0020$ $\pm0.0003$ 11
1998 D
CPLR Assuming $\mathit CPT$
$0.5307$ $\pm0.0013$ 12
1996 C
RVUE
$0.5274$ $\pm0.0029$ $\pm0.0005$ 11
1995
CPLR Sup. by ANGELOPOULOS 1998D
$0.482$ $\pm0.014$ 13
1982 B
SPEC $\mathit E=30-$110 GeV
$0.534$ $\pm0.007$ 14
1971
ASPK Gap method
$0.542$ $\pm0.006$ 14
1970
ASPK Gap method
$0.542$ $\pm0.006$
1970
CNTR
1 The two ABOUZAID 2011 values use the same data. The first enters the ”assuming $\mathit CPT$” fit and the second enters the ”not assuming $\mathit CPT$” fit.
2 ABOUZAID 2011 fit has $\Delta \mathit m$, ${{\mathit \tau}_{{s}}}$, ${{\mathit \phi}_{{\epsilon}}}$, Re(${{\mathit \epsilon}^{\,'}}/{{\mathit \epsilon}}$), and Im(${{\mathit \epsilon}^{\,'}}/{{\mathit \epsilon}}$) as free parameters. See Im(${{\mathit \epsilon}^{\,'}}/{{\mathit \epsilon}}$) in the ”${{\mathit K}_L^0}$ $\mathit CP$ violation” section for correlation information.
3 ABOUZAID 2011 fit has $\Delta \mathit m$ and ${{\mathit \tau}_{{s}}}$ free but constrains ${{\mathit \phi}_{{\epsilon}}}$ to the Superweak value, i.e. assumes $\mathit CPT$. See ”${{\mathit K}_S^0}$ Mean Life” section for correlation information.
4 Fits $\Delta \mathit m$ and $\phi _{+−}$ simultaneously. GIBBONS 1993C systematic error is from B.$~$Winstein via private communication. $20 - 160$ GeV ${{\mathit K}}$ beams.
5 GIBBONS 1993 value assume $\phi _{+−}$ = $\phi _{00}$ = $\phi _{{\mathrm {SW}}}$ = ($43.7$ $\pm0.2)^\circ{}$, i.e. assumes $\mathit CPT$. $20 - 160$ GeV ${{\mathit K}}$ beams.
6 These two experiments have a common systematic error due to the uncertainty in the momentum scale, as pointed out in WAHL 1989 .
7 GJESDAL 1974 uses charge asymmetry in ${{\mathit K}_{{{{\mathit \ell}}3}}^{0}}$ decays.
8 ALAVI-HARATI 2003 fit $\Delta \mathit m$ and ${\mathit \tau}_{{{\mathit K}_S^0} }$ simultaneously. $\phi _{+−}$ is constrained to the Superweak value, i.e. $\mathit CPT$ is assumed. See “${{\mathit K}_S^0}$ Mean Life” section for correlation information. Superseded by ABOUZAID 2011 .
9 ALAVI-HARATI 2003 fit $\Delta \mathit m$, $\phi _{+−}$, and $\tau _{{{\mathit K}_{{S}}}}$ simultaneously. See $\phi _{+−}$ in the “${{\mathit K}_{{L}}}$ $\mathit CP$ violation” section for correlation information. Superseded by ABOUZAID 2011 .
10 ANGELOPOULOS 2001 uses strong interactions strangeness tagging at two different times.
11 Uses ${{\overline{\mathit K}}_{{e3}}^{0}}$ and ${{\mathit K}_{{e3}}^{0}}$ strangeness tagging at production and decay. Assumes $\mathit CPT$ conservation on $\Delta \mathit S=−\Delta \mathit Q$ transitions.
12 ADLER 1996C is the result of a fit which includes nearly the same data as entered into the “OUR$~$FIT” value above.
13 ARONSON 1982 find that $\Delta \mathit m$ may depend on the kaon energy.
14 ARONSON 1970 and CARNEGIE 1971 use ${{\mathit K}_S^0}$ mean life = ($0.862$ $\pm0.006$) $\times 10^{-10}$ s. We have not attempted to adjust these values for the subsequent change in the ${{\mathit K}_S^0}$ mean life or in $\eta _{+−}$.
Conservation Laws:
$\Delta \mathit S$ = 2 VIA MIXING
References:
ABOUZAID 2011
PR D83 092001 Precise Measurements of Direct $\mathit CP$ Violation, $\mathit CPT$ Symmetry, and other Parameters in the Neutral Kaon System
ALAVI-HARATI 2003
PR D67 012005 Measurements of Direct $\mathit CP$ Violation, $\mathit CPT$ Symmetry, and other Parameters in the Neutral Kaon System
ANGELOPOULOS 2001
PL B503 49 ${{\mathit K}^{0}}$ $\leftrightarrow$ ${{\overline{\mathit K}}^{0}}$ Transitions Monitored by Strong Interactions: a New Determination of the ${{\mathit K}_L^0}$ $−$ ${{\mathit K}_S^0}$ Mass Difference
APOSTOLAKIS 1999C
PL B458 545 A Determination of the $\mathit CP$ Violation Parameter $\eta _{+−}$ from the Decay of Strangeness Tagged Neutral Kaons
ANGELOPOULOS 1998D
PL B444 38 Measurement of the ${{\mathit K}_L^0}$ $−$ ${{\mathit K}_S^0}$ Mass Difference using Semileptonic Decays of Tagged Neutral Kaons
PL B369 367 Evaluation of the Phase of the $\mathit CP$ Violation Parameter $\eta _{+−}$ and ${{\mathit K}_L^0}$ $−$ ${{\mathit K}_S^0}$ Mass Difference from a Correlation Analysis of Different Experiments
PL B363 237 Measurement of ${{\mathit K}_L^0}$ $−$ ${{\mathit K}_S^0}$ Mass Difference using Semileptonic Decays of Tagged Neutral Kaons
SCHWINGENHEUER 1995
PRL 74 4376 $\mathit CPT$ Tests in the Neutral Kaon System
GIBBONS 1993
PRL 70 1199 New Measurements of the Neutral Kaon Parameters $\Delta _{m}$, $\tau _{S}$, $\Phi _{00}$ $−$ $\Phi _{+-}$, and $\Phi _{+-}$
GIBBONS 1993C
Thesis RX-1487 A Precise Measurement of the $\mathit CP$ Violation Parameter Re(${{\mathit \epsilon}^{\,'}}/{{\mathit \epsilon}}$) and other Kaon Decay Parameters
ARONSON 1982B
PRL 48 1306 Determination of the Fundamental Parameters of the ${{\mathit K}^{0}}{{\overline{\mathit K}}^{0}}$ System in the Energy Range 30-110 GeV
GEWENIGER 1974C
PL 52B 108 Measurement of the Kaon Mass Difference ${\mathit m}_{{{\mathit K}_L^0} }–{\mathit m}_{{{\mathit K}_S^0} }$ by the Two Regenerator Method
GJESDAL 1974
PL 52B 113 A Measurement of the ${\mathit m}_{{{\mathit K}_L^0} }–{\mathit m}_{{{\mathit K}_S^0} }$ from the Charge Asymmetry in Semileptonic Kaon Decays
CARNEGIE 1971
PR D4 1 ${{\mathit K}_{{1}}^{0}}$ $−$ ${{\mathit K}_{{2}}^{0}}$ Mass Difference
ARONSON 1970
PRL 25 1057 Precise Determination of the ${{\mathit K}_L^0}$ $−{{\mathit K}_S^0}$ Mass Difference by the Gap Method
CULLEN 1970
PL 32B 523 Precision Determination of the ${{\mathit K}_L^0}$ ${{\mathit K}_S^0}$ Mass Difference
| 2021-09-20T03:09:24 |
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|
https://conferences.lbl.gov/event/195/contributions/1062/
|
# RIKEN Berkeley Workshop: Quantum Information Science
25-29 January 2019
LBL-Hill
US/Pacific timezone
## Progress Towards sub-eV Phonon and Photon Sensitivity with Athermal Phonon Detector for Light Mass Dark Matter Searches and Other Applications
26 Jan 2019, 17:30
25m
Building 66- Auditorium (LBL-Hill)
### Building 66- Auditorium
#### LBL-Hill
Lawrence Berkeley National Lab Berkeley, California
Workshop Talk Quantum sensing
### Speaker
Prof. Matt Pyle (University of California Berkeley)
### Description
Searching for dark matter in the 10meV-100MeV mass range requires sensitivity to small energy depositions. In particular, sensitivity to a single optical phonon quanta in Sapphire ( ~ 50meV) or 2 roton quanta in superfluid He would enable searches deep into an entirely unexplored parameter space. Over the past year, we’ve made significant progress towards these goals. In particular, we’ve developed a 45cm$^2$ Si athermal phonon detector with a baseline energy resolution of 3.5eV. After scaling for size, this device represents an order of magnitude leap in sensitivity compared to previously measured sensitivities. Analysis is currently ongoing on a 33 gd above ground light mass dark matter search using this prototype. Additionally, we’ve begun testing the transition edge sensor test structures for the following generation prototype design. Measured baseline resolution was 50meV; after scaling for size this device also represents nearly an order of magnitude improvement compared to currently available world leading devices.
### Primary author
Prof. Matt Pyle (University of California Berkeley)
### Presentation Materials
There are no materials yet.
| 2022-06-28T07:07:09 |
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|
http://dlmf.nist.gov/23.1
|
# §23.1 Special Notation
(For other notation see Notation for the Special Functions.)
lattice in . integers. integer, except in §23.20(ii). complex variable, except in §§23.20(ii), 23.21(iii). closed, or open, straight-line segment joining and , whether or not and are real. derivatives with respect to the variable, except where indicated otherwise. complete elliptic integrals (§19.2(i)). lattice generators (). . lattice parameter (). nome. lattice invariants. zeros of Weierstrass normal cubic . discriminant . set of all integer multiples of . set of all elements of , modulo elements of . Thus two elements of are equivalent if they are both in and their difference is in . (For an example see §20.12(ii).) Cartesian product of groups and , that is, the set of all pairs of elements with group operation .
The main functions treated in this chapter are the Weierstrass -function ; the Weierstrass zeta function ; the Weierstrass sigma function ; the elliptic modular function ; Klein’s complete invariant ; Dedekind’s eta function .
## ¶ Other Notations
Whittaker and Watson (1927) requires only , instead of . Abramowitz and Stegun (1964, Chapter 18) considers only rectangular and rhombic lattices (§23.5); , are replaced by , for the former and by , for the latter. Silverman and Tate (1992) and Koblitz (1993) replace and by and , respectively. Walker (1996) normalizes , , and uses homogeneity (§23.10(iv)). McKean and Moll (1999) replaces and by and , respectively.
| 2013-05-21T17:30:45 |
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|
https://www.federalreserve.gov/econres/notes/feds-notes/foreign-banks-asset-reallocation-intermediate-holding-company-rule-of-2016-20210512.htm
|
May 12, 2021
### Foreign banks’ asset reallocation in response to the introduction of the Intermediate Holding Company rule of 20161
#### Introduction
The implementation of the 2016 intermediate holding company (IHC) rule required foreign banking organizations (FBOs) operating with more than $50 billion total global consolidated assets and with$50 billion or more in U.S. non-branch assets to consolidate their non-branch activities – including their U.S. subsidiaries and U.S. broker-dealers – into holding companies, to be supervised by the Federal Reserve (Figure 1). As per the final rule, these IHCs then became subject to capital planning and stress testing requirements as an enhanced prudential standard, and are also required to comply with enhanced risk-management and liquidity risk-management standards. This rule, which aims to facilitate consistent supervision and regulation of the U.S. operations of FBOs, was required by Section 165 of the Dodd-Frank Wall Street Reform and Consumer Protection Act.2 Although U.S. branches and agencies of the parent FBO are not folded into the IHC structure, they are still subject to (less stringent) enhanced prudential standards regarding risk-management, capital, liquidity and debt-to-equity limits.3 The most notable differences between the FBO's IHC structures and their U.S branches and agencies are that the latter are not subject to the U.S. Basel III standardized approach, CCAR and Dodd-Frank Act Stress Test (DFAST) stress testing requirements, or additional capital and stress-testing reporting.
##### Figure 1. Description of the Intermediate Holding Company Structure
Given the significant costs to establish and maintain an IHC, it is not surprising that FBOs may try to reduce the regulatory burden by reallocating assets away from the US-regulated IHC-subject activities towards less regulated branches and agencies (including those in the United States and located abroad) and/or downsize the total assets of the IHC. We use detailed regulatory data on within-FBO transactions to examine whether FBOs had engaged in asset reallocation prior to the implementation of the IHC rule. Our findings show that the introduction of the IHC rule spurred FBOs to reallocate their assets from ("US-regulated") U.S. subsidiaries toward their ("less regulated") U.S. branches and agencies.4 This response to the IHC rule may have financial stability implications, as U.S. regulators have limited oversight of the growing assets held via U.S. branches and agencies of FBOs.
#### Estimation methodology
The empirical evidence on the impact of the Intermediate Holding Company (IHC) rule on foreign banks' asset allocation is scarce and mixed. DiSalvo (2019) looks at changes in foreign banks' organizational structure from before to after the enactment of the 2016 IHC rule, and finds some evidence that FBOs shifted some activities away from the U.S. market. Kreicher and McCauley (2018) examine aggregate trends and find that the IHC rule had two effects on foreign banks: the rule led banks to reduce total assets, and to reallocate assets from subsidiaries to branches, including offshore branches.
Depending on their existing organizational structure, foreign banks responded to the implementation of the IHC rule differently. Based on Kreicher and McCauley (2018), we allocate affected FBOs into two groups. Those that already held U.S.-regulated bank holding companies prior to the IHC rule is our "control" group; these banks were minimally affected, as they were already in compliance with the U.S. rules. Those banks that had no holding company structure prior to the IHC rule, and thus had to set up new U.S.-regulated IHCs altogether, form our "treatment" group. We also include here those IHC-subject banks that were able to reduce their U.S. non-branch and agency assets below $50 billion, and thus avoided the IHC rule.5 Our testable hypothesis is that IHC-affected banks that had to set up new holding companies to comply with the IHC rule responded by transferring assets from their US-regulated entities (i.e., subsidiaries, broker-dealers, etc.) to their less regulated entities – namely, U.S. branches and agencies.6 We use the rarely accessed FR Y-7Q reports for our analysis, which collect quarterly consolidated regulatory data on assets and capitalization from all FBOs that were on the path to become holding companies.7 In our difference-in-differences analysis, we compare changes in the branch (less regulated) and non-branch (US-regulated) assets of our control and treatment groups. We focus on the 2014 Q4 to 2018 Q1 period, comprising a symmetric window of seven quarters before vs. seven quarters after the IHC rule became binding in July of 2016. For our "benchmark date," we choose the end of Q4 of 2015. We choose this date for two reasons. First, January 2016 was the deadline for banks to submit any written request for multiple IHCs or alternative structures to the Federal Reserve – and the Federal Reserve provided a decision on the majority of such requests in February 2016. Therefore, FBOs learned of their post-IHC organizational structure prior to end-Q1 2016.8 Second, a test of parallel trends indicates 2016 Q1 as the period at which asset trends for our treatment and control groups start to diverge.9 A quick review of the data reveals that FBOs that were required to form a new holding company to meet the IHC rule (our treatment group) have increased their less regulated U.S. branch assets (Figures 2 and 3). Furthermore, FBOs have reduced their US-regulated non-branch assets (Figure 4) substantially relative to those banks which already had a holding company in place (our control group). In fact, the reduction in FBO assets that would be subject to the IHC rule began in advance of the benchmark date in 2015 (Figure 4), as affected FBOs not only shifted assets to branches, but also migrated assets abroad. As banks reduced their US-based assets primarily by cutting their IHC rule-affected non-branch assets, the ratio of less regulated branch assets to US-regulated non-branch assets shows a similar evolution as the ratio of branch to total US assets (Figure 5). Notably, the overall migration from IHC-subject assets to less regulated units (either their US-based branches and agencies or foreign entities) has continued for a long time period, past the end of our sample in 2018 Q1. Most assets have moved from primary dealer and repo operations, together with US loans and commercial paper funding, all of which are USD denominated. ##### Figure 2. Non-US regulated US branch assets before/after IHC rule ##### Figure 3. Non-US regulated US branch over total US-based assets ##### Figure 4. US-regulated IHC assets before/after IHC rule ##### Figure 5. Non-US regulated US branch over US-regulated IHC assets Table A1 provides summary statistics for our control and treatment groups. We estimate the following difference-in-differences specifications: $(1) \ \ \ {ln(X)}_{j,t} = \alpha_1 + \alpha_2 {POST\_IHC}_t + \alpha_3 {Post\_IHC}_t \times {Treated}_j + {Controls}_{j,t} + \varepsilon_{j,t}$ where $ln(X)_{j,t}$ denotes the natural logarithm of US-based branch assets of bank $j$ in year-quarter $t$. The vector $Controls$ contains lagged total assets and combinations of bank and time fixed effects. In additional estimations, we also use the share of bank j's US-based branch assets in total US assets as the dependent variable. We do not have a prior on the sign of $\alpha_2$ – it depends on whether our control banks chose to reduce their US-based branch assets relative to the pre-IHC period. Importantly for our identification, we expect FBOs which were required to set up new IHCs to reallocate assets from US-regulated non-branches to less regulated U.S. branches. As such, we expect that these banks increased their branch assets more relative to banks that already had holding companies in place: $\alpha_3>0$. Similarly, for the share of FBOs' holdings of US-regulated non-branch assets, we estimate: $(2) \ \ \ {ln(Y)}_{j,t}=\beta_1+\beta_2{Post\_IHC}_t+\beta_3{Post\_IHC}_t\times{Treated}_j+\beta_4{Treated}_j+{Controls}_{j,t}+\varepsilon_{j,t}$ where ${ln(Y)}_{j,t}$ denotes the natural logarithm of US-based non-branch assets of bank $j$ in year-quarter $t$. Again, we do not have priors for the sign of $\beta_2$. But, importantly, we expect FBOs which were required to set up new IHCs to reduce US-regulated non-branch assets more relative to banks that already had holding companies: $\beta_3<0$. Lastly, we look at the overall composition of FBOs' US-based assets, and examine the ratio of less-regulated branch assets to US-regulated non-branch assets. $(3) \ \ \ Z_{j,t}=\gamma_1+\gamma_2{Post\_IHC}_t+\gamma_3{Post\_IHC}_t\times{Treated}_j+\gamma_4{Treated}_j+{Controls}_{j,t}+\varepsilon_{j,t}$ where $Z_{j,t}$ denotes the ratio of branch to non-branch assets of bank $j$ in year-quarter $t$. We expect FBOs, which were required to set up new IHCs, to increase branch assets relative to non-branch assets more relative to banks that already had holding companies: $\gamma_3>0$. #### Estimation results We find compelling evidence that US-based FBOs with no pre-existing holding companies increased their less regulated branch assets and reduced their US-regulated non-branch assets relative to those FBOs which already had a holding company in place. Table 1 shows the results of estimating Equations (1) and (2), using total branch assets (Columns 1 and 2) and total non-branch assets (Columns 3 and 4) as dependent variables. Columns 1 and 3 include lagged total assets as controls, and Columns 2 and 4 add bank and time fixed effects. Consistent with our hypothesis, we find significant and positive coefficient estimates on the interaction terms: after their IHC status became certain at the end of 2015 Q4, FBOs with no pre-existing holding companies increased their less regulated branch assets in the U.S. by around 27 percent more than banks in our control group. At the same time, they also lowered their non-branch assets that would be subject to the IHC regulations by around 20 percent (top row). Validating our difference-in-differences setup, there is no systematic difference in the branch or non-branch assets of banks in our control group before vs. after 2015 Q4 (second row). In addition, there is no systematic difference between our treatment or control groups before 2015 Q4 (third row). ##### Table 1 VARIABLES Assets of U.S. Branches and Agencies Assets of U.S. Branches and Agencies US-regulated IHC-subject Assets US-regulated IHC-subject Assets Post-IHC dummy * Treatment dummy 0.273** 0.288** -0.212* -0.192* [0.122] [0.127] [0.125] [0.0915] Post-IHC dummy -0.0805 0.0373 [0.0627] [0.0321] Treatment dummy 0.496 0.11 [0.491] [0.179] Total U.S. assets (t-1) 0.615*** 0.663*** 0.690*** 0.646*** [0.163] [0.174] [0.184] [0.203] Constant 2.909 2.696 3.496 4.01 [1.870] [2.171] [2.241] [2.544] Observations 190 190 196 196 Number of banks 14 14 14 14 Bank Fixed Effects No Yes No Yes Time Fixed Effects No Yes No Yes Robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 In Table 2, we study the share of branch assets in total assets (Columns 1 and 2) and the ratio of branch to non-branch assets (Columns 3 and 4) as dependent variables. These results also consistently and significantly support the asset reallocation story. We find that FBOs with no pre-existing holding companies increased the share of branch assets in total U.S. assets by about 10 percentage points (Columns 1 and 2), and the gap in the share of branch vs non-branch assets also increased by nearly 20 percentage points (top row). As before, and supporting our empirical specification, there is no significant difference in the branch or non-branch assets of banks in our control group before vs. after 2015 Q4 and there is no systematic difference between our treatment or control groups before 2015 Q4. ##### Table 2 VARIABLES Ratio of Assets of U.S. Branches and Agencies to total US-based assets Ratio of Assets of U.S. Branches and Agencies to total US-based assets Ratio of Assets of U.S. Branches and Agencies to US-regulated IHC-subject assets Ratio of Assets of U.S. Branches and Agencies to US-regulated IHC-subject assets Post-IHC dummy * Treatment dummy 0.0947** 0.0947** 0.189** 0.163** [0.0396] [0.0407] [0.0793] [0.0722] Post-IHC dummy -0.0156 -0.0312 [0.0133] [0.0265] Treatment dummy 0.00969 0.0194 [0.0814] [0.163] Constant 0.242*** 0.277*** -0.516*** -0.447*** [0.0617] [0.0193] [0.123] [0.0363] Observations 196 196 196 196 Number of banks 14 14 14 14 Bank Fixed Effects No Yes No Yes Time Fixed Effects No Yes No Yes Robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 #### Conclusion We use detailed regulatory data to examine whether FBOs responded to the implementation of the IHC rule, and find consistent evidence that this rule had spurred FBOs to reallocate their assets from their US-regulated non-branch assets toward their less regulated branches in the US. This behavior highlights an additional consequence of the IHC rule, and is consistent with regulatory arbitrage — with possible financial stability implications, as U.S. regulators have limited purview of growing assets held via US-based branches of FBOs. #### References David Polk (2014). "U.S. Intermediate Holding Company: Structuring and Regulatory Considerations for Foreign Banks" (April 2). DiSalvo, James (2019). "Banking trends: How Foreign Banks Changed after Dodd–Frank," FRB Philadelphia Research Department Fillat, José L., Stefania Garetto and Arthur V. Smith. "Global banking, local stress: How multinational banks transmit shocks," voxeu.org (November 2018). Financial Times (2019). "European banks slash$280bn from main U.S. businesses," November 24.
Kreicher, Lawrence L and Robert N McCauley (2018). "The new U.S. intermediate holding companies: reducing or shifting assets?," BIS Quarterly Review (March 2018)
Parchimowicz, Katarzyna M. (2019). "Missed targets and misplaced incentives? The case of parent undertaking requirement in the USA and in the EU," Journal of Banking Regulation, pp. 1–12.
Wall, Larry D. (2017). "Recent changes in U.S. regulation of large foreign banking organizations," Journal of Financial Regulation and Compliance 25(3), pp. 318-332
#### Appendix
##### Table A1
VARIABLES mean sd p25 p50 p75 N
Total US assets ($million) 263,658 94,321 193,486 270,656 336,957 204 Total US non-branch assets ($ million) 188,282 77,576 134,654 152,764 260,388 168
Total US branch assets (\$ million) 68,529 49,518 31,471 61,305 91,602 168
Post-IHC dummy 0.529 0.5 0 1 1 204
Treatment dummy 0.417 0.494 0 0 1 204
Ratio of Assets of U.S. Branches and Agencies to total US-based assets 0.262 0.152 0.144 0.261 0.371 168
Ratio of Assets of U.S. Branches and Agencies to US-regulated IHC-subject assets -0.477 0.303 -0.712 -0.478 -0.257 168
1. We thank Mark Fischer at the FRB of New York and Jose Berrospide and Rebecca Zarutskie at the Federal Reserve Board for useful comments. Return to text
3. For example, each large FBO is required to establish a U.S. risk committee with at least one independent director which oversees all U.S. operations. Furthermore, U.S. branches and agencies must certify they meet capital standards on a consolidated basis consistent with Basel capital standards, and they have to maintain a 14-day U.S. liquidity buffer. Return to text
4. In the note we use the term US-regulated assets/subsidiaries to refer to those assets that are subject to the IHC, and less regulated assets refer to U.S. branches and agencies that are outside the IHC. Return to text
5. In alternative specifications, we exclude the two banks that had avoided the IHC rule through asset reduction, and find that our results are robust to the exclusion of these banks. Return to text
6. A similarly important issue, which we do not address in this note, is the cross-border asset migration from the US-based entities of FBOs to units of the global bank in other countries, in response to the IHC rule implementation (see, for instance, Financial Times, 2019). Return to text
7. Comprehensive FBO-level data on total U.S. assets, broken down by total US-regulated assets and less regulated assets, is available starting in Q4 of 2014: https://www.federalreserve.gov/apps/reportforms/reportdetail.aspx?sOoYJ+5BzDYZF7OsZFXqBA==. Return to text
9. An alternative benchmark date is of course the date the IHC rule became binding, July 1, 2016. However, we prefer the earlier benchmark as banks, aware of their upcoming structural changes, began the reallocation of their assets several quarters ahead of the binding deadline (Kreicher and McCauley, 2018). Our results are robust to using July 1 2016 as the benchmark date. Return to text
Paligorova, Teodora, and Judit Temesvary (2021). "Foreign banks' asset reallocation in response to the introduction of the Intermediate Holding Company rule of 2016," FEDS Notes. Washington: Board of Governors of the Federal Reserve System, May 12, 2021, https://doi.org/10.17016/2380-7172.2886.
Disclaimer: FEDS Notes are articles in which Board staff offer their own views and present analysis on a range of topics in economics and finance. These articles are shorter and less technically oriented than FEDS Working Papers and IFDP papers.
| 2021-06-15T06:31:26 |
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|
https://tjyj.stats.gov.cn/CN/Y2012/V29/I12/69
|
• 论文 •
### 通货膨胀的宏观经济影响因素分析
• 出版日期:2012-12-15 发布日期:2012-12-19
### Analysis of Macroeconomic Influencing Factors to Inflation
Zhao Jinwen&Ding Lintao
• Online:2012-12-15 Published:2012-12-19
Abstract: Firstly, we establish a Bayesian Vector Auto-regression (BVAR) model and analyze the impulse responses of inflation to macroeconomic factors and its intensity. In addition, we establish a Threshold model and analyze the threshold effects of inflation when different variables are used as threshold variables. Through the empirical researches, we find that the impulse responses of inflation to shocks from six factors are different. The temporary response to excess liquidity is the most strongest and those to stock price, output gap and oil price are moderate. Then the intensity responding to real exchange rate and house price are the weakest. The stock price, real exchange rate and oil price have obvious threshold characteristics, which can separately divide the inflation into high and low status. These findings help us understand and recognize the responding mechanism of inflation better. Thus we can take sound economic policies to deal with inflation.
| 2022-07-02T04:48:50 |
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|
http://dlmf.nist.gov/33.6
|
# §33.6 Power-Series Expansions in $\rho$
33.6.1 $\mathop{F_{\ell}\/}\nolimits\!\left(\eta,\rho\right)=\mathop{C_{\ell}\/}% \nolimits\!\left(\eta\right)\sum_{k=\ell+1}^{\infty}A_{k}^{\ell}(\eta)\rho^{k},$
33.6.2 ${\mathop{F_{\ell}\/}\nolimits^{\prime}}\!\left(\eta,\rho\right)=\mathop{C_{% \ell}\/}\nolimits\!\left(\eta\right)\sum_{k=\ell+1}^{\infty}kA_{k}^{\ell}(\eta% )\rho^{k-1},$
where $A_{\ell+1}^{\ell}=1$, $A_{\ell+2}^{\ell}=\eta/(\ell+1)$, and
33.6.3 $(k+\ell)(k-\ell-1)A_{k}^{\ell}=2\eta A_{k-1}^{\ell}-A_{k-2}^{\ell},$ $k=\ell+3,\ell+4,\dots$,
or in terms of the hypergeometric function (§§15.1, 15.2(i)),
33.6.4 $A_{k}^{\ell}(\eta)=\dfrac{(-i)^{k-\ell-1}}{(k-\ell-1)!}\*\mathop{{{}_{2}F_{1}}% \/}\nolimits\!\left(\ell+1-k,\ell+1-i\eta;2\ell+2;2\right).$
33.6.5 $\mathop{{H^{\pm}_{\ell}}\/}\nolimits\!\left(\eta,\rho\right)=\frac{e^{\pm i% \mathop{{\theta_{\ell}}\/}\nolimits\!\left(\eta,\rho\right)}}{(2\ell+1)!% \mathop{\Gamma\/}\nolimits\!\left(-\ell+i\eta\right)}\left(\sum_{k=0}^{\infty}% \frac{\left(a\right)_{k}}{\left(2\ell+2\right)_{k}k!}(\mp 2i\rho)^{a+k}\left(% \mathop{\ln\/}\nolimits\!\left(\mp 2i\rho\right)+\mathop{\psi\/}\nolimits\!% \left(a+k\right)-\mathop{\psi\/}\nolimits\!\left(1+k\right)-\mathop{\psi\/}% \nolimits\!\left(2\ell+2+k\right)\right)-\sum_{k=1}^{2\ell+1}\frac{(2\ell+1)!(% k-1)!}{(2\ell+1-k)!\left(1-a\right)_{k}}(\mp 2i\rho)^{a-k}\right),$
where $a=1+\ell\pm i\eta$ and $\mathop{\psi\/}\nolimits\!\left(x\right)={\mathop{\Gamma\/}\nolimits^{\prime}}% \!\left(x\right)/\mathop{\Gamma\/}\nolimits\!\left(x\right)$5.2(i)).
The series (33.6.1), (33.6.2), and (33.6.5) converge for all finite values of $\rho$. Corresponding expansions for ${\mathop{{H^{\pm}_{\ell}}\/}\nolimits^{\prime}}\!\left(\eta,\rho\right)$ can be obtained by combining (33.6.5) with (33.4.3) or (33.4.4).
| 2014-10-31T17:16:07 |
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|
https://mooseframework.inl.gov/source/kernels/PorousFlowAdvectiveFlux.html
|
## Information and Tools
Fully-upwinded advective flux of the component given by fluid_component
This Kernel implements the weak form of where all parameters are defined in the nomenclature.
note
A fully-upwinded version is implemented, where the mobility of the upstream nodes is used.
See upwinding for details. Other Kernels implement Kuzmin-Turek TVD stabilization.
## Input Parameters
• variableThe name of the variable that this Kernel operates on
C++ Type:NonlinearVariableName
Options:
Description:The name of the variable that this Kernel operates on
• PorousFlowDictatorThe UserObject that holds the list of PorousFlow variable names
C++ Type:UserObjectName
Options:
Description:The UserObject that holds the list of PorousFlow variable names
• gravityGravitational acceleration vector downwards (m/s^2)
C++ Type:libMesh::VectorValue
Options:
Description:Gravitational acceleration vector downwards (m/s^2)
### Required Parameters
• blockThe list of block ids (SubdomainID) that this object will be applied
C++ Type:std::vector
Options:
Description:The list of block ids (SubdomainID) that this object will be applied
• fallback_schemequickquick: use nodal mobility without preserving mass. harmonic: use a harmonic mean of nodal mobilities and preserve fluid mass
Default:quick
C++ Type:MooseEnum
Options:quick harmonic
Description:quick: use nodal mobility without preserving mass. harmonic: use a harmonic mean of nodal mobilities and preserve fluid mass
• displacementsThe displacements
C++ Type:std::vector
Options:
Description:The displacements
• full_upwind_threshold5If, for each timestep, the number of upwind-downwind swaps in an element is less than this quantity, then full upwinding is used for that element. Otherwise the fallback scheme is employed.
Default:5
C++ Type:unsigned int
Options:
Description:If, for each timestep, the number of upwind-downwind swaps in an element is less than this quantity, then full upwinding is used for that element. Otherwise the fallback scheme is employed.
• fluid_component0The index corresponding to the fluid component for this kernel
Default:0
C++ Type:unsigned int
Options:
Description:The index corresponding to the fluid component for this kernel
### Optional Parameters
• enableTrueSet the enabled status of the MooseObject.
Default:True
C++ Type:bool
Options:
Description:Set the enabled status of the MooseObject.
• save_inThe name of auxiliary variables to save this Kernel's residual contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)
C++ Type:std::vector
Options:
Description:The name of auxiliary variables to save this Kernel's residual contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)
• use_displaced_meshFalseWhether 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:False
C++ Type:bool
Options:
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.
• control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector
Options:
Description:Adds user-defined labels for accessing object parameters via control logic.
• seed0The seed for the master random number generator
Default:0
C++ Type:unsigned int
Options:
Description:The seed for the master random number generator
• diag_save_inThe name of auxiliary variables to save this Kernel's diagonal Jacobian contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)
C++ Type:std::vector
Options:
Description:The name of auxiliary variables to save this Kernel's diagonal Jacobian contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)
• implicitTrueDetermines whether this object is calculated using an implicit or explicit form
Default:True
C++ Type:bool
Options:
Description:Determines whether this object is calculated using an implicit or explicit form
• vector_tagsnontimeThe tag for the vectors this Kernel should fill
Default:nontime
C++ Type:MultiMooseEnum
Options:nontime time
Description:The tag for the vectors this Kernel should fill
• extra_vector_tagsThe extra tags for the vectors this Kernel should fill
C++ Type:std::vector
Options:
Description:The extra tags for the vectors this Kernel should fill
• matrix_tagssystemThe tag for the matrices this Kernel should fill
Default:system
C++ Type:MultiMooseEnum
Options:nontime system
Description:The tag for the matrices this Kernel should fill
• extra_matrix_tagsThe extra tags for the matrices this Kernel should fill
C++ Type:std::vector
Options:
Description:The extra tags for the matrices this Kernel should fill
| 2019-02-23T13:39:47 |
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|
https://par.nsf.gov/biblio/10258070-uncertain-times-redshifttime-relation-from-cosmology-stars
|
skip to main content
Uncertain times: the redshift–time relation from cosmology and stars
ABSTRACT Planck data provide precise constraints on cosmological parameters when assuming the base ΛCDM model, including a 0.17 per cent measurement of the age of the Universe, $t_0=13.797 \pm 0.023\, {\rm Gyr}$. However, the persistence of the ‘Hubble tension’ calls the base ΛCDM model’s completeness into question and has spurred interest in models such as early dark energy (EDE) that modify the assumed expansion history of the Universe. We investigate the effect of EDE on the redshift–time relation z↔t and find that it differs from the base ΛCDM model by at least ${\approx } 4{{\ \rm per\ cent}}$ at all t and z. As long as EDE remains observationally viable, any inferred t ← z or z ← t quoted to a higher level of precision do not reflect the current status of our understanding of cosmology. This uncertainty has important astrophysical implications: the reionization epoch – 10 > z > 6 – corresponds to disjoint lookback time periods in the base ΛCDM and EDE models, and the EDE value of t0 = 13.25 ± 0.17 Gyr is in tension with published ages of some stars, star clusters, and ultrafaint dwarf galaxies. However, most published stellar ages do not include an uncertainty in accuracy (due to, e.g. uncertain more »
Authors:
;
Award ID(s):
Publication Date:
NSF-PAR ID:
10258070
Journal Name:
Monthly Notices of the Royal Astronomical Society
Volume:
505
Issue:
2
Page Range or eLocation-ID:
2764 to 2783
ISSN:
0035-8711
Sponsoring Org:
National Science Foundation
##### More Like this
1. ABSTRACT The canonical Lambda cold dark matter (ΛCDM) cosmological model makes precise predictions for the clustering and lensing properties of galaxies. It has been shown that the lensing amplitude of galaxies in the Baryon Oscillation Spectroscopic Survey (BOSS) is lower than expected given their clustering properties. We present new measurements and modelling of galaxies in the BOSS LOWZ sample. We focus on the radial and stellar mass dependence of the lensing amplitude mismatch. We find an amplitude mismatch of around $35{{\ \rm per\ cent}}$ when assuming ΛCDM with Planck Cosmological Microwave Background (CMB) constraints. This offset is independent of halomore »
2. ABSTRACT Stellar and supernova nucleosynthesis in the first few billion years of the cosmic history have set the scene for early structure formation in the Universe, while little is known about their nature. Making use of stellar physical parameters measured by GALAH Data Release 3 with accurate astrometry from the Gaia EDR3, we have selected ∼100 old main-sequence turn-off stars (ages ≳12 Gyr) with kinematics compatible with the Milky Way stellar halo population in the Solar neighbourhood. Detailed homogeneous elemental abundance estimates by GALAH DR3 are compared with supernova yield models of Pop III (zero-metal) core-collapse supernovae (CCSNe), normal (non-zero-metal) CCSNe,more »
3. ABSTRACT We use FIRE simulations to study disc formation in z ∼ 0, Milky Way-mass galaxies, and conclude that a key ingredient for the formation of thin stellar discs is the ability for accreting gas to develop an aligned angular momentum distribution via internal cancellation prior to joining the galaxy. Among galaxies with a high fraction ($\gt 70{{\ \rm per\ cent}}$) of their young stars in a thin disc (h/R ∼ 0.1), we find that: (i) hot, virial-temperature gas dominates the inflowing gas mass on halo scales (≳20 kpc), with radiative losses offset by compression heating; (ii) this hot accretion proceedsmore »
4. ABSTRACT We study stellar-halo formation using six Milky-Way-mass galaxies in FIRE-2 cosmological zoom simulations. We find that $5{-}40{{\ \rm per\ cent}}$ of the outer (50–300 kpc) stellar halo in each system consists of in-situ stars that were born in outflows from the main galaxy. Outflow stars originate from gas accelerated by superbubble winds, which can be compressed, cool, and form co-moving stars. The majority of these stars remain bound to the halo and fall back with orbital properties similar to the rest of the stellar halo at z = 0. In the outer halo, outflow stars are more spatially homogeneous, metal-rich, and alpha-element-enhancedmore »
5. ABSTRACT Recent searches for the hosts of z ∼ 4 damped Ly α absorbers (DLAs) have detected bright galaxies at distances of tens of kpc from the DLA. Using the FIRE-2 cosmological zoom simulations, we argue that these relatively large distances are due to a predominantly cool and neutral inner circumgalactic medium (CGM) surrounding high-redshift galaxies. The inner CGM is cool because of the short cooling time of hot gas in ${\lesssim}10^{12}\, {\rm M_{\odot }}$ haloes, which implies that accretion and feedback energy are radiated quickly, while it is neutral due to high volume densities and column densities at high redshiftmore »
| 2022-08-19T22:29:53 |
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|
https://pos.sissa.it/398/790/
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Volume 398 - The European Physical Society Conference on High Energy Physics (EPS-HEP2021) - T12: Detector R&D and Data Handling
First results of the newly installed, MAPS based, ALICE Inner Tracking System
J. Liu
Full text: Not available
Abstract
The ALICE Inner Tracking System (ITS) has recently been replaced with a full silicon pixel detector constructed entirely with CMOS monolithic active pixel sensors. It consists of three inner layers ($50\ \mu m$ thick sensors) and four outer layers ($100\ \mu m$ thick sensors) covering $10\ m^{2}$ and containing 12.5 billion pixels with a pixel size of $27 \ \mu \times 29\ \mu m$. Its increased granularity, the very low material budget ($0.35\%\ X_{0}/layer$ in the inner barrel) as well as a small radius of the innermost layer combined with a thin beam pipe, will result in a significant improvement of impact-parameter resolution and tracking efficiency at low $p_{T}$ with respect to the previous tracker.
The assembly of the full detector and services finished in December 2019. A comprehensive commissioning phase (on surface) was completed in December 2020, including detector calibration, fake-hit rate determination, data transmission tests and preliminary evaluation of the detector efficiency and the alignment of the sensors, based on a reconstruction of cosmic-ray tracks. The commissioning of the new ITS within the ALICE apparatus has started in May 2021. After a first phase of standalone tests and detector performance optimization, the detector has been included in the global commissioning activities from July 2021. In this paper, the detector design as well as the first results of the performance studied during the commissioning for the detector will be discussed.
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.
| 2022-01-19T04:25:13 |
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|
https://www-physics.lbl.gov/seminars/old/feldman.html
|
The NO$\nu$A Experiment:
Abstract:
The NO$\nu$A experiment will be a second-generation experiment on the Fermilab NuMI neutrino beamline. It is designed to improve the measurements of the $\theta_{23}$ and $\theta_{13}$ neutrino mixing parameters by approximately an order of magnitude from what is possible with the MINOS experiment. A non-zero value of $\theta_{13}$ will open the door to measurements of the ordering of the neutrino masses and CP violation in the lepton sector. The long baseline of the NO$\nu$A experiment gives it a unique opportunity to measure the mass ordering.
| 2022-09-29T07:41:16 |
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|
https://tangentiaventures.com/unepic-switch-afozev/what-is-meant-by-common-ion-effect-1f3fce
|
# what is meant by common ion effect
Video on YouTube Creative Commons Attribution/Non-Commercial/Share-Alike http://en.wikipedia.org/wiki/Le_Chatelier The common ion effect describes the effect on âequilibrium that occurs when a common ion (an ion that is already contained in the solution) is added to a solution. Boundless vets and curates high-quality, openly licensed content from around the Internet. The result is that some of the chloride is removed and made into lead(II) chloride. She has taught science courses at the high school, college, and graduate levels. Or in other words, superposition of the degree of dissociation of weak electrolyte due to the addition of strong electrolyte having common ion ⦠Does the presence of a common ion increase or decrease the solubility of the insoluble salt? As one salt dissolves, it affects how well the other salt can dissolve, essentially making it less soluble. OK, this sounds complicated, but it is actually easy to understand. Odd-ion effect occurs when any ion from other electrolyte consumes any ion from interfering electrolyte and hence neutralises common ion effect so degree of dissociation of weak electrolyte is increased. What is the common ion effect? Briefly explain what is meant by the common ion effect. The common-ion effect occurs whenever you have a sparingly soluble compound. What does a large x value mean? The sodium chloride ionizes into sodium and chloride ions: The additional chlorine anion from this reaction decreases the solubility of the lead(II) chloride (the common-ion effect), shifting the lead chloride reaction equilibrium to counteract the addition of chlorine. Then if we add HF, since it is a weak acid, the high concentration of F- already present in solution shifts the equilibrium to the left, hence fewer H+ forms than expected so higher pH. Wiktionary So that's one use for the common ion effect in the laboratory separation. Common ion effect. Wiktionary The common ion effect also plays a role in the regulation of buffers. When we are at equilibrium, the IAP and Ksp have the same value. This equilibrium is established when the rates of migration between the solid and aqueous phases of the molecules (or ions) are equal. Sodium Chloride: The Molecular Formula of Table Salt. Lets look at barium sulfate, which in chapter 3.4 we learned was an insoluble salt. Chemical equilibrium is the chemical state where there are no net physical or chemical changes between the reactant and the products of a reaction. Boundless Learning Helmenstine, Anne Marie, Ph.D. "Common-Ion Effect Definition." b) The shift in an ionic equilibrium caused by the addition of a solute that furnishes an ion that doesn't take part in the equilibrium. Ex: Silver ions are precipitated as silver chloride, Barium ions as Barium sulphate, and Ferric ion as Ferric chloride or Ferric sulphate. Ans: By adding common ions to a saturated solution, the equilibrium shifts towards the left. While the lead chloride example featured a common anion, the same principle applies to a common cation. The common ion effect is the suppression of the degree of dissociation of a weak electrolyte containing a common ion. For example, when calcium fluoride dissolves into calcium and fluoride ions, the solubility product expression is: $CaF_{2(s) }\leftrightarrow { Ca^{+2} }_{ (aq) }+{ 2F^{-} }_{ (aq) }$. The common ion effect is used to reduce the concentration of one of the products in an aqueous equilibrium. If the salts share a common cation or anion, both contribute to the concentration of the ion and need to be included in concentration calculations. The common ion effect can be explained by Le Chatelier’s principle of chemical equilibrium: $AB_{(s) }\leftrightarrow { A^+ }_{ (aq) } + { B^-}_{ (aq) }$. The percent dissociation of the hydrogen cyanide will decrease, therefore decreasing the H+ ions and increasing the pH of the solution. http://en.wiktionary.org/wiki/conjugate_acid, http://en.wiktionary.org/wiki/conjugate_base, http://www.chem1.com/acad/webtext/solut/solut-6a.html#SEC1, http://en.wikipedia.org/wiki/Le_Chatelier, http://en.wikipedia.org/wiki/Common-ion_effect, http://commons.wikimedia.org/wiki/File:Lithium_hydroxide_with_carbonate_growths.JPG, https://www.boundless.com/chemistry/textbooks/boundless-chemistry-textbook/. It states that if the concentration of any one of the ions is increased, then, according to Le Chatelier 's principle , the ions in excess should combine with ⦠Jun 15 2015 02:26 AM. The common ion effect is responsible for the reduction in solubility of an ionic precipitate when a soluble compound combining one of the ions of the precipitate is added to the solution in equilibrium with the precipitate. According to Le Chatelier’s principle, addition of more ions alters the equilibrium and shifts the reaction to favor the solid or deionized form. Solubility equilibrium refers to the state of chemical equilibrium between a chemical compound in the solid state and a solution composed of that dissolved compound. Or in other words, superposition of the degree of dissociation of weak electrolyte due to the addition of strong electrolyte having common ion is called as common ion effect. The addition of either of these two ions (from a compound or solution with an ion in common) will decrease the solubility of the compound with low solubility. Wiktionary Common-Ion Effect Definition. Therefore, the common ion effect takes a role in pH regulation. $HCN_{(aq)}\leftrightarrow {H^+}_{(aq)} + {CN^-}_{(aq)}$. This phenomenon is the common ion effect and plays important roles in pharmaceutical and environmental areas. This expression must always hold, even if some ionic species come from other sources. CC BY-SA 3.0. http://en.wiktionary.org/wiki/buffer For a simple dissolution process, the addition of more of one of the ions (A+) from another compound will shift the composition to the left, reducing the concentration of the other ion (B–), effectively reducing the solubility of the solid (AB). In common ion effect, weak electrolytes get suppressed when a strong electrolyte is added to the solution. General Chemistry (11th Edition) Edit edition. (a) (i) What is meant by the common ion effect? Examples. If we add a basic salt NaF, it will fully dissociate to give F-. How many grams of Fe(OH)2 (K = 1.8 x 10¯15) will dissolve in one liter of water buffered at ⦠Give an example. Therefore, precipitation occurs rapidly. Common-ion effect describes the suppressing effect on ionization of an electrolyte when another electrolyte is added that shares a common ion. For example, table salt (NaCl) placed in water eventually dissolves. This topic also discuss the effect of a common ion on the dissociation of weak acids in water. The common-ion effect is a term used to describe the effect on a solution of two For example Identify common neurotransmitters and their effect in the body respond by opening nearby ion channels in the for example, exert their effects primarily on the What is meant by the common-ion effect? The presence of a common ion suppresses the ionization of a weak acid or a weak base. [1] (ii) Give the conjugate acid and the conjugate base for NH 3. CC BY-SA 3.0. http://commons.wikimedia.org/wiki/File:Lithium_hydroxide_with_carbonate_growths.JPG If to an ionic equilibrium, AB A + + Bâ¾ , a salt containing a common ion is added, the equilibrium shifts in the backward direction. Common Ion Effect on Solubility 3 9. conjugate baseThe species that is created after the donation of a proton. Problem 11QP from Chapter 16: What is meant by the common-ion effect? The latter case is known as buffering. That is, do large x values mean more solid has dissolved? From my textbook, it is stated that: e.g. A combination of salts in an aqueous solution will all ionize according to the solubility products, which are equilibrium constants describing a mixture of two phases. Wikimedia (adsbygoogle = window.adsbygoogle || []).push({}); Solubility refers to the amount of material that is able to be dissolved in a particular solvent. This is called common Ion effect. Q.34. You ⦠bufferA solution used to stabilize the pH (acidity) of a liquid. Common ion effect is used for the complete precipitation of one of the ions as its sparingly soluble salt with a very low value of solubility product for gravimetric estimation. Whenever a solution of an ionic substance comes into contact with another ionic compound with a common ion, the solubility of the ionic substance decreases significantly. The common ion effect generally decreases âsolubility of a solute. Addition of excess ions will alter the pH of the buffer solution. This particular resource used the following sources: http://www.boundless.com/ As the concentration of one ion increases, the concentration of other ion decreases to satisfy the Ksp value. The amount of NaCl that could dissolve to reach the saturation point would be lowered. It also can have an effect on buffering solutions, as adding more conjugate ions may shift the pH of the solution. CC BY-SA 3.0. http://en.wikipedia.org/wiki/Common-ion_effect conjugate acidThe species created when a base accepts a proton. For example, consider what happens when you dissolve lead(II) chloride in water and then add sodium chloride to the saturated solution. It is called common ion effect. The common ion effect can change the ion activity product (IAP) as long as the solution is not at equilibrium and this in turn will change the saturation index (SI), some use a saturation ratio, where the SI = log (IAP)/Ksp. A buffer solution is composed of a weak acid and its conjugate base, or a weak base and its conjugate acid. The common-ion effect refers to the decrease in solubility of an ionic precipitate by the addition to the solution of a soluble compound with an ion in common with the precipitate. A compound of low solubility forms two ions in a saturated solution. common-ion effect, decrease in solubility of an ionic salt, i.e., one that dissociates in solution into its ions, caused by the presence in solution of another solute that contains one of the same ions as the salt. Get solutions In the case of an an acidic buffer, the hydrogen ion concentration decreases, and the resulting solution is less acidic than a solution containing the pure weak acid. The common ion effect is the phenomenon in which the addition of an ion common to two solutes causes precipitation or reduces ionization. Is Dissolving Salt in Water a Chemical Change or Physical Change? Precipitate Definition and Example in Chemistry, Why Adding Salt to Water Increases the Boiling Point, Make Potassium Chlorate from Bleach and Salt Substitute, Ph.D., Biomedical Sciences, University of Tennessee at Knoxville, B.A., Physics and Mathematics, Hastings College. What is meant by common ion effect? Whenever a solution of an ionic substance comes into contact with another ionic compound with a common ion, the solubility of the ionic substance decreases significantly. ThoughtCo. Le Chatelier’s principleThe principle used to predict the effect of a change in conditions on a chemical equilibrium. Dr. Helmenstine holds a Ph.D. in biomedical sciences and is a science writer, educator, and consultant. What is a solubility product? For example, this would be like trying to dissolve solid table salt (NaCl) in a solution where the chloride ion (Cl–) is already present. However, if more table salt is continuously added, the solution will reach a point at which no more can be dissolved; in other words, the solution is saturated, and the table salt has effectively reached its solubility limit. The role that the common ion effect plays in solutions is mostly visible in the decrease of solubility of solids. Steve Lower’s Website The F- is the common ion shifting it to the left is a common ion effect. This may mean reducing the concentration of a toxic metal ion, or controlling the pH of a solution. Therefore, if more $Ca^{+2}$ ions are placed in solution, the equilibrium will shift to the left, favoring the solid form and decreasing the solubility of the solid. Due to the common ion effect that decreases the solubility of lead two chloride which means we are gonna get more of our solid because our goal is to isolate as much of our solid as possible. Sup-port your answer with evidence from Model 1. ⦠After watching this video you will be able to: Describe the effect of common ions on the percent ionization of weak acids and bases. You will decrease the ionization of that acid and you will have in solution a fair amount of both the acid form, and the base form of that buffer. Cecilia answered on ⦠In common ion effect, weak electrolytes get suppressed when a strong electrolyte is added to the solution. Common ion effect 1 answer below » sir i did not understand what is meant by common ion effect in acids and bases concept .so please explain about that. Helmenstine, Anne Marie, Ph.D. (2020, August 28). Public domain. Determine the pH of the solution made from the weak acid / weak base in the presence of the common ion. a) The shift in an ionic equilibrium caused by the removal of some ions that take part in the equilibrium. Helmenstine, Anne Marie, Ph.D. "Common-Ion Effect Definition." CC BY-SA 3.0. http://en.wiktionary.org/wiki/conjugate_acid CC BY-SA 3.0. http://www.chem1.com/acad/webtext/solut/solut-6a.html#SEC1 The common-ion effect is used to describe the effect on an equilibrium involving a substance that adds an ion that is a part of the equilibrium. Addition of more like conjugate ions will ultimately shift the pH of the solution. Double Displacement Reaction Definition and Examples. This behaviour is a consequence of Le Chatelier's principle for the equilibrium reaction of the ionic association/dissociation. The common ion effect must be taken into consideration when determining solution equilibrium upon addition of ions that are already present in the solution. Wikipedia The common ion effect is a decrease in the solubility of an ionic compound as a result of the addition of a common ion. The addition of cyanide ions (CN–) will suppress the ionization of hydrogen cyanide (HCN) and shift its equilibrium to the left. Common-ion effect describes the suppressing effect on ionization of an electrolyte when another electrolyte is added that shares a common ion. Lead(II) chloride is slightly soluble in water, resulting in the following equilibrium: The resulting solution contains twice as many chloride ions and lead ions. The common-ion effect is a term used to describe the effect on a solution of two dissolved solutes that contain the same ion. Through the addition of common ions, the solubility of a compound generally decreases due to a shift in equilibrium. 10. CC BY-SA 3.0. http://en.wiktionary.org/wiki/conjugate_base 14. The standard reaction potentials of Ag + /Ag and Cd 2+ /Cd are +0.80 volt and -0.40 volt, respectively. What Is an Ionic Equation and How Is It Used? https://www.thoughtco.com/definition-of-common-ion-effect-604938 (accessed February 5, 2021). Buffering solutions contain either an acid or base, accompanied by its conjugate counterpart. Retrieved from https://www.thoughtco.com/definition-of-common-ion-effect-604938. Wikipedia CC BY-SA. Le Chatelier's principle states equilibrium will shift to counter a change when more of a reactant is added. ThoughtCo, Aug. 28, 2020, thoughtco.com/definition-of-common-ion-effect-604938. Q.33. If you add sodium chloride to this solution, you have both lead(II) chloride and sodium chloride containing the chlorine anion. The compound will become less soluble in any solution containing a common ion. The effect of adding a soluble salt with a common ion to an insoluble salt of that ion, which causes more of the insoluble salt to precipitate out (ie., suppresses its ionization). The common-ion effect is an example of chemical equilibrium. To illustrate the "diverse ion effect", we will study how the solubility of $\ce{AgCl}$ changes in absence and presence of $\ce{NaNO3}$, given that the molar solubility product of $\ce{AgCl}$ is $1.76 \times 10^{-10}$. This is because the rate of the forward (reactant to product) and reverse (product to reactant) reactions are equal. [1] (b) Consider the reaction 2Ag + + Cd â 2Ag + Cd 2+. 1 Approved Answer. And this is, in a buffer always what happens when you add the salt that contains the conjugate base, for example. Ions ) are equal chloride example featured a common ion effect in the equilibrium chloride! Conjugate baseThe species that is, in a saturated solution in any solution containing a common cation between the and! One use for the common ion effect is the common ion removed and made into (! The F- is the common ion to describe the effect of a liquid openly licensed from! Low solubility forms two ions in a saturated solution, the solubility of an ionic Equation and is. Is because the rate of the solution of other ion decreases to satisfy the Ksp value holds Ph.D.. Therefore, the solubility of the solution, weak electrolytes get suppressed when a base accepts a proton used. Buffering solutions contain either an acid or base, accompanied by its conjugate acid and its conjugate acid 28. The forward ( reactant to product ) and reverse ( product to reactant ) are. Is composed of a compound generally decreases due to a shift in an ionic equilibrium caused by removal. Is established when the rates of migration between the solid and aqueous phases of the hydrogen cyanide will,! Standard reaction potentials of Ag + /Ag and Cd 2+ soluble compound change in conditions a. The compound will become less soluble in any solution containing a common cation Table (! A shift in an aqueous equilibrium solubility forms two ions in a solution. / weak base in the solubility what is meant by common ion effect solids and this is, do large x values mean more has! Weak acid / weak base and its conjugate counterpart 3.4 we learned was insoluble... Ok, this sounds complicated, but it is stated that:.! Forward ( reactant to product ) and reverse ( product to reactant ) reactions are equal increase or decrease solubility! Ions to a common ion effect 2Ag + Cd â 2Ag + Cd 2+ /Cd are +0.80 volt and volt. / weak base in the solution reducing the concentration of one of the salt... ( a ) ( i ) What is an ionic Equation and how is used... Openly licensed content from around the Internet, Anne Marie, Ph.D. 2020! Therefore, the equilibrium reaction of the solution sparingly soluble compound by its conjugate acid and the base! Use for the equilibrium pH regulation takes a role in pH regulation ion on dissociation. Stated that: e.g is stated that: e.g lead ( II ) chloride and sodium chloride containing the anion... ) of a liquid must always hold, even if some ionic species come from other sources that contains conjugate. Principle for the common ion effect also plays a role in the decrease solubility! Sparingly soluble compound ok, this sounds complicated, but it is stated that:.... 28 ) shifting it to the solution to understand the standard reaction of! ( NaCl ) placed in water eventually dissolves of a common ion effect takes a role in pH regulation 's... Or chemical changes between the solid and aqueous phases of the solution ) of solute... //Www.Thoughtco.Com/Definition-Of-Common-Ion-Effect-604938 ( accessed February 5, 2021 ) a common cation that some of the insoluble.. Of dissociation of the molecules ( or ions ) are equal chemical changes between the solid aqueous! Increase or decrease what is meant by common ion effect solubility of a common ion buffering solutions contain either an or. Product to reactant ) reactions are equal roles in pharmaceutical and environmental areas chloride sodium... Suppresses the ionization of an ionic compound as a result of the made. Around the Internet of le Chatelier ’ s principleThe principle used to stabilize the pH of the solution its counterpart! Visible in the solution forms two ions in a saturated solution, you have sparingly. Electrolyte is added that shares a common cation increases, the common ion NH 3 shift in an aqueous.... Give the conjugate acid and the products of a solution you ⦠the F- is the state. How is it used https: //www.thoughtco.com/definition-of-common-ion-effect-604938 ( accessed February 5, 2021 ) add a basic salt,. Acidity ) of a common ion shifting it to the solution a common ion effect takes a role pH. And curates high-quality, openly licensed content from around the Internet actually to! Answered on ⦠common ion effect takes a role in pH regulation baseThe species that is, in a solution... My textbook, it is actually easy to understand a basic salt NaF, it is actually easy understand. Is an example of chemical equilibrium is established when the rates of migration between reactant. Common cation, it affects how well the other salt can dissolve, essentially making it less.. Example, Table salt pH of the addition of common ions, the IAP Ksp! Mean more solid has dissolved on a solution helmenstine, Anne Marie, Ph.D. common-ion! An electrolyte when another electrolyte is added to the solution Ag + /Ag and Cd 2+ are... Solution equilibrium upon addition of common ions to a shift in an aqueous equilibrium the rate of solution. Equilibrium upon addition of ions that take part in the presence of change... The reactant and the conjugate base, accompanied by its conjugate base, or the. Solution used to stabilize the pH of the solution solutions contain either an or! Species that is created after the donation of a reactant is added shares. Behaviour is a consequence of le Chatelier 's principle for the equilibrium whenever have... Potentials of Ag + /Ag and Cd 2+ /Cd are +0.80 volt and volt. This topic also discuss the effect of a common ion what is meant by common ion effect on buffering solutions as. The H+ ions and increasing the pH of the forward ( reactant to )! A term used to predict the effect of a common ion effect is a decrease in the laboratory separation in. A buffer always What happens when you add the salt that contains conjugate. Reverse ( product to reactant ) reactions are equal affects how well the other can... Species created when a strong electrolyte is added more conjugate ions may the... Conjugate acid and its conjugate counterpart NaF, it will fully dissociate to give F- in sciences. Give the conjugate acid as one salt dissolves, it affects how well the other salt can dissolve essentially. Role that the common ion effect equilibrium will shift to counter a when. Chloride is removed and made into lead ( II ) give the base... Salt can dissolve, essentially making it less soluble 2+ /Cd are +0.80 volt and -0.40 volt,.. Solution of two dissolved solutes that contain the same value effect generally decreases âsolubility of a reactant added! We are at equilibrium, the concentration of one of the molecules ( or ions ) are equal saturation would. Created when a base accepts a proton the saturation point would be lowered water a chemical change or change... The H+ ions and increasing the pH of a proton dissolved solutes that the... Add the salt that contains the conjugate acid and its conjugate acid and the products in ionic! Is actually easy to understand of ions that take part in the presence a. If some ionic species come from other sources removed and made into lead ( II chloride. Of solubility of a common anion, the IAP and Ksp have same! Ph of the degree of dissociation of the solution ionic compound as a of! Equilibrium reaction of the products of a reactant is added to the.! Effect on ionization of an electrolyte when another electrolyte is added to the solution as a result of insoluble! Of buffers this behaviour is a science writer, educator, and consultant another electrolyte added. Physical or chemical changes between the reactant and the conjugate base, accompanied its... Generally decreases âsolubility of a compound of low solubility forms two ions in a buffer What! ) and reverse ( product to reactant ) reactions are equal le Chatelier 's states. Determine the pH of the forward ( reactant to product ) and (! Base in the decrease of solubility of the insoluble salt shift the pH of solution... ) chloride a Ph.D. in biomedical sciences and is a common ion effect come other... Same principle applies to a common ion effect must be taken into consideration when determining equilibrium! ) the shift in an ionic Equation and how is it used dissociate to give F- concentration one..., for example, Table salt ( NaCl ) placed in water eventually dissolves the common effect! You ⦠the F- is the common ion shifting it to the left accompanied its... Role that the common ion effect and plays important roles in pharmaceutical and environmental areas contains conjugate! But it is stated that: e.g is stated that: e.g product ) and reverse product. Product ) and reverse ( product to reactant ) reactions are equal Cd /Cd! Products of a compound generally decreases due to a shift in an aqueous equilibrium change! We add a basic salt NaF, it will fully dissociate to give F- compound generally decreases due a... Dissolving salt in water eventually dissolves ionic species come from other sources where there are no net or... To this solution, you have both lead ( II ) chloride barium,. Of some ions that take part in the solubility of a solute of. X values mean more solid has dissolved can have an effect on 3... The solution â 2Ag + Cd 2+ /Cd are +0.80 volt and -0.40 volt, respectively amount NaCl...
| 2021-05-11T20:25:48 |
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https://www.usgs.gov/center-news/volcano-watch-when-hual-lai-turned-viscous
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Volcano Watch — When Hualālai Turned Viscous
Release Date:
As you make the drive from Waimea to Kona, you may notice a peculiar grassy knoll and an associated hummocky ridge on the northern slope of Hualālai, directly mauka of Kiholo Bay.
The old Mamalahoa Highway, the mountain road to Kona, takes you up and over the Puu Anahulu Ridge and beside the base of Puu Waawaa, Hawaiian for "many-furrowed hill."
The cone stands 372 m (1,220 feet) tall and measures more than 1.6 km (1 mile) in diameter. The ridge runs nearly 9 km (5.5 miles) down Hualālai's slope and rises 275 m (900 feet) from the landscape.
These prominent features seem foreign to Hawaiian topography, because they are composed of rock with an unusual chemical composition that is rare in Hawaii and found nowhere else on the surface of the Big Island. Trachyte, pronounced tra- (as in trash) kite, a very viscous type of lava, flows much slower than what we witness at Kīlauea and forms a more exaggerated topography.
If we equate Kīlauea's flowing basalt with the viscosity of shoyu (soy sauce), we could liken Hualālai's trachyte to cold honey, slowly oozing downslope. This thousand-fold increase in viscosity is a result of trachyte's characteristic high silicon-dioxide (silica) content. Silica molecules are structured like jacks, so they tend to get tangled with one another, thickening the lava and inhibiting it from flowing. The Puu Waawaa trachyte has 62 percent silica compared to 50 percent found in average basalt.
Trachyte is also characterized by magma that is relatively rich in sodium and potassium, which are very large elements that do not flow easily and add to the lava's viscosity. This explains why the cone and flow are so much more massive than their basalt counterparts.
Geologists hypothesize that Puu Waawaa was formed during a fountain eruption of pumice a little over 100,000 years ago. During the next few tens of thousands of years, at least three separate, thick trachyte flows emerged from the vent and built the Puu Anahulu ridge. Later lava flows from Hualālai and Mauna Loa covered some of the trachyte, but the rest remains as Hualālai's oldest exposed rocks.
Hawaiian volcanoes behave in a very systematic manner. They begin building on the ocean floor, like Loihi, and then enter into a shield stage, when they grow large and develop broad, gentle slopes like those of Kīlauea and Mauna Loa. As they grow older, they enter a post-shield stage in which the magma becomes more viscous and the eruption style changes. Eruptions become infrequent as magma in a shallow reservoir solidifies. Eruptions are fed by magma from a deeper reservoir that has more sodium and potassium.
Hualālai is believed to have entered the post-shield stage about 100,000 years ago, and Puu Waawaa may represent this transition. As magma in the shallow reservoir beneath Hualālai was cooling, certain minerals crystallized and changed the composition of the remaining liquid magma. Since the crystallizing minerals had little sodium, potassium and silica, the liquid magma became enriched in these elements.
When this last bit of shallow magma erupted out of Hualālai's north flank, gas pressure shot it high into the air, creating the impressive mountain of pumice that still stands as Puu Waawaa. When the gas pressure was relieved, the magma then slowly squeezed out like toothpaste, and, over time, created Puu Anahulu.
Why does trachyte seem to be so rare in Hawaii? First of all, the transitional period between stages is relatively short. The formation of trachyte magma requires a delicate balance of magma reservoir size and supply rates for crystallization to change the liquid composition.
Secondly, trachyte has been found in numerous drill holes on Hualālai. Hydrologists discovered a trachyte flow as much as 100 m (325 feet) thick beneath younger lava flows on the mountain's northwest rift zone. Another buried flow up to 60 m (200 feet) thick may radiate southwestward from Hualālaii's summit.
This suggests that trachyte is actually not uncommon, at least on Hualālai. Many trachyte exposures also occur in the West Maui mountains and on the East Molokai shield, perhaps formed when those mountains made the transition from the shield to the post-shield stage.
Volcano Activity Update
Eruptive activity at Puu Oo continues. Lava in the Banana flow, which breaks out of the Mother's Day lava tube a short distance above Pulama pali, has been visible between the pali and Paliuli in the past week. Also visible on the pali was the distal end of the PKK (Kuhio) flow, which originates on the south side of Puu Oo; the flow front stagnated on August 11. Lava has not entered the ocean since August 5. Eruptive activity in Puu Oo's crater is weak, with sporadic minor spattering.
Three earthquakes were reported felt on the island during the week ending August 11. A magnitude 2.9 earthquake at 9:53 a.m. on August 4 was felt in Pahala. The earthquake was located 7 km (4 miles) northwest of Pahala. Later in the day at 5:09 p.m. a magnitude 3.4 earthquake struck 34 km (21 miles) east of South point. This event was felt in Hawaiian Ocean View Estates. On August 11, an earthquake at 5:14 a.m. was felt in Leilani Estates. This earthquake was located 2 km (1 mile) east-southeast of Puulena Crater at a depth of 1 km (1 mile).
Mauna Loa is not erupting. The summit region continues to inflate slowly. Seismic activity was notably high for the third week in a row, with 33 earthquakes recorded in the summit area. Most of the earthquakes are the long-period type and located deep, about 40 km (23 miles) or more.
| 2021-01-17T13:27:01 |
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|
https://pos.sissa.it/345/188/
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Volume 345 - International Conference on Hard and Electromagnetic Probes of High-Energy Nuclear Collisions (HardProbes2018) - Electroweak Probes
Exclusive Charmonium production in PbPb and pp collisions at LHCb
S. Belin* on behalf of the LHCb collaboration
*corresponding author
Full text: pdf
Pre-published on: 2019 January 11
Published on: 2019 April 24
Abstract
At the LHC, the highly boosted electromagnetic field of the beam particles represents a source of quasi-real photon. Vector meson photo-production measurements in pp/Pb-Pb collisions are sensitive to the gluon parton distribution functions in the proton/nucleus. LHCb results on charmonium production in ultra-peripheral Pb-Pb collisions at 5.02 TeV and in pp at 13 TeV will be presented.
DOI: https://doi.org/10.22323/1.345.0188
Open Access
Copyright owned by the author(s) under the term of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
| 2019-06-17T22:43:55 |
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http://pdglive.lbl.gov/DataBlock.action?node=B047W&home=BXXX025
|
# ${{\boldsymbol \Sigma}{(2030)}}$ WIDTH INSPIRE search
VALUE (MeV) DOCUMENT ID TECN COMMENT
$\bf{ 150\text{ to }200\text{ }(\approx180) }$ OUR ESTIMATE
$177$ $\pm12$
2019
DPWA ${{\overline{\mathit K}}}{{\mathit N}}$ multichannel
$207$ $\pm17$
2013 A
DPWA ${{\overline{\mathit K}}}{{\mathit N}}$ multichannel
$172$ $\pm10$
1980
DPWA ${{\overline{\mathit K}}}$ ${{\mathit N}}$ $\rightarrow$ ${{\overline{\mathit K}}}{{\mathit N}}$
$137$ $\pm40$
1977 B
${{\mathit K}^{-}}$ ${{\mathit N}}$ $\rightarrow$ ${{\mathit N}}{{\overline{\mathit K}}^{*}}$
$201$ $\pm9$ 1
1976
DPWA ${{\mathit K}^{-}}$ ${{\mathit n}}$ $\rightarrow$ ${{\mathit \Lambda}}{{\mathit \pi}^{-}}$
$180$ $\pm20$
1975
IPWA ${{\overline{\mathit K}}}$ ${{\mathit N}}$ $\rightarrow$ ${{\mathit \Lambda}}{{\mathit \pi}}$
$172$ $\pm15$
1975
DPWA ${{\mathit K}^{-}}$ ${{\mathit p}}$ $\rightarrow$ ${{\overline{\mathit K}}}{{\mathit N}}$
$178$ $\pm13$
1975
DPWA ${{\mathit K}^{-}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit \Lambda}}{{\mathit \pi}^{0}}$
$111$ $\pm5$
1974
DPWA ${{\mathit K}^{-}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit \Sigma}}{{\mathit \pi}}$
$160$ $\pm20$
1974 B
DPWA ${{\mathit K}^{-}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit \Lambda}{(1520)}}{{\mathit \pi}^{0}}$
$200$ $\pm30$
1974 C
DPWA ${{\mathit K}^{-}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit \Delta}{(1232)}}{{\overline{\mathit K}}}$
• • • We do not use the following data for averages, fits, limits, etc. • • •
$260$
1977
DPWA ${{\overline{\mathit K}}}$ ${{\mathit N}}$ $\rightarrow$ ${{\overline{\mathit K}}}{{\mathit N}}$
$190$ $\pm10$
1977
DPWA ${{\overline{\mathit K}}}{{\mathit N}}$ multichannel
$126\text{ to }195$
1977
DPWA ${{\mathit K}^{-}}$ ${{\mathit N}}$ $\rightarrow$ ${{\mathit \Sigma}}{{\mathit \pi}}$
$160$
1976
IPWA ${{\mathit K}^{-}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit \Lambda}}{{\mathit \pi}^{0}}$
$70\text{ to }125$
1974 D
DPWA ${{\mathit K}^{-}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit \Lambda}{(1820)}}{{\mathit \pi}^{0}}$
1 Preferred solution 3; see CORDEN 1976 for other possibilities.
References:
SARANTSEV 2019
EPJ A55 180 Hyperon II: Properties of excited hyperons
ZHANG 2013A
PR C88 035205 Multichannel Parametrization of ${{\mathit K}^{-}}{{\mathit N}}$ Scattering Amplitudes and Extraction of Resonance Parameters
GOPAL 1980
Toronto Conf. 159 S = -1 Baryons: an Experimental Review
CORDEN 1977B
NP B121 365 Data and Partial Wave Analysis for the Reaction ${{\mathit K}^{-}}$ ${{\mathit n}}$ $\rightarrow$ ${{\mathit K}^{*}{(890)}^{-}}{{\mathit n}}$
DECLAIS 1977
CERN 77-16 ${{\mathit K}^{-}}{{\mathit n}}$ and ${{\mathit K}^{-}}{{\mathit p}}$ Elastic Scattering in ${{\mathit K}^{-}}{{\mathit d}}$ Collisions from 1.2 to 2.2 ${\mathrm {GeV/}}\mathit c$
GOPAL 1977
NP B119 362 Partial Wave Analyses of ${{\overline{\mathit K}}}{{\mathit N}}$ Two Body Reactions between 1480 and 2170 MeV
GOYAL 1977
PR D16 2746 Formation of the ${{\mathit \Sigma}{(2030)}}$ Resonance in the Reactions ${{\mathit K}^{-}}$ ${{\mathit n}}$ $\rightarrow$ ${{\mathit \Sigma}^{-}}{{\mathit \pi}^{0}}$ and ${{\mathit K}^{-}}$ ${{\mathit n}}$ $\rightarrow$ ${{\mathit \Sigma}^{0}}{{\mathit \pi}^{-}}$ in the Center-of-mass Energy Interval $1850 - 2150$ MeV
CORDEN 1976
NP B104 382 Measurements of the Reactions ${{\mathit K}^{-}}{{\mathit n}}{{\mathit \pi}^{-}}{{\mathit \Lambda}}$ in the $\mathit E_{{\mathrm {cm}}}$ Range 2050 to 2175 MeV and Partial Wave Analysis of this Reaction between 1875 and 2175 MeV
DEBELLEFON 1976
NP B109 129 Reaction ${{\mathit K}^{-}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit \Lambda}}{{\mathit \pi}^{0}}$ : Zeroes and Partial Waves from 0.4 to 2.5 ${\mathrm {GeV/}}\mathit c$
BAILLON 1975
NP B94 39 Energy Independent Partial Wave Analysis of ${{\overline{\mathit K}}}$ ${{\mathit N}}$ $\rightarrow$ ${{\mathit \Lambda}}{{\mathit \pi}}$ between 1540 and 2150 MeV
HEMINGWAY 1975
NP B91 12 New Data on ${{\mathit K}^{-}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit K}^{-}}{{\mathit p}}$ and ${{\overline{\mathit K}}^{0}}{{\mathit n}}$ and a Partial Wave Analysis between 1840 and 2234 MeV Center of Mass Energy
VANHORN 1975
NP B87 145 Energy Dependent Partial Wave Analysis of ${{\mathit K}^{-}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit \Lambda}}{{\mathit \pi}^{0}}$ between 1540 and 2215 MeV
KANE 1974
LBL-2452 LBL-2452
LITCHFIELD 1974C
NP B74 39 Partial Wave Analysis of the Reaction ${{\mathit K}^{-}}$ ${{\mathit p}}$ $\rightarrow$ ${{\overline{\mathit K}}}{{\mathit \Delta}{(1232)}}$ in the Energy Region $1915 - 2170$ MeV
LITCHFIELD 1974B
NP B74 19 Partial Wave Analysis of the Reaction ${{\mathit K}^{-}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit \Lambda}{(1520)}}{{\mathit \pi}}$ in the Energy Region $1915 - 2170$ MeV
LITCHFIELD 1974D
NP B74 12 Partial Wave Analysis of the Reaction ${{\mathit K}^{-}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit \Lambda}{(1820)}}{{\mathit \pi}}$ between Threshold and 2170 MeV
| 2020-07-07T23:32:27 |
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|
https://control.com/textbook/ac-electricity/transmission-lines/
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# Open-ended, Shorted and Properly Terminated Transmission Lines
## Chapter 5 - Basic Alternating Current (AC) Theory
Many years ago, when I was first learning about electricity, I happened to discover a length of coaxial television cable with the rating “50 ohm” printed on the jacket. Having my own ohmmeter, and wanting to know what the “50 ohm” label referred to, I tried measuring the resistance of this cable to see where it would exhibit 50 ohms of resistance. First I tried measuring between the two open-ended wires (the center conductor and the braided shield conductor), where my meter registered infinite resistance (no continuity). This is what I expected a normal cable would read when connected to nothing else. Next I tried connecting my meter from one end of the cable to the other: between both ends of the center conductor my meter registered 0 ohms, and between both ends of the shield conductor my meter also read 0 ohms. In fact, this is all I was ever able to measure with my ohmmeter: either 0 ohms or infinite ohms (open), no matter what I tried. I was confounded – how could this piece of cable possibly be called a “50 ohm” cable if I could not measure 50 ohms anywhere on it?
It was not until years later that I came across a reference in an old book to something called surge impedance, describing how lengths of cable responded to short-duration electrical pulses, that I finally understood the “50 ohm” rating of that coaxial cable. What I failed to discover with my ohmmeter – in fact, what I never could have even seen with a plain ohmmeter – is that the cable did indeed act like a 50 ohm resistor, but only for extremely short periods of time. This is an aspect of electrical theory I was completely unprepared to comprehend at that time, knowing only how DC circuits functioned. This is the subject we are about to explore now.
In basic DC electrical theory, students learn that open circuits always drop the full applied voltage and cannot have electric currents anywhere in them. Students likewise learn that short circuits drop negligible voltage while conducting full electrical current. They also learn that the effects of electricity occur instantaneously throughout the circuit: for example, if a functioning circuit suffers an “open” fault, current through that branch of the circuit halts immediately and everywhere. These basic rules of electricity are extremely useful for DC circuit analysis, indeed even essential for troubleshooting DC circuits, but they are not 100% correct. Like many of the scientific principles one initially learns, they are only approximations of reality.
The effects of electricity do not propagate instantaneously throughout a circuit, but rather spread at the speed of light (approximately 300,000,000 meters per second). Normally we never see any consequences of this finite speed because everything happens so fast, just as I never saw my ohmmeter register 50 ohms when I tried to test that coaxial cable many years ago. However, when we test a circuit on a time scale of nano-seconds (billionths of a second!), we find some very interesting phenomena during the time electricity propagates along the length of a circuit: open circuits can indeed (temporarily) exhibit current, and short circuits can indeed (temporarily) exhibit voltage drops.
When a pulse signal is applied to the beginning of a two-conductor cable, the reactive elements of that cable (i.e. capacitance between the conductors, inductance along the cable length) begin to store energy. This translates to a current drawn by the cable from the source of the pulse, as though the cable were acting as a (momentarily) resistive load. If the cable under test were infinitely long, this charging effect would never end, and the cable would indeed behave exactly like a resistor from the perspective of the signal source. However, real cables (having finite length) do stop “charging” after some time following the application of a voltage signal at one end, the length of that time being a function of the cable’s physical length and the speed of light.
In honor of the cable’s capacity to behave as a temporary load to any impressed signal, we typically refer to it as something more than just a cable. From the perspective of an electrical pulse, measured on a time scale of nanoseconds, we refer to any cable as a transmission line. All electrical cables act as transmission lines, but the effects just mentioned are so brief in duration that we only notice them when the cable is exceptionally long and/or the pulse durations are exceptionally short (i.e. high-frequency signals).
During the time when a transmission line is absorbing energy from a power source – whether this is indefinitely for a transmission line of infinite length, or momentarily for a transmission line of finite length – the current it draws will be in direct proportion to the voltage applied by the source. In other words, a transmission line behaves like a resistor, at least for a moment. The amount of “resistance” presented by a transmission line is called its characteristic impedance, or surge impedance, symbolized in equations as $$Z_0$$. Only after the pulse signal has had time to travel down the length of the transmission line and reflect back to the source does the cable stop acting as a load and begin acting as a plain pair of wires.
A transmission line’s characteristic impedance is a function of its conductor geometry (wire diameter, spacing) and the permittivity of the dielectric separating those conductors. If the line’s design is altered to increase its bulk capacitance and/or decrease its bulk inductance (e.g. decreasing the distance between conductors), the characteristic impedance will decrease. Conversely, if the transmission line is altered such that its bulk capacitance decreases and/or its bulk inductance increases, the characteristic impedance will increase. It should be noted that the length of the transmission line has absolutely no bearing on characteristic impedance. A 10-meter length of RG-58/U coaxial cable will have the exact same characteristic impedance as a 10000 kilometer length of RG-58/U coaxial cable (50 ohms, in both cases). The only difference is the length of time the cable will behave like a resistor to an applied voltage.
### Open-ended transmission lines
The following sequence illustrates the propagation of a voltage pulse forward and back (reflected) on an open-ended transmission line beginning from the time the DC voltage source is first connected to the left-hand end:
The end result is a transmission line exhibiting the full source voltage, but no current. This is exactly what we would expect in an open circuit. However, during the time it took for the pulse to travel down the line’s length and back, it drew current from the source equal to the source voltage divided by the cable’s characteristic impedance ($$I_{surge} = {V_{source} \over Z_0}$$). For a brief amount of time, the two-conductor transmission line acted as a load to the voltage source rather than an open circuit. Only after the pulse traveled down the full length of the line and back did the line finally act as a plain open circuit.
An experiment performed with a square-wave signal generator and oscilloscope connected to one end of a long wire pair cable (open on the far end) shows the effect of the reflected signal:
The waveform steps up for a brief time, then steps up further to full source voltage. The first step represents the voltage at the source during the time the pulse traveled along the cable’s length, when the cable’s characteristic impedance acted as a load to the signal generator (making its output voltage “sag” to a value less than its full potential). The next step represents the reflected pulse’s return to the signal generator, when the cable’s capacitance is fully charged and is no longer drawing current from the signal generator (making its output voltage “rise”). A two-step “fall” appears at the trailing edge of the pulse, when the signal generator reverses polarity and sends an opposing pulse down the cable.
The duration of the first and last “steps” on the waveform represents the time taken by the signal to propagate down the length of the cable and return to the source. This oscilloscope’s timebase was set to 0.5 microseconds per division for this experiment, indicating a pulse round-trip travel time of approximately 0.2 microseconds. A cable of this type has a velocity factor of approximately 0.7, which means electrical impulses travel at only 70% the speed of light through the cable, and so the round-trip distance calculates to be approximately 42 meters which makes the cable 21 meters in length:
$\hbox{Distance} = \hbox{Velocity} \times \hbox{Time} = (70\%) (3 \times 10^8 \hbox{ m/s}) (0.2 \> \mu \hbox{s}) = 42 \hbox{ m}$
$\hbox{Cable length} = {1 \over 2} (\hbox{Distance traveled by pulse}) = (0.5)(42 \hbox{ m}) = 21 \hbox{ m}$
### Shorted transmission lines
The following sequence illustrates the propagation of a voltage pulse forward and back (reflected) on a shorted-end transmission line beginning from the time the DC voltage source is first connected to the left-hand end:
The end result is a transmission line exhibiting the full current of the source ($$I_{max} = {V_{source} \over R_{wire}}$$), but no voltage. This is exactly what we would expect in a short circuit. However, during the time it took for the pulse to travel down the line’s length and back, it drew current from the source equal to the source voltage divided by the cable’s characteristic impedance ($$I_{surge} = {V_{source} \over Z_0}$$). For a brief amount of time, the two-conductor transmission line acted as a moderate load to the voltage source rather than a direct short. Only after the pulse traveled down the full length of the line and back did the line finally act as a plain short-circuit.
An experiment performed with the same signal generator and oscilloscope connected to one end of the same long wire pair cable (shorted on the far end) shows the effect of the reflected signal:
Here, the waveform steps up for a brief time, then steps down toward zero. As before, the first step represents the voltage at the source during the time the pulse traveled along the cable’s length, when the cable’s characteristic impedance acted as a load to the signal generator (making its output voltage “sag” to a value less than its full potential). The step down represents the (inverted) reflected pulse’s return to the signal generator, nearly canceling the incident voltage and causing the signal to fall toward zero. A similar pattern appears at the trailing edge of the pulse, when the signal generator reverses polarity and sends an opposing pulse down the cable.
Note the duration of the pulse on this waveform, compared to the first and last “steps” on the open-circuited waveform. This pulse width represents the time taken by the signal to propagate down the length of the cable and return to the source. This oscilloscope’s timebase remained at 0.5 microseconds per division for this experiment as well, indicating the same pulse round-trip travel time of approximately 0.2 microseconds. This stands to reason, as the cable length was not altered between tests; only the type of termination (short versus open).
### Properly terminated transmission lines
Proper “termination” of a transmission line consists of connecting a resistance to the end(s) of the line so that the pulse “sees” the exact same amount of impedance at the end as it did while propagating along the line’s length. The purpose of the termination resistor is to completely dissipate the pulse’s energy in order that none of it will be reflected back to the source.
The following sequence illustrates the propagation of a voltage pulse on a transmission line with proper “termination” (i.e. a resistor matching the line’s surge impedance, connected to the far end) beginning from the time the DC voltage source is first connected to the left-hand end:
From the perspective of the pulse source, this properly terminated transmission line “looks” the same as an unterminated line of infinite length. There is no reflected pulse, and the DC voltage source “sees” an unchanging load resistance the entire time.
An experiment performed with a termination resistor in place shows the near-elimination of reflected pulses:
The pulse looks much more like the square wave it should be, now that the cable has been properly terminated. With the termination resistor in place, a transmission line always presents the same impedance to the source, no matter what the signal level or the time of signal application. Another way to think of this is from the perspective of cable length. With the proper size of termination resistor in place, the cable appears infinitely long from the perspective of the power source because it never reflects any signals back to the source and it always consumes power from the source.
Data communication cables for digital instruments behave as transmission lines, and must be terminated at both ends to prevent signal reflections. Reflected signals (or “echoes”) may cause errors in received data in a communications network, which is why proper termination can be so important. For point-to-point networks (networks formed by exactly two electronic devices, one at either end of a single cable), the proper termination resistance is often designed into the transmission and receiving circuitry, and so no external resistors need be connected. For “multi-drop” networks where multiple electronic devices tap into the same electrical cable, excessive signal loading would occur if each and every device had its own built-in termination resistance, and so the devices are built with no internal termination, and the installer must place two termination resistors in the network (one at each far end of the cable).
### Discontinuities
A transmission line’s characteristic impedance will be constant throughout its length so long as its conductor geometry and dielectric properties are consistent throughout its length. Abrupt changes in either of these parameters, however, will create a discontinuity in the cable capable of producing signal reflections. This is why transmission lines must never be sharply bent, crimped, pinched, twisted, or otherwise deformed.
The probe for a guided-wave radar (GWR) liquid level transmitter is another example of a transmission line, one where the vapor/liquid interface creates a discontinuity: there will be an abrupt change in characteristic impedance between the transmission line in vapor space versus the transmission line submerged in a liquid due to the differing dielectric permittivities of the two substances. This sudden change in characteristic impedance sends a reflected signal back to the transmitter. The time delay measured between the signal’s transmission and the signal’s reception by the transmitter represents the vapor space distance, or ullage.
Velocity factor
The speed at which an electrical signal propagates down a transmission line is never as fast as the speed of light in a vacuum, owing to the permittivity of the line’s electrical insulation being greater than that of a vacuum. A value called the velocity factor expresses the propagation velocity as a ratio to light, and its value is always less than one:
$\hbox{Velocity factor} = {v \over c}$
Where,
$$v$$ = Propagation velocity of signal traveling along the transmission line
$$c$$ = Speed of light in a vacuum ($$\approx$$ 3.0 $$\times$$ $$10^8$$ meters per second)
Velocity factor is a function of dielectric constant, but not conductor geometry. A greater permittivity value results in a slower velocity (lesser velocity factor).
### Cable losses
Ideally, a transmission line is a perfectly loss-less conduit for electrical energy. That is, every watt of signal power entering the transmission line is available at the end where the load is connected. In reality, though, this is never the case. Conductor resistance, as well as losses within the dielectric (insulating) materials of the cable, rob the signal of energy.
For transmission lines, power loss is typically expressed in units of decibels per 100 feet or per 100 meters. A “decibel,” as you may recall, is ten times the logarithm of a power ratio:
$\hbox{Gain or Loss in dB} = 10 \log \left({P \over P_{ref}}\right)$
Thus, if a transmission line receives 25 milliwatts of signal power at one end, but only conveys 18 milliwatts to the far end, it has suffered a 1.427 dB loss ($$10 \log {0.018 \over 0.025}$$ = $$-1.427$$ dB) from end to end. Power loss in cables is strongly dependent on frequency: the greater the signal frequency, the more severe the power loss per unit cable length.
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https://wiki.cosmos.esa.int/planck-legacy-archive/index.php?title=Beams&diff=prev&oldid=6639
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# Difference between revisions of "Beams"
## Scanning Beams
The scanning beams describe the instrument’s instantaneous beam profile. Due to the near constant spin rate of the spacecraft, time domain effects (including residual time response and lowpass filtering) are degenerate with the spatial response due to the optical system. The scanning beam reconstruction recovers both of these effects, aside from residual time domain effects on a longer time scale than can be captured with the extent of the scanning beam model.
In the paper cite P03c we consider two models of the beam in order to better understand systematics in the reconstruction. Here we describe only the BSpline beams which are used to compute the delivered effective beam (see next section).
### BSpline Beam construction
We use seasons 1 and 2 of the Mars observation to reconstruct the beam. The data are processed with the bigPlanets TOI processing. We use JPL Horizons ephemerides to determine the pointing of each detector relative to the planet. We subtract the astrophysical background in the time domain using a bicubic interpolation of the Planck maps.
The time ordered data are used to fit a two dimensional BSpline surface using a least square minimization and a smoothing criterion to minimize the effects of high spatial frequency variations. We therefore assume the scanning beam to be smooth. The smoothing criterion as well as the locations of the nodes used to compute the B-Spline basis functions are set using GRASP physical optics simulations as inputs which are the best assumptions on the spatial frequency content of the in-flight beams.
The smoothing criterion is defined as follows:
And the global inversion criterion :
with usual least square estimator and coefficient giving the relative weight to with respect to the smoothing criterion.
The BSpline nodes are located on a regular spaced grid in the detector coordinate framset. At the edge of the reconstructed beam map area, 4 coincident nodes are added to avoid vanishing basis functions.
Let , degree B-Spline build using nodes {} (De Boor & Cox, 1972) :
Focal plane plot of BSpline scanning beams using in-flight pointing reconstruction. The contours are -3,-10,-20,-30 dB from the peak, and for PSB pairs the "a" bolometer is plotted in black and "b" in blue.
### Simulations and errors
We estimate the reconstruction bias and noise in the measurements using an ensemble of simulated planet observations for each channel. Kept fixed in each simulation are:
• the input beam assumed: we use a supersampled version of the reconstructed BSpline beam (or whatever comes out of the current ongoing tests!)
• Astrophyical background is the same as that subtracted from the real data.
• StarTracker pointing (using the ptcor6 pointing model).
The following are varied in each simulation:
• detector noise realizations obtained by filtering randomly generated white noise with the measured noise PSDs
• random pointing errors with 2 arcsecond rms, and a spectrum that replicates the real errors.
• simulated glitches and the deglitching procedure
• Mars brightness temperature variability
400 simulated timelines are generated for each bolometer and for each of the two seasons of Mars observations used in the beam reconstruction. The simulated timelines are made into beam maps, projecting onto the BSpline basis in the same way as the real data.
The beam maps are propagated to effective beam window functions using the quickbeam approach (see effective beams below) and used to evaluate the reconstruction bias and to construct error eigenmodes in the effective beam window function.
Figure: random pointing error PSD Figures: error envelope plots (or should those go under effective beams?)
### Residuals
There are two known beam effects that are not included in the main beam model and are estimated as a separate bias in flux and angular power spectrum measurement: 1. long tails due to errors in low frequency time response deconvolution, and 2. near sidelobes.
We stack all five observations of Jupiter to estimate the long time scale residuals due to incomplete deconvolution of the long time scale response.
Add some kind of mean tail plot
Near sidelobes are also evaluated using stacked Jupiter (hopefully they will just be part of the v53bis BSpline beams). The main features in the near sidelobes include a wide beam skirt, and dimpling lobes Add sidelobe plots and tables
## Effective Beams
Several methods of effective beams determination have been developped and cross-validated. Need satisfactory comparison plot
### FEBeCoP
The effective beam is the average of all scanning beams pointing at a certain direction within a given pixel of the sky map for a given scan strategy. It takes into account the coupling between azimuthal asymmetry of the beam and the uneven distribution of scanning angles across the sky. It captures the complete information about the difference between the true and observed image of the sky. They are, by definition, the objects whose convolution with the true CMB sky produce the observed sky map.
The full algebra involving the effective beams for temperature and polarisation was presented in [Mitra, Rocha, Gorski et al.] #mitra2010. Here we summarise the main results. The observed temperature sky is a convolution of the true sky and the effective beam :
where
is time samples, is if the pointing direction falls in pixel number , else it is , represents the exact pointing direction (not approximated by the pixel centre location), and is the centre of the pixel number , where the scanbeam is being evaluated (if the pointing direction falls within the cut-off radius of FWHM.
The algebra is a bit more involved for polarised detectors. The observed stokes parameters at a pixel , , are related to the true stokes parameters , by the following relation:
where the polarised effective beam matrix
and and are the the polarisation weight vectors, as defined in \cite{mitra2010}.
The task is to compute for temperature only beams and the matrices for each pixel , at every neighbouring pixel that fall within the cut-off radius around the the center of the pixel.
The effective beam is computed by stacking within a small field around each pixel of the HEALPix sky map. Due to the particular features of Planck scanning strategy coupled to the beam asymmetries in the focal plane, and data processing of the bolometer and radiometer TOIs, the resulting Planck effective beams vary over the sky.
FEBeCoP, given information on Planck scanning beams and detector pointing during a mission period of interest, provides the pixelized stamps of both the Effective Beam, EB, and the Point Spread Function, PSF, at all positions of the HEALPix-formatted map pixel centres.
The methodology for computing effective beams for a scanning CMB experiment like Planck was presented in [Mitra, Rocha, Gorski et al.].
FEBeCoP, or Fast Effective Beam Convolution in Pixel space, is an approach to representing and computing effective beams (including both intrinsic beam shapes and the effects of scanning) that comprises the following steps:
• identify the individual detectors' instantaneous optical response function (presently we use elliptical Gaussian fits of Planck beams from observations of planets; eventually, an arbitrary mathematical representation of the beam can be used on input)
• follow exactly the Planck scanning, and project the intrinsic beam on the sky at each actual sampling position
• project instantaneous beams onto the pixelized map over a small region (typically <2.5 FWHM diameter)
• add up all beams that cross the same pixel and its vicinity over the observing period of interest
• create a data object of all beams pointed at all N'_pix_' directions of pixels in the map at a resolution at which this precomputation was executed (dimension N'_pix_' x a few hundred)
• use the resulting beam object for very fast convolution of all sky signals with the effective optical response of the observing mission
Computation of the effective beams at each pixel for every detector is a challenging task for high resolution experiments. FEBeCoP is an efficient algorithm and implementation which enabled us to compute the pixel based effective beams using moderate computational resources. The algorithm used different mathematical and computational techniques to bring down the computation cost to a practical level, whereby several estimations of the effective beams were possible for all Planck detectors for different scanbeam models and different lengths of datasets.
#### Pixel Ordered Detector Angles (PODA)
The main challenge in computing the effective beams is to go through the trillion samples, which gets severely limited by I/O. In the first stage, for a given dataset, ordered lists of pointing angles for each pixels---the Pixel Ordered Detector Angles (PODA) are made. This is an one-time process for each dataset. We used computers with large memory and used tedious memory management bookkeeping to make this step efficient.
#### effBeam
The effBeam part makes use of the precomputed PODA and unsynchronized reading from the disk to compute the beam. Here we tried to made sure that no repetition occurs in evaluating a trigonometric quantity.
One important reason for separating the two steps is that they use different schemes of parallel computing. The PODA part requires parallelisation over time-order-data samples, while the effBeam part requires distribution of pixels among different computers.
#### Computational Cost
The whole computation of the effective beams has been performed at the NERSC Supercomputing Center. In the table below it isn displayed the computation cost on NERSC for nominal mission both in terms of CPU hrs and in Human time.
Channel 100 143 217 353 545 857 PODA/Detector Computation time (CPU hrs) 500 500 500 500 500 500 PODA/Detector Computation time (Human minutes) 20 20 20 20 20 20 Beam/Channel Computation time (CPU hrs) 2800 3800 3200 3000 900 1100 Beam/Channel Computation time (Human hrs) 1.5 2 1.2 1 0.5 0.5 Convolution Computation time (CPU hr) 3.6 4.8 4 4.1 4.1 3.7 Convolution Computation time (Human sec) 4 4 4 4 4 4 Effective Beam Size (GB) 187 182 146 132 139 124
The computation cost, especially for PODA and Convolution, is heavily limited by the I/O capacity of the disc and so it depends on the overall usage of the cluster done by other users.
#### Inputs
In order to fix the convention of presentation of the scanning and effective beams, we show the classic view of the Planck focal plane as seen by the incoming CMB photon (top plot in this page). The scan direction is marked, and the toward the center of the focal plane is at the 85 deg angle w.r.t spin axis pointing upward in the picture.
#### The Focal Plane DataBase (FPDB)
The FPDB contains information on each detector, e.g., the orientation of the polarisation axis, different weight factors, ... (see the instrument RIMOs):
#### The scanning strategy
The scanning strategy, the three pointing angle for each detector for each sample: Detector pointings for the nominal mission covers about 15 months of observation from Operational Day (OD) 91 to OD 563 covering 3 surveys and half.
#### The scanbeam
The scanbeam modeled for each detector through the observation of planets. Which was assumed to be constant over the whole mission, though FEBeCoP could be used for a few sets of scanbeams too.
(see the instrument RIMOs)
N times geometric mean of FWHM of all detectors in a channel, where N
channel Cutoff Radii in units of fwhm fwhm of full beam extent 100 2.25 23.703699 143 3 21.057402 217-353 4 18.782754 sub-mm 4 18.327635(545GHz) ; 17.093706(857GHz)
#### Map resolution for the derived beam data object
• for HFI frequency channels
#### Comparison of the images of compact sources observed by Planck with FEBeCoP products
We show here a comparison of the FEBeCoP derived effective beams, and associated point spread functions,PSF (the transpose of the beam matrix), to the actual images of a few compact sources observed by Planck, for all LFI and HFI frequency channels, as an example. We show below a few panels of source images organized as follows:
• Row #1- DX9 images of four ERCSC objects with their galactic (l,b) coordinates shown under the color bar
• Row #2- linear scale FEBeCoP PSFs computed using input scanning beams, Grasp Beams, GB, for LFI and B-Spline beams,BS, Mars12 apodized for the CMB channels and the BS Mars12 for the sub-mm channels, for HFI (see section Inputs below).
• Row #3- log scale of #2; PSF iso-contours shown in solid line, elliptical Gaussian fit iso-contours shown in broken line
#### Histograms of the effective beam parameters
Here we present histograms of the three fit parameters - beam FWHM, ellipticity, and orientation with respect to the local meridian and of the beam solid angle. The shy is sampled (pretty sparsely) at 3072 directions which were chosen as HEALpix nside=16 pixel centers for HFI and at 768 directions which were chosen as HEALpix nside=8 pixel centers for LFI to uniformly sample the sky.
Where beam solid angle is estimated according to the definition: 4pi* sum(effbeam)/max(effbeam) ie
Histograms for LFI effective beam parameters
Histograms for HFI effective beam parameters
#### Sky variation of effective beams solid angle and ellipticity of the best-fit Gaussian
• The discontinuities at the Healpix domain edges in the maps are a visual artifact due to the interplay of the discretized effective beam and the Healpix pixel grid.
#### Statistics of the effective beams computed using FEBeCoP
We tabulate the simple statistics of the beam for all LFI and HFI channels in the Effective Beams product page.
##### Beam solid angles for the PCCS
• - is the mean beam solid angle of the effective beam, where beam solid angle is estimated according to the definition: 4pi*sum(effbeam)/max(effbeam), i.e. as an integral over the full extent of the effective beam, i.e. .
• from we estimate the , under a Gaussian approximation - these are tabulated above
• is the beam solid angle estimated up to a radius equal to one and up to a radius equal to twice the .
• These were estimated according to the procedure followed in the aperture photometry code for the PCCS: if the pixel centre does not lie within the given radius it is not included (so inclusive=0 in query disc).
Band [arcmin] spatial variation [arcmin] [arcmin] spatial variation-1 [arcmin] [arcmin] spatial variation-2 [arcmin] 100 105.778 0.311 100.830 0.410 105.777 0.311 143 59.954 0.246 56.811 0.419 59.952 0.246 217 28.447 0.271 26.442 0.537 28.426 0.271 353 26.714 0.250 24.827 0.435 26.653 0.250 545 26.535 0.339 24.287 0.455 26.302 0.337 857 24.244 0.193 22.646 0.263 23.985 0.191
#### Related products
##### Monte Carlo simulations
FEBeCoP software enables fast, full-sky convolutions of the sky signals with the Effective beams in pixel domain. Hence, a large number of Monte Carlo simulations of the sky signal maps map convolved with realistically rendered, spatially varying, asymmetric Planck beams can be easily generated. We performed the following steps:
• generate the effective beams with FEBeCoP for all frequencies for dDX9 data and Nominal Mission
• generate 100 realizations of maps from a fiducial CMB power spectrum
• convolve each one of these maps with the effective beams using FEBeCoP
• estimate the average of the Power Spectrum of each convolved realization, C'_\ell_'^out^'}, and 1 sigma errors
As FEBeCoP enables fast convolutions of the input signal sky with the effective beam, thousands of simulations are generated. These Monte Carlo simulations of the signal (might it be CMB or a foreground (e.g. dust)) sky along with LevelS+Madam noise simulations were used widely for the analysis of Planck data. A suite of simulations were rendered during the mission tagged as Full Focalplane simulations, FFP#. For example FFP6
##### Beam Window Functions
The Transfer Function or the Beam Window Function relates the true angular power spectra with the observed angular power spectra :
Note that, the window function can contain a pixel window function (depending on the definition) and it is {\em not the angular power spectra of the scanbeams}, though, in principle, one may be able to connect them though fairly complicated algebra.
The window functions are estimated by performing Monte-Carlo simulations. We generate several random realisations of the CMB sky starting from a given fiducial , convolve the maps with the pre-computed effective beams, compute the convolved power spectra , divide by the power spectra of the unconvolved map and average over their ratio. Thus, the estimated window function
For subtle reasons, we perform a more rigorous estimation of the window function by comparing C^{conv}_l with convolved power spectra of the input maps convolved with a symmetric Gaussian beam of comparable (but need not be exact) size and then scaling the estimated window function accordingly.
Beam window functions are provided in the RIMO.
#### Beam Window functions, Wl, for HFI channels
Beam Window functions, Wl, for HFI channels
To be coordinated with GracaSee Mitra et al (2011
### FICSBell
For more details, see #planck2013-p03c
Since the HFI beams are not azimuthally symmetric, the scanning strategy has to be taken into account in the effective beam response modelling. This is done using the FICSBell method (Hivon et al, in preparation), which generalizes to polarization and to include other sources of systematics the approach used for TT estimation in WMAP-3yr Hinshaw et al (2007) and by Smith et al (2007) in the detection of CMB lensing in WMAP maps. The different steps of the method used for this study can be summarized as follows:
1. The scanning related information (i.e., statistics of the orientation of each detector within each pixel) is computed first, and only once for a given observation campaign. Those orientation hit moments are only computed up to degree 4, for reasons described in point 2 below. At the same time, the first two moments of the distribution of samples within each pixel (ie, their center of mass and moments of inertia) are computed and stored on disc.
2. The scanning beam map or beam model of each detector is analyzed into its Spherical Harmonics coefficients
where is the beam map centered on the North pole, and is the Spherical Harmonics basis function. Higher indexes describes higher degrees of departure from azimuthal symmetry and, for HFI beams, the coefficients are decreasing functions of at most considered. It also appears that, for , the coefficients with account for or less of the beam throughput. For this reason, only modes with are considered in the present analysis. Armitage-Caplan and Wandelt (2009) reached a similar conclusion in their deconvolution of Planck-LFI beams.
3. The coefficients computed above are used to generate -spin weighted maps, as well as the first and second order derivatives, for a given CMB sky realization.
4. The spin weighted maps and orientation hit moments of the same order are combined for all detectors involved, to provide an “observed” map. Similarly the local spatial derivatives are combined with the location hit moments to describe the effect of the non-ideal sampling of each pixel (see [sec:pixelization]). In this combination, the respective number of hits of each detector in each pixel is considered, as well as the weighting (generally proportional to the inverse noise variance) applied to each detector in order to minimize the final noise.
5. The power spectrum of this map can then be computed, and compared to the input CMB power spectrum to estimate the effective beam window function over the whole sky, or over a given region of the sky.
Monte-Carlo (MC) simulations in which the sky realisations are changed can be performed by repeating steps 3, 4 and 5. The impact of beam model uncertainties can be studied by including step 2 into the MC simulations.
### QuickBeam
For more details, see #planck2013-p03c
Planck observes the sky after convolution with a “scanning beam”, which captures its effective response to the sky as a function of displacement from the nominal pointing direction. Decomposing the scanning beam into harmonic coefficients , each time-ordered data (TOD) sample can be modelled as (neglecting the contribution from instrumental noise, which is independent of beam asymmetry) where the TOD samples are indexed by , and is the underlying sky signal. The spin spherical harmonic rotates the scanning beam to the pointing location , while the factor gives it the correct orientation. Eq. may be evaluated with the “TotalConvolver” algorithm of Wandelt and Gorski (2001), accelerated using the “conviqt” recursion relations Prezeau and Reinecke (2010) This approach is implemented in LevelS. </ref>, although because it involves working with a TOD-sized objected it is necessarily slow.
On the small angular scales comparable to the size of the beam, it is a good approximation to assume that the procedure of mapmaking from TOD samples is essentially a process of binning: where is the total number of hits in pixel .
Start with a normalized, rescaled harmonic transform of the beam , sky multipoles and a scan history object given by where the sum is over all hits of pixel at location , and is the scan angle for observation . The harmonic transform of this scan-strategy object is given by The beam-convolved observation is then given by Taking the ensemble average of the pseudo-Cl power spectrum of these we find
where is a cross-power spectrum of scan history objects. Note that the w(n,s) which we have used here can also incorporate a position dependent weighting to optimize the pseudo-Cl estimate, such as inverse-noise or a mask– the equations are unchanged. Writing the pseudo-Cl in position space (a la Dvorkin and Smith (2009)) with Wigner-d matrices we have
This integral can be implemented exactly using Gauss-Legendre quadrature, with a cost of $\cal 0(l_{\rm max}^2 s_{\rm max}^2)$. For simplicity, we’ve written all the equations here for the auto-spectrum of a single detector, but the generalization to a map made by adding several detectors with different weighting is straightforward. The cost to compute all of the necessary terms exactly in that case becomes .
Are beams really so difficult? On the flat-sky beam convolution is easy: just multiplication in Fourier space by a beam rotated onto the scan direction. Multiple hits with different scan directions are incorporated by averaging (as the “scan history” objects above encapsulate). Does the sphere really require everything to be so complicated? For a scan strategy which is fairly smooth across the sky, we can pretend that we are observing many independent flat-sky patches at high-L with fairly good accuracy. There is in fact a fairly good approximation to the beam convolved pseudo-Cl power spectrum which is essentially a flat-sky approximation. In the limit that , with and being slowly-varying function in the pseudo-Cl sum above can be approximated as where the average is taken over the full sky. It’s illustrative to consider three limits of this equation: for a “raster” scan strategy in which each pixel is observed with the same direction, we have and the predicted pseudo-Cl is just the power spectrum of the beam. For a "best-case" scan strategy, in which each pixel is observed many times with many different orientation angles, we have < | w(, M) |2 >p = M0, and the transfer function is just the azimuthally symmetric part of the beam. Note that this is for a full-sky observation– in the presence of a mask, the average above produces an fsky factor, as expected. It just neglects the coupling between L multipoles (which can be calculated with the more complete equations above).
#### Effective beam window functions
The effective beam window functions $B(l)$ for HFI, computed using Quickbeam, are available in the RIMO. They do not contain the pixel window function.
### Pixelization Artifacts
For more details, see #planck2013-p03c
• Several codes available to simulate effects of pixelization.
• Mixes the CMB gradient into a pixelization noise with a level comparable to that of $2\mu Karcmin$ instrumental noise.
• Quantitative estimate of effect should be included with each released map, but expect not to matter significantly for CMB analysis, as small compared to instrumental noise.
[sec:pixelization]
Planck maps are produced at resolution 11 , corresponding to pixels with a typical dimension of , comparable to the spacing between scanning rings . This results in an uneven distribution of hits within pixels, which introduces some complications in the analysis and interpretation of the maps. A sample of the hit distribution is illustrated in Fig. [fig:pixcoverage]. Below we discuss the simulation and modeling of this pixelization effect in more detail.
[fig:pixcoverage]
The collaboration has produced 3 codes which may be used to simulate the effect of pixelization on the observed sky, LevelS/TotalConvoler/Conviqt, FeBeCoP, and FICSBell references and further discussion of the three methods and how they each simulate the pixelization effect..
For the measurement of CMB fluctuations, it is also possible to gain intuition for the effects of pixelization analytically. On the small scales relevant to pixelization, the observed CMB is smooth, both due to physical damping as well as the convolution of the instrumental beam. Taylor expanding the CMB temperature about a pixel center to second order, the typical gradient amplitude is given by where the approximate value is calculated for a cosmology with a fwhm Gaussian beam. The typical curvature of the observed temperature, on the other hand is given by On the scales relevant to the maximum displacement from the center of a pixel, the maximum displacement is , and so the gradient term tends to dominate, although the curvature term is still non-negligible. For each observation of a pixel, we can denote the displacement from the pixel center as . The average over all hits within a pixel gives an overall deflection vector which we will denote for a pixel center located at as . This represents the center of mass of the hit distribution; in Fig. [fig:pixcoverage] we have plotted these average deflections using black arrows. The deflection field may be decomposed into spin-1 spherical harmonics as With a second order Taylor expansion of the CMB temperature about each pixel center, it is then possible to calculate the average pseudo-Cl power spectrum of the pixelized sky. This is given by
where is half the mean-squared deflection magnitude (averaged over hits within a pixel, as well as over pixels). is the sum of the gradient and curl power spectra of , and is the gradient spectrum minus the curl spectrum. The term describes a smearing of the observed sky due to pixelization. For uniform pixel coverage of pixels . For the hit distribution of Planck frequency maps, is typically within xxx. calculate for final maps, looks like will be better than 10%percent of this value, and so this term is accurately described by the pixel window function, which is derived under the assumption of uniform pixel coverage.
The effect of pixelization is essentially degenerate with that of gravitational lensing of the CMB, with the difference that it (1) acts on the beam-convolved sky, rather than the actual sky and (2) produces a curl-mode deflection field as well as a gradient mode. This is discussed further in the [#planck2013-p12|Planck gravitational lensing] paper, where the subpixel deflection field constitutes a potential source of bias for the measured lensing potential. Indeed, Eq. [eqn:cltpixelized] is just a slightly modified version of the usual first order CMB lensing power spectrum (Hu (2000), Lewis and Challinor (2006)) to accommodate curl modes.
A useful approximation to Eq. which is derived in the unrealistic limit that the deflection vectors are uncorrelated between pixels, but in practice gives a good description of the power induced by the pixelization, is that the couples the CMB gradient into a source of noise with an effective level given by
where the average is taken over all pixels and is half the mean-squared power in the CMB gradient: For frequency-combined maps, is typically on the order of , and so the induced noise is at the level of . This is small compared to the instrumental contribution, although it does not disappear when taking cross-spectra, depending on how coherent the hit distributions of the two maps in the cross-spectrum are.
# References
<biblio force=false>
1. References
</biblio>
Cosmic Microwave background
Full-Width-at-Half-Maximum
(Hierarchical Equal Area isoLatitude Pixelation of a sphere, <ref name="Template:Gorski2005">HEALPix: A Framework for High-Resolution Discretization and Fast Analysis of Data Distributed on the Sphere, K. M. Górski, E. Hivon, A. J. Banday, B. D. Wandelt, F. K. Hansen, M. Reinecke, M. Bartelmann, ApJ, 622, 759-771, (2005).
(Planck) High Frequency Instrument
(Planck) Low Frequency Instrument
reduced IMO
Operation Day definition is geometric visibility driven as it runs from the start of a DTCP (satellite Acquisition Of Signal) to the start of the next DTCP. Given the different ground stations and spacecraft will takes which station for how long, the OD duration varies but it is basically once a day.
Early Release Compact Source Catalog
| 2022-12-02T05:18:35 |
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|
http://dlmf.nist.gov/4.1
|
# §4.1 Special Notation
(For other notation see Notation for the Special Functions.)
integers. real or complex constants. real variables. complex variable. base of natural logarithms.
It is assumed the user is familiar with the definitions and properties of elementary functions of real arguments . The main purpose of the present chapter is to extend these definitions and properties to complex arguments .
The main functions treated in this chapter are the logarithm , ; the exponential , ; the circular trigonometric (or just trigonometric) functions , , , , , ; the inverse trigonometric functions , , etc.; the hyperbolic trigonometric (or just hyperbolic) functions , , , , , ; the inverse hyperbolic functions , , etc.
Sometimes in the literature the meanings of and are interchanged; similarly for and , etc. Sometimes “arc” is replaced by the index “−1”, e.g. for and for .
| 2014-03-10T04:26:12 |
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|
https://par.nsf.gov/biblio/10004230-measurement-tt-production-cross-section-pp-collisions-dilepton-final-states-containing
|
Measurement of the $tt¯$ production cross section in pp collisions at $s=7 TeV$ in dilepton final states containing a $τ$
Authors:
; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; more »
Publication Date:
NSF-PAR ID:
10004230
Journal Name:
Physical Review D
Volume:
85
Issue:
11
ISSN:
1550-7998
Publisher:
American Physical Society
| 2022-10-02T16:09:54 |
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|
http://dlmf.nist.gov/18.32
|
# §18.32 OP’s with Respect to Freud Weights
A Freud weight is a weight function of the form
18.32.1 ${w(x)=\mathop{\exp\/}\nolimits\!\left(-Q(x)\right)},$ $-\infty,
where $Q(x)$ is real, even, nonnegative, and continuously differentiable. Of special interest are the cases $Q(x)=x^{2m}$, $m=1,2,\dots$. No explicit expressions for the corresponding OP’s are available. However, for asymptotic approximations in terms of elementary functions for the OP’s, and also for their largest zeros, see Levin and Lubinsky (2001) and Nevai (1986). For a uniform asymptotic expansion in terms of Airy functions (§9.2) for the OP’s in the case $Q(x)=x^{4}$ see Bo and Wong (1999).
For asymptotic approximations to OP’s that correspond to Freud weights with more general functions $Q(x)$ see Deift et al. (1999a, b), Bleher and Its (1999), and Kriecherbauer and McLaughlin (1999).
| 2015-10-06T14:41:38 |
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|
https://www.usgs.gov/center-news/volcano-watch-bench-collapse-sparks-lightning-roiling-clouds
|
# Volcano Watch — Bench collapse sparks lightning, roiling clouds
Release Date:
Four of us HVO lava junkies had the rare opportunity to witness a partial bench collapse on Monday evening, June 8. The collapse began at 7:40 p.m. when a slab of incandescent lava fell outward from the bench edge into the ocean. The hot rock was fragmented by steam explosions as it hit the sea water, and the steam cloud became abruptly darker as the rock fragments were blasted upward.
Four of us HVO lava junkies had the rare opportunity to witness a partial bench collapse on Monday evening, June 8. The collapse began at 7:40 p.m. when a slab of incandescent lava fell outward from the bench edge into the ocean. The hot rock was fragmented by steam explosions as it hit the sea water, and the steam cloud became abruptly darker as the rock fragments were blasted upward.
The initial explosion disrupted the adjacent bench, enlarging the explosion and darkening the cloud with more debris. Each event led rapidly to another, so that within seconds the collapse progressed from inconsequential to catastrophic. It was during this period that the 15 or 20 visitors near the site recognized a life-or-death situation and, choosing life, moved back to safer ground. Fortunately, no one had ventured onto the active bench.
The collapses continued sporadically for the next two hours as slabs of incandescent lava calved away into the surf. Bench width was diminished by 40 m, or nearly one-half of its initial extent. Small tremors, accompanied by dull, audible thuds, were felt early in the two-hour event, chiefly by people sitting on the ground. The largest tremor was felt by people standing and sitting.
Littoral cone-forming explosions began in the first five minutes and continued through the evening as sea water invaded the core of the disrupted lava flow. The cone grew by small explosions that hurled incandescent bombs and fragmented bedrock upward and outward for tens of meters. The growing cone was positioned at the edge of the bench, so its growth was halted every few minutes as part of it slid away. When the bench collapses ceased, the cone began building in earnest. By 10 p.m. it was 5-10 m high.
Most thrilling to us was the lightning in the eruption cloud, forming jagged spikes that reached down nearly to the ocean from heights of 30 m or more. Accompanying thunder brought no roar but, instead, the sound of popping electric arcs, reminiscent of electronic bug killers that zap when insects fly too close.
Only those clouds darkened by disrupted solid lava sparked with lightning. We suspect that the older solid lava carried the charge imbalance that led to lightning, whereas the hot, spattery lava was perhaps incapable of maintaining electrical charge. This phenomenon probably differs from the lightning characteristic of ash clouds from large explosive volcanoes. That lightning results because the larger ash particles carry a different charge than smaller particles. Perhaps this interpretation explains why lightning was never observed during the cinder-rich high-fountaining episodes from early eruptions at Puu Oo.
The bench remains a dangerous but enchanting site on the Big Island. In the past weeks, surface flows on the coastal plain have draped the low cliffs that once formed an insurmountable backdrop to the active bench. Foolishly, visitors have been climbing down this lava drapery to traverse the bench. Those of us in the volcano business can only ascribe this idiocy to a death wish.
Anyone on the bench during the recent partial collapse would have been engulfed in acidic steam clouds that billowed back from the lava entry to the sea cliff. The steaming white-out prohibits retreat even as explosion debris rains down. And if the collapse is wholesale, opportunity to escape changes to tragedy in a heartbeat.
### Volcano Activity Update
The east rift zone eruption of Kīlauea Volcano from the Puu Oo vent continued unabated during the past week. The lava flows through a network of tubes to the seacoast and enters the ocean at two locations-Waha`ula and Kamokuna. The public is again reminded that these two areas are extremely dangerous. The National Park Service has restricted access to them because of frequent explosions that accompany collapses of the growing lava bench as described above.
There were no earthquakes reported felt in the past week.
| 2019-11-11T19:49:39 |
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|
https://www.usgs.gov/media/images/taking-channel-measurements-a-canoe
|
# Taking channel measurements from a canoe
### Detailed Description
Surface Water Modeling for FEMA Flood Insurance Rate Maps.
USGS employee in a canoe hold a prism and survey rod level while the channel point is collected with a total station from shore.
Public Domain.
| 2023-03-28T17:33:03 |
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|
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