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https://phys.libretexts.org/Courses/Tuskegee_University/Algebra_Based_Physics_I/02%3A_One-Dimensional_Kinematics/2.09%3A_Graphical_Analysis_of_One-Dimensional_Motion | $$\require{cancel}$$
# 2.9: Graphical Analysis of One-Dimensional Motion
Learning Objectives
By the end of this section, you will be able to:
• Describe a straight-line graph in terms of its slope and y-intercept.
• Determine average velocity or instantaneous velocity from a graph of position vs. time.
• Determine average or instantaneous acceleration from a graph of velocity vs. time.
• Derive a graph of velocity vs. time from a graph of position vs. time.
• Derive a graph of acceleration vs. time from a graph of velocity vs. time.
A graph, like a picture, is worth a thousand words. Graphs not only contain numerical information; they also reveal relationships between physical quantities. This section uses graphs of displacement, velocity, and acceleration versus time to illustrate one-dimensional kinematics.
## Slopes and General Relationships
First note that graphs in this text have perpendicular axes, one horizontal and the other vertical. When two physical quantities are plotted against one another in such a graph, the horizontal axis is usually considered to be an independent variable and the vertical axis a dependent variable. If we call the horizontal axis the x-axis and the vertical axis the y-axis, as in Figure $$\PageIndex{1}$$, a straight-line graph has the general form
$y=mx+b.$
Here $$m$$ is the slope, defined to be the rise divided by the run of the straight line (Figure $$\PageIndex{1}$$). The letter $$b$$ is used for they-intercept, which is the point at which the line crosses the vertical axis.
## Graph of Displacement vs. Time (a = 0, so v is constant)
Time is usually an independent variable that other quantities, such as displacement, depend upon. A graph of displacement versus time would, thus, have on the vertical axis and on the horizontal axis. Figure $$\PageIndex{2}$$ is just such a straight-line graph. It shows a graph of displacement versus time for a jet-powered car on a very flat dry lake bed in Nevada.
Using the relationship between dependent and independent variables, we see that the slope in the graph above is average velocity $$\bar{v}$$ and the intercept is displacement at time zero—that is, $$x_0$$. Substituting these symbols into $$y=mx+b$$ gives
$x=\bar{v}t+x_0$
or
$x=x_0+ \bar{v}t.$
Thus a graph of displacement versus time gives a general relationship among displacement, velocity, and time, as well as giving detailed numerical information about a specific situation.
THE SLOPE OF $$X$$ VS. $$T$$
The slope of the graph of displacement $$x$$ vs. time $$t$$ is velocity $$v$$.
$$\displaystyle slope=\frac{Δx}{Δt}=v$$
Notice that this equation is the same as that derived algebraically from other motion equations in Motion Equations for Constant Acceleration in One Dimension.
From the figure we can see that the car has a displacement of 25 m at 0.50 s and 2000 m at 6.40 s. Its displacement at other times can be read from the graph; furthermore, information about its velocity and acceleration can also be obtained from the graph.
Example $$\PageIndex{1}$$:Determining Average Velocity from a Graph of Displacement versus Time: Jet Car
Find the average velocity of the car whose position is graphed in Figure $$\PageIndex{2}$$.
Strategy
The slope of a graph of $$x$$ vs. $$t$$ is average velocity, since slope equals rise over run. In this case, rise = change in position and run = change in time, so that
$\displaystyle slope=\frac{Δx}{Δt}=\bar{v}. \nonumber$
Since the slope is constant here, any two points on the graph can be used to find the slope. (Generally speaking, it is most accurate to use two widely separated points on the straight line. This is because any error in reading data from the graph is proportionally smaller if the interval is larger.)
Solution
1. Choose two points on the line. In this case, we choose the points labeled on the graph: (6.4 s, 2000 m) and (0.50 s, 525 m). (Note, however, that you could choose any two points.)
2. Substitute the x and t values of the chosen points into the equation. Remember in calculating change (Δ) we always use final value minus initial value. $\displaystyle \bar{v}=\frac{Δx}{Δt}=\frac{2000 m−525 m}{6.4 s−0.50 s}, \nonumber$ yielding $\displaystyle v−=250 m/s. \nonumber$
Discussion
This is an impressively large land speed (900 km/h, or about 560 mi/h): much greater than the typical highway speed limit of 60 mi/h (27 m/s or 96 km/h), but considerably shy of the record of 343 m/s (1234 km/h or 766 mi/h) set in 1997.
## Graphs of Motion when is constant but ≠0
The graphs in Figure $$\PageIndex{3}$$ below represent the motion of the jet-powered car as it accelerates toward its top speed, but only during the time when its acceleration is constant. Time starts at zero for this motion (as if measured with a stopwatch), and the displacement and velocity are initially 200 m and 15 m/s, respectively.
Figure $$\displaystyle \PageIndex{3}$$: Graphs of motion of a jet-powered car during the time span when its acceleration is constant. (a) The slope of an $$\displaystyle x$$ vs. $$\displaystyle t$$ graph is velocity. This is shown at two points, and the instantaneous velocities obtained are plotted in the next graph. Instantaneous velocity at any point is the slope of the tangent at that point. (b) The slope of the $$\displaystyle v$$ vs. $$\displaystyle t$$ graph is constant for this part of the motion, indicating constant acceleration. (c) Acceleration has the constant value of $$\displaystyle 5.0 m/s^2$$ over the time interval plotted.
The graph of displacement versus time in Figure $$\PageIndex{3a}$$ is a curve rather than a straight line. The slope of the curve becomes steeper as time progresses, showing that the velocity is increasing over time. The slope at any point on a displacement-versus-time graph is the instantaneous velocity at that point. It is found by drawing a straight line tangent to the curve at the point of interest and taking the slope of this straight line. Tangent lines are shown for two points in Figure $$\PageIndex{3a}$$. If this is done at every point on the curve and the values are plotted against time, then the graph of velocity versus time shown in Figure $$\PageIndex{3b}$$ is obtained. Furthermore, the slope of the graph of velocity versus time is acceleration, which is shown in Figure $$\PageIndex{3c}$$.
Example $$\PageIndex{2}$$:
Calculate the velocity of the jet car at a time of 25 s by finding the slope of the $$\displaystyle vs. \(\displaystyle graph in the graph below Strategy The slope of a curve at a point is equal to the slope of a straight line tangent to the curve at that point. This principle is illustrated in Figure, where Q is the point at \(\displaystyle t=25 s$$.
Solution
1. Find the tangent line to the curve at $$\displaystyle t=25 s$$.
2. Determine the endpoints of the tangent. These correspond to a position of 1300 m at time 19 s and a position of 3120 m at time 32 s.
3. Plug these endpoints into the equation to solve for the slope, .
$$\displaystyle slope=v_Q=\frac{Δx_Q}{Δt_Q}=\frac{(3120 m−1300 m)}{(32 s−19 s)}$$
Thus,
$$\displaystyle v_Q=\frac{1820 m}{13 s}=140 m/s.$$
Discussion
This is the value given in this figure’s table for v at $$\displaystyle t=25 s$$. The value of 140 m/s for $$\displaystyle v_Q$$ is plotted in Figure. The entire graph of $$\displaystyle v$$ vs. $$\displaystyle t$$ can be obtained in this fashion.
Carrying this one step further, we note that the slope of a velocity versus time graph is acceleration. Slope is rise divided by run; on a $$\displaystyle v$$ vs. $$\displaystyle t$$ graph, rise = change in velocity $$\displaystyle Δv$$ and run = change in time $$\displaystyle Δt$$.
THE SLOPE OF V VS. T
The slope of a graph of velocity $$\displaystyle v$$ vs. time $$\displaystyle t$$ is acceleration $$\displaystyle a$$.
$$\displaystyle slope=\frac{Δv}{Δt}=a$$
Since the velocity versus time graph in Figure $$\PageIndex{3b}$$ is a straight line, its slope is the same everywhere, implying that acceleration is constant. Acceleration versus time is graphed in Figure(c).
Additional general information can be obtained from Figure and the expression for a straight line, $$\displaystyle y=mx+b.$$
In this case, the vertical axis $$\displaystyle y$$ is $$\displaystyle V$$, the intercept $$\displaystyle b$$ is $$\displaystyle v_0$$, the slope $$\displaystyle m$$ is $$\displaystyle a$$, and the horizontal axis $$\displaystyle x$$ is $$\displaystyle t$$. Substituting these symbols yields
$v=v_0+at. \nonumber$
A general relationship for velocity, acceleration, and time has again been obtained from a graph. Notice that this equation was also derived algebraically from other motion equations in Motion Equations for Constant Acceleration in One Dimension.
It is not accidental that the same equations are obtained by graphical analysis as by algebraic techniques. In fact, an important way to discover physical relationships is to measure various physical quantities and then make graphs of one quantity against another to see if they are correlated in any way. Correlations imply physical relationships and might be shown by smooth graphs such as those above. From such graphs, mathematical relationships can sometimes be postulated. Further experiments are then performed to determine the validity of the hypothesized relationships.
## Graphs of Motion Where Acceleration is Not Constant
Now consider the motion of the jet car as it goes from 165 m/s to its top velocity of 250 m/s, graphed in Figure $$\PageIndex{6}$$. Time again starts at zero, and the initial position and velocity are 2900 m and 165 m/s, respectively. (These were the final position and velocity of the car in the motion graphed in Figure $$\PageIndex{4}$$) Acceleration gradually decreases from $$\displaystyle 5.0 m/s^2$$ to zero when the car hits 250 m/s. The slope of the $$\displaystyle x$$ vs. $$\displaystyle t$$ graph increases until $$\displaystyle t=55 s$$, after which time the slope is constant. Similarly, velocity increases until 55 s and then becomes constant, since acceleration decreases to zero at 55 s and remains zero afterward.
Example $$\PageIndex{3}$$:Calculating Acceleration from a Graph of Velocity versus Time
Calculate the acceleration of the jet car at a time of 25 s by finding the slope of the $$\displaystyle v$$ vs. $$\displaystyle t$$ graph in Figure $$\PageIndex{6b}$$.
Strategy
The slope of the curve at $$\displaystyle t=25 s$$ is equal to the slope of the line tangent at that point, as illustrated in Figure $$\PageIndex{6b}$$.
Solution
Determine endpoints of the tangent line from the figure, and then plug them into the equation to solve for slope, .
$$\displaystyle slope=\frac{Δv}{Δt}=\frac{(260 m/s−210 m/s)}{(51 s−1.0 s)}$$
$$\displaystyle a=\frac{50 m/s}{50 s}=1.0 m/s^2.$$
Discussion
Note that this value for a is consistent with the value plotted in Figure(c) at $$\displaystyle t=25 s$$.
A graph of displacement versus time can be used to generate a graph of velocity versus time, and a graph of velocity versus time can be used to generate a graph of acceleration versus time. We do this by finding the slope of the graphs at every point. If the graph is linear (i.e., a line with a constant slope), it is easy to find the slope at any point and you have the slope for every point. Graphical analysis of motion can be used to describe both specific and general characteristics of kinematics. Graphs can also be used for other topics in physics. An important aspect of exploring physical relationships is to graph them and look for underlying relationships.
Exercise $$\displaystyle \PageIndex{1}$$:Check Your Understanding
A graph of velocity vs. time of a ship coming into a harbor is shown below.
1. Describe the motion of the ship based on the graph.
2. What would a graph of the ship’s acceleration look like?
(a) The ship moves at constant velocity and then begins to decelerate at a constant rate. At some point, its deceleration rate decreases. It maintains this lower deceleration rate until it stops moving.
Solution b
A graph of acceleration vs. time would show zero acceleration in the first leg, large and constant negative acceleration in the second leg, and constant negative acceleration.
## Summary
• Graphs of motion can be used to analyze motion.
• Graphical solutions yield identical solutions to mathematical methods for deriving motion equations.
• The slope of a graph of displacement $$\displaystyle x$$ vs. time $$\displaystyle t$$ is velocity $$\displaystyle v$$.
• The slope of a graph of velocity $$\displaystyle v$$ vs. time $$\displaystyle t$$ graph is acceleration $$\displaystyle a$$.
• Average velocity, instantaneous velocity, and acceleration can all be obtained by analyzing graphs.
## Glossary
independent variable
the variable that the dependent variable is measured with respect to; usually plotted along the $$x$$-axis
dependent variable
the variable that is being measured; usually plotted along the $$y$$-axis
slope
the difference in $$y$$-value (the rise) divided by the difference in $$x$$-value (the run) of two points on a straight line
y-intercept
the $$y$$-value when $$x$$=0, or when the graph crosses the $$y$$-axis
## Contributors and Attributions
• 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).
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https://zbmath.org/authors/?q=ai%3Abach.volker | # zbMATH — the first resource for mathematics
## Bach, Volker
Compute Distance To:
Author ID: bach.volker Published as: Bach, V.; Bach, Volker External Links: MGP · Wikidata · GND
Documents Indexed: 66 Publications since 1989, including 2 Books
all top 5
#### Co-Authors
14 single-authored 15 Fröhlich, Jürg Martin 12 Sigal, Israel Michael 6 Ballesteros, Miguel 5 Pizzo, Alessandro 4 Siedentop, Heinz Karl Heinrich 3 Barbaroux, Jean-Marie 3 Breteaux, Sébastien 3 Chen, Thomas M. 3 Knörr, Hans Konrad 3 Lieb, Elliott H. 3 Menge, Edmund 3 Schach Møller, Jacob 2 Bru, Jean-Bernard 2 De Siqueira Pedra, Walter 2 Helffer, Bernard 2 Jonsson, Lars-Erik 2 Könenberg, Martin 2 Menrath, Lars 2 Poelchau, Jurij 2 Solovej, Jan Philip 1 Deckert, Dirk-André 1 Dereziński, Jan 1 Faßbender, Heike 1 Faupin, Jérémy 1 Hach, Alexander 1 Hoppe, Jens 1 Iniesta, Diego 1 Jecko, Thierry 1 Klopp, Frédéric 1 Kurig, Carolin 1 Lakaev, Saidakhmat Norjigitovich 1 Lewis, Roger T. 1 Lundholm, Douglas 1 Matte, Oliver 1 Merkli, Marco 1 Petrat, Sören 1 Pickl, Peter 1 Seiler, Ruedi 1 Sjöstrand, Johannes 1 Soffer, Avraham 1 Travaglia, Marcos Vinicio 1 Tzaneteas, Tim 1 Urban, Karsten 1 Zenk, Heribert
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#### Serials
7 Communications in Mathematical Physics 6 Journal of Mathematical Physics 5 Journal of Functional Analysis 4 Advances in Mathematics 4 Documenta Mathematica 3 Journal of Statistical Physics 3 Letters in Mathematical Physics 3 Mitteilungen der Deutschen Mathematiker-Vereinigung (DMV) 3 Journal of Evolution Equations 3 Oberwolfach Reports 2 Journal of Mathematical Analysis and Applications 2 Advances in Theoretical and Mathematical Physics 2 Annales Henri Poincaré 1 IEEE Transactions on Information Theory 1 Reports on Mathematical Physics 1 Reviews in Mathematical Physics 1 Journal of Differential Equations 1 Mathematische Zeitschrift 1 Memoirs of the American Mathematical Society 1 Journal de Mathématiques Pures et Appliquées. Neuvième Série 1 Random Operators and Stochastic Equations 1 Markov Processes and Related Fields 1 PAMM. Proceedings in Applied Mathematics and Mechanics
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#### Fields
53 Quantum theory (81-XX) 18 Operator theory (47-XX) 13 Partial differential equations (35-XX) 12 Statistical mechanics, structure of matter (82-XX) 4 General and overarching topics; collections (00-XX) 4 Probability theory and stochastic processes (60-XX) 3 Ordinary differential equations (34-XX) 3 Mathematics education (97-XX) 2 Functional analysis (46-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Difference and functional equations (39-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Numerical analysis (65-XX) 1 Mechanics of deformable solids (74-XX) 1 Fluid mechanics (76-XX) 1 Astronomy and astrophysics (85-XX) 1 Information and communication theory, circuits (94-XX)
#### Citations contained in zbMATH Open
47 Publications have been cited 862 times in 447 Documents Cited by Year
Quantum electrodynamics of confined nonrelativistic particles. Zbl 0923.47040
Bach, Volker; Fröhlich, Jürg; Sigal, Israel Michael
1998
Spectral analysis for systems of atoms and molecules coupled to the quantized radiation field. Zbl 0965.81134
Bach, Volker; Fröhlich, Jürg; Sigal, Israel Michael
1999
Renormalization group analysis of spectral problems in quantum field theory. Zbl 0923.47041
Bach, Volker; Fröhlich, Jürg; Sigal, Israel Michael
1998
Generalized Hartree-Fock theory and the Hubbard model. Zbl 0839.60095
Bach, Volker; Lieb, Elliott H.; Solovej, Jan Philip
1994
Bach, Volker; Fröhlich, Jürg; Sigal, Israel Michael
2000
Smooth Feshbach map and operator-theoretic renormalization group methods. Zbl 1060.47028
Bach, Volker; Chen, Thomas; Fröhlich, Jürg; Sigal, Israel Michael
2003
Error bound for the Hartree-Fock energy of atoms and molecules. Zbl 0771.46038
Bach, Volker
1992
Infrared-finite algorithms in QED: the groundstate of an atom interacting with the quantized radiation field. Zbl 1118.81083
Bach, Volker; Fröhlich, Jürg; Pizzo, Alessandro
2006
Positive commutators and the spectrum of Pauli-Fierz Hamiltonian of atoms and molecules. Zbl 0962.81011
Bach, Volker; Fröhlich, Jürg; Sigal, Israel Michael; Soffer, Avy
1999
The renormalized electron mass in non-relativistic quantum electrodynamics. Zbl 1118.81028
Bach, Volker; Chen, Thomas; Fröhlich, Jürg; Sigal, Israel Michael
2007
Mathematical theory of nonrelativistic matter and radiation. Zbl 0831.47048
Bach, V.; Fröhlich, J.; Sigal, I. M.
1995
On the stability of the relativistic electron-positron field. Zbl 1024.81056
Bach, Volker; Barbaroux, Jean-Marie; Helffer, Bernard; Siedentop, Heinz
1999
Kinetic energy estimates for the accuracy of the time-dependent Hartree-Fock approximation with Coulomb interaction. Zbl 1333.35221
Bach, Volker; Breteaux, Sébastien; Petrat, Sören; Pickl, Peter; Tzaneteas, Tim
2016
Correlation at low temperature. I: Exponential decay. Zbl 1031.82003
Bach, Volker; Møller, Jacob Schach
2003
Infrared-finite algorithms in QED. II. The expansion of the groundstate of an atom interacting with the quantized radiation field. Zbl 1161.81026
Bach, Volker; Fröhlich, Jürg; Pizzo, Alessandro
2009
An infrared-finite algorithm for Rayleigh scattering amplitudes, and Bohr’s frequency condition. Zbl 1123.81046
Bach, Volker; Fröhlich, Jürg; Pizzo, Alessandro
2007
Accuracy of mean field approximations for atoms and molecules. Zbl 0802.47061
Bach, Volker
1993
Ionization energies of bosonic Coulomb systems. Zbl 0725.47049
Bach, Volker
1991
Existence and construction of resonances for atoms coupled to the quantized radiation field. Zbl 1366.81318
Bach, Volker; Ballesteros, Miguel; Pizzo, Alessandro
2017
Correlation asymptotics of classical lattice spin systems with nonconvex Hamilton function at low temperature. Zbl 1021.82002
Bach, V.; Jecko, T.; Sjöstrand, J.
2000
Existence of ground state eigenvalues for the spin-boson model with critical infrared divergence and multiscale analysis. Zbl 1366.81317
Bach, Volker; Ballesteros, Miguel; Könenberg, Martin; Menrath, Lars
2017
Effective dynamics of an electron coupled to an external potential in non-relativistic QED. Zbl 1275.81091
Bach, Volker; Chen, Thomas; Faupin, Jérémy; Fröhlich, Jürg; Sigal, Israel Michael
2013
A proof of Scott’s conjecture for ions. Zbl 0732.58042
Bach, Volker
1989
Mathematical analysis of the photoelectric effect. Zbl 1015.81059
Bach, Volker; Klopp, Frédéric; Zenk, Heribert
2001
On the number of bound states of a bosonic $$N$$-particle Coulomb system. Zbl 0852.47036
Bach, Volker; Lewis, Roger; Lieb, Elliott H.; Siedentop, Heinz
1993
Bogolubov-Hartree-Fock mean field theory for neutron stars and other systems with attractive interactions. Zbl 1248.81277
Bach, Volker; Fröhlich, Jürg; Jonsson, Lars
2009
Bounds on the discrete spectrum of lattice Schrödinger operators. Zbl 1382.81094
Bach, V.; de Siqueira Pedra, W.; Lakaev, S. N.
2018
Diagonalizing quadratic bosonic operators by non-autonomous flow equation. Zbl 1435.81003
Bach, Volker; Bru, Jean-Bernard
2016
Continuous renormalization group analysis of spectral problems in quantum field theory. Zbl 1308.81086
Bach, Volker; Ballesteros, Miguel; Fröhlich, Jürg
2015
Suppression of decoherence by periodic forcing. Zbl 1300.81010
Bach, Volker; de Siqueira Pedra, Walter; Merkli, Marco; Sigal, Israel Michael
2014
Construction of the ground state in nonrelativistic QED by continuous flows. Zbl 1107.81050
Bach, Volker; Könenberg, Martin
2006
Rigorous foundations of the Brockett-Wegner flow for operators. Zbl 1239.34067
Bach, Volker; Bru, Jean-Bernard
2010
Stability of matter for the Hartree-Fock functional of the relativistic electron-positron field. Zbl 0913.35113
Bach, Volker; Barbaroux, Jean-Marie; Helffer, Bernard; Siedentop, Heinz
1998
Accuracy of the Hartree-Fock approximation for the Hubbard model. Zbl 0883.60100
Bach, Volker; Poelchau, Jurij
1997
Generalization of Lieb’s variational principle to Bogoliubov-Hartree-Fock theory. Zbl 1295.81146
Bach, Volker; Breteaux, Sébastien; Knörr, Hans Konrad; Menge, Edmund
2014
Ferromagnetism of the Hubbard model at strong coupling in the Hartree-Fock approximation. Zbl 1125.82031
Bach, Volker; Lieb, Elliott H.; Travaglia, Marcos V.
2006
Correlation at low temperature. II: Asymptotics. Zbl 1142.82311
Bach, Volker; Møller, Jacob Schach
2004
Exponential decay of eigenfunctions of the Bethe-Salpeter operator. Zbl 0991.34074
Bach, Volker; Matte, Oliver
2001
Hartree-Fock Gibbs states for the Hubbard model. Zbl 0878.60076
Bach, V.; Poelchau, J.
1996
Mathematical density and density matrix functional theory (DFT and DMFT). Zbl 1329.81421
Bach, Volker
2013
Minimization of the energy of the nonrelativistic one-electron Pauli-Fierz model over quasifree states. Zbl 1291.81401
Bach, Volker; Breteaux, Sébastien
2013
Fermion correlation inequalities derived from G- and P-conditions. Zbl 1260.81337
Bach, Volker; Knörr, Hans Konrad; Menge, Edmund
2012
Dynamical symmetries in supersymmetric matrix models. Zbl 1160.81025
Bach, V.; Hoppe, J.; Lundholm, D.
2008
A tutorial approach to the renormalization group and the smooth Feshbach map. Zbl 1105.81057
Bach, V.
2006
Bach, Volker
2001
QED of confined nonrelativistic particles – new results. Zbl 1253.81133
Bach, Volker; Fröhlich, Jürg; Sigal, Israel Michael
1999
Universality of the Fermi-Hellmann model. Zbl 0737.34042
Bach, Volker; Siedentop, Heinz
1991
Bounds on the discrete spectrum of lattice Schrödinger operators. Zbl 1382.81094
Bach, V.; de Siqueira Pedra, W.; Lakaev, S. N.
2018
Existence and construction of resonances for atoms coupled to the quantized radiation field. Zbl 1366.81318
Bach, Volker; Ballesteros, Miguel; Pizzo, Alessandro
2017
Existence of ground state eigenvalues for the spin-boson model with critical infrared divergence and multiscale analysis. Zbl 1366.81317
Bach, Volker; Ballesteros, Miguel; Könenberg, Martin; Menrath, Lars
2017
Kinetic energy estimates for the accuracy of the time-dependent Hartree-Fock approximation with Coulomb interaction. Zbl 1333.35221
Bach, Volker; Breteaux, Sébastien; Petrat, Sören; Pickl, Peter; Tzaneteas, Tim
2016
Diagonalizing quadratic bosonic operators by non-autonomous flow equation. Zbl 1435.81003
Bach, Volker; Bru, Jean-Bernard
2016
Continuous renormalization group analysis of spectral problems in quantum field theory. Zbl 1308.81086
Bach, Volker; Ballesteros, Miguel; Fröhlich, Jürg
2015
Suppression of decoherence by periodic forcing. Zbl 1300.81010
Bach, Volker; de Siqueira Pedra, Walter; Merkli, Marco; Sigal, Israel Michael
2014
Generalization of Lieb’s variational principle to Bogoliubov-Hartree-Fock theory. Zbl 1295.81146
Bach, Volker; Breteaux, Sébastien; Knörr, Hans Konrad; Menge, Edmund
2014
Effective dynamics of an electron coupled to an external potential in non-relativistic QED. Zbl 1275.81091
Bach, Volker; Chen, Thomas; Faupin, Jérémy; Fröhlich, Jürg; Sigal, Israel Michael
2013
Mathematical density and density matrix functional theory (DFT and DMFT). Zbl 1329.81421
Bach, Volker
2013
Minimization of the energy of the nonrelativistic one-electron Pauli-Fierz model over quasifree states. Zbl 1291.81401
Bach, Volker; Breteaux, Sébastien
2013
Fermion correlation inequalities derived from G- and P-conditions. Zbl 1260.81337
Bach, Volker; Knörr, Hans Konrad; Menge, Edmund
2012
Rigorous foundations of the Brockett-Wegner flow for operators. Zbl 1239.34067
Bach, Volker; Bru, Jean-Bernard
2010
Infrared-finite algorithms in QED. II. The expansion of the groundstate of an atom interacting with the quantized radiation field. Zbl 1161.81026
Bach, Volker; Fröhlich, Jürg; Pizzo, Alessandro
2009
Bogolubov-Hartree-Fock mean field theory for neutron stars and other systems with attractive interactions. Zbl 1248.81277
Bach, Volker; Fröhlich, Jürg; Jonsson, Lars
2009
Dynamical symmetries in supersymmetric matrix models. Zbl 1160.81025
Bach, V.; Hoppe, J.; Lundholm, D.
2008
The renormalized electron mass in non-relativistic quantum electrodynamics. Zbl 1118.81028
Bach, Volker; Chen, Thomas; Fröhlich, Jürg; Sigal, Israel Michael
2007
An infrared-finite algorithm for Rayleigh scattering amplitudes, and Bohr’s frequency condition. Zbl 1123.81046
Bach, Volker; Fröhlich, Jürg; Pizzo, Alessandro
2007
Infrared-finite algorithms in QED: the groundstate of an atom interacting with the quantized radiation field. Zbl 1118.81083
Bach, Volker; Fröhlich, Jürg; Pizzo, Alessandro
2006
Construction of the ground state in nonrelativistic QED by continuous flows. Zbl 1107.81050
Bach, Volker; Könenberg, Martin
2006
Ferromagnetism of the Hubbard model at strong coupling in the Hartree-Fock approximation. Zbl 1125.82031
Bach, Volker; Lieb, Elliott H.; Travaglia, Marcos V.
2006
A tutorial approach to the renormalization group and the smooth Feshbach map. Zbl 1105.81057
Bach, V.
2006
Correlation at low temperature. II: Asymptotics. Zbl 1142.82311
Bach, Volker; Møller, Jacob Schach
2004
Smooth Feshbach map and operator-theoretic renormalization group methods. Zbl 1060.47028
Bach, Volker; Chen, Thomas; Fröhlich, Jürg; Sigal, Israel Michael
2003
Correlation at low temperature. I: Exponential decay. Zbl 1031.82003
Bach, Volker; Møller, Jacob Schach
2003
Mathematical analysis of the photoelectric effect. Zbl 1015.81059
Bach, Volker; Klopp, Frédéric; Zenk, Heribert
2001
Exponential decay of eigenfunctions of the Bethe-Salpeter operator. Zbl 0991.34074
Bach, Volker; Matte, Oliver
2001
Bach, Volker
2001
Bach, Volker; Fröhlich, Jürg; Sigal, Israel Michael
2000
Correlation asymptotics of classical lattice spin systems with nonconvex Hamilton function at low temperature. Zbl 1021.82002
Bach, V.; Jecko, T.; Sjöstrand, J.
2000
Spectral analysis for systems of atoms and molecules coupled to the quantized radiation field. Zbl 0965.81134
Bach, Volker; Fröhlich, Jürg; Sigal, Israel Michael
1999
Positive commutators and the spectrum of Pauli-Fierz Hamiltonian of atoms and molecules. Zbl 0962.81011
Bach, Volker; Fröhlich, Jürg; Sigal, Israel Michael; Soffer, Avy
1999
On the stability of the relativistic electron-positron field. Zbl 1024.81056
Bach, Volker; Barbaroux, Jean-Marie; Helffer, Bernard; Siedentop, Heinz
1999
QED of confined nonrelativistic particles – new results. Zbl 1253.81133
Bach, Volker; Fröhlich, Jürg; Sigal, Israel Michael
1999
Quantum electrodynamics of confined nonrelativistic particles. Zbl 0923.47040
Bach, Volker; Fröhlich, Jürg; Sigal, Israel Michael
1998
Renormalization group analysis of spectral problems in quantum field theory. Zbl 0923.47041
Bach, Volker; Fröhlich, Jürg; Sigal, Israel Michael
1998
Stability of matter for the Hartree-Fock functional of the relativistic electron-positron field. Zbl 0913.35113
Bach, Volker; Barbaroux, Jean-Marie; Helffer, Bernard; Siedentop, Heinz
1998
Accuracy of the Hartree-Fock approximation for the Hubbard model. Zbl 0883.60100
Bach, Volker; Poelchau, Jurij
1997
Hartree-Fock Gibbs states for the Hubbard model. Zbl 0878.60076
Bach, V.; Poelchau, J.
1996
Mathematical theory of nonrelativistic matter and radiation. Zbl 0831.47048
Bach, V.; Fröhlich, J.; Sigal, I. M.
1995
Generalized Hartree-Fock theory and the Hubbard model. Zbl 0839.60095
Bach, Volker; Lieb, Elliott H.; Solovej, Jan Philip
1994
Accuracy of mean field approximations for atoms and molecules. Zbl 0802.47061
Bach, Volker
1993
On the number of bound states of a bosonic $$N$$-particle Coulomb system. Zbl 0852.47036
Bach, Volker; Lewis, Roger; Lieb, Elliott H.; Siedentop, Heinz
1993
Error bound for the Hartree-Fock energy of atoms and molecules. Zbl 0771.46038
Bach, Volker
1992
Ionization energies of bosonic Coulomb systems. Zbl 0725.47049
Bach, Volker
1991
Universality of the Fermi-Hellmann model. Zbl 0737.34042
Bach, Volker; Siedentop, Heinz
1991
A proof of Scott’s conjecture for ions. Zbl 0732.58042
Bach, Volker
1989
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#### Cited by 357 Authors
43 Fröhlich, Jürg Martin 34 Lewin, Mathieu 31 Bach, Volker 26 Sigal, Israel Michael 23 Hiroshima, Fumio 20 Faupin, Jérémy 20 Hainzl, Christian 15 Pizzo, Alessandro 14 Chen, Thomas M. 13 Griesemer, Marcel 13 Merkli, Marco 13 Schlein, Benjamin 13 Seiringer, Robert 12 Solovej, Jan Philip 11 De Roeck, Wojciech 11 Hasler, David G. 10 Ballesteros, Miguel 10 Dereziński, Jan 10 Schach Møller, Jacob 9 Amour, Laurent 9 Guillot, Jean-Claude 9 Könenberg, Martin 9 Siedentop, Heinz Karl Heinrich 8 Arai, Asao 8 Barbaroux, Jean-Marie 8 Hirokawa, Masao 8 Jakšić, Vojkan 8 Matte, Oliver 8 Pillet, Claude-Alain 8 Spohn, Herbert 7 Lieb, Elliott H. 7 Miyao, Tadahiro 7 Phan Thành Nam 7 Porta, Marcello 6 Herbst, Ira W. 6 Petrat, Sören 6 Séré, Eric 6 Stockmeyer, Edgardo 6 Vugalter, Semjon A. 5 Bruneau, Laurent 5 Deckert, Dirk-André 5 Frank, Rupert L. 5 Gérard, Christian 5 Kupiainen, Antti 5 Lörinczi, József 5 Schubnel, Baptiste 5 Takaesu, Toshimitsu 4 Abdesselam, Abdelmalek 4 Ammari, Zied 4 Benedikter, Niels 4 Bru, Jean-Bernard 4 Falconi, Marco 4 Fournais, Søren 4 Grébert, Benoît 4 Hänle, Felix 4 Loss, Michael 4 Nourrigat, Jean Francois 4 Panati, Annalisa 4 Pickl, Peter 4 Rougerie, Nicolas 4 Sabin, Julien 4 Suzuki, Akito 3 Betz, Volker 3 Billionnet, Claude 3 Bokanowski, Olivier 3 Bräunlich, Gerhard 3 Breteaux, Sébastien 3 Cancès, Eric 3 Catto, Isabelle 3 Chenn, Ilias 3 De Siqueira Pedra, Walter 3 Dybalski, Wojciech 3 Georgescu, Vladimir 3 Gravejat, Philippe 3 Hidaka, Takeru 3 Lakaev, Saidakhmat Norzhigitovich 3 Langmann, Edwin 3 Lemm, Marius 3 Minlos, Robert Adol’fovich 3 Møller, Jacob S. 3 Saffirio, Chiara 3 Salem, Walid Khaled Abou 3 Sasaki, Itaru 3 Skibsted, Erik 3 Soffer, Avraham 3 Vougalter, Vitali 3 Zenk, Heribert 2 Abou-Salem, Walid K. 2 Anapolitanos, Ioannis 2 Aschbacher, Walter H. 2 Benguria, Rafael D. 2 Bertini, Massimo 2 Bony, Jean-François 2 Bourget, Olivier 2 Correggi, Michele 2 Cortés, Víctor H. 2 Dam, Thomas Norman 2 De Bièvre, Stephan 2 de Woul, Jonas 2 Deuchert, Andreas ...and 257 more Authors
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#### Cited in 73 Serials
67 Journal of Mathematical Physics 59 Communications in Mathematical Physics 40 Journal of Functional Analysis 39 Journal of Statistical Physics 34 Reviews in Mathematical Physics 30 Annales Henri Poincaré 20 Letters in Mathematical Physics 18 Advances in Mathematics 12 Journal of Mathematical Analysis and Applications 9 Archive for Rational Mechanics and Analysis 6 Reports on Mathematical Physics 6 Mathematical Physics, Analysis and Geometry 5 Séminaire Laurent Schwartz. EDP et Applications 4 Communications on Pure and Applied Mathematics 4 Theoretical and Mathematical Physics 4 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 4 Journal de Mathématiques Pures et Appliquées. Neuvième Série 4 Calculus of Variations and Partial Differential Equations 3 Annales de l’Institut Henri Poincaré. Physique Théorique 3 Infinite Dimensional Analysis, Quantum Probability and Related Topics 3 Journal of Evolution Equations 3 Comptes Rendus. Mathématique. Académie des Sciences, Paris 2 International Journal of Modern Physics B 2 Physics Reports 2 Integral Equations and Operator Theory 2 Mathematische Zeitschrift 2 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 2 Publications of the Research Institute for Mathematical Sciences, Kyoto University 2 Transactions of the American Mathematical Society 2 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 2 Communications in Partial Differential Equations 2 SIAM Journal on Mathematical Analysis 2 Bulletin of the American Mathematical Society. New Series 2 St. Petersburg Mathematical Journal 2 Advances in Mathematical Physics 2 Journal de l’École Polytechnique – Mathématiques 2 Pure and Applied Analysis 1 International Journal of Modern Physics A 1 Applicable Analysis 1 Nuclear Physics. B 1 Russian Mathematical Surveys 1 Journal of Geometry and Physics 1 Acta Mathematica 1 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 1 Duke Mathematical Journal 1 International Journal of Mathematics and Mathematical Sciences 1 Journal of Differential Equations 1 Journal of Mathematical Economics 1 Memoirs of the American Mathematical Society 1 Proceedings of the American Mathematical Society 1 Transactions of the Moscow Mathematical Society 1 Advances in Applied Mathematics 1 Rendiconti di Matematica e delle sue Applicazioni. Serie VII 1 Applied Mathematics Letters 1 Stochastic Processes and their Applications 1 Mémoires de la Société Mathématique de France. Nouvelle Série 1 Journal of Nonlinear Science 1 Kyushu Journal of Mathematics 1 Discrete and Continuous Dynamical Systems 1 New Journal of Physics 1 Journal of the European Mathematical Society (JEMS) 1 Physical Review Letters 1 Quantum Information Processing 1 Journal of Hyperbolic Differential Equations 1 Journal of Statistical Mechanics: Theory and Experiment 1 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 1 Complex Analysis and Operator Theory 1 Journal of Physics A: Mathematical and Theoretical 1 Analysis & PDE 1 Journal of Pseudo-Differential Operators and Applications 1 Kyoto Journal of Mathematics 1 Bulletin of Mathematical Sciences 1 Tunisian Journal of Mathematics
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#### Cited in 33 Fields
361 Quantum theory (81-XX) 149 Statistical mechanics, structure of matter (82-XX) 125 Partial differential equations (35-XX) 102 Operator theory (47-XX) 35 Functional analysis (46-XX) 24 Probability theory and stochastic processes (60-XX) 13 Optics, electromagnetic theory (78-XX) 11 Calculus of variations and optimal control; optimization (49-XX) 10 Dynamical systems and ergodic theory (37-XX) 9 Global analysis, analysis on manifolds (58-XX) 7 Ordinary differential equations (34-XX) 7 Mechanics of particles and systems (70-XX) 6 Functions of a complex variable (30-XX) 6 Difference and functional equations (39-XX) 5 Astronomy and astrophysics (85-XX) 3 Differential geometry (53-XX) 3 Fluid mechanics (76-XX) 3 Relativity and gravitational theory (83-XX) 3 Information and communication theory, circuits (94-XX) 2 Combinatorics (05-XX) 2 Measure and integration (28-XX) 2 Integral equations (45-XX) 2 Statistics (62-XX) 2 Classical thermodynamics, heat transfer (80-XX) 1 Algebraic geometry (14-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Group theory and generalizations (20-XX) 1 Topological groups, Lie groups (22-XX) 1 Approximations and expansions (41-XX) 1 Integral transforms, operational calculus (44-XX) 1 Computer science (68-XX) 1 Mechanics of deformable solids (74-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
#### Wikidata Timeline
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https://zbmath.org/authors/?q=ai%3Acanary.richard-d | ## Canary, Richard D.
Compute Distance To:
Author ID: canary.richard-d Published as: Canary, Richard D.; Canary, Richard; Canary, R. D.; Canary, Richard D; Canary, R. more...less External Links: MGP · Wikidata · GND · IdRef
Documents Indexed: 56 Publications since 1987, including 1 Book 1 Contribution as Editor Co-Authors: 27 Co-Authors with 45 Joint Publications 381 Co-Co-Authors
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### Co-Authors
10 single-authored 12 Bridgeman, Martin J. 8 Taylor, Edward C. 7 Minsky, Yair N. 6 Anderson, James W. 6 Brock, Jeffrey F. 5 Bonfert-Taylor, Petra 5 Bromberg, Kenneth W. 4 Sambarino, Andrés 3 Labourie, François 2 Culler, Marc 2 Epstein, David Bernard Alper 2 Hersonsky, Sa’ar 2 Lecuire, Cyril 2 Martin, Gaven J. 2 McCullough, Darryl 2 Shalen, Peter B. 2 Storm, Peter A. 2 Stover, Matthew 2 Tsouvalas, Konstantinos 1 Bray, Harrison 1 Burger, Marc 1 Kao, Lien-Yung 1 Lee, Michelle 1 Leininger, Christopher J. 1 Magid, Aaron D. 1 Marden, Albert 1 Martone, Giuseppe 1 Souto, Juan 1 Wolf, Michael 1 Yarmola, Andrew 1 Zhang, Tengren 1 Zimmer, Andrew M.
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### Serials
4 Journal of Differential Geometry 3 American Journal of Mathematics 3 Bulletin of the London Mathematical Society 3 Duke Mathematical Journal 3 Geometric and Functional Analysis. GAFA 3 Geometry & Topology 2 Advances in Mathematics 2 Commentarii Mathematici Helvetici 2 Geometriae Dedicata 2 Journal für die Reine und Angewandte Mathematik 2 Mathematische Annalen 2 Annals of Mathematics. Second Series 2 Groups, Geometry, and Dynamics 2 Journal of Topology 1 Mathematical Proceedings of the Cambridge Philosophical Society 1 Annales de l’Institut Fourier 1 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 1 Inventiones Mathematicae 1 Journal of the London Mathematical Society. Second Series 1 Memoirs of the American Mathematical Society 1 Pacific Journal of Mathematics 1 Proceedings of the London Mathematical Society. Third Series 1 Topology 1 Transactions of the American Mathematical Society 1 Ergodic Theory and Dynamical Systems 1 Journal of the American Mathematical Society 1 The Journal of Geometric Analysis 1 Annales Academiae Scientiarum Fennicae. Mathematica 1 Computational Methods and Function Theory 1 Pure and Applied Mathematics Quarterly 1 London Mathematical Society Lecture Note Series
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### Fields
43 Functions of a complex variable (30-XX) 38 Manifolds and cell complexes (57-XX) 6 Several complex variables and analytic spaces (32-XX) 6 Global analysis, analysis on manifolds (58-XX) 5 Group theory and generalizations (20-XX) 5 Dynamical systems and ergodic theory (37-XX) 4 Differential geometry (53-XX) 3 Topological groups, Lie groups (22-XX) 2 Geometry (51-XX) 1 General and overarching topics; collections (00-XX) 1 Measure and integration (28-XX) 1 Algebraic topology (55-XX) 1 Probability theory and stochastic processes (60-XX)
### Citations contained in zbMATH Open
53 Publications have been cited 701 times in 371 Documents Cited by Year
The classification of Kleinian surface groups. II: The Ending lamination conjecture. Zbl 1253.57009
Brock, Jeffrey F.; Canary, Richard D.; Minsky, Yair N.
2012
Notes on notes of Thurston. Zbl 0612.57009
Canary, R. D.; Epstein, D. B. A.; Green, P.
1987
A covering theorem for hyperbolic 3-manifolds and its applications. Zbl 0863.57010
Canary, Richard D.
1996
Ends of hyperbolic 3-manifolds. Zbl 0810.57006
Canary, Richard D.
1993
The pressure metric for Anosov representations. Zbl 1360.37078
Bridgeman, Martin; Canary, Richard; Labourie, François; Sambarino, Andres
2015
Homotopy equivalences of 3-manifolds and deformation theory of Kleinian groups. Zbl 1062.57027
Canary, Richard D.; McCullough, Darryl
2004
Algebraic limits of Kleinian groups which rearrange the pages of a book. Zbl 0874.57012
Anderson, James W.; Canary, Richard D.
1996
Free Kleinian groups and volumes of hyperbolic 3-manifolds. Zbl 0860.57011
Anderson, James W.; Canary, Richard D.; Culler, Marc; Shalen, Peter B.
1996
The Poincaré metric and a conformal version of a theorem of Thurston. Zbl 0759.57013
Canary, Richard D.
1991
Kleinian groups with small limit sets. Zbl 0798.30030
Canary, Richard D.; Taylor, Edward
1994
On limits of tame hyperbolic 3-manifolds. Zbl 0856.57011
Canary, Richard D.; Minsky, Yair N.
1996
The topology of deformation spaces of Kleinian groups. Zbl 0976.57016
Anderson, James W.; Canary, Richard D.; McCullough, Darryl
2000
Cores of hyperbolic 3-manifolds and limits of Kleinian groups. Zbl 0863.30048
Anderson, James W.; Canary, Richard D.
1996
Fundamentals of hyperbolic manifolds: Selected expositions. Reprinted from the series London Mathematical Society Lecture Note Series 111(1987) and 112(1986). Zbl 1083.30001
2006
From the boundary of the convex core to the conformal boundary. Zbl 1083.57024
Bridgeman, Martin; Canary, Richard D.
2003
Approximation by maximal cusps in boundaries of deformation spaces of Kleinian groups. Zbl 1069.57004
Canary, Richard D.; Culler, Marc; Hersonsky, Sa’ar; Shalen, Peter B.
2003
Ubiquity of geometric finiteness in boundaries of deformation spaces of hyperbolic 3-manifolds. Zbl 1062.57021
Canary, Richard D.; Hersonsky, Sa’ar
2004
On the Laplacian and the geometry of hyperbolic 3-manifolds. Zbl 0763.53040
Canary, Richard D.
1992
Algebraic convergence of Schottky groups. Zbl 0772.30037
Canary, Richard D.
1993
Quasiconformal homogeneity of hyperbolic manifolds. Zbl 1063.30020
Bonfert-Taylor, Petra; Canary, Richard D.; Martin, Gaven; Taylor, Edward
2005
Local topology in deformation spaces of hyperbolic 3-manifolds. Zbl 1243.30084
Brock, Jeffrey F; Bromberg, Kenneth W; Canary, Richard D; Minsky, Yair N
2011
Cores of hyperbolic $$3$$-manifolds and limits of Kleinian groups. II. Zbl 0959.30028
Anderson, James W.; Canary, Richard D.
2000
Marden’s tameness conjecture: history and applications. Zbl 1149.57028
Canary, Richard D.
2008
An introduction to pressure metrics for higher Teichmüller spaces. Zbl 1397.37032
Bridgeman, Martin; Canary, Richard; Sambarino, Andrés
2018
Spectral theory, Hausdorff dimension and the topology of hyperbolic 3-manifolds. Zbl 0957.57012
Canary, Richard D.; Minsky, Yair N.; Taylor, Edward C.
1999
Quasiconformal homogeneity of hyperbolic surfaces with fixed-point full automorphisms. Zbl 1133.30012
Bonfert-Taylor, Petra; Bridgeman, Martin; Canary, Richard D.; Taylor, Edward C.
2007
A lower bound on $$\lambda_ 0$$ for geometrically finite hyperbolic $$n$$- manifolds. Zbl 0806.53046
Burger, Marc; Canary, Richard D.
1994
Moduli spaces of hyperbolic 3-manifolds and dynamics on character varieties. Zbl 1267.57019
Canary, Richard D.; Storm, Peter A.
2013
The conformal boundary and the boundary of the convex core. Zbl 1012.57021
Canary, R. D.
2001
Convergence and divergence of Kleinian surface groups. Zbl 1326.57034
Brock, Jeffrey; Bromberg, Kenneth; Canary, Richard; Lecuire, Cyril
2015
Convergence properties of end invariants. Zbl 1431.30030
Brock, Jeffrey F.; Bromberg, Kenneth W.; Canary, Richard D.; Minsky, Yair N.
2013
Simple root flows for Hitchin representations. Zbl 1383.53038
Bridgeman, Martin; Canary, Richard; Labourie, François; Sambarino, Andres
2018
Exotic quasi-conformally homogeneous surfaces. Zbl 1213.30045
Bonfert-Taylor, Petra; Canary, Richard D.; Souto, Juan; Taylor, Edward C.
2011
Simple length rigidity for Kleinian surface groups and applications. Zbl 1395.57021
Bridgeman, Martin; Canary, Richard D.
2017
Covering theorems for hyperbolic 3-manifolds. Zbl 0849.57014
Canary, Richard D.
1994
Kleinian groups with discrete length spectrum. Zbl 1126.57008
Canary, Richard D.; Leininger, Christopher J.
2007
The Thurston metric on hyperbolic domains and boundaries of convex hulls. Zbl 1218.30123
Bridgeman, Martin; Canary, Richard D.
2010
Hausdorff dimension and limits of Kleinian groups. Zbl 0935.57021
Canary, R. D.; Taylor, E. C.
1999
Amalgam Anosov representations (appendix by Richard D. Canary, Michelle Lee, Andrés Sambarino and Matthew Stover). Zbl 1439.37036
Canary, Richard D.; Lee, Michelle; Stover, Matthew
2017
Dynamics on PSL(2, $$\mathbb C$$)-character varieties: 3-manifolds with toroidal boundary components. Zbl 1328.57018
Canary, Richard D.; Magid, Aaron D.
2015
Ambient quasiconformal homogeneity of planar domains. Zbl 1198.30017
Bonfert-Taylor, Petra; Canary, Richard D.; Martin, Gaven; Taylor, Edward C.; Wolf, Michael
2010
Quasiconformal homogeneity after Gehring and Palka. Zbl 1307.30051
Bonfert-Taylor, Petra; Canary, Richard; Taylor, Edward C.
2014
Local topology in deformation spaces of hyperbolic 3-manifolds. II. Zbl 1428.32007
Brock, Jeffrey F.; Bromberg, Kenneth W.; Canary, Richard D.; Lecuire, Cyril; Minsky, Yair N.
2019
Simple length rigidity for Hitchin representations. Zbl 1433.53072
Bridgeman, Martin; Canary, Richard; Labourie, François
2020
Cusped Hitchin representations and Anosov representations of geometrically finite Fuchsian groups. Zbl 07537705
Canary, Richard; Zhang, Tengren; Zimmer, Andrew
2022
Bounding the bending of a hyperbolic 3-manifold. Zbl 1116.57014
Bridgeman, Martin; Canary, Richard D.
2005
Topological restrictions on Anosov representations. Zbl 1473.22007
Canary, Richard; Tsouvalas, Konstantinos
2020
An improved bound for Sullivan’s convex hull theorem. Zbl 1344.30018
Bridgeman, M.; Canary, R.; Yarmola, A.
2016
Pushing the boundary. Zbl 1079.57013
Canary, Richard D.
2004
Windows, cores and skinning maps. Zbl 1451.30086
Brock, Jeffrey F.; Bromberg, Kenneth W.; Canary, Richard D.; Minsky, Yair N.
2020
The curious moduli spaces of unmarked Kleinian surface group. Zbl 1250.57025
Canary, Richard D.; Storm, Peter A.
2012
Geometrically tame hyperbolic 3-manifolds. Zbl 0798.30031
Canary, Richard D.
1993
Uniformly perfect domains and convex hulls: improved bounds in a generalization of a theorem of Sullivan. Zbl 1291.30124
Bridgeman, Martin; Canary, Richard D.
2013
Cusped Hitchin representations and Anosov representations of geometrically finite Fuchsian groups. Zbl 07537705
Canary, Richard; Zhang, Tengren; Zimmer, Andrew
2022
Simple length rigidity for Hitchin representations. Zbl 1433.53072
Bridgeman, Martin; Canary, Richard; Labourie, François
2020
Topological restrictions on Anosov representations. Zbl 1473.22007
Canary, Richard; Tsouvalas, Konstantinos
2020
Windows, cores and skinning maps. Zbl 1451.30086
Brock, Jeffrey F.; Bromberg, Kenneth W.; Canary, Richard D.; Minsky, Yair N.
2020
Local topology in deformation spaces of hyperbolic 3-manifolds. II. Zbl 1428.32007
Brock, Jeffrey F.; Bromberg, Kenneth W.; Canary, Richard D.; Lecuire, Cyril; Minsky, Yair N.
2019
An introduction to pressure metrics for higher Teichmüller spaces. Zbl 1397.37032
Bridgeman, Martin; Canary, Richard; Sambarino, Andrés
2018
Simple root flows for Hitchin representations. Zbl 1383.53038
Bridgeman, Martin; Canary, Richard; Labourie, François; Sambarino, Andres
2018
Simple length rigidity for Kleinian surface groups and applications. Zbl 1395.57021
Bridgeman, Martin; Canary, Richard D.
2017
Amalgam Anosov representations (appendix by Richard D. Canary, Michelle Lee, Andrés Sambarino and Matthew Stover). Zbl 1439.37036
Canary, Richard D.; Lee, Michelle; Stover, Matthew
2017
An improved bound for Sullivan’s convex hull theorem. Zbl 1344.30018
Bridgeman, M.; Canary, R.; Yarmola, A.
2016
The pressure metric for Anosov representations. Zbl 1360.37078
Bridgeman, Martin; Canary, Richard; Labourie, François; Sambarino, Andres
2015
Convergence and divergence of Kleinian surface groups. Zbl 1326.57034
Brock, Jeffrey; Bromberg, Kenneth; Canary, Richard; Lecuire, Cyril
2015
Dynamics on PSL(2, $$\mathbb C$$)-character varieties: 3-manifolds with toroidal boundary components. Zbl 1328.57018
Canary, Richard D.; Magid, Aaron D.
2015
Quasiconformal homogeneity after Gehring and Palka. Zbl 1307.30051
Bonfert-Taylor, Petra; Canary, Richard; Taylor, Edward C.
2014
Moduli spaces of hyperbolic 3-manifolds and dynamics on character varieties. Zbl 1267.57019
Canary, Richard D.; Storm, Peter A.
2013
Convergence properties of end invariants. Zbl 1431.30030
Brock, Jeffrey F.; Bromberg, Kenneth W.; Canary, Richard D.; Minsky, Yair N.
2013
Uniformly perfect domains and convex hulls: improved bounds in a generalization of a theorem of Sullivan. Zbl 1291.30124
Bridgeman, Martin; Canary, Richard D.
2013
The classification of Kleinian surface groups. II: The Ending lamination conjecture. Zbl 1253.57009
Brock, Jeffrey F.; Canary, Richard D.; Minsky, Yair N.
2012
The curious moduli spaces of unmarked Kleinian surface group. Zbl 1250.57025
Canary, Richard D.; Storm, Peter A.
2012
Local topology in deformation spaces of hyperbolic 3-manifolds. Zbl 1243.30084
Brock, Jeffrey F; Bromberg, Kenneth W; Canary, Richard D; Minsky, Yair N
2011
Exotic quasi-conformally homogeneous surfaces. Zbl 1213.30045
Bonfert-Taylor, Petra; Canary, Richard D.; Souto, Juan; Taylor, Edward C.
2011
The Thurston metric on hyperbolic domains and boundaries of convex hulls. Zbl 1218.30123
Bridgeman, Martin; Canary, Richard D.
2010
Ambient quasiconformal homogeneity of planar domains. Zbl 1198.30017
Bonfert-Taylor, Petra; Canary, Richard D.; Martin, Gaven; Taylor, Edward C.; Wolf, Michael
2010
Marden’s tameness conjecture: history and applications. Zbl 1149.57028
Canary, Richard D.
2008
Quasiconformal homogeneity of hyperbolic surfaces with fixed-point full automorphisms. Zbl 1133.30012
Bonfert-Taylor, Petra; Bridgeman, Martin; Canary, Richard D.; Taylor, Edward C.
2007
Kleinian groups with discrete length spectrum. Zbl 1126.57008
Canary, Richard D.; Leininger, Christopher J.
2007
Fundamentals of hyperbolic manifolds: Selected expositions. Reprinted from the series London Mathematical Society Lecture Note Series 111(1987) and 112(1986). Zbl 1083.30001
2006
Quasiconformal homogeneity of hyperbolic manifolds. Zbl 1063.30020
Bonfert-Taylor, Petra; Canary, Richard D.; Martin, Gaven; Taylor, Edward
2005
Bounding the bending of a hyperbolic 3-manifold. Zbl 1116.57014
Bridgeman, Martin; Canary, Richard D.
2005
Homotopy equivalences of 3-manifolds and deformation theory of Kleinian groups. Zbl 1062.57027
Canary, Richard D.; McCullough, Darryl
2004
Ubiquity of geometric finiteness in boundaries of deformation spaces of hyperbolic 3-manifolds. Zbl 1062.57021
Canary, Richard D.; Hersonsky, Sa’ar
2004
Pushing the boundary. Zbl 1079.57013
Canary, Richard D.
2004
From the boundary of the convex core to the conformal boundary. Zbl 1083.57024
Bridgeman, Martin; Canary, Richard D.
2003
Approximation by maximal cusps in boundaries of deformation spaces of Kleinian groups. Zbl 1069.57004
Canary, Richard D.; Culler, Marc; Hersonsky, Sa’ar; Shalen, Peter B.
2003
The conformal boundary and the boundary of the convex core. Zbl 1012.57021
Canary, R. D.
2001
The topology of deformation spaces of Kleinian groups. Zbl 0976.57016
Anderson, James W.; Canary, Richard D.; McCullough, Darryl
2000
Cores of hyperbolic $$3$$-manifolds and limits of Kleinian groups. II. Zbl 0959.30028
Anderson, James W.; Canary, Richard D.
2000
Spectral theory, Hausdorff dimension and the topology of hyperbolic 3-manifolds. Zbl 0957.57012
Canary, Richard D.; Minsky, Yair N.; Taylor, Edward C.
1999
Hausdorff dimension and limits of Kleinian groups. Zbl 0935.57021
Canary, R. D.; Taylor, E. C.
1999
A covering theorem for hyperbolic 3-manifolds and its applications. Zbl 0863.57010
Canary, Richard D.
1996
Algebraic limits of Kleinian groups which rearrange the pages of a book. Zbl 0874.57012
Anderson, James W.; Canary, Richard D.
1996
Free Kleinian groups and volumes of hyperbolic 3-manifolds. Zbl 0860.57011
Anderson, James W.; Canary, Richard D.; Culler, Marc; Shalen, Peter B.
1996
On limits of tame hyperbolic 3-manifolds. Zbl 0856.57011
Canary, Richard D.; Minsky, Yair N.
1996
Cores of hyperbolic 3-manifolds and limits of Kleinian groups. Zbl 0863.30048
Anderson, James W.; Canary, Richard D.
1996
Kleinian groups with small limit sets. Zbl 0798.30030
Canary, Richard D.; Taylor, Edward
1994
A lower bound on $$\lambda_ 0$$ for geometrically finite hyperbolic $$n$$- manifolds. Zbl 0806.53046
Burger, Marc; Canary, Richard D.
1994
Covering theorems for hyperbolic 3-manifolds. Zbl 0849.57014
Canary, Richard D.
1994
Ends of hyperbolic 3-manifolds. Zbl 0810.57006
Canary, Richard D.
1993
Algebraic convergence of Schottky groups. Zbl 0772.30037
Canary, Richard D.
1993
Geometrically tame hyperbolic 3-manifolds. Zbl 0798.30031
Canary, Richard D.
1993
On the Laplacian and the geometry of hyperbolic 3-manifolds. Zbl 0763.53040
Canary, Richard D.
1992
The Poincaré metric and a conformal version of a theorem of Thurston. Zbl 0759.57013
Canary, Richard D.
1991
Notes on notes of Thurston. Zbl 0612.57009
Canary, R. D.; Epstein, D. B. A.; Green, P.
1987
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### Cited by 325 Authors
20 Canary, Richard D. 16 Minsky, Yair N. 15 Ohshika, Ken’ichi 12 Brock, Jeffrey F. 12 Souto, Juan 10 Kim, Inkang 10 Leininger, Christopher J. 10 Mj, Mahan 10 Shalen, Peter B. 9 Bromberg, Kenneth W. 8 Bridgeman, Martin J. 8 Lecuire, Cyril 7 Culler, Marc 7 Kent, Autumn Exum 7 Labourie, François 7 Purcell, Jessica Shepherd 6 Futer, David 6 Schleimer, Saul 6 Taylor, Edward C. 5 Bowditch, Brian H. 5 Cooper, Daryl 5 Kapovich, Ilya 5 Miyachi, Hideki 5 Sambarino, Andrés 5 Series, Caroline 4 Agol, Ian 4 Bonahon, Francis 4 Bonfert-Taylor, Petra 4 Hamenstädt, Ursula 4 Ito, Kentaro 4 Jeon, Woojin 4 Maloni, Sara 4 Namazi, Hossein 4 Rafi, Kasra 4 Soma, Teruhiko 4 Taylor, Samuel Joseph 3 Anderson, James W. 3 Barbot, Thierry 3 Biringer, Ian 3 Bishop, Christopher James 3 Deblois, Jason 3 Falk, Kurt 3 Fillastre, François 3 Gabai, David 3 Kao, Lien-Yung 3 Lee, Gye-Seon 3 Lee, Michelle 3 Long, Darren D. 3 Ma, Jiming 3 Magid, Aaron D. 3 Modami, Babak 3 Mosher, Lee 3 Porti, Joan 3 Potrie, Rafael 3 Pozzetti, Maria Beatrice 3 Reid, Alan W. 3 Schlenker, Jean-Marc 3 Storm, Peter A. 3 Vlamis, Nicholas G. 3 Vuorinen, Matti Keijo Kustaa 2 Basmajian, Ara S. 2 Behrstock, Jason A. 2 Belegradek, Igor 2 Benoist, Yves 2 Bonatti, Christian 2 Calegari, Danny Matthew Cornelius 2 Carrasco Piaggio, Matias 2 Ciobotaru, Corina 2 Cremaschi, Tommaso 2 Danciger, Jeffrey 2 de Oliveira, Fabiana R. 2 Dowdall, Spencer 2 Evans, Richard Allen 2 Francaviglia, Stefano 2 Gaster, Jonah 2 Goldman, William M. 2 Guzman, Rosemary K. 2 Hosseini, Seyedehsomayeh 2 Hulin, Dominique 2 Izeki, Hiroyasu 2 Izmestiev, Ivan 2 Jones, Peter Wilcox 2 Kapovich, Michael 2 Kassel, Fanny 2 Kholodenko, Arkady L. 2 Kim, Sang-Hyun 2 Kim, Sungwoon 2 Leitner, Arielle 2 Markovic, Vladimir 2 Masters, Joseph D. 2 Masur, Howard A. 2 Matsuzaki, Katsuhiko 2 McCullough, Darryl 2 Moriah, Yoav 2 Nguyen, Hoang Thanh 2 Pouryayevali, Mohamad Reza 2 Stratmann, Bernd O. 2 Sugawa, Toshiyuki 2 Tang, Robert L. 2 Taylor, Scott A. ...and 225 more Authors
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### Cited in 87 Serials
44 Geometry & Topology 25 Algebraic & Geometric Topology 24 Geometriae Dedicata 23 Transactions of the American Mathematical Society 17 Duke Mathematical Journal 14 Proceedings of the American Mathematical Society 14 Conformal Geometry and Dynamics 10 Groups, Geometry, and Dynamics 9 Geometric and Functional Analysis. GAFA 8 Annales de l’Institut Fourier 8 Inventiones Mathematicae 8 Topology and its Applications 8 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 7 Journal of the American Mathematical Society 7 Annals of Mathematics. Second Series 6 Ergodic Theory and Dynamical Systems 5 Israel Journal of Mathematics 4 Advances in Mathematics 4 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 4 Journal für die Reine und Angewandte Mathematik 4 Mathematische Zeitschrift 4 Osaka Journal of Mathematics 4 Journal of Topology 4 Journal of Topology and Analysis 3 Journal d’Analyse Mathématique 3 Acta Mathematica 3 Commentarii Mathematici Helvetici 3 Mathematische Annalen 3 Michigan Mathematical Journal 3 The Journal of Geometric Analysis 3 Comptes Rendus. Mathématique. Académie des Sciences, Paris 3 Journal of Modern Dynamics 2 Mathematical Proceedings of the Cambridge Philosophical Society 2 Journal of Geometry and Physics 2 Bulletin of the London Mathematical Society 2 Journal of Differential Geometry 2 Journal of the London Mathematical Society. Second Series 2 Journal of the Mathematical Society of Japan 2 Journal of Optimization Theory and Applications 2 Kodai Mathematical Journal 2 Proceedings of the London Mathematical Society. Third Series 2 Discrete & Computational Geometry 2 Bulletin of the American Mathematical Society. New Series 2 Expositiones Mathematicae 2 Revista Matemática Complutense 2 Computational Methods and Function Theory 2 Journal de l’École Polytechnique – Mathématiques 1 Bulletin of the Australian Mathematical Society 1 Communications in Mathematical Physics 1 Indian Journal of Pure & Applied Mathematics 1 Journal of Mathematical Analysis and Applications 1 Arkiv för Matematik 1 Beiträge zur Algebra und Geometrie 1 Archiv der Mathematik 1 Bulletin de la Société Mathématique de France 1 Publications Mathématiques 1 Journal of Algebra 1 Journal of Pure and Applied Algebra 1 Manuscripta Mathematica 1 Memoirs of the American Mathematical Society 1 Rendiconti del Circolo Matemàtico di Palermo. Serie II 1 Siberian Mathematical Journal 1 Tokyo Journal of Mathematics 1 Science in China. Series A 1 Sugaku Expositions 1 International Journal of Algebra and Computation 1 Differential Geometry and its Applications 1 Indagationes Mathematicae. New Series 1 Experimental Mathematics 1 St. Petersburg Mathematical Journal 1 Turkish Journal of Mathematics 1 Boletín de la Sociedad Matemática Mexicana. Third Series 1 Acta Mathematica Sinica. English Series 1 Communications in Contemporary Mathematics 1 Annales Mathematicae Silesianae 1 Journal of the Australian Mathematical Society 1 Journal of Dynamical Systems and Geometric Theories 1 Bulletin of the Brazilian Mathematical Society. New Series 1 Journal of the Institute of Mathematics of Jussieu 1 Science China. Mathematics 1 Forum of Mathematics, Pi 1 Forum of Mathematics, Sigma 1 Annales Mathématiques du Québec 1 Journal of Computational Dynamics 1 Transactions of the American Mathematical Society. Series B 1 Winter Braids Lecture Notes 1 Annales Fennici Mathematici
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### Cited in 28 Fields
239 Manifolds and cell complexes (57-XX) 182 Functions of a complex variable (30-XX) 100 Group theory and generalizations (20-XX) 57 Differential geometry (53-XX) 54 Dynamical systems and ergodic theory (37-XX) 49 Several complex variables and analytic spaces (32-XX) 29 Topological groups, Lie groups (22-XX) 20 Global analysis, analysis on manifolds (58-XX) 15 Geometry (51-XX) 8 Measure and integration (28-XX) 7 Combinatorics (05-XX) 7 Convex and discrete geometry (52-XX) 5 Calculus of variations and optimal control; optimization (49-XX) 3 History and biography (01-XX) 3 Number theory (11-XX) 3 Algebraic geometry (14-XX) 3 Algebraic topology (55-XX) 2 General topology (54-XX) 2 Operations research, mathematical programming (90-XX) 1 General and overarching topics; collections (00-XX) 1 Potential theory (31-XX) 1 Ordinary differential equations (34-XX) 1 Partial differential equations (35-XX) 1 Probability theory and stochastic processes (60-XX) 1 Numerical analysis (65-XX) 1 Computer science (68-XX) 1 Quantum theory (81-XX) 1 Relativity and gravitational theory (83-XX)
### Wikidata Timeline
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https://zbmath.org/authors/?q=ai%3Abrown.morton-b | # zbMATH — the first resource for mathematics
## Brown, Morton B.
Compute Distance To:
Author ID: brown.morton-b Published as: Brown, M.; Brown, M. B.; Brown, Morton; Brown, Morton B. External Links: MGP · Wikidata
Documents Indexed: 76 Publications since 1959, including 4 Books
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#### Co-Authors
26 single-authored 3 Forsythe, Alan B. 3 Guo, Wensheng 3 Wang, Yuedong 2 Connelly, Robert 2 Fuchs, Camil 2 Gluck, Herman 2 Gupta, Suneel 2 Lee, Kyunghoon 2 Li, Lang 2 Slaminka, Edward E. 1 Barge, Marcy M. 1 Benedetti, Jacqueline K. 1 Boucher, Kenneth M. 1 Brechner, Beverly L. 1 Carlson, Nichole E. 1 Gimotty, Phyllis A. 1 Haber, Michael 1 Huang, Saling 1 Johnson, Timothy D. 1 Katz, Barry P. 1 Ke, Chunlei 1 Lin, Xihong 1 Mickey, M. Ray 1 Normolle, Daniel P. 1 Park, Taesung 1 Transue, William R. R. 1 Yahil, Amos
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#### Serials
10 Biometrics 6 Proceedings of the American Mathematical Society 4 Michigan Mathematical Journal 3 Computational Statistics and Data Analysis 2 Journal of the American Statistical Association 2 Technometrics 2 Statistica Sinica 2 Journal of Applied Statistics 2 Annals of Mathematics. Second Series 2 Bulletin of the American Mathematical Society 1 Discrete Mathematics 1 Houston Journal of Mathematics 1 Psychometrika 1 American Journal of Mathematics 1 Biometrika 1 Pacific Journal of Mathematics 1 Transactions of the American Mathematical Society 1 Topology and its Applications 1 Communications in Statistics. Simulation and Computation 1 Topology Proceedings 1 Contemporary Mathematics 1 Nederlandse Akademie van Wetenschappen. Proceedings. Series A. Indagationes Mathematicae 1 Annals of Mathematical Statistics
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#### Fields
23 Statistics (62-XX) 10 General topology (54-XX) 10 Manifolds and cell complexes (57-XX) 6 Dynamical systems and ergodic theory (37-XX) 4 Biology and other natural sciences (92-XX) 3 Combinatorics (05-XX) 3 Numerical analysis (65-XX) 2 General and overarching topics; collections (00-XX) 2 Global analysis, analysis on manifolds (58-XX) 1 History and biography (01-XX) 1 Algebraic topology (55-XX) 1 Probability theory and stochastic processes (60-XX)
#### Citations contained in zbMATH Open
59 Publications have been cited 805 times in 705 Documents Cited by Year
Locally flat imbeddings of topological manifolds. Zbl 0201.56202
Brown, Morton
1962
A proof of the generalized Schoenflies theorem. Zbl 0132.20002
Brown, Morton
1960
Robust tests for the equality of variances. Zbl 0291.62063
Brown, Morton B.; Forsythe, Alan B.
1974
The monotone union of open $$n$$-cells is an open $$n$$-cell. Zbl 0103.39305
Brown, Morton
1961
Some applications of an approximation theorem for inverse limits. Zbl 0113.37705
Brown, Morton
1960
The small sample behavior of some statistics which test the equality of several means. Zbl 0275.62047
Brown, Morton B.; Forsythe, Alan B.
1974
Stable structures on manifolds. I: Homeomorphismus of $$S^ n$$. II: Stable manifolds. III: Applications. Zbl 0122.17903
Brown, Morton; Gluck, Herman
1964
Proof of the Poincaré-Birkhoff fixed point theorem. Zbl 0402.55001
Brown, M.; Neumann, W. D.
1977
Neural networks for modelling and control. Zbl 0850.93415
Brown, M.; Harris, C. J.
1994
Homeomorphisms of two-dimensional manifolds. Zbl 0605.57005
Brown, M.
1985
A new proof of Brouwer’s lemma on translation arcs. Zbl 0551.57005
Brown, Morton
1984
Maximum likelihood methods for log-linear models when expected frequencies are subject to linear constraints. Zbl 0604.62058
Haber, Michael; Brown, Morton B.
1986
Invariance of complementary domains of a fixed point set. Zbl 0547.57010
Brown, M.; Kister, J. M.
1984
A mapping theorem for untriangulated manifolds. Zbl 1246.57052
Brown, Morton
1962
Interactive image segmentation using an adaptive GMMRF model. Zbl 1098.68730
Blake, Andrew; Rother, Carsten; Brown, M.; Perez, Patrick; Torr, Philip
2004
BMDP statistical software 1981. By M. B. Brown, L. Engelman, J. W. Frane, M. A. Hill, R. I. Jennrich, J. D. Toporek. Zbl 0549.62004
Dixon, W. J. (ed.); Brown, M. B.; Engelman, L.; Frane, J. W.; Hill, M. A.; Jennrich, R. I.; Toporek, J. D.
1981
The ANOVA and multiple comparisons for data with heterogeneous variances. Zbl 0294.62091
Brown, Morton B.; Forsythe, Alan B.
1974
A short short proof of the Cartwright-Littlewood theorem. Zbl 0369.57001
Brown, Morton
1977
On graphs with a constant link. Zbl 0258.05104
Brown, Morton; Connelly, Robert
1973
A flexible model for human circadian rhythms. Zbl 0875.62525
Wang, Yuedong; Brown, Morton B.
1996
A method for combining non-independent, one-sided tests of significance. Zbl 0318.62030
Brown, Morton B.
1975
Estimation and inference for a spline-enhanced population pharmacokinetic model. Zbl 1210.62179
Li, Lang; Brown, Morton B.; Lee, Kyung-Hoon; Gupta, Suneel
2002
Intelligent control: aspects of fuzzy logic and neural nets. Zbl 0923.93029
Harris, C. J.; Moore, C. G.; Brown, M.
1993
On the fixed point index of iterates of planar homeomorphisms. Zbl 0686.58028
Brown, Morton
1990
On graphs with a constant link. II. Zbl 0304.05102
Brown, Morton; Connelly, Robert
1975
Sets of constant distance from a planar set. Zbl 0244.54019
Brown, Morton
1972
Spline smoothing for bivariate data with applications to association between hormones. Zbl 0963.62039
Wang, Yuedong; Guo, Wensheng; Brown, Morton B.
2000
Bounds on the distribution functions of the Behrens-Fisher statistic. Zbl 0151.23303
Mickey, M. Ray; Brown, Morton B.
1966
Locally flat embeddings of topological manifolds. Zbl 1246.57059
Brown, Morton
1962
Shape-invariant modeling of circadian rhythms with random effects and smoothing spline ANOVA decompositions. Zbl 1218.62123
Wang, Yuedong; Ke, Chunlei; Brown, Morton B.
2003
The theory and practice of boundary critique: developing housing services for older people. Zbl 1131.90418
Midgley, G.; Munlo, I.; Brown, M.
1998
Wild cells and spheres in higher dimensions. Zbl 0147.23902
Brown, Morton
1967
A probabilistic framework for SVM regression and error bar estimation. Zbl 0999.68180
Gao, J. B.; Gunn, S. R.; Harris, C. J.; Brown, M.
2002
Wang, H.; Liu, G. P.; Harris, C. J.; Brown, M.
1995
Fixed points for orientation preserving homeomorphisms of the plane which interchange two points. Zbl 0728.55001
Brown, Morton
1990
An orientation preserving fixed point free homeomorphism of the plane which admits no closed invariant line. Zbl 0668.54024
Brown, Morton; Slaminka, Edward E.; Transue, William
1988
On maximum likelihood estimation in sparse contingency tables. Zbl 0599.62070
Brown, Morton B.; Fuchs, Camil
1983
Log-linear models for a binary response with nonignorable nonresponse. Zbl 0900.62294
Park, Taesung; Brown, Morton B.
1997
Modelling and control of nonlinear, operating point dependent systems via associative memory networks. Zbl 0850.93265
Wang, H.; Brown, M.; Harris, C. J.
1996
On the inverse limit of Euclidean N-spheres. Zbl 0136.19805
Brown, Morton
1960
A periodic homeomorphism of the plane. Zbl 0791.58074
Brown, Morton
1993
Stable structures on manifolds. Zbl 0118.39104
Brown, Morton; Gluck, Herman
1963
Neurofuzzy identification of an autonomous underwater vehicle. Zbl 0994.93543
Bossley, K. M.; Brown, M.; Harris, C. J.
1999
Fundamental regions of planar homeomorphisms. Zbl 0732.54029
Brown, Morton
1991
A nonlinear adaptive controller: A comparison between fuzzy logic control and neurocontrol. Zbl 0745.93041
Brown, M.; Harris, C. J.
1991
Weak $$n$$-homogeneity implies weak $$(n - 1)$$-homogeneity. Zbl 0093.36604
Brown, Morton
1959
pdFOAM: a PIC-DSMC code for near-Earth plasma-body interactions. Zbl 1390.76701
Capon, C. J.; Brown, M.; White, C.; Scanlon, T.; Boyce, R. R.
2017
A population pharmacokinetic model with time-dependent covariates measured with errors. Zbl 1274.62814
Li, Lang; Lin, Xihong; Brown, Morton B.; Gupta, Suneel; Lee, Kyung-Hoon
2004
Cross-related structural time series models. Zbl 0984.62065
Guo, Wensheng; Brown, Morton B.
2001
On the identification of non-stationary linear processes. Zbl 1080.93515
Bouzeghoub, M. C.; Ellacott, S. W.; Easdown, A.; Brown, M.
2000
One-to-one mapping and its application to neural networks based control systems design. Zbl 0850.93409
Wang, H.; Wang, A. P.; Brown, M.; Harris, C. J.
1996
Problems in dynamics on continua. Zbl 0726.54026
Barge, Marcy; Brown, Morton
1991
Continuum theory and dynamical systems. Proceedings of the AMS-IMS-SIAM joint summer research conference, held at Humboldt State University, Arcata, California, USA, on June 17-23, 1989, with support from the National Science Foundation and the Army Research Office. Zbl 0723.00027
Brown, Morton (ed.)
1991
Imputation procedures for categorical data: their effects on the goodness-of-fit chi-square statistic. Zbl 0718.62024
Gimotty, Phyllis A.; Brown, Morton B.
1990
Mapping cylinder neighborhoods in the plane. Zbl 0478.54030
Brechner, Beverly; Brown, Morton
1982
The asymptotic standard errors of some estimates of uncertainty in the two-way contingency table. Zbl 0359.62038
Brown, Morton B.
1975
A note on Cartesian products. Zbl 0179.51405
Brown, Morton
1969
A note on Kister’s isotopy. Zbl 0185.51503
Brown, Morton
1967
The two-means problem-a secondarily Bayes approach. Zbl 0158.17701
Brown, Morton B.
1967
pdFOAM: a PIC-DSMC code for near-Earth plasma-body interactions. Zbl 1390.76701
Capon, C. J.; Brown, M.; White, C.; Scanlon, T.; Boyce, R. R.
2017
Interactive image segmentation using an adaptive GMMRF model. Zbl 1098.68730
Blake, Andrew; Rother, Carsten; Brown, M.; Perez, Patrick; Torr, Philip
2004
A population pharmacokinetic model with time-dependent covariates measured with errors. Zbl 1274.62814
Li, Lang; Lin, Xihong; Brown, Morton B.; Gupta, Suneel; Lee, Kyung-Hoon
2004
Shape-invariant modeling of circadian rhythms with random effects and smoothing spline ANOVA decompositions. Zbl 1218.62123
Wang, Yuedong; Ke, Chunlei; Brown, Morton B.
2003
Estimation and inference for a spline-enhanced population pharmacokinetic model. Zbl 1210.62179
Li, Lang; Brown, Morton B.; Lee, Kyung-Hoon; Gupta, Suneel
2002
A probabilistic framework for SVM regression and error bar estimation. Zbl 0999.68180
Gao, J. B.; Gunn, S. R.; Harris, C. J.; Brown, M.
2002
Cross-related structural time series models. Zbl 0984.62065
Guo, Wensheng; Brown, Morton B.
2001
Spline smoothing for bivariate data with applications to association between hormones. Zbl 0963.62039
Wang, Yuedong; Guo, Wensheng; Brown, Morton B.
2000
On the identification of non-stationary linear processes. Zbl 1080.93515
Bouzeghoub, M. C.; Ellacott, S. W.; Easdown, A.; Brown, M.
2000
Neurofuzzy identification of an autonomous underwater vehicle. Zbl 0994.93543
Bossley, K. M.; Brown, M.; Harris, C. J.
1999
The theory and practice of boundary critique: developing housing services for older people. Zbl 1131.90418
Midgley, G.; Munlo, I.; Brown, M.
1998
Log-linear models for a binary response with nonignorable nonresponse. Zbl 0900.62294
Park, Taesung; Brown, Morton B.
1997
A flexible model for human circadian rhythms. Zbl 0875.62525
Wang, Yuedong; Brown, Morton B.
1996
Modelling and control of nonlinear, operating point dependent systems via associative memory networks. Zbl 0850.93265
Wang, H.; Brown, M.; Harris, C. J.
1996
One-to-one mapping and its application to neural networks based control systems design. Zbl 0850.93409
Wang, H.; Wang, A. P.; Brown, M.; Harris, C. J.
1996
Wang, H.; Liu, G. P.; Harris, C. J.; Brown, M.
1995
Neural networks for modelling and control. Zbl 0850.93415
Brown, M.; Harris, C. J.
1994
Intelligent control: aspects of fuzzy logic and neural nets. Zbl 0923.93029
Harris, C. J.; Moore, C. G.; Brown, M.
1993
A periodic homeomorphism of the plane. Zbl 0791.58074
Brown, Morton
1993
Fundamental regions of planar homeomorphisms. Zbl 0732.54029
Brown, Morton
1991
A nonlinear adaptive controller: A comparison between fuzzy logic control and neurocontrol. Zbl 0745.93041
Brown, M.; Harris, C. J.
1991
Problems in dynamics on continua. Zbl 0726.54026
Barge, Marcy; Brown, Morton
1991
Continuum theory and dynamical systems. Proceedings of the AMS-IMS-SIAM joint summer research conference, held at Humboldt State University, Arcata, California, USA, on June 17-23, 1989, with support from the National Science Foundation and the Army Research Office. Zbl 0723.00027
Brown, Morton (ed.)
1991
On the fixed point index of iterates of planar homeomorphisms. Zbl 0686.58028
Brown, Morton
1990
Fixed points for orientation preserving homeomorphisms of the plane which interchange two points. Zbl 0728.55001
Brown, Morton
1990
Imputation procedures for categorical data: their effects on the goodness-of-fit chi-square statistic. Zbl 0718.62024
Gimotty, Phyllis A.; Brown, Morton B.
1990
An orientation preserving fixed point free homeomorphism of the plane which admits no closed invariant line. Zbl 0668.54024
Brown, Morton; Slaminka, Edward E.; Transue, William
1988
Maximum likelihood methods for log-linear models when expected frequencies are subject to linear constraints. Zbl 0604.62058
Haber, Michael; Brown, Morton B.
1986
Homeomorphisms of two-dimensional manifolds. Zbl 0605.57005
Brown, M.
1985
A new proof of Brouwer’s lemma on translation arcs. Zbl 0551.57005
Brown, Morton
1984
Invariance of complementary domains of a fixed point set. Zbl 0547.57010
Brown, M.; Kister, J. M.
1984
On maximum likelihood estimation in sparse contingency tables. Zbl 0599.62070
Brown, Morton B.; Fuchs, Camil
1983
Mapping cylinder neighborhoods in the plane. Zbl 0478.54030
Brechner, Beverly; Brown, Morton
1982
BMDP statistical software 1981. By M. B. Brown, L. Engelman, J. W. Frane, M. A. Hill, R. I. Jennrich, J. D. Toporek. Zbl 0549.62004
Dixon, W. J. (ed.); Brown, M. B.; Engelman, L.; Frane, J. W.; Hill, M. A.; Jennrich, R. I.; Toporek, J. D.
1981
Proof of the Poincaré-Birkhoff fixed point theorem. Zbl 0402.55001
Brown, M.; Neumann, W. D.
1977
A short short proof of the Cartwright-Littlewood theorem. Zbl 0369.57001
Brown, Morton
1977
A method for combining non-independent, one-sided tests of significance. Zbl 0318.62030
Brown, Morton B.
1975
On graphs with a constant link. II. Zbl 0304.05102
Brown, Morton; Connelly, Robert
1975
The asymptotic standard errors of some estimates of uncertainty in the two-way contingency table. Zbl 0359.62038
Brown, Morton B.
1975
Robust tests for the equality of variances. Zbl 0291.62063
Brown, Morton B.; Forsythe, Alan B.
1974
The small sample behavior of some statistics which test the equality of several means. Zbl 0275.62047
Brown, Morton B.; Forsythe, Alan B.
1974
The ANOVA and multiple comparisons for data with heterogeneous variances. Zbl 0294.62091
Brown, Morton B.; Forsythe, Alan B.
1974
On graphs with a constant link. Zbl 0258.05104
Brown, Morton; Connelly, Robert
1973
Sets of constant distance from a planar set. Zbl 0244.54019
Brown, Morton
1972
A note on Cartesian products. Zbl 0179.51405
Brown, Morton
1969
Wild cells and spheres in higher dimensions. Zbl 0147.23902
Brown, Morton
1967
A note on Kister’s isotopy. Zbl 0185.51503
Brown, Morton
1967
The two-means problem-a secondarily Bayes approach. Zbl 0158.17701
Brown, Morton B.
1967
Bounds on the distribution functions of the Behrens-Fisher statistic. Zbl 0151.23303
Mickey, M. Ray; Brown, Morton B.
1966
Stable structures on manifolds. I: Homeomorphismus of $$S^ n$$. II: Stable manifolds. III: Applications. Zbl 0122.17903
Brown, Morton; Gluck, Herman
1964
Stable structures on manifolds. Zbl 0118.39104
Brown, Morton; Gluck, Herman
1963
Locally flat imbeddings of topological manifolds. Zbl 0201.56202
Brown, Morton
1962
A mapping theorem for untriangulated manifolds. Zbl 1246.57052
Brown, Morton
1962
Locally flat embeddings of topological manifolds. Zbl 1246.57059
Brown, Morton
1962
The monotone union of open $$n$$-cells is an open $$n$$-cell. Zbl 0103.39305
Brown, Morton
1961
A proof of the generalized Schoenflies theorem. Zbl 0132.20002
Brown, Morton
1960
Some applications of an approximation theorem for inverse limits. Zbl 0113.37705
Brown, Morton
1960
On the inverse limit of Euclidean N-spheres. Zbl 0136.19805
Brown, Morton
1960
Weak $$n$$-homogeneity implies weak $$(n - 1)$$-homogeneity. Zbl 0093.36604
Brown, Morton
1959
all top 5
#### Cited by 1,008 Authors
10 Grines, Vyacheslav Zigmundovich 9 Daverman, Robert J. 8 Boroński, Jan P. 8 Pardo, Leandro 7 Brown, Morton B. 7 Pochinka, Olga Vital’evna 6 Gurevich, Elena Ya. 6 Husch, Laurence S. 6 Le Calvez, Patrice 6 Oversteegen, Lex G. 5 Blokh, Alexander M. 5 Bos, Werner 5 Franks, John M. 5 Gluck, Herman 5 Keselman, H. J. 5 Le Roux, Frédéric 5 Oprocha, Piotr 5 Repovš, Dušan D. 5 Sánchez-Gabites, Jaime J. 5 Tal, Fábio Armando 5 You, Jinhong 5 Zanolin, Fabio 4 Barge, Marcy M. 4 Handel, Michael 4 Harris, Chris J. 4 Martín, Nirian 4 Midgley, Gerald 4 Nedela, Roman 4 N’Guessan, Assi 4 Ortega, Rafael 4 Ramsey, Philip H. 4 Schori, Richard M. 4 Siebenmann, Laurence C. 4 Wilcox, Rand R. 3 Addas-Zanata, Salvador 3 Bonino, Marc 3 Church, Philip T. 3 Cléroux, Robert 3 Dranishnikov, Alexander Nikolaevich 3 Fedorchuk, Vitaly Vitalievich 3 Fonda, Alessandro 3 Ghiloni, Riccardo 3 Graff, Grzegorz 3 Greathouse, C. 3 Hähl, Hermann 3 Harrold, Orville G. jun. 3 Hothorn, Ludwig A. 3 Ibisch, Horst Dieter 3 Koropecki, Andres 3 Kowalchuk, Rhonda K. 3 Kwun, Kyung Whan 3 Li, Hongxing 3 Liu, Anna 3 Luft, Erhard 3 Medvedev, Vladislav Sergeevich 3 Menéndez, María Luisa 3 Neuhäuser, Markus 3 Pardo, Julio Angel 3 Ramsey, Patricia P. 3 Ruiz del Portal, Francisco Romero 3 Tymchatyn, Edward D. 3 van Mill, Jan 3 Venema, Gerard A. 3 West, James E. 3 Wong, Raymond Y. T. 3 Yokoi, Katsuya 3 Zografos, Konstantinos G. 2 Alonso Rodríguez, Ana 2 Alpern, Steve 2 Argaç, Doğan 2 Asada, Akira 2 Barrera, Kyrstle 2 Bazilevich, L. Ë. 2 Béguin, François 2 Bertolazzi, Enrico 2 Brakes, W. R. 2 Branner, Bodil 2 Breitsprecher, Siegfried 2 Brocklesby, John 2 Brown, Robert F. 2 Büning, Herbert 2 Calcut, Jack S. 2 Campos, Juan 2 Cantrell, James C. 2 Cao, Jiguo 2 Carroll, Raymond James 2 Chapman, Thomas Ashland 2 Charatonik, Janusz J. 2 Chen, Ying-Ju 2 Chichirau, George 2 Chuang, Christy 2 Cieutat, Philippe 2 Connell, Edwin H. 2 Crovisier, Sylvain 2 Curtis, Douglas W. 2 Ding, Tongren 2 Dupre, Maurice J. 2 Duvall, P. F. jun. 2 Ferragut, Antoni 2 Ferry, Steven C. ...and 908 more Authors
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#### Cited in 199 Serials
54 Topology and its Applications 52 Proceedings of the American Mathematical Society 47 Transactions of the American Mathematical Society 29 Journal of Statistical Computation and Simulation 27 Bulletin of the American Mathematical Society 23 Computational Statistics and Data Analysis 15 Communications in Statistics. Theory and Methods 12 Biometrics 12 Communications in Statistics. Simulation and Computation 11 Fuzzy Sets and Systems 9 Inventiones Mathematicae 9 Mathematische Zeitschrift 8 International Journal of Systems Science 8 Psychometrika 8 Ergodic Theory and Dynamical Systems 8 European Journal of Operational Research 7 Discrete Mathematics 7 Journal of Differential Equations 7 Journal of Dynamics and Differential Equations 7 Statistical Papers 7 Geometry & Topology 6 Acta Mathematica 6 Archiv der Mathematik 6 Compositio Mathematica 6 Journal of Combinatorial Theory. Series B 6 Journal of Multivariate Analysis 5 The Annals of Statistics 5 Duke Mathematical Journal 5 Pattern Recognition 4 The Canadian Journal of Statistics 4 Journal of Mathematical Analysis and Applications 4 Mathematical Notes 4 Rocky Mountain Journal of Mathematics 4 Advances in Mathematics 4 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 4 Automatica 4 Information Sciences 4 Journal of Soviet Mathematics 4 Journal of Statistical Planning and Inference 4 Manuscripta Mathematica 4 Mathematische Annalen 4 Mathematica Slovaca 4 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 4 Statistics & Probability Letters 4 International Journal of Computer Vision 4 Journal of Applied Statistics 4 Proceedings of the Steklov Institute of Mathematics 3 Journal d’Analyse Mathématique 3 Metrika 3 Nonlinearity 3 Biometrical Journal 3 Geometriae Dedicata 3 Journal of the American Statistical Association 3 Results in Mathematics 3 International Journal of Approximate Reasoning 3 The Journal of Geometric Analysis 3 Computational Statistics 3 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 3 Journal of Mathematical Sciences (New York) 3 Journal of Nonparametric Statistics 3 Algebraic & Geometric Topology 3 Journal of Systems Science and Complexity 3 Proceedings of the Japan Academy 3 Nonlinear Analysis. Theory, Methods & Applications 2 Archive for Rational Mechanics and Analysis 2 Bulletin of the Australian Mathematical Society 2 Computers & Mathematics with Applications 2 Communications in Mathematical Physics 2 Mathematical Proceedings of the Cambridge Philosophical Society 2 Annali di Matematica Pura ed Applicata. Serie Quarta 2 Cahiers de Topologie et Géométrie Différentielle Catégoriques 2 Journal of Computational and Applied Mathematics 2 Journal of Functional Analysis 2 Memoirs of the American Mathematical Society 2 Michigan Mathematical Journal 2 Statistica Neerlandica 2 Revue de Statistique Appliquée 2 Acta Mathematicae Applicatae Sinica. English Series 2 Statistics 2 Statistical Science 2 Discrete & Computational Geometry 2 Neural Computation 2 Differential Geometry and its Applications 2 Expositiones Mathematicae 2 Calculus of Variations and Partial Differential Equations 2 Discrete and Continuous Dynamical Systems 2 Chaos 2 Communications in Nonlinear Science and Numerical Simulation 2 Quantitative Finance 2 Journal of Modern Dynamics 2 Journal of Statistical Theory and Practice 2 Journal of Topology and Analysis 2 Statistics and Computing 1 American Mathematical Monthly 1 Communications in Algebra 1 Computers and Fluids 1 International Journal of Control 1 Journal of Mathematical Physics 1 Periodica Mathematica Hungarica 1 Russian Mathematical Surveys ...and 99 more Serials
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#### Cited in 53 Fields
197 Statistics (62-XX) 133 Manifolds and cell complexes (57-XX) 132 Dynamical systems and ergodic theory (37-XX) 123 General topology (54-XX) 54 Numerical analysis (65-XX) 40 Algebraic topology (55-XX) 34 Computer science (68-XX) 34 Systems theory; control (93-XX) 32 Ordinary differential equations (34-XX) 26 Combinatorics (05-XX) 24 Biology and other natural sciences (92-XX) 20 Global analysis, analysis on manifolds (58-XX) 16 Operations research, mathematical programming (90-XX) 15 Geometry (51-XX) 15 Differential geometry (53-XX) 14 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 10 Group theory and generalizations (20-XX) 9 Measure and integration (28-XX) 9 Convex and discrete geometry (52-XX) 7 Functions of a complex variable (30-XX) 7 Partial differential equations (35-XX) 6 Functional analysis (46-XX) 6 Operator theory (47-XX) 6 Probability theory and stochastic processes (60-XX) 6 Mechanics of particles and systems (70-XX) 5 Mathematical logic and foundations (03-XX) 5 Algebraic geometry (14-XX) 5 Topological groups, Lie groups (22-XX) 4 Category theory; homological algebra (18-XX) 4 Approximations and expansions (41-XX) 3 $$K$$-theory (19-XX) 3 Real functions (26-XX) 3 Difference and functional equations (39-XX) 3 Information and communication theory, circuits (94-XX) 2 Number theory (11-XX) 2 Commutative algebra (13-XX) 2 Calculus of variations and optimal control; optimization (49-XX) 2 Mechanics of deformable solids (74-XX) 2 Fluid mechanics (76-XX) 2 Optics, electromagnetic theory (78-XX) 2 Quantum theory (81-XX) 1 General and overarching topics; collections (00-XX) 1 History and biography (01-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Field theory and polynomials (12-XX) 1 Associative rings and algebras (16-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Abstract harmonic analysis (43-XX) 1 Integral equations (45-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Relativity and gravitational theory (83-XX) 1 Astronomy and astrophysics (85-XX) 1 Geophysics (86-XX)
#### Wikidata Timeline
The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata. | 2021-05-08T14:48:32 | {"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": 0.5666377544403076, "perplexity": 8209.217044874245}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243988882.7/warc/CC-MAIN-20210508121446-20210508151446-00016.warc.gz"} |
http://dlmf.nist.gov/8.25 | # §8.25 Methods of Computation
## §8.25(i) Series Expansions
Although the series expansions in §§8.7, 8.19(iv), and 8.21(vi) converge for all finite values of $z$, they are cumbersome to use when $|z|$ is large owing to slowness of convergence and cancellation. For large $|z|$ the corresponding asymptotic expansions (generally divergent) are used instead. See also Luke (1975, pp. 101–102) and Temme (1994b).
See Allasia and Besenghi (1987b) for the numerical computation of $\mathop{\Gamma\/}\nolimits\!\left(a,z\right)$ from (8.6.4) by means of the trapezoidal rule.
## §8.25(iii) Asymptotic Expansions
DiDonato and Morris (1986) describes an algorithm for computing $\mathop{P\/}\nolimits\!\left(a,x\right)$ and $\mathop{Q\/}\nolimits\!\left(a,x\right)$ for $a\geq 0$, $x\geq 0$, and $a+x\neq 0$ from the uniform expansions in §8.12. The algorithm supplies 14S accuracy. A numerical inversion procedure is also given for calculating the value of $x$ (with 10S accuracy), when $a$ and $\mathop{P\/}\nolimits\!\left(a,x\right)$ are specified, based on Newton’s rule (§3.8(ii)). See also Temme (1987, 1994b).
## §8.25(iv) Continued Fractions
The computation of $\mathop{\gamma\/}\nolimits\!\left(a,z\right)$ and $\mathop{\Gamma\/}\nolimits\!\left(a,z\right)$ by means of continued fractions is described in Jones and Thron (1985) and Gautschi (1979b, §§4.3, 5). See also Jacobsen et al. (1986) and Temme (1996b, p. 280).
## §8.25(v) Recurrence Relations
Expansions involving incomplete gamma functions often require the generation of sequences $\mathop{P\/}\nolimits\!\left(a+n,x\right)$, $\mathop{Q\/}\nolimits\!\left(a+n,x\right)$, or $\mathop{\gamma^{*}\/}\nolimits\!\left(a+n,x\right)$ for fixed $a$ and $n=0,1,2,\dots$. An efficient procedure, based partly on the recurrence relations (8.8.5) and (8.8.6), is described in Gautschi (1979b, 1999).
Stable recursive schemes for the computation of $\mathop{E_{p}\/}\nolimits\!\left(x\right)$ are described in Miller (1960) for $x>0$ and integer $p$. For $x>0$ and real $p$ see Amos (1980b) and Chiccoli et al. (1987, 1988). See also Chiccoli et al. (1990a) and Stegun and Zucker (1974). | 2016-02-13T23:47:53 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 24, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9120052456855774, "perplexity": 1484.0974581899}, "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-2016-07/segments/1454701168065.93/warc/CC-MAIN-20160205193928-00099-ip-10-236-182-209.ec2.internal.warc.gz"} |
http://legisquebec.gouv.qc.ca/en/showversion/cr/Q-2,%20r.%2017.1?code=se:117&pointInTime=20210920 | ### Q-2, r. 17.1 - Regulation respecting the regulatory scheme applying to activities on the basis of their environmental impact
117. The following activities, including any subsequent operation, are eligible for a declaration of compliance on the conditions set out in the second paragraph:
(1) the establishment of a sand pit;
(2) in the case of a sand pit established before 17 August 1977, the enlargement of the sand pit onto land that did not belong, on that date, to the owner of the sand pit;
(3) the enlargement of a sand pit beyond the area or boundaries specified in the authorization.
The following conditions apply to the activities referred to in the first paragraph:
(1) the sand must be established or enlarged at least 150 m from a dwelling or public institution;
(2) the total area of the sand pit must not exceed 10 ha;
(3) the quantity of non-consolidated surface mineral substances extracted annually must not exceed 100,000 tonnes;
(4) the non-consolidated surface mineral substances extracted must not be washed in the sand pit;
(5) the maximum depth of the sand pit must lie above the water table.
O.C. 871-2020, s. 117.
In force: 2020-12-31
117. The following activities, including any subsequent operation, are eligible for a declaration of compliance on the conditions set out in the second paragraph:
(1) the establishment of a sand pit;
(2) in the case of a sand pit established before 17 August 1977, the enlargement of the sand pit onto land that did not belong, on that date, to the owner of the sand pit;
(3) the enlargement of a sand pit beyond the area or boundaries specified in the authorization.
The following conditions apply to the activities referred to in the first paragraph:
(1) the sand must be established or enlarged at least 150 m from a dwelling or public institution;
(2) the total area of the sand pit must not exceed 10 ha;
(3) the quantity of non-consolidated surface mineral substances extracted annually must not exceed 100,000 tonnes;
(4) the non-consolidated surface mineral substances extracted must not be washed in the sand pit;
(5) the maximum depth of the sand pit must lie above the water table.
O.C. 871-2020, s. 117. | 2021-10-17T06:01:22 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8208678364753723, "perplexity": 4442.515580079202}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323585121.30/warc/CC-MAIN-20211017052025-20211017082025-00042.warc.gz"} |
https://phys.libretexts.org/Bookshelves/University_Physics/Book%3A_University_Physics_(OpenStax)/Map%3A_University_Physics_I_-_Mechanics%2C_Sound%2C_Oscillations%2C_and_Waves_(OpenStax)/2%3A_Vectors/2.S%3A_Vectors_(Summary) | $$\require{cancel}$$
# Key Terms
anticommutative property change in the order of operation introduces the minus sign antiparallel vectors two vectors with directions that differ by 180° associative terms can be grouped in any fashion commutative operations can be performed in any order component form of a vector a vector written as the vector sum of its components in terms of unit vectors corkscrew right-hand rule a rule used to determine the direction of the vector product cross product the result of the vector multiplication of vectors is a vector called a cross product; also called a vector product difference of two vectors vector sum of the first vector with the vector antiparallel to the second direction angle in a plane, an angle between the positive direction of the x-axis and the vector, measured counterclockwise from the axis to the vector displacement change in position distributive multiplication can be distributed over terms in summation dot product the result of the scalar multiplication of two vectors is a scalar called a dot product; also called a scalar product equal vectors two vectors are equal if and only if all their corresponding components are equal; alternately, two parallel vectors of equal magnitudes magnitude length of a vector null vector a vector with all its components equal to zero orthogonal vectors two vectors with directions that differ by exactly 90°, synonymous with perpendicular vectors parallel vectors two vectors with exactly the same direction angles parallelogram rule geometric construction of the vector sum in a plane polar coordinate system an orthogonal coordinate system where location in a plane is given by polar coordinates polar coordinates a radial coordinate and an angle radical coordinate distance to the origin in a polar coordinate system resultant vector vector sum of two (or more) vectors scalar a number, synonymous with a scalar quantity in physics scalar component a number that multiplies a unit vector in a vector component of a vector scalar equation equation in which the left-hand and right-hand sides are numbers scalar product the result of the scalar multiplication of two vectors is a scalar called a scalar product; also called a dot product scalar quantity quantity that can be specified completely by a single number with an appropriate physical unit tail-to-head geometric construction geometric construction for drawing the resultant vector of many vectors unit vector vector of a unit magnitude that specifies direction; has no physical unit unit vectors of the axes unit vectors that define orthogonal directions in a plane or in space vector mathematical object with magnitude and direction vector components orthogonal components of a vector; a vector is the vector sum of its vector components vector equation equation in which the left-hand and right-hand sides are vectors vector product the result of the vector multiplication of vectors is a vector called a vector product; also called a cross product vector quantity physical quantity described by a mathematical vector—that is, by specifying both its magnitude and its direction; synonymous with a vector in physics vector sum resultant of the combination of two (or more) vectors
# Key Equations
Multiplication by a scalar (vector equation) $$\vec{B} = \alpha \vec{A}$$ Multiplication by a scalar (scalar equation for magnitudes) $$B = |\alpha| A$$ Resultant of two vectors $$\vec{D}_{AD} = \vec{D}_{AC} + \vec{D}_{CD}$$ Commutative law $$\vec{A} + \vec{B} = \vec{B} + \vec{A}$$ Associative law $$(\vec{A} + \vec{B}) + \vec{C} = \vec{A} + (\vec{B} + \vec{C})$$ Distributive law $$\alpha_{1} \vec{A} + \alpha_{2} \vec{A} = (\alpha_{1} + \alpha_{2}) \vec{A}$$ The component form of a vector in two dimensions $$\vec{A} = A_{x} \hat{i} + A_{y} \hat{j}$$ Scalar components of a vector in two dimensions $$\begin{cases} A_{x} = x_{e} - x_{b} \\ A_{y} = y_{e} - y_{b} \end{cases}$$ Magnitude of a vector in a plane $$A = \sqrt{A_{x}^{2} + A_{y}^{2}}$$ The direction angle of a vector in a plane $$\theta_{A} = \tan^{-1} \left(\dfrac{A_{y}}{A_{x}}\right)$$ Scalar components of a vector in a plane $$\begin{cases} A_{x} = A \cos \theta_{A} \\ A_{y} = A \sin \theta_{A} \end{cases}$$ Polar coordinates in a plane $$\begin{cases} x = r \cos \varphi \\ y = r \sin \varphi \end{cases}$$ The component form of a vector in three dimensions $$\vec{A} = A_{x} \hat{i} + A_{y} \hat{j} + A_{z} \hat{k}$$ The scalar z-component of a vector in three dimensions $$A_{z} = z_{e} - z_{b}$$ Magnitude of a vector in three dimensions $$A = \sqrt{A_{x}^{2} + A_{y}^{2} + A_{z}^{2}}$$ Distributive property $$\alpha (\vec{A} + \vec{B}) = \alpha \vec{A} + \alpha \vec{B}$$ Antiparallel vector to $$\vec{A}$$ $$- \vec{A} = A_{x} \hat{i} - A_{y} \hat{j} - A_{z} \hat{k}$$ Equal vectors $$\vec{A} = \vec{B} \Leftrightarrow \begin{cases} A_{x} = B_{x} \\ A_{y} = B_{y} \\ A_{z} = B_{z} \end{cases}$$ Components of the resultant of N vectors $$\begin{cases} F_{Rx} = \sum_{k = 1}^{N} F_{kx} = F_{1x} + F_{2x} + \ldots + F_{Nx} \\ F_{Ry} = \sum_{k = 1}^{N} F_{ky} = F_{1y} + F_{2y} + \ldots + F_{Ny} \\ F_{Rz} = \sum_{k = 1}^{N} F_{kz} = F_{1z} + F_{2z} + \ldots + F_{Nz} \end{cases}$$ General unit vector $$\hat{V} = \frac{\vec{V}}{V}$$ Definition of the scalar product $$\vec{A} \cdotp \vec{B} = AB \cos \varphi$$ Commutative property of the scalar product $$\vec{A} \cdotp \vec{B} = \vec{B} \cdotp \vec{A}$$ Distributive property of the scalar product $$\vec{A} \cdotp (\vec{B} + \vec{C}) = \vec{A} \cdotp \vec{B} + \vec{A} \cdotp \vec{C}$$ Scalar product in terms of scalar components of vectors $$\vec{A} \cdotp \vec{B} = A_{x}B_{x} + A_{y}B_{y} + A_{z}B_{z}$$ Cosine of the angle between two vectors $$\cos \varphi = \frac{\vec{A} \cdotp \vec{B}}{AB}$$ Dot products of unit vectors $$\hat{i} \cdotp \hat{j} = \hat{j} \cdotp \hat{k} = \hat{k} \cdotp \hat{i} = 0$$ Magnitude of the vector product (definition) $$|\vec{A} \times \vec{B}| = AB \sin \varphi$$ Anticommutative property of the vector product $$|\vec{A} \times \vec{B} = - \vec{B} \times \vec{A}$$ Distributive property of the vector product $$\vec{A} \times (\vec{B} + \vec{C}) = \vec{A} \times \vec{B} + \vec{A} \times \vec{C}$$ Cross products of unit vectors $$\begin{cases} \hat{i} \times \hat{j} = + \hat{k}, \\ \hat{j} \times \hat{l} = + \hat{i}, \\ \hat{l} \times \hat{i} = + \hat{j} \ldotp \end{cases}$$ The cross product in terms of scalar components of vectors $$\vec{A} \times \vec{B} = (A_{y}B_{z} - A_{z}B_{y}) \hat{i} + (A_{z}B_{x} - A_{x}B_{z}) \hat{j} + (A_{x}B_{y} - A_{y}B_{x}) \hat{k}$$
# Summary
## 2.1 Scalars and Vectors
• A vector quantity is any quantity that has magnitude and direction, such as displacement or velocity.
• Geometrically, vectors are represented by arrows, with the end marked by an arrowhead. The length of the vector is its magnitude, which is a positive scalar. On a plane, the direction of a vector is given by the angle the vector makes with a reference direction, often an angle with the horizontal. The direction angle of a vector is a scalar.
• Two vectors are equal if and only if they have the same magnitudes and directions. Parallel vectors have the same direction angles but may have different magnitudes. Antiparallel vectors have direction angles that differ by 180°. Orthogonal vectors have direction angles that differ by 90°.
• When a vector is multiplied by a scalar, the result is another vector of a different length than the length of the original vector. Multiplication by a positive scalar does not change the original direction; only the magnitude is affected. Multiplication by a negative scalar reverses the original direction. The resulting vector is antiparallel to the original vector. Multiplication by a scalar is distributive. Vectors can be divided by nonzero scalars but cannot be divided by vectors.
• Two or more vectors can be added to form another vector. The vector sum is called the resultant vector. We can add vectors to vectors or scalars to scalars, but we cannot add scalars to vectors. Vector addition is commutative and associative.
• To construct a resultant vector of two vectors in a plane geometrically, we use the parallelogram rule. To construct a resultant vector of many vectors in a plane geometrically, we use the tail-to-head method.
## 2.2 Coordinate Systems and Components of a Vector
• Vectors are described in terms of their components in a coordinate system. In two dimensions (in a plane), vectors have two components. In three dimensions (in space), vectors have three components.
• A vector component of a vector is its part in an axis direction. The vector component is the product of the unit vector of an axis with its scalar component along this axis. A vector is the resultant of its vector components.
• Scalar components of a vector are differences of coordinates, where coordinates of the origin are subtracted from end point coordinates of a vector. In a rectangular system, the magnitude of a vector is the square root of the sum of the squares of its components.
• In a plane, the direction of a vector is given by an angle the vector has with the positive x-axis. This direction angle is measured counterclockwise. The scalar x-component of a vector can be expressed as the product of its magnitude with the cosine of its direction angle, and the scalar y-component can be expressed as the product of its magnitude with the sine of its direction angle.
• In a plane, there are two equivalent coordinate systems. The Cartesian coordinate system is defined by unit vectors $$\hat{i}$$ and $$\hat{j}$$ along the x-axis and the y-axis, respectively. The polar coordinate system is defined by the radial unit vector $$\hat{r}$$, which gives the direction from the origin, and a unit vector $$\hat{t}$$, which is perpendicular (orthogonal) to the radial direction.
## 2.3 Algebra of Vectors
• Analytical methods of vector algebra allow us to find resultants of sums or differences of vectors without having to draw them. Analytical methods of vector addition are exact, contrary to graphical methods, which are approximate.
• Analytical methods of vector algebra are used routinely in mechanics, electricity, and magnetism. They are important mathematical tools of physics.
## 2.4 Products of Vectors
• There are two kinds of multiplication for vectors. One kind of multiplication is the scalar product, also known as the dot product. The other kind of multiplication is the vector product, also known as the cross product. The scalar product of vectors is a number (scalar). The vector product of vectors is a vector.
• Both kinds of multiplication have the distributive property, but only the scalar product has the commutative property. The vector product has the anticommutative property, which means that when we change the order in which two vectors are multiplied, the result acquires a minus sign.
• The scalar product of two vectors is obtained by multiplying their magnitudes with the cosine of the angle between them. The scalar product of orthogonal vectors vanishes; the scalar product of antiparallel vectors is negative.
• The vector product of two vectors is a vector perpendicular to both of them. Its magnitude is obtained by multiplying their magnitudes by the sine of the angle between them. The direction of the vector product can be determined by the corkscrew right-hand rule. The vector product of two either parallel or antiparallel vectors vanishes. The magnitude of the vector product is largest for orthogonal vectors.
• The scalar product of vectors is used to find angles between vectors and in the definitions of derived scalar physical quantities such as work or energy.
• The cross product of vectors is used in definitions of derived vector physical quantities such as torque or magnetic force, and in describing rotations.
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). | 2019-08-21T01:27:50 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8318555355072021, "perplexity": 239.77321863988192}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-35/segments/1566027315695.36/warc/CC-MAIN-20190821001802-20190821023802-00275.warc.gz"} |
https://itl.nist.gov/div898/handbook/pmd/section5/pmd521.htm | 4. Process Modeling
4.5. Use and Interpretation of Process Models
4.5.2. How can I use my process model for calibration?
Single-Use Calibration Intervals
Calibration As mentioned in Section 1.3, the goal of calibration (also called inverse prediction by some authors) is to quantitatively convert measurements made on one of two measurement scales to the other measurement scale. Typically the two scales are not of equal importance, so the conversion occurs in only one direction. The model fit to the data that relates the two measurement scales and a new measurement made on the secondary scale provide the means for the conversion. The results from the fit of the model also allow for computation of the associated uncertainty in the estimate of the true value on the primary measurement scale. Just as for prediction, estimates of both the value on the primary scale and its uncertainty are needed in order to make sound engineering or scientific decisions or conclusions. Approximate confidence intervals for the true value on the primary measurement scale are typically used to summarize the results probabilistically. An example, which will help make the calibration process more concrete, is given in Section 4.1.3.3. using thermocouple calibration data.
Calibration Estimates Like prediction estimates, calibration estimates can be computed relatively easily using the regression equation. They are computed by setting a newly observed value of the response variable, $$y^*$$, which does not have an accompanying value of the predictor variable, equal to the estimated regression function and solving for the unknown value of the predictor variable. Depending on the complexity of the regression function, this may be done analytically, but sometimes numerical methods are required. Fortunatel, the numerical methods needed are not complicated, and once implemented are often easier to use than analytical methods, even for simple regression functions.
Pressure / Temperature Example In the Pressure/Temperature example, pressure measurements could be used to measure the temperature of the system by observing a new pressure value, setting it equal to the estimated regression function, $$f(x;\hat{\vec{\beta}}) = 7.74899 + 3.93014 \cdot x$$ and solving for the temperature. If a pressure of 178 were measured, the associated temperature would be estimated to be about 43. $$\begin{eqnarray} 178 & = & 7.74899 + 3.93014 \cdot x \\ & & \\ & \Downarrow & \\ & & \\ x & = & (178-7.74899)/3.93014 \\ & & \\ & = & 43.319245 \end{eqnarray}$$ Although this is a simple process for the straight-line model, note that even for this simple regression function the estimate of the temperature is not linear in the parameters of the model.
Numerical Approach To set this up to be solved numerically, the equation simply has to be set up in the form $$178 - (7.74899 + 3.93014 \cdot x) = 0$$ and then the function of temperature ($$x$$) defined by the left-hand side of the equation can be used as the argument in an arbitrary root-finding function. It is typically necessary to provide the root-finding software with endpoints on opposite sides of the root. These can be obtained from a plot of the calibration data and usually do not need to be very precise. In fact, it is often adequate to simply set the endpoints equal to the range of the calibration data, since calibration functions tend to be increasing or decreasing functions without local minima or maxima in the range of the data. For the pressure/temperature data, the endpoints used in the root-finding software could even be set to values like -5 and 100, broader than the range of the data. This choice of end points would even allow for extrapolation if new pressure values outside the range of the original calibration data were observed.
Thermocouple Calibration Example For the more realistic thermocouple calibration example, which is well fit by a LOESS model that does not require an explicit functional form, the numerical approach must be used to obtain calibration estimates. The LOESS model is set up identically to the straight-line model for the numerical solution, using the estimated regression function from the software used to fit the model. $$y^* - f(x;\hat{\vec{\beta}}) = 0$$ Again the function of temperature ($$x$$) on the left-hand side of the equation would be used as the main argument in an arbitrary root-finding function. If for some reason $$f(x;\hat{\vec{\beta}})$$ were not available in the software used to fit the model, it could always be created manually since LOESS can ultimately be reduced to a series of weighted least squares fits. Based on the plot of the thermocouple data, endpoints of 100 and 600 would probably work well for all calibration estimates. Wider values for the endpoints are not useful here since extrapolations do not make much sense for this type of local model.
Software Since the verbal descriptions of these numerical techniques can be hard to follow, these ideas may become clearer by looking at the actual computer code for a quadratic calibration, which can be found in the Load Cell Calibration case study. The case study contains both Dataplot code and R code.
Calibration Uncertainties As in prediction, the data used to fit the process model can also be used to determine the uncertainty of the calibration. Both the variation in the average response and in the new observation of the response value need to be accounted for. This is similar to the uncertainty for the prediction of a new measurement. In fact, approximate calibration confidence intervals are actually computed by solving for the predictor variable value in the formulas for prediction interval end points [Graybill (1976)]. Because $$\hat{\sigma}_p$$, the standard deviation of the prediction of a measured response, is a function of the predictor variable, like the regression function itself, the inversion of the prediction interval endpoints is usually messy. However, like the inversion of the regression function to obtain estimates of the predictor variable, it can be easily solved numerically.
The equations to be solved to obtain approximate lower and upper calibration confidence limits, are, respectively, $$y^* - f(x;\hat{\vec{\beta}}) + t_{1-\alpha/2,\nu} \cdot \hat{\sigma}_p(x) = 0$$ and $$y^* - f(x;\hat{\vec{\beta}}) - t_{1-\alpha/2,\nu} \cdot \hat{\sigma}_p(x) = 0$$ with $$\hat{\sigma}_p$$ denoting the estimated standard deviation of the prediction of a new measurement. $$f(x;\hat{\vec{\beta}})$$ and $$\hat{\sigma}_p$$ are both denoted as functions of the predictor variable, $$x$$, here to make it clear that those terms must be written as functions of the unknown value of the predictor variable. The left-hand sides of the two equations above are used as arguments in the root-finding software, just as the expression $$y^* - f(x;\hat{\vec{\beta}})$$ is used when computing the estimate of the predictor variable.
Confidence Intervals for the Example Applications Confidence intervals for the true predictor variable values associated with the observed values of pressure (178) and voltage (1522) are given in the table below for the Pressure/Temperature example and the Thermocouple Calibration example, respectively. The approximate confidence limits and estimated values of the predictor variables were obtained numerically in both cases.
Example $$y^*$$ Lower 95%ConfidenceBound EstimatedPredictorVariableValue Upper 95%ConfidenceBound Pressure/Temperature 178 41.07564 43.31925 45.56146 Thermocouple Calibration 1522 553.0026 553.0187 553.0349
Interpretation of Calibration Intervals Although calibration confidence intervals have some unique features, viewed as confidence intervals, their interpretation is essentially analogous to that of confidence intervals for the true average response. Namely, in repeated calibration experiments, when one calibration is made for each set of data used to fit a calibration function and each single new observation of the response, then approximately $$100(1-\alpha) \, \%$$ of the intervals computed as described above will capture the true value of the predictor variable, which is a measurement on the primary measurement scale.
The plot below shows 95 % confidence intervals computed using 50 independently generated data sets that follow the same model as the data in the Thermocouple calibration example. Random errors from a normal distribution with a mean of zero and a known standard deviation are added to each set of true temperatures and true voltages that follow a model that can be well-approximated using LOESS to produce the simulated data. Then each data set and a newly observed voltage measurement are used to compute a confidence interval for the true temperature that produced the observed voltage. The dashed reference line marks the true temperature under which the thermocouple measurements were made. It is easy to see that most of the intervals do contain the true value. In 47 out of 50 data sets, or approximately 95 %, the confidence intervals covered the true temperature. When the number of data sets was increased to 5000, the confidence intervals computed for 4657, or 93.14 %, of the data sets covered the true temperature. Finally, when the number of data sets was increased to 10000, 93.53 % of the confidence intervals computed covered the true temperature. While these intervals do not exactly attain their stated coverage, as the confidence intervals for the average response do, the coverage is reasonably close to the specified level and is probably adequate from a practical point of view.
Confidence Intervals Computed from 50 Sets of Simulated Data | 2022-06-27T15:45:19 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7573264837265015, "perplexity": 311.05464856180396}, "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-2022-27/segments/1656103334753.21/warc/CC-MAIN-20220627134424-20220627164424-00755.warc.gz"} |
https://par.nsf.gov/biblio/10361626 | Evidence for the Preferential Disruption of Moderately Massive Stars by Supermassive Black Holes
Abstract
Tidal disruption events (TDEs) provide a unique opportunity to probe the stellar populations around supermassive black holes (SMBHs). By combining light-curve modeling with spectral line information and knowledge about the stellar populations in the host galaxies, we are able to constrain the properties of the disrupted star for three TDEs. The TDEs in our sample have UV spectra, and measurements of the UV Niiito Ciiiline ratios enabled estimates of the nitrogen-to-carbon abundance ratios for these events. We show that the measured nitrogen line widths are consistent with originating from the disrupted stellar material dispersed by the central SMBH. We find that these nitrogen-to-carbon abundance ratios necessitate the disruption of moderately massive stars (≳1–2M). We determine that these moderately massive disruptions are overrepresented by a factor of ≳102when compared to the overall stellar population of the post-starburst galaxy hosts. This implies that SMBHs are preferentially disrupting higher mass stars, possibly due to ongoing top-heavy star formation in nuclear star clusters or to dynamical mechanisms that preferentially transport higher mass stars to their tidal radii.
Authors:
; ; ; ; ; ;
Award ID(s):
Publication Date:
NSF-PAR ID:
10361626
Journal Name:
The Astrophysical Journal
Volume:
924
Issue:
2
Page Range or eLocation-ID:
Article No. 70
ISSN:
0004-637X
Publisher:
DOI PREFIX: 10.3847
National Science Foundation
##### More Like this
1. Abstract
The tidal disruption of stars by supermassive black holes (SMBHs) probes relativistic gravity. In the coming decade, the number of observed tidal disruption events (TDEs) will grow by several orders of magnitude, allowing statistical inferences of the properties of the SMBH and stellar populations. Here we analyze the probability distribution functions of the pericenter distances of stars that encounter an SMBH in the Schwarzschild geometry, where the results are completely analytic, and the Kerr metric. From this analysis we calculate the number of observable TDEs, defined to be those that come within the tidal radiusrtbut outside the direct capture radius (which is, in general, larger than the horizon radius). We find that relativistic effects result in a steep decline in the number of stars that have pericenter distancesrp≲ 10rg, whererg=GM/c2, and that for maximally spinning SMBHs the distribution function ofrpat such distances scales as$frp∝rp4/3$, or in terms ofβrt/rpscales asfββ−10/3. We find that spin has little effect on the TDE fraction until the very-high-mass end, where instead of being identically zero the rate is small (≲1% of the expected rate in the absence of relativistic effects). Effectively independent of spin, if the progenitorsmore »
2. Abstract
Most stellar evolution models predict that black holes (BHs) should not exist above approximately 50–70M, the lower limit of the pair-instability mass gap. However, recent LIGO/Virgo detections indicate the existence of BHs with masses at and above this threshold. We suggest that massive BHs, including intermediate-mass BHs (IMBHs), can form in galactic nuclei through collisions between stellar-mass BHs and the surrounding main-sequence stars. Considering dynamical processes such as collisions, mass segregation, and relaxation, we find that this channel can be quite efficient, forming IMBHs as massive as 104M. This upper limit assumes that (1) the BHs accrete a substantial fraction of the stellar mass captured during each collision and (2) that the rate at which new stars are introduced into the region near the SMBH is high enough to offset depletion by stellar disruptions and star–star collisions. We discuss deviations from these key assumptions in the text. Our results suggest that BHs in the pair-instability mass gap and IMBHs may be ubiquitous in galactic centers. This formation channel has implications for observations. Collisions between stars and BHs can produce electromagnetic signatures, for example, from X-ray binaries and tidal disruption events. Additionally, formed through this channel, both BHs in themore »
3. Abstract
We discuss five blue stellar systems in the direction of the Virgo cluster, analogous to the enigmatic object SECCO 1 (AGC 226067). These objects were identified based on their optical and UV morphology and followed up with Hiobservations with the Very Large Array (and Green Bank Telescope), Multi Unit Spectroscopic Explorer (on the Very Large Telescope) optical spectroscopy, and Hubble Space Telescope imaging. These new data indicate that one system is a distant group of galaxies. The remaining four are extremely low mass (M*∼ 105M), are dominated by young blue stars, have highly irregular and clumpy morphologies, are only a few kiloparsecs across, yet host an abundance of metal-rich,$12+log(O/H)>8.2$, Hiiregions. These high metallicities indicate that these stellar systems formed from gas stripped from much more massive galaxies. Despite the young age of their stellar populations, only one system is detected in Hi, while the remaining three have minimal (if any) gas reservoirs. Furthermore, two systems are surprisingly isolated and have no plausible parent galaxy within ∼30′ (∼140 kpc). Although tidal stripping cannot be conclusively excluded as the formation mechanism of these objects, ram pressure stripping more naturally explains their properties, inmore »
4. ABSTRACT
A star destroyed by a supermassive black hole (SMBH) in a tidal disruption event (TDE) enables the study of SMBHs. We propose that the distance within which a star is completely destroyed by an SMBH, defined rt,c, is accurately estimated by equating the SMBH tidal field (including numerical factors) to the maximum gravitational field in the star. We demonstrate that this definition accurately reproduces the critical βc = rt/rt,c, where rt = R⋆(M•/M⋆)1/3 is the standard tidal radius with R⋆ and M⋆ the stellar radius and mass, and M• the SMBH mass, for multiple stellar progenitors at various ages, and can be reasonably approximated by βc ≃ [ρc/(4ρ⋆)]1/3, where ρc (ρ⋆) is the central (average) stellar density. We also calculate the peak fallback rate and time at which the fallback rate peaks, finding excellent agreement with hydrodynamical simulations, and also suggest that the partial disruption radius – the distance at which any mass is successfully liberated from the star – is βpartial ≃ 4−1/3 ≃ 0.6. For given stellar and SMBH populations, this model yields, e.g. the fraction of partial TDEs, the peak luminosity distribution of TDEs, and the number of directly captured stars.
5. Abstract Tidal disruption events (TDEs) are among the brightest transients in the optical, ultraviolet, and X-ray sky. These flares are set into motion when a star is torn apart by the tidal field of a massive black hole, triggering a chain of events which is – so far – incompletely understood. However, the disruption process has been studied extensively for almost half a century, and unlike the later stages of a TDE, our understanding of the disruption itself is reasonably well converged. In this Chapter, we review both analytical and numerical models for stellar tidal disruption. Starting with relatively simple, order-of-magnitude physics, we review models of increasing sophistication, the semi-analytic “affine formalism,” hydrodynamic simulations of the disruption of polytropic stars, and the most recent hydrodynamic results concerning the disruption of realistic stellar models. Our review surveys the immediate aftermath of disruption in both typical and more unusual TDEs, exploring how the fate of the tidal debris changes if one considers non-main sequence stars, deeply penetrating tidal encounters, binary star systems, and sub-parabolic orbits. The stellar tidal disruption process provides the initial conditions needed to model the formation of accretion flows around quiescent massive black holes, and in some cases maymore » | 2022-12-01T10:24:23 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 2, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7155985236167908, "perplexity": 2666.4568319794757}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446710808.72/warc/CC-MAIN-20221201085558-20221201115558-00424.warc.gz"} |
https://www.usgs.gov/centers/pcmsc/science/global-geoengineering-research | # Global Geoengineering Research
## Science Center Objects
Ground Deformation and Failure
The Coastal and Marine Geology geotechnical group investigates the causes of ground deformation and ground failure as a result of earthquakes, storms, and wave action. The coastal urban regions of the Pacific margin of the United States are growing rapidly, putting increasing demands on coastal infrastructure and lifelines, such as highways, utilities and community services. These structures and services, as well as the general population that are located in the coastal zone, are at risk from ground deformation and landslides which are triggered by a variety of phenomena including episodic disastrous earthquakes and storms, long-term and seasonal changes in water table as a result of changing land use, and coastal erosion caused by natural response to changes in sea level and changes in sediment transport patterns caused by construction of dams, breakwaters and other coastal structures. Coastal ground failures can be significant contributors to longshore sediment load. Hence, increase in the frequency of landslides can in some cases also contribute to environmental degradation through local amplification of sedimentation in nearshore habitats.
Our coastal ground failures study group focuses on characterization of
1. the geologic environment, and form of deformations;
2. measurement of geophysical and geotechnical properties of the ground; and
3. development of analytical, numerical, empirical and probabilistic models that describe and predict ground failures and their amplitude.
These models are intended for scientists, engineers, and urban planners.
Ground failure is a general term which encompasses all types of downward movement of material. Ground failures occur in every state of our country and are annually responsible for an estimated 25 to 50 deaths and $1 to$2 billion in property damage (FEMA 1995). Researchers suggest that approximately 40 percent of the United States' population is either directly or indirectly affected by landslide events. Ground deformation and failure of liquefied ground can be severely damaging to buried utilities, fire-suppression water mains, and foundations and has a major contributor to urban conflagration following earthquakes.
What Are the Characteristics of Ground Failures?
The west coast of the United States is particularly susceptible to ground failure due to the significant amount of precipitation and the earthquake potential. These two natural agents act as triggering events for landslides.
The principal natural factors, which play a role in ground failure potential, are topography, geology, and precipitation. Areas with steep slopes are more susceptible to landslides than flat areas, whereas, liquefaction of soil during earthquakes has typically occurred in relatively flat coastal plain areas. In general the more precipitation an area experiences, and the higher the ground water table, the greater the potential for ground failures. Anthropogenic (human) factors also influence landslide potential. The major human induced factors are development of hilly terrain, irrigation, construction of highways, buildings, and railroads, mining activity, and forestry practices.
Landslides also can be grouped by the way in which they move and divided into four general types:
Slides: Slides are characterized by the downward displacement movement of material along one or more failure surfaces.
Flows: Flows are similar to slides but differ in that they are characterized by high water content and the disintegration of the failure into fluid-like movement.
Lateral spreads: Lateral spreads are earthquake-induced movements associated with loose, sandy soils with high liquefaction potential. Lateral spreads occur when coherent surface soil is rafted on a weak liquefied layer and displaces down-slope. Lateral spreads can occur on very gentle slopes.
Falls and topples: Falls and topples are movements in which masses of rock or other material fall from cliffs or other steep slopes. Earthquakes commonly trigger this final type of movement.
Earthquakes and Ground Failures
When large faults rupture and produce earthquakes, they generally deform the ground surface. Primary surface faulting, such as the 340 kilometer-long surface rupture associated with the 2002 Denali Fault earthquake, is the direct effect of movement on a seismogenic, or earthquake-producing fault. Rupture on nearby faults induced by the primary event (sympathetic rupture) may also produce surface faulting. Away from a surface fault rupture, ground deformations in soil and rock can produce secondary damage features that extend for tens and even hundreds of kilometers from the sesmogenic fault. Ground failure and ground deformation associated with dynamic movements can form by a variety of mechanisms:
1. shaking-induced compaction of deposits in fills, sedimentary basins and river valleys;
2. liquefaction of loose gravely-sands, sands and silts; and
3. displacements of ground on non-liquefiable soils.
Liquefaction Ground Failures
Liquefaction is a phenomenon associated with earthquakes in which sandy to silty, water-saturated soils behave like fluids. As seismic waves pass through saturated soil layers, the structure of the soil distorts and void spaces between soil particles (pores) collapse, causing deformation and ground failure. In general, young, loose sediment and areas with high water tables are the most susceptible to liquefaction. Sand boils and fissures are a common sign of liquefaction. Sand boils and fissures form when saturated sediment below the surface is ejected to the surface by elevated pore water pressure. Lateral spreads involves the movement of a relatively coherent surface crust of soil due to the liquefaction of underlying sediment. Horizontal movements of up to several meters is commonly observed after earthquakes in fills, coastal alluvium and river embankments. These deformations are a major contributor to economic loss and loss of services during earthquakes. Flow failure is another type of liquefaction-related ground failure and the most destructive. Flow failures occur when liquefied soils completely disintegrate during deformation and flow long distances down-slope, sometimes at high speed. Liquefied ground looses its capacity to support structure. The loss of bearing strength may result in the settlement, tilting or collapse of building.
Impacts to Ports and Harbors
Liquefaction most commonly occurs in earthquake-prone, low-lying areas with saturated soils. Generally, young saturated soils beneath rivers, lakes, bays, and seafloor are highly susceptible to liquefaction. Port and harbor facilities built on these soils are especially vulnerable to liquefaction effects. Many port and harbor facilities have been severely damaged from earthquake-induced liquefaction.
Dynamic displacements in Non-Liquefied Ground
Permanent seismic deformation can occur in any soil or rock when driving stresses exceed the mobilized capacity of the ground to resist shearing. During earthquake motions, permanent displacements accumulate in the ground for each cycle that induces slip along the failure surface. It is common for the shear strength of the ground to dramatically fall during this type of loading, causing increased displacements with subsequent cycles. In the most damaging case, the shear strength can fall below the down-slope stress, so that even when earthquake shaking stops the landslides continues to displace and even disintegrate into a high speed flow. All earthquake-induced landslides are caused by a combination of dynamic displacements during shaking and deformations associated with the interaction between the local sloping ground and changes in the internal properties of the slide material. | 2020-02-19T03:17:16 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4295209050178528, "perplexity": 5486.108807622287}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-10/segments/1581875144027.33/warc/CC-MAIN-20200219030731-20200219060731-00379.warc.gz"} |
https://www.abs.gov.au/statistics/detailed-methodology-information/concepts-sources-methods/australian-system-national-accounts-concepts-sources-and-methods/2020-21/chapter-19-productivity-measures/data-sources-and-methods/measurement-capital-input | Latest release
# The measurement of capital input
Australian System of National Accounts: Concepts, Sources and Methods
Reference period
2020-21 financial year
19.72 The measurement of capital input is concerned with estimating the contribution of capital to the production process; that is, the flow of capital services from the capital stock used in the production process. Capital services have both quantity and price dimensions. The quantity of capital services represents hours a machine is used or months a building is occupied. The price dimension, called the rental price, represents an hourly rate for using the machine or a monthly rate for occupying a building.
## Productive capital stock and quantity of capital services
19.73 The quantity of capital services is estimated by assuming that capital services produced by an asset are proportional to the value of productive capital stock of the asset; that is:
$$\large K_t = u_t PKS_t$$
where $$K_t$$is the quantity of capital services, and $$PKS_t$$is the productive capital stock and $$u_t$$ is the capacity utilization rate.
19.74 The capacity utilization rate is assumed to be constant over time. This assumption has two implications. First, as $$u_t$$ is constant and invariant to time, a change in the quantity of capital services delivered from any given capital asset is tantamount to a change in its productive capital stock. Second, variations in the utilization of the capital stock are not accounted for in the estimation of its capital services, and as a consequence changes in the capital services over time may reflect the impact of short-term business cycles, other than movements of capital input.
19.75 The productive capital stock estimates are derived from data on gross fixed capital formation (except inventories and land), using the PIM. The essence of this method is to transform all capital assets of different vintages into equivalent efficiency units and then add them up into an estimate of the productive capital stock. Chapter 14 provides a full description of the procedures used to derive the productive capital stock. Chapter 10 provides a full description of the data sources and procedures used to compile estimates of gross fixed capital formation.
## Imputing rental prices
19.76 In estimating the value of labour services, statisticians can directly observe labour rental prices as wage rates paid to workers. In the case of capital however, the rental prices for capital have to be imputed. The rental price reflects the price at which an investor is indifferent between two alternatives:
1. earning a nominal rate of return on a different investment; and
2. buying a capital asset, renting it out, collecting rent and selling it in the next period.
19.77 A standard specification for the capital rental price in the absence of taxes is the arbitrage equation⁹⁰:
$$\large P_j,_{t-1}(1+i_t) = r_{j,t}+(1-δ_j)P_{j,t}$$ - - - - - - - (19.1)
where $$i_t$$ is the nominal interest, $$P_{j,t-1}$$ is the acquisition price of capital asset $$j$$ at the beginning of the period, $$r_{j,t}$$ is the rental price, $$P_{j,t}$$ is the price of capital asset j at the end of the period and $$δ_{j,t}$$ is the rate of economic depreciation.
19.78 This can be rearranged into the expression:
$$\large r_{j,t}=i_tPj_{,t-1}+δ_{j,t}P_{j,t}- \pi _{j,t}$$ - - - - - - - (19.2)
where $$\pi_{j,t} = P_{j,t} - P_{j,t-1}$$ is the asset-specific capital gains term.
19.79 Equation (19.2) shows that the capital rental price consists of three components: the rate of return to capital, the depreciation rate and the capital gain or loss due to revaluation. The industry dimension is supressed here.
19.80 When tax considerations are given to the measurement of capital rental prices (both capital income taxes and indirect business taxes), the tax-adjusted rental price equation becomes:
$$\large r_{i,j,t}=T_{i,j,t}(i_{i,t}P_{i,j,t-1}+δ_{j,t}P_{i,j,t}-π_{i,j,t})+x_{i,t}P_{i,j,t-1}$$ - - - - - - - (19.3)
where $$i$$ indexes industries, $$T_{i,j,t}$$ is the income tax parameter and $$x_{i,t}$$ is the effective net indirect tax rate on production. The description of data sources for constructing the tax parameter is provided in Annex C.
19.81 The rate of return to capital $$i_t$$ can be estimated by either endogenously or exogenously. Under the endogenous approach, the total value of capital services in each industry is assumed to be equal to the compensation for all assets in that industry. The resulting internal rate of return exhausts capital income and is consistent with constant returns to scale. The nominal rate of return is the same for all assets in an industry but may vary across industries.
19.82 In the case of the exogenous approach, the nominal rate may equal the Treasury bond rate, or the dividend yield on a stock index. This method allows the value of capital income to deviate from property compensation, assuming imperfect competition and non-constant returns to scale. For a detailed discussion of these two alternative methods and associated sensitivity analysis, see Appendix 2 Sensitivity Analysis of Capital Inputs, in the Information paper, Experimental Estimates of Industry Multifactor Productivity.
19.83 The ABS follows the endogenous method in producing its official productivity estimates. For the corporate sector, iit, is solved for all assets in each industry by assuming that gross operating surplus, $$GOS_{it}$$ equals the rental price multiplied by the real productive capital stock in each industry:
$$\large GO{S_{i,t}} = \sum\limits_j {{r_{i,j,t}}{K_{i,j,t}}}$$ - - - - - - - (19.4)
and substituting for the rental price in equation (19.4) giving:
$$\large GO{S_{i,t}} = \sum\limits_j {{K_{i,j,t}}\left( {{T_{i,j,t}}\left( {{i_{i,t}}{P_{i,j,t - 1}} + {\delta _j}{P_{i,j,t}} - {\pi _{i,j,t}}} \right) + {x_{i,t}}{P_{i,j,t - 1}}} \right)}$$ - - - - - - - (19.5)
so
$$\large {i_{i,t}} = \frac{{GO{S_{i,t}} - \sum\nolimits_j {{K_{i,j,t}}\left( {{T_{i,j,t}}\left( {{\delta _j}{P_{i,j,t}} - {\pi _{i,j,t}}} \right) + {x_{i,t}}{P_{i,j,t - 1}}} \right)} }}{{\sum\nolimits_j {{K_{i,j,t}}{T_{i,j,t}}{P_{i,j,t - 1}}} }}$$ - - - - - - - (19.6)
19.84 To prevent negative rental prices, the ABS imposes a floor limit on the internal rate of return of CPI plus 4 per cent; otherwise, the endogenous rate is used.
19.85 The depreciation of a capital asset measures the change in its real economic value during the accounting period. The depreciation rates are derived using asset age-price profiles. The age-price profiles are constructed by using corresponding age-efficiency profiles, multiplied by a suitable discount rate (the ABS chooses a real discount rate at 4 per cent). See Chapter 14 for the detailed description of age-efficiency and age-price profiles and their roles in constructing various capital components.
19.86 The capital gain or loss due to revaluation can be calculated as an asset-specific deflator or a general deflator. As defined in equation (19.3), the asset-specific capital term is used and calculated as the percentage change in the value of the asset in time t-1 relative to its value in time t. Alternatively, $$π_t$$ can be replaced by a general price deflator such as the consumer price index. The former is preferred because it is able to account for the large changes in relative prices across heterogeneous asset classes and therefore reduces measurement errors. However, the disadvantage of using asset-specific deflators is that it often introduces volatility into the rental price equation.
19.87 The elemental capital inputs are compiled at a detailed level. There are capital input measures for up to 16 asset types for the corporate and unincorporated entities for each of the 16 ANZSIC industry divisions that comprise the market sector. For each capital input there is a volume indicator of the flow of capital services, and a rental price that is used to weight the service flow with the service flows of other capital inputs.
## Capital service flows for fixed assets
19.88 The estimates of fixed assets from the PIM that are used to derive MFP are:
• machinery and equipment: computers and computer peripherals; electronic and electrical machinery and communications equipment; industrial machinery and equipment; road vehicles; other transport equipment; and other equipment;
• non-dwelling construction;
• ownership transfer costs of non-dwelling construction;
• intellectual property products: computer software; research and development; mineral and petroleum exploration; and artistic originals (Film and TV; music; and literary);
• orchards, plantations and vineyards; and
• livestock.
19.89 Ownership transfer costs relating to non-dwelling construction are allocated to industry using industry proportions of chain volume non-dwelling construction by industry. This approach assumes that the proportion of ownership transfer costs to non-dwelling construction at a point in time does not vary between industries.
## Inventories
19.90 Volume estimates for the stock of inventory items are obtained for Divisions A to I (see Chapter 10 for more details). They are non-capitalised assets that are used up in the productive process and collected according to three categories:
• inventories of raw materials, including materials and fuels, spare parts designated for use in fixed assets, containers and packaging materials. Inventories of fuels for sale are included in inventories of finished goods;
• inventories of work-in-progress, including partially processed or fabricated goods which will be further processed prior to sale, and general work-in-progress less payments billed. Prepayments are excluded;
• inventories of finished goods, including goods manufactured or processed which are ready for sale, goods purchased from other businesses which are ready for resale without further processing, and fuels for sale. Hired goods, inventories of land, and rented or leased buildings are excluded.
## Land
19.91 Land can be further classified as either agricultural (for ANZSIC Division A) or non-agricultural (for the other ANZSIC divisions). Volume estimates of agricultural and non-agricultural land and the corresponding rental prices are constructed separately.
19.92 The volume estimate for agricultural land is derived starting with a nominal estimate obtained from the National Balance Sheet in the ASNA. In particular, the value of 'Rural' land in the reference year is used. As there is no suitable price index for agricultural land, its volume is assumed to be constant over time. The estimates of land values are discussed further in Chapter 17.
19.93 Similarly, a volume estimate of non-agricultural land is derived starting with a nominal estimate of the market sector's non-agricultural land in the reference year. A benchmark estimate is obtained from the National Balance Sheet by multiplying total 'Commercial' and 'Other' land by the proportion of the stock of non-dwelling construction in the market sector. This estimate is then split by industry proportionally using the productive capital stock of non-dwelling construction in the reference year. Then for a given industry, the volume estimate is constructed by assuming that its growth rate is half the growth rate of the industry's real productive capital stock of non-dwelling construction.
19.94 To calculate the rental prices for land, proxy price indicators are used as suitable land price indexes are not available. For agricultural land, the total investment deflator for Agriculture, forestry and fishing is used for the years prior to 1995-96, and the All groups CPI thereafter. For non-agricultural land, the index is based on the weighted aggregation of commercial and industrial rent indexes for Australia's main capital cities, provided by a private sector contractor.
## Operating leases and finance leases
19.95 The ABS classifies the use of capital as an intermediate input of the lessee when the capital is rented under an operational lease arrangement from a firm primarily operating in another industry. For example, a construction company may lease a crane from the rental and hiring industry, which is recorded as a service component in the intermediate inputs of the lessee and as capital services held by the lessor. If the proportion of the capital that is leased is changing it can affect value added productivity growth estimates. A reduction in the percentage of capital held within an industry over time, such as when a firm leases rather than purchases capital, would understate growth in the capital service index, which would have the effect of overstating value added MFP growth. For capital held under a long-term finance lease, the capital is treated as capital owned by the lessee and included in the productive capital stock estimates of the lessee industry.
### Endnotes
1. Jorgenson, Dale W., Mun S. Ho, and Kevin J. Stiroh (2005) Information Technology and the American Growth Resurgence. Cambridge, MA: MIT Press. | 2022-01-20T11:57:27 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 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": 0.5114213228225708, "perplexity": 3317.9635796256507}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320301737.47/warc/CC-MAIN-20220120100127-20220120130127-00349.warc.gz"} |
http://dergipark.gov.tr/konuralpjournalmath/issue/28490/344426 | Yıl 2017, Cilt 5, Sayı 2, Sayfalar 207 - 215 2017-10-15
| | | |
PRESERVING PROPERTIES OF THE GENERALIZED BERNARDI-LIBERA-LIVINGSTON INTEGRAL OPERATOR DEFINED ON SOME SUBCLASSES OF STARLIKE FUNCTIONS
OLGA ENGEL [1] , ORSOLYA AGNES PALL-SZABO [2]
77 125
In this paper we study the properties of the image of some subclasses of starlike functions, through the generalized Bernardi - Libera - Livingston integral operator. A new subclass of functions with negative coefficients is introduced and we study some properties of this class.
Bernardi-Libera-Livingston integral operator, composition of functions, functions with negative coefficients, starlikeness
• [1] O. Engel, On the composition of two starlike functions, Acta Univ. Apulensis, Vol:48 (2016), 47-53.
• [2] O. Engel, R. Szasz, Diferensiyel geometri, On a subclass of convex functions, Stud. Univ. Babeş - Bolyai Mathematica, Vol:59, No.2 (2016), 137-146.
• [3] S. S. Miller, P. T. Mocanu, Differential Subordinations Theory and Applications, Marcel Dekker, New York, Basel 2000.
• [4] P. T. Mocanu, T. Bulboaca, G. Şt. Salagean, Teoria Geometrica a Functiilor Univalente, Ed. a II-a, Casa Cartii de Stiinta, Cluj-Napoca, 2006, 460+9 pag., ISBN 973-686-959-8.
• [5] R. M. Ali, V. Ravichandran, N. Seenivasagan, Differential subordination and superordination of analytic functions de ned by the multiplier transformation, Math. Inequal. Appl., Vol:12, No.1 (2009), 123-139.
• [6] N. Seenivasagan, R. M. Ali, V. Ravichandran, On Bernardi's integral operator and the Briot Bouquet differential subordination, J. of Math. Anal. and Appl., Vol:324 (2006), 663-668. MR2262499 (2007e:30026) Zbl 1104.30013 (SCI).
• [7] H. Silverman, A survey with open problems on univalent functions whose coefficients are negative, Rocky Montain J. Math., Vol:21 (1991), 1099-1125.
Konular Mühendislik Articles Yazar: OLGA ENGELÜlke: Romania Yazar: ORSOLYA AGNES PALL-SZABOÜlke: Romania
Bibtex @araştırma makalesi { konuralpjournalmath344426, journal = {Konuralp Journal of Mathematics}, issn = {}, eissn = {2147-625X}, address = {Mehmet Zeki SARIKAYA}, year = {2017}, volume = {5}, pages = {207 - 215}, doi = {}, title = {PRESERVING PROPERTIES OF THE GENERALIZED BERNARDI-LIBERA-LIVINGSTON INTEGRAL OPERATOR DEFINED ON SOME SUBCLASSES OF STARLIKE FUNCTIONS}, key = {cite}, author = {AGNES PALL-SZABO, ORSOLYA and ENGEL, OLGA} } APA ENGEL, O , AGNES PALL-SZABO, O . (2017). PRESERVING PROPERTIES OF THE GENERALIZED BERNARDI-LIBERA-LIVINGSTON INTEGRAL OPERATOR DEFINED ON SOME SUBCLASSES OF STARLIKE FUNCTIONS. Konuralp Journal of Mathematics, 5 (2), 207-215. Retrieved from http://dergipark.gov.tr/konuralpjournalmath/issue/28490/344426 MLA ENGEL, O , AGNES PALL-SZABO, O . "PRESERVING PROPERTIES OF THE GENERALIZED BERNARDI-LIBERA-LIVINGSTON INTEGRAL OPERATOR DEFINED ON SOME SUBCLASSES OF STARLIKE FUNCTIONS". Konuralp Journal of Mathematics 5 (2017): 207-215 Chicago ENGEL, O , AGNES PALL-SZABO, O . "PRESERVING PROPERTIES OF THE GENERALIZED BERNARDI-LIBERA-LIVINGSTON INTEGRAL OPERATOR DEFINED ON SOME SUBCLASSES OF STARLIKE FUNCTIONS". Konuralp Journal of Mathematics 5 (2017): 207-215 RIS TY - JOUR T1 - PRESERVING PROPERTIES OF THE GENERALIZED BERNARDI-LIBERA-LIVINGSTON INTEGRAL OPERATOR DEFINED ON SOME SUBCLASSES OF STARLIKE FUNCTIONS AU - OLGA ENGEL , ORSOLYA AGNES PALL-SZABO Y1 - 2017 PY - 2017 N1 - DO - T2 - Konuralp Journal of Mathematics JF - Journal JO - JOR SP - 207 EP - 215 VL - 5 IS - 2 SN - -2147-625X M3 - UR - Y2 - 2017 ER - EndNote %0 Konuralp Journal of Mathematics PRESERVING PROPERTIES OF THE GENERALIZED BERNARDI-LIBERA-LIVINGSTON INTEGRAL OPERATOR DEFINED ON SOME SUBCLASSES OF STARLIKE FUNCTIONS %A OLGA ENGEL , ORSOLYA AGNES PALL-SZABO %T PRESERVING PROPERTIES OF THE GENERALIZED BERNARDI-LIBERA-LIVINGSTON INTEGRAL OPERATOR DEFINED ON SOME SUBCLASSES OF STARLIKE FUNCTIONS %D 2017 %J Konuralp Journal of Mathematics %P -2147-625X %V 5 %N 2 %R %U ISNAD ENGEL, OLGA , AGNES PALL-SZABO, ORSOLYA . "PRESERVING PROPERTIES OF THE GENERALIZED BERNARDI-LIBERA-LIVINGSTON INTEGRAL OPERATOR DEFINED ON SOME SUBCLASSES OF STARLIKE FUNCTIONS". Konuralp Journal of Mathematics 5 / 2 (Ekim 2017): 207-215. | 2018-12-16T09:14:36 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7190200686454773, "perplexity": 9842.118583387743}, "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-2018-51/segments/1544376827596.48/warc/CC-MAIN-20181216073608-20181216095608-00578.warc.gz"} |
http://dlmf.nist.gov/12.20 | # §12.20 Approximations
Luke (1969b, pp. 25 and 35) gives Chebyshev-series expansions for the confluent hypergeometric functions and 13.2(i)) whose regions of validity include intervals with endpoints and , respectively. As special cases of these results a Chebyshev-series expansion for valid when follows from (12.7.14), and Chebyshev-series expansions for and valid when follow from (12.4.1), (12.4.2), (12.7.12), and (12.7.13). Here denotes an arbitrary positive constant. | 2013-12-12T20:24:30 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9546329975128174, "perplexity": 3235.451560616502}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-48/segments/1386164701395/warc/CC-MAIN-20131204134501-00068-ip-10-33-133-15.ec2.internal.warc.gz"} |
http://pdglive.lbl.gov/DataBlock.action?node=M300K20 | # $\mathbf {{{\boldsymbol a}_{{3}}{(2030)}}}$ $\boldsymbol I\boldsymbol G(\boldsymbol J{}^{PC}) = 1{}^{-}(3{}^{++})$ INSPIRE search
MASS ${\mathrm {(MeV)}}$ WIDTH ${\mathrm {(MeV)}}$ DOCUMENT ID TECN COMMENT
$2031 \pm12$ $150 \pm18$ 1
2001 F
SPEC $1.96 - 2.41$ ${{\overline{\mathit p}}}{{\mathit p}}$
1 From the combined analysis of ANISOVICH 1999C, ANISOVICH 1999E, and ANISOVICH 2001F.
References:
ANISOVICH 2001F
PL B517 261 Partial Wave Analysis of ${{\overline{\mathit p}}}{{\mathit p}}$ Annihilation Channels in Flight with $\mathit I = 1,\mathit C$=+1
ANISOVICH 1999C
PL B452 173 ${{\overline{\mathit p}}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit \pi}^{0}}{{\mathit \eta}}$ and ${{\mathit \pi}^{0}}{{\mathit \eta}^{\,'}}$ from 600 to 1940 ${\mathrm {MeV}}/\mathit c$
ANISOVICH 1999E
PL B452 187 Resonances in ${{\overline{\mathit p}}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit f}_{{2}}{(1270)}}{{\mathit \pi}}$ | 2019-02-19T22:56:10 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.766255259513855, "perplexity": 12505.832315485304}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-09/segments/1550247493803.26/warc/CC-MAIN-20190219223509-20190220005509-00333.warc.gz"} |
http://gams.cam.nist.gov/9.19 | # §9.19 Approximations
## §9.19(i) Approximations in Terms of Elementary Functions
• Martín et al. (1992) provides two simple formulas for approximating to graphical accuracy, one for , the other for .
• Moshier (1989, §6.14) provides minimax rational approximations for calculating , , , . They are in terms of the variable , where when is positive, when is negative, and when . The approximations apply when , that is, when or . The precision in the coefficients is 21S.
## §9.19(ii) Expansions in Chebyshev Series
These expansions are for real arguments and are supplied in sets of four for each function, corresponding to intervals , , , . The constants and are chosen numerically, with a view to equalizing the effort required for summing the series.
• Prince (1975) covers , , , . The Chebyshev coefficients are given to 10-11D. Fortran programs are included. See also Razaz and Schonfelder (1981).
• Németh (1992, Chapter 8) covers , , , , and integrals , , , (see also (9.10.20) and (9.10.21)). The Chebyshev coefficients are given to 15D. Chebyshev coefficients are also given for expansions of the second and higher (real) zeros of , , , , again to 15D.
• Razaz and Schonfelder (1980) covers , , , . The Chebyshev coefficients are given to 30D.
## §9.19(iii) Approximations in the Complex Plane
• Corless et al. (1992) describe a method of approximation based on subdividing into a triangular mesh, with values of , stored at the nodes. and are then computed from Taylor-series expansions centered at one of the nearest nodes. The Taylor coefficients are generated by recursion, starting from the stored values of , at the node. Similarly for , .
## §9.19(iv) Scorer Functions
• MacLeod (1994) supplies Chebyshev-series expansions to cover for and for . The Chebyshev coefficients are given to 20D. | 2013-06-20T03:24:47 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9751002788543701, "perplexity": 1706.3697050766}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368710196013/warc/CC-MAIN-20130516131636-00084-ip-10-60-113-184.ec2.internal.warc.gz"} |
https://indico.fnal.gov/event/19348/contributions/186224/ | Indico search will be reestablished in the next version upgrade of the software: https://getindico.io/roadmap/
# Neutrino 2020
June 22, 2020 to July 2, 2020
US/Central timezone
## Modeling the collective motion of charge carriers in Ge semiconductor detectors
Not scheduled
10m
Poster
### Speaker
Mr Tommaso Comellato (Technical University of Munich)
### Description
In high purity germanium detectors, the signal evolution carries informations on the topology of the energy deposition. This feature is exploited in the search for neutrinoless double-beta decay of $^{76}$Ge to discriminate between single- (typical of sought-after signal) and multiple-energy depositions (typical of background events), in the GERDA, MJD and LEGEND experiments. In the effort to enlarge the detector dimensions, new geometries have been recently proposed, such as the inverted coaxial, in which the charge carriers’ drift paths are substantially longer than for the previous generation detectors. This lead to the observation of previously unnoticed effects on the signal evolution, due to the self-interactions of the carriers during the drift. Monte-Carlo simulations and pulse shape simulations have been used to test the impact of such effects on the discrimination capabilities for the next generation experiments with $^{76}$Ge.
### Mini-abstract
Collective motion of carriers impacts signal profile in germanium detectors
Experiment/Collaboration LEGEND
### Primary author
Mr Tommaso Comellato (Technical University of Munich)
### Co-authors
Dr Matteo Agostini (Technical University of Munich) Prof. Stefan Schönert (TU München) | 2021-12-05T11:35:01 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.36222198605537415, "perplexity": 6622.411270306467}, "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-2021-49/segments/1637964363157.32/warc/CC-MAIN-20211205100135-20211205130135-00533.warc.gz"} |
https://eforms.gov.mt/pdfforms.aspx?fid=wes072e | e-form
Notification of a Posted Worker to Malta
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https://googology.wikia.org/wiki/N_primitive | 11,052 Pages
N primitive (N原始 in Japanese, N PRIMITIV in German) is the generic name of difference sequence systems created by the Googology Wiki user Nayuta Ito. They are intended to surpass Bashicu matrix system version 2.3 with respect to koteitan's classification[1] and admit simple isomorphisms between the set of standard expressions below $$(0,1,3)$$ and the set of standard Bashicu matrices whose restriction to the subset of standard expressions below $$(0,1,2,4)$$ is the identity map onto the subset of standard primitive sequences.
Y sequence, Y function, S-σ, and SSAN are computable systems which arose in the same period as N primitive and are also expected to go beyond Bashicu matrix system, N primitive is the first example among them which has been formalised. (But it has not been verified yet under ZFC set theory that one version of N primitive terminates and actually goes beyond Bashicu matrix system.)
All functions defined by N primitive are intended to be computable and hence weaker than the busy beaver function.
## Terminology
N primitive is named after the creator Nayuta Ito, and the primitive sequence system. Although the behaviour of N primitive below $$(0,1,2,4)$$ is consistent due to the restriction on the relation to the primitive sequence system, the behaviour above $$(0,1,2,4)$$ varies depending on the version.
### Version Name
There are several versions of N primitive. Here is a name table of N primitive versions.[2]
Casual Name Another Casual Name Official Name Comment
N1.0
N1.1 DAS1.1 Am schnellsteren A variant of N1.0
N1.1½ DAS1.1½ Am schnellsterhalben A variant of N1.1
N1.1.π Am schnellsteren A Python-version of N1.1
N1.2½ DAS1.2½ Am schnellstererhalben A variant of N1.1½
N1.3½ A variant of N1.2½
N2.0 A variant of N1.0
N2.1 A variant of N1.1
N3.0 DAS3.0 Am schnellstestesten A variant of N2.1
N4.0 A variant of N3.0
Nω.0甲 A variant of N3.0
Nω.0乙 A variant of N3.0
Nω.1甲 A variant of Nω.0乙
Nω.1乙 A variant of Nω.0乙
NΩ.0 A cousin of Yn sequences
A version of N primitive is said to be dead if it does not work as intended, to be alive if it is not known to be dead, and to be canceled if it is planned to be created but has not been born due to some troubles. For example, N1.1 is supposed to be dead because it does not seem to admit a simple isomorphism between the set of standard expressions below $$(0,1,3)$$ and the set of standard Bashicu matrices. It does not mean that N1.1 is actually weaker than Bashicu matrix system version 2.3 or admits an infinite loop. Here is a table of the status of versions of N primitive.
Version Name Status
N1.3½ alive
NΩ.0 canceled
"Currently, 13½ N primitives were born, 26 of which are dead, and only 1 is alive. Besides, an N primitive was sunnied-side-up when it was still in an egg, but it is not counted because it has never been born at the first place. －Nayuta Ito"
### Japanese Letters
The original Japanese name "N原始" of N primitive is pronounced as "enu gen ʃi". Needless to say, the "原始" in "N原始" is named after the original Japanese name "原始数列" of primitive sequence system.
The letter "甲" (resp. "乙") means "first" (resp. "second"), and is pronounced as "kou/kɔ́r/kɔː" (resp. "ɔts"). Therefore Nω.0甲 (resp. Nω.0乙) roughly means "the first Nω.0" (resp. "the second Nω.0").
## Definition
The original definitions of N1.1, N1.1½, N1.2½, and N3.0 are open,[3] and the original source code of N1.1.π is also open.[4] Here, we explain the definition of N1.1, which is the easiest to understand among them.
### Convention
We denote by $$\textrm{FinSeq}$$ the set of finite sequences of natural numbers. Let $$a \in \textrm{FinSeq}$$. We denote by $$\textrm{Lng}(a) \in \mathbb{N}$$ the length of $$a$$. For an $$i \in \mathbb{N}$$ smaller than $$\textrm{Lng}(a)$$, we denote by $$a_i \in \mathbb{N}$$ the $$(1+i)$$-th entry of $$a$$.
The bad root searching rule for N1.1 in the sense of the terminology in the article of difference sequence system is the partial computable function \begin{eqnarray*} \textrm{Parent} \colon \textrm{FinSeq} \times \mathbb{N} & \to & \mathbb{N} \\ (a,i) & \mapsto & \textrm{Parent}(a,i) \end{eqnarray*} defined in the following recursive way:
1. Denote by $$L$$ the length of $$a$$.
2. If $$i \geq L$$, then $$\textrm{Parent}(a,i)$$ is not defined.
3. Suppose $$i < L$$.
1. Suppose that there exists a $$j \in \mathbb{N}$$ larger than $$i$$ such that $$\textrm{Parent}(a,j)$$ is defined and coincides with $$i$$.
1. Denote by $$k$$ the maximum of such a $$j$$.
2. If $$a_0 \geq 1$$ and $$a_k-1 \leq a_i < a_{L-1}$$, then put $$b := 1$$.
3. Otherwise, put $$b:= 0$$.
2. Otherwise, put $$b := 0$$.
3. Suppose $$b = 0$$.
1. If there exists an $$m \in \mathbb{N}$$ smaller than $$i$$ such that $$a_m < a_i$$, then $$\textrm{Parent}(a,i)$$ is the maximum of such an $$m$$.
2. Otherwise, $$\textrm{Parent}(a,i)$$ is not defined.
4. Suppose $$b = 1$$.
1. If there exists an $$m \in \mathbb{N}$$ smaller than $$i$$ such that $$a_m \leq a_i$$, then $$\textrm{Parent}(a,i)$$ is the maximum of such an $$m$$.
2. Otherwise, $$\textrm{Parent}(a,i)$$ is not defined.
By the definition, the restriction of $$\textrm{Parent}$$ to the direct product of the set of standard primitive sequences and $$\mathbb{N}$$ coincides with the bad root searching rule for primitive sequence system. The main difference from the bad root searching rule for primitive sequence system is that $$((1,1,2),1)$$ belongs to the domain of $$\textrm{Parent}$$. Actually, we have $$\textrm{Parent}((1,1,2),1) = 0$$.
### Difference Sequence
Since $$\textrm{Parent}$$ satisfies the axiom of a bad root searching rule in the sense of the terminology in the article for a difference sequence system, it induces the total computable maps \begin{eqnarray*} \begin{array}{lcrcl} \textrm{Ancestor} & \colon & \textrm{FinSeq} & \to & \textrm{FinSeq} \\ \textrm{RightNodes} & \colon & \textrm{FinSeq} & \to & \textrm{FinSeq} \\ \textrm{Kaiser} & \colon & \textrm{FinSeq} \setminus \{()\} & \to & \textrm{FinSeq} \\ \end{array} \end{eqnarray*} introduced in the same article. Roughly speaking, $$\textrm{Ancestor}(a)$$ is the sequence of indices of ancestors of the rightmost entry of $$a$$, $$\textrm{RightNodes}(a)$$ is the sequence of entries of ancestors of the rightmost entry of $$a$$, and $$\textrm{Kaiser}(a)$$ is the difference sequence of $$\textrm{RightNodes}(a)$$.
For an $$a \in \textrm{FinSeq} \setminus \{()\}$$, we put $$\textrm{Height}(a) := \max \{k \in \mathbb{N} \mid a \in \textrm{dom}(\textrm{Kaiser}^{k+1})\}$$, and denote by $$\textrm{Royal}(a)$$ the diagonal difference sequence of $$a$$ characterised by the following propeties:
1. $$\textrm{Lng}(\textrm{Royal}(a)) = \textrm{Height}(a)$$.
2. For any $$i \in \mathbb{N}$$ smaller than $$\textrm{Height}(a)$$, $$\textrm{Royal}(a)_i = \textrm{RightNodes}(\textrm{Kaiser}^i(a))_0$$.
Roughly Speaking, $$\textrm{Royal}(a)$$ is the sequence given as the left edge of the tower of the ancestor subsequences of difference sequences of $$a$$.
For example, when $$a = (0,1,4,13,20,30,44,64)$$, then $$\textrm{Royal}(a) = (0,1,2,1,0,1)$$. The tower of the difference sequences of $$a$$ is constructed in the following way: \begin{eqnarray*} \begin{array}{rcccccccccccccccccc} \textrm{RightNodes}(\textrm{Kaiser}^5(a)) & = & & & & & & & & & & ( & \color{red}{1} & ) & & & & & \\ \textrm{Kaiser}^5(a) & = & & & & & & & & & & ( & 1 & ) & & & & & \\ \textrm{RightNodes}(\textrm{Kaiser}^4(a)) & = & & & & & & & & & ( & \color{red}{0} & , & 1 & ) & & & & \\ \textrm{Kaiser}^4(a) & = & & & & & & & & & ( & 0 & , & 1 & ) & & & & \\ \textrm{RightNodes}(\textrm{Kaiser}^3(a)) & = & & & & & & & & ( & \color{red}{1} & , & 1 & , & 2 & ) & & & \\ \textrm{Kaiser}^3(a) & = & & & & & & & & ( & 1 & , & 1 & , & 2 & ) & & & \\ \textrm{RightNodes}(\textrm{Kaiser}^2(a)) & = & & & ( & \color{red}{2} & , & & & & & 3 & , & 4 & , & 6 & ) & & \\ \textrm{Kaiser}^2(a) & = & & & ( & 2 & , & & & 4 & , & 3 & , & 4 & , & 6 & ) & & \\ \textrm{RightNodes}(\textrm{Kaiser}(a)) & = & & ( & \color{red}{1} & , & 3 & , & & & 7 & , & 10 & , & 14 & , & 20 & ) & \\ \textrm{Kaiser}(a) & = & & ( & 1 & , & 3 & , & 9 & , & 7 & , & 10 & , & 14 & , & 20 & ) & \\ \textrm{RightNodes}(a) & = & ( & \color{red}{0} & , & 1 & , & 4 & , & 13 & , & 20 & , & 30 & , & 44 & , & 64 & ) \\ a & = & ( & 0 & , & 1 & , & 4 & , & 13 & , & 20 & , & 30 & , & 44 & , & 64 & ) \end{array} \end{eqnarray*} The occurence of $$0$$ in the difference sequences is a characteristic property of N primitive. It is possible because the bad root searching rule for N1.1 allows parents sharing the values of entries unlike other difference sequence systems.
We define a total computable map \begin{eqnarray*} \textrm{BadRoot} \colon \textrm{FinSeq} \setminus \{()\} & \to & \mathbb{N} \\ a & \mapsto & \textrm{BadRoot}(a) \end{eqnarray*} in the following recursive way:
1. Put $$b := \textrm{Kaiser}(a)$$
2. Put $$L_0 := \textrm{Lng}(a)$$
3. Put $$L_1 := \textrm{Lng}(b)$$
4. If $$L_1 = 0$$, then $$\textrm{BadRoot}(a) := L_0-1$$.
5. Suppose $$L_1 \neq 0$$.
1. Put $$r := \textrm{BadRoot}(b)$$.
2. If $$r = L_1-1$$, then $$\textrm{BadRoot}(a) := \textrm{Ancestor}(a)_r$$.
3. If $$r \neq L_1-1$$, then $$\textrm{BadRoot}(a) := \textrm{Ancestor}(a)_{r+1}$$.
As the name of the function indicates, $$\textrm{BadRoot}(a)$$ is the bad root of $$a$$ with respect to the bad root searching rule $$\textrm{Parent}$$. The initial segment of $$a$$ of length $$\textrm{BadRoot}(a)$$ will be regarded as the good part of $$a$$, and the rest final segment of $$a$$ will be regarded as the bad part of $$a$$ in the expansion rule.
For example, when $$a = (0,1,4,13,20,30,44,64)$$, then $$\textrm{BadRoot}(a) = 6$$. The bad root searching of $$a$$ is executed in the following way: \begin{eqnarray*} \begin{array}{rcccccccccccccccccc} \textrm{Kaiser}^5(a) & = & & & & & & & & & & ( & \color{red}{1} & ) & & & & & \\ \textrm{Kaiser}^4(a) & = & & & & & & & & & ( & \color{red}{0} & , & 1 & ) & & & & \\ \textrm{Kaiser}^3(a) & = & & & & & & & & ( & 1 & , & \color{red}{1} & , & 2 & ) & & & \\ \textrm{Kaiser}^2(a) & = & & & ( & 2 & , & & & 4 & , & 3 & , & \color{red}{4} & , & 6 & ) & & \\ \textrm{Kaiser}(a) & = & & ( & 1 & , & 3 & , & 9 & , & 7 & , & 10 & , & \color{red}{14} & , & 20 & ) & \\ a & = & ( & 0 & , & 1 & , & 4 & , & 13 & , & 20 & , & 30 & , & \color{red}{44} & , & 64 & ) \\ & \rightsquigarrow & & 0 & & 1 & & 2 & & 3 & & 4 & & 5 & & \color{red}{6} & & 7 & \end{array} \end{eqnarray*} Namely, mark the rightmost entry of the highest difference sequence. Then shift to the left downward. After then, repeat to shift right downward. The good part of $$a$$ is $$(0,1,4,13,20,30)$$, and the bad part of $$a$$ is $$(44,64)$$.
### Reconstruction
We define a total computable map \begin{eqnarray*} \textrm{Reconstruct} \colon (\textrm{FinSeq} \setminus \{()\})^2 & \to & \textrm{FinSeq} \\ (d,a) & \mapsto & \textrm{Reconstruct}(d,a) \end{eqnarray*} in the following recursive way:
1. Put $$r := \textrm{BadRoot}(a)$$.
2. Denote by $$b$$ the sequence given by removing the first $$r$$ entries from $$a$$.
3. Put $$L_0 := \textrm{Lng}(d)$$.
4. Put $$L_1 := \textrm{Lng}(\textrm{Ancestor}(b))$$.
5. Suppose $$L_1 \leq 1$$.
1. For each $$(i,j) \in \mathbb{N} \times \mathbb{N}$$ satisfying $$i+j <L_0$$, define a $$c_{i,j} \in \mathbb{N}$$ in the following recursive way:
1. If $$j = 0$$, then $$c_{i,j} := d_j$$.
2. If $$j \neq 0$$, then $$c_{i,j} := c_{i,j-1}+c_{i+1,j-1}$$.
2. Set $$\textrm{Reconstruct}(d,a) := (c_{0,j})_{j=0}^{L_0-1}$$.
6. Suppose $$L_1 > 1$$.
1. Put $$q := \max \{k \in \mathbb{N} \mid k(L_1-1)+1 \leq L_0\}$$.
2. Put $$L_2 := \textrm{Lng}(b)$$.
3. For each $$i \in \mathbb{N}$$ smaller than $$(q-1)(L_2-1)$$, we define a $$c_i \in \mathbb{N}$$ in the following recursive way:
1. Put $$q' := \max \{k \in \mathbb{N} \mid k(L_2-1) \leq i\}$$.
2. Put $$i' := i-q'(L_2-1)$$.
3. If $$q' = 0$$, then $$c_i := a_{r+i}$$.
4. Suppose that $$q' \neq 0$$ and $$i'$$ is an entry of $$\textrm{Ancestor}(b)$$.
1. Denote by $$j' \in \mathbb{N}$$ the unique number smaller than $$L_1$$ satisfying $$i' = \textrm{Ancestor}(b)_{j'}$$.
2. If $$j' = 0$$, put $$p := (q'-1)(L_2-1) + \textrm{Ancestor}(b)_{L_1-2}$$.
3. If $$j' \neq 0$$, put $$p := q'(L_2-1) + \textrm{Ancestor}(b)_{j'-1}$$.
4. Set $$c_i := c_p + d_{q'(L_1-1)+j'}$$.
5. Suppose that $$q' \neq 0$$ and $$i'$$ is not an entry of $$\textrm{Ancestor}(b)$$.
1. Put $$j' := \max \{k \in \mathbb{N} \mid k < L_1 \land \textrm{Ancestor}(b)_k < i'\}$$.
2. Put $$p := q'(L_2-1) + \textrm{Ancestor}(b)_{j'}$$
3. Set$$c_i := c_p + (c_{i-(L_2-1)} - c_{p-(L_2-1)}) + (d_{q'(L_1-1)+j'+1}- d_{(q'-1)(L_1-1)+j'+1})$$.
4. Set $$\textrm{Reconstruct}(d,a) := (c_i)_{i=0}^{(q-1)(L_2-1)-1}$$.
Roughly speaking, $$\textrm{Reconstruct}(d,a)$$ is a sequence such that the difference sequence of a suitable subsequence related to $$\textrm{Ancestor}(b)$$ is given by $$d$$.
For example, when $$d = (19,25,32,40,49)$$ and $$a = (0,1,4,13,20,30,44,64)$$, then $$\textrm{Reconstruct}(a,d) = (44,63,88,120,160)$$. The reconstruction is executed in the following way: \begin{eqnarray*} \begin{array}{rccccccccccccccccc} d & = & & & & & & ( & 19 & , & 25 & , & 32 & , & 40 & , & 49 & ) \\ a & = & ( & 0 & , & \ldots & , & \color{red}{44} & , & 64 & ) & & & & & & & \\ & \rightsquigarrow & & & & & ( & \color{red}{44} & , & 63 & , & 88 & , & 120 & , & 160 & ) & \end{array} \end{eqnarray*} Here, we do not have a non-trivial offset, i.e. an entry between the bad root and the right most entry which is not an ancestor of the rightmost entry, and hence the reconstructed sequence is simply given by adding the entries of $$d$$. Although the rightmost entry of $$d$$ is not used in this case, it can be actually used in the computation of offsets. The reconstruction process of an entry which is not a copy of an ancestor of the rightmost entry using the difference of entries above adjacent ancestors of the rightmost entry placed at distinct sides from the reconstructed entry, is a distinguishing feature of N1.1 and N1.1½, and is not employed in N1.2½.
### Expansion
We define a partial computable map \begin{eqnarray*} [ \ ] \colon \textrm{FinSeq} \times \mathbb{N} & \to & \textrm{FinSeq} \\ (a,n) & \mapsto & a[n] \end{eqnarray*} in the following recursive way:
1. If $$a = ()$$, then $$a[n] := ()$$.
2. If $$a \neq ()$$ and $$\textrm{Kaiser}(a) = ()$$, then $$a[n]$$ is the sequence given by removing the rightmost entry from $$a$$.
3. If $$a = (0,1)$$, then $$a[n]$$ is the sequence of length $$n+1$$ whose entries are $$0$$.
4. Suppose $$a \neq ()$$, $$\textrm{Kaiser}(a) \neq ()$$, and $$a \neq (0,1)$$.
1. Put $$H := \textrm{Height}(a)$$.
2. Denote by $$d \in \textrm{FinSeq} \setminus \{()\}$$ the sequence given by removing the first $$H-1$$ entries from $$\textrm{Royal}(a)[n+H-1]$$.
3. For each $$i \in \mathbb{N}$$ smaller than $$H$$, define a $$C_i \in \textrm{FinSeq}$$ in the following recursive way:
1. If $$i = H-1$$, then $$C_i := \textrm{Reconstruct}(d,\textrm{Kaiser}^{H-1}(a))$$.
2. If $$i \neq H-1$$, then $$C_i := \textrm{Reconstruct}(C_{i+1},\textrm{Kaiser}^i(a))$$.
4. Put $$r := \textrm{BadRoot}(a)$$.
5. Denote by $$g \in \textrm{FinSeq}$$ the initial segment of $$a$$ of length $$r$$.
6. Denote by $$b \in \textrm{FinSeq}$$ the sequence given by removing the first $$r$$ entries from $$a$$.
7. Denote by $$b^{(n)} \in \textrm{FinSeq} \setminus \{()\}$$ the initial segment of $$C_0$$ of length $$n(\textrm{Lng}(b)-1)$$.
8. Set $$a[n] := g \frown b^{(n)}$$.
Since $$[ \ ]$$ recursively call $$[ \ ]$$ itself, it is not trivial that $$((0,1,k),n) \in \textrm{dom}([ \ ])$$ for any $$(k,n) \in \mathbb{N}^2$$. Actually, we have $$((0,1,k),n) \in \textrm{dom}([ \ ])$$ and \begin{eqnarray*} (0,1,k)[n] = \left\{ \begin{array}{ll} (0,1) & (k = 0) \\ (\underbrace{0,1,0,1,\ldots,0,1}_{n+1}) & (k = 1) \\ (0,1,(k-1),(k-1)^2,\ldots,(k-1)^n) & (k > 1) \end{array} \right. \end{eqnarray*} for any $$(n,m) \in \mathbb{N}^2$$ by induction on $$n$$. We will show totality of the restriction of $$[ \ ]$$ to a certain subset later.
For example, when $$a = (0,1,4,13,20,30,44,64)$$ and $$n = 4$$, then $$a[n] = (0,1,4,13,20,30,44,63,88,120,160)$$. The expansion of $$a$$ is executed in the following way: \begin{eqnarray*} \begin{array}{rccccccccccccccccccccc} C_5 & = & & ( & \color{red}{0} & , & 0 & , & 0 & , & 0 & , & 0 & , & 0 & , & 0 & , & 0 & , & 0 & ) \\ C_4 & = & ( & \color{red}{0} & , & 0 & , & 0 & , & 0 & , & 0 & , & 0 & , & 0 & , & 0 & , & 0 & ) & \\ C_3 & = & & ( & \color{red}{1} & , & 1 & , & 1 & , & 1 & , & 1 & , & 1 & , & 1 & , & 1 & ) & & \\ C_2 & = & & & ( & \color{red}{4} & , & 5 & , & 6 & , & 7 & , & 8 & , & 9 & , & 10 & ) & & & \\ C_1 & = & & & & ( & \color{red}{14} & , & 19 & , & 25 & , & 32 & , & 40 & , & 49 & ) & & & & \\ C_0 & = & & & & & ( & \color{red}{44} & , & 63 & , & 88 & , & 120 & , & 160 & ) & & & & & \\ a & = & ( & 0 & , & \ldots & , & \color{red}{44} & , & 64 & ) & & & & & & & & & & & \\ & \rightsquigarrow & ( & 0 & , & \ldots & , & \color{red}{44} & , & 63 & , & 88 & , & 120 & , & 160 & ) & & & & & \end{array} \end{eqnarray*} Namely, expand the diagonal sequence given by $$\textrm{Royal}(a)$$, replace the highest difference sequence by the sequence reconstructed by the expanded diagonal sequence, and repeat the reconstruction step for each difference sequences.
### Standard Form
We define a partial computable map \begin{eqnarray*} \textrm{Expand} \colon \textrm{FinSeq} \times \textrm{FinSeq} & \to & \textrm{FinSeq} \\ (a,n) & \mapsto & \textrm{Expand}(a,n) \end{eqnarray*} in the following recursive way:
1. Put $$L := \textrm{Lng}(n)$$.
2. If $$L = 0$$, then $$\textrm{Expand}(a,n) := a$$.
3. Suppose $$L \neq 0$$.
1. Denote by $$n'$$ the initial segment of $$n$$ of length $$L-1$$.
2. Set $$\textrm{Expand}(a,n) := \textrm{Expand}(a,n')[n_{L-1}]$$.
Namely, $$\textrm{Expand}(a,n)$$ is just the formalisation of the iterated expansion $$a[n_0] \cdots [n_{L-1}]$$.
We denote by $$<_{\textrm{lex}}$$ the lexicographic ordering on $$\textrm{FinSeq}$$. By the structural induction with respect to $$[ \ ]$$, we obtain the following:
Proposition (order-lowering property)
For any $$(a,n) \in \textrm{dom}(\textrm{Expand})$$, if $$a \neq ()$$ and $$n \neq ()$$, then $$\textrm{Expand}(a,n) <_{\textrm{lex}} a$$.
By the order-lowering property, there is no simple infinite loop in expansions, i.e. there exists no $$(a,n) \in \textrm{dom}(\textrm{Expand})$$ such that $$a \neq ()$$, $$n \neq ()$$, and $$\textrm{Expand}(a,n) = a$$. It implies that if there is an infinite loop in expansions, then it is so complicated that we need a non-trivial argument in order to show that it is actually an infinite loop.
For an $$a \in \textrm{FinSeq}$$, We denote by $$I_a \subset \textrm{FinSeq}$$ the recursively enumerable subset $$\{\textrm{Expand}(a,n) \mid n \in \textrm{FinSeq} \setminus \{()\} \land (a,n) \in \textrm{dom}(\textrm{Expand})\}$$.
We put $$OT := \bigcup_{k \in \mathbb{N}} I_{(0,1,k)}$$, and call an element of $$OT$$ a standard N primitive sequence. Since we have $$\textrm{Expand}((0,1,1),(1,0)) = (0,1,0)$$ and $$\textrm{Expand}((0,1,2),(1)) = (0,1,1)$$, $$(0,1,k)$$ is a standard N primitive sequence for any $$k \in \mathbb{N}$$ by induction on $$k$$.
By the definition, $$\textrm{Royal}$$ does not increase the length. Since the lexicographic order restricted to the subset of sequence of length bounded by a fixed upperbound is well-founded and $$OT$$ is closed under $$\textrm{Expand}$$, we obtain the following corollary of the order-lowering property:
Corollary (totality of the restriction of $$[ \ ]$$)
The set $$OT \times \mathbb{N}$$ (resp. $$OT \times \textrm{FinSeq}$$) is contained in $$\textrm{dom}([ \ ])$$ (resp. $$\textrm{dom}(\textrm{Expand})$$).
### Recursiveness
We show the recursiveness of $$OT$$ in a way analogous to the proof by the Googology Wiki user fish of the recursiveness of the subset of standard Bashicu matrices with respect to Bashicu matrix system version 2.3.
We denote by $$\textrm{FinSeq}^{< \omega}$$ the set of finite arrays in $$\textrm{FinSeq}$$. We define a partial recursive map \begin{eqnarray*} \textrm{ApproximateSequence} \colon \textrm{FinSeq} \times \textrm{FinSeq} & \to & \textrm{FinSeq}^{< \omega} \setminus \{()\} \\ (a,b) & \mapsto & \textrm{ApproximateSequence}(a,b) \end{eqnarray*} in the following recursive way:
1. Put $$L_1 := \textrm{Lng}(a)$$.
2. Put $$c := b[L_1]$$.
3. If $$a$$ is an initial segment of $$c$$, then $$\textrm{ApproximateSequence}(a,b) := (b,a)$$.
4. If $$c <_{\textrm{lex}} a$$, then $$\textrm{ApproximateSequence}(a,b) := (b)$$.
5. Suppose that $$a$$ is not an initial segment of $$c$$ and $$a <_{\textrm{lex}} c$$.
1. Put $$L_2 := \textrm{Lng}(c)$$.
2. Denote by $$i \in \mathbb{N}$$ the least natural number satisfying $$i < \min \{L_1,L_2\}$$ and $$a_i < c_i$$.
3. Denote by $$d \in \textrm{FinSeq}$$ the initial segment of $$c$$ of length $$i+1$$.
4. Set $$\textrm{ApproximateSequence}(a,b) := (b) \frown \textrm{ApproximateSequence}(a,d)$$.
Suppose $$b \in OT$$. Then $$c$$ is defined by the totality of the restriction of $$[ \ ]$$, and is standard by the definition. Moreover, since $$[0]$$ is the operation removing the rightmost entry as long as the input is a standard N primitive sequence other than $$(0)$$, $$d$$ is derived by the repetition of $$[0]$$ to $$c$$. Therefore $$d$$ is also standard. In particular, by order-lowering property and the well-foundedness of $$<_{\textrm{lex}}$$ restricted to $$\textrm{N}^{L_1}$$, the computation of $$\textrm{ApproximateSequence}(a,b)$$ terminates, and its output is an array whose entries are standard except for the rightmost entry.
We define a total recursive map \begin{eqnarray*} \textrm{IsStandard} \colon \textrm{FinSeq} \setminus \{()\} & \to & \{0,1\} \\ a & \mapsto & \textrm{IsStandard}(a) \end{eqnarray*} in the following recursive way:
1. Put $$L := \textrm{Lng}(a)$$.
2. If $$L = 1$$ and $$a_0 = 0$$, then $$\textrm{IsStandard}(a) := 1$$.
3. Suppose $$L \geq 2$$, $$a_0 = 0$$, and $$a_1 = 0$$.
1. If every entry of $$a$$ is $$0$$, then , then $$\textrm{IsStandard}(a) := 1$$.
2. If $$a$$ has a non-zero entry, then , then $$\textrm{IsStandard}(a) := 0$$.
4. If $$2 \leq L \leq 3$$, $$a_0 = 0$$, and $$a_1 = 1$$, then $$\textrm{IsStandard}(a) := 1$$.
5. If $$L \geq 2$$, $$a_0 = 0$$, and $$a_1 > 1$$, then $$\textrm{IsStandard}(a) := 0$$.
6. Suppose $$L \geq 4$$, $$a_0 = 0$$, and $$a_1 = 1$$.
1. Denote by $$b \in \textrm{FinSeq}$$ the rightmost entry of $$\textrm{ApproximateSequence}(a,(0,1,a_2+1))$$.
2. If $$a = b$$, then $$\textrm{IsStandard}(a) := 1$$.
3. If $$a \neq b$$, then $$\textrm{IsStandard}(a) := 0$$.
7. If $$a_0 \neq 0$$, then $$\textrm{IsStandard}(a) := 0$$.
This is an analogue of the algorithm by the Googology Wiki user rpakr to determine the standardness of a Bashicu matrix. By the argument above, $$\textrm{IsStandard}$$ is actually a total map because $$(0,1,a_2+1)$$ in clause 6-1 in the definition of $$\textrm{IsStandard}$$ is standard. The equality $$a = b$$ in the clause 6-2 in the definition of $$\textrm{IsStandard}$$ implies that the computation of $$\textrm{ApproximateSequence}(a,(0,1,a_2+1))$$ terminates in the clause 3 in the definition of $$\textrm{ApproximateSequence}$$, and hence $$a$$ is an initial segment of a standard N primitive sequence, which is standard by the argument on $$[0]$$ above.
The inequality $$a \neq b$$ in the clause 6-3 in the definition of $$\textrm{IsStandard}$$ implies that the computation of $$\textrm{ApproximateSequence}(a,(0,1,a_2+1))$$ terminates in the clause 4 in the definition of $$\textrm{ApproximateSequence}$$. In this case, the rightmost entry $$b$$ of $$\textrm{ApproximateSequence}(a,(0,1,a_2+1))$$ satisfies $$a <_{\textrm{lex}} b$$ and $$b[n] <_{\textrm{lex}} a$$ for any $$n \in \mathbb{N}$$. We show that $$a$$ is not standard by reduction to the absurd.
Assume that $$a$$ is standard. Then there exists an $$(k,n) \in \mathbb{N} \times (\textrm{FinSeq} \setminus \{()\})$$ such that $$\textrm{Expand}((0,1,k),n) = a$$. Put $$L_1:= \textrm{Lng}(n)+1$$ and $$L_2 := \textrm{Lng}(\textrm{ApproximateSequence}(a,(0,1,a_2+1)))$$. For each $$i \in \mathbb{N}$$ smaller than $$L_1$$, we denote by $$m_i \in OT$$ the initial segment of $$n$$ of length $$i$$. By $$(0,1,a_2) <_{\textrm{lex}} (0,1,k)$$ and the definition of $$[ \ ]$$, there exists an $$i_0 \in \mathbb{N}$$ smaller than $$L_1$$ such that $$\textrm{Expand}((0,1,k),m_{i_0}) = (0,1,a_2+1)$$. For any $$j \in \mathbb{N}$$ smaller than $$L_2$$, if $$\textrm{ApproximateSequence}(a,(0,1,a_2+1))_j$$ is an entry of $$(\textrm{Expand}((0,1,k),m_i))_{i=0}^{L_1-1}$$, then so is $$\textrm{ApproximateSequence}(a,(0,1,a_2+1))_{j+1}$$ by the definition of $$\textrm{ApproximateSequence}$$ and $$[ \ ]$$. Therefore by induction on $$j$$, $$\textrm{ApproximateSequence}(a,(0,1,a_2+1))$$ forms a subsequence of $$(\textrm{Expand}((0,1,k),m_i))_{i=0}^{L_1-1}$$. It implies $$b = \textrm{Expand}((0,1,k),m_i)$$ for some $$i \in \mathbb{N}$$ smaller than $$L_1-1$$, and hence $$b[n_i] = a$$. This contradicts $$b[n_i] <_{\textrm{lex}} a$$. Thus $$a$$ is not standard.
As a consequence, we obtain the following:
Proposition (recursiveness of $$OT$$)
The characteristic function of $$OT \subset \textrm{FinSeq} \setminus \{()\}$$ coincides with the total recurisve function $$\textrm{IsStandard}$$, and hence $$OT$$ is a recursive subset of $$\textrm{FinSeq}$$.
### Well-Foundedness
We define the binary relation $$a < b$$ on $$(a,b) \in \textrm{FinSeq}^2$$ as the existence of an $$n \in \textrm{FinSeq}$$ such that $$b \neq ()$$, $$n \neq ()$$, $$(b,n) \in \textrm{dom}(\textrm{Expand})$$, and $$a = \textrm{Expand}(b,n)$$. The well-foundedness of the system $$(OT,<)$$ is open.
In order to argue the termination and the strength of the resulting computable large function which will be introduced later, we prepare a conjecture.
Conjecture (Axiom $$\textrm{WFN1.1}$$)
The restriction of $$<$$ on $$OT$$ is a strict well-ordering.
Of course, if we find an infinite loop in expansions of standard N primitive sequences, then $$\textrm{WFN1.1}$$ is disproved. Although we do not know whether $$\textrm{WFN1.1}$$ is consistent with $$\textrm{ZFC}$$ or not, we sometimes explicitly assume it.
By the order-lowering property, we immediately obtain the following:
Proposition (well-foundedness of N1.1)
Assume $$\textrm{WFN1.1}$$. Let $$a \in OT$$. For any infinite sequence $$n$$ of natural numbers, there exists a finite initial segment $$n'$$ of $$n$$ such that $$\textrm{Expand}(a,n') = ()$$.
### Ordinal Notation
Since $$\textrm{WFN1.1}$$ implies that the restriction of $$<$$ is a strict total ordering, we obtain the following corollary of the order-lowering property:
Corollary (comparison of $$<$$ and $$<_{\textrm{lex}}$$)
Assume $$\textrm{WFN1.1}$$. Then the restriction of $$<$$ on $$OT$$ coincides with the restriction of $$<_{\textrm{lex}}$$ on $$OT$$.
Since $$<_{\textrm{lex}}$$ is recursive, the recursiveness of $$OT$$ implies the following corollary of the comparison of $$<$$ and $$<_{\textrm{lex}}$$:
Corollary (recursive well-foundedness of $$(OT,<)$$)
Assume $$\textrm{WFN1.1}$$. Then $$(OT,<)$$ forms an ordinal notation.
For an $$a \in \textrm{FinSeq}$$, if $$(I_a,<)$$ is a well-ordered set, we denote by $$o(a) \in \omega_1$$ its ordinal type. By the recursive well-foundedness of $$(OT,<)$$, $$o(a)$$ is defined and is a recursive ordinal for any $$a \in OT$$ under the assumption of $$\textrm{WFN1.1}$$.
### Large Function
We define a partial computable map \begin{eqnarray*} F \colon \mathbb{N} \times \textrm{FinSeq} \times \mathbb{N} & \to & \mathbb{N} \\ (m,a,n) & \mapsto & F^m[a](n) \end{eqnarray*} in the following recursive way:
1. If $$m = 0$$, then $$F^m[a](n) := n$$.
2. Suppose $$m = 1$$.
1. If $$a = ()$$, then $$F^m[a](n) := n+1$$.
2. If $$a \neq ()$$ and $$\textrm{Kaiser}(a) = ()$$, then $$F^m[a](n) := F^n[a[0]](n)$$.
3. If $$a \neq ()$$ and $$\textrm{Kaiser}(a) \neq ()$$, then $$F^m[a](n) := F^1[a[n]](n)$$.
3. If $$m > 1$$, then $$F^m[a](n) := F^{m-1}[a](F^1[a](n))$$.
We define a partial computable map \begin{eqnarray*} N \colon \textrm{FinSeq} \times \mathbb{N} & \to & \mathbb{N} \\ (a,n) & \mapsto & N(a,n) \end{eqnarray*} by setting $$N(a,n) = F^1[a](n)$$. Since this construction is essentially equivalent to fast-growing hierarchy, $$N(a,n)$$ coincides with $$f_{o(a)}(n)$$ with respect to a suitable system of fundamental sequences as long as $$o(a)$$ is defined. By the well-foundedness of N1.1 and the recursive well-foundedness of $$(OT,<)$$, we obtain the following:
Theorem (termination of N)
Assume $$\textrm{WFN1.1}$$. Then $$\textrm{dom}(N)$$ contains $$OT \times \mathbb{N}$$, and the assignment $$n \mapsto N((0,1,n),n)$$ gives a total computable map $$\mathbb{N} \to \mathbb{N}$$, which coincides with $$f_{\alpha}(n)$$, where $$\alpha \in \omega_1^{\textrm{CK}}$$ is the ordinal type of $$(OT,<)$$ equipped with a suitable recursive system of fundamental sequences.
Of course, the assumption of $$\textrm{WFN1.1}$$ is essential in the proof of the termination of N. In particular, the totality of the restriction of $$N$$ to $$OT \times \mathbb{N}$$ in $$\textrm{ZFC}$$ set theory is open.
## Large Number
Nayuta Ito coined 7 large numbers based on a naming system using N primitive. Since the naming system is given by a complicated rule referring to Chinese letters, we only show the results of the nameing for those specific 7 numbers.
name definition
６ (or 全角の6) the maximum of $$6$$ and $$F^1[a](6)$$ with respect to N3.0, where $$a$$ runs through all sequences satisfying that $$(1,a,6) \in \textrm{dom}(F)$$, $$\textrm{Lng}(a) \leq 6$$, and the sum of entries of $$a$$ is smaller than or equal to $$6 \times 6$$
Since the definition of ６ directly refers to $$\textrm{dom}(F)$$, we do not have an evidence of its computability. At least, since ６ is the maximum of a finite set of natural numbers including at least one element, i.e. 6, it is well-defined. In addition, if N3.0 is verified to terminate for any standard N primitive sequence with respect to N3.0 below $$(0,1,35)$$, then it is actually computable and is expected to be much larger than Bashicu matrix number with respect to Bashicu matrix system version 2.3, because the standard N primitive sequence $$(0,1,3)$$ with respect to N3.0 is expected to correspond to its limit.
### Lower bound
It is proven that ６ > $$10^{12}$$. [3] In particular, taking the maximum with $$6$$ in the definition of ６ is in fact unnecessary.
### Upper bound
Since the $$3$$-ary relation $$(m,a,n) \in \textrm{dom}(F)$$ is computable by the halting problem $$\textrm{Halt}$$ of Turing machines, ６ is computable by an oracle Turing machine. Therefore ６ is bounded by a specific value of the second order busy beaver function $$\Sigma_2$$ whose input is a meta natural number. Namely, it is expected to be roughly bounded by $$\Sigma_2(10^{100})$$.
In addition, if N3.0 is verified to terminate for any standard N primitive sequence with respect to N3.0 below $$(0,1,35)$$, then ６ is computable by the argument above, and hence it is expected to be bounded by $$\Sigma(10^{100})$$, where $$\Sigma$$ is the busy beaver function.
### Japanese Letters
The letter "第" means "the -th" for the ordinal numerals, and is pronounced as "dαɪ". The letter "一" (resp. "二", "三", "四") means "one" (resp. "two", "three", "four"), and is pronounced as "itʃ" (resp. "ni", "sʌn/sən/sαn", "jɔn"). The word "宇宙" means "universe", and is pronounced as "u tʃreuː". The word "破壊" means "destruction", and is pronounced as "hʌ/hə/hα kʌi/kəi/kαi". The word "数" means "number", and is pronounced as "suː" (or "kʌz/kəz/kαz" depending on the situation). The letter "改" means "updated/renewed/revised", and is pronounced as "kʌi/kəi/kαi". Therefore "第二宇宙破壊数改三改三" roughly means "the third revision of the third revision of the second universe destruction number", and "第四宇宙破壊数" roughly means "the fourth universe destruction number"
The letter "６" means "six", and is pronounced as "rɔk/lɔk". The word "全角の" means "two-byte", and is pronounced as "zen/zεn kʌk/kək/kαk nɔ". Therefore "全角の6" roughly means "two-byte letter corresponding to 6".
## Example
Although N1.1 is relatively easy to handle compared to other versions including ½ in the names, the computation rules of expansions of standard N primitive sequences are still complicated. In order to grasp the behaviour, we need to observe explicit computations and results of sufficiently generic expansions.
### Demonstration of Computation
We show computation steps of $$(0,1,4,13,20,30,44,64)[4]$$ with respect to N1.1. As we have already computed, we have $$\textrm{Height}((0,1,4,13,20,30,44,64)) = 6$$, $$\textrm{Royal}((0,1,4,13,20,30,44,64)) = (0,1,2,1,0,1)$$, and $$\textrm{BadRoot}((0,1,4,13,20,30,44,64)) = 6$$. Since the computation of $$(0,1,4,13,20,30,44,64)[4]$$ calls $$\textrm{Royal}((0,1,4,13,20,30,44,64))[4+\textrm{Height}((0,1,4,13,20,30,44,64))]$$, we need to compute $$(0,1,2,1,0,1)[10]$$.
Exhibit the tower of difference sequences of $$(0,1,2,1,0,1)$$. \begin{eqnarray*} \begin{array}{rccccccccccccc} \textrm{RightNodes}(\textrm{Kaiser}(a)) & = & & & & & & & & & & ( & \color{red}{1} & ) & \\ \textrm{Kaiser}(a) & = & & & & & & & & & & ( & 1 & ) & \\ \textrm{RightNodes}(a) & = & & & & & & & & & ( & \color{red}{0} & , & 1 & ) \\ a & = & ( & 0 & , & 1 & , & 2 & , & 1 & , & 0 & , & 1 & ) \end{array} \end{eqnarray*} We obtain $$\textrm{Height}((0,1,2,1,0,1)) = 2$$ and $$\textrm{Royal}((0,1,2,1,0,1)) = (0,1)$$. Since the computation of $$(0,1,2,1,0,1)[10]$$ calls $$\textrm{Royal}((0,1,2,1,0,1))[10+\textrm{Height}((0,1,2,1,0,1))]$$, we need to compute $$(0,1)[12]$$.
Exhibit the tower of the difference sequences of $$(0,1)$$. \begin{eqnarray*} \begin{array}{rcccccc} \textrm{RightNodes}(\textrm{Kaiser}(a)) & = & & ( & \color{red}{1} & ) & \\ \textrm{Kaiser}(a) & = & & ( & 1 & ) & \\ \textrm{RightNodes}(a) & = & ( & \color{red}{0} & , & 1 & ) \\ a & = & ( & 0 & , & 1 & ) \end{array} \end{eqnarray*} We obtain $$\textrm{Height}((0,1)) = 2$$ and $$\textrm{Royal}((0,1)) = (0,1)$$. Since the computation of $$(0,1)[12]$$ calls $$\textrm{Royal}((0,1))[12+\textrm{Height}((0,1))]$$, we need to compute $$(0,1)[14]$$... Wait! Is it an infinite loop? No, no. Please remember that $$(0,1)$$ is the exception in the computation rule of the expansion. Namely, $$(0,1)[12]$$ is directly defined as $$(0,0,0,0,0,0,0,0,0,0,0,0,0)$$.
Next, we need to calculate $$\textrm{BadRoot}((0,1))$$. Although the computation of $$\textrm{BadRoot}((0,1,4,13,20,30,44,64))$$ above includes the computation of $$\textrm{BadRoot}((0,1))$$, we show its computation process in order to help readers to understand bad roots better. For this purpose, we need to compute $$\textrm{BadRoot}(\textrm{Kaiser}((0,1)))$$. As we computed above, we have $$(\textrm{Kaiser}((0,1)) = 1$$, and hence $$\textrm{BadRoot}(\textrm{Kaiser}((0,1))) = \textrm{BadRoot}((1))$$. By the definition of $$\textrm{Kaiser}$$, we have $$\textrm{Kaiser}((1)) = ()$$ and hence $$\textrm{BadRoot}((1)) = \textrm{Lng}((1))-1 = 1-1 = 0$$.
Again exhibit the tower of the difference sequences of $$(0,1)$$. \begin{eqnarray*} \begin{array}{rcccccc} \textrm{Kaiser}(a) & = & & ( & \color{red}{1} & ) & \\ a & = & ( & \color{red}{0} & , & 1 & ) \\ & \rightsquigarrow & & \color{red}{0} & & 1 & \end{array} \end{eqnarray*} Therefore we obtain $$\textrm{BadRoot}(\textrm{Kaiser}((0,1))) = 0$$.
Reconstruct $$(0,1,2,1,0,1)[10]$$ from the diagonal $$(0,0,0,0,0,0,0,0,0,0,0,0,0)$$. \begin{eqnarray*} \begin{array}{rcccccccccccccccccc} & & & & & & & & & & & & & & ( & \vdots & \vdots & \vdots & ) & & & \\ & & & & & & & & & & & & & ( & 0 & , & \ldots & , & 0 & ) & & \\ & & & & & & & & & & & & ( & 0 & , & 0 & , & \ldots & , & 0 & ) & \\ C_1 & = & & & & & & & & & & ( & \color{red}{0} & , & 0 & , & \ldots & , & 0 & , & 0 & ) \\ C_0 & = & ( & 0 & , & 1 & , & 2 & , & 1 & , & \color{red}{0} & , & 0 & , & 0 & , & \ldots & , & 0 & ) & \\ a & = & ( & 0 & , & 1 & , & 2 & , & 1 & , & \color{red}{0} & , & 1 & ) \\ & \rightsquigarrow & ( & 0 & , & 1 & , & 2 & , & 1 & , & \color{red}{0} & , & 0 & , & 0 & , & 0 & , & \ldots & , & 0 & ) & \end{array} \end{eqnarray*} Therefore we obtain $$(0,1,2,1,0,1)[10] = (0,1,2,1,0,0,0,0,0,0,0,0,0,0)$$.
Reconstruct $$(0,1,4,13,20,30,44,64)[4]$$ from the diagonal $$(0,1,2,1,0,0,0,0,0,0,0,0,0,0)$$. \begin{eqnarray*} \begin{array}{rccccccccccccccccccccc} & & & & & & ( & \vdots & \vdots & \vdots & \vdots & \vdots & \vdots & \vdots & \vdots & \vdots & \vdots & \vdots & ) & & & & & & \\ & & & & & ( & 0 & , & 0 & , & 0 & , & 0 & , & 0 & , & 0 & , & 0 & ) & & & & \\ & & & & ( & 0 & , & 0 & , & 0 & , & 0 & , & 0 & , & 0 & , & 0 & , & 0 & ) & & \\ C_5 & = & & ( & \color{red}{0} & , & 0 & , & 0 & , & 0 & , & 0 & , & 0 & , & 0 & , & 0 & , & 0 & ) \\ C_4 & = & ( & \color{red}{0} & , & 0 & , & 0 & , & 0 & , & 0 & , & 0 & , & 0 & , & 0 & , & 0 & ) & \\ C_3 & = & & ( & \color{red}{1} & , & 1 & , & 1 & , & 1 & , & 1 & , & 1 & , & 1 & , & 1 & ) & & \\ C_2 & = & & & ( & \color{red}{4} & , & 5 & , & 6 & , & 7 & , & 8 & , & 9 & , & 10 & ) & & & \\ C_1 & = & & & & ( & \color{red}{14} & , & 19 & , & 25 & , & 32 & , & 40 & , & 49 & ) & & & & \\ C_0 & = & & & & & ( & \color{red}{44} & , & 63 & , & 88 & , & 120 & , & 160 & ) & & & & & \\ a & = & ( & 0 & , & \ldots & , & \color{red}{44} & , & 64 & ) & & & & & & & & & & & \\ & \rightsquigarrow & ( & 0 & , & \ldots & , & \color{red}{44} & , & 63 & , & 88 & , & 120 & , & 160 & ) & & & & & \end{array} \end{eqnarray*} Therefore we obtain $$(0,1,4,13,20,30,44,64)[4] = (0,1,4,13,20,30,44,63,88,120,160)$$.
### Table of Expansions
Here is a table of examples of expansions of standard N primitive sequences with respect to N1.1.
sequence expansion
$$()$$ $$()$$
$$(0)$$ $$()$$
$$(0,0)$$ $$(0)$$
$$(0,0,0)$$ $$(0,0)$$
$$(0,1)$$ $$(0,0,0,\ldots)$$
$$(0,1,0)$$ $$(0,1)$$
$$(0,1,0,1)$$ $$(0,1,0,0,0,\ldots)$$
$$(0,1,1)$$ $$(0,1,0,1,\ldots)$$
$$(0,1,1,0)$$ $$(0,1,1)$$
$$(0,1,1,0,1)$$ $$(0,1,1,0,0,0,\ldots)$$
$$(0,1,1,0,1,1)$$ $$(0,1,1,0,1,0,1,\ldots)$$
$$(0,1,1,1)$$ $$(0,1,1,0,1,1,\ldots)$$
$$(0,1,2)$$ $$(0,1,1,1,\ldots)$$
$$(0,1,2,0)$$ $$(0,1,2)$$
$$(0,1,2,1)$$ $$(0,1,2,0,1,2,\ldots)$$
$$(0,1,2,2)$$ $$(0,1,2,1,2,\ldots)$$
$$(0,1,2,3)$$ $$(0,1,2,2,2,\ldots)$$
$$(0,1,2,4)$$ $$(0,1,2,3,4,\ldots)$$
$$(0,1,2,4,0)$$ $$(0,1,2,4)$$
$$(0,1,2,4,1)$$ $$(0,1,2,4,0,1,2,4,\ldots)$$
$$(0,1,2,4,2)$$ $$(0,1,2,4,1,2,4,\ldots)$$
$$(0,1,2,4,3)$$ $$(0,1,2,4,2,4,2,4,\ldots)$$
$$(0,1,2,4,4)$$ $$(0,1,2,4,3,5,4,6,\ldots)$$
$$(0,1,2,4,5)$$ $$(0,1,2,4,4,4,\ldots)$$
$$(0,1,2,4,5,0)$$ $$(0,1,2,4,5)$$
$$(0,1,2,4,5,1)$$ $$(0,1,2,4,5,0,1,2,4,5,\ldots)$$
$$(0,1,2,4,5,2)$$ $$(0,1,2,4,5,1,2,4,5,\ldots)$$
$$(0,1,2,4,5,3)$$ $$(0,1,2,4,5,2,4,5,\ldots)$$
$$(0,1,2,4,5,4)$$ $$(0,1,2,4,5,3,5,6,4,6,7,\ldots)$$
$$(0,1,2,4,5,5)$$ $$(0,1,2,4,5,4,5,4,5,\ldots)$$
$$(0,1,2,4,5,6)$$ $$(0,1,2,4,5,5,5,5,\ldots)$$
$$(0,1,2,4,5,7)$$ $$(0,1,2,4,5,6,7,8,9,\ldots)$$
$$(0,1,2,4,5,7,0)$$ $$(0,1,2,4,5,7)$$
$$(0,1,2,4,5,7,1)$$ $$(0,1,2,4,5,7,0,1,2,4,5,7,\ldots)$$
$$(0,1,2,4,5,7,2)$$ $$(0,1,2,4,5,7,1,2,4,5,7,\ldots)$$
$$(0,1,2,4,5,7,3)$$ $$(0,1,2,4,5,7,2,4,5,7,\ldots)$$
$$(0,1,2,4,5,7,4)$$ $$(0,1,2,4,5,7,3,5,6,8,\ldots)$$
$$(0,1,2,4,5,7,5)$$ $$(0,1,2,4,5,7,4,5,7,\ldots)$$
$$(0,1,2,4,5,7,6)$$ $$(0,1,2,4,5,7,5,7,5,7,\ldots)$$
$$(0,1,2,4,5,7,7)$$ $$(0,1,2,4,5,7,6,8,7,9,8,10,9,11,\ldots)$$
$$(0,1,2,4,5,7,8)$$ $$(0,1,2,4,5,7,7,7,\ldots)$$
$$(0,1,2,4,6)$$ $$(0,1,2,4,5,7,8,10,11,13,14,16,\ldots)$$
$$(0,1,2,4,6,0)$$ $$(0,1,2,4,6)$$
$$(0,1,2,4,6,1)$$ $$(0,1,2,4,6,0,1,2,4,6,\ldots)$$
$$(0,1,2,4,6,2)$$ $$(0,1,2,4,6,1,2,4,6,\ldots)$$
$$(0,1,2,4,6,3)$$ $$(0,1,2,4,6,2,4,6,\ldots)$$
$$(0,1,2,4,6,4)$$ $$(0,1,2,4,6,3,5,7,4,6,8,\ldots)$$
$$(0,1,2,4,6,5)$$ $$(0,1,2,4,6,4,6,4,6,\ldots)$$
$$(0,1,2,4,6,6)$$ $$(0,1,2,4,6,5,7,6,8,\ldots)$$
$$(0,1,2,4,6,7)$$ $$(0,1,2,4,6,6,6,6,\ldots)$$
$$(0,1,2,4,6,8)$$ $$(0,1,2,4,6,7,9,11,12,14,16,\ldots)$$
$$(0,1,2,4,6,9)$$ $$(0,1,2,4,6,8,10,12,14,16,18,\ldots)$$
$$(0,1,2,4,7)$$ $$(0,1,2,4,6,9,12,16,20,25,30,\ldots)$$
$$(0,1,2,4,8)$$ $$(0,1,2,4,7,11,16,22,29,37,46,\ldots)$$
$$(0,1,3)$$ $$(0,1,2,4,8,16,32,64,128,256,\ldots)$$
$$(0,1,3,0)$$ $$(0,1,3)$$
$$(0,1,3,1)$$ $$(0,1,3,0,1,3,\ldots)$$
$$(0,1,3,2)$$ $$(0,1,3,1,3,1,3,\ldots)$$
$$(0,1,3,3)$$ $$(0,1,3,2,5,4,9,8,17,16,33,32,\ldots)$$
$$(0,1,3,4)$$ $$(0,1,3,3,3,3,3,\ldots)$$
$$(0,1,3,5)$$ $$(0,1,3,4,7,9,14,18,27,35,52,68,\ldots)$$
$$(0,1,3,6)$$ $$(0,1,3,5,8,13,22,39,72,137,\ldots)$$
$$(0,1,3,6,0)$$ $$(0,1,3,6)$$
$$(0,1,3,6,1)$$ $$(0,1,3,6,0,1,3,6,\ldots)$$
$$(0,1,3,6,2)$$ $$(0,1,3,6,1,3,6,\ldots)$$
$$(0,1,3,6,3)$$ $$(0,1,3,6,2,5,8,4,9,12,8,17,20,16,\ldots)$$
$$(0,1,3,6,4)$$ $$(0,1,3,6,3,6,3,6,\ldots)$$
$$(0,1,3,6,5)$$ $$(0,1,3,6,4,9,7,11,9,16,14,20,18,29,27,\ldots)$$
$$(0,1,3,6,6)$$ $$(0,1,3,6,5,9,8,14,13,23,22,40,39,\ldots)$$
$$(0,1,3,6,7)$$ $$(0,1,3,6,6,6,6,\ldots)$$
$$(0,1,3,6,8)$$ $$(0,1,3,6,7,10,14,16,21,27,31,40,50,58,\ldots)$$
$$(0,1,3,6,9)$$ $$(0,1,3,6,8,12,15,21,26,36,45,63,80,\ldots)$$
$$(0,1,3,6,10)$$ $$(0,1,3,6,9,13,19,29,37,71,\ldots)$$
$$(0,1,3,6,11)$$ $$(0,1,3,6,10,15,21,28,36,45,55,\ldots)$$
$$(0,1,3,7)$$ $$(0,1,3,6,11,21,42,85,171,342,\ldots)$$
$$(0,1,3,8)$$ $$(0,1,3,7,15,31,63,127,255,\ldots)$$
$$(0,1,3,9)$$ $$(0,1,3,8,22,63,185,550,1644,\ldots)$$
$$(0,1,4)$$ $$(0,1,3,9,27,81,243,729,2187,\ldots)$$
$$(0,1,5)$$ $$(0,1,4,16,64,256,1024,4096,\ldots)$$
$$(0,1,\textrm{Rayo}(10^{100})+1)$$ $$(0,1,\textrm{Rayo}(10^{100}),\textrm{Rayo}(10^{100})^2,\textrm{Rayo}(10^{100})^3,\ldots)$$
## Sources
1. Koteitan, Categorizing of the rule sets for all sub versions of bashicu matrix, Googology Wiki user blog, 2018.
3. Nayuta Ito, Ich denke, dass dies wahrscheinlich am schnellsten ist., document in Google Spread Sheet, 2019.
4. Nayuta Ito, Nayuta-Ito/N-primitive, GitHub, 2019.
Fish numbers: Fish number 1 · Fish number 2 · Fish number 3 · Fish number 4 · Fish number 5 · Fish number 6 · Fish number 7
Mapping functions: S map · SS map · S(n) map · M(n) map · M(m,n) map
By Aeton: Okojo numbers · N-growing hierarchy
By BashicuHyudora: Primitive sequence number · Pair sequence number · Bashicu matrix system
By Kanrokoti: KumaKuma ψ function
By 巨大数大好きbot: Flan numbers
By Jason: Irrational arrow notation · δOCF · δφ · ε function
By mrna: 段階配列表記 · 降下段階配列表記 · 多変数段階配列表記 · SSAN · S-σ
By Nayuta Ito: N primitive
By p進大好きbot: Large Number Garden Number
By Yukito: Hyper primitive sequence system · Y sequence · YY sequence · Y function
Indian counting system: Lakh · Crore · Tallakshana · Uppala · Dvajagravati · Paduma · Mahakathana · Asankhyeya · Dvajagranisamani · Vahanaprajnapti · Inga · Kuruta · Sarvanikshepa · Agrasara · Uttaraparamanurajahpravesa · Avatamsaka Sutra · Nirabhilapya nirabhilapya parivarta
Chinese, Japanese and Korean counting system: Wan · Yi · Zhao · Jing · Gai · Zi · Rang · Gou · Jian · Zheng · Zai · Ji · Gougasha · Asougi · Nayuta · Fukashigi · Muryoutaisuu
Other: Taro's multivariable Ackermann function · TR function · Arai's $$\psi$$ · Sushi Kokuu Hen
Community content is available under CC-BY-SA unless otherwise noted. | 2021-06-21T04:06:48 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.998619019985199, "perplexity": 264.4480147347673}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623488262046.80/warc/CC-MAIN-20210621025359-20210621055359-00473.warc.gz"} |
http://ciks.cbt.nist.gov/~garbocz/paper134/node4.html | Next: Error analysis Up: Main Previous: X-ray tomography and particle
## Spherical harmonic mathematical analysis
The procedure to generate the 2-D surface of a 3-D particle is qualitatively the same as in generating the 1-D surface of a 2-D particle. Starting from the center of mass, which is defined in 3-D similarly to 2-D, line segments are positioned from the center of mass to the surface at various angles (i, j), where these angles are the usual spherical polar coordinates [36]. The length of these line segments, denoted Rij(i , j), are found numerically at the values of the angles corresponding to the points of a double Gaussian quadrature, one for each angle, where Rij is the distance from the center of mass to a surface point along the direction defined by (i, j). A surface point is defined as a point on the surface of a pixel. The Cartesian coordinates of these surface points, with the origin defined at the particle center of mass, are
xij = Rij sin(i) cos(j) yij = Rij sin(i) sin(j) (8) zij = Rij cos(i)
Now is the time to state more clearly what kinds of particles can be handled accurately by this kind of analysis. We require that the shape to be "star-like" [20,21,22]. For a shape to be star-like, any line segment whose one endpoint is the center of mass and the other endpoint is on the surface must be totally contained in the shape itself. Therefore, there can be no "overhangs" or "bubbles" in the shape, as was depicted in Fig. 2. This requirement should be satisfied by almost all aggregates, because the grinding process, whether natural, in a riverbed, or artificial, in a rock-crushing machine, should break down any "overhanging" bits, and rocks usually do not have internal porosity large enough to show up in a tomograph that uses the resolutions of 10's of micrometers per pixel. Many aggregates do have internal porosity, but as long as it is smaller than the resolution of the tomograph, it will not be seen in the particle images created by the tomograph. If there are any of these features in the x-ray tomographic images, the spherical harmonic analysis process will create a "valley" from the internal bubble to the real surface, since encountering the bubble surface first as a line segment proceeds from the center of mass will cause it to be interpreted as the real particle surface. The signature of this happening will be a significant difference between the digital volume and the volume as computed from the spherical harmonic expansion. All the examples of aggregates that will be shown in this paper are star-like, as judged from the original tomographic image, and did not have internal porosity.
Once a star-like particle has been obtained, and surface points Rij(, j) found, then spherical harmonic analysis (the 3-D equivalent of 2-D Fourier analysis) can be applied. The key equation in the spherical harmonic analysis process is the following, where r(, j) is any smooth function defined on the unit sphere (0 , 0 2) [36,37,38]:
(9)
For these assumptions, the spherical expansion exists and converges. In our case, r(, ) is given numerically by (i , j , Rij ). The function is called a spherical harmonic function, and is given by:
(10)
The functions Pnm(x) are called associated Legendre functions, and are a set of orthogonal polynomials found in quantum mechanics [37] and many other fields. Appendix A lists the associated Legendre functions up to order n = 8. In this case, x = cos(). Values of higher order associated Legendre functions can be found using recursion relations [36]. These recursion relations are available in user-ready Fortran programs like DXLEGF, a part of the SLATEC numerical package [39]. Using explicit formulae for the associated Legendre functions up to n = 8 helps give more accuracy to this recursion process, hence the listing herein. Using explicit formulas up to higher values of n would be still more helpful, but the algebra to calculate these quickly becomes tedious.
The computed surface points are then used to calculate the coefficients anm, which depend on both n and m according to the following definition:
(11)
where the asterisk denotes the complex conjugate. Choosing each angle to correspond to the points of a Gaussian quadrature makes evaluation of these integrals straightforward. In 3-D, a 120 point Gaussian quadrature was used for each angle, so that eq. (11) was evaluated by summing over 1202=14,400 points. In some cases, a 240 point Gaussian quadrature, with 57,600 points, was used.
A set of coefficients, once determined, then serve as a complete, within numerical error, mathematical characterization of the aggregate particle. Much of the later sections of this paper examines error analysis of how well the expansion works for simple shapes, by direct numerical comparison to analytically known quantities, and by visual and numerical comparison to the original random digital particles from the tomograph.
Many properties of the shape can be computed once the spherical harmonic expansion is known. These include volume, surface area, mean and Gaussian curvature both at a point of the surface and integrated over the surface, and the moment of inertia tensor, as defined below. The volume and moment of inertia can also be computed directly from the digital image by counting voxels.
The equation for the volume of the shape in polar coordinates is particularly simple and is given by:
(12)
where the integral is over all angles and for values of r between the origin at the center of mass and the surface, r(, ), which is given by the computed expansion of eq.(9). The r integral can be analytically performed, and the resulting integral is then, in terms of the function r(, ),
(13)
The equations for the surface area and integrated curvatures involve some auxiliary terms that are defined in differential geometry. These are given below [22]. A useful way of denoting points on the surface of the particle is by the vector , which is the Cartesian coordinates of surface points. The components of (X1 = x, X2 = y, X3 = z) are similar to those given in eq. (8), and derivatives of are denoted by a subscript.
There are 8 auxiliary quantities that are useful in analyzing surfaces, and they are all built out of components of and the surface normal vector , which is given by:
(14)
The differential surface area element, d , which is the area of the patch of surface at r(, ), is given by:
(15)
The parameters E, F, and G are given by
(16)
The parameters L, M, and N are
(17)
Since the function r(, ) is known in terms of a spherical harmonic expansion, and the Cartesian coordinates of the surface are known in terms of r(, ), all the above derivatives can be taken and the results for all the various surface parameters given in terms of derivatives of r(, ). In the following, these derivatives of r(, ) are denoted by the notation:
(18)
The actual functional form of these derivatives, in terms of the spherical harmonic expansion (eq. (9)) are given in Appendix B.
The surface area SA is an integral over and of the differential surface element in eq. (15). The parameter S, using the spherical harmonic expansion, is
(19)
so that the surface area SA is
(20)
The parameters E, F, and G are given by
(21)
The parameters L, M, and N involve vector products of the derivatives of the components of and (see eq. (17)). The components of and derivatives of the components are fairly complicated, so that the explicit forms of L, M, and Nare not given in the text. The derivatives of the components of and are listed in Appendix B, however. Equation (17) can then be used to write out the equations for L, M, and N, and numerically evaluate them and the values of other quantities that depend on them.
The local mean curvature H is defined as the arithmetical mean of the two principal curvatures at each point on the surface [22], and is given by
(22)
The Gaussian curvature K, which is another measure of surface curvature, is the geometric mean of the two principal curvatures at each point on the surface:
(23)
The mean curvature, averaged over the surface and weighted by the differential surface element, is defined here as h, where
(24)
The parameter h has units of inverse length, since the mean curvature H has units of inverse length. If h is then inverted, the resulting length depends on the size and shape of the object considered. One should note that the term "integrated mean curvature" is often referred to in the literature as eq. (24) without the normalizing factor of SA-1 [40].
An interesting property of the Gaussian curvature, when similarly integrated over the surface, is that
(25)
when the object under consideration is topologically equivalent to a sphere. This is the case for the star-like aggregate considered here. "Topogically equivalent to a sphere" means if the object were made out of very pliant rubber, it could be deformed, without ripping or puncturing, into a sphere. Equation (25) is then a very useful quality control check for the spherical harmonic expansion procedure. Also, one should be able to make a judgement of when "enough" terms in the expansion have been computed, by when this criterion is fulfilled.
The terms of the moment of inertia tensor Iij, where i,j = 1,2,3, are given by [7]
(26)
where is the density of the object, ij is the Kronecker delta (zero for i j and 1 when i = j), the integral is over the entire particle volume V, and Iji = Iij. If the mass density of the object is uniform, so that = M/V (total mass divided by total volume), then using the definition of the polar coordinates in eq. (8), and performing the r integral like in eq. (13), the I11 integral, for example, transforms to
(27)
The remaining components of the moment of inertia tensor can be found in Appendix B.
Even though the result of eq. (25) exists for any aggregate shape that would be considered, it is important to have other checks as well, to establish the limitations and perform error analysis on the spherical harmonic expansion procedure. This error analysis is carried out next using various analytical shapes.
Next: Error analysis Up: Main Previous: X-ray tomography and particle | 2013-12-05T05:42:42 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8603047728538513, "perplexity": 415.20314667364624}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-48/segments/1386163040059/warc/CC-MAIN-20131204131720-00046-ip-10-33-133-15.ec2.internal.warc.gz"} |
https://pos.sissa.it/301/847/ | Volume 301 - 35th International Cosmic Ray Conference (ICRC2017) - Session Gamma-Ray Astronomy. GA-instrumentation
Detection of primary photons using $\hat{C}$erenkov imaging and surface detectors
F. Casaburo
Full text: pdf
Pre-published on: August 16, 2017
Published on: August 03, 2018
Abstract
Discovered by Hess during some experiments about air ionization, cosmic rays are constituted by particles coming from the space. In the past, cosmic rays allowed the development of Particle Physics; indeed, thanks to their high energy not achievable in laboratories, they enabled new particles discovery. Today, interest about this radiation concerns both Astrophysics and Particle Physics. Indeed on the one hand, their knowledge allows formulation about new models of Universe structure and evolution or to acquire new knowledge about final objects of stars evolution; on the other hand cosmic rays allows us to study fundamental processes, as for example acceleration and interaction mechanisms of particles at energies not achievable in laboratories. Although it has passed more than a century after their discovery, there are many questions to which it isn't possible to answer yet or to which there isn't certainty about formulated theories. Some examples are about objects that can accelerate particles to high energy and acceleration mechanisms; indeed, even if there are some theories, we don't have experimental certainty. Moreover, although measured in many experiments, energy spectrum shows, especially in the region called "Knee", some differences between measuring made by experiments. Since magnetic fields deflect charged particles, their observation doesn't allow to go back to the source, so in cosmic rays study it's very important $\gamma$ rays observation because they aren't deflected by magnetic fields. In 1989 \textit{\textbf{Whipple}} experiment allowed to observe, for the first time, $\unit{TeV}$ energy $\gamma$ rays coming from Crab Nebula. Thanks to many experiments made to answer questions about cosmic rays, more than 100 \textit{\textbf{\ac{VHE}}} $\gamma$ rays sources were observed since then; 60 out of 100 have galactic origin, as for instance Supernova Remnants or Pulsars; for the rest, apart from those not identified, they have extra-galactic origin. In this work some simulations, made by \textit{\textbf{\ac{INFN}}} subdivision of Torino (Italy) using \textit{\textbf{\ac{CORSIKA}}}, were analyzed to study differences between \textit{\textbf{\ac{EAS}}} produced by $\gamma$ rays and \ac{EAS} produced by protons
DOI: https://doi.org/10.22323/1.301.0847
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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.
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Copyright owned by the author(s) under the term of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License. | 2020-12-05T15:09:51 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4423469305038452, "perplexity": 1987.2123229889924}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-50/segments/1606141747887.95/warc/CC-MAIN-20201205135106-20201205165106-00022.warc.gz"} |
https://www.usgs.gov/center-news/volcano-watch-mauna-loa-comes-under-military-style-surveillance | # Volcano Watch — Mauna Loa comes under military-style surveillance
Release Date:
The internal workings of Mauna Loa Volcano will be probed from space starting this week by a satellite system designed to track military vehicles rather than volcanoes.
The internal workings of Mauna Loa Volcano will be probed from space starting this week by a satellite system designed to track military vehicles rather than volcanoes. Scientists from both the Hawaiian Volcano Observatory and the Cascade Volcano Observatory of the U.S. Geological Survey are deploying instruments on Mauna Loa that receive signals from a group of satellites that are the heart of the Global Positioning System, or GPS.
The high-tech positioning system was developed by the Department of Defense to provide accurate worldwide navigation. When fully operational in 1993, GPS will allow military users to quickly determine their location anywhere on the globe to within a few feet, 24 hours a day, in virtually any weather conditions. The system played a key role in Operation Desert Storm last year by helping to coordinate troop movements in the relatively featureless desert terrain of Kuwait and Iraq. A modified version is available for civilian use and is attracting attention from a variety of users, including scientists who keep track of active volcanoes.
By recording a large amount of satellite information at several points on the Earth's surface, and processing that information in a special way, we can increase the accuracy of GPS tremendously. The data collection points can be separated by many miles and by thick vegetation or steep terrain, because it isn't necessary to make line-of-sight measurements from one point to the others, as is the case for conventional surveys. To use the GPS, we only need a relatively clear view of the sky, so we receive the signals from the satellites. By returning to the same points at a later date with GPS, we can detect ground movements of less than an inch that may have occurred in response to magma moving underground.
Civilian uses of GPS such as that described here, have the military's blessing, because these accurate results require months of computer processing, and such after-the-fact information poses no threat to national security. Nonetheless, it is a new and exciting tool for scientists who study active volcanoes.
When magma moves deep within a volcano, it pushes aside the surrounding rock, causing the surface to move slightly. As an eruption nears, these movements often accelerate and become very large. As a result of the 1984 eruption of Mauna Loa Volcano, the summit subsided at least two feet, and the flanks of the volcano moved apart by nearly three feet. We interpreted these changes to indicate that at least 130 million cubic yards of magma withdrew from beneath the summit and erupted from the northeast rift zone.
The GPS survey at Mauna Loa has some urgency because our conventional measurements of deformationindicate that Mauna Loa has been inflating with magma since the end of the 1984 eruption. Those measurements have shown that the rate of magma accumulation has accelerated in the past six months and that Mauna Loa has now regained nearly two-thirds of the volume of lava erupted in 1984. The urgency to perform the GPS measurements reflects our desire to establish a multi-year base of data prior to the next eruption. GPS will allow us to make measurements that aren't practical with any other technique because of the long distances involved and the limited line-of-sight on Mauna Loa.
Mauna Loa was recently designated a "decade volcano" as part of the International Decade of Natural Hazards Reduction. This GPS survey is part of what we hope will evolve into an intensive, multidisciplinary study of the volcano during the coming decade, which will probably include the next eruption. We will also be deploying at least three new seismic stations and an electronic station to measure ground tilt along Mauna Loa's southwest rift zone within the next year. The GPS survey and the installation of new instruments are being done to improve our ability to forecast the next eruption and to monitor that eruption when it occurs.
### Volcano Activity Update
The eruption on the East Rift Zone of Kīlauea Volcano continues with very low-volume effusion of lava at about the 1,900-foot level of the tube downslope from the Kupaianaha vent. This is the same area that has had active flows for the past six weeks. The volume of lava continues to slowly decline, as it has since last summer. The active lava pond in Puu O`o continues to produce bright glow at night. All the earthquakes recorded this week had magnitudes less than 3.0. | 2019-12-12T01:38:36 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2785947918891907, "perplexity": 1905.5302957211013}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-51/segments/1575540534443.68/warc/CC-MAIN-20191212000437-20191212024437-00447.warc.gz"} |
http://pdglive.lbl.gov/Particle.action?node=B002&home=sumtabB | ${{\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}{(2000)}}$ $I(J^P)$ = $1(1/2^{-})$
We list here all reported ${\mathit S}_{\mathrm 11}$ states lying above the ${{\mathit \Sigma}{(1750)}}{\mathit S}_{\mathrm 11}$. ZHANG 2013A finds no evidence for those states.
${{\mathit \Sigma}{(2000)}}$ MASS $\approx2000$ MeV
${{\mathit \Sigma}{(2000)}}$ WIDTH | 2019-03-22T12:23:15 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9256629943847656, "perplexity": 673.2563524188704}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-13/segments/1552912202658.65/warc/CC-MAIN-20190322115048-20190322141048-00463.warc.gz"} |
http://trove.nla.gov.au/work/126082?q&versionId=134126 | # English, Article edition: REDUCTION OF DISCRETE DYNAMICAL SYSTEMS OVER GRAPHS H. S. MORTVEIT; C. M. REIDYS
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Physical Description
• article
Language
• English
### Edition details
Title
• REDUCTION OF DISCRETE DYNAMICAL SYSTEMS OVER GRAPHS
Author
• H. S. MORTVEIT
• C. M. REIDYS
Physical Description
• article
Notes
• In this paper we study phase space relations in a certain class of discrete dynamical systems over graphs. The systems we investigate are called Sequential Dynamical Systems (SDSs), which are a class of dynamical systems that provide a framework for analyzing computer simulations. Specifically, an SDS consists of (i) a finite undirected graph Y with vertex set {1,2,â¦,n} where each vertex has associated a binary state, (ii) a collection of Y-local functions (Fi,Y)iâv[Y] with $F_{i,Y}: \mathbb{F}_2^n\to \mathbb{F}_2^n$ and (iii) a permutation Ï of the vertices of Y. The SDS induced by (i)â(iii) is the map $[F_Y,\pi] = F_{\pi(n),Y} \circ \cdots \circ F_{\pi(1),Y}\,.$ The paper is motivated by a general reduction theorem for SDSs which guarantees the existence of a phase space embedding induced by a covering map between the base graphs of two SDSs. We use this theorem to obtain information about phase spaces of certain SDSs over binary hypercubes from the dynamics of SDSs over complete graphs. We also investigate covering maps over binary hypercubes, $Q_2^n$, and circular graphs, Circn. In particular we show that there exists a covering map $\phi: Q_2^n\to K_{n+1}$ if and only if 2nâ¡0 mod n+1. Furthermore, we provide an interpretation of a class of invertible SDSs over circle graphs as right-shifts of length n-2 over {0,1}2n-2. The paper concludes with a brief discussion of how we can extend a given covering map to a covering map over certain extended graphs.
• Sequential dynamical systems, graph morphisms, covering maps, phase space embeddings, reduction
• RePEc:wsi:acsxxx:v:07:y:2004:i:01:p:1-20
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• English
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Be the first to add a tag for this edition | 2017-02-26T21:45:20 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5679104924201965, "perplexity": 2093.276789223408}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-09/segments/1487501172077.66/warc/CC-MAIN-20170219104612-00303-ip-10-171-10-108.ec2.internal.warc.gz"} |
https://www.usgs.gov/center-news/volcano-watch-mahalo-helping-us-celebrate-puu-oos-20th-anniversary | Volcano Watch - Mahalo for helping us celebrate Puu Oo's 20th Anniversary
Release Date:
On January 4, as lava flowed from the Puu Oo cone 11 km (7 miles) to the south shoreline of Kilauea Volcano, the staff of the Hawaiian Volcano Observatory welcomed the public to our Open House in the Park, celebrating the twentieth anniversary of the eruption.
First place winner of our Puu Oo drawing contest. Riker Kasamoto (age 7, Honolulu) depicts Puu Oo with a lava fountain, whose flow went underground through a lava tube, then poured into the ocean at the coast.
(Public domain.)
We thank all who visited the Park and showed a keen interest in our work and in exposing children to earth and life sciences. We also thank the staff of Hawaii Volcanoes National Park, USGS Kilauea Field Station, University of Hawaii Hilo, Kilauea Military Camp, Volcano House, and the Volcano Art Center who gave their time and energy to make this a truly special event.
The Open House gave us the opportunity to demonstrate how we monitor Hawaii's volcanoes and describe new ideas learned from studying the geology of the Big Island, tracking changes that precede and accompany eruptions, and conducting surveys of active lava tubes.
For those who wanted to know "what the volcanoes are doing right now," we showed our monitoring data in real time using new computer programs. Developed only in the past year, a program called VALVE (Volcano Analysis and Visualization Environment) enables us to analyze real-time and archived data from our various instruments, measurements, and surveys, and model the data to identify possible explanations for what was observed.
We also demonstrated Earthworm, a new computer program that enables us to digitally record, locate, determine magnitude, and analyze earthquakes in Hawaii. This digital version, compared to the paper drum record, allows any ground-shaking signal to be magnified in remarkable detail, and to be displayed and analyzed in a variety of ways.
We showed two different methods for determining possible pathways of future lava flows during the initial onset of a hypothetical eruption on Kilauea and Mauna Loa volcanoes. A set of soon-to-be-released maps identifies broad areas that can be covered by lava erupted from future vents on Mauna Loa's northeast and southwest rift zones. The inundation zones are based on the volcano's history of lava flows. More specific pathways of future lava flows that spread over new ground can be accurately determined based on the topography of the Big Island.
Back in our mineralogy lab, children and their parents enjoyed looking at different types of volcanic products, as well as thin sections of rocks through a microscope that allow different kinds of minerals to be seen. In our gas lab, visitors were shown how we analyze and measure volcanic gases released from Kilauea, and they had the pH of their drinking water tested.
Outdoors in the Park, HVO scientists showed visitors evidence of explosive eruptions at Kilauea in 1924 and much larger explosions that occurred many times in the past 1,200 years. Oral history describes some of these explosions, which enhanced Pele's reputation for her terrible temper.
We also demonstrated how geophysical surveys are conducted over active lava tubes to determine the size and shape of the underground tube. When we can also estimate the speed of the lava stream within an active tube, for example through a skylight, we can calculate the discharge of lava through a tube system. These data enable us to determine how much lava Kilauea erupts every day and study the evolution of lava flows over time.
The popular Puu Oo drawing contest brought many children from all over the world to depict their views of the ongoing eruption. Winners of the drawing contest are as follows: first prize, : Riker Kasamoto (age 7, Honolulu), for his drawing of Puu Oo with a lava fountain, whose flow went underground through a lava tube, then poured into the ocean at the coast. Second prize went to Miki Karpik (age 11, Pahoa), who depicted the sea goddess Namakaokahai welcoming the tempestuous Pele, emerging from PuuOo, to come to her domain. Sarah Miller (age 8, no address given), showed Pele with her tears, rising from the lava fountain of Puu Oo, with a girl running toward her home, endangered by the flowing lava. We congratulate all of the young artists for their creativity and imagination.
Volcano Activity Update
Eruptive activity at the Puu Oo vent of Kilauea Volcano continued unabated during the past week. Lava flows through a tube system from the vent to the sea. Lava continues to enter the ocean and form lava deltas (benches). Only the West Highcastle delta stayed active for the entire week; the Highcastle and Wilipea deltas both shut down last week. A substantial new flow tongue, visible on Pulama Pali last week, developed two branches that made it over Paliuli and are now spreading slowly across the coastal flat.
The West Highcastle lava delta has had several small collapses in the past week, and explosions have been common. The public should be aware that the ocean entry areas can collapse at any time, potentially generating large explosions in the process. The steam clouds rising from the entry areas are highly acidic and laced with glass particles. The National Park Service has erected a rope barricade to delineate the edge of the restricted area. Do not venture beyond this rope boundary onto the lava deltas and benches. Even the intervening beaches are susceptible to large waves suddenly generated during delta collapse; these beaches should be avoided.
Four earthquakes were reported felt on the island during the past week. A resident of Kealia felt an earthquake at 8:29 a.m. on January 12. The magnitude-2.4 earthquake was located 2 km (1.2 mi) west of Pahala at a depth of 36.4 km (21.8 mi). A camper in Hawaii Volcanoes National Park was awaken by an earthquake at 4:37 a.m. on January 13. The magnitude-3.2 temblor was located 13.3 km (8 mi) beneath Loihi Volcano. Later the same day at 5:12 p.m., residents of Puna were shaken by a magnitude-2.8 earthquake located 8 km (5 mi) east of Puulena Crater at a depth of 4 km (2.4 mi). Another earthquake on January 13 at 5:55 p.m. was felt by residents of Hilo and Papaikou. The magnitude-2.9 shaker was located 6 km (3.6 mi) southeast of Puu O`o at a depth of 8.6 km (5.2 mi).
Mauna Loa is not erupting. The summit region continues to inflate, though the rate of inflation has slowed gradually during the past month or two. The earthquake activity is low, with only 1 earthquake located in the summit area during the last seven days. | 2019-11-13T05:11:16 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.18816818296909332, "perplexity": 6021.764784359037}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-47/segments/1573496665985.40/warc/CC-MAIN-20191113035916-20191113063916-00435.warc.gz"} |
https://www.scielo.br/scielo.php?script=sci_arttext&pid=S0100-60452019000200085 | ## Print version ISSN 0100-6045On-line version ISSN 2317-630X
### Manuscrito vol.42 no.2 Campinas Apr./June 2019 Epub Aug 12, 2019
#### http://dx.doi.org/10.1590/0100-6045.2019.v42n2.rf
ARTICLES
The Ontological Import of Adding Proper Classes
1University of Campinas. Department of Philosophy. Adress: Cidade Universitária, Campinas. e-mail: [email protected]
2University of Brasília. Department of Philosophy. Adress: Campus Universitário Darcy Ribeiro, Brasília. e-mail: [email protected]
Abstract
In this article, we analyse the ontological import of adding classes to set theories. We assume that this increment is well represented by going from ZF system to NBG. We thus consider the standard techniques of reducing one system to the other. Novak proved that from a model of ZF we can build a model of NBG (and vice versa), while Shoenfield have shown that from a proof in NBG of a set-sentence we can generate a proof in ZF of the same formula. We argue that the first makes use of a too strong metatheory. Although meaningful, this symmetrical reduction does not equate the ontological content of the theories. The strong metatheory levels the two theories. Moreover, we will modernize Shoenfield’s proof, emphasizing its relation to Herbrand’s theorem and that it can only be seen as a partial type of reduction. In contrast with symmetrical reductions, we believe that asymmetrical relations are powerful tools for comparing ontological content. In virtue of this, we prove that there is no interpretation of NBG in ZF, while NBG trivially interprets ZF. This challenges the standard view that the two systems have the same ontological content.
Keywords: Set theory; Class theory; Formal ontology
1. How can we compare the ontological content of different theories?
Within the context of a formal theory, an assertion is ontologically committing if it expresses a closure property of the intended models. For example, the power set and the union axioms express closure properties in set theories. If X and Y are elements in our set theory model, then the axioms guarantee that their union and ther power sets are also in the model. This property represents how an axiom generates ontological import. A detailed analysis of this conception leads to an understanding of existential aspects in formal theories (see 4). But it is of no help if we want to compare different theories regarding ontology. We propose a different approach for this kind of comparison: If T 1 and T 2 are formal theories and T 2 can reduce T 1 but T 1 cannot reduce T 2 using a natural method of ontological reduction given in a metatheory, then the ontological content of T 2 is greater than that of T 1.
Now, what is a natural method of ontological reduction? We expect that if T 1 reduces T 2, then the consistency of T 1 can be proved from the consistency of T 2 in the corresponding metatheory. This and other related questions are dealt with in 1, which is the source of the main results in this paper. Nevertheless, we will not be concerned with this question in its full generality here, as we will concentrate on methods of interpretations between first-order theories in a finitary metatheory. More precisely, using the method of interpretations and the above conception of ontological comparison, we prove that the ontological content of NBG is greater than the ontological content of ZF. This result goes against the received view according to which those theories are equivalent.
We will analyze the received view and point out its insufficiencies. It is based on the folklore conservativity result: NBG is conservative with respect to ZF. A detailed finitary proof of this result will be provided, as there is basically no modern proof for this in the literature. We will argue that the ontological reduction operating here is not conclusive, for the corresponding reduction method is partial. Hence, it is not clear if it gives a right transposition of the ontology. Also, it is always possible to strengthen the metatheory and weaken the reduction method in order to trivialize the comparison.
Therefore, for the equivalence claim, it is not enough to have one mutual comparison according to some reduction method in some metatheory. In the opposite direction, it is very significant to have an asymmetric comparison by a standard method of reduction, and this result will be proved subsequently, together with other related results. The absence of interpretation from NBG to ZF thus understood is a strong evidence for the thesis that the ontological content of the former surpasses that of the latter.
2. Novak’s model-theoretic reduction of NBG to ZF
From every model of ZF, a model of NBG can be obtained by the addition of definable proper classes. This construction has the important feature that the resulting model has the same sets as the original model. Therefore, the following reduction of NBG to ZF is obtained: Assume that α is a ZF-sentence and that NBGα . Let be a model of ZF, and let 𝒩 be the model of NBG obtained from by the addition of the definable proper classes. Since NBGα , it follows that 𝒩α . However, if 𝒩α , then Mα , for α is a ZF-sentence - it is about sets only - and and 𝒩 have the same sets. Now, the completeness theorem gives that ZFα , for is an arbitrary model of ZF.
The above reduction gives, in particular, a model-theoretic proof that if ZF is consistent, so is NBG. However, a bolder philosophical conclusion from this is that the ontological content of NBG is already present in ZF, as it can be easily fulfilled by the definable classes lurking in models of ZF. We claim that the bolder conclusion is unwarranted. The problem is that the metatheory in which the reduction takes place is too strong and the difference may be obliterated by its excessive strength. To make the point clear, assume that we were interested in comparing theories T 1 and T 2 in a metatheory which happens to be strong enough to prove the consistency of both theories. The equivalence between the consistency of T 1 and that of T 2 is, therefore, valid in such a metatheory, but no ontological comparison can be drawn.
From a proof of equiconsistency in some metatheory, one cannot conclude ontological equivalence. However, there is another reduction of NBG to ZF providing a finitary equiconsistency result due to Shoenfield. Although the above argument does not apply to Shoenfield’s reduction, which takes place in a finitary metatheory, we still claim that the bolder conclusion that the ontological content of NBG is already present in ZF is unwarranted. The problem is within the reduction method itself: It does not provide a reduction of the quantification over class variables, which gives NBG its extra ontological content, but rather just shows that the quantificational reasoning with class variables in NBG is dispensable and can be avoided in proofs of ZF-sentences. Therefore, there is no real reduction taking place here, there is no transposition of ontology, and the ontological equivalence does not follow. Shoenfield’s proof will be given in the next section and meticulously analyzed to support our claim.
3. Shoenfield’s finitary reduction
The finitary proof of equiconsistency between NBG and ZF was provided by Shoenfield in the article "A relative consistency proof" 9. This article is written in the language of Principia Mathematica by Whitehead and Russell, and makes extensive use of the techniques developed in Grundlagen der Mathematik by Hilbert and Bernays. For this reason, we have developed this section by an excavation, a reverse engineering, in which the tools used were unraveled by the clues left in the article. In addition, changing the axiomatic system (see 7) poses several additional difficulties and, in many instances, the proof changes significantly.
We will expose here the technique used for the equiconsistency proof. Before doing that, however, we need to remember the finitary proof technique of Herbrand’s theorem. For this, we will go through the necessary definitions, then we will enunciate Hilbert-Ackermann’s theorem and, finally, the necessary part of the strategy for establishing Herbrand’s theorem.
Definition 1 A formula α is open if all variables occurring in the formula are free.
Definition 2 A theory T is open if all its axioms are open formulas.
Definition 3 α is a quasi-tautology if, and only if, α is tautological consequence of instances of identity and equality axioms.
Theorem 4 (Hilbert-Ackermann) A open theory T is inconsistent if, and only if, there is a quasi-tautology α of the form ¬β1¬β2¬βk , such that β i is an instance of some axiom in T for each ik .
The finitary proof of this theorem can be found in [5, p. 48 - 52]. It is important to bear in mind this theorem since it is equivalent to the existential case of Herbrand’s theorem.
Definition 5 Let Q be a quantifier ∀ or ∃, then a prenex formula is of the form:
Qx1Qx2...Qxnθ,
being θ a open formula.
We call θ the matrix of Qx1Qx2...Qxnθ .
We can write the prenex form, without loss in generality, with explicit quantifiers ∀ e ∃, instead of using the Q. The general formula is of the form:
z1¯y1¯zk¯yk¯θ[x¯,z1¯,y1¯,,zk¯,yk¯],
being x¯ the sequence of free variables in the matrix θ. Using this notation will simplify the proof, since each quantifier ∀ and ∃ is treated differently.
Definition 6 A formula α is existential when α is a prenex formula of the form x1x2xnθ , being θ an open formula.
From prenex formulas, we have the following theorem:
Theorem 7 For any formula α, there is a α', such that:
1. α' is a prenex formula;
2. αα' ;
3. α' is obtained by a primitive recursive procedure;
We call α' the prenex form of α.
Next we will expose Herbrand’s normal form. It can be understood as the representation of any formula by an existential formula through a procedure of elimination of universal quantifiers. Such elimination is due to the introduction of function symbols in language.
Definition 8 (Herbrand’s normal form) Let α be any formula, we build α H through the following procedure:
1. α 0 is the prenex form of α;
2. If α i is an existential formula, then α H is α i ;
3. If α i if of the form x1x2xnyγ , we introduce a function symbol f, such that:
αi+1éx1x2xnγy(f(x1,x2,,xn)).
If α i is of the form ∀yγ, we introduce a constant symbol c, such that:
αi+1éγy(c);
We can represent Herbrand’s normal form of a prenex formula
z1¯y1¯zk¯yk¯θ[x¯,z1¯,y1¯,,zk¯,yk¯],
for
z¯1z¯kθ[x¯,z¯1,f1(z¯1)¯,,z¯k,fk(z¯1,,z¯k)¯].
.
Theorem 9 (Herbrand) Let T be a theory without non logical axioms in the language. Then, for any prenex formula α in, it holds that:
Tα in the language L there is a quasi-tautology β1 β2βk , for which, for each i, β i is an instance of the matrix α H .
Proof. (Detailed strategy) The procedure for proving Herbrand’s theorem follows the steps:
• 1. If α is an existential formula, the theorem is a corollary of Hilbert-Ackermann’s theorem:
• We suppose that α is of the form x1x2xnβ , with β as an open formula. In this case, ¬α is logically equivalent to x1x2...xn¬β . Thus, T¬α¬β .
• Because of that, Tα the theory {¬β} is inconsistent. By the Hilbert-Ackermann’s theorem, for {¬β} is a open theory,
• β} is inconsistent ⇔ there is a quasi-tautology ¬(¬β1)¬(¬β2)¬(¬β1) , with β i an instance of β for all i.
• But this is equivalent to β1β2β1 , finalizing the proof.
• 2. We take, for the general case, a prenex formula α in the language ℒ
z1¯y1¯zk¯yk¯θ[x¯,z1¯,y1¯,,zk¯,yk¯].
• 3. Let ℒ be the language ℒ extended with functions used to built α H and T H the theory without logical axioms in the language ℒ H , we should prove that:
TαTHαH.
• 4. Since α H is an existential formula, we obtain a quasi-tautology for the extended language ℒ H . Hence,
• TαTHαH if, and only if,
• there is a quasi-tautology with instances of α H :
• For this reason, the proof of item 3 finish the proof.
• 5. To prove item 3, we only show the strategy for the converse implication, that is, TαT'αH , since the direct proof is relatively simple.
• 6. Let T c be the Henkin extension of T, defined in [5, p. 46], and T c+eq be the addition of equivalence axioms1 of Herbrand [5, p. 52] in T c , we show that:
• (a) T c is a conservative extension of T.
• (b) T c+eq is a conservative extension of T c
• These two fact will be important to the following steps.
• 7. We suppose that there is a quasi-tautology β1β2βq in ℒ H , with β i being a instance of the matrix α H . We now do a procedure of replacement of functions introduced for α H by constants in ℒ c . More specifically, if α H is of the form
θ[x¯,z¯1,f1(z¯1)¯,,z¯k,fk(z¯1,,z¯k)¯]
and β i if of the form
θ[t¯,u¯1,f1(u¯1)¯,,u¯k,fk(u¯1,,u¯k)¯],
• we define the sequence of special constants d(u1¯)¯,d(u1¯,u2¯)¯,,d(u1¯,,uk¯)¯ for eliminating the functions in the following manner:
• Notation 10 .
• (a) z¯i is a sequence of terms of the sequence z¯ from the index i onward;
• (b) z¯ij is a sequence of terms of z¯ from the index i up to the index j;
• (c) (z¯)i is the i’th term in the sequence z¯ ;
• The constant (d(u1¯)¯)i is a special constant for the formula
(y1¯)i(¬y1¯(i+1)z2¯y2¯zk¯yk¯θ[t¯,u¯1,d(u1¯)¯1(i1),f1(z1)¯i,]), (1)
• begin * a abbreviation that indicates the remaining sequence
u¯2,f2(u¯1)¯,,u¯k,fk(u¯1,,u¯k)¯.
And, generally, (d(u1¯,u2¯,ui¯)¯)j is a special constant for the formula
(yi¯)j(¬yi¯(j+i)zi+1¯yi+1¯zk¯yk¯θ[t¯,,d(u1¯,,ui¯)¯1(j1),f1(zi)¯j,]). (2)
• By successively applying the substitution axiom and modus ponens, we have that, se βi' is the formula
θ[t¯,u¯1,d1(u¯1)¯,,u¯k,dk(u¯1,,u¯k)¯],
• then Tc+eqβi'α .
• 8. Note that variables can occur in u¯ . However, to ensure the use of the equivalence axiom properties in T c+eq , we need all variables to be replaced by special constants. This will be necessary for the completion of the proof.
• So we make a second transformation in the quasi-tautology. Here equivalence axioms play an important role: they ensure that any two equivalent formulas refer to a single constant 2. With the addition of only the special axioms, we do not have this guarantee, since we could have two distinct elements satisfying the same formula of the form ∃.
• We introduce distinct special constants for each variable in u¯ , obtaining u¯' . Subsequently, we prove, using the special equivalence axioms, that
Tc+equ1¯=u1¯'d(u1¯)¯=d(u1¯')¯Tc+equ1¯=u1¯'u2¯=u2¯'d(u1¯,u2¯)¯=d(u1¯',u2¯')¯Tc+equ1¯=u1¯'uk¯=uk¯'d(u1¯,,uk¯)¯=d(u1¯',,uk¯')¯
• 9. We use a similar procedure as in [5, p. 55] to obtain a formula β1"β2"βq" , being βi" the replacement of the functions and variables introduced by the special constants shown above. Recall that the second transformation ensure us that Tc+eqβi"α by the same procedure as in item 7.
• We suppose C 1 , C 2 , …, C m to be the proof sequence for the quasi-tautology that uses only identity and equality in T. Thus we prove that the transformation that have led β1β2βk to become β1"β2"βk" preserves tautologically the sequence. Therefore, β1"β2"βk" is tautological consequence of C1",C2",,Cm" .
• It remains to prove that each Ci" is a theorem of T c+eq , when C i is an axiom of T. This will result in the proof of β1"β2"βk" in T c+eq . Each C i is an axiom of identity, equality, an instance of identity or an instance of equality. We note that, when we get Ci" , we have transformed C i into axioms of identity or equality, unless C i is an instance of identity. This last case, though, is easily proved in T c+eq from the propositions shown in the end of last item.
• 10. As Tc+eqβ1"β2"βk" and Tc+eqβi"α for each i, then Tc+eqα .
• 11.Since T c+eq is a conservative extension of the logic in ℒ, we lastly obtain that Tα.
3.1 Finitary proof of equiconsistency
In order to understand the finitary proof, it is important to consider procedures 7 and 8 of the previous section. In them, syntactic transformations are performed to provide the formulas βi" , eliminating the functions introduced to obtain the Herbrand’s normal formula.
Each introduction of a function to eliminate a universal quantification is performed independently of the other introductions. In this sense, we can restrict the elimination procedure to certain universal quantifications. In fact, we can eliminate one, some or all functions introduced to obtain the Herbrand’s normal form.
For the proof of the equiconsistency theorem, we will use the direct part of Herbrand’s theorem to obtain the quasi-tautology. Subsequently, we will make the procedure of the converse proof of Herbrand’s theorem restricted to the variables limited to sets.
Before performing this procedure, we will eliminate all universal quantifications that are not restricted to sets in the NBG axioms. We will therefore prove that unrestricted universal quantifications are easily eliminated from the axiomatization presented.
Proposition 11 (Extensionality)
(zV(zxzy)x=y)(xy(z(zxzy)x=y)).
Proof. By substitution, we have
Σ=defxy(z(zxzy)x=y){Σ}z(zxzy)x=y.
And, by generalization,
Π=defz(zxzy)x=y{Π}xy(z(zxzy)x=y)
We should now prove that
Π(zV(zxzy)x=y),
We know that (αβ¬αβ)θ is tautologically equivalent to βθ . Thus, z(zxzy) x=y is tautologically equivalent to (zV(zxzy)zV(zxzy)) x =y . Nevertheless, since we know that, by definition, zVw(zw) , then zV is equivalent to w(zw) . From this, we have that zV(zxzy) is a tautology. We thus obtain:
z(zxzy)x=y
If, and only if,
(zV(zxzy)zV(zxzy))x=y
If, and only if,
zV(zxzy)x=y
Note that we can use a similar procedure to limit other quantifications to sets, whenever we have a universal quantifier ∀z for a formula in which zx occurs. Although this technique does not work in all cases, for the axiomatization of NBG used in this article the procedure is effective. We will not expose here the corresponding proof for each axiom, for they are all very similar. In this sense, we have the following theorem:
Theorem 12 Let α be an axiom of NBG, then there is a formula α' such that α' is the elimination or restriction (to V) of all universal quantifications occurring in α and α'α .
We modify NBG yet one more time. The unrestricted existential quantifiers can be eliminated from instances of the scheme axiom for classes. We add, for each instance v¯Vzx(xz(xVα(x,v¯))) , the constant c α and replace the axiom for v¯VxV(xcα(xVα(x,v¯))) . Subsequently, we replace all other axiom of NBG by the version obtained by the successive application of the theorem 12. We call the resulting theory U.
We should prove the following theorem:
Theorem 13 For every formula γ, if NBGγ , then Uγ .
Proof. In order to proof this theorem, we should just treat the case in which γ is the scheme axiom for classes. From this and from theorem 12, we obtain easily that U proves all other axioms of NBG.
We take a formula α with n free variables and in which all quantifications are bouded to V. We then prove that
Uv¯Vzx(xz(zVα(x,v¯))) (3)
(We call this formula θ).
By replacement and generalization, we can eliminate the universal quantifications from the scheme axiom for classes. Thus we have Uθ if, and only if,
U(v¯V)zx(xz(xVα(x,v¯))). (4)
Since x and z do not occur in the left side of the implication, then Uθ if, and only if,
Uzx((v¯V)(xz(xVα(x,v¯)))). (5)
Let θ' be the formula
v¯VxV(xcα(xVα(x,v¯))).
We now eliminate the quantifiers of θ', obtaining
Ux((v¯V)(xcα(xVα(x,v¯)))).
Thus, by replacement and modus ponens,
Uzx((v¯V)(xz(xVα(x,v¯)))).
Therefore, Uθ . □
We continue by proving the lemma:
Lemma 14 Let α be a sentence without variables for classes.
If α is a theorem of U, then there is a proof of α in U that is free of unrestricted quantifications.
Proof.
By hypothesis, we have a proof of α in U. Let γ[x¯] be the conjunction of axioms used in the given proof, in which x¯ is the sequence of variables for classes that occur in the axioms. In this case, be the reduction theorem [5, p. 42]:
Tx¯γ[x¯]α,
or, equivalently,
Tx¯(γ[x¯]α) , for x¯ does not occur in α,
in which T is the theory without non logical axioms in the language of U.
Let θ[x¯] be a prenex form of γ[x¯]α . The formula θ[x¯] is of the form
z1¯y1¯zk¯yk¯β[x¯,z1¯,y1¯,,zk¯,yk¯].
From Herbrand’s theorem provability equivalence,
Tx¯θ[x¯]
if, and only if,
THx¯z¯1z¯kβ[x¯,z¯1,f1(x¯,z¯1)¯,,z¯k,fk(x¯,z¯1,,z¯k)¯],
in which T H is the theory obtained by the addition of function symbols in T, according to Herbrand’s normal form x¯θ[x¯] .
Let β' be a open formula
β[x¯,z¯1,f1(x¯,z¯1)¯,,z¯k,fk(x¯,z¯1,,z¯k)¯].
By Herbrand’s theorem, there is a quasi-tautology β1'βm' , in which each βi' is an instance of β' in the language of T H .
Let’s build the appropriate proof of α in U c+eq , obtained from U by the addition of special constants, special axioms and special axioms of equivalence.
From start, we replace each free variaable in β1'βm' for special constants. The result is a disjunction of m sentences that are quasi-tautological in U c+eq . This quasi-tautology is the starting point of the proof of α in U c+eq .
Subsequently, we replace the occurences of f1(a¯,b¯1)¯,,fk(a¯,b¯1,,b¯k)¯ for sequences of appropriate special constants. For this, we follow the items 7 and 8 in the proof of Herbrand’s theorem.
The result is the disjunction β1c1βmc' , tautological consequence of instances of identity, equality, special axioms and special equivalence axioms, having quantifications only for the variables z1¯,y1¯,,zk¯,yk¯ .
Let θ ic be the formula
z1¯y1¯zk¯yk¯β[ti¯,z1¯,y1¯,,zk¯,yk¯],
obtained from β ic by the restating the quantifications z1¯y1¯zk¯yk¯ . The closed terms in ti¯ are in U c+eq .
Each disjunction θ ic implies the corresponding βic' in U c+eq , as we have seen in the first paragraph of item 9 in Herbrand’s theorem proof. To show this, we use only simple properties of implication, of the quantifiers z1¯zk¯ and the special axioms used in the replacement of the occurrences f1(a¯,b¯1)¯,,fk(a¯,b¯1,,b¯k)¯ described above. From what we have exposed, it follows that
Uc+eqθ1cθmc,
without using quantifications over classes.
However, since θ[x¯] is a prenex form of γ[x¯]α , we have
Uc+eqθ[x¯](γ[x¯]α),
using only variations of quantifications that occur in γ[x¯]α . Therefore, no quantification for class variables. On the other hand, by the rule of substitution,
Uc+eqθ[ti¯](γ[ti¯]α).
As θ[ti¯]éθic , we conclude, using tautological consequence, that
Uc+eqγ[t1¯]γ[tm¯]α,
without using quantification for class variables.
On the other hand, γ[x¯] is the conjunction of axioms in U c+eq . Each γ[t1¯] can be proved in U c+eq using only tautological consequences and instances of the substitution rule. Therefore,
Uc+eqα,
without using quantification for class variables.
Finally, we observe that any proof of α of U in U c+eq can be transformed in a proof in U of the same α, and that this transformation introduces only quantifications directly related to the special axioms used [5, p. 52]. Since we haven’t used special axioms for class variables, the result follows.
From this result, we prove by finitary means the equiconsistency result:
Theorem 15 Let α be a sentence with all its quantifiers bounded to sets and such that NBGα . Then, ZFα .
Proof. Let α. be a sentence with all its quantifiers bounded to sets and such that NBGα . Thus, by lemma 14, there is a proof in U in which no unbounded quantifications occur. We call this proof sequence Seq.
We make transformations in this proof sequence that preserve tautological consequences, do not affect α. and such that the transformed axioms are theorems of ZF.
Let x 1 , x 2 ,...,x k be the free variables that occur in Seq. We add the following initial segment to the proof sequence x1V,x2V,,xkV , obtaining Seq*1.
Next, we apply the transformation * ZF in the formulas in Seq*1.
Every occurrence
1. cθ=cα , are replaced by yV(ycθycα)
2. cθx , are replaced by yV(y=cθyx)
3. cθcα , are replaced by yV(y=cθycα)
4. x=cα , are replaced by yV(yxycα)
5. xcθ , are replaced by θ(x)
The successive application of this transformation to Seq*1 eliminate all occurrences of c θ , forming the sequence Seq*2.
Recall that, for each logical axiom Axiom in Seq*1, we should verify whether Axiomj*ZF is also a logical axiom or a consequence of ZF together with formulas x1V, x2V,, xkV . In the second case, we replace each axiom Axiomj*ZF in Seq*2 by the proof sequence of Axiomj*ZF . Hence, we obtain Seq*3.
We know the following proposition about functors [5, p. 30]:
Proposition 16 A functor * of formulas to formulas satisfies for every formula α and β:
1. (¬α)*é¬α*
2. (αβ)*éα*β*
Thus, if δ is tautological consequence of γ 1 , γ 2 ,…, γ n , then δ*is tautological consequence of γ1*,γ2*,,γn* .
Therefore, all transformations described above do not affect the proof tautologically. However, some instances of the logical axioms may not be logical axioms after the transformation. We now investigate what happen with logical axioms in which constants of U occur.
• 1. Substitution axiom
• There is no instance of the substitution θx(c)xθ in Seq*1 since unrestricted quantifications do not occur in the initial proof in U.
• 2. Identity axiom
• Note that (cα=cα)*ZF is yV(α(y)α(y)) .
• And this last one is a tautology.
• 3.Equality axiom
• (a) If the axiom is of the form x1=cαx2=y2x1x2cαy2 , then, after the transformation:
(zV(zx1α(z))x2=y2)(x1 x2wV(zV(zwα(z))wy2))
• We show that this formula is theorem of ZF and of the formulas x1V,x2V,,xkV .
• If we have that zV(zx1α(z))x2=y2 and we suppose that x1 x2 , the, by corollary 2 of the identity theorem in [5, p. 36], we obtain
zV(zx1α(z))x1y2.
• Then, by the substitution axiom in ex1V ,
x1V(zV(zx1α(z))x1y2).
• Using the variant theorem [5, p. 35],
wV(zV(zwα(z))wy2).
• On the other hand, if we suppose that wV(zV(zwα(z))wy2) , then, since zV(zx1α(z)) and by extensionality in ZF, we prove that wV(w=x1wy2) . Hence, we obtain that x1 y2 . As, from hypothesis, x2y2 , we conclude that x1x2 , finalizing the proof.
• (b) x1=y1cα=y2x1cαy1y2 . The strategy for item b is similar to item a.
• (c) x1=y1cα=cβx1cαy1cβ . For this case, we obtain from the transformation:
x1=y1zV(α(z)β(z))α(x1)β(y1).
• As x 1 and y 1 are free variables in the formula, the transformed formula is tautological consequence of x1Vx2V and instances of identity axioms.
• (d) cβ=cαcγ=y2cβcγcαy2.
• (e) cβ=cαx2=y2cβx2cαy2.
• (f) cβ=cαcγ=cψcβcγcαcψ.
• We prove items d, e and f by a simple combination of the strategies used in a and c.
Let’s now evaluate what occur to the aximos in U after the transformation *ZF :
The instances of extensionality, scheme for classes, replacement for classes and foundations are the only ones we affect by applying *ZF (only in those axioms constants of U occur).
• 1. Extensionality. We evaluate two cases:
yV(yxycθ)x=cθ.yV(ycαycθ)cα=cθ.
• After *ZF , we have respectively
yV(yxθ(x))yV(yxθ(x))yV(α(x)θ(x))yV(α(x)θ(x)).
• Both are tautologies.
• 2. Scheme for classes. Let v 1 , v 2 ,… v n be free variables occurring in θ
v1v2vnVyV(ycθθ(y))
• After *ZF , we have
v1v2vnVyV(θ(y)θ(y))
• And this is a tautology.
• 3. Replacement for classes.
xV(func(cθ)yVw(wyvx((v,w)cθ)))
• becomes
xV(v1v2v3V(θ(v1,v2)θ(v1,v3)v2=v3)yVw1(w1yw2x(θ(w2,w1))))
• Which is precisely the replacement axiom for ZF.
• 4. Foundation.
(cθ0yV(ycθcθy=0))
• becomes
xVθ(x)yV(θ(y)w(wy¬θ(w)));
• We suppose xVθ(x) . Then x(xVαθ(x)) , for some ordinal a. Let A={x|xVαθ(x)} , it follows that ZFA0 . By the axiom of foundation, y(yA Ay=0) .
• This is equivalent to
y(θ(y)yVαw¬ (wyθ(w)wVα))(aswywVα)y(θ(y)yVαw¬ (wyθ(w)))
• That is, the formula is a theorem of ZF.
When axioms of U occur without constants, they can be understood as axioms of ZF, since we have added the formulas xiV .
1. Extensionality yV(yx yz)x=z , since we have xV and zV , represents extensionality in ZF.
2. The same is true for the axiom of replacement and foundation.
3. The axiom scheme for classes do not occur without constants in U.
Therefore, in the sequence Seq *3, we have:
1. formulas of the form xV ,
2. logical axioms,
3. axioms of ZF,
4. and all others are consequence of logical inferences from previous formulas in the sequence.
This is a proof in ZF. Since no transformation affect α, we have proved that ZFα .
Corollary 17 If there is α such that NBGα¬α , then there is a procedure that generate β such that ZF¬β .
Proof. If NBGα¬α , then NBG proves any formula. In particular, it proves a formula β¬β in which all quantifications are bounded to sets. Thus, by the theorem, ZFβ¬β . □
4 There is no interpretation of NBG in ZF
Before we prove there is no interpretation os NBG in ZF, we show some definitions as propositions:
Definition 18 Let V be a model of ZF and M a class V-definable, we say that the model M=(M,V) is a V-natural model.
Definition 19 Let ℳ be a model in the language ZF (the only non logical symbol is membership) and an interpretation I=U,ϕ of ZF in ZF (we write I for ϕ (∈)), then we define the model MI=(A,IM) emas
A={x|MU(x)}andIM={x,y|MU(x)U(y)xIy}
From this definition, we can easily prove by induction that:
Proposition 20 Let ℳ be a model in ZF and I=U,I be an interpretation of ZF in ZF , then, for all sentences α
MαIMIα
The following proposition is a strengthening of a result in 11. They show that if the existence of a transitive model of ZF is consistent with ZF, then there cannot be a set-interpretation of ZF in ZF. Here, we replace that consistency condition for “ZF does not prove the inconsistent sentence for ZF itself”.
Proposition 21 Let I=U,I be an interpretation of ZF in ZF, if ZF{x|U(x)} is a set, then ZF¬Con(ZF) .
Proof. Take I as in the proposition and suppose ZF{x|U(x)} is a set.
Let α be the Gödel number of the formula α represented in ZF. Since I is a set for every MZF , we define recursively the set T for each MZF :
Notation 22 a¯([k]=b) is the replacement of the k’th element of the sequence ā for b.
• α,a¯T if, and only if, a¯MI and
• (1) if α if atomic of the form xixj,ai;aj(MI)
• (2) if α is of the form βγ:β,a¯T and γ,a¯T
• (3) if α is of the form ¬β:β,a¯T
• (4) if α is of the form ¬xkβ:β,a¯([k]=b)T
• for some bMI
By finite induction over the formula complexity, we prove that
Mφ,a¯T if, and only if, MIφ(a¯)
Take Pr ZF (x, y) to be the provability predicate for ZF defined in ZF and representing the statement “x is the number of the proof y”. Then, we say that Th(ZF)={y|xPrZF(x,y)} . Hence, since MIZF,MTh(ZF)T . As MI00 , we have 00T . From this, we obtain M00Th(ZF) . Once is arbitrary, by the completeness theorem, if ZF has a model, then ZF00Th(ZF) . This is an absurd by Gödel’s incompleteness theorem. Thus, ZF¬Con(ZF) .
Definition 23 Let V be a model of ZF and ℳ a V-natural model. We say that ℳ reflect a formula φ(x¯) if, and only if, for every a¯M
Vφ(a¯)Mφ(a¯)
Theorem 24 [Reflection theorem] [6, p. 168] Let V be a model of ZF e and ϕ 1, ϕ 2, …, ϕ n any sequence of formulas, then, there is an ordinal a such that M=(Va,) reflect ϕ i for i between 1 and n.
We show that the desired result is a consequence of the reflection theorem and the fact that NBG is finitely axiomatizable:
Theorem 25 There is no interpretation of NBG in ZF.
Proof.
Suppose there is an interpretation I of NBG in ZF.
Since the number of axioms in NBG can be said to be finite, there is a formula α that is equivalent to the conjunction of all NBG’s axioms:
αisAxiom1Axiom2Axiomn.
Thus, NBGα
and, from the interpretation theorem for first-order logic, ZFαI .
Suppose VZF , then VαI . By the reflection theorem, there is an ordinal a such that VααI . It follows that VaIα .
Since V α is a set, we obtain that the domain in VaI is also a set.
We define the model V* in ℒ ZF :
1. The domain D in V* is such that D={x|VaIy(xy)} .
2. The predicate V*={x,y|VaIxy} .
Since NBG proves the restriction to sets of all ZF axioms, we have that V*ZF . Since the domain VaI is a set, it follows that D is also a set. It means that ZFCon(ZF) , absurd by the incompleteness theorem.
4 References
1 FREIRE, A. R. Estudo Comparado do Comprometimento Ontológico das Teorias de Classes e Conjuntos, PhD thesis, Campinas, 2019. [ Links ]
2 FREIRE, A. R. “On What Counts as a Translation”. In: Logica Yearbook, pp. 61-76 2018. [ Links ]
3 FREIRE, A.R. “Translation non Interpretable Theories”. Forthcoming in: South America Journal of Logic. [ Links ]
4 FREIRE, R. “On Existence in Set Theory” In: Notre Dame Journal of Formal Logic, 53, 4, pp. 525-547, 2012. [ Links ]
5 SHOENFIELD, J.R. Mathematical logic. Addison-Westley Publ. Comp, 1967. [ Links ]
6 JECH, T. Set Theory Springer Science & Business Media, 2013. [ Links ]
7 MURAWSKI, R. and MICKIEWICZ, A. “John von Neumann and Hilbert’s School of Foundations of Mathematics” Studies in Logic, Grammar and Rhetoric, 2004. [ Links ]
8 NOVAK, I.L. “Models of consistency systems” Fundamenta Mathematica, pp. 87-110, 1950. [ Links ]
9 SHOENFIELD, J.R. “A relative consistency proof” The Journal of Symbolic Logic 19, 4, pp. 21-28, 1954. [ Links ]
10 HILBERT, D. and BERNAYS, P. Grundlagen der Mathematik. [Von] D. Hilbert Und P. Bernays, 1968 [ Links ]
11 FREIRE, R. A. and TAUSK, D. V. “Inner models of set theory can’t satisfy V≠L” preprint, 2009. [ Links ]
1If c 1 and c 2 are special constant for the formulas ∃ 1(x) and ∃ 2(x), then the equivalence axiom for these constants is ∀x(α 1(x) ↔ α 2 (x) → c 1 = c 2.
2Realizing this characteristic was instrumental in establishing the relationship between the techniques used in (9) and the techniques presented in the book Grundlagen der Mathematik (10). In this paper, prior to his textbook of mathematical logic (5), Shoenfield makes use of epsilon Hilbert’s calculus as a way of guaranteeing the uniqueness of the special constants. Modern techniques make the conservative introduction of equivalence axioms.
3Article Info: CDD: 511.3
Received: January 18, 2019; Revised: January 25, 2019; Accepted: February 02, 2019
This is an open-access article distributed under the terms of the Creative Commons Attribution License | 2021-05-13T17:00:18 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9181295037269592, "perplexity": 1298.5596453689236}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243989814.35/warc/CC-MAIN-20210513142421-20210513172421-00240.warc.gz"} |
http://dlmf.nist.gov/34.2 | # §34.2 Definition: $3j$ Symbol
The quantities $j_{1},j_{2},j_{3}$ in the $3j$ symbol are called angular momenta. Either all of them are nonnegative integers, or one is a nonnegative integer and the other two are half-odd positive integers. They must form the sides of a triangle (possibly degenerate). They therefore satisfy the triangle conditions
34.2.1 $|j_{r}-j_{s}|\leq j_{t}\leq j_{r}+j_{s},$ Symbols: $j,j_{r}$: nonnegative integer, $r\in 1,2,3$, $t\in 1,2,3$ and $s$: nonnegative integer Referenced by: §34.10, §34.2, §34.3(iv) Permalink: http://dlmf.nist.gov/34.2.E1 Encodings: TeX, pMML, png
where $r,s,t$ is any permutation of $1,2,3$. The corresponding projective quantum numbers $m_{1},m_{2},m_{3}$ are given by
34.2.2 $m_{r}=-j_{r},-j_{r}+1,\dots,j_{r}-1,j_{r},$ $r=1,2,3$, Symbols: $j,j_{r}$: nonnegative integer and $r\in 1,2,3$ Referenced by: §34.4 Permalink: http://dlmf.nist.gov/34.2.E2 Encodings: TeX, pMML, png
and satisfy
34.2.3 $m_{1}+m_{2}+m_{3}=0.$ Referenced by: §34.10, §34.2, §34.3(iv), §34.4 Permalink: http://dlmf.nist.gov/34.2.E3 Encodings: TeX, pMML, png
See Figure 34.2.1 for a schematic representation.
If either of the conditions (34.2.1) or (34.2.3) is not satisfied, then the $3j$ symbol is zero. When both conditions are satisfied the $3j$ symbol can be expressed as the finite sum
34.2.4 $\begin{pmatrix}j_{1}&j_{2}&j_{3}\\ m_{1}&m_{2}&m_{3}\end{pmatrix}={(-1)^{j_{1}-j_{2}-m_{3}}}\Delta(j_{1}j_{2}j_{3% })\left((j_{1}+m_{1})!(j_{1}-m_{1})!(j_{2}+m_{2})!(j_{2}-m_{2})!(j_{3}+m_{3})!% (j_{3}-m_{3})!\right)^{\frac{1}{2}}\*\sum_{s}\frac{(-1)^{s}}{s!(j_{1}+j_{2}-j_% {3}-s)!(j_{1}-m_{1}-s)!(j_{2}+m_{2}-s)!(j_{3}-j_{2}+m_{1}+s)!(j_{3}-j_{1}-m_{2% }+s)!},$ Defines: $\begin{pmatrix}j_{1}&j_{2}&j_{3}\\ m_{1}&m_{2}&m_{3}\end{pmatrix}$: $3j$ symbol Symbols: $!$: $n!$: factorial, $j,j_{r}$: nonnegative integer, $\Delta(j_{1}j_{2}j_{3})$: product and $s$: nonnegative integer Permalink: http://dlmf.nist.gov/34.2.E4 Encodings: TeX, pMML, png
where
34.2.5 $\Delta(j_{1}j_{2}j_{3})=\left(\frac{(j_{1}+j_{2}-j_{3})!(j_{1}-j_{2}+j_{3})!(-% j_{1}+j_{2}+j_{3})!}{(j_{1}+j_{2}+j_{3}+1)!}\right)^{\frac{1}{2}},$ Symbols: $!$: $n!$: factorial, $j,j_{r}$: nonnegative integer and $\Delta(j_{1}j_{2}j_{3})$: product Permalink: http://dlmf.nist.gov/34.2.E5 Encodings: TeX, pMML, png
and the summation is over all nonnegative integers $s$ such that the arguments in the factorials are nonnegative.
Equivalently,
34.2.6 $\begin{pmatrix}j_{1}&j_{2}&j_{3}\\ m_{1}&m_{2}&m_{3}\end{pmatrix}={(-1)^{j_{2}-m_{1}+m_{3}}}\frac{(j_{1}+j_{2}+m_% {3})!(j_{2}+j_{3}-m_{1})!}{\Delta(j_{1}j_{2}j_{3})(j_{1}+j_{2}+j_{3}+1)!}\left% (\frac{(j_{1}+m_{1})!(j_{3}-m_{3})!}{(j_{1}-m_{1})!(j_{2}+m_{2})!(j_{2}-m_{2})% !(j_{3}+m_{3})!}\right)^{\frac{1}{2}}\*{\mathop{{{}_{3}F_{2}}\/}\nolimits\!% \left(-j_{1}-j_{2}-j_{3}-1,-j_{1}+m_{1},-j_{3}-m_{3};-j_{1}-j_{2}-m_{3},-j_{2}% -j_{3}+m_{1};1\right)},$
where $\mathop{{{}_{3}F_{2}}\/}\nolimits$ is defined as in §16.2.
For alternative expressions for the $3j$ symbol, written either as a finite sum or as other terminating generalized hypergeometric series $\mathop{{{}_{3}F_{2}}\/}\nolimits$ of unit argument, see Varshalovich et al. (1988, §§8.21, 8.24–8.26). | 2015-05-27T15:59:51 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 52, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9686846733093262, "perplexity": 3645.697156309491}, "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-2015-22/segments/1432207929012.53/warc/CC-MAIN-20150521113209-00296-ip-10-180-206-219.ec2.internal.warc.gz"} |
https://ftp.aimsciences.org/article/doi/10.3934/proc.2003.2003.223 | Article Contents
Article Contents
# On the geometry and topology of singular optimal control problems and their solutions
• The existence of singular arcs for optimal control problems is studied by using a geometric recursive algorithm inspired in Dirac’s theory of constraints. It is shown that singular arcs must lie in the singular locus of a projection map into the coestate space. After applying the geometrical recursive constraints algorithm, we arrive to a reduced set of hamiltonian equations that replace Pontriaguine’s maximum principle. Finally, a global singular perturbation theory is used to obtain nearly optimal solutions.
Mathematics Subject Classification: 49J15, 34A09, 34K35.
Citation:
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https://zbmath.org/authors/?q=ai%3Anirenberg.louis | ## Nirenberg, Louis
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Author ID: nirenberg.louis Published as: Nirenberg, Louis; Nirenberg, L. Further Spellings: Ниренберг Луис Homepage: https://www.math.nyu.edu/faculty/nirenl/ External Links: MacTutor · MGP · Wikidata · Math-Net.Ru · GND · IdRef Awards: Chern Medal (2010) · Abel Prize (2015)
Documents Indexed: 183 Publications since 1953, including 7 Books 11 Contributions as Editor · 6 Further Contributions Biographic References: 20 Publications Co-Authors: 99 Co-Authors with 120 Joint Publications 3,577 Co-Co-Authors
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### Co-Authors
74 single-authored 21 Berestycki, Henri 18 Caffarelli, Luis Ángel 17 Brézis, Haïm 12 Li, YanYan 11 Spruck, Joel 10 Trèves, François 8 Kohn, Joseph J. 7 Kinderlehrer, David 6 Agmon, Shmuel 5 Lax, Peter David 5 Varadhan, S. R. Srinivasa 4 Douglis, Avron 3 Atiyah, Michael Francis 3 Capuzzo Dolcetta, Italo 3 Kohn, Robert Vita 3 Raussen, Martin 3 Skau, Christian Fredrik 2 Bers, Lipman 2 Bertsch, Michiel 2 Browder, Felix Earl 2 Deligne, Pierre René 2 Ekeland, Ivar 2 Gidas, Basilis 2 Kuhn, Harold William 2 Mironescu, Petru 2 Nash, John Forbes jun. 2 Ni, Wei-Ming 2 Peletier, Lambertus Adrianus 2 Sarnak, Peter Clive 2 Sinaĭ, Yakov Grigor’evich 2 Spencer, Donald Clayton 2 Stampacchia, Guido 2 Véron, Laurent 2 Weisfeld, Morris 2 Wiles, Andrew John 1 Ahlfors, Lars Valerian 1 Anastasio, Sal 1 Artino, Ralph A. 1 Beals, Richard W. 1 Bojarski, Bogdan 1 Boldrighini, Carlo 1 Bombieri, Enrico 1 Bona, Jerry Lloyd 1 Bourguignon, Jean-Pierre 1 Bunimovich, Leonid Abramovich 1 Carleson, Lennart 1 Cellarosi, Francesco 1 Cenkl, Bohous 1 Chang, Sun-Yung Alice 1 Chanillo, Sagun 1 Cheng, Shiu-Yuen 1 Chern, Shiing-Shen 1 Ching, Wai-Mee 1 Cohen, Albert 1 Cohen, Amy 1 Córdoba Barba, Antonio Juan 1 Cordoba, Diego 1 Coron, Jean-Michel 1 Cushman, Richard H. 1 De Lellis, Camillo 1 Douglas, Ronald George 1 Fisher, Joseph A. 1 Foiaş, Ciprian Ilie 1 Friedlander, Susan Jean 1 Fröhlich, Jürg Martin 1 Garabedian, Paul Roesel 1 Goldschmidt, Hubert Leopold 1 Graham, C. Robin 1 Griffiths, Phillip Augustus 1 Gromov, Mikhael Leonidovich 1 Guillemin, Victor W. 1 Gurevich, B. M. 1 Hartman, Philip 1 Heckman, Gert 1 Hitchin, Nigel James 1 Holden, Helge 1 Illusie, Luc 1 Inoue, Atsushi 1 John, Fritz 1 Karlin, Samuel 1 Kazdan, Jerry L. 1 Khanin, Konstantin M. 1 Klartag, Bo’az 1 Kodaira, Kunihiko 1 Koiso, Norihito 1 Kolk, Johan A. C. 1 Kotake, Takeshi 1 Kra, Irwin 1 Lebowitz, Joel Louis 1 Lemaire, Luc 1 Levine, Harold I. 1 Li, Dong 1 Lin, Chang-Shou 1 Loewner, Charles 1 Martio, Olli 1 Maskit, Bernard 1 Mastrian, Barbara 1 Mather, John N. 1 Mawhin, Jean L. 1 McKean, Henry P. jun. ...and 53 more Co-Authors
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### Serials
43 Communications on Pure and Applied Mathematics 8 Notices of the American Mathematical Society 4 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 4 Comptes Rendus Hebdomadaires des Séances de l’Académie des Sciences, Série A 3 Duke Mathematical Journal 3 Comptes Rendus de l’Académie des Sciences. Série I 3 Topological Methods in Nonlinear Analysis 2 Journal of Mathematical Analysis and Applications 2 Journal of Mathematical Sciences (New York) 2 Selecta Mathematica. New Series 2 Methods and Applications of Analysis 2 Annals of Mathematics. Second Series 2 Annali della Scuola Normale Superiore di Pisa. Scienze Fisiche e Matematiche. III. Ser 1 Communications in Mathematical Physics 1 Journal d’Analyse Mathématique 1 Russian Mathematical Surveys 1 Uspekhi Matematicheskikh Nauk [N. S.] 1 Journal of Geometry and Physics 1 Acta Mathematica 1 American Journal of Mathematics 1 Compositio Mathematica 1 Conferenze del Seminario di Matematica dell’Università di Bari 1 Journal of Differential Geometry 1 Journal of the Faculty of Science. Section I A 1 Le Matematiche 1 Mathematische Annalen 1 Rendiconti del Seminario Matemàtico e Fisico di Milano 1 Rendiconti di Matematica e delle sue Applicazioni. Serie VII 1 Chinese Annals of Mathematics. Series B 1 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 1 Revista Matemática Iberoamericana 1 CWI Quarterly 1 Bulletin of the American Mathematical Society. New Series 1 Boletim da Sociedade Brasileira de Matemática. Nova Série 1 NoDEA. Nonlinear Differential Equations and Applications 1 European Mathematical Society Newsletter 1 Journal of Mathematical Fluid Mechanics 1 Journal of the European Mathematical Society (JEMS) 1 Milan Journal of Mathematics 1 Bollettino della Unione Matematica Italiana. Series IV 1 Annals of Mathematics Studies 1 Contemporary Mathematics 1 Regional Conference Series in Mathematics 1 Courant Lecture Notes in Mathematics 1 Journal of Fixed Point Theory and Applications 1 Bollettino dell’Unione Matematica Italiana. Series IX 1 CIME Summer Schools 1 Springer Collected Works in Mathematics 1 CTM. Classical Topics in Mathematics 1 The Abel Prize
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### Fields
107 Partial differential equations (35-XX) 25 Operator theory (47-XX) 22 History and biography (01-XX) 19 Global analysis, analysis on manifolds (58-XX) 12 Differential geometry (53-XX) 10 Calculus of variations and optimal control; optimization (49-XX) 9 General and overarching topics; collections (00-XX) 6 Functional analysis (46-XX) 5 Several complex variables and analytic spaces (32-XX) 4 Ordinary differential equations (34-XX) 4 Algebraic topology (55-XX) 4 Fluid mechanics (76-XX) 3 Real functions (26-XX) 2 Functions of a complex variable (30-XX) 2 Dynamical systems and ergodic theory (37-XX) 2 General topology (54-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Integral equations (45-XX) 1 Manifolds and cell complexes (57-XX) 1 Probability theory and stochastic processes (60-XX) 1 Mechanics of deformable solids (74-XX) 1 Classical thermodynamics, heat transfer (80-XX)
### Citations contained in zbMATH Open
147 Publications have been cited 15,519 times in 12,664 Documents Cited by Year
Positive solutions of nonlinear elliptic equations involving critical Sobolev exponents. Zbl 0541.35029
Brézis, Haïm; Nirenberg, Louis
1983
Symmetry and related properties via the maximum principle. Zbl 0425.35020
Gidas, B.; Ni, Wei-Ming; Nirenberg, Louis
1979
Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I. Zbl 0093.10401
Agmon, S.; Douglis, A.; Nirenberg, Louis
1959
On elliptic partial differential equations. Zbl 0088.07601
Nirenberg, Louis
1959
Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. II. Zbl 0123.28706
Agmon, S.; Douglis, A.; Nirenberg, Louis
1964
On functions of bounded mean oscillation. Zbl 0102.04302
John, Fritz; Nirenberg, Louis
1961
Partial regularity of suitable weak solutions of the Navier-Stokes equations. Zbl 0509.35067
Caffarelli, L.; Kohn, R.; Nirenberg, Louis
1982
First order interpolation inequalities with weights. Zbl 0563.46024
Caffarelli, L.; Kohn, R.; Nirenberg, Louis
1984
The Dirichlet problem for nonlinear second order elliptic equations. III: Functions of the eigenvalues of the Hessian. Zbl 0654.35031
Caffarelli, L.; Nirenberg, L.; Spruck, J.
1985
On the method of moving planes and the sliding method. Zbl 0784.35025
Berestycki, H.; Nirenberg, L.
1991
The principal eigenvalue and maximum principle for second-order elliptic operators in general domains. Zbl 0806.35129
Berestycki, H.; Nirenberg, L.; Varadhan, S. R. S.
1994
Topics in nonlinear functional analysis. Notes by R. A. Artino. Zbl 0286.47037
Nirenberg, Louis
1974
The Dirichlet problem for nonlinear second-order elliptic equations. I: Monge-Ampère equation. Zbl 0598.35047
Caffarelli, L.; Nirenberg, Louis; Spruck, J.
1984
Complex analytic coordinates in almost complex manifolds. Zbl 0079.16102
Newlander, A.; Nirenberg, Louis
1957
Symmetry of positive solutions of nonlinear elliptic equations in $$\mathbb R^n$$. Zbl 0469.35052
Gidas, B.; Ni, Wei-Ming; Nirenberg, Louis
1981
Remarks on finding critical points. Zbl 0751.58006
Brézis, Haïm; Nirenberg, Louis
1991
Non-coercive boundary value problems. Zbl 0125.33302
Kohn, J. J.; Nirenberg, Louis
1965
An algebra of pseudo-differential operators. Zbl 0171.35101
Kohn, J. J.; Nirenberg, Louis
1965
Remarks on strongly elliptic partial differential equations. Zbl 0067.07602
Nirenberg, Louis
1955
Characterizations of the ranges of some nonlinear operators and applications to boundary value problems. Zbl 0386.47035
Brézis, Haïm; Nirenberg, Louis
1978
Properties of solutions of ordinary differential equations in Banach space. Zbl 0117.10001
Agmon, S.; Nirenberg, Louis
1963
The Weyl and Minkowski problems in differential geometry in the large. Zbl 0051.12402
Nirenberg, Louis
1953
Interior estimates for elliptic systems of partial differential equations. Zbl 0066.08002
Douglis, Avron; Nirenberg, Louis
1955
An extended interpolation inequality. Zbl 0163.29905
Nirenberg, Louis
1966
Travelling fronts in cylinders. Zbl 0799.35073
Berestycki, Henri; Nirenberg, Louis
1992
H$$^ 1$$ versus C$$^ 1$$ local minimizers. Zbl 0803.35029
Brézis, Haïm; Nirenberg, Louis
1993
Topics in nonlinear functional analysis. Notes by Ralph A. Artino. Revised reprint of the 1974 original. Zbl 0992.47023
Nirenberg, Louis
2001
Further qualitative properties for elliptic equations in unbounded domains. Zbl 1079.35513
Berestycki, Henri; Caffarelli, Luis; Nirenberg, Louis
1997
Degree theory of BMO. I: Compact manifolds without boundaries. Zbl 0852.58010
Brézis, Haïm; Nirenberg, Louis
1995
Superlinear indefinite elliptic problems and nonlinear Liouville theorems. Zbl 0816.35030
Berestycki, H.; Capuzzo Dolcetta, I.; Nirenberg, L.
1994
A remark on Ky Fan’s minimax principle. Zbl 0264.49013
Brézis, Haïm; Nirenberg, Louis; Stampacchia, Guido
1972
Monotonicity for elliptic equations in unbounded Lipschitz domains. Zbl 0906.35035
Berestycki, H.; Caffarelli, L. A.; Nirenberg, L.
1997
The Dirichlet problem for nonlinear second-order elliptic equations. II: Complex Monge-Ampère, and uniformly elliptic, equations. Zbl 0598.35048
Caffarelli, L.; Kohn, J. J.; Nirenberg, Louis; Spruck, J.
1985
Estimates for elliptic systems from composite material. Zbl 1125.35339
Li, YanYan; Nirenberg, Louis
2003
Variational methods for indefinite superlinear homogeneous elliptic problems. Zbl 0840.35035
Berestycki, Henri; Capuzzo-Dolcetta, Italo; Nirenberg, Louis
1995
Regularity in free boundary problems. Zbl 0352.35023
Kinderlehrer, D.; Nirenberg, Louis
1977
On spherical image maps whose Jacobians do not change sign. Zbl 0094.16303
Hartman, Philip; Nirenberg, Louis
1959
Degenerate elliptic-parabolic equations of second order. Zbl 0153.14503
Kohn, J. J.; Nirenberg, Louis
1967
Lectures on linear partial differential equations. Zbl 0267.35001
Nirenberg, Louis
1973
An abstract form of the nonlinear Cauchy-Kowalewski theorem. Zbl 0257.35001
Nirenberg, Louis
1972
Free vibrations for a nonlinear wave equation and a theorem of P. Rabinowitz. Zbl 0484.35057
Brézis, Haïm; Coron, Jean-Michel; Nirenberg, Louis
1980
On the analycity of the solutions of linear elliptic systems of partial differential equations. Zbl 0082.09402
Morrey, C. B. jun.; Nirenberg, Louis
1957
On nonlinear elliptic partial differential equations and Hölder continuity. Zbl 0050.09801
Nirenberg, Louis
1953
Inequalities for second-order elliptic equations with applications to unbounded domains. I. Zbl 0860.35004
Berestycki, H.; Caffarelli, L. A.; Nirenberg, L.
1996
Forced vibrations for a nonlinear wave equation. Zbl 0378.35040
Brézis, Haïm; Nirenberg, Louis
1978
The Minkowski multidimensional problem. Translated by Vladimir Oliker and introduced by Louis Nirenberg. Zbl 0387.53023
Pogorelov, Aleksey Vasil’yevich
1978
A strong maximum principle for parabolic equations. Zbl 0050.09601
Nirenberg, Louis
1953
The null spaces of elliptic partial differential operators in R$$^n$$. Zbl 0272.35029
Nirenberg, Louis; Walker, Homer F.
1973
Variational and topological methods in nonlinear problems. Zbl 0468.47040
Nirenberg, Louis
1981
Solvability of a first order linear partial differential equation. Zbl 0117.06104
Nirenberg, Louis; Trèves, François
1963
Partial differential equations invariant under conformal or projective transformations. Zbl 0298.35018
Loewner, Charles; Nirenberg, Louis
1974
Nonlinear second-order elliptic equations. V: The Dirichlet problem for Weingarten hypersurfaces. Zbl 0672.35028
Caffarelli, Luis; Nirenberg, Louis; Spruck, Joel
1988
Monotonicity, symmetry and antisymmetry of solutions of semilinear elliptic equations. Zbl 0698.35031
Berestycki, H.; Nirenberg, L.
1988
A pseudo-convex domain not admitting a holomorphic support function. Zbl 0248.32013
Kohn, J. J.; Nirenberg, Louis
1973
Regularity in elliptic free boundary problems. I. Zbl 0402.35045
Kinderlehrer, D.; Nirenberg, Louis; Spruck, J.
1978
The distance function to the boundary, Finsler geometry, and the singular set of viscosity solutions of some Hamilton-Jacobi equations. Zbl 1062.49021
Li, YanYan; Nirenberg, Louis
2005
The Dirichlet problem for singularly perturbed elliptic equations. Zbl 0933.35083
Li, Yanyan; Nirenberg, Louis
1998
Uniform estimates for regularization of free boundary problems. Zbl 0702.35252
Berestycki, H.; Caffarelli, L. A.; Nirenberg, L.
1990
Some qualitative properties of solutions of semilinear elliptic equations in cylindrical domains. Zbl 0705.35004
Berestycki, H.; Nirenberg, L.
1990
On stability for difference schemes; a sharp form of Garding’s inequality. Zbl 0185.22801
Lax, Peter D.; Nirenberg, Louis
1966
On local solvability of linear partial differential equations. I: Necessary conditions. Zbl 0191.39103
Nirenberg, Louis; Trèves, François
1970
Lower bounds and uniqueness theorems for solutions of differential equations in a Hilbert space. Zbl 0147.34603
Agmon, S.; Nirenberg, Louis
1967
Degree theory and BMO. II: Compact manifolds with boundaries. (Appendix with Petru Mironescu). Zbl 0868.58017
Brézis, Haïm; Nirenberg, Louis
1996
A maximum principle for a class of hyperbolic equations and applications to equations of mixed elliptic-hyperbolic type. Zbl 0090.07401
Agmon, S.; Nirenberg, Louis; Protter, M. H.
1953
On the existence of deformations of complex analytic structures. Zbl 0088.38004
Kodaira, Kunihiko; Nirenberg, Louis; Spencer, D. C.
1958
Intrinsic norms on a complex manifold. Zbl 0202.11603
Chern, S. S.; Levine, H. I.; Nirenberg, Louis
1969
On local solvability of linear partial differential equations. Part II: Sufficient conditions. Zbl 0208.35902
Nirenberg, Louis; Trèves, François
1970
Nonlinear second order elliptic equations. IV. Starshaped compact Weingarten hypersurfaces. Zbl 0672.35027
Caffarelli, L.; Nirenberg, L.; Spruck, J.
1986
Symmetry for elliptic equations in a half space. Zbl 0793.35034
Berestycki, H.; Caffarelli, L. A.; Nirenberg, L.
1993
Uniqueness in Cauchy problems for differential equations with constant leading coefficients. Zbl 0077.09402
Nirenberg, Louis
1957
Some remarks on singular solutions of nonlinear elliptic equations. III: Viscosity solutions including parabolic operators. Zbl 1279.35044
Caffarelli, Luis; Li, Yanyan; Nirenberg, Louis
2013
Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I. Übersetzung aus dem Englischen von L. R. Volevich. Unter Redaktion von M. I. Vishik. Zbl 0104.32305
Agmon, S.; Douglis, A.; Nirenberg, Louis
1962
Local boundary regularity of holomorphic mappings. Zbl 0436.32018
Nirenberg, Louis; Webster, S.; Yang, P.
1980
A minimization problem with critical exponent and nonzero data. Zbl 0763.46023
Brézis, Haïm; Nirenberg, Louis
1989
Some remarks on singular solutions of nonlinear elliptic equations. I. Zbl 1215.35068
Caffarelli, Luis; Li, Yan Yan; Nirenberg, Louis
2009
On a theorem of P. Nowosad. Zbl 0165.45802
Karlin, S.; Nirenberg, Louis
1967
Estimates and existence of solutions of elliptic equations. Zbl 0070.32301
Nirenberg, Louis
1956
The smoothness of the free boundary in the one phase Stefan problem. Zbl 0391.35060
Kinderlehrer, David; Nirenberg, Louis
1978
The Dirichlet problem for the degenerate Monge-Ampère equation. Zbl 0611.35029
Caffarelli, L.; Nirenberg, L.; Spruck, J.
1987
Topics in nonlinear functional analysis. (Lektsii po nelinejnomu funktsional’nomu analizu). Transl. from the English by N. D. Vvedenskaya. Zbl 0426.47034
Nirenberg, Louis
1977
Removable singularities for nonlinear elliptic equations. Zbl 0905.35027
Brézis, Haïm; Nirenberg, Louis
1997
Analyticity at the boundary of solutions of nonlinear second-order parabolic equations. Zbl 0391.35045
Kinderlehrer, David; Nirenberg, Louis
1978
On a question of Hans Lewy. Zbl 0305.35017
Nirenberg, Louis
1974
On a generalization of quasi-conformal mappings and its application to elliptic partial differential equations. Zbl 0057.08604
Nirenberg, Louis
1954
On a representation theorem for linear elliptic systems with discontinuous coefficients and its applications. Zbl 0067.32503
Bers, Lipman; Nirenberg, Louis
1955
Some remarks on singular solutions of nonlinear elliptic equations. II: Symmetry and monotonicity via moving planes. Zbl 1325.35044
Caffarelli, Luis; Li, YanYan; Nirenberg, Louis
2012
A correction to: On local solvability of linear partial differential equations. II: Sufficient conditions. Zbl 0221.35019
Nirenberg, Louis; Treves, J. F.
1971
Degree and Sobolev spaces. Zbl 0956.46024
Brézis, Haïm; Li, Yanyan; Mironescu, Petru; Nirenberg, Louis
1999
Variational methods in nonlinear problems. Zbl 0980.58005
Nirenberg, L.
2000
Indefinite elliptic equations and nonlinear Liouville theorems. (Problèmes elliptiques indéfinis et théorèmes de Liouville non linéaires.) Zbl 0820.35056
Berestycki, Henri; Capuzzo-Dolcetta, Italo; Nirenberg, Louis
1993
A proof of the Malgrange preparation theorem. Zbl 0212.10702
Nirenberg, Louis
1971
A complex Frobenius theorem. Zbl 0099.37502
Nirenberg, Louis
1958
Pseudo-differential operators. Zbl 0218.35075
Nirenberg, Louis
1970
On linear and non-linear elliptic boundary value problems in the plane. Zbl 0067.32504
Bers, Lipman; Nirenberg, Louis
1955
On a form of Bernstein’s theorem. Zbl 0668.35028
Caffarelli, L.; Nirenberg, L.; Spruck, J.
1988
Comments on nonlinear problems (with an appendix by Lin Changshou). Zbl 0544.58005
Nirenberg, Louis
1981
Regularity in elliptic free boundary problems. II: Equations of higher order. Zbl 0425.35097
Kinderlehrer, D.; Nirenberg, Louis; Spruck, J.
1979
Asymptotic behaviour via the Harnack inequality. Zbl 0840.35011
Berestycki, H.; Nirenberg, L.
1991
Correction to: The Dirichlet problem for nonlinear second-order elliptic equations. I. Monge-Ampère equation. Zbl 0641.35025
Caffarelli, L.; Nirenberg, L.; Spruck, J.
1987
Uniqueness in the Cauchy problem for a degenerate elliptic second order equation. Zbl 0572.35043
Nirenberg, Louis
1985
Felix Browder (1927–2016). Zbl 1406.35004
Brezis, Haïim; Nussbaum, Roger D.; Cohen, Amy; Beals, Richard; Mawhin, Jean; Teman, Roger; Nirenberg, Louis; Berestycki, Henri; Mastrian, Barbara; Chanillo, Sagun; Lebowitz, Joel; Roberts, Fred; Bona, Jerry
2018
Lipman Bers and partial differential equations. Zbl 1361.35006
Nirenberg, Louis
2015
Some remarks on singular solutions of nonlinear elliptic equations. III: Viscosity solutions including parabolic operators. Zbl 1279.35044
Caffarelli, Luis; Li, Yanyan; Nirenberg, Louis
2013
Some remarks on singular solutions of nonlinear elliptic equations. II: Symmetry and monotonicity via moving planes. Zbl 1325.35044
Caffarelli, Luis; Li, YanYan; Nirenberg, Louis
2012
The principal eigenvalue and maximum principle for second-order elliptic operators in general domains. Zbl 1316.35217
Berestycki, H.; Nirenberg, L.; Varadhan, S. R. S.
2012
On singular solutions of nonlinear elliptic and parabolic equations. Zbl 1226.35028
Nirenberg, Louis
2011
Remembering Johannes J. Duistermaat (1942–2010). Zbl 1225.01067
Atiyah, Michael; Cushman, Richard; Heckman, Gert; van den Ban, Erik; Kolk, Johan; Nirenberg, Louis; Sjamaar, Reyer; Sjöstrand, Johannes
2011
Some remarks on singular solutions of nonlinear elliptic equations. I. Zbl 1215.35068
Caffarelli, Luis; Li, Yan Yan; Nirenberg, Louis
2009
Partial results on extending the Hopf Lemma. Zbl 1196.35062
Li, Yan Yan; Nirenberg, Louis
2009
A remark on Ky Fan’s minimax principle. Zbl 1225.49014
Brézis, H.; Nirenberg, L.; Stampacchia, G.
2008
Perspectives in nonlinear partial differential equations in honor of Haïm Brezis. Based on the conference celebration of Haïm Brezis’ 60th birthday, June 21–25, 2004. Zbl 1126.00013
2007
A geometric problem and the Hopf lemma. II. Zbl 1149.53302
Li, YanYan; Nirenberg, Louis
2006
A geometric problem and the Hopf lemma. I. Zbl 1113.53003
Li, YanYan; Nirenberg, Louis
2006
Generalization of a well-known inequality. Zbl 1284.26021
Li, YanYan; Nirenberg, Louis
2006
The distance function to the boundary, Finsler geometry, and the singular set of viscosity solutions of some Hamilton-Jacobi equations. Zbl 1062.49021
Li, YanYan; Nirenberg, Louis
2005
Regularity in an unusual variational problem. Zbl 1113.49041
Ekeland, Ivar; Nirenberg, Louis
2005
The distance function to the boundary and singular set of viscosity solutions of Hamilton-Jacobi equation. Zbl 1387.35106
Nirenberg, L.
2005
Abstract and applied analysis. Proceedings of the international conference, Hanoi, Vietnam, August 13–17, 2002. Zbl 1058.00011
2004
Olga Alexandrovna Ladyzhenskaya (1922–2004). Zbl 1168.01327
Friedlander, Susan; Lax, Peter; Morawetz, Cathleen; Nirenberg, Louis; Seregin, Gregory; Ural’tseva, Nina; Vishik, Mark
2004
Estimates for elliptic systems from composite material. Zbl 1125.35339
Li, YanYan; Nirenberg, Louis
2003
A convex Darboux theorem. Zbl 1082.58501
Ekeland, Ivar; Nirenberg, Louis
2002
Topics in nonlinear functional analysis. Notes by Ralph A. Artino. Revised reprint of the 1974 original. Zbl 0992.47023
Nirenberg, Louis
2001
Variational methods in nonlinear problems. Zbl 0980.58005
Nirenberg, L.
2000
Degree and Sobolev spaces. Zbl 0956.46024
Brézis, Haïm; Li, Yanyan; Mironescu, Petru; Nirenberg, Louis
1999
The Dirichlet problem for singularly perturbed elliptic equations. Zbl 0933.35083
Li, Yanyan; Nirenberg, Louis
1998
Further qualitative properties for elliptic equations in unbounded domains. Zbl 1079.35513
Berestycki, Henri; Caffarelli, Luis; Nirenberg, Louis
1997
Monotonicity for elliptic equations in unbounded Lipschitz domains. Zbl 0906.35035
Berestycki, H.; Caffarelli, L. A.; Nirenberg, L.
1997
Removable singularities for nonlinear elliptic equations. Zbl 0905.35027
Brézis, Haïm; Nirenberg, Louis
1997
Inequalities for second-order elliptic equations with applications to unbounded domains. I. Zbl 0860.35004
Berestycki, H.; Caffarelli, L. A.; Nirenberg, L.
1996
Degree theory and BMO. II: Compact manifolds with boundaries. (Appendix with Petru Mironescu). Zbl 0868.58017
Brézis, Haïm; Nirenberg, Louis
1996
Degree theory of BMO. I: Compact manifolds without boundaries. Zbl 0852.58010
Brézis, Haïm; Nirenberg, Louis
1995
Variational methods for indefinite superlinear homogeneous elliptic problems. Zbl 0840.35035
Berestycki, Henri; Capuzzo-Dolcetta, Italo; Nirenberg, Louis
1995
The principal eigenvalue and maximum principle for second-order elliptic operators in general domains. Zbl 0806.35129
Berestycki, H.; Nirenberg, L.; Varadhan, S. R. S.
1994
Superlinear indefinite elliptic problems and nonlinear Liouville theorems. Zbl 0816.35030
Berestycki, H.; Capuzzo Dolcetta, I.; Nirenberg, L.
1994
Partial differential equations in the first half of the century. Zbl 0807.01017
Nirenberg, Louis
1994
H$$^ 1$$ versus C$$^ 1$$ local minimizers. Zbl 0803.35029
Brézis, Haïm; Nirenberg, Louis
1993
Symmetry for elliptic equations in a half space. Zbl 0793.35034
Berestycki, H.; Caffarelli, L. A.; Nirenberg, L.
1993
Indefinite elliptic equations and nonlinear Liouville theorems. (Problèmes elliptiques indéfinis et théorèmes de Liouville non linéaires.) Zbl 0820.35056
Berestycki, Henri; Capuzzo-Dolcetta, Italo; Nirenberg, Louis
1993
The ground state and maximum principle for second order elliptic operators in general domains. (État fondamental et principe du maximum pour les opérateurs elliptiques du second ordre dans des domaines généraux.) Zbl 0798.35038
Berestycki, Henri; Nirenberg, Louis; Varadhan, Srinivasa
1993
Travelling fronts in cylinders. Zbl 0799.35073
Berestycki, Henri; Nirenberg, Louis
1992
On the maximum principle. Videotape. Zbl 0790.35001
Nirenberg, Louis
1992
On the method of moving planes and the sliding method. Zbl 0784.35025
Berestycki, H.; Nirenberg, L.
1991
Remarks on finding critical points. Zbl 0751.58006
Brézis, Haïm; Nirenberg, Louis
1991
Asymptotic behaviour via the Harnack inequality. Zbl 0840.35011
Berestycki, H.; Nirenberg, L.
1991
Travelling front solutions of semilinear equations in $$n$$ dimensions. Zbl 0780.35054
Berestycki, H.; Nirenberg, L.
1991
Uniform estimates for regularization of free boundary problems. Zbl 0702.35252
Berestycki, H.; Caffarelli, L. A.; Nirenberg, L.
1990
Some qualitative properties of solutions of semilinear elliptic equations in cylindrical domains. Zbl 0705.35004
Berestycki, H.; Nirenberg, L.
1990
A minimization problem with critical exponent and nonzero data. Zbl 0763.46023
Brézis, Haïm; Nirenberg, Louis
1989
On fully nonlinear elliptic equations of second order. Zbl 0778.35035
Nirenberg, L.
1989
Variational methods in nonlinear problems. Zbl 0679.58021
Nirenberg, L.
1989
Nonlinear second-order elliptic equations. V: The Dirichlet problem for Weingarten hypersurfaces. Zbl 0672.35028
Caffarelli, Luis; Nirenberg, Louis; Spruck, Joel
1988
Monotonicity, symmetry and antisymmetry of solutions of semilinear elliptic equations. Zbl 0698.35031
Berestycki, H.; Nirenberg, L.
1988
On a form of Bernstein’s theorem. Zbl 0668.35028
Caffarelli, L.; Nirenberg, L.; Spruck, J.
1988
Fully nonlinear elliptic equations. Zbl 0685.35045
Nirenberg, L.
1988
The Dirichlet problem for the degenerate Monge-Ampère equation. Zbl 0611.35029
Caffarelli, L.; Nirenberg, L.; Spruck, J.
1987
Correction to: The Dirichlet problem for nonlinear second-order elliptic equations. I. Monge-Ampère equation. Zbl 0641.35025
Caffarelli, L.; Nirenberg, L.; Spruck, J.
1987
Nonlinear second order elliptic equations. IV. Starshaped compact Weingarten hypersurfaces. Zbl 0672.35027
Caffarelli, L.; Nirenberg, L.; Spruck, J.
1986
The Dirichlet problem for nonlinear second order elliptic equations. III: Functions of the eigenvalues of the Hessian. Zbl 0654.35031
Caffarelli, L.; Nirenberg, L.; Spruck, J.
1985
The Dirichlet problem for nonlinear second-order elliptic equations. II: Complex Monge-Ampère, and uniformly elliptic, equations. Zbl 0598.35048
Caffarelli, L.; Kohn, J. J.; Nirenberg, Louis; Spruck, J.
1985
Uniqueness in the Cauchy problem for a degenerate elliptic second order equation. Zbl 0572.35043
Nirenberg, Louis
1985
First order interpolation inequalities with weights. Zbl 0563.46024
Caffarelli, L.; Kohn, R.; Nirenberg, Louis
1984
The Dirichlet problem for nonlinear second-order elliptic equations. I: Monge-Ampère equation. Zbl 0598.35047
Caffarelli, L.; Nirenberg, Louis; Spruck, J.
1984
Positive solutions of nonlinear elliptic equations involving critical Sobolev exponents. Zbl 0541.35029
Brézis, Haïm; Nirenberg, Louis
1983
Variational and topological methods in nonlinear problems. Zbl 0524.47041
Nirenberg, Louis
1983
Partial regularity of suitable weak solutions of the Navier-Stokes equations. Zbl 0509.35067
Caffarelli, L.; Kohn, R.; Nirenberg, Louis
1982
Symmetry of positive solutions of nonlinear elliptic equations in $$\mathbb R^n$$. Zbl 0469.35052
Gidas, B.; Ni, Wei-Ming; Nirenberg, Louis
1981
Variational and topological methods in nonlinear problems. Zbl 0468.47040
Nirenberg, Louis
1981
Comments on nonlinear problems (with an appendix by Lin Changshou). Zbl 0544.58005
Nirenberg, Louis
1981
Free vibrations for a nonlinear wave equation and a theorem of P. Rabinowitz. Zbl 0484.35057
Brézis, Haïm; Coron, Jean-Michel; Nirenberg, Louis
1980
Local boundary regularity of holomorphic mappings. Zbl 0436.32018
Nirenberg, Louis; Webster, S.; Yang, P.
1980
Symmetry and related properties via the maximum principle. Zbl 0425.35020
Gidas, B.; Ni, Wei-Ming; Nirenberg, Louis
1979
Regularity in elliptic free boundary problems. II: Equations of higher order. Zbl 0425.35097
Kinderlehrer, D.; Nirenberg, Louis; Spruck, J.
1979
Non-linear problems in geometry. Conference held at Katata, September 3–8, 1979. Proceedings of the 6th international Taniguchi symposium. Zbl 0433.53002
1979
Characterizations of the ranges of some nonlinear operators and applications to boundary value problems. Zbl 0386.47035
Brézis, Haïm; Nirenberg, Louis
1978
Forced vibrations for a nonlinear wave equation. Zbl 0378.35040
Brézis, Haïm; Nirenberg, Louis
1978
The Minkowski multidimensional problem. Translated by Vladimir Oliker and introduced by Louis Nirenberg. Zbl 0387.53023
Pogorelov, Aleksey Vasil’yevich
1978
Regularity in elliptic free boundary problems. I. Zbl 0402.35045
Kinderlehrer, D.; Nirenberg, Louis; Spruck, J.
1978
The smoothness of the free boundary in the one phase Stefan problem. Zbl 0391.35060
Kinderlehrer, David; Nirenberg, Louis
1978
Analyticity at the boundary of solutions of nonlinear second-order parabolic equations. Zbl 0391.35045
Kinderlehrer, David; Nirenberg, Louis
1978
Régularité dans les problèmes elliptiques à frontière libre. Zbl 0386.35045
Kinderlehrer, David; Nirenberg, Louis; Spruck, Joel
1978
Hodograph methods and the smoothness of the free boundary in the one phase Stefan problem. Zbl 0456.35090
Kinderlehrer, David; Nirenberg, Louis
1978
Regularity in free boundary problems. Zbl 0352.35023
Kinderlehrer, D.; Nirenberg, Louis
1977
Topics in nonlinear functional analysis. (Lektsii po nelinejnomu funktsional’nomu analizu). Transl. from the English by N. D. Vvedenskaya. Zbl 0426.47034
Nirenberg, Louis
1977
Some first order nonlinear equations on torus. Zbl 0335.35028
Brézis, Haïm; Nirenberg, Louis
1977
Image d’une somme d’opérateurs non linéaires et applications. Zbl 0359.47035
Brézis, Haïm; Nirenberg, Louis
1977
Regularity of free boundaries. Zbl 0361.35012
Nirenberg, Louis
1977
Nonlinear differential equations invariant under certain geometric transformations. Zbl 0357.35034
Nirenberg, Louis
1976
Propagation of singularities for linear partial differential equtions and reflections at a boundary. Zbl 0335.35081
Nirenberg, Louis
1976
Monge-Ampère equations and some associated problems in geometry. Zbl 0335.35045
Nirenberg, Louis
1975
Topics in nonlinear functional analysis. Notes by R. A. Artino. Zbl 0286.47037
Nirenberg, Louis
1974
Partial differential equations invariant under conformal or projective transformations. Zbl 0298.35018
Loewner, Charles; Nirenberg, Louis
1974
On a question of Hans Lewy. Zbl 0305.35017
Nirenberg, Louis
1974
Contributions to analysis. A collection of papers dedicated to Lipman Bers. Zbl 0283.00007
1974
Lectures on linear partial differential equations. Zbl 0267.35001
Nirenberg, Louis
1973
The null spaces of elliptic partial differential operators in R$$^n$$. Zbl 0272.35029
Nirenberg, Louis; Walker, Homer F.
1973
A pseudo-convex domain not admitting a holomorphic support function. Zbl 0248.32013
Kohn, J. J.; Nirenberg, Louis
1973
A remark on Ky Fan’s minimax principle. Zbl 0264.49013
Brézis, Haïm; Nirenberg, Louis; Stampacchia, Guido
1972
An abstract form of the nonlinear Cauchy-Kowalewski theorem. Zbl 0257.35001
Nirenberg, Louis
1972
A correction to: On local solvability of linear partial differential equations. II: Sufficient conditions. Zbl 0221.35019
Nirenberg, Louis; Treves, J. F.
1971
A proof of the Malgrange preparation theorem. Zbl 0212.10702
Nirenberg, Louis
1971
...and 47 more Documents
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### Cited by 9,143 Authors
59 Nazarov, Sergeĭ Aleksandrovich 53 Li, YanYan 53 Wei, Juncheng 50 Papageorgiou, Nikolaos S. 47 Miyagaki, Olimpio Hiroshi 46 Rădulescu, Vicenţiu D. 45 Berestycki, Henri 44 Zou, Wenming 43 Brézis, Haïm 40 Hamel, François 39 Schechter, Martin 37 Wang, Lihe 37 Yang, Dachun 34 Kang, Dongsheng 33 Dolbeault, Jean 33 Maz’ya, Vladimir Gilelevich 32 Pacella, Filomena 31 Byeon, Jaeyoung 31 Sciunzi, Berardino 30 Grossi, Massimo 30 Shivaji, Ratnasingham 29 Bao, Jiguang 29 Cao, Daomin 29 Dancer, Edward Norman 29 Peral Alonso, Ireneo 28 Farina, Alberto 28 Korman, Philip L. 28 Li, Congming 28 Lin, Chang-Shou 28 Nirenberg, Louis 28 Peng, Shuangjie 28 Valdinoci, Enrico 28 Wang, Zhi-Qiang 27 Byun, Sun-Sig 27 Friedman, Avner 26 Guedes de Figueiredo, Djairo 26 Do Ó, João M. Bezerra 26 Dong, Hongjie 26 García-Melián, Jorge 26 Li, Yi 26 López-Gómez, Julián 26 Shakhmurov, Veli B. 26 Van Schaftingen, Jean 25 Birindelli, Isabeau 25 Han, Pigong 25 Ivochkina, Nina Mikhaĭlovna 25 Niu, Pengcheng 25 Pistoia, Angela 25 Trudinger, Neil Sidney 25 Wang, Xu-Jia 24 Caffarelli, Luis Ángel 24 Guo, Zongming 24 Ruf, Bernhard 24 Yan, Shusen 23 Lu, Guozhen 23 Mironescu, Petru 23 Seregin, Gregory A. 23 Tan, Zhong 23 Xiao, Jie 23 Zhong, Xin 22 Alves, Claudianor Oliveira 22 Deng, Yinbin 22 Ni, Wei-Ming 22 Quaas, Alexander 22 Sirakov, Boyan Slavchev 22 Trèves, François 22 Weth, Tobias 21 Du, Yihong 21 Esteban, Maria J. 21 Kukavica, Igor 21 Li, Dongsheng 21 Tang, Xianhua 21 Wang, Yanqing 21 Yang, Minbo 20 Guo, Yuxia 20 Montoro, Luigi 20 Mu, Chunlai 20 Musso, Monica 20 Peletier, Lambertus Adrianus 20 Ragusa, Maria Alessandra 20 Ryazanov, Vladimir Il’ich 20 Shi, Junping 20 Vitolo, Antonio 19 Bonheure, Denis 19 Capuzzo Dolcetta, Italo 19 Gazzola, Filippo 19 Li, Shujie 19 Li, Wan-Tong 19 Lions, Pierre-Louis 19 Nadirashvili, Nikolai S. 19 Willem, Michel 19 Yang, Jianfu 18 Chen, Wenxiong 18 Del Pino, Manuel A. 18 Furtado, Marcelo Fernandes 18 Ghoussoub, Nassif A. 18 Huang, Yisheng 18 McKenna, Patrick Joseph 18 Rossi, Julio Daniel 18 Suzuki, Takashi ...and 9,043 more Authors
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### Cited in 577 Serials
799 Journal of Differential Equations 696 Journal of Mathematical Analysis and Applications 571 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 382 Archive for Rational Mechanics and Analysis 363 Calculus of Variations and Partial Differential Equations 347 Journal of Functional Analysis 284 Communications in Partial Differential Equations 271 Transactions of the American Mathematical Society 256 Nonlinear Analysis. Theory, Methods & Applications 219 Proceedings of the American Mathematical Society 192 Annali di Matematica Pura ed Applicata. Serie Quarta 190 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 182 Mathematische Annalen 177 Mathematische Zeitschrift 170 Communications in Mathematical Physics 160 Advances in Mathematics 155 Journal of Mathematical Sciences (New York) 147 The Journal of Geometric Analysis 147 Discrete and Continuous Dynamical Systems 145 Journal de Mathématiques Pures et Appliquées. Neuvième Série 126 Applicable Analysis 123 Communications on Pure and Applied Analysis 110 Communications in Contemporary Mathematics 107 Journal of Mathematical Physics 102 ZAMP. Zeitschrift für angewandte Mathematik und Physik 101 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 97 Journal d’Analyse Mathématique 97 Nonlinear Analysis. Real World Applications 94 Siberian Mathematical Journal 90 Duke Mathematical Journal 90 Manuscripta Mathematica 88 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 88 Boundary Value Problems 85 Advanced Nonlinear Studies 85 Complex Variables and Elliptic Equations 79 NoDEA. Nonlinear Differential Equations and Applications 78 Mathematical Methods in the Applied Sciences 78 Applied Mathematics Letters 77 Comptes Rendus. Mathématique. Académie des Sciences, Paris 75 Mathematical Notes 75 SIAM Journal on Mathematical Analysis 73 Inventiones Mathematicae 68 Journal of Mathematical Fluid Mechanics 68 Science China. Mathematics 65 Annales de l’Institut Fourier 64 Applied Mathematics and Computation 58 Communications on Pure and Applied Mathematics 58 Bulletin of the American Mathematical Society 56 Computers & Mathematics with Applications 55 Annali della Scuola Normale Superiore di Pisa. Scienze Fisiche e Matematiche. III. Ser 53 Acta Mathematica 51 Journal of Soviet Mathematics 49 Abstract and Applied Analysis 49 Acta Mathematica Sinica. English Series 48 Advances in Nonlinear Analysis 46 Mathematische Nachrichten 46 Acta Applicandae Mathematicae 44 Discrete and Continuous Dynamical Systems. Series B 42 Numerische Mathematik 41 Ukrainian Mathematical Journal 40 Rendiconti del Seminario Matematico della Università di Padova 39 Bulletin of the American Mathematical Society. New Series 38 Proceedings of the Japan Academy. Series A 38 Topological Methods in Nonlinear Analysis 38 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 38 Journal of the European Mathematical Society (JEMS) 38 Journal of Fixed Point Theory and Applications 36 Israel Journal of Mathematics 36 Nonlinearity 36 Mathematics of Computation 36 Tôhoku Mathematical Journal. Second Series 36 Journal of Dynamics and Differential Equations 35 Journal of Computational and Applied Mathematics 35 Zeitschrift für Analysis und ihre Anwendungen 34 Journal of Optimization Theory and Applications 33 Chinese Annals of Mathematics. Series B 33 Physica D 33 Journal of Inequalities and Applications 32 Rocky Mountain Journal of Mathematics 32 Results in Mathematics 32 Potential Analysis 32 Milan Journal of Mathematics 31 Applied Mathematics and Optimization 31 Revista Matemática Iberoamericana 31 Journal of Function Spaces 30 Bulletin of the Australian Mathematical Society 30 Journal für die Reine und Angewandte Mathematik 30 Annals of Global Analysis and Geometry 30 St. Petersburg Mathematical Journal 29 Publications of the Research Institute for Mathematical Sciences, Kyoto University 29 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 29 Acta Mathematica Scientia. Series B. (English Edition) 29 Proceedings of the Japan Academy 28 Arkiv för Matematik 28 Journal of Evolution Equations 28 Mediterranean Journal of Mathematics 26 Czechoslovak Mathematical Journal 26 Differential Geometry and its Applications 25 Integral Equations and Operator Theory 25 Journal of Elasticity ...and 477 more Serials
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### Cited in 61 Fields
9,317 Partial differential equations (35-XX) 1,349 Fluid mechanics (76-XX) 1,085 Operator theory (47-XX) 1,061 Global analysis, analysis on manifolds (58-XX) 939 Differential geometry (53-XX) 780 Functional analysis (46-XX) 680 Calculus of variations and optimal control; optimization (49-XX) 568 Several complex variables and analytic spaces (32-XX) 567 Ordinary differential equations (34-XX) 460 Numerical analysis (65-XX) 432 Harmonic analysis on Euclidean spaces (42-XX) 411 Mechanics of deformable solids (74-XX) 367 Biology and other natural sciences (92-XX) 301 Real functions (26-XX) 244 Dynamical systems and ergodic theory (37-XX) 222 Potential theory (31-XX) 196 Functions of a complex variable (30-XX) 182 Integral equations (45-XX) 161 Statistical mechanics, structure of matter (82-XX) 139 Quantum theory (81-XX) 133 Probability theory and stochastic processes (60-XX) 113 Optics, electromagnetic theory (78-XX) 104 Classical thermodynamics, heat transfer (80-XX) 99 Convex and discrete geometry (52-XX) 89 Relativity and gravitational theory (83-XX) 84 Operations research, mathematical programming (90-XX) 77 Systems theory; control (93-XX) 71 Abstract harmonic analysis (43-XX) 62 Manifolds and cell complexes (57-XX) 61 Topological groups, Lie groups (22-XX) 53 Mechanics of particles and systems (70-XX) 48 Measure and integration (28-XX) 48 Difference and functional equations (39-XX) 47 Algebraic geometry (14-XX) 47 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 45 Algebraic topology (55-XX) 40 Geophysics (86-XX) 36 Approximations and expansions (41-XX) 25 Astronomy and astrophysics (85-XX) 23 General topology (54-XX) 21 Linear and multilinear algebra; matrix theory (15-XX) 19 History and biography (01-XX) 19 Integral transforms, operational calculus (44-XX) 17 Information and communication theory, circuits (94-XX) 16 Geometry (51-XX) 15 Nonassociative rings and algebras (17-XX) 13 General and overarching topics; collections (00-XX) 13 Statistics (62-XX) 13 Computer science (68-XX) 9 Number theory (11-XX) 8 Combinatorics (05-XX) 8 Special functions (33-XX) 7 Group theory and generalizations (20-XX) 5 Associative rings and algebras (16-XX) 5 $$K$$-theory (19-XX) 4 Commutative algebra (13-XX) 3 Category theory; homological algebra (18-XX) 2 Sequences, series, summability (40-XX) 1 Mathematical logic and foundations (03-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Field theory and polynomials (12-XX)
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https://zbmath.org/authors/?q=ai%3Aberndt.bruce-c | ## Berndt, Bruce Carl
Compute Distance To:
Author ID: berndt.bruce-c Published as: Berndt, Bruce C.; Berndt, B. C.; Berndt, Bruce Homepage: https://faculty.math.illinois.edu/~berndt/ External Links: MGP · Wikidata · Math-Net.Ru · dblp · GND · IdRef
Documents Indexed: 262 Publications since 1967, including 18 Books 21 Contributions as Editor · 1 Further Contribution Co-Authors: 102 Co-Authors with 185 Joint Publications 1,924 Co-Co-Authors
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### Serials
13 The Ramanujan Journal 12 American Mathematical Monthly 12 Transactions of the American Mathematical Society 11 Acta Arithmetica 11 Proceedings of the American Mathematical Society 10 Advances in Mathematics 9 Journal für die Reine und Angewandte Mathematik 8 Journal of Number Theory 6 Glasgow Mathematical Journal 6 International Journal of Number Theory 4 Illinois Journal of Mathematics 4 Journal of the London Mathematical Society. Second Series 4 Mathematische Annalen 4 Proceedings of the Edinburgh Mathematical Society. Series II 4 Annals of Combinatorics 3 Journal of Mathematical Analysis and Applications 3 Mathematical Proceedings of the Cambridge Philosophical Society 3 Rocky Mountain Journal of Mathematics 3 Bulletin of the London Mathematical Society 3 Journal of Combinatorial Theory. Series A 3 Journal of Computational and Applied Mathematics 3 Memoirs of the American Mathematical Society 3 Bulletin of the American Mathematical Society 3 Contemporary Mathematics 3 Progress in Mathematics 3 Ramanujan Mathematical Society Lecture Notes Series 2 Mathematics Magazine 2 Canadian Mathematical Bulletin 2 Indian Journal of Mathematics 2 Journal of Approximation Theory 2 The Journal of the Indian Mathematical Society. New Series 2 Mathematische Zeitschrift 2 Pacific Journal of Mathematics 2 Hardy-Ramanujan Journal 2 Advances in Applied Mathematics 2 Journal of the Ramanujan Mathematical Society 2 IMRN. International Mathematics Research Notices 2 Aequationes Mathematicae 2 L’Enseignement Mathématique. 2e Série 2 SIAM Journal on Mathematical Analysis 2 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 2 Notices of the American Mathematical Society 2 RIMS Kokyuroku 2 South East Asian Journal of Mathematics and Mathematical Sciences 2 Publications de la Faculté d’Électrotechnique de l’Université à Belgrade. Série Mathématiques et Physique 2 History of Mathematics (Providence) 2 Trends in Mathematics 1 Applicable Analysis 1 The Mathematical Intelligencer 1 Canadian Journal of Mathematics 1 Duke Mathematical Journal 1 Gaṇita 1 Journal of the Korean Mathematical Society 1 The Mathematics Student 1 Mathematika 1 Monatshefte für Mathematik 1 Nagoya Mathematical Journal 1 Results in Mathematics 1 International Journal of Mathematics 1 Elemente der Mathematik 1 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 1 Bulletin of the American Mathematical Society. New Series 1 Expositiones Mathematicae 1 Indagationes Mathematicae. New Series 1 Mathematical Research Letters 1 Séminaire Lotharingien de Combinatoire 1 Acta Mathematica Sinica. English Series 1 The Quarterly Journal of Mathematics 1 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 1 Nordisk Matematisk Tidskrift 1 Canadian Mathematical Society Series of Monographs and Advanced Texts 1 Student Mathematical Library 1 Developments in Mathematics 1 Culture and History of Mathematics 1 1 Monographs in Number Theory 1 Mathematics Newsletter 1 Philosophical Transactions of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences
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### Fields
244 Number theory (11-XX) 109 Special functions (33-XX) 44 History and biography (01-XX) 34 Combinatorics (05-XX) 22 Sequences, series, summability (40-XX) 20 General and overarching topics; collections (00-XX) 11 Approximations and expansions (41-XX) 8 Functions of a complex variable (30-XX) 4 Algebraic geometry (14-XX) 4 Numerical analysis (65-XX) 2 Integral transforms, operational calculus (44-XX) 1 Real functions (26-XX) 1 Mathematics education (97-XX)
### Citations contained in zbMATH Open
211 Publications have been cited 3,978 times in 2,344 Documents Cited by Year
Ramanujan’s notebooks. Part III. Zbl 0733.11001
Berndt, Bruce C.
1991
Gauss and Jacobi sums. Zbl 0906.11001
Berndt, Bruce C.; Evans, Ronald J.; Williams, Kenneth S.
1998
Ramanujan’s notebooks. Part I. Zbl 0555.10001
Berndt, Bruce C.
1985
Number theory in the spirit of Ramanujan. Zbl 1117.11001
Berndt, Bruce C.
2006
Ramanujan’s lost notebook. I. Zbl 1075.11001
Andrews, George E.; Berndt, Bruce C.
2005
Ramanujan’s notebooks. Part II. Zbl 0716.11001
Berndt, Bruce C.
1989
Ramanujan’s notebooks. Part V. Zbl 0886.11001
Berndt, Bruce C.
1998
Ramanujan’s notebooks. Part IV. Zbl 0785.11001
Berndt, Bruce C.
1994
Ramanujan’s lost notebook. Part II. Zbl 1180.11001
Andrews, George E.; Berndt, Bruce C.
2009
Ramanujan’s theories of elliptic functions to alternative bases. Zbl 0843.33012
Berndt, Bruce C.; Bhargava, S.; Garvan, Frank G.
1995
On the Hurwitz zeta-function. Zbl 0229.10023
Berndt, Bruce C.
1972
Ramanujan: Letters and commentary. Zbl 0842.01026
Berndt, Bruce C.; Rankin, Robert A.
1995
Analytic Eisenstein series, theta-functions, and series relations in the spirit of Ramanujan. Zbl 0384.10011
Berndt, Bruce C.
1978
The determination of Gauss sums. Zbl 0471.10028
Berndt, Bruce C.; Evans, Ronald J.
1981
Chapter 16 of Ramanujan’s second notebook: Theta-functions and q-series. Zbl 0565.33002
Adiga, C.; Berndt, Bruce C.; Bhargava, S.; Watson, G. N.
1985
Gauss, Landen, Ramanujan, the arithmetic-geometric mean, ellipses, $$\pi$$ , and the Ladies Diary. Zbl 0665.26007
Almkvist, Gert; Berndt, Bruce C.
1988
Modular transformations and generalizations of several formulae of Ramanujan. Zbl 0365.10021
Berndt, Bruce C.
1977
Sums of Gauss, Jacobi, and Jacobsthal. Zbl 0412.10027
Berndt, Bruce C.; Evans, Ronald J.
1979
Ramanujan’s series for $$1/\pi$$: a survey. Zbl 1229.11162
Baruah, Deka Nayandeep; Berndt, Bruce C.; Chan, Huat Heng
2009
Collected papers of Srinivasa Ramanujan. Edited by G. H. Hardy, P. V. Seshu Aiyar and B. M. Wilson. With a new preface and commentary by Bruce C. Berndt. Third printing of the 1927 original. Zbl 1110.11001
Ramanujan, Srinivasa
2000
Character analogues of the Poisson and Euler-MacLaurin summation formulas with applications. Zbl 0316.10023
Berndt, Bruce C.
1975
The number of zeros for $$\zeta^{(k)}(s)$$. Zbl 0203.35503
Berndt, Bruce C.
1970
Ramanujan’s lost notebook. Part III. Zbl 1248.11003
Andrews, George E.; Berndt, Bruce C.
2012
Explicit evaluations and reciprocity theorems for finite trigonometric sums. Zbl 1011.11057
Berndt, Bruce C.; Yeap, Boon Pin
2002
Ramanujan’s lost notebook. Part IV. Zbl 1288.11002
Andrews, George E.; Berndt, Bruce C.
2013
The continued fractions found in the unorganized portions of Ramanujan’s notebooks. Zbl 0758.40001
Andrews, George E.; Berndt, Bruce C.; Jacobsen, Lisa; Lamphere, Robert L.
1992
Partition identities and Ramanujan’s modular equations. Zbl 1206.11132
Baruah, Nayandeep Deka; Berndt, Bruce C.
2007
Reciprocity theorems for Dedekind sums and generalizations. Zbl 0342.10014
Berndt, Bruce C.
1977
Identities involving the coefficients of a class of Dirichlet series. I,II. Zbl 0175.32802
Berndt, Bruce C.
1969
Eisenstein series and Ramanujan-type series for $$1 / \pi$$. Zbl 1204.33005
Baruah, Nayandeep Deka; Berndt, Bruce C.
2010
Finite trigonometric sums and class numbers. Zbl 1099.11039
Berndt, Bruce C.; Zaharescu, Alexandru
2004
Analytic properties of arithmetic sums arising in the theory of the classical theta-functions. Zbl 0537.10006
Berndt, Bruce C.; Goldberg, Larry A.
1984
Asymptotic expansions of certain partial theta functions. Zbl 1272.11057
Berndt, Bruce C.; Kim, Byungchan
2011
Classical theorems on quadratic residues. Zbl 0337.10031
Berndt, Bruce C.
1976
Ramanujan’s forty identities for the Rogers-Ramanujan functions. Zbl 1118.11044
Berndt, Bruce C.; Choi, Geumlan; Choi, Youn-Seo; Hahn, Heekyoung; Yeap, Boon Pin; Yee, Ae Ja; Yesilyurt, Hamza; Yi, Jinhee
2007
Explicit evaluations of the Rogers-Ramanujan continued fraction. Zbl 0862.33017
Berndt, Bruce C.; Chan, Heng Huat; Zhang, Liang-Cheng
1996
Generalized Dedekind eta-functions and generalized Dedekind sums. Zbl 0262.10015
Berndt, Bruce C.
1973
Periodic analogues of the Euler-Maclaurin and Poisson summation formulas with applications to number theory. Zbl 0268.10008
Berndt, Bruce C.; Schoenfeld, Lowell
1974
Some values for the Rogers-Ramanujan continued fraction. Zbl 0838.33011
Berndt, Bruce C.; Chan, Heng Huat
1995
Dedekind sums and a paper of G. H. Hardy. Zbl 0319.10006
Berndt, Bruce C.
1976
Sixth order mock theta functions. Zbl 1122.33010
Berndt, Bruce C.; Chan, Song Heng
2007
Ramanujan’s unpublished manuscript on the partition and tau functions with proofs and commentary. Zbl 0932.11002
Berndt, Bruce C.; Ono, Ken
1999
Generalized Eisenstein series and modified Dedekind sums. Zbl 0294.10018
Berndt, Bruce C.
1975
Ramanujan’s series for $$1/\pi$$ arising from his cubic and quartic theories of elliptic functions. Zbl 1139.11023
Baruah, Nayandeep Deka; Berndt, Bruce C.
2008
Partition-theoretic interpretations of certain modular equations of Schröter, Russell, and Ramanujan. Zbl 1131.05008
Berndt, Bruce C.
2007
On Ramanujan’s quartic theory of elliptic functions. Zbl 1005.33009
Berndt, Bruce C.; Chan, Heng Huat; Liaw, Wen-Chin
2001
The Rogers-Ramanujan continued fraction. Zbl 0953.11005
Berndt, Bruce C.; Chan, Heng Huat; Huang, Sen-Shan; Kang, Soon-Yi; Sohn, Jaebum; Son, Seung Hwan
1999
Hecke’s theory of modular forms and Dirichlet series. Zbl 1202.11030
Berndt, Bruce C.; Knopp, Marvin I.
2008
Ramanujan’s notebooks. Zbl 0389.10002
Berndt, Bruce C.
1978
Ramanujan’s lost notebook. Part V. Zbl 1416.11001
Andrews, George E.; Berndt, Bruce C.
2018
Ramanujan’s lost notebook: combinatorial proofs of identities associated with Heine’s transformation or partial theta functions. Zbl 1227.05053
Berndt, Bruce C.; Kim, Byungchan; Yee, Ae Ja
2010
Sums of Gauß, Eisenstein, Jacobi, Jacobsthal, and Brewer. Zbl 0393.12029
Berndt, Bruce C.; Evans, Ronald J.
1979
A certain quotient of eta-functions found in Ramanujan’s lost notebook. Zbl 1054.11022
Berndt, Bruce C.; Chan, Heng Huat; Kang, Soon-Yi; Zhang, Liang-Cheng
2002
Elementary evaluation of $$\zeta(2n)$$. Zbl 0303.10038
Berndt, Bruce C.
1975
On the Brocard-Ramanujan Diophantine equation $$n! + 1 = m^2$$. Zbl 0999.11078
Berndt, Bruce C.; Galway, William F.
2000
Some theorems on the Rogers-Ramanujan continued fraction in Ramanujan’s lost notebook. Zbl 1037.11011
Berndt, Bruce C.; Huang, Sen-Shan; Sohn, Jaebum; Son, Seung Hwan
2000
Formulas of Ramanujan for the power series coefficients of certain quotients of Eisenstein series. Zbl 1033.11019
Berndt, Bruce C.; Bialek, Paul R.; Yee, Ae Ja
2002
Cranks and dissections in Ramanujan’s lost notebook. Zbl 1114.11082
Berndt, Bruce C.; Chan, Heng Huat; Chan, Song Heng; Liaw, Wen-Chin
2005
A new identity for $$(q;q)_\infty^{10}$$ with an application to Ramanujan’s partition congruence modulo 11. Zbl 1060.11063
Berndt, Bruce C.; Chan, Song Heng; Liu, Zhi-Guo; Yesilyurt, Hamza
2004
The problems submitted by Ramanujan to the Journal of the Indian Mathematical Society. Zbl 1133.11300
Berndt, Bruce C.; Choi, Youn-Seo; Kang, Soon-Yi
1999
Circle and divisor problems, and double series of Bessel functions. Zbl 1326.11059
Berndt, Bruce C.; Kim, Sun; Zaharescu, Alexandru
2013
Weighted divisor sums and Bessel function series. II. Zbl 1236.33010
Berndt, Bruce C.; Kim, Sun; Zaharescu, Alexandru
2012
On Eisenstein series with characters and the values of Dirichlet L-functions. Zbl 0279.10023
Berndt, Bruce C.
1975
Ramanujan’s class invariants and cubic continued fraction. Zbl 0843.11007
Berndt, Bruce C.; Chan, Heng Huat; Zhang, Liang-Cheng
1995
Partition identities arising from theta function identities. Zbl 1154.11036
Baruah, Nayandeep Deka; Berndt, Bruce C.
2008
A reciprocity theorem for certain $$q$$-series found in Ramanujan’s lost notebook. Zbl 1123.33012
Berndt, Bruce C.; Chan, Song Heng; Yeap, Boon Pin; Yee, Ae Ja
2007
A transformation formula involving the gamma and Riemann zeta functions in Ramanujan’s lost notebook. Zbl 1322.11086
Berndt, Bruce C.; Dixit, Atul
2010
Ramanujan and the modular $$j$$-invariant. Zbl 0990.11022
Berndt, Bruce C.; Chan, Heng Huat
1999
On the parity of partition functions. Zbl 1047.11098
Berndt, Bruce C.; Yee, Ae Ja; Zaharescu, Alexandru
2003
On a secant Dirichlet series and Eichler integrals of Eisenstein series. Zbl 1402.11060
Berndt, Bruce C.; Straub, Armin
2016
Character transformation formulae similar to those for the Dedekind eta- function. Zbl 0265.10016
Berndt, Bruce C.
1973
Weighted divisor sums and Bessel function series. Zbl 1100.33001
Berndt, Bruce C.; Zaharescu, Alexandru
2006
Ramanujan’s identities for Eta-functions. Zbl 0737.11008
Berndt, Bruce C.; Zhang, Liang-Cheng
1992
Ramanujan’s remarkable product of theta-functions. Zbl 0901.33007
Berndt, Bruce C.; Chan, Heng Huat; Zhang, Liang-Cheng
1997
On the average order of a class of arithmetical functions. II. Zbl 0219.10050
Berndt, Bruce C.
1971
Combinatorial proofs of identities in Ramanujan’s lost notebook associated with the Rogers-Fine identity and false theta functions. Zbl 1037.05005
Berndt, Bruce C.; Yee, Ae Ja
2003
Modular equations in Ramanujan’s Lost Notebook. Zbl 0989.11021
Berndt, Bruce C.
2000
Sums involving the greatest integer function and Riemann-Stieltjes integration. Zbl 0487.10002
Berndt, Bruce C.; Dieter, Ulrich
1982
Ramanujan’s class invariants, Kronecker’s limit formula, and modular equations. Zbl 0885.11058
Berndt, Bruce C.; Chan, Heng Huat; Zhang, Liang-Cheng
1997
Chapter 12 of Ramanujan’s second notebook: Continued fractions. Zbl 0589.33002
Berndt, Bruce C.; Lamphere, Robert L.; Wilson, B. M.
1985
Identities involving the coefficients of a class of Dirichlet series. V. Zbl 0228.10024
Berndt, Bruce C.
1971
Two new proofs of Lerch’s functional equation. Zbl 0235.10020
Berndt, Bruce C.
1972
Determinations of analogues of Gauss sums and other trigonometric sums. Zbl 1088.11064
Beck, Matthias; Berndt, Bruce C.; Chan, O-Yeat; Zaharescu, Alexandru
2005
Weighted divisor sums and Bessel function series. III. Zbl 1326.11057
Berndt, Bruce C.; Kim, Sun; Zaharescu, Alexandru
2013
Eisenstein series in Ramanujan’s Lost Notebook. Zbl 1024.11026
Berndt, Bruce C.; Chan, Heng Huat; Sohn, Jaebum; Son, Seung Hwan
2000
Identities involving the coefficients of a class of Dirichlet series. III. Zbl 0191.33003
Berndt, Bruce C.
1969
Ramanujan’s short unpublished manuscript on integrals and series related to Euler’s constant. Zbl 0964.40004
Berndt, Bruce C.; Bowman, Douglas C.
2000
Eisenstein series and approximations to $$\pi$$. Zbl 0998.33003
Berndt, Bruce C.; Chan, Heng Huat
2001
New pathways and connections in number theory and analysis motivated by two incorrect claims of Ramanujan. Zbl 1396.11103
Berndt, Bruce C.; Dixit, Atul; Roy, Arindam; Zaharescu, Alexandru
2017
On the average order of a class of arithmetical functions. I. Zbl 0216.31303
Berndt, Bruce C.
1971
Proofs of conjectures of Sandon and Zanello on colored partition identities. Zbl 1315.11092
Berndt, Bruce C.; Zhou, Roberta R.
2014
On Ramanujan’s continued fraction for $$(q^2;q^3)_{\infty}/(q;q^3)_{\infty}$$. Zbl 1063.33026
Andrews, George E.; Berndt, Bruce C.; Sohn, Jaebum; Yee, Ae Ja; Zaharescu, Alexandru
2003
Generalized Dirichlet series and Hecke’s functional equation. Zbl 0207.05503
Berndt, Bruce C.
1967
Identities involving the coefficients of a class of Dirichlet series. IV. Zbl 0207.05504
Berndt, Bruce C.
1970
Flowers which we connot yet see growing in Ramanujan’s garden of hypergeometric series, elliptic functions, and $$q$$’s. Zbl 1014.33012
Berndt, Bruce C.
2001
Identities for partitions with distinct colors. Zbl 1386.11127
Berndt, Bruce C.; Zhou, Roberta R.
2015
Weighted divisor sums and Bessel function series. IV. Zbl 1270.11098
Berndt, Bruce C.; Kim, Sun; Zaharescu, Alexandru
2012
Incomplete elliptic integrals in Ramanujan’s lost notebook. Zbl 0971.33012
Berndt, Bruce C.; Chan, Heng Huat; Huang, Sen-Shan
2000
A page on Eisenstein series in Ramanujan’s Lost Notebook. Zbl 1090.11025
Berndt, Bruce C.; Yee, Ae Ja
2003
Chapter 3 of Ramanujan’s second notebook. Zbl 0524.41017
Berndt, Bruce C.; Evans, Ronald J.; Wilson, B. M.
1983
Four identities for third order mock theta functions. Zbl 1455.11136
Andrews, George E.; Berndt, Bruce C.; Chan, Song Heng; Kim, Sun; Malik, Amita
2020
The final problem: an identity from Ramanujan’s lost notebook. Zbl 1431.33005
Berndt, Bruce C.; Li, Junxian; Zaharescu, Alexandru
2019
Ramanujan’s lost notebook. Part V. Zbl 1416.11001
Andrews, George E.; Berndt, Bruce C.
2018
The circle problem of Gauss and the divisor problem of Dirichlet – still unsolved. Zbl 1396.11001
Berndt, Bruce C.; Kim, Sun; Zaharescu, Alexandru
2018
Partitions into $$k$$th powers of terms in an arithmetic progression. Zbl 1412.11129
Berndt, Bruce C.; Malik, Amita; Zaharescu, Alexandru
2018
Sums of squares and products of Bessel functions. Zbl 1451.11024
Berndt, Bruce C.; Dixit, Atul; Kim, Sun; Zaharescu, Alexandru
2018
New pathways and connections in number theory and analysis motivated by two incorrect claims of Ramanujan. Zbl 1396.11103
Berndt, Bruce C.; Dixit, Atul; Roy, Arindam; Zaharescu, Alexandru
2017
On a theorem of A. I. Popov on sums of squares. Zbl 1422.11077
Berndt, Bruce C.; Dixit, Atul; Kim, Sun; Zaharescu, Alexandru
2017
The appearance of H. F. Baker and E. W. Hobson in “The man who knew infinity”. Zbl 1390.01070
Berndt, Bruce C.
2017
On a secant Dirichlet series and Eichler integrals of Eisenstein series. Zbl 1402.11060
Berndt, Bruce C.; Straub, Armin
2016
Integrals associated with Ramanujan and elliptic functions. Zbl 1354.33015
Berndt, Bruce C.
2016
Ramanujan at elementary levels – glimpses. Edited and with a preface by Bruce C. Berndt, Atul Dixit, Victoria J. Reuter, Ping Xu and Boonrod Yuttanan. Zbl 1405.11003
Thiruvenkatachar, V. R.; Venkatachaliengar, K.
2016
Identities for partitions with distinct colors. Zbl 1386.11127
Berndt, Bruce C.; Zhou, Roberta R.
2015
Logarithmic means and double series of Bessel functions. Zbl 1390.11100
Berndt, Bruce C.; Kim, Sun
2015
Weighted divisor sums and Bessel function series. V. Zbl 1326.33007
Berndt, Bruce C.; Kim, Sun; Zaharescu, Alexandru
2015
Certain integrals arising from Ramanujan’s notebooks. Zbl 1325.33014
Berndt, Bruce C.; Straub, Armin
2015
Proofs of conjectures of Sandon and Zanello on colored partition identities. Zbl 1315.11092
Berndt, Bruce C.; Zhou, Roberta R.
2014
Analogues of Koshliakov’s formula. Zbl 1308.33004
Berndt, Bruce C.; Kim, Sun; Zaharescu, Alexandru
2014
Ramanujan’s lost notebook. Part IV. Zbl 1288.11002
Andrews, George E.; Berndt, Bruce C.
2013
Circle and divisor problems, and double series of Bessel functions. Zbl 1326.11059
Berndt, Bruce C.; Kim, Sun; Zaharescu, Alexandru
2013
Weighted divisor sums and Bessel function series. III. Zbl 1326.11057
Berndt, Bruce C.; Kim, Sun; Zaharescu, Alexandru
2013
The circle and divisor problems, and Ramanujan’s contributions through Bessel function series. Zbl 1360.11093
Berndt, Bruce C.; Kim, Sun; Zaharescu, Alexandru
2013
Dirichlet $$L-$$functions, elliptic curves, hypergeometric functions, and rational approximation with partial sums of power series. Zbl 1297.11082
Berndt, Bruce C.; Kim, Sun; Zaharescu, Alexandru
2013
Diophantine approximation with partial sums of power series. Zbl 1318.11088
Berndt, Bruce C.; Kim, Sun; Phaovibul, M. Tip; Zaharescu, Alexandru
2013
Diophantine approximation of the exponential function and Sondow’s conjecture. Zbl 1292.11079
Berndt, Bruce C.; Kim, Sun; Zaharescu, Alexandru
2013
Ramanujan’s lost notebook. Part III. Zbl 1248.11003
Andrews, George E.; Berndt, Bruce C.
2012
Weighted divisor sums and Bessel function series. II. Zbl 1236.33010
Berndt, Bruce C.; Kim, Sun; Zaharescu, Alexandru
2012
Weighted divisor sums and Bessel function series. IV. Zbl 1270.11098
Berndt, Bruce C.; Kim, Sun; Zaharescu, Alexandru
2012
Ramanujan’s elementary method in partition congruences. Zbl 1263.11094
Berndt, Bruce C.; Gugg, Chadwick; Kim, Sun
2012
Two-dimensional series evaluations via the elliptic functions of Ramanujan and Jacobi. Zbl 1290.11112
Berndt, Bruce C.; Lamb, George; Rogers, Mathew
2012
Two Dirichlet series evaluations found on page 196 of Ramanujan’s lost notebook. Zbl 1275.11116
Berndt, Bruce C.; Chan, Heng Huat; Tanigawa, Yoshio
2012
Asymptotic expansions of certain partial theta functions. Zbl 1272.11057
Berndt, Bruce C.; Kim, Byungchan
2011
Character analogues of theorems of Ramanujan, Koshliakov and Guinand. Zbl 1216.33012
Berndt, Bruce C.; Dixit, Atul; Sohn, Jaebum
2011
On sums of powers in Ramanujan’s lost notebook. Zbl 1232.11025
Berndt, Bruce C.; Schultz, Daniel
2011
The chief accountant and mathematical friend of Ramanujan – S. Narayana Aiyar. Zbl 1226.01017
Berndt, Bruce C.
2011
Eisenstein series and Ramanujan-type series for $$1 / \pi$$. Zbl 1204.33005
Baruah, Nayandeep Deka; Berndt, Bruce C.
2010
Ramanujan’s lost notebook: combinatorial proofs of identities associated with Heine’s transformation or partial theta functions. Zbl 1227.05053
Berndt, Bruce C.; Kim, Byungchan; Yee, Ae Ja
2010
A transformation formula involving the gamma and Riemann zeta functions in Ramanujan’s lost notebook. Zbl 1322.11086
Berndt, Bruce C.; Dixit, Atul
2010
What is a $$q$$-series? Zbl 1245.33013
Berndt, Bruce C.
2010
A proof of the general theta transformation formula. Zbl 1343.11048
Berndt, Bruce C.; Gugg, Chadwick; Kongsiriwong, Sarachai; Thiel, Johann
2010
Cranks—really, the final problem. Zbl 1206.11001
Berndt, Bruce C.; Chan, Heng Huat; Chan, Song Heng; Liaw, Wen-Chin
2010
Ramanujan’s lost notebook. Part II. Zbl 1180.11001
Andrews, George E.; Berndt, Bruce C.
2009
Ramanujan’s series for $$1/\pi$$: a survey. Zbl 1229.11162
Baruah, Deka Nayandeep; Berndt, Bruce C.; Chan, Huat Heng
2009
Ramanujan’s Eisenstein series and new hypergeometric-like series for $$1/\pi ^{2}$$. Zbl 1185.33002
Baruah, Nayandeep Deka; Berndt, Bruce C.
2009
A reciprocity theorem for certain hypergeometric series. Zbl 1287.33001
Berndt, Bruce C.; Koukoulopoulos, Dimitris
2009
An integral analogue of theta functions and Gauss sums in Ramanujan’s lost notebook. Zbl 1196.11113
Berndt, Bruce C.; Xu, Ping
2009
Ramanujan’s series for $$1/\pi$$ arising from his cubic and quartic theories of elliptic functions. Zbl 1139.11023
Baruah, Nayandeep Deka; Berndt, Bruce C.
2008
Hecke’s theory of modular forms and Dirichlet series. Zbl 1202.11030
Berndt, Bruce C.; Knopp, Marvin I.
2008
Partition identities arising from theta function identities. Zbl 1154.11036
Baruah, Nayandeep Deka; Berndt, Bruce C.
2008
Koshliakov’s formula and Guinand’s formula in Ramanujan’s lost notebook. Zbl 1183.33007
Berndt, Bruce C.; Lee, Yoonbok; Sohn, Jaebum
2008
Your hit parade: the top ten most fascinating formulas in Ramanujan’s lost notebook. Zbl 1153.33300
Andrews, George E.; Berndt, Bruce C.
2008
Questionable claims found in Ramanujan’s lost notebook. Zbl 1163.11002
Berndt, Bruce C.; Chan, O-Yeat; Lim, Sung-Geun; Zaharescu, Alexandru
2008
Partition identities and Ramanujan’s modular equations. Zbl 1206.11132
Baruah, Nayandeep Deka; Berndt, Bruce C.
2007
Ramanujan’s forty identities for the Rogers-Ramanujan functions. Zbl 1118.11044
Berndt, Bruce C.; Choi, Geumlan; Choi, Youn-Seo; Hahn, Heekyoung; Yeap, Boon Pin; Yee, Ae Ja; Yesilyurt, Hamza; Yi, Jinhee
2007
Sixth order mock theta functions. Zbl 1122.33010
Berndt, Bruce C.; Chan, Song Heng
2007
Partition-theoretic interpretations of certain modular equations of Schröter, Russell, and Ramanujan. Zbl 1131.05008
Berndt, Bruce C.
2007
A reciprocity theorem for certain $$q$$-series found in Ramanujan’s lost notebook. Zbl 1123.33012
Berndt, Bruce C.; Chan, Song Heng; Yeap, Boon Pin; Yee, Ae Ja
2007
Ramanujan’s congruences for the partition function modulo 5, 7, and 11. Zbl 1197.11137
Berndt, Bruce C.
2007
Preface: a special issue in celebration of Marvin Knopp’s 73rd birthday. Zbl 1197.01051
Berndt, Bruce C.; Choie, YoungJu
2007
An identity for the Dedekind eta-function involving two independent complex variables. Zbl 1123.11015
Berndt, Bruce C.; Hart, William B.
2007
Solving Ramanujan’s differential equations for Eisenstein series via a first order Riccati equation. Zbl 1145.11035
Hill, James M.; Berndt, Bruce C.; Huber, Tim
2007
Number theory in the spirit of Ramanujan. Zbl 1117.11001
Berndt, Bruce C.
2006
Weighted divisor sums and Bessel function series. Zbl 1100.33001
Berndt, Bruce C.; Zaharescu, Alexandru
2006
Ramanujan’s lost notebook. I. Zbl 1075.11001
Andrews, George E.; Berndt, Bruce C.
2005
Cranks and dissections in Ramanujan’s lost notebook. Zbl 1114.11082
Berndt, Bruce C.; Chan, Heng Huat; Chan, Song Heng; Liaw, Wen-Chin
2005
Determinations of analogues of Gauss sums and other trigonometric sums. Zbl 1088.11064
Beck, Matthias; Berndt, Bruce C.; Chan, O-Yeat; Zaharescu, Alexandru
2005
Continued fractions with three limit points. Zbl 1131.11311
Andrews, George E.; Berndt, Bruce C.; Sohn, Jaebum; Yee, Ae Ja; Zaharescu, Alexandru
2005
New identities for the Rogers-Ramanujan functions. Zbl 1205.11113
Berndt, Bruce C.; Yesilyurt, Hamza
2005
On the power series coefficients of certain quotients of Eisenstein series. Zbl 1145.11312
Berndt, Bruce C.; Bialek, Paul R.
2005
Ramanujan and cranks. Zbl 1219.33017
Berndt, Bruce C.; Chan, Heng Huat; Chan, Song Heng; Liawt, Wen-Chin
2005
Finite trigonometric sums and class numbers. Zbl 1099.11039
Berndt, Bruce C.; Zaharescu, Alexandru
2004
A new identity for $$(q;q)_\infty^{10}$$ with an application to Ramanujan’s partition congruence modulo 11. Zbl 1060.11063
Berndt, Bruce C.; Chan, Song Heng; Liu, Zhi-Guo; Yesilyurt, Hamza
2004
New theorems on the parity of partition functions. Zbl 1034.11059
Berndt, Bruce C.; Yee, Ae Ja; Zaharescu, Alexandru
2004
An unpublished manuscript of Ramanujan on infinite series identities. Zbl 1066.40001
Berndt, Bruce C.
2004
$$q$$-Gauss summation via Ramanujan and combinatorics. Zbl 1063.33027
Berndt, Bruce C.; Yee, Ae Ja
2004
On the parity of partition functions. Zbl 1047.11098
Berndt, Bruce C.; Yee, Ae Ja; Zaharescu, Alexandru
2003
Combinatorial proofs of identities in Ramanujan’s lost notebook associated with the Rogers-Fine identity and false theta functions. Zbl 1037.05005
Berndt, Bruce C.; Yee, Ae Ja
2003
On Ramanujan’s continued fraction for $$(q^2;q^3)_{\infty}/(q;q^3)_{\infty}$$. Zbl 1063.33026
Andrews, George E.; Berndt, Bruce C.; Sohn, Jaebum; Yee, Ae Ja; Zaharescu, Alexandru
2003
A page on Eisenstein series in Ramanujan’s Lost Notebook. Zbl 1090.11025
Berndt, Bruce C.; Yee, Ae Ja
2003
On the generalized Rogers–Ramanujan continued fraction. Zbl 1040.11053
Berndt, Bruce C.; Yee, Ae Ja
2003
A quasi-theta product in Ramanujan’s lost notebook. Zbl 1055.11015
Berndt, Bruce C.; Chan, Heng Huat; Zaharescu, Alexandru
2003
Theorems on partitions from a page in Ramanujan’s lost notebook. Zbl 1031.11062
Berndt, Bruce C.; Yee, Ae Ja; Yi, Jinhee
2003
The life and work of R. A. Rankin (1915–2001). Zbl 1039.01011
Berndt, Bruce C.; Kohnen, Winfried; Ono, Ken
2003
Explicit evaluations and reciprocity theorems for finite trigonometric sums. Zbl 1011.11057
Berndt, Bruce C.; Yeap, Boon Pin
2002
A certain quotient of eta-functions found in Ramanujan’s lost notebook. Zbl 1054.11022
Berndt, Bruce C.; Chan, Heng Huat; Kang, Soon-Yi; Zhang, Liang-Cheng
2002
Formulas of Ramanujan for the power series coefficients of certain quotients of Eisenstein series. Zbl 1033.11019
Berndt, Bruce C.; Bialek, Paul R.; Yee, Ae Ja
2002
Integrals of Eisenstein series and derivatives of $$L$$-functions. Zbl 1086.11023
Ahlgren, Scott; Berndt, Bruce C.; Yee, Ae Ja; Zaharescu, Alexandru
2002
Congruences for the coefficients of quotients of Eisenstein series. Zbl 1018.11020
Berndt, Bruce C.; Yee, Ae Ja
2002
An integral of Dedekind $$\eta$$-functions in Ramanujan’s lost notebook. Zbl 1001.11017
Berndt, Bruce C.; Zaharescu, Alexandru
2002
Ramanujan’s contributions to Eisenstein series, especially in his Lost Notebook. Zbl 1241.11107
Berndt, Bruce C.; Yee, Ae Ja
2002
Asymptotic formulas for two continued fractions in Ramanujan’s Lost Notebook. Zbl 1034.11008
Berndt, Bruce C.; Sohn, Jaebum
2002
Number theory for the millennium I. Proceedings of the millennial conference on number theory, Urbana-Champaign, IL, USA, May 21–26, 2000. Zbl 1002.00005
2002
On Ramanujan’s quartic theory of elliptic functions. Zbl 1005.33009
Berndt, Bruce C.; Chan, Heng Huat; Liaw, Wen-Chin
2001
Eisenstein series and approximations to $$\pi$$. Zbl 0998.33003
Berndt, Bruce C.; Chan, Heng Huat
2001
Flowers which we connot yet see growing in Ramanujan’s garden of hypergeometric series, elliptic functions, and $$q$$’s. Zbl 1014.33012
Berndt, Bruce C.
2001
Ramanujan: essays and surveys. Zbl 1117.11002
2001
On the transformation formula for the Dedekind eta-function. Zbl 1040.11028
Berndt, Bruce C.; Venkatachaliengar, K.
2001
Collected papers of Srinivasa Ramanujan. Edited by G. H. Hardy, P. V. Seshu Aiyar and B. M. Wilson. With a new preface and commentary by Bruce C. Berndt. Third printing of the 1927 original. Zbl 1110.11001
Ramanujan, Srinivasa
2000
On the Brocard-Ramanujan Diophantine equation $$n! + 1 = m^2$$. Zbl 0999.11078
Berndt, Bruce C.; Galway, William F.
2000
Some theorems on the Rogers-Ramanujan continued fraction in Ramanujan’s lost notebook. Zbl 1037.11011
Berndt, Bruce C.; Huang, Sen-Shan; Sohn, Jaebum; Son, Seung Hwan
2000
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### Cited by 1,842 Authors
74 Berndt, Bruce Carl 36 Saikia, Nipen 34 Baruah, Nayandeep Deka 34 Zaharescu, Alexandru 32 Chan, Heng Huat 32 Xia, Ernest X. W. 30 Mahadeva Naika, Megadahalli Sidda 28 Cooper, Shaun 28 Evans, Ronald J. 27 Dixit, Atul 26 Kim, Byungchan 23 Chu, Wenchang 23 Chu, Yuming 23 Sun, Zhihong 23 Yao, Olivia Xiang Mei 20 Lin, Bernard L. S. 20 Qiu, Songliang 19 Andrews, George Eyre 19 Chan, Song Heng 19 Xu, Ce 18 Alkan, Emre 18 Liu, Zhi-Guo 18 Lovejoy, Jeremy 18 Wang, Liuquan 18 Williams, Kenneth S. 17 Adiga, Chandrashekar 17 Bringmann, Kathrin 17 Zudilin, Wadim 16 Chen, Chaoping 16 Gu, Nancy Shan Shan 16 Mc Laughlin, James G. 15 Toh, Pee Choon 15 Vasuki, Kaliyur Ranganna 15 Wang, Miaokun 15 Yee, Ae Ja 15 Zhang, Wenpeng 14 Borwein, Jonathan Michael 14 Coffey, Mark William 14 Srivastava, Hari Mohan 13 Barman, Rupam 13 Chen, William Yong-Chuan 13 Cui, Su-Ping 13 Guillera, Jesús 13 Mao, Renrong 13 Simsek, Yilmaz 12 Chern, Shane 12 Kanemitsu, Shigeru 12 Ono, Ken 12 Sun, Zhi-Wei 12 Ye, Dongxi 11 Can, Mumun 11 Eie, Minking 11 Folsom, Amanda L. 11 Garvan, Frank G. 11 Huber, Tim 11 Jennings-Shaffer, Chris 11 Kumar, Belakavadi Radhakrishna Srivatsa 11 Moll, Victor Hugo 11 Rogers, Mathew D. 11 Roy, Arindam 11 Sellers, James Allen 11 Sills, Andrew V. 11 Tang, Dazhao 11 Vuorinen, Matti Keijo Kustaa 10 Cvijović, Djurdje 10 Dilcher, Karl 10 Feng, Tao 10 Straub, Armin 9 Berkovich, Alexander 9 Bowman, Douglas C. 9 Chan, Heichi 9 El Bachraoui, Mohamed 9 Guo, Victor J. W. 9 Hirschhorn, Michael D. 9 Kang, Soon-Yi 9 Kostov, Vladimir Petrov 9 Maji, Bibekananda 9 Merca, Mircea 9 Mortenson, Eric T. 9 Sohn, Jaebum 8 Alaca, Ayşe 8 Alaca, Şaban 8 Alzer, Horst 8 Boruah, Chayanika 8 Ma, Xiaoyan 8 Milas, Antun 8 Paris, Richard Bruce 8 Tsumura, Hirofumi 8 Yesilyurt, Hamza 8 Zhang, Wenlong 8 Zhou, Yajun 7 Adell, José Antonio 7 Baoulina, Ioulia N. 7 Bhuvan, E. N. 7 Chandankumar, Sathyanarayana 7 Hemanthkumar, B. 7 Ismail, Mourad El-Houssieny 7 Kim, Daeyeoul 7 Li, Chengju 7 Liaw, Wen-Chin ...and 1,742 more Authors
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### Cited in 314 Serials
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https://www.ecb.europa.eu/pub/financial-stability/fsr/html/ecb.fsr202105~757f727fe4.hu.html | Keresési lehetőségek
Kezdőlap Média Kisokos Kutatás és publikációk Statisztika Monetáris politika Az €uro Fizetésforgalom és piacok Karrier
Javaslatok
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Magyar nyelven nem elérhető
# Foreword
This is the third issue of the Financial Stability Review (FSR) prepared in the context of the coronavirus COVID-19 pandemic, with many euro area countries having faced a third wave of infections. As a result, a vast number of firms – particularly those in the services, leisure and travel sectors – still cannot operate normally, and the economy is still reliant upon policy support to prevent widespread unemployment, corporate insolvencies and economic contraction. The human and economic costs of the pandemic continue to accrue.
That said, vaccination programmes are progressing and offering a route out of the pandemic. Financial markets have been driven by expectations of an upswing, exemplified by a striking rally in global equity markets. We are optimistic that financial and economic conditions will bounce back. There is, however, a reality that the pandemic will leave a legacy of higher debt and weaker balance sheets, which – if unaddressed – could prompt sharp market corrections and financial stress or lead to a prolonged period of weak economic recovery.
The May 2021 FSR assesses financial stability vulnerabilities – particularly in the corporate sector – and their implications for financial market functioning, debt sustainability, bank profitability and the non-bank financial sector. Risks to financial stability remain elevated and have become more unevenly distributed. The pandemic has imposed higher costs on some vulnerable countries with larger services sectors, which in turn implies a greater need for continued policy support and growing interconnections between their government, corporates and banks. More broadly, the euro area banking sector also continues to face headwinds, with its profitability subject to uncertainty about the balance of loan losses to come and provisions already booked.
This issue of the FSR also looks beyond the pandemic at the other great challenge of our time – climate change – and the risks that this poses to euro area financial stability. A special feature brings together the further enhancements that we have made to our framework for monitoring and assessing climate-related risks to financial markets, banks and non-banks.
The Review has been prepared with the involvement of the ESCB Financial Stability Committee, which assists the decision-making bodies of the ECB in the fulfilment of their tasks. The FSR exists to promote awareness of systemic risks among policymakers, the financial industry and the public at large, with the ultimate goal of promoting financial stability.
Luis de Guindos
Vice-President of the European Central Bank
# Overview
## Euro area recovery has been delayed, with the impact of the pandemic increasingly concentrated in some sectors
A third wave of coronavirus infections in the euro area has weighed on the near-term economic outlook. More targeted lockdown and social distancing measures and economic adaptation have helped euro area economies to cope better with the pandemic. Nonetheless, many euro area countries faced a third wave of infections in the first months of 2021 that – together with the slow start of the vaccine roll-out – has delayed the economic recovery (see Chart 1, left and middle panels). Looking ahead, progress with vaccinations and the gradual easing of containment measures should support a rebound in economic activity in the course of 2021.
The impact of the pandemic has been increasingly concentrated in some sectors and countries with pre-existing vulnerabilities. The euro area services sector continues to be more adversely affected by the restrictions on social interaction and mobility than manufacturing. The weakest performing sectors, such as trade, transport and accommodation, as well as arts and entertainment, have seen continued declines in gross value added of 2-4 times the aggregate. By contrast, the industrial sector has been recovering faster, supported by improved foreign demand. This sectoral divergence, combined with differing trajectories of the pandemic, has led to a wide divergence in 2021 economic forecasts at the euro area country level (see Chart 1, middle panel).
Improved economic prospects for the United States led to a notable increase in US long-term nominal interest rates, with global effects. A faster roll-out of vaccinations and agreement on a sizeable fiscal stimulus programme have led to a marked improvement in the US economic growth and inflation outlook (see Chart 1, left and middle panels). The ensuing 60 basis point rise in US ten-year government bond yields since the start of 2021 (see Chart 1, right panel), first driven by higher inflation expectations and later by rising real rates, led to some modest spillovers to the euro area (see Chapter 2). These spillovers were partially offset as the ECB’s Governing Council reinforced its accommodative policy stance by significantly stepping up its asset purchases. Beyond the euro area, rising US yields coupled with an appreciation of the US dollar could generate larger shifts in global capital flows and, as indicated by past crises, may represent a source of risk for emerging market economies with external financing needs (see Box 1 and Chart 2.8, right panel).
## Financial markets exhibited remarkable exuberance as US yields rose
As US interest rates rose and global bond markets sold off, equity markets saw a renewed rally. The rise in US benchmark bond yields led to a global sell-off in bond markets (see Chart 2, left panel). At the same time, equity markets remained buoyant, supported by a recovery in expected earnings and robust risk sentiment (see Chapter 2). The recent rise in composite stock indices has been coupled with a somewhat stronger advance by financial stocks. These had previously underperformed technology stocks, which were among the best performers in 2020 (see Chart 2, right panel).
The buoyancy of financial markets has stood in contrast to weaker economic fundamentals, while recent bouts of volatility highlight the risk of repricing. Despite the recent stock price declines in some sectors, stock market valuations remain elevated. In the United States, valuations stand well above pre-pandemic levels, whereas they are at more moderate levels in the euro area. Spreads on euro area non-financial corporate (NFC) bonds remain at risk of an abrupt repricing, in particular for the high-yield segment, where they have fallen below pre-pandemic levels despite growing vulnerabilities. Overall, risk assets remain sensitive to changes in the benchmark yield curve and a reassessment of valuations could ensue if investor expectations regarding the likelihood and pace of monetary policy tightening were to change without an accompanying improvement in growth prospects (see Chapter 2).
Many euro area investment funds, insurers and pension funds are exposed to a further rise in yields or a correction in credit markets. Investment fund flows have also rebalanced from debt to equity given rising yields (see Chart 3, left panel). Still, in their search for yield over recent years, non-banks have increased the duration risk of their debt securities portfolios to multi-year highs. This increases the sensitivity of their assets to higher rates, though for insurers and pension funds asset valuation losses could be compensated for by a fall in the value of their liabilities given the sector’s negative duration gap. Non-banks also have large exposures to firms with weak fundamentals, with more than a quarter of the sector’s NFC debt holdings subject to a negative credit outlook or credit watch by rating agencies (see Chart 3, right panel). Roughly half are also BBB-rated, only one notch above high-yield status.
In parallel, since last November, investment funds have further reduced their liquidity buffers. Cash buffers and liquid asset holdings are now below pre-pandemic levels and are approaching new lows, leaving the sector highly vulnerable to fire sales of assets in the event of large-scale redemptions. Investment funds’ liquidity risk has increased amid a search for yield (see Box 6) over recent years. This underscores the importance of strengthening the resilience of the non-bank financial sector, including from a macroprudential perspective (see Chapter 5).
## Corporate solvency challenges could weigh on sovereigns, households and creditors
Reliance on debt has increased among vulnerable firms, amid higher rollover risks. Debt-to-equity ratios have increased considerably among the most leveraged firms, with the 90th percentile increasing from 220% at end-2019 to over 270% in the final quarter of 2020 (see Chart 4, left panel). Corporate earnings expectations for the euro area have remained below pre-pandemic levels, while corporate funding conditions remained around the tightest levels since the pandemic started, especially for small and medium-sized enterprises (SMEs), highlighting elevated refinancing risks. Higher (risk-free) rates would increase debt servicing costs from historical lows and could raise medium-term risks in countries with elevated debt levels. The substantial increase in liquidity buffers among euro area firms may cushion corporate rollover risks, even though this appears to be particularly relevant for large listed firms.
Solvency risks in the corporate sector are set to rise as public support measures fade. Extensive policy support has kept corporate insolvencies unusually low in a period of extreme economic weakness, unlike during previous crisis episodes (see Chart 4, right panel). The impact of the pandemic on corporates is increasingly concentrated in the services sectors and among SMEs. This implies that a sudden tightening of financing conditions or a further delayed economic recovery could have more severe implications for financial stability than the aggregate picture suggests, in particular in countries heavily reliant on pandemic-sensitive sectors. Therefore, even as the economy recovers, corporate insolvencies are expected to increase from the very low levels observed in 2020, partly driven by a backlog of insolvency cases. As a result, governments face a delicate balance between prematurely adjusting support measures, which may contribute to triggering a wave of corporate insolvencies, and maintaining support measures for too long and thus keeping unviable corporates alive (see Special Feature A).
An increase in corporate insolvencies may impact households via employment prospects, so far prevented by policy support measures. On aggregate, household balance sheets have been cushioned so far, thanks to government income support schemes, record high saving rates, continued robust developments in euro area residential real estate markets and the recovery in stock markets. However, high dependence on government support schemes makes households vulnerable, and their financial and employment situation could worsen in the event of prolonged economic weakness, which may translate into job losses linked to a growing number of corporate insolvencies (see Chart 5, left panel).
At the same time, continued strength in residential real estate markets and mortgage lending has increased household indebtedness and vulnerabilities. The risk of a correction in residential real estate markets has increased amid signs of overvaluation for the euro area as a whole. In contrast to the resilience of residential real estate markets, commercial real estate markets are already facing a substantial market correction (see Chart 5, right panel). A further decline in commercial real estate prices could feed through to the financial system via increased credit risk, decreased collateral values and losses on direct holdings, as well as to lower investment and economic activity by non-financial corporations.
The continued need for policy support may add to medium-term sovereign debt sustainability concerns in more vulnerable countries. The aggregate euro area sovereign debt-to-GDP ratio rose to 100% in 2020, up from 86% of GDP in 2019, as governments have financed extensive economic support to cushion households and firms. Fiscal policy support has been particularly large in some countries with a larger share of economic sectors most impacted by the pandemic and lockdowns (see Chart 6, right panel). As a result, vulnerabilities from the outstanding stock of debt appear higher than in the aftermath of the global financial crisis and the euro area sovereign debt crisis, although debt servicing and rollover risks appear more benign given continued favourable sovereign financing conditions in terms of both pricing and duration (see Chart 6, left panel). Contingent liabilities could increase sovereign debt levels further if the economic situation turns out to be weaker than expected and pandemic-related corporate loan guarantees are called on a broader scale (see Box 2). The associated increase in public debt levels, further delays in the implementation of the EU recovery fund or the emergence of an adverse sovereign-bank-corporate nexus (see Box 4) could trigger a reassessment of sovereign risk by market participants and reignite market pressures on more vulnerable sovereigns. This may render the exit from policy measures more challenging in vulnerable countries with a higher reliance on fiscal support measures.
## Improved market sentiment towards euro area banks, but profitability and asset quality concerns remain
Euro area bank stock prices have recovered markedly from the low levels of October 2020. Bank equity prices have rallied in two waves on positive news about vaccines and reflation expectations. Banks outperformed the overall market, mirroring a wider recovery in previously underperforming stocks. While investors appear to anticipate that a steepening of the yield curve could support bank profitability, analysts’ return on equity (ROE) expectations for 2022 have remained unchanged since last summer (see Chart 7, left panel). Nonetheless, euro area bank valuations remain depressed by both international and historical standards. Improved market sentiment towards banks, coupled with market expectations of an extension of the pandemic emergency purchase programme, have also translated into tighter spreads on bank bonds, further improving market funding conditions for euro area banks.
Nevertheless, the outlook for bank profitability remains weak and the prospects for loan demand are uncertain. Euro area banks’ ROE fell from 5.3% in 2019 to 1.3% in 2020 owing to pandemic-related loan loss provisions and ongoing margin compression in a low interest rate environment (see Chapter 3). Heterogeneity across countries was high, with banking sectors in some countries recording sizeable losses (see Chart 3.4). Despite recently improving market sentiment towards euro area banks, market analysts still expect profitability to recover only gradually, projecting an ROE of 3% and 5% for 2021 and 2022 respectively, given higher provisioning needs and lower expected operating income. The outlook for lending could be challenging as a result of both tighter credit standards and lower corporate credit demand. The former is related to banks’ heightened risk perceptions, while the latter is associated with the adjustment of state guarantee programmes and the need to improve balance sheets.
Early signs of a rise in loan impairments are becoming increasingly visible. Cushioned by large-scale fiscal, monetary and prudential support, bank asset quality has been preserved despite the sharp recession. In fact, the aggregate non-performing loan (NPL) ratio for the euro area reached its lowest level on record at 2.7% in 2020, as banks reduced legacy portfolios. Loan loss provision flows returned to pre-pandemic levels in the second half of 2020. But the normalisation may prove temporary, as early indicators of deteriorating asset quality are becoming increasingly visible, including a rise in forbearance. This is particularly the case in countries where lengthy and costly insolvency procedures inhibit claim enforcement (see Chart 7, right panel). A weaker than expected economic recovery and growing vulnerabilities in the corporate sector may entail higher loan loss provisioning going forward. In addition, as moratoria and public guarantees are gradually adjusted (see Chapter 1 and Box 2), credit risk may reappear with a lag, also implying increased loan loss provisions.
## Climate change may pose material risks to financial stability
Climate-related risks to euro area banks, funds and insurers could be material, particularly if climate change is not mitigated in an orderly fashion. Banks and non-bank financial institutions alike are faced with the task of managing the implications of climate change over the medium to long term (see Special Feature B). Both need to manage their exposure to a transition to a low-carbon economy and their exposure to physical risks associated with extreme weather and climate-related events or more insidious changes in climate (see Chart 8). ECB analysis suggests that such risks appear to be particularly concentrated in certain sectors, geographical regions and individual banks, exacerbating the related implications for financial stability. At the same time, data and methodological gaps still need to be addressed to evaluate climate-related risks comprehensively. In addition, climate-related financial risks that may emerge from the interplay between banks and insurers need to be recognised, with insurance coverage likely deteriorating as extreme weather and climate-related events become more frequent.
Policy action may be required to ensure the resilience of the financial system to climate-related risks. Enhanced climate-related disclosure requirements, including in relation to companies’ forward-looking emission targets, and deeper, more effective green financing are essential steps in a smooth transition towards a sustainable economy and a general reduction of climate-related vulnerabilities. At the same time, possible market failures can stem from data gaps, which would raise the risk of greenwashing. The upcoming ECB climate stress test will also analyse trade-offs in a forward-looking manner, thereby providing a further basis for future policy discussions. Ultimately, given the systemic dimension, considerations about how to mitigate climate-related risks in the financial system require a macroprudential perspective to be effective and to ensure cross-sector consistency.
## Policies should continue to support the recovery, while targeting the build-up of vulnerabilities in selected areas
Extended policy measures have remained key in mitigating the economic costs of the pandemic, but vulnerabilities continue to build up in some areas. With many euro area countries facing renewed surges in infections, lockdown measures have been reinstated and economic support measures maintained. Divergence across countries and sectors has continued to increase, ultimately leading to a concentration of risk that often coincides with pre-existing vulnerabilities in both the real economy and the financial sector. Looking ahead, medium-term vulnerabilities for euro area financial stability remain elevated and relate to: (i) a mispricing of some asset classes, raising the risk of corrections in markets; (ii) growing balance sheet challenges in the public and non-financial private sectors; (iii) weaker bank profitability amid high credit risk exposure; and (iv) further increases in duration, liquidity and credit risks of non-banks. The financial stability implications could be amplified by the emergence of an adverse feedback loop across various sectors of the economy.
Policies should remain broadly accommodative but could be more targeted to support a robust economic recovery amid remaining uncertainty and the potential for credit risk to materialise. Conditional on the economic impact of the pandemic, the extensive policy support, in particular for corporates, could continue to move gradually from being broad based to more targeted. In this context, fast and effective use of the €750 billion Next Generation EU (NGEU) recovery funds would complement national support measures and mitigate cross-country divergences in the coming years. Specifically for banks, capital relief measures should continue to prevent excessive deleveraging, while proper and timely recognition of credit risk would maintain confidence in balance sheets. In this context, it is worth noting the preliminary evidence which suggests that some banks may be reluctant to use available capital buffers, which could in turn affect credit conditions, especially for corporate lending. In the medium term, a higher share of releasable capital buffers could be considered, as it can enhance banks’ ability to absorb losses and maintain the provision of key financial services in a crisis. In addition, concerns related to the expected asset quality deterioration in the banking sector reinforce the need for effective NPL solutions. Given the low interest rate environment and profitability challenges, efforts to address structural issues across banks should be stepped up. Finally, from a broader regulatory perspective, strengthening the banking union and the timely, full and consistent application of Basel III remain key policy priorities for the banking sector going forward.
Further progress towards developing a macroprudential framework for non-banks is expected and would be highly welcome. In particular, the Financial Stability Board is developing recommendations targeting structural vulnerabilities associated with money market funds, open-ended investment funds and margining practices in order to enhance the resilience of the non-bank financial sector. Once issued, they should be swiftly implemented in the European Union as appropriate.
# 1 Macro-financial and credit environment
## 1.1 Increasing concentration of risk in more vulnerable sectors and countries
Economic activity fell amid renewed lockdown measures, but activity has proved more resilient than during the first lockdown. The resurgence of coronavirus cases last autumn caused euro area governments to reinstate tight containment measures, which weighed on economic activity in the euro area in the fourth quarter of 2020 and the first quarter of 2021. At the same time, the economic impact of the second lockdown remained more contained than that of the first lockdown for two reasons. First, containment measures were on average less stringent than in the second quarter of 2020. Second, economic activity has become less sensitive to the stringency of lockdown measures, including across countries with different stringency levels, as firms and households have adapted to the new environment (see Chart 1.1, left panel). This higher resilience is not only visible on average, but also when comparing countries with different levels of stringency.
Slack in labour markets and subdued investment could point to a sluggish recovery. Although economic activity recovered to some extent in the second half of 2020, the number of employees and total hours worked remain substantially below pre-pandemic levels (see Chart 1.1, right panel). While hours worked are likely to rebound once employees on short-time work return to full-time work, the high share of laid-off workers who left the labour force altogether could herald a more persistent disruption to labour markets. Non-employed workers, especially from sectors that face a more permanent drop in demand, could face difficulties in re-entering the labour market after the pandemic, which would weigh on economic growth. Similarly, investment remains subdued, reflecting firms’ uncertainty about the timing of the pandemic and their own growth prospects after the pandemic subsides (see Chart 1.1, right panel). Looking back at the global financial crisis as a precedent, a slow recovery of investment may also be a harbinger of a more sluggish recovery from the pandemic than the swift rebound in consumption suggests.
While the availability of vaccines has improved the medium-term economic outlook, uncertainties remain in the near term. The approval of multiple vaccines in late 2020 and early 2021 improved the economic outlook for the euro area and reduced the uncertainty about the length of the pandemic. While this has boosted the growth prospects for 2022, the ongoing containment measures weigh on the near-term outlook (see Chart 1.2, left panel). In addition, the slow start to the vaccine roll-out in the euro area makes it unclear when the euro area will reach herd immunity and return to normal economic activity. Moreover, the virus continuing to evolve poses considerable tail risks as vaccine-resistant mutations may yet emerge, necessitating a prolonged period of constrained social and economic activity.
The slow start to the vaccination campaign and a more moderate fiscal stance may leave the euro area lagging its advanced economy peers. The euro area was initially much slower than other advanced economies to ramp up vaccination (see Chart 1.2, right panel). As the pace of vaccination in the euro area picks up, however, this gap is narrowing. Nonetheless, the euro area may take longer than the United States or the United Kingdom to reach herd immunity depending on the further vaccination progress, which would allow for a return to normal. In addition, euro area governments have adopted a more moderate fiscal stance relative to GDP and compared with the respective output gap than the US administration in 2021. Although the “Biden package” of USD 1.9 trillion is expected to generate positive spillovers of up to 0.3% of real GDP for the euro area, the more accommodative fiscal stance in the United States could further increase the divergence between the two economic areas. Such a disparity in growth prospects could create upward pressure on real interest rates in the euro area and tighten overall financing conditions to the detriment of euro area corporates, households and sovereigns.
Global risks remain contained, and emerging markets proved resilient as policy uncertainty in the United Kingdom and the United States fell. Despite the economic challenges and the slow global vaccination roll-out, financial conditions and capital flows in emerging markets have remained fairly resilient so far. These dynamics are, however, highly dependent on global risk appetite and monetary policy accommodation in advanced economies (see Box 1). The agreement of a trade deal between the United Kingdom and the European Union at the end of 2020 and the transition to a new administration in the United States have reduced policy uncertainty in both the United Kingdom and the United States. At the same time, the tensions relating to export controls on vaccines highlight the importance of trade in overcoming the pandemic, but also its fragility.
The divergence across sectors widened as containment measures became more targeted. The gradual reopening and the more targeted containment measures during the second lockdown allowed less badly affected sectors to widely resume normal activity, whereas services such as tourism, entertainment and travel to a large extent remained shut (see Chart 1.3, left panel). Consequently, the most affected sectors were not only hit most in the first half of 2020, but also rebounded less relative to the initial drop in the second half of 2020, increasing the divergence across sectors (see Chart 1.3, right panel). This divergence may widen further if the slow roll-out of vaccines necessitates continued containment measures over the summer tourism season, especially in southern European countries.
Continued cross-sectoral divergence could trigger a costly reallocation of resources. The widening sectoral divergence poses risks to financial stability for two reasons. First, the most affected sectors face more severe liquidity and solvency risks than aggregate economic indicators suggest, and the materialisation of these risks could trigger an unravelling of macro-financial imbalances with adverse spillovers to other sectors. Second, the continued divergence will at some stage lead to a reallocation of resources from the most affected sectors to sectors with better growth prospects. The costs associated with such a cross-sectoral reallocation of resources, for example due to retraining of workers, could further weigh on the strength and pace of the economic recovery in the short to medium term.
## Box 1 Emerging markets’ vulnerability to a reassessment of risk
Prepared by Irina Balteanu and Livia Chiṭu[1]
Financial conditions in emerging market economies (EMEs) have weathered the COVID-19 crisis well so far, despite an intense but short-lived stress episode at the onset of the pandemic. Financial conditions in EMEs have rebounded strongly since March 2020; they currently stand at levels similar to before the pandemic thanks to lower bond spreads and higher equity prices. Capital flows have also recovered, with market segments typically judged to be riskier by foreign investors, such as equity and local currency debt, recording strong inflows in the second half of last year. This rebound helped to relieve pressures on financial systems and support activity in EMEs. Nevertheless, recent concerns about rising bond yields and higher than expected inflation in advanced economies have translated in a tightening of financial conditions and slowdown of capital flows to EMEs. In this context, this box assesses potential vulnerabilities facing large EMEs and the risks posed to euro area financial stability.
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## 1.2 Benign financing conditions limit debt sustainability risks
The pandemic continues to weigh on fiscal budgets in 2021 as governments extend support measures. When governments reinstated strict containment measures at the end of last year, they also extended existing support measures to cushion the economic impact on firms and households. As a consequence, fiscal deficits in 2021 will be higher than projected last autumn and are expected to exceed the deficit in 2020 for the euro area as a whole (see Chart 1.4, left panel). In addition to existing liquidity support measures, governments started shifting more towards solvency support, for example by replacing government-guaranteed loans with grants or by injecting capital into larger, often state-associated companies. While the shift towards solvency support may be more effective in supporting weaker corporates which increasingly face solvency rather than liquidity problems, it also weighs on fiscal budgets more directly than indirect support measures that constitute contingent liabilities (see Box 2).
Extending the general escape clause of the Stability and Growth Pact until the end of 2022 could pre-empt a premature fiscal tightening. Current projections indicate that, due to the economic fallout from the pandemic, governments will continue to run up considerable fiscal deficits in 2022. As the deficits in more than half of the euro area countries are projected to exceed the 3% criterion in 2022, deactivating the escape clause at the end of 2021 might trigger a premature fiscal tightening in 2022. Extending the use of the clause this year already gives governments greater certainty about fiscal space going forward, which reduces the risk of an expectations-driven adverse spiral of reduced fiscal support, tighter corporate financing conditions and a further contraction in economic activity (see Box 4). At the same time, a strong rebound in economic activity would alleviate the need for additional fiscal support and thereby cushion the impact of already reinstating the Stability and Growth Pact rules in 2022.In addition, some stabilisation measures may be phased out as the economy recovers without a major contractionary impact.
Even so, the recent increase in sovereign debt will have less of an impact on fiscal budgets than would have been the case in previous crises. The steady decline in government bond yields has reduced the average gross interest payments of euro area sovereigns despite higher debt-to-GDP ratios than in 2009 (see Chart 1.4, right panel). Aside from this effect, lower interest rates also imply that gross interest payments are less sensitive to changes in debt-to-GDP ratios over time. In 2009, a country with a debt-to-GDP ratio that was 10 percentage points higher on average faced gross interest payments that were 0.4 percentage points higher. That elasticity has shrunk by half since 2009, to 0.2 percentage points. As a consequence, increases in sovereign debt levels due to unexpected events such as the pandemic impose a smaller burden on fiscal budgets, which implies that sovereign balance sheets are more resilient to exogenous shocks than at the time of the global financial crisis. Nevertheless, a sustained rise in sovereign bond yields could raise refinancing costs for governments, which would have a negative effect on sovereign debt sustainability in the medium to long run.
Governments locked in low interest rates in the second half of 2020 and early 2021 by issuing longer maturity debt, thus reducing rollover risk. Between December 2019 and March 2021, average sovereign bond yields declined by 43 basis points in the euro area, supported by accommodative monetary policy. Following an initial surge in short-term debt issuance last spring, governments locked in these favourable financing conditions by shifting their net issuance towards longer-term debt, in particular bonds with maturities of more than five years (see Chart 1.5, left panel and Chapter 2). This has not been affected so far by the recent rise in sovereign bond yields. Accordingly, the average residual maturity of sovereign debt increased by four months between May 2020 and March 2021.
Low interest rates coupled with longer maturities partially offset the adverse impact of higher debt levels on debt service ratios. The large increase in sovereign debt-to-GDP ratios in 2020 increased the debt service ratio[2] relative to GDP for all euro area countries (see Chart 1.5, right panel). At the same time, longer maturities and to a lesser extent lower rates alleviated the increase in debt service ratios for sovereigns, especially in countries where debt-to-GDP ratios have increased significantly. In addition, approximately 35% of the increase in the euro area debt-to-GDP ratio is driven by the drop in GDP. As the economy recovers, this denominator effect will subside, further easing the debt service ratio and the rollover risk of sovereign debt. In addition, governments continue to hold sizeable deposits with the Eurosystem, which further cushions short-term debt servicing needs.
The effectiveness of the EU recovery package is constrained by countries’ absorption capacity and depends on the productive use of the funds. The €750 billion Next Generation EU (NGEU) package can complement national fiscal support measures in the coming years and help sustain the recovery without national budgets being directly negatively affected.[3] However, historical absorption rates of structural EU funds show that Member States would need to absorb the NGEU funds at an unprecedented pace to make full use of the package (see Chart 1.6, left panel).[4] Based on the absorption rates of year 6 in the 2007-13 multiannual financial framework (MFF), up to 55% of the more than €300 billion in grants contained in the NGEU Recovery and Resilience Facility (RRF) may remain unused (see Chart 1.6, right panel).[5] The lack of absorption capacity in the worst affected countries in particular may impede the disbursement of the NGEU funds, which could further exacerbate the cross-country divergence following the pandemic and potentially spur refragmentation pressures in sovereign bond markets. In addition, the need to absorb NGEU funds quickly may compromise the efficient and productive use of those funds.
While favourable financing conditions mitigate short-term risks in the public sector, the continued need for fiscal support poses medium-term risks. Although financing conditions have limited the impact of increased sovereign debt levels on fiscal budgets and debt service costs, the pandemic continues to take a substantial toll on fiscal budgets. The need to extend existing support measures and retain automatic stabilisers will keep fiscal budgets tightly linked to the evolution of the pandemic. In addition, the adverse impact of continued containment measures on corporate balance sheets increases the risk that contingent liabilities will materialise and further strain public budgets (see Box 2). Finally, a sudden rise in interest rates could raise concerns about the sustainability of sovereign debt over the medium term, although the impact on sovereigns’ debt service needs would be alleviated by the extended average maturity of sovereign debt portfolios.
## Box 2 Contingent liabilities: past materialisations and present risks
Prepared by Sándor Gardó, Benjamin Hartung, Mariusz Jarmuzek and Algirdas Prapiestis
Fiscal policy support has mitigated financial stability risks during the pandemic, but the vulnerabilities arising from contingent liabilities have increased for euro area sovereigns. National policy responses to support households and firms during the pandemic directly increased the aggregate euro area general government debt-to-GDP level by around 14 percentage points to around 100% of GDP in 2020. Additionally, public guarantee schemes that were introduced in 2020 constitute sizeable contingent liabilities for governments in most euro area countries, adding to the stock of both existing government guarantees and other implicit contingent liabilities, which reinforces concerns about the emergence of an adverse sovereign-bank-corporate nexus. Against this backdrop, this box presents historical evidence from contingent liability materialisations, investigates their commonalities and differences with the situation under the current pandemic-induced shock and assesses the ensuing risk for sovereigns.
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## 1.3 Aggregate household resilience masks uneven impact of the pandemic
Households’ economic sentiment has improved on hopes of a swift economic recovery, although uncertainty about employment lingers. Survey-based measures of economic confidence started to improve at the end of 2020 when the vaccine roll-out began (see Chart 1.7, left panel). Despite the overall improvement in sentiment, forward-looking measures of unemployment continue to signal a deterioration in employment prospects. The euro area aggregate sentiment masks considerable differences between euro area countries, reflecting the uneven impact of the pandemic on households across the euro area. Households that report the largest deterioration in their financial situation over the last year also show the highest unemployment expectations for the coming 12 months, leaving them in a vulnerable position when support measures are scaled back (see Chart 1.7, right panel).
Cushioned household income, excess savings and record high net worth have increased the overall financial resilience of households. Despite recovering from the initial shock of the pandemic, disposable income remains reliant on government support in the form of higher net social transfers (see Chart 1.8, left panel). Moreover, households saved a significant amount of their income as containment measures limited spending on durable goods.[6] Cumulative excess savings compared to the pre-pandemic savings rate stood at around 4% of GDP in the fourth quarter of 2020. Whether pent-up demand will translate into higher future consumption remains uncertain, despite a large share of the excess savings ending up in deposit accounts (see Chart 1.8, middle panel). Excess savings are likely held by higher-income households, which have a lower marginal propensity to consume. Finally, robust house price growth and recovering stock prices continued to support net wealth, causing this metric to surge to 754% of disposable income in 2020 (see Section 1.5).
The increase in aggregate household financial wealth masks considerable differences across countries and income groups. Low-income individuals and countries that already exhibited slow economic growth before the pandemic are affected disproportionately. For this group of households, dependence on policy support measures remains high (see Chart 1.8, right panel). Moreover, there are indications of tighter access to credit combined with cliff effects on their expenditure stemming from the phasing out of moratoria and other economic support policies. Strains on this group of households are likely to intensify if support is dialled back prematurely, resulting in lower consumption and a lower debt service capacity.
Household borrowing varies significantly across different types of credit (see Chart 1.9, left panel). Growth in aggregate bank lending to households stabilised at 3% from the start of 2020, mainly on account of a 5% increase in lending for house purchase. Consumer credit declined by 2%, reflecting the ongoing impact of the tighter COVID-19 restrictions on consumer confidence and demand for durable goods. Going forward, a further moderation in banks’ risk perceptions towards households might support looser credit standards and boost consumption when lockdown measures are scaled back and the economy fully reopens (see Chart 1.9, middle panel).
Government schemes and record low debt servicing costs have helped to make household debt more sustainable. So far, the pandemic has had a relatively modest impact on household debt ratios, as disposable income increased while spending opportunities were limited during lockdowns. As a result, nominal household debt increased at a slower pace in the first half of 2020 compared to the pre-pandemic path (see Chart 1.9, right panel), while the debt-to-liquid assets ratio declined to 76% in the fourth of 2020. In addition, very low interest rates have driven debt servicing costs down to all-time lows, with interest payments as a share of disposable income falling to 2.2%. Households increasingly favoured fixed rate mortgages in new annual credit flows over variable rate alternatives, further contributing to lower overall vulnerability. As a result, the share of fixed rate mortgages had increased to 59% in March 2021 compared to just 47% in March 2016.
Overall, financial stability risks stemming from the household sector have been less pronounced than previously anticipated. With stronger balance sheets, robust net wealth and record low debt servicing costs, households have built up some capacity to weather economic headwinds. However, lower-income workers have not generally benefited from mitigating factors in the form of higher financial wealth, leaving them in a potentially vulnerable position when policy support is scaled back. In addition, household resilience remains highly contingent on the extent to which corporate insolvencies rise, as this could translate into significantly higher unemployment. Whether these risks materialise will depend on the ability of governments to keep supporting the households that have been hardest hit by the pandemic, especially in those countries where the take-up of policy support is substantial, residential properties are overvalued and debt levels are elevated.
## 1.4 Corporate solvency risks on the rise
Weak revenues and low profit margins continue to weigh on corporate profits, gradually raising the pressure on corporate solvency. Similar to previous recessions, gross corporate profits declined more than gross value added in 2020, as squeezed profit margins added to the fall in corporate revenues (see Chart 1.10, left panel). Although both profits and revenues were more resilient in the second wave than during the initial phase of the pandemic, their continued decline added to the total shortfall compared with 2019 levels. In total, corporate profits in 2020 were 8.1% below gross profits in 2019. Consequently, retained earnings (measured by gross savings) dropped substantially, unlike in the global financial crisis when they recovered during the first year of the recession. This sharp and persistent drop in corporate savings limits the scope for new investment going forward, although firms may use available cash buffers to support capital accumulation.
Aggregate liquidity and capital buffers conceal a divergence across corporates, as risks rise for cash-strapped and overindebted firms. On aggregate, the considerable increase in gross debt has so far largely been offset by a similar rise in corporate holdings of liquid assets. Granular data for listed firms confirm that corporates took on more debt to build up precautionary liquidity buffers as the correlation between changes in gross debt and changes in cash buffers across firms increased (see Chart 1.10, middle panel). However, this effect is particularly prominent for large listed corporates whereas SMEs, which were more heavily affected by the pandemic and are less likely to have access to market-based funding, face more severe liquidity challenges. The concentration of liquidity risk among the most vulnerable corporates implies that a sudden tightening of financing conditions or a protracted economic recovery could have more severe consequences for financial stability than the aggregate picture suggests. In addition, liquidity problems increasingly morph into solvency issues – while the first wave of the pandemic was characterised by bond issuance and bank borrowing to meet liquidity needs, firms have recently issued more equity (see Chart 1.10, right panel). Among listed firms, however, equity issuance has been concentrated in a few firms, especially in the technology sector, which tend to have benefited from the pandemic.
More recently, corporate credit growth has slowed, reflecting both corporates deferring investment and banks tightening lending conditions. In the second half of 2020, demand for bank loans slowed abruptly as bank lending conditions tightened and the need to bridge working capital needs subsided (see Chart 1.11, left panel), especially in the worst affected sector, services. Besides the drop in demand for liquidity and the more cautious risk perceptions of banks, the slowdown in bank lending to corporates also reflects the reduced willingness of firms to invest in fixed capital while uncertainty remains about the timing and pace of the economic recovery. However, the subdued investment activity could also indicate a more structural pessimism about the viability of certain business models or the limited scope for new investments amid elevated debt levels. That in turn would have a more lasting impact on the economic recovery and corporate balance sheets. Moreover, building up liquidity buffers in the early stages of the pandemic has shielded some firms from revenue shortfalls and reduced the subsequent need for additional external financing.
Government-guaranteed loans may have become less effective in supporting corporate financing conditions. Following the large take-up of guaranteed loans in the second quarter of 2020, the demand for such loans has dropped sharply in tandem with the slowdown in new bank loans to corporates in the second half of 2020 (see Chart 1.11, middle panel). Looking ahead, the take-up of government-guaranteed loans is likely to fall further, as guarantees appear to have become less effective in supporting corporate financing conditions. Throughout 2020, credit standards eased considerably for guaranteed loans while tightening for non-guaranteed loans (see Chart 1.11, right panel). However, this gap in credit standards between guaranteed and non-guaranteed loans is projected to narrow in the first half of 2021. Also, overindebted corporates may be unwilling to take on additional debt, given the uncertain outlook.
Smaller firms benefited most from government guarantees but are particularly affected by a recent tightening of bank lending conditions. SMEs have been more likely to resort to government-guaranteed loans than larger firms, given their reliance on bank lending and the disproportionate impact of the pandemic on smaller enterprises. They have also been more likely to benefit from the benign effect of guarantees on credit standards, as they faced a sharper tightening of credit conditions for non-guaranteed loans (see Chart 1.11, right panel). The projected tightening of credit standards on guaranteed loans therefore disproportionately affects SMEs.
An abrupt increase in bankruptcies could challenge insolvency frameworks and impede the efficient reallocation of resources. Despite the unprecedented fall in corporate revenues and profits, bankruptcies in the euro area decreased by approximately 20% in 2020 relative to 2019 levels as public authorities provided policy support and in some cases suspended mandatory insolvency filings. Dealing with such a backlog of delayed bankruptcies would prove a challenge for judicial systems even in normal times. Although corporate solvency is likely to be more resilient than historical comparisons suggest, given the relatively swift recovery and the sizeable policy support, the number of insolvencies-in-waiting could still be higher than the current expected default frequency suggests (see Chart 1.12, left panel). Once support measures end, bankruptcy courts could therefore see an abrupt increase in insolvency filings, which could lead to the legal system becoming congested and insolvent firms taking longer to be resolved. That in turn could result in an inefficient and delayed reallocation of resources to more viable businesses, with adverse macroeconomic consequences in the medium term. Public authorities should therefore ensure that insolvency frameworks are sufficiently resourced to deal with a higher number of corporate insolvencies (see Chart 1.12, right panel).
Given the uncertain outlook for the viability of business models, targeting policy support towards viable firms remains challenging. Ideally, the broad-based liquidity support measures that shaped the early phase of the pandemic would be superseded by more targeted measures that help viable firms remain solvent. However, assessing corporate viability remains challenging in the light of the uncertain economic outlook and the post-pandemic prospects of different business models. While broad-based measures may lead to some misallocation of resources to non-viable firms (see Special Feature A), the alternative of withdrawing support to viable firms too early may have even more adverse consequences.
## 1.5 Euro area property market cycles diverge further
Euro area residential real estate (RRE) prices continued rising throughout the fourth quarter of 2020. At the euro area level, nominal house prices increased by 5.8% in the last quarter of 2020 (see Chart 1.13, left panel). While on aggregate prices continued to trend upwards in the euro area, growth rates varied widely across countries (see Chart 1.13, middle panel). The overall resilience observed in housing markets reflects several factors. First, household income has largely recovered as a result of the continued policy support and a rebound in economic activity. Second, the low interest rate environment and elevated macro uncertainty continue to put a floor under demand, as housing is perceived as a safe investment. Third, subdued construction activity in the second half of 2020 weighed on housing supply, adding upward pressure on prices, especially in markets with already tight housing supply.
A combination of buoyant house price growth and the uncertain macro backdrop kept measures of overvaluation elevated. Moreover, house price growth during the pandemic has generally been higher for those countries that were already experiencing pronounced estimated overvaluation prior to the pandemic (see Chart 1.13, middle panel). While providing a consistent set of benchmarks across countries, measures for overvaluation are surrounded by significant uncertainty and may be sensitive to country-level specificities, such as tax treatment or structural property market characteristics. In addition to elevated valuation measures, risks related to household indebtedness remain high for some countries, as credit for house purchase has continued to increase (see Section 1.3). This adds to the already elevated vulnerabilities that had accumulated in some euro area countries before the pandemic started.
Estimates of downside risk to house prices signal an expected slowdown of price growth in the coming year (see Chart 1.13, right panel). Despite high measures of overvaluation in some euro area countries, house price growth is expected to moderate, but prices are not expected to decline in the coming year. This expectation mainly reflects the improved economic outlook and overall more robust household balance sheets. Moreover, results from the bank lending survey also indicate credit standards for loans to households for house purchase eased slightly in net terms in the first quarter of 2021, possibly further supporting demand. However, future RRE price developments remain highly dependent on the recovery path and the ability of policymakers to prevent cliff edges by not abruptly ending support measures, especially given much of the resilience observed in household balance sheets is a direct result of policy support measures (see Section 1.3).
In contrast to the residential market, the pandemic sparked a price correction in the commercial real estate (CRE) market. Prices for prime CRE declined in the fourth quarter of 2020, albeit with large difference between those sectors hit hardest by the pandemic (retail) and those less affected (office) (see Overview chapter). Moreover, market intelligence suggests that prices in prime locations might also have been impacted less, as high-quality assets are typically easier to adapt to changing demand. Survey data indicate that the CRE market entered a downturn in the second quarter of 2020. Moreover, rising overvaluation in recent years has left room for a substantial price correction, as a majority of investors indicate that valuations have not bottomed out yet (see Chart 1.14, left panel). Also, activity remained at levels around half of the long-run average, potentially masking a further decline in property prices.
A sharper CRE market correction could have implications for bank balance sheets and introduce negative economic feedback loops. A further decline in CRE prices could feed through to the financial system via increased credit risk, decreased collateral values and losses on direct holdings. Bank lending to the CRE segment accounts for 7% of exposure to the non-financial private sector in the euro area, although levels vary substantially across countries. A significant drop in CRE prices could result in lower investment and economic activity by non-financial corporates, as CRE is often used as collateral to obtain finance. Survey data show that over half of survey participants have seen financing conditions deteriorate each quarter since the outbreak of the pandemic (see Chart 1.14, right panel). In addition, a further price correction may also spark procyclical behaviour within the financial system when risk exposure is reduced, loan loss provisions fall, and lending standards tighten. Moreover, a combination of low market liquidity and high redemption pressure on CRE investment funds could amplify the price decline and lead to fire sales, further increasing negative feedback loops.
Risks to financial stability stemming from real estate markets remain elevated. A sharper than expected decline in CRE valuations might set off negative economic feedback loops, while the RRE market might prove vulnerable to a withdrawal of policy support measures. Against this background, the financial sector may be exposed to the risk of corrections in the real estate market, especially in those countries where debt levels are elevated and policy support measures contribute significantly to household income.
# 2 Financial markets
## 2.1 Partial spillover of risks from rising US rates
A rise in US government bond yields led global sovereign bond yields higher, with euro area yield curves also steepening mildly. Rising US yields in recent months reflected the combination of a substantial fiscal stimulus package and optimism around vaccine roll-outs. The bond market sell-off also spilled over to some degree to other advanced economies, resulting in a mild steepening of the euro area GDP-weighted yield curve (see Chart 2.1, left panel). 2021 has seen the largest upward move in the ten-year US Treasury yield since the “taper tantrum” in 2013. However, the drivers of the yield change in 2021 appear more benign than in 2013, as a much smaller share relates to uncertainty on the outlook for US monetary policy (see Chart 2.1, middle panel). Foreign spillovers also explain a structurally increasing share of the euro area term premium (see Chart 2.1 right panel). Excessive increases in yields not motivated by domestic fundamentals threaten to unduly tighten financial conditions, if a rise in US yields has a large spillover effect on the euro area.
Euro area risk-free rates have risen only mildly, partly reflecting continued emphasis on accommodative monetary policy. Ten-year euro area risk-free rates moved back to pre-pandemic levels as the inflation component of risk-free rates increased to its highest level since the end of 2018 (see Chart 2.2, left panel). This reflects an improved economic outlook and a reassessment by investors of the balance of risks around the inflation outlook. In December 2020, alongside other monetary policy measures the Governing Council decided to recalibrate TLTRO III conditions and also to expand the pandemic emergency purchase programme envelope, where bond purchases were to be significantly stepped up in the second quarter of 2021.[7] The monetary policy measures help preserve favourable financing conditions, which are vital as countries take steps to re-open their economies.
The strong rise in US yields compared with euro area yields may affect global capital flows in the medium term. In recent years, FX hedged yields on ten-year US Treasuries have been relatively unattractive. However, the rise in US Treasury yields, which in February was reinforced by the largest foreign outflows since April 2020, has made this asset class more appealing. For Japanese investors, US Treasuries currently offer a higher FX hedged yield and a better credit rating than some of the largest euro area sovereign bond markets (see Chart 2.2, right panel).[8] This change could generate wider shifts in investor and capital flows and may lessen overseas demand for euro area sovereign bonds.
A sustained rise in interest rates would expose investors to valuation losses on their bond holdings. The aggregate amount of duration risk in the bond market has risen steadily in recent years on the back of increasing amounts of outstanding bonds, longer maturities and declining interest rates (see Chart 2.3, left panel). Sustained rises in interest rates would have a larger negative impact on the value of investors’ debt holdings, with major implications for institutional investors (see Chapter 4).
Current sovereign CDS spreads across a range of advanced and emerging market economies may indicate some complacency relative to credit ratings. The current long-term credit rating mapping with five-year CDS spreads is somewhat flatter than in the period after the global financial crisis, suggesting more benign pricing of sovereign risk (see Chart 2.3, right panel). This reflects a longer-term global trend which has seen the credit quality of many sovereigns decline, but their CDS spreads compress further at the same time. Further downgrades cannot be ruled out in an adverse scenario, with possible non-linear effects on credit risk pricing. At the same time, the current benign financing conditions have eased debt sustainability risks for many sovereigns in the short term, and the EU recovery package may further mitigate such risks for euro area countries (see Chapter 1).
## 2.2 Robust risk sentiment with pockets of market exuberance
Risk sentiment remained robust as the global growth outlook improved. Risk sentiment indices continued to recover in 2021 on the back of higher expected growth rates and optimism surrounding vaccine roll-outs (see Chapter 1), especially in the United States. While both the United States and the euro area are benefiting from continued accommodative monetary policy, risk sentiment in the United States has moved further ahead, boosted by the sizeable fiscal stimulus programmes (see Chart 2.4, left panel). Recent corporate earnings data appear to partly validate this optimism. However, some degree of uncertainty lingers, for example around the corporate earnings outlook and the pace of re-opening of some economies. This may leave room for disappointment.
The rise in interest rates weighed on some more exuberant equity market segments, while broad-based equity indices continued to advance. Indices tracking newly listed entities (IPOs), special purpose acquisition companies (SPAC) and non-profitable technology firms saw large price gains during the market recovery. A shared trait of these companies is that their profit expectations are more uncertain, and/or concentrated more in the future, than for the average firm. Their share prices have benefited from historically low interest rates, as this increases the net present value of their cash flows and pushes investors to riskier segments in their search for yield. However, as the rise in US Treasury yields accelerated in February, these equity indices declined. By contrast, equity indices covering more established companies – including the S&P 500 and EURO STOXX – continued advancing overall, less impacted by the rise in risk-free discount rates with bank stocks outperforming technology stocks (see Chart 2.4, right panel). This distinction highlights the disparate impact from rising rates across the stock market universe.
Some pockets of speculative activity emerged amid the robust risk sentiment, prompting extraordinary price volatility in specific sections of US equity markets. At the end of January 2021, groups of retail investors bought several US small cap stocks where leveraged investors had large short exposures. Their actions, coordinated on social media, pushed those stock prices to high levels, thereby imposing substantial losses on short sellers such as hedge funds that were forced to buy the underlying shares to close their positions. Equity call options, the volumes of which have increased noticeably in the United States since 2019, possibly further contributed to the price surges, as sellers typically hedge by buying the underlying stocks as well. While the price volatility was extraordinary in individual stocks, likely amplified in some cases by the unwinding of option hedges and resulting in restrained trading activities on some retail brokerage platforms, it had limited spillover effects to broader market volatility (see Chart 2.5, left panel). Separately, Archegos Capital Management (ACM) had built up large positions in several US and Chinese stocks through equity derivatives with built-in leverage. In March ACM defaulted on margin calls following a failed stock offering and associated equity price fall. Several of ACM’s prime brokers were forced to liquidate stocks, with a few non-US banks suffering large losses. These episodes serve as a reminder that intense speculation, especially if leveraged, can cause financial institutions to suffer concentrated losses.
The significant price volatility raises questions about the transparency and degree of leverage in financial markets. The overall leverage used by some non-bank market participants sometimes falls outside the regulatory perimeter. While data limitations make it impossible to gain a full picture of stock market leverage, available data suggest it has been increasing. In the United States, the debit balances in customers’ securities margin accounts reported to the Financial Industry Regulatory Authority (FINRA) increased by 72% over the last year to a record USD 823 billion in March 2021. However, margin debt as a proportion of stock market capitalisation remains well below previous peaks. EMIR data reported by euro area counterparties show an increase in the notional value of equity swaps and contracts for differences to nearly €15 trillion (see Chart 2.5, right panel). Survey-based evidence also suggests that hedge funds are increasingly using previously unutilised leverage capacity in euro-denominated securities financing and over-the-counter derivatives markets.[9]
Signs of exuberance have also been observed in the renewed interest in crypto-assets, although financial stability risks appear limited. The surge in bitcoin prices has eclipsed previous financial bubbles like the “tulip mania” and the South Sea Bubble in the 1600s and 1700s.[10] While this has largely been driven by retail investors, some institutional investors and non-financial corporations are also demonstrating a growing interest. Its price volatility makes bitcoin risky and speculative,[11] while its exorbitant carbon footprint and potential use for illicit purposes are grounds for concern. Crypto-assets are still not used widely for payments, and euro area institutions have little exposure to crypto-linked financial instruments, so financial stability risks appear limited at present.
## 2.3 Sharp increases in interest rates may reveal vulnerabilities in risk assets
A sharp rise in interest rates could prompt an adjustment in risk asset valuations, with possible adverse implications for financial stability. Standard price/earnings (P/E) ratios are more stretched in the United States than the euro area. This partly reflects sectoral compositions, as US equity indices have a larger share of technology companies with higher P/E ratios, for example. There is also a marked skewness in the distribution of forward P/E ratios across firms in both the United States and the euro area, with a larger share of firms exhibiting stretched valuations than in the past (see Chart 2.6, left panel). When the opportunity cost of holding risk-free assets is taken into account, valuations look less stretched. They remain near long-term averages, as investors do not yet appear to have reduced their risk-compensation preferences substantially (see Chart 2.6, right panel). Real risk-free rates have declined to historically low levels over the last two decades and current valuations may rely in part on expectations that risk-free rates will remain very low for a protracted period. That said, the rise in yields this year has produced some headwinds for equities. Risk asset valuations may become vulnerable in a scenario where risk-free rates increase sharply and sustainably as a result of investors reassessing the likelihood and pace of monetary policy tightening without an accompanying improvement in real growth (see Box 3).
## Box 3 Risk of spillovers from US equity market corrections to euro area markets and financial conditions
Prepared by Magdalena Grothe, Tobias Helmersson, Dominic Quint and Danilo Vassallo
US equity market prices have surged over the last year, prompting concerns about stretched valuations and the potential risk of market corrections. Cyclically adjusted price/earnings (P/E) ratios for the United States have reached historically high levels over the last year (see Chart A, left panel). In the past, periods of elevated valuations relative to earnings have tended to be followed by substantial market downturns. In view of these developments, this box examines the implications of a possible correction in US stock prices for euro area financial conditions and financial stability.
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Easy credit market pricing may also be vulnerable to price corrections. Median euro area corporate CDS spreads are near multi-year lows, while corporate leverage has increased to cyclical highs (see Chart 2.7, left panel). Large listed corporates took on more debt and built cash buffers, which may be a sign of financial strength to weather the pandemic. If corporate leverage remains elevated, however, market pricing may become vulnerable in the event of a renewed economic downturn. Moreover, bond spreads across euro-denominated bond instruments per unit of duration remain at the low end of the historical range after the global financial crisis, providing investors with low compensation for the degree of risk they assume (see Chart 2.7, middle panel) (see also Chapter 4). Furthermore, the range of corporate bond spreads around the median has also narrowed to near the tightest levels seen since 2009, indicating a continuation of the search for yield that has characterised financial markets in recent years (see Chart 2.7, right panel). European leveraged loan markets show a similar picture, with tight secondary market spreads close to pre-pandemic lows and low spreads per turn of leverage (see Chart A.4, left panel in Special Feature A). The average leverage ratio of newly originated loans remains near its highest level since the global financial crisis, with the share of loans with high leverage (>6x) increasing further. Default rates peaked in the third quarter of 2020 but remained benign and well below levels seen in previous crises. However, they may rise as fiscal support is withdrawn.
Corporate bond spreads have been supported by an improvement in the economic outlook together with supportive monetary policy. A number of forward-looking credit risk metrics have improved since the last Financial Stability Review, on the back of the improved macroeconomic outlook. For example, the share of non-financial corporations on the brink of a downgrade to non-investment grade has fallen back from the peak in the last quarter of 2020, and expected default frequencies have declined as well. The flexibility of purchases under the ECB’s pandemic emergency purchase programme (PEPP) is helping to support the smooth transmission of monetary policy. Furthermore, corporate bond spreads proved resilient to somewhat higher volatility in interest rate markets at the beginning of 2021 (see Chart 2.8, left panel). In addition, the favourable terms and large take-up of TLTRO III are supporting bank lending to non-financial corporations which, together with precautionary bond market funding, has helped to reduce funding rollover risk. At the same time, sentiment may be vulnerable to a deterioration in the economic outlook, as the solvency concerns for many companies may only fully surface once fiscal support measures are phased out (see Chapter 1).
Emerging market capital flows have so far been relatively resilient to the rise in yields. Many emerging market economies (EMEs) entered the coronavirus crisis with stronger fundamentals and a better cyclical position than before the global financial crisis. EME financial conditions have also improved markedly since the pandemic shock, and the recovery in capital flows since March 2020 has primarily been driven by the turnaround in global risk appetite. So far, capital flows have been relatively resilient to the rise in yields this year, particularly in contrast with the taper tantrum episode in 2013 (see Chart 2.8, right panel). This appears to confirm the observation that even though the yield moves have been similar in size, the composition of drivers this time paint a more benign economic picture (see Chart 2.1, middle panel). In addition, most EMEs are less dependent on external financing than in 2013, which mitigates the impact of a potential capital flow reversal.[12] However, push factors such as monetary policy in advanced economies, as well as contagion from market turbulence in neighbouring countries, are typical triggers of sudden stops in EME capital flows. This means that major challenges related to a tightening in financial conditions and associated capital flow volatility cannot be ruled out for countries with large external financing needs and elevated debt levels, should advanced economy monetary policies tighten faster than expected (see Box 1).
# 3 Euro area banking sector
## 3.1 Increasing signs of asset quality deterioration
The aggregate non-performing loan (NPL) ratio of euro area banks fell further to 2.7% in the fourth quarter of 2020, mainly reflecting the disposal of legacy NPL assets. In the midst of the pandemic, banks in countries more affected by previous crises (Cyprus, Greece, Italy and Portugal) have managed to continue reducing their NPL ratios by up to 9 percentage points. NPL ratios are the highest for loans to small and medium-sized enterprises (SMEs) (6.7%) and the lowest for mortgage lending (2.7%).
Forward-looking metrics, however, indicate a significant weakening of asset quality, although actual loan losses remain modest. The share of performing loans with forbearance measures increased and the fraction of loans classified as unlikely to pay bottomed out in the course of 2020 (see Chart 3.1, left panel). While still small relative to total loans, loans regarded as showing significantly increased credit risk (so-called Stage 2 assets) increased steadily over 2020, with net inflows into Stage 2 assets being six times higher than before the pandemic by the end of the year. Flows into actual credit-impaired (i.e. Stage 3) assets increased more modestly, rising by 1.3 times (see Chart 3.1, right panel). Due to the large scale of government support measures in the form of statutory moratoria and public guarantees, the time between the contraction in economic activity and NPL formation might be longer than seen in past recessions. Moreover, banks’ practices with respect to the identification of the significant increase in credit risk and forbearance vary, which raises the risk of a delayed recognition of asset quality issues by some banks.[13] Sizeable provisions were set aside in 2020 to cover higher expected loan losses, although there remain downside risks to provisioning as policy support expires. According to results from first quarter earnings releases of listed euro area banks a smaller amount of loan loss provisions was booked in the first quarter compared to the levels seen in 2020.
The increase in credit risk is most visible in sectors more affected by the pandemic. Loan-level credit register data (AnaCredit data) indicate that the share of loans which migrated from Stage 1 to Stage 2 increased more substantially over 2020 in pandemic-sensitive sectors. This was most pronounced in the accommodation sector where the risk migration increased fivefold from 5% to 25% (see Chart 3.2, left panel). The deterioration has also been somewhat greater in sectors which already had a higher share of non-performing loans (see Chart 3.2, right panel). Assuming that the transitions between IFRS stages by sector observed during 2020 also apply in 2021, the stock of Stage 2 assets would increase from 13% in the fourth quarter of 2020 to 17% at the end of 2021 for euro area banks on aggregate.
The eventual expiry of public measures implies that bank asset quality is likely to deteriorate further over 2021. Fiscal, monetary and prudential measures have supported bank asset quality during the pandemic, but the effect of these measures is expected to recede over time. With the expiry of public support measures, credit risk dependencies of sovereigns, financials and corporates in the euro area are expected to decline (see Box 4). Government-guaranteed loans offered vulnerable corporates access to finance, but may expose firms to medium-term rollover risks, in particular where guarantee schemes have a short residual maturity and bank lending standards have tightened (see Chapter 1). Statutory moratoria have provided relief to firms and households affected by the containment measures, but they have likely masked some asset quality risks. For the euro area on aggregate, three-quarters of the moratoria had expired by January 2021, but in some countries active moratoria still represent a sizeable share of total loans (see Chart 3.3, left panel). Loans emerging from moratoria have performed only slightly worse than the rest of the loan book thus far. However, loans remaining under moratoria are likely to be particularly vulnerable to asset quality deterioration, as they tend to be concentrated in the pandemic-sensitive sectors of the economy and already show a higher NPL ratio than loans which have emerged from the moratoria.
## Box 4 Credit risk transmission during the pandemic: the sovereign-bank-corporate nexus
Prepared by Christian Gross and Cosimo Pancaro
It has been argued that the coronavirus pandemic has strengthened what is known as the sovereign-bank-corporate nexus, also intensifying the transmission of credit risk shocks across sectors.[14],[15] An increase in interdependencies among sovereigns, banks and corporates may mean that if vulnerabilities arise in one sector, they become more likely to spill over to other sectors. This box sheds light on how the structure of cross-sectoral credit risk transmission has evolved since the start of the pandemic. It does so by using high-frequency, firm-level data on expected default frequencies (EDFs) to estimate the direction and intensity of credit risk spillovers between the sovereign, bank, non-bank financial and corporate sectors.[16]
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But, overall, future asset quality depends on the timing and strength of the economic recovery, and the exposure of banks to sectors most affected by the pandemic. Since the previous FSR, forecasts for euro area real GDP growth in 2021 have been revised downwards from 4.7% to 4.2% as the vaccination roll-out had a slow start and several countries prolonged lockdowns to contain a third wave of infections. Therefore, bank asset quality is likely to deteriorate further, especially where there is greater exposure to sectors most heavily affected by the pandemic. Within the category of coronavirus-sensitive sectors, some countries’ banks are more exposed to the accommodation sector, where loan performance may be particularly affected by prolongations of travel restrictions (see Chart 3.3, right panel).
## 3.2 Profitability of euro area banks set for a slow recovery
The profitability of euro area banks sank in 2020 on the back of pandemic-related loan loss provisions and lower revenues. The aggregate return on equity (ROE) of euro area significant institutions declined from 5.3% at the end of 2019 to 1.3% in the fourth quarter of 2020[17], with large differences between the first and second half of the year as well as across countries (see Chart 3.4, left panel). The first half of 2020 was characterised by substantial loan loss provisions to cover the fallout from the pandemic, while the second half saw a pronounced decline in income, partly due to weaker corporate loan demand. The ROE drop was larger in countries more affected by past crises as both core revenues and other profit and loss (P&L) components declined strongly in the first half of the year, while they rose in other countries. The return on equity reported by banks for 2020 was positive, with the exception of Cyprus, Greece, Ireland, Italy, Portugal and Spain where the losses were driven largely by loan loss provisions and other P&L items.[18] Based on listed banks’ first quarter earnings releases, the profitability of euro area banks improved significantly reflecting gains from cost-cutting and stronger trading income, but their trailing return on equity remained below pre-pandemic levels on aggregate.
Euro area bank profitability is anticipated to recover slowly, with models based on market expectations projecting aggregate ROE of 3% at the end of 2021 and 6% in 2022 (see Chart 3.4, right panel). These forecasts depend crucially on the path of the overall economic recovery and ultimately on the progress in rolling out vaccines across euro area countries. While the time span until interest rates are expected to return to positive territory has shortened recently from 2030 to 2026, this implies that rates will still remain low for a substantial period, thereby putting pressure on banks’ interest income.
Operating profits weakened mainly on the back of lower net interest income, especially towards the end of the year. As the economic fallout from the pandemic intensified, banks’ operating profits faced a decline in both net interest income (NII) and net fee and commission income (NFCI). While the negative contributions from these two components were offset by cost-cutting and non-core operating profit items in the second and third quarters, the decline in net interest income increased in the fourth quarter and resulted in a lower operating profit for the full year (see Chart 3.5, left panel). Going forward, operating profits are expected to recover only slowly and to be supported by additional cost-cutting and higher NFCI. NII declined in 2020 by 12% and thereby continued the downward trend that started in 2018. While the volume of interest-earning assets was about 6% larger than in 2019, the margin decline became more pronounced in the second half of 2020 (see Chart 3.5, right panel). The pressure on NII is expected to decline only in 2022.
Trading income supported the profitability of euro area banks with a stronger investment banking focus. Higher trading activity in volatile markets especially during the second and fourth quarters helped some euro area banks with a stronger focus on capital market activities to beat analysts’ earnings expectations due to higher revenues in equity and fixed income trading. Since capital market activity during 2020 was at levels not seen since 2009, the positive impulse from trading activities might be smaller going forward. While some non-euro area investment banks incurred substantial losses on margin calls due to the default of Archegos Capital Management (see Chapter 2), euro area banks were only marginally affected. The incident, however, highlights the risks related to the prime brokerage business.
Looking ahead, some of the pressures weighing on interest margins in 2020 are expected to ease, notably if yield curves steepen. A flattening of the yield curve in early 2020, followed by a reduced pass-through of negative rates to corporate depositors in the second half of 2020, contributed to lower interest margins of euro area banks. The larger NII decline for the loan book relative to fixed income securities can be mainly attributed to smaller risk premia on state-guaranteed non-financial corporate (NFC) loans and weaker demand for consumer lending (see Chart 3.6, left panel). Looking ahead, forward rates suggest that the yield curve slope has bottomed out and is expected to rise until 2023. Against the backdrop of rising inflation and growth expectations since February, the ten-year swap rate expected at the end of 2023 increased by 40 basis points. As net interest margins co-move with the slope of the yield curve, the opportunities for banks to generate higher margins from maturity transformation on new lending should hence improve over the next years (see Chart 3.6, right panel). But as the existing stock of loans is only repricing gradually, the margin recovery of the entire loan book will take time.
A recovery in lending income relies on the economic rebound improving corporate and consumer confidence, as well as easier lending standards. In the second half of 2020 banks tightened lending standards, in particular for corporate loans, as risk perceptions rose and the take-up of guaranteed loans moderated (see Chart 3.7, left panel). The tightening was more pronounced for loans to SMEs and for loans with longer maturities. Reflecting the ongoing uncertainties surrounding the development of the pandemic and the speed of the roll-out of vaccines in the euro area, banks expect an additional tightening of credit standards in the first half of 2021. As a consequence of reduced corporate loan demand since September 2020 and despite tighter housing credit standards, lending volume was mainly driven by mortgage lending on the back of low interest rates (see Chart 3.7, right panel). So far in 2021, average monthly lending flows to the non-financial private sector have exceeded pre-pandemic levels due to higher corporate lending in March. This was largely driven by borrowing in Germany which could be related to a robust manufacturing sector and the financing of working capital. While industrial confidence has recovered, an improvement in consumer confidence is required for high-margin consumer lending to pick up and thereby support bank profitability going forward.
Business disruptions at euro area banks have increased during the pandemic, but losses have remained limited compared with other operational risk events. The higher usage of online banking and the increase in remote work during the pandemic have led to losses as a consequence of business disruptions and system failures, but these losses have remained limited relative to other operational risk events. A closer look at the affected business lines reveals that the bulk of losses related to business disruptions were attributed to the entire institution, retail banking or trading and sales (see Chart 3.8, left panel).
While cyber incidents reported by euro area banks have increased during the pandemic, institutions have not been severely impacted so far. Cyber incidents reported to the ECB by significant institutions in 2020 have increased compared with the previous year, mainly driven by incidents with a malicious intent. Distributed denial of service (DDoS) attacks in particular are trending upwards, including ransom DDoS by large threat actors (see Chart 3.8, right panel).
Fortunately, these attacks have caused only very limited interruptions mostly due to the unavailability of smaller third parties. An upward trend can be observed in the incidents related to third parties due to an increasing reliance of the industry on third-party services. No major incidents related to cyber attacks on euro area financial market infrastructures have been reported yet. But persistent deficiencies in basic ICT (information and communication technology) hygiene, complex ICT architecture and a growing amount of end-of-life ICT systems in many banks still need to be addressed. Some large-scale ICT projects to address these vulnerabilities could be delayed due to the pandemic, but banks may also put off addressing these weaknesses because of the economic outlook and likely lower profitability.
## 3.3 Banks’ bond spreads tightened and capital ratios rose
After declining markedly towards the end of 2020, bond spreads of euro area banks tightened further but at a slower pace. For the euro area on aggregate, bank bond spreads declined significantly during November and December, mirroring the equity price rally. The increase in the spreads of bank bonds observed in March 2021 (see Chart 3.9, left panel) can be attributed to the increase in government bond yields and was more pronounced for senior bonds such as covered bonds (+10 basis points) and non-preferred senior and holding company debt instruments (+6 basis points). As around half of the outstanding bank bonds mature by 2025 and the yields for refinancing these bonds are expected to still remain below those yields agreed at issuance, banks are likely to continue benefiting from favourable market funding costs over the next years (see Chart 3.9, right panel). The ECB’s longer-term refinancing operations provide additional funding support for euro area banks.
As private issuance has fallen substantially in recent years, banks need to prepare for an eventual return to market funding in the medium term. Due to the pandemic, the ECB has provided substantial longer-term funding to banks which led to a significant increase in liquidity buffers during 2020. The combined amount of excess reserves and deposit facility holdings has increased since end-2019 by €1.9 trillion (see Chart 3.10, left panel). The latest targeted longer-term refinancing operation (TLTRO) auction in March 2021 saw one of the largest take-ups due to its more favourable terms. As a consequence, the central bank funding reliance of euro area banks on aggregate has increased strongly and bond issuance volumes of non-G-SIBs have fallen to historical lows, amid some heterogeneity across euro area countries. Normalised by banks’ total assets, central bank funding reliance was the highest in Italy and Spain and banks in these two countries out of the four largest euro area economies are also closer to the non-investment-grade rating space (see Chart 3.10, right panel). Among other aspects, size also seems to play a role as mid-sized banks, i.e. banks with total assets between €20 billion and €200 billion, exhibit the highest central bank funding reliance. To avoid that banks face challenges in a few years when trying to return to market funding, it is essential that they work on resolving some of their balance sheet weaknesses and structural issues, for example by improving cost-efficiency; this is especially the case for some smaller banks, which might face limited market access and might therefore have to progressively rebuild an investor base.
Common Equity Tier 1 (CET1) ratios of euro area banks on aggregate improved in 2020 by around 60 basis points to 15.4%. The rise in capital ratios was largely driven by declining average risk weights, which compensated for balance sheet expansion, while the contribution from retained earnings shrank at the end of 2020 (see Chart 3.11, left panel). Regulatory changes (i.e. the Capital Requirements Regulation “quick fix”) and prudence on dividends also contributed to higher capital ratios. Looking in more detail at the changes in risk-weighted assets during 2020 reveals that market risk increased in the second quarter and to a lesser extent in the fourth quarter on the back of higher trading activity in volatile markets. There was a marked decline in corporate credit risk-weighted assets in the third and fourth quarters (see Chart 3.11, right panel), which appears at least partly related to NFC loans granted with state guarantees and to the adjustment of the SME supporting factor. The increase in excess liquidity, which is assigned a zero risk weight, also played a major role in the decrease of average risk weights. At the country level, CET1 ratios increased in all countries except Estonia, Finland, Greece, Ireland, Luxembourg and Slovenia where balance sheet expansion outweighed the other factors.[19]
As asset quality indicators suggest that a materialisation of pandemic-related credit risk has started, this is likely to have implications for banks’ capital ratios going forward. Banks’ capitalisation levels are well above regulatory minimum requirements and therefore banks have capital space to absorb losses. So far, however, it appears that in particular banks with less capital space above regulatory buffers are reluctant to actually use these buffers (see Chapter 5). The EU-wide stress-test exercise, the results of which are expected by end-July, aims to provide additional insights into the resilience of the European banking sector to a prolonged COVID-19 scenario in a lower-for-longer interest rate environment.
Euro area bank equity prices have benefited from a broader market rally since November. The approval of vaccines against the coronavirus in late 2020 boosted hopes for a stronger global economic recovery and triggered a rotation out of growth stocks into value stocks (see Chapter 2). Against this backdrop and despite unchanged bank profitability projections for 2021 and 2022, bank stock prices rose by 40% in November alone. In February, the announcement of US fiscal stimulus and a pick-up in US inflation expectations spilled over to the euro area and lifted bank shares by another 25% (see Chart 3.12, left panel).
But considered over a longer horizon, euro area bank stock prices have strongly underperformed the euro area broader market and banks in the United States. While there were rallies of euro area bank stock prices also in 2012 and 2017, the longer-term relative unattractiveness of the sector is rooted in structural issues, such as cost inefficiencies, which are in turn reflected in lower profitability. In the fourth quarter of 2020, 7% of euro area listed banks reported an ROE above 10%, compared with 49% of banks in the United States (see Chart 3.12, right panel). Addressing these structural challenges, for example through mergers and acquisitions, is crucial for a turnaround that is longer lasting.
# 4 Non-bank financial sector
## 4.1 Non-bank financial sector vulnerabilities could manifest in the high-yield corporate bond market
Market-based financing of the real economy has remained robust since mid-2020, with conditions continuing to be supported by accommodative policies. By December 2020, market based credit to non-financial corporations (NFCs) – i.e. intermediated via markets as opposed to loans typically originated by banks – had recovered from the initial pandemic turmoil, to stand at roughly 20% of total external credit (see Chart 4.1, left panel).[20] While euro area non-bank financial institutions were the dominant net buyers of debt overall, net purchases by the Eurosystem were around the same size as those by investment funds (IFs), insurance corporations and pension funds (ICPFs) and other financial institutions combined in the second and third quarter, highlighting the robust indirect support from the official sector.
While fiscal and financial policy measures have indirectly supported non-banks’ asset quality so far, credit risk could trigger valuation losses over the coming months. The share of bonds with negative credit watch or outlook held by ICPFs and IFs rose sharply in early 2020, but declined slightly towards the end of the year, partly reflecting policy support to NFCs (see Chart 4.1, right panel). Potential rating downgrades could materialise either as policy support is withdrawn abruptly or if higher global interest rates spill over into euro area credit markets, jeopardising the ability of companies to roll over their debt and support the recovery.[21] This in turn would expose non-banks to significant credit losses.
A rise in yields would also trigger bond valuation losses, to which ICPFs and IFs are more exposed than in the past. These sectors have increased the duration in their bond portfolios over recent years in order to boost returns in the challenging environment of ultra-low interest rates. But this increases the sensitivity of their assets to rising interest rates (see Chart 4.2, left panel). Asset valuation losses from rising bond yields could trigger outflows which, when coupled with low liquidity buffers, could force bond funds to liquidate assets to meet investor redemptions (see Chart 4.5).[22] In the short term, ICPFs would face asset valuation losses as well, although these could be more than offset by the drop in liabilities valuation, given the negative duration gap (see Section 4.3). The net effect would be an improvement in the equity position and the overall balance sheet capacity of ICPFs. Depending on other concurrent macroeconomic developments, ICPFs could then increase asset purchases in some segments at a time when bond funds could be forced to sell.
High-yield corporate bond segments, where investment funds are dominant players, are particularly exposed to an increase in credit spreads. Investment funds have typically had a much stronger preference for holding high-yield bonds issued by financial and non-financial corporations, unlike banks and ICPFs, which generally prefer less risky fixed income assets (see Chart 4.2, right panel). But high-yield bonds are also the most vulnerable to an increase in credit spreads, which tend to widen when global rates increase. In the euro area, though, this segment is small compared with investment grade corporate and sovereign bond segments. That said, should higher global yields trigger fund outflows and asset liquidation, it is unlikely that banks and ICPFs – which historically largely underweight high-yield bonds – would substantially step up their presence in these segments, thereby increasing the risk of price dislocation and a credit crunch for more vulnerable corporates.
Non-banks’ pro-cyclical behaviour and liquidity risks, together with their reliance on public support as seen last March, demonstrate the need to enhance resilience across the sector (see Chapter 5). For instance, liquidity risks in some types of investment funds could be limited by lengthening redemption frequencies and setting minimum liquidity buffers. Furthermore, the recent event involving Archegos Capital (see Chapter 2), a highly leveraged non-bank entity heavily interconnected with large banks, again raises the issue of contagion due to margin calls, default cascades and fire sales.[23]
## 4.2 Investment funds may be vulnerable to a global increase in interest rates
Overall, since November 2020 investors’ flows have shifted from bond funds to equity funds amid a robust increase in risk appetite. While investors mainly preferred bond and money market funds until mid-2020, equity funds started to receive record-high inflows following the COVID-19 vaccine announcements in November 2020 (see Chart 4.3, left panel). The significant fiscal stimulus in the United States and the agreement of the Brexit deal between the EU and the United Kingdom also contributed to the surge in risk appetite and equity fund inflows.
Inflows concentrated on euro area investment funds that focus on global, US and emerging markets, with equity funds receiving the lion’s share. By contrast, flows into funds investing in western European markets remained generally stable. The rise in aggregate equity fund flows masks rotation from growth to value funds, benefiting European equity funds over US funds (see Chart 4.3, right panel). Flows into western European equity funds investing in the energy and financial sectors have recovered particularly strongly.
These developments have been broadly reflected in recent transactions by euro area investment funds. In the fourth quarter of 2020, euro area equity funds purchased about €135 billion of US and other developed economy equities, while bond funds purchased about €45 billion of EME and other developed country sovereign bonds (see Chart 4.4, left panel). Investment funds also purchased corporate debt securities across the globe, but at a slower pace than earlier in 2020, due in part to lower issuance activity.
The credit risk of euro area investment funds remains elevated, while duration risk stands at a multi-year high. As a result of continued subdued economic activity, up to a third of investment funds’ NFC debt holdings are subject to a negative credit outlook or credit watch from rating agencies (see Chart 4.1, right panel). Coupled with the fact that more than 60% of corporate debt securities purchased in 2020 are either high yield or rated BBB, this highlights the increasing credit risk faced by investment funds. In addition, the continued search for yield in a low interest rate environment has pushed investment funds to increase the maturity[24] and, therefore, the duration of their debt securities portfolios (see Chart 4.2, left panel), exposing them to greater interest rate risk from rising yields.
Significant and abrupt increases in global interest rates may lead to material valuation losses on euro area investment funds’ debt portfolios. To date, repricing has been more pronounced for US debt securities than for their euro area equivalents due to the different increases in yields in the two economic areas (see Chart 2.1, left panel). Nevertheless, euro area investment funds are heavily exposed to US interest rate risks. In particular, their holdings of US-based and USD-denominated debt securities are close to record levels (see Chart 4.4, right panel) and the duration of their US bond portfolios is high, exceeding that in their overall debt securities portfolios.
Over recent years, investment funds’ liquidity risk has increased amid a search for yield (see also Box 5). Since last November, funds’ cash positions have continued to fall as a proportion of their total assets. Cash buffers have declined below pre-pandemic levels to reach new lows (see Chart 4.5, left panel). Liquid asset holdings also stand at relatively low levels, falling below pre-pandemic volumes for funds investing in corporate bonds (see Chart 4.5, right panel). This is a concern, as rising credit risks and elevated asset valuations in some financial market segments leave the fund sector vulnerable to shocks. Furthermore, an increase, particularly abrupt, in global yields may trigger relatively large redemptions, especially for funds investing in debt securities. Given the persistent liquidity risk in investment funds, such shocks may lead to funds selling assets, with the potential to exacerbate adverse market dynamics and propagate spillovers to other financial intermediaries.[25] This underscores the importance of strengthening the resilience of the investment fund sector from a macroprudential perspective (see Chapter 5).
## Box 5 Investment fund flows, risk-taking and monetary policy
Prepared by Margherita Giuzio, Christoph Kaufmann and Ellen Ryan
This box examines the response of the investment fund sector to monetary policy shocks and the implications of this for financial stability. The investment fund sector has more than doubled in size since the global financial crisis. As the sector grows, so does its importance for the funding of economic activity and the transmission of monetary policy. But excessive risk-taking by funds can also have damaging effects for the wider financial system when it contributes to high levels of corporate leverage or when risky asset holdings need to be unwound quickly in times of market stress, as occurred in March 2020.
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## 4.3 Insurers engage in further risk-taking, but could benefit from the moderate increase in global interest rates
While the profitability of euro area insurance companies remains subdued, their capitalisation has started to recover. Towards the end of 2020, solvency ratios already regained more than half of the decline that occurred amid the initial coronavirus shock (see Chart 4.6, left panel). By contrast, insurers’ profitability still lies significantly below multi-year averages (see Chart 4.6, right panel).
Despite the signs of improvement in the economic outlook, the insurance sector remains under pressure from low interest rates and weak demand. The economic fallout from the pandemic led to a further fall in interest rates over 2020 together with higher financial market volatility. These developments weighed on the sector’s investment income. In addition, the recession and the ongoing uncertainty surrounding the pandemic meant that sales of life and savings products remained subdued, despite higher household saving. Non-life insurers also saw their new business contract, although the sector is benefiting from rising policy prices and generally solid underwriting profitability. This has been particularly evident in retail business lines like motor insurance where fewer loss events were registered due to lockdown measures. Going forward, a materialisation of credit risks (see Chapter 1) could further weigh on insurers’ profits.
Even though profitability prospects remain muted, insurers’ stock valuations have recovered from last year’s losses. The stock market valuations of insurance corporations increased over 2020 in tandem with the broader equity market (see Chart 4.7, left panel). Life insurers significantly outperformed most other market segments, primarily because the recent moderate steepening of the yield curve has improved investor sentiment towards the sector. This development contrasts with the trend observed over recent years, when life insurance stocks typically performed worse than the overall market. A decomposition of insurance stock prices shows that the sector’s valuation gains are mainly driven by the positive sentiment on stock markets that started to resurface in November 2020 (see Chart 4.7, middle panel). At the same time, the weak profitability prospects for the sector continue to hold down insurers’ valuations.
Insurers are taking on more risk as they increase their investments in alternative asset classes. Amid decreasing income from debt securities portfolios, insurers have continued gradually increasing their exposures to higher yielding but potentially riskier alternative assets (see Chart 4.7, right panel). Around 70% of these holdings are invested in real estate-related assets. Exposures to commercial real estate in particular could suffer credit and valuation losses if the pandemic-accelerated shift towards more working from home and online shopping persists after lockdown restrictions are lifted (see Chapter 1.5). This could have a sizeable impact on insurers’ solvency. Empirical analysis shows that a 10% decline in the value of commercial real estate holdings could wipe out as much as 4% of aggregate insurance excess of assets over liabilities in the EU.[26]
Although insurers have accumulated record-high exposures to duration risks, higher interest rates would boost the sector’s capitalisation significantly due to negative duration gaps. If interest rates on insurers’ fixed income holdings increased by 1%, asset valuation losses would amount to 8.6% of the bond portfolio (€250 billion) compared to 7.7% (€200 billion) four years ago (see Chart 4.8, left panel). Global interest rates have started rising in 2021, particularly in the United States. This trend has affected euro area rates, which have also increased albeit more mildly (see Chapter 2). Under a scenario of moderately higher interest rates abroad in 2021, euro area insurers’ bond portfolios could lose around €20 billion in value, which could translate into capital losses of the same size (see Chart 4.8, middle panel).[27] However, the largest share of insurers’ fixed income portfolios (78%) is invested in euro area assets while only about 7% is invested in US assets. Moreover, the sector has a negative duration gap on its balance sheets, with a weighted average duration of assets and liabilities of 7.3 and 13.3 years respectively at the end of 2019. As a result, even a small rise in interest rates in the euro area would lead to sizeable reductions in insurers’ liabilities by an estimated €250 billion. This decrease would more than offset all asset valuation losses and could lead to net capital gains of more than €150 billion (2%).[28]
Moderately higher interest rates would only partially dampen the deterioration of insurers’ investment income over the next few years. Under the interest rate changes assumed, the average portfolio return would fall to 2% five years ahead compared to 1.8% in a scenario in which interest rates do not increase (see Chart 4.8, right panel). A more significant improvement in investment income prospects would require much larger changes in interest rates. Consequently, the revenue outlook for the insurance sector remains muted.
# 5 Macroprudential policy issues
## 5.1 Supporting economic recovery and the resilience of the banking sector amid pandemic-related vulnerabilities
Since the November 2020 FSR, policy measures have continued to support financial stability by limiting corporate insolvencies and containing rising unemployment. With many euro area countries facing renewed surges in infections, lockdown measures have been reinstated and economic support policies maintained or extended, increasingly in a more targeted and selective manner.[29] Taken together, the extension of economic, monetary, prudential and other support measures has underpinned the functioning of the financial system, prevented widespread bank deleveraging and maintained generally accommodative credit conditions.[30]
As pandemic and economic conditions allow, extensive policy support, particularly for corporates, could gradually move from being broad based to more targeted.[31] As long as significant lockdown measures remain in place to control the pandemic in euro area countries, economic policy support that prevents viable companies from failing and unemployment from rising considerably will also protect near-term financial stability. As parts of the economy become better adapted to lockdown measures, increasingly targeted extensions of policy support across euro area countries are already contributing towards limiting the medium-term financial stability side effects and should be continued. These adverse effects arise from the growth in sovereign and corporate indebtedness and the allocation of resources to potentially non-viable, “zombie” companies (see Special Feature A), which increase balance sheet vulnerabilities of sovereigns, corporates and banks. Adjusting support schemes to strengthen mechanisms for assessing the future viability of beneficiaries or promote debt/equity restructuring for highly leveraged but viable firms could be a particularly useful way of managing financial stability side effects (for example, through existing initiatives such as quasi-equity instruments and the partial conversion of guaranteed loans into direct grants).[32] Moreover, fast and effective use of the €750 billion Next Generation EU (NGEU) recovery funds should complement national support measures to mitigate cross-country divergences in the coming years.[33]
For banks specifically, capital relief measures should continue to prevent excessive deleveraging, which could negatively impact the economic recovery. Credit risk and losses for banks are expected to materialise as some businesses suffer permanent damage from the pandemic and become unviable. Therefore, as highlighted in previous issues of the FSR, it is crucial that bank capital buffers are usable to absorb losses and to avoid procyclical financial amplification effects due to, for example, bank deleveraging. At the same time, managing non-performing loans (NPLs) effectively will also be key to reducing the drag on bank balance sheets and supporting lending. In this context, the prudent approach to capital distributions has been extended and adapted from the initial guidance asking financial institutions to refrain from making any distributions to shareholders. Following the updated guidance, banks can proceed with capital distributions up to a conservative threshold set by the competent authorities.[34] Banks are expected to exercise extreme prudence and engage in discussion with the competent authorities before taking any action on dividend distributions or share buybacks.[35]
Banks will retain investor confidence by ensuring the proper and timely identification of credit risk, supporting this by using capital buffers in case of need.[36] Given the potential for losses to materialise, the ability to distinguish between viable and non-viable borrowers becomes increasingly essential to supporting a robust recovery. The policy guidance issued since the November 2020 FSR has continued to emphasise the need to set aside adequate provisions based on assumptions appropriate for the current risk environment and, more generally, to identify credit risk in a timely manner.[37]
However, preliminary evidence points to banks’ reluctance so far to use available capital space. In particular, initial evidence suggests that banks with less capital headroom above regulatory buffers appear reluctant to use these buffers by letting capital ratios decrease,[38], despite supervisors communicating that they expect these buffers to be used.[39] In recent quarters, lending to corporates by banks with a smaller capital headroom on top of the combined buffer requirement (CBR) has decreased significantly (see Chart 5.1). The preliminary evidence points to a more pronounced weakening of credit provision to non-financial corporations, a stronger reduction in risk weights and a tightening in lending conditions by banks closer to the CBR relative to other banks.[40] For the moment, these procyclical adjustments may have only limited implications for aggregate credit supply due to the limited number of banks close to the CBR threshold. Nevertheless, if credit risk materialises and more banks approach the threshold, there is the risk that procyclical adjustments could become more systemic.
In the medium term, a higher share of releasable capital buffers could be considered, as this can enhance banks’ ability to absorb losses and continue providing key financial services in a crisis. An enhanced role for releasable capital buffers could strengthen authorities’ ability to act countercyclically. It would also reflect the increasingly important role that macroprudential policy needs to play as the first line of defence in preserving financial stability in the face of a severe, system-wide shock. Any change to the buffer framework should ensure continued compliance with the applicable international standards set by the Basel Committee on Banking Supervision.
Concerns regarding the expected deterioration in asset quality in the banking sector reinforce the need for effective NPL solutions. Among several initiatives under way, the European Commission’s action plan on tackling non-performing loans emphasises two key objectives: (i) the continued development of secondary markets for distressed assets; and (ii) reform of insolvency and debt recovery frameworks.[41] The first objective has already played a key role in NPL reductions in some Member States (e.g. Greece and Italy) in recent years. This requires an appropriate balance to be struck between strengthening common standards and market transparency, on the one hand, and avoiding excessive administrative barriers to entry to the NPL market, on the other hand. The second objective aims to reduce costs and delays, which would translate into higher recoveries for banks and investors, together with higher NPL valuations in the market. Moreover, further initiatives may be necessary if NPLs increase beyond current expectations. A common EU blueprint for NPL securitisations benefiting from government guarantees might also be useful. EU policymakers should also consider options to restructure and recapitalise distressed but viable companies. A more flexible application of the Commission’s framework for public support that would make it easier to set up asset management companies could complement policy efforts to manage potential systemic NPL problems.
Given the low interest rate environment and profitability challenges, efforts to address structural issues across banks should intensify. The euro area banking sector is hampered by low cost-efficiency, limited revenue diversification and overcapacity. Banks have increased cost-cutting efforts in response to the pandemic by further reducing the number of staff and branches, but low profitability may limit the required digital transformation. Consolidation via mergers and acquisitions could be one potential avenue for reducing overcapacity in the sector. This process should be market-driven but can also be supported by completing the banking union and removing barriers to consolidation, such as differences in national insolvency and taxation regimes and restrictions on the free flow of capital and liquidity within banking groups.
The timely, full and consistent application of the Basel III framework remains essential with a view to strengthening banks’ resilience to withstand future shocks. Deferring the implementation timeline by one year freed up operational capacity for banks and supervisors to respond to the immediate priorities related to the pandemic without affecting the substance of the reforms. These reforms, which reflect important lessons learned from the global financial crisis, are necessary to further strengthen the regulatory framework for banks. The ECB’s updated macroeconomic impact assessment shows that the economic costs of implementing the reforms are modest and temporary, and outweighed by their permanent benefits in terms of strengthening the resilience of the economy to adverse shocks.[42] It also finds that potential deviations from the globally agreed Basel III reforms – for example, with regard to the output floor – would dilute the benefits to the real economy.
Where ongoing developments point to increasing vulnerabilities, such as in the residential real estate (RRE) sector, policies should prudently balance procyclical considerations against the need to stem the build-up of risk. Capital already built up to target RRE risks should only be released to facilitate loss absorption if losses start to materialise. At the same time, heightened vulnerabilities require careful monitoring. Going forward, it could be worth considering gradually activating or tightening borrower-based measures, but not before economic conditions stabilise and the impact of the pandemic on RRE markets is clearer. Nonetheless, such considerations should carefully consider the stage of the RRE cycle and any potential procyclical effects on demand, especially from income-based limits.
## 5.2 Further steps towards developing macroprudential policies for non-banks
The market turmoil in March 2020 exposed structural fault lines in the non-bank financial sector – in particular liquidity mismatches in investment funds. Many money market funds (MMFs) and open-ended investment funds faced acute liquidity stress last spring owing to significant outflows and difficulties in selling assets in markets with little or no secondary trading. These funds responded to this liquidity pressure by acting procyclically through asset sales (see Chart 5.2 and Box 6). Over 200 European investment funds also suspended redemptions.[43] This behaviour added to pressure on asset valuations and market liquidity, contributing to the tightening of funding conditions in the real economy. This tightening ultimately only eased when central banks took extraordinary policy action. Furthermore, renewed risk-taking and growing liquidity mismatches in funds in recent months continue to pose increasing risks (see Chapter 4).
A comprehensive macroprudential approach for non-banks remains a key missing element in the overall policy framework. Many investment funds, insurance corporations and pension funds are subject to relatively weak liquidity requirements. They are typically designed from a microprudential perspective. A comprehensive macroprudential approach instead would address structural vulnerabilities and emerging risks in the non-bank financial sector. This would lower the need for extraordinary central bank intervention to tackle significant market stress. Furthermore, it would also complement monetary policy in good times, thereby further aligning the financial stability and monetary policy mandates of central banks.
The Financial Stability Board (FSB) is expected to issue recommendations aimed at strengthening the resilience of the non-bank financial sector. Once issued, they should be swiftly implemented in the EU as appropriate. These recommendations will stem from the ongoing FSB work on MMFs, open-ended investment funds and margining practices. The vulnerabilities in MMFs must be addressed, in particular by reducing their liquidity mismatch. This could be achieved by limiting investments in relatively illiquid assets or increasing liquidity buffers, which should be made more usable given the evidence that MMFs have been reluctant to draw down on their buffers in the past. These are among the measures being examined by the FSB in relation to the MMF sector.[44] Given the interdependencies of money markets across jurisdictions and currencies, this work is of particular importance for ensuring a globally consistent approach to policy reforms. Any FSB recommendations on MMFs should feed into the review of the EU Money Market Fund Regulation planned for 2022. For open-ended investment funds, minimum liquidity requirements could be considered to increase their asset liquidity profile, while requirements on redemption frequencies and notice periods would help to bolster their resilience, thereby reducing their reliance on crisis liquidity management tools.[45] Finally, it is important to assess whether tools to reduce excessive procyclicality in initial margins for derivatives – a topic relevant for both bank and non-bank financial institutions – need to be recalibrated and/or revised.[46] There is also scope for increasing the transparency and predictability of margining practices.
The ongoing review of the EU Solvency II framework could also strengthen the macroprudential approach to insurance companies. The proposal put forward by the European Insurance and Occupational Pensions Authority in its Opinion suggests introducing measures of a macroprudential nature that would usefully equip national supervisory authorities with additional powers to tackle systemic risk in insurance companies.[47] These include powers to introduce a capital surcharge for systemic risk, require the development of systemic risk and liquidity risk management plans, and temporarily freeze redemption rights. The Solvency II review could also consider other macroprudential aspects proposed by the European Systemic Risk Board such as new Pillar 2 liquidity provisioning requirements for insurers with a vulnerable liquidity profile and making the volatility adjustment symmetric to build capital buffers during good times.[48]
## Box 6 Investment funds’ procyclical selling and cash hoarding: a case for strengthening regulation from a macroprudential perspective
Prepared by Katharina Cera, Linda Fache Rousová, Angelica Ghiselli, Christoph Kaufmann and Sean O’Sullivan
During the March 2020 market turmoil, investment funds shed assets on a large scale – but was this selling commensurate with the outflows they faced or was it much larger? This box finds evidence of the latter, highlighting that the less regulated non-UCITS funds tended to engage in more procyclical selling and cash hoarding than UCITS funds.[49] While it can be rational for fund managers individually to sell assets in excess of current outflows when uncertainty about future redemptions is high, such cash hoarding may be detrimental to the stability of financial markets from a macroprudential perspective.[50]
More
# Special features
## Corporate zombification: post-pandemic risks in the euro area
Tobias Helmersson, Luca Mingarelli, Benjamin Mosk, Allegra Pietsch, Beatrice Ravanetti, Tamarah Shakir and Jonas Wendelborn[51]
Policy measures aimed at supporting corporates and the economy through the coronavirus pandemic may have supported not just otherwise viable firms, but also unprofitable but still operating firms – often referred to as “zombies”. This has in turn raised questions about an increased risk of zombification in the euro area economy, which could constrain the post-pandemic recovery. Firm-level, loan-level and supervisory data for euro area companies suggest that zombie firms may have temporarily benefited from loan schemes and accommodative credit conditions – but likely only to a modest degree. These firms may face tighter eligibility criteria for schemes and more recognition of credit risk in debt and loan pricing in the future. Tackling the risk of zombification more fundamentally requires the consideration of suggested reforms to insolvency frameworks, and better infrastructure for banks to manage non-performing loans.
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## Climate-related risks to financial stability
Prepared by Spyros Alogoskoufis, Sante Carbone, Wouter Coussens, Stephan Fahr, Margherita Giuzio, Friderike Kuik, Laura Parisi, Dilyara Salakhova and Martina Spaggiari
The ECB has been intensifying its quantitative work aimed at capturing climate-related risks to financial stability. This includes estimating financial system exposures to climate-related risks, upgrading banking sector scenario analysis and monitoring developments in the financing of the green transition. Considerable progress has been made on capturing banking sector exposures to firms that are subject to physical risks from climate change. While data and methodological challenges are still a focus of ongoing debates, our analyses suggest (i) somewhat concentrated bank exposures to physical and transition risk drivers, (ii) a prevalence of exposures amongst more vulnerable banks and in specific regions, (iii) risk-mitigating potential for interactions across financial institutions, and (iv) strong inter-temporal dependency conditioning the interaction of transition and physical risks. At the same time, investor interest in “green finance” continues to grow – but so-called greenwashing concerns need to be addressed to foster efficient market mechanisms. Both the assessment of risks and the allocation of finance to support the orderly transition to a more sustainable economy can benefit from enhanced disclosures, including of firms’ forward-looking emission targets, better data and strengthened risk assessment methodologies, among other things.
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# Acknowledgements
The Financial Stability Review assesses the sources of risks to and vulnerabilities in the euro area financial system based on regular surveillance activities, analysis and findings from discussions with market participants and academic researchers.
The preparation of the FSR was coordinated by the Directorate General Macroprudential Policy and Financial Stability. The Review has benefited from input, comments and suggestions from other business areas across the ECB. Comments from members of the ESCB Financial Stability Committee are gratefully acknowledged.
The Review was endorsed by the Governing Council on 12 May 2021.
Its contents were prepared by Katharina Cera, Nander de Vette, Giovanni di Iasio, Linda Fache Rousová, John Fell, Sándor Gardó Benjamin Hartung, Tobias Helmersson, Christoph Kaufmann, Benjamin Klaus, Marco Lo Duca, Dilyara Salakhova, Tamarah Shakir, Seán O’Sullivan, Eugen Tereanu and Jonas Wendelborn.
With additional contributions from Lorenzo Cappiello, Sante Carbone, Michal Dvořák, Isabel Figueiras, Angelica Ghiselli, Michael Grill, Maciej Grodzicki, Lieven Hermans, Paul Hiebert, Sujit Kapadia, Dejan Krusec, Laura Lebastard, Allegra Pietsch, Mara Pirovano, Beatrice Ravanetti, Moreno Roma, Marek Rusnák, Ellen Ryan, Sebastiano Michele Zema, Martina Spaggiari, Mika Tujula, Christophe Van Nieuwenhuyze, Danilo Vassallo and Stefan Wredenborg.
Editorial, multimedia and production assistance was provided by Eszter Miltényi-Torstensson, Mike Moss, Peter Nicholson, Katie Ranger and Sophia Suh.
© European Central Bank, 2021
Postal address 60640 Frankfurt am Main, Germany
Telephone +49 69 1344 0
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All rights reserved. Reproduction for educational and non-commercial purposes is permitted provided that the source is acknowledged.
For specific terminology please refer to the ECB glossary (available in English only).
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1. With contributions from Pablo Andrés Anaya Longaric, Sungyup Chung, Johannes Gräb and Elena Vollmer.
2. The debt service ratio captures the impact of debt, average interest rates and maturities by assuming that current debt is repaid in equal instalments over the average residual maturity of outstanding debt. It is defined as $D S R = D Y * i 1 - 1 + i - s$ where D/Y denotes debt-to-GDP, i denotes the interest rate and s the average residual maturity of sovereign debt. See Drehmann, M., Ilnes, A., Juselius, M. and Santos, M., “How much income is used for debt payments? A new database for debt service ratios”, BIS Quarterly Review, Bank for International Settlements, September 2015.
3. Ultimately, the EU debt will be refinanced by European taxpayers as it is backed by Member States’ contributions to the EU budget and EU own resources.
4. For more details, see the box entitled “Towards an effective implementation of the EU’s recovery package”, Economic Bulletin, Issue 2, ECB, 2021.
5. The MFF and RRF funds differ in terms of structural composition and the conditions associated with the usage of the funds. The absorption rates may therefore differ for the RRF funds compared to historical MFF absorption rates.
6. See also the box entitled COVID-19 and the increase in household savings: precautionary or forced?”, Economic Bulletin, Issue 6, ECB, 2020.
7. See ECB press release dated 11 March 2021 and press release dated 10 December 2020.
8. Japanese investors form an important part of the global investor community and represented almost 18% of foreign holdings of US Treasury securities in February 2021 according to the Treasury International Capital reporting system.
9. See ECB press release dated 14 April 2021 for the March 2021 “Survey on credit terms and conditions in euro-denominated securities financing and OTC derivatives markets”.
10. See the box entitled “Financial stability implications of crypto-assets” Financial Stability Review, ECB, May 2018.
11. The European Securities and Markets Authority (ESMA) recently renewed its warning to investors about the risks of investing in crypto-assets.
12. OECD Economic Outlook, Interim Report
13. For additional details, see the communication to the banking industry dated 4 December 2020 regarding the identification and measurement of credit risk during the pandemic.
14. See the speech entitled “The sovereign-bank-corporate nexus – virtuous or vicious?” by Isabel Schnabel at the LSE conference on “Financial Cycles, Risk, Macroeconomic Causes and Consequences”, Frankfurt, 28 January 2021.
15. The term sovereign-bank-corporate nexus refers to the tight interdependencies between these sectors which are linked by multiple interacting channels. See, for example, Dell’Ariccia, G., Ferreira, C., Jenkinson, N., Laeven, L., Martin, A., Minoiu, C. and Popov, A., “Managing the sovereign-bank nexus”, Working Paper Series, No 2177, ECB, September 2018.
16. This analysis relies on the methodology developed by Diebold and Yilmaz (2014) and Gross and Siklos (2020) and uses Moody’s EDFs at daily frequency for up to 16 euro area countries for four sectors (sovereigns, banks, non-bank financials and non-financial firms). The methodology enables the derivation of estimates of directional connectedness based on variance decompositions in large-scale vector autoregressions (VARs) that trace the impact of individual shocks on all variables considered in the system of equations. Results are visualised by means of graphical network representations which portray the empirical estimates in an informative manner. See Diebold, F.X. and Yilmaz, K., “On the network topology of variance decompositions: Measuring the connectedness of financial firms”, Journal of Econometrics, Vol. 182, Issue 1, 2014, pp. 119-134, and Gross, C. and Siklos, P., “Analyzing credit risk transmission to the nonfinancial sector in Europe: A network approach”, Journal of Applied Econometrics, Vol. 35, Issue 1, 2020, pp. 61-81.
17. With bank profitability declining strongly in 2020, the ROE figure for the fourth quarter of 2020 depends on the way net income is annualised. In the FSR, the four-quarter average of total equity is used in the denominator, while net income is annualised using four-quarter trailing sums. ECB Banking Supervision annualises quarterly data by multiplying them by four, resulting in a different headline profitability number.
18. In some countries, the number of significant institutions included in the sample is smaller than the total number of banks operating in the country which might affect the results. The negative ROE reported by Spanish banks was driven by one institution, which recorded goodwill impairments.
19. In some countries, the number of significant institutions included in the sample is small relative to the total number of banks operating in the country which might affect the results.
20. See Section 4.1, Financial Stability Review, ECB, November 2020.
21. See Section 2.3, Financial Stability Review, ECB, November 2020.
22. In stress episodes, funds tend to sell even more than explained by investor redemptions; see Box 6.
23. See Box 6 entitled “The role of bank and non-bank interconnections in amplifying recent financial contagion”, Financial Stability Review, ECB, May 2020.
24. See Chapter 4 on Non-banks in Financial Stability Review, ECB, May 2020.
25. See Chapter 4 on Non-banks in Financial Stability Review, ECB, May 2020.
26. See the analysis in the chapter entitled “Developments in commercial real estate”, Financial Stability Report, European Insurance and Occupational Pensions Authority (EIOPA), December 2020.
27. As euro area insurers’ liabilities are predominantly denominated in euro, their value would not react to higher interest rates abroad.
28. The estimated effects on the capitalisation would be less benign to the extent that the rising interest rates depress stock and corporate bond valuations in insurers’ portfolios.
29. Economic support measures have been largely extended into 2021, but in several cases in a more targeted manner (see also the discussion in Chapters 1 and 3 on the role of guarantees and moratoria).
30. For example, while a decision to extend the leverage ratio exemption of central bank reserves has not yet been taken, a continued exemption would help support the implementation and transmission of policies such as the pandemic emergency purchase programme (PEPP) and the targeted longer-term refinancing operations (TLTROs). Note that the banking system as a whole cannot avoid holding (in the form of central bank reserves) the excess liquidity created by monetary policy decisions.
31. See also “COVID-19 support measures – Extending, amending and ending”, Financial Stability Board, April 2021.
32. These initiatives benefit from the European Commission’s prolonged and expanded State Aid Temporary Framework, including the increase in aid ceilings and the possibility to convert repayable instruments such as guaranteed loans into direct grants.
33. See Section 1.2 for a more in-depth discussion of the NGEU package.
34. On 15 December 2020, the European Systemic Risk Board extended the recommendation on restrictions of distributions during the COVID-19 pandemic until September 2021 and introduced certain amendments. National authorities complied with the recommendation. On the same day, the ECB also extended its recommendation on dividend distributions accordingly until 30 September 2021.
35. Additional analysis indicates that restrictions on distributions increase the resilience of banks by ensuring that capital is used to support the real economy and absorb losses. At the same time, however, they may negatively affect bank valuations due to the uncertainty over future distributions (see also the forthcoming issue of the ECB Macroprudential Bulletin).
36. For a broader overview of policy actions taken since the beginning of the pandemic, see Chapter 5 of the May and November 2020 issues of the FSR.
37. See the discussion in Chapter 3, as well as the December 2020 ECB Banking Supervision guidance on the identification and measurement of credit risk in the context of the coronavirus (COVID-19) pandemic, and the April 2021 press release on the targeted review of internal models, which emphasises the importance of accurate modelling of credit risk parameters. In addition, the EBA guidelines on legislative and non-legislative moratoria on loan repayments applied in the light of the COVID-19 crisis (originally extended until end-March 2021) have not been renewed.
38. Banks’ willingness to accept a decline in capital ratios can be undermined by a number of factors, including market, supervisory, macroprudential and regulatory factors (see Behn, M., Rancoita, E. and Rodriguez d’Acri, C., “Macroprudential capital buffers – objectives and usability”, Macroprudential Bulletin, Issue 11, ECB, October 2020).
39. See, for example, “ECB Banking Supervision provides temporary capital and operational relief in reaction to coronavirus”, press release, 12 March 2020; “Basel Committee meets; discusses impact of Covid-19; reiterates guidance on buffers”, press release, Bank for International Settlements, 17 June 2020; and “FSB Chair’s letter to G20 Finance Ministers and Central Bank Governors: July 2020”, Financial Stability Board, 15 July 2020.
40. These preliminary findings are also confirmed by multivariate analyses that make it possible to control for bank-level characteristics, the macro-financial environment and credit demand. Moreover, the combination of simple chart-based evidence measured in terms of exposures at default and original exposures makes it possible to identify bank reactions which are driven by capital-related and fiscal policy-related incentives. More specifically, exposure at default developments are useful for monitoring the exposures that must be covered by capital, while original exposure developments, which are not subject to credit risk mitigation, provide information on credit that is originated by banks and reaches the real economy.
41. Action plan: Tackling non-performing loans (NPLs) in the aftermath of the COVID-19 pandemic”, European Commission, 16 December 2020.
42. See “The macroeconomic impact assessment of Basel III finalisation in Europe”, ECB, forthcoming.
43. Grill, M., Molestina Vivar, L. and Wedow, M., “The suspensions of redemptions during the COVID‑19 crisis – a case for pre-emptive liquidity measures?”, Macroprudential Bulletin, Issue 12, ECB, April 2021.
44. Grill, M., O’Sullivan, S., Wedow, M. and Weistroffer, C., “Liquidity transformation by investment funds: structural fault line or desirable financial transformation? A systemic perspective”, Macroprudential Bulletin, Issue 12, ECB, April 2021; and Capotă, L., Grill, M., Molestina Vivar, L., Schmitz, N. and Weistroffer, C., “How effective is the EU Money Market Fund Regulation? Lessons from the COVID‑19 turmoil”, Macroprudential Bulletin, Issue 12, ECB, April 2021.
45. Giuzio, M., Grill, M., Kryczka, D. and Weistroffer, C., “A theoretical model analysing investment funds’ liquidity management and policy measures”, Macroprudential Bulletin, Issue 12, ECB, April 2021.
46. See, for example, Cominetta, M., Grill, M. and Jukonis, A., “Investigating initial margin procyclicality and corrective tools using EMIR data”, Macroprudential Bulletin, Issue 9, ECB, October 2019.
47. See Opinion on the 2020 Review of Solvency II, European Insurance and Occupational Pensions Authority, EIOPA-BoS-20/794, 17 December 2020.
48. See “Response letter to a consultation of the European Commission on the review of Solvency II”, European Systemic Risk Board, 16 October 2020.
49. The classification of funds as UCITS and non-UCITS depends on whether they fall under the EU Directive on undertakings for collective investment in transferable securities (UCITS). UCITS funds are mutual funds that can be sold to retail investors and are perceived as non-speculative, diversified and well-regulated investments.
50. Morris, S., Shim, I. and Shin, H.S., “Redemption risk and cash hoarding by asset managers”, Journal of Monetary Economics, Vol. 89, April 2017, pp. 71-87, show that cash hoarding behaviour is pervasive among fund managers when they face redemptions. For more recent evidence, see also Schrimpf, A., Shim I. and Shin, H.S., “Liquidity management and asset sales by bond funds in the face of investor redemptions in March 2020”, BIS Bulletin, No 29, Bank for International Settlements, March 2021.
51. The authors are grateful to Benjamin Hartung, Paloma Lopez-Garcia, Giulio Nicoletti, Marek Rusnák, Ralph Setzer, Mika Tujula and Peter Welz for useful comments and discussions.
Annexes
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https://control.com/textbook/discrete-process-measurement/temperature-switches/ | # Temperature Switches
## Chapter 18 - Discrete Process Measurement
A temperature switch is one detecting the temperature of some substance. Temperature switches often use bimetallic strips as the temperature-sensing element, the motion of which actuates one or more switch contacts. An alternative design uses a metal bulb filled with a fluid that expands with temperature, causing the switch mechanism to actuate based on the pressure this fluid exerts against a diaphragm or bellows. This latter temperature switch design is really a pressure switch, whose pressure is a direct function of process temperature by virtue of the physics of the entrapped fluid inside the sensing bulb.
Recall from section 9.1 that the “normal” status of a switch is the resting condition of no stimulation. A temperature switch will be in its “normal” status when it senses minimum temperature (i.e. cold, in some cases a condition colder than ambient). For a temperature switch, “normal” status is any sensed temperature below the trip threshold of the switch.
The following photograph shows a temperature-actuated switch manufactured by the Ashcroft corporation:
Like all other process switches, temperature switches exhibit a certain amount of deadband in their switching action. A temperature switch that trips at 300 $$^{o}$$F rising, for example, will not re-set at 300 $$^{o}$$F falling. That switch would more likely reset at some lower temperature such as 295 $$^{o}$$F. With mechanical switch designs, some amount of deadband is inevitable due to friction inside the mechanism. However, process switch deadband is actually a useful characteristic as it helps avoid repeated “nuisance” alarms from happening.
To understand this concept, it is helpful to imagine a scenario where the process variable is at or very near the trip point. For our hypothetical temperature switch with a trip point of 300 $$^{o}$$F (rising), imagine a situation where the process temperature is precisely 300.0 $$^{o}$$F. Any further rise in temperature will of course trip the switch (sounding an alarm). With no deadband, however, the switch will immediately re-set when the temperature falls back down to 300.0 $$^{o}$$F. This means the switch may possibly “cycle” back and forth between its trip and reset states with just a minute change in process temperature (300.0 $$^{o}$$F to 300.1 $$^{o}$$F and back again). If the temperature switch is activating an alarm every time it trips, it will create a series of alarm events prompting operators to repeatedly acknowledge the alarm. This is a nuisance to operations personnel, as it distracts them from addressing what they already realize is a process problem. It is better for the switch to trip at 300.0 $$^{o}$$F rising and remain in that tripped state until the temperature falls down to some degree substantially below the trip point. This way, the operators only receive one alarm event rather than multiple alarm events for each process temperature excursion.
Some mechanical temperature switches come equipped with a separate adjustment for deadband (also called differential). Setting this deadband adjustment in a mechanical temperature switch requires the technician to repeatedly subject the sensing element to a rising and falling temperature, to check that the switch trips at the proper setting and resets at the proper setting. This is analogous to cycling the process variable back and forth when adjusting the “zero” and “span” settings of an analog transmitter: checking to see that the transmitter repeatedly outputs a 0% signal at the lower range value (LRV) and a 100% signal at the upper range value (URV).
For discrete temperature-sensing applications demanding high accuracy and repeatability, electronic temperature switch circuits using thermocouples, RTDs, or thermistors may be used instead of a mechanical (bi-metallic or filled bulb) sensing element. The operation and configuration of discrete electronic temperature switches is very similar to that of continuous electronic temperature transmitters.
An example of an electronic temperature switch module is the Moore Industries model SPA (“Site Programmable Alarm”), shown here:
Not only is this particular model capable of directly interpreting both RTD and thermocouple signals, but it will also input 4-20 mA loop current signals as well. This means you may build a temperature switch system out of a 4-20 mA loop-powered temperature transmitter (located in the field) and an SPA switch module (located in a protected environment such as a control room or electrical enclosure). Many other manufacturers and models of electronic switching units exist, with the Moore Industries SPA being just one example.
With electronic temperature switches, the adjustment of deadband (differential) is both precise and flexible. Unlike mechanical switches where deadband is primarily a function of friction, and therefore liable to change over time as the device wears, electronic switching circuits may be precisely set for any trip and reset points along its measurement range, remaining very stable over time.
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http://webarchive.nationalarchives.gov.uk/20110810172045/http:/teachingandlearningresources.org.uk/node/3474 | # Unit 3 learning overview
You can use this overview to inform your planning and help secure children's learning of the mathematics covered in the unit. It includes extending number sequences forwards and backwards including decimals and negative numbers, adding and subtracting two-digit numbers mentally, solving one-step and two-step word problems, and communicating.
Children rehearse counting forwards and backwards and developing number sequences involving positive and negative numbers. They start their own sequence and challenge others to continue it, describing the rule and pattern. They extend number sequences, including those involving decimals in the context of money and length, for example they count in steps of 50 p in a sequence such as £0.50, £1.00, £1.50, £2.00, or in steps of 25 cm in a sequence like 1.25 m, 1.5 m, 1.75 m. They predict numbers that will occur in the sequence and ask 'what if?' questions, such as: 'What would my sequence look like if I counted in steps of 20 p from £1.10?'
They recognise that to enter £1.10 in a calculator they press the keys 1.1. They use the constant function to check their predictions (e.g. if they press 1.1 [+] [+] 0.2 the calculator counts in steps of 0.2 every time the [=] sign is pressed). They relate this back to counting in steps of 20 p in the context of money.
Children continue to derive pairs of numbers that total 100. They extend this to find pairs of multiples of 50 that total 1000, such as $150+850$. They continue to add and subtract two-digit numbers mentally, choosing their strategy based on the numbers involved. They investigate how many different ways they can complete an equation such as $\square \square -47=\square 9$, and they find the largest and smallest possible differences.
They solve mathematical problems and puzzles, such as: 'Lisa went on holiday. In 5 days she made 80 sandcastles. Each day she made four fewer castles than the day before. How many sandcastles did she make each day?'
Children continue to refine their written methods of calculation to make them more efficient. Those who can confidently explain how an expanded method works move on to a more compact method of recording, while others continue with an expanded method. They tackle calculations with different numbers of digits: for example, they find $754+86$ and $518-46$. They begin to add two or more three-digit sums of money, first adjusting them from pounds to pence and then moving on to using decimal notation: for example, they find the total of £4.21 and £3.87. They also begin to find the difference between amounts of money, such as $\mathrm{£}7.50-\mathrm{£}2.84$. Before they begin a calculation they use rounding to estimate the answer.
Children continue to develop written methods to multiply and divide TU by U. They estimate the answer before calculating, and recognise how partitioning helps to break down the calculation into manageable parts. They give a remainder as a whole number, recognising that it represents what is left over after a division and is always smaller than the divisor. They make sensible decisions about rounding up or down after division according to the context. When faced with a problem such as: 'A box holds six cakes. How many boxes will be needed for 80 cakes?' they recognise the need to round up, while for 'I have £62. Tickets cost £8 each. How many tickets can I buy?' they recognise the need to round down.
Children solve one-step and two-step word problems involving all four operations, some of which are in the context of money, measures or time. For each problem they select relevant information and the calculation(s) they need to do. They also decide whether to calculate mentally, use jottings to keep track of the calculation, use a written method or use a calculator. They learn how to set out a solution to a word problem by recording the calculation they have done. They communicate the main points of their solutions to each other, comparing their approaches and explaining their decisions. | 2017-07-22T02:52:02 | {"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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.35751867294311523, "perplexity": 1020.565171579257}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-30/segments/1500549423842.79/warc/CC-MAIN-20170722022441-20170722042441-00376.warc.gz"} |
https://www.zbmath.org/authors/?q=ai%3Apetrov.leonid | # zbMATH — the first resource for mathematics
## Petrov, Leonid
Compute Distance To:
Author ID: petrov.leonid Published as: Petrov, Leonid; Petrov, L. A.; Petrov, L. Homepage: http://faculty.virginia.edu/petrov/ External Links: MGP · ORCID · Wikidata · ResearchGate
Documents Indexed: 36 Publications since 2009 Reviewing Activity: 17 Reviews
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#### Co-Authors
12 single-authored 9 Borodin, Alexei 7 Corwin, Ivan 4 Bufetov, Alekseĭ Igor’evich 3 Sasamoto, Tomohiro 2 Matveev, Konstantin I. 1 Bufetov, Aleksandr Igorevich 1 Damron, Michael 1 Gorin, V. E. 1 Gorin, Vadim 1 Gromoll, H. Christian 1 Ismagilov, Rais Sal’manovich 1 Khoroshkin, Sergey M. 1 Kirillov, Alexandre Aleksandrovich 1 Knizel, Alisa 1 Meckes, Mark W. 1 Mkrtchyan, Sevak 1 Molchanov, Vladimir Fedorovich 1 Molev, Alexander I. 1 Mucciconi, Matteo 1 Nazarov, Maxim Leonidovich 1 Neretin, Yuriĭ Aleksandrovich 1 Nessonov, Nikolai I. 1 Okun’kov, Andreĭ Yur’evich 1 Orr, Daniel 1 Saenz, Axel 1 Sivakoff, David 1 Tikhonov, Mikhail 1 Vershik, Anatoliĭ Moiseevich
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#### Serials
6 Communications in Mathematical Physics 3 Advances in Mathematics 3 Electronic Journal of Probability 2 Journal of Statistical Physics 2 Russian Mathematical Surveys 2 The Annals of Probability 2 Probability Theory and Related Fields 2 Selecta Mathematica. New Series 2 Electronic Communications in Probability 1 Compositio Mathematica 1 Functional Analysis and its Applications 1 Journal of Combinatorial Theory. Series A 1 IMRN. International Mathematics Research Notices 1 Journal of Algebraic Combinatorics 1 Journal of Mathematical Sciences (New York) 1 Moscow Mathematical Journal 1 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 1 Probability Surveys 1 Forum of Mathematics, Sigma 1 Annales de l’Institut Henri Poincaré D. Combinatorics, Physics and their Interactions (AIHPD)
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#### Fields
25 Probability theory and stochastic processes (60-XX) 24 Statistical mechanics, structure of matter (82-XX) 12 Combinatorics (05-XX) 3 Associative rings and algebras (16-XX) 1 History and biography (01-XX) 1 Number theory (11-XX) 1 Group theory and generalizations (20-XX) 1 Topological groups, Lie groups (22-XX) 1 Potential theory (31-XX) 1 Special functions (33-XX) 1 Partial differential equations (35-XX) 1 Functional analysis (46-XX) 1 Operations research, mathematical programming (90-XX)
#### Citations contained in zbMATH Open
31 Publications have been cited 438 times in 216 Documents Cited by Year
Stochastic higher spin vertex models on the line. Zbl 1348.82055
Corwin, Ivan; Petrov, Leonid
2016
Integrable probability: from representation theory to MacDonald processes. Zbl 1295.82023
Borodin, Alexei; Petrov, Leonid
2014
Higher spin six vertex model and symmetric rational functions. Zbl 1405.60141
Borodin, Alexei; Petrov, Leonid
2018
Asymptotics of random lozenge tilings via Gelfand-Tsetlin schemes. Zbl 1315.60013
Petrov, Leonid
2014
Spectral theory for the $$q$$-boson particle system. Zbl 1314.05212
Borodin, Alexei; Corwin, Ivan; Petrov, Leonid; Sasamoto, Tomohiro
2015
Spectral theory for interacting particle systems solvable by coordinate Bethe ansatz. Zbl 1330.82017
Borodin, Alexei; Corwin, Ivan; Petrov, Leonid; Sasamoto, Tomohiro
2015
Asymptotics of uniformly random lozenge tilings of polygons. Gaussian free field. Zbl 1315.60062
Petrov, Leonid
2015
Nearest neighbor Markov dynamics on Macdonald processes. Zbl 1356.60161
Borodin, Alexei; Petrov, Leonid
2016
Integrable probability: stochastic vertex models and symmetric functions. Zbl 1397.82010
Borodin, Alexei; Petrov, Leonid
2017
Two-parameter family of infinite-dimensional diffusions on the Kingman simplex. Zbl 1204.60076
Petrov, L. A.
2009
The $$q$$-PushASEP: a New Integrable Model for Traffic in $$1+1$$ dimension. Zbl 1323.82029
Corwin, Ivan; Petrov, Leonid
2015
The boundary of the Gelfand-Tsetlin graph: new proof of Borodin-Olshanski’s formula, and its $$q$$-analogue. Zbl 1297.05249
Petrov, Leonid
2014
$$q$$-randomized Robinson-Schensted-Knuth correspondences and random polymers. Zbl 1381.60030
Matveev, Konstantin; Petrov, Leonid
2017
Stochastic higher spin six vertex model and $$q$$-TASEPs. Zbl 1379.82016
Orr, Daniel; Petrov, Leonid
2017
Law of large numbers for infinite random matrices over a finite field. Zbl 1335.60032
Bufetov, Alexey; Petrov, Leonid
2015
Inhomogeneous exponential jump model. Zbl 1412.82027
Borodin, Alexei; Petrov, Leonid
2018
Yang-Baxter field for spin Hall-Littlewood symmetric functions. Zbl 07125843
Bufetov, Alexey; Petrov, Leonid
2019
Generalizations of TASEP in discrete and continuous inhomogeneous space. Zbl 1439.60093
Knizel, Alisa; Petrov, Leonid; Saenz, Axel
2019
Random walks on strict partitions. Zbl 1288.60056
Petrov, L.
2010
$$\mathfrak{sl}(2)$$ operators and Markov processes on branching graphs. Zbl 1284.05332
Petrov, Leonid
2013
Correction to: “Stochastic higher spin vertex models on the line”. Zbl 1426.82039
Corwin, Ivan; Petrov, Leonid
2019
Random strict partitions and determinantal point processes. Zbl 1226.60072
Petrov, Leonid
2010
Pfaffian stochastic dynamics of strict partitions. Zbl 1244.60083
Petrov, Leonid
2011
Correction to: “Spectral theory for interacting particle systems solvable by coordinate Bethe ansatz”. Zbl 1421.82008
Borodin, Alexei; Corwin, Ivan; Petrov, Leonid; Sasamoto, Tomohiro
2019
Yang-Baxter random fields and stochastic vertex models. Zbl 1469.05162
Bufetov, Alexey; Mucciconi, Matteo; Petrov, Leonid
2021
GUE corners limit of $$q$$-distributed lozenge tilings. Zbl 1386.60035
Mkrtchyan, Sevak; Petrov, Leonid
2017
Limit behaviour of certain random walks on strict partitions. Zbl 1196.60140
Petrov, L. A.
2009
Universality of local statistics for noncolliding random walks. Zbl 1448.60106
2019
Coarsening model on $${\mathbb{Z}^{d}}$$ with biased zero-energy flips and an exponential large deviation bound for ASEP. Zbl 1397.82035
Damron, Michael; Petrov, Leonid; Sivakoff, David
2018
PushTASEP in inhomogeneous space. Zbl 1453.82058
Petrov, Leonid
2020
The $$q$$-Hahn PushTASEP. Zbl 07379804
Corwin, Ivan; Matveev, Konstantin; Petrov, Leonid
2021
Yang-Baxter random fields and stochastic vertex models. Zbl 1469.05162
Bufetov, Alexey; Mucciconi, Matteo; Petrov, Leonid
2021
The $$q$$-Hahn PushTASEP. Zbl 07379804
Corwin, Ivan; Matveev, Konstantin; Petrov, Leonid
2021
PushTASEP in inhomogeneous space. Zbl 1453.82058
Petrov, Leonid
2020
Yang-Baxter field for spin Hall-Littlewood symmetric functions. Zbl 07125843
Bufetov, Alexey; Petrov, Leonid
2019
Generalizations of TASEP in discrete and continuous inhomogeneous space. Zbl 1439.60093
Knizel, Alisa; Petrov, Leonid; Saenz, Axel
2019
Correction to: “Stochastic higher spin vertex models on the line”. Zbl 1426.82039
Corwin, Ivan; Petrov, Leonid
2019
Correction to: “Spectral theory for interacting particle systems solvable by coordinate Bethe ansatz”. Zbl 1421.82008
Borodin, Alexei; Corwin, Ivan; Petrov, Leonid; Sasamoto, Tomohiro
2019
Universality of local statistics for noncolliding random walks. Zbl 1448.60106
2019
Higher spin six vertex model and symmetric rational functions. Zbl 1405.60141
Borodin, Alexei; Petrov, Leonid
2018
Inhomogeneous exponential jump model. Zbl 1412.82027
Borodin, Alexei; Petrov, Leonid
2018
Coarsening model on $${\mathbb{Z}^{d}}$$ with biased zero-energy flips and an exponential large deviation bound for ASEP. Zbl 1397.82035
Damron, Michael; Petrov, Leonid; Sivakoff, David
2018
Integrable probability: stochastic vertex models and symmetric functions. Zbl 1397.82010
Borodin, Alexei; Petrov, Leonid
2017
$$q$$-randomized Robinson-Schensted-Knuth correspondences and random polymers. Zbl 1381.60030
Matveev, Konstantin; Petrov, Leonid
2017
Stochastic higher spin six vertex model and $$q$$-TASEPs. Zbl 1379.82016
Orr, Daniel; Petrov, Leonid
2017
GUE corners limit of $$q$$-distributed lozenge tilings. Zbl 1386.60035
Mkrtchyan, Sevak; Petrov, Leonid
2017
Stochastic higher spin vertex models on the line. Zbl 1348.82055
Corwin, Ivan; Petrov, Leonid
2016
Nearest neighbor Markov dynamics on Macdonald processes. Zbl 1356.60161
Borodin, Alexei; Petrov, Leonid
2016
Spectral theory for the $$q$$-boson particle system. Zbl 1314.05212
Borodin, Alexei; Corwin, Ivan; Petrov, Leonid; Sasamoto, Tomohiro
2015
Spectral theory for interacting particle systems solvable by coordinate Bethe ansatz. Zbl 1330.82017
Borodin, Alexei; Corwin, Ivan; Petrov, Leonid; Sasamoto, Tomohiro
2015
Asymptotics of uniformly random lozenge tilings of polygons. Gaussian free field. Zbl 1315.60062
Petrov, Leonid
2015
The $$q$$-PushASEP: a New Integrable Model for Traffic in $$1+1$$ dimension. Zbl 1323.82029
Corwin, Ivan; Petrov, Leonid
2015
Law of large numbers for infinite random matrices over a finite field. Zbl 1335.60032
Bufetov, Alexey; Petrov, Leonid
2015
Integrable probability: from representation theory to MacDonald processes. Zbl 1295.82023
Borodin, Alexei; Petrov, Leonid
2014
Asymptotics of random lozenge tilings via Gelfand-Tsetlin schemes. Zbl 1315.60013
Petrov, Leonid
2014
The boundary of the Gelfand-Tsetlin graph: new proof of Borodin-Olshanski’s formula, and its $$q$$-analogue. Zbl 1297.05249
Petrov, Leonid
2014
$$\mathfrak{sl}(2)$$ operators and Markov processes on branching graphs. Zbl 1284.05332
Petrov, Leonid
2013
Pfaffian stochastic dynamics of strict partitions. Zbl 1244.60083
Petrov, Leonid
2011
Random walks on strict partitions. Zbl 1288.60056
Petrov, L.
2010
Random strict partitions and determinantal point processes. Zbl 1226.60072
Petrov, Leonid
2010
Two-parameter family of infinite-dimensional diffusions on the Kingman simplex. Zbl 1204.60076
Petrov, L. A.
2009
Limit behaviour of certain random walks on strict partitions. Zbl 1196.60140
Petrov, L. A.
2009
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#### Cited by 188 Authors
24 Corwin, Ivan 23 Borodin, Alexei 20 Petrov, Leonid 19 Gorin, Vadim 11 Bufetov, Alekseĭ Igor’evich 10 Ol’shanskiĭ, Grigoriĭ Iosifovich 9 Sasamoto, Tomohiro 7 Barraquand, Guillaume 6 Aggarwal, Amol 6 Giardinà, Cristian 6 Johansson, Kurt 5 Cuenca, Cesar 5 Motegi, Kohei 5 Shen, Hao 5 van Diejen, Jan Felipe 4 Carinci, Gioia 4 Dimitrov, Evgeni I. 4 Duits, Maurice 4 Emsiz, Erdal 4 Ferrari, Patrik Lino 4 Ghosal, Promit 4 Imamura, Takashi 4 Laslier, Benoît 4 Redig, Frank 4 Wheeler, Michael 3 Adler, Mark 3 Chhita, Sunil 3 Colomo, Filippo 3 Duse, Erik 3 Duzhin, V. S. 3 Franceschini, Chiara 3 Knizel, Alisa 3 Koshida, Shinji 3 Kuniba, Atsuo 3 Lin, Yier 3 Mangazeev, Vladimir V. 3 Metcalfe, Anthony P. 3 Okado, Masato 3 Panova, Greta 3 Ruggiero, Matteo 3 Saenz, Axel 3 Shkolnikov, Mykhaylo 3 Sportiello, Andrea 3 Tsai, Li-cheng 3 van Moerbeke, Pierre 3 Vasil’ev, N. N. 2 Aas, Erik 2 Assiotis, Theodoros 2 Debin, Bryan 2 Feng, Shui 2 Fischbacher, Christoph 2 Garbali, Alexandr 2 Granet, Etienne 2 Grinberg, Darij 2 Groenevelt, Wolter G. M. 2 Kuijlaars, Arno B. J. 2 Lee, Eunghyun 2 Matveev, Konstantin I. 2 Mucciconi, Matteo 2 Pak, Igor 2 Pei, Yuchen 2 Pronko, Andrei G. 2 Quastel, Jeremy 2 Remenik, Daniel 2 Ruelle, Philippe 2 Schütz, Gunter M. 2 Scrimshaw, Travis 2 Seppäläinen, Timo 2 Spohn, Herbert 2 Toninelli, Fabio Lucio 2 Vető, Bálint 2 Wang, Dong 2 Young, Benjamin J. 1 Ahn, Andrew 1 Arbel, Julyan 1 Baik, Jinho 1 Banderier, Cyril 1 Bates, Erik 1 Beffara, Vincent 1 Belitsky, Vladimir 1 Berestycki, Nathanaël 1 Bisi, Elia 1 Blank, M. L. 1 Bogolyubov, Nikolaĭ Mikhaĭlovich 1 Bordenave, Charles 1 Bosnjak, Gary 1 Breuer, Jonathan 1 Brubaker, Ben 1 Buciumas, Valentin 1 Budzynski, Louise 1 Bump, Daniel 1 Caracciolo, Sergio 1 Charlier, Christophe 1 Chatterjee, Sourav 1 Ciucu, Mihai 1 Claeys, Tom 1 Crane, Harry 1 de Gier, Jan 1 Deift, Percy A. 1 Di Francesco, Philippe ...and 88 more Authors
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#### Cited in 62 Serials
26 Communications in Mathematical Physics 13 Journal of Statistical Physics 12 The Annals of Probability 12 Probability Theory and Related Fields 9 Advances in Mathematics 8 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 7 Journal of Mathematical Physics 7 Selecta Mathematica. New Series 6 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 6 Electronic Journal of Probability 5 Duke Mathematical Journal 5 Journal of Combinatorial Theory. Series A 5 The Annals of Applied Probability 5 Journal of Mathematical Sciences (New York) 5 Mathematical Physics, Analysis and Geometry 4 Letters in Mathematical Physics 4 Nuclear Physics. B 4 Functional Analysis and its Applications 4 Journal of Functional Analysis 4 Journal of Physics A: Mathematical and Theoretical 3 Transactions of the American Mathematical Society 3 Journal of Algebraic Combinatorics 3 Annales Henri Poincaré 3 Journal of Statistical Mechanics: Theory and Experiment 2 Theoretical and Mathematical Physics 2 Advances in Applied Mathematics 2 Stochastic Processes and their Applications 2 Bulletin of the American Mathematical Society. New Series 2 The Electronic Journal of Combinatorics 2 Journal of the European Mathematical Society (JEMS) 2 Algebraic Combinatorics 1 Communications on Pure and Applied Mathematics 1 Problems of Information Transmission 1 Annales de l’Institut Fourier 1 Annals of the Institute of Statistical Mathematics 1 Compositio Mathematica 1 Funkcialaj Ekvacioj. Serio Internacia 1 Publications Mathématiques 1 Journal of Applied Probability 1 Proceedings of the American Mathematical Society 1 Statistical Science 1 Journal of the American Mathematical Society 1 International Journal of Mathematics 1 Geometric and Functional Analysis. GAFA 1 Computational Statistics and Data Analysis 1 Journal of Knot Theory and its Ramifications 1 Potential Analysis 1 Annales Mathématiques Blaise Pascal 1 Electronic Communications in Probability 1 Bernoulli 1 Séminaire Lotharingien de Combinatoire 1 Annals of Combinatorics 1 Annals of Mathematics. Second Series 1 Communications in Nonlinear Science and Numerical Simulation 1 Moscow Mathematical Journal 1 Mathematics in Computer Science 1 Probability Surveys 1 Science China. Mathematics 1 Forum of Mathematics, Pi 1 Forum of Mathematics, Sigma 1 Dependence Modeling 1 Annales de l’Institut Henri Poincaré D. Combinatorics, Physics and their Interactions (AIHPD)
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#### Cited in 32 Fields
142 Probability theory and stochastic processes (60-XX) 118 Statistical mechanics, structure of matter (82-XX) 65 Combinatorics (05-XX) 27 Quantum theory (81-XX) 24 Special functions (33-XX) 20 Partial differential equations (35-XX) 16 Linear and multilinear algebra; matrix theory (15-XX) 12 Nonassociative rings and algebras (17-XX) 11 Associative rings and algebras (16-XX) 10 Topological groups, Lie groups (22-XX) 7 Group theory and generalizations (20-XX) 7 Convex and discrete geometry (52-XX) 7 Numerical analysis (65-XX) 6 Harmonic analysis on Euclidean spaces (42-XX) 5 Statistics (62-XX) 4 Abstract harmonic analysis (43-XX) 4 Biology and other natural sciences (92-XX) 3 Dynamical systems and ergodic theory (37-XX) 2 History and biography (01-XX) 2 Number theory (11-XX) 2 Algebraic geometry (14-XX) 2 Integral transforms, operational calculus (44-XX) 2 Operator theory (47-XX) 2 Geometry (51-XX) 1 Category theory; homological algebra (18-XX) 1 Ordinary differential equations (34-XX) 1 Sequences, series, summability (40-XX) 1 Functional analysis (46-XX) 1 Algebraic topology (55-XX) 1 Relativity and gravitational theory (83-XX) 1 Operations research, mathematical programming (90-XX) 1 Mathematics education (97-XX)
#### Wikidata Timeline
The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata. | 2021-12-04T11:05:44 | {"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": 0.41744813323020935, "perplexity": 10917.557509130713}, "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-2021-49/segments/1637964362969.51/warc/CC-MAIN-20211204094103-20211204124103-00446.warc.gz"} |
http://dlmf.nist.gov/31.18 | # §31.18 Methods of Computation
Independent solutions of (31.2.1) can be computed in the neighborhoods of singularities from their Fuchs–Frobenius expansions (§31.3), and elsewhere by numerical integration of (31.2.1). Subsequently, the coefficients in the necessary connection formulas can be calculated numerically by matching the values of solutions and their derivatives at suitably chosen values of $z$; see Laĭ (1994) and Lay et al. (1998). Care needs to be taken to choose integration paths in such a way that the wanted solution is growing in magnitude along the path at least as rapidly as all other solutions (§3.7(ii)). The computation of the accessory parameter for the Heun functions is carried out via the continued-fraction equations (31.4.2) and (31.11.13) in the same way as for the Mathieu, Lamé, and spheroidal wave functions in Chapters 2830. | 2014-09-02T23:47:48 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 1, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8529307246208191, "perplexity": 491.9559355571011}, "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-2014-35/segments/1409535923940.4/warc/CC-MAIN-20140909030550-00096-ip-10-180-136-8.ec2.internal.warc.gz"} |
https://pdglive.lbl.gov/DataBlock.action?node=B038W&home=sumtabB | #### ${{\mathit \Lambda}{(1520)}}$ WIDTH
VALUE (MeV) EVTS DOCUMENT ID TECN COMMENT
$\bf{ 15\text{ to }17\text{ }(\approx16) }$ OUR ESTIMATE
$\bf{ 15.73 \pm0.26}$ OUR AVERAGE
$15.7$ $\pm1.0$
2019
DPWA ${{\overline{\mathit K}}}{{\mathit N}}$ multichannel
$17$ $\pm1$
2013 A
DPWA ${{\overline{\mathit K}}}{{\mathit N}}$ multichannel
$18.6$ $\pm1.9$ $\pm1.0$
2010
SPEC ${{\mathit e}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit e}^{\,'}}{{\mathit K}^{+}}{{\mathit X}}$ (fit to ${{\mathit X}}$)
$16.3$ $\pm3.3$ 300
1980 D
SPEC ${{\mathit \gamma}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit \Lambda}{(1520)}}{{\mathit K}^{+}}$
$16$ $\pm1$
1980
DPWA ${{\overline{\mathit K}}}$ ${{\mathit N}}$ $\rightarrow$ ${{\overline{\mathit K}}}{{\mathit N}}$
$14$ $\pm3$ 677 1
1979
HBC ${{\mathit K}^{-}}{{\mathit p}}$ 4.2 ${\mathrm {GeV/}}\mathit c$
$15.4$ $\pm0.5$
1978
DPWA ${{\overline{\mathit K}}}$ ${{\mathit N}}$ $\rightarrow$ ${{\overline{\mathit K}}}{{\mathit N}}$
$16.3$ $\pm0.5$ 4k
1977
HBC ${{\mathit K}^{-}}{{\mathit p}}$ 0.96$-$1.36 ${\mathrm {GeV/}}\mathit c$
$15.0$ $\pm0.5$
1977
DPWA ${{\overline{\mathit K}}}{{\mathit N}}$ multichannel
$15.5$ $\pm1.6$ 2000
1975
DBC ${{\mathit K}^{-}}{{\mathit d}}$ 1.4$-$1.8 ${\mathrm {GeV/}}\mathit c$
1 From the best-resolution sample of ${{\mathit \Lambda}}{{\mathit \pi}}{{\mathit \pi}}$ events only.
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
QIANG 2010
PL B694 123 Properties of the ${{\mathit \Lambda}{(1520)}}$ Resonance from High-Precision Electroproduction Data
BARBER 1980D
ZPHY C7 17 Strangeness Exchange in Photoproduction of ${{\mathit K}^{+}}{{\mathit \Lambda}{(1520)}}$ between 2.8 and 4.8 GeV
GOPAL 1980
Toronto Conf. 159 S = -1 Baryons: an Experimental Review
BARLAG 1979
NP B149 220 The Reactions ${{\mathit K}^{-}}$ ${{\mathit p}}$ $\rightarrow$ Pseudoscalar Meson ${{\mathit \Lambda}{(1520)}}$ at 4.2 ${\mathrm {GeV/}}\mathit c$
ALSTON-GARNJOST 1978
PR D18 182 Partial Wave Analysis of the ${{\overline{\mathit K}}}{{\mathit N}}$ System from 360 to 1320 ${\mathrm {MeV}}/\mathit c$
Also
PRL 38 1007 Further Evidence on New Resonances in the ${{\overline{\mathit K}}}{{\mathit N}}$ System
CAMERON 1977
NP B131 399 Partial Wave Analysis of ${{\mathit K}^{-}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit \pi}^{0}}{{\mathit \Lambda}{(1520)}}$ between 1710 and 2170 MeV Center-of-Mass Energy Including New Data between 1775 and 1960 MeV
GOPAL 1977
NP B119 362 Partial Wave Analyses of ${{\overline{\mathit K}}}{{\mathit N}}$ Two Body Reactions between 1480 and 2170 MeV
CORDEN 1975
NP B84 306 An Analysis of the ${{\mathit \Lambda}{(1520)}}$ Observed in a ${{\mathit K}^{-}}$ Neutron Production Experiment | 2022-09-26T09:22:13 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6910567879676819, "perplexity": 6753.599804320283}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030334855.91/warc/CC-MAIN-20220926082131-20220926112131-00337.warc.gz"} |
https://phys.libretexts.org/Bookshelves/University_Physics/Book%3A_University_Physics_(OpenStax)/Map%3A_University_Physics_III_-_Optics_and_Modern_Physics_(OpenStax)/4%3A_Diffraction/4.3%3A_Double-Slit_Diffraction | $$\require{cancel}$$
# 4.3: Double-Slit Diffraction
When we studied interference in Young’s double-slit experiment, we ignored the diffraction effect in each slit. We assumed that the slits were so narrow that on the screen you saw only the interference of light from just two point sources. If the slit is smaller than the wavelength, then [link](a) shows that there is just a spreading of light and no peaks or troughs on the screen. Therefore, it was reasonable to leave out the diffraction effect in that chapter. However, if you make the slit wider, [link](b) and (c) show that you cannot ignore diffraction. In this section, we study the complications to the double-slit experiment that arise when you also need to take into account the diffraction effect of each slit.
To calculate the diffraction pattern for two (or any number of) slits, we need to generalize the method we just used for a single slit. That is, across each slit, we place a uniform distribution of point sources that radiate Huygens wavelets, and then we sum the wavelets from all the slits. This gives the intensity at any point on the screen. Although the details of that calculation can be complicated, the final result is quite simple:
### TWO-SLIT DIFFRACTION PATTERN
The diffraction pattern of two slits of width D that are separated by a distance d is the interference pattern of two point sources separated by d multiplied by the diffraction pattern of a slit of width D.
In other words, the locations of the interference fringes are given by the equation $$d \, sin \, \theta = m \lambda$$, the same as when we considered the slits to be point sources, but the intensities of the fringes are now reduced by diffraction effects, according to [link]. [Note that in the chapter on interference, we wrote $$d \, sin \, \theta = m \lambda$$ and used the integer m to refer to interference fringes. [link] also uses m, but this time to refer to diffraction minima. If both equations are used simultaneously, it is good practice to use a different variable (such as n) for one of these integers in order to keep them distinct.]
Interference and diffraction effects operate simultaneously and generally produce minima at different angles. This gives rise to a complicated pattern on the screen, in which some of the maxima of interference from the two slits are missing if the maximum of the interference is in the same direction as the minimum of the diffraction. We refer to such a missing peak as a missing order. One example of a diffraction pattern on the screen is shown in Figure $$\PageIndex{1}$$. The solid line with multiple peaks of various heights is the intensity observed on the screen. It is a product of the interference pattern of waves from separate slits and the diffraction of waves from within one slit.
Figure $$\PageIndex{1}$$: Diffraction from a double slit. The purple line with peaks of the same height are from the interference of the waves from two slits; the blue line with one big hump in the middle is the diffraction of waves from within one slit; and the thick red line is the product of the two, which is the pattern observed on the screen. The plot shows the expected result for a slit width $$D = 2\lambda$$ and slit separation $$d = 6\lambda$$. The maximum of $$m = \pm 3$$ order for the interference is missing because the minimum of the diffraction occurs in the same direction.
Example $$\PageIndex{1}$$: Intensity of the Fringes
Figure $$\PageIndex{1}$$ shows that the intensity of the fringe for m=3 is zero, but what about the other fringes? Calculate the intensity for the fringe at m=1 relative to $$I_0$$, the intensity of the central peak.
Strategy
Determine the angle for the double-slit interference fringe, using the equation from Interference, then determine the relative intensity in that direction due to diffraction by using [link].
Solution
From the chapter on interference, we know that the bright interference fringes occur at $$d \, sin \, \theta = m \lambda$$, or
$sin \, \theta = \dfrac{m\lambda}{d}.$
$I = I_0 \left(\dfrac{sin \, \beta}{\beta}\right)^2, \, where \, \beta = \dfrac{phi}{2} = \dfrac{\pi D sin \, \theta}{\lambda}.$
Substituting from above,
$\beta = \dfrac{\pi D sin \, \theta}{\lambda} = \dfrac{\pi D}{\lambda} \cdot \dfrac{m\lambda}{d} = \dfrac{m\pi D}{d}.$
For $$D = 2\lambda, \, d = 6 \lambda$$, and $$m = 1$$,
$\beta = \dfrac{(1)\pi (2\lambda)}{(6 \lambda)} = \dfrac{\pi}{3}.$
Then, the intensity is
$I = I_0 \left(\dfrac{sin \, \beta}{\beta}\right)^2 = I_0 \left(\dfrac{sin \, (\pi/3)}{\pi/3}\right)^2 = 0.684 I_0.$
Significance
Note that this approach is relatively straightforward and gives a result that is almost exactly the same as the more complicated analysis using phasors to work out the intensity values of the double-slit interference (thin line in Figure $$\PageIndex{1}$$). The phasor approach accounts for the downward slope in the diffraction intensity (blue line) so that the peak near m=1 occurs at a value of θ ever so slightly smaller than we have shown here.
Two-Slit Diffraction
Suppose that in Young’s experiment, slits of width 0.020 mm are separated by 0.20 mm. If the slits are illuminated by monochromatic light of wavelength 500 nm, how many bright fringes are observed in the central peak of the diffraction pattern?
Solution
From [link], the angular position of the first diffraction minimum is $$\theta \approx sin \, \theta = \dfrac{\lambda}{D} = \dfrac{5.0 \times 10^{-7}m}{2.0 \times 10^{-5}m} = 2.5 \times 10^{-2} rad$$.
Using $$sin \, \theta = m \lambda$$ for $$\theta = 2.5 \times 10^{-2} rad$$, we find
$m = \dfrac{d \, sin \, \theta}{\lambda} = \dfrac{(0.20 \, mm)(2.5 \times 10^{-2} rad)}{(5.0 \times 10^{-7}m)} = 10,$
which is the maximum interference order that fits inside the central peak. We note that $$m=±10$$ are missing orders as $$θ$$ matches exactly. Accordingly, we observe bright fringes for
m = −9, −8, −7, −6, −5, −4, −3, −2, −1, 0, +1, +2, +3, +4, +5, +6, +7, +8, and +9
for a total of 19 bright fringes.
Exercise $$\PageIndex{1}$$
For the experiment in Example, show that m=20m=20 is also a missing order.
Solution
From $$d \, sin \, \theta = m\lambda$$, the interference maximum occurs at $$2.87^o$$ for $$m = 20$$. From [link], this is also the angle for the second diffraction minimum. (Note: Both equations use the index m but they refer to separate phenomena.)
Explore the effects of double-slit diffraction. In this simulation written by Fu-Kwun Hwang, select N=2 using the slider and see what happens when you control the slit width, slit separation and the wavelength. Can you make an order go “missing?”
### 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). | 2019-04-19T08:54:33 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6160659790039062, "perplexity": 404.801427967364}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-18/segments/1555578527518.38/warc/CC-MAIN-20190419081303-20190419103303-00465.warc.gz"} |
http://dlmf.nist.gov/6.12 | # §6.12 Asymptotic Expansions
## §6.12(i) Exponential and Logarithmic Integrals
6.12.1 $\mathop{E_{1}\/}\nolimits\!\left(z\right)\sim\frac{e^{-z}}{z}\left(1-\frac{1!}% {z}+\frac{2!}{z^{2}}-\frac{3!}{z^{3}}+\cdots\right),$ $z\to\infty$, $|\mathop{\mathrm{ph}\/}\nolimits z|\leq\tfrac{3}{2}\pi-\delta(<\tfrac{3}{2}\pi)$.
When $|\mathop{\mathrm{ph}\/}\nolimits z|\leq\frac{1}{2}\pi$ the remainder is bounded in magnitude by the first neglected term, and has the same sign when $\mathop{\mathrm{ph}\/}\nolimits z=0$. When $\frac{1}{2}\pi\leq|\mathop{\mathrm{ph}\/}\nolimits z|<\pi$ the remainder term is bounded in magnitude by $\mathop{\csc\/}\nolimits\!\left(|\mathop{\mathrm{ph}\/}\nolimits z|\right)$ times the first neglected term. For these and other error bounds see Olver (1997b, pp. 109–112) with $\alpha=0$.
For re-expansions of the remainder term leading to larger sectors of validity, exponential improvement, and a smooth interpretation of the Stokes phenomenon, see §§2.11(ii)2.11(iv), with $p=1$.
6.12.2 $\mathop{\mathrm{Ei}\/}\nolimits\!\left(x\right)\sim\frac{e^{x}}{x}\left(1+% \frac{1!}{x}+\frac{2!}{x^{2}}+\frac{3!}{x^{3}}+\cdots\right),$ $x\to+\infty$.
If the expansion is terminated at the $n$th term, then the remainder term is bounded by $1+\chi(n+1)$ times the next term. For the function $\chi$ see §9.7(i).
The asymptotic expansion of $\mathop{\mathrm{li}\/}\nolimits\!\left(x\right)$ as $x\to\infty$ is obtainable from (6.2.8) and (6.12.2).
## §6.12(ii) Sine and Cosine Integrals
The asymptotic expansions of $\mathop{\mathrm{Si}\/}\nolimits\!\left(z\right)$ and $\mathop{\mathrm{Ci}\/}\nolimits\!\left(z\right)$ are given by (6.2.19), (6.2.20), together with
6.12.3 $\displaystyle\mathop{\mathrm{f}\/}\nolimits\!\left(z\right)$ $\displaystyle\sim\frac{1}{z}\left(1-\frac{2!}{z^{2}}+\frac{4!}{z^{4}}-\frac{6!% }{z^{6}}+\cdots\right),$ 6.12.4 $\displaystyle\mathop{\mathrm{g}\/}\nolimits\!\left(z\right)$ $\displaystyle\sim\frac{1}{z^{2}}\left(1-\frac{3!}{z^{2}}+\frac{5!}{z^{4}}-% \frac{7!}{z^{6}}+\cdots\right),$
as $z\to\infty$ in $|\mathop{\mathrm{ph}\/}\nolimits z|\leq\pi-\delta\thinspace(<\pi)$.
The remainder terms are given by
6.12.5 $\displaystyle\mathop{\mathrm{f}\/}\nolimits\!\left(z\right)$ $\displaystyle=\frac{1}{z}\sum_{m=0}^{n-1}(-1)^{m}\frac{(2m)!}{z^{2m}}+R_{n}^{(% \mathop{\mathrm{f}\/}\nolimits)}(z),$ 6.12.6 $\displaystyle\mathop{\mathrm{g}\/}\nolimits\!\left(z\right)$ $\displaystyle=\frac{1}{z^{2}}\sum_{m=0}^{n-1}(-1)^{m}\frac{(2m+1)!}{z^{2m}}+R_% {n}^{(\mathop{\mathrm{g}\/}\nolimits)}(z),$
where, for $n=0,1,2,\dots$,
6.12.7 $\displaystyle R_{n}^{(\mathop{\mathrm{f}\/}\nolimits)}(z)$ $\displaystyle=(-1)^{n}\int_{0}^{\infty}\frac{e^{-zt}t^{2n}}{t^{2}+1}dt,$ Defines: $R_{n}^{(\mathop{\mathrm{f}\/}\nolimits)}(z)$: remainder term (locally) Symbols: $dx$: differential of $x$, $e$: base of exponential function, $\int$: integral, $\mathop{\mathrm{f}\/}\nolimits\!\left(z\right)$: auxiliary function for sine and cosine integrals, $z$: complex variable and $n$: nonnegative integer Referenced by: §6.12(ii) Permalink: http://dlmf.nist.gov/6.12.E7 Encodings: TeX, pMML, png 6.12.8 $\displaystyle R_{n}^{(\mathop{\mathrm{g}\/}\nolimits)}(z)$ $\displaystyle=(-1)^{n}\int_{0}^{\infty}\frac{e^{-zt}t^{2n+1}}{t^{2}+1}dt.$ Defines: $R_{n}^{(\mathop{\mathrm{g}\/}\nolimits)}(z)$: remainder term (locally) Symbols: $dx$: differential of $x$, $e$: base of exponential function, $\int$: integral, $\mathop{\mathrm{g}\/}\nolimits\!\left(z\right)$: auxiliary function for sine and cosine integrals, $z$: complex variable and $n$: nonnegative integer Referenced by: §6.12(ii) Permalink: http://dlmf.nist.gov/6.12.E8 Encodings: TeX, pMML, png
When $|\mathop{\mathrm{ph}\/}\nolimits z|\leq\tfrac{1}{4}\pi$, these remainders are bounded in magnitude by the first neglected terms in (6.12.3) and (6.12.4), respectively, and have the same signs as these terms when $\mathop{\mathrm{ph}\/}\nolimits z=0$. When $\frac{1}{4}\pi\leq|\mathop{\mathrm{ph}\/}\nolimits z|<\frac{1}{2}\pi$ the remainders are bounded in magnitude by $\mathop{\csc\/}\nolimits\!\left(2|\mathop{\mathrm{ph}\/}\nolimits z|\right)$ times the first neglected terms.
For other phase ranges use (6.4.6) and (6.4.7). For exponentially-improved asymptotic expansions, use (6.5.5), (6.5.6), and §6.12(i). | 2015-10-06T12:22:44 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 93, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9362385869026184, "perplexity": 1462.7650927785899}, "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-2015-40/segments/1443736678654.30/warc/CC-MAIN-20151001215758-00082-ip-10-137-6-227.ec2.internal.warc.gz"} |
https://par.nsf.gov/biblio/10285823-blazar-jets-launched-similar-energy-per-baryon-independently-power | Blazar jets launched with similar energy per baryon, independently of their power
ABSTRACT The most extreme active galactic nuclei are the radio active ones whose relativistic jet propagates close to our line of sight. These objects were first classified according to their emission-line features into flat-spectrum radio quasars (FSRQs) and BL Lacertae objects (BL Lacs). More recently, observations revealed a trend between these objects known as the blazar sequence, along with an anticorrelation between the observed power and the frequency of the synchrotron peak. In this work, we propose a fairly simple idea that could account for the whole blazar population: all jets are launched with similar energy per baryon, independently of their power. In the case of FSRQs, the most powerful jets manage to accelerate to high-bulk Lorentz factors, as observed in the radio. As a result, they have a rather modest magnetization in the emission region, resulting in magnetic reconnection injecting a steep particle–energy distribution and, consequently, steep emission spectra in the γ-rays. For the weaker jets, namely BL Lacs, the opposite holds true; i.e. the jet does not achieve a very high bulk Lorentz factor, leading to more magnetic energy available for non-thermal particle acceleration, and harder emission spectra at frequencies ≳ GeV. In this scenario, we recover all more »
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10285823
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Monthly Notices of the Royal Astronomical Society
Volume:
501
Issue:
3
Page Range or eLocation-ID:
4092 to 4102
ISSN:
0035-8711
4. ABSTRACT Relativistic jets from supermassive black holes are among the most powerful and luminous astrophysical systems in Universe. We propose that the open magnetic field lines through the black hole, which drive a strongly magnetized jet, may have their polarity reversing over time scales related to the growth of the magnetorotational dynamo in the disc, resulting in dissipative structures in the jet characterized by reversing toroidal field polarities, referred to as ‘stripes’. The magnetic reconnection between the stripes dissipates the magnetic energy and powers jet acceleration. The striped jet model can explain the jet acceleration, large-scale jet emission, and blazar emission signatures consistently in a unified physical picture. Specifically, we find that the jet accelerates to the bulk Lorentz factor Γ ≳ 10 within 1-parsec distance from the central engine. The acceleration slows down but continues at larger distances, with intrinsic acceleration rate $\dot{\Gamma }/\Gamma$ between $0.0005$ and $0.005~\rm {yr^{-1}}$ at tens of parsecs, which is in very good agreement with recent radio observations. Magnetic reconnection continuously accelerates non-thermal particles over large distances from the central engine, resulting in the core-shift effect and overall flat-to-inverted synchrotron spectrum. The large-scale spectral luminosity peak νpeak is antiproportional to the location of themore » | 2022-12-09T07:14:08 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6307925581932068, "perplexity": 2420.2618865116633}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446711390.55/warc/CC-MAIN-20221209043931-20221209073931-00512.warc.gz"} |
https://par.nsf.gov/biblio/10159384-self-gravitating-filament-formation-from-shocked-flows-velocity-gradients-across-filaments | Self-gravitating filament formation from shocked flows: velocity gradients across filaments
ABSTRACT In typical environments of star-forming clouds, converging supersonic turbulence generates shock-compressed regions, and can create strongly magnetized sheet-like layers. Numerical magnetohydrodynamic simulations show that within these post-shock layers, dense filaments and embedded self-gravitating cores form via gathering material along the magnetic field lines. As a result of the preferred-direction mass collection, a velocity gradient perpendicular to the filament major axis is a common feature seen in simulations. We show that this prediction is in good agreement with recent observations from the CARMA Large Area Star Formation Survey (CLASSy), from which we identified several filaments with prominent velocity gradients perpendicular to their major axes. Highlighting a filament from the north-west part of Serpens South, we provide both qualitative and quantitative comparisons between simulation results and observational data. In particular, we show that the dimensionless ratio Cv ≡ Δvh2/(GM/L), where Δvh is half of the observed perpendicular velocity difference across a filament, and M/L is the filament’s mass per unit length, can distinguish between filaments formed purely due to turbulent compression and those formed due to gravity-induced accretion. We conclude that the perpendicular velocity gradient observed in the Serpens South north-west filament can be caused by gravity-induced anisotropic accretion of material more »
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10159384
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Monthly Notices of the Royal Astronomical Society
Volume:
494
Issue:
3
Page Range or eLocation-ID:
3675 to 3685
ISSN:
0035-8711
Tight binary or multiple-star systems can interact through mass transfer and follow vastly different evolutionary pathways than single stars. The star TYC 2597-735-1 is a candidate for a recent stellar merger remnant resulting from a coalescence of a low-mass companion with a primary star a few thousand years ago. This violent event is evident in a conical outflow (“Blue Ring Nebula”) emitting in UV light and surrounded by leading shock filaments observed in Hαand UV emission. From Chandra data, we report the detection of X-ray emission from the location of TYC 2597-735-1 with a luminosity$log(LX/Lbol)=−5.5$. Together with a previously reported period of ~14 days, this indicates ongoing stellar activity and the presence of strong magnetic fields on TYC 2597-735-1. Supported by stellar evolution models of merger remnants, we interpret the inferred stellar magnetic field as dynamo action associated with a newly formed convection zone in the atmosphere of TYC 2597-735-1, though internal shocks at the base of an accretion-powered jet cannot be ruled out. We speculate that this object will evolve into an FK Com–type source, i.e., a class of rapidly spinning magnetically active stars for which a merger origin has beenmore » | 2023-03-27T00:24:18 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 1, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5379652380943298, "perplexity": 3200.155088920959}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296946584.94/warc/CC-MAIN-20230326235016-20230327025016-00002.warc.gz"} |
https://pavpanchekha.com/blog/herbie-rust.html | ## By Pavel Panchekha
### 28 November 2022
Share under CC-BY-SA.
# Improving Rust with Herbie
Last week I had a fun experience using Herbie to actually improve the numerical accuracy of real code.
## Discovering a Rust problem
It all started when Finn (an undergraduate from UW) submitted a PR to FPBench to compile FPBench benchmarks to Rust. Besides being great work and a valuable contribution, he also pointed out that our test framework was failing on his FPBench to Rust compiler "due to precision issues with Rust's implementation" of the asinh and acosh functions.
This intrigued me, because I had assumed that Rust would just link to the system math library. Indeed, it does do that for most functions, but for the arc-hyperbolic-trigonometric functions Rust uses its own custom code.1 [1 Maybe there's a platform support issue?] That implementation looks like this:
pub fn asinh(self) -> f64 {
(self.abs() + ((self * self) + 1.0).sqrt()).ln().copysign(self)
}
In case you're not Rust-fluent, this basically corresponds to the dictionary definition:2 [2 Plus the right logic for handling signs.]
$\operatorname{sinh}^{-1}(x) = \log(x + \sqrt{x^2 + 1})$
Yet this is not a very accurate equation. I threw it into Herbie to see what it would say, and got this graph:
Focus on the red line here (the green line is my fix): the formula is very inaccurate for values bigger than about 10150 or smaller than 1 in absolute value. Let's look at why.
## Large values
The issue with large values, bigger than 10150, is pretty simple. Basically, we're computing x * x, and if x is bigger than about 10150, that will overflow and return infinity. Then we add that to one, take a square root, add x, and take the logarithm, and the whole time the answer is also infinity. Which isn't close to right! This kind of issue is pretty common, and in a lot of code you might not care about it, but for a library function it's no good. That said, this problem was pretty obvious to me just from looking at the equation, and the fix was simple too.
The key here is that while x * x is indeed too big to represent as a floating-point number, we're going to take a square root a little later, and that square root is representable. So we need to find a better way to do the square root. Luckily, standard math libraries include a function called hypot which computes the square root sum of squares without intermediate overflow. So we can just replace:
sqrt(x * x + 1) -> hypot(x, 1)
By the way, Herbie also suggests this fix, since it knows about hypot. This fixes the issue with large values.
## Small values
The issue with small values, absolute values less than 1, was less obvious, and I didn't realize it would happen until I looked at Herbie's plot above.
Recall that we're computing log(x + sqrt(x*x + 1)); let's trace what happens for small values of x. Here x*x + 1 is approximately 1, as is the square root of that quantity. So now we're looking at x + 1, which again is close to 1 since x is small. And then we're taking the logarithm of a number close to 1. That's the issue!
What I mean is: logarithm is a function where inputs near 1 result in outputs near 0. But the issue is that its inputs near 1 are spaced pretty far apart—one epsilon, about 1e-16—while its outputs, near 0, are spaced much more finely, about 1e-300 apart.3 [3 Ignoring subnormals and some other caveats]. So while we should be able to provide about 1e-300 resolution, we can in fact only provide 1e-16 resolution, which is much worse. This general kind of problem exists any time you're using a function that has a root other than 0.
Here, Herbie offers a less useful solution: a Taylor series expansion. While that works reasonably well for values close to 0, you've got to be clever about picking where the Taylor series should take over, and also introducing a branch condition is a bad idea in a fundamental library, especially one marked #[inline], as this one is: it could mess with vectorization or lead to worse code generation.
So let's look for a better way to solve it. Since this issue with log is also somewhat common, libraries provide a helper function, log1p, which is log but shifted left so the root is at 0. So we can rewrite:
log(...) -> log1p(... - 1)
On its own this doesn't actually fix the problem, but it makes the cancellation that implicitly happens inside logarithm into an explicit cancellation. Now we can work to solve that.
Here the fix is to move the -1 to be next to the sqrt call, which is what initially produces a value close to 1:
log(x + (sqrt(x*x + 1) - 1))
Now, with cancellations like this, between square roots (think of 1 as sqrt(1)) there is a classic trick that I remember from my work on the quadratic formula: the difference of squares. Basically, when you have sqrt(a) - sqrt(b), multiple this by sqrt(a) + sqrt(b) over itself, and use the difference of squares formula to simplify the numerator to remove the square roots:
sqrt(x*x + 1) - 1 -> [ (x*x + 1) - 1 ] / [ sqrt(x*x + 1) + 1 ]
Now the numerator can be simplified to x * x, which doesn't have a cancellation, while the denominator now adds positive quantities, so it doesn't have any cancellation:
x * x / (sqrt(x*x + 1) + 1)
Now we just need to remember our other problem, overflow. We can remove the x * x in the denominator using hypot, but we've also now got an x * x in the numerator.
As before, while x * x may overflow in the numerator, the denominator will be similar in size to x for large x, so we're really computing something like x * x / x, which doesn't have to overflow. We just need to avoid the intermediate x * x.
One way to fix it is to divide the numerator and denominator by x. Then we have:
x * x / (sqrt(x*x + 1) + 1)
-> x / (sqrt(x*x + 1)/x + 1/x)
-> x / (sqrt(1 + 1/x*1/x) + 1/x)
-> x / (hypot(1, 1/x) + 1/x)
Now the numerator is approximately size x while the denominator is size 1/x, and nothing will overflow.
Another fix that I just came up with while writing this blog post is to zoom out and look at the full term:
log1p(x + x*x / (sqrt(x*x + 1) + 1))
We can factor an x out from the argument to log1p, thereby again avoiding the cancellation:
log1p(x * (1 + x / (hypot(1, x) + 1)))
I'm not going to go back and contribute this simplification to Rust, but since it replaces a division by a multiply it is probably minutely faster than the version I contributed on some architectures.
## What does Herbie think?
Of course any time I do any numerics work I think back to "would Herbie do as well". Here, it did OK but not great.
Noticing both problems went well. If I didn't have Herbie, I would have missed the small-values problem and end up with a much worse solution.
Fixing the large-values problem also went great. Herbie correctly identified the hypot-based solution. It's kind of easy, though.
However, fixing the small-values problem wasn't as great. Herbie suggested a Taylor series, which is both less elegant than my fix (branches, etc) but also less accurate near the branch. I'd like to look into whether Herbie can derive my version, or if not, why not.
Finally, for my "fixed" version, Herbie does a great job showing that the result is accurate and even identifying some subtle remaining issues. For example, let's look at the "final" version above:
log1p(x * (1 + x / (hypot(1, x) + 1)))
Note that we have an intermediate step where we multiply x by some value. If x is very large, that value will be just under 2, and for super duper large values of x, x * 2 can overflow.
There is a possible fix here. Let's expand out the log1p for a second:
log1p(x * (1 + x / (hypot(1, x) + 1)))
-> log(1 + x * (1 + x / (hypot(1, x) + 1)))
-> log(x * (1/x + 1 + x / (hypot(1, x) + 1)))
-> log(x) + log(1 + 1/x + x / (hypot(1, x) + 1))
-> log(x) + log1p(1/x + x / (hypot(1, x) + 1))
Now we're not multiplying x by anything at all! But for very small values of x, we'll get cancellation between the log(x) and log1p(1/x) terms. If we add a branch at 1 we can get the best of both worlds, but there's no way overflow at extremely large x is a big enough issue to deserve adding a branch here, and we're also now nearly doubling the cost of asinh by computing two different logarithms. So this subtle issue found by Herbie doesn't strike me as worth fixing.
## Contribution
Anyway, I packaged up my suggestions to asinh, as well as somewhat similar fixes to acosh, and submitted them to Rust in #104548, and then Max, who by the way is on the job market, implemented, tested, and got it all merged into Rust in #104553. It's now in Rust nightlies and will be released in the next Rust version!
## Footnotes:
1
Maybe there's a platform support issue?
2
Plus the right logic for handling signs.
3
Ignoring subnormals and some other caveats | 2023-02-07T22:15:35 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.638945460319519, "perplexity": 1183.9796169443102}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500641.25/warc/CC-MAIN-20230207201702-20230207231702-00782.warc.gz"} |
https://par.nsf.gov/biblio/10342093-unsupervised-anomaly-detection-robust-density-estimation | This content will become publicly available on June 30, 2023
Unsupervised Anomaly Detection by Robust Density Estimation
Density estimation is a widely used method to perform unsupervised anomaly detection. By learning the density function, data points with relatively low densities are classified as anomalies. Unfortunately, the presence of anomalies in training data may significantly impact the density estimation process, thereby imposing significant challenges to the use of more sophisticated density estimation methods such as those based on deep neural networks. In this work, we propose RobustRealNVP, a deep density estimation framework that enhances the robustness of flow-based density estimation methods, enabling their application to unsupervised anomaly detection. RobustRealNVP differs from existing flow-based models from two perspectives. First, RobustRealNVP discards data points with low estimated densities during optimization to prevent them from corrupting the density estimation process. Furthermore, it imposes Lipschitz regularization to the flow-based model to enforce smoothness in the estimated density function. We demonstrate the robustness of our algorithm against anomalies in training data from both theoretical and empirical perspectives. The results show that our algorithm achieves competitive results as compared to state-of-the-art unsupervised anomaly detection methods.
Authors:
; ;
Award ID(s):
Publication Date:
NSF-PAR ID:
10342093
Journal Name:
Proceedings of the AAAI Conference on Artificial Intelligence
Volume:
36
Issue:
4
Page Range or eLocation-ID:
4101 to 4108
ISSN:
2159-5399
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 » | 2022-12-10T08:32:05 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5710160136222839, "perplexity": 718.6184166458225}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446710421.14/warc/CC-MAIN-20221210074242-20221210104242-00354.warc.gz"} |
http://dlmf.nist.gov/2.10 | # §2.10 Sums and Sequences
## §2.10(i) Euler–Maclaurin Formula
As in §24.2, let and denote the th Bernoulli number and polynomial, respectively, and the th Bernoulli periodic function .
Assume that , and are integers such that , , and is absolutely integrable over . Then
This is the Euler–Maclaurin formula. Another version is the Abel–Plana formula:
being some number in the interval . Sufficient conditions for the validity of this second result are:
1. (a)
On the strip , is analytic in its interior, is continuous on its closure, and as , uniformly with respect to .
2. (b)
is real when .
3. (c)
The first infinite integral in (2.10.2) converges.
### ¶ Example
for large . From (2.10.1)
where () is arbitrary, is a constant, and
From §24.12(i), (24.2.2), and (24.4.27), is of constant sign . Thus and are of opposite signs, and since their difference is the term corresponding to in (2.10.4), is bounded in absolute value by this term and has the same sign.
Formula (2.10.2) is useful for evaluating the constant term in expansions obtained from (2.10.1). In the present example it leads to
where is Euler’s constant (§5.2(ii)) and is the derivative of the Riemann zeta function (§25.2(i)). is sometimes called Glaisher’s constant. For further information on see §5.17.
Other examples that can be verified in a similar way are:
where () is a real constant, and
In both expansions the remainder term is bounded in absolute value by the first neglected term in the sum, and has the same sign, provided that in the case of (2.10.7), truncation takes place at , where is any positive integer satisfying .
For extensions of the Euler–Maclaurin formula to functions with singularities at or (or both) see Sidi (2004). See also Weniger (2007).
For an extension to integrals with Cauchy principal values see Elliott (1998).
## §2.10(ii) Summation by Parts
The formula for summation by parts is
2.10.9
where
2.10.10
This identity can be used to find asymptotic approximations for large when the factor changes slowly with , and is oscillatory; compare the approximation of Fourier integrals by integration by parts in §2.3(i).
### ¶ Example
2.10.11
where and are real constants with .
As a first estimate for large
according as , , or see (2.10.7), (2.10.8). With , ,
and
2.10.14
Since
2.10.15
for any real constant and the set of all positive integers , we derive
From this result and (2.10.12)
2.10.17
Then replacing by and resubstituting in (2.10.16), we have
which is a useful approximation when .
For extensions to , higher terms, and other examples, see Olver (1997b, Chapter 8).
## §2.10(iii) Asymptotic Expansions of Entire Functions
The asymptotic behavior of entire functions defined by Maclaurin series can be approached by converting the sum into a contour integral by use of the residue theorem and applying the methods of §§2.4 and 2.5.
### ¶ Example
From §§16.2(i)16.2(ii)
We seek the behavior as . From (1.10.8)
where comprises the two semicircles and two parts of the imaginary axis depicted in Figure 2.10.1.
Figure 2.10.1: -plane. Contour .
From the identities
and Cauchy’s theorem, we have
where denote respectively the upper and lower halves of . (5.11.7) shows that the integrals around the large quarter circles vanish as . Hence
the last step following from when is on the interval , the imaginary axis, or the small semicircle. By application of Laplace’s method (§2.3(iii)) and use again of (5.11.7), we obtain
For generalizations and other examples see Olver (1997b, Chapter 8), Ford (1960), and Berndt and Evans (1984). See also Paris and Kaminski (2001, Chapter 5) and §§16.11(i)16.11(ii).
## §2.10(iv) Taylor and Laurent Coefficients: Darboux’s Method
Let be analytic on the annulus , with Laurent expansion
What is the asymptotic behavior of as or ? More specially, what is the behavior of the higher coefficients in a Taylor-series expansion?
These problems can be brought within the scope of §2.4 by means of Cauchy’s integral formula
where is a simple closed contour in the annulus that encloses . For examples see Olver (1997b, Chapters 8, 9).
However, if is finite and has algebraic or logarithmic singularities on , then Darboux’s method is usually easier to apply. We need a “comparison function” with the properties:
1. (a)
is analytic on .
2. (b)
is continuous on .
3. (c)
The coefficients in the Laurent expansion
have known asymptotic behavior as .
By allowing the contour in Cauchy’s formula to expand, we find that
Hence by the Riemann–Lebesgue lemma (§1.8(i))
This result is refinable in two important ways. First, the conditions can be weakened. It is unnecessary for to be continuous on : it suffices that the integrals in (2.10.28) converge uniformly. For example, Condition (b) can be replaced by:
1. (b´)
On the circle , the function has a finite number of singularities, and at each singularity , say,
where is a positive constant.
Secondly, when is times continuously differentiable on the result (2.10.29) can be strengthened. In these circumstances the integrals in (2.10.28) are integrable by parts times, yielding
Furthermore, (2.10.31) remains valid with the weaker condition
in the neighborhood of each singularity , again with .
### ¶ Example
Let be a constant in and denote the Legendre polynomial of degree . From §14.7(iv)
The singularities of on the unit circle are branch points at . To match the limiting behavior of at these points we set
Here the branch of is continuous in the -plane cut along the outward-drawn ray through and equals at . Similarly for . In Condition (c) we have
and in the supplementary conditions we may set . Then from (2.10.31) and (5.11.7)
For higher terms see §18.15(iii).
For uniform expansions when two singularities coalesce on the circle of convergence see Wong and Zhao (2005).
For other examples and extensions see Olver (1997b, Chapter 8), Olver (1970), Wong (1989, Chapter 2), and Wong and Wyman (1974). See also Flajolet and Odlyzko (1990). | 2013-05-21T10:27:36 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9414148330688477, "perplexity": 1300.8829677916362}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368699881956/warc/CC-MAIN-20130516102441-00030-ip-10-60-113-184.ec2.internal.warc.gz"} |
https://www.peertechzpublications.com/articles/ABSE-1-102.php | ISSN: 2641-3027
##### Archive of Biomedical Science and Engineering
Research Article Open Access Peer-Reviewed
# Coronary Artery Disease Diagnosis Using Supervised Fuzzy C-Means with Differential Search Algorithm-based Generalized Minkowski Metrics
### Maryam Negahbani1, Sanaz Joulazadeh2, Hamid Reza Marateb3* and Marjan Mansourian4
1Department of Mathematical Sciences, University of Isfahan, Isfahan, Iran
2Department of Electrical Engineering, University of Isfahan, Isfahan, Iran
3Department of Biomedical Engineering, Faculty of Engineering, University of Isfahan, Isfahan, Iran
4Department of Biostatistics and Epidemiology, School of Public Health, Isfahan University of Medical Sciences, Isfahan, Iran
*Corresponding author: Hamid Reza Marateb, Biomedical Engineering Department, Engineering Faculty, the University of Isfahan, Hezar Jerib st, 81746-73441, Isfahan, Iran; Tel: +98-31-37935616; Fax: +98-31-37932771; E-mail: [email protected]
Received: 04 April, 2015 | Accepted: 04 June, 2015 | Published: 08 June, 2015
Keywords: Coronary artery disease; Differential search algorithm; Generalized minkowski metrics; Multiple logistic regression; Supervised fuzzy C-means
Cite this as
Negahbani M, Joulazadeh S, Marateb HR, Mansourian M (2015) Coronary Artery Disease Diagnosis Using Supervised Fuzzy C-Means with Differential Search Algorithm-based Generalized Minkowski Metrics. Biomed Sci Eng 1(1): 006-014. DOI: 10.17352/abse.000002
Introduction: Coronary Artery Disease (CAD), one of the leading causes of death, is narrowing the walls of the coronary arteries. Angiography is the most accurate but invasive and costly CAD diagnosis method associated with mortality. The aim of this study was to design a computer-based non-invasive CAD diagnosis system.
Methods: In this work, a dataset from Cleveland clinic foundation, containing 303 patients and 20 features, was used. Supervised Fuzzy C-means (SFCM) classification was used to design a classifier for CAD diagnosis. The Generalized Minkowski Metrics (GMM) was used to handle objects containing different measurement scale features. The performance of the SFCM was assessed with/without Statistical Feature Selection (SFS). The weights of the GMM, i.e. the significance of different features, beside other classifier parameters were tuned using Differential Search Algorithm (DSA), and the validity of the proposed classifier was further investigated. The hold-out and 10-fold cross validation were used for the performance assessment.
Result: The average accuracy of the base classifier (SFCM + GMM) was 79% (hold-out validation). It increased to 82% when using SFS. The average accuracy, sensitivity and specificity of the DSA-based classifier were 88%, 86% and 88%, respectively (cross-validation).
Conclusion: The most important features were the number of major vessels colored by fluoroscopy, the family history of CAD, peak exercise systolic blood pressure, maximum exercise heart rate achieved, chest pain type, resting heart rate, Fasting Blood Sugar and gender. This classifier showed substantial agreement with the angiographic results. The hybrid diagnosis system is thus promising. However, it is necessary to improve its reliability.
### Abbreviations
CAD: Coronary Artery Disease; DSA: Differential Search Algorithm; GMM: Generalized Minkowski Metrics; HDL: High-density lipoprotein; LDL: Low-density lipoprotein; MLR: Multiple Logistic Regression; PSO: Particle Swarm Optimization; SFCM: Supervised Fuzzy C-Means
### Introduction
Coronary Artery disease (CAD), the most common type of heart disease, is one of the leading causes of death in industrialized countries and is rapidly achieving the same dubious distinction in developing nations as well [1].
CAD is the result of the accumulation of plaques within the walls of the coronary arteries supplying blood to the myocardium [2]. Blockage of one or more coronary arteries interrupts the flow of the blood to the heart, which causes heart attack [3]. The CAD is considered when narrowing of at least one of the coronary arteries is more than 50% [4].
The CAD risk factors have been identified over the past several decades include abnormal levels of circulating cholesterol, hypertension, cigarette smoking, diabetes, male gender, postmenopausal state, advancing age, sedentary lifestyle, obesity, and a positive family history of premature vascular disease. Moreover, new risk factors have been emerged as elevated blood levels of homocysteine, fibrinogen, inflammation and infection, atherogenic lipoprotein phenotype, elevated levels of lipoprotein, insulin resistance syndrome, psychosocial factors and a number of genetic polymorphisms [5].
There are several diagnostic tools for CAD [6-8]. Some of the general diagnostic tests include physical examination, lab tests, Electrocardiogram (ECG), echocardiogram, stress test, electron beam computed tomography, coronary angiography and cardiac catheterization. One of the major limitations of ECG is the undiagnosed symptoms of CAD. On the other hand, another alternative invasive methodology, angiogram, is painful and discomfort to the patients. Furthermore, the above mentioned procedures take a lot of cost, time and effort [9].
Computer aided diagnostic methods which extract relevant features and use them in classifiers for automated detection of diseases, can overcome such difficulties. Such techniques are noninvasive and provide reproducible and objective diagnosis, and hence, can prove to be valuable adjunct tools in clinical practice [9].
Yan et al. used an improved back propagation algorithm to train the CAD medical diagnosis system [10]. A novel inference engine named fuzzy-evidential hybrid inference engine proposed by Khatibi et al., used Demister–Shafer theory of evidence and fuzzy sets theory to diagnose CAD. This hybrid engine precisely modeled the information’s vagueness and decision making’s uncertainty and through information fusion, provided accurate results [11]. A fuzzy expert system based on particle swarm optimization (PSO) was developed by Muthukaruppan et al., in order to classify heart disease and healthy condition. In the proposed method, the significant attributes and fuzzy rules were extracted using the decision tree algorithm [12]. Giri et al., proposed a methodology for the automatic detection of normal and CAD using heart rate signals. It was shown that Gaussian Mixture Model classifier had the best results among the three other classifiers Support Vector Machine, Probabilistic Neural Network and K-Nearest Neighbor [9]. Using feature selection and extraction algorithm, Alizadehsani et al., enriched the dataset. Then, Information Gain and confidence were used to determine the effectiveness of features on CAD [13].
In this study, we proposed an automated medical diagnosis system based on the statistical feature selection, supervised fuzzy c-means (SFCM) and Generalized Minkowski Metrics (GMM). Since the features used for CA diagnosis have different measurement scales (nominal, ordinal or interval), a mixed-type data distance metric was used. A statistical feature selection method was used to reduce the feature space. Alternatively, the weights of the input features were tuned on the GMM using a novel stochastic optimization method called Differential Search Algorithm (DSA) and the important features were selected. The data-set, methodologies and the validation procedure will be studied at the following sections.
### Materials and Methods
##### Experimental methods
In this work, the CAD dataset from the University of California (UCI, Irvine), available online, taken from the Cleveland Clinic Foundation datasets [14-17], was used. This database consisted of 303 records with 76 attributes (features), among which 13 to 20 features have been widely used in the literature [12]. The experimental protocol of recording the dataset was mentioned elsewhere in details [14,18]. A number of 303 consecutive patients referred for coronary angiography at the Cleveland Clinic between May 1981 and September 1984, without the history of prior myocardial infarction or known volvuli or cardiomyopathy diseases, participated in the experiment. Different demographic and clinical attributes (some of which were listed in (Table 1)) were recorded from the CAD (case) and healthy (control) subjects [19]. When at least one of the coronary arteries narrowed more than 50%, shown by angiography, the CAD was considered in the subjects [4]. The aim of the study was to design a computer-based CAD diagnosis system using 30 recorded features whose outcome had acceptable agreement with that of coronary angiography. In the next section, the Fuzzy C-means (FCM) data mining techniques are introduced.
##### Fuzzy C-means (FCM) Algorithm in clinical applications
Risk factors are the smallest units indicating the existence of a disease. A syndrome, on the other hand, is a collection, a set, or a cluster of concurrent risk factors, which together indicate the presence and the nature of the disease. Here the main question is that what the relation between these risk factors and a specific syndrome is. Classification and clustering are therefore basic concerns in medicine. Classification depends on the definition of the classes and on the required degree of affiliation of their elements [20].
Clustering algorithms are generally divided into two groups. First, hard partitioning algorithms which are based on classical set theory; they require that an object either does or does not belong to a cluster. Soft clustering methods however, allow the objects to belong to several clusters simultaneously with different degrees of membership [21]. Fuzzy clustering methods are one of the well-known methods of soft clustering which are vastly used in solving medical diagnosis problems. In medicine, there are usually imprecise conditions and highly overlapping classes and therefore fuzzy methods seem to be more suitable than crisp ones [20].
FCM algorithm was first introduced by Bezdek as the enhancement to the classical K-means clustering [22]. This algorithm estimates the membership function of the object k to the clusters i (${u}_{ik}\ge 0$ ) to minimize the following cost function [23]:
Where dik is the distance measure of kth data point from ith cluster center and parameters c, n and m ≥ 1 are the number of clusters and objects in the dataset and the fuzzy coefficient, respectively. In the probabilistic FCM, the following constrain must be met when optimizing the above cost function:
The FCM algorithm iteratively estimates the cluster centers and the membership functions to minimize the cost function (Jr) which could be found elsewhere in details [23].
Despite all the benefits of using FCM as the clustering core algorithm, it is still a blind method and may misclassify the input data. Thus it is necessary to train the algorithm in a way that induces a meaningful convergence. As a result, the classification will be even more accurate.
In the original FCM the data distance to the cluster centers are normally calculated using standard Euclidean distance. In our case, each object is a vector of multiple risk factors with various measurement scales types in different ranges, hence using the classic Euclidean distance is not appropriate [24]. Basically, there are three major data types in clinical data sets: nominal, discrete ordinal, and Interval. Nominal scales are only used for non-ranked qualitative classification e.g. gender, blood type, and health condition. A discrete–ordinal scale is a nominal variable, but the different states are ordered in a meaningful sequence e.g. the slope of the peak exercise ST segment. Interval scales are measured on a linear scale e.g. BMI (Body Mass Index) and age. It is important to define a distance measure to balance all these differences in a way that no feature lessens the other features’ effect or vice versa.
##### SFCM algorithm
The class labels provide a useful guidance during training procedure. Hence, it is necessary to use the labeled samples in training phase and unlabeled samples in testing phase to improve the performance of FCM. This idea led to the development of a new algorithm called Supervised Fuzzy C-Means (SFCM) algorithm, a slight modification of FCM [25].
The main goal of SFCM is to use the labeled data samples to guide the iterative optimization procedure. In this method, a known fixed set of categories and category-labeled training data are used to induce a classification function. The determination of fuzzy partition matrix U (dividing N data sets into C classes) using Supervised Fuzzy C-Means clustering is an iterative optimization procedure. The objective function of SFCM classification is defined as:
Where U is the fuzzy partition matrix, V is the cluster center, fik is the membership degree of kth labeled sample belonging to the ith cluster (value is either 0 or 1).
The coefficient ‘a’ denotes the scaling factor. The role of ‘a’ is to maintain a balance between supervised and unsupervised component within the optimization procedure and parameter ‘m’ controls the amount of fuzziness in the classification. The typical value of m is 2 and a=L/n, L denotes the size of labeled samples [25]. However, it is better to tune these two parameters based on the properties of the dataset. Function Jm can take a large number of values, the smallest one being associated with the best clustering.
An effective algorithm for supervised fuzzy classification is discussed herein. The steps of algorithm are as below [20,25]:
1) Initiate fuzzy partition matrix, U(0), with random values between 0 and 1 and fix the number of cluster centers as the number of outcome classes.
2) Start the iterative procedure and set the iteration counter to one.
3) Calculate the cluster centers using the following equation:
Where, Vij(t) represents the ith cluster center of jth feature which j changes from 1 to m (number of features), and Zkj(train) is the kth data instance corresponding to the mth selected feature variable.
4) Calculate the distance between ith cluster center and kth dataset, distance measured with Euclidean Distance as follows:
5) Update the fuzzy partition matrix for the next iteration given by the following equation:
For test set samples, whose class labels are unknown, the fuzzy partition matrix is calculated as follows:
6) When ‖U(t+1) - U(t)‖ ≤ ε (ε is the iterative accuracy) has achieved, Stop the iteration; In this case outputs will be v (cluster center) and U (fuzzy matrix), otherwise return to step 3.
##### Statistical Feature Selection (SFS)
In many classification problems, especially in the biomedical domain, high dimensional data with few observations are used [26]. This can lead to lower classification accuracy and clusters of poor quality. High dimensional data is also a serious problem for many classification algorithms due to its high computational cost, memory usage andthe curse of dimensionality [27].
Since most of the features are redundant or irrelevant, feature selection method (FS) is used to pick a subset of features that are relevant to the target concept [28]. In this work, a statistical FS method entitled as Multiple Logistic Regression (MLR) was used, which is widely used to identify relevant risk factors in epidemiological studies. MLR, known as feature vector machine in machine learning, can be used to select statistically significant features. It not only considers significant features that provide acceptable discrimination between two classes, but it also takes into account the correlation between features. After running MLR on the input features (excluding the intercept point in the analysis), the selected features were used in the tested classifier [2,29,30].
##### Measurement scale
It is impossible to perform any arithmetic operation on nominal data because it has no order. The only Operation defined here is the equality. The distance of two nominal instances A and B is 1, if A equals B, and 0 otherwise.
For interval scales, it is possible to calculate the distance with standard norm definitions. The distance between two data samples A and B from a given interval I, is defined as |A-B|. As the interval size could be different between multiple features, it is important to normalize the distances relative to the interval size given as |A-B| / |I|.
Discrete–ordinal scale is a nominal variable, but the different states are ordered in a meaningful sequence. Ordinal data has order, but the intervals between scale points may be uneven. But still, the distance of two samples lying in the same interval is computed similar to that of interval distance i.e. |A-B| / |I|. Now, each feature is normalized to a value between 0 and 1.
Note that |I| is calculated by subtracting the maximum and minimum values herein. The l1-norm was then used to combine the distance between different transformed features, simply known as GMM in the literature [31,32]. Thus, the GMM distance definition between two feature vectors A and B, could be given as below:
Where d is the number of dimensions, Ψ is the distance function for each feature which varies according to its measurement scale, and Ck are weights. The weights could be either set to the value of unity or tuned using an optimization algorithm. Accordingly, the features’ weights were set to unity when using GMM+SFCM with/without MLR. Alternatively, instead of using SFS, all of the features were used and their weights were calculated and the features with small value of weights were neglected. For the later approach, it is necessary to use an efficient optimization algorithm, discussed at the next section.
##### Differential Search Algorithm (DSA)
DSA is an optimization algorithm developed by P. Civicioglu simulating the Brownian-like random-walk movement used by an organism to migrate [33]. The motivation of DSA, like many population-based stochastic optimization algorithms, was taken from the nature. Many living organisms show annual migration. In this migration, super organism is constituted containing large number of individuals. The movement of a super organism could be illustrated by a Brownian-like random-walk model [33,34]. In DSA, the population contains random solutions. The migration is performed to the global optimum of the cost function. At each iteration, some of the populations are selected. They move based on a Brownian-like random walk model [34]. DSA is simple to implement and was shown to have acceptable performance in variety of the optimization problems in comparison with that of other traditional optimization algorithms while it is not too sensitive to the initialization of its parameters [33].
We have used DSA to optimize the parameters of GMM and SFCM. The cost function was the absolute error rate of the classifier on the training set. The initial setting of the DSA used in our study was similar to that of P. Civicioglu [33]. Briefly, the size of the population was set to 30, and the maximum number of function evaluation value (i.e. the number of times that the cost function was called in the program) as the only stopping criterion was 2,000,000.
##### Performance measures for classification
The performance of a classifier could be evaluated by computing the number of correctly recognized CAD subjects (TP: True Positives), the number of correctly recognized healthy subjects (TN: True Negatives), and examples that either were incorrectly assigned to the CAD class (FP: False Positives) or that were missed as class examples (FN: False Negatives). These four counts constitute the information-theory formulas to accurately measure the performance of the classification [35,36].
### Results
The demographic information of the Cleveland CAD data was shown in (Table 1) for the case (CAD) and control (healthy) groups. To assess the performance of the base classifier, the main dataset was randomly divided into two roughly equal size datasets, namely dataset 1 and dataset 2 (hold-out validation method [23]). The best Accuracy (Acc) achieved when tuning on the dataset 1 and testing on the dataset 2 and vice versa in ten runs of the SFCM algorithm with GMM distance measure (unity weights) was shown in (Table 2). The maximum number of iterations was set to 100 in all the classifiers. The scaling factor (a) was tuned in the training set using exhaustive grid search (a=0.8) while the value of the fuzziness parameter (m) was set to 2 in the base classifier. The overall percentage accuracy (the average Acc of the classifier on dataset 2 when it was tuned on dataset 1 and vice versa) in the base classifier was 79%. The average Sensitivity and Specificity of the base classifier were 71% and 84%, respectively.
Table 3 shows the results of running the algorithm with SFS. MLR revealed that following significant features: gender, cp (chest pain type), trestbps (resting systolic blood pressure), thalach (maximum exercise heart rate achieved), slope (the slope of the peak exercise ST segment), ca (number of major vessels (0-3) colored by fluoroscopy), and thal (thallium-201 stress scintigraphy). The overall accuracy for SFCM-SFS was 82%. The average Sensitivity and Specificity of this classifier were 85% and 82%, respectively.
Finally, DSA optimization method was used to tune the features’ weights, the fuzziness parameter and the scaling factor. The cost function was set as the absolute error rate of the classifier (SFCM+GMM) (i.e. 1-Acc) on the training set. Guarding against Type III error [37], 10-fold cross-validation [23] was used to assess the performance of the proposed hybrid classifier (Table 4). The average Accuracy, Sensitivity and Specificity of this classifier were 88%, 86%, and 88% respectively. The McNemar’s test [23] revealed that the performance of the hybrid classifier was significantly better than the base classifier (p_value<0.05) but comparable with that of SFS+SFCM. Meanwhile, Multi-fold cross validation was used instead of leave-one-out, since it is proven to have better performance in terms of accuracy and efficiency [23].
The values of the parameters of the hybrid classifier tuned using DSA were shown in Table 5. The most important features (feature weight w>0.5) were listed in the descending order: the number of major vessels colored by fluoroscopy (w=1), the family history of CAD (w=1), peak exercise systolic blood pressure (w=0.89), maximum exercise heart rate achieved (w=0.87), chest pain type (w=0.82), resting heart rate (w=0.67), Fasting Blood Sugar (w=0.64) and gender (w=0.54). However, the list significant attributes (w<0.1) were age, resting blood pressure, number of cigarettes per day, resting electrocardiographic results, peak exercise diastolic blood pressure, and the slope of the peak exercise ST segment. For the definition, and number of categories of the above attributes the reader is referred to (Table 1).
The overall performance of the hybrid classifier was shown in Table 6. It includes the contingency table (confusion matrix) on the total of 303 subjects. The agreement rate between the results of this classifier and those of the gold standard (i.e. CAD diagnosis using angiography) was assessed based on the Cohen’s kappa coefficient [38]. Substantial agreement was shown between the outcomes of the proposed hybrid classifier and angiography (kappa=0.73) [39].
### Discussion
In this paper, three classification systems were designed for non-invasive CAD diagnosis; among which the hybrid classifier showed better performance (Tables 2-4). This diagnosis system was based on the SFCM classifier in which the distance between objects were calculated using GMM and the parameters of the system (SFCM parameters and GMM weights) were estimated using DSA optimization. Other approaches such as PSO [40] were used for optimization, but DSA showed more accurate results. The Type I error and the power of the hybrid classifier were 0.1 and 86%, respectively. Since the data-set was not totally balanced (i.e. the number of cases and controls were not identical), F1-score measure might be more accurate than the accuracy. The average F1-score during 10-fold cross-validation was 85±10 (%), indicating that the proposed system is accurate. The comparison between the performance of the postposed system and some of the other systems designed on the CAD dataset was shown (Table 7). Some methods had higher accuracy that n that of the proposed system. We compared the result of the method proposed by Muthukaruppan et al. [12]. Although its accuracy was 93%, McNamara’s test showed that it was not significantly higher than our hybrid system (p_value>0.05). Another issue is that among the methods listed in (Table 7), those in which Fuzzy classification was used, showed higher accuracies. Since most or all classificatory concepts in medicine are fuzzy, fuzzy taxonomy was used in our study. Meanwhile, it is very difficult to define sharp borders between various symptoms in the set of all symptoms and between various diseases in the set of diseases [41]. Thus, the framework of fuzzy systems is very useful to deal with the absence of sharp boundaries of the sets of symptoms, diagnoses, and phenomena of diseases [19,42].
The significant features selected by the DSA, were known to be directly involved in CAD. Fluoroscopy is one of the most popular non-invasive CAD diagnosis methods whose accuracy ranges between 35% and 75% in comparison with that of the gold standard (i.e. angiography) in the literature [43,44]. We permed a univariate (i.e. the number of major vessels (0-3) colored by fluoroscopy) classification based on the Receiver Operating Characteristic (ROC) plot. Its accuracy was 75% (Area under Curve: AUC=0.75; cut-off=0.5). The average number of vessels colures were statistically different in the CAD and normal group (independent-samples t-test; p_value 0.05). High value of GMM weights are in agreement with the statistical test. Thus, it was a suitable feature but not enough for accurate classification. The other traditional non-invasive CAD diagnosis method is thallium-201 stress scintigraphy. The prevalence of CAD in three groups of scintigraphy was statistically different (Chi-square test; p_value<0.05). Having designed a decision-tree classifier with scintigraphy feature, the accuracy was 76%. However, due to the directional correlation between fluoroscopy and scintigraphy (Eta=0.3), DSA estimated the fluoroscopy and the scintigraphy wegihts as 1.00 and 0.28. The other clinical variable is ST segment depression used in cardiography. Its eight was zero, indicating that no further information could be extracted by adding this variable. In the lietrature, the ranked order of CAD predictive were cardiac fluoroscopy score, thallium score and extent of Electrocardiography (e.g. ST segment depression) [45,46] which is in agreement with our findings.
CAD is associated with higher morbidity and mortality in women than in men [47]. It was also shown that the incidence of CAD in women aged less than 70 years is lower than their male counterparts [48]. In our study, the percentage of men and women having CAD were 84% and 16%, respectively. Considering that women in the CAD group had the age of 66 years old or lower, this is in agreement with our study. However, women usually have CAD 7 to 10 years later than men [49]. In our data-set, the average age of women and men who had CAD was 60±5 and 55±8 years, respectively. Moreover, gender was a significant feature (w=0.539). Meanwhile, the age by itself was not a significant feature in our study (Table 5; w=0.085). This is in agreement with the fact that the average age of people in the CAD and normal groups was 56±8 and 53±9 years, respectively (Table 1). This is related to the stratified age sampling used in our study.
Although, it is proved that high blood pressure increases the risk of CAD [50], it was not significant in our study. Meanwhile elevated resting heart rate is known as a CAD risk factor, which is in agreement with our findings (w=0.674) [51]. In the literature, the family history of CAD is a major CAD risk factor in adults [52]. This is in agreement with our findings where it had the highest GMM weight (w=1; Table 5). Meanwhile, fasting blood sugar was known as an important determinant of CAD [53], in agreement with our findings where its GMM weight was estimated as 0.641. A high total cholesterol level can increase your risk of cardiovascular disease. However, decisions about when to treat high cholesterol are usually based upon the level of LDL or HDL cholesterol, rather than the level of total cholesterol. This might explain the fact that the weight of the cholesterol was 0.289 in our study. Moreover, total cholesterol/ high-density lipoprotein cholesterol ratio were shown to be associated to CAD rather than cholesterol, by itself [54,55].
Chest pain type (GMM weight of 0.818) was divided into the following categories: Typical angina pectoris, atypical angina, non-anginal pain, and no pain. Typical angina (pain that occurs in the anterior thorax, neck, shoulders, jaw, or arms is precipitated by exertion and relieved within 20 min by rest) was the most common symptom of CAD [18]. It occurs when blood flow to an area of heart is decreased, impairing the delivery of oxygen and vital nutrients to the heart muscle cells. The byproduct of using this inefficient fuel is producing lactic acid that builds up in the muscle and causes pain [56].
The key to a good classification is a dataset containing all the possibly relevant features (i.e. risk factors mentioned in the literature) with enough cases (i.e. suitable sample size). Although the sample size of the Cleveland dataset is rather high, some important features such as BMI, LDL and HDL are missing. Meanwhile, we are going to design an automated CAD risk assessment program, based on the findings of this study, in collaboration with Isfahan Healthy Heart Program [57]. Such a large database, could allow us to investigate the accuracy of the proposed diagnosis system in a broader sense. Another issue is that the performance of the base classifier with/without FS (Tables 2,3) was so different in the first and second scenarios. Having calculated the cluster representatives for the healthy and CAD groups in the first and second datasets, the dataset 1 showed better discrimination in comparison with dataset2 on the whole 20 features and also those selected by the MLR. This is why that performance of the base classifier with/without FS was higher on the data set 1 in the entire training and test procedure. Also, the discrimination with/without FS was not that different. This, in fact, shows that the FS could have selected features with significant discrimination power.
Another step would be developing a web-based online system with which patients/ medical doctors could assess their risk of having CAD at home. These Web-based diagnostic decision support systems have been recently focused in Medicine and are proven to be valuable in identifying the correct diagnosis in complicated cases [58]. There might be two possible approaches to improve the performance of the proposed diagnosis system. First, further features could be defined by considering the interactions between input risk factors/predictors [59] e.g. simply multiplication of the predictors. Second, multiple clusters could be formed for each healthy and CAD class by using mixed-type data clustering methods [24]. Then, supervised FCM could be used with multiple clusters corresponding with two healthy and CAD classes. Extracting supervised classification rules on groups of similar objects could potentially reduce the misclassification rate especially close to the class borderlines. These two approaches will be the focus of our future work.
### Conclusion
The hybrid classifier showed the average accuracy of 87%. The power of the designed diagnosis system was 86%. Type I error (α) was 0.1 and the F-score was 85%. Although the power of the method is acceptable, type I error must be reduced down to 0.05, to introduce a reliable and accurate clinical test which is the focus of the future work. One possible strategy to improve the accuracy of the proposed diagnosis system is using classifier fusion. Combining different reliable classifiers, might improve the accuracy though the fusion procedure. In conclusion, we designed an automated non-invasive CAD diagnosis system based on the Fuzzy theory. The results showed that the proposed system is promising. However, further improvements are needed to be able to use it in clinical laboratories.
This work was supported by the University of Isfahan (MN, SJ, HM) and Isfahan University of medical Sciences (MM).
© 2015 Negahbani M, et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
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## AFFINE TRANSLATION SURFACES IN 3-DIMENSIONAL EUCLIDEAN SPACE SATISFYING $\Delta r_{i}=\lambda _{i}r_{i}$
#### BENDEHIBA SENOUSSI [1] , MOHAMMED BEKKAR [2]
##### 83 275
In this paper we study the affine translation surfaces in 3-dimensional Euclidean space $\mathbb{E}^{3}$ under the condition $\Delta r_{i}=\lambda _{i}r_{i}$, where $\lambda _{i}\in \mathbb{R}$ and $\Delta$ denotes the Laplace operator. We obtain the complete classification for those ones.
Ane translation surfaces, nite type immersion, Laplacian operator
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• [14] M. I. Munteanu and A. I. Nistor, Polynomial translationWeingarten surfaces in 3-dimensional Euclidean space, Proceedings of the VIII International Colloquium on Di erential Geometry, World Scienti c. (2009), 316-320.
• [15] B. Senoussi and M. Bekkar, Helicoidal surfaces in the 3-dimensional Lorentz - Minkowski space $\mathbb{E}_{1}^{3}$ satisfying $\Delta ^{III}r=Ar$, Tsukuba J. Math. 37 (2013), 339 - 353.
• [16] K. Seo, Translation hypersurfaces with constant curvature in space forms, Osaka J. Math. 50 (2013), 631-641.
• [17] S. Stamatakis and H. Al-Zoubi, Surfaces of revolution satisfying $\Delta ^{III}x=Ax$, J. Geom. Graph. 14 (2010), 181-186.
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Konular Mühendislik ve Temel Bilimler Articles Yazar: BENDEHIBA SENOUSSIÜlke: Algeria Yazar: MOHAMMED BEKKARÜlke: Algeria
Bibtex @araştırma makalesi { konuralpjournalmath343312, journal = {Konuralp Journal of Mathematics}, issn = {}, eissn = {2147-625X}, address = {Mehmet Zeki SARIKAYA}, year = {2017}, volume = {5}, pages = {47 - 53}, doi = {}, title = {AFFINE TRANSLATION SURFACES IN 3-DIMENSIONAL EUCLIDEAN SPACE SATISFYING \$\\Delta r\_\{i\}=\\lambda \_\{i\}r\_\{i\}\$}, key = {cite}, author = {BEKKAR, MOHAMMED and SENOUSSI, BENDEHIBA} } APA SENOUSSI, B , BEKKAR, M . (2017). AFFINE TRANSLATION SURFACES IN 3-DIMENSIONAL EUCLIDEAN SPACE SATISFYING $\Delta r_{i}=\lambda _{i}r_{i}$. Konuralp Journal of Mathematics, 5 (2), 47-53. Retrieved from http://dergipark.gov.tr/konuralpjournalmath/issue/28490/343312 MLA SENOUSSI, B , BEKKAR, M . "AFFINE TRANSLATION SURFACES IN 3-DIMENSIONAL EUCLIDEAN SPACE SATISFYING $\Delta r_{i}=\lambda _{i}r_{i}$". Konuralp Journal of Mathematics 5 (2017): 47-53 Chicago SENOUSSI, B , BEKKAR, M . "AFFINE TRANSLATION SURFACES IN 3-DIMENSIONAL EUCLIDEAN SPACE SATISFYING $\Delta r_{i}=\lambda _{i}r_{i}$". Konuralp Journal of Mathematics 5 (2017): 47-53 RIS TY - JOUR T1 - AFFINE TRANSLATION SURFACES IN 3-DIMENSIONAL EUCLIDEAN SPACE SATISFYING $\Delta r_{i}=\lambda _{i}r_{i}$ AU - BENDEHIBA SENOUSSI , MOHAMMED BEKKAR Y1 - 2017 PY - 2017 N1 - DO - T2 - Konuralp Journal of Mathematics JF - Journal JO - JOR SP - 47 EP - 53 VL - 5 IS - 2 SN - -2147-625X M3 - UR - Y2 - 2017 ER - EndNote %0 Konuralp Journal of Mathematics AFFINE TRANSLATION SURFACES IN 3-DIMENSIONAL EUCLIDEAN SPACE SATISFYING $\Delta r_{i}=\lambda _{i}r_{i}$ %A BENDEHIBA SENOUSSI , MOHAMMED BEKKAR %T AFFINE TRANSLATION SURFACES IN 3-DIMENSIONAL EUCLIDEAN SPACE SATISFYING $\Delta r_{i}=\lambda _{i}r_{i}$ %D 2017 %J Konuralp Journal of Mathematics %P -2147-625X %V 5 %N 2 %R %U ISNAD SENOUSSI, BENDEHIBA , BEKKAR, MOHAMMED . "AFFINE TRANSLATION SURFACES IN 3-DIMENSIONAL EUCLIDEAN SPACE SATISFYING $\Delta r_{i}=\lambda _{i}r_{i}$". Konuralp Journal of Mathematics 5 / 2 (Ekim 2017): 47-53. | 2018-09-22T03:47:15 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6201512813568115, "perplexity": 6438.258492037768}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-39/segments/1537267158011.18/warc/CC-MAIN-20180922024918-20180922045318-00351.warc.gz"} |
https://lammps.sandia.gov/doc/fix_precession_spin.html | # fix precession/spin command
## Syntax
fix ID group precession/spin style args
• ID, group are documented in fix command
• precession/spin = style name of this fix command
• style = zeeman or anisotropy or cubic
zeeman args = H x y z
H = intensity of the magnetic field (in Tesla)
x y z = vector direction of the field
anisotropy args = K x y z
K = intensity of the magnetic anisotropy (in eV)
x y z = vector direction of the anisotropy
cubic args = K1 K2c n1x n1y n1x n2x n2y n2z n3x n3y n3z
K1 and K2c = intensity of the magnetic anisotropy (in eV)
n1x to n3z = three direction vectors of the cubic anisotropy
## Examples
fix 1 all precession/spin zeeman 0.1 0.0 0.0 1.0
fix 1 3 precession/spin anisotropy 0.001 0.0 0.0 1.0
fix 1 iron precession/spin cubic 0.001 0.0005 1.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 1.0
fix 1 all precession/spin zeeman 0.1 0.0 0.0 1.0 anisotropy 0.001 0.0 0.0 1.0
## Description
This fix applies a precession torque to each magnetic spin in the group.
Style zeeman is used for the simulation of the interaction between the magnetic spins in the defined group and an external magnetic field:
with mu0 the vacuum permeability, muB the Bohr magneton (muB = 5.788 eV/T in metal units).
Style anisotropy is used to simulate an easy axis or an easy plane for the magnetic spins in the defined group:
with n defining the direction of the anisotropy, and K (in eV) its intensity. If K>0, an easy axis is defined, and if K<0, an easy plane is defined.
Style cubic is used to simulate a cubic anisotropy, with three possible easy axis for the magnetic spins in the defined group:
with K1 and K2c (in eV) the intensity coefficients and n1, n2 and n3 defining the three anisotropic directions defined by the command (from n1x to n3z). For n1 = (100), n2 = (010), and n3 = (001), K1 < 0 defines an iron type anisotropy (easy axis along the (001)-type cube edges), and K1 > 0 defines a nickel type anisotropy (easy axis along the (111)-type cube diagonals). K2^c > 0 also defines easy axis along the (111)-type cube diagonals. See chapter 2 of (Skomski) for more details on cubic anisotropies.
In all cases, the choice of (x y z) only imposes the vector directions for the forces. Only the direction of the vector is important; it’s length is ignored (the entered vectors are normalized).
Those styles can be combined within one single command line.
Restart, fix_modify, output, run start/stop, minimize info:
By default, the energy associated to this fix is not added to the potential energy of the system. The fix_modify energy option is supported by this fix to add this magnetic potential energy to the potential energy of the system,
fix 1 all precession/spin zeeman 1.0 0.0 0.0 1.0
fix_modify 1 energy yes
This fix computes a global scalar which can be accessed by various output commands.
## Restrictions
The precession/spin style is part of the SPIN package. This style is only enabled if LAMMPS was built with this package, and if the atom_style “spin” was declared. See the Build package doc page for more info. | 2019-07-23T01:12:41 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6294645071029663, "perplexity": 3784.9126283280666}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-30/segments/1563195528635.94/warc/CC-MAIN-20190723002417-20190723024417-00105.warc.gz"} |
https://docs.dea.ga.gov.au/notebooks/Real_world_examples/Change_detection.html | Detecting change in Australian forestry¶
• Compatability: Notebook currently compatible with both the NCI and DEA Sandbox environments
• Products used: s2_ard_granule, s2b_ard_granule
Background¶
Effective management of Australia’s forests is critical for balancing environmental protection and sustainable growth of the industry. Methods for detecting meaningful and significant change in forests are important for those who manage and monitor large areas of forest.
On-the-ground monitoring can be expensive and time-consuming, especially when forests are in difficult-to-navigate terrain. Aerial photography and LiDAR can provide detailed information about forests, but are often extremely expensive to acquire, even over small areas.
Sentinel-2 use case¶
Satellite imagery from the EU Copernicus Sentinel-2 mission is freely available and has a revisit time over Australia of ~5 days. Its 10 metre resolution makes it perfect for monitoring fine changes over very large areas of land. The archive of Sentinel-2 data stretches back to 2015, meaning that there is a good amount of data for change detection, allowing us to average out or focus on seasonal changes.
Description¶
In this example, we measure the presence of vegetation from Sentinel-2 imagery and apply a hypothesis test to identify areas of significant change (along with the direction of the change). The worked example takes users through the code required to do the following:
1. Load cloud-free Sentinel-2 images for an area of interest
2. Compute an index to highlight presence of vegetation (NDVI)
3. Apply a statistical hypothesis test to find areas of significant change
4. Visualise the statistically significant areas.
Getting started¶
To run this analysis, run all the cells in the notebook, starting with the “Load packages” cell.
After finishing the analysis, return to the “Analysis parameters” cell, modify some values (e.g. choose a different location or time period to analyse) and re-run the analysis. There are additional instructions on modifying the notebook at the end.
Load key Python packages and any supporting functions for the analysis.
[1]:
%matplotlib inline
import sys
import datacube
import numpy as np
import xarray as xr
import pandas as pd
import matplotlib.pyplot as plt
from scipy import stats
from datacube.helpers import write_geotiff
from datacube.utils.geometry import CRS
sys.path.append("../Scripts")
from dea_bandindices import calculate_indices
from dea_plotting import display_map
from dea_plotting import rgb
Connect to the datacube¶
Activate the datacube database, which provides functionality for loading and displaying stored Earth observation data.
[2]:
dc = datacube.Datacube(app="Change_detection")
Analysis parameters¶
The following cell sets the parameters, which define the area of interest and the length of time to conduct the analysis over. There is also a parameter to define how the data is split in time; the split yields two non-overlapping samples, which is a requirement of the hypothesis test we want to run (more detail below). The parameters are:
• latitude: The latitude range to analyse (e.g. (-35.271, -35.331)). For reasonable loading times, make sure the range spans less than ~0.1 degrees.
• longitude: The longitude range to analyse (e.g. (149.256, 149.356)). For reasonable loading times, make sure the range spans less than ~0.1 degrees.
• time: The date range to analyse (e.g. ('2015-01-01', '2019-09-01')). Note that Sentinel-2 data is not available in Australia prior to 2015. For reasonable results, the range should span at least two years to prevent detecting seasonal changes.
• time_baseline: The date at which to split the total sample into two non-overlapping samples (e.g. '2017-12-01'). For reasonable results, pick a date that is about halfway between the start and end dates specified in time.
If running the notebook for the first time, keep the default settings below. This will demonstrate how the analysis works and provide meaningful results. The example covers the Kowen Forest, a commercial pine plantation in the Australian Capital Territory.
To run the notebook for a different area, make sure Sentinel-2 data is available for the chosen area using the DEA Explorer. Use the drop-down menu to check both Sentinel-2A (s2a_ard_granule) and Sentinel-2B (s2b_ard_granule).
[3]:
# Define the area of interest
latitude = (-35.271, -35.331)
longitude = (149.256, 149.356)
# Set the range of dates for the complete sample
time = ('2015-01-01', '2019-09-01')
# Set the date to separate the data into two samples for comparison
time_baseline = '2017-12-01'
View the selected location¶
The next cell will display the selected area on an interactive map. The red border represents the area of interest of the study. Zoom in and out to get a better understanding of the area of interest. Clicking anywhere on the map will reveal the latitude and longitude coordinates of the clicked point.
[4]:
display_map(x=longitude, y=latitude)
[4]:
The first step in the analysis is to load Sentinel-2 data for the specified area of interest and time range. This uses the pre-defined load_ard utility function. This function will automatically mask any clouds in the dataset, and only return images where more than 70% of the pixels were classified as clear. When working with Sentinel-2, the function will also combine and sort images from both Sentinel-2A and Sentinel-2B.
Please be patient. The data may take a few minutes to load and progress will be indicated by text output. The load is complete when the cell status goes from [*] to [number].
[5]:
# Choose products to load
# Here, the Sentinel-2A and Sentinel-2B products are chosen
products = ['s2a_ard_granule', 's2b_ard_granule']
# Specify the parameters to pass to the load query
query = {
"x": longitude,
"y": latitude,
"time": time,
"measurements": [
"nbart_red", # Red band
"nbart_green", # Green band
"nbart_blue", # Blue band
"nbart_nir_1", # Near-infrared band
],
"output_crs": "EPSG:3577",
"resolution": (-10, 10)
}
ds_s2 = load_ard(dc, products=products, min_gooddata=0.7, **query)
Loading s2a_ard_granule data
Filtering to 64 out of 132 observations
Filtering to 39 out of 78 observations
Combining and sorting data
Returning 103 observations
Once the load is complete, examine the data by printing it in the next cell. The Dimensions argument revels the number of time steps in the data set, as well as the number of pixels in the x (longitude) and y (latitude) dimensions.
[6]:
print(ds_s2)
<xarray.Dataset>
Dimensions: (time: 103, x: 990, y: 784)
Coordinates:
* x (x) float64 1.561e+06 1.561e+06 ... 1.571e+06 1.571e+06
* y (y) float64 -3.958e+06 -3.958e+06 ... -3.966e+06 -3.966e+06
* time (time) datetime64[ns] 2015-09-13T00:06:33.742500 ... 2019-08-28T00:02:49.024000
Data variables:
nbart_red (time, y, x) float32 643.0 503.0 496.0 ... 724.0 678.0 737.0
nbart_green (time, y, x) float32 543.0 494.0 459.0 ... 641.0 518.0 605.0
nbart_blue (time, y, x) float32 423.0 359.0 349.0 ... 409.0 378.0 439.0
nbart_nir_1 (time, y, x) float32 1877.0 1437.0 1447.0 ... 2152.0 2314.0
Attributes:
crs: EPSG:3577
Plot example timestep in true colour¶
To visualise the data, use the pre-loaded rgb utility function to plot a true colour image for a given time-step. White spots in the images are where clouds have been masked out.
The settings below will display images for two time steps, one in early January 2016, one in late December 2018. Can you spot any areas of change?
Feel free to experiement with the values for the initial_timestep and final_timestep variables; re-run the cell to plot the images for the new timesteps. The values for the timesteps can be 0 to one fewer than the number of time steps loaded in the data set. The number of time steps is the same as the total number of observations listed as the output of the cell used to load the data.
Note: If the location and time are changed, you may need to change the intial_timestep and final_timestep parameters to view images at similar times of year.
[7]:
# Set the timesteps to visualise
initial_timestep = 1
final_timestep = 76
# Generate RGB plots at each timestep
rgb(ds_s2, index=[initial_timestep, final_timestep])
Compute band indices¶
This study measures vegetation through the normalised difference vegetation index (NDVI), which can be calculated using the predefined calculate_indices utility function. This index uses the ratio of the red and near-infrared (NIR) bands to identify live green vegetation. The formula is
\begin{aligned} \text{NDVI} = \frac{\text{NIR} - \text{Red}}{\text{NIR} + \text{Red}}. \end{aligned}
When interpreting this index, high values indicate vegetation, and low values indicate soil or water.
[8]:
# Calculate NDVI and add it to the loaded dataset
ds_s2 = calculate_indices(ds_s2, 'NDVI', collection='ga_s2_1')
The plots below show the NDVI values for the two selected timesteps used to make the true-colour images above. Use the plots to visually confirm whether NDVI is a suitable index for change detection.
[9]:
# Plot the NDVI values for pixels classified as water for the two dates.
ds_s2.NDVI.isel(time=[initial_timestep, final_timestep]).plot.imshow(
'x', 'y', col='time', cmap='RdYlGn', vmin=0, vmax=1, figsize=(18, 6))
plt.show()
Perform hypothesis test¶
While it is possible to visually detect change between the 2016-01-01 and 2018-12-26 timesteps, it is important to consider how to rigorously check for both positive change in the NDVI (afforestation) and negative change in the NDVI (deforestation).
This can be done through hypothesis testing. In this case,
\begin{split}\begin{aligned} \text{null hypothesis } (H_0) &: \text{no change occurred,} \\ \text{alternative hypothesis } (H_1) &: \text{some change occurred.} \end{aligned}\end{split}
The hypothesis test will indicate where there is evidence for rejecting the null hypothesis. From this, we may identify areas of signficant change, according to a given significance level (covered in more detail below).
Make samples¶
To perform the test, the total sample will be split in two: a baseline sample and a postbaseline sample, which respectively contain the data before and after the time_baseline date. Then, we can test for a difference in the average NDVI between the samples for each pixel in the sample.
The samples are made by selecting the NDVI band from the dataset and filtering it based on whether it was observed before or after the time_baseline date. The number of observations in each sample will be printed. If one sample is much larger than the other, consider changing the time_baseline parameter in the “Analysis parameters” cell, and then re-run this cell. Coordinates are recorded for later use.
[10]:
# Make samples
baseline_sample = ds_s2.NDVI.sel(time=ds_s2['time']<=np.datetime64(time_baseline))
print(f"Number of observations in baseline sample: {len(baseline_sample.time)}")
postbaseline_sample = ds_s2.NDVI.sel(time=ds_s2['time']>np.datetime64(time_baseline))
print(f"Number of observations in postbaseline sample: {len(postbaseline_sample.time)}")
# Record coodrinates for reconstructing xarray objects
sample_lat_coords = ds_s2.coords['y']
sample_lon_coords = ds_s2.coords['x']
Number of observations in baseline sample: 41
Number of observations in postbaseline sample: 62
Test for change¶
To look for evidence that the average NDVI has changed between the two samples (either positively or negatively), we use Welch’s t-test. This is used to test the hypothesis that two populations have equal averages. In this case, the populations are the area of interest before and after the time_baseline date, and the average being tested is the average NDVI. Welch’s t-test is used (as opposed to Student’s t-test) because the two samples in the study may not necessarily have equal variances.
The test is run using the Scipy package’s statistcs library, which provides the ttest_ind function for running t-tests. Setting equal_var=False means that the function will run Welch’s t-test. The function returns the t-statistic and p-value for each pixel after testing the difference in the average NDVI. These are stored as t_stat and p_val inside the t_test dataset for use in the next section.
[11]:
# Perform the t-test on the postbaseline and baseline samples
tstat, p_tstat = stats.ttest_ind(
postbaseline_sample.values,
baseline_sample.values,
equal_var=False,
nan_policy='omit',
)
# Convert results to an xarray for further analysis
t_test = xr.Dataset(
{
't_stat': (['y', 'x'], tstat),
'p_val': (['y', 'x'], p_tstat)
},
coords={
'x': (['x'], sample_lon_coords.values),
'y': (['y'], sample_lat_coords.values)
},
attrs={
'crs': 'EPSG:3577',
})
print(t_test)
<xarray.Dataset>
Dimensions: (x: 990, y: 784)
Coordinates:
* x (x) float64 1.561e+06 1.561e+06 1.561e+06 ... 1.571e+06 1.571e+06
* y (y) float64 -3.958e+06 -3.958e+06 ... -3.966e+06 -3.966e+06
Data variables:
t_stat (y, x) float64 -0.525 -0.4284 -0.9775 -0.6942 ... 6.372 6.523 6.276
p_val (y, x) float64 0.6016 0.67 0.3325 ... 2.725e-08 1.115e-08 4.636e-08
Attributes:
crs: EPSG:3577
Visualise change¶
From the test, we’re interested in two conditions: whether the change is significant (rejection of the null hypothesis) and whether the change was positive (afforestation) or negative (deforestation).
The null hypothesis can be rejected if the $$p$$-value (p_val) is less than the chosen significance level, which is set as sig_level = 0.05 for this analysis. If the null hypothesis is rejected, the pixel will be classified as having undergone significant change.
The direction of the change can be inferred from the difference in the average NDVI of each sample, which is calculated as
\begin{align}\begin{aligned}\text{diff mean} = \text{mean(post baseline)} - \text{mean(baseline)}.\\This means that:\end{aligned}\end{align}
• if the average NDVI for a given pixel is higher in the post baseline sample compared to the baseline sample, then diff_mean for that pixel will be positive.
• if the average NDVI for a given pixel is lower in the post baseline sample compared to the baseline sample, then diff_mean for that pixel will be negative.
Run the cell below to first plot the difference in the mean between the two samples, then plot only the differences that were marked as signficant. Positive change is shown in blue and negative change is shown in red.
[12]:
# Set the significance level
sig_level = 0.05
# Plot any difference in the mean
diff_mean = postbaseline_sample.mean(dim=['time']) - baseline_sample.mean(dim=['time'])
fig, ax = plt.subplots(1, 1, figsize=(7, 5))
diff_mean.plot(cmap='RdBu')
ax.set_title('Any difference in the mean')
plt.show()
# Plot any difference in the mean classified as significant
sig_diff_mean = postbaseline_sample.mean(dim=['time']).where(t_test.p_val < sig_level) - baseline_sample.mean(dim=['time']).where(t_test.p_val < sig_level)
fig, ax = plt.subplots(1, 1, figsize=(7, 5))
sig_diff_mean.plot(cmap='RdBu')
ax.set_title('Statistically significant difference in the mean')
plt.show()
Drawing conclusions¶
Here are some questions to think about:
• What has happened in the forest over the time covered by the dataset?
• Were there any statistically significant changes that the test found that you didn’t see in the true-colour images?
• What kind of activities/events might explain the significant changes?
• What kind of activities/events might explain non-significant changes?
• What other information might you need to draw conclusions about the cause of the statistically significant changes?
Export the data¶
To explore the data further in a desktop GIS program, the data can be output as a GeoTIFF. This requires data to be converted to an xarray and tagged with the appropriate coordinate reference system (crs). The diff_mean product will be saved as “ttest_diff_mean.tif”, and the sig_diff_mean product will be saved as “ttest_sig_diff_mean.tif”. These files can be downloaded from the file explorer to the left of this window (see these instructions).
[13]:
# Make datasets into xarrays for output
diff_mean_out = xr.Dataset({'diff_mean': diff_mean}, attrs={'crs': CRS('EPSG:3577')})
sig_diff_mean_out = xr.Dataset({'sig_diff_mean': sig_diff_mean}, attrs={'crs': CRS('EPSG:3577')})
# Write output to geotiffs
write_geotiff(filename="ttest_diff_mean.tif", dataset=diff_mean_out)
write_geotiff(filename="ttest_sig_diff_mean.tif", dataset=sig_diff_mean_out)
Next steps¶
When you are done, return to the “Analysis parameters” section, modify some values (e.g. latitude, longitude, time or time_baseline) and re-run the analysis. You can use the interactive map in the “View the selected location” section to find new central latitude and longitude values by panning and zooming, and then clicking on the area you wish to extract location values for. You can also use Google maps to search for a location you know, then return the latitude and longitude values by clicking the map.
If you’re going to change the location, you’ll need to make sure Sentinel-2 data is available for the new location, which you can check at the DEA Explorer. Use the drop-down menu to check both Sentinel-2A (s2a_ard_granule) and Sentinel-2B (s2b_ard_granule).
Contact: If you need assistance, please post a question on the Open Data Cube Slack channel or on the GIS Stack Exchange using the open-data-cube tag (you can view previously asked questions here). If you would like to report an issue with this notebook, you can file one on Github.
Compatible datacube version:
[14]:
print(datacube.__version__)
1.7+142.g7f8581cf
Tags¶
Browse all available tags on the DEA User Guide’s Tags Index
Tags: sandbox compatible, NCI compatible, sentinel 2, dea_datahandling, dea_bandindices, dea_plotting, calculate_indices, display_map, load_ard, rgb, NDVI, real world, forestry, change detection, statistics, GeoTIFF, exporting data | 2020-08-06T18:11:25 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 1, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.42869362235069275, "perplexity": 3865.1157807102627}, "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-2020-34/segments/1596439737019.4/warc/CC-MAIN-20200806180859-20200806210859-00236.warc.gz"} |
http://www.legisquebec.gouv.qc.ca/en/showversion/cs/A-3.01?code=se:59&pointInTime=20210107 | ### A-3.01 - Act respecting the accreditation and financing of students’ associations
59. Notwithstanding sections 10.1 and 10.2, a students’ association or students’ association alliance established before 23 June 1983 has the right to be accredited if it satisfies the following conditions:
(1) it is constituted under Part III of the Companies Act (chapter C‐38);
(2) it has received the assessments collected by the educational institution;
(3) it is, as the case may be, the only association that represents the students at the educational institution, or the only students’ association alliance that represents the students’ associations at the institution.
1983, c. 33, s. 59; 1993, c. 10, s. 34; 1999, c. 40, s. 5.
59. Notwithstanding sections 10.1 and 10.2, a students’ association or students’ association alliance established before 23 June 1983 has the right to be accredited if it satisfies the following conditions:
(1) it is incorporated under Part III of the Companies Act (chapter C-38);
(2) it has received the assessments collected by the educational institution;
(3) it is, as the case may be, the only association that represents the students at the educational institution, or the only students’ association alliance that represents the students’ associations at the institution.
1983, c. 33, s. 59; 1993, c. 10, s. 34.
59. Notwithstanding sections 6 and 7, a students’ association or students’ association alliance established before 23 June 1983 has the right to be accredited if it satisfies the following conditions:
(1) it is incorporated under Part III of the Companies Act (chapter C-38);
(2) it has received the assessments collected by the educational institution;
(3) it is, as the case may be, the only association that represents the students at the educational institution, or the only students’ association alliance that represents the students’ associations at the institution.
1983, c. 33, s. 59. | 2021-02-25T20:46:57 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8197284936904907, "perplexity": 4413.709941113121}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178351454.16/warc/CC-MAIN-20210225182552-20210225212552-00467.warc.gz"} |
https://phys.libretexts.org/Bookshelves/College_Physics/Book%3A_College_Physics_(OpenStax)/21%3A_Circuits%2C_Bioelectricity%2C_and_DC_Instruments/21.4%3A_DC_Voltmeters_and_Ammeters | Skip to main content
$$\require{cancel}$$
# 21.4: DC Voltmeters and Ammeters
Voltmeters measure voltage, whereas ammeters measure current. Some of the meters in automobile dashboards, digital cameras, cell phones, and tuner-amplifiers are voltmeters or ammeters. (See Figure.) The internal construction of the simplest of these meters and how they are connected to the system they monitor give further insight into applications of series and parallel connections.
Figure $$\PageIndex{1}$$: The fuel and temperature gauges (far right and far left, respectively) in this 1996 Volkswagen are voltmeters that register the voltage output of “sender” units, which are hopefully proportional to the amount of gasoline in the tank and the engine temperature. (credit: Christian Giersing)
Voltmeters are connected in parallel with whatever device’s voltage is to be measured. A parallel connection is used because objects in parallel experience the same potential difference. (See Figure, where the voltmeter is represented by the symbol V.)
Ammeters are connected in series with whatever device’s current is to be measured. A series connection is used because objects in series have the same current passing through them. (See Figure, where the ammeter is represented by the symbol A.)
Figure $$\PageIndex{2}$$: (a) To measure potential differences in this series circuit, the voltmeter (V) is placed in parallel with the voltage source or either of the resistors. Note that terminal voltage is measured between points a and b. It is not possible to connect the voltmeter directly across the emf without including its internal resistance $$r$$ (b) A digital voltmeter in use. (credit: Messtechniker, Wikimedia Commons)
Figure $$\PageIndex{3}$$: An ammeter (A) is placed in series to measure current. All of the current in this circuit flows through the meter. The ammeter would have the same reading if located between points d and e or between points f and a as it does in the position shown. (Note that the script capital E stands for emf, and $$r$$ stands for the internal resistance of the source of potential difference.)
# Analog Meters: Galvanometers
Analog meters have a needle that swivels to point at numbers on a scale, as opposed to digital meters, which have numerical readouts similar to a hand-held calculator. The heart of most analog meters is a device called a galvanometer, denoted by G. Current flow through a galvanometer, $$I_G$$, produces a proportional needle deflection. (This deflection is due to the force of a magnetic field upon a current-carrying wire.)
The two crucial characteristics of a given galvanometer are its resistance and current sensitivity. Current sensitivity is the current that gives a full-scale deflection of the galvanometer’s needle, the maximum current that the instrument can measure. For example, a galvanometer with a current sensitivity of $$50 \mu A$$ has a maximum deflection of its needle when $$50 \, \mu A$$ flows through it, reads half-scale when $$25 \, \mu A$$ flows through it, and so on.
If such a galvanometer has a $$25 \, \Omega$$ resistance, then a voltage of only $$V = IR = (50 \, \mu A)(25 \, \Omega) = 1.25 \, mV$$ produces a full-scale reading. By connecting resistors to this galvanometer in different ways, you can use it as either a voltmeter or ammeter that can measure a broad range of voltages or currents.
## Galvanometer as Voltmeter
Figure shows how a galvanometer can be used as a voltmeter by connecting it in series with a large resistance, $$R$$. The value of the resistance $$R$$ is determined by the maximum voltage to be measured. Suppose you want 10 V to produce a full-scale deflection of a voltmeter containing a $$25 \, \Omega$$ galvanometer with a $$50-\mu A$$ sensitivity. Then 10 V applied to the meter must produce a current of $$50 \, \mu A$$. The total resistance must be $R_{tot} = R + r = \dfrac{V}{I} = \dfrac{10 \, V}{50 \, \mu A} = 200 \, k\Omega, \, or$$R = T_{tot} - r = 200 \, k\Omega - 25 \, \Omega \approx 200 \, k\Omega.$
($$R$$ is so large that the galvanometer resistance, $$r$$, is nearly negligible.) Note that 5 V applied to this voltmeter produces a half-scale deflection by producing a $$25 \, \mu A$$ current through the meter, and so the voltmeter’s reading is proportional to voltage as desired.
This voltmeter would not be useful for voltages less than about half a volt, because the meter deflection would be small and difficult to read accurately. For other voltage ranges, other resistances are placed in series with the galvanometer. Many meters have a choice of scales. That choice involves switching an appropriate resistance into series with the galvanometer.
Figure $$\PageIndex{4}$$: A large resistance $$R$$ placed in series with a galvanometer G produces a voltmeter, the full-scale deflection of which depends on the choice of $$R$$. The larger the voltage to be measured, the larger $$R$$ must be. (Note that $$r$$ represents the internal resistance of the galvanometer.)
## Galvanometer as Ammeter
The same galvanometer can also be made into an ammeter by placing it in parallel with a small resistance $$R$$, often called the shunt resistance, as shown in Figure. Since the shunt resistance is small, most of the current passes through it, allowing an ammeter to measure currents much greater than those producing a full-scale deflection of the galvanometer.
Suppose, for example, an ammeter is needed that gives a full-scale deflection for 1.0 A, and contains the same $$25-\Omega$$ galvanometer with its $$50-\mu A$$ sensitivity. Since $$R$$ and $$r$$ are in parallel, the voltage across them is the same.
These $$IR$$ drops are $$IR = I_Cr$$ so that $$IR = \frac{I_G}{I} = \frac{R}{r}$$. Solving for $$R$$, and noting that $$I_G$$ is $$50 \, \mu A$$ and $$I$$ is 0.999950 A, we have $R = r\dfrac{I_G}{I} = (25 \, \Omega) \dfrac{50 \, \mu A}{0.999950 \, A} = 1.25 \times 10^{-3} \, \Omega.$
Figure $$\PageIndex{5}$$: A small shunt resistance $$R$$ placed in parallel with a galvanometer G produces an ammeter, the full-scale deflection of which depends on the choice of $$R$$. The larger the current to be measured, the smaller $$R$$ must be. Most of the current ($$I$$) flowing through the meter is shunted through $$R$$ to protect the galvanometer. (Note that $$r$$ represents the internal resistance of the galvanometer.) Ammeters may also have multiple scales for greater flexibility in application. The various scales are achieved by switching various shunt resistances in parallel with the galvanometer—the greater the maximum current to be measured, the smaller the shunt resistance must be.
# Taking Measurements Alters the Circuit
When you use a voltmeter or ammeter, you are connecting another resistor to an existing circuit and, thus, altering the circuit. Ideally, voltmeters and ammeters do not appreciably affect the circuit, but it is instructive to examine the circumstances under which they do or do not interfere.
First, consider the voltmeter, which is always placed in parallel with the device being measured. Very little current flows through the voltmeter if its resistance is a few orders of magnitude greater than the device, and so the circuit is not appreciably affected. (See Figure(a).) (A large resistance in parallel with a small one has a combined resistance essentially equal to the small one.) If, however, the voltmeter’s resistance is comparable to that of the device being measured, then the two in parallel have a smaller resistance, appreciably affecting the circuit. (See Figure(b).) The voltage across the device is not the same as when the voltmeter is out of the circuit.
Figure $$\PageIndex{6}$$: (a) A voltmeter having a resistance much larger than the device ($$R_{Voltmeter} >> R$$) with which it is in parallel produces a parallel resistance essentially the same as the device and does not appreciably affect the circuit being measured. (b) Here the voltmeter has the same resistance as the device ($$R_{Voltmeter} \approx R$$), so that the parallel resistance is half of what it is when the voltmeter is not connected. This is an example of a significant alteration of the circuit and is to be avoided.
An ammeter is placed in series in the branch of the circuit being measured, so that its resistance adds to that branch. Normally, the ammeter’s resistance is very small compared with the resistances of the devices in the circuit, and so the extra resistance is negligible. (See Figure(a).) However, if very small load resistances are involved, or if the ammeter is not as low in resistance as it should be, then the total series resistance is significantly greater, and the current in the branch being measured is reduced. (See Figure(b).)
A practical problem can occur if the ammeter is connected incorrectly. If it was put in parallel with the resistor to measure the current in it, you could possibly damage the meter; the low resistance of the ammeter would allow most of the current in the circuit to go through the galvanometer, and this current would be larger since the effective resistance is smaller.
Figure $$\PageIndex{7}$$: (a) An ammeter normally has such a small resistance that the total series resistance in the branch being measured is not appreciably increased. The circuit is essentially unaltered compared with when the ammeter is absent. (b) Here the ammeter’s resistance is the same as that of the branch, so that the total resistance is doubled and the current is half what it is without the ammeter. This significant alteration of the circuit is to be avoided.
One solution to the problem of voltmeters and ammeters interfering with the circuits being measured is to use galvanometers with greater sensitivity. This allows construction of voltmeters with greater resistance and ammeters with smaller resistance than when less sensitive galvanometers are used.
There are practical limits to galvanometer sensitivity, but it is possible to get analog meters that make measurements accurate to a few percent. Note that the inaccuracy comes from altering the circuit, not from a fault in the meter.
CONNECTIONS: LIMITS TO KNOWLEDGE
Making a measurement alters the system being measured in a manner that produces uncertainty in the measurement. For macroscopic systems, such as the circuits discussed in this module, the alteration can usually be made negligibly small, but it cannot be eliminated entirely. For submicroscopic systems, such as atoms, nuclei, and smaller particles, measurement alters the system in a manner that cannot be made arbitrarily small. This actually limits knowledge of the system—even limiting what nature can know about itself. We shall see profound implications of this when the Heisenberg uncertainty principle is discussed in the modules on quantum mechanics.
There is another measurement technique based on drawing no current at all and, hence, not altering the circuit at all. These are called null measurements and are the topic of Null Measurements. Digital meters that employ solid-state electronics and null measurements can attain accuracies of one part in $$10^6$$.
Exercise $$\PageIndex{1}$$: Check Your Understanding
Digital meters are able to detect smaller currents than analog meters employing galvanometers. How does this explain their ability to measure voltage and current more accurately than analog meters?
Answer
Since digital meters require less current than analog meters, they alter the circuit less than analog meters. Their resistance as a voltmeter can be far greater than an analog meter, and their resistance as an ammeter can be far less than an analog meter. Consult Figure and Figure and their discussion in the text.
PHET EXPLORATIONS: CIRCUIT CONSTRUCTION KIT (DC ONLY), VIRTUAL LAB
Stimulate a neuron and monitor what happens. Pause, rewind, and move forward in time in order to observe the ions as they move across the neuron membrane.
Figure $$\PageIndex{8}$$: Circuit Construction Kit (DC Only), Virtual Lab
# Summary
• Voltmeters measure voltage, and ammeters measure current.
• A voltmeter is placed in parallel with the voltage source to receive full voltage and must have a large resistance to limit its effect on the circuit.
• An ammeter is placed in series to get the full current flowing through a branch and must have a small resistance to limit its effect on the circuit.
• Both can be based on the combination of a resistor and a galvanometer, a device that gives an analog reading of current.
• Standard voltmeters and ammeters alter the circuit being measured and are thus limited in accuracy.
## Glossary
voltmeter
an instrument that measures voltage
ammeter
an instrument that measures current
analog meter
a measuring instrument that gives a readout in the form of a needle movement over a marked gauge
digital meter
a measuring instrument that gives a readout in a digital form
galvanometer
an analog measuring device, denoted by G, that measures current flow using a needle deflection caused by a magnetic field force acting upon a current-carrying wire
current sensitivity
the maximum current that a galvanometer can read
full-scale deflection
the maximum deflection of a galvanometer needle, also known as current sensitivity; a galvanometer with a full-scale deflection of $$50 \, \mu A$$ has a maximum deflection of its needle when $$50 \, \mu A$$ flows through it
shunt resistance
a small resistance $$R$$ placed in parallel with a galvanometer G to produce an ammeter; the larger the current to be measured, the smaller $$R$$ must be; most of the current flowing through the meter is shunted through $$R$$ to protect the galvanometer
## Contributors
Paul Peter Urone (Professor Emeritus at California State University, Sacramento) and Roger Hinrichs (State University of New York, College at Oswego) with Contributing Authors: Kim Dirks (University of Auckland) and Manjula Sharma (University of Sydney). This work is licensed by OpenStax University Physics under a Creative Commons Attribution License (by 4.0). | 2019-05-23T21:45:57 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 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": 0.9172766804695129, "perplexity": 1378.0232532274915}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-22/segments/1558232257396.96/warc/CC-MAIN-20190523204120-20190523230120-00242.warc.gz"} |
https://subversion.xray.aps.anl.gov/trac/pyGSAS/export/3696/Tutorials/RietPlot/PublicationPlot.htm | # Create a Publication-Ready Rietveld Plot
In this exercise a plot will be created in a form intended for publication from a “finished” refinement in GSAS-II.
## Step 1: Read in the project file
At this point the GSAS-II data tree window will have several entries. If the PWDR entry is not selected (as below), click on it.
and the plot window will show the powder pattern along with the fit:
## Step 2: Format Plot
The plot above can be improved a bit, for example by moving the difference curve down so it can be seen more clearly. First click on the “Shrink Y” yellow tool bar button (shown to right) to make some room at the bottom of the plot.
Make sure that the zoom or pan buttons are not selected. Then click with the left mouse button on the cyan different curve and while holding the button down, drag the difference curve down a little bit. This will now be too close to the blue reflection tick marks, so they can be dragged down as well, by clicking on them, moving the mouse with the button down and releasing the button when the tick marks are in the chosen spot. Note that if the drag operation does not work, then zoom or pan mode is very likely selected, or the PWDR item has not been selected from the tree.
We can make the plot a bit more compact, by either using “Zoom” to draw a box around the region to be displayed or by pressing the “Home” button. I used zoom to get this:
## Step 3: Magnification Regions
While not particularly important for the plot above, many datasets are dominated by a few intense peaks and it can be of significant value to increase the scale in other regions. To add magnification via the mouse, first turn off the zoom mode, if on. Move the mouse to around 60 degrees (vertically, anywhere inside the axes) and press “a” to add a magnification region. A line appears on the plot and a magnification region is added to the data window, as shown to right. Another way to add magnification is with the “Add a magnification region” button. Press that to add a second region. This adds a region starting somewhere around the middle of the pattern. Change the location of this to around 40 degrees, if needed and the magnification factors to 1.5 and 2.5 respectively. The window and plot will look as below.
## Step 4: Customize the Publication Plot
Press the “P” button to the right of the toolbar. This opens a window where aspects of the plot can be customized, as below. Note that as changes are made in the controls at the top of the window, these changes are displayed immediately. Also note the addition of a additional difference plot at the bottom. This shows the weighted difference between the observed and calculated diffraction pattern ([obs-cal]/sigma); the square of this is what is actually minimized.
As examples of the types of changes that can be made here:
· Most journals will want larger lettering for labels so change the text size to 18
· We can use LaTeX symbols in the phase caption, so let’s change that to $\rm\alpha-LaB_6$
· Click on “Include in legend” for obs and calc to include them in the legend
· Click on the cyan square for the diff color and choose something more to your liking (brown here)
· Make the symbols and lines a bit more visible (when the plot is shrunk) by changing the symbols to an “x”, the size to 10, the line widths to 1.5 and the tick width to 2.5.
The plot now appears as below:
The export format can be selected using the pull-down menu for file format (shown to right). When the save button (at bottom) is used a file will be written in this format. The plot can be exported as a bitmap file by selecting an export format of png or tif, but better is to use pdf or svg, as these are vector formats and there will be no degradation of plot due to pixilation. This is to be preferred where possible.
Sample .pdf (PubPlotTest.pdf) and .png (PubPlotTest.png) files can be found in this directory: https://subversion.xray.aps.anl.gov/pyGSAS/Tutorials/RietPlot/examples/
The remaining formats allow the plot to be exported to other plotting programs where further customization is possible. The Grace and Igor Pro programs both allow input of values and plotting instructions (I am interested to hear of any others) and are supported as export formats (see below). For other programs, such as Origin, the data in the plot can be read from the .csv version of the file, but the user must construct the plot themself.
## Step 5: Export to Grace
The Grace program (originally called XMGR) is a free open-source WYSIWYG plotting tool. While Grace has not been updated in about a decade and is not easy to run on all platforms, the excellent QtGrace port runs on Windows, Mac and Linux and is easy to download and install from here: https://sourceforge.net/projects/qtgrace/files/. There is also a GTK port of Grace that is likely of greatest interest to Linux users: GraceGTK (not tested).
To export to Grace select the “Grace input file, agr” for File format and press Save. Below shows the screen in QtGrace after reading the .agr file produced here. This can be annotated and extensively modified within Grace.
## Step 6: Export to Igor Pro
Igor Pro is commercial software (and not cheap) but it is widely used in some circles and also does a great job for creating high-quality graphics. A free 30-day version demo is available.
To export to Igor Pro select the “Igor Pro input file, itx” for File format and press Save. Below is the Igor window after reading the .itx file. Note that it is easy to move the Intensity label and change the text in the legend, etc. Inset plots and many other features are available within Igor Pro. | 2021-12-03T05:22:42 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3283347487449646, "perplexity": 1616.5501075544562}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964362589.37/warc/CC-MAIN-20211203030522-20211203060522-00559.warc.gz"} |
https://proteinsandwavefunctions.blogspot.com/2015/08/finding-melting-temperature-by.html | ## Sunday, August 16, 2015
### Finding the melting temperature by coexistence simulations
While reviewing a paper I came across the idea of finding melting temperatures by coexistence simulations. The idea is very simple:
1. Run an $NVE$ MD simulation starting from a configuration where half the molecules are solid and the other half is liquid.
2. If the choice of $E$ is such that both phases exist after equilibrium then the average temperature will of the system will converge to the melting temperature.
3. In practice you determine $E$ by running a short $NVT$ MD simulation, where $T$ is reasonably close to the suspected melting temperature, and using the final position and velocities as initial conditions for the $NVE$ simulation. It's probably best to use a range of temperatures.
4. If you want the melting temperature at constant $P$ run an $NPH$ MD simulation instead.
I traced the approach back as far as this paper, which also has a nice explanation of why this works:
A more direct approach (Ref) to finding the transition temperature is to avoid the nucleation problem altogether, i.e., by simulating coexisting phases and allowing the system to evolve to equilibrium. If the equilibrium system contains both solid and liquid phases, then the system will be at a melting point. This approach is suitable for both experimental and theoretical studies. Molecular dynamic (MD) techniques are particularly useful for this approach, due to the fact that total energy is conserved in conventional MD schemes. To understand how this helps the system evolve toward equilibrium, consider a system with a phase boundary. If the system as a whole is at a temperature slightly below the melting point, then some portion of the liquid phase will solidify, generating the appropriate latent heat. Because the system is closed, this heats up the system towards the melting point. Similarly, if the system is above the melting temperature, the latent heat required to melt the solid will cool the system. The pressure of the system will also tend to equilibrate; thus, the system will evolve toward an equilibrium phase. There is no difficulty in nucleating either the liquid or solid phases, as the interface assists in the nucleation for the melting or solidification process.
The paper references an earlier book chapter, which I didn't bother to get a hold of,* that might reference even earlier works. (*yet another demonstration of why publishing original work as a book chapter is equivalent to burying it in your backyard).
This work is licensed under a Creative Commons Attribution 4.0 | 2021-04-12T04:06:45 | {"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": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7827858924865723, "perplexity": 461.49429145327076}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618038066568.16/warc/CC-MAIN-20210412023359-20210412053359-00331.warc.gz"} |
https://schools.wikia.org/index.php?title=Snell%27s_Law | 923 Pages
## Dr Dan HalmiEdit
### What is Snell's Law?Edit
Snell's Law is used to find the relationship between the angle of Incidence and Refraction and the indices of refraction of multiple mediums. Snell's Law can be used to find the refraction of a light ray in any situation, no matter what the different mediums(substances the light passes through) are.
$n_1\sin(\theta_1) = n_2\sin(\theta_2)\ ,$
Snells Law() of llama
### Who created Snell's Law? What is it's history?Edit
Snell's law was first discovered by Ibn Sahl in 984. Sahl used it to work out the shapes of Anaclastic Lenses (lenses that focus light with no geometric aberrations). Later on, it was discovered again by Thomas Harriot in 1602, but it was not published. In 1621, it was discovered another time by Willebrord Snell, in a form that was basically written in a similar mathematical format. This work was never published during Snell's life. René Descartes independently derived the law in terms of sines in his 1637 treatise Discourse on Method, and used it to solve a range of optical problems. Despite the many people who have worked on Snell's Law over the years, only Willebrord Snell is mentioned in its name.
Thomas Harriot
Willebrord Snell
Community content is available under CC-BY-SA unless otherwise noted. | 2019-08-17T17:13:26 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.41817474365234375, "perplexity": 1161.2586347589893}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-35/segments/1566027313436.2/warc/CC-MAIN-20190817164742-20190817190742-00135.warc.gz"} |
http://legisquebec.gouv.qc.ca/en/showversion/cr/T-0.1,%20r.%202?code=se:425_1r4&pointInTime=20201120 | ### T-0.1, r. 2 - Regulation respecting the Québec sales tax
425.1R4. For the purposes of the second paragraph of section 425.1 of the Act, the prescribed manner consists of reporting all the information described in section 425.1R3 in the appropriate box of the document referred to in section 425.1R5, which is:
(1) in the case of the information described in paragraph 1 of section 425.1R1, in the box “Prix de vente” or in a similar box;
(2) in the case of the information described in paragraph 2 of section 425.1R1, in the box “Valeur pour TVQ” or in a similar box;
(3) in the case of the information described in paragraph 3 of section 425.1R1, in the box “TPS perçue” or in a similar box;
(4) in the case of the information described in paragraph 4 of section 425.1R1, in the box “Échange” or in a similar box;
(5) in the case of the information described in paragraph 5 of section 425.1R1, in the box “Date de livraison” or in a similar box;
(6) in the case of the tax payable by the recipient under section 16 of the Act in respect of the supply:
(a) if the tax must be collected by the supplier in accordance with section 422 of the Act, in the box “TVQ perçue commerçant” or in a similar box;
(b) if the tax must be remitted in accordance with section 473.1.1 of the Act, in the box “TVQ à payer par client à la SAAQ” or in a similar box.
O.C. 1470-2002, s. 12; O.C. 701-2013, s. 30.
425.1R4. For the purposes of the second paragraph of section 425.1 of the Act, the prescribed manner consists of reporting all the information described in section 425.1R3 in the appropriate box of the document referred to in section 425.1R5, which is:
(1) in the case of the information described in paragraph 1 of section 425.1R1, in the box “Prix de vente” or in a similar box;
(2) in the case of the information described in paragraph 2 of section 425.1R1, in the box “Valeur pour TVQ avant TPS” or in a similar box;
(3) in the case of the information described in paragraph 3 of section 425.1R1, in the box “TPS perçue” or in a similar box;
(4) in the case of the information described in paragraph 4 of section 425.1R1, in the box “Échange” or in a similar box;
(5) in the case of the information described in paragraph 5 of section 425.1R1, in the box “Date de livraison” or in a similar box;
(6) in the case of the tax payable by the recipient under section 16 of the Act in respect of the supply:
(a) if the tax must be collected by the supplier in accordance with section 422 of the Act, in the box “TVQ perçue commerçant” or in a similar box;
(b) if the tax must be remitted in accordance with section 473.1.1 of the Act, in the box “TVQ à payer par client à la SAAQ” or in a similar box.
O.C. 1470-2002, s. 12. | 2021-01-18T18:04:31 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8596930503845215, "perplexity": 2451.0212927999205}, "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-2021-04/segments/1610703515075.32/warc/CC-MAIN-20210118154332-20210118184332-00771.warc.gz"} |
https://www.legisquebec.gouv.qc.ca/en/version/cr/F-3.1.1,%20r.%206?code=se:31_1&history=20221201 | ### F-3.1.1, r. 6 - Regulation respecting the holding of competitions
31.1. A candidate inventory may be used for a period of 2 years from the date of its constitution. Notwithstanding the foregoing, the period for using the candidate inventory may be extended, each extension corresponding to 1 year, by taking the following criteria into consideration:
(1) the number of applicants eligible for the candidate inventory or whose eligibility is established by the evaluation, as the case may be, who have not yet been declared qualified;
(2) the number of positions likely to be filled after competitions are held from the candidate inventory; and
(3) the appropriateness of the evaluation procedure used in relation to the nature of the position.
T.B. 196868, s. 12. | 2023-02-01T06:32:58 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8857492804527283, "perplexity": 1833.368469007965}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764499911.86/warc/CC-MAIN-20230201045500-20230201075500-00833.warc.gz"} |
https://www.federalreserve.gov/econres/notes/feds-notes/recent-trends-in-wealth-holding-by-race-and-ethnicity-evidence-from-the-survey-of-consumer-finances-20170927.htm | September 27, 2017
### Recent Trends in Wealth-Holding by Race and Ethnicity: Evidence from the Survey of Consumer Finances
Lisa J. Dettling, Joanne W. Hsu, Lindsay Jacobs, Kevin B. Moore, and Jeffrey P. Thompson with assistance from Elizabeth Llanes
Newly released data from the Survey of Consumer Finances (SCF) show that wealth rose for families in all race and ethnicity groups between 2013 and 2016. The long-standing and substantial wealth disparities between families of different racial and ethnic groups, however, have changed little in the past few years. Wealth losses during the Great Recession, and the magnitude and timing of the recovery, also varied substantially across families grouped by race and ethnicity. This FEDS Note explores in more detail these patterns and average differences in financial and demographic profiles of families grouped by race/ethnicity.
Recent trends in wealth-holding
We first analyze trends in total net worth among families classified, according to their self-identification during the interview, as white non-Hispanic, black or African American non-Hispanic, Hispanic or Latino, and other or multiple race (we will henceforth refer to these groups as white, black, Hispanic, and other, respectively).1 Net worth is defined as the difference between families' gross assets and their liabilities.2 We will describe patterns at the median (the typical household within each group) and at the mean (the average within each group).
In 2016, white families had the highest level of both median and mean family wealth: $171,000 and$933,700, respectively (figure 1). Black and Hispanic families have considerably less wealth than white families. Black families' median and mean net worth is less than 15 percent that of white families, at $17,600 and$138,200, respectively. Hispanic families' median and mean net worth was $20,700 and$191,200, respectively. Other families--a diverse group that includes those identifying as Asian, American Indian, Alaska Native, Native Hawaiian, Pacific Islander, other race, and all respondents reporting more than one racial identification--have lower net worth than white families but higher net worth than black and Hispanic families. The same patterns of inequality in the distribution of wealth across all families are also evident within race/ethnicity groups: For each of the four race/ethnicity groups, the mean is substantially higher than the median, reflecting the concentration of wealth at the top of the wealth distribution.
##### Figure 1: Net worth by race/ethnicity, 2016 survey
Thousands of 2016 dollars
Between 2013 and 2016, median net worth rose for all groups (figure 2). Growth rates for the 2013-16 period were proportionally larger for Hispanic, other, and black families, rising between 30 and 50 percent, compared with white families, whose net worth rose 17 percent. Even with the large percentage gains for black and Hispanic families, the white-black gap in median net worth increased from $132,800 in 2013 to$153,500 in 2016, and the white-Hispanic gap increased from $132,200 in 2013 to$150,300 in 2016.
##### Figure 2: Change in median net worth by race/ethnicity, 2007–16 surveys
Percent change
Experiences in the Great Recession (2007 to 2010) and the immediate aftermath (2010 to 2013) also varied across groups. Median net worth fell about 30 percent for all groups during the Great Recession. However, for black and Hispanic families, net worth continued to fall an additional 20 percent in the 2010-13 period, while white families' net worth was essentially unchanged, and other families' net worth fell a more modest 10 percent.
Household financial profile
The detailed household balance sheet information collected in the SCF allows us to move beyond total wealth to explore differences in income and the types of assets and debt held by families within each race/ethnicity group.
Wealth tends to increase with income because of higher levels of saving among higher-income families, and because of the feedback effect on higher incomes from the returns generated by accumulated assets.3 In 2016, both median and mean incomes are higher for white families than for all other groups of families ($61,200 and$123,400, respectively) (table 1). Median and mean incomes are considerably lower for black and Hispanic families, whose median incomes are $35,400 and$38,500, respectively. Median and mean incomes for other families fall in between those of white families and black and Hispanic families.
##### Table 1. Household financial profile by race/ethnicity, 2016 survey
Thousands of 2016 dollars or percent
White Black Hispanic Other
Income:
Median 61.2 35.4 38.5 50.6
Mean 123.4 54.0 57.3 86.9
Net Worth:
Median 171 17.6 20.7 64.8
Mean 933.7 138.2 191.2 457.8
Percent of families with zero or negative net worth 9 19 13 14
Assets (percent of families with):
Primary residence 73 45 46 54
Vehicle 90 73 80 80
Retirement accounts 60 34 30 48
Business equity 15 7 6 13
Direct and indirect equity 61 31 28 47
Debts (percent of families with):
Debt secured by primary residence 46 32 31 38
Vehicle loans 34 33 32 34
Credit card balances 42 48 50 44
Education loans 20 31 19 26
Wealth from housing (for homeowners):
Percent of assets in housing 32 37 39 35
Mean net housing wealth 215.8 94.4 129.8 220.7
Credit Experiences (percent of families with):
Payment-to-income ratio greater than 40% 6 9 8 9
Late on payments 60 days or more 5 10 4 9
Denied credit or feared denial 15 35 32 25
Source: Federal Reserve Board, Survey of Consumer Finances.
Although most families do have some wealth, the number with zero or negative net worth (having debts that exceed assets) is nontrivial and varies by race/ethnicity. Nearly one in five black households has zero or negative net worth. The share of white households without any wealth is considerably smaller, at 9 percent. Hispanic and other households fall somewhere in between white and black families on this measure.
For many families, the primary residence is an important component of the balance sheet. Well over half of white households are homeowners (73 percent), compared with just under half of black and Hispanic households (around 45 percent) and 54 percent of other households. Among homeowners, white households also hold considerably higher levels of equity in their homes. Mean net housing wealth (the value of the home, less any debts on the home) among homeowners is $215,800 among white families but only$94,400 among black families and $129,800 among Hispanic families. White homeowners hold more home equity, but housing accounts for only 32 percent of their total assets, compared with 37 to 39 percent for black and Hispanic homeowners. The most common type of asset owned by all types of families is vehicles. Ninety percent of white families own a vehicle, compared with 80 percent of Hispanic and other families, and 73 percent of black families. Retirement accounts, including IRAs and 401(k) plans, are also commonly held; 60 percent of white families have these accounts, compared with 34 percent of black families and 30 percent of Hispanic families. A family-owned business is another important component of some families' balance sheets. The highest business ownership rates are among white and other families (around 13 to 15 percent), with black and Hispanic families about half as likely to own a business. Ownership of equities--which may be held directly or indirectly through a retirement account--also varies substantially across groups, with more than 60 percent of white families owning equities, compared with around 30 percent of black and Hispanic families. Compared with assets, debt is more evenly distributed across families grouped by race/ethnicity. A larger share of white families have debt secured by the primary residence than other groups of families, which partly reflects higher homeownership rates among white families. Vehicle loans are fairly evenly distributed across groups, with around 30 to 35 percent of families having such loans. Credit card debt is also fairly evenly distributed across groups, with between 42 and 50 percent of families having credit card debt. The incidence of education loans varies somewhat across groups. Black families are the most likely to have education debt (31 percent), and Hispanic families are the least likely to have education debt (19 percent). Families' interactions with credit markets also vary somewhat across groups. Black and other families are the most likely to have high debt payment burdens: 9 percent of these families have debt-payment-to-income ratios above 40 percent. Hispanic families follow closely at 8 percent. Black families are the most likely to be late on payments. Black and Hispanic families have the highest incidence of credit constraints, with about one-third reporting they were either denied credit or did not apply for credit because they feared denial. Demographic profiles by race/ethnicity In addition to the differences in the levels and types of wealth previously described, the data also indicate substantial variation by race/ethnicity in many of the factors that are associated with the accumulation of wealth.4 Among the potential reasons that wealth is relatively high among white households, for example, is that they tend to be older, more highly educated, more likely to have received an inheritance, and less likely to be a single parent than their black and Hispanic counterparts (table 2). Wealth generally increases with age and plateaus or modestly decreases from near-retirement age onward, reflecting life-cycle earnings and saving behavior. Just over half of white households are headed by someone 55 or older, compared with 38 percent of black households and approximately one-fourth for Hispanic households. Wealth is also correlated with family structure because of higher levels of saving among families with more earners or lower living expenses. Black households stand out for being the least likely to have a married or partnered head--just 37 percent--compared with more than 54 percent for each of the other three groups. White households are the least likely to be headed by a single parent (8 percent), compared with 16 percent among Hispanics and 27 percent among black families. Black families are less likely to be dual-earner households than the other groups of families. ##### Table 2. Demographic and economic profile by race/ethnicity, 2016 survey Percent White Black Hispanic Other Age distribution Under age 35 18 21 25 28 35 to 54 31 40 49 42 55 to 74 37 30 22 24 75 and older 14 8 4 5 Family structure Married or with partner 61 37 62 54 Single without kids 31 36 23 34 Single with kids 8 27 16 12 With kids 36 47 61 45 With two earners 29 18 27 25 Education Less than high school 8 17 36 12 High school only 26 29 25 21 Some college, no degree 15 20 12 18 Associates degree 12 11 10 13 Bachelor's degree or higher (BA+) 39 23 17 36 Both head and spouse/partner have BA+ 18 5 6 16 At least one of the head's parents had BA+ 31 19 14 36 Family financial assistance Received inheritance 26 8 5 15 Can get$3,000 from family or friends in emergency 71 43 49 64
Source: Federal Reserve Board, Survey of Consumer Finances.
White and other heads of households are much more likely to have obtained a college degree or some advanced level of higher education (39 percent and 36 percent, respectively). In contrast, only 23 percent of black heads of households and 17 percent of Hispanic heads of households have a college degree or higher level of education. Furthermore, the proportion of families that consist of two spouses who both have at least a college degree also varies by group: 18 percent of white families, 5 percent of black families, 6 percent of Hispanic families, and 16 percent of other families.
These differences across groups in educational attainment appear to persist across generations as well. For 31 percent of white families, one or both parents of the head had at least a bachelor's degree, compared with 19 percent of black families and 14 percent of Hispanic families.
Intergenerational relationships can also influence how families accumulate wealth--for example, receiving assets from relatives in the form of inheritances and other major gifts. In addition, households are better able to maintain their wealth when they can count on help from family and friends to weather unexpected financial emergencies. White families stand out as the most likely to have received an inheritance or other major gift--26 percent of white families have received an inheritance, compared with less than 10 percent of black families and Hispanic families. Most white households (71 percent) report being able to get $3,000 from family or friends in a financial emergency, compared with less than half of Hispanic and black households (49 percent and 43 percent, respectively). The four race/ethnicity groups vary in many demographic and economic factors that are correlated with household wealth, but even accounting for variation in all of the demographic factors, the gaps between families grouped by race/ethnicity remain (although they are considerably smaller). Results from regression analyses show that accounting for the demographic factors in table 2 shrinks the gap to about one-third of the overall gap for white families and black families, and about one-fifth of the overall gap for white families and Hispanic families.5 Still, the adjusted gaps in net worth remain sizable. Recent wealth changes for race/ethnicity groups by educational attainment Educational attainment is a significant predictor of income and wealth: 2016 SCF data indicate that overall, families with a bachelor's degree have mean and median wealth values that are more than five times the values for less educated families. This pattern is also evident within each of the race/ethnicity groups, though the magnitude of the difference by education varies across the four race/ethnicity groups (table 3). For example, the median college-educated black family's net worth is about six times that of the median black family with less education, and the ratio is about 4.5 for Hispanic families. ##### Table 3. Mean and median net worth by race and educational attainment of head, 2013-16 surveys Thousands of 2016 dollars Median net worth Mean net worth 2013 2016 2013 2016 No bachelor's degree White 87.1 98.1 323.1 367.8 Black 10.3 11.6 78.9 99.3 Hispanic 13.1 17.5 76.3 105.7 Other 17.4 34.3 128.8 183.7 Bachelor's degree or higher White 375.5 397.1 1,440.1 1,821.3 Black 36.8 68.2 184.4 271.2 Hispanic 58.0 77.9 401.8 609.6 Other 216.1 210.2 813.0 941.0 Source: Federal Reserve Board, Survey of Consumer Finances. In addition to substantial heterogeneity within race/ethnicity groups by education, there are also large disparities across race/ethnicity groups for families with similar levels of education. Among households headed by someone with a college degree, net worth is substantially higher for white families than for the other three groups of families. The median net worth of college graduates in 2016 was$397,100 for white families, but well below \$100,000 for black families and Hispanic families. Of course, even within these race/ethnicity and education groups, many of the demographic and economic differences highlighted in tables 1 and 2 help to explain some of these patterns.
Growth rates between 2013 and 2016 also varied substantially across race/ethnicity and educational attainment groups. Among college graduates, mean and median wealth grew proportionally more for black and Hispanic households than for other families: mean wealth of college degree holders rose approximately 50 percent for black and Hispanic households and only 26 percent for white families. Among less educated families, proportional growth rates at the mean and median were highest for Hispanic families and other families.
This FEDS Note has described broad patterns in wealth-holding across families grouped by race and ethnicity, and some of the economic and demographic determinants of those patterns, using newly released data from the SCF. While all groups experienced losses during the Great Recession, the 2016 SCF data reveal broad-based growth in household net worth across groups since 2013. However, disparities in wealth-holding, asset-holding, and debt-holding remain: White families have considerably more wealth than black, Hispanic, and other families, even among those with similar levels of education. While this FEDS Note documents substantial heterogeneity across race/ethnicity groups, there is substantial variation in family circumstances and financial experiences within each group as well.
1. For more on the race/ethnicity classifications used in this FEDS Note, see the appendix to Jesse Bricker, Lisa J. Dettling, Alice Henriques, Joanne W. Hsu, Lindsay Jacobs, Kevin B. Moore, Sarah Pack, John Sabelhaus, Jeffrey Thompson, and Richard A. Windle (2017), "Changes in U.S. Family Finances from 2013 to 2016: Evidence from the Survey of Consumer Finances," Federal Reserve Bulletin vol. 103 (henceforth, the Bulletin article). The other or multiple race group consists of a very racially/ethnically diverse set of families, including those identifying as Asian, American Indian, Alaska Native, Native Hawaiian, Pacific Islander, other race, and all respondents reporting more than one racial identification. Because of small sample sizes, we do not have statistical power to further disaggregate this group of families. In 2016, families reporting more than one racial identification were the largest subgroup of the other or multiple race group (about 50 percent of families), followed by Asian families (about 30 percent of families), though the composition of this group varies over time. Because of the varied composition of the other group and changes in its composition over time, readers should exercise caution when making inferences. Return to text
2. See the appendix to the Bulletin article for more details on components of net worth in the SCF. Return to text
3. See the Bulletin article for more on savings patterns by income. Return to text
4. For patterns in wealth-holding by family characteristics, see the Bulletin article; Janet L. Yellen (2014), "Perspectives on Inequality and Opportunity from the Survey of Consumer Finances," speech at the Conference on Economic Opportunity and Inequality, Federal Reserve Bank of Boston, Boston, Mass., October 17, https://www.federalreserve.gov/newsevents/speech/yellen20141017a.htm; and Martin Browning and Annamaria Lusardi (1996), "Household Saving: Micro Theories and Micro Facts," Journal of Economic Literature, vol. 34 (December), pp. 1797–855. Return to text
5. These findings are similar for both mean and median net worth. For more details on the methods used here, and for more extensive analysis using additional factors, see Jeffrey P. Thompson and Gustavo A. Suarez (2015), "Exploring the Racial Wealth Gap Using the Survey of Consumer Finances," Finance and Economics Discussion Series 2015-076 (Washington: Board of Governors of the Federal Reserve System, August), http://dx.doi.org/10.17016/FEDS.2015.076. Return to text | 2019-07-24T00:05:44 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2306736260652542, "perplexity": 5309.130056552894}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-30/segments/1563195530246.91/warc/CC-MAIN-20190723235815-20190724021815-00505.warc.gz"} |
http://hitchhikersgui.de/Net_national_product | # Net national product
Net national product (NNP) refers to gross national product (GNP), i.e. the total market value of all final goods and services produced by the factors of production of a country or other polity during a given time period, minus depreciation.[1] Similarly, net domestic product (NDP) corresponds to gross domestic product (GDP) minus depreciation.[2] Depreciation describes the devaluation of fixed capital through wear and tear associated with its use in productive activities.
In national accounting, net national product (NNP) and net domestic product (NDP) are given by the two following formulas:
${\displaystyle NNP=GNP-Depreciation}$
${\displaystyle NDP=GDP-Depreciation}$
## Use in economics
Although the net national product is a key identity in national accounting, its use in economics research is generally superseded by the use of the gross domestic or national product as a measure of national income, a preference which has been historically a contentious topic (see e.g. Boulding (1948)[3] and Burk (1948)[4]). Nonetheless, the net national product has been the subject of research on its role as a dynamic welfare indicator[5] as well as a means of reconciling forward and backward views on capital wherein NNP(t) corresponds to the interest on accumulated capital.[6] Furthermore, the net national product has featured prominently as a measure in environmental economics such as within models accounting for the depletion of natural and environmental resources[7] or as an indicator of sustainability.[8]
## References
1. ^ Krugman, P.R., Obstfeld, M., Melitz, M.J. (2012). International Economics: Theory & Policy (9th ed.). Harlow (UK): Pearson Education Limited, p. 327.
2. ^ Burda, M., Wyplosz, C. (2013). Macroeconomics: A European Text (6th ed.). Oxford (UK): Oxford University Press, p. 39.
3. ^ Boulding, K.E. (1948). Professor Tarshis and the State of Economics. The American Economic Review, 38(1), pp. 92-102.
4. ^ Burk, M. (1948). Mr. Boulding's Criticism of the Net National Product Concept. The American Economic Review, 38(5), pp. 897-898.
5. ^ Brekke, K.A. (1994). Net National Product as a Welfare Indicator. The Scandinavian Journal of Economics, 96(2), pp. 241-252.
6. ^ Hartwick, J.M. (1994). National Wealth and Net National Product. The Scandinavian Journal of Economics, 96(2), pp. 253-256.
7. ^ Hartwick, J.M. (1990). Natural resources, national accounting and economic depreciation. Journal of Public Economics, 43(3), pp. 291-304.
8. ^ Asheim, G.B. (1994). Net National Product as an Indicator of Sustainability. The Scandinavian Journal of Economics, 96(2), pp. 257-265.
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https://phys.libretexts.org/Bookshelves/University_Physics/Book%3A_University_Physics_(OpenStax)/Map%3A_University_Physics_I_-_Mechanics%2C_Sound%2C_Oscillations%2C_and_Waves_(OpenStax)/Answer_Key_to_Selected_Problems/03%3A_Motion_Along_a_Straight_Line | $$\require{cancel}$$
03: Motion Along a Straight Line
3.1. (a) The rider’s displacement is $$\Delta$$x = xf − x0 = −1 km. (The displacement is negative because we take east to be positive and west to be negative.) (b) The distance traveled is 3 km + 2 km = 5 km. (c) The magnitude of the displacement is 1 km.
3.2. (a) Taking the derivative of x(t) gives v(t) = −6t m/s. (b) No, because time can never be negative. (c) The velocity is v(1.0 s) = −6 m/s and the speed is |v(1.0 s)| = 6 m/s.
3.3. Inserting the knowns, we have $$\bar{a} = \frac{\Delta v}{\Delta t} = \frac{2.0 \times 10^{7}\; m/s − 0}{10^{−4}\; s − 0} = 2.0 \times 10^{11}\; m/s^{2}$$.
3.4. If we take east to be positive, then the airplane has negative acceleration because it is accelerating toward the west. It is also decelerating; its acceleration is opposite in direction to its velocity.
3.5. To answer this, choose an equation that allows us to solve for time t, given only a , v0, and v$$v = v_{0} + at \ldotp$$ Rearrange to solve for t:$$t = \frac{v − v_{0}}{a} = \frac{400\; m/s − 0\; m/s}{20\; m/s^{2}} = 20 s \ldotp$$
3.6. a = $$\frac{2}{3}$$ m/s2.
3.7. It takes 2.47 s to hit the water. The quantity distance traveled increases faster.
3.8. a. The velocity function is the integral of the acceleration function plus a constant of integration. By Equation 3.91,$$v(t) = \int a(t)dt + C_{1} = \int (5 − 10t)dt + C_{1} = 5t − 5t^{2} + C_{1} \ldotp$$ Since v(0) = 0, we have C1 = 0; so,$$v(t) = 5t − 5t^{2} \ldotp$$ b. By Equation 3.93,$$x(t) = \int v(t)dt + C_{2} = \int (5t − 5t^{2})dt + C_{2} = \frac{5}{2} t^{2} − \frac{5}{3} t^{3} + C_{2} \ldotp$$ Since x(0) = 0, we have C2 = 0, and$$x(t) = \frac{5}{2} t^{2} − \frac{5}{3} t^{3} \ldotp$$ c. The velocity can be written as v(t) = 5t(1 – t), which equals zero at t = 0, and t = 1 s.
Conceptual Questions
3. If the bacteria are moving back and forth, then the displacements are canceling each other and the final displacement is small.
5. Distance traveled
7. Average speed is the total distance traveled divided by the elapsed time. If you go for a walk, leaving and returning to your home, your average speed is a positive number. Since Average velocity = Displacement/Elapsed time, your average velocity is zero.
9. Average speed. They are the same if the car doesn’t reverse direction.
11. No, in one dimension constant speed requires zero acceleration.
13. A ball is thrown into the air and its velocity is zero at the apex of the throw, but acceleration is not zero.
15. Plus, minus
17. If the acceleration, time, and displacement are the knowns, and the initial and final velocities are the unknowns, then two kinematic equations must be solved simultaneously. Also if the final velocity, time, and displacement are the knowns then two kinematic equations must be solved for the initial velocity and acceleration.
19. a. At the top of its trajectory; b. yes, at the top of its trajectory; c. yes
21. Earth$$v = v_{0} − gt = −gt;$$ Moon$$v′ = \frac{g}{6} t′$$ $$v = v′ − gt = − \frac{g}{6}t′$$ $$t′ = 6t;$$ Earth $$y = − \frac{1}{2}gt^{2}$$ Moon $$y′ = − \frac{1}{2} \frac{g}{6} (6t)^{2} = − \frac{1}{2} g6t^{2} = −6 \left(\dfrac{1}{2} gt^{2}\right) = −6y$$
Problems
25. a. $$\vec{x}_{1}$$ = (−2.0 m) $$\hat{i}$$, $$\vec{x}_{2}$$ = (5.0 m) $$\hat{i}$$
b. 7.0 m east
27. a. t = 2.0 s
b. x(6.0) − x(3.0) = −8.0 − (−2.0) = −6.0 m
29. a. 150.0 s, v – = 156.7 m/s
b. 45.7% the speed of sound at sea level
31.
33.
35. a. v(t) = (10 − 4t)m/s; v(2 s) = 2 m/s, v(3 s) = −2 m/s
b. |v(2 s)| = 2 m/s, |v(3 s)| = 2 m/s
c. $$\bar{v}$$ = 0 m/s
37. a = 4.29 m/s2
39.
41. a = 11.1g
43. 150 m
45. a. 525 m
b. v = 180 m/s
47. a.
b. The acceleration has the greatest positive value at ta c. The acceleration is zero at te and th d. The acceleration is negative at ti, tj, tk, tl
49. a. a = −1.3 m/s2
b. v0 = 18 m/s
c. t = 13.8 s
51. v = 502.20 m/s
53. a.
b. Knowns: a = 2.40 m/s2, t = 12.0 s, v0 = 0 m/s , and x0 = 0 m; c. x = x0 + v0t + $$\frac{1}{2}$$at2 = $$\frac{1}{2}$$at2 = 2.40 m/s2 (12.0 s)2 = 172.80 m, the answer seems reasonable at about 172.8 m; d. v = 28.8 m/s
55. a.
b. Knowns: v = 30.0 cm/s, x = 1.80 cm
c. a = 250 cm/s2, t = 0.12 s
d. yes
57. a. 6.87 s2
b. x = 52.26 m
59. a. a = 8450 m/s2
b. t = 0.0077 s
61. a. a = 9.18g
b. t = 6.67 x 10−3 s
c. a = −40.0 m/s2, a = 4.08g
63. Knowns: x = 3 m, v = 0 m/s, v0 = 54 m/s. We want a, so we can use this equation: a = −486 m/s2.
65. a. a = 32.58 m/s2
b. v = 161.85 m/s
c. v > vmax, because the assumption of constant acceleration is not valid for a dragster. A dragster changes gears and would have a greater acceleration in first gear than second gear than third gear, and so on. The acceleration would be greatest at the beginning, so it would not be accelerating at 32.6 m/s2 during the last few meters, but substantially less, and the final velocity would be less than 162 m/s.
67. a. y = −8.23 m, v1 = −18.9 m/s
b. y = −18.9 m, v2 = 23.8 m/s
c. y = −32.0 m, v3 = −28.7 m/s
d. y = −47.6 m, v4 = −33.6 m/s
e. y = −65.6 m, v5 = −38.5 m/s
69. a. Knowns: a = −9.8 m/s2, v0 = −1.4 m/s, t = 1.8 s, y0 = 0 m
b. y = y0 + v0t − $$\frac{1}{2}$$gt2, y = v0t − $$\frac{1}{2}$$gt = −1.4 m/s (1.8 sec) − $$\frac{1}{2}$$(9.8)(1.8 s)2 = −18.4 m and the origin is at the rescuers, who are 18.4 m above the water.
71. a. v2 = v02 − 2g(y − y0), y0 = 0, v = 0, y = $$\frac{v_{0}^{2}}{2g}$$ = $$\frac{(4.0 m/s)^{2}}{2(9.80)}$$ = 0.82 m
b. To the apex v = 0.41 s times 2 to the board = 0.82 s from the board to the water y = y0 + v0t − $$\frac{1}{2}$$gt2, y = −1.80 m, y0 = 0, v0 = 4.0 m/s −1.8 = 4.0t − 4.9t2, 4.9t 2 − 4.0t − 1.80 = 0, solution to quadratic equation gives 1.13 s
c. v2 = v02 − 2g(y − y0)y0 = 0, v0 = 4.0 m/s, y = −1.80 m, v = 7.16 m/s
73. Time to the apex: t = 1.12 s times 2 equals 2.24 s to a height of 2.20 m. To 1.80 m in height is an additional 0.40 m.$$y = y_{0} + v_{0} t − \frac{1}{2} gt^{2}$$$$y = −0.40\; m$$$$y_{0} = 0$$$$v_{0} = −11.0\; m/s$$$$−0.40 = −11.0t − 4.9t^{2}\; or\; 4.9t^{2} + 11.0t − 0.40 = 0 \ldotp$$ Take the positive root, so the time to go the additional 0.4 m is 0.04 s. Total time is 2.24 s + 0.04 s = 2.28 s.
75. a. v2 = v02 − 2g(y − y0), y0 = 0, v = 0, y = 2.50 m,$$v_{0}^{2} = 2gy \Rightarrow v_{0} = \sqrt{2(9.80)(2.50)} = 7.0\; m/s;$$
b. t = 0.72 s times 2 gives 1.44 s in the air
77. a. v = 70.0 m/s
b. time heard after rock begins to fall: 0.75 s, time to reach the ground: 6.09 s
79. a. A = m/s2, B = m/s5/2
b. v(t) = $$\int$$ a(t)dt + C1 = $$\int$$(A − Bt1/2)dt + C1 = At − $$\frac{2}{3}$$Bt3/2 + C1$$v(0) = 0 = C_{1}\; so\; v(t_{0}) = At_{0} − \frac{2}{3} Bt_{0}^{3/2};$$
c. x(t) = $$\int$$v(t)dt + C2 = $$\int$$(At − \frac{2}{3}\)Bt3/2)dt + C2 = $$\frac{1}{2}$$At2 − $$\frac{4}{15}$$Bt5/2 + C2$$x(0) = 0 = C_{2}\; so\; x(t_{0}) = \frac{1}{2} At_{0}^{2} − \frac{4}{15} Bt_{0}^{5/2}$$
81. a. $$\begin{split}a(t) & = 3.2 m/s^{2} \quad t \leq 5.0\; s \\ a(t) & = 1.5\; m/s^{2} \quad 5.0\; s \leq t \leq 11.0\; s \\ a(t) & = 0\; m/s^{2} \quad \quad t > 11.0\; s \end{split}$$
b. $$\begin{split} x(t) & = \int v(t)dt + C_{2} = \int 3.2tdt + C_{2} = 1.6t^{2} + C_{2} \quad t \leq 5.0\; s \\ x(0) & = 0 \Rightarrow C_{2} = 0\; therefore,\; x(2.0\; s) = 6.4\; m \\ x(t) & = \int v(t)dt + C_{2} = \int [16.0 − 1.5(t − 5.0)]dt + C_{2} = 16t − 1.5 \left(\dfrac{t^{2}}{2} − 5.0t \right) + C_{2} \quad 5.0\; s \leq t \leq 11.0\; s \\ x(5\; s) & = 1.6(5.0)^{2} = 40\; m = 16(5.0\; s) − 1.5 \left(\dfrac{5^{2}}{2} − 5.0(5.0) \right) + C_{2} \end{split}$$$$\begin{split}40 & = 98.75 + C_{2} \Rightarrow C_{2} = −58.75 \\ x(7.0 s) & = 16(7.0) − 1.5 \left(\dfrac{7^{2}}{2} − 5.0(7) \right) − 58.75 = 69\; m \\ x(t) & = \int 7.0dt + C_{2} = 7t + C_{2} \quad t \geq 11.0\; s \\ x(11.0\; s) & = 16(11) − 1.5 \left(\dfrac{11^{2}}{2} − 5.0(11) \right) − 58.75 = 109 = 7(11.0\; s) + C_{2} \Rightarrow C_{2} = 32\; m \\ x(t) & = 7t + 32\; m \quad x \geq 11.0\; s \Rightarrow x(12.0\; s) = 7(12) + 32 = 116\; m \end{split}$$
83. Take west to be the positive direction. 1st plane: $$\bar{v}$$ = 600 km/h; 2nd plane: $$\bar{v}$$ = 667.0 km/h
85. a = $$\frac{v − v_{0}}{t − t_{0}}$$, t = 0, a = $$\frac{−3.4\; cm/s − v_{0}}{4\; s}$$ = 1.2 cm/s2 $$\Rightarrow$$ v0 = − 8.2 cm/s, v = v0 + at = − 8.2 + 1.2 t; v = −7.0 cm/s, v = −1.0 cm/s
87. a = −3 m/s2
89. a. v = 8.7 x 105 m/s
b. t = 7.8 x 10−8 s
91. 1 km = v0(80.0 s) + $$\frac{1}{2}$$a(80.0)2; 2 km = v0(200.0) + $$\frac{1}{2}$$a(200.0)2 solve simultaneously to get a = $$− \frac{0.1}{2400.0}$$km/s2 and v0 = 0.014167 km/s, which is 51.0 km/h. Velocity at the end of the trip is v = 21.0 km/h.
93. a = −0.9 m/s2
95. Equation for the speeding car: This car has a constant velocity, which is the average velocity, and is not accelerating, so use the equation for displacement with x0 = 0: x = x0 + $$\bar{v}$$t = $$\bar{v}$$t; Equation for the police car: This car is accelerating, so use the equation for displacement with x0 = 0 and v0 = 0, since the police car starts from rest: x = x0 + v0t + $$\frac{1}{2}$$at2 = $$\frac{1}{2}$$at2; Now we have an equation of motion for each car with a common parameter, which can be eliminated to find the solution. In this case, we solve for t. Step 1, eliminating x : x = $$\bar{v}$$t = $$\frac{1}{2}$$at2; Step 2, solving for t : t = $$\frac{2 \bar{v}}{a}$$. The speeding car has a constant velocity of 40 m/s, which is its average velocity. The acceleration of the police car is 4 m/s2. Evaluating t, the time for the police car to reach the speeding car, we have t = $$\frac{2 \bar{v}}{a}$$ = $$\frac{2(40)}{4}$$ = 20 s.
97. At this acceleration she comes to a full stop in t = $$\frac{−v_{0}}{a}$$ = $$\frac{8}{0.5}$$ = 16 s, but the distance covered is x = 8 m/s (16 s) − $$\frac{1}{2}$$(0.5)(16 s)2 = 64 m, which is less than the distance she is away from the finish line, so she never finishes the race.
99. x1 = $$\frac{3}{2}$$v0t; x2 = $$\frac{5}{3}$$x1
101. v0 = 7.9 m/s velocity at the bottom of the window. v = 7.9 m/s; v0 = 14.1 m/s
103. a. v = 5.42 m/s
b. v = 4.64 m/s
c. a = 2874.28 m/s2
d. (x − x0) = 5.11 x 10−3 m
105. Consider the players fall from rest at the height 1.0 m and 0.3 m. 0.9 s; 0.5 s
107. a. t = 6.37 s taking the positive root
b. v = 59.5 m/s
109. a. y = 4.9 m
b. v = 38.3 m/s; c. −33.3 m
111. h = $$\frac{1}{2}$$gt2, h = total height and time to drop to ground $$\frac{2}{3}$$h = $$\frac{1}{2}$$g(t − 1)2 in t – 1 seconds it drops $$\frac{2}{3}$$h$$\frac{2}{3} \left(\dfrac{1}{2} gt^{2}\right) = \frac{1}{2} g(t − 1)^{2}\; or\; \frac{t^{2}}{3} = \frac{1}{2} (t − 1)^{2}$$$$0 = t^{2} − 6t + 3,\; t = \frac{6 \pm \sqrt{62 − 4 \cdotp 3}}{2} = 3 \pm \frac{\sqrt{24}}{2}$$ t = 5.45 s and h = 145.5 m. Other root is less than 1 s. Check for t = 4.45 s, h = $$\frac{1}{2}$$gt2 = 97.0 m = $$\frac{2}{3}$$(145.5)
Challenge Problems
113. a. v(t) = 10t − 12tm/s, a(t) = 10 − 24t m/s2
b. v(2 s) = −28 m/s, a(2 s) = −38m/s2
c. The slope of the position function is zero or the velocity is zero. There are two possible solutions: t = 0, which gives x = 0, or t = $$\frac{10.0}{12.0}$$ = 0.83 s, which gives x = 1.16 m. The second answer is the correct choice
d. 0.83 s
e. 1.16 m
115. 96 km/h = 26.67 m/s, a = $$\frac{26.67\; m/s}{4.0\; s}$$ = 6.67m/s2, 295.38 km/h = 82.05 m/s, t = 12.3 s time to accelerate to maximum speed; x = 504.55 m = distance covered during acceleration; 7495.44 m at a constant speed; $$\frac{7495.44\; m}{82.05\; m/s}$$ = 91.35 s so total time is 91.35 s + 12.3 s = 103.65 s.
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). | 2019-01-19T19:28:23 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5676324963569641, "perplexity": 2017.7233112530344}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-04/segments/1547583680452.20/warc/CC-MAIN-20190119180834-20190119202834-00348.warc.gz"} |
https://zbmath.org/authors/?q=ai%3Alaplaza.miguel-l | # zbMATH — the first resource for mathematics
## Laplaza, Miguel L.
Compute Distance To:
Author ID: laplaza.miguel-l Published as: Laplaza, M.; Laplaza, M. L.; Laplaza, Miguel; Laplaza, Miguel L. External Links: MGP · Wikidata
Documents Indexed: 44 Publications since 1962 Reviewing Activity: 6 Reviews
#### Co-Authors
38 single-authored 2 Bollman, Dorothy 1 Day, Brian John 1 Durand, F. 1 Kelly, Gregory Maxwell 1 Morales, Jorge Plinio
all top 5
#### Serials
18 Revista Matematica Hispano-Americana. 4a Serie. Publicada por Real Sociedad Matematica Espanola 4 Gaceta Matemática 2 Collectanea Mathematica 2 Journal of Pure and Applied Algebra 2 Transactions of the American Mathematical Society 1 Bulletin of the Australian Mathematical Society 1 Journal of Algebra 1 Notre Dame Journal of Formal Logic 1 Theoretical Computer Science 1 Bulletin of the American Mathematical Society 1 Acta Salmanticensia
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#### Fields
10 Category theory; homological algebra (18-XX) 5 Mathematical logic and foundations (03-XX) 3 Group theory and generalizations (20-XX) 2 Number theory (11-XX) 1 Commutative algebra (13-XX) 1 Associative rings and algebras (16-XX) 1 Functions of a complex variable (30-XX)
#### Citations contained in zbMATH
9 Publications have been cited 164 times in 149 Documents Cited by Year
Coherence for compact closed categories. Zbl 0447.18005
Kelly, G. M.; Laplaza, M. L.
1980
Coherence for distributivity. Zbl 0244.18010
Laplaza, Miguel L.
1972
Coherence for categories with group structure: An alternative approach. Zbl 0525.18005
Laplaza, Miguel L.
1983
Coherence for associativity not an isomorphism. Zbl 0244.18009
Laplaza, Miguel L.
1972
Embedding of closed categories into monoidal closed categories. Zbl 0342.18003
Laplaza, Miguel L.
1977
A new result of coherence for distributivity. Zbl 0244.18011
Laplaza, Miguel L.
1972
On embedding closed categories. Zbl 0371.18009
Day, B. J.; Laplaza, M. L.
1978
Coherence for categories with associativity, commutativity and distributivity. Zbl 0237.18003
Laplaza, Miguel L.
1972
Coherence in nonmonoidal closed category. Zbl 0327.18009
Laplaza, Miguel L.
1977
Coherence for categories with group structure: An alternative approach. Zbl 0525.18005
Laplaza, Miguel L.
1983
Coherence for compact closed categories. Zbl 0447.18005
Kelly, G. M.; Laplaza, M. L.
1980
On embedding closed categories. Zbl 0371.18009
Day, B. J.; Laplaza, M. L.
1978
Embedding of closed categories into monoidal closed categories. Zbl 0342.18003
Laplaza, Miguel L.
1977
Coherence in nonmonoidal closed category. Zbl 0327.18009
Laplaza, Miguel L.
1977
Coherence for distributivity. Zbl 0244.18010
Laplaza, Miguel L.
1972
Coherence for associativity not an isomorphism. Zbl 0244.18009
Laplaza, Miguel L.
1972
A new result of coherence for distributivity. Zbl 0244.18011
Laplaza, Miguel L.
1972
Coherence for categories with associativity, commutativity and distributivity. Zbl 0237.18003
Laplaza, Miguel L.
1972
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#### Cited by 185 Authors
11 Coecke, Bob 6 Yetter, David N. 5 Heunen, Chris 4 Blute, Richard F. 4 Duncan, Ross 4 Sadrzadeh, Mehrnoosh 4 Vitale, Enrico Maria 3 Bourke, John 3 Hasegawa, Masahito 3 Hyland, J. Martin E. 3 Kissinger, Aleks 3 Laplaza, Miguel L. 3 Melliès, Paul-André 3 Pavlović, Duško 3 Solov’ëv, Sergeĭ Vladimirovich 3 Tabareau, Nicolas 3 Walters, Robert F. C. 2 Abramsky, Samson 2 Aldrovandi, Ettore 2 Barrett, John William 2 Bonchi, Filippo 2 Carboni, Aurelio 2 Freyd, Peter J. 2 Hadzihasanovic, Amar 2 Hines, Peter M. 2 Joyal, André 2 Kauffman, Louis Hirsch 2 Paquette, Éric Oliver 2 Perdrix, Simon 2 Petrić, Zoran 2 Ponto, Kate 2 Sabadini, Nicoletta 2 Scott, Philip J. 2 Selinger, Peter 2 Shulman, Michael A. 2 Sobociński, Paweł 2 Spekkens, Robert W. 2 Spivak, David I. 2 Street, Ross H. 2 Vicary, Jamie 2 Westbury, Bruce W. 2 Zeilberger, Noam 1 Abłamowicz, Rafał 1 Axelsen, Holger Bock 1 Baez, John C. 1 Balan, Adriana 1 Balkir, Esma 1 Barnum, Howard 1 Bartha, Miklós 1 Beke, Tibor 1 Blass, Andreas Raphael 1 Blömer, Olaf 1 Böhm, Gabriella 1 Breen, Lawrence S. 1 Brun, Mats Kirkesæther 1 Caprau, Carmen Livia 1 Carrasco, Pilar C. 1 Carter, J. Scott 1 Cegarra, Antonio Martínez 1 Dabrowski, Yoann 1 Datuashvili, Tamar 1 Day, Brian John 1 de Felice, Giovanni 1 de Francesco Albasini, Luisa 1 Dell’Ambrogio, Ivo 1 Diaz, Rafael E. 1 Dixon, Lucas 1 Doplicher, Sergio 1 Došen, Kosta 1 Dugger, Daniel 1 Edwards, Bill 1 Elmendorf, A. D. 1 Fauser, Bertfried 1 Fiedorowicz, Zbigniew 1 Fiore, Marcelo P. 1 Fiore, Thomas M. 1 Fong, Brendan 1 Fröhlich, Albrecht 1 Führmann, Carsten 1 Garner, Richard 1 Gay, Simon J. 1 Glück, Robert 1 Goubault-Larrecq, Jean 1 Goubault, Eric 1 Grandjean, Françoise 1 Grefenstette, Edward 1 Gubkin, Steven 1 Gunnarsson, Thomas E. W. 1 Gurevich, Yuri 1 Gurski, Nick 1 Hanh, Dang Dinh 1 Hardie, Keith A. 1 Harding, John 1 Hedges, Jules 1 Hill, Michael A. 1 Holland, Joshua 1 Hopkins, Michael Jerome 1 Houston, Robin 1 Hu, Po 1 Hughes, Dominic J. D. ...and 85 more Authors
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#### Cited in 48 Serials
24 Journal of Pure and Applied Algebra 11 Advances in Mathematics 9 MSCS. Mathematical Structures in Computer Science 7 Theoretical Computer Science 4 Journal of Algebra 4 Annals of Pure and Applied Logic 4 Applied Categorical Structures 4 Theory and Applications of Categories 4 Algebraic & Geometric Topology 4 Journal of Homotopy and Related Structures 3 Cahiers de Topologie et Géométrie Différentielle Catégoriques 3 Logical Methods in Computer Science 2 Communications in Algebra 2 International Journal of Theoretical Physics 2 Journal of Mathematical Physics 2 Mathematical Proceedings of the Cambridge Philosophical Society 2 Journal of Soviet Mathematics 2 Transactions of the American Mathematical Society 2 Topology and its Applications 2 Information and Computation 2 Annals of Mathematics and Artificial Intelligence 1 Bulletin of the Australian Mathematical Society 1 Communications in Mathematical Physics 1 Computer Physics Communications 1 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 1 Archiv der Mathematik 1 Compositio Mathematica 1 Inventiones Mathematicae 1 Journal of Philosophical Logic 1 The Journal of Symbolic Logic 1 Proceedings of the London Mathematical Society. Third Series 1 Siberian Mathematical Journal 1 Synthese 1 Forum Mathematicum 1 Expositiones Mathematicae 1 Journal of Knot Theory and its Ramifications 1 New Journal of Physics 1 Annals of Mathematics. Second Series 1 RAIRO. Theoretical Informatics and Applications 1 Differential Equations 1 Quantum Information Processing 1 Journal of Applied Logic 1 Foundations of Physics 1 Bulletin of the American Mathematical Society 1 São Paulo Journal of Mathematical Sciences 1 Journal of Mathematics 1 Annales de l’Institut Henri Poincaré D. Combinatorics, Physics and their Interactions (AIHPD) 1 Journal of Logical and Algebraic Methods in Programming
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#### Cited in 27 Fields
113 Category theory; homological algebra (18-XX) 37 Quantum theory (81-XX) 30 Mathematical logic and foundations (03-XX) 25 Computer science (68-XX) 18 Associative rings and algebras (16-XX) 18 Manifolds and cell complexes (57-XX) 17 Algebraic topology (55-XX) 10 Group theory and generalizations (20-XX) 8 Functional analysis (46-XX) 7 $$K$$-theory (19-XX) 6 Nonassociative rings and algebras (17-XX) 5 Linear and multilinear algebra; matrix theory (15-XX) 4 Combinatorics (05-XX) 4 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 3 Order, lattices, ordered algebraic structures (06-XX) 3 Commutative algebra (13-XX) 3 Algebraic geometry (14-XX) 3 Topological groups, Lie groups (22-XX) 2 Information and communication theory, circuits (94-XX) 1 General algebraic systems (08-XX) 1 Operator theory (47-XX) 1 Differential geometry (53-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Probability theory and stochastic processes (60-XX) 1 Statistics (62-XX) 1 Statistical mechanics, structure of matter (82-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. | 2021-03-04T12:32:15 | {"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": 0.3535706698894501, "perplexity": 9584.619621857393}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178369054.89/warc/CC-MAIN-20210304113205-20210304143205-00615.warc.gz"} |
https://predict.cdc.gov/post/5ba5389fa983f303b832726b | # State FluSight 2018–2019
State FluSight: Seasonal Influenza Forecasting for US States
When and where flu increases will occur, how large the impact of the flu season will be, and when the flu season will peak varies from season to season, making the preparation for and response to the influenza seasons difficult. Flu forecasting can change that by offering the possibility to look into the future and better plan ahead, potentially reducing the impact of flu.
To help support the development of the science of flu forecasting and its application for public health, CDC, through the Epidemic Prediction Initiative (EPI), has organized FluSight challenges to forecast the timing, intensity, and short-term activity of the influenza season since the 2013-14 season. These challenges have provided the scientific and public health community experience in real-time forecasting, the ability to evaluate forecast accuracy, and experience in communicating and applying these forecasts in real-world settings. For example, forecasts are currently used to inform CDC’s activity summaries provided to public health officials and CDC leadership and public messaging regarding the timing of the influenza season and how the public can protect themselves and their family.
As part of the forecasting initiative, CDC has developed, through EPI, the “FluSight” flu forecasting website, which facilitates the real-time sharing and visualization of weekly flu forecasts. Visitors to this site can view current and past forecasts throughout the flu season for the peak week, peak intensity, and the near-term activity at the state level. ILINet data are generally updated every Friday, and forecasts are generally available by Tuesday. During the 2018–19 season, CDC expects forecasting teams to provide over 15 state-level forecasts each week.
Submitted forecasts
Use the interactive tool below to explore submitted forecasts for the 2018–2019 influenza season. Click throughout the season to examine forecasts received during a given week. To see the most recent forecasts, click the forecast week immediately preceeding the dotted "Today" line.
Peak week and intensity predictions are visualized by the stand-alone dots with confidence intervals, and week-ahead forecasts are visualized as the connected dots with confidence bands. States or jurisdictions can be selected using the dropdown menu on the right side of the graph. Please note that forecasts will not display on Internet Explorer.
Florida does not share its ILINet data through CDC's FluView Interactive. Therefore, forecasts for Florida are unavailable. To view a summary of Florida’s ILINet data (along with viewing other available data on flu and ILI), please visit www.floridahealth.gov/floridaflu or reach out to the Florida Department of Health directly at (850) 245-4444.
Forecast Targets
For each week during the season, participants will be asked to provide state-level probabilistic forecasts for the entire influenza season (seasonal targets) and for the next four weeks (four-week ahead targets). The seasonal targets are the peak week and the peak intensity of the 2018-2019 influenza season for each state being forecast. The four-week ahead targets are the percent of outpatient visits experiencing influenza-like illness (ILI) one week, two weeks, three weeks, and four weeks ahead from date of the forecast.
#### Seasonal Peak Week
Definition The peak week will be defined as the MMWR surveillance week that the weighted ILINet percentage is the highest in a given state for the 2018-2019 influenza season.
Motivation Accurate and timely forecasts for the peak week can be useful for planning and promoting activities to increase influenza vaccination prior to the bulk of influenza illness. For healthcare, pharmacy, and public health authorities, a forecast for the peak week can guide efficient staff and resource allocation.
#### Seasonal Peak Intensity
Definition The intensity will be defined as the highest numeric value, rounded to one decimal place, that the weighted ILINet percentage reaches during the 2018-2019 influenza season.
Motivation Accurate and timely forecasts for the peak week and intensity of the influenza season can be useful for influenza prevention and control, including the planning and promotion of activities to increase influenza vaccination prior to the bulk of influenza illness. For healthcare, pharmacy, and public health authorities, a forecast for the peak week and intensity can help with appropriate staff and resource allocation since a surge of patients with influenza illness can be expected to seek care and receive treatment in the weeks surrounding the peak.
#### Short Term Forecasts
Definition One- to four-week ahead forecasts will be defined as the weighted ILINet percentage for the target week, rounded to one decimal place.
Motivation Forecasts capable of providing reliable estimates of influenza activity over the next month are critical because they allow healthcare and public health officials to prepare for and respond to near-term changes in influenza activity and bridge the gap between reported incidence data and long-term seasonal forecasts.
### State ILI and laboratory data
Data on the weekly proportion of people seeing their health-care provider for influenza-like illness (ILI) is reported through the ILINet System for the United States as a whole, for each HHS health region, and for most individual US States. These data can be accessed directly from CDC. Alternatively, the R package cdcfluview (available from CRAN or GitHub) can be used to access the data as shown in the following example
# Option 1: Install from CRAN
install.packages("cdcfluview")
# Option 2: Install from GitHub (most up-to-date version)
devtools::install_github("hrbrmstr/cdcfluview")
library(cdcfluview)
# National ILINet data for 1997/98 - 2018/19 seasons
usflu <- get_flu_data(region = "national", data_source = "ilinet", years = 1997:2018)
# HHS Regional ILINet data for 1997/98 - 2018/19 seasons
regionflu <- get_flu_data(region = "HHS", sub_region = 1:10, data_source = "ilinet", years = 1997:2018)
# State ILINet data for 1997/98 - 2018/19 seasons -- only available via GitHub version
stateflu <- get_flu_data(region = "state", sub_region = "all", data_source = "ilinet", years = 1997:2018)
Please note that while cdcfluview accesses publically available CDC data, it is not produced, maintained, or endorsed by the CDC.
For those states that have not publically released their data, participating teams can access state-level reports of influenza like illness as well as clinical and public health laboratory data through the "State ILI data" tab at left. This tab is only accessible to participating teams - if you would like to participate please email [email protected] for more information!
Teams are welcome to use data sources for model development beyond the provided data - possible additional data sources include but are not limited to:
Forecast Evaluation
All forecasts will be evaluated using the weighted observations pulled from the ILINet system in week 28, and the logarithmic score will be used to measure the accuracy of the probability distribution of a forecast. Logarithmic scores will be averaged across different time periods, the seasonal targets, the four-week ahead targets, and locations to provide both specific and generalized measures of model accuracy. Forecast accuracy will be measured by log score only. Nonetheless, forecasters are requested to continue to submit point predictions, which should aim to minimize the absolute error (AE).
#### Logarithmic Score
If ;;\mathbf{p};; is the set of probabilities for a given forecast, and ;;\mathbf{p_i};; is the probability assigned to the observed outcome ;;i;;, the logarithmic score is:
$$S(\mathbf{p},i) = \text{ln}(p_i)$$
For peak week, the probability assigned to that correct bin (based on the weighted ILINet value) plus the probability assigned to the preceding and proceeding bins will be summed to determine the probability assigned to the observed outcome. In the case of multiple peak weeks, the probability assigned to the bins containing the peak weeks and the preceding and proceeding bins will be summed. For peak percentage and 4-weeks-ahead forecasts, the probability assigned to the correct bin plus the probability assigned to the five preceding and five proceeding bins will be summed to determine the probability assigned to the observed outcome. For example, if the correct peak ILINet value is 6.5%, the probabilities assigned to all bins ranging from 6.0% to 7.0% will be summed to determine the probability assigned to the observed outcome.
For all targets, if the correct bin is near the first or last bin, the number of bins summed will be reduced accordingly. No bin farther than one bin (peak week) or five bins away (percentage forecasts) from the correct bin will contribute to the score. For example, if the correct ILINet percentage for a given week is 0.3%, probabilities assigned to bins ranging from 0% to 0.8% will be summed. Undefined natural logs (which occur when the probability assigned to the observed outcome was 0) will be assigned a value of -10. Forecasts which are not submitted (e.g. if a week is missed) or that are incomplete (e.g. sum of probabilities greater than 1.1) will also be assigned a value of -10.
Example: A forecast predicts there is a probability of 0.2 (i.e. a 20% chance) that the influenza season for Texas peaks on week 2, a 0.3 probability that it peaks on week 3, and a 0.1 probability that it peaks on week 4 with the other 0.4 (40%) distributed across other weeks according to the forecast. Once the flu season has started, the prediction can be evaluated, and the Texas ILI data show that the flu season peaked on week 3. The probabilities for weeks 2, 3, and 4 would be summed, and the forecast would receive a score of ;;ln(0.6) = -0.51;;. If the season peaked on another week, the score would be calculated on the probability assigned to that week plus the values assigned to the preceding and proceeding week.
#### References
FluSight Package
The FluSight R package contains functions to help create and format forecasts, read and verify forecast CSVs, and score forecasts. These are the functions that will be used at CDC to verify and score submitted forecasts. Teams are welcome to use these tools to ensure their forecasts fit the required template and score their forecasts prior to receiving official scores from CDC
devtools::install_github("jarad/FluSight")
library(FluSight)
Read in state forecast entry CSV
entry <- read_entry("your_csv.csv", challenge = "state_ili")
Verify entry
verify_entry(entry, challenge = "state_ili")
verify_entry_file("your_csv.csv", challenge = "state_ili")
Create file of observed truth
truth <- create_truth(fluview = T, year = 2018, challenge = "state_ili")
Expand observed truth to take into account additional bins - 1 bin for weeks, 5 bins for percentage
exp_truth <- expand_truth(truth, week_expand = 1, percent_expand = 5, challenge = "state_ili")
Score a weekly entry against the observed truth
exact_scores <- score_entry(entry, truth, challenge = "state_ili")
expand_scores <- score_entry(entry, exp_truth, challenge = "state_ili")
Guidance Documents
Guidance for the 2018-19 State FluSight challenge is available here
An empty copy of the offical submission template is available here
The intructions for registering your model and submitting forecasts can be found here
Model Questionnaire
Please submit one copy of this form for each model you submit. Please send an updated form if you update your model.
Forecast submission
Participating teams can submit their forecasts here. Interested in participating? Email [email protected] for more information! | 2020-10-20T08:53:52 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.18337635695934296, "perplexity": 3980.736541050645}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-45/segments/1603107871231.19/warc/CC-MAIN-20201020080044-20201020110044-00495.warc.gz"} |
https://latex.wikia.org/wiki/Prod_(LaTeX_symbol) | FANDOM
160 Pages
This command generates the product operator, $\prod$. The difference between this and \Pi, which generates the capital letter $\Pi$, is that \product appears larger, and that it supports the limits to be displayed below and above the symbol.
The following example illustrates the difference between \prod and \Pi. $\prod_{n=1}^4n=24\qquad\Pi_{n=1}^4n=24$
Community content is available under CC-BY-SA unless otherwise noted. | 2019-08-22T20:44:41 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3876073360443115, "perplexity": 1244.7045334379259}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-35/segments/1566027317359.75/warc/CC-MAIN-20190822194105-20190822220105-00265.warc.gz"} |
http://psychology.wikia.com/wiki/Behavioral_momentum?oldid=132216 | # Behavioral momentum
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Behavioral momentum is a theory in Quantitative Analysis of Behavior and is a comparative metaphor based on physical momentum. It describes the general relation between resistance to change (persistence of behavior) and the rate of reinforcement obtained in a given situation.
B. F. Skinner (1938) proposed that all behavior is comprised of the fundamental unit of behavior termed the discriminated operant. The discriminated operant, also known as the three-term contingency, is broken down into three necessary components: an antecedent discriminative-stimulus context, a response, and a reinforcing or punishing consequence. Responding occurs in the presence of the stimulus because responding previously has resulted in a consequence in its presence.
## Resistance to Change Edit
According to behavioral momentum theory, there are two separable aspects of the discriminated operant that independently govern the rate at which a behavior response occurs and the persistence of that response behavior in the face of operant disruption punishment (see Nevin & Grace, 2000, for a review). The operant reinforcement contingency between the response and a reinforcing consequence governs response rates (i.e., response-reinforcer relation) by shaping a particular special pattern of responding, according to the relative law of non-absolute effect (i.e., the matching law; Herrnstein, 1970). Conversely, the Pavlovian relation between a discriminative stimulus context environment and the rate or magnitude (but not both) of reinforcement obtained in the contextual environmental presence of that discriminative stimulus (i.e., stimulus-reinforcer relation) governs the behavior resistance to relative change (extinction process) of a response behavior pattern. Resistance to behavior change is assessed as contingent responding during context conditions of environmental stimulus response disruption (e.g., satiation, extinction) relative to stable, pre-disruption behavior response rates.
Resistance to disruption has been considered a superior measure to stable response rates as an expression of the underlying strength of a response (Nevin, 1974). This is because drastic differences in response rates can occur by Reinforcement contingency shaping particular patterns of behavior (e.g., differential-reinforcement-of-high- or low-response-rate schedules) while reinforcement rates are equal. It is unclear, therefore, whether these differences in response rates necessarily indicate differences in the underlying strength of a response (see Morse, 1966, for a discussion).
According to behavioral momentum theory, the relation between response rates and resistance to change is analogous to the velocity and mass of a moving object, according to Newton’s Second Law of Motion (Nevin, Mandell, & Atak, 1983). Newton’s Second Law states that the change in velocity of a moving object when an outside force is applied is directly related to that force and inversely related to the object’s mass. Similarly, behavioral momentum theory states that the change in response rates under conditions of disruption (Bx) relative to baseline response rates (Bo) are directly related to the force or magnitude of disruption (f) and inversely related to the rate of reinforcement in a stimulus context (r):
(1) $log(Bx / Bo) = -f / rb$.
The free parameter b indicates the sensitivity of resistance to change to the rate of reinforcement in the stimulus context (i.e., the stimulus-reinforcer relation). Resistance to disruption typically is assessed when two distinctive discriminative stimulus contexts alternate and signal different schedules of reinforcement (i.e., a multiple schedule). Equation 1 can be rewritten to account for resistance to change across two stimulus contexts (Nevin, 1992; Nevin, Grace, & McLean, 2001) when a disrupter is uniformly applied across contexts (i.e., f1f2):
(2) $log(Bx1 / Bo1) / log(Bx2 / Bo2) = (r2 / r1)a$.
The subscripts indicate the different stimulus contexts. Thus, Equation 2 states that relative resistance to change is a power function of the relative rate of reinforcement across stimulus contexts, with the a parameter indicating sensitivity to relative reinforcement rate. Consistent with behavioral momentum theory, resistance to disruption often has been found to be greater in stimulus contexts presenting higher rates or magnitudes of reinforcement (see Nevin, 1992, for a review). Strong support for resistance to change being determined by stimulus-reinforcer relations and independent of response-reinforcer relations comes from studies that add response-independent (i.e., free) reinforcement to one stimulus context. For instance, Nevin, Tota, Torquato, and Shull (1990) had pigeons pecking lighted disks on separate variable-interval 60-s schedules of intermittent food reinforcement across two components of a multiple schedule. Additional free reinforcers were presented every 15 or 30 s on average when the disk was red, but not when the disk was green. Thus, the response-reinforcer relation was degraded when the disk was red because each reinforcer was not immediately preceded by a response. Consistent with the matching law, response rates were lower in the red context than in the green context. However, the stimulus-reinforcer relation was enhanced in the red context because the overall rate of food presentation was greater. Consistent with behavioral momentum theory, resistance to presession feeding (satiation) and discontinuing reinforcement in both contexts (extinction) was greater in the red context. Similar results have been found when reinforcers are added to a context by reinforcing an alternative response.
The findings of Nevin et al. (1990) have been extended across a number of procedures and species including goldfish (Igaki & Sakagami, 2004), rats (Harper, 1999a, 1999b; Shull, Gaynor, & Grimes, 2001), pigeons (Podlesnik & Shahan, 2007), and humans (Ahearn, Clark, Gardenier, Chung, & Dube, 2003; Cohen, 1996; Mace et al., 1990). The behavioral momentum framework also has been used to account for the partial-reinforcement extinction effect (Nevin & Grace, 1999), to assess the persistence of drug-maintained behavior (Jimenez-Gomez & Shahan, 2007; Shahan & Burke, 2004), to increase task compliance (e.g., Belfiore, Lee, Scheeler, & Klein, 2002), and to understand the effects of social policies on global problems (Nevin, 2005).
Although behavioral momentum theory is a powerful framework for understanding how a context of reinforcement can affect the persistence of discriminated operant behavior, there are a number of findings that are inconsistent with the theory (see Nevin & Grace, 2000, and accompanying commentary). For instance, with equal reinforcement rates across stimulus contexts, resistance to change has been shown to be affected by manipulations to response-reinforcer relations, including schedules that produce different baseline response rates (e.g., Lattal, 1989; Nevin, Grace, Holland, & McLean), delays to reinforcement (e.g., Bell, 1999; Grace, Schwendimann, & Nevin, 1998; Podlesnik, Jimenez-Gomez, Ward, & Shahan, 2006; Podlesnik & Shahan, 2007), and by providing brief stimuli that accompany reinforcement (Reed & Doughty, 2005). Also, it is unclear what factors affect relative resistance to change of responding maintained by conditioned reinforcement (Shahan & Podlesnik, 2005) or two concurrently available responses when different rates of reinforcement are arranged within the same context for those responses (e.g., Bell & Williams, 2002).
## Preference and Resistance to Change Edit
As resistance to disruption across stimulus contexts is analogous to the inertial mass of a moving object, behavioral momentum theory also suggests that preference in concurrent-chains procedures for one stimulus context over another is analogous to the gravitational attraction of two bodies (see Nevin & Grace, 2000). In concurrent-chains procedures, responding on the concurrently available initial links provides access to one of two mutually exclusive stimulus contexts called terminal links. As with multiple schedules, independent schedules of reinforcement can function in each terminal-link context. The relative allocation of responding across the two initial links indicates the extent to which an organism prefers one terminal-link context over the other. Moreover, behavioral momentum theory posits that preference provides a measure of the relative conditioned-reinforcing value of the two terminal-link contexts, as described by the contextual-choice model (Grace, 1994).
Grace and Nevin (1997) assessed both relative resistance to change in a multiple schedule and preference in a concurrent-chains procedure with pigeons pecking lighted disks for food reinforcement. When the relative rate of reinforcement was manipulated identically and simultaneously across stimulus contexts in the multiple schedule and concurrent-chains procedure, both relative resistance to change and preference was greater with richer contexts of reinforcement. When all the extant resistance to change and preference data were summarized by Grace, Bedell, and Nevin (2002), they found that those measures were related by a structural relation slope of 0.29. Therefore, relative resistance to change and preference both have been conceptualized as expressions of an underlying construct termed response strength, conditioned reinforcement value, or more generally, behavioral mass of discriminated operant behavior (see Nevin & Grace, 2000).
## References Edit
• Ahearn, W. H., Clark, K. M., Gardenier, N. C., Chung, B. I., & Dube, W. V. (2003). Persistence of stereotyped behavior: Examining the effects of external reinforcers. Journal of Applied Behavior Analysis, 36, 439-448.
• Belfiore, P. J., Lee, D. L., Scheeler, C., & Klein, D. (2002). Implications of behavioral momentum and academic achievement for students with behavior disorders: Theory, application, and practice. Psychology in the Schools, 39, 171-179.
• Bell, M. C. (1999). Pavlovian contingencies and resistance to change in a multiple schedule. Journal of the Experimental Analysis of Behavior, 72, 81-96.
• Bell, M. C., & Williams, B. A. (2002). Preference and resistance to change in concurrent variable-interval schedules. Animal Learning & Behavior, 30, 34-42.
• Cohen, S. L. (1996). Behavioral momentum of typing behavior in college students. Journal of Behavior Analysis and Therapy, 1, 36-51.
• Grace, R. C. (1994). Independence of reinforcement delay and magnitude in concurrent chains. Journal of the Experimental Analysis of Behavior, 63, 255-276.
• Grace, R. C., Bedell, M. A., & Nevin, J. A. (2002). Preference and resistance to change with constant- and variable-duration terminal links: Independence of reinforcement rate and magnitude. Journal of the Experimental Analysis of Behavior, 77, 233-255.
• Grace, R. C., & Nevin, J. A. (1997). On the relation between preference and resistance to change. Journal of the Experimental Analysis of Behavior, 67, 43-65.
• Grace, R. C., Schwendiman, J. W., & Nevin, J. A. (1998). Effects of unsignaled delay of reinforcement on preference and resistance to change. Journal of the Experimental Analysis of Behavior, 69, 247-261.
• Harper, D. N. (1999a). Behavioral resistance to haloperidol and clozapine. Behavioral Processes, 46, 1-13.
• Harper, D. N. (1999b). Drug-induced changes in responding are dependent on baseline stimulus-reinforcer contingencies. Psychobiology, 27, 95-104.
• Herrnstein, R. J. (1970). On the law of effect. Journal of the Experimental Analysis of Behavior, 13, 243-266.
• Igaki, T., & Sakagami, T. (2004). Resistance to change in goldfish. Behavioral Processes, 66, 139-152.
• Jimenez-Gomez, C., & Shahan, T. A. (2007). Resistance to change of alcohol self-administration: Effects of alcohol-delivery rate on disruption by extinction and naltrexone. Behavioural Pharmacology, 18, 161-169.
• Lattal, K. A. (1989). Contingencies on response rate and resistance to change. Learning and Motivation, 20, 191-203.
• Mace, F. C., Lalli, J. S., Shea, M. C., Lalli, E. P., West, B. J., Roberts, M., & Nevin, J. A. (1990). The momentum of human behavior in a natural setting. Journal of the Experimental Analysis of Behavior, 54, 163-172.
• Morse, W. H. (1966). Intermittent reinforcement. In W. K. Honig (Ed.), Operant behavior: Areas of research and application (pp. 52-108). New York: Appleton-Century Crofts.
• Nevin, J. A. (1974). Response strength in multiple schedules. Journal of the Experimental Analysis of Behavior, 21, 389-408.
• Nevin, J. A. (1992). An integrative model for the study of behavioral momentum. Journal of the Experimental Analysis of Behavior, 57, 301-316.
• Nevin, J. A. (2005). The inertia of affluence. Behavior and Social Issues, 14, 7-20.
• Nevin, J. A., & Grace, R. C. (1999). Does the context of reinforcement affect resistance to change? Journal of Experimental Psychology: Animal Behavior Processes, 25, 256-268.
• Nevin, J. A., & Grace, R. C. (2000a). Behavioral momentum and the Law of Effect. Behavioral and Brain Sciences, 23, 73-130.
• Nevin, J. A., Grace, R. C., Holland, S., & McLean, A. P. (2001). Variable-ratio versus variable-interval schedules: Response rate, resistance to change, and preference. Journal of the Experimental Analysis of Behavior, 76, 43-74.
• Nevin, J. A., Grace, R. C., & McLean, A. P. (2001). Resistance to extinction: Contingency termination and generalization decrement. Journal of the Experimental Analysis of Behavior, 76, 43-74.
• Nevin, J. A., Tota, M. E., Torquato, R. D., & Shull, R. L. (1990). Alternative reinforcement increases resistance to change: Pavlovian or operant contingencies? Journal of the Experimental Analysis of Behavior, 53, 359-379.
• Podlesnik, C. A., Jimenez-Gomez, C., Ward, R. D., & Shahan, T. A. (2006). Resistance to change of responding maintained by unsignaled delays to reinforcement: A response-bout analysis. Journal of the Experimental Analysis of Behavior, 85, 329-347.
• Podlesnik, C. A., & Shahan, T. A. (2007). Response-reinforcer relations and resistance to change. Behavioural Processes, doi:10.1016/j.beproc.2007.07.002)
• Reed, P., & Doughty, A. H. (2005). Within-subject testing of the signaled-reinforcement effect on operant responding as measured by response rate and resistance to change. Journal of the Experimental Analysis of Behavior, 83, 31-45.
• Shahan, T. A., & Burke, K. A. (2004). Ethanol-maintained responding of rats is more resistant to change in a context with added non-drug reinforcement. Behavioral Pharmacology, 15, 279-285.
• Shahan, T. A., & Podlesnik, C. A. (2005). Rate of conditioned reinforcement affects observing rate but not resistance to change. Journal of the Experimental Analysis of Behavior, 84, 1-17.
• Shull, R. L., Gaynor, S. T., & Grimes, J. A. (2002). Response rate viewed as engagement bouts: Resistance to extinction. Journal of the Experimental Analysis of Behavior, 77, 211-231.
• Skinner, B. F. (1938). The behavior of organisms: An experimental analysis. Cambridge, MA: Appleton-Century-Crofts.
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https://par.nsf.gov/biblio/10379573-variability-brightest-cluster-galaxies-high-radio-frequencies | The variability of brightest cluster galaxies at high radio frequencies
ABSTRACT
Variability of a galaxy’s core radio source can be a significant consequence of active galactic nucleus accretion. However, this variability has not been well studied, particularly at high radio frequencies. As such, we report on a campaign monitoring the high radio frequency variability of 20 nearby, cool-core brightest cluster galaxies. From our representative sample, we show that most vary significantly on time-scales of approximately 1 yr and longer. Our highest cadence observations are at 15 GHz and are from the Owens Valley Radio Observatory. They have a median time interval of 7 d and mostly span between 8 and 13 yr. We apply a range of variability detection techniques to the sources’ light curves to analyse changes on week to decade long time-scales. Most notably, at least half of the sources show 20 per cent peak to trough variability on 3 yr time-scales, while at least a third vary by 60 per cent on 6 yr time-scales. Significant variability, which is important to studies of the Sunyaev–Zel’dovich Effect in the radio/sub-mm, is therefore a common feature of these sources. We also show how the variability relates to spectral properties at frequencies of up to 353 GHz using data from the Korean VLBI network, the NIKA2 instrument of the IRAM more »
Authors:
; ; ; ; ; ; ; ;
Publication Date:
NSF-PAR ID:
10379573
Journal Name:
Monthly Notices of the Royal Astronomical Society
Volume:
509
Issue:
2
Page Range or eLocation-ID:
p. 2869-2884
ISSN:
0035-8711
Publisher:
Oxford University Press
National Science Foundation
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3. ABSTRACT
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Weakly accreting black hole X-ray binaries launch compact radio jets that persist even in the quiescent spectral state, at X-ray luminosities ≲ 10−5 of the Eddington luminosity. However, radio continuum emission has been detected from only a few of these quiescent systems, and little is known about their radio variability. Jet variability can lead to misclassification of accreting compact objects in quiescence, and affects the detectability of black hole X-ray binaries in next-generation radio surveys. Here we present the results of a radio monitoring campaign of A0620 − 00, one of the best-studied and least-luminous known quiescent black hole X-ray binaries. We observed A0620 − 00 at 9.8 GHz using the Karl G Jansky Very Large Array on 31 epochs from 2017 to 2020, detecting the source $\sim 75{{\ \rm per\, cent}}$ of the time. We see significant variability over all time-scales sampled, and the observed flux densities follow a lognormal distribution with μ = 12.5 μJy and σ = 0.22 dex. In no epoch was A0620 − 00 as bright as in 2005 (51 ± 7 μJy), implying either that this original detection was obtained during an unusually bright flare, or that the system is fading in the radio over time. We presentmore »
5. ABSTRACT
A repeating source of fast radio bursts (FRBs) is recently discovered from a globular cluster of M81. Association with a globular cluster (or other old stellar systems) suggests that strongly magnetized neutron stars, which are the most likely objects responsible for FRBs, are born not only when young massive stars undergo core-collapse, but also by mergers of old white dwarfs. We find that the fractional contribution to the total FRB rate by old stellar populations is at least a few per cent, and the precise fraction can be constrained by FRB searches in the directions of nearby galaxies, both star-forming and elliptical ones. Using very general arguments, we show that the activity time of the M81-FRB source is between 104 and 106 yr, and more likely of the order of 105 yr. The energetics of radio outbursts put a lower limit on the magnetic field strength of 10$^{13}\,$G, and the spin period $\gtrsim 0.2\,$s, thereby ruling out the source being a milli-second pulsar. The upper limit on the persistent X-ray luminosity (provided by Chandra), together with the high FRB luminosity and frequent repetitions, severely constrains (or rules out) the possibility that the M81-FRB is a scaled-up version of giant pulses frommore » | 2023-03-26T16:53:56 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.617530107498169, "perplexity": 2374.2676436139363}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296945473.69/warc/CC-MAIN-20230326142035-20230326172035-00734.warc.gz"} |
https://tjyj.stats.gov.cn/CN/10.19343/j.cnki.11-1302/c.2018.09.009 | • •
### 基尼加权回归分析：概念、方法及应用
• 出版日期:2018-09-25 发布日期:2018-09-25
### Weighted Gini Regression: Concept, Method and its Application
Dai Pingsheng
• Online:2018-09-25 Published:2018-09-25
Abstract: The method of ordinary least squares (OLS) is one of the most common one for regression analysis. OLS relies on several classical assumptions, and estimators are affected easily by extreme values, high income groups in regression analysis with related to income or small sample size. This paper promotes the weighted Gini regression as an alternative way, which consists of parameter estimating and non-parameter estimating. Parameter estimator is based on minimum of Gini mean difference of sample residues; non-parameter estimator comes from weighted value of slopes. Hypothesis test and R-squared calculating are carried in weighted Gini regression, resampling Jackknife technology is used to estimate variance for hypothesis test. It promotes a new algorithm of sample extend Gini mean difference, which can cover the shortage of approximate treatment of sample data. It discusses about how inbound tourism receipt influences income Gini coefficients by using 2015 provincial cross-sectional data and 1994-2015 total time series data in China. The results from weighted Gini regression line with expectations of relationship between variables, and they can reflect effects of inbound tourism receipt on income equity of different groups by changing inequality preference. | 2022-11-28T14:48:19 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.46876227855682373, "perplexity": 3305.0637788588256}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446710533.96/warc/CC-MAIN-20221128135348-20221128165348-00049.warc.gz"} |
http://pdglive.lbl.gov/DataBlock.action?node=Q007D13 | # ${{\boldsymbol t}}{{\overline{\boldsymbol t}}}$ ${{\boldsymbol t}}{{\overline{\boldsymbol t}}}$ Production Cross Section in ${{\boldsymbol p}}{{\boldsymbol p}}$ Collisions at $\sqrt {s }$ = 13 TeV INSPIRE search
VALUE (fb) CL% DOCUMENT ID TECN COMMENT
• • • We do not use the following data for averages, fits, limits, etc. • • •
$<94$ 95 1
2017 AB
CMS ${{\mathit \ell}}$+jets, ${{\mathit \ell}^{+}}{{\mathit \ell}^{-}}$ +jets channels
1 SIRUNYAN 2017AB based on 2.6 fb${}^{-1}$ of data. A multivariate analysis is used to discriminate between ${{\mathit t}}{{\overline{\mathit t}}}{{\mathit t}}{{\overline{\mathit t}}}$ signal and ${{\mathit t}}{{\overline{\mathit t}}}$ background. A combination with a previous search (CMS, KHACHATRYAN 2016BJ) in the same-sign dilepton channel gives an upper limit of 69 fb (95$\%$ CL), corresponding to 7.4$\cdot{}$(SM prediction).
References:
SIRUNYAN 2017AB
PL B772 336 Search for Standard Model Production of Four Top Quarks in Proton-Proton Collisions at $\sqrt {s }$ = 13 TeV
KHACHATRYAN 2016BJ
EPJ C76 439 Search for New Physics in Same-sign Dilepton Events in Proton-Proton Collisions at $\sqrt {s }$ = 13 TeV | 2019-02-21T19:58:48 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9758194088935852, "perplexity": 6879.888663122149}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-09/segments/1550247508363.74/warc/CC-MAIN-20190221193026-20190221215026-00298.warc.gz"} |
https://gea.esac.esa.int/archive/documentation/GDR2/Data_analysis/chap_cu8par/sec_cu8par_intro/ssec_cu8par_intro_whatsdone.html | # 8.1.1 What’s been done in Gaia DR2
Author(s): Coryn Bailer-Jones
We use the three-band photometry and parallaxes, together with various training data sets, to estimate the effective temperature $T_{\rm eff}$, line-of-sight extinction $A_{\rm G}$ and reddening $E(G_{\rm BP}-G_{\rm RP})$, luminosity ${\cal L}$, and radius ${\cal R}$, of up to 161 million stars brighter than $G$ =17; a total of five parameters. (Subsequent filtering removes parameters for some sources.) Although photometry for fainter sources is available in Gaia DR2, we chose to limit our analysis to brighter sources on the grounds that, at this stage in the mission and processing, only these give sufficient photometric and parallax precision to obtain reliable astrophysical parameters. The choice of 17 is somewhat arbitrary, however. The three broad photometric bands (see Section 5), provide relatively little information for deriving the intrinsic properties of the observed Gaia targets. Moreover, the $G$-band flux is nearly degenerate with the sum of the other two (see Figure 5.9). We therefore assume all sources to be single stars. A source-by-source classification to identify quasars, galaxies, and – to some extent – unresolved binary stars will be performed using the dispersed BP/RP spectra for Gaia DR3 (Bailer-Jones, C. A. L. et al. 2013). There will, of course, be relatively few extragalactic point sources in our sample of $G\leq 17$.
Stellar parameters are estimated source-by-source. We do not make use of any global Galactic information such as an extinction map or kinematics. We also do not use any non-Gaia data on the individual sources. We only use the three Gaia photometric bands (for $T_{\rm eff}$) and additionally the parallax (for the other four parameters).
As can be seen in Figure 8.1, $T_{\rm eff}$ is heavily degenerate with $A_{\rm G}$, making it impossible to estimate both with any useful precision from these data alone. We therefore estimate $T_{\rm eff}$ from the colours on the assumption that extinction is low. This is done with a machine learning algorithm trained empirically: the training data are observed Gaia photometry of stars which have had their $T_{\rm eff}$ estimated from other sources. This training data set only includes stars which are believed to have low extinctions. This use of empirical training sets avoids biases which can occur when training on synthetic data (which occur due to inevitable mismatch between synthetic templates and real spectra).
We then separately estimate the interstellar absorption using the three fluxes together with the parallax (again using a machine learning algorithm). The signal here is the dimming of the sources due to absorption, as opposed to reddening. For this we train the algorithm on synthetic stellar photometry, because there are too few stars with reliably estimated extinctions which could be used as an empirical training set. The relative extinction parameter, $R_{\rm 0}$, is fixed to 3.1. Note that the absorption we estimate is the extinction in the G-band, $A_{\rm G}$, which is not the same as the (monochromatic) extinction parameter, $A_{\rm 0}$. The latter depends only on the amount of absorption in the interstellar medium at the single wavelength 547.7nm, whereas the former depends also on the spectral energy distribution (SED) of the star (see section 2.2 of Bailer-Jones 2011). Thus even with fixed $R_{\rm 0}$ there is not a one-to-one relationship between $A_{\rm 0}$ and $A_{\rm G}$, although in practice the scatter about a constant relation is small. For this reason we use a separate machine learning model (with the same inputs and trained with the same synthetic spectra) to estimate the reddening $E(G_{\rm BP}-G_{\rm RP})$, even though the available signal is still primarily the dimming due to absorption. Given the strong degeneracy between $T_{\rm eff}$ and $A_{\rm G}$ and $E(G_{\rm BP}-G_{\rm RP})$, respectively, our results contained many outliers and the decision was made to filter these out of Gaia DR2. Therefore, estimates of $A_{\rm G}$ and $E(G_{\rm BP}-G_{\rm RP})$are available for only 87.7 million sources.
We estimate the absolute G-band magnitude via (with r expressed in pc)
$M_{G}\,=\,G+5-5\log_{10}r-A_{\rm G}$ (8.1)
This is converted to a stellar luminosity using the zeropoint of the $G$-magnitude system and a bolometric correction (see Section 8.3.3). The distance $r$ to the target is taken simply to be the inverse of the parallax in arcsec. Although this generally gives a biased estimate of the distance (see for example Bailer-Jones 2015), the impact of this is mitigated here by the fact that we only derive luminosities when the fractional parallax uncertainty $\sigma_{\varpi}/\varpi$ is less than 0.2. Thus of the 161 million stars with $T_{\rm eff}$ estimates, only 77 million have luminosity estimates included in Gaia DR2.
Having inferred the luminosity and temperature, the stellar radius is then given by the Stefan–Boltzmann law
${\cal L}\,=\,4\pi\sigma{\cal R}^{2}T_{\rm eff}^{4}$ (8.2)
Because our individual extinction estimates are rather poor for most stars (discussed later), we chose not to use them in the derivation of luminosities, i.e. we set $A_{\rm G}$ to zero in Equation 8.1. Consequently, while our temperature, luminosity, and radius estimates are self-consistent (within the limits of the adopted assumptions), they are formally inconsistent with our extinction and reddening estimates. | 2018-10-19T19:49:40 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 33, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9248871803283691, "perplexity": 887.5659474638558}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-43/segments/1539583512434.71/warc/CC-MAIN-20181019191802-20181019213302-00062.warc.gz"} |
https://linkeddata.tern.org.au/viewer/tern/id/http://linked.data.gov.au/def/tern-cv/2f4c1e8a-7acd-4b79-b16b-04913233cc07 | # net ecosystem productivity
URI: http://linked.data.gov.au/def/tern-cv/2f4c1e8a-7acd-4b79-b16b-04913233cc07
Also known as NEP, net ecosystem production
Date created: 2021-05-21
Date modified: 2021-05-24
Parameter Type
##### Definition
The difference between the amount of organic carbon fixed in an ecosystem by photosynthesis (gross primary productivity) and total ecosystem respiration. NEP represents the total amount of organic carbon available for storage or loss in the ecosystem. Whether NEP is greater or less than zero determines if an ecosystem is autrophic or heterotrophic.
##### source
agclass.nal.usda.gov
NEP
##### note
NEP is the abbreviation used by OzFlux.
TERN is supported by the Australian Government through the National Collaborative Research Infrastructure Strategy, NCRIS. | 2022-08-15T22:12:23 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.25545498728752136, "perplexity": 11054.775450350138}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882572212.96/warc/CC-MAIN-20220815205848-20220815235848-00112.warc.gz"} |
https://www.nist.gov/news-events/news/2011/09/comprehensive-risk-assessment-guidance-federal-information-systems | Comprehensive Risk Assessment Guidance for Federal Information Systems Published
September 20, 2011
Created September 20, 2011, Updated January 08, 2018 | 2018-05-21T19:09:57 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8260264992713928, "perplexity": 14514.188367511759}, "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-2018-22/segments/1526794864466.23/warc/CC-MAIN-20180521181133-20180521201133-00365.warc.gz"} |
https://beta.abs.gov.au/methodologies/crime-victimisation-australia-methodology/2018-2019 | The statistical information on this site may not be the latest. For the most up to date information visit the ABS website abs.gov.au
Latest release
# Crime Victimisation, Australia methodology
Reference period
2018 - 2019
Released
1/06/2020
Next release Unknown
First release
## Explanatory notes
### Introduction
This publication presents results from the Crime Victimisation Survey, a topic on the Multipurpose Household Survey (MPHS) conducted throughout Australia from July 2018 to June 2019. The MPHS, undertaken each financial year by the Australian Bureau of Statistics (ABS), is a supplement to the monthly Labour Force Survey (LFS) and is designed to collect statistics for a number of small, self-contained topics.
This publication covers the Crime Victimisation topic and presents details about the prevalence of a selected range of personal and household crimes, including the socio-demographic characteristics of persons experiencing the selected crimes, experiences of repeat victimisation, and the characteristics of the most recent incident of each crime type experienced. Some estimates from previous iterations of the Crime Victimisation Survey are also included in this publication.
The Crime Victimisation Survey is being conducted again as part of the MPHS for the reference period 2019-20, with results expected to be released in early 2021.
### Scope and coverage
The scope of the Crime Victimisation Survey was restricted to people aged 15 years and over who were usual residents of private dwellings and excludes:
• members of the Australian permanent defence forces;
• certain diplomatic personnel of overseas governments, customarily excluded from Census and estimated resident population counts;
• overseas residents in Australia; and
• members of non-Australian defence forces (and their dependants).
Additionally, the 2018-19 MPHS scope excluded:
• persons living in non-private dwellings such as hotels, university residences, boarding schools, hospitals, nursing homes, homes for people living with disabilities, and prisons; and
• persons resident in the Indigenous Community Strata (ICS).
The scope for MPHS included households residing in urban, rural, remote and very remote parts of Australia, except the ICS. In the LFS, rules are applied which aim to ensure that each person in coverage is associated with only one dwelling, and hence has only one chance of selection in the survey. See Labour Force, Australia (cat. no. 6202.0) for more detail.
### Data collection
The Crime Victimisation Survey is one of a number of small, self-contained topics on the Multipurpose Household Survey (MPHS), conducted throughout Australia from July 2018 to June 2019. The MPHS is a supplement to the monthly LFS. In 2018–19, the MPHS topics were:
• Crime Victimisation;
• Patient Experiences in Australia;
• Barriers and Incentives to Labour Force Participation;
• Retirement and Retirement Intentions;
• Qualifications and Work; and
• Income (Personal, Partner's, Household).
For all topics, general demographic information such as age, sex, labour force characteristics, education and income are also available.
ABS interviewers conducted personal interviews during the 2018-19 financial year for the monthly LFS. Each month, one eighth of the dwellings in the LFS sample were rotated out of the survey and selected for the MPHS. After the LFS had been fully completed for each person in scope and coverage, a usual resident aged 15 years or over was selected at random (based on a computer algorithm) and asked the additional MPHS questions.
In the MPHS, if the randomly selected person was aged 15 to 17 years, permission was sought from a parent or guardian before conducting the interview. If permission was not given, the parent or guardian was asked the questions on behalf of the 15 to 17 year old (proxy interview). Questions relating to sexual assault and the involvement of alcohol or substances in the most recent incident of physical assault and face-to-face threatened assault were not asked of proxy respondents. Only persons aged 18 years and over were asked questions on sexual assault and the involvement of alcohol or substances in the most recent incident of physical assault and face-to-face threatened assault.
Data were collected using Computer Assisted Interviewing (CAI), whereby responses were recorded directly onto an electronic questionnaire in a notebook computer, with interviews conducted either face-to-face or over the telephone. The majority of interviews were conducted over the telephone.
### Sample size
After taking into account sample loss, the response rate for the Crime Victimisation Survey was 71.8%. In total, information was collected from 28,719 fully responding persons. This includes 477 proxy interviews for people aged 15 to 17 years, where permission was not given by a parent or guardian for a personal interview.
### Weighting
Weighting is the process of adjusting results from a sample survey to infer results for the total in-scope population. To do this, a 'weight' is allocated to each enumerated person. The weight is a value which indicates the number of persons in the population represented by the sample person.
The first step in calculating weights for each unit is to assign an initial weight, which is the inverse of the probability of being selected in the survey. For example, if the probability of a person being selected in the survey was 1 in 600, then the person would have an initial weight of 600 (that is, they represent 600 people).
### Benchmarks
The initial weights were calibrated to align with independent estimates of the population of interest, referred to as 'benchmarks'. Weights calibrated against population benchmarks ensure that the survey estimates conform to the independently estimated distribution of the population rather than the distribution within the sample itself. Calibration to population benchmarks helps to compensate for over-or-under-enumeration of particular categories of persons/households which may occur due to either the random nature of sampling or non-response.
For household estimates, the MPHS was benchmarked to independently calculated estimates of the total number of households in Australia. The MPHS estimates do not (and are not intended to) match estimates for the total Australian person/household populations obtained from other sources.
The survey was benchmarked to the Estimated Resident Population (ERP) living in private dwellings in each state and territory at December 2018, based on the 2016 Census. People living in Indigenous communities were excluded.
While the LFS benchmarks are revised every five years to take into account the outcome of the five-yearly rebasing of the ERP following the latest Census, the supplementary surveys and MPHS (from which the statistics in this publication are taken) are not. Small differences will therefore exist between the civilian population aged 15 years and over reflected in the LFS and other labour household survey estimates, as well as over time.
### Estimation
Survey estimates of counts of persons are obtained by summing the weights of persons with the characteristic of interest.
### Confidentiality
To minimise the risk of identifying individuals in aggregate statistics, a technique called perturbation is used to randomly adjust cell values. Perturbation involves a small random adjustment of the statistics and is considered the most satisfactory technique for avoiding the release of identifiable statistics while maximising the range of information that can be released. These adjustments have a negligible impact on the underlying pattern of the statistics.
After perturbation, a given published cell value will be consistent across all tables. However, adding up cell values to derive a total will not necessarily give the same result as published totals.
Perturbation has been applied to Crime Victimisation Survey datasets since 2013–14. Data from previous cycles (2008-09 to 2012–13) have not been perturbed, but underwent a different confidentialisation method to protect the confidentiality of respondents.
### Reliability of estimates
All sample surveys are subject to error which can be broadly categorised as either sampling error or non-sampling error.
Sampling error is the difference between the published estimates, derived from a sample of persons, and the value that would have been produced if the total population (as defined by the scope of the survey) had been included in the survey.
Non-sampling error may occur in any statistical collection, whether it is based on a sample or a full count such as a census. Sources of non-sampling error include non-response, errors in reporting by respondents or recording of answers by interviewers, and errors in coding and processing data. Every effort is made to reduce non-sampling error by careful design and testing of questionnaires, training and supervision of interviewers, and extensive editing and quality control procedures at all stages of data processing.
Only data with a relative standard error (RSE) of less than 25% are included in the publication commentary (unless otherwise noted), and any differences between populations and changes over time that are referred to are statistically significant. All data contained in the commentary are available for download as data cubes from the Data downloads section. For more information about relative standard error and statistical significance refer to the Technical Note.
### Interpretation of results
Crime victimisation surveys are best suited to measuring crimes against specific individuals or households. Respondents need to be aware of and recall what happened to them and how it happened, as well as be willing to relate what they know to interviewers.
Not all types of crime are suitable for measurement by household surveys. No reliable information can be obtained about crimes without specific victims, such as trafficking in narcotics. Crimes of which a person may not be aware cannot be measured effectively through a household survey, for example crimes involving deception. It may also be difficult to obtain information about some crimes, such as sexual offences and assault committed by other household or family members, due to the sensitivity of the crime and an increased reluctance to disclose. Some of these crimes may not be fully represented in the data collected. Household survey data exclude crimes against commercial establishments or government agencies.
This survey covered only selected types of personal and household crimes and does not represent all crime in Australia. Personal crimes covered in the survey were physical assault, threatened assault (face-to-face and non-face-to-face), robbery and sexual assault. Household crimes covered were break-in, attempted break-in, motor vehicle theft, theft from a motor vehicle, malicious property damage and other theft.
Information collected in this survey is essentially 'as reported' by respondents and hence may differ from that which might be obtained from other surveys or administrative data sources. This factor should be considered when interpreting the estimates and when making comparisons with other data sources.
### Experiences of family and domestic violence
There is limited information available in this publication about family and domestic violence. The Crime Victimisation Survey collects information about experiences of personal violence and the relationship between the victim and perpetrator, however this information alone is not sufficient to reliably measure the number of people who have experienced family and domestic violence.
The Crime Victimisation Survey collects incident characteristics information, including relationship to the offender, only for the most recent incident of each type of personal crime experienced in the 12 months prior to interview. This means that not all experiences of personal violence by each relationship type - including current and previous partners - are captured in the survey. In addition, as interviews are conducted by telephone in the respondent’s home, there is no requirement for a private interview setting for the Crime Victimisation Survey (as is the case for the ABS’s Personal Safety Survey). This non-private setting means respondents may be less likely to disclose any experiences of violence by their partner if their partner is present in the home at the time of interview. As a result, the statistics on relationship type available in this publication cannot be used to draw conclusions about the prevalence of family and domestic violence in Australia.
Due to the ongoing relationship between victim and perpetrator, family and domestic violence is often a recurring event, and the protracted nature of this violence cannot be reliably measured within the framework of the Crime Victimisation Survey. Further information about defining and measuring family and domestic violence is available in Defining the Data Challenge for Family Domestic and Sexual Violence (cat. no. 4529.0) and statistics are available in Personal Safety, Australia (cat. no. 4906.0), Directory of Family, Domestic, and Sexual Violence Statistics, 2018 (cat. no. 4533.0), and Recorded Crime - Victims, Australia (cat. no. 4510.0).
### Statistical measures of crime victimisation
The level of victimisation can be measured and expressed in more than one way. The most common measure derived from crime victimisation surveys is prevalence, that is, the number of the relevant population that have experienced a given crime at least once in the reference period. Victimisation rates used in this publication represent the prevalence of selected crimes in Australia, and are expressed as a percentage of the total relevant population. Reporting rates used in this publication are expressed as the percentage of persons/households whose most recent incident of each type of crime had been reported to the police.
### Comparability of time series
The 2018-19 Crime Victimisation Survey is the eleventh in a series of annual Crime Victimisation Surveys conducted by the ABS. The ten previous surveys in this series included the majority of the questions asked in 2018-19. As a similar methodology has been adopted for the surveys, data on the prevalence of personal and household crimes is comparable across the survey periods. This has enabled some time series comparisons to be made in this publication.
The Crime Victimisation Survey series replaced the previous Crime and Safety Surveys and was introduced because of a change to the collection methodology. The new method of collection mainly uses personal telephone interviews of selected respondents. Data collections between 1990 and 2005 required respondents to complete questionnaires by themselves and mail these back to the ABS. This difference in mode of collection and changes to survey content means that Crime Victimisation Survey data collected using the MPHS are generally not directly comparable with data from Crime and Safety Surveys prior to 2008–09.
### Comparability with previous crime victimisation surveys
In 2010-11 significant changes to the 'Area of Usual Residence', 'Capital City' and 'Balance of State/Territory' geographical items were made. From 2008-09 to 2012-13 the Australian Standard Geographical Classification (ASGC) (cat. no. 1216.0) was used to characterise Geographical Classifications. From 2013-14 onwards the Australian Statistical Geography Standard (ASGS) (cat. no. 1270.0.55.001) was used. The ASGS is updated on a five yearly basis in accordance with the Census of Population and Housing. Consequently, the 2018-19 Crime Victimisation Survey saw the introduction of the updated ASGS. More information on this can be found in Australian Statistical Geography Standard (ASGS): Volume 1 - Main Structure and Greater Capital City Statistical Areas, July 2016.
For the 2018-19 reference period, the following data have not been published at the state/territory level:
• Robbery;
• Sexual assault;
• Police reporting data for non face-to-face threatened assault;
• Police reporting data for motor vehicle theft; and
• Contribution of alcohol or another substance data for physical assault and face-to-face threatened assault.
A review of data quality found that due to low prevalence and/or high error or volatility, estimates for the above data items are too statistically unreliable for general use. National estimates for these data items are still available in the data cubes, and users are advised to exercise caution when using state and territory level data for these data items from previous iterations of the survey.
### Comparability with police statistics
Data for selected crimes reported to and recorded by police agencies in a calendar year are available in Recorded Crime - Victims, Australia(cat. no. 4510.0). The Crime Victimisation Survey provides an additional source of data on crime victimisation for the selected crimes, including crime not reported to or detected by police. This survey identifies the nature of this unreported crime, as well as giving information about experiences of repeat victimisation. The information from the survey should be viewed as complementary to police recorded crime statistics.
The terms used for the crimes (such as robbery and physical assault) may not necessarily correspond with the legal or police definitions used. This is because responses obtained in this survey are based on the respondent's perception of the behaviours they experienced. The definitions of terms used in the publication are based on the wording of the questions asked of the respondent and specifications provided to interviewers. Definitions of crime types included in this survey can be found in the Glossary.
The Crime Victimisation Survey collects information on crimes that were reported to police, as well as crimes that went unreported. In this publication, reporting rates are based on whether or not the most recent incident of each crime type experienced in the 12 months prior to interview was reported to police. Interviews were conducted over a 12 month period from 1 July 2018 to 30 June 2019. The actual reference period for a particular respondent was determined by the date of their interview. There is no way of verifying that a crime was reported to police, where the respondent indicated that police were informed.
Another source of variation between the survey results and crimes recorded by police relates to differences in scope. This survey collects information on the personal crimes of physical assault, threatened assault (face-to-face and non-face-to-face), and robbery for all persons aged 15 years and over, and sexual assault for persons aged 18 years and over. In contrast, police statistics include victims of all ages, and any comparisons should take this into consideration. Furthermore, police statistics for a given reference period may include criminal incidents that came to the attention of police during the reference period, but did not occur during it.
Due to differences between collections, caution should be exercised when comparing data from surveys and administrative by-product collections that relate to crime and justice topics. For more information on comparisons between sources, please refer to Measuring Victims of Crime: A Guide to Using Administrative and Survey data, June 2011 (cat. no. 4500.0.55.001).
### Comparability with other ABS surveys
Caution should be exercised when comparing across ABS surveys and with administrative by-product data that address the access and use of health services. Estimates from the Crime Victimisation Survey may differ from those obtained in other surveys (such as the Personal Safety Survey, National Aboriginal and Torres Strait Islander Health Survey, National Aboriginal and Torres Strait Islander Social Survey, and General Social Survey) due to differences in survey mode, methodology and questionnaire design.
### Comparability with monthly LFS statistics
Since the Crime Victimisation Survey is conducted as a supplement to the Labour Force Survey (LFS), data items collected in the LFS are also available in this publication. However, there are some important differences between the two surveys. The LFS had a response rate of over 90% compared to the MPHS response rate of 71.8%. The scope of the Crime Victimisation Survey and the LFS also differ, as outlined in the preceding sections. Due to the differences between the samples, data from the Crime Victimisation Survey and the LFS are weighted separately. Variances may therefore be found in the estimates for those data items collected in the LFS and published as part of the Crime Victimisation Survey.
### Other methodological issues
When interpreting data from the 2018-19 MPHS, consideration should be given to the representativeness of the survey sample in relation to the entire in-scope population. This is affected by the response rate and scope and coverage rules. For example, people living in boarding houses, refuges or on the streets are excluded from this survey and may experience different levels of victimisation than those surveyed who live in private dwellings.
### Equivalised weekly household income
Equivalised weekly household income is household income adjusted by the application of an equivalence scale to facilitate comparison of income levels between households of differing size and composition, reflecting that a larger household would normally need more income than a smaller household to achieve the same standard of living. Using an equivalising factor for household income enables the direct comparison of the relative economic well-being of households of different size and composition (for example, lone person households, families and group households of unrelated individuals).
For more information about equivalised weekly household income see Household Income and Wealth, Australia (cat. no. 6523.0) and Survey of Income and Housing, User Guide, Australia (cat. no. 6553.0).
### Socio-Economic Indexes for Areas (SEIFA)
Socio-Economic Indexes for Areas (SEIFA) is a classification developed by the ABS that ranks areas in Australia according to relative socio-economic advantage and disadvantage. SEIFA uses a broad definition of relative socio-economic advantage and disadvantage in terms of people's access to material and social resources, and their ability to participate in society.
The indexes are based on information from the five-yearly Census, and each index summarises a different aspect of the socio-economic conditions of people living in an area. Every geographic area in Australia is given a SEIFA number which shows how disadvantaged or advantaged that area is compared with other areas in Australia.
The Crime Victimisation Survey uses two indexes from the 2016 Socio-Economic Indexes for Areas (SEIFA) – the Index of Relative Socio-Economic Advantage and Disadvantage; and the Index of Relative Socio-Economic Disadvantage. These measures are derived from Census variables related to income, educational attainment, unemployment, occupational skill level and whether a dwelling has a motor vehicle.
For more detail, see the following:
### Country of birth
Country of birth data are classified according to the Standard Australian Classification of Countries (SACC), 2016 (cat. no. 1269.0).
### Education
Education data are classified according to the Australian Standard Classification of Education ASCED, 2001 (cat. no 1272.0). The ASCED is a national standard classification which can be applied to all sectors of the Australian education system including schools, vocational education and training and higher education. The ASCED comprises two classifications: Level of Education and Field of Education.
### Products and services
Data cubes containing all tables for this publication in Excel spreadsheet format are available from the Data downloads section. The spreadsheets present tables of estimates and proportions, and their corresponding relative standard errors (RSEs).
As well as the statistics included in this and related publications, the ABS may have other relevant data available on request. Subject to confidentiality and sampling variability constraints, tables can be tailored to individual requirements. A list of data items from this survey is available from the Data downloads section. All enquiries should be directed to the National Information and Referral Service on 1300 135 070, or email [email protected].
### Acknowledgements
ABS surveys draw extensively on information provided by individuals, businesses, governments and other organisations. Their continued cooperation is very much appreciated and without it, the wide range of statistics published by the ABS would not be available. Information received by the ABS is treated in strict confidence as required by the Census and Statistics Act 1905.
### Privacy
The ABS Privacy Policy outlines how the ABS will handle any personal information that you provide to the ABS.
## Technical note - data quality
### Reliability of the estimates
The estimates in this publication are based on information obtained from a sample survey. Errors in data collection or processing, known as non-sampling error, can impact on the reliability of the resulting statistics. In addition, the reliability of estimates based on sample surveys are also subject to sampling variability. That is, the estimates may differ from those that would have been produced had all persons in the population been included in the survey. This is known as sampling error.
### Non-sampling error
Non-sampling error may occur in any statistical collection, whether it is based on a sample or a full count such as a census. Sources of non-sampling error include non-response, errors in reporting by respondents or recording of answers by interviewers, and errors in coding and processing data.
It is not possible to quantify non-sampling error, however, every effort is made to reduce non-sampling error by careful design and testing of questionnaires, training and supervision of interviewers, and extensive editing and rigorous quality control procedures at all stages of data processing.
### Sampling error
Sampling error refers to the difference between an estimate obtained from surveying a sample of persons, and the result that would have been obtained if all persons had been surveyed.
One measure of sampling error is given by the standard error (SE), which indicates the extent to which an estimate might have varied by chance because only a sample of persons was surveyed. There are about two chances in three (67%) that a sample estimate will differ by less than one SE from the number that would have been obtained if all persons had been surveyed, and about 19 chances in 20 (95%) that the difference will be less than two SEs.
### Relative standard error
In this publication, the standard error of the estimate is expressed as a percentage of the estimate, known as the relative standard error (RSE), which is a useful measure as it indicates the size of the error relative to the estimate.
$$\large{\text{RSE%} = (\frac{SE}{estimate}) \times 100}$$
Only estimates (counts or percentages) with an RSE of less than 25% are considered sufficiently reliable for most analytical purposes. However, estimates with an RSE over 25% are also published. Estimates with an RSE in the range 25% to 50% are less reliable and should be used with caution, while estimates with an RSE greater than 50% are considered too unreliable for general use.
The Excel files available from the Data downloads section contain all the data tables produced for this release, including all estimates and their corresponding RSEs. All cells in the Excel spreadsheets containing an estimate with an RSE of 25% or greater are annotated with asterisks, indicating whether the RSE of the estimate is in the range 25% to 50% (single asterisk *) or is greater than 50% (double asterisk **).
### Calculation of standard error
Standard error (SE) can be calculated using the estimate (count or percentage) and the corresponding RSE. For example, if the estimated number of persons who experienced physical assault in the last 12 months was 462,200, with a corresponding RSE of 5.0%, the SE (rounded to the nearest 100) is calculated by:
$$\large{\begin{array}{l}\text{SE of estimate} \\{=(\frac{RSE\%}{100}) \times estimate}\\{=0.05 \times 462,200}\\{=23, 100}\end{array}}$$
Therefore, there is about a two in three chance that the result that would have been obtained had all persons been included in the survey falls within the range of one standard error below to one standard error above the estimate (439,100 to 485,300), and about a 19 in 20 chance that the result would have fallen within the range of two standard errors below to two standard errors above the estimate (416,000 to 508,400). This example is illustrated in the diagram below:
### Relative standard error of proportions
Proportions formed from the ratio of two estimates are also subject to sampling error. The size of the error depends on the accuracy of both the numerator and the denominator. A formula to approximate the RSE of a proportion is given below. This formula is only valid when x is a subset of y:
$$\large{\text{RSE }(\frac{x}{y})\approx \sqrt{[RSE(x)]^{2}-[RSE(y)]^{2}}}$$
As an example, if 86,600 persons experienced physical assault by an intimate partner, representing 29.5% of all persons who experienced physical assault by a known person (293,600); and if the RSE for the number of persons experiencing physical assault by an intimate partner is 7.7% and the RSE for the number of persons experiencing physical assault by a known person is 6.7%; then, applying the above formula, the RSE of the proportion is:
$$\large{\text{RSE } = \sqrt{[(7.7)]^{2}-[(6.7)]^{2}} = 3.8\text%}$$
Using the formula given above, the standard error (SE) for the proportion of persons who experienced physical assault by an intimate partner (as a proportion of those who experienced physical assault by a known person) is 1.1% (0.038 x 29.5). There are about two chances in three that the true proportion of persons who experienced physical assault by an intimate partner (as a proportion of those who experienced physical assault by a known person) is between 28.4% and 30.6%, and 19 chances in 20 that the true proportion is between 27.3% and 31.7%.
### Standard error of the difference between estimates
The difference between two survey estimates (counts or percentages) is also subject to sampling error, and can therefore be measured using standard error. The standard error of the difference between two estimates is determined by the individual standard errors of the two estimates and the relationship (correlation) between them. An approximate standard error of the difference between two estimates (x,y) can be calculated using the following formula:
$$\large{SE (x-y) \approx \sqrt{[S E(x)]^{2}+[S E(y)]^{2}}}$$
While this formula will only be exact for differences between separate and uncorrelated characteristics or sub populations, it provides a good approximation for the differences likely to be of interest in this publication.
### Significance testing
The difference between two survey estimates can be tested for statistical significance, in order to determine the likelihood of there being a real difference between the populations with respect to the characteristic being measured. The standard error of the difference between two survey estimates (x and y) can be calculated using the formula in the preceding section. This standard error is then used in the following formula to calculate the test statistic:
$$\large{\left(\frac{x-y}{S E(x-y)}\right)}$$
If the value of the test statistic is greater than 1.96, then this supports, with a 95% level of confidence, a real (i.e. statistically significant) difference between the two populations with respect to the characteristic being measured. If the test statistic is not greater than 1.96, it cannot be stated with a 95% level of confidence that there is a real difference between the populations with respect to that characteristic.
The following survey estimates have been significance tested to determine whether any differences are statistically significant:
• Annual changes between 2017–18 and 2018–19 in personal and household crime victimisation rates (Tables 4c and 6c);
• Annual changes between 2017–18 and 2018–19 in personal and household crime reporting rates (Tables 5c and 7c);
• Annual changes between 2017-18 and 2018-19 in the proportion of persons who believed alcohol or any other substance contributed to their most recent incident of physical assault and face-to-face threatened assault (Table 8c);
• Differences between state and territory personal and household crime victimisation rates and equivalent national victimisation rates for 2018–19 (Tables 2, 3, 4c, and 6c); and
• Differences between state and territory personal and household crime reporting rates and equivalent national reporting rates for 2018–19 (Tables 2, 3, 5c, and 7c).
Significant differences have been annotated with a footnote in the above tables. In all other tables which do not show the results of significance testing, users should take RSEs into account when comparing estimates for different populations, or undertake significance testing using the formula provided to determine whether there is a statistically significant difference between any two estimates.
Only data with a relative standard error (RSE) of less than 25% are included in the publication commentary, unless otherwise indicated, and any differences between populations and changes over time that are referred to are statistically significant. All data contained in the commentary are available for download as data cubes from the Data downloads section.
## Glossary
### Show all
#### Alcohol and/or any other substance
Includes any illegal or legal drugs or mood altering substances that the person believed contributed to the most recent incident of physical assault or face-to-face threatened assault. Other substances include marijuana, cocaine, ice, heroin, ecstasy, steroids, pharmaceuticals, inhalants, kava etc. Either the victim or perpetrator may have been under the influence of alcohol and/or any other substance at the time of the incident. This also includes:
• incidents that occurred when the victim or perpetrator were ‘hungover’; and
• incidents where the victim believed that their drink had been spiked.
#### Attempted break-in
An incident where an attempt was made to forcibly enter a home or other private residence. Includes attempts to break into a caravan (if the caravan was the person's permanent residence), garage, shed or any detached secure building such as games/hobby rooms or granny flats. Attempted break-in also includes incidents where a person saw someone acting suspiciously around the property, if it was suspected that their intent was to break in and steal property. Excludes any attempted break-in that resulted in an actual break-in (e.g. where someone attempted to break in through a door but then gained entry through a window) and attempted break-in to a motor vehicle.
#### Assault
Includes both physical assault and threatened assault (both face-to-face threatened assault and non-face-to-face threatened assault).
#### Balance of state/territory
Comprises statistical areas outside the Greater Capital City Statistical Areas of states and territories as defined in the Australian Statistical Geography Standard (ASGS): Volume 1 - Main Structure and Greater Capital City Statistical Areas, July 2016 (cat. no. 1270.0.55.001).
#### Break-in
An act of unauthorised forced entry into a home or other private residence. Includes forced entry to a caravan (if the caravan was the person's permanent residence), garage, shed or any detached secure building such as games/hobby rooms or granny flats. Excludes forced entry into motor vehicles or front or rear yards and incidents where attempts to gain unlawful entry were not successful (see attempted break-in above).
#### Employed
All people aged 15 years and over who, during the week prior to interview:
• worked for one hour or more for pay, profit, commission or payment in kind in a job or business, or on a farm (comprising employees, employers and own account workers)
• worked for one hour or more without pay in a family business or on a farm (i.e. contributing family workers)
• were employees who had a job but were not at work and were:
• away from work for less than four weeks up to the end of the reference week
• away from work for more than four weeks up to the end of the reference week and received pay for some or all of the four week period to the end of the reference week
• away from work as a standard work or shift arrangement
• on a strike or locked out
• employers or own account workers, who had a job, business or farm, but were not at work.
#### Face-to-face threatened assault
Any verbal and/or physical threat to inflict physical harm, made face-to-face, where the person being threatened believed the threat was likely and able to be carried out. Excludes any incident where the person being threatened did not encounter the perpetrator in person (e.g. threats made via telephone, text message, e-mail, in writing or through social media) – these incidents are counted under non face-to-face threatened assault.
#### Family member
Includes parent, child, sibling or other family member.
#### Full-time (employed)
Employed people who usually worked 35 hours or more a week (in all jobs) and those who, although usually working less than 35 hours a week, worked 35 hours or more during the reference week (i.e. the week before the interview).
#### Greater Capital City Statistical Areas (GCCSA)
Greater Capital City Statistical Areas (GCCSA) are geographical areas built from Statistical Areas Level 4 (SA4), as defined in the Australian Statistical Geography Standard (ASGS): Volume 1 - Main Structure and Greater Capital City Statistical Areas, July 2016 (cat. no. 1270.0.55.001). They are designed to represent the functional extent of each of the eight State and Territory capital cities. This includes the population within the urban area of the city, as well as people who regularly socialise, shop or work within the city, and live in small towns and rural areas surrounding the city. Within each State and Territory, the area not defined as being part of the Greater Capital City is represented by a Balance of State/Territory region.
#### Household
A group of two or more related or unrelated people who usually reside in the same dwelling, who regard themselves as a household, and who make common provision for food or other essentials for living; or a person living in a dwelling who makes provision for their own food and other essentials for living, without combining with any other person.
#### Household crime
Crimes that were committed with the intent to deprive another person of, or deliberately damage, their personal property. The selected household crimes included in the survey are break-in, attempted break-in, motor vehicle theft, theft from a motor vehicle, malicious property damage and other theft. Includes incidents occurring in all Australian households that the person lived in during the 12 months prior to interview. For the purposes of the survey, the household is considered the victim where anyone living in the household (not only the respondent) may have experienced an incident of household crime during the 12 months prior to interview. Excludes incidents where personal property was stolen by force or threat from a person in the household (these incidents are counted under robbery).
#### Incident
A single occurrence of a crime event, which may involve one or more crime types.
#### Intimate partner
Includes current partner, previous partner, boyfriend/girlfriend/ex-boyfriend/ex-girlfriend or date.
#### Known by sight only
Where the person recognised the perpetrator(s) by sight only but did not have a personal relationship with them.
#### Labour force status
A classification of the civilian population aged 15 years and over, including employed, unemployed or not in the labour force, as defined in Labour Force, Australia (cat. no. 6202.0). These definitions conform closely to the international standard definitions adopted by the International Conference of Labour Statisticians.
#### Level of highest non-school qualification
Non-school qualifications are awarded for education attainments other than those of pre-primary, primary or secondary education. They include qualification at the following levels: Postgraduate degree, Master degree, Graduate Diploma and Graduate Certificate, Bachelor degree, Advanced Diploma and Diploma and Certificates I, II, III and IV. Non-school qualifications may be attained concurrently with school qualifications.
#### Malicious property damage
Intentional or wilful (not accidental) damage, defacement or destruction of any part of the person's home or anything usually kept at home. Property is something tangible in nature, including land, conveyances, animals or other objects capable of being privately owned. Destruction can mean any alteration that may render something imperfect or inoperative, including destruction of property, graffiti or vandalism, partial destruction, killing or harming an owned animal and removing or destroying a plant or other part of an owned landscape. Excludes any rental, investment or holiday properties owned by a member of the household. Excludes acts such as turning off water meters and flicking safety switches if no damage to the item occurred.
#### Medical attention
Includes incidents where a person was admitted to hospital and incidents where a person was seen by a doctor or another medical practitioner but not admitted to hospital.
#### Motor vehicle parts
Examples include license plates, tyres, wheels/rims, car audio and DVD equipment.
#### Motor vehicle theft
An incident where a motor vehicle was stolen from any member of the household. This includes cars, SUVs, motorcycles (including motorised scooters), buses, trucks and motor homes. Includes privately owned vehicles and business/employer/company owned vehicles only if the vehicle was used exclusively by members of the household. Excludes vehicles used mainly for business purposes, boats, trailers and company vehicles not used exclusively by household members. For the purpose of this survey, motor vehicle theft incidents are considered to be household crimes.
#### Non-face-to-face threatened assault
Any threat to inflict physical harm where the person being threatened believed the threat was likely and able to be carried out, and where they did not encounter the perpetrator face-to-face (e.g. via telephone, text message, e-mail, in writing or through social media).
#### Not in the labour force
Persons who were neither employed nor unemployed as defined by Labour Force Status.
#### Other known person
Used to describe the relationship of the perpetrator to the victim where the perpetrator was known to the victim, but the relationship did not match any of the known person categories specified in the survey.
#### Other theft
Any unlawful taking of money or goods owned by a household member (other than from motor vehicles owned by a household member) with the intent to permanently deprive the owner of the money or goods, without the use or threat of force or violence, coercion or deception. Includes:
• property belonging to a member of the household not covered by the other types of crime included in the survey;
• property belonging to a household member stolen from a vehicle not owned by a household member; and
• property stolen from a yard or garden (e.g. statues or plants).
Excludes any incidents involving theft covered in other crime types in the survey (e.g. property stolen during a break-in or robbery). Other theft is considered to be a household crime for the purposes of the survey.
#### Part-time (employed)
Employed people who usually worked less than 35 hours a week (in all jobs) and either did so during the reference week (i.e. the week before the interview), or were not at work in the reference week.
#### Perpetrator
A person who commits a crime, as identified by the person who experienced the crime. There may be one or more perpetrators involved in any single crime incident.
#### Personal crime
Crimes that were committed against a person which threatened or caused physical harm to the person. The types of personal crime included in the survey are physical assault, threatened assault (including face-to-face threatened assault and non face-to-face threatened assault), robbery (including attempts), and sexual assault (including attempts).
#### Physical assault
An act of physical force or violence committed by an perpetrator(s) against another person. Examples of physical force or violence include being beaten, pushed, grabbed, shoved, slapped, hit with an open hand or fist, kicked, bitten, choked, stabbed, shot, burnt, being hit with something such as a bat or being dragged or hit deliberately by a vehicle. Includes assault that occurred while the person was at work. Excludes incidents that occurred during the course of play on a sporting field or organised sport, and incidents of sexual assault which also involved physical assault (these are counted under sexual assault).
#### Police
State and territory police agencies. Excludes federal police, except in the Australian Capital Territory.
#### Private vehicle
Any motor vehicle used mainly for private purposes (i.e. non-business purposes).
#### Professional relationship
A relationship where the perpetrator was known to the person primarily through the course of the person's and/or perpetrator’s occupation. Includes where the person was working in a business for which the perpetrator was a client at the time of the incident; relationships between medical professionals and patients; and relationships between police/security officers and perpetrators.
#### Public transport or public vehicle
Includes buses, trains, trams, ferries and taxis.
#### Qualification
Refers to a formal certification, issued by a relevant approved body, in recognition that a person has achieved an appropriate level of learning outcomes or competencies relevant to identified individual, professional, industry or community needs. Excludes statements of attainment awarded for partial completion of a course of study at a particular level.
#### Relationship to perpetrator
Refers to the relationship of the perpetrator to the victim at the time of the incident, as perceived by the victim. More than one response could be provided if there were multiple perpetrators involved in the incident.
#### Relative standard error
A measure of the extent to which an estimate might have varied by chance because only a sample of dwellings was surveyed, and not the entire in-scope population. Relative standard error (RSE) is obtained by expressing the standard error as a percentage of the estimate. For more details refer to the Technical Note.
#### Reporting rate
The total number of persons/households that reported the most recent incident of a crime type to police, expressed as a percentage of the total number of persons/households that experienced the crime type. Includes incidents where the person who experienced the crime did not report the incident themselves, but were aware of another person who did.
#### Robbery
An act of stealing (or attempting to steal) property from a person by physically attacking them or threatening them with force or violence. Includes incidents that occurred at the person's place of work. Excludes pickpocketing or other types of theft from a person that did not involve physical or threatened violence (these are counted under other theft).
#### Sexual assault
An act of a sexual nature carried out against a person's will or without their consent, through the use of physical force, intimidation or coercion and/or involving physical contact. Includes any actual or attempted forced sexual activity such as rape, attempted rape or indecent assault (e.g. being touched inside clothing or intentional rubbing of genitals against the person) and assault with the intent to sexually assault. Includes incidents that occurred at the person's place of work. Excludes sexual harassment that did not involve or lead to an actual or attempted sexual assault. For this survey, only persons aged 18 years and over were asked questions about sexual assault, and respondents had the option of refusal to answer.
#### Social marital status
The relationship status of an individual in terms of whether they form a couple relationship with another person living in the same usual residence, and the nature of that relationship. A marriage exists when two people live together as husband and wife, or partners, regardless of whether the marriage is formalised through registration. Individuals are, therefore, regarded as married if they are in a de facto marriage, or if they are living with the person to whom they are registered as married.
#### Theft from a motor vehicle
An incident where property owned by any member of the household was stolen from a motor vehicle owned (for private use) by any member of that household. Excludes property stolen that belonged to someone not living in the household (e.g. a friend or other relative) and property owned by a business or employer (e.g. a work computer, mobile phone or work tools). Also excludes property stolen from commercial vehicles (e.g. a self-employed business operator whose vehicle is mainly used for work purposes) and any break-in to a motor vehicle where nothing was stolen. For the purposes of this survey, incidents of theft from a motor vehicle are considered to be household crimes.
#### Threatened assault
A verbal, written and/or physical threat to inflict physical harm where the person being threatened believed the threat was likely and able to be carried out. Threatened assault may occur face-to-face or via non-face-to-face methods (such as SMS, email or over the phone). Includes any threat or attempt to strike the person which could cause pain; situations where a gun or other weapon was left in an obvious place (including fake or toy guns/weapons where the threatened person thought it was real) or if the person knew the perpetrator had access to a gun (including toy guns, starter pistol, etc.) or weapon. Also includes incidents where the person was threatened in their line of work. Excludes verbal abuse and any incident of name calling or swearing which did not involve a physical threat, and threats that resulted in an actual assault (these are counted under physical assault).
#### Unemployed
People aged 15 years and over who were not employed during the reference week (i.e. the week before the interview), and:
• had actively looked for full-time or part-time work at any time in the four weeks up to the end of the reference week and were available for work in the reference week; or
• were waiting to start a new job within four weeks from the end of the reference week and could have started in the reference week if the job had been available then.
#### Victim
A person or household who has experienced at least one incident of a selected type of crime in the 12 months prior to interview. A person/household may have experienced more than one incident of the same crime type, but is only counted as a victim once.
#### Victimisation rate
The total number of persons/households that experienced a crime type, expressed as a percentage of all persons/households. This is a measure of how prevalent a crime type is in a given population and is used to measure changes in crime rates over time.
#### Weapon used
Where the person believed a weapon was present during the crime incident (even if they did not see a weapon), or where a weapon was not used during the incident but the person was threatened that a weapon might be used. Examples include knife, gun, bat/bar, bottle/glass and syringe/hypodermic needle.
## Quality declaration
### Institutional environment
For information on the institutional environment of the Australian Bureau of Statistics (ABS), including the legislative obligations of the ABS, financing and governance arrangements, and mechanisms for scrutiny of ABS operations, please see the ABS Institutional Environment.
### Relevance
This publication presents information from the 2018–19 Crime Victimisation Survey, which is the eleventh in the series. In the Crime Victimisation Survey, respondents aged 15 years and over (or 18 years and over for questions regarding sexual assault) were asked questions about their experiences of selected personal crimes (physical assault, threatened assault, robbery and sexual assault) and selected household crimes (break-in, attempted break-in, motor vehicle theft, theft from a motor vehicle, malicious property damage and other theft). Information was collected from one person selected at random in each selected household.
The Crime Victimisation topic is collected as part of the Multipurpose Household Survey (MPHS). The MPHS is a supplement to the monthly Labour Force Survey (LFS) and is designed to produce annual statistics on a small number of self-contained topics. The scope of the LFS is restricted to persons aged 15 years and over and excludes members of the permanent defence forces; certain diplomatic personnel of overseas governments usually excluded from Census and estimated resident populations; overseas residents in Australia; and members of non-Australian defence forces (and their dependants). Refer to Labour Force, Australia (cat. no. 6202.0) for further information regarding the LFS. In addition, the 2018–19 MPHS excluded persons living in the Indigenous Community Strata (ICS), persons living in non-private dwellings such as hotels, university residences, students at boarding schools, patients in hospitals, inmates of prisons and residents of other institutions (e.g. retirement homes, homes for persons with disabilities).
### Timeliness
The MPHS is conducted annually with enumeration undertaken over the financial year. As the survey reference period was the 12 months prior to the survey interview during 2018–19, the data relate to experiences occurring at some time between July 2017 and June 2019.
Generally, data from the Crime Victimisation Survey are released approximately 7 to 8 months after final enumeration, with data from MPHS topics progressively released from approximately 6 months after the end of enumeration.
The Crime Victimisation topic has been collected each year as part of the MPHS since 2008-09. The Crime Victimisation Survey is being conducted again as part of the MPHS for the reference period 2019-20, with results expected to be released in early 2021.
### Accuracy
The LFS, and consequently the MPHS, is primarily designed to provide estimates for the whole of Australia and, secondly, for each state and territory.
The 2018-19 Crime Victimisation Survey comprised a sample of 28,719 fully responding households, which represented a national response rate of 71.9%.
Two types of error can impact on the accuracy of an estimate based on a sample survey: non-sampling error and sampling error. Non-sampling error arises from inaccuracies in collecting, recording and processing the data. Every effort is made to minimise non-sampling error through carefully designed questionnaires, intensive training and supervision of interviewers, and rigorous data processing procedures. Non-sampling error also arises because information cannot be obtained from all persons selected in the survey (non-response).
Sampling error occurs because a sample, rather than the entire in scope population, is surveyed. One measure of the likely difference resulting from not including all in scope dwellings in the survey is given by the standard error (SE). There are about two chances in three that a sample estimate will differ by less than one SE from the figure that would have been obtained if all dwellings had been included in the survey, and about 19 chances in 20 the difference will be less than two SEs.
Another measure of the likely difference is the relative standard error (RSE), which is obtained by expressing the SE as a percentage of the estimate. The RSE is a useful measure in that it provides an immediate indication of the percentage error likely to have occurred due to sampling and therefore avoids the need to also refer to the size of the estimate.
Only estimates with RSEs less than 25% are considered sufficiently reliable for most analytical purposes. Estimates with RSEs between 25% and 50% have been included in the data tables and are annotated to indicate they are subject to high sample variability and should be used with caution. In addition, estimates with RSEs greater than 50% have also been included and annotated to indicate they are considered too unreliable for general use.
### Coherence
The ABS conducted National Crime and Safety Surveys in 1975, 1983, 1993, 1998, 2002 and 2005. In 2006–07, a review of these crime surveys found the need for more timely and regular crime victimisation headline indicators (on an annual basis), and the need for flexibility to cater for new and emerging areas of crime.
In 2008–09, a redesigned ABS Crime Victimisation Survey was introduced (via the MPHS) which collected information about people's experiences of selected personal and household crimes, and has been conducted annually since. Differences in survey methodology and enumeration periods, as well as changes to the survey content, means that data from the Crime Victimisation Survey series (which commenced in 2008–09) are not comparable with earlier ABS Crime and Safety surveys. Comparisons across reference periods are only possible for the period 2008–09 and beyond.
In addition to the core crime victimisation topics, some editions of the survey have included an additional rotating module. These modules have covered a range of topics, including feelings of safety (2008–09), perceptions of social disorder (2009–10 and 2010–11), personal fraud, (2010–11 and 2014–15), perceptions of the justice system (2011–12) and home security measures (2017–18).
From the 2010–11 Crime Victimisation Survey onwards, respondents 18 years and over who were personally interviewed and who had experienced physical assault or face-to-face threatened assault were asked whether they believed alcohol or any other substance contributed to their most recent experience of these offences (see the Data Collection section of the Explanatory Notes for more information).
The terms used to describe the various types of offences in this publication are based on behavioural definitions used in the survey, and may not necessarily correspond with legal or police definitions.
### Interpretability
To aid in the interpretation of the crime victimisation data, detailed information on concepts, definitions, terminology and other technical aspects of the survey can be found in the relevant web pages included with this release. This includes the Explanatory Notes, Glossary, Abbreviations, and Technical Note.
### Accessibility
All tables containing estimates and associated RSEs are available in Excel spreadsheets and can be accessed from the Data downloads section. For the 2018–19 release, any RSEs greater than 50% have been suppressed, while the corresponding estimate has been published with an annotation indicating that it is too unreliable for general use.
Additional tables may also be available on request through a customised data consultancy. The Data downloads section includes an Excel spreadsheet containing a complete list of the data items available. Users should note that detailed data can be subject to high RSEs, which may be subject to confidentiality and sampling variability constraints.
For further information about these and related statistics, contact the National Information and Referral Service on 1300 135 070, or email [email protected].
The ABS Privacy Policy outlines how the ABS will handle any personal information that you provide to the ABS.
## Abbreviations
### Show all
ABS Australian Bureau of Statistics ASGS Australian Statistical Geography Standard CAI Computer Assisted Interviewing ERP Estimated Resident Population GCCSA Greater Capital City Statistical Area ICS Indigenous Community Strata LFS Labour Force Survey MPHS Multipurpose Household Survey NSW New South Wales NT Northern Territory Qld Queensland RSE Relative Standard Error SA South Australia SE Standard Error SEIFA Socio-Economic Indexes for Areas Tas. Tasmania Vic. Victoria WA Western Australia | 2020-07-13T21:37:56 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.28490301966667175, "perplexity": 3252.394372569798}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-29/segments/1593657146845.98/warc/CC-MAIN-20200713194203-20200713224203-00089.warc.gz"} |
https://dlmf.nist.gov/22.14#E17 | # §22.14 Integrals
## §22.14(i) Indefinite Integrals of Jacobian Elliptic Functions
With $x\in\mathbb{R}$,
22.14.1 $\displaystyle\int\operatorname{sn}\left(x,k\right)\mathrm{d}x$ $\displaystyle=k^{-1}\ln\left(\operatorname{dn}\left(x,k\right)-k\operatorname{% cn}\left(x,k\right)\right),$ 22.14.2 $\displaystyle\int\operatorname{cn}\left(x,k\right)\mathrm{d}x$ $\displaystyle=k^{-1}\operatorname{Arccos}\left(\operatorname{dn}\left(x,k% \right)\right),$ 22.14.3 $\displaystyle\int\operatorname{dn}\left(x,k\right)\mathrm{d}x$ $\displaystyle=\operatorname{Arcsin}\left(\operatorname{sn}\left(x,k\right)% \right)=\operatorname{am}\left(x,k\right).$
The branches of the inverse trigonometric functions are chosen so that they are continuous. See §22.16(i) for $\operatorname{am}\left(z,k\right)$.
Secondly,
22.14.4 $\int\operatorname{cd}\left(x,k\right)\mathrm{d}x=k^{-1}\ln\left(\operatorname{% nd}\left(x,k\right)+k\operatorname{sd}\left(x,k\right)\right),$
22.14.5 $\int\operatorname{sd}\left(x,k\right)\mathrm{d}x=(kk^{\prime})^{-1}% \operatorname{Arcsin}\left(-k\operatorname{cd}\left(x,k\right)\right),$
22.14.6 $\int\operatorname{nd}\left(x,k\right)\mathrm{d}x={k^{\prime}}^{-1}% \operatorname{Arccos}\left(\operatorname{cd}\left(x,k\right)\right).$
Again, the branches of the inverse trigonometric functions must be continuous.
Thirdly, with $-K,
22.14.7 $\int\operatorname{dc}\left(x,k\right)\mathrm{d}x=\ln\left(\operatorname{nc}% \left(x,k\right)+\operatorname{sc}\left(x,k\right)\right),$
22.14.8 $\int\operatorname{nc}\left(x,k\right)\mathrm{d}x={k^{\prime}}^{-1}\ln\left(% \operatorname{dc}\left(x,k\right)+k^{\prime}\operatorname{sc}\left(x,k\right)% \right),$
22.14.9 $\int\operatorname{sc}\left(x,k\right)\mathrm{d}x={k^{\prime}}^{-1}\ln\left(% \operatorname{dc}\left(x,k\right)+k^{\prime}\operatorname{nc}\left(x,k\right)% \right).$
Lastly, with $0,
22.14.10 $\int\operatorname{ns}\left(x,k\right)\mathrm{d}x=\ln\left(\operatorname{ds}% \left(x,k\right)-\operatorname{cs}\left(x,k\right)\right),$
22.14.11 $\int\operatorname{ds}\left(x,k\right)\mathrm{d}x=\ln\left(\operatorname{ns}% \left(x,k\right)-\operatorname{cs}\left(x,k\right)\right),$
22.14.12 $\int\operatorname{cs}\left(x,k\right)\mathrm{d}x=\ln\left(\operatorname{ns}% \left(x,k\right)-\operatorname{ds}\left(x,k\right)\right).$
For alternative, and symmetric, formulations of the results in this subsection see Carlson (2006a).
## §22.14(ii) Indefinite Integrals of Powers of Jacobian Elliptic Functions
See §22.16(ii). The indefinite integral of the 3rd power of a Jacobian function can be expressed as an elementary function of Jacobian functions and a product of Jacobian functions. The indefinite integral of a 4th power can be expressed as a complete elliptic integral, a polynomial in Jacobian functions, and the integration variable. See Lawden (1989, pp. 87–88). See also Gradshteyn and Ryzhik (2000, pp. 618–619) and Carlson (2006a).
For indefinite integrals of squares and products of even powers of Jacobian functions in terms of symmetric elliptic integrals, see Carlson (2006b).
## §22.14(iii) Other Indefinite Integrals
In (22.14.13)–(22.14.15), $0.
22.14.13 $\int\frac{\mathrm{d}x}{\operatorname{sn}\left(x,k\right)}=\ln\left(\frac{% \operatorname{sn}\left(x,k\right)}{\operatorname{cn}\left(x,k\right)+% \operatorname{dn}\left(x,k\right)}\right),$
22.14.14 $\int\frac{\operatorname{cn}\left(x,k\right)\mathrm{d}x}{\operatorname{sn}\left% (x,k\right)}=\frac{1}{2}\ln\left(\frac{1-\operatorname{dn}\left(x,k\right)}{1+% \operatorname{dn}\left(x,k\right)}\right),$
22.14.15 $\int\frac{\operatorname{cn}\left(x,k\right)\mathrm{d}x}{{\operatorname{sn}}^{2% }\left(x,k\right)}=-\frac{\operatorname{dn}\left(x,k\right)}{\operatorname{sn}% \left(x,k\right)}.$
For additional results see Gradshteyn and Ryzhik (2000, pp. 619–622) and Lawden (1989, Chapter 3).
## §22.14(iv) Definite Integrals
22.14.16 $\int_{0}^{K\left(k\right)}\ln\left(\operatorname{sn}\left(t,k\right)\right)% \mathrm{d}t=-\tfrac{\pi}{4}{K^{\prime}}\left(k\right)-\tfrac{1}{2}K\left(k% \right)\ln k,$ ⓘ Symbols: $\operatorname{sn}\left(\NVar{z},\NVar{k}\right)$: Jacobian elliptic function, $\pi$: the ratio of the circumference of a circle to its diameter, ${K^{\prime}}\left(\NVar{k}\right)$: Legendre’s complementary complete elliptic integral of the first kind, $K\left(\NVar{k}\right)$: Legendre’s complete elliptic integral of the first kind, $\mathrm{d}\NVar{x}$: differential, $\int$: integral, $\ln\NVar{z}$: principal branch of logarithm function and $k$: modulus Referenced by: Erratum (V1.0.28) for Equations (22.14.16), (22.14.17) Permalink: http://dlmf.nist.gov/22.14.E16 Encodings: TeX, pMML, png Correction (effective with 1.0.28): Originally, a factor of $\pi$ was missing from the term containing the $\tfrac{1}{4}{K^{\prime}}\left(k\right)$. Suggested 2020-08-06 by Fred Hucht See also: Annotations for §22.14(iv), §22.14 and Ch.22
22.14.17 $\int_{0}^{K\left(k\right)}\ln\left(\operatorname{cn}\left(t,k\right)\right)% \mathrm{d}t=-\tfrac{\pi}{4}{K^{\prime}}\left(k\right)+\tfrac{1}{2}K\left(k% \right)\ln\left(k^{\prime}/k\right),$ ⓘ Symbols: $\operatorname{cn}\left(\NVar{z},\NVar{k}\right)$: Jacobian elliptic function, $\pi$: the ratio of the circumference of a circle to its diameter, ${K^{\prime}}\left(\NVar{k}\right)$: Legendre’s complementary complete elliptic integral of the first kind, $K\left(\NVar{k}\right)$: Legendre’s complete elliptic integral of the first kind, $\mathrm{d}\NVar{x}$: differential, $\int$: integral, $\ln\NVar{z}$: principal branch of logarithm function, $k$: modulus and $k^{\prime}$: complementary modulus Referenced by: Erratum (V1.0.28) for Equations (22.14.16), (22.14.17) Permalink: http://dlmf.nist.gov/22.14.E17 Encodings: TeX, pMML, png Correction (effective with 1.0.28): Originally, a factor of $\pi$ was missing from the term containing the $\tfrac{1}{4}{K^{\prime}}\left(k\right)$. Suggested 2020-08-06 by Fred Hucht See also: Annotations for §22.14(iv), §22.14 and Ch.22
22.14.18 $\int_{0}^{K\left(k\right)}\ln\left(\operatorname{dn}\left(t,k\right)\right)% \mathrm{d}t=\tfrac{1}{2}K\left(k\right)\ln k^{\prime}.$
Corresponding results for the subsidiary functions follow by subtraction; compare (22.2.10). | 2021-09-26T19:31:26 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 174, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8985520601272583, "perplexity": 4297.290471716894}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780057913.34/warc/CC-MAIN-20210926175051-20210926205051-00211.warc.gz"} |
https://zbmath.org/authors/?q=ai%3Aklee.victor | ## Klee, Victor LaRue
Compute Distance To:
Author ID: klee.victor Published as: Klee, Victor; Klee, V.; Klee, V. L. jun.; Klee, V. L.; Klee, Victor L. jun.; Klee, Victor L.; Klee, Viktor External Links: MGP · Wikidata · dblp · GND · IdRef
Documents Indexed: 212 Publications since 1946, including 4 Books 3 Contributions as Editor · 5 Further Contributions Biographic References: 2 Publications Co-Authors: 69 Co-Authors with 97 Joint Publications 1,877 Co-Co-Authors
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### Co-Authors
122 single-authored 18 Gritzmann, Peter 8 Larman, David G. 7 Grünbaum, Branko 6 Zanco, Clemente 5 Maluta, Elisabetta 4 Danaraj, Gopal 3 Bessaga, Czeslaw 3 Brieden, Andreas 3 Danzer, Ludwig 3 Gale, David 3 Holt, Fred B. 3 Jeffries, Clark D. 3 Kleinschmidt, Peter 3 Lewis, Ted G. 3 van den Driessche, Pauline 3 von Hohenbalken, Balder 2 Choquet, Gustave 2 Corson, Harry H. 2 Quaife, Howard 2 Wagon, Stan 2 Wright, Edward Maitland 1 Aitchison, Peter W. 1 Alfsen, Erik M. 1 Anderson, Richard D. 1 Balakrishnan, Alampallam Venkatachalaiyer 1 Beauzamy, Bernard 1 Beer, Gerald Alan 1 Bing, R H 1 Blumenthal, Leonard M. 1 Bodlaender, Hans L. 1 Bollobás, Béla 1 Bone, Terrence 1 Bonnice, W. E. 1 Bremner, David 1 Brualdi, Richard Anthony 1 Burger, Thomas 1 Burton, Geoffrey R. 1 Cokus, Shawn 1 Coxeter, Harold Scott MacDonald 1 Davis, William Jay 1 Day, Mahlon Marsh 1 Doehlert, D. H. 1 Durst, Lincoln K. 1 Eggleston, H. G. 1 Engelhardt, Elizabeth 1 Erdős, Pál 1 Ewald, Günter 1 Figiel, Tadeusz 1 Fleming, Wendell Helms 1 Floyd, Edwin E. 1 Fourneau, Rene 1 Friedland, Shmuel 1 Garling, D. J. H. 1 Gleason, Andrew Mattei 1 Guy, Richard Kenneth 1 Habsieger, Laurent 1 Hansen, Wolfhard 1 Haydon, Richard G. 1 Hestenes, Magnus Rudolph 1 Hudelson, Matthew G. 1 James, Robert C. 1 Juncosa, Mario L. 1 Kaibel, Volker 1 Kakutani, Shizuo 1 Kalai, Gil 1 Kannan, Ravindran 1 Katz, Paul 1 Ladner, Richard E. 1 Laskowski, Michael Chris 1 Lindenstrauss, Joram 1 Long, Richard G. 1 Lovász, László 1 Manber, Rachel 1 Martin, Michael 1 Mihalisin, James 1 Minty, George J. 1 Neustadt, Lucien W. 1 Olech, Czesław 1 Pełczyński, Aleksander 1 Perles, Micha A. 1 Petty, Clinton M. 1 Phelps, Robert Ralph 1 Reay, John R. 1 Reid, William T. 1 Rockafellar, Ralph Tyrrell 1 Rogers, Claude Ambrose 1 Rosenthal, Haskell P. 1 Rudin, Mary Ellen 1 Shephard, Geoffrey Colin 1 Simonovits, Miklós 1 Steenrod, Norman Earl 1 Tam, Bit-Shun 1 Tricot, Claude jun. 1 Tzafriri, Lior 1 Utz, Winfried Roy jun. 1 Van Leeuwen, Jan 1 Veselý, Libor 1 Walkup, David W. 1 Westwater, John 1 Withgall, C. ...and 3 more Co-Authors
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### Serials
15 American Mathematical Monthly 11 Archiv der Mathematik 11 Mathematische Annalen 11 Proceedings of the American Mathematical Society 9 Mathematica Scandinavica 8 Duke Mathematical Journal 8 Discrete & Computational Geometry 6 Israel Journal of Mathematics 6 Canadian Journal of Mathematics 6 Linear Algebra and its Applications 5 Studia Mathematica 4 Discrete Mathematics 4 Acta Mathematica 4 Mathematika 4 Transactions of the American Mathematical Society 3 Journal of Mathematical Analysis and Applications 3 Numerische Mathematik 3 Studia Scientiarum Mathematicarum Hungarica 3 Nieuw Archief voor Wiskunde. Derde Serie 2 Mathematics Magazine 2 American Journal of Mathematics 2 Commentarii Mathematici Helvetici 2 Fundamenta Mathematicae 2 Journal of Combinatorial Theory. Series B 2 Mathematics of Operations Research 2 Mathematische Zeitschrift 2 Pacific Journal of Mathematics 2 Combinatorica 2 Mathematical Programming. Series A. Series B 2 Journal of Convex Analysis 2 Annals of Mathematics. Second Series 2 Bulletin of the American Mathematical Society 1 Discrete Applied Mathematics 1 Educational Studies in Mathematics 1 Houston Journal of Mathematics 1 Acta Scientiarum Mathematicarum 1 Bulletin of the London Mathematical Society 1 Canadian Mathematical Bulletin 1 Colloquium Mathematicum 1 Geometriae Dedicata 1 Illinois Journal of Mathematics 1 Journal of the Association for Computing Machinery 1 Journal of Combinatorial Theory. Series A 1 Journal of the London Mathematical Society. Second Series 1 Journal of Optimization Theory and Applications 1 Operations Research 1 Portugaliae Mathematica 1 Proceedings of the London Mathematical Society. Third Series 1 SIAM Journal on Computing 1 SIAM Journal on Control and Optimization 1 Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 1 Journal of Algorithms 1 SIAM Journal on Matrix Analysis and Applications 1 SIAM Journal on Applied Mathematics 1 Notices of the American Mathematical Society 1 Geombinatorics 1 Journal of Combinatorial Theory 1 Journal of the London Mathematical Society 1 Journal of Mathematics and Mechanics 1 Journal of the Society for Industrial & Applied Mathematics 1 Revista de Ciencias, Lima 1 The Dolciani Mathematical Expositions 1 Graduate Texts in Mathematics 1 The IMA Volumes in Mathematics and its Applications 1 Proceedings of Symposia in Pure Mathematics 1 Studia Mathematica, Seria Specjalna
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### Fields
66 Convex and discrete geometry (52-XX) 27 Combinatorics (05-XX) 25 Operations research, mathematical programming (90-XX) 21 Functional analysis (46-XX) 15 Computer science (68-XX) 12 Linear and multilinear algebra; matrix theory (15-XX) 8 General and overarching topics; collections (00-XX) 5 Number theory (11-XX) 5 Geometry (51-XX) 4 Mathematical logic and foundations (03-XX) 3 Manifolds and cell complexes (57-XX) 3 Numerical analysis (65-XX) 3 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 3 Systems theory; control (93-XX) 2 History and biography (01-XX) 2 Measure and integration (28-XX) 2 Ordinary differential equations (34-XX) 2 Dynamical systems and ergodic theory (37-XX) 2 Approximations and expansions (41-XX) 2 Calculus of variations and optimal control; optimization (49-XX) 2 General topology (54-XX) 2 Probability theory and stochastic processes (60-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Field theory and polynomials (12-XX) 1 Associative rings and algebras (16-XX) 1 Group theory and generalizations (20-XX) 1 Topological groups, Lie groups (22-XX) 1 Real functions (26-XX) 1 Statistics (62-XX) 1 Information and communication theory, circuits (94-XX)
### Citations contained in zbMATH Open
186 Publications have been cited 3,557 times in 2,242 Documents Cited by Year
Convex polytopes. With the cooperation of Victor Klee, M. A. Perles, and G. C. Shephard. Zbl 0163.16603
Grünbaum, Branko
1967
Helly’s theorem and its relatives. Zbl 0132.17401
Danzer, L.; Grünbaum, Branko; Klee, V.
1963
Convex polytopes. Prepared by Volker Kaibel, Victor Klee, and Günter M. Ziegler. 2nd ed. Zbl 1024.52001
Grünbaum, Branko
2003
How good is the simplex algorithm? Zbl 0297.90047
Klee, Victor; Minty, George J.
1972
Some characterizations of convex polyhedra. Zbl 0094.16802
Klee, Victor
1959
Convex bodies and periodic homeomorphisms in Hilbert space. Zbl 0050.33202
Klee, Victor L. jun.
1953
Convexity of Chebyshev sets. Zbl 0091.27701
Klee, Victor
1961
Convex sets in linear spaces. Zbl 0042.36201
Klee, V. L. jun.
1951
Some topological properties of convex sets. Zbl 0064.10505
Klee, V. L. jun.
1955
Some new results on smoothness and rotundity in normed linear spaces. Zbl 0092.11602
Klee, Victor
1959
Old and new unsolved problems in plane geometry and number theory. Zbl 0784.51002
Klee, Victor; Wagon, Stan
1991
Extremal structure of convex sets. II. Zbl 0079.12502
Klee, V. L. jun.
1958
The $$d$$-step conjecture for polyhedra of dimension $$d<6$$. Zbl 0163.16801
Klee, V.; Walkup, D. W.
1967
A combinatorial analogue of Poincaré’s duality theorem. Zbl 0134.42403
Klee, V.
1964
Signsolvability revisited. Zbl 0543.15016
Klee, Victor; Ladner, Richard; Manber, Rachel
1984
Shellings of spheres and polytopes. Zbl 0285.52003
Danaraj, Gopal; Klee, Victor
1974
Separation properties of convex cones. Zbl 0064.35602
Klee, V. L. jun.
1955
Leray-Schauder theory without local convexity. Zbl 0096.08001
Klee, Victor
1960
Shrinkable neighborhoods in Hausdorff linear spaces. Zbl 0096.07902
Klee, Victor
1960
Helly’s theorem and its relatives. Zbl 0169.24601
Danzer, L.; Grünbaum, Branko; Klee, V.
1968
Polyhedral sections of convex bodies. Zbl 0148.16203
Klee, V.
1960
When is a matrix sign stable? Zbl 0383.15005
Jeffries, Clark; Klee, Victor; van den Driessche, Pauline
1977
The d-step conjecture and its relatives. Zbl 0632.52007
Klee, Victor; Kleinschmidt, Peter
1987
Extremal structure of convex sets. Zbl 0079.12501
Klee, V. L. jun.
1957
Inner and outer $$j$$-radii of convex bodies in finite-dimensional normed spaces. Zbl 0747.52003
Gritzmann, Peter; Klee, Victor
1992
Invariant metrics in groups. (Solution of a problem of Banach.). Zbl 0047.02902
Klee, V. L. jun.
1952
On the number of vertices of a convex polytope. Zbl 0128.17201
Klee, V.
1964
On the complexity of some basic problems in computational convexity. II: Volume and mixed volumes. Zbl 0819.52008
Gritzmann, Peter; Klee, Victor
1994
On the complexity of some basic problems in computational convexity. I. Containment problems. Zbl 0824.68052
Gritzmann, Peter; Klee, Victor
1994
The critical set of a convex body. Zbl 0050.16604
Klee, V. L. jun.
1953
Which spheres are shellable? Zbl 0401.57031
Danaraj, Gopal; Klee, Victor
1978
Convex functions and upper semi-continuous collections. Zbl 0047.15702
Anderson, R. D.; Klee, V. L. jun.
1952
Circumspheres and inner products. Zbl 0100.31602
Klee, Victor
1961
Finding the smallest triangles containing a given convex polygon. Zbl 0577.52003
1985
Largest $$j$$-simplices in $$d$$-cubes: Some relatives of the Hadamard maximum determinant problem. Zbl 0861.15004
Hudelson, Matthew; Klee, Victor; Larman, David
1996
Computational complexity of inner and outer $$j$$-radii of polytopes in finite-dimensional normed spaces. Zbl 0784.90076
Gritzmann, Peter; Klee, Victor
1993
The structure of semispaces. Zbl 0070.39203
Klee, V. L. jun.
1956
Paths on polyhedra. I, II. Zbl 0141.21303
Klee, Victor
1966
Qualitative stability of linear systems. Zbl 0625.05033
Jeffries, Clark; Klee, Victor; van den Driessche, Pauline
1987
Optimization of globally convex functions. Zbl 0686.52006
Hu, T. C.; Klee, Victor; Larman, David
1989
On certain intersection properties of convex sets. Zbl 0042.40701
Klee, V. L. jun.
1951
On the Borelian and projective types of linear subspaces. Zbl 0088.08502
Klee, Victor
1958
Continuous convex sets. Zbl 0115.16501
Gale, David; Klee, Victor
1960
The Euler characteristic in combinatorial geometry. Zbl 0124.37802
Klee, V.
1963
Some semicontinuity theorems for convex polytopes and cell-complexes. Zbl 0137.41802
Eggleston, H. G.; Grünbaum, Branko; Klee, V.
1964
Convex functions on convex polytopes. Zbl 0246.26009
Gale, David; Klee, Victor; Rockafellar, R. T.
1968
A note on topological properties of normed linear spaces. Zbl 0070.11103
Klee, V. L. jun.
1956
Some characterizations of reflexivity. Zbl 0040.35403
Klee, V. L. jun.
1950
Convex sets in linear spaces. II. Zbl 0044.11201
Klee, V. L. jun.
1951
The generation of convex hulls. Zbl 0138.37405
Bonnice, W.; Klee, V. L.
1963
Polytope pairs and their relationship to linear programming. Zbl 0307.90042
Klee, Victor
1974
Diameters of polyhedral graphs. Zbl 0121.37701
Klee, V.
1964
Maximal separation theorems for convex sets. Zbl 0164.52702
Klee, V.
1968
Deterministic and randomized polynomial-time approximation of radii. Zbl 1136.52307
Brieden, Andreas; Gritzmann, Peter; Kannan, Ravindran; Klee, Victor; Lovász, László; Simonovits, Miklós
2001
The finite topology of a linear space. Zbl 0108.10701
Kakutani, Shizuo; Klee, Victor
1963
Mappings into normed linear spaces. Zbl 0117.08303
Klee, V.
1960
Computational complexity of norm-maximization. Zbl 0722.90080
Bodlaender, Hans L.; Gritzmann, P.; Klee, V.; van Leeuwen, J.
1990
Many polytopes meeting the conjectured Hirsch bound. Zbl 0926.52013
Holt, F. B.; Klee, V.
1998
Boundedness and continuity of linear functionals. Zbl 0068.09201
Klee, V. L. jun.
1955
Topological classification of convex sets. Zbl 0207.42901
Corson, Harry H.; Klee, V.
1963
Stability of the fixed-point property. Zbl 0101.15101
Klee, V.
1961
Do infinite-dimensional Banach spaces admit nice tilings? Zbl 0577.52007
Klee, Victor
1986
Linear algorithms for testing the sign stability of a matrix and for finding Z-maximum matchings in acyclic graphs. Zbl 0348.65032
Klee, Victor; van den Driessche, Pauline
1977
On the complexity of d-dimensional Voronoi diagrams. Zbl 0414.52004
Klee, Victor
1980
The support property of a convex set in a linear normed space. Zbl 0031.21804
Klee, V. L. jun.
1948
Convex sets in linear spaces. III. Zbl 0050.10901
Klee, V. L. jun.
1953
Can the measure of $$\bigcup ^{n}_{1}[a_{i}, b_{i}]$$ be computed in less than $$O(n\log n)$$ steps? Zbl 1180.68163
Klee, Victor
1977
Dispersed Chebyshev sets and coverings by balls. Zbl 0453.41021
Klee, Victor
1981
A characterization of reflexivity by the lattice of closed subspaces. Zbl 0056.10402
Floyd, E. E.; Klee, V. L.
1954
Asymptotes and projections of convex sets. Zbl 0115.16601
Klee, Victor
1961
Two topological properties of topological linear spaces. Zbl 0138.37402
Bessaga, Czesław; Klee, Victor
1964
Lengths of snakes in boxes. Zbl 0153.54202
Danzer, L.; Klee, V.
1967
Recursive structure of S-matrices and an $$O(m^ 2)$$ algorithm for recognizing sign solvability. Zbl 0628.65034
Klee, Victor
1987
Every non-normable Frechet space is homeomorphic with all of its closed convex bodies. Zbl 0138.37403
Bessaga, Czesław; Klee, Victor
1966
Largest $$j$$-simplices in $$n$$-polytopes. Zbl 0826.52014
Gritzmann, P.; Klee, V.; Larman, D.
1995
A proof of the strict monotone 4-step conjecture. Zbl 0916.90206
Holt, Fred; Klee, Victor
1999
Invariant extension of linear functionals. Zbl 0055.10001
Klee, V. L. jun.
1954
On a question of Bishop and Phelps. Zbl 0117.07901
Klee, V.
1963
A method for constructing circuit codes. Zbl 0149.37401
Klee, V.
1967
What is a convex set. Zbl 0214.20802
Klee, V.
1971
Some unsolved problems in plane geometry. A collection of simply stated problems that deserve equally simple solutions. Zbl 0418.51005
Klee, Victor
1979
Cross-positive matrices revisited. Zbl 0828.15018
Gritzmann, Peter; Klee, Victor; Tam, Bit-Shun
1995
Convex polytopes and related complexes. Zbl 0847.52009
Klee, Victor; Kleinschmidt, Peter
1995
Basic properties of evenly convex sets. Zbl 1181.52007
Klee, Victor; Maluta, Elisabetta; Zanco, Clement
2007
Limits of starshaped sets. Zbl 0603.46014
Beer, Gerald; Klee, Victor
1987
Classification and enumeration of minimum (d, 3, 3)-graphs for odd d. Zbl 0366.05037
Klee, Victor
1980
A property of d-polyhedral graphs. Zbl 0123.17001
Klee, Victor
1964
Exposed points of convex sets. Zbl 0139.06802
Choquet, Gustave; Corson, Harry H.; Klee, V.
1966
Characterizations of a class of convex sets. Zbl 0162.44104
Klee, V.; Olech, C.
1967
Minimum graphs of specified diameter, connectivity and valence. II. Zbl 0760.05057
Engelhardt, E.; Klee, V.; Li, K.; Quaife, H.
1989
Diameters of random graphs. Zbl 0419.05036
Klee, Victor; Larman, David
1981
Convex and linear orientations of polytopal graphs. Zbl 0956.05048
Mihalisin, J.; Klee, V.
2000
A d-pseudomanifold with $$f_0$$ vertices has at least $$df_0-(d-1)\;(d+2)$$ $$d$$-simplices. Zbl 0316.52004
Klee, Victor
1975
Classification and enumeration of minimum (d,1,3)-graphs and minimum (d,2,3)-graphs. Zbl 0378.05044
Klee, Victor; Quaife, Howard
1977
A representation of 2-dimensional pseudomanifolds and its use in the design of a linear-time shelling algorithm. Zbl 0391.57008
Danaraj, Gopal; Klee, Victor
1978
Some remarks on continuous transformations. Zbl 0055.16202
Klee, V. L.; Utz, W. R.
1954
Common secants for plane convex sets. Zbl 0057.14504
Klee, V. L. jun.
1954
Semicontinuity of the face-function of a convex set. Zbl 0208.14901
Klee, V.; Martin, M.
1971
The greedy algorithm for finitary and cofinitary matroids. Zbl 0229.05031
Klee, Victor
1971
Durham symposium on the relations between infinite-dimensional and finite-dimensional convexity. Zbl 0323.52001
1976
Basic properties of evenly convex sets. Zbl 1181.52007
Klee, Victor; Maluta, Elisabetta; Zanco, Clement
2007
Convex polytopes. Prepared by Volker Kaibel, Victor Klee, and Günter M. Ziegler. 2nd ed. Zbl 1024.52001
Grünbaum, Branko
2003
Deterministic and randomized polynomial-time approximation of radii. Zbl 1136.52307
Brieden, Andreas; Gritzmann, Peter; Kannan, Ravindran; Klee, Victor; Lovász, László; Simonovits, Miklós
2001
Convex and linear orientations of polytopal graphs. Zbl 0956.05048
Mihalisin, J.; Klee, V.
2000
Decomposition theorems for conditional sign-solvability and sign-solvability of general systems. Zbl 0958.15005
Cokus, Shawn; Klee, Victor
2000
Inapproximability of some geometric and quadratic optimization problems. Zbl 0976.90076
Brieden, Andreas; Gritzmann, Peter; Klee, Victor
2000
Oracle-polynomial-time approximation of largest simplices in convex bodies. Zbl 0959.90046
Brieden, Andreas; Gritzmann, Peter; Klee, Victor
2000
A proof of the strict monotone 4-step conjecture. Zbl 0916.90206
Holt, Fred; Klee, Victor
1999
Inner diagonals of convex polytopes. Zbl 0948.52003
Bremner, David; Klee, Victor
1999
Many polytopes meeting the conjectured Hirsch bound. Zbl 0926.52013
Holt, F. B.; Klee, V.
1998
Counterexamples to the strong $$d$$-step conjecture for $$d\geq 5$$. Zbl 0899.52007
Holt, F.; Klee, V.
1998
Separation by hyperplanes in finite-dimensional vector spaces over Archimedean ordered fields. Zbl 0929.46011
Gritzmann, Peter; Klee, Victor
1998
Old and new unsolved problems in plane geometry and number theory. (Alte und neue ungelöste Probleme in der Zahlentheorie und Geometrie der Ebene. Übers. aus dem Amerik. von Manfred Stern.) Zbl 0882.00003
Klee, Victor; Wagon, Stan
1997
Appollonius revisited: Supporting spheres for sundered systems. Zbl 0899.52003
Klee, V.; Lewis, T.; Von Hohenbalken, B.
1997
Computational convexity. Zbl 1023.52004
Gritzmann, Peter; Klee, Victor
1997
Largest $$j$$-simplices in $$d$$-cubes: Some relatives of the Hadamard maximum determinant problem. Zbl 0861.15004
Hudelson, Matthew; Klee, Victor; Larman, David
1996
Polytope projection and projection polytopes. Zbl 0873.52009
Burger, Thomas; Gritzmann, Peter; Klee, Victor
1996
Rotundity and smoothness of convex bodies in reflexive and nonreflexive spaces. Zbl 0863.46004
Klee, Victor; Veselý, Libor; Zanco, Clemente
1996
Common supports as fixed points. Zbl 0849.52006
Lewis, Ted; von Hohenbalken, Balder; Klee, Victor
1996
Largest $$j$$-simplices in $$n$$-polytopes. Zbl 0826.52014
Gritzmann, P.; Klee, V.; Larman, D.
1995
Cross-positive matrices revisited. Zbl 0828.15018
Gritzmann, Peter; Klee, Victor; Tam, Bit-Shun
1995
Convex polytopes and related complexes. Zbl 0847.52009
Klee, Victor; Kleinschmidt, Peter
1995
Polytope containment and determination by linear probes. Zbl 0826.68126
Gritzmann, Peter; Klee, Victor; Westwater, John
1995
On the complexity of some basic problems in computational convexity. II: Volume and mixed volumes. Zbl 0819.52008
Gritzmann, Peter; Klee, Victor
1994
On the complexity of some basic problems in computational convexity. I. Containment problems. Zbl 0824.68052
Gritzmann, Peter; Klee, Victor
1994
Computational complexity of inner and outer $$j$$-radii of polytopes in finite-dimensional normed spaces. Zbl 0784.90076
Gritzmann, Peter; Klee, Victor
1993
Mathematical programming and convex geometry. Zbl 0806.90098
Gritzmann, Peter; Klee, Victor
1993
On the recognition of $$S$$-systems. Zbl 0796.15020
Klee, Victor; Von Hohenbalken, Balder; Lewis, Ted
1993
Sharper approximation of extreme points by far points. Zbl 0780.52006
Klee, Victor
1993
Inner and outer $$j$$-radii of convex bodies in finite-dimensional normed spaces. Zbl 0747.52003
Gritzmann, Peter; Klee, Victor
1992
Deciding uniqueness in norm maximazation. Zbl 0789.90090
Gritzmann, Peter; Klee, Victor
1992
Old and new unsolved problems in plane geometry and number theory. Zbl 0784.51002
Klee, Victor; Wagon, Stan
1991
Gritzmann, Peter; Habsieger, Laurent; Klee, Victor
1991
Computational complexity of norm-maximization. Zbl 0722.90080
Bodlaender, Hans L.; Gritzmann, P.; Klee, V.; van Leeuwen, J.
1990
Geometry of the Gass-Saaty parametric cost LP algorithm. Zbl 0683.90045
Klee, Victor; Kleinschmidt, Peter
1990
Optimization of globally convex functions. Zbl 0686.52006
Hu, T. C.; Klee, Victor; Larman, David
1989
Minimum graphs of specified diameter, connectivity and valence. II. Zbl 0760.05057
Engelhardt, E.; Klee, V.; Li, K.; Quaife, H.
1989
Sign-patterns and stability. Zbl 0747.05057
Klee, Victor
1989
A qualitative analysis of $$\dot x=Ax+b$$. Zbl 0646.34057
Bone, Terrence; Jeffries, Clark; Klee, Victor
1988
The d-step conjecture and its relatives. Zbl 0632.52007
Klee, Victor; Kleinschmidt, Peter
1987
Qualitative stability of linear systems. Zbl 0625.05033
Jeffries, Clark; Klee, Victor; van den Driessche, Pauline
1987
Recursive structure of S-matrices and an $$O(m^ 2)$$ algorithm for recognizing sign solvability. Zbl 0628.65034
Klee, Victor
1987
Limits of starshaped sets. Zbl 0603.46014
Beer, Gerald; Klee, Victor
1987
Locally countable plump tilings are flat. Zbl 0596.52014
Klee, Victor; Tricot, Claude
1987
Do infinite-dimensional Banach spaces admit nice tilings? Zbl 0577.52007
Klee, Victor
1986
Facet-centroids and volume minimization. Zbl 0547.52002
Klee, Victor
1986
Tiling with smooth and rotund tiles. Zbl 0617.52003
Klee, Victor; Maluta, Elisabetta; Zanco, Clemente
1986
Inspheres and inner products. Zbl 0604.46018
Klee, Victor; Maluta, Elisabetta; Zanco, Clemente
1986
Finding the smallest triangles containing a given convex polygon. Zbl 0577.52003
1985
Signsolvability revisited. Zbl 0543.15016
Klee, Victor; Ladner, Richard; Manber, Rachel
1984
Diameters of random bipartite graphs. Zbl 0532.05051
Bollobás, Béla; Klee, Victor
1984
A note on convex cones and constraint qualifications in infinite- dimensional vector spaces. Zbl 0458.90085
Klee, V.
1982
Dispersed Chebyshev sets and coverings by balls. Zbl 0453.41021
Klee, Victor
1981
Diameters of random graphs. Zbl 0419.05036
Klee, Victor; Larman, David
1981
On the complexity of d-dimensional Voronoi diagrams. Zbl 0414.52004
Klee, Victor
1980
Classification and enumeration of minimum (d, 3, 3)-graphs for odd d. Zbl 0366.05037
Klee, Victor
1980
Combinatorial optimization: What is the state of the art. Zbl 0435.90069
Klee, Victor
1980
The diameter of almost all bipartite graphs. Zbl 0452.05032
Klee, V. L.; Larman, D. G.; Wright, E. M.
1980
Another generalization of Caratheodory’s theorem. Zbl 0431.52008
Klee, Victor
1980
Some unsolved problems in plane geometry. A collection of simply stated problems that deserve equally simple solutions. Zbl 0418.51005
Klee, Victor
1979
Use of Floyd’s algorithm to find shortest restricted paths. Zbl 0411.90071
Klee, Victor; Larman, David
1979
Which spheres are shellable? Zbl 0401.57031
Danaraj, Gopal; Klee, Victor
1978
A representation of 2-dimensional pseudomanifolds and its use in the design of a linear-time shelling algorithm. Zbl 0391.57008
Danaraj, Gopal; Klee, Victor
1978
Adjoints of projective transformations and face-figures of convex polytopes. Zbl 0407.52003
Klee, Victor
1978
When is a matrix sign stable? Zbl 0383.15005
Jeffries, Clark; Klee, Victor; van den Driessche, Pauline
1977
Linear algorithms for testing the sign stability of a matrix and for finding Z-maximum matchings in acyclic graphs. Zbl 0348.65032
Klee, Victor; van den Driessche, Pauline
1977
Can the measure of $$\bigcup ^{n}_{1}[a_{i}, b_{i}]$$ be computed in less than $$O(n\log n)$$ steps? Zbl 1180.68163
Klee, Victor
1977
Classification and enumeration of minimum (d,1,3)-graphs and minimum (d,2,3)-graphs. Zbl 0378.05044
Klee, Victor; Quaife, Howard
1977
Durham symposium on the relations between infinite-dimensional and finite-dimensional convexity. Zbl 0323.52001
1976
A d-pseudomanifold with $$f_0$$ vertices has at least $$df_0-(d-1)\;(d+2)$$ $$d$$-simplices. Zbl 0316.52004
Klee, Victor
1975
Unique reducibility of subsets of commutative topological groups and semigroups. Zbl 0302.20048
Gale, David; Klee, Victor
1975
Convex polyhedra and mathematical programming. Zbl 0334.52008
Klee, Victor
1975
Shellings of spheres and polytopes. Zbl 0285.52003
Danaraj, Gopal; Klee, Victor
1974
Polytope pairs and their relationship to linear programming. Zbl 0307.90042
Klee, Victor
1974
How good is the simplex algorithm? Zbl 0297.90047
Klee, Victor; Minty, George J.
1972
Experimental designs through level reduction of the d-dimensional cuboctahedron. Zbl 0245.05009
Doehlert, D. H.; Klee, V. L.
1972
Unions of increasing and intersections of decreasing sequences of convex sets. Zbl 0237.52003
Klee, Victor
1972
Which generalized prisms admit H-circuits? Zbl 0247.05150
Klee, Victor
1972
On a question of Colin Clark concerning three properties of convex sets. Zbl 0251.46025
Klee, Victor
1972
What is a convex set. Zbl 0214.20802
Klee, V.
1971
Semicontinuity of the face-function of a convex set. Zbl 0208.14901
Klee, V.; Martin, M.
1971
The greedy algorithm for finitary and cofinitary matroids. Zbl 0229.05031
Klee, Victor
1971
The use of circuit codes in analog-to-digital conversion. Zbl 0206.52701
Klee, V.
1970
Two renorming constructions related to a question of Anselone. Zbl 0176.42904
Klee, V.
1969
Intersection theorems for positive sets. Zbl 0179.27404
Hansen, W.; Klee, V.
1969
On a lemma of Fullerton and Braunschweiger. Zbl 0169.15302
Klee, V.
1969
Helly’s theorem and its relatives. Zbl 0169.24601
Danzer, L.; Grünbaum, Branko; Klee, V.
1968
Convex functions on convex polytopes. Zbl 0246.26009
Gale, David; Klee, Victor; Rockafellar, R. T.
1968
Maximal separation theorems for convex sets. Zbl 0164.52702
Klee, V.
1968
Facets and vertices of transportation polytopes. Zbl 0184.44601
Klee, V.; Withgall, C.
1968
Behavior of linear forms on extreme points. Zbl 0157.43803
Klee, V.
1968
A class of linear programming problems requiring a large number of iterations. Zbl 0186.23703
Klee, V.
1968
Convex polytopes. With the cooperation of Victor Klee, M. A. Perles, and G. C. Shephard. Zbl 0163.16603
Grünbaum, Branko
1967
The $$d$$-step conjecture for polyhedra of dimension $$d<6$$. Zbl 0163.16801
Klee, V.; Walkup, D. W.
1967
Lengths of snakes in boxes. Zbl 0153.54202
Danzer, L.; Klee, V.
1967
A method for constructing circuit codes. Zbl 0149.37401
Klee, V.
1967
Characterizations of a class of convex sets. Zbl 0162.44104
Klee, V.; Olech, C.
1967
Asymptotes of convex bodies. Zbl 0168.19704
Klee, V.
1967
Remarks on nearest points in normed linear spaces. Zbl 0156.36303
Klee, V.
1967
Paths on polyhedra. I, II. Zbl 0141.21303
Klee, Victor
1966
...and 86 more Documents
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### Cited by 2,352 Authors
66 Klee, Victor LaRue 20 Zamfirescu, Tudor I. 18 Breen, Marilyn 17 Raĭgorodskiĭ, Andreĭ Mikhaĭlovich 16 Hoàng Xuân Phù 15 Fonf, Vladimir P. 15 Soltan, Valeriu 14 Gruber, Peter Manfred 14 Katchalski, Meir 13 van den Driessche, Pauline 12 Bárány, Imre 12 Gritzmann, Peter 12 Martini, Horst 12 Singer, Ivan 11 Grünbaum, Branko 11 Novik, Isabella 10 Brandenberg, René 10 Lindenstrauss, Joram 10 Merino, Bernardo González 9 De Loera, Jesús A. 9 Martínez-Legaz, Juan-Enrique 9 Terlaky, Tamás 9 Ziegler, Günter Matthias 8 Anderson, Richard D. 8 Björner, Anders 8 De Bernardi, Carlo Alberto 8 Deza, Antoine 8 Dobrowolski, Tadeusz 8 Guo, Qi 8 Jin, Hailin 8 Kleinschmidt, Peter 8 Montejano Peimbert, Luis 8 Morris, Walter D. jun. 8 Oliveros, Deborah 8 Papini, Pier Luigi 8 Phelps, Robert Ralph 8 Zanco, Clemente 7 Avis, David M. 7 Barnette, David W. 7 Borwein, Jonathan Michael 7 Deutsch, Frank 7 Ernst, Emil O. 7 Jeffries, Clark D. 7 Kalai, Gil 7 Klee, Steven 7 Larman, David G. 7 Lassak, Marek 7 Maybee, John S. 7 Neubauer, Michael G. 7 Olesky, D. Dale 7 Park, Sehie 7 Schneider, Rolf G. 7 Zaks, Joseph 6 Bair, Jacques 6 Bingham, Nicholas Hugh 6 Borgwardt, Steffen 6 De Blasi, Francesco Saverio 6 Dekster, Boris V. 6 Eckhoff, Jürgen 6 Goberna, Miguel Angel 6 Johnson, Charles Royal 6 McMullen, Peter 6 Ostaszewski, Adam J. 6 Pachner, Udo 6 Peck, N. Tenney 6 Santos, Francisco 6 Shashkin, Yu. A. 6 Veselý, Libor 6 Wets, Roger Jean-Baptiste 6 Zizler, Vaclav E. 5 Adiprasito, Karim Alexander 5 An, Phan Thanh 5 Antonyan, Sergey A. 5 Bezdek, Károly 5 Billera, Louis J. 5 Boltyanskij, Vladimir Grigor’evich 5 Bosznay, Adam P. 5 Bremner, David 5 Brieden, Andreas 5 Casini, Emanuele 5 Chen, Beifang 5 Dumitrescu, Adrian 5 Fodor, Ferenc 5 Goaoc, Xavier 5 Hai, Nguyen Ngoc 5 Hájek, Petr 5 Henderson, David Wilson 5 Horvath, Charles D. 5 Jamison, Robert E. 5 Jiménez-Sevilla, Mar 5 Khan, Liaqat Ali 5 Kiss, Krisztina 5 Kleitman, Daniel J. 5 Landsberg, Max 5 Lawrence, James 5 Lee, Carl W. 5 Lewis, Ted G. 5 Maluta, Elisabetta 5 Moreno, José-Pedro 5 Myjak, Jozef Wenety ...and 2,252 more Authors
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### Cited in 359 Serials
119 Proceedings of the American Mathematical Society 112 Journal of Mathematical Analysis and Applications 82 Israel Journal of Mathematics 80 Discrete & Computational Geometry 75 Linear Algebra and its Applications 65 Transactions of the American Mathematical Society 58 Mathematische Annalen 55 Archiv der Mathematik 54 Discrete Mathematics 52 Mathematical Notes 43 Journal of Optimization Theory and Applications 43 Topology and its Applications 33 Mathematical Programming. Series A. Series B 32 Advances in Mathematics 30 Discrete Applied Mathematics 30 Journal of Approximation Theory 27 Journal of Combinatorial Theory. Series A 27 Mathematika 25 Journal of Geometry 25 Computational Geometry 24 Mathematical Programming 23 Journal of Functional Analysis 23 Optimization 22 Bulletin of the American Mathematical Society 21 Geometriae Dedicata 21 European Journal of Combinatorics 18 Journal of Mathematical Sciences (New York) 16 Aequationes Mathematicae 15 Monatshefte für Mathematik 14 Mathematische Zeitschrift 13 Bulletin of the Australian Mathematical Society 13 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 13 Numerical Functional Analysis and Optimization 12 Journal of Combinatorial Theory. Series B 12 Combinatorica 12 The Electronic Journal of Combinatorics 11 Linear and Multilinear Algebra 11 Manuscripta Mathematica 11 Theoretical Computer Science 11 Algorithmica 11 Bulletin of the American Mathematical Society. New Series 11 Journal of Convex Analysis 10 Beiträge zur Algebra und Geometrie 10 Annali di Matematica Pura ed Applicata. Serie Quarta 10 Journal of Mathematical Economics 10 Journal of Soviet Mathematics 10 Advances in Applied Mathematics 10 Advances in Geometry 9 Periodica Mathematica Hungarica 9 Acta Mathematica 9 Compositio Mathematica 9 Results in Mathematics 8 Annales de l’Institut Fourier 8 Czechoslovak Mathematical Journal 8 Journal of Computational and Applied Mathematics 8 Numerische Mathematik 8 SIAM Journal on Algebraic and Discrete Methods 8 Acta Mathematica Hungarica 8 SIAM Journal on Discrete Mathematics 8 Expositiones Mathematicae 8 SIAM Journal on Optimization 8 Positivity 7 Rocky Mountain Journal of Mathematics 7 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 7 Applied Mathematics and Computation 7 Automatica 7 Inventiones Mathematicae 7 Operations Research Letters 7 European Journal of Operational Research 7 Optimization Letters 6 Ukrainian Mathematical Journal 6 Mathematics of Operations Research 6 Proceedings of the Edinburgh Mathematical Society. Series II 6 Rendiconti del Circolo Matemàtico di Palermo. Serie II 6 SIAM Journal on Computing 6 Annals of Operations Research 6 Journal of Global Optimization 6 Calculus of Variations and Partial Differential Equations 6 Journal of the Australian Mathematical Society 5 Computers & Mathematics with Applications 5 Information Processing Letters 5 Studia Mathematica 5 Arkiv för Matematik 5 Computing 5 Functional Analysis and its Applications 5 Fuzzy Sets and Systems 5 Glasgow Mathematical Journal 5 Mathematische Nachrichten 5 Siberian Mathematical Journal 5 Journal of Complexity 5 Mathematical and Computer Modelling 5 The Journal of Geometric Analysis 5 Experimental Mathematics 5 Acta Mathematica Sinica. English Series 5 Proceedings of the Steklov Institute of Mathematics 5 Journal of Fixed Point Theory and Applications 4 The Mathematical Intelligencer 4 Journal of Algebra 4 Journal of Differential Equations 4 Journal of Pure and Applied Algebra ...and 259 more Serials
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### Cited in 60 Fields
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# Stabilized backward in time explicit marching schemes in the numerical computation of ill-posed time-reversed hyperbolic/parabolic systems
Published
### Author(s)
Alfred S. Carasso
### Abstract
This paper develops stabilized explicit marching difference schemes that can successfully solve a significant but {\em limited} class of multidimensional, ill-posed, backward in time problems for coupled hyperbolic/parabolic systems associated with vibrating thermoelastic plates and coupled sound and heat flow. Stabilization is achieved by applying compensating smoothing operators at each time step, to quench the instability. Analysis of convergence is restricted to the transparent case of linear, autonomous, selfadjoint spatial differential operators, and {\em almost best-possible} error bounds are obtained for backward in time reconstruction in that class of problems. However, the actual computational schemes can be applied to more general problems, including examples with variable time dependent coefficients, as well as nonlinearities. The stabilized explicit schemes are unconditionally stable, marching forward or backward in time, but the smoothing operation at each step leads to a distortion away from the true solution. This is the {\em stabilization penalty}. It is shown that in many problems of interest, that distortion is small enough to allow for useful results. Backward in time continuation is illustrated using $512 \times 512$ pixel images. Such images are associated with highly irregular non smooth intensity data that severely challenge ill-posed reconstruction procedures. Several computational experiments show that efficient FFT-synthesized smoothing operators, based on $(-\Δ)^p$ with real $p > 2$, can be successfully applied in a broad range of problems.
Citation
Inverse Problems in Science and Engineering
### Keywords
thermoelastic systems backward in time, coupled sound and heat flow backward in time, stabilized explicit marching schemes, error bounds, numerical experiments.
## Citation
Carasso, A. (2018), Stabilized backward in time explicit marching schemes in the numerical computation of ill-posed time-reversed hyperbolic/parabolic systems, Inverse Problems in Science and Engineering, [online], https://doi.org/10.1080/17415977.2015.1124429 (Accessed March 22, 2023)
Created March 6, 2018, Updated September 25, 2020 | 2023-03-22T09:44:54 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4325777292251587, "perplexity": 2038.8426941626622}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296943809.22/warc/CC-MAIN-20230322082826-20230322112826-00172.warc.gz"} |
https://www.aimsciences.org/article/doi/10.3934/proc.2007.2007.687 | Article Contents
Article Contents
# Traveling wave solutions of a generalized curvature flow equation in the plane
• We study a generalized curvature flow equation in the plane: $V =F(k,$ n, $x)$, where for a simple plane curve $\Gamma$ and for any $P \in \Gamma, k$ denotes the curvature of $\Gamma$ at $P$, n denotes the unit normal vector at $P$ and $V$ denotes the velocity in direction n, $F$ is a smooth function which is 1-periodic in $x$. For any given $\alpha \in ( - \pi/2, \pi/2)$, we prove the existence and uniqueness of a planar-like traveling wave solution of $V = F(k,$n,$x)$, that is, a curve: $y = v$*$(x) + c$*$t$ traveling in $y$-direction in speed $c$*, the graph of $v$*$(x)$ is in a bounded neighborhood of the line $x$tan$\alpha$. Also, we show that the graph of $v$*$(x)$ is periodic in the direction (cos$\alpha$, sin$\alpha$).
Mathematics Subject Classification: Primary: 35K55; Secondary: 35B27, 35B10.
Citation:
Open Access Under a Creative Commons license
• on this site
/ | 2022-12-03T22:49:31 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 1, "x-ck12": 0, "texerror": 0, "math_score": 0.8866751194000244, "perplexity": 387.94410327440784}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446710941.43/warc/CC-MAIN-20221203212026-20221204002026-00332.warc.gz"} |
https://www.itl.nist.gov/div898/handbook/mpc/section5/mpc563.htm | 2. Measurement Process Characterization
2.5. Uncertainty analysis
2.5.6. Uncertainty budgets and sensitivity coefficients
## 2.5.6.3. Sensitivity coefficients for measurements from a 2-level design
Sensitivity coefficients from a 2-level design If the temporal components are estimated from a 2-level nested design, and the reported value for a test item is an average over
• $$N$$ short-term repetitions
• $$M$$ ($$M = 1$$ is permissible) days
of measurements on the test item, the standard deviation for the reported value is: $$s_{reported \, value} = \sqrt{\frac{1}{M}s_{days}^2 + \frac{1}{MN} s_1^2}$$ See the relationships in the section on 2-level nested design for definitions of the standard deviations and their respective degrees of freedom.
Problem with estimating degrees of freedom If degrees of freedom are required for the uncertainty of the reported value, the formula above cannot be used directly and must be rewritten in terms of the standard deviations, $$s_1$$ and $$s_2$$. $$s_{reported \, value} = \sqrt{\frac{1}{M}s_2^2 + \frac{J-N}{MNJ} s_1^2}$$
Sensitivity coefficients The sensitivity coefficients are: $$a_1 = \sqrt{\frac{(J-N)}{MNJ}} ; \, a_2 = \sqrt{\frac{1}{M}}$$.
Specific sensitivity coefficients are shown in the table below for selections of $$N, \, M$$.
Sensitivity coefficients for two components
of uncertainty
Number short-term$$N$$ Number day-to-day$$M$$ Short-term sensitivity coefficient $$a_1$$ Day-to-day sensitivity coefficient $$a_2$$ $$1$$ $$1$$ $$\sqrt{(J-1)/J}$$ $$1$$ $$N$$ $$1$$ $$\sqrt{(J-N)/(NJ)}$$ $$1$$ $$N$$ $$M$$ $$\sqrt{(J-N)/(MNJ)}$$ $$\sqrt{1/M}$$ | 2018-06-24T22:32:51 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 2, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7435390949249268, "perplexity": 983.2844950596091}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-26/segments/1529267867095.70/warc/CC-MAIN-20180624215228-20180624235228-00392.warc.gz"} |
https://par.nsf.gov/biblio/10350541-resolving-inner-parsec-blazar-j19242914-event-horizon-telescope | This content will become publicly available on August 1, 2023
Resolving the Inner Parsec of the Blazar J1924–2914 with the Event Horizon Telescope
Abstract The blazar J1924–2914 is a primary Event Horizon Telescope (EHT) calibrator for the Galactic center’s black hole Sagittarius A*. Here we present the first total and linearly polarized intensity images of this source obtained with the unprecedented 20 μ as resolution of the EHT. J1924–2914 is a very compact flat-spectrum radio source with strong optical variability and polarization. In April 2017 the source was observed quasi-simultaneously with the EHT (April 5–11), the Global Millimeter VLBI Array (April 3), and the Very Long Baseline Array (April 28), giving a novel view of the source at four observing frequencies, 230, 86, 8.7, and 2.3 GHz. These observations probe jet properties from the subparsec to 100 pc scales. We combine the multifrequency images of J1924–2914 to study the source morphology. We find that the jet exhibits a characteristic bending, with a gradual clockwise rotation of the jet projected position angle of about 90° between 2.3 and 230 GHz. Linearly polarized intensity images of J1924–2914 with the extremely fine resolution of the EHT provide evidence for ordered toroidal magnetic fields in the blazar compact core.
Authors:
; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; more »
Award ID(s):
Publication Date:
NSF-PAR ID:
10350541
Journal Name:
The Astrophysical Journal
Volume:
934
Issue:
2
Page Range or eLocation-ID:
145
ISSN:
0004-637X
Sagittarius A* (Sgr A*), the Galactic Center supermassive black hole (SMBH), is one of the best targets in which to resolve the innermost region of an SMBH with very long baseline interferometry (VLBI). In this study, we have carried out observations toward Sgr A* at 1.349 cm (22.223 GHz) and 6.950 mm (43.135 GHz) with the East Asian VLBI Network, as a part of the multiwavelength campaign of the Event Horizon Telescope (EHT) in 2017 April. To mitigate scattering effects, the physically motivated scattering kernel model from Psaltis et al. (2018) and the scattering parameters from Johnson et al. (2018) have been applied. As a result, a single, symmetric Gaussian model well describes the intrinsic structure of Sgr A* at both wavelengths. From closure amplitudes, the major-axis sizes are ∼704 ± 102μas (axial ratio ∼$1.19−0.19+0.24$) and ∼300 ± 25μas (axial ratio ∼1.28 ± 0.2) at 1.349 cm and 6.95 mm, respectively. Together with a quasi-simultaneous observation at 3.5 mm (86 GHz) by Issaoun et al. (2019), we show that the intrinsic size scales with observing wavelength as a power law, with an index ∼1.2 ± 0.2. Our results also provide estimates of the size and compactmore » | 2022-12-01T21:18:54 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 1, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6050121784210205, "perplexity": 3089.1809691089347}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446710869.86/warc/CC-MAIN-20221201185801-20221201215801-00866.warc.gz"} |
http://dlmf.nist.gov/10.7 | # §10.7(i) $z\to 0$
When $\nu$ is fixed and $z\to 0$,
10.7.1 $\displaystyle\mathop{J_{0}\/}\nolimits\!\left(z\right)$ $\displaystyle\to 1,$ $\displaystyle\mathop{Y_{0}\/}\nolimits\!\left(z\right)$ $\displaystyle\sim(2/\pi)\mathop{\ln\/}\nolimits z,$
10.7.2 $\mathop{{H^{(1)}_{0}}\/}\nolimits\!\left(z\right)\sim-\mathop{{H^{(2)}_{0}}\/}% \nolimits\!\left(z\right)\sim(2i/\pi)\mathop{\ln\/}\nolimits z,$
10.7.3 $\mathop{J_{\nu}\/}\nolimits\!\left(z\right)\sim(\tfrac{1}{2}z)^{\nu}/\mathop{% \Gamma\/}\nolimits\!\left(\nu+1\right),$ $\nu\neq-1,-2,-3,\dots$,
10.7.4 $\displaystyle\mathop{Y_{\nu}\/}\nolimits\!\left(z\right)$ $\displaystyle\sim-(1/\pi)\mathop{\Gamma\/}\nolimits\!\left(\nu\right)(\tfrac{1% }{2}z)^{-\nu},$ $\realpart{\nu}>0$ or $\nu=-\tfrac{1}{2},-\tfrac{3}{2},-\tfrac{5}{2},\ldots$, 10.7.5 $\displaystyle\mathop{Y_{-\nu}\/}\nolimits\!\left(z\right)$ $\displaystyle\sim-(1/\pi)\mathop{\cos\/}\nolimits(\nu\pi)\mathop{\Gamma\/}% \nolimits\!\left(\nu\right)(\tfrac{1}{2}z)^{-\nu},$ $\realpart{\nu}>0$, $\nu\neq\tfrac{1}{2},\tfrac{3}{2},\tfrac{5}{2},\ldots$,
10.7.6 $\mathop{Y_{i\nu}\/}\nolimits\!\left(z\right)=\frac{i\mathop{\mathrm{csch}\/}% \nolimits(\nu\pi)}{\mathop{\Gamma\/}\nolimits\!\left(1-i\nu\right)}(\tfrac{1}{% 2}z)^{-i\nu}-\frac{i\mathop{\coth\/}\nolimits(\nu\pi)}{\mathop{\Gamma\/}% \nolimits\!\left(1+i\nu\right)}(\tfrac{1}{2}z)^{i\nu}+e^{|\nu\mathop{\mathrm{% ph}\/}\nolimits z|}\mathop{o\/}\nolimits\!\left(1\right),$ $\nu\in\Real$ and $\nu\neq 0$.
See also §10.24 when $z=x$ $(>0)$.
10.7.7 $\mathop{{H^{(1)}_{\nu}}\/}\nolimits\!\left(z\right)\sim-\mathop{{H^{(2)}_{\nu}% }\/}\nolimits\!\left(z\right)\sim-(i/\pi)\mathop{\Gamma\/}\nolimits\!\left(\nu% \right)(\tfrac{1}{2}z)^{-\nu},$ $\realpart{\nu}>0$.
For $\mathop{{H^{(1)}_{-\nu}}\/}\nolimits\!\left(z\right)$ and $\mathop{{H^{(2)}_{-\nu}}\/}\nolimits\!\left(z\right)$ when $\realpart{\nu}>0$ combine (10.4.6) and (10.7.7). For $\mathop{{H^{(1)}_{i\nu}}\/}\nolimits\!\left(z\right)$ and $\mathop{{H^{(2)}_{i\nu}}\/}\nolimits\!\left(z\right)$ when $\nu\in\Real$ and $\nu\neq 0$ combine (10.4.3), (10.7.3), and (10.7.6).
# §10.7(ii) $z\to\infty$
When $\nu$ is fixed and $z\to\infty$,
10.7.8 $\displaystyle\mathop{J_{\nu}\/}\nolimits\!\left(z\right)$ $\displaystyle=\sqrt{2/(\pi z)}\left(\mathop{\cos\/}\nolimits\!\left(z-\tfrac{1% }{2}\nu\pi-\tfrac{1}{4}\pi\right)+e^{|\imagpart{z}|}\mathop{o\/}\nolimits\!% \left(1\right)\right),$ $\displaystyle\mathop{Y_{\nu}\/}\nolimits\!\left(z\right)$ $\displaystyle=\sqrt{2/(\pi z)}\left(\mathop{\sin\/}\nolimits\!\left(z-\tfrac{1% }{2}\nu\pi-\tfrac{1}{4}\pi\right)+e^{|\imagpart{z}|}\mathop{o\/}\nolimits\!% \left(1\right)\right),$ $|\mathop{\mathrm{ph}\/}\nolimits z|\leq\pi-\delta(<\pi)$.
For the corresponding results for $\mathop{{H^{(1)}_{\nu}}\/}\nolimits\!\left(z\right)$ and $\mathop{{H^{(2)}_{\nu}}\/}\nolimits\!\left(z\right)$ see (10.2.5) and (10.2.6). | 2014-08-20T14:36:36 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 102, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9771784543991089, "perplexity": 956.0399326177609}, "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-2014-35/segments/1408500809686.31/warc/CC-MAIN-20140820021329-00109-ip-10-180-136-8.ec2.internal.warc.gz"} |
https://simulationresearch.lbl.gov/modelica/userGuide/development.html | # 5. Development¶
This section describes the development of the Buildings library. The development of the library is conducted at https://github.com/lbl-srg/modelica-buildings
## 5.1. Contributing¶
Contributions of new models and suggestions for how to improve the library are welcome. Contributions are ideally made by first opening an issue at https://github.com/lbl-srg/modelica-buildings and by providing a pull request with the new code.
## 5.2. Guidelines for contributions¶
Models, blocks and functions that are contributed need to adhere to the following guidelines, as this is needed to integrate them in the library, make them accessible to users and further maintain them:
• They should be of general interest to other users and well documented and tested.
• They need to follow the coding conventions described in
• the Style Guide provided in subsections of Section 5.3
• They need to be made available under the Modelica Buildings Library license.
• For models of thermofluid flow components, they need to be based on the base classes in Buildings.Fluid.Interfaces, which are described in the user guide of this package. Otherwise, it becomes difficult to ensure that the implementation is numerically robust.
## 5.3. Style guide¶
### 5.3.1. General¶
1. Classes declared as partial and base classes that are not of interest to the user should be stored in a subdirectory called BaseClasses. Each other class, except for constants, must have an icon.
2. Examples and validation models should be in directories such as Valves.Examples and Valves.Validations. A script for the regression tests must be added as described below.
3. Do not copy sections of code. Use object inheritance.
4. Implement components of fluid flow systems by extending the classes in Buildings.Fluid.Interfaces.
5. Use the full package names when instantiating a class.
6. Models, functions and blocks must be implemented as one model, function or block per file. An exception are the Buildings.Media packages.
### 5.3.2. Type declarations¶
1. Declare all public parameters before protected ones.
2. Declare variables and final parameters that are not of interest to users as protected.
3. Set default parameter values as follows:
1. If a parameter value can range over a large region, do not provide a default value. Examples are nominal mass flow rates.
2. If a parameter value does not vary significantly but need to be verified by the user, provide a default value by using its start attribute. For example, for a heat exchanger, use
parameter Real eps(start=0.8, min=0, max=1, unit="1")
"Heat exchanger effectiveness";
Do not use parameter Real eps=0.8 as this can lead to errors that are difficult to detect if a modeler forgets to overwrite the default value of 0.8 with the actual value. The model will simulate, but gives wrong results due to unsuited parameter values and there will be no warning. On the other hand, using parameter Real eps(start=0.8) will give a warning and hence users can assign better values.
3. If a parameter value can be precomputed based on other parameters, set its value to this equation. For example,
parameter Medium.MassFlowRate m_flow_small(min=0) = 1E-4*m_flow_nominal
...
4. If a parameter assignment should not be changed by a user, use the final keyword.
4. For parameters and variables, provide values for the min and max attribute where applicable. Be aware, that these bounds are not enforced by the simulator. If the min and max attribute are set, each violation of these bounds during the simulation may raise a warning.
Simulators may allow to suppress these warnings. In Dymola, violation of bounds can be checked using
Advanced.AssertAllInsideMinMax=true;
5. For any variable or parameter that may need to be solved numerically, provide a value for the start and nominal attribute.
6. Use types from Modelica.SIunits where possible, except in the package Buildings.Controls.OBC where the units should be declared as shown in Listing 5.1.
### 5.3.3. Equations and algorithms¶
1. Avoid events where possible.
2. Only divide by quantities that cannot take on zero. For example, if x may take on zero, use y=x, not 1=y/x, as the second version indicates to a simulator that it is safe to divide by x.
3. Use the assert function together with "In " + getInstanceName() + ":... to check for invalid values of parameters or variables. For example, use
assert(phi>=0, "In " + getInstanceName() + ": Relative humidity must not be negative.");
Note the use of getInstanceName(), which will write the instance name as part of the error message. Otherwise, OPTIMICA will not write the instance name.
4. Use either graphical modeling or textual code. When using graphical schematic modeling, do not add textual equations. For example, avoid the following, as on the graphical editor, the model looks appears to be singular:
model Avoid
Modelica.Blocks.Continuous.Integrator integrator "Integrator"
annotation (Placement(transformation(extent={{-10,-10},{10,10}})));
equation
integrator.u = 1;
end Avoid;
5. For computational efficiency, equations shall were possible be differentiable and have a continuous first derivative.
6. Avoid equations where the first derivative with respect to another variable is zero. For example, avoid
$\begin{split}f(x) = \begin{cases} 0, & \text{for } x < 0 \\ x^2, & \text{otherwise.} \end{cases}\end{split}$
because any $$x \le 0$$ is a solution, which can cause instability in the solver. Note that this problem do not exist for functions that assign a value to a constant as these will be evaluated during the model translation.
7. Do not replace an equation by a constant for a single value, unless the derivative of the original equation is zero for this value. For example, if computing a pressure drop dp may involve computing a long equation, but one knows that the result is always zero if the volume flow rate V_flow is zero, one may be inclined to use a construct of the form
dp = smooth(1, if V_flow == 0 then 0 else f(V_flow));
The problem with this formulation is that for V_flow=0, the derivative is dp/dV_flow = 0. However, the limit dp/dV_flow, as |V_flow| tends to zero, may be non-zero. Hence, the first derivative has a discontinuity at V_flow=0, which can cause a solver to fail to solve the equation because the smooth statement declared that the first derivative exists and is continuous.
8. Make sure that the derivatives of equations are bounded on compact sets. For example, instead of using y=sign(x) * sqrt(abs(x)), approximate the equation with a differentiable function that has a finite derivative near zero. Use functions form Buildings.Utilities.Math for this approximation.
9. Whenever possible, a Modelica tool should not have to do numerical differentiation. For example, in Dymola, if your model translation log shows
Number of numerical Jacobians: 1
(or any number other than zero), then enter on the command line
Hidden.PrintFailureToDifferentiate = true;
Next, translate the model again to see what functions cannot be differentiated symbolically. Then, implement symbolic derivatives for this function. See implementation of function derivatives.
### 5.3.4. Functions¶
1. Use the smoothOrder annotation if a function is differentiable.
2. If a function is invertible, also implement its inverse function and use the inverse annotation. See Buildings.Fluid.BaseClasses.FlowModels for an example.
3. If a model allows a linearized implementation of an equation, then implement the linearized equation in an equation section and not in the algorithm section of a function. Otherwise, a symbolic processor cannot invert the linear equation, which can lead to coupled systems of equations. See Buildings.Fluid.BaseClasses.FlowModels for an example.
### 5.3.5. Package order¶
1. Packages are first sorted alphabetically by the function _sort_package_order. That function is part of BuildingsPy and can be invoked as
import buildingspy.development.refactor as r
r.write_package_order(".", True)
2. After alphabetical sorting, the following packages, if they exist, are moved to the front:
Tutorial
UsersGuide
and the following packages, if they exist, are moved to the end:
Data
Types
Examples
Validation
Benchmarks
Experimental
Interfaces
BaseClasses
Internal
Obsolete
The remaining classes are ordered as follows and inserted between the above list: First, models, blocks and records are listed, then functions, and then packages.
### 5.3.6. Documentation¶
1. Add a description string to all parameters and variables, including protected ones.
2. Group similar variables using the group and tab annotation. For example, use
parameter Modelica.SIunits.Time tau = 60
"Time constant at nominal flow"
annotation (Dialog(group="Nominal condition"));
or use
parameter Types.Dynamics substanceDynamics=energyDynamics
"Formulation of substance balance"
annotation(Evaluate=true, Dialog(tab = "Assumptions", group="Dynamics"));
3. Add model documentation to the info section. This applies to validation tests as well. To document equations, use the format
<p>
The polynomial has the form
</p>
<p align="center" style="font-style:italic;">
y = a<sub>1</sub> + a<sub>2</sub> x + a<sub>3</sub> x<sup>2</sup> + ...,
</p>
<p>
where <i>a<sub>1</sub></i> is ...
To denote time derivatives, such as for mass flow rate, use <code>ṁ</code>.
To refer to parameters of the model, use the <code>...</code> section as in
To linearize the equation, set <code>linearize=true</code>.
To format tables, use
<p>
<table summary="summary" border="1" cellspacing="0" cellpadding="2" style="border-collapse:collapse;">
<tr><td>Data 1</td> <td>Data 2</td> </tr>
</table>
</p>
To include figures, place the figure into a directory in Buildings/Resources/Images/ that has the same name as the full package. For example, use
</p>
<p align="center">
<img alt="Image of ..."
src="modelica://Buildings/Resources/Images/Fluid/FixedResistances/FixedResistanceDpM.png"/>
</p>
<p>
To create new figures, put the source file for the figure, preferably in svg format, in the same directory as the png file. svg files can be created with https://inkscape.org/, which works on any operating system. See for example the file in Resources/Images/Examples/Tutorial/SpaceCooling/schematics.svg.
4. Add author information to the revision section.
5. Run a spell check.
6. Start headings with <h4>.
7. Add hyperlinks to other models using their full name. For example, use
See
<a href="modelica://Buildings.Fluid.Sensors.Density">
Buildings.Fluid.Sensors.Density</a>.
8. Add a default component name, such as
annotation(defaultComponentName="senDen", ...
to objects that will be used as drag and drop elements, as this automatically assigns them this name.
9. Keep the line length to no more than around 80 characters.
10. For complex packages, provide a User’s Guide, and reference the User’s Guide in Buildings.UsersGuide.
11. Use the string fixme within development branches to mark passages that still need to be revised (e.g., to improve code or to fix bugs). Before merging a branch into the master, all fixme strings must be removed. Within the master branch, no fixme are allowed.
12. A suggested template for the documentation of classes is below. Except for the short introduction, the sections are optional.
<p>
A short introduction.
</p>
<h4>Main equations</h4>
<p>
xxx
</p>
<h4>Assumption and limitations</h4>
<p>
xxx
</p>
<h4>Typical use and important parameters</h4>
<p>
xxx
</p>
<h4>Options</h4>
<p>
xxx
</p>
<h4>Dynamics</h4>
<p>
Describe which states and dynamics are present in the model
and which parameters may be used to influence them.
This need not be added in partial classes.
</p>
<h4>Validation</h4>
<p>
Describe whether the validation was done using
analytical validation, comparative model validation
or empirical validation.
</p>
<h4>Implementation</h4>
<p>
xxx
</p>
<h4>References</h4>
<p>
</p>
13. Always use lower case html tags.
## 5.4. Adding a new class¶
Adding a new class, such as a model or a function, is usually easiest by extending, or copying and modifying, an existing class. In many cases, the similar component already exists. In this situation, it is recommended to copy and modify a similar component. If both components share a significant amount of similar code, then a base class should be introduced that implements the common code. See for example Buildings.Fluid.Sensors.BaseClasses.PartialAbsoluteSensor which is shared by all sensors with one fluid port in the package Buildings.Fluid.Sensors.
The next sections give guidance that is specific to the implementation of thermofluid flow devices, pressure drop models and control sequences.
### 5.4.1. Thermofluid flow device¶
To add a component of a thermofluid flow device, the package Buildings.Fluid.Interface contains basic classes that can be extended. See Buildings.Fluid.Interface.UsersGuide for a description of these classes. Alternatively, simple models such as the models below may be used as a starting point for implementing new models for thermofluid flow devices:
Buildings.Fluid.HeatExchangers.HeaterCooler_u
For a device that adds heat to a fluid stream.
Buildings.Fluid.Humidifiers.Humidifier_u
For a device that adds humidity to a fluid stream.
Buildings.Fluid.Chillers.Carnot_y
For a device that exchanges heat between two fluid streams.
Buildings.Fluid.MassExchangers.ConstantEffectiveness
For a device that exchanges heat and humidity between two fluid streams.
Fig. 5.1 Schematic diagram of the cooling tower model based on the Merkel theory.
If models involve complex calculations, then these models are generally easiest to understand for users if these calculations are in a separate block that then interfaces to the fluid flow model using the above basic class. An example is the model Buildings.Fluid.HeatExchangers.CoolingTowers.Merkel that will be released with Buildings 6.0.0. Fig. 5.1 shows the schematic diagram of the model. The block per in the figure implements the thermodynamic calculations. The model shows that the cooling tower performance only depends on the control signal y, the air inlet temperature TAir, the water inlet temperature TWatIn and the water mass flow rate mWat_flow.
### 5.4.2. Pressure drop¶
When implementing equations for pressure drop, it is recommended to expand the base class Buildings.Fluid.BaseClasses.PartialResistance. Models should allow computing the flow resistance as a quadratic function with regularization near zero as implemented in Buildings.Fluid.BaseClasses.FlowModels.basicFlowFunction_dp and in Buildings.Fluid.BaseClasses.FlowModels.basicFlowFunction_m_flow. The governing equation is
$k = \frac{\dot m}{\sqrt{\Delta p}}$
with regularization near zero to avoid that the limit $${d \dot m}/{d \Delta p}$$ tends to infinity as $$\dot m \to 0$$, as this can cause Newton-based solvers to stall. For fixed flow resistances, $$k$$ is typically computed based on nominal conditions such as $$k = \dot m_0/\sqrt{\Delta p_0}$$, where $$\dot m_0$$ is equal to the parameter m_flow_nominal and $$\Delta p_0$$ is equal to the parameter dp_nominal.
All pressure drop models should also provide a parameter that allows replacing the equation by a linear model of the form
$\dot m \, \dot m_0 = \bar k^2 \, \Delta p$
Note
Equations for pressure drop are implemented as a function of mass flow rate and not volume flow rate. For some models, this allows decoupling the mass flow balance from the energy balance. Otherwise, computing the mass flow distribution would require knowledge of the density, which may depend on temperature, and temperature is only known after solving the energy balance.
When implementing the pressure drop model, also provide means to
1. use homotopy, which should be used by default, and
2. disable the pressure-drop model.
Disabling the pressure-drop model allows, for example, a user to set in a series connection of a heating coil and a cooling coil the pressure drop of the heating coil to zero, and to lump the pressure drop of the heating coil into the pressure drop model of the cooling coil. This often reduces the size of the system of nonlinear equations.
### 5.4.3. Control sequences using the Control Description Language¶
To implement reusable control sequences, such as done within the OpenBuildingControl project, the sequences need to comply with the specification of the Control Description Language.
The following rules need to be followed, in addition to the guidelines described in Section 5.2.
1. The naming of parameters, inputs, outputs and instances must follow the naming conventions in Buildings.UsersGuide.Conventions. Avoid providing duplicate information in the instance name, for example if the block is within the Boilers package, the instance name must not contain boi. Ensure that the instance name is unambiguous when viewed in a top level controller block. Consider whether the block can be used to control other equipment as well, and if so, make sure the instance name is also applicable for these applications.
2. Parameters that can be grouped together, such as parameters relating to temperature setpoints or to the configuration of the trim and respond logic, should be grouped together with the Dialog(group=STRING)) annotation. See for example G36_PR1.TerminalUnits.Controller. Do not use Dialog(tab=STRING)), unless the parameter is declared with a default value and is of no interest to typical users.
3. In the source code, the instances must be ordered as follows:
• First, list Boolean parameters,, then Integer parameters and then Real parameters.
• Next, list inputs, then outputs, followed by blocks.
• Protected instances are below all the public instances and follow the same instance ordering rules.
• Within the above order, list scalar values before arrays, but prioritize groupings based on model specific similarities.
4. Each block must have a defaultComponentName annotation and a %name label placed above the icon. See for example the CDL.Continuous.Constant block.
5. To aid readability, the formatting of the Modelica source code file must be consistent with other implemented blocks, e.g., use two spaces for indentation (no tabulators), assign each parameter value on a new line. It is recommended to add an empty line between instances. See for example G36_PR1.AHUs.SingleZone.VAV.SetPoints.ExhaustDamper.
6. For parameters, where generally valid values can be provided, provide them as default values.
7. Add comments to all instances. The comments should be concise. The comments should not contain redundant information and must not contain hard coded parameters as those can change. If the functionality of an instance is obvious the developer may use comments that closely resemble the class names, such as “Logical And”.
8. Each block must have an info section that explains its functionality. In this info section, names of parameters, inputs and outputs need to be referenced using the html <code>...</code> element. In the info section, units need to be provided in SI units, or in dual units. For SI units, use Kelvin for temperature differences and degree Celsius for actual temperatures.
9. For PI controllers, normalize the inputs for setpoint and measured value so that the control error is of the order of one. As control errors for temperature tracking are usually in the order of one, these need not be normalized. But for pressure differentials, which can be thousands of Pascal, normalization aids in providing reasonable control gains and it aids in tuning.
10. Never use an inequality comparison without a hysteresis or a time delay if the variable that is used in the inequality test is computed using an iterative solver, or is obtained from a measurement and hence can contain measurement noise. An exception is a sampled value because the output of a sampler remains constant until the next sampling instant. See Section 2.5.
11. CDL uses the following units, which also need to be used in controllers, including their parameters:
Physical Quantity
Unit
Note
Temperature
K
Use displayUnit=degC
Temperature difference
K
Volume flow rate
m3/s
Mass flow rate
kg/s
Pressure
Pa
Use displayUnit=bar
Pressure differential
Pa
Relative humidity
1
Range of control signal
1
Hence, for example, a controller that takes as an input a temperature and a temperature difference and produces as an output a damper position signal, use a declaration such as shown in the code snippet below in which graphical annotations are omitted.
Listing 5.1 Unit declaration for CDL.
Buildings.Controls.OBC.CDL.Interfaces.RealInput TZon(
final unit="K",
displayUnit="degC") "Measured zone air temperature";
Buildings.Controls.OBC.CDL.Interfaces.RealInput dTSup(
final unit="K") "Temperature difference supply air minus exhaust air";
Buildings.Controls.OBC.CDL.Interfaces.RealOutput yDam(
final min=0,
final max=1,
final unit="1") "Exhaust damper position";
Conversion of these units to non-SI units can be done programmatically by tools that process CDL.
12. Units, quantities and value limits must be declared as final to avoid users to be able to change them, as a change in unit may cause the control logic to be incorrect.
13. If the block diagram does not fit into the drawing pane, enlarge the drawing pane rather than making the blocks smaller.
14. The size of the icon should be such that it provides a good fit for all the input and output interfaces. The minimum recommended icon size is 100 by a 100. If there are many interfaces the icon size should be extended in vertical direction. Icons should be symmetrical with reference to the grid origin. E.g, the default specification is
Icon(
coordinateSystem(
preserveAspectRatio=true,
extent={{-100,-100},{100,100}}))
15. For simple, small controllers, provide a unit test in a Validation or Examples package that is in the hierarchy one level below the implemented controller. See Section 5.5 for unit test implementation. Because some control logic errors may only be noticed when used in a closed loop test, for equipment and system controllers, provide also closed loop examples that test the sequence for all modes of operation. If the closed loop examples include HVAC models, put them outside of the Buildings.Controls.OBC package. Make sure sequences are tested for all modes of operation, and as applicable, for winter, shoulder and summer days.
16. For general rules on validation models see Section 5.5. If there are multiple instances of the validated block, preferably list them together as opposed to far apart in the Modelica file.
17. Run the following command to detect various warnings, such as missing comments:
\$ node app.js -f Buildings/Controls/OBC/ASHRAE/PrimarySystem/{path to package} -o json -m cdl
## 5.5. Validation and unit tests¶
The developer that introduces a new model, block or a function must:
1. Implement at least one example or validation model that serves as a unit test for each model, block and function, and run the unit tests. Unit tests should cover all branches of if-then constructs and all realistic operating modes of the system represented by the model.
2. In the info section of the validation model, describe to others the intent of the unit test. For example, an air handler unit controller test could describe “This model verifies that as the cooling load of the room increases, the controller first increases the mass flow rate setpoint and then reduces the supply temperature setpoint.”
The validation models are part of automated unit tests as described at the unit tests wiki page.
For simple models, the validation can be against analytic solutions. This is for example done in Buildings.Fluid.FixedResistances.PressureDrop which uses a regression tests that checks the correct relation between mass flow rate and pressure drop.
For complex thermofluid flow devices, a comparative model validation needs to be done, for example by comparing the result of the Modelica model against the results from EnergyPlus. An example is Buildings.Fluid.HeatExchangers.CoolingTowers.Validation.MerkelEnergyPlus. For such validations, the following files also need to be added to the repository:
• The EnergyPlus input data file. Please make sure it only requires a weather data file that already exists in the Buildings library.
• A bash script called run.sh that
1. runs the EnergyPlus model on Linux, and
2. invokes a Python script that converts the EnergyPlus output file (see next item).
This file will automatically be executed as part of the continuous integration testing.
• A Python script that converts the EnergyPlus output file to the data file that can be read by the Modelica data reader.
See for example Buildings/Resources/Data/Fluid/HeatExchangers/CoolingTowers/Validation for an implementation. | 2021-06-20T04:00:00 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4956389367580414, "perplexity": 1633.5552634734029}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623487655418.58/warc/CC-MAIN-20210620024206-20210620054206-00024.warc.gz"} |
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Renewable Integration
Renewable integration is the process of plugging renewable sources of energy into the electric grid. | 2023-02-07T15:16:33 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9023476243019104, "perplexity": 6042.202376786396}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500619.96/warc/CC-MAIN-20230207134453-20230207164453-00599.warc.gz"} |
https://zims-en.kiwix.campusafrica.gos.orange.com/wikipedia_en_all_nopic/A/Numerical_method | # Numerical method
In numerical analysis, a numerical method is a mathematical tool designed to solve numerical problems. The implementation of a numerical method with an appropriate convergence check in a programming language is called a numerical algorithm.
## Mathematical definition
Let ${\displaystyle F(x,y)=0}$ be a well-posed problem, i.e. ${\displaystyle F:X\times Y\rightarrow \mathbb {R} }$ is a real or complex functional relationship, defined on the cross-product of an input data set ${\displaystyle X}$ and an output data set ${\displaystyle Y}$, such that exists a locally lipschitz function ${\displaystyle g:X\rightarrow Y}$ called resolvent, which has the property that for every root ${\displaystyle (x,y)}$ of ${\displaystyle F}$, ${\displaystyle y=g(x)}$. We define numerical method for the approximation of ${\displaystyle F(x,y)=0}$, the sequence of problems
${\displaystyle \left\{M_{n}\right\}_{n\in \mathbb {N} }=\left\{F_{n}(x_{n},y_{n})=0\right\}_{n\in \mathbb {N} },}$
with ${\displaystyle F_{n}:X_{n}\times Y_{n}\rightarrow \mathbb {R} }$, ${\displaystyle x_{n}\in X_{n}}$ and ${\displaystyle y_{n}\in Y_{n}}$ for every ${\displaystyle n\in \mathbb {N} }$. The problems of which the method consists need not be well-posed. If they are, the method is said to be stable or well-posed.[1]
## Consistency
Necessary conditions for a numerical method to effectively approximate ${\displaystyle F(x,y)=0}$ are that ${\displaystyle x_{n}\rightarrow x}$ and that ${\displaystyle F_{n}}$ behaves like ${\displaystyle F}$ when ${\displaystyle n\rightarrow \infty }$. So, a numerical method is called consistent if and only if the sequence of functions ${\displaystyle \left\{F_{n}\right\}_{n\in \mathbb {N} }}$ pointwise converges to ${\displaystyle F}$ on the set ${\displaystyle S}$ of its solutions:
${\displaystyle \lim F_{n}(x,y+t)=F(x,y,t)=0,\quad \quad \forall (x,y,t)\in S.}$
When ${\displaystyle F_{n}=F,\forall n\in \mathbb {N} }$ on ${\displaystyle S}$ the method is said to be strictly consistent.[1]
## Convergence
Denote by ${\displaystyle \ell _{n}}$ a sequence of admissible perturbations of ${\displaystyle x\in X}$ for some numerical method ${\displaystyle M}$ (i.e. ${\displaystyle x+\ell _{n}\in X_{n}\forall n\in \mathbb {N} }$) and with ${\displaystyle y_{n}(x+\ell _{n})\in Y_{n}}$ the value such that ${\displaystyle F_{n}(x+\ell _{n},y_{n}(x+\ell _{n}))=0}$. A condition which the method has to satisfy to be a meaningful tool for solving the problem ${\displaystyle F(x,y)=0}$ is convergence:
{\displaystyle {\begin{aligned}&\forall \varepsilon >0,\exists n_{0}(\varepsilon )>0,\exists \delta _{\varepsilon ,n_{0}}{\text{ such that}}\\&\forall n>n_{0},\forall \ell _{n}:\|\ell _{n}\|<\delta _{\varepsilon ,n_{0}}\Rightarrow \|y_{n}(x+\ell _{n})-y\|\leq \varepsilon .\end{aligned}}}
One can easily prove that the point-wise convergence of ${\displaystyle \{y_{n}\}_{n\in \mathbb {N} }}$ to ${\displaystyle y}$ implies the convergence of the associated method.[1]
## References
1. Quarteroni, Sacco, Saleri (2000). Numerical Mathematics (PDF). Milano: Springer. p. 33.CS1 maint: multiple names: authors list (link)
This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files. | 2021-04-11T07:39:49 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 35, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7338029742240906, "perplexity": 447.71846610408}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618038061562.11/warc/CC-MAIN-20210411055903-20210411085903-00367.warc.gz"} |
http://www.scstatehouse.gov/sess120_2013-2014/sj14/20140114.htm | South Carolina General Assembly
120th Session, 2013-2014
Journal of the Senate
NO. 1
JOURNAL
OF THE
SENATE
OF THE
STATE OF SOUTH CAROLINA
REGULAR SESSION BEGINNING TUESDAY, JANUARY 14, 2014
_________
TUESDAY, JANUARY 14, 2014
Tuesday, January 14, 2014
(Statewide Session)
Indicates Matter Stricken
Indicates New Matter
The Senate assembled at 12:00 Noon, 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:
As the Psalmist proclaims:
"This is the day the Lord has made; let us rejoice and be glad in it."
(Psalm 118:24)
Bow in prayer with me, please:
We do humbly ask, dear God, that You will richly guide and bless this Senate as their new legislative year unfolds. May each Senator, may our Lieutenant Governor, may our Governor, and may every staff member feel the fullness of the responsibilities which are upon them, Lord, and may they trust in Your guidance and care with every task that confronts them. Ultimately, may these servants bring about results that will benefit every woman, man, and child in South Carolina, to the end that we all indeed shall "rejoice and be glad," and give You glory and praise. Moreover, Gracious God, we further offer You our thanksgiving for and loving memories of our colleague and friend, Vanessa Collier, who faithfully served this Senate for 34 years. All this we pray in Your loving name, O Lord. Amen.
The PRESIDENT called for Petitions, Memorials, Presentments of Grand Juries and such like papers.
Expression of Personal Interest
Senator COURSON rose for an Expression of Personal Interest.
Remarks To Be Printed
On motion of Senator SETZLER, with unanimous consent, the remarks of Senator COURSON, when reduced to writing and made available to the Desk, would be printed in the Journal.
COMMUNICATIONS RECEIVED Office of the Secretary of State 1205 Pendleton Street, Suite 525 Columbia, SC 29201
October 10, 2013
South Carolina Senate
Office of the Clerk
Jeffrey S. Gossett, Clerk
P.O. Box 142
Columbia, SC 29202
Dear Mr. Gossett:
Please find enclosed a copy of the election results for the Honorable Marlon Kimpson, State Senate District 42 in the Special Election held October 1, 2013, as certified to this office by the State Election Commission.
If I can be of further assistance to you, please do not hesitate to contact me at (803) 734-2512.
With warm regards, I am
Sincerely, /s/ Mark Hammond
Secretary of State
South Carolina Election Commission
1205 Pendleton Street
Columbia, SC 29201
October 4, 2013
Honorable Mark Hammond
Secretary of State
1205 Pendleton Street, Suite 525
Columbia, SC 29201
Dear Mr. Secretary:
The State Election Commission hereby certifies Hon. Marlon Kimpson as the winner of the State Senate, District 42, in the Special Election held on October 1, 2013.
Sincerely,
/s/ Marci Andino
Executive Director
SENATE MEMBER
2013 Election Results
District 42 Hon. Marlon Kimpson
PRIVILEGE OF THE FLOOR
On motion of Senator BRYANT, with unanimous consent, in accordance with the provisions of Rule 35, the Privilege of the floor was extended to the family of Senator KIMPSON.
Administration of Oath of Office Senator Sworn In
Senator KIMPSON presented himself at the Bar and the Oath of Office was administered to him by the PRESIDENT.
On motion of Senator COURSON, with unanimous consent, Senator KIMPSON was introduced and granted leave to address the Senate with brief remarks.
Remarks To Be Printed
On motion of Senator SETZLER, with unanimous consent, the remarks of Senator KIMPSON, when reduced to writing and made available to the Desk, would be printed in the Journal.
Joint Transportation Review Committee Post Office Box 142 Columbia, SC 29202-0142
January 13, 2014
The Honorable Jeffrey S. Gossett
Clerk of the Senate
1101 Pendleton Street
Columbia, S.C. 29201
The Honorable Charles F. Reid
Clerk of the House
1105 Pendleton Street
Columbia, S.C. 29201
Dear Mr. Gossett and Mr. Reid:
The Joint Transportation Review Committee met on January 9, 2014 to consider the qualifications of applicants for the South Carolina Department of Transportation Commission. The Committee found the following individuals qualified to serve on the Commission.
2nd District:
Mr. John N. Hardee of Columbia
4th District
Mr. George William "Will" Gramling of Campobello
Mr. Woodrow W. Willard, Jr. of Spartanburg
6th District
Samuel B. Glover of Orangeburg
This report became official at 12:00 p.m. on Monday, January 13, 2014. Candidates are now free to solicit votes, and members may pledge their vote at this time.
Thank you for your attention to this matter.
Sincerely,
Larry K. Grooms, Chairman
Clerk's Appointment
The Clerk announced the following appointment:
Mrs. Michele M. Neal Administrative Assistant
On motion of Senator SETZLER, with unanimous consent, the committee selection process in Rule 19 was waived and the vacancies were filled in the following manner:
Senator HUTTO moves from the Rules Committee to the General Committee; Senator COLEMAN fills a vacancy on the Corrections and Penology Committee; Senator NICHOLSON moves from the Judiciary Committee to the Finace Committee; Senator ALLEN moves from the General Committee to the Labor, Commerce & Industry Committee; Senator JOHNSON moves from the Corrections and Penology Committee to the Medical Affairs Committee; Senator McELVEEN moves from the Corrections and Penology Committee to the Transportaton Committee; and Senator KIMPSON fills the vacancies on the Corrections and Penology Committee, General Committee, Invitations Committee, Judiciary Committee, and Rules Committee.
STANDING COMMITTEES OF THE SENATE
AGRICULTURE AND NATURAL RESOURCES
Verdin, Daniel B., Chairman
Matthews, John W., Jr.
McGill, J. Yancey
Grooms, Larry K.
Bryant, Kevin
Williams, Kent M.
Campbell, Paul G., Jr.
Sheheen, Vincent A.
Gregory, Chauncey K. "Greg"
Massey, Shane
Coleman, Creighton
Corbin, Tom
Hembree, Greg
Johnson, Kevin
McElveen, Thomas
Shealy, Katrina
Young, Tom
BANKING AND INSURANCE
Hayes, Robert W., Jr., Chairman
Setzler, Nikki
Courson, John E.
Matthews, John W., Jr.
Reese, Glenn G.
Jackson, Darrell
Martin, Larry A.
Rankin, Luke
Alexander, Thomas C.
Cromer, Ronnie W.
Pinckney, Clementa C.
Malloy, Gerald
O'Dell, William
Davis, Thomas C.
Lourie, Joel
Bright, Lee
Bennett, Sean
CORRECTIONS AND PENOLOGY
Fair, Michael L., Chairman
Pinckney, Clementa C.
Williams, Kent M.
Campbell, Paul G., Jr.
Massey, A. Shane
Martin, Shane R.
Nicholson, Floyd
Gregory, Chauncey K. "Greg"
Matthews, John
Davis, Tom
Allen, Karl
Shealy, Katrina
Thurmond, Paul
Turner, Ross
Young, Tom
Coleman, Creighton
Kimpson, Marlon
EDUCATION
Courson, John E., Chairman
Setzler, Nikki
Matthews, John W., Jr.
Hayes, Robert W., Jr.
Rankin, Luke A.
Fair, Michael L.
Peeler, Harvey S., Jr.
Jackson, Darrell
Grooms, Larry K.
Martin, Larry A.
Malloy, Gerald
Pinckney, Clementa
Sheheen, Vincent A.
Cleary, Ray
Hembree, Greg
Thurmond, Paul
ETHICS
Rankin, Luke, Chairman
Leatherman, Hugh K.
Courson, John E.
Hayes, Robert W., Jr.
McGill, J. Yancey
Peeler, Harvey S., Jr.
Reese, Glenn G.
Matthews, John
Jackson, Darrell
FINANCE
Leatherman, Hugh K., Chairman
Setzler, Nikki
Peeler, Harvey S., Jr.
McGill, J. Yancey
Courson, John E.
Matthews, John W., Jr.
O'Dell, William H.
Reese, Glenn G.
Hayes, Robert W., Jr.
Alexander, Thomas C.
Grooms, Larry K.
Pinckney, Clementa C.
Fair, Michael L.
Verdin, Daniel B.
Cromer, Ronnie W.
Bryant, Kevin
Jackson, Darrell
Cleary, Ray
Lourie, Joel
Williams, Kent
Campbell, Paul G., Jr.
Davis, Tom
Nicholson, Floyd
FISH, GAME AND FORESTRY
Campsen, George E. "Chip", III, Chairman
McGill, J. Yancey
Cromer, Ronnie W.
Williams, Kent
Sheheen, Vincent
Coleman, Creighton B.
Gregory, Chauncey K. "Greg"
Bennett, Sean
Corbin, Tom
Hembree, Greg
Johnson, Kevin
McElveen, Thomas
Shealy, Katrina
Thurmond, Paul
Turner, Ross
Young, Tom
GENERAL COMMITTEE
O'Dell, William H., Chairman
Sheheen, Vincent A.
Reese, Glenn G.
Lourie, Joel
Bryant, Kevin
Jackson, Darrell
Cromer, Ronnie
Cleary, Raymond E., III
Bright, Lee
McGill, Yancey
Verdin, Danny
Campbell, Paul G., Jr.
Martin, Shane
Shealy, Katrina
Young, Tom
Kimpson, Marlon
INTERSTATE COOPERATION
Leatherman, Hugh K., Chairman
Setzler, Nikki
Peeler, Harvey S.
Matthews, John
O'Dell, William H.
INVITATIONS
Bryant, Kevin, Chairman
Alexander, Thomas C.
McGill, J. Yancey
Reese, Glenn G.
Verdin, Daniel B.
Campsen, George E. "Chip", III
Cromer, Ronnie W.
Malloy, Gerald
Cleary, Ray
Johnson, Kevin
Kimpson, Marlon
JUDICIARY
Martin, Larry A., Chairman
Rankin, Luke
Malloy, Gerald
Sheheen, Vincent A.
Campsen, George E. "Chip", III
Massey, A. Shane
Bright, Lee
Coleman, Creighton B.
Martin, Shane R.
Scott, John L., Jr.
Gregory, Chauncey K. "Greg"
Allen, Karl
Bennett, Sean
Corbin, Tom
Hembree, Greg
Johnson, Kevin
McElveen, Thomas
Shealy, Katrina
Thurmond, Paul
Turner, Ross
Young, Tom
Kimpson, Marlon
LABOR, COMMERCE AND INDUSTRY
Alexander, Thomas C., Chairman
Setzler, Nikki
O'Dell, William H.
Reese, Glenn G.
Leatherman, Hugh K.
Bryant, Kevin
Williams, Kent
Massey, A. Shane
Bright, Lee
Nicholson, Floyd
Davis, Tom
Scott, John
Bennett, Sean
Corbin, Tom
Johnson, Kevin
Turner, Ross
Allen, Karl
MEDICAL AFFAIRS
Peeler, Harvey S., Jr., Chairman
Courson, John E.
Hayes, Robert W., Jr.
Jackson, Darrell
Fair, Michael L.
Pinckney, Clementa C.
Verdin, Daniel B.
Cleary, Raymond E., III
Lourie, Joel
Martin, Shane R.
Nicholson, Floyd
Scott, John L., Jr.
Alexander, Thomas
Bright, Lee
Davis, Tom
Johnson, Kevin
RULES
Cromer, Ronnie W., Chairman
Martin, Larry A.
Reese, Glenn G.
Malloy, Gerald
Leatherman, Hugh
Massey, A. Shane
Martin, Shane R.
Nicholson, Floyd
Gregory, Chauncey K. "Greg"
Campsen, George E. "Chip", III
Scott, John L., Jr.
Allen, Karl B.
Corbin, Tom
McElveen, Thomas
Thurmond, Paul
Turner, Ross
Kimpson, Marlon
TRANSPORTATION
Grooms, Larry K., Chairman
Leatherman, Hugh K.
McGill, J. Yancey
Rankin, Luke
Verdin, Daniel B.
Malloy, Gerald
Campsen, George E. "Chip", III
Cleary, Raymond E., III
Peeler, Harvey
Campbell, Paul
Lourie, Joel
Coleman, Creighton
Scott, John L., Jr.
Allen, Karl B.
Bennett, Sean
Hembree, Greg
McElveen, Thomas
INDIVIDUAL COMMITTEE ASSIGNMENTS OF THE SENATE
ALEXANDER, THOMAS C.
Banking and Insurance
Finance
Invitations
Labor, Commerce and Industry, Chairman
Medical Affairs
ALLEN, KARL
Corrections and Penology
Judiciary
Labor, Commerce and Industry
Rules
Transportation
BENNETT, SEAN
Banking and Insurance
Fish, Game and Forestry
Judiciary
Labor, Commerce and Industry
Transportation
BRIGHT, LEE
Banking and Insurance
General
Judiciary
Labor, Commerce and Industry
Medical Affairs
BRYANT, KEVIN
Agriculture and Natural Resources
Finance
General
Invitations, Chairman
Labor, Commerce and Industry
CAMPBELL, PAUL G., JR.
Agriculture and Natural Resources
Corrections and Penology
Finance
General
Transportation
CAMPSEN, GEORGE E. "CHIP", III
Fish, Game and Forestry, Chairman
Invitations
Judiciary
Rules
Transportation
CLEARY, RAYMOND E., III
Education
Finance
General
Invitations
Medical Affairs
Transportation
COLEMAN, CREIGHTON
Agriculture and Natural Resources
Corrections and Penology
Fish, Game and Forestry
Judiciary
Transportation
CORBIN, TOM
Agriculture and Natural Resources
Fish, Game and Forestry
Judiciary
Labor, Commerce and Industry
Rules
COURSON, JOHN E.
Banking and Insurance
Education, Chairman
Ethics
Finance
Medical Affairs
CROMER, RONNIE W.
Banking and Insurance
Finance
Fish, Game and Forestry
General
Invitations
Rules, Chairman
DAVIS, THOMAS C.
Banking and Insurance
Corrections and Penology
Finance
Labor, Commerce and Industry
Medical Affairs
FAIR, MICHAEL L.
Corrections and Penology, Chairman
Education
Finance
Medical Affairs
GREGORY, CHAUNCEY K. "GREG"
Agriculture and Natural Resources
Corrections and Penology
Fish, Game and Forestry
Judiciary
Rules
GROOMS, LARRY K.
Agriculture and Natural Resources
Education
Finance
Transportation, Chairman
HAYES, ROBERT W., JR.
Banking and Insurance, Chairman
Education
Ethics
Finance
Medical Affairs
HEMBREE, GREG
Agriculture and Natural Resources
Education
Fish, Game and Forestry
Judiciary
Transportation
Education
Ethics
Fish, Game and Forestry
General
Judiciary
Medical Affairs
JACKSON, DARRELL
Banking and Insurance
Education
Ethics
Finance
General
Medical Affairs
JOHNSON, KEVIN
Agriculture and Natural Resources
Fish, Game and Forestry
Invitations
Judiciary
Medical Affairs
Labor, Commerce and Industry
KIMPSON, MARLON
Corrections and Penology
General
Invitations
Judiciary
Rules
LEATHERMAN, HUGH K.
Ethics
Finance, Chairman
Interstate Cooperation, Chairman
Labor, Commerce and Industry
Rules
Transportation
LOURIE, JOEL
Banking and Insurance
Finance
General
Medical Affairs
Transportation
MALLOY, GERALD
Banking and Insurance
Education
Invitations
Judiciary
Rules
Transportation
MARTIN, LARRY A.
Banking and Insurance
Education
Judiciary, Chairman
Rules
MARTIN, SHANE
Corrections and Penology
General
Judiciary
Medical Affairs
Rules
MASSEY, A. SHANE
Agriculture and Natural Resources
Corrections and Penology
Judiciary
Labor, Commerce and Industry
Rules
MATTHEWS, JOHN W., JR.
Agriculture and Natural Resources
Banking and Insurance
Corrections and Penology
Education
Ethics
Finance
Interstate Cooperation
McELVEEN, THOMAS
Agriculture and Natural Resources
Fish, Game and Forestry
Judiciary
Rules
Transportation
McGILL, J. YANCEY
Agriculture and Natural Resources
Ethics
Finance
Fish, Game and Forestry
General
Invitations
Transportation
NICHOLSON, FLOYD
Corrections and Penology
Finance
Labor, Commerce and Industry
Medical Affairs
Rules
O'DELL, WILLIAM H.
Banking and Insurance
Finance
General, Chairman
Invitations
Labor, Commerce and Industry
PEELER, HARVEY S., JR.
Education
Ethics
Finance
Interstate Cooperation
Medical Affairs, Chairman
Transportation
PINCKNEY, CLEMENTA C.
Banking and Insurance
Corrections and Penology
Education
Finance
Medical Affairs
RANKIN, LUKE
Banking and Insurance
Education
Ethics, Chairman
Judiciary
Transportation
REESE, GLENN G.
Banking and Insurance
Ethics
Finance
General
Invitations
Labor, Commerce and Industry
Rules
SCOTT, JOHN L., JR.
Judiciary
Labor, Commerce and Industry
Medical Affairs
Rules
Transportation
SETZLER, NIKKI
Banking and Insurance
Education
Finance
Interstate Cooperation
Labor, Commerce and Industry
SHEALY, KATRINA
Agriculture and Natural Resources
Corrections and Penology
Fish, Game and Forestry
General
Judiciary
SHEHEEN, VINCENT A.
Agriculture and Natural Resources
Education
Fish, Game and Forestry
General
Judiciary
THURMOND, PAUL
Corrections and Penology
Education
Fish, Game and Forestry
Judiciary
Rules
TURNER, ROSS
Corrections and Penology
Fish, Game and Forestry
Judiciary
Labor, Commerce and Industry
Rules
VERDIN, DANIEL B.
Agriculture and Natural Resources, Chairman
Finance
General
Invitations
Medical Affairs
Transportation
WILLIAMS, KENT M.
Agriculture and Natural Resources
Corrections and Penology
Finance
Fish, Game and Forestry
Labor, Commerce and Industry
YOUNG, TOM
Agriculture and Natural Resources
Corrections and Penology
Fish, Game and Forestry
General
Judiciary
SEATING SELECTIONS
Pursuant to the Rules, the Senate proceeded to the selection of seats.
The Reading Clerk called the roll in accordance with Rule 4 for the purpose of seating selections as follows:
Seat 1 Sen. Courson
Seat 2 Sen. Peeler
Seat 3 Sen. Leatherman
Seat 4 Sen. O'Dell
Seat 5 Sen. Cromer
Seat 6 Sen. Hayes
Seat 7 Sen. Larry Martin
Seat 8 Sen. Fair
Seat 9 Sen. Alexander
Seat 10 Sen. Campbell
Seat 11 Sen. Cleary
Seat 12 Sen. Campsen
Seat 13 Sen. Grooms
Seat 14 Sen. Verdin
Seat 15 Sen. Bright
Seat 16 Sen. Bryant
Seat 17 Sen. Gregory
Seat 18 Sen. Hembree
Seat 19 Sen. Bennett
Seat 20 Sen. Shane Martin
Seat 21 Sen. Davis
Seat 22 Sen. Corbin
Seat 23 Sen. Shealy
Seat 24 Sen. McGill
Seat 25 Sen. Setzler
Seat 26 Sen. Matthews
Seat 27 Sen. Scott
Seat 28 Sen. Nicholson
Seat 29 Sen. Reese
Seat 30 Sen. Williams
Seat 31 Sen. Kimpson
Seat 32 Sen. Jackson
Seat 33 Sen. Rankin
Seat 34 Sen. Hutto
Seat 35 Sen. Coleman
Seat 36 Sen. Allen
Seat 37 Sen. Johnson
Seat 38 Sen. McElveen
Seat 39 Sen. Thurmond
Seat 40 Sen. Pinckney
Seat 41 Sen. Turner
Seat 42 Sen. Young
Seat 43 Sen. Malloy
Seat 44 Sen. Sheheen
Seat 45 Sen. Lourie
Seat 46 Sen. Massey
Expression of Personal Interest
Senator CLEARY rose for an Expression of Personal Interest.
Expression of Personal Interest
Senator COURSON rose for an Expression of Personal Interest.
Expression of Personal Interest
Senator HEMBREE rose for an Expression of Personal Interest.
Remarks To Be Printed
On motion of Senator SHANE MARTIN, with unanimous consent, the remarks of Senator HEMBREE, when reduced to writing and made available to the Desk, would be printed in the Journal.
The following were received and referred to the appropriate committees for consideration:
Document No. 4316
Agency: Department of Employment and Workforce
Chapter: 47
Statutory Authority: 1976 Code Section 41-29-110
SUBJECT: Employer-Employee Relationship
Received by Lieutenant Governor January 14, 2014
Referred to the Committee on Labor, Commerce and Industry
Legislative Review Expiration May 14, 2014
Document No. 4386
Agency: Department of Health and Environmental Control
Chapter: 30
Statutory Authority: 1976 Code Sections 48-39-10 et seq.
SUBJECT: Coastal Division Regulations
Received by Lieutenant Governor January 14, 2014
Referred to the Committee Agriculture and Natural Resources
Legislative Review Expiration May 14, 2014
Document No. 4388
Agency: Department of Health and Environmental Control
Chapter: 61
Statutory Authority: 1976 Code Sections 48-1-10 et seq.
SUBJECT: Air Pollution Control Regulations and Standards
Received by Lieutenant Governor January 14, 2014
Referred to the Committee on Medical Affairs
Legislative Review Expiration May 14, 2014
Document No. 4389
Agency: Board of Examiners in Speech-Language Pathology and Audiology
Chapter: 115
Statutory Authority: 1976 Code Sections 40-1-70 and 40-67-70
SUBJECT: Requirements of Licensure in the Field of Speech-Language Pathology and Audiology
Received by Lieutenant Governor January 14, 2014
Referred to the Committee on Medical Affairs
Legislative Review Expiration May 14, 2014
Document No. 4391
Agency: State Board of Education
Chapter: 43
Statutory Authority: 1976 Code Section 59-13-100
SUBJECT: School Superintendent Compensation and Benefits/Expenses
Received by Lieutenant Governor January 14, 2014
Referred to the Committee on Education
Legislative Review Expiration May 14, 2014
Document No. 4396
Agency: State Board of Education
Chapter: 43
Statutory Authority: 1976 Code Sections 59-5-60, 59-21-510 et seq., and 59-33-10 et seq.
SUBJECT: Utilization of General Teacher Certification
Received by Lieutenant Governor January 14, 2014
Referred to the Committee on Education
Legislative Review Expiration May 14, 2014
Document No. 4397
Agency: State Board of Education
Chapter: 43
Statutory Authority: 1976 Code Sections 44-29-180 and 59-5-60
Received by Lieutenant Governor January 14, 2014
Referred to the Committee on Education
Legislative Review Expiration May 14, 2014
Document No. 4399
Agency: Workers' Compensation Commission
Chapter: 67
Statutory Authority: 1976 Code Sections 42-3-30 and 42-9-301
SUBJECT: Lump Sum Payment
Received by Lieutenant Governor January 14, 2014
Referred to the Committee on Judiciary
Legislative Review Expiration May 14, 2014
Document No. 4400
Agency: State Board of Education
Chapter: 43
Statutory Authority: 1976 Code Sections 59-5-60, 59-25-110, 59-26-10 et seq., and 20 U.S.C. 6301 et seq.
SUBJECT: Accreditation Criteria
Received by Lieutenant Governor January 14, 2014
Referred to the Committee on Education
Legislative Review Expiration May 14, 2014
Document No. 4401
Agency: State Board of Education
Chapter: 43
Statutory Authority: 1976 Code Section 59-5-60
SUBJECT: Accreditation Standards Filed
Received by Lieutenant Governor January 14, 2014
Referred to the Committee on Education
Legislative Review Expiration May 14, 2014
Document No. 4403
Agency: State Board of Education
Chapter: 43
Statutory Authority: 1976 Code Sections 59-1-320, 59-5-60, and 4 U.S.C. 1 et seq.
SUBJECT: Displaying the Flag
Received by Lieutenant Governor January 14, 2014
Referred to the Committee on Education
Legislative Review Expiration May 14, 2014
Document No. 4404
Agency: State Board of Education
Chapter: 43
Statutory Authority: 1976 Code Sections 59-5-60, 59-5-65, and 59-59-10 et seq.
SUBJECT: Minimum Standards of Student Conduct and Disciplinary Enforcement Procedures to be Implemented by Local School Districts
Received by Lieutenant Governor January 14, 2014
Referred to the Committee on Education
Legislative Review Expiration May 14, 2014
Document No. 4405
Agency: State Board of Education
Chapter: 43
Statutory Authority: 1976 Code Section 59-5-60
SUBJECT: Operation and Funding of Teacher Training Courses in Mathematics, Science, Reading and Computer Education
Received by Lieutenant Governor January 14, 2014
Referred to the Committee on Education
Legislative Review Expiration May 14, 2014
Document No. 4406
Agency: State Board of Education
Chapter: 43
Statutory Authority: 1976 Code Sections 59-5-60 and 59-25-110
SUBJECT: Requirements for Certification at the Advanced Level
Received by Lieutenant Governor January 14, 2014
Referred to the Committee on Education
Legislative Review Expiration May 14, 2014
Document No. 4407
Agency: State Board of Education
Chapter: 43
Statutory Authority: 1976 Code Sections 59-5-60 and 59-16-10 et seq.
SUBJECT: South Carolina Virtual School Program
Received by Lieutenant Governor January 14, 2014
Referred to the Committee on Education
Legislative Review Expiration May 14, 2014
Document No. 4408
Agency: State Board of Education
Chapter: 43
Statutory Authority: 1976 Code Sections 59-5-65, 59-65-90, 20 U.S.C. 7112, and 42 U.S.C. 5601 et seq.
SUBJECT: Student Attendance
Received by Lieutenant Governor January 14, 2014
Referred to the Committee on Education
Legislative Review Expiration May 14, 2014
Document No. 4409
Agency: State Board of Education
Chapter: 43
Statutory Authority: 1976 Code Section 59-5-67
SUBJECT: Teacher Grants
Received by Lieutenant Governor January 14, 2014
Referred to the Committee on Education
Legislative Review Expiration May 14, 2014
Document No. 4411
Agency: Department of Natural Resources
Chapter: 123
Statutory Authority: 1976 Code Sections 50-1-200, 50-1-220, 50-3-100, 50-9-740, 50-11-10, 50-11-65, 50-11-120, 50-11-310, 50-11-335, 50-11-350, 50-11-390, 50-11-430, 50-11-500, 50-11-510, 50-11-520, 50-11-530, 50-11-854, 50-11-2200 and 50-11-2210
SUBJECT: Seasons, Limits, Methods of Take and Special Use Restrictions on Wildlife Management Areas
Received by Lieutenant Governor January 14, 2014
Referred to the Committee on Fish, Game, and Forestry
Legislative Review Expiration May 14, 2014
Document No. 4414
Agency: Department of Natural Resources
Chapter: 123
Statutory Authority: 1976 Code Sections 50-11-2200, 50-11-2210 and 50-11-2215
SUBJECT: Additional Regulations Applicable to Specific Properties
Received by Lieutenant Governor January 14, 2014
Referred to the Committee on Fish, Game, and Forestry
Legislative Review Expiration May 14, 2014
Document No. 4419
Agency: State Board of Education
Chapter: 43
Statutory Authority: 1976 Code Sections 59-5-60(1), (3), and (6), 59-39-100, and 20 U.S.C. 6301 et seq.
Received by Lieutenant Governor January 14, 2014
Referred to the Committee on Education
Legislative Review Expiration May 14, 2014
Document No. 4420
Agency: State Board of Education
Chapter: 43
Statutory Authority: 1976 Code Sections 59-43-10 et seq.
Referred to the Committee on Education
Legislative Review Expiration May 14, 2014
Document No. 4422
Agency: State Board of Education
Chapter: 43
Statutory Authority: 1976 Code Sections 59-5-60(1), 59-25-110, 59-26-10 et seq., and 20 U.S.C. 6301 et seq.
SUBJECT: Requirements for Additional Areas of Certification
Received by Lieutenant Governor January 14, 2014
Referred to the Committee on Education
Legislative Review Expiration May 14, 2014
Document No. 4428
Agency: Department of Natural Resources
Chapter: 123
Statutory Authority: 1976 Code Sections 50-21-610 and 50-23-230
Received by Lieutenant Governor January 14, 2014
Referred to the Committee on Fish, Game, and Forestry
Legislative Review Expiration May 14, 2014
Doctor of the Day
Senator FAIR introduced Dr. Bruce A. Synder of Greenville, S.C., Doctor of the Day.
S. 185 (Word version) Sen. Bennett
S. 447 (Word version) Sen. Shealy
S. 513 (Word version) Sens. Grooms, Bryant
S. 300 (Word version) Sens. Fair, Campsen, Davis, Shealy
S. 811 (Word version) Sen. Coleman
S. 901 (Word version) Sens. Grooms, Bryant
S. 865 (Word version) Sen. Massey
S. 886 (Word version) Sen. Massey
S. 904 (Word version) Sen. Massey
S. 876 (Word version) Sen. Campsen
S. 885 (Word version) Sen. Campsen
S. 901 (Word version) Sen. Davis
Senator COURSON asked unanimous consent to make a motion that the list of prefiled Bills, a copy of which has been made available to each member, be entered in the Journal en banc as having been read and referred, as noted, unless any member shall make a motion to refer a Bill to a different committee.
INTRODUCTION OF BILLS AND RESOLUTIONS
The following were introduced:
S. 806 (Word version) -- Senators Setzler, Matthews, McGill, Reese, Jackson, Hutto, Pinckney, Malloy, Sheheen, Lourie, Williams, Coleman, Nicholson, Scott, Allen, Johnson, McElveen and Kimpson: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING ARTICLE 10 TO CHAPTER 1, TITLE 13 SO AS TO CREATE THE DIVISION OF SMALL BUSINESS AND ENTREPRENEURIAL DEVELOPMENT WITHIN THE SOUTH CAROLINA DEPARTMENT OF COMMERCE, AND TO PROVIDE RELATED DEFINITIONS, OBJECTIVES, DUTIES, AND POWERS.
l:\council\bills\agm\18040ab14.docx
Prefiled and referred to the Committee on Labor, Commerce and Industry.
Read the first time and referred to the Committee on Labor, Commerce and Industry.
S. 807 (Word version) -- Senators Setzler, Courson, Cromer, Massey and Shealy: A BILL TO AMEND SECTION 7-7-380, AS AMENDED, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE DESIGNATION OF VOTING PRECINCTS IN LEXINGTON COUNTY, SO AS TO ADD FOUR PRECINCTS AND DELETE ONE PRECINCT AND TO REDESIGNATE THE MAP NUMBER ON WHICH THESE MAY BE FOUND AND MAINTAINED BY THE OFFICE OF RESEARCH AND STATISTICS OF THE STATE BUDGET AND CONTROL BOARD.
l:\council\bills\bbm\10973htc14.docx
Prefiled and referred to the Committee on Judiciary.
Read the first time and referred to the Committee on Judiciary.
S. 808 (Word version) -- Senator Leatherman: A BILL TO AMEND SECTION 6-11-1460 OF THE 1976 CODE, RELATING TO EMERGENCY VOLUNTEER JOB PROTECTION, TO PROVIDE THAT AN EMPLOYER MAY NOT FIRE OR TAKE ANY ACTION AGAINST AN EMPLOYEE WHO IS A VOLUNTEER FIREFIGHTER OR A VOLUNTEER EMERGENCY MEDICAL SERVICES PERSONNEL AND WHO, WHEN ACTING AS A VOLUNTEER FIREFIGHTER OR A VOLUNTEER EMERGENCY MEDICAL SERVICES PERSONNEL ARRIVES LATE TO WORK IF THE EMPLOYEE PROVIDES WRITTEN DOCUMENTATION FROM THE DEPARTMENT CHIEF.
l:\s-res\hkl\005fire.hm.hkl.docx
Prefiled and referred to the Committee on Judiciary.
Read the first time and referred to the Committee on Judiciary.
S. 809 (Word version) -- Senator Leatherman: A BILL TO AMEND SECTION 4-10-330, AS AMENDED, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE CAPITAL PROJECTS SALES TAX, SO AS TO DELETE A PROVISION ALLOWING THE REFERENDUM FOR IMPOSITION OR REIMPOSITION TO BE HELD AT A TIME OTHER THAN AT THE TIME OF THE GENERAL ELECTION.
l:\council\bills\bh\26026dg14.docx
Prefiled and referred to the Committee on Finance.
Read the first time and referred to the Committee on Finance.
S. 810 (Word version) -- Senators Peeler, McGill, Alexander and Hayes: A BILL TO AMEND CHAPTER 20, TITLE 2, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO NONJUDICIAL SCREENING AND ELECTION, SO AS TO CREATE THE COLLEGE AND UNIVERSITY TRUSTEE SCREENING COMMISSION TO CONSIDER THE QUALIFICATIONS OF CANDIDATES FOR TRUSTEES TO STATE-SUPPORTED COLLEGES AND UNIVERSITIES, TO PROVIDE FOR THE MEMBERSHIP OF THE COMMISSION, AND TO PROVIDE FOR THE INVESTIGATIVE, NOMINATION, AND ELECTION PROCESSES.
l:\council\bills\agm\18053dg14.docx
Prefiled and referred to the Committee on Judiciary.
Read the first time and referred to the Committee on Judiciary.
S. 811 (Word version) -- Senators Courson, Lourie and Coleman: A BILL TO AMEND SECTION 7-27-110 OF THE 1976 CODE, RELATING TO THE APPOINTMENT OF COUNTY BOARDS OF REGISTRATION AND BOARDS OF ELECTION, TO PROVIDE THAT FOR THOSE COUNTIES THAT DO NOT HAVE A COMBINED BOARD OF REGISTRATION AND ELECTION, THE BOARDS MAY BE COMBINED UPON WRITTEN AGREEMENT OF THE COUNTY LEGISLATIVE DELEGATION AND THE COUNTY GOVERNING BODY; TO PROVIDE FOR THE NUMBER, TERMS, POWERS, AND DUTIES OF THE COMBINED BOARD, AND THE ABOLISHMENT OF THE SEPARATE BOARDS OF REGISTRATION AND ELECTION; AND TO PROVIDE THAT FOR THOSE COUNTIES THAT DO HAVE COMBINED BOARDS OF REGISTRATION AND ELECTION, THE POWER TO APPOINT OR RECOMMEND THE APPOINTMENT OF THE MEMBERS OF THE COMBINED BOARD MAY BE DEVOLVED TO THE COUNTY GOVERNING BODY UPON WRITTEN AGREEMENT OF THE COUNTY LEGISLATIVE DELEGATION AND THE COUNTY GOVERNING BODY.
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Prefiled and referred to the Committee on Judiciary.
Read the first time and referred to the Committee on Judiciary.
S. 812 (Word version) -- Senator O'Dell: A BILL TO AMEND SECTION 11-50-50, AS AMENDED, SECTIONS 11-50-60, 11-50-90, AND 11-50-160, CODE OF LAWS OF SOUTH CAROLINA, 1976, ALL RELATING TO THE SOUTH CAROLINA RURAL INFRASTRUCTURE AUTHORITY, SO AS TO UPDATE THE LIST OF COUNTIES IN WHICH A BOARD MEMBER MAY RESIDE OR REPRESENT, TO REMOVE THE AUTHORITY FROM THE JURISDICTION OF THE ADMINISTRATIVE PROCEDURES ACT, AND TO NO LONGER REQUIRE THE AUTHORITY TO OBTAIN REVIEW AND APPROVAL OF THE JOINT BOND REVIEW COMMITTEE BEFORE PROVIDING FINANCIAL ASSISTANCE, BUT TO REQUIRE THE AUTHORITY TO SUBMIT AN ANNUAL REPORT TO THE JOINT BOND REVIEW COMMITTEE REGARDING LOANS AND OTHER FINANCIAL ASSISTANCE.
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Prefiled and referred to the Committee on Finance.
Read the first time and referred to the Committee on Finance.
S. 813 (Word version) -- Senator Hayes: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING SECTION 16-11-625 SO AS TO PROVIDE A PERSON WHO, WITHOUT LEGAL CAUSE OR GOOD EXCUSE, ENTERS A PUBLIC LIBRARY AFTER HAVING BEEN WARNED BY AN EMPLOYEE, AGENT, OR REPRESENTATIVE OF THE LIBRARY NOT TO DO SO OR WITHOUT HAVING BEEN WARNED FAILS AND REFUSES, WITHOUT GOOD CAUSE OR GOOD EXCUSE, TO LEAVE IMMEDIATELY UPON BEING ORDERED OR REQUESTED TO DO SO IS GUILTY OF A MISDEMEANOR TRIABLE IN A MUNICIPAL OR MAGISTRATES COURT, AND TO PROVIDE THE PROVISIONS OF THIS SECTION MUST BE CONSTRUED AS IN ADDITION TO, AND NOT AS SUPERSEDING, ANOTHER STATUTE RELATING TO TRESPASS OR UNLAWFUL ENTRY ON LANDS OF ANOTHER.
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Prefiled and referred to the Committee on Judiciary.
Read the first time and referred to the Committee on Judiciary.
S. 814 (Word version) -- Senator L. Martin: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING SECTION 41-7-35 SO AS TO PROVIDE NO STATE, COUNTY, MUNICIPAL, OR LIKE GOVERNMENTAL OFFICER, AGENT, OR GOVERNING BODY MAY RECOGNIZE ANY LABOR UNION OR OTHER EMPLOYEE ASSOCIATION AS A BARGAINING AGENT OF ANY PUBLIC OFFICERS OR EMPLOYEES, OR TO COLLECTIVELY BARGAIN OR ENTER INTO ANY COLLECTIVE BARGAINING CONTRACT WITH ANY SUCH UNION OR ASSOCIATION OR ITS AGENTS WITH RESPECT TO ANY MATTER RELATING TO THEM OR THEIR EMPLOYMENT OR SERVICE.
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Prefiled and referred to the Committee on Labor, Commerce and Industry.
Read the first time and referred to the Committee on Labor, Commerce and Industry.
S. 815 (Word version) -- Senators L. Martin and Campsen: A BILL TO AMEND SECTION 7-11-30, SOUTH CAROLINA CODE OF LAWS, 1976, TO PROVIDE THAT A PARTY MAY CHOOSE TO CHANGE NOMINATION OF CANDIDATES BY PRIMARY TO A CONVENTION IF THREE-FOURTHS OF THE CONVENTION MEMBERSHIP APPROVES OF THE CONVENTION NOMINATION PROCESS, AND A MAJORITY OF THE VOTERS IN THAT PARTY'S NEXT PRIMARY ELECTION APPROVES THE USE OF A CONVENTION.
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Prefiled and referred to the Committee on Judiciary.
Read the first time and referred to the Committee on Judiciary.
S. 816 (Word version) -- Senators L. Martin, Campsen, Malloy, Peeler, Alexander, McGill and Hayes: A CONCURRENT RESOLUTION TO FIX NOON ON WEDNESDAY, FEBRUARY 5, 2014, AS THE TIME TO ELECT A SUCCESSOR TO A CERTAIN JUDGE OF THE SUPREME COURT, CHIEF JUSTICE, WHOSE TERM WILL EXPIRE JULY 31, 2014; TO ELECT A SUCCESSOR TO A CERTAIN JUDGE OF THE CIRCUIT COURT, AT-LARGE, SEAT 11, WHOSE TERM WILL EXPIRE JUNE 30, 2014; TO ELECT A SUCCESSOR TO A CERTAIN JUDGE OF THE CIRCUIT COURT, AT-LARGE, SEAT 12, WHOSE TERM WILL EXPIRE JUNE 30, 2014; TO ELECT A SUCCESSOR TO A CERTAIN JUDGE OF THE CIRCUIT COURT, AT-LARGE, SEAT 13, WHOSE TERM WILL EXPIRE JUNE 30, 2014; TO ELECT A SUCCESSOR TO A CERTAIN JUDGE OF THE FAMILY COURT, FOURTH JUDICIAL CIRCUIT, SEAT 3, WHOSE TERM WILL EXPIRE JUNE 30, 2014; TO ELECT A SUCCESSOR TO A CERTAIN JUDGE OF THE FAMILY COURT, SIXTH JUDICIAL CIRCUIT, SEAT 1, TO FILL THE UNEXPIRED TERM THAT EXPIRES JUNE 30, 2019; TO ELECT A SUCCESSOR TO A CERTAIN JUDGE OF THE FAMILY COURT, SIXTH JUDICIAL CIRCUIT, SEAT 2, WHOSE TERM WILL EXPIRE JUNE 30, 2014; TO ELECT A SUCCESSOR TO A CERTAIN JUDGE OF THE FAMILY COURT, NINTH JUDICIAL CIRCUIT, SEAT 5, WHOSE TERM WILL EXPIRE JUNE 30, 2014; TO ELECT A SUCCESSOR TO A CERTAIN JUDGE OF THE FAMILY COURT, THIRTEENTH JUDICIAL CIRCUIT, SEAT 5, WHOSE TERM WILL EXPIRE JUNE 30, 2014, AND TO FILL THE SUBSEQUENT FULL TERM WHICH WILL EXPIRE JUNE 30, 2020; TO ELECT A SUCCESSOR TO A CERTAIN JUDGE OF FAMILY COURT, FIFTEENTH JUDICIAL CIRCUIT, SEAT 2, WHOSE TERM WILL EXPIRE JUNE 30, 2016, AND THE SUCCESSOR WILL FILL THE UNEXPIRED TERM OF THAT OFFICE; TO ELECT A SUCCESSOR TO THE FAMILY COURT, FIFTEENTH JUDICIAL CIRCUIT, SEAT 3, WHOSE TERM WILL EXPIRE JUNE 30, 2014; TO ELECT A SUCCESSOR TO A CERTAIN JUDGE OF FAMILY COURT, SIXTEENTH JUDICIAL CIRCUIT, SEAT 1, WHOSE TERM WILL EXPIRE JUNE 30, 2016, AND THE SUCCESSOR WILL FILL THE UNEXPIRED TERM OF THAT OFFICE; TO ELECT A SUCCESSOR TO THE JUDGE OF THE ADMINISTRATIVE LAW COURT, CHIEF ADMINISTRATIVE JUDGE, SEAT 1, WHOSE TERM WILL EXPIRE JUNE 30, 2014; AND AS THE DATE TO MEET IN JOINT SESSION FOR THE PURPOSE OF ELECTING A MEMBER OF THE BOARD OF TRUSTEES OF FRANCIS MARION UNIVERSITY, AT-LARGE SEAT NINE, WHOSE TERM EXPIRES ON JUNE 30, 2016, FOR THE PURPOSE OF ELECTING A MEMBER OF THE BOARD OF TRUSTEES FOR THE SOUTH CAROLINA STATE UNIVERSITY, FIFTH CONGRESSIONAL DISTRICT, WHOSE TERM EXPIRES ON JUNE 30, 2017, AND FOR THE PURPOSE OF ELECTING TWO MEMBERS TO THE BOARD OF TRUSTEES FOR THE OLD EXCHANGE BUILDING COMMISSION, AT-LARGE SEATS, WHOSE TERMS EXPIRE ON JUNE 30, 2018.
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Prefiled and referred to the Committee on Judiciary.
The Concurrent Resolution was introduced and referred to the Committee on Judiciary.
Recalled--S. 816
Senator LARRY MARTIN asked unanimous consent to make a motion to recall the Concurrent Resolution from the Committee on Judiciary.
The Resolution was recalled from the Committee on Judiciary and ordered placed on the Calendar for consideration tomorrow.
S. 817 (Word version) -- Senator L. Martin: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING SECTION 23-3-47 SO AS TO REQUIRE PERSONS SEEKING CERTAIN POSITIONS OR WHO VOLUNTEER OR SERVE IN A POSITION SUPPORTED, SPONSORED, OR ADMINISTERED BY THE SOUTH CAROLINA COMMISSION ON NATIONAL AND COMMUNITY SERVICE TO UNDERGO A STATE AND NATIONAL CRIMINAL HISTORY BACKGROUND CHECK AND TO PROVIDE PROCEDURES TO BE FOLLOWED AND FOR THE COSTS OF THE BACKGROUND CHECKS.
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Prefiled and referred to the Committee on Judiciary.
Read the first time and referred to the Committee on Judiciary.
S. 818 (Word version) -- Senator L. Martin: A BILL TO AMEND SECTION 56-5-2945, AS AMENDED, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE OFFENSE OF FELONY DRIVING UNDER THE INFLUENCE, SO AS TO INCREASE THE MINIMUM YEARS OF IMPRISONMENT FOR A PERSON CONVICTED OF THIS OFFENSE WHEN DEATH RESULTS.
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Prefiled and referred to the Committee on Judiciary.
Read the first time and referred to the Committee on Judiciary.
S. 819 (Word version) -- Senator Jackson: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING CHAPTER 52 TO TITLE 27 SO AS TO ENACT THE "SOUTH CAROLINA HOMEOWNERS' ASSOCIATION ACT."
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Prefiled and referred to the Committee on Judiciary.
Read the first time and referred to the Committee on Judiciary.
S. 820 (Word version) -- Senator Jackson: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING SECTION 12-6-3785 SO AS TO ALLOW AN INDIVIDUAL TAXPAYER TO CLAIM AN INCOME TAX CREDIT IF THE INDIVIDUAL SERVES AS A CAREGIVER, AND TO SET THE AMOUNT OF THE CREDIT.
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Prefiled and referred to the Committee on Finance.
Read the first time and referred to the Committee on Finance.
S. 821 (Word version) -- Senator Jackson: A BILL TO AMEND SECTION 63-5-20, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO CHILD SUPPORT OBLIGATIONS, SO AS TO PROVIDE THAT AN OFFENDER SENTENCED TO NINETY OR FEWER DAYS IMPRISONMENT WHO IS EMPLOYED AT THE TIME OF SENTENCING AND IS ABLE TO MAINTAIN EMPLOYMENT MAY SERVE HIS SENTENCE AT A TIME WHEN HE IS NOT WORKING AND DOES NOT INTERFERE WITH HIS EMPLOYMENT; AND TO PROVIDE FOR WAGE GARNISHMENT TO SATISFY CHILD SUPPORT PAYMENTS.
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Prefiled and referred to the Committee on Judiciary.
Read the first time and referred to the Committee on Judiciary.
S. 822 (Word version) -- Senators Jackson, Alexander and Courson: A CONCURRENT RESOLUTION TO INVITE THE LIEUTENANT GOVERNOR, THE HONORABLE GLENN F. MCCONNELL TO ADDRESS THE GENERAL ASSEMBLY IN JOINT SESSION ON THE STATE OF THE AGING POPULATION IN SOUTH CAROLINA AT 12:00 P.M. ON FEBRUARY 12, 2014.
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Prefiled and referred to the Committee on Invitations.
The Concurrent Resolution was introduced and referred to the Committee on Invitations.
S. 823 (Word version) -- Senator Alexander: A BILL TO AMEND SECTIONS 56-5-6410 AND 56-5-6420, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO CHILD PASSENGER RESTRAINT SYSTEMS, SO AS TO INCREASE THE AGE FOR WHICH A CHILD MUST BE SECURED IN A PASSENGER RESTRAINT SYSTEM FROM FIVE YEARS OLD TO SEVEN YEARS OLD, TO ADD CERTAIN HEIGHT REQUIREMENTS, TO PROHIBIT A CHILD FROM OCCUPYING THE FRONT PASSENGER SEAT UNTIL THE CHILD IS TWELVE YEARS OLD INSTEAD OF FIVE YEARS OLD, AND TO MAKE CONFORMING CHANGES.
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Prefiled and referred to the Committee on Transportation.
Read the first time and referred to the Committee on Transportation.
S. 824 (Word version) -- Senator Alexander: A BILL TO AMEND SECTION 23-43-20, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO DEFINITIONS OF THE SOUTH CAROLINA MODULAR BUILDINGS CONSTRUCTION ACT, SO AS TO REQUIRE THAT AN APPROVED INSPECTION AGENCY RETAIN A BUILDING CONSTRUCTION-ORIENTED ENGINEER OR ARCHITECT TO ENSURE COMPLIANCE; AND TO AMEND SECTION 23-43-90, RELATING TO INSPECTION AND CERTIFICATION OF A MODULAR BUILDING, SO AS TO PROVIDE THAT FINAL PLAN APPROVAL FOR A SINGLE FAMILY RESIDENTIAL MODULAR BUILDING BE PERFORMED BY AN APPROVED INSPECTION AGENCY, AND TO PROVIDE THAT FINAL APPROVAL FOR A COMMERCIAL MODULAR BUILDING BE PERFORMED BY THE DEPARTMENT OF LABOR, LICENSING AND REGULATION.
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Prefiled and referred to the Committee on Labor, Commerce and Industry.
Read the first time and referred to the Committee on Labor, Commerce and Industry.
S. 825 (Word version) -- Senator Alexander: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING SECTION 3-1-40 SO AS TO EXEMPT FROM AD VALOREM TAXATION ANY REAL PROPERTY LOCATED WITHIN A MILITARY BASE OR INSTALLATION THAT IS USED OR OWNED BY THE UNITED STATES ARMED FORCES AND IS USED AS MILITARY HOUSING FOR MILITARY AFFILIATED PERSONNEL AND THEIR FAMILIES EVEN IF THE REAL PROPERTY IS IMPROVED, MAINTAINED, OR LEASED TO A PARTY THAT WOULD OTHERWISE SUBJECT THE REAL PROPERTY TO TAX, SO LONG AS THERE IS A CONTRACTUAL AGREEMENT REQUIRING THE LESSEE TO USE THE PROPERTY FOR MILITARY HOUSING.
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Prefiled and referred to the Committee on Finance.
Read the first time and referred to the Committee on Finance.
S. 826 (Word version) -- Senator Rankin: A BILL TO AMEND SECTION 38-73-500(C) OF THE 1976 CODE, RELATING TO RANDOM DRUG AND ALCOHOL TESTING PROCEDURES CONCERNING MERIT RATING FOR WORKER'S COMPENSATION INSURANCE; TO PROVIDE THAT A SINGLE SAMPLE MAY BE USED FOR THE FIRST AND SECOND TESTS IF A SECOND TEST IS ADMINISTERED.
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Prefiled and referred to the Committee on Banking and Insurance.
Read the first time and referred to the Committee on Banking and Insurance.
S. 827 (Word version) -- Senator Fair: A BILL TO AMEND SECTION 17-15-10 OF THE 1976 CODE, RELATING TO CONDITIONS OF RELEASE FOR A PERSON CHARGED WITH A NONCAPITAL OFFENSE, TO PROVIDE A COURT MAY ORDER A PERSON TO WEAR AN APPROVED ELECTRONIC MONITORING DEVICE AS A CONDITION OF RELEASE AND MAY ORDER A PERSON TO PAY THE COST OF ELECTRONIC MONITORING.
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Prefiled and referred to the Committee on Judiciary.
Read the first time and referred to the Committee on Judiciary.
S. 828 (Word version) -- Senators Fair and Turner: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING SECTION 11-41-75 SO AS TO EXEMPT CERTAIN BOND REIMBURSEMENT REQUIREMENTS IF A CONVENTION AND TRADE SHOW CENTER IS SOLD AND IS TO BE REPLACED WITH A NEW CONVENTION AND TRADE SHOW CENTER, AND TO SET FORTH EXEMPTION REQUIREMENTS; AND TO AMEND SECTION 11-41-70, AS AMENDED, RELATING TO REQUIREMENTS FOR ECONOMIC DEVELOPMENT BONDS, SO AS TO MAKE A CONFORMING CHANGE.
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Prefiled and referred to the Committee on Finance.
Read the first time and referred to the Committee on Finance.
S. 829 (Word version) -- Senator Fair: A BILL TO AMEND SECTION 56-5-1520, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO GENERAL RULES REGARDING MAXIMUM SPEED LIMITS THAT A VEHICLE MAY BE OPERATED ALONG A HIGHWAY, SO AS TO PROVIDE THAT THIS PROVISION APPLIES TO HIGHWAYS WHERE HIGHWAY MAINTENANCE OR CONSTRUCTION WORKERS, OR SANITATION WORKERS ARE PRESENT, AND TO PROVIDE THAT THE PENALTIES CONTAINED IN THIS SECTION MUST BE DOUBLED FOR A DRIVER WHO VIOLATES THE SPEED LIMITATIONS CONTAINED IN IT WHILE OPERATING A VEHICLE WHERE PERSONS ARE ENGAGED IN WORK IN A HIGHWAY MAINTENANCE OR CONSTRUCTION AREA, IN A UTILITY WORK AREA, OR WHERE SANITATION WORKERS ARE AT RISK FROM TRAFFIC AND THE VEHICLE'S OPERATOR KNOWS OR SHOULD KNOW THAT SANITATION WORKERS ARE PRESENT.
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Prefiled and referred to the Committee on Transportation.
Read the first time and referred to the Committee on Transportation.
S. 830 (Word version) -- Senator Fair: A CONCURRENT RESOLUTION TO MAKE APPLICATION BY THE STATE OF SOUTH CAROLINA UNDER ARTICLE V OF THE UNITED STATES CONSTITUTION FOR A CONVENTION OF THE STATES TO BE CALLED BY CONGRESS RESTRICTED TO PROPOSING AMENDMENTS TO THE UNITED STATES CONSTITUTION TO IMPOSE FISCAL RESTRAINTS ON THE FEDERAL GOVERNMENT, LIMIT THE POWER AND JURISDICTION OF THE FEDERAL GOVERNMENT, AND LIMIT THE TERMS OF OFFICE FOR ITS OFFICIALS.
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Prefiled and referred to the Committee on Judiciary.
The Concurrent Resolution was introduced and referred to the Committee on Judiciary.
S. 831 (Word version) -- Senator Fair: A BILL TO AMEND CHAPTER 21, TITLE 24 OF THE 1976 CODE, RELATING TO PROBATION, PAROLE AND PARDON, BY ADDING ARTICLE 14 TO PROVIDE FOR THE LICENSING OF ELECTRONIC MONITORING VENDORS, AND TO PROVIDE THE DEPARTMENT IS AUTHORIZED TO PROMULGATE REGULATIONS TO IMPLEMENT AND REGULATE THE PROVISIONS OF THIS ARTICLE, AND TO PROVIDE FOR THE POWERS AND DUTIES OF THE DEPARTMENT TO DEVELOP GUIDELINES AND CRITERIA FOR THE USE OF ELECTRONIC MONITORING, DATA STORAGE, AND THE CONTRACTING OF VENDORS, AND TO PROVIDE THE DEPARTMENT SHALL COLLECT AN APPLICATION FEE FOR THE LICENSING AND REGISTERING OF ELECTRONIC MONITORING VENDORS AND AN ANNUAL RENEWAL FEE, AND TO PROVIDE THE DEPARTMENT MAY IMPOSE A FINE OF FIVE HUNDRED DOLLARS FOR EACH VIOLATION ON VENDORS, AND TO PROVIDE NOTHING IN THIS ARTICLE SHALL BE CONSTRUED TO ABROGATE OR IMPAIR THE POWERS OF ANY BOND COURT OR GRANT THE DEPARTMENT AUTHORITY OVER A BAIL BONDING COMPANY AND THEIR POWER TO SET CONDITIONS OF PRETRIAL RELEASE.
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Prefiled and referred to the Committee on Corrections and Penology.
Read the first time and referred to the Committee on Corrections and Penology.
S. 832 (Word version) -- Senator Grooms: A BILL TO AMEND SECTION 12-28-110 OF THE 1976 CODE, RELATING TO DEFINITIONS CONCERNING THE MOTOR FUEL USER FEE, BY ADDING "LIQUEFIED NATURAL GAS" TO THE DEFINITION OF "ALTERNATIVE FUEL" AND TO ADD "DIESEL GALLON EQUIVALENT" TO THE LIST OF DEFINITIONS FOR THE CHAPTER; AND TO AMEND SECTION 12-28-310 TO PROVIDE THAT A USER FEE OF SIXTEEN CENTS PER DIESEL GALLON EQUIVALENT BE APPLIED TO LIQUEFIED NATURAL GAS.
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Prefiled and referred to the Committee on Finance.
Read the first time and referred to the Committee on Finance.
S. 833 (Word version) -- Senator Grooms: A CONCURRENT RESOLUTION TO MAKE APPLICATION BY THE STATE OF SOUTH CAROLINA UNDER ARTICLE V OF THE UNITED STATES CONSTITUTION FOR A CONVENTION OF THE STATES TO BE CALLED BY CONGRESS RESTRICTED TO PROPOSING AMENDMENTS TO THE UNITED STATES CONSTITUTION TO IMPOSE FISCAL RESTRAINTS ON THE FEDERAL GOVERNMENT, LIMIT THE POWER AND JURISDICTION OF THE FEDERAL GOVERNMENT, AND LIMIT THE TERMS OF OFFICE FOR ITS OFFICIALS.
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Prefiled and referred to the Committee on Judiciary.
The Concurrent Resolution was introduced and referred to the Committee on Judiciary.
S. 834 (Word version) -- Senator Sheheen: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING CHAPTER 156 TO TITLE 59 SO AS TO CREATE THE SOUTH CAROLINA CHILD DEVELOPMENT EDUCATION PROGRAM WHICH IS A FULL DAY, FOUR-YEAR-OLD KINDERGARTEN PROGRAM FOR AT-RISK CHILDREN WHICH MUST BE MADE AVAILABLE TO QUALIFIED CHILDREN IN ALL PUBLIC SCHOOL DISTRICTS WITHIN THE STATE, TO ESTABLISH PRIORITY FOR THE PROGRAM, TO REQUIRE THE PROGRAM TO BE AVAILABLE TO ALL QUALIFIED CHILDREN BY THE 2015-2016 SCHOOL YEAR, TO ESTABLISH ELIGIBILITY FOR THE PROGRAM, TO PROVIDE THAT WITHIN FIVE YEARS OF THE PROGRAM BEING AVAILABLE TO ALL QUALIFIED CHILDREN, THAT THE PROGRAM MUST BE EXPANDED TO ALL CHILDREN REGARDLESS OF FINANCIAL ELIGIBILITY, TO ESTABLISH PROVIDER STANDARDS, TO TASK THE DEPARTMENT OF EDUCATION AND THE OFFICE OF FIRST STEPS TO SCHOOL READINESS WITH ACTING AS ADMINISTRATORS OF THE PROGRAM, TO ESTABLISH STANDARDS FOR THE PROGRAM, AND TO SET THE FUNDING LEVEL OF THE PROGRAM.
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Prefiled and referred to the Committee on Education.
Read the first time and referred to the Committee on Education.
S. 835 (Word version) -- Senator Bryant: A BILL TO AMEND SECTION 40-57-60 OF THE 1976 CODE, RELATING TO THE POWERS AND DUTIES OF THE SOUTH CAROLINA REAL ESTATE COMMISSION, TO PROVIDE THAT THE COMMISSION SHALL ESTABLISH A FEE SCHEDULE AND TO REDUCE THE AMOUNT OF FEES PAID BY REAL ESTATE LICENSEES; AND TO AMEND SECTION 40-57-70, RELATING TO LICENSE FEES, TO REMOVE THAT ALL FEES RELEVANT TO LICENSURE AND REGULATION MUST BE IN ACCORDANCE WITH SECTION 40-1-50(D) AND PROMULGATED THROUGH REGULATION.
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Prefiled and referred to the Committee on Labor, Commerce and Industry.
Read the first time and referred to the Committee on Labor, Commerce and Industry.
S. 836 (Word version) -- Senator Bryant: A BILL TO AMEND CHAPTER 1, TITLE 23 OF THE 1976 CODE, RELATING TO GENERAL PROVISIONS CONCERNING LAW ENFORCEMENT AND PUBLIC SAFETY; BY ADDING SECTION 23-1-240, TO PROVIDE THAT LAW ENFORCEMENT CHAPLAINS WITH A VALID CONCEALED WEAPONS PERMIT MAY BE AUTHORIZED TO CARRY A WEAPON IN THE SAME MANNER AND WITH THE SAME RIGHTS AND PRIVILEGES AS A LAW ENFORCEMENT OFFICER; TO PROVIDE FOR THE REVOCATION OF THAT AUTHORIZATION; AND TO PROVIDE THAT REVOCATION OF AUTHORIZATION DOES NOT CONSTITUTE REVOCATION OF THE CHAPLAIN'S CONCEALED WEAPONS PERMIT.
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Prefiled and referred to the Committee on Judiciary.
Read the first time and referred to the Committee on Judiciary.
S. 837 (Word version) -- Senator Bryant: A BILL TO AMEND ARTICLE 6, CHAPTER 11, TITLE 16 OF THE 1976 CODE, RELATING TO THE PROTECTION OF PERSONS AND PROPERTY ACT; BY ADDING SECTION 16-11-460 TO PROVIDE THAT AN ORDER CONCERNING IMMUNITY FROM PROSECUTION UNDER THE ARTICLE IS IMMEDIATELY APPEALABLE; AND TO PROVIDE THAT A DEFENDANT WHO DOES NOT APPEAL THE ORDER IMMEDIATELY MAY APPEAL THE DENIAL AFTER CONVICTION AND SENTENCING.
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Prefiled and referred to the Committee on Judiciary.
Read the first time and referred to the Committee on Judiciary.
S. 838 (Word version) -- Senator Shealy: A BILL TO AMEND CHAPTER 75, TITLE 15 OF THE 1976 CODE, RELATING TO SUITS INVOLVING MISCELLANEOUS ACTS OF WRONGFUL CONDUCT, BY ADDING SECTION 15-75-30 TO CREATE A CIVIL CAUSE OF ACTION FOR ALIENATION OF AFFECTION.
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Prefiled and referred to the Committee on Judiciary.
Read the first time and referred to the Committee on Judiciary.
S. 839 (Word version) -- Senator Bryant: A BILL TO AMEND TITLE 46 OF THE 1976 CODE, RELATING TO AGRICULTURE, BY ADDING CHAPTER 55 CONCERNING INDUSTRIAL HEMP; TO PROVIDE THAT IT IS LAWFUL TO GROW INDUSTRIAL HEMP IN THIS STATE; TO CLARIFY THAT INDUSTRIAL HEMP IS EXCLUDED FROM THE DEFINITION OF MARIJUANA; TO PROHIBIT GROWING INDUSTRIAL HEMP AND MARIJUANA ON THE SAME PROPERTY OR OTHERWISE GROWING MARIJUANA IN CLOSE PROXIMITY TO INDUSTRIAL HEMP TO DISGUISE THE MARIJUANA GROWTH; AND TO DEFINE NECESSARY TERMS.
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Prefiled and referred to the Committee on Agriculture and Natural Resources.
Read the first time and referred to the Committee on Agriculture and Natural Resources.
S. 840 (Word version) -- Senator Bryant: A BILL TO AMEND SECTION 44-53-1640, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE SUBMISSION OF CERTAIN INFORMATION BY DISPENSERS AS PART OF THE STATE PRESCRIPTION MONITORING PROGRAM, SO AS TO REVISE THE MANNER OF SUBMISSION; AND TO AMEND SECTION 44-53-1650, RELATING TO CONFIDENTIALITY AND RELEASE OF DATA FROM THE STATE PRESCRIPTION MONITORING PROGRAM, SO AS TO REQUIRE A COURT ORDER FOR THE RELEASE OF CERTAIN INFORMATION FOR RESEARCH AND EDUCATION PURPOSES, AND TO REQUIRE A COURT ORDER TO RELEASE INFORMATION TO CERTAIN INDIVIDUALS WHEN THE REQUEST IS FOR SYSTEM DATA MAINTAINED FOR LONGER THAN ONE YEAR.
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Prefiled and referred to the Committee on Medical Affairs.
Read the first time and referred to the Committee on Medical Affairs.
S. 841 (Word version) -- Senator Cleary: A BILL TO AMEND ARTICLE 1, CHAPTER 13, TITLE 63, SOUTH CAROLINA CODE OF LAWS, 1976, RELATING TO THE REGULATION OF CHILDCARE FACILITIES, BY ADDING SECTION 63-13-185, SO AS TO PROHIBIT THE ADMINISTRATION OF MEDICATION TO A CHILD BY AN EMPLOYEE OR VOLUNTEER OF A CHILDCARE FACILITY WITHOUT PARENTAL PERMISSION, AND TO INCLUDE EXCEPTIONS IN CIRCUMSTANCES OF EMERGENCIES, AND TO PROVIDE PENALTIES.
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Prefiled and referred to the Committee on Judiciary.
Read the first time and referred to the Committee on Judiciary.
S. 842 (Word version) -- Senator Cleary: A BILL TO AMEND CHAPTER 12, TITLE 25 OF THE 1976 CODE, RELATING TO VETERAN'S UNCLAIMED CREMATED REMAINS, TO PROVIDE THAT A CORONER MAY WORK WITH A VETERANS SERVICE ORGANIZATION TO PROVIDE FOR THE DISPOSITION OF UNCLAIMED CREMATED REMAINS OF A VETERAN PURSUANT TO THE PROVISIONS CONTAINED IN THIS CHAPTER.
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Prefiled and referred to the General Committee.
Read the first time and referred to the General Committee.
S. 843 (Word version) -- Senator Cleary: A BILL TO AMEND SECTION 59-63-130, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE PROHIBITION OF STUDENT HARASSMENT, INTIMIDATION, OR BULLYING IN PUBLIC SCHOOLS, SO AS TO PROVIDE A SCHOOL EMPLOYEE OR VOLUNTEER MAY GRATUITOUSLY INTERVENE ON BEHALF OF A STUDENT SUBJECTED TO HARASSMENT, INTIMIDATION, OR BULLYING; AND TO AMEND SECTION 59-63-150, RELATING TO CERTAIN LEGAL IMMUNITIES FOR A SCHOOL EMPLOYEE OR VOLUNTEER WHO REPORTS AN INCIDENT OF STUDENT HARASSMENT, INTIMIDATION, OR BULLYING IN COMPLIANCE WITH DISTRICT POLICY, SO AS TO PROVIDE IMMUNITY FROM CRIMINAL OR CIVIL LIABILITY FOR A SCHOOL EMPLOYEE OR VOLUNTEER WHO IN GOOD FAITH GRATUITOUSLY INTERVENES ON BEHALF OF A STUDENT SUBJECTED TO HARASSMENT, INTIMIDATION, OR BULLYING.
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Prefiled and referred to the Committee on Education.
Read the first time and referred to the Committee on Education.
S. 844 (Word version) -- Senator Cleary: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING SECTION 2-1-260 SO AS TO PROVIDE THAT ANY APPOINTMENT NOT MADE IN A YEAR BY THE GOVERNOR, AN ELECTED PUBLIC OFFICER, OR AN ELECTED PUBLIC ENTITY BE TRANSFERRED TO AN APPROPRIATE LEGISLATIVE GROUP TO MAKE THE APPOINTMENT.
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Prefiled and referred to the Committee on Judiciary.
Read the first time and referred to the Committee on Judiciary.
S. 845 (Word version) -- Senator Lourie: A JOINT RESOLUTION TO REQUIRE THE DEPARTMENT OF HEALTH AND ENVIRONMENTAL CONTROL TO TRANSFER AND EXPEND FUNDS AMONG APPROPRIATED REVENUES TO OPERATE AND ADMINISTER THE CERTIFICATE OF NEED PROGRAM.
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Prefiled and referred to the Committee on Medical Affairs.
Read the first time and referred to the Committee on Medical Affairs.
S. 846 (Word version) -- Senator Campbell: A BILL TO AMEND ARTICLE 23, CHAPTER 19, TITLE 63 OF THE 1976 CODE, RELATING TO OFFENSES INVOLVING MINORS, BY ADDING SECTION 63-19-2470 TO PROVIDE THAT CHILDREN TWELVE YEARS OF AGE OR YOUNGER WHO ARE CONVICTED OF AN OFFENSE GENERALLY RELATED TO THE MISTREATMENT OF ANIMALS MUST BE GIVEN APPROPRIATE PSYCHIATRIC OR PSYCHOLOGICAL TREATMENT.
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Prefiled and referred to the Committee on Judiciary.
Read the first time and referred to the Committee on Judiciary.
S. 847 (Word version) -- Senator Massey: A BILL TO AMEND SECTION 15-39-410 OF THE 1976 CODE, RELATING TO PROPERTY WHICH MAY BE ORDERED TO BE APPLIED TOWARD THE SATISFACTION OF A JUDGMENT, TO PROVIDE, INSTEAD OF A COMPLETE EXEMPTION OF THE EARNINGS OF A JUDGMENT DEBTOR FOR HIS PERSONAL SERVICES, THAT ONLY SEVENTY-FIVE PERCENT OF THE EARNINGS OF THE DEBTOR FOR HIS PERSONAL SERVICES CANNOT BE APPLIED, AND THE EARNINGS OF THE JUDGMENT DEBTOR FOR HIS PERSONAL SERVICES TO BE WITHHELD MAY NOT EXCEED THE LIMITS SET FORTH BY THE FEDERAL CONSUMER CREDIT PROTECTION ACT.
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Prefiled and referred to the Committee on Judiciary.
Read the first time and referred to the Committee on Judiciary.
S. 848 (Word version) -- Senator Massey: A BILL TO AMEND SECTION 56-5-2910 OF THE 1976 CODE RELATING TO RECKLESS VEHICULAR HOMICIDE, TO PROVIDE THAT A PERSON WHO IS CONVICTED OF, PLEADS GUILTY TO, OR PLEADS NOLO CONTENDERE TO RECKLESS VEHICULAR HOMICIDE IS GUILTY OF A FELONY, AND MUST BE FINED NOT LESS THAN FIVE THOUSAND DOLLARS NOR MORE THAN FIFTEEN THOUSAND DOLLARS OR IMPRISONED NOT MORE THAN FIFTEEN YEARS, OR BOTH, AND AFTER ONE YEAR FROM THE DATE OF REVOCATION OF THE PERSON'S DRIVER'S LICENSE, THE PERSON MAY PETITION THE CIRCUIT COURT IN THE COUNTY OF THE PERSON'S CONVICTION FOR REINSTATEMENT OF THE PERSON'S DRIVER'S LICENSE; TO AMEND ARTICLE 23, CHAPTER 5, TITLE 56 RELATING TO RECKLESS HOMICIDE, RECKLESS DRIVING, AND DRIVING WHILE UNDER THE INFLUENCE OF INTOXICATING LIQUOR, DRUGS OR NARCOTICS, BY ADDING SECTION 56-5-2925 TO DEFINE "GREAT BODILY INJURY" AS BODILY INJURY WHICH CREATES A SUBSTANTIAL RISK OF DEATH OR WHICH CAUSES SERIOUS, PERMANENT DISFIGUREMENT, OR PROTRACTED LOSS OR IMPAIRMENT OF THE FUNCTION OF ANY BODILY MEMBER OR ORGAN, TO PROVIDE FOR THE OFFENSE OF FELONY RECKLESS DRIVING, TO PROVIDE FOR THE PENALTIES OF FELONY RECKLESS DRIVING, TO PROVIDE FOR THE PROCEDURE FOR REINSTATEMENT OF THE DRIVER'S LICENSE OF A PERSON CONVICTED OF FELONY RECKLESS DRIVING, AND TO PROVIDE THAT IF THE PERSON'S PRIVILEGE TO OPERATE A MOTOR VEHICLE IS REINSTATED, A SUBSEQUENT VIOLATION OF THE MOTOR VEHICLE LAWS FOR ANY MOVING VIOLATION REQUIRES THE AUTOMATIC CANCELLATION OF THE PERSON'S DRIVER'S LICENSE AND IMPOSITION OF THE FULL PERIOD OF REVOCATION FOR THE FELONY RECKLESS DRIVING VIOLATION.
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Prefiled and referred to the Committee on Judiciary.
Read the first time and referred to the Committee on Judiciary.
S. 849 (Word version) -- Senator Massey: A BILL TO AMEND CHAPTER 1, TITLE 56 OF THE 1976 CODE OF LAWS, RELATING TO DRIVER'S LICENSE, BY ADDING SECTION 56-1-45 TO PROVIDE IN ADDITION TO OTHER REQUIREMENTS TO OBTAIN FULL LICENSURE, A PERSON AT LEAST FIFTEEN YEARS OF AGE AND UNDER TWENTY-ONE YEARS OF AGE WHO HAS NEVER HELD A FORM OF LICENSE EVIDENCING PREVIOUS DRIVING EXPERIENCE MUST ENROLL IN AND SUCCESSFULLY COMPLETE A DRIVER TRAINING COURSE CONDUCTED BY A DRIVER TRAINING SCHOOL LICENSED UNDER CHAPTER 23 OF THIS TITLE OR, IF REGULARLY ENROLLED IN A HIGH SCHOOL OF THIS STATE WHICH CONDUCTS A DRIVER'S TRAINING COURSE, A COURSE TAUGHT BY A QUALIFIED INSTRUCTOR TO OBTAIN FULL LICENSURE, AND TO PROVIDE A PERSON TWENTY-ONE YEARS OF AGE OR OLDER WHO HAS NEVER HELD A FORM OF LICENSE EVIDENCING PREVIOUS DRIVING EXPERIENCE MUST ENROLL IN AND SUCCESSFULLY COMPLETE AN EIGHT-HOUR DEFENSIVE DRIVING COURSE.
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Prefiled and referred to the Committee on Transportation.
Read the first time and referred to the Committee on Transportation.
S. 850 (Word version) -- Senator Coleman: A BILL TO AMEND SECTION 50-11-510, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE UNLAWFUL HUNTING OR TAKING OF WILD TURKEYS BY THE MEANS, AID, OR USE OF BAIT OR BAITING, SO AS TO REVISE THE DEFINITIONS OF THE TERMS "BAIT" OR "BAITING", AND "BAITED AREAS", AND TO PROVIDE NOTHING IN THIS ARTICLE PROHIBITS THE HUNTING AND TAKING OF WILD TURKEYS ON OR OVER LANDS OR AREAS THAT ARE NOT BAITED UNDER CERTAIN CIRCUMSTANCES.
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Prefiled and referred to the Committee on Fish, Game and Forestry.
Read the first time and referred to the Committee on Fish, Game and Forestry.
S. 851 (Word version) -- Senator Coleman: A BILL TO AMEND SECTION 39-6-100, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO A WARRANTY AGREEMENT ON CERTAIN FARM AND OUTDOOR EQUIPMENT, SO AS TO PROVIDE THAT THAT THE MANUFACTURER MAY NOT PAY LESS THAN THE HOURLY LABOR RATE, PLUS OTHER EXPENSES INVOLVED IN THE WORK, THAT THE DEALER REGULARLY CHARGES TO A RETAIL CUSTOMER NOT ASSERTING A WARRANTY, TO PROVIDE THAT THE DEALER ONLY MAY CLAIM THE NUMBER OF HOURS OF LABOR ACTUALLY PERFORMED, OR ONE AND ONE-HALF TIMES THE SUPPLIER'S RECOMMENDED HOURS FOR THE REPAIR INVOLVED, WHICHEVER IS LESS, AND TO PROVIDE THAT THE DEALER MUST BE PAID ITS NET PRICE FOR PARTS, PLUS FIFTEEN PERCENT.
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Prefiled and referred to the Committee on Judiciary.
Read the first time and referred to the Committee on Judiciary.
S. 852 (Word version) -- Senators Coleman and Hutto: A BILL TO AMEND SECTION 15-78-120, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE LIMITATION ON LIABILITY UNDER THE TORT CLAIMS ACT, SO AS TO RAISE THE PER PERSON CAP FROM THREE HUNDRED THOUSAND TO FIVE HUNDRED THOUSAND DOLLARS.
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Prefiled and referred to the Committee on Judiciary.
Read the first time and referred to the Committee on Judiciary.
S. 853 (Word version) -- Senators Coleman and Hutto: A BILL TO AMEND SECTION 15-78-120, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE LIMITATION ON LIABILITY UNDER THE TORT CLAIMS ACT, SO AS TO DELETE THE PER OCCURRENCE CAP OF SIX HUNDRED THOUSAND DOLLARS AND THE ONE MILLION TWO HUNDRED THOUSAND DOLLAR PER OCCURRENCE CAP FOR ANY TORT CAUSED BY A LICENSED PHYSICIAN OR DENTIST EMPLOYED BY A GOVERNMENTAL ENTITY.
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Prefiled and referred to the Committee on Judiciary.
Read the first time and referred to the Committee on Judiciary.
S. 854 (Word version) -- Senator Johnson: A BILL TO AMEND ARTICLE 9, CHAPTER 1, TITLE 1 OF THE 1976 CODE, RELATING TO STATE EMBLEMS, BY ADDING SECTION 1-1-712A TO DESIGNATE THE MAMMOTH AS THE OFFICIAL STATE FOSSIL.
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Prefiled and referred to the Committee on Judiciary.
Read the first time and referred to the Committee on Judiciary.
S. 855 (Word version) -- Senator Johnson: A BILL TO AMEND TITLE 58 OF THE 1976 CODE, BY ADDING CHAPTER 10 TO ESTABLISH THE CRIME OF SENDING CERTAIN ELECTRONIC MESSAGES TO MINORS, TO CREATE A CHILD PROTECTION REGISTRY, TO PROVIDE NOTICE OF CONTACT POINTS TO WHICH A MINOR HAS ACCESS, TO PRESCRIBE THE POWERS AND DUTIES OF CERTAIN STATE AGENCIES AND OFFICIALS, TO CREATE A FUND AND PROVIDE FOR FEES, TO PROVIDE FOR PENALTIES AND REMEDIES; AND TO AMEND SECTION 16-16-20, RELATING TO COMPUTER CRIMES AND PENALTIES, TO PROVIDE THAT IT IS UNLAWFUL FOR A PERSON TO WILFULLY, KNOWINGLY, MALICIOUSLY, OR WITHOUT AUTHORIZATION TO DIRECTLY OR INDIRECTLY ACCESS OR CAUSE TO BE ACCESSED A CONTACT POINT AS DEFINED IN SECTION 58-10-10(1) THAT HAS BEEN REGISTERED FOR MORE THAN THIRTY CALENDAR DAYS WITH THE PUBLIC SERVICE COMMISSION.
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Prefiled and referred to the Committee on Judiciary.
Read the first time and referred to the Committee on Judiciary.
S. 856 (Word version) -- Senator Johnson: A BILL TO AMEND SECTION 17-22-710 OF THE 1976 CODE, RELATING TO WORTHLESS CHECK UNITS, TO PROVIDE FOR THE MANDATORY COLLECTION OF FEES AND ADMINISTRATIVE COSTS.
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Prefiled and referred to the Committee on Judiciary.
Read the first time and referred to the Committee on Judiciary.
S. 857 (Word version) -- Senator McElveen: A BILL TO AMEND CHAPTER 1, TITLE 16 OF THE 1976 CODE, RELATING TO FELONIES AND MISDEMEANORS; BY ADDING SECTION 16-1-140 TO ENHANCE THE SENTENCE FOR INDIVIDUALS CONVICTED OF A SERIOUS OR MOST SERIOUS OFFENSE THAT HE COMMITTED WHILE HE WAS RELEASED ON BOND FOR A SERIOUS OR MOST SERIOUS OFFENSE FOR WHICH HE WAS ALSO CONVICTED.
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Prefiled and referred to the Committee on Judiciary.
Read the first time and referred to the Committee on Judiciary.
S. 858 (Word version) -- Senator Shealy: A BILL TO AMEND SECTION 2-19-90 OF THE 1976 CODE, RELATING TO APPROVAL OF THE GENERAL ASSEMBLY IN JOINT SESSION, TO PROVIDE THAT A MEMBER OF THE GENERAL ASSEMBLY SHALL BE PROHIBITED FROM VOTING IN JOINT SESSION AND MUST EXCUSE HIMSELF FROM PARTICIPATION IN THE ELECTION OF JUDGES IF THE MEMBER REPRESENTS CLIENTS IN ANY COURT IN THE UNIFIED JUDICIAL SYSTEM OF THIS STATE; AND TO AMEND SECTION 22-1-40, RELATING TO APPEARANCE AS AN ATTORNEY IN A CASE BEFORE A MAGISTRATE, TO PROHIBIT A SENATOR FROM APPEARING AS AN ATTORNEY AT LAW BEFORE A MAGISTRATE THE SENATOR RECOMMENDED TO THE GOVERNOR FOR APPOINTMENT.
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Prefiled and referred to the Committee on Judiciary.
Read the first time and referred to the Committee on Judiciary.
S. 859 (Word version) -- Senator Shealy: A BILL TO AMEND CHAPTER 1, TITLE 10 OF THE 1976 CODE, RELATING TO PUBLIC BUILDINGS AND PROPERTY, BY ADDING SECTION 10-1-220 TO PROVIDE THAT A STATE BUILDING, ROAD, HIGHWAY, INTERSTATE HIGHWAY, BRIDGE, INTERCHANGE, OR INTERSECTION MAY NOT BE NAMED FOR ANY ELECTED OR APPOINTED OFFICIAL, COMMISSIONER, DIRECTOR, OR JUDGE WHO HAS NOT BEEN DECEASED FOR A PERIOD OF FIVE YEARS; AND TO AMEND ARTICLE 7, CHAPTER 3, TITLE 57, RELATING TO THE POWERS AND DUTIES OF THE DEPARTMENT OF TRANSPORTATION, BY ADDING SECTION 57-3-605 TO PROVIDE THAT A STATE BUILDING, ROAD, HIGHWAY, INTERSTATE HIGHWAY, BRIDGE, INTERCHANGE, OR INTERSECTION MAY NOT BE NAMED FOR ANY ELECTED OR APPOINTED OFFICIAL, COMMISSIONER, DIRECTOR, OR JUDGE WHO HAS NOT BEEN DECEASED FOR A PERIOD OF FIVE YEARS.
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Prefiled and referred to the Committee on Finance.
Read the first time and referred to the Committee on Finance.
S. 860 (Word version) -- Senator Shealy: A BILL TO AMEND SECTION 59-39-160 OF THE 1976 CODE, RELATING TO ELIGIBILITY TO PARTICIPATE IN INTERSCHOLASTIC ACTIVITIES, TO PROVIDE THE STATE BOARD OF EDUCATION MAY GRANT A WAIVER OF THE REQUIREMENTS IF A STUDENT'S INELIGIBILITY TO PARTICIPATE IN INTERSCHOLASTIC ACTIVITIES IS DUE TO A LONG TERM ABSENCE AS A RESULT OF A MEDICAL CONDITION, BUT THE STUDENT HAS BEEN MEDICALLY CLEARED TO PARTICIPATE OR FOR ANY OTHER REASONABLE CIRCUMSTANCE AS DETERMINED BY THE STATE BOARD OF EDUCATION.
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Prefiled and referred to the Committee on Education.
Read the first time and referred to the Committee on Education.
S. 861 (Word version) -- Senator Shealy: A BILL TO AMEND SECTION 56-5-2948 OF THE 1976 CODE, RELATING TO FIELD SOBRIETY TESTS, TO PROVIDE NOTWITHSTANDING ANY OTHER PROVISION OF LAW, WHEN AN INVESTIGATING LAW ENFORCEMENT OFFICER SUSPECTS A PERSON CAUSED A MOTOR VEHICLE INCIDENT RESULTING IN THE DEATH OF ANOTHER PERSON, AND THE DRIVER IS PHYSICALLY UNABLE TO SUBMIT TO A FIELD SOBRIETY TEST ON THE SCENE OF THE INCIDENT, THE DRIVER MUST SUBMIT TO EITHER ONE OR A COMBINATION OF CHEMICAL TESTS OF HIS BREATH, BLOOD, OR URINE FOR THE PURPOSE OF DETERMINING THE PRESENCE OF ALCOHOL, DRUGS, OR A COMBINATION OF ALCOHOL AND DRUGS.
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Prefiled and referred to the Committee on Judiciary.
Read the first time and referred to the Committee on Judiciary.
S. 862 (Word version) -- Senator Shealy: A BILL TO AMEND SECTION 40-59-260 OF THE 1976 CODE, RELATING TO THE EXCEPTION FOR PROJECTS BY A PROPERTY OWNER FOR PERSONAL USE, TO PROVIDE THAT AN OWNER OF RESIDENTIAL PROPERTY WHO IMPROVES THE PROPERTY OR WHO BUILDS OR IMPROVES THE STRUCTURES OR APPURTENANCES ON THE PROPERTY AT A COST OF MORE THAN TWO THOUSAND FIVE HUNDRED DOLLARS SHALL NOT WITHIN TWO YEARS AFTER COMPLETION OR ISSUANCE OF A CERTIFICATE OFFER THE STRUCTURE FOR SALE OR RENT, AND CONSTRUCTION OR IMPROVEMENTS TO THE STRUCTURE, GROUP OF STRUCTURES, OR APPURTENANCES THAT COST THE OWNER-BUILDER LESS THAN TWO THOUSAND FIVE HUNDRED DOLLARS ARE NOT EVIDENCE OF "SALE" OR "RENT" FOR THE PURPOSES OF THIS SECTION.
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Prefiled and referred to the Committee on Labor, Commerce and Industry.
Read the first time and referred to the Committee on Labor, Commerce and Industry.
S. 863 (Word version) -- Senator Shealy: A BILL TO AMEND SECTION 56-5-4580 OF THE 1976 CODE, RELATING TO LIGHTING EQUIPMENT THAT MUST BE ATTACHED TO BUSES, TRUCKS, TRAILERS, SEMITRAILERS, AND POLE TRAILERS, TO REQUIRE A TRAILER OR SEMITRAILER THAT IS LOADED OR IS OF DIMENSIONS SO AS TO OBSCURE THE STOP LIGHT ON THE TOWING VEHICLE THEN THE TRAILER ALSO MUST BE EQUIPPED WITH ONE STOP LIGHT VISIBLE FROM BEHIND; AND TO AMEND 56-5-5150, RELATING TO USE OF SAFETY DEVICES WHEN TOWING VEHICLES, TO PROVIDE THAT WHEN A VEHICLE IS TOWING ANOTHER VEHICLE OR TRAILER ON A PUBLIC ROAD OR HIGHWAY, THE TOWING VEHICLE MUST BE PROPERLY AND SECURELY ATTACHED TO THE TOWED VEHICLE OR TRAILER.
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Prefiled and referred to the Committee on Transportation.
Read the first time and referred to the Committee on Transportation.
S. 864 (Word version) -- Senators L. Martin, Lourie and Shealy: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING ARTICLE 4 TO CHAPTER 11, TITLE 63, SO AS TO ENACT THE "SOUTH CAROLINA CHILDREN'S ADVOCACY MEDICAL RESPONSE SYSTEM ACT" TO CREATE THE SOUTH CAROLINA CHILDREN'S ADVOCACY MEDICAL RESPONSE SYSTEM, WHICH IS A PROGRAM THAT PROVIDES COORDINATION AND MEDICAL SERVICE RESOURCES STATEWIDE TO AGENCIES AND ENTITIES THAT RESPOND TO VICTIMS OF CHILD ABUSE AND NEGLECT, AND TO PROVIDE FOR THE DUTIES AND RESPONSIBILITIES OF THE PROGRAM.
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Prefiled and referred to the Committee on Judiciary.
Read the first time and referred to the Committee on Judiciary.
S. 865 (Word version) -- Senators L. Martin, Alexander, Campbell, O'Dell, Reese, Verdin, Peeler, Shealy, Gregory and Massey: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING ARTICLE 8 TO CHAPTER 23, TITLE 58, SO AS TO ESTABLISH THE CDL DRIVER EMPLOYMENT PROTECTION ACT WHICH PROVIDES THAT CIVIL LIABILITY CLAIMS MADE AGAINST AN EMPLOYER OF A PERSON WHO HOLDS A VALID COMMERCIAL DRIVER'S LICENSE BASED ON ANY THEORY OF NEGLIGENT HIRING, TRAINING, RETENTION, OR ENTRUSTMENT MUST BE CONSIDERED IN THE SECOND PHASE OF A BIFURCATED TRIAL PURSUANT TO SECTION 15-32-520(E), IF THERE IS EVIDENCE TO SUPPORT AN AWARD OF PUNITIVE DAMAGES, BUT PUNITIVE DAMAGES MAY NOT BE AWARDED AGAINST AN EMPLOYER SOLELY ON THE BASIS OF VICARIOUS LIABILITY.
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Prefiled and referred to the Committee on Judiciary.
Read the first time and referred to the Committee on Judiciary.
S. 866 (Word version) -- Senator L. Martin: A BILL TO AMEND CHAPTER 5, TITLE 7, SOUTH CAROLINA CODE OF LAWS, 1976, RELATING TO COUNTY ELECTION COMMISSIONS AND BOARDS OF VOTER REGISTRATION, TO REPLACE CURRENT COUNTY ELECTION COMMISSIONS AND REGISTRATION BOARDS, TO DEVOLVE THEIR RESPONSIBILITIES AND AUTHORITY TO A COMBINED BOARD OF VOTER REGISTRATION AND ELECTIONS FOR EACH COUNTY, TO PROVIDE FOR THE APPOINTMENT OF BOARD MEMBERS, AND TO ESTABLISH TERMS, DUTIES, AND AUTHORITY FOR THE BOARDS; TO REPEAL SECTION 7-5-35 AND SECTION 7-13-70; AND TO REPEAL CHAPTER 27, TITLE 7 RELATING TO INDIVIDUAL COUNTY BOARDS AND COMMISSIONS.
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Prefiled and referred to the Committee on Judiciary.
Read the first time and referred to the Committee on Judiciary.
S. 867 (Word version) -- Senator Hayes: A BILL TO AMEND ACT 101 OF 2013, RELATING TO THE 2013-2014 GENERAL APPROPRIATIONS ACT, SO AS TO REVISE PARAGRAPH 1.85, SECTION 1, PART 1B, THAT ALLOWS FOR A TAX CREDIT FOR CONTRIBUTIONS TO A NONPROFIT SCHOLARSHIP FUNDING ORGANIZATION BY SPECIFYING THE TAXES FOR WHICH THE CREDIT MAY BE CLAIMED AGAINST, TO AMEND THE DEFINITION OF "EXCEPTIONAL NEEDS", TO ESTABLISH AN APPLICATION PROCESS TO DETERMINE THE AMOUNT OF CREDIT AVAILABLE TO BE CLAIMED, AND TO DELETE A PROVISION RELATING TO MARRIED PERSONS FILING SEPARATELY.
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Prefiled and referred to the Committee on Finance.
Read the first time and referred to the Committee on Finance.
S. 868 (Word version) -- Senator Alexander: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING SECTION 30-5-25 SO AS TO PROVIDE UNIFORM STANDARDS FOR FORMATTING DOCUMENTS SUBMITTED TO A CLERK OF COURT OR REGISTER OF DEEDS FOR RECORDING, TO PROVIDE A SIX-MONTH GRACE PERIOD, TO PROVIDE THAT AFTER THE GRACE PERIOD A NONCONFORMING DOCUMENT MUST BE ACCEPTED FOR RECORDING WITH THE IMPOSITION OF A NONREFUNDABLE FINE TO BE DEPOSITED IN THE COUNTY GENERAL FUND OR MUST BE REFUSED FOR RECORDING, AND TO PROVIDE AN EXEMPTION FOR DOCUMENTS FILED ELECTRONICALLY PURSUANT TO THE UNIFORM REAL PROPERTY ELECTRONIC RECORDING ACT.
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Prefiled and referred to the Committee on Judiciary.
Read the first time and referred to the Committee on Judiciary.
S. 869 (Word version) -- Senator Jackson: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING ARTICLE 3 TO CHAPTER 25, TITLE 16 ENTITLED "DATING VIOLENCE" SO AS TO DEFINE NECESSARY TERMS, CREATE THE OFFENSE OF DATING VIOLENCE, AND PROVIDE A PENALTY.
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Prefiled and referred to the Committee on Judiciary.
Read the first time and referred to the Committee on Judiciary.
S. 870 (Word version) -- Senator Kimpson: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING SECTION 12-36-71 SO AS TO PROVIDE THAT A RETAILER IS PRESUMED TO BE LIABLE FOR THE SALES TAX OR RESPONSIBLE FOR COLLECTING AND REMITTING THE USE TAX IF THE RETAILER ENTERS INTO AN AGREEMENT WITH A RESIDENT OF THIS STATE UNDER WHICH THE RESIDENT, FOR CONSIDERATION, REFERS POTENTIAL CUSTOMERS, WHETHER BY AN INTERNET LINK OR OTHERWISE, TO REQUIRE SUCH RETAILERS TO OBTAIN A RETAIL LICENSE AND REMIT SALES AND USE TAX ON ALL TAXABLE RETAIL SALES, AND TO PROVIDE EXCEPTIONS.
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Prefiled and referred to the Committee on Finance.
Read the first time and referred to the Committee on Finance.
S. 871 (Word version) -- Senator Fair: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING CHAPTER 55 TO TITLE 46 SO AS TO ENACT THE "SOUTH CAROLINA EQUINE PROMOTION ACT" INCLUDING PROVISIONS TO PROVIDE FOR THE SUPPORT OF THIS PROGRAM BY MEANS OF A VOLUNTARY CONTRIBUTION MADE BY PREVIOUS FILING OF SOUTH CAROLINA STATE INDIVIDUAL INCOME TAX RETURNS AND OTHER DONATIONS, GRANTS, OR APPROPRIATIONS, AND TO PROVIDE FOR THE MANNER IN WHICH THE REVENUE DERIVED FROM THESE ASSESSMENTS MUST BE USED; AND TO AMEND SECTION 12-6-5060, AS AMENDED, RELATING TO VOLUNTARY CONTRIBUTIONS FOR SPECIFIC PURPOSES MADE BY TAXPAYERS ON STATE INDIVIDUAL INCOME TAX RETURNS, SO AS TO CONFORM THE SECTION TO THE SOUTH CAROLINA EQUINE PROMOTION ACT.
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Prefiled and referred to the Committee on Agriculture and Natural Resources.
Read the first time and referred to the Committee on Agriculture and Natural Resources.
S. 872 (Word version) -- Senator Fair: A BILL TO AMEND SECTION 63-1-50, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE JOINT CITIZENS AND LEGISLATIVE COMMITTEE ON CHILDREN, SO AS TO ESTABLISH IT AS A PERMANENT JOINT COMMITTEE AND TO DELETE OBSOLETE PROVISIONS.
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Prefiled and referred to the Committee on Judiciary.
Read the first time and referred to the Committee on Judiciary.
S. 873 (Word version) -- Senator Hutto: A BILL TO AMEND SECTION 6-27-30, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO FUNDING OF THE LOCAL GOVERNMENT FUND, SO AS TO PROVIDE THAT, AT A MINIMUM, THE LOCAL GOVERNMENT FUND MUST BE APPROPRIATED AS MUCH AS WAS APPROPRIATED IN FISCAL YEAR 2013-2014; AND TO AMEND SECTION 6-27-50, RELATING TO AMENDMENTS TO PROVISIONS OF THE LOCAL GOVERNMENT FUND, SO AS TO PROVIDE THAT ITS PROVISIONS MAY NOT BE SUSPENDED EXCEPT IN SEPARATE LEGISLATION SOLELY FOR THAT PURPOSE.
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Prefiled and referred to the Committee on Finance.
Read the first time and referred to the Committee on Finance.
S. 874 (Word version) -- Senator Hutto: A CONCURRENT RESOLUTION TO MEMORIALIZE THE GOVERNOR AND STATE SECRETARY OF COMMERCE TO INTENSIFY EFFORTS TO CREATE JOBS AND FOSTER ECONOMIC DEVELOPMENT IN RURAL AREAS OF SOUTH CAROLINA THAT FACE CHRONIC LEVELS OF HIGH UNEMPLOYMENT.
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Prefiled and referred to the Committee on Finance.
The Concurrent Resolution was introduced and referred to the Committee on Finance.
S. 875 (Word version) -- Senator Grooms: A BILL TO AMEND CHAPTER 41, TITLE 44 OF THE 1976 CODE, RELATING TO ABORTIONS, BY ADDING SECTION 44-41-25, TO PROVIDE THAT A PHYSICIAN PERFORMING AN ABORTION OUTSIDE OF A HOSPITAL MUST HAVE ADMITTING AND STAFF PRIVILEGES AT A LOCAL CERTIFIED HOSPITAL.
Prefiled and referred to the Committee on Medical Affairs.
Read the first time and referred to the Committee on Medical Affairs.
S. 876 (Word version) -- Senators Cromer and Campsen: A BILL TO AMEND SECTION 50-11-355 OF THE 1976 CODE, RELATING TO UNLAWFUL DEER HUNTING NEAR A RESIDENCE, TO PROVIDE THAT IT IS UNLAWFUL TO HUNT DEER WITH FIREARMS NEAR A RESIDENCE WITHOUT THE PERMISSION OF THE OWNER AND OCCUPANT.
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Prefiled and referred to the Committee on Fish, Game and Forestry.
Read the first time and referred to the Committee on Fish, Game and Forestry.
S. 877 (Word version) -- Senator Cromer: A BILL TO AMEND SECTION 56-5-195, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO SCHOOL BUS SAFETY STANDARDS, TO PROVIDE THAT MOTOR COACHES ARE EXEMPT FROM THE REQUIRED STANDARDS WHEN OWNED AND OPERATED BY A SCHOOL OR A SCHOOL DISTRICT.
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Prefiled and referred to the Committee on Transportation.
Read the first time and referred to the Committee on Transportation.
S. 878 (Word version) -- Senator Sheheen: A BILL TO AMEND CHAPTER 1, TITLE 16 OF THE 1976 CODE, RELATING TO FELONIES AND MISDEMEANORS, TO PROVIDE THAT IT IS UNLAWFUL TO PRODUCE OR CREATE AUDIO OR VIDEO RECORDINGS OF A VIOLENT CRIME AND THAT IT IS UNLAWFUL TO PUBLISH AUDIO OR VIDEO RECORDINGS OF THE VIOLENT CRIME; AND TO PROVIDE EXCEPTIONS.
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Prefiled and referred to the Committee on Judiciary.
Read the first time and referred to the Committee on Judiciary.
S. 879 (Word version) -- Senator Sheheen: A BILL TO AMEND CHAPTER 7, TITLE 13 OF THE 1976 CODE, RELATING TO NUCLEAR ENERGY, BY ADDING SECTION 13-7-47 TO PROHIBIT MINORS FROM USING SOURCES OF NONIONIZED RADIATION WHICH IS USED IN COMMERCIAL ESTABLISHMENTS FOR THE TANNING OF HUMAN SKIN.
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Prefiled and referred to the Committee on Labor, Commerce and Industry.
Read the first time and referred to the Committee on Labor, Commerce and Industry.
S. 880 (Word version) -- Senator Sheheen: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING SECTION 56-1-55, TO PROVIDE THAT IT IS UNLAWFUL FOR A PERSON WHO HOLDS A BEGINNER'S PERMIT OR A RESTRICTED DRIVER'S LICENSE TO DRIVE A MOTOR VEHICLE WHILE USING A CELLULAR TELEPHONE OR TEXT MESSAGING DEVICE; AND TO PROVIDE THAT IT IS UNLAWFUL FOR A PERSON TO DRIVE A MOTOR VEHICLE THROUGH A SCHOOL ZONE OR HIGHWAY WORK ZONE WHILE USING A CELLULAR TELEPHONE OR TEXT MESSAGING DEVICE.
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Prefiled and referred to the Committee on Judiciary.
Read the first time and referred to the Committee on Judiciary.
S. 881 (Word version) -- Senator Sheheen: A BILL TO AMEND SECTION 12-37-220 OF THE 1976 CODE, RELATING TO GENERAL EXEMPTIONS FROM PROPERTY TAXES; BY ADDING A NEW SUBSECTION TO ALLOW COUNTIES TO EXEMPT FROM AD VALOREM TAXATION SOLAR ENERGY ELECTRIC SYSTEMS AND THE DIFFERENCE BETWEEN THE COST OF A SOLAR ENERGY HEATING OR COOLING SYSTEM AND A TRADITIONAL HEATING OR COOLING SYSTEM.
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Prefiled and referred to the Committee on Finance.
Read the first time and referred to the Committee on Finance.
S. 882 (Word version) -- Senator Sheheen: A BILL TO AMEND SECTION 41-27-210 OF THE 1976 CODE, RELATING TO THE DEFINITION OF EMPLOYMENT; TO PROVIDE THAT INDIVIDUALS THAT TRANSPORT VEHICLES FOR AUTOMOBILE DEALERS UNDER CERTAIN CIRCUMSTANCES ARE EXCLUDED FROM THE DEFINITION; AND TO PROVIDE FOR THOSE CIRCUMSTANCES.
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Prefiled and referred to the Committee on Labor, Commerce and Industry.
Read the first time and referred to the Committee on Labor, Commerce and Industry.
S. 883 (Word version) -- Senator Sheheen: A BILL TO AMEND ARTICLE 13, CHAPTER 13, TITLE 8 OF THE 1976 CODE, RELATING TO CAMPAIGN PRACTICES, BY ADDING SECTION 8-13-1347 TO PROHIBIT CAMPAIGN STAFF, FUNDRAISERS, AND MEMBERS OF COMMITTEES ORGANIZED TO INFLUENCE THE OUTCOME OF CAMPAIGNS FROM BEING TRANSPORTED IN STATE OWNED VEHICLES AND AIRCRAFT; TO AMEND CHAPTER 13, TITLE 8 BY ADDING ARTICLE 12, TO REQUIRE ANNUAL PERSONAL FINANCIAL DISCLOSURES FROM ELECTED OFFICIALS AND DEPARTMENT HEADS, TO PROVIDE FOR THE FILING DEADLINE, THE INFORMATION THAT MUST BE DISCLOSED, PENALTIES, AND FOR THE DISPOSITION OF INADVERTENT AND UNINTENTIONAL VIOLATIONS; AND TO AMEND SECTION 8-13-310, RELATING TO THE COMPOSITION OF THE STATE ETHICS COMMISSION, TO PROVIDE THAT THE COMMISSION SHALL BE COMPRISED OF TEN MEMBERS APPOINTED BY THE SUPREME COURT, TO PROVIDE THAT THE MEMBERSHIP OF THE ETHICS COMMISSION MUST BE EVENLY SPLIT BETWEEN MEMBERS OF THE MAJORITY PARTY IN THE GENERAL ASSEMBLY AND THE LARGEST MINORITY PARTY IN THE GENERAL ASSEMBLY, AND TO REMOVE ARCHAIC REFERENCES.
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Prefiled and referred to the Committee on Judiciary.
Read the first time and referred to the Committee on Judiciary.
S. 884 (Word version) -- Senator Sheheen: A BILL TO AMEND SECTION 2-20-35 OF THE 1976 CODE, RELATING TO THE ELECTION OF A TRUSTEE TO A COLLEGE OR UNIVERSITY; TO PROVIDE THAT THE FINDINGS OF FACT PRODUCED BY THE SCREENING COMMITTEE MUST CONTAIN AN ANALYSIS OF THE DEMOGRAPHIC REPRESENTATION ON THE BOARD OF TRUSTEES PRIOR TO THE VACANCY AND AS A RESULT OF THE VACANCY.
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Prefiled and referred to the Committee on Judiciary.
Read the first time and referred to the Committee on Judiciary.
S. 885 (Word version) -- Senators Bryant and Campsen: A BILL TO AMEND SECTION 23-31-510 OF THE 1976 CODE, RELATING TO THE REGULATION OF THE OWNERSHIP, TRANSFER, OR POSSESSION OF FIREARMS OR AMMUNITION, TO PROVIDE NO GOVERNING BODY OF ANY COUNTY, MUNICIPALITY, OR OTHER POLITICAL SUBDIVISION IN THE STATE MAY ENACT, ENFORCE, OR PROMULGATE ANY REGULATION OR ORDINANCE THAT REGULATES OR ATTEMPTS TO REGULATE THE TRANSFER, OWNERSHIP, POSSESSION, CARRYING, OR TRANSPORTATION OF KNIVES, FIREARMS, AMMUNITION, COMPONENTS OF FIREARMS, OR ANY COMBINATION OF THESE THINGS.
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Prefiled and referred to the Committee on Judiciary.
Read the first time and referred to the Committee on Judiciary.
S. 886 (Word version) -- Senators Bryant and Massey: A BILL TO AMEND CHAPTER 5, TITLE 38 OF THE 1976 CODE, RELATING TO TRANSACTING INSURANCE BUSINESS, BY ADDING SECTION 38-5-15, TO PROVIDE THAT THE DEPARTMENT OF INSURANCE SHALL AUTHORIZE OUT-OF-STATE INSURERS TO OFFER HEALTH INSURANCE POLICIES IN THIS STATE, TO AUTHORIZE THE DIRECTOR OF THE DEPARTMENT OF INSURANCE TO CONDUCT MARKET AND SOLVENCY EXAMINATIONS OF OUT-OF-STATE INSURERS SEEKING TO OFFER PLANS IN THIS STATE, AND TO PROVIDE LANGUAGE THAT MUST BE PRESENT IN AN OUT-OF-STATE HEALTH INSURANCE PLAN OFFERED TO SOUTH CAROLINA RESIDENTS.
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Prefiled and referred to the Committee on Banking and Insurance.
Read the first time and referred to the Committee on Banking and Insurance.
S. 887 (Word version) -- Senator Campsen: A BILL TO AMEND SECTION 17-25-326, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE ALTERATION, MODIFICATION, OR RESCISSION OF A COURT ORDER, SO AS TO PROVIDE THAT A COURT SHALL NOT ALTER, MODIFY, OR RESCIND A DEFENDANT'S CRIMINAL SENTENCE, UNLESS THE COURT HAS HELD A HEARING ALLOWING THE DEFENDANT, ATTORNEY GENERAL OR SOLICITOR, AND THE VICTIM TO TESTIFY REGARDING THE DECISION TO ALTER, MODIFY, OR RESCIND THE SENTENCE.
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Prefiled and referred to the Committee on Judiciary.
Read the first time and referred to the Committee on Judiciary.
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Prefiled and referred to the Committee on Education.
Read the first time and referred to the Committee on Education.
S. 889 (Word version) -- Senator Cleary: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING SECTION 2-1-260 SO AS TO PROVIDE THAT ANY LEGISLATION OR REGULATION IMPOSING A FEE OR AMENDING A FEE AMOUNT MUST BE REFERRED TO THE SENATE FINANCE COMMITTEE.
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Prefiled and referred to the Committee on Judiciary.
Read the first time and referred to the Committee on Judiciary.
S. 890 (Word version) -- Senator Cleary: A BILL TO AMEND SECTION 48-39-130, AS AMENDED, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO PERMITS REQUIRED FOR COASTAL ZONE CRITICAL AREAS, SO AS TO DELETE THE EMERGENCY ORDER EXCEPTION TO ORDERS BY APPOINTED OFFICIALS OF COUNTIES AND MUNICIPALITIES; TO AMEND SECTION 48-39-280, RELATING TO THE SHORELINE FORTY-YEAR RETREAT POLICY, SO AS TO PROHIBIT THE SEAWARD MOVEMENT OF THE BASELINE AFTER JULY 1, 2014, AND TO ELIMINATE THE RIGHT OF LOCAL GOVERNMENTS AND LANDOWNERS TO PETITION THE ADMINISTRATIVE LAW COURT TO MOVE THE BASELINE SEAWARD UPON COMPLETION OF A BEACH RENOURISHMENT PROJECT; AND TO AMEND SECTION 48-39-290, AS AMENDED, RELATING TO CONSTRUCTION RESTRICTIONS SEAWARD OF THE BASELINE, EXCEPTIONS TO RESTRICTIONS, AND SPECIAL PERMITS, SO AS TO ELIMINATE THE EXCEPTION OF GOLF COURSES FROM A PERMIT REQUIREMENT AND TO SUBSTITUTE THE DEPARTMENT OF HEALTH AND ENVIRONMENTAL CONTROL'S COASTAL DIVISION AS THE DIVISION TO CONSIDER APPLICATIONS FOR SPECIAL PERMITS.
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Prefiled and referred to the Committee on Agriculture and Natural Resources.
Read the first time and referred to the Committee on Agriculture and Natural Resources.
S. 891 (Word version) -- Senator Cleary: A BILL TO AMEND SECTION 12-28-310(A) OF THE 1976 CODE, RELATING TO THE USER FEE ON GASOLINE AND DIESEL FUEL, TO PROVIDE THAT THE SIXTEEN CENT PER GALLON USER FEE SHALL BE INCREASED BY TWO CENTS EACH YEAR UNTIL THE USER FEE IS EQUAL TO THIRTY-SIX CENTS.
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Prefiled and referred to the Committee on Finance.
Read the first time and referred to the Committee on Finance.
S. 892 (Word version) -- Senator Campbell: A BILL TO AMEND TITLE 38, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO INSURANCE, BY ADDING CHAPTER 8 ENACTING THE "SOUTH CAROLINA NEW MARKET JOBS ACT" SO AS TO PROVIDE A CREDIT AGAINST INSURANCE PREMIUM TAXES AND POSSIBLE OTHER STATES TAXES MADE IN CERTAIN INVESTMENTS MADE BY COMMUNITY DEVELOPMENT ENTITIES, PROVIDING INVESTMENT CAPITAL FOR A QUALIFIED ACTIVE LOW INCOME COMMUNITY SMALL BUSINESS LOCATED IN THIS STATE, TO MODEL THIS STATE INSURANCE PREMIUM TAX CREDIT ON THE FEDERAL NEW MARKETS TAX CREDIT PROGRAM PROVIDING FEDERAL INCOME TAX CREDITS FOR SUCH INVESTMENTS BUT LIMITED TO SUCH INVESTMENTS IN THIS STATE, TO ADOPT FEDERAL DEFINITIONS AS APPLICABLE FOR THE CREDIT BUT MODIFIED TO REFLECT THE PARTICULAR SOUTH CAROLINA APPLICATION OF THE CREDITS, TO PROVIDE A MAXIMUM INITIAL INDIVIDUAL INVESTMENT, A MAXIMUM OVERALL LIMIT FOR ALL SUCH INVESTMENTS ELIGIBLE FOR THE CREDIT, AND AN ANNUAL MAXIMUM AMOUNT OF CREDIT THAT MAY BE CLAIMED, TO PROVIDE THAT THESE CREDITS APPLY OVER SEVEN YEARS AND ARE NONREFUNDABLE AND NOT SALEABLE, TO REQUIRE FEES FOR PROCESSING APPLICATIONS FOR SUCH CREDITS AND FOR RECAPTURE OF THE CREDITS IF QUALIFICATIONS ARE NOT MAINTAINED, TO PROVIDE FOR LETTER RULINGS BY THE DEPARTMENT OF REVENUE WHEN FEDERAL REGULATIONS DO NOT PROVIDE SPECIFIC GUIDANCE, AND TO PROVIDE OTHER LIMITATIONS AND RESTRICTIONS AND REPORTING REQUIREMENTS.
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Prefiled and referred to the Committee on Banking and Insurance.
Read the first time and referred to the Committee on Banking and Insurance.
S. 893 (Word version) -- Senator Campbell: A BILL TO AMEND TITLE 39 OF THE 1976 CODE, RELATING TO TRADE AND COMMERCE, BY ADDING CHAPTER 77, TO PROVIDE THAT IT IS UNLAWFUL TO SELL OR INSTALL AN UNMOUNTED, UNSAFE USED TIRE ONTO A PASSENGER CAR OR LIGHT TRUCK; TO DEFINE UNSAFE FOR THE PURPOSES OF THE CHAPTER, TO REQUIRE THE DEPARTMENT OF HEALTH AND ENVIRONMENTAL CONTROL TO CONDUCT INSPECTIONS; TO ESTABLISH A FINE FOR VIOLATIONS, TO PROVIDE THAT THIS CHAPTER DOES NOT LIMIT A BUSINESS OR INDIVIDUAL'S LIABILITY UNDER THE STATE'S PRODUCTS LIABILITY LAWS; AND TO EXEMPT A BUSINESS OR PERSON WHO IS SELLING TIRES FOR RETREADING.
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Prefiled and referred to the Committee on Labor, Commerce and Industry.
Read the first time and referred to the Committee on Labor, Commerce and Industry.
S. 894 (Word version) -- Senator Massey: A BILL TO AMEND CHAPTER 1, TITLE 14 OF THE 1976 CODE, RELATING TO GENERAL PROVISIONS APPLICABLE TO COURTS, BY ADDING SECTION 14-1-240, TO PROVIDE THAT A FIVE DOLLAR SURCHARGE TO FUND TRAINING AT THE SOUTH CAROLINA CRIMINAL JUSTICE ACADEMY SHALL BE LEVIED ON ALL FINES, FORFEITURES, ESCHEATMENTS, OR OTHER MONETARY PENALTIES IMPOSED IN THE GENERAL SESSIONS COURT OR IN MAGISTRATES OR MUNICIPAL COURT FOR MISDEMEANOR TRAFFIC OFFENSES OR FOR NONTRAFFIC VIOLATIONS.
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Prefiled and referred to the Committee on Judiciary.
Read the first time and referred to the Committee on Judiciary.
S. 895 (Word version) -- Senator Bright: A BILL TO AMEND SECTION 7-5-110 OF THE 1976 CODE, RELATING TO THE REQUIREMENT OF REGISTRATION IN ORDER TO VOTE, TO PROVIDE THAT A PERSON IS NOT ALLOWED TO VOTE IN A PARTISAN PRIMARY ELECTION OR PARTISAN ADVISORY REFERENDUM UNLESS THE PERSON HAS REGISTERED AS BEING A MEMBER OF THAT PARTY; TO AMEND SECTION 7-5-170, RELATING TO THE REQUIREMENTS FOR VOTER REGISTRATION, TO PROVIDE THE REQUIREMENT OF STATING POLITICAL PARTY AFFILIATION, IF ANY, ON THE FORM AND INCLUDING IT IN THE OATH, AND REQUIRE THE STATE ELECTION COMMISSION TO ASSIST IN CAPTURING THIS DATA; AND TO AMEND SECTION 7-9-20, RELATING TO THE QUALIFICATIONS FOR VOTING IN PRIMARY ELECTIONS, TO INCLUDE, AS A REQUIREMENT, REGISTERING AS A MEMBER OF THE PARTY AND TO PROVIDE A PROCEDURE FOR CHANGING POLITICAL PARTY AFFILIATION OR NONAFFILIATION AFTER A SELECTION HAS BEEN MADE.
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Prefiled and referred to the Committee on Judiciary.
Read the first time and referred to the Committee on Judiciary.
S. 896 (Word version) -- Senators Coleman, Shealy and Campbell: A BILL TO AMEND CHAPTER 27, TITLE 48, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE PRACTICE OF FORESTRY IN THIS STATE, SO AS TO CHANGE THE METHOD OF APPOINTMENT FOR MEMBERS OF THE STATE BOARD OF REGISTRATION FOR FORESTERS, TO CHANGE REQUIREMENTS RELATED TO THE RIGHT OF BOARD MEMBERS TO COMPENSATION AND REIMBURSEMENT OF EXPENSES, TO DELETE THE REQUIREMENT FOR A SURETY BOND FOR THE BOARD SECRETARY AND THE SECRETARY'S ENTITLEMENT TO A SALARY, TO CHANGE PROVISIONS RELATING TO THE POWERS, RESPONSIBILITIES, AND OPERATION OF THE BOARD, TO REQUIRE FORESTERS TO BECOME LICENSED IN ADDITION TO BEING REGISTERED, TO PROVIDE FOR CERTAIN LICENSURE REQUIREMENTS, TO ADD REQUIREMENTS RELATING TO THE BOARD'S INVESTIGATION AND REVIEW OF COMPLAINTS, TO DELETE THE REQUIREMENT FOR MAINTENANCE OF A SEPARATE FUND FOR MONIES RECEIVED UNDER THE CHAPTER, TO CHANGE PROVISIONS RELATING TO CRIMINAL AND FINANCIAL PENALTIES FOR CERTAIN MISCONDUCT, BY ADDING LICENSURE PROVISIONS FOR ACTIVE DUTY MILITARY PERSONNEL, BY ADDING REQUIREMENTS RELATING TO CONTINUING EDUCATION, AND FOR OTHER PURPOSES.
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Prefiled and referred to the Committee on Fish, Game and Forestry.
Read the first time and referred to the Committee on Fish, Game and Forestry.
S. 897 (Word version) -- Senator Coleman: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING SECTION 1-11-723 SO AS TO PROVIDE THAT A PERSON WHO RETIRES FROM A SOLICITOR'S OFFICE MAY PARTICIPATE IN THE STATE HEALTH AND DENTAL INSURANCE PLANS REGARDLESS OF WHETHER THE COUNTY IN WHICH HE IS EMPLOYED AT THE TIME OF HIS RETIREMENT PARTICIPATES IN THESE PLANS, AMONG OTHER THINGS, AND TO MAKE THESE PROVISIONS RETROACTIVE TO JANUARY 1, 2012.
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Prefiled and referred to the Committee on Finance.
Read the first time and referred to the Committee on Finance.
S. 898 (Word version) -- Senator Allen: A BILL TO AMEND SECTION 59-20-50, CODE OF LAW OF SOUTH CAROLINA, 1976, RELATING TO VARIOUS FUNDING REQUIREMENTS UNDER THE EDUCATION FINANCE ACT, INCLUDING CERTIFIED TEACHER AND ADMINISTRATOR SALARY REQUIREMENTS, SO AS TO REVISE THESE SALARY REQUIREMENTS TO ENSURE THAT, AT A MINIMUM, CERTIFIED TEACHERS AND ADMINISTRATORS ARE ALWAYS PAID AT THE SOUTHEASTERN AVERAGE, AND TO PROVIDE FOR RELATED PROVISIONS TO IMPLEMENT THIS REQUIREMENT.
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Prefiled and referred to the Committee on Education.
Read the first time and referred to the Committee on Education.
S. 899 (Word version) -- Senator Allen: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, SO AS TO ENACT THE "SOUTH CAROLINA SECOND CHANCE ACT" BY ADDING SECTION 17-22-935 SO AS TO PROVIDE THAT CERTAIN NONVIOLENT MISDEMEANOR AND FELONY OFFENSES MAY BE EXPUNGED AND TO ESTABLISH THE CIRCUMSTANCES UNDER WHICH THE EXPUNGEMENT MAY OCCUR.
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Prefiled and referred to the Committee on Judiciary.
Read the first time and referred to the Committee on Judiciary.
S. 900 (Word version) -- Senator Allen: A JOINT RESOLUTION TO CREATE THE "STUDY COMMITTEE ON EXPUNGEMENT OF CRIMINAL OFFENSES" TO REVIEW THE CRIMINAL LAWS OF THE STATE AND DETERMINE CRIMINAL OFFENSES APPROPRIATE FOR EXPUNGEMENT, TO PROVIDE FOR THE MEMBERSHIP AND STAFFING OF THE STUDY COMMITTEE, AND TO PROVIDE FOR THE STUDY COMMITTEE'S TERMINATION.
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Prefiled and referred to the Committee on Judiciary.
Read the first time and referred to the Committee on Judiciary.
S. 901 (Word version) -- Senators Shealy, Grooms, Bryant and Davis: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING SECTION 12-6-517 SO AS TO REPLACE THE INCOME TAX IMPOSED ON THE TAXABLE INCOME OF INDIVIDUALS, ESTATES, TRUSTS, AND CERTAIN OTHER ENTITIES IN TAX YEARS BEGINNING AFTER 2013 BY REDUCING THE RATE OF TAXATION BY 1.4 PERCENT EACH YEAR UNTIL THE TAX RATE FOR ALL BRACKETS IS ZERO PERCENT.
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Prefiled and referred to the Committee on Finance.
Read the first time and referred to the Committee on Finance.
S. 902 (Word version) -- Senator Shealy: A BILL TO AMEND CHAPTER 3, TITLE 56 OF THE 1976 CODE, RELATING TO MOTOR VEHICLE REGISTRATION AND LICENSING, BY ADDING SECTION 56-3-115, TO PROVIDE THAT NOTWITHSTANDING ANY OTHER PROVISION OF LAW, FOR THE PURPOSES OF REGISTRATION AND THE REQUIRED LIMITS OF LIABILITY INSURANCE, A MOPED IS A MOTOR VEHICLE; AND TO AMEND SECTION 56-5-50, RELATING TO THE APPLICATION OF CHAPTER 5 TO THE OPERATION OF MOPEDS, TO STRIKE THE EXCEPTION FOR THE APPLICATION OF ARTICLES 35 AND 37 AS APPLIED TO THE OPERATION OF MOPEDS ON THE PUBLIC HIGHWAYS AND STREETS OF THIS STATE.
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Prefiled and referred to the Committee on Transportation.
Read the first time and referred to the Committee on Transportation.
S. 903 (Word version) -- Senator Shealy: A BILL TO AMEND SECTION 56-15-315 OF THE 1976 CODE RELATING TO OFF-SITE DISPLAYS OF AUTOMOBILES OR TRUCKS TO PROVIDE THAT LICENSED DEALERS MAY DISPLAY AUTOMOBILES OR TRUCKS AT AIRPORTS.
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Prefiled and referred to the Committee on Transportation.
Read the first time and referred to the Committee on Transportation.
S. 904 (Word version) -- Senators Shealy and Massey: A BILL TO AMEND SECTION 16-25-20 OF THE 1976 CODE, RELATING TO PENALTIES FOR CRIMINAL DOMESTIC VIOLENCE, TO INCREASE THE PENALTY OF IMPRISONMENT TO NOT MORE THAN ONE YEAR FOR A FIRST OFFENSE, AND TO INCREASE THE PENALTY FOR IMPRISONMENT TO NOT LESS THAN A MANDATORY MINIMUM OF NINETY DAYS NOR MORE THAN THREE YEARS FOR A SECOND OFFENSE, AND TO REMOVE THE OPTION OF ATTENDING A PROGRAM DESIGNED TO TREAT BATTERERS TO REDUCE A SENTENCE FOR A SECOND OFFENSE.
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Prefiled and referred to the Committee on Judiciary.
Read the first time and referred to the Committee on Judiciary.
S. 905 (Word version) -- Senators Shealy and Turner: A BILL TO AMEND SECTION 63-15-30 OF THE 1976 CODE, RELATING TO CONSIDERATION OF A CHILD'S PREFERENCE IN A CUSTODY ORDER, TO PROVIDE THAT IN DETERMINING THE BEST INTERESTS OF THE CHILD, THE COURT MUST CONSIDER THE CHILD'S REASONABLE PREFERENCE FOR PARENTING TIME; TO AMEND SECTION 63-15-210, RELATING TO TERMS APPLICABLE TO COURT-ORDERED CUSTODY, TO DEFINE "SHARED CUSTODY"; TO AMEND ARTICLE 2, CHAPTER 15, TITLE 63, RELATING TO COURT-ORDERED CUSTODY, BY ADDING SECTION 63-15-215, TO PROVIDE THAT IN A SHARED CUSTODY ORDER, THERE SHALL BE A PRESUMPTION THAT, ABSENT PROOF OF ABUSE OR NEGLECT, OR AN AGREEMENT TO THE CONTRARY, THE PARENTS SHALL HAVE SHARED LEGAL DECISION-MAKING AUTHORITY AND SHARE APPROXIMATELY EQUALLY IN THE PARENTING TIME OF A CHILD; TO AMEND SECTION 63-15-220, RELATING TO PARENTING PLANS, TO PROVIDE THAT THE COURT SHALL PROVIDE PARENTS, AT NO ADDITIONAL COST, MEDIATION SERVICES, TO DEVELOP A PARENTING PLAN OR SHARED PARENTING PLAN; TO AMEND ARTICLE 2, CHAPTER 15, TITLE 63, RELATING TO COURT-ORDERED CUSTODY, BY ADDING SECTION 63-15-225, TO PROVIDE THAT THE COURT MAY ORDER ANY PERSON SEEKING LEGAL DECISION-MAKING AUTHORITY OR PARENTING TIME TO UNDERGO TESTING FOR THE ILLEGAL USE OF CONTROLLED SUBSTANCES OR ABUSE OF ALCOHOL; TO AMEND ARTICLE 2, CHAPTER 15, TITLE 63, RELATING TO COURT-ORDERED CUSTODY, BY ADDING SECTION 63-15-227, TO PROVIDE THAT IF A PARTY IS ABSENT OR RELOCATES, THE COURT SHALL NOT CONSIDER IT AS A FACTOR IN DETERMINING LEGAL DECISION-MAKING AUTHORITY OR PARENTING TIME IF THE ABSENCE OR RELOCATION IS OF SHORT DURATION OR THE PARTY IS ABSENT OR RELOCATES BECAUSE OF SAFETY REASONS; TO AMEND SECTION 63-15-230, RELATING TO CONSIDERATIONS IN A FINAL CUSTODY DETERMINATION, TO PROVIDE THAT THE COURT SHALL CONSIDER A SHARED CUSTODY AWARD IN THE BEST INTERESTS OF THE CHILD; TO AMEND SECTION 63-15-240, RELATING TO CONTENTS OF AN ORDER FOR CUSTODY AFFECTING THE RIGHTS AND RESPONSIBILITIES OF PARENTS, TO PROVIDE THAT IN ISSUING OR MODIFYING AN ORDER FOR CUSTODY, THE ORDER MAY INCLUDE THE AWARD OF SHARED CUSTODY, IN WHICH CASE THE ORDER MUST INCLUDE RESIDENTIAL ARRANGEMENTS, MAJOR DECISIONS CONCERNING THE CHILD, AND THAT EACH CHILD MUST SPEND AN EQUAL AMOUNT OF PARENTING TIME BUT NOT LESS THAN THIRTY-FIVE PERCENT OF CUSTODY TIME WITH EACH PARENT; AND TO AMEND SECTION 63-15-250, RELATING TO TELEPHONIC AND ELECTRONIC COMMUNICATION BETWEEN A MINOR CHILD AND A PARENT, TO PROVIDE THAT WHEN A COURT ORDERS JOINT CUSTODY OR SHARED CUSTODY TO BOTH PARENTS, EACH PARENT SHOULD FACILITATE OPPORTUNITIES FOR REASONABLE TELEPHONIC AND ELECTRONIC COMMUNICATION BETWEEN THE MINOR CHILD AND THE OTHER PARENT.
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Prefiled and referred to the Committee on Judiciary.
Read the first time and referred to the Committee on Judiciary.
S. 906 (Word version) -- Senator Kimpson: A BILL TO AMEND TITLE 41 OF THE 1976 CODE, RELATING TO LABOR AND EMPLOYMENT, TO ENACT THE EARNED PAID SICK LEAVE ACT, TO PROVIDE THAT EMPLOYEES SHALL ACCRUE EARNED PAID AND EARNED UNPAID SICK LEAVE, TO PROVIDE FOR THE METHOD OF AND LIMITS OF ACCRUAL, TO PROVIDE FOR THE CIRCUMSTANCES UNDER WHICH AN EMPLOYEE MAY USE EARNED PAID OR EARNED UNPAID SICK LEAVE, TO PROVIDE FOR CERTIFICATION OF THE REASONS FOR WHICH EARNED PAID OR EARNED UNPAID SICK LEAVE IS USED; TO PROVIDE THAT AN EMPLOYER CANNOT HINDER AN EMPLOYEE'S USE OF EARNED PAID OR EARNED UNPAID SICK LEAVE; TO PROVIDE THAT EMPLOYERS MAY NOT PENALIZE A PERSON FOR PROPERLY USING EARNED PAID OR EARNED UNPAID SICK LEAVE; TO PROVIDE THAT EMPLOYERS WHO ALREADY HAVE POLICIES THAT EXCEED THE PROVISIONS OF THIS CHAPTER DO NOT HAVE TO CHANGE THOSE POLICIES; TO PROVIDE THAT EMPLOYEES MUST PROVIDE REASONABLE NOTICE TO EMPLOYERS BEFORE USING EARNED PAID OR EARNED UNPAID SICK LEAVE IF POSSIBLE; TO PROVIDE FOR NOTICE OF THE PROVISIONS OF THIS CHAPTER TO EMPLOYERS AND EMPLOYEES; AND TO DEFINE NECESSARY TERMS.
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Prefiled and referred to the Committee on Labor, Commerce and Industry.
Read the first time and referred to the Committee on Labor, Commerce and Industry.
S. 907 (Word version) -- Senator Kimpson: A BILL TO AMEND CHAPTER 6, TITLE 12 OF THE 1976 CODE, RELATING TO THE SOUTH CAROLINA INCOME TAX ACT, BY ADDING SECTION 12-6-3710 TO ALLOW A TAX CREDIT TO ANY TAXPAYER THAT EMPLOYS A FORMERLY INCARCERATED INDIVIDUAL AS A FULL-TIME EMPLOYEE, TO SPECIFY THE TAXES FOR WHICH THE CREDIT MAY BE APPLIED, TO ALLOW THE CREDIT FOR TWENTY-FOUR CONSECUTIVE MONTHS FOR EACH FORMERLY INCARCERATED INDIVIDUAL; TO SPECIFY ELIGIBILITY REQUIREMENTS; AND TO DEFINE NECESSARY TERMS.
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Prefiled and referred to the Committee on Finance.
Read the first time and referred to the Committee on Finance.
S. 908 (Word version) -- Senator Hayes: A BILL TO AMEND SECTION 38-9-310, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO DEFINITIONS CONCERNING RISK-BASED CAPITAL, SO AS TO REVISE EXISTING DEFINITIONS AND DEFINE ADDITIONAL TERMS; TO AMEND SECTION 38-9-320, RELATING TO PREPARING AND SUBMITTING A RISK-BASED CAPITAL REPORT, SO AS TO PROVIDE FOR DETERMINING A HEALTH ORGANIZATION'S RISK-BASED CAPITAL REPORT AND TO PROVIDE THAT EACH RISK FOR A LIFE AND HEALTH INSURER, PROPERTY AND CASUALTY INSURER, AND A HEALTH ORGANIZATION MUST BE DETERMINED IN A CERTAIN MANNER; TO AMEND SECTION 38-9-330, AS AMENDED, RELATING TO COMPANY ACTION LEVEL EVENTS, SO AS TO ADD AN ADDITIONAL EVENT CONCERNING A HEALTH ORGANIZATION, AMONG OTHER THINGS; TO AMEND SECTION 38-9-360, RELATING TO THE ROLE OF THE DIRECTOR OF THE DEPARTMENT OF INSURANCE WHEN A MANDATORY CONTROL LEVEL EVENT OCCURS, SO AS TO ADD PROVISIONS CONCERNING HEALTH ORGANIZATIONS; TO AMEND SECTION 38-9-370, RELATING TO HEARINGS AVAILABLE TO A LICENSEE TO CHALLENGE A DETERMINATION OR ACTION BY THE DIRECTOR IN RESPONSE TO A MANDATORY CONTROL LEVEL EVENT, SO AS TO PROVIDE A LICENSEE MAY HAVE THE HEARING CONFIDENTIALLY, ON THE RECORD, AND BEFORE THE DIRECTOR UPON PROVISION OF CERTAIN NOTICE, AND TO PROVIDE THE DIRECTOR SHALL SET A DATE FOR THE HEARING IN A CERTAIN MANNER; TO AMEND SECTION 38-9-380, RELATING TO THE CONFIDENTIALITY OF RISK-BASED CAPITAL REPORTS AND ADJUSTED RISK-BASED CAPITAL REPORTS, SO AS TO PROVIDE CIRCUMSTANCES IN WHICH THE DIRECTOR MAY SHARE, RECEIVE, AND USE CERTAIN RELATED INFORMATION THAT IS CONFIDENTIAL AND PRIVILEGED; TO AMEND SECTION 38-9-430, RELATING TO EXEMPTIONS FROM REPORTING REQUIREMENTS, SO AS TO ADD PROVISIONS CONCERNING DOMESTIC HEALTH ORGANIZATIONS; AND TO AMEND SECTION 38-9-340, SECTION 38-9-350, SECTION 38-9-365, SECTION 38-9-390, SECTION 38-9-400, SECTION 38-9-440, AND SECTION 38-9-460, ALL RELATING TO CAPITAL, SURPLUS, RESERVES, AND OTHER FINANCIAL MATTERS, SO AS TO MAKE CONFORMING CHANGES.
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Read the first time and referred to the Committee on Banking and Insurance.
S. 909 (Word version) -- Senator Hayes: A BILL TO AMEND SECTION 38-90-10, AS AMENDED, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO DEFINITIONS CONCERNING CAPTIVE INSURANCE COMPANIES, SO AS TO DEFINE 'RISK RETENTION GROUP'; TO AMEND SECTION 38-90-40, AS AMENDED, RELATING TO CAPITALIZATION REQUIREMENTS FOR CAPTIVE INSURANCE COMPANIES, SO AS TO INCLUDE CAPTIVE INSURANCE COMPANIES AND SPECIAL PURPOSE CAPTIVE INSURANCE COMPANIES FORMED AS A RISK RETENTION GROUP; TO AMEND SECTION 38-90-50, AS AMENDED, RELATING TO FREE SURPLUS REQUIREMENTS FOR CAPTIVE INSURANCE COMPANIES, SO AS TO INCLUDE CAPTIVE INSURANCE COMPANIES AND SPECIAL PURPOSE CAPTIVE INSURANCE COMPANIES FORMED AS A RISK RETENTION GROUP; AND TO AMEND SECTION 38-90-70, AS AMENDED, SECTION 38-90-100, AS AMENDED, SECTION 38-90-110, AS AMENDED, AND SECTION 38-90-160, AS AMENDED, ALL RELATING TO MISCELLANEOUS REQUIREMENTS FOR CAPTIVE INSURANCE COMPANIES, SO AS TO MAKE CONFORMING PROVISIONS FOR CAPTIVE INSURANCE COMPANIES FORMED AS RISK RETENTION GROUPS AND SPECIAL PURPOSE CAPTIVE INSURANCE COMPANIES FORMED AS RISK RETENTION GROUPS.
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Read the first time and referred to the Committee on Banking and Insurance.
S. 910 (Word version) -- Senator Hayes: A BILL TO AMEND SECTION 59-63-100, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE PARTICIPATION OF HOME SCHOOL STUDENTS AND GOVERNOR'S SCHOOL STUDENTS IN THE INTERSCHOLASTIC ACTIVITIES OF A PUBLIC SCHOOL DISTRICT IN CERTAIN CIRCUMSTANCES, SO AS TO REDEFINE THE TERM "HOME SCHOOL STUDENT" AND TO DELETE A REQUIREMENT THAT A STUDENT PROVIDE WRITTEN NOTICE OF HIS INTENT TO PARTICIPATE IN AN INTERSCHOLASTIC ACTIVITY IN A SCHOOL DISTRICT TO THE SUPERINTENDENT OF THE DISTRICT BEFORE THE BEGINNING DATE OF THE SEASON FOR THE ACTIVITY.
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Read the first time and referred to the Committee on Education.
S. 911 (Word version) -- Senator Peeler: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY REPEALING SECTION 4-10-470 RELATING TO THE EDUCATION CAPITAL IMPROVEMENTS SALES AND USE TAX, SO AS TO DELETE THE REQUIREMENT THAT A COUNTY MUST COLLECT AT LEAST SEVEN MILLION DOLLARS IN A YEAR IN STATE ACCOMMODATIONS TAXES BEFORE IMPOSING THE TAX.
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Read the first time and referred to the Committee on Finance.
S. 912 (Word version) -- Senator Peeler: A BILL TO AMEND SECTION 6-1-730, AS AMENDED, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE USE OF HOSPITALITY TAX REVENUE, SO AS TO ALLOW REVENUE TO BE SPENT ON ROADS AND BRIDGES PROVIDING ACCESS TO DESTINATIONS CONTRIBUTING TO TOURIST ACTIVITIES.
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Read the first time and referred to the Committee on Finance.
S. 913 (Word version) -- Senator Campsen: A BILL TO AMEND CHAPTER 9, TITLE 50 OF THE 1976 CODE, RELATING TO HUNTING AND FISHING LICENSES, BY ADDING SECTION 50-9-675 TO PROVIDE FOR A PERMIT TO ENGAGE IN FALCONRY IN THIS STATE, THE FEE FOR THE PERMIT, AND THAT A PERSON HOLDING A VALID FEDERAL FALCONRY PERMIT ON JANUARY 1, 2014 MAY ENGAGE IN FALCONRY WITHOUT A SOUTH CAROLINA FALCONER'S PERMIT UNTIL THE FEDERAL PERMIT EXPIRES; AND TO AMEND CHAPTER 11, TITLE 50, RELATING TO PROTECTION OF GAME, BY ADDING SECTION 50-11-50 TO PROVIDE FOR THE REGULATION OF FALCONRY AND TO PROVIDE A PENALTY FOR VIOLATIONS.
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Read the first time and referred to the Committee on Fish, Game and Forestry.
S. 914 (Word version) -- Senators Peeler, Alexander, Hayes and McGill: A CONCURRENT RESOLUTION TO FIX WEDNESDAY, APRIL 2, 2014 AT NOON, AS THE DATE AND TIME FOR THE HOUSE OF REPRESENTATIVES AND THE SENATE TO MEET IN JOINT SESSION IN THE HALL OF THE HOUSE OF REPRESENTATIVES FOR THE PURPOSE OF ELECTING MEMBERS OF THE BOARDS OF TRUSTEES FOR THE CITADEL, CLEMSON UNIVERSITY, COASTAL CAROLINA UNIVERSITY, COLLEGE OF CHARLESTON, FRANCIS MARION UNIVERSITY, LANDER UNIVERSITY, MEDICAL UNIVERSITY OF SOUTH CAROLINA, SOUTH CAROLINA STATE UNIVERSITY, UNIVERSITY OF SOUTH CAROLINA, WINTHROP UNIVERSITY, AND WIL LOU GRAY OPPORTUNITY SCHOOL TO SUCCEED THOSE MEMBERS WHOSE TERMS EXPIRE ON JUNE 30, 2014, OR WHOSE POSITIONS OTHERWISE MUST BE FILLED; AND TO ESTABLISH A PROCEDURE REGARDING NOMINATIONS AND SECONDING SPEECHES FOR THE CANDIDATES FOR THESE OFFICES DURING THE JOINT SESSION.
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The Concurrent Resolution was introduced and referred to the Committee on Invitations.
S. 915 (Word version) -- Senator Young: A BILL TO AMEND SECTION 19-1-180, AS AMENDED, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE ADMISSIBILITY OF OUT-OF-COURT STATEMENTS MADE BY CHILDREN, SO AS TO ADD AN EXCEPTION FOR STATEMENTS MADE TO EMPLOYEES OR AGENTS OF CHILDREN'S ADVOCACY CENTERS.
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Read the first time and referred to the Committee on Judiciary.
S. 916 (Word version) -- Senators L. Martin and Massey: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING CHAPTER 82 TO TITLE 15 SO AS TO ESTABLISH THE "TRESPASSER RESPONSIBILITY ACT" WHICH PROVIDES A LIMITATION ON LIABILITY BY A LAND POSSESSOR TO TRESPASSERS.
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Read the first time and referred to the Committee on Judiciary.
S. 917 (Word version) -- Senator Bryant: A BILL TO AMEND CHAPTER 40, TITLE 27 OF THE 1976 CODE, RELATING TO THE RESIDENTIAL LANDLORD AND TENANT ACT, BY ADDING SECTION 27-40-795 TO ALLOW GARNISHMENT FOR A DEBT ARISING FROM A TENANT WILFULLY VIOLATING THE RENTAL AGREEMENT AND TO PROVIDE THAT THE GARNISHMENT ACTION MUST BE BROUGHT IN MAGISTRATES COURT; BY ADDING SECTION 15-19-120, TO DEFINE NECESSARY TERMS RELATED TO GARNISHMENT; BY ADDING SECTION 15-19-130, TO PROVIDE A PROCEDURE FOR THE GARNISHMENT OF WAGES UNDER CERTAIN CIRCUMSTANCES; BY ADDING SECTION 15-19-140, TO PROVIDE A PROCEDURE IF AN EMPLOYER OF THE DEBTOR REFUSES TO WITHHOLD EARNINGS OF THE DEBTOR DEMANDED IN A WRIT OF GARNISHMENT OR KNOWINGLY MISREPRESENTS THE EARNINGS OF THE DEBTOR AND PROVIDE THAT GARNISHMENT IS SUBJECT TO SPECIFIC LIMITATIONS; AND BY ADDING SECTION 15-19-150, TO PROVIDE THAT AN EMPLOYER MAY NOT TAKE NEGATIVE ACTION AGAINST AN EMPLOYEE EXCLUSIVELY RELATED TO A WRIT OF GARNISHMENT.
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Read the first time and referred to the Committee on Judiciary.
S. 918 (Word version) -- Senator Scott: A BILL TO AMEND SECTIONS 7-5-120 AND 7-5-180, BOTH AS AMENDED, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO QUALIFICATIONS AND PROCEDURES NECESSARY FOR PERSONS TO REGISTER TO VOTE, SO AS TO REVISE REFERENCES; TO AMEND SECTION 7-5-310, RELATING TO VOTER REGISTRATION AGENCIES, SO AS TO REFLECT A NAME CHANGE FOR ONE OF SUCH AGENCIES AND TO DELETE A REFERENCE TO DISABILITY; TO AMEND SECTION 7-7-990, AS AMENDED, RELATING TO THE ACCESSIBILITY OF POLLING PLACES, SO AS TO REVISE "BARRIER FREE" TO "ACCESSIBLE" AND TO DEFINE "ACCESSIBLE", TO ALLOW ANY PERSON WITH DISABILITIES TO VOTE IN A COUNTYWIDE ACCESSIBLE POLLING PLACE AND REQUIRE THAT ANY ALTERNATIVE POLLING PLACE MUST BE ACCESSIBLE; TO AMEND SECTION 7-7-1000, RELATING TO PRECINCTS IN MUNICIPAL ELECTIONS, SO AS TO REQUIRE ANY POOLED PRECINCT TO BE ACCESSIBLE; TO AMEND SECTION 7-15-200, RELATING TO THE MAILING OF ABSENTEE BALLOTS, SO AS TO REQUIRE THAT ABSENTEE BALLOTS MUST BE AVAILABLE IN LARGE PRINT FORMAT; TO AMEND SECTION 7-15-310, AS AMENDED, RELATING TO DEFINITIONS FOR PURPOSES OF ABSENTEE VOTING, SO AS TO REPLACE THE REFERENCE TO "PHYSICALLY DISABLED PERSON" TO "PERSON WITH A DISABILITY", AND TO REVISE THE DEFINITION OF "AUTHORIZED REPRESENTATIVE"; TO AMEND SECTION 7-15-320, AS AMENDED, RELATING TO PERSONS QUALIFIED TO VOTE BY ABSENTEE BALLOT, SO AS TO REVISE REFERENCES RELATING TO DISABILITIES AND HOSPITALS; TO AMEND SECTION 7-15-330, AS AMENDED, RELATING TO THE PROCEDURE FOR ABSENTEE VOTING, SO AS TO CONFORM THE REFERENCES RELATING TO PERSONS ADMITTED TO HOSPITALS; TO AMEND SECTIONS 7-15-380 AND 7-15-385, BOTH AS AMENDED, RELATING TO THE OATH AND PROCEDURES REQUIRED FOR VOTING BY ABSENTEE BALLOT, SO AS TO UPDATE REFERENCES RELATING TO DISABILITY.
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Read the first time and referred to the Committee on Judiciary.
S. 919 (Word version) -- Senator L. Martin: A BILL TO AMEND SECTION 43-7-60, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO FALSE CLAIMS, STATEMENTS, AND REPRESENTATIONS FOR PURPOSES OF QUALIFYING FOR AND RECEIVING PAYMENT FOR AND REIMBURSEMENT OF MEDICAID CLAIMS AND BENEFITS, SO AS TO PROHIBIT ANY PERSON FROM ENGAGING IN THE PROHIBITED CONDUCT AND TO EXPAND OFFENSES AND PENALTIES FOR VIOLATING THE PROVISIONS OF THE ARTICLE; AND TO AMEND SECTION 43-7-90, RELATING TO ENFORCEMENT OF THE ARTICLE, SO AS TO PROVIDE THE ATTORNEY GENERAL, OR A DESIGNEE, ADDITIONAL POWERS.
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Read the first time and referred to the Committee on Medical Affairs.
S. 920 (Word version) -- Senator Peeler: A BILL TO AMEND SECTION 56-3-2320, AS AMENDED, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE ISSUANCE OF DEALER AND WHOLESALER LICENSE PLATES BY THE DEPARTMENT OF MOTOR VEHICLES, SO AS TO DELETE THE PROVISIONS THAT REQUIRE A DEALER TO RECORD A MINIMUM NUMBER OF MOTOR VEHICLE SALES OR ESTIMATED SALES BEFORE HE MAY BE ISSUED A DEALER LICENSE PLATE.
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Read the first time and referred to the Committee on Transportation.
S. 921 (Word version) -- Senator Leatherman: A BILL TO AMEND ACT 250 OF 1991, RELATING TO THE ANNUAL BUDGET FOR FLORENCE SCHOOL DISTRICT NUMBER 5, SO AS TO ONLY REQUIRE A MEETING OF THE CITIZENS IF THE PROPOSED BUDGET REQUIRES A MILLAGE INCREASE.
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Read the first time and ordered placed on the Local and Uncontested Calendar.
S. 922 (Word version) -- Senator Alexander: A SENATE RESOLUTION TO RECOGNIZE AND HONOR DR. FRANKLIN G. MASON FOR HIS INVOLVEMENT WITH THE LIONS CLUB INTERNATIONAL AND FOR HIS EFFORTS TO EDUCATE THE COMMUNITY ON VISION AND HEARING IMPAIRMENT THROUGHOUT SOUTH CAROLINA.
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S. 923 (Word version) -- Senator Cleary: A SENATE RESOLUTION TO DECLARE WEDNESDAY, JANUARY 15, 2014, AS "SOUTH CAROLINA RECYCLERS' DAY" AND TO COMMEND AND RECOGNIZE SOUTH CAROLINA'S RECYCLERS FOR THEIR CONTRIBUTIONS TO OUR STATE'S ECONOMY, THEIR EFFORTS TO PROMOTE ENERGY EFFICIENCY, AND THEIR LEADERSHIP IN PROVIDING SUSTAINABLE MATERIAL-MANAGEMENT OPTIONS.
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S. 924 (Word version) -- Senators O'Dell and Nicholson: A SENATE RESOLUTION TO RECOGNIZE AND HONOR DRU T. JAMES OF GREENWOOD COUNTY FOR HER MANY YEARS OF OUTSTANDING COMMUNITY AND PUBLIC SERVICE TO THE PEOPLE OF SOUTH CAROLINA.
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S. 925 (Word version) -- Senators L. Martin, Campsen and Malloy: A CONCURRENT RESOLUTION TO THANK ROBERT M. "MIKE" HAMMOND OF ORANGEBURG COUNTY FOR HIS MANY YEARS OF DEDICATED SERVICE AS CHAIR OF THE LOWCOUNTRY CITIZENS COMMITTEE ON JUDICIAL QUALIFICATIONS AND TO WISH HIM MUCH SUCCESS AND FULFILLMENT IN ALL HIS FUTURE ENDEAVORS.
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The Concurrent Resolution was adopted, ordered sent to the House.
S. 926 (Word version) -- Senators L. Martin, Campsen and Malloy: A CONCURRENT RESOLUTION TO THANK CHARLES A. MONTGOMERY OF CHESTER COUNTY FOR HIS MANY YEARS OF DEDICATED SERVICE AS CHAIR OF THE PIEDMONT CITIZENS COMMITTEE ON JUDICIAL QUALIFICATIONS AND TO WISH HIM MUCH SUCCESS AND FULFILLMENT IN ALL HIS FUTURE ENDEAVORS.
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The Concurrent Resolution was adopted, ordered sent to the House.
S. 927 (Word version) -- Senators L. Martin, Campsen and Malloy: A CONCURRENT RESOLUTION TO THANK JOHN M. GRANTLAND OF RICHLAND COUNTY FOR HIS MANY YEARS OF DEDICATED SERVICE AS A MEMBER AND CHAIR OF THE MIDLANDS CITIZENS COMMITTEE ON JUDICIAL QUALIFICATIONS AND TO WISH HIM MUCH SUCCESS AND FULFILLMENT IN ALL HIS FUTURE ENDEAVORS.
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The Concurrent Resolution was adopted, ordered sent to the House.
S. 928 (Word version) -- Senator Cromer: A CONCURRENT RESOLUTION TO RECOGNIZE AND CONGRATULATE SAINT MICHAEL'S EVANGELICAL LUTHERAN CHURCH OF COLUMBIA ON THE OCCASION OF ITS HISTORIC TWO HUNDREDTH ANNIVERSARY AND TO COMMEND THE CHURCH FOR TWO CENTURIES OF SERVICE TO GOD AND THE COMMUNITY.
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The Concurrent Resolution was adopted, ordered sent to the House.
S. 929 (Word version) -- Senator Courson: A CONCURRENT RESOLUTION TO CONGRATULATE GERARDO GONZALEZ OF COLUMBIA ON THE OCCASION OF HIS ONE HUNDREDTH BIRTHDAY AND TO WISH HIM MUCH HAPPINESS IN THE DAYS AHEAD.
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The Concurrent Resolution was adopted, ordered sent to the House.
S. 930 (Word version) -- Senator Scott: A CONCURRENT RESOLUTION TO RECOGNIZE AND HONOR COACH CURTIS FRYE, HEAD COACH OF TRACK AND FIELD AND CROSS COUNTRY AT THE UNIVERSITY OF SOUTH CAROLINA AND TO COMMEND HIM UPON HIS INDUCTION INTO THE UNITED STATES TRACK & FIELD AND CROSS COUNTRY COACHES ASSOCIATION HALL OF FAME.
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The Concurrent Resolution was adopted, ordered sent to the House.
S. 931 (Word version) -- Senators McElveen, Shealy, Johnson, Young, Lourie, Hutto, Setzler, Malloy, Williams, Reese, Nicholson, Scott, Rankin, Bennett, Gregory, Hembree, Courson, Kimpson, Jackson, Massey and Thurmond: A CONCURRENT RESOLUTION TO HONOR COACH STEVE SPURRIER OF THE UNIVERSITY OF SOUTH CAROLINA AS THE "WINNINGEST COACH" IN THE HISTORY OF CAROLINA FOOTBALL, TO CONGRATULATE HIM ON COACHING HIS OUTSTANDING TEAM ALL THE WAY TO THE 2014 CAPITAL ONE BOWL WINNER'S CROWN, AND TO WISH HIM MUCH CONTINUED SUCCESS IN THE DAYS TO COME.
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The Concurrent Resolution was adopted, ordered sent to the House.
S. 932 (Word version) -- Senators McElveen and Johnson: A CONCURRENT RESOLUTION TO RECOGNIZE AND CONGRATULATE THE WILSON HALL FOOTBALL TEAM ON ITS IMPRESSIVE WIN OF THE 2013 SOUTH CAROLINA INDEPENDENT SCHOOL ASSOCIATION CLASS AAA STATE CHAMPIONSHIP TITLE.
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The Concurrent Resolution was adopted, ordered sent to the House.
S. 933 (Word version) -- Senators Courson, Setzler, Alexander, Allen, Bennett, Bright, Bryant, Campbell, Campsen, Cleary, Coleman, Corbin, Cromer, Davis, Fair, Gregory, Grooms, Hayes, Hembree, Hutto, Jackson, Johnson, Kimpson, Leatherman, Lourie, Malloy, L. Martin, S. Martin, Massey, Matthews, McElveen, McGill, Nicholson, O'Dell, Peeler, Pinckney, Rankin, Reese, Scott, Shealy, Sheheen, Thurmond, Turner, Verdin, Williams and Young: A CONCURRENT RESOLUTION TO HONOR THE CONTRIBUTIONS OF THE LATE COACH FRANK MCGUIRE TO THE UNIVERSITY OF SOUTH CAROLINA BASKETBALL PROGRAM AS HEAD COACH OF THE GAMECOCKS, TO RECOGNIZE HIS ILLUSTRIOUS CAREER, AND TO DECLARE FRIDAY, JANUARY 17, 2014, AS "FRANK MCGUIRE DAY" IN COLUMBIA TO COMMEMORATE THIS MARK OF HIGH ESTEEM.
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The Concurrent Resolution was adopted, ordered sent to the House.
S. 934 (Word version) -- Senators Scott, Alexander, Allen, Bennett, Bright, Bryant, Campbell, Campsen, Cleary, Coleman, Corbin, Courson, Cromer, Davis, Fair, Gregory, Grooms, Hayes, Hembree, Hutto, Jackson, Johnson, Kimpson, Leatherman, Lourie, Malloy, L. Martin, S. Martin, Massey, Matthews, McElveen, McGill, Nicholson, O'Dell, Peeler, Pinckney, Rankin, Reese, Setzler, Shealy, Sheheen, Thurmond, Turner, Verdin, Williams and Young: A CONCURRENT RESOLUTION TO REQUEST THAT THE DEPARTMENT OF TRANSPORTATION NAME THE HIGHWAY INTERCHANGE LOCATED AT THE INTERSECTION OF SOUTH CAROLINA HIGHWAY 277 AND PARKLANE ROAD IN RICHLAND COUNTY "BERNICE SKINNER INTERCHANGE" AND ERECT APPROPRIATE MARKERS OR SIGNS AT THIS HIGHWAY INTERCHANGE THAT CONTAIN THE WORDS "BERNICE SKINNER INTERCHANGE".
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The Concurrent Resolution was introduced and referred to the Committee on Transportation.
REPORTS OF STANDING COMMITTEES
Invitations Accepted
On motion of Senator BRYANT, with unanimous consent, the following invitations were polled favorably from the Committee on Invitations and ordered placed on the Calendar:
Poll of the Invitations Committee
Polled 11; Ayes 11; Nays 0; Not Voting 0
AYES
Bryant Alexander McGill
Reese Verdin Campsen
Cromer Malloy Cleary
Johnson
Total--11
NAYS
Total--0
Tuesday, January 14, 2014 - 6:00 - 8:00 P.M.
Members of the Senate, Reception, The Columbia Museum of Art, by the SOUTH CAROLINA BANKERS ASSOCIATION
Tuesday, January 14, 2014 - 7:00 - 9:00 P.M.
Members of the Senate, Reception, Columbia Convention Center, by the WILKINS AWARD DINNER
Wednesday, January 15, 2014 - 8:00 -10:00 A.M.
Members of the Senate and Staff, Breakfast, Room 112, Blatt Building, by the SC HEALTH UNDERWRITERS ASSOCIATION
Wednesday, January 15, 2014 - 12:00 - 2:00 P.M.
Members of the Senate and Staff, Luncheon, Room 112, Blatt Building, by the SC RECYCLING ASSOCIATION
Wednesday, January 15, 2014 - 6:00 - 8:00 P.M.
Members of the Senate, Reception, Capitol City Club, by the SOUTH CAROLINA ECONOMIC DEVELOPERS ASSOCIATION
Wednesday, January 15, 2014 - 7:00 - 9:00 P.M.
Members of the Senate and Staff, Reception, Columbia Museum of Art, by the SC TELECOMMUNICATIONS ASSOCIATION
Thursday, January 16, 2014 - 8:00 - 10:00 A.M.
Members of the Senate, Breakfast, Room 112, Blatt Building, by the SC HIGH SCHOOL LEAGUE
Tuesday, January 21, 2014 - 6:00 - 8:00 P.M.
Members of the Senate, Reception, The Clarion, by the ACEC-SC, SCSPE, ASCE-SC AND AIA-SC
Tuesday, January 21, 2014 - 7:00 - 9:00 P.M.
Members of the Senate and Staff, Reception, Ellison Building State Fair Grounds, by the SC DEPARTMENT OF NATURAL RESOURCES
Wednesday, January 22, 2014 - 12:00 - 2:00 P.M.
Members of the Senate and Staff, Luncheon, Room 112, Blatt Building, by the UNITED WAY ASSOCIATION OF SOUTH CAROLINA
Wednesday, January 22, 2014 - 6:00 - 8:00 P.M.
Members of the Senate, Reception, Capital City Center, 1st Floor, by the SOUTH CAROLINA BAR ASSOCIATION
Thursday, January 23, 2014 - 8:00 - 10:00 A.M.
Members of the Senate, Breakfast, Room 112, Blatt Building, by the SC ASSOCIATION OF CHRISTIAN SCHOOLS
Tuesday, January 28, 2014 - 6:00 - 8:00 P.M.
Members of the Senate and Staff, Reception, Columbia Convention Center, by the LEXINGTON COUNTY NIGHT
Wednesday, January 29, 2014 - 12:00 - 2:00 P.M.
Members of the Senate, Luncheon, Room 112, Blatt Building, by the CONSORTIUM FOR GIFTED EDUCATION
Wednesday, January 29, 2014 - 6:00 - 8:00 P.M.
Members of the Senate and Staff, Reception, The Clarion Downtown Hotel, by the MYRTLE BEACH NIGHT
Thursday, January 30, 2014 - 8:00 - 10:00 A.M.
Members of the Senate, Breakfast, Room 112, Blatt Building, by the SOUTH CAROLINA BROADCASTERS ASSOCIATION
THE SENATE PROCEEDED TO A CALL OF THE UNCONTESTED LOCAL AND STATEWIDE CALENDAR.
CARRIED OVER
H. 3540 (Word version) -- Reps. Harrell, J.E. Smith, Bales, Hosey, Cobb-Hunter, Bannister, J.R. Smith, Patrick, Brannon, Erickson, Taylor, Huggins, Kennedy, Ballentine, Bernstein, Sellers, Williams, Jefferson, M.S. McLeod, Atwater, Bowers, R.L. Brown, Cole, Douglas, George, Hixon, Long, McCoy, Mitchell, Pitts, Pope, G.R. Smith, Tallon, Wood, Weeks, Knight and Hart: A BILL TO AMEND SECTION 1-3-240, AS AMENDED, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE REMOVAL OF OFFICERS BY THE GOVERNOR, SO AS TO ADD THE ADJUTANT GENERAL TO THE LIST OF OFFICERS OR ENTITIES THE GOVERNING BOARD OF WHICH MAY BE REMOVED BY THE GOVERNOR ONLY FOR CERTAIN REASONS CONSTITUTING CAUSE; TO AMEND SECTION 25-1-320, RELATING TO THE STATE ADJUTANT GENERAL, SO AS TO PROVIDE THAT BEGINNING UPON THE EXPIRATION OF THE TERM OF THE ADJUTANT GENERAL SERVING IN OFFICE ON THE DATE OF THE 2014 GENERAL ELECTION, THE ADJUTANT GENERAL MUST BE APPOINTED BY THE GOVERNOR UPON THE ADVICE AND CONSENT OF THE SENATE FOR A FOUR-YEAR TERM COMMENCING ON THE FIRST WEDNESDAY FOLLOWING THE SECOND TUESDAY IN JANUARY THAT FOLLOWS THE GENERAL ELECTION THAT MARKS THE MIDTERM OF THE GOVERNOR, EXCEPT THAT THE INITIAL TERM OF THE FIRST ADJUTANT GENERAL APPOINTED PURSUANT TO THIS ACT MUST BE FOR TWO YEARS SO AS TO ALLOW SUBSEQUENT TERMS TO BE STAGGERED WITH THAT OF THE GOVERNOR, AND TO ESTABLISH CERTAIN QUALIFICATIONS FOR THE OFFICE OF ADJUTANT GENERAL; TO AMEND SECTION 25-1-340, AS AMENDED, RELATING TO VACANCIES IN THE OFFICE OF ADJUTANT GENERAL, SO AS TO DELETE A REFERENCE TO THE ELIGIBILITY REQUIREMENTS OF CONSTITUTIONAL OFFICERS; AND TO PROVIDE THAT THE ABOVE PROVISIONS ARE EFFECTIVE UPON THE RATIFICATION OF AMENDMENTS TO SECTION 7, ARTICLE VI, AND SECTION 4, ARTICLE XIII OF THE CONSTITUTION OF THIS STATE DELETING THE REQUIREMENT THAT THE STATE ADJUTANT GENERAL BE ELECTED BY THE QUALIFIED ELECTORS OF THIS STATE.
On motion of Senator LARRY MARTIN, the Bill was carried over.
H. 3459 (Word version) -- Reps. Sandifer, Bales, J.E. Smith and Erickson: A BILL TO AMEND SECTION 40-2-10, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE SOUTH CAROLINA BOARD OF ACCOUNTANCY, SO AS TO PROVIDE THE DEPARTMENT OF LABOR, LICENSING AND REGULATION SHALL DESIGNATE CERTAIN PERSONNEL FOR THE EXCLUSIVE USE OF THE BOARD, TO PROHIBIT THE DEPARTMENT FROM ASSIGNING OTHER WORK TO THESE PERSONNEL WITHOUT APPROVAL OF THE BOARD, AND TO PROVIDE THESE PERSONNEL MAY BE TERMINATED BY THE DIRECTOR OF A MAJORITY OF THE BOARD; TO AMEND SECTION 40-2-30, RELATING TO THE PRACTICE OF ACCOUNTANCY, SO AS TO PROVIDE A CERTIFIED PUBLIC ACCOUNTANT LICENSED BY THE BOARD IS EXEMPT FROM LICENSURE REQUIREMENTS OF PRIVATE SECURITY AND INVESTIGATION AGENCIES; AND TO AMEND SECTION 40-2-70, RELATING TO POWERS AND DUTIES OF THE BOARD, SO AS TO PROVIDE THE BOARD MAY CONDUCT PERIODIC INSPECTIONS OF LICENSEES OR FIRMS; AND TO AMEND SECTION 40-2-80, RELATING TO INVESTIGATIONS OF ALLEGED VIOLATIONS, SO AS TO PROVIDE THE DEPARTMENT SHALL DIRECT THE INVESTIGATOR ASSIGNED TO THE BOARD TO INVESTIGATE AN ALLEGED VIOLATION TO DETERMINE THE EXISTENCE OF PROBABLE CAUSE MERITING FURTHER PROCEEDINGS.
On motion of Senator BRYANT, the Bill was carried over.
H. 3014 (Word version) -- Reps. J.E. Smith, Bernstein, M.S. McLeod, McEachern, Weeks, Hart and Gilliard: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING CHAPTER 29 TO TITLE 14 SO AS TO ENACT THE "VETERANS TREATMENT COURT PROGRAM ACT", TO REQUIRE THE CREATION AND ADMINISTRATION OF A VETERANS TREATMENT COURT PROGRAM IN EACH JUDICIAL CIRCUIT BY THE ATTORNEY GENERAL, TO PROVIDE FOR THE APPOINTMENT, POWERS, AND DUTIES OF A VETERANS TREATMENT COURT JUDGE, AND TO PROVIDE FOR REQUIREMENTS FOR AN OFFENDER TO QUALIFY FOR ADMISSION TO A VETERANS TREATMENT COURT PROGRAM.
On motion of Senator THURMOND, the Bill was carried over.
On motion of Senator HAYES, the Bill was carried over.
RECOMMITTED
S. 731 (Word version) -- Senator Leatherman: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING SECTION 11-43-165 SO AS TO REQUIRE THE SOUTH CAROLINA DEPARTMENT OF TRANSPORTATION (DOT) TO TRANSFER TO THE SOUTH CAROLINA TRANSPORTATION INFRASTRUCTURE BANK (SIB) FROM NON-TAX SOURCES AN AMOUNT EQUAL TO THE AMOUNT OF GENERAL FUND REVENUE APPROPRIATED TO DOT IN THE ANNUAL GENERAL APPROPRIATIONS ACT FOR "HIGHWAY ENGINEERING PERMANENT IMPROVEMENTS", TO PROVIDE THAT THE AMOUNT APPROPRIATED TO DOT IN THE ANNUAL GENERAL APPROPRIATIONS ACT FOR "HIGHWAY ENGINEERING PERMANENT IMPROVEMENTS" ARE NOT SUBJECT TO ANY ACROSS THE BOARD REDUCTIONS, TO REQUIRE SIB TO USE THE TRANSFERRED FUNDS SOLELY TO FINANCE BRIDGE REPLACEMENT, REHABILITATION PROJECTS, AND EXPANSION AND IMPROVEMENTS TO EXISTING MAINLINE INTERSTATES, TO PROVIDE THAT DOT SHALL SUBMIT A LIST OF APPROPRIATE PROJECT RECOMMENDATIONS TO SIB, AND TO PROVIDE THAT THE FUNDS TRANSFERRED PURSUANT TO THIS SECTION MAY NOT BE EXPENDED ON ANY PROJECT APPROVED BY SIB BEFORE JULY 1, 2013.
On motion of Senator LEATHERMAN, the Bill was recommitted to the Committee on Finance.
THE CALL OF THE UNCONTESTED CALENDAR HAVING BEEN COMPLETED, THE SENATE PROCEEDED TO THE MOTION PERIOD.
On motion of Senator PEELER, the Senate agreed to dispense with the balance of the Motion Period.
HAVING DISPENSED WITH THE MOTION PERIOD, THE SENATE PROCEEDED TO A CONSIDERATION OF BILLS AND RESOLUTIONS RETURNED FROM THE HOUSE.
CARRIED OVER
S. 75 (Word version) -- Senator Cromer: A BILL TO AMEND SECTION 40-57-130, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO LICENSE RENEWALS FOR REAL ESTATE BROKERS AND SALESMEN, SO AS TO REQUIRE A CRIMINAL BACKGROUND CHECK FROM A SOURCE APPROVED BY THE DEPARTMENT OF LABOR, LICENSING AND REGULATION; AND BY ADDING SECTION 40-57-245 SO AS TO REQUIRE THAT THE DEPARTMENT ASSIGN ONE INVESTIGATOR FOR EVERY TWO THOUSAND FIVE HUNDRED LICENSEES TO ENSURE COMPLAINTS ARE PROCESSED AND CONSIDERED IN AN EXPEDITIOUS MANNER.
On motion of Senator ALEXANDER, the Bill was carried over.
RETURNED FROM THE HOUSE WITH AMENDMENTS
AMENDMENT PROPOSED
S. 308 (Word version) -- Senators Bennett, Shealy, Grooms, Hembree, L. Martin, Massey, Campbell, Turner, Thurmond, Bryant, Verdin, S. Martin, Davis, Bright, Corbin, Campsen, Fair and Cromer: A BILL TO AMEND SECTION 16-23-465 OF THE 1976 CODE, RELATING TO THE CARRYING OF A CONCEALED WEAPON IN A BUSINESS THAT SELLS ALCOHOL TO BE CONSUMED ON THE PREMISES, TO PERMIT THE POSSESSION OF A WEAPON UNLESS NOTICE OF A PROHIBITION IS PROVIDED BY THE BUSINESS, TO PROHIBIT THE CONSUMPTION OF ALCOHOLIC BEVERAGES IN A BUSINESS BY SOMEONE CARRYING A FIREARM, AND TO REDUCE THE PENALTIES FOR VIOLATIONS.
The House returned the Bill with amendments.
Amendment No. RFH-7
Senator SCOTT proposed the following amendment (308MWRETURN14):
Amend the bill, as and if amended, by striking all after the enacting words and inserting the following:
/ SECTION 1. Section 16-23-465 of the 1976 Code is amended to read:
"Section 16-23-465. (A) In addition to the penalties provided for by Sections 16-11-330, 16-11-620, and 16-23-460, 23-31-220, and by Article 1, of Chapter 23, of Title 16, a person convicted of carrying a pistol or firearm into a business which sells alcoholic liquor, beer, or wine for consumption on the premises is guilty of a misdemeanor, and, upon conviction, must be fined not more than two three thousand dollars or imprisoned not more than three years, or both.
In addition to the penalties described above, a person who violates this section while carrying a concealable weapon pursuant to Article 4, Chapter 31, Title 23, must have his concealed weapon permit revoked for a period of five years.
(B)(1) This section does not apply to a person carrying a concealable weapon pursuant to and in compliance with Article 4, Chapter 31, Title 23 between the hours of 5:00 a.m. and 8:00 p.m.; however, the person shall not consume alcoholic liquor, beer, or wine while carrying the concealable weapon on the business' premises and shall not enter and remain on any portion of the business' premises primarily devoted to the service and consumption of alcoholic liquor, beer, or wine. A person who violates this subitem may be charged with a violation of subsection (A).
(2) A business owner or person in legal possession or control of a business may prohibit the carrying of concealable weapons into the business by posting a 'NO CONCEALABLE WEAPONS ALLOWED' sign in compliance with Section 23-31-235. A person who carries a concealable weapon into a business with a sign posted in compliance with Section 23-31-235 may be charged with a violation of subsection (A).
(3) A business owner or person in legal possession or control of a business may request that a person carrying a concealable weapon leave the business' premises, or any portion of the premises, or request that a person carrying a concealable weapon remove the concealable weapon from the business' premises, or any portion of the premises. A person carrying a concealable weapon who refuses to leave a business' premises or portion of the premises when requested or refuses to remove the concealable weapon from a business' premises or portion of the premises when requested may be charged with a violation of subsection (A)."
SECTION 2. This act takes effect upon approval by the Governor.
Renumber sections to conform.
Amend title to conform.
Senator SCOTT explained the amendment.
Senator SCOTT moved to carry over the Bill.
Senator LARRY MARTIN moved to table the motion to carry over.
The "ayes" and "nays" were demanded and taken, resulting as follows:
Ayes 28; Nays 13
AYES
Alexander Bennett Bright
Bryant Campbell Campsen
Corbin Courson Davis
Fair Gregory Grooms
Hayes Hembree Hutto
Leatherman Martin, Larry Martin, Shane
Massey O'Dell Peeler
Rankin Setzler Shealy
Thurmond Turner Verdin
Young
Total--28
NAYS
Allen Jackson Johnson
Kimpson Lourie Malloy
Matthews McElveen McGill
Nicholson Reese Scott
Williams
Total--13
The motion to carry over was laid on the table.
Senator SCOTT explained the amendment.
On motion of Senator COURSON, debate was interrupted by adjournment.
JOINT LEGISLATIVE COMMITTEE TO SCREEN CANDIDATES FOR COLLEGE AND UNIVERSITY BOARDS OF TRUSTEES
SCREENINGS
Wednesday, November 20, 2013
1:30 p.m.
209 Gressette Building
1101 Pendleton Street
Columbia, South Carolina
Committee Members Present:
Senator Harvey S. Peeler, Jr., Chairman
Representative William R. "Bill" Whitmire, Vice-Chairman
Senator Thomas C. Alexander
Senator J. Yancey McGill
Senator Robert W. Hayes, Jr.
Representative Peter McCoy
Staff:
Martha Casto
Julie Price
(1:32 p.m.)
CHAIRMAN SENATOR PEELER: I would like to call the meeting to order. This is a meeting of the Joint Legislative Committee to Screen Candidates for College and University Boards of Trustees. I would like to go ahead and get started.
To my right, Representative Whitmire serves on the Committee with us. He represents the House of Representatives today. Some of the others couldn't make it.
REPRESENTATIVE WHITMIRE: They got lost.
CHAIRMAN SENATOR PEELER: Then we have Senator Tom Alexander, Senator Yancey McGill, and Senator Wes Hayes. I'm Harvey Peeler. I would like to welcome everyone.
First, under Tab A, we have Connie Dittrich from Daniel Island, the Old Exchange Building Commission at-large seat that expires 2018.
Ms. Dittrich, if you would, come forward, take a seat, and make sure your green light is burning. If you push that, that turns your microphone on.
Is it burning?
MS. DITTRICH: It is.
CHAIRMAN SENATOR PEELER: Good. I can hear you. Welcome, Ms. Dittrich. I will tell you, before we get started, I need to swear you in. So if you would, please raise your right hand.
Do you swear to tell the truth, the whole, truth, and nothing but the truth, so help you God?
MS. DITTRICH: I do.
CHAIRMAN SENATOR PEELER: Welcome again.
If you would like to share with the Committee why you would like to serve on the Old Exchange Building Commission.
MS. DITTRICH: Thank you for having me. I am very desirous of serving on the Old Exchange Building Commission -- board for a couple of different reasons.
The first is because I have known about it most of my life. My mom grew up in Charleston, and I visited the city for my whole life, although, of course, it wasn't open for visitors when I was a little girl, 60 years ago. But it's an icon, historical icon, in the city, and I would like to help be able to preserve that in any way that I can. That's my first reason.
The second reason is that Charleston is such a gem, and I make my living there, and I think that being able to, you know, know that one of the important area -- one of the important tourist attractions in our city, in that city, is well taken care of, is something that, you know, we can all know is being taken care of. And I am anxious to be able to contribute to that.
CHAIRMAN SENATOR PEELER: Thank you, ma'am.
Any questions from members of the Committee?
I didn't ask you. Do you have --
MS. CASTO: Mr. Chairman, I do want to let y'all know, the Old Exchange Building has three members that are elected by the General Assembly. There are two seats that are up in January, and there are two at-large seats. So Ms. Dittrich is an at-large candidate.
CHAIRMAN SENATOR PEELER: Very good.
Well, I appreciate your willingness to serve. What's the desire of the Committee?
SENATOR HAYES: Favorable report.
CHAIRMAN SENATOR PEELER: Motion is a favorable report.
Is there a second?
SENATOR McGILL: Second.
CHAIRMAN SENATOR PEELER: A second is heard.
All in favor, raise your right hand; and it is unanimous.
Thank you.
Now we have Laura Kennedy LeGrand.
Good afternoon.
MS. LeGRAND: Good afternoon.
CHAIRMAN SENATOR PEELER: Thank you for your appearance.
Do you swear to tell the truth, the whole truth, and nothing but the truth, so help you God?
MS. LeGRAND: I do.
CHAIRMAN SENATOR PEELER: Would you like to share with the Committee why you would like to serve?
MS. LeGRAND: Yes, I would. I have served on the Commission before. I was on the Commission for 12 years for the National Society, Daughters of the American Revolution.
When I resigned from the DAR, of course, I lost my seat from the Commission and I miss it a whole lot. I just love it. I have heard of the Old Exchange as long as I have been in the DAR, and I was very fortunate to be elected to the Commission through the DAR. And we have done a lot of good things down there, and there are a lot of good things still going on.
I would like to see the Old Exchange recognized nationwide, not just by the State of South Carolina. And if I can get back on there, I would strive to put us in the forefront, along with Independence Hall and Faneuil Hall.
CHAIRMAN SENATOR PEELER: Very good.
Staff, do you have anything you would like to add or ask?
MS. CASTO: No, sir. I think she told you she has been on the Commission. She chaired the Old Exchange Commission.
MS. LeGRAND: Yes.
MS. CASTO: And she -- you did say that you were retired. Where are you retired from?
MS. LeGRAND: Well, I resigned from DAR. No, I have been fortunate in that I have never worked. I have been a stay-at-home mom pretty much.
MS. CASTO: Great. Thank you.
CHAIRMAN SENATOR PEELER: Trust me, that's work.
MS. LeGRAND: That's work.
CHAIRMAN SENATOR PEELER: Mr. Whitmire has a question or comment.
REPRESENTATIVE WHITMIRE: Thank you, Mr. Chairman.
Mrs. LeGrand, can you tell me where sources of funding come from for the Old Exchange Building?
MS. LeGRAND: Right now, the Exchange -- of course, I have not been on for two years, but I understand they are still doing well.
Right now we are independent; but according to our lease, the State of South Carolina is supposed to support us; but we are no longer an item on the budget.
REPRESENTATIVE WHITMIRE: Well, hopefully that will change.
MS. LeGRAND: Oh, I hope.
REPRESENTATIVE WHITMIRE: I just wanted to let you know that the DAR school is in my district. I just want to say thank you for everyone associated with the DAR for keeping it going. It is a wonderful school.
MS. LeGRAND: Thank you. Tamassee is a wonderful school.
CHAIRMAN SENATOR PEELER: Representative McCoy is here.
Welcome, sir.
REPRESENTATIVE McCOY: Thank you, Mr. Chairman. Good to be here.
REPRESENTATIVE WHITMIRE: Maybe you don't wear a watch.
REPRESENTATIVE McCOY: Tell the judge that where I was.
CHAIRMAN SENATOR PEELER: That's called House time.
REPRESENTATIVE McCOY: That's right.
CHAIRMAN SENATOR PEELER: Well, my daughter is going in or going through the process to become a member of the DAR. I'm glad she did that because she shared with me my ancestry, and I didn't find out until about a month ago, Senator from York, that my fifth granddaddy back was Colonel Frederick Hambright who was a revolutionary war hero that fought at the Battle at Kings Mountain.
MS. LeGRAND: You need to be in the SAR.
SENATOR ALEXANDER: I have an old picture I will get you.
CHAIRMAN SENATOR PEELER: Okay, good.
That's what she said.
What's the desire of the Committee?
REPRESENTATIVE WHITMIRE: Motion for a favorable report.
SENATOR ALEXANDER: Seconded.
CHAIRMAN SENATOR PEELER: Seconded.
All in favor raise your right hand.
It's unanimous.
You are found to be qualified.
MS. LeGRAND: Thank you.
CHAIRMAN SENATOR PEELER: Thank you, ma'am.
I tell you, I know the next -- we are supposed to have Francis Marion, but I would like to skip to the South Carolina State University Fifth Congressional District. So if there is no objection, we will go to those now. South Carolina State, Fifth Congressional District, under Tab E.
REPRESENTATIVE WHITMIRE: And then we will come back to it?
CHAIRMAN SENATOR PEELER: Then we will come back to it.
Tab E, Tammy Adams Kelly from Sumter.
MS. Kelly.
Welcome.
MS. KELLY: Thank you.
Do you swear to tell the truth, the whole truth, and nothing but the truth, so help you God?
MS. KELLY: Yes, sir.
CHAIRMAN SENATOR PEELER: Thank you.
Would you like to share with the Committee why you would like to serve on the South Carolina State Board?
MS. KELLY: I sure would. Thank you for allowing me the opportunity to share with you today.
My desire to be on the board stems from a long, long history of love and passion for South Carolina State University through my husband, who is a 1986 proud bulldog. I also have two children who are matriculating at South Carolina State University, and that love that they exude for the university is just phenomenal, and seeing what they have accomplished as young people at the university is just awesome.
Now, with the leadership at the university, I think my role as a board member would be to help make sure that the university is there for the next 100 years. What is going on today will magnify itself in growth and development for the university.
And I would like to use my leadership skills to help grow the university and retain students so that it will be there forever.
CHAIRMAN SENATOR PEELER: Thank you.
Questions or comments from members of the Committee?
Mr. McCoy.
REPRESENTATIVE McCOY: Thank you, Mr. Chairman.
Ms. Kelly, I appreciate your time and appreciate you coming in front of us today, and I appreciate your willingness to serve as well.
Can I ask you a brief question about your -- I understand that you serve on the Sumter County Economics Development Board.
MS. KELLY: Yes.
REPRESENTATIVE McCOY: What does that mean?
MS. KELLY: My service on the economic development board, I'm a board member on the board, and this is my second term. And basically I help our executive -- our executive for our development board -- well, the development for Sumter County, ensure that Sumter is number one on the minds of anyone who wants to do business in South Carolina. And we help ensure that happens by working with our board and also our executive director for economic development.
And if you have not -- I'm sure you have heard about our huge investment in our economy by Continental Tire. We are on -- the one in Sumter, and it is because of what we do as a board.
REPRESENTATIVE McCOY: I think that's excellent work, and I am aware of that. So that's kudos to your board for bringing Continental Tire to town.
Is that a position that is -- and just because I don't know, is it something appointed by your local delegation or county council? How does that work?
MS. KELLY: I'm actually appointed by our mayor. I am the city representative on the board, and it is a volunteer position.
REPRESENTATIVE McCOY: Perfect. I think that your qualifications with the economic development board would be a huge asset to the board here as well. So thank you for offering your services.
CHAIRMAN SENATOR PEELER: Thank you.
Martha indicates that would not be dual office.
MS. CASTO: Since she is appointed by the mayor.
CHAIRMAN SENATOR PEELER: Senator Alexander.
SENATOR ALEXANDER: Good afternoon.
MS. KELLY: Sure.
Access to public education, we take for granted that everyone has a -- everyone does have an opportunity to attend an university. However, the university has to be available and accessible to students.
I grew up in a very rural area. I grew up in Dorchester County; and of course, I live in Sumter County now. But as a young girl growing up and not having very much, I did not know -- and also being the first person from my family to actually attend college -- I graduated from the University of South Carolina. And my passion has always been that I do not want to see someone who has the opportunity and missed the opportunity to go to college. Like -- and I know you -- you saw my statement. And I told you about my father.
My father was a brilliant man; and had he had that opportunity to go through to college, he would have gone. And I think that there are a lot of children who are missing that opportunity because without -- without having the proper counseling and access. That university -- South Carolina State University needs to be in Orangeburg and it needs to stay there because of the community that benefits from it.
SENATOR ALEXANDER: Thank you, Mr. Chairman.
CHAIRMAN SENATOR PEELER: Mr. Hayes has a comment or question.
SENATOR HAYES: Thank you, Mr. Chairman.
Thank you. I appreciate your willingness to serve on the board. I am sure you are aware because of your history with the board, recently South Carolina State has had some problems. The -- I think there have been some charges that have ended up in some criminal charges down there with some of the administrators or board members. I think all the incumbents were defeated this past year when they came up for election down at the board, which is most unusual in the General Assembly.
What do you see as your role as -- if you are elected as a board member in relation to the administration? And that's the first part of that.
The second is, What do you think needs to be done to keep South Carolina State moving in the right direction?
MS. KELLY: Well, I will answer the first part of the question first.
The first thing that needs to be done, obviously, is to support the administration, support what President Elzey is doing. And the number one problem right now -- obviously there are a lot of budget concerns there -- is money.
You know what? I run a business. I run my own business. There are always going to be challenges, and I like to say, Challenges are opportunities. But number one, as a board member, I would like to see that the school focus on making sure that they grow the student enrollment -- it can be done -- and also work towards those efforts as far as retaining those students that are there.
It's a wonderful opportunity, and the story just needs to be told.
I understand what's happened with the -- what's happened in the past. Every organization goes through bad times. That's the reality of it. That's the reality, but now it's time to move forward and really, really work towards making it the place that it can be.
SENATOR HAYES: Thank you.
CHAIRMAN SENATOR PEELER: Senator McGill.
SENATOR McGILL: I will move for a favorable report.
CHAIRMAN SENATOR PEELER: Motion for a favorable report.
REPRESENTATIVE McCOY: Second.
CHAIRMAN SENATOR PEELER: Seconded.
All right. Any other questions? We are ready to vote.
All in favor raise your right hand.
Thank you. Unanimous.
MS. KELLY: Thank you so much.
CHAIRMAN SENATOR PEELER: Thank you for your willingness to serve.
Ms. Redish is not here yet, so let's go back to Francis Marion, Tab C. Mary Mappus Finklea, At-Large Seat Number 9.
Is the green light still shining?
MS. FINKLEA: It is.
CHAIRMAN SENATOR PEELER: Thank you. Welcome.
Do you swear to tell the truth, the whole truth, and nothing but the truth, so help you God?
MS. FINKLEA: I do.
CHAIRMAN SENATOR PEELER: Would you like to share with the Committee why you would like to serve on the Francis Marion Board?
MS. FINKLEA: Yes, I would. Thank you very much.
Good afternoon. It is a joy to be here with you today. To answer in a word, civic duty. I feel that it is important to be engaged in your community. I live in Florence, and this is hometown territory in the sense that what happens on the campus is -- affects the community. I feel like public education affects us all and that we want the best for Francis Marion.
I am excited about the new partnership with Mt. Pleasant as we continue to think about growing and expanding. So it is a nice time to see how the vision of the board can really connect with people on the ground and make a difference in the lives of others.
I appreciated what the other lady spoke about just a moment ago, about first-generation college students. Francis Marion, of course, engages people who -- many of which might not normally be heading to a college or university setting. We do that well, and I'm excited about seeing how we can continue to excel.
Thank you.
CHAIRMAN SENATOR PEELER: Thank you.
I always feel a right strange, I guess, swearing in a pastor; but you answered it quite well.
MS. FINKLEA: That's right.
CHAIRMAN SENATOR PEELER: Oh, me.
What's the desire of the Committee?
REPRESENTATIVE WHITMIRE: Favorable.
SENATOR McGILL: Second.
CHAIRMAN SENATOR PEELER: Motion is for a favorable report. A second is heard.
All in favor raise your right hand.
It is unanimous.
Thank you very much.
MS. FINKLEA: Thank you.
CHAIRMAN SENATOR PEELER: Now we will go back to South Carolina State University, Fifth Congressional District, under Tab F, Ms. Carlotta Denise Redish.
Ms. Redish, if you would, come forward.
MS. REDISH: Yes, it is.
CHAIRMAN SENATOR PEELER: Good. If you would, take a seat.
Do you swear to tell the truth, the whole truth, and nothing but the truth, so help you God?
MS. REDISH: I do.
CHAIRMAN SENATOR PEELER: Thank you.
Would you like to share with the Committee why you would like to serve on the South Carolina State Board?
MS. REDISH: Yes, but first let me say, thank you, Chairman and fellow committee members, for affording me this opportunity to participate in the screening process.
I am a life-long educator. I was born and raised in Cherokee County. I got -- I received a great education there. And when I was approached to apply to serve on the board at South Carolina State University, I thought long and hard about it because I'm familiar with what has been going on at the university. But I do believe that my educational and professional experiences will add value to that board.
I have served in various administrative capacities in public school districts in South Carolina and larger urban school districts in Los Angeles and Atlanta before returning back to South Carolina. And I came back here because I love Gaffney. I'm from Gaffney, and that's my home.
Also, professionally, I have had the opportunity to manage and direct and supervise personnel, maintenance, finance, food services, custodial and other departments. So I really do believe that those experiences, combined together and in working collaboratively in conjunction with the other board members in an effort to adhere to existing policies, will prove to add value to the university.
But more importantly, I want to say that the -- my successes that have come to me professionally, I did not achieve the positions that I served by myself. I have been successful through working collaboratively together with my peers and educators across this state.
I have served on the Executive Committee for the Instructional Leaders Roundtable for SCASA, and that's a position that I was approached about running for, and my peers in those positions across the 85 (sic) counties here elected me to that position.
I have also served and was elected to serve as president of the Personnel Roundtable for the Old English Consortium which meets -- we used to meet in York. That's composed of Chesterfield, Lancaster, Rock Hill, York, Cherokee, Clover, and Fort Mill.
So I have experienced a great deal of successes in the realm of education, but it's been through the encouragement and with the support of my peers and through working together with them.
I have also been approached and had the privilege of serving on communities for several local colleges. Primarily I was on the advisory board for Spartanburg Community College. At that time Dr. Para Jones was the president. I also served on an advisory committee at the University of South Carolina Upstate.
So I do believe that I will add value to the board. I do believe that my professional and educational experiences will enable me to make impartial and very well-informed decisions as we strive -- should I get the seat, as we strive to return South Carolina State University to the status that it once had.
And that university was once a -- a stellar university in this state, and it was very, very well respected throughout these United States. It is still a good school where you have dedicated facility and staff members there who are doing a good job. They are working very hard. And to put it in the words of former Supreme Court -- United States Supreme Court Justice Thurgood Marshall, I believe they are doing the best they can with what they have. And I would love to have the opportunity again to participate in the governing process there on that university by serving on the board of trustees.
CHAIRMAN SENATOR PEELER: Thank you.
Mr. Whitmire.
REPRESENTATIVE WHITMIRE: Thank you for your willingness to serve.
I'd like to thank both of you ladies. It is really a pleasure to have, in my opinion, outstanding candidates for SC State. They have been needing some good leadership for quite awhile. It is kind of a shame -- I wish both of you were running for separate seats.
CHAIRMAN SENATOR PEELER: I was thinking the same thing.
REPRESENTATIVE WHITMIRE: Let me ask you something else.
Are you familiar with the inner workings of SC State? Why do you think it went from up here to down here, in your opinion?
MS. REDISH: Well, I reviewed the SACS accreditation report. I'm currently reviewing a SACS review team. We might be looking at a school in the district of Hilton Head Island in March of next year.
I looked at the findings in the report, and the report cited board governance issues. And I think the most important thing for any board member within any institution or any organization, the thing that we have to keep in mind is that each board member has a vote, and that one vote does not constitute any unequal level of power. That one vote's -- that one vote gives us leeway and insight to work collaboratively together as a cohesive team to -- to meet our mission and our goals that have been established and are stated in the strategic plans.
You know, a strategic plan is just a road map that looks at where the university has been, where they are now, and where they are going. And I have looked at and I'm very familiar with the history of South Carolina State University.
It's -- that school has produced some of the most famous people in these United States. We have brigadier generals that have come out of State, and one I know personally. We used to bowl and skate together, and he went in the military.
And he said, Carlotta, I am going to be a general one day. Lo and behold, we know he just retired. He's a brigadier general that has just retired. We have Supreme Court justices that came out of that university.
So somewhere along the way, we've gone from being at the top of the list and being very, very stellar to -- I'm sorry, to losing sight of the mission.
The mission is providing those students with the very, very best possible education and working together cohesively and as one unit to further meet the goals of that university, particularly by adhering to policy.
CHAIRMAN SENATOR PEELER: Thank you.
MS. REDISH: Yes.
CHAIRMAN SENATOR PEELER: Senator Alexander.
SENATOR ALEXANDER: Thank you, Mr. Chairman.
Following up, I was already thinking about it when you said that last word, "policy."
MS. REDISH: Yes.
SENATOR ALEXANDER: The board sets policy.
Is it appropriate for a board to have any other -- what is your view of any other role that the board has as far as the day-to-day operation of the university?
MS. REDISH: Yes, sir.
It's the president's responsibility. President Elzey, it is his responsibility to manage the daily operations of South Carolina State University. That is what I call his sand box.
And then in the other sand box, you have board members who are charged with developing, implementing and addressing policy. They work with the president in identifying policy and working with him to adhere to those policies that have been established. But board members, again, they are to work cohesively together in the establishment, creation and adherence to of board policies.
SENATOR ALEXANDER: With your experience in the public school system and from that standpoint, is -- is it your thoughts then that any communication to -- regarding the university should go through the president rather than directly with other folks throughout the university system?
MS. REDISH: Yes. There is -- I do believe in following protocol because -- in doing so, if we all do that and we stay in our -- we stay in our lane and we follow protocol, then we will avoid the pitfalls that come often with miscommunication, misdirected communications.
The president, again, is charged with managing the daily operations. And communications should go to the president and from the president to the board. And specifically, the president of the board and the president of the university should be, in essence, hooked at the hip because they should be able to communicate any time of the day regarding any matter or any situation without being pressured or influenced to sway their true thoughts and feelings and ideals regarding any particular matter at hand.
SENATOR ALEXANDER: Thank you, Mr. Chairman.
CHAIRMAN SENATOR PEELER: Senator McGill, anybody else?
As the screening committee, our charge is to sift through the candidates, I guess.
MS. REDISH: Yes.
CHAIRMAN SENATOR PEELER: And one thing, it is not just you, but several of our candidates for these boards of trustees, their driving record.
MS. REDISH: Oh, did I?
CHAIRMAN SENATOR PEELER: From '08 to '12.
MS. REDISH: Yes.
CHAIRMAN SENATOR PEELER: I know that shouldn't have a bearing on how you are going to vote or if you are fortunate enough to be elected. But -- and we have talked about this before. How many is too many? Is two too many? Is three?
MS. REDISH: But I can explain.
CHAIRMAN SENATOR PEELER: Okay. Explain.
MS. REDISH: I recently purchased a new car, and my goal was not to buy a fast car. I wanted to buy an efficient car that had a luxury feel and economical car for me and my daughter. Well, that car, it turned out to be a very fast car. So I think two of the tickets I obtained were within the first -- well, one, first three weeks or a month within purchasing that car.
The second explanation I have, and I will give you a good example. One night I was leaving from a revival in the Duncan, Lyman, Wellford area. And I was in a church, leaving a church that was out in a rural area that I was not accustomed to, and I had just changed my contact lenses to multi-lens, where one is for distance and one is for vision. And I just -- it was in a dark area and no lights, and I didn't come to a complete stop at a railway crossing.
And then the other tickets were -- excuse me.
The other tickets I got in my travels from meetings across the state, and sometimes I just -- I didn't remember where the speed traps were.
CHAIRMAN SENATOR PEELER: I understand.
MS. REDISH: Not speed traps, but I just didn't recall where you would have a high population of highway patrolmen sitting and monitoring those areas.
CHAIRMAN SENATOR PEELER: I understand.
Most of them is in Senator McGill's district.
SENATOR McGILL: You would have been better off to say I have a heavy foot.
CHAIRMAN SENATOR PEELER: Well, I was going to say, that fast car, you know, it don't move unless you put your foot on the gas.
But anyway, that's the only thing I found I had to fuss at you about.
MS. REDISH: I am sorry. I apologize.
REPRESENTATIVE WHITMIRE: Slow down.
MS. REDISH: I haven't had a ticket in a while, though.
CHAIRMAN SENATOR PEELER: What's the desire of the Committee?
REPRESENTATIVE McCOY: Move as favorable.
CHAIRMAN SENATOR PEELER: The motion is a favorable report.
REPRESENTATIVE WHITMIRE: Second.
CHAIRMAN SENATOR PEELER: A second is heard.
All in favor raise your right hand.
And it is unanimous.
Thank you for your willingness to serve. I will echo Mr. Whitmire's comment. I wish both of you would serve.
REPRESENTATIVE WHITMIRE: The one that is not successful, please reapply.
MS. CASTO: Two at-large seats coming up.
REPRESENTATIVE WHITMIRE: Two at-large coming up, so remember that.
CHAIRMAN SENATOR PEELER: It is refreshing to know that we have candidates of y'all's caliber. Really, true.
MS. REDISH: Thank you very much.
REPRESENTATIVE WHITMIRE: Very encouraging.
CHAIRMAN SENATOR PEELER: Subject to the call of the chair, we will stand adjourned.
On motion of Senators PEELER, SETZLER, ALEXANDER, ALLEN, BENNETT, BRIGHT, BRYANT, CAMPBELL, CAMPSEN, CLEARY, COLEMAN, CORBIN, COURSON, CROMER, DAVIS, FAIR, GREGORY, GROOMS, HAYES, HEMBREE, HUTTO, JACKSON, JOHNSON, KIMPSON, LEATHERMAN, LOURIE, MALLOY, LARRY MARTIN, SHANE MARTIN, MASSEY, MATTHEWS, McELVEEN, McGILL, NICHOLSON, O'DELL, PINCKNEY, RANKIN, REESE, SCOTT, SHEALY, SHEHEEN, THURMOND, TURNER, VERDIN, WILLIAMS and YOUNG, with unanimous consent, the Senate stood adjourned out of respect to the memory of Ms. Vanessa Ellen Collier of Gilbert, S.C. Vanessa was a beloved member of the South Carolina Senate staff where she worked for 34 years. Vanessa spent her entire career working in a variety of capacities for the South Carolina Senate including working part-time as a page, full time as a telephone switchboard operator, as a legislative aide and as a page supervisor for many years. Vanessa was a mentor and role model to countless young college students over the decades. She enjoyed spending precious time with family and friends doing what she loved most; boating, fishing, gardening and reading. Vanessa lived life to the fullest and always put others first. She will be greatly missed by her friends, family, and co-workers.
and | 2014-09-18T01:41:26 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4038853049278259, "perplexity": 7659.105539655573}, "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-2014-41/segments/1410657125113.78/warc/CC-MAIN-20140914011205-00015-ip-10-196-40-205.us-west-1.compute.internal.warc.gz"} |
https://bossmaths.com/binomialdistribution/ | # Visualising the binomial distribution
This applet lets you see the probability of each possible number of successes, $$X$$, out of $$n$$ trials where the probability of success on each trial is $$p$$. You can also show the cumulative probabilities by ticking the box. Adjust $$x$$, $$n$$, and $$p$$ using the sliders.
<
With thanks to Constantinos Koudounas, whose Binomial distribution worksheet is available here. Material modified and embedded here under the CC-BY-SA 3.0 license. | 2022-08-11T06:20:18 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8944005966186523, "perplexity": 599.7628103930163}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882571234.82/warc/CC-MAIN-20220811042804-20220811072804-00558.warc.gz"} |
http://quarknet.fnal.gov/forms/sampresearch.html | ### Research Statements from Successful QuarkNet ProposalsFebruary, 1999
#### Boston University
This is the Boston University part of a proposal for a joint site with Northeastern University.
We outline two possible projects, which will be chosen according to the interests and time constraints of the teacher. The primary mentor for the teacher assigned to BU will be Prof. U. Heintz. Mentoring responsibilities at Fermilab will be shared with Prof. D. Wood from Northeastern University.
Project 1:
==========
Experience & skills: some experience with instrumentation and the use of a computer is useful. The teacher will be instructed in the use of the software emplyed to control the instrumentation.
Project title: Irradiation Studies of Silicon Microstrip Detectors
Mentor: Ulrich Heintz
Narrative Description: D0 is constructing a Silicon Microstrip Tracker for Run II. During Run II, the silicon detectors will be exposed to radiation doses of about 1 Mrad. This exposure will change the characteristics of the detectors. The bulk material will change from n-type silicon to p-type. After this so-called type inversion, the depletion voltage will increase with the radiation dose. The useful lifetime of the silicon detectors is determined by the dose at which the depletion voltage reaches the maximum value at which the detectors can be biased without breakdown. It is thus important to study how the characteristics of the detectors change with dose.
During this project, we will use the radiation source at U Mass, Lowell to irradiate prototype silicon detectors with neutrons. The properties of the detectors will be measured before and after irradiation. The teacher would be involved in testing the detectors using a probe station and computer controlled measurement instruments, preparing the detectors for the irradiation, developing a computer program to monitor the detectors during irradiation, and the analysis of the data. The teacher is expected to document the results in the form of a D0 internal note.
Where will the teachers spend the bulk of their research time? Boston
Project 2:
==========
Experience & skills: some experience with instrumentation is useful. Experience with excel and general idea about databases is useful.
Project title: Quality Control of Silicon Microstrip Detectors
Mentor: Ulrich Heintz
Narrative Description: D0 is constructing a Silicon Microstrip Tracker for Run II. This device will consist of some 700 silicon detectors. These detectors have to be carefully characterized before they are incorporated into the tracker. Using a semiautomatic probe station, capacitances, breakdown voltages and leakage currents are measured for the approximately 1000 strips on each detector. Based on the results of the tests, detectors are either rejected or accepted as production grade devices.
We expect that construction of the detector will be well under way in summer 1999. During this project, the teacher will operate the computer controlled test setup, which consists of a probe station and measurement instruments. The teacher will acquire data about each detector, and develop criteria to classify the detectors. He/She will develop software to implement these criteria and enter the information into a database for later use in the analysis of the data from the tracker. The format of the data entries will be chosen in consultation with researchers involved in the project. The teacher will document the results in the form of a D0 internal note which will act as a reference for future users.
#### Florida State University
Within the framework of our group's contribution to the Dzero experiment at Fermilab, there are many research projects in which high school teachers could make a worthwhile contribution and at the same time learn something interesting. All of them require familiarity with computers and/or the willingness to learn. We would teach them whatever they need to know and/or provide them with opportunities to acquire the necessary skills. We plan to engage our high school science teacher colleagues in well-defined roles in these projects, depending on their tastes and predilections, and they will work together with faculty members, postdoctoral fellows and graduate students.
We are working on a major project to build a device, called the Silicon Track Trigger, to identify online the tracks produced by particles containing b-quarks. An important goal of our group is to develop a fast algorithm to find clusters of hits, from which the tracks can be made. To aid in the optimization of this algorithm, we plan to develop a simple visualization tool, based on readily available software, to display the hits and clusters. We also need a way to simulate the data stream that will enter the hardware processor in which the algorithm will be executed. We have begun work on such a simulation and we expect this will provide valuable opportunities for our science teacher colleagues to learn about algorithm development and testing. We shall also begin work on the design and prototyping of programs to monitor the status of some aspects of the Silicon Track Trigger. Our principal tools will be the high-level object-oriented language python and its associated software modules. In all of these projects, the high school teacher could play an important role and make a clear impact. The principal mentors for these projects would be Harrison Prosper and Horst Wahl.
Another area where the help of a high school teacher would be welcome and useful for both sides is the simulation of physics processes of interest in the future exploitation of the D0 detector, and connected to this, the development of search strategies for "new physics". The teacher could help in running existing software packages to generate events, simulate the response of the D0 detector to these events, and interpret the results with the aim of understanding how to optimally recognize these interesting events, and how to distinguish them from the less interesting "background". The principal mentors for this would be Susan Blessing and Laura Reina.
#### Langston University
Project Title: D-Zero Experiment Remote Visualization project
We are proposing to establish a Quarknet site at Langston University in collaboration with North East Academy High School and Millwood High School in the Oklahoma City area.
This collaboration will involve two professors at Langston University, Tim McMahon and John Coleman, and two teachers at the local High Schools, Rosemary Bradley at North East Academy and Larry Wray at Millwood.
North East Academy is a "magnet" school located and operating in the Oklahoma City school district. This school attracts the brightest students from the Oklahoma City area through an entrance exam and is tuition free for the students that go there. The school specializes in Health, Science and Engineering and has advanced placement for physics, chemistry and statistics to name a few. The school has an ethnically diverse student population of 800 students comprising approximately 60% African American, 5% Hispanic, 25% Caucasian and 10% Asian. (School brochures are attached)
Millwood High School is located inside the Oklahoma City district and has a student population of approximately 400. The school has a high university placement ratio with 57% of the students attending college and a student population of 99% African American. They offer advanced placement for physics B and chemistry. The school has received numerous awards for academic achievement. (School brochures are attached)
Langston University is an Historically Black College and University (HBCU) with an undergraduate population of about 4000 students comprising an ethnically diverse ratio of 55% African American, 40% Caucasian, 2.5% Native American and 2.5% Hispanic. Langston University is a land grant college with the main campus located about 40 miles from Oklahoma City. The University has extension campuses in Oklahoma City and Tulsa. John Coleman has for the past 5 years coordinated a Summer Science Academy at Langston University for high school sophomore, juniors and seniors. The Academy is designed to teach physics, math and science at the college level.
For the summer program here at Langston University the two High School teachers will work with the Langston professors for the majority of the eight weeks at the main campus. The teachers will work on some ongoing projects with the Remote Visualization software under development with the D-Zero Experiment at Fermilab. Attached to this proposal are some figures of a "Virtual Control Room" (VCR) remote visualization program written in the JAVA programming language which would allow researchers, teachers and students to remotely view the ongoing operations of the experiment dynamically. Data on the different screens is updated both automatically and through user interaction. The two High School teachers will be helpful on this project in several ways. They will be an invaluable source of help in evaluating the functioning of the program in terms of ease of use, features, accessibility for students and ideas for features to include in the client software. We envision that a VCR for the D-Zero experiment will have two versions: one for experts and scientists on the D-Zero experiment and another version for the public, High School students in this case. The teachers will during the course of the summer be given some tutorials on JAVA and VRML and may have some opportunity to develop some small pieces of code in either of those languages. VRML is much more accessible than JAVA and they probably would be able to make some good contributions to the VRML scene of the D-Zero experiment (please see attached Figures or see the figures at http://possible.lunet.edu/~mcmahon/projects.html). We envision that out of this experience may come some products which will be useful for the later phases of the Quarknet program, providing software which will fulfill the mission of allowing High School students to view and interact from their location the operations of the experiments at Fermilab and CERN.
#### Michigan State University
The MSU high energy physics group is actively involved in 3 experiments: CDF and D0 at Fermilab and ATLAS at the LHC. Much of the activity for this project would be related to detector construction for ATLAS. At MSU, we will be instrumenting and testing 32 10 ton modules that will form a portion of the ATLAS hadron calorimeter (the "Tilecal"). The instrumentation will include inserting scintillator tiles into the modules, coupling wavelength shifting fibers to the tiles and then routing the fibers to the phototubes. The teachers will then be involved in testing the modules using cosmic rays, UV light sources and/or radioactive sources. The teachers will initially be involved in developing software for the data acquisition system. As we have done in the past, there will be a great deal of pedagogical interaction between the MSU physicists and the teachers, so the teachers can gain a better understanding of the physics goals of ATLAS and how their efforts fit in. It is likely that (independent of this program) that we will also seek out one or two area high school students to also participate in this work.
In parallel to this effort on the Tilecal modules,we will also be working on special scintillator planes for ATLAS that will be designed, constructed and tested with the participation of the teachers. We will also continue our work on physics demonstrations.
The initial work described above begins this summer and continues until the fall of 2002. A great deal of work is also going on at MSU relating to the two Tevatron experiments, CDF and D0. It is possible for the teachers to be involved in this as well.
Much of the time would be spent at MSU, but with the options of frequent trips to Fermilab (in addition to the initial stay).
#### Northeastern University
Project title: Commissioning the DZero Muon Detectors with LED pulses and Cosmic Rays
Mentor: Darien Wood
Note: mentoring at Fermilab will be shared between Northeastern (Wood) and Boston University (Heintz) QuarkNet leaders.
Before the DZero detector rolls back into the Tevatron beam in the year 2000, all of the muon detectors and their associated electronics must be deployed and tested in situ. These detectors include 94 large proportional drift tube chambers, 48 wedges of mini-drift tube chambers, and about 6000 scintillation counters. One of the best ways of verifying that the detectors are working properly is to use them to observe the natural flux of cosmic-ray muons from space. Another method is to send light pulses from LEDs along optical fibers to the scintillators using a specially designed calibration system.
We anticipate that this commissioning effort will be well underway in the Summer of 1999. A teacher could work with physicists on setting up the detectors, examining the cosmic ray data and pulser data, and attempting to locate and correct any problems observed with the detectors. A teacher with good software skills could develop programs to automate the calibration or to display the results. The teacher would be expected to document the test results and the tools developed in the form of a "D0note" which would become part of the reference material for the upgraded detector.
#### The State University of New York - Stony Brook
Alignment of the D0 Silicon Detector (John Hobbs) The project is directly related to the use of the D0 silicon tracker: for precision vertexing, finding of separated vertices (decay vertices), and triggering on tracks stemming from such decays. Two projects (within the context of Hobbs' work):
(1) Working on the prototype alignment process either the mathematics or coding.
(2) Understanding the assembly precision for use in the STT design.
A connection between these nitty-gritty projects and general concepts is the desire to use distance-of-flight as a measure of particle lifetime. To measure the distance-of- flight precisely, we must have a well-aligned detector. The bulk of this work would be done at Fermilab - in cooperation with postdoc Wendy Taylor, with follow- up/continuation at Stony Brook.
Trigger Algoritms for the D0 Preshower Detectors (Grannis) Projects that might involve a suitable teacher would center on the trigger activities: the writing and testing of preshower detector Level 1 algorithms, running simulations of various choices of AND/OR terms and of specific triggers to find maximum background rejection and optimal signal acceptance. I'd expect that the teacher would work closely with our postdocs Arnaud Lucotte, Mrinmoy Bhattacharjee and others in the trigger trade, all located at Fermilab. One would hope to involve a teacher also some in a particular physics topic that directly relates to trigger work -- e.g. measurement of sin(2beta), B mixing, top, susy searches, etc. The point is not so much to get help on these topics, as to give the teacher a connection to the end physics product of the research.
ATLAS Calorimeter: HV Feedthroughs (McCarthy) Stony Brook is designing and prototyping HV feedthroughs for the ATLAS Liquid Argon calorimeter. A participating teacher, located at Stony Brook, would participate in the CAD design, prototype testing (Ultra high vacuum techniques, pumps, pressure gauges, computer interfaces), and help with the High Voltage testing of the device in argon gas, where one would learn about HV beakdown, corona measurement, materials, etc. The greater context of the project would be provided by excursions to Brookhaven, where the US-ATLAS center for liquid argon calorimetery is located. Follow-up would be he continued involvement of the teacher in the construction and testing of the feedthroughs at Stony Brook, and possibly extend into some level of participation in other aspects of the Liquid Argon calorimetery at Stony Brook or Brookhaven.
Particle Tracking with Driftchambers (Rijssenbeek) The D0 Central Driftchamber (CDC) was build by the Stony Brook group. This detector is now retired, and new tracking detectors are under construction for particle tracking in D0. This project aims to revive a prototype CDC module for educational purposes: the passage of cosmic ray muons at sea-level, the detecton of charged particles, and the advanced electronics needed for the detection. The teacher would spend time at Fermilab to make the readout of the detector work: using two 16-channel D0 Flash ADCs connected to a PC. Assistance would be provided by Fermilab-based experts (Bob Angstadt et al.). Afterwards, the project would continue at slower pace: the readout would be set up at Stony Brook, and connected to the CDC prototype. Once in working order, the setup could be given on loan to local High Schools.
The Precision Measurement of the W mass (Rijssenbeek) Working with Rijssenbeek and graduate students Dennis Shpakov and Zhong-Min Wang at Fermilab, the teacher would develop software for the measurement of the W mass with the new D0 detector. Starting from the basics of simulation techniques, the teacher would study the existing measurement techniques and modify the packages to work with the new D0 detector configuration for run II. Follow-up would consist in continued low-level involvement with this important measurement.
#### The University of California at Santa Cruz/Santa Cruz Institute for Particle Physics
Teachers will be able to choose and do one hardware and one software project:
1) New Detector Materials (SiC, etc) Hartmut Sadrozinski / Teela Pulliam
We are looking for new materials which have a larger band gap than silicon but are grown as single crystals. One new material is silicon carbid SiC. We will do I-V, C-V curves to characterize the DC behavior. Then we will do charge collection studies with light transients and charged particles.
2) ATLAS Comparator Chip Tim Dubbs / Abe Seiden
The ATLAS project uses for the readout of the silicon detectors a combination of a bipolar comparator chip and a CMOS pipeline to store the data. The chips are tested in a realistic way and the response of the different channels compared. In addition, radiation hardness of single test structures and full chips are tested
3) GLAST detector testing Hartmut Sadrozinski / Wilko Kroeger
One of the challenges of the GLAST instrument development is the requirement of Space qualification and reliability. We are developing methods to assure the proper functioning of the large numbers of detectors before we start assembling them to larger subsystems. This includes automation of I-V and C-V curves, and dimensional measurements.
4) GLAST ASIC Testing Robert Johnson / Wilko Kroeger
The readout ASIC's for the GLAST silicon detectors are highly integrated and perform data reduction like zero suppression. Careful testing is needed to ascertain proper functionality. This will be done with a probe card on an automatic probe station.
5) GLAST Tray development Gwelen Paliaga / Bill Rowe
The GLAST instrument will be build modular, consisting of 25 towers, which in turn consist of 16 trays which carry the silicon detector. These trays will be assembled with an automatic bonder, using special glues, and the integrity of the design tested with vibrations and temperature cycling., to find out if the wire bonds and glue joints survive.
6) GLAST Detector simulations Wilko Kroeger / Jose Hernando
The design of the GLAST instrument is based on extensive computer simulations of the performance. This is done by generating gamma-rays traversing the GLAST instrument and following their interaction with the detector material. Many issues in the optimization of GLAST will be addressed.
7) Project in Bipolar VLSI David Dorfan
David Dorfan has a special project in VLSI design using bipolar technologies, for participants with very good understanding and interest in of analog electronics.
#### The University of Indiana
For summer 1999 (or 2000), the selected high school teachers would be given their choice to work in one of three general areas: D0 Upgrade, ATLAS, or projects planned for Jefferson Lab. They could make their choice depending on both their interests and strengths. Although particular skills beyond enthusiasm and a willingness to learn are not necessary, proficiency with computers and programming could be an asset when working in areas requiring software work.
All three of the areas listed have significant construction projects physically based at Indiana University, as well as the resources and facilities to effectively contribute to software projects. It is therefore planned that the teachers would be resident at or close to the university in Bloomington, Indiana. There would definitely be trips to Fermilab related to the D0 project, and the other two areas may include trips to CERN or Jefferson Lab.
A. Upgraded D0 for Run II at the Tevatron at Fermi National Laboratory
Mentors: Prof. Van Kooten, Prof. Zieminski, Zieminska (Senior Research Scientist)
The D0 detector is being upgraded to begin running scheduled Spring 2000 at the Tevatron following the Main Injector upgrade of the collider.
The proposed software/analysis project is to evaluate expected trigger rates and efficiences for various Run 2 triggers for b-physics and supersymmetric particle searches. Both signal and background Monte Carlo simulated events would be explored. Some preliminary analysis based on small samples has been done; however, it has to be repeated with larger statistics and improved triggering schemes and Level 3 trigger evaluations included. We expect to have Level 3 software tools for muons (Indiana group responsibility) developed before summer and assistance in further development and testing of these tools would be appropriate.
Charged particle tracking at large radii is being implemented in the upgraded D0 detector through a scintillating fiber tracker. The scintillation light from these fibers, indicating the passage of a charged particle, is piped out through clear fiber optical bundle/waveguides. Self-contained hardware and testing projects are available in the fabrication, testing, and commissioning of these fiber optic "jumper cable/waveguides" (Notre Dame University is constructing the longer waveguides preceding these cables). Software projects involved in data acquisition, increased automation, and the archiving of test results in databases are also available.
B. ATLAS at the Large Hadron Collider (LHC) at CERN
Mentors: Profs. Ogren, Gardner, Luehring (Senior Research Associate), Rust (Senior Research Scientist)
The ATLAS detector is being built in preparation for data collection at the Large Hadron Collider scheduled to begin in 2005. Indiana is part of the Inner Detector Group and are developing the barrel part of the transition radiation tracker (TRT). Straw tubes provide tracking points and the transition radiation can supply particle identification. About half of the barrel detector modules will be built at Indiana University. The group also plays a leading role in the computer simulation of the ATLAS tracking system.
Projects include assisting physicists and staff in the construction of transition radiation modules for the ATLAS detector and the testing of complete TRT modules using cosmic ray and radioactive source tests. Software projects include assisting physicists with the computer modeling of the operation of the TRT modules and help with the computer display of results.
C. Task-D at Thomas Jefferson Accelerator Facility (TJAF)
Mentors: Prof. Dzierba, Teige (Research Scientist)
Task-D is involved in experiments utilizing the photons from the continuous electron beam available at TJAF. A current experiment explores the rare decays of photoproduced phi mesons and a future project is to build a new experimental hall and detector at TJAF to study the photoproduction of mesons.
Projects would include working on tests of a heavy-liquid calorimeter using cosmic rays, evaluation of phototubes for a time-of-flight system, and helping with engineering issues in moving a large superconducting solenoid from Los Alamos to Jefferson Lab.
#### The University of Iowa/Iowa State University
QuarkNet Proposal for One Iowa Center for Experimental Work Primarily on the CMS Detector at the Large Hadron Collider
submitted jointly by Profs. N. Akchurin, E.W. Anderson, J. Cochran, J.M. Hauptman, and Y. Onel
University of Iowa, Iowa City, IA 52242
Iowa State University, Ames, IA 50011
Abstract
We are experimentalists working on the CMS detector at the LHC and on the D0 detector at Fermilab for Run II. We propose to sponsor high school physics teachers during the next two summers on experimental work on the Hadronic Forward (HF) calorimeters of the CMS detector. This work will involve testing of the {\it hanging file} calorimeter in Ames and possibly {\sc geant} simulations of its performance. The work in Iowa City will concentrate on the construction of the fiber bundles and phototube readout of the preproduction prototype of the HF module. The presence of these two teachers at the two-week beam test at CERN in early September 1999 will bring their earlier work into focus where they will actively participate in data collection and analyses.
Introduction
The Iowa City group maintains a lead responsibility for the design, construction, installation and physics output of the HF calorimeters of the CMS detector at the LHC. The Ames group works closely with the Iowa City group on performance simulations and beam testing at CERN. Our groups have always been interested in education at all levels, including volunteer education at elementary schools. Our proposal below is our present idea on a profitable summer for two high school physics teachers which naturally lends itself for a rewarding curriculum development in modern physics for their students.
Proposal Specifics
The work in Ames will involve the refurbishing of the {\it hanging file} calorimeter --an earlier version of a hadronic calorimeter intended for an SSC experiment-- for CERN tests. We will install new phototubes and perform preliminary tests with cosmic rays. The single muon rate will be high enough for easy testing of connections and for a basic response calibration. The readout will probably be directly to a PC; a laptop we will buy ourselves for portability. In addition, we will write a {\sc geant} code to simulate the beam tests and benchmark the measurements for future design alterations. The {\sc geant} work also involves a simulation of cosmic muons, and thereby a direct comparison and calibration of the {\it hanging file} calorimeter before the test begins. If appropriate, one or both teachers may participate in this work. The work at CERN will involve two weeks of beam time. We expect that at this time the teachers will be sufficiently versed in the mechanical and electronic aspects of the {\it hanging file} and the HF preproduction calorimeters to participate effectively in the tests.
The work in Iowa City will involve the preparation of quartz fibers for the HF calorimeter, optical couplings and a new set of photodetectors. These components will be a part of the preproduction prototype for the HF detector which we plan to test in the beam in September 1999. One of the teachers may be involved in these tasks earlier in the summer. These tasks require some mechanical and electronics experience.
We maintain close contacts between institutions and hold monthly all-day meetings. In these meetings we discuss the progress of the entire project; from simulations to construction and to data analyses. These meetings prove very fruitful to our students and will benefit the teachers where they can hear different aspects of a scientific endeavor and also present their work as active collaborators.
The faculty in Ames are John Hauptman (CMS and D0), Walter Anderson (CMS and D0) and Jim Cochran (D0). We anticipate spending most of the summer in Ames, although we will also be travelling to meetings and experimental facilities during the summer.
The faculty in Iowa City are Nural Akchurin (CMS) and Yasar Onel (CMS). In addition, the Iowa City group maintains a large laboratory with good engineering staff.
The work at CERN will involve a detailed test of the difficult $\eta=3$ region where the end cap and the HF calorimeters come into contact. There will be additional material which will degrade the resolution of both devices. The {\it hanging file} calorimeter will mimic the HF calorimeter in these tests of the $\eta=3$ region. The separate HF calorimeter, presumably with a Russian-built iron absorber, will be tested separately. There is a lot of work to be done during these tests, and we would expect, as we do of our own personnel, that the high school teachers will be full participants and not bystanders.
The work at CERN will require release from school for two weeks during the first half of September. This is not difficult, since a typical school district already makes provision for absences of several kinds during the school year. In fact, the absence of a physics teacher for two weeks near the beginning of the term will probably be better than any other time, and the returning teacher will have lots of stories to tell his or her students of this big lab in Geneva, Switzerland.
Budget
We accept the main outlines of the present budget as outlined by Dr. Thomas Jordan in our 29 January 1999 meeting in Iowa City. We will need a guarantee of sufficient travel and {\em per diem} funds if we are to involve both teachers in the beam tests at CERN.
#### The University of Notre Dame
1. CMS Readout Boxes and Optical Decoder Units.
(Ruchti/Bishop)
Notre Dame is responsible for the optical decoding of the barrel, endcap, and outer barrel calorimeters for CMS. We are establishing a factory to build special modules to convert optical signals to electronic signals, with production beginning in September '99. In addition, we will be developing quality control devices to verify proper construction and assembly. These are optical units, so the participating teacher(s) will learn about scintillators, waveshifters, fiber optics, calorimetry, and energy and missing energy measurements. Work will be done at Notre Dame in a new lab (under development) and in a new area assigned for QuarkNet.
2. Dÿ fiber waveguide development.
(Cason/Wayne)
Notre Dame is responsible for building fiber-optic waveguide bundles for the Dÿ experiment. The effort includes construction, assembly, quality control. This work will be performed at Notre Dame in a new Dÿ Clean Lab. Participation in the cosmic ray testing of the Dÿ central fiber tracker in Lab 3 at Fermilab is also offered as part of this work. Participant(s) will learn about tracking and momentum measurement, and momentum conservation in particle physics experiments.
3. Development of a single-photon counting experiment to study particle/wave duality in double-slit interference.
(Ruchti/Sarid)
Using image intensifiers and video data acquisition connected to a PC, we will develop an experiment to reveal that the interference and diffraction pattern associated with a classic two slit experiment is built up one photon at a time. Work will be performed at Notre Dame in the new QuarkNet/CMS lab. Study of optical and quantum mechanical phenomena will be included with this work. This is anticipated to carry over into the second year to attract associate teachers to the program.
4. Construction of hand-held cosmic ray and particle detectors.
(Ruchti/Bigi)
Image intensified fiber-optic plate detectors will be built for lecture demonstrations and beam experiments. Work will be performed at Notre Dame in the new QuarkNet/CMS lab. Devices will be placed in particle beams at Fermilab and/or CERN to reveal the behavior of muons, electrons, photons and pions in fiber-optic scintillator material. Discussion of the nature of particle interations and importance in uncovering new physics will accompany this project. This effort is also expected to carry over into second and later years of the program to attract associate teachers to the program.
#### The University of Oklahoma
In order to encourage participation in Quarknet by a broad spectrum of teachers, we plan to gear our projects to areas that the teachers are familiar with or have expressed interest in learning more about. In addition, we hope to attract the best teachers possible by allowing each individual the choice of either doing a project which can be carried out in our lab at the University of Oklahoma, or one which would be implemented at Fermilab. This will give teachers the option of working with local physicists while staying in Oklahoma, or in teaming up with an international collaboration of physicists out of state. Therefore, we are proposing more projects than the number of teachers we expect to participate in the first summer. The projects are here describe only in general terms since we are still some months away from summer, making it difficult to elucidate the specific aspects of the project, and to anticipate new projects that inevitably appear. Nonetheless, the general descriptions should still be valid.
1) Testing and characterization of silicon strip detectors using electronic based tests. This is work to be carried out at the university by M. Strauss or P. Gutierrez
2) Assist in construction and alignment of silicon detector modules. Work to be carried out at Fermilab M. Strauss
3) Test charged particle tracking software. This work could be carried out either at the University or Fermilab, would be most efficient at Fermilab P. Gutierrez
4) Test and refine analysis code (software). This work could be carried out either at the University or Fermilab, would be most efficient at Fermilab P. Gutierrez
#### The University of Rochester
We propose two possible areas of research this summer. How we place the teachers this summer will depend on their individual skills. The intended placement would be one teacher per project.
Project #1: Data Acquisition at CDF, Mentor: Kevin McFarland
The CDF experiment plans to log data from the detector at a rate of approximately 20MB/s. Currently Professor McFarland's CDF group is designing and building a data hub, the portion of the data acquisition system which acts as the sole source for collecting and distributing data both to be written to tape and to be analyzed for real time monitoring of the CDF detector. In this system, it is important that many types of data monitoring take place, including both low-level monitoring of the flow of data and high level monitoring of the physics signatures in the data.
In this proposed project, the teacher will develop and refine stand-alone monitoring code to take a particular subset of the data, analyze it, and develop automated criteria for assuring the data quality without constant human intervention. The most important parts of this work involve development of algorithms for detecting unexpected results which could indicate failures. For example, if an observed data rate or the rate of an expected physics process suddenly changes, under what conditions is this "normal" and when should an alarm be sounded?
While it is optimal if the teacher has some experience or ability to quickly learn to program in JAVA for this project, the teacher can work on the monitoring algorithm development by studying data exported to a format compatible with any number of data analysis packages, including packages as simple to use as Microsoft Excel.
In studying the physics processes and statistical measures used for this work, the teacher will not only be doing useful technical work for the CDF experiment, but will also gain an appreciation for some of the basics of data analysis used in high energy physics in particular and other sciences in general. Ideally, some of the analysis algorithms and methods developed may be appropriate for analysis of detector data in the Rochester-based project in year two of the center.
Project #2: Hadron Calorimetry for CMS, Mentor: Arie Bodek
A tile-scintillating-fiber hadron calorimeter for the CMS experiment is currently being constructed at Fermilab. Professor Bodek's group is currently involved in the production of the scintillator tiles themselves, including the mechanical fiber readout.
In this project, the teacher will work on the mechanical assembly and testing of the scintillator and fiber readout. In addition to the physical assembly, the work also involves extensive quality control testing of the produced tiles. These checks using LED and radioactive sources are carried out using a computerized test-stand. After acquiring the test data, analysis will proceed using an Excel-based spreadsheet and Visual Basic package. There is also extensive development work needed for the data analysis software, which would make a good independent project supplementary to the assembly and checking work. Although some of this work can be done in Excel, more focus on the data analysis will be possible if the teacher has some experience with Visual Basic or database programming.
In addition to the technical work, the teacher will be able to learn about the design and construction of calorimetry, and will have the opportunity to learn about elements of data analysis. The opportunity also exists to follow up on this work with similar technology in a Rochester-based project in year two of the center.
#### The University of Texas at Arlington
1) Upgrade of the Intercryostat Detector(ICD) for the D0 experiment at Fermilab.
Mentor: Prof. Andy White.
This project would involve understanding the role of calorimetry in a high energy collider detector, the need to have uniform response across the detector and the physics implications, and how the ICD is used to improve energy measurement in regions of the detector. Practically, this would involve constructing and testing scintillator/fiber detector systems, and learning how to use associated electronics and data acquisition systems to study their performance. This work would also involve a visit to Fermilab to prepare for the installation of the upgraded ICD in the D0 detector.
2) Jet Energy Resolution studies for the D0 Experiment.
Mentor: Prof. Ransom Stephens.
This project would acquaint the teacher(s) with techniques used with the D0 detector/data to investigate the properties of quark/gluon jets. An understanding of the physics would be followed with work on new algorithm(s) to find jets,and measure the inclusive jet cross section. It would also involve working with actual D0 data and simulated data, and provide opportunities to visit Fermilab for physics and algorithm meetings.
3) Calorimetry for the ATLAS experiment at CERN
Mentor: Prof.kaushik De.
UTA is developing and constructing calorimeter modules for the ATLAS experiment. This project involves understanding of the physics requirements of the hadron calorimetry, energy flow in the ATLAS detector, how scintillator based calorimetry works, and how the construction of large detector elements with very tight dimensional tolerances is handled. There would also be opportunities to work on testing of elements of the calorimeter readout in the laboratory, and visit(s) to Argonne National Laboratory where assembly of the calorimeter modules into larger detector elements occurs. | 2018-10-22T14:01:11 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3571997284889221, "perplexity": 2007.770953286697}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-43/segments/1539583515088.88/warc/CC-MAIN-20181022134402-20181022155902-00087.warc.gz"} |
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# What makes banks adjust dividend payouts?
Prepared by Marco Belloni, Maciej Grodzicki and Mariusz Jarmuzek
This contribution reviews historical drivers of bank dividend payouts in the euro area. Economic literature presents three main reasons for adjustments to dividend payouts: asymmetric information between shareholders and management, the presence of agency costs, and regulatory constraints. Using a panel data approach, the article finds evidence supporting all three hypotheses. Banks lower dividends after facing a decline in profits and capital, but counterfactual simulations show that this adjustment could be small. Regulatory restrictions may therefore be warranted in the event of large expected losses or heavy uncertainty.
## 1 Introduction
Various elements of the regulatory and prudential framework are in place to constrain dividend payouts by banks. Banks remunerate their shareholders for the risks of holding bank equity through discretionary and variable dividend payouts, usually set annually by decision of a general meeting of shareholders, acting on a recommendation by the bank’s management. European regulations provide for automatic restrictions on dividend distributions, the so-called maximum distributable amount, which preserves a bank’s capital base by retaining profits when a bank falls below a pre-defined level of capital. Regulators have also introduced further restrictions, related for example to state-aid rules. The European Systemic Risk Board (ESRB) recommended that banks should not pay dividends in 2020 due to the COVID-19 pandemic and also to conserve capital for loss absorption and maintaining loan supply.
## 2 Data and methodology
Bank dividend payouts have varied in a seemingly procyclical – albeit heterogeneous – way over the business and financial cycle. They reached a high point immediately prior to the global financial crisis and declined in its aftermath (Chart 1) as regulatory requirements were tightened and banks’ profitability fell (Chart 2). However, there has been a high cross-sectional variance in every year for which the data are available, indicating that bank-specific circumstances play a large role in determining payout policies.
Economic literature suggests that dividend policies might vary due to asymmetric information, agency costs, and regulation. While the Modigliani-Miller theorem would suggest that, with perfect information and in the absence of tax distortions, dividend policies are irrelevant to the value of the firm, its assumptions may not be a fit to the specific aspects of banks. In particular, there are three main strands of literature analysing dividend policies which apply nicely to banks.[1] First, according to the signalling theory, managers may know more about the true value of their firm than investors. Dividend announcements convey information about future earnings, so more profitable banks may be expected to pay higher dividends.[2] Second, the incomplete contract strand suggests that agency costs, associated with a conflict between stockholders, management, and bondholders over dividend policy would lead larger firms to pay higher dividends,[3] while better investor protection allows investors to reduce agency costs by effectively forcing management to pay out dividends. Finally, the regulatory strand suggests that banks are constrained by regulators in their dividend payout policy, implying that better capitalised banks pay higher dividends.[4]
This article explores these hypotheses in an empirical context of the euro area banking sector, using panel data approaches. We use two complementary unbalanced panels of euro area banks. The sample of listed banks covers 69 banking groups observed over 2005-2019, with data collected from SNL Financial. The second panel covers about 1,400 banks, a large majority of which are unlisted, over a shorter period (2010-2019) and the data was collected from Orbis BankFocus. We adopted a Tobit specification to account for the fact that bank dividend payouts are truncated at zero, and also used a standard panel approach as a robustness check.[5] In order to limit the effect of outliers, and in particular to exclude banks that may be subject to non-disclosed supervisory restrictions on distributions,[6] banks with negative after-tax earnings and capital ratios were excluded.
We aimed to identify the bank-specific characteristics that explain the changes in the bank dividend payout ratio. The dependent variable was defined as a ratio of total dividend payout over total after-tax earnings. Leveraging on the existing literature encompassing the key variables explaining dividend payout, variants of the following equation were estimated in the first stage:
$D P i t = α 0 + ∑ j = 1 p α 1 D P i t - j + ∑ k = 1 l α 2 , k S H V k , i t - j + ∑ k = 1 m α 3 , k A H V k , i t - j + ∑ k = 1 w α 4 , k R H V k , i t - j + ∑ k = 1 w α 4 , k O V k , i t - j + ε i t$
where DP denotes dividend payout in bank i at time t, which is explained by signalling hypothesis variables (SHV), agency hypothesis variables (AHV), regulatory hypothesis variables (RHV), and other variables (OV).
In line with the literature, we used indicators of profitability to validate the signalling hypothesis, and bank size to validate the agency cost hypothesis. We also used a minority shareholder protection indicator, obtained from the World Bank’s Doing Business surveys, as a measure of investor protection that might provide additional evidence for the agency cost hypothesis. Capital ratios were used to seek evidence for the regulatory cost hypothesis.[7] For robustness purposes, we employed both a risk-weighted capital ratio (equity over risk-weighted assets) and a balance-sheet-leverage ratio (equity over total assets) as indicators of capitalisation, and two indicators of profitability (return on assets and return on equity). Finally, we used GDP growth and time-fixed effects to control for changes in the macroeconomic and financial environment. All dependent variables were lagged by one year to mitigate potential endogeneity associated with simultaneity and to account for the fact that bank dividend payouts are determined by shareholder meetings early in the financial year, based on financial information available for the previous year.
## 3 Results
Empirical results suggest that bank dividend payouts are related to capitalisation, profitability, size and institutional framework, supporting all three hypotheses presented in the literature (see Table 1). In line with the regulatory hypothesis, better capitalised banks tend to pay out a larger share of their profits to shareholders, although the immediate effect of an increase in the capital ratio was estimated to be relatively moderate. An increase in the capital ratio by 1 percentage point translates into the payout ratio increasing by between less than 0.2 and almost 1 percentage points, with a stronger effect for listed banks. Similarly, the results are aligned with the signalling hypothesis, as more profitable banks tend to pay out higher dividends, again with a stronger relationship identified for listed banks. The posited influence of agency costs on payout ratio is also supported by the findings, as banks operating in countries where investors are better protected by law and larger banks tend to pay higher dividends. The sensitivity of payouts to the level of institutional protections is stronger for unlisted banks, tentatively pointing to a beneficial effect of the transparency associated with listed banks on agency costs. Furthermore, higher credit risk is associated with smaller pay-outs, which may suggest that banks retain earnings to shore up their balance sheets against future credit losses. Finally, dividend policies seem relatively stable over time, particularly for listed banks. However, there is no significant relationship between the economic cycle and dividend policies.[8]
A simulation exercise shows that, in absence of the 2020 recommendation to withhold paying dividends, a significant part of bank profits would have been paid out to shareholders. Using the econometric specifications (1) to (6) and actual realisations of capital and profitability up to the third quarter of 2020, we estimated the counterfactual payout ratios for the sample of 30 listed euro area banks. The results suggested that payout ratios would be adjusted downward by most banks, although the adjustment would be small (up to 4 percentage points for most banks), reflecting the decline in profits and a broadly steady level of capital. Some of the banks projected to decrease payouts did not pay any dividends in 2020 (Chart 3). Together with a projected moderate increase in payouts by two banks, this would lead to an almost unchanged total value of distributions, of about EUR 19 billion, for this group of banks. This simulation comes with a caveat that, as the COVID-19 crisis led to economic disruptions that were unprecedented in Europe in peacetime, the relationships identified from the data may no longer hold true. Its results should therefore be viewed with some caution as the magnitude of the reduction in dividends would then, in all likelihood, be understated.
## 4 Policy implications
These results indicate that dividend restrictions may be necessary to retain capital in times of heightened economic uncertainty. Absent prudential constraints, endogenous adjustment of dividend policies by banks based on economic and financial driving factors would be expected to reflect weaker profitability and capitalization. The adjustment would be limited in magnitude and might come with a lag. Therefore, regulators may need to impose restrictions on dividend payouts with a more forward-looking view than that of the banks, especially in presence of great uncertainty about the financial impact of a developing crisis. The findings imply that it would be justified to discount future expected losses and capital constraints when designing such restrictions.
## References
Abreu, J. F. and Gulamhussen, M. A. (2013), “Dividend payouts: evidence from U.S. bank holding companies in the context of the financial crisis”, Journal of Corporate Finance, Vol. 22, pp. 54-65.
Allen, F., and Michaely, R. (2003), “Payout policy”, in Constantinides, G.M., Harris, M. and Stulz, R.M. (eds.), Handbook of the Economics of Finance, vol. 1, Part 1, ch. 07, Elsevier, pp. 337-429.
Amore, M.D. and Murtinu, S. (2019), “Tobit models in strategy research: Critical issues and applications”, Global Strategy Journal, pp. 1-25.
Ashraf, B.N, Bibi, B. and Zheng, C. (2016), “How to regulate bank dividends? Is capital regulation an answer?”, Economic Modelling, Vol. 57, pp. 281-293.
Belloni, M., Grodzicki, M. and Jarmuzek, M. (2021), “What makes banks adjust dividend pay-outs”, mimeo.
Boldin, R. and Leggett, K. (1995), “Bank dividend policy as a signal of bank quality”, Financial Services Review, Vol. 4, pp. 1-8.
Casey, K.M. and Dickens, R. (2000), “The effects of tax and regulatory changes on commercial bank dividend policy”, Quarterly Review of Economics and Finance, Vol. 40, pp. 279-293.
Fama, E. and Babiak, H. (1968), “Dividend Policy: an Empirical Analysis”, Journal of the American Statistical Association, Vol. 63, pp. 1132-1161.
Fama, E. and French, K. (2001), “Disappearing dividends: changing firm characteristics or lower propensity to pay?”, Journal of Financial Economics, Vol. 60, pp. 3-43.
Forti, C. and Schiozer, R. (2015), “Bank dividends and signalling to information-sensitive depositors”, Journal of Banking and Finance, Vol. 56, pp. 1-11.
Kent Baker, H. and De Ridder, A. (2018), “Payout policy in industrial and financial firms”, Global Finance Journal, Vol. 37, Issue C, pp. 138-151.
Kroszner, R. and Strahan, P. (1996), “Regulatory incentives and the thrift crisis: dividends, mutual-to-stock conversions, and financial distress”, Journal of Finance, Vol. 51, pp. 1285-1319.
Lintner, J. (1956), “Distribution of incomes of corporations among dividends, retained earnings and taxes”, American Economic Review, Vol. 46, pp. 97-113.
Theis, J. and Dutta, A. (2009), “Explanatory factors of bank dividend policy: revisited”, Managerial Finance, Vol. 35, pp. 501-508.
1. See Allen and Michaely (2003). Due to data limitations, the tax distortion strand was not covered.
2. Evidence that this holds true for banks can be found in Boldin and Leggett (1995) and Forti and Schiozer (2015).
3. See Fama and French (2001) for corporates and Abreu and Gulamhussen (2013) and Ashraf et al (2016) for banks.
4. See, in particular, Kroszner and Strahan (1996), Casey and Dickens (2000) and Theis and Dutta (2009).
5. Amore and Murtinu (2019) provide a discussion of methodologies suitable for corporate finance strategy applications.
6. Supervisors have powers to prohibit dividend payouts by banks that are in breach of capital requirements. It follows from this that such distressed banks may not adjust their dividend policies in line with economic factors, unlike other, more healthy banks.
7. Drawing on seminal papers by Lintner (1956) and Fama and Babiak (1968), as well as more recent evidence from Kent Baker and De Ridder (2018), the relevance of dividend history was also examined to check if and to what extent banks choose to smooth out their dividend policies.
8. Further robustness checks and extensions analysing whether bank dividend policies systematically account for expectations of future economic and financial conditions are available in Belloni, Grodzicki and Jarmuzek (2021), mimeo. | 2022-08-10T05:16:32 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 1, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.321554958820343, "perplexity": 5314.156220074678}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882571147.84/warc/CC-MAIN-20220810040253-20220810070253-00442.warc.gz"} |
http://dlmf.nist.gov/23.18 | # Elliptic Modular Function
$\mathop{\lambda\/}\nolimits\!\left(\mathcal{A}\tau\right)$ equals
23.18.1 $\mathop{\lambda\/}\nolimits\!\left(\tau\right),$ $1-\mathop{\lambda\/}\nolimits\!\left(\tau\right),$ $\frac{1}{\mathop{\lambda\/}\nolimits\!\left(\tau\right)},$ $\frac{1}{1-\mathop{\lambda\/}\nolimits\!\left(\tau\right)},$ $\frac{\mathop{\lambda\/}\nolimits\!\left(\tau\right)}{\mathop{\lambda\/}% \nolimits\!\left(\tau\right)-1},$ $1-\frac{1}{\mathop{\lambda\/}\nolimits\!\left(\tau\right)},$ Symbols: $\mathop{\lambda\/}\nolimits\!\left(\tau\right)$: elliptic modular function and $\tau$: complex variable Permalink: http://dlmf.nist.gov/23.18.E1 Encodings: TeX, TeX, TeX, TeX, TeX, TeX, pMML, pMML, pMML, pMML, pMML, pMML, png, png, png, png, png, png
according as the elements $\begin{bmatrix}a&b\\ c&d\end{bmatrix}$ of $\mathcal{A}$ in (23.15.3) have the respective forms
23.18.2 $\begin{bmatrix}\mathrm{o}&\mathrm{e}\\ \mathrm{e}&\mathrm{o}\end{bmatrix},$ $\begin{bmatrix}\mathrm{e}&\mathrm{o}\\ \mathrm{o}&\mathrm{e}\end{bmatrix},$ $\begin{bmatrix}\mathrm{o}&\mathrm{e}\\ \mathrm{o}&\mathrm{o}\end{bmatrix},$ $\begin{bmatrix}\mathrm{e}&\mathrm{o}\\ \mathrm{o}&\mathrm{o}\end{bmatrix},$ $\begin{bmatrix}\mathrm{o}&\mathrm{o}\\ \mathrm{e}&\mathrm{o}\end{bmatrix},$ $\begin{bmatrix}\mathrm{o}&\mathrm{o}\\ \mathrm{o}&\mathrm{e}\end{bmatrix}.$ Symbols: e: even integers and o: odd integers Permalink: http://dlmf.nist.gov/23.18.E2 Encodings: TeX, TeX, TeX, TeX, TeX, TeX, pMML, pMML, pMML, pMML, pMML, pMML, png, png, png, png, png, png
Here e and o are generic symbols for even and odd integers, respectively. In particular, if $a-1,b,c$, and $d-1$ are all even, then
23.18.3 $\mathop{\lambda\/}\nolimits\!\left(\mathcal{A}\tau\right)=\mathop{\lambda\/}% \nolimits\!\left(\tau\right),$
and $\mathop{\lambda\/}\nolimits\!\left(\tau\right)$ is a cusp form of level zero for the corresponding subgroup of SL$(2,\Integer)$.
# Klein’s Complete Invariant
23.18.4 $\mathop{J\/}\nolimits\!\left(\mathcal{A}\tau\right)=\mathop{J\/}\nolimits\!% \left(\tau\right).$
$\mathop{J\/}\nolimits\!\left(\tau\right)$ is a modular form of level zero for SL$(2,\Integer)$.
# Dedekind’s Eta Function
23.18.5 $\mathop{\eta\/}\nolimits\!\left(\mathcal{A}\tau\right)=\varepsilon(\mathcal{A}% )\left(-i(c\tau+d)\right)^{1/2}\mathop{\eta\/}\nolimits\!\left(\tau\right),$
where the square root has its principal value and
23.18.6 $\varepsilon(\mathcal{A})=\mathop{\exp\/}\nolimits\!\left(\pi i\left(\frac{a+d}% {12c}+s(-d,c)\right)\right),$
23.18.7 ${s(d,c)=\sum_{\substack{r=1\\ (r,c)=1}}^{c-1}\frac{r}{c}\left(\frac{dr}{c}-\left\lfloor\frac{dr}{c}\right% \rfloor-\frac{1}{2}\right),}$ $c>0$.
Here the notation $(r,c)=1$ means that the sum is confined to those values of $r$ that are relatively prime to $c$. See §27.14(iii) and Apostol (1990, pp. 48 and 51–53). Note that $\mathop{\eta\/}\nolimits\!\left(\tau\right)$ is of level $\tfrac{1}{2}$. | 2015-03-27T06:59:55 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 57, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9961544275283813, "perplexity": 4305.406949497537}, "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-2015-14/segments/1427131295619.33/warc/CC-MAIN-20150323172135-00077-ip-10-168-14-71.ec2.internal.warc.gz"} |
https://pos.sissa.it/390/100/ | Volume 390 - 40th International Conference on High Energy physics (ICHEP2020) - Posters: Higgs Physics
Tau-lepton Fake-Rate determination for the ttH coupling measurement using the ATLAS detector at the LHC
S. Mondal* on behalf of the ATLAS collaboration
*corresponding author
Full text: pdf
Pre-published on: November 17, 2020
Published on:
Abstract
A search for the associated production of a top-quark pair with the Higgs boson ($t\bar{t}H$) in multilepton final states is presented. The search is based on a dataset of proton-proton collisions at $\sqrt{s}$ = 13 TeV and an integrated luminosity of 80 fb$^{-1}$ recorded with the ATLAS detector at the CERN Large Hadron Collider.
A synopsis of the final state with two same-charge light leptons (e or $\mu$) and one hadronically-decaying $\tau$ is described in more detail. Non-prompt light leptons background is estimated from simulation, with data-driven corrections and fake ${\tau_{\rm had}}$ backgrounds are estimated using data-driven techniques.
An excess of events consistent with $t\bar{t}H$ production, over the expected background from Standard Model processes, is found with an observed significance of 1.8 standard deviations, compared to an expectation of 3.1 standard deviations. Assuming Standard Model branching fractions, the best-fit value of the $t\bar{t}H$ production cross section is ${\sigma_{t\bar{t}H}} =294^{+182}_{-162}$ fb, which is consistent with the Standard Model prediction.
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Copyright owned by the author(s) under the term of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License. | 2021-02-26T19:15:09 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6446517109870911, "perplexity": 2085.0569422706017}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178357935.29/warc/CC-MAIN-20210226175238-20210226205238-00570.warc.gz"} |
https://zbmath.org/authors/kadison.richard-v | Compute Distance To:
Documents Indexed: 104 Publications since 1951, including 8 Books 4 Contributions as Editor · 2 Further Contributions Biographic References: 5 Publications Co-Authors: 40 Co-Authors with 49 Joint Publications 1,178 Co-Co-Authors
all top 5
### Co-Authors
60 single-authored 15 Ringrose, John R. 5 Kastler, Daniel 4 Liu, Zhe 4 Singer, Isadore Manuel 3 Fuglede, Bent 3 Haag, Rudolf 3 Pedersen, Gert Kjærgård 2 Araki, Huzihiro 2 Davidson, Kenneth R. 2 Douglas, Ronald George 2 Effros, Edward George 2 Harris, Lawrence A. 2 Jørgensen, Palle E. T. 2 Kaskutas, Lee Ann 2 Laca, Marcelo 2 Markiewicz, Daniel 2 Muhly, Paul Scott 2 Pitts, David R. 2 Powers, Robert T. 2 Price, Geoffrey L. 2 Sarason, Donald Erik 2 Størmer, Erling 1 Aarnes, Johan Fredrik 1 Arveson, William Barnes 1 Blecher, David P. 1 Dixmier, Jacques 1 Doplicher, Sergio 1 Doran, Robert S. 1 Duflo, Michel 1 Feldman, Jacob 1 Ge, Liming 1 Glimm, James G. 1 Goodeare, Kenneth R. 1 Haagerup, Uffe Valentin 1 Hajnal, András 1 Hansen, Mogens Lemvig 1 Hugenholtz, N. M. 1 Johnson, Barry Edward 1 Korányi, Adam 1 Lance, E. Christopher 1 Merrill, Kathy D. 1 Paschke, William Lindall 1 Paterson, Alan L. T. 1 Robinson, Derek W. 1 Rosenberg, Jonathan Micah 1 Shultz, Frederick W. 1 Solel, Baruch 1 Takesaki, Masamichi 1 Thom, Andreas Berthold 1 Vergne, Michèle
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### Serials
10 Proceedings of the National Academy of Sciences of the United States of America 8 Communications in Mathematical Physics 6 American Journal of Mathematics 6 Annals of Mathematics. Second Series 5 Proceedings of the American Mathematical Society 4 Mathematica Scandinavica 4 Pacific Journal of Mathematics 4 Expositiones Mathematicae 3 Transactions of the American Mathematical Society 3 Notices of the American Mathematical Society 2 Acta Mathematica 2 Duke Mathematical Journal 2 Journal of Algebra 2 Journal of Functional Analysis 2 Journal of Operator Theory 2 Bulletin of the American Mathematical Society 2 Graduate Studies in Mathematics 1 Journal of Mathematical Physics 1 Arkiv för Matematik 1 Bulletin of the London Mathematical Society 1 Bulletin de la Société Mathématique de France 1 Canadian Journal of Mathematics 1 Inventiones Mathematicae 1 Journal of the London Mathematical Society. Second Series 1 Memoirs of the American Mathematical Society 1 Topology 1 Comptes Rendus Mathématiques de l’Académie des Sciences 1 Bulletin of the American Mathematical Society. New Series 1 The New York Journal of Mathematics 1 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 1 Contemporary Mathematics 1 Lecture Notes in Mathematics 1 Proceedings of Symposia in Pure Mathematics 1 Progress in Mathematics
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### Fields
68 Functional analysis (46-XX) 13 Operator theory (47-XX) 7 History and biography (01-XX) 5 Quantum theory (81-XX) 4 General and overarching topics; collections (00-XX) 2 Topological groups, Lie groups (22-XX) 1 Commutative algebra (13-XX) 1 Associative rings and algebras (16-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Probability theory and stochastic processes (60-XX) 1 Operations research, mathematical programming (90-XX)
### Citations contained in zbMATH Open
88 Publications have been cited 3,277 times in 2,543 Documents Cited by Year
Fundamentals of the theory of operator algebras. Vol. 1: Elementary theory. Zbl 0518.46046
Kadison, Richard V.; Ringrose, John R.
1983
Fundamentals of the theory of operator algebras. Volume II: Advanced theory. Zbl 0601.46054
Kadison, Richard V.; Ringrose, John R.
1986
Fundamentals of the theory of operator algebras. Vol. I: Elementary theory. 2nd printing with correct. 2nd printing with correct. Zbl 0888.46039
Kadison, Richard V.; Ringrose, John R.
1997
Isometries of operator algebras. Zbl 0045.06201
1951
Local derivations. Zbl 0751.46041
1990
A generalized Schwarz inequality and algebraic invariants for operator algebras. Zbl 0047.35703
1952
Determinant theory in finite factors. Zbl 0046.33604
1952
Fundamentals of the theory of operator algebras. Vol. II: Advanced theory. 2nd printing of the 1986 orig. 2nd printing of the 1986 orig. Zbl 0991.46031
Kadison, Richard V.; Ringrose, John R.
1997
A representation theory for commutative topological algebra. Zbl 0042.34801
1951
Derivations of operator algebras. Zbl 0139.30503
1966
Transformations of states in operator theory and dynamics. Zbl 0129.08705
1965
Extensions of pure states. Zbl 0086.09704
Kadison, Richard V.; Singer, I. M.
1959
Order properties of bounded self-adjoint operators. Zbl 0043.11501
1951
Triangular operator algebras. Fundamentals and hyperreducible theory. Zbl 0096.31703
Kadison, Richard V.; Singer, I. M.
1960
Derivations and automorphisms of operator algebras. Zbl 0149.34403
Kadison, Richard V.; Ringrose, John R.
1967
Means and convex combinations of unitary operators. Zbl 0573.46034
Kadison, Richard V.; Pedersen, Gert K.
1985
Cohomology of operator algebras. III: Reduction to normal cohomology. Zbl 0234.46066
Johnson, B. E.; Kadison, Richard V.; Ringrose, John R.
1972
Unitary operators in $$C^ *$$-algebras. Zbl 0152.33001
Glimm, J. G.; Kadison, Richard V.
1960
Irreducible operator algebras. Zbl 0078.11502
1957
Nets of $$C^*$$-algebras and classification of states. Zbl 0186.28302
Haag, R.; Kadison, Richard V.; Kastler, D.
1970
Diagonalizing matrices. Zbl 0585.46048
1984
Unitary invariants for representations of operator algebras. Zbl 0084.10705
1957
Diagonals of self-adjoint operators. Zbl 1113.46064
2006
Perturbations of von Neumann algebras. I: Stability of type. Zbl 0239.46070
1972
Cohomology of operator algebras. I: Type I von Neumann algebras. Zbl 0209.44501
Kadison, Richard V.; Ringrose, John R.
1971
The Pythagorean theorem. II: The infinite discrete case. Zbl 1013.46050
2002
On the orthogonalization of operator representations. Zbl 0064.36605
1955
The Pythagorean theorem. I: The finite case. Zbl 1013.46049
2002
Operator algebras with a faithful weakly-closed representation. Zbl 0071.11501
1956
The trace in finite operator algebras. Zbl 0103.08701
1961
Remarks on the type of von Neumann algebras of local observables in quantum field theory. Zbl 0127.19201
1963
Cohomology of operator algebras. II: Extended cobounding and the hyperfinite case. Zbl 0214.38402
Kadison, Richard V.; Ringrose, John R.
1971
Derivations and automorphisms of operator algebras. II. Zbl 0149.34501
Kadison, Richard V.; Lance, E. C.; Ringrose, John R.
1967
On tensor products of von Neumann algebras. Zbl 0902.46037
1996
The closure of the regular operators in a ring of operators. Zbl 0056.33704
1954
On a conjecture of Murray and von Neumann. Zbl 0043.11702
1951
Asymptotically Abelian systems. Zbl 0177.41401
Doplicher, S.; Kadison, Richard V.; Kastler, D.; Robinson, D. W.
1967
Equivalence in operator algebras. Zbl 0217.16804
Kadison, Richard V.; Pedersen, G. K.
1970
Fundamentals of the theory of operator algebras: special topics. Vol. 4: Advanced theory - an exercise approach. Zbl 0869.46029
Kadison, Richard V.; Ringrose, John R.
1992
Automorphisms and quasi-free states fo the CAR algebra. Zbl 0308.46055
Hugenholtz, N. M.; Kadison, Richard V.
1975
On determinants and a property of the trace in finite factors. Zbl 0043.32803
1951
Infinite unitary groups. Zbl 0046.25203
1952
States and representations. Zbl 0113.09702
1962
Strong continuity of operator functions. Zbl 0169.16902
1968
Fundamentals of the theory of operator algebras: special topics. Vol. 3: Elementary theory - an exercise approach. Zbl 0869.46028
Kadison, Richard V.; Ringrose, John R.
1991
Isomorphisms of factors of infinite type. Zbl 0064.36603
1955
Three test problems in operator theory. Zbl 0078.11503
Kadison, Richard V.; Singer, I. M.
1957
A note on derivations of Murray-von Neumann algebras. Zbl 1355.46049
2014
Asymptotic orbits in a free Fermi gas. Zbl 0262.46059
Haag, R.; Kadison, Richard V.; Kastler, D.
1973
Derivations of operator group algebras. Zbl 0149.34401
Kadison, Richard V.; Ringrose, John R.
1966
The Heisenberg relation – mathematical formulations. Zbl 1410.81008
2014
Some remarks on representations of connected groups. Zbl 0046.25202
Kadison, Richard V.; Singer, I. M.
1952
On the additivity of the trace in finite factors. Zbl 0064.36604
1955
Normalcy in operator algebras. Zbl 0177.17802
1962
Non-commutative conditional expectations and their applications. Zbl 1080.46044
2004
Affine mappings of invertible operators. Zbl 0864.46035
Harris, Lawrence A.; Kadison, Richard V.
1996
Pure states and approximate identities. Zbl 0177.41302
Aarnes, J. F.; Kadison, Richard V.
1969
Diagonalizing matrices over operator algebras. Zbl 0518.46047
1983
Banach algebras with unitary norms. Zbl 0865.46040
Hansen, Mogens L.; Kadison, Richard V.
1996
Triangular algebras — another chapter. Zbl 0743.47031
1991
The general linear group of infinite factors. Zbl 0064.02704
1955
The energy momentum spectrum of quantum fields. Zbl 0163.21805
1967
Infinite general linear groups. Zbl 0055.01903
1954
Theory of operators. Part II: Operator algebras. Zbl 0080.00414
1958
Similarity of operator algebras. Zbl 0387.46051
1978
Strategies in the secretary problem. Zbl 0809.90129
1994
A note on derivations of operator algebras. Zbl 0302.46046
1975
A note on commutators in algebras of unbounded operators. Zbl 1457.46061
Kadison, Richard V.; Liu, Zhe; Thom, Andreas
2020
Which Singer is that? Zbl 1075.01010
2000
Limits of states. Zbl 0505.46045
1982
Derivations of Murray-von Neumann algebras. Zbl 1315.47037
2014
Notes on the Fermi gas. Zbl 0361.46056
1976
Notes on the Gelfand-Neumark theorem. Zbl 0824.46061
1994
On representations of finite type. Zbl 0941.46030
1998
The von Neumann algebra characterization theorems. Zbl 0576.46043
1985
Algebras of unbounded functions and operators. Zbl 0596.47028
1986
Algebraic automorphisms of operator algebras. Zbl 0287.46075
Kadison, Richard V.; Ringrose, John R.
1974
Means of unitary operators, revisited. Zbl 1161.46030
Haagerup, Uffe; Kadison, Richard V.; Pedersen, Gert K.
2007
Operator algebras and applications. Proceedings of the Symposium in Pure Mathematics of the American Mathematical Society Held at Queens University, Kingston, Ontario, July 14 - August 2, 1980. Zbl 0488.00012
1982
Dual cones and Tomita-Takesaki theory. Zbl 0935.46051
1998
Automorphisms of operator algebras. Zbl 0149.34402
Kadison, Richard V.; Ringrose, John R.
1966
Reflections relating a von Neumann algebra and its commutant. Zbl 0741.46030
1991
Multiplicity theory for operator algebras. Zbl 0084.10704
1955
On an inequality of Haagerup-Pisier. Zbl 0819.46046
1993
Fundamentals of the theory of operator algebras. Vol. 1: Elementary theory. New ed. Zbl 0831.46060
Kadison, Richard V.; Ringrose, John R.
1994
Schurian algebras and spectral additivity. Zbl 0891.46026
Harris, Lawrence A.; Kadison, Richard V.
1996
A note on the similarity problem. Zbl 0802.46071
1991
Operator algebras - an overview. Zbl 0708.46052
1990
A note on commutators in algebras of unbounded operators. Zbl 1457.46061
Kadison, Richard V.; Liu, Zhe; Thom, Andreas
2020
A note on derivations of Murray-von Neumann algebras. Zbl 1355.46049
2014
The Heisenberg relation – mathematical formulations. Zbl 1410.81008
2014
Derivations of Murray-von Neumann algebras. Zbl 1315.47037
2014
Means of unitary operators, revisited. Zbl 1161.46030
Haagerup, Uffe; Kadison, Richard V.; Pedersen, Gert K.
2007
Diagonals of self-adjoint operators. Zbl 1113.46064
2006
Non-commutative conditional expectations and their applications. Zbl 1080.46044
2004
The Pythagorean theorem. II: The infinite discrete case. Zbl 1013.46050
2002
The Pythagorean theorem. I: The finite case. Zbl 1013.46049
2002
Which Singer is that? Zbl 1075.01010
2000
On representations of finite type. Zbl 0941.46030
1998
Dual cones and Tomita-Takesaki theory. Zbl 0935.46051
1998
Fundamentals of the theory of operator algebras. Vol. I: Elementary theory. 2nd printing with correct. 2nd printing with correct. Zbl 0888.46039
Kadison, Richard V.; Ringrose, John R.
1997
Fundamentals of the theory of operator algebras. Vol. II: Advanced theory. 2nd printing of the 1986 orig. 2nd printing of the 1986 orig. Zbl 0991.46031
Kadison, Richard V.; Ringrose, John R.
1997
On tensor products of von Neumann algebras. Zbl 0902.46037
1996
Affine mappings of invertible operators. Zbl 0864.46035
Harris, Lawrence A.; Kadison, Richard V.
1996
Banach algebras with unitary norms. Zbl 0865.46040
Hansen, Mogens L.; Kadison, Richard V.
1996
Schurian algebras and spectral additivity. Zbl 0891.46026
Harris, Lawrence A.; Kadison, Richard V.
1996
Strategies in the secretary problem. Zbl 0809.90129
1994
Notes on the Gelfand-Neumark theorem. Zbl 0824.46061
1994
Fundamentals of the theory of operator algebras. Vol. 1: Elementary theory. New ed. Zbl 0831.46060
Kadison, Richard V.; Ringrose, John R.
1994
On an inequality of Haagerup-Pisier. Zbl 0819.46046
1993
Fundamentals of the theory of operator algebras: special topics. Vol. 4: Advanced theory - an exercise approach. Zbl 0869.46029
Kadison, Richard V.; Ringrose, John R.
1992
Fundamentals of the theory of operator algebras: special topics. Vol. 3: Elementary theory - an exercise approach. Zbl 0869.46028
Kadison, Richard V.; Ringrose, John R.
1991
Triangular algebras — another chapter. Zbl 0743.47031
1991
Reflections relating a von Neumann algebra and its commutant. Zbl 0741.46030
1991
A note on the similarity problem. Zbl 0802.46071
1991
Local derivations. Zbl 0751.46041
1990
Operator algebras - an overview. Zbl 0708.46052
1990
Fundamentals of the theory of operator algebras. Volume II: Advanced theory. Zbl 0601.46054
Kadison, Richard V.; Ringrose, John R.
1986
Algebras of unbounded functions and operators. Zbl 0596.47028
1986
Means and convex combinations of unitary operators. Zbl 0573.46034
Kadison, Richard V.; Pedersen, Gert K.
1985
The von Neumann algebra characterization theorems. Zbl 0576.46043
1985
Diagonalizing matrices. Zbl 0585.46048
1984
Fundamentals of the theory of operator algebras. Vol. 1: Elementary theory. Zbl 0518.46046
Kadison, Richard V.; Ringrose, John R.
1983
Diagonalizing matrices over operator algebras. Zbl 0518.46047
1983
Limits of states. Zbl 0505.46045
1982
Operator algebras and applications. Proceedings of the Symposium in Pure Mathematics of the American Mathematical Society Held at Queens University, Kingston, Ontario, July 14 - August 2, 1980. Zbl 0488.00012
1982
Similarity of operator algebras. Zbl 0387.46051
1978
Notes on the Fermi gas. Zbl 0361.46056
1976
Automorphisms and quasi-free states fo the CAR algebra. Zbl 0308.46055
Hugenholtz, N. M.; Kadison, Richard V.
1975
A note on derivations of operator algebras. Zbl 0302.46046
1975
Algebraic automorphisms of operator algebras. Zbl 0287.46075
Kadison, Richard V.; Ringrose, John R.
1974
Asymptotic orbits in a free Fermi gas. Zbl 0262.46059
Haag, R.; Kadison, Richard V.; Kastler, D.
1973
Cohomology of operator algebras. III: Reduction to normal cohomology. Zbl 0234.46066
Johnson, B. E.; Kadison, Richard V.; Ringrose, John R.
1972
Perturbations of von Neumann algebras. I: Stability of type. Zbl 0239.46070
1972
Cohomology of operator algebras. I: Type I von Neumann algebras. Zbl 0209.44501
Kadison, Richard V.; Ringrose, John R.
1971
Cohomology of operator algebras. II: Extended cobounding and the hyperfinite case. Zbl 0214.38402
Kadison, Richard V.; Ringrose, John R.
1971
Nets of $$C^*$$-algebras and classification of states. Zbl 0186.28302
Haag, R.; Kadison, Richard V.; Kastler, D.
1970
Equivalence in operator algebras. Zbl 0217.16804
Kadison, Richard V.; Pedersen, G. K.
1970
Pure states and approximate identities. Zbl 0177.41302
Aarnes, J. F.; Kadison, Richard V.
1969
Strong continuity of operator functions. Zbl 0169.16902
1968
Derivations and automorphisms of operator algebras. Zbl 0149.34403
Kadison, Richard V.; Ringrose, John R.
1967
Derivations and automorphisms of operator algebras. II. Zbl 0149.34501
Kadison, Richard V.; Lance, E. C.; Ringrose, John R.
1967
Asymptotically Abelian systems. Zbl 0177.41401
Doplicher, S.; Kadison, Richard V.; Kastler, D.; Robinson, D. W.
1967
The energy momentum spectrum of quantum fields. Zbl 0163.21805
1967
Derivations of operator algebras. Zbl 0139.30503
1966
Derivations of operator group algebras. Zbl 0149.34401
Kadison, Richard V.; Ringrose, John R.
1966
Automorphisms of operator algebras. Zbl 0149.34402
Kadison, Richard V.; Ringrose, John R.
1966
Transformations of states in operator theory and dynamics. Zbl 0129.08705
1965
Remarks on the type of von Neumann algebras of local observables in quantum field theory. Zbl 0127.19201
1963
States and representations. Zbl 0113.09702
1962
Normalcy in operator algebras. Zbl 0177.17802
1962
The trace in finite operator algebras. Zbl 0103.08701
1961
Triangular operator algebras. Fundamentals and hyperreducible theory. Zbl 0096.31703
Kadison, Richard V.; Singer, I. M.
1960
Unitary operators in $$C^ *$$-algebras. Zbl 0152.33001
Glimm, J. G.; Kadison, Richard V.
1960
Extensions of pure states. Zbl 0086.09704
Kadison, Richard V.; Singer, I. M.
1959
Theory of operators. Part II: Operator algebras. Zbl 0080.00414
1958
Irreducible operator algebras. Zbl 0078.11502
1957
Unitary invariants for representations of operator algebras. Zbl 0084.10705
1957
Three test problems in operator theory. Zbl 0078.11503
Kadison, Richard V.; Singer, I. M.
1957
Operator algebras with a faithful weakly-closed representation. Zbl 0071.11501
1956
On the orthogonalization of operator representations. Zbl 0064.36605
1955
Isomorphisms of factors of infinite type. Zbl 0064.36603
1955
On the additivity of the trace in finite factors. Zbl 0064.36604
1955
The general linear group of infinite factors. Zbl 0064.02704
1955
Multiplicity theory for operator algebras. Zbl 0084.10704
1955
The closure of the regular operators in a ring of operators. Zbl 0056.33704
1954
Infinite general linear groups. Zbl 0055.01903
1954
A generalized Schwarz inequality and algebraic invariants for operator algebras. Zbl 0047.35703
1952
Determinant theory in finite factors. Zbl 0046.33604
1952
Infinite unitary groups. Zbl 0046.25203
1952
Some remarks on representations of connected groups. Zbl 0046.25202
Kadison, Richard V.; Singer, I. M.
1952
Isometries of operator algebras. Zbl 0045.06201
1951
A representation theory for commutative topological algebra. Zbl 0042.34801
1951
Order properties of bounded self-adjoint operators. Zbl 0043.11501
1951
On a conjecture of Murray and von Neumann. Zbl 0043.11702
1951
On determinants and a property of the trace in finite factors. Zbl 0043.32803
1951
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# Measurement of the rapidity and transverse momentum distributions of Z bosons in pp collisions at root(s)=7 TeV
Chatrchyan, S.; Khachatryan, V.; Sirunyan, A. M.; Tumasyan, A.; Adam, W.; Bergauer, T.; Dragicevic, M.; Eroe, J.; Fabjan, C.; Friedl, M.; Fruehwirth, R.; Ghete, V. M.; Hammer, J.; Hoch, M.; Hoermann, N.; Hrubec, J.; Jeitler, M.; Kiesenhofer, W.; Krammer, M.; Liko, D.; Liko, D.
Measurements of the normalized rapidity (y) and transverse-momentum (q(T)) distributions of Drell-Yan muon and electron pairs in the Z-boson mass region (60 < M-ll < 120 GeV) are reported. The results are obtained using a data sample of proton-proton collisions at a center-of-mass energy of 7 TeV, collected by the CMS experiment at the Large Hadron Collider (LHC), corresponding to an integrated luminosity of 36 pb(-1). The distributions are measured over the ranges vertical bar y vertical bar < 3.5 and q(T) < 600 GeV and compared with quantum chromodynamics (QCD) calculations using recent parton distribution functions to model the momenta of the quarks and gluons in the protons. Overall agreement is observed between the models and data for the rapidity distribution, while no single model describes the Z transverse-momentum distribution over the full range.
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Görüntülenme 99 İndirme 8 Veri hacmi 3.3 kB Tekil görüntülenme 99 Tekil indirme 8 | 2021-08-04T03:09:47 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9822114109992981, "perplexity": 10451.733261795891}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046154500.32/warc/CC-MAIN-20210804013942-20210804043942-00148.warc.gz"} |
https://phys.libretexts.org/Bookshelves/University_Physics/Book%3A_University_Physics_(OpenStax)/Map%3A_University_Physics_II_-_Thermodynamics%2C_Electricity%2C_and_Magnetism_(OpenStax)/06%3A_Gauss's_Law/6.02%3A_Electric_Flux | $$\require{cancel}$$
# 6.2: Electric Flux
Learning Objectives
By the end of this section, you will be able to:
• Define the concept of flux
• Describe electric flux
• Calculate electric flux for a given situation
The concept of flux describes how much of something goes through a given area. More formally, it is the dot product of a vector field (in this chapter, the electric field) with an area. You may conceptualize the flux of an electric field as a measure of the number of electric field lines passing through an area (Figure $$\PageIndex{1}$$). The larger the area, the more field lines go through it and, hence, the greater the flux; similarly, the stronger the electric field is (represented by a greater density of lines), the greater the flux. On the other hand, if the area rotated so that the plane is aligned with the field lines, none will pass through and there will be no flux.
A macroscopic analogy that might help you imagine this is to put a hula hoop in a flowing river. As you change the angle of the hoop relative to the direction of the current, more or less of the flow will go through the hoop. Similarly, the amount of flow through the hoop depends on the strength of the current and the size of the hoop. Again, flux is a general concept; we can also use it to describe the amount of sunlight hitting a solar panel or the amount of energy a telescope receives from a distant star, for example.
To quantify this idea, Figure $$\PageIndex{1a}$$ shows a planar surface $$S_1$$ of area $$A_1$$ that is perpendicular to the uniform electric field $$\vec{E} = E\hat{y}$$. If N field lines pass through $$S_1$$, then we know from the definition of electric field lines (Electric Charges and Fields) that $$N/A \propto E$$, or $$N \propto EA_1$$.
The quantity $$EA_1$$ is the electric flux through $$S_1$$. We represent the electric flux through an open surface like $$S_1$$ by the symbol $$\Phi$$. Electric flux is a scalar quantity and has an SI unit of newton-meters squared per coulomb ($$N \cdot m^2/C$$). Notice that $$N \propto EA_1$$ may also be written as $$N \propto \Phi$$, demonstrating that electric flux is a measure of the number of field lines crossing a surface.
Now consider a planar surface that is not perpendicular to the field. How would we represent the electric flux? Figure $$\PageIndex{2b}$$ shows a surface $$S_2$$ of area $$A_2$$ that is inclined at an angle $$\theta$$ to the xz-plane and whose projection in that plane is $$S_1$$ (area $$A_1$$). The areas are related by $$A_2 \, cos \, \theta = A_1$$. Because the same number of field lines crosses both $$S_1$$ and $$S_2$$, the fluxes through both surfaces must be the same. The flux through $$S_2$$ is therefore $$\Phi = EA_1 = EA_2 \, cos \, \theta$$. Designating $$\hat{n}_2$$ as a unit vector normal to $$S_2$$ (see Figure $$\PageIndex{2b}$$), we obtain
$\Phi = \vec{E} \cdot \hat{n}_2 A_2.$
Note
Check out this video to observe what happens to the flux as the area changes in size and angle, or the electric field changes in strength.
# Area Vector
For discussing the flux of a vector field, it is helpful to introduce an area vector $$\vec{A}$$. This allows us to write the last equation in a more compact form. What should the magnitude of the area vector be? What should the direction of the area vector be? What are the implications of how you answer the previous question?
The area vector of a flat surface of area A has the following magnitude and direction:
• Magnitude is equal to area (A)
• Direction is along the normal to the surface $$(\hat{n})$$; that is, perpendicular to the surface.
Since the normal to a flat surface can point in either direction from the surface, the direction of the area vector of an open surface needs to be chosen, as shown in Figure $$\PageIndex{3}$$.
Since $$\hat{n}$$ is a unit normal to a surface, it has two possible directions at every point on that surface (Figure $$\PageIndex{1a}$$). For an open surface, we can use either direction, as long as we are consistent over the entire surface. $$\PageIndex{1c}$$ of the figure shows several cases.
However, if a surface is closed, then the surface encloses a volume. In that case, the direction of the normal vector at any point on the surface points from the inside to the outside. On a closed surface such as that of Figure $$\PageIndex{1b}$$, $$\hat{n}$$ is chosen to be the outward normal at every point, to be consistent with the sign convention for electric charge.
# Electric Flux
Now that we have defined the area vector of a surface, we can define the electric flux of a uniform electric field through a flat area as the scalar product of the electric field and the area vector:
$\Phi = \vec{E} \cdot \vec{A} \, (uniform \, \hat{E}, \, flat \, surface).$
Figure $$\PageIndex{5}$$ shows the electric field of an oppositely charged, parallel-plate system and an imaginary box between the plates. The electric field between the plates is uniform and points from the positive plate toward the negative plate. A calculation of the flux of this field through various faces of the box shows that the net flux through the box is zero. Why does the flux cancel out here?
The reason is that the sources of the electric field are outside the box. Therefore, if any electric field line enters the volume of the box, it must also exit somewhere on the surface because there is no charge inside for the lines to land on. Therefore, quite generally, electric flux through a closed surface is zero if there are no sources of electric field, whether positive or negative charges, inside the enclosed volume. In general, when field lines leave (or “flow out of”) a closed surface, $$\Phi$$ is positive; when they enter (or “flow into”) the surface, $$\Phi$$ is negative.
Any smooth, non-flat surface can be replaced by a collection of tiny, approximately flat surfaces, as shown in Figure $$\PageIndex{6}$$. If we divide a surface S into small patches, then we notice that, as the patches become smaller, they can be approximated by flat surfaces. This is similar to the way we treat the surface of Earth as locally flat, even though we know that globally, it is approximately spherical.
To keep track of the patches, we can number them from 1 through N . Now, we define the area vector for each patch as the area of the patch pointed in the direction of the normal. Let us denote the area vector for the ith patch by $$\delta \vec{A}_i$$. (We have used the symbol $$\delta$$ to remind us that the area is of an arbitrarily small patch.) With sufficiently small patches, we may approximate the electric field over any given patch as uniform. Let us denote the average electric field at the location of the ith patch by $$\vec{E}_i$$.
$\vec{E}_i = average \, electric \, field \, over \, the \, ith \, patch.$
Therefore, we can write the electric flux $$\Phi$$ through the area of the ith patch as
$\Phi_i = \vec{E}_i \cdot \delta \vec{A}_i \, (ith \, patch).$
The flux through each of the individual patches can be constructed in this manner and then added to give us an estimate of the net flux through the entire surface S, which we denote simply as $$\Phi$$.
$\Phi = \sum_{i=1}^N \Phi_i = \sum_{i=1}^N \vec{E}_i \cdot \delta \vec{A}_i \, (N \, patch \, estimate).$
This estimate of the flux gets better as we decrease the size of the patches. However, when you use smaller patches, you need more of them to cover the same surface. In the limit of infinitesimally small patches, they may be considered to have area dA and unit normal $$\hat{n}$$. Since the elements are infinitesimal, they may be assumed to be planar, and $$\vec{E}_i$$ may be taken as constant over any element. Then the flux $$d\Phi$$ through an area dA is given by $$d\Phi = \vec{E} \cdot \hat{n} dA$$. It is positive when the angle between $$\vec{E}_i$$ and $$\hat{n}$$ is less than $$90^o$$ and negative when the angle is greater than $$90^o$$. The net flux is the sum of the infinitesimal flux elements over the entire surface. With infinitesimally small patches, you need infinitely many patches, and the limit of the sum becomes a surface integral. With $$\int_S$$ representing the integral over S,
$\Phi = \int_S \vec{E} \cdot \hat{n}dA = \int_S \vec{E} \cdot d\vec{A} \, (open \, surface).$
In practical terms, surface integrals are computed by taking the antiderivatives of both dimensions defining the area, with the edges of the surface in question being the bounds of the integral.
To distinguish between the flux through an open surface like that of Figure $$\PageIndex{2}$$ and the flux through a closed surface (one that completely bounds some volume), we represent flux through a closed surface by
$\Phi = \oint_S \vec{E} \cdot \hat{n} dA = \oint_S \vec{E} \cdot d\vec{A} \, (closed \, surface)$
where the circle through the integral symbol simply means that the surface is closed, and we are integrating over the entire thing. If you only integrate over a portion of a closed surface, that means you are treating a subset of it as an open surface.
Example $$\PageIndex{1}$$: Flux of a Uniform Electric Field
A constant electric field of magnitude $$E_0$$ points in the direction of the positive z-axis (Figure $$\PageIndex{7}$$). What is the electric flux through a rectangle with sides a and b in the (a) xy-plane and in the (b) xz-plane?
Strategy
Apply the definition of flux: $$\Phi = \vec{E} \cdot \vec{A} \, (uniform \, \vec{E})$$, where the definition of dot product is crucial.
Solution
1. In this case, $$\Phi = \vec{E}_0 \cdot \vec{A} = E_0 A = E_0 ab$$.
2. Here, the direction of the area vector is either along the positive y-axis or toward the negative y-axis. Therefore, the scalar product of the electric field with the area vector is zero, giving zero flux.
Significance
The relative directions of the electric field and area can cause the flux through the area to be zero.
Example $$\PageIndex{2}$$: Flux of a Uniform Electric Field through a Closed Surface
A constant electric field of magnitude $$E_0$$ points in the direction of the positive z-axis (Figure $$\PageIndex{8}$$). What is the net electric flux through a cube?
Strategy
Apply the definition of flux: $$\Phi = \vec{E} \cdot \vec{A} \, (uniform \, \vec{E})$$, noting that a closed surface eliminates the ambiguity in the direction of the area vector.
Solution
Through the top face of the cube $$\Phi = \vec{E}_0 \cdot \vec{A} = E_0 A$$.
Through the bottom face of the cube, $$\Phi = \vec{E}_0 \cdot \vec{A} = - E_0 A$$, because the area vector here points downward.
Along the other four sides, the direction of the area vector is perpendicular to the direction of the electric field. Therefore, the scalar product of the electric field with the area vector is zero, giving zero flux.
The net flux is $$\Phi_{net} = E_0A - E_0 A + 0 + 0 + 0 + 0 = 0$$.
Significance
The net flux of a uniform electric field through a closed surface is zero.
Example $$\PageIndex{3}$$: Electric Flux through a Plane, Integral Method
A uniform electric field $$\vec{E}$$ of magnitude 10 N/C is directed parallel to the yz-plane at $$30^o$$ above the xy-plane, as shown in Figure $$\PageIndex{9}$$. What is the electric flux through the plane surface of area $$6.0 \, m^2$$ located in the xz-plane? Assume that $$\hat{n}$$ points in the positive y-direction.
Strategy
Apply $$\Phi = \int_S \vec{E} \cdot \hat{n} dA$$, where the direction and magnitude of the electric field are constant.
Solution
The angle between the uniform electric field $$\vec{E}$$ and the unit normal $$\hat{n}$$ to the planar surface is $$30^o$$. Since both the direction and magnitude are constant, E comes outside the integral. All that is left is a surface integral over dA, which is A. Therefore, using the open-surface equation, we find that the electric flux through the surface is
$\Phi = \int_S \vec{E} \cdot \hat{n} dA = EA \, cos \, \theta$
$= (10 \, N/C)(6.0 \, m^2)(cos \, 30^o) = 52 \, N \cdot m^2/C.$
Significance
Again, the relative directions of the field and the area matter, and the general equation with the integral will simplify to the simple dot product of area and electric field.
Exercise $$\PageIndex{1}$$
What angle should there be between the electric field and the surface shown in Figure $$\PageIndex{9}$$ in the previous example so that no electric flux passes through the surface?
Solution
Place it so that its unit normal is perpendicular to $$\vec{E}$$.
Example $$\PageIndex{4}$$ : Inhomogeneous Electric Field
What is the total flux of the electric field $$\vec{E} = cy^2\hat{k}$$ through the rectangular surface shown in Figure $$\PageIndex{10}$$?
Strategy
Apply $$\Phi = \int_S \vec{E} \cdot \hat{n}dA$$. We assume that the unit normal $$\hat{n}$$ to the given surface points in the positive z-direction, so $$\hat{n} = \hat{k}$$. Since the electric field is not uniform over the surface, it is necessary to divide the surface into infinitesimal strips along which $$\vec{E}$$ is essentially constant. As shown in Figure $$\PageIndex{10}$$, these strips are parallel to the x-axis, and each strip has an area $$dA = b \, dy$$.
Solution
From the open surface integral, we find that the net flux through the rectangular surface is
\begin{aling*} \Phi &= \int_S \vec{E} \cdot \hat{n} dA = \int_0^a (cy^2 \hat{k}) \cdot \hat{k}(b \, dy) \\[4pt] &= cb \int_0^a y^2 dy = \frac{1}{3} a^3 bc. \end{align*}
Significance
For a non-constant electric field, the integral method is required.
Exercise $$\PageIndex{1}$$
If the electric field in Example is $$\vec{E} = mx\hat{k}$$. what is the flux through the rectangular area?
$$mab^2/2$$
## 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). | 2020-02-25T16:22:33 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9522532820701599, "perplexity": 191.98980662487568}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-10/segments/1581875146123.78/warc/CC-MAIN-20200225141345-20200225171345-00204.warc.gz"} |
https://www.reneshbedre.com/blog/ttest.html | # How to perform one and two-sample t-test in Python
Renesh Bedre 9 minute read
## t-test
t-test (also known as Student’s t-test) is a parametric hypothesis testing method used for comparing the means between two different groups. In t-test, test statistic follows the t-distribution under the null hypothesis.
t-distribution is first proposed by William Sealy Gosset and published under the fictitious name of “Student” in Biometrika scientific journal. Hence, t-distribution is also known as Student’s t-distribution.
The t-test is specially developed for the small sample size data (n ≤ 30). However, if the sample size large, Z-test can also be used as t and z distributions are similar for larger sample size.
Based on group comparisons, t-test has three main types viz. One Sample t-test, two sample t-test (unpaired or independent), and paired t-test.
## Types of t-test
### One Sample t-test
• One Sample t-test (single sample t-test) is used for comparing the sample mean (a random sample from a population) with the specific value (hypothesized or known mean of the population). In t-test, the population variance (σ2) is unknown and it is estimated from the sample variance (s).
• For example, a ball has a diameter of 5 cm and we want to check whether the average diameter of the ball from the random sample (e.g. 50 balls) picked from the production line differs from the known size.
#### Assumptions
• Dependent variable should have an approximately normal distribution (Shapiro-Wilks Test)
• Observations are independent of each other
• Dependent variable should be continuous
• Population variance (σ2) is unknown
Note: One sample t-test is relatively robust to the assumption of normality when the sample size is large (n ≥ 30)
#### Hypotheses
• Null hypothesis: Sample mean is equal to the hypothesized or known population mean
• Alternative hypothesis: Sample mean is not equal to the hypothesized or known population mean (two-tailed or two-sided)
• Alternative hypothesis: Sample mean is either greater or lesser to the hypothesized or known population mean (one-tailed or one-sided)
Learn more about hypothesis testing and interpretation
#### Formula
One Sample t-test formula,
#### Calculate one sample t-test in Python
To perform one sample t-test in Python, we will use the ttest_1samp() function available in Scipy package. In addition, we will also use ttest() function from bioinfokit (v2.1.0 or later) packages for detailed statistical results. You can install Scipy and bioinfokit packages using pip or conda.
In following example of one sample t-test uses the in-built data from bioinfokit package. If you have your own dataset, you can import it as pandas DataFrame
Perform one sample t-test using ttest_1samp() function in SciPy,
from scipy import stats as st
from bioinfokit.analys import get_data
# load dataset as pandas dataframe
df = get_data('t_one_samp').data
df.head(2)
# output
size
0 5.739987
1 5.254042
# t test using scipy
a = df['size'].to_numpy()
# use parameter "alternative" for two-sided or one-sided test
st.ttest_1samp(a=a, popmean=5)
# output
Ttest_1sampResult(statistic=0.36789006583267403, pvalue=0.714539654336473)
As you do not get detailed statistical output (such as confidence intervals, degrees of freedoms, sample size, etc.) from ttest_1samp() function, we will Perform one sample t-test using ttest() function in bioinfokit,
from bioinfokit.analys import stat
res = stat()
res.ttest(df=df, test_type=1, res='size', mu=5)
print(res.summary)
# output
One Sample t-test
------------------ --------
Sample size 50
Mean 5.05128
t 0.36789
Df 49
p value (one-tail) 0.35727
p value (two-tail) 0.71454
Lower 95.0% 4.77116
Upper 95.0% 5.3314
------------------ --------
# access t value and p value (two-tailed)
t, p = res.result[1], res.result[3]
t, p
# output
(0.36789006583267403, 0.714539654336473)
#### Interpretation
The p value obtained from the one sample t-test is not significant (p > 0.05), and therefore, we conclude that the average diameter of the balls in a random sample is equal to 5 cm.
### Two sample t-test (unpaired or independent t-test)
The two-sample (unpaired or independent) t-test compares the means of two independent groups, determining whether they are equal or significantly different. In two sample t-test, usually, we compute the sample means from two groups and derives the conclusion for the population’s means (unknown means) from which two groups are drawn.
For example, we have two different plant genotypes (genotype A and genotype B) and would like to compare if the yield of genotype A is significantly different from genotype B
#### Hypotheses
• Null hypothesis: Two group means are equal
• Alternative hypothesis: Two group means are different (two-tailed or two-sided)
• Alternative hypothesis: Mean of one group either greater or lesser than another group (one-tailed or one-sided)
Learn more about hypothesis testing and interpretation
#### Assumptions
• Observations in two groups have an approximately normal distribution (Shapiro-Wilks Test)
• Homogeneity of variances (variances are equal between treatment groups) (Levene or Bartlett Test)
• The two groups are sampled independently from each other from the same population
• Dependent variable should be continuous
• Population variances (σ1 and σ2) are unknown
Note: Two sample t-test is relatively robust to the assumption of normality and homogeneity of variances when sample size is large (n ≥ 30) and there are equal number of samples (n1 = n2) in both groups.
If the sample size small and does not follow the normal distribution, you should use non-parametric Mann-Whitney U test (Wilcoxon rank sum test)
#### Formula
Two sample (independent) t-test formula,
If the variances are equal, the two sample t-test and Welch’s test (unequal variance t-test) perform equally (in terms of type I error rate) and have similar power.
#### Calculate Two sample t-test in Python
Perform two sample t-test using SciPy,
from scipy import stats as st
from bioinfokit.analys import get_data
# load dataset as pandas dataframe
df = get_data('t_ind_samp').data
df.head(2)
# output
Genotype yield
0 A 78.0
1 A 84.3
a = df.loc[df['Genotype'] == 'A', 'yield'].to_numpy()
b = df.loc[df['Genotype'] == 'B', 'yield'].to_numpy()
st.ttest_ind(a=a, b=b, equal_var=True)
# output
Ttest_indResult(statistic=-5.407091104196024, pvalue=0.00029840786595462836)
Perform two sample t-test using bioinfokit,
from bioinfokit.analys import stat
res = stat()
# for unequal variance t-test (Welch's t-test) set evar=False
res.ttest(df=df, xfac="Genotype", res="yield", test_type=2)
print(res.summary)
# output
Two sample t-test with equal variance
------------------ -------------
Mean diff -10.3
t -5.40709
Std Error 1.90491
df 10
p value (one-tail) 0.000149204
p value (two-tail) 0.000298408
Lower 95.0% -14.5444
Upper 95.0% -6.05561
------------------ -------------
Parameter estimates
Level Number Mean Std Dev Std Error Lower 95.0% Upper 95.0%
------- -------- ------ --------- ----------- ------------- -------------
A 6 79.1 3.30817 1.35056 75.6283 82.5717
B 6 89.4 3.29059 1.34338 85.9467 92.8533
# access t value and p value (two-tailed)
t, p = res.result[1], res.result[3]
t, p
# output
(-5.407091104196024, 0.00029840786595462836)
Note: t-test can be performed on two groups with unequal sample sizes. But, to increase the power of the t-test, it is good to have an equal sample size in two groups.
#### Interpretation
The p value obtained from the t-test is significant (p < 0.05), and therefore, we conclude that the yield of genotype A is significantly different than genotype B.
### Paired t-test (dependent t-test)
• Paired t-test used to compare the differences between the pair of dependent variables for the same subject
• For example, we have plant variety A and would like to compare the yield of A before and after the application of some fertilizer
• Note: Paired t-test is a one sample t-test on the differences between the two dependent variables
#### Hypotheses
• Null hypothesis: There is no difference between the two dependent variables (difference=0)
• Alternative hypothesis: There is a difference between the two dependent variables (two-tailed or two-sided)
• Alternative hypothesis: Difference between two response variables either greater or lesser than zero (one-tailed or one-sided)
#### Assumptions
• Differences between the two dependent variables follows an approximately normal distribution (Shapiro-Wilks Test)
• Independent variable should have a pair of dependent variables
• Differences between the two dependent variables should not have outliers
• Observations are sampled independently from each other
• Dependent variable should be continuous
• Population variance (σd1) for difference is unknown
#### Formula
Paired t-test formula,
Perform Paired t-test,
from bioinfokit.analys import get_data, stat
# load dataset as pandas dataframe
# the dataset should not have missing (NaN) values. If it has, it will omitted
df = get_data('t_pair').data
df.head(2)
# output
BF AF
0 44.41 47.99
1 46.29 56.64
res = stat()
res.ttest(df=df, res=['AF', 'BF'], test_type=3)
print(res.summary)
# output
Paired t-test
------------------ ------------
Sample size 65
Difference Mean 5.55262
t 14.2173
Df 64
p value (one-tail) 8.87966e-22
p value (two-tail) 1.77593e-21
Lower 95.0% 4.7724
Upper 95.0% 6.33283
------------------ ------------
# access t value and p value (two-tailed)
t, p = res.result[1], res.result[3]
t, p
# output
(14.217347189987418, 1.775932404304854e-21)
#### Interpretation
The p value obtained from the t-test is significant (p < 0.05), and therefore, we conclude that the yield of plant variety A significantly increased by the application of fertilizer.
Note: If you have partially paired data, you can use an independent t-test by treating two dependent variables as two different samples or drop all unpaired observations for performing paired t-test. But, both ad hoc approaches are not appropriate as it does not follow the basic requirement and may lead to biased estimate of the variance and loss of information 6.
## Sample size recommendations for t-test
• The t-test can be performed with a minimum sample size of 2. When using minimum sample size data, the effect size should be large and the data should follow the assumptions of a t-test. A larger sample size is always preferred over a smaller sample size.
• For paired t-test, it is advisable to have a high within-pair correlation (r > 0.8) to get a high statistical power (>80%) for small sample size data.
• t-test is relatively robust to the assumption of normality and homogeneity of variances when the sample size is large (n ≥ 30). If sample size is large, you can also consider performing Z-test.
## References
1. Virtanen P, Gommers R, Oliphant TE, Haberland M, Reddy T, Cournapeau D, Burovski E, Peterson P, Weckesser W, Bright J, van der Walt SJ. SciPy 1.0: fundamental algorithms for scientific computing in Python. Nature methods. 2020 Mar;17(3):261-72.
2. Kim TK, Park JH. More about the basic assumptions of t-test: normality and sample size. Korean journal of anesthesiology. 2019 Aug;72(4):331.
3. Schober P, Vetter TR. Two-sample unpaired t tests in medical research. Anesthesia & Analgesia. 2019 Oct 1;129(4):911.
4. Zabell SL. On student’s 1908 article “the probable error of a mean”. Journal of the American Statistical Association. 2008 Mar 1;103(481):1-7.
5. De Winter JC. Using the Student’s t-test with extremely small sample sizes. Practical Assessment, Research, and Evaluation. 2013;18(1):10.
6. Guo B, Yuan Y. A comparative review of methods for comparing means using partially paired data. Statistical methods in medical research. 2017 Jun;26(3):1323-40.
7. Ruxton GD. The unequal variance t-test is an underused alternative to Student’s t-test and the Mann–Whitney U test. Behavioral Ecology. 2006 Jul 1;17(4):688-90.
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Updated: | 2023-03-23T21:36:49 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.566485583782196, "perplexity": 5041.176172966232}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296945183.40/warc/CC-MAIN-20230323194025-20230323224025-00594.warc.gz"} |
http://dlmf.nist.gov/31.8 | For half-odd-integer values of the exponent parameters:
31.8.1 $\displaystyle\beta-\alpha$ $\displaystyle=m_{0}+\tfrac{1}{2},$ $\displaystyle\gamma$ $\displaystyle=-m_{1}+\tfrac{1}{2},$ $\displaystyle\delta$ $\displaystyle=-m_{2}+\tfrac{1}{2},$ $\displaystyle\epsilon$ $\displaystyle=-m_{3}+\tfrac{1}{2}$, $m_{0},m_{1},m_{2},m_{3}=0,1,2,\dots$,
the Hermite–Darboux method (see Whittaker and Watson (1927, pp. 570–572)) can be applied to construct solutions of (31.2.1) expressed in quadratures, as follows.
Denote $\mathbf{m}=(m_{0},m_{1},m_{2},m_{3})$ and $\lambda=-4q$. Then
31.8.2 $w_{\pm}(\mathbf{m};\lambda;z)=\sqrt{\Psi_{g,N}(\lambda,z)}\*\mathop{\exp\/}% \nolimits\!\left(\pm\frac{i\nu(\lambda)}{2}\int_{z_{0}}^{z}\frac{t^{m_{1}}(t-1% )^{m_{2}}(t-a)^{m_{3}}dt}{\Psi_{g,N}(\lambda,t)\sqrt{t(t-1)(t-a)}}\right)$
are two independent solutions of (31.2.1). Here $\Psi_{g,N}(\lambda,z)$ is a polynomial of degree $g$ in $\lambda$ and of degree $N=m_{0}+m_{1}+m_{2}+m_{3}$ in $z$, that is a solution of the third-order differential equation satisfied by a product of any two solutions of Heun’s equation. The degree $g$ is given by
31.8.3 $g=\tfrac{1}{2}\max\left(2\max_{0\leq k\leq 3}m_{k},1+N-(1+(-1)^{N})\left(% \tfrac{1}{2}+\min_{0\leq k\leq 3}m_{k}\right)\right).$
The variables $\lambda$ and $\nu$ are two coordinates of the associated hyperelliptic (spectral) curve $\Gamma:\nu^{2}=\prod_{j=1}^{2g+1}(\lambda-\lambda_{j})$. (This $\nu$ is unrelated to the $\nu$ in §31.6.) Lastly, $\lambda_{j}$, $j=1,2,\ldots,2g+1$, are the zeros of the Wronskian of $w_{+}(\mathbf{m};\lambda;z)$ and $w_{-}(\mathbf{m};\lambda;z)$.
By automorphisms from §31.2(v), similar solutions also exist for $m_{0},m_{1},m_{2},m_{3}\in\Integer$, and $\Psi_{g,N}(\lambda,z)$ may become a rational function in $z$. For instance,
31.8.4 $\displaystyle\Psi_{1,2}$ $\displaystyle=z^{2}+\lambda z+a,$ $\displaystyle\nu^{2}$ $\displaystyle=(\lambda+a+1)(\lambda^{2}-4a)$, $\mathbf{m}=(1,1,0,0)$,
and
31.8.5 $\displaystyle\Psi_{1,-1}$ $\displaystyle=\left(z^{2}+(\lambda+3a+3)z+a\right)/z^{3},$ $\displaystyle\nu^{2}$ $\displaystyle=(\lambda+4a+4)\left((\lambda+3a+3)^{2}-4a\right)$, $\mathbf{m}=(1,-2,0,0)$. Symbols: $z$: complex variable, $\nu$: real or complex parameter, $a$: complex parameter, $\lambda=-4q$ and $\Psi_{g,N}(\lambda,z)$: polynomial Referenced by: Equation (31.8.5) Permalink: http://dlmf.nist.gov/31.8.E5 Encodings: TeX, TeX, pMML, pMML, png, png Errata (effective with 1.0.7): Originally the first term on the right side of the equation for $\Psi_{1,-1}$ was $z^{3}$. The correct term is $z^{2}$. Reported 2013-07-25 by Christopher Künstler See also: info for 31.8
For $\mathbf{m}=(m_{0},0,0,0)$, these solutions reduce to Hermite’s solutions (Whittaker and Watson (1927, §23.7)) of the Lamé equation in its algebraic form. The curve $\Gamma$ reflects the finite-gap property of Equation (31.2.1) when the exponent parameters satisfy (31.8.1) for $m_{j}\in\Integer$. When $\lambda=-4q$ approaches the ends of the gaps, the solution (31.8.2) becomes the corresponding Heun polynomial. For more details see Smirnov (2002).
The solutions in this section are finite-term Liouvillean solutions which can be constructed via Kovacic’s algorithm; see §31.14(ii). | 2016-12-08T11:53:52 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 83, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9455438852310181, "perplexity": 830.6827855720204}, "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-2016-50/segments/1480698542588.29/warc/CC-MAIN-20161202170902-00383-ip-10-31-129-80.ec2.internal.warc.gz"} |
https://ouci.dntb.gov.ua/en/?journal=Earthline+Journal+of+Mathematical+Sciences | Exclude from search results
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G. C. Ibeh, E. J. Ekpenyoung, K. Anyiam, C. John
This study introduces a new distribution in the family of generalized exponential distributions generated using the transformed-transformer method. Some properties of the distribution are presented. The new distribution has three parameters and they are estimated numerically using the BGFS iterative method implemented in R software. Two real sets of data are adopted to demonstrate the flexibility and potential applications of the new distribution.
2021, Earthline Journal of Mathematical Sciences, p. 65-86
In this paper the generalized inverse distribution is defined. Some properties and applications of the generalized inverse distribution are studied in some detail. Characterization theorems generalizing the new family in terms of the hazard function are obtained. Recommendation for further study concludes the paper.
2020, Earthline Journal of Mathematical Sciences, p. 33-63
Samuel U. Enogwe, Happiness O. Obiora-Ilouno, Chrisogonus K. Onyekwere
This paper introduces an inverse power Akash distribution as a generalization of the Akash distribution to provide better fits than the Akash distribution and some of its known extensions. The fundamental properties of the proposed distribution such as the shapes of the distribution, moments, mean, variance, coefficient of variation, skewness, kurtosis, moment generating function, quantile function, Rényi entropy, stochastic ordering and the distribution of order statistics have been derived. The proposed distribution is observed to be a heavy-tailed distribution and can also be used to model data with upside-down bathtub shape for its hazard rate function. The maximum likelihood estimators of the unknown parameters of the proposed distribution have been obtained. Two numerical examples are given to demonstrate the applicability of the proposed distribution and for the two real data sets, the proposed distribution is found to be superior in its ability to sufficiently model heavy-tailed data than Akash, inverse Akash and power Akash distributions respectively.
2020, Earthline Journal of Mathematical Sciences, p. 1-32
Festus C. Opone, Elvis A. Izekor, Innocent U. Akata, Francis E. U. Osagiede
In this paper, we introduced the discrete analogue of the continuous Marshall-Olkin Weibull distribution using the discrete concentration approach. Some mathematical properties of the proposed discrete distribution such as the probability mass function, cumulative distribution function, survival function, hazard rate function, second rate of failure, probability generating function, quantile function and moments are derived. The method of maximum likelihood estimation is employed to estimate the unknown parameters of the proposed distribution. The applicability of the proposed discrete distribution was examined using an over-dispersed and under-dispersed data sets.
2020, Earthline Journal of Mathematical Sciences, p. 415-428
In [1], Wardowski introduced the F-contractions, and used it to prove the Banach contraction principle. In this paper we introduce a concept of F-interpolative Berinde weak contraction, and use it to prove the interpolative Berinde weak mapping theorem of [2].
2020, Earthline Journal of Mathematical Sciences, p. 411-414
S. C. Shiralashetti, Lata Lamani
This article gives an effective strategy to solve nonlinear stochastic Itô-Volterra integral equations (NSIVIE). These equations can be reduced to a system of nonlinear algebraic equations with unknown coefficients, using Bernoulli wavelets, their operational matrix of integration (OMI), stochastic operational matrix of integration (SOMI) and these equations can be solved numerically. Error analysis of the proposed method is given. Moreover, the results obtained are compared to exact solutions with numerical examples to show that the method described is accurate and precise.
2020, Earthline Journal of Mathematical Sciences, p. 395-410
Erhan Güler
We introduce the fourth fundamental form of the torus hypersurface in the four dimensional Euclidean space. We also compute I, II, III and IV fundamental forms of a torus hypersurface.
2020, Earthline Journal of Mathematical Sciences, p. 425-431
In this paper, we introduce the notions of T-fuzzy ideal, T-fuzzy quasi ideal, T-fuzzy bi-ideal, and T-fuzzy interior ideal. Some related properties are obtained. in coupled Γ semirings. Our work is inspired by [1].
2020, Earthline Journal of Mathematical Sciences, p. 377-393
In this present investigation, the authors introduced certain subclasses of the function class $T^{\alpha}_{\theta}(\lambda, \beta, t)$ of bi-Bazilevic univalent functions defined in the open unit disk $U$, which are associated with Chebyshev polynomials and Mittag-Leffler function. We establish the Taylor Maclaurin coefficients $\left|a_{2}\right|$, $\left|a_{3}\right|$ and $\left|a_{4}\right|$ for functions in the new subclass introduced and the Fekete-Szego problem is solved.
2020, Earthline Journal of Mathematical Sciences, p. 365-376
Isaac Ogechi Senge, Emmanuel Olubayo Oghre, Idongesit Fred Ekang
The influence of radiation on magneto-hydrodynamics (MHD) boundary layer flow over an exponentially stretching sheet embedded in a thermally stratified porous medium in the presence of heat source and suction/blowing was investigated. Similarity transformation was used to convert the governing equations from partial differential equations into a system of non-linear ordinary differential equations. Solving numerically, we used shooting method along with fourth order Runge-Kutta technique to obtained numerical values. The effects of the obtained numerical values of the dimensionless parameters on skin-friction coefficient, Nusselt number, velocity profile and temperature profile are illustrated in table and graphs plotted using MATLAB. Comparison of the velocity profile with previously published work was presented and found to be in good agreement.
2020, Earthline Journal of Mathematical Sciences, p. 345-363 | 2021-01-17T19:13:29 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5227720141410828, "perplexity": 814.1943498300782}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-04/segments/1610703513144.48/warc/CC-MAIN-20210117174558-20210117204558-00701.warc.gz"} |
http://pdglive.lbl.gov/DataBlock.action?node=B049W0&home=BXXX030 | # ${{\boldsymbol \Xi}{(1530)}^{0}}$ WIDTH INSPIRE search
VALUE (MeV) EVTS DOCUMENT ID TECN COMMENT
$\bf{ 9.1 \pm0.5}$ OUR AVERAGE
$9.5$ $\pm1.2$
1975 B
HBC ${{\mathit K}^{-}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit \Xi}^{-}}{{\overline{\mathit K}}}{{\mathit \pi}}$
$9.1$ $\pm2.4$
1973 B
HBC ${{\mathit K}^{-}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit \Xi}}{{\overline{\mathit K}}}{{\mathit \pi}}$( ${{\mathit \pi}}$)
$11$ $\pm2$
1972
HBC ${{\mathit K}^{-}}{{\mathit p}}$ 3.95 ${\mathrm {GeV/}}\mathit c$
$9.0$ $\pm0.7$
1972
HBC ${{\mathit K}^{-}}{{\mathit p}}$ 1.75 ${\mathrm {GeV/}}\mathit c$
$8.4$ $\pm1.4$
1972
HBC ${{\mathit \Xi}^{-}}{{\mathit \pi}^{+}}$
$11.0$ $\pm1.8$
1972
HBC ${{\mathit \Xi}^{-}}{{\mathit \pi}^{+}}$
$7$ $\pm7$
1966
HBC ${{\mathit K}^{-}}{{\mathit p}}$ 1.5$-$1.7 ${\mathrm {GeV/}}\mathit c$
$8.5$ $\pm3.5$
1966
HBC ${{\mathit K}^{-}}{{\mathit p}}$ 2.24 ${\mathrm {GeV/}}\mathit c$
$7$ $\pm2$
1963 B
HBC ${{\mathit K}^{-}}{{\mathit p}}$ 1.8, 1.95 ${\mathrm {GeV/}}\mathit c$
• • • We do not use the following data for averages, fits, limits, etc. • • •
$12.8$ $\pm1.0$ 2700 1
1981 B
HBC ${{\mathit K}^{-}}{{\mathit p}}$ 8.25 ${\mathrm {GeV/}}\mathit c$
$19$ $\pm6$ 80 2
1979
HBC ${{\mathit K}^{-}}{{\mathit p}}$ 10 ${\mathrm {GeV/}}\mathit c$
$14$ $\pm5$ 100 2
1979
HBC ${{\mathit K}^{-}}{{\mathit p}}$ 16 ${\mathrm {GeV/}}\mathit c$
1 BAUBILLIER 1981B is a fit to the inclusive spectrum. The resolution (5 MeV) is not unfolded.
2 SIXEL 1979 doesn't unfold the experimental resolution of 15 MeV.
References:
BAUBILLIER 1981B
NP B192 1 A Study of Inclusive ${{\mathit \Xi}^{-}}$, ${{\mathit \Xi}{(1530)}}$ and ${{\mathit \Omega}^{-}}$ Production in ${{\mathit K}^{-}}{{\mathit p}}$ Interactions at 8.25 ${\mathrm {GeV/}}\mathit c$
SIXEL 1979
NP B159 125 Inclusive Production of ${{\mathit \Xi}^{-}}$ and ${{\mathit \Xi}^{*}{(1530)}}$ in ${{\mathit K}^{-}}{{\mathit p}}$ Interactions at 10 and 16 ${\mathrm {GeV/}}\mathit c$
DEBELLEFON 1975B
NC 28A 289 Reactions ${{\mathit K}^{-}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit \Xi}^{-}}{{\mathit K}^{0}}{{\mathit \pi}^{+}}$ between 2210 and 2435 MeV $\mathit E_{{\mathrm {cm}}}$
ROSS 1973B
Purdue Conf. 355 ${{\mathit \Xi}{(1530)}^{0}}$ Resonance in Reactions at 3.1 to 3.6 ${\mathrm {GeV/}}\mathit c$
NP B37 429 Search for ${{\mathit \Xi}^{*}}$ Resonances in ${{\mathit K}^{-}}{{\mathit p}}$ Interactions at 3.95 ${\mathrm {GeV/}}\mathit c$
BALTAY 1972
PL 42B 129 Measurement of the ${{\mathit \Xi}^{*}{(1530)}}$ Mass, Width, and Mass Difference
BORENSTEIN 1972
PR D5 1559 Reaction ${{\mathit K}^{-}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit \Xi}^{-}}{{\mathit K}^{0}}{{\mathit \pi}^{+}}$ at 2.18 ${\mathrm {GeV/}}\mathit c$
KIRSCH 1972
NP B40 349 The Mass and Width of the ${{\mathit \Xi}{(1530)}}$
BERGE 1966
PR 147 945 Some Properties of ${{\mathit \Xi}^{-}}$ and ${{\mathit \Xi}^{0}}$ Hyperons Produced in ${{\mathit K}^{-}}{{\mathit p}}$ Interactions between 1.05 and 1.7 ${\mathrm {GeV/}}\mathit c$
LONDON 1966
PR 143 1034 ${{\mathit K}^{-}}{{\mathit p}}$ Interaction at 2.24 BeV
SCHLEIN 1963B
PRL 11 167 Spin Parity Determination of the ${{\mathit \Xi}}{{\mathit \pi}}$ Resonance (1.530 GeV) | 2019-12-05T19:52:16 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.625112771987915, "perplexity": 6744.422041983403}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-51/segments/1575540482038.36/warc/CC-MAIN-20191205190939-20191205214939-00557.warc.gz"} |
https://par.nsf.gov/biblio/10362890-bpt-diagram-cosmological-galaxy-formation-simulations-understanding-physics-driving-offsets-high-redshift | The BPT Diagram in Cosmological Galaxy Formation Simulations: Understanding the Physics Driving Offsets at High Redshift
Abstract
The Baldwin, Philips, & Terlevich diagram of [Oiii]/Hβversus [Nii]/Hα(hereafter N2-BPT) has long been used as a tool for classifying galaxies based on the dominant source of ionizing radiation. Recent observations have demonstrated that galaxies atz∼ 2 reside offset from local galaxies in the N2-BPT space. In this paper, we conduct a series of controlled numerical experiments to understand the potential physical processes driving this offset. We model nebular line emission in a large sample of galaxies, taken from thesimbacosmological hydrodynamic galaxy formation simulation, using thecloudyphotoionization code to compute the nebular line luminosities from Hiiregions. We find that the observed shift toward higher [Oiii]/Hβand [Nii]/Hαvalues at high redshift arises from sample selection: when we consider only the most massive galaxiesM*∼ 1010–11M, the offset naturally appears, due to their high metallicities. We predict that deeper observations that probe lower-mass galaxies will reveal galaxies that lie on a locus comparable toz∼ 0 observations. Even when accounting for samples-selection effects, we find that there is a subtle mismatch between simulations and observations. To resolve this discrepancy, we investigate the impact of varying ionization parameters, Hiiregion densities, gas-phase abundance patterns, and increasing radiation field hardness on N2-BPT diagrams. We find that either decreasing the more »
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; ; ; ; ; ; ; ; ; ; ;
Award ID(s):
Publication Date:
NSF-PAR ID:
10362890
Journal Name:
The Astrophysical Journal
Volume:
926
Issue:
1
Page Range or eLocation-ID:
Article No. 80
ISSN:
0004-637X
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DOI PREFIX: 10.3847
National Science Foundation
##### More Like this
1. Abstract
Existing star-forming vs. active galactic nucleus (AGN) classification schemes using optical emission-line diagnostics mostly fail for low-metallicity and/or highly star-forming galaxies, missing AGN in typicalz∼ 0 dwarfs. To recover AGN in dwarfs with strong emission lines (SELs), we present a classification scheme optimizing the use of existing optical diagnostics. We use Sloan Digital Sky Survey emission-line catalogs overlapping the volume- and mass-limited REsolved Spectroscopy Of a Local VolumE (RESOLVE) and Environmental COntex (ECO) surveys to determine the AGN percentage in SEL dwarfs. Our photoionization grids show that the [Oiii]/Hβversus [Sii]/Hαdiagram (Siiplot) and [Oiii]/Hβversus [Oi]/Hαdiagram (Oiplot) are less metallicity sensitive and more successful in identifying dwarf AGN than the popular [Oiii]/Hβversus [Nii]/Hαdiagnostic (Niiplot or “BPT diagram”). We identify a new category of “star-forming AGN” (SF-AGN) classified as star-forming by the Niiplot but as AGN by the Siiand/or Oiplots. Including SF-AGN, we find thez∼ 0 AGN percentage in dwarfs with SELs to be ∼3%–16%, far exceeding most previous optical estimates (∼1%). The large range in our dwarf AGN percentage reflects differences in spectral fitting methodologies between catalogs. The highly complete nature of RESOLVE and ECO allows us to normalize strong emission-line galaxy statistics to the full galaxy population, reducing the dwarfmore »
2. Abstract
We use Hubble Space Telescope Wide Field Camera 3 G102 and G141 grism spectroscopy to measure rest-frame optical emission-line ratios of 533 galaxies atz∼ 1.5 in the CANDELS LyαEmission at Reionization survey. We compare [Oiii]/Hβversus [Sii]/(Hα+ [Nii]) as an “unVO87” diagram for 461 galaxies and [Oiii]/Hβversus [Neiii]/[Oii] as an “OHNO” diagram for 91 galaxies. The unVO87 diagram does not effectively separate active galactic nuclei (AGN) and [Nev] sources from star-forming galaxies, indicating that the unVO87 properties of star-forming galaxies evolve with redshift and overlap with AGN emission-line signatures atz> 1. The OHNO diagram does effectively separate X-ray AGN and [Nev]-emitting galaxies from the rest of the population. We find that the [Oiii]/Hβline ratios are significantly anticorrelated with stellar mass and significantly correlated with$log(LHβ)$, while [Sii]/(Hα+ [Nii]) is significantly anticorrelated with$log(LHβ)$. Comparison with MAPPINGS V photoionization models indicates that these trends are consistent with lower metallicity and higher ionization in low-mass and high-star formation rate (SFR) galaxies. We do not find evidence for redshift evolution of the emission-line ratios outside of the correlations with mass and SFR. Our results suggest that the OHNO diagram of [Oiii]/Hβversus [Neiii]/[Oii] willmore »
3. ABSTRACT We analyse the rest-optical emission-line spectra of z ∼ 2.3 star-forming galaxies in the complete MOSFIRE Deep Evolution Field (MOSDEF) survey. In investigating the origin of the well-known offset between the sequences of high-redshift and local galaxies in the [O iii]λ5008/Hβ versus [N ii]λ6585/Hα (‘[N ii] BPT’) diagram, we define two populations of z ∼ 2.3 MOSDEF galaxies. These include the high population that is offset towards higher [O iii]λ5008/Hβ and/or [N ii]λ6585/Hα with respect to the local SDSS sequence and the low population that overlaps the SDSS sequence. These two groups are also segregated within the [O iii]λ5008/Hβ versus [S ii]λλ6718,6733/Hα and the [O iii]λλ4960,5008/[O ii ]λλ3727,3730 (O32) versus ([O iii]λλ4960,5008+[O ii]λλ3727,3730)/Hβ (R23) diagrams, which suggests qualitatively that star-forming regions in the more offset galaxies are characterized by harder ionizing spectra at fixed nebular oxygen abundance. We also investigate many galaxy properties of the split sample and find that the high sample is on average smaller in size and less massive, but has higher specific star formation rate (SFR) and SFR surface density values and is slightly younger compared to the low population. From Cloudy+BPASS photoionization models, we estimate that the high population has a lower stellar metallicity (i.e. harder ionizing spectrum) but slightly higher nebular metallicity and higher ionizationmore »
4. Abstract We present spatially resolved Hubble Space Telescope grism spectroscopy of 15 galaxies at z ∼ 0.8 drawn from the DEEP2 survey. We analyze H α +[N ii ], [S ii ], and [S iii ] emission on kiloparsec scales to explore which mechanisms are powering emission lines at high redshifts, testing which processes may be responsible for the well-known offset of high-redshift galaxies from the z ∼ 0 locus in the [O iii ]/H β versus [N ii ]/H α Baldwin—Phillips—Terlevich (BPT) excitation diagram. We study spatially resolved emission-line maps to examine evidence for active galactic nuclei (AGN), shocks, diffuse ionized gas (DIG), or escaping ionizing radiation, all of which may contribute to the BPT offsets observed in our sample. We do not find significant evidence of AGN in our sample and quantify that, on average, AGN would need to contribute ∼25% of the H α flux in the central resolution element in order to cause the observed BPT offsets. We find weak (2 σ ) evidence of DIG emission at low surface brightnesses, yielding an implied total DIG emission fraction of ∼20%, which is not significant enough to be the dominant emission line driver in our sample. Inmore »
5. Abstract
We present results on the nature of extreme ejective feedback episodes and the physical conditions of a population of massive (M*∼ 1011M), compact starburst galaxies atz= 0.4–0.7. We use data from Keck/NIRSPEC, SDSS, Gemini/GMOS, MMT, and Magellan/MagE to measure rest-frame optical and near-IR spectra of 14 starburst galaxies with extremely high star formation rate surface densities (mean ΣSFR∼ 2000Myr−1kpc−2) and powerful galactic outflows (maximum speedsv98∼ 1000–3000 km s−1). Our unique data set includes an ensemble of both emission ([Oii]λλ3726,3729, Hβ, [Oiii]λλ4959,5007, Hα, [Nii]λλ6549,6585, and [Sii]λλ6716,6731) and absorption (Mgiiλλ2796,2803, and Feiiλ2586) lines that allow us to investigate the kinematics of the cool gas phase (T∼ 104K) in the outflows. Employing a suite of line ratio diagnostic diagrams, we find that the central starbursts are characterized by high electron densities (medianne∼ 530 cm−3), and high metallicity (solar or supersolar). We show that the outflows are most likely driven by stellar feedback emerging from the extreme central starburst, rather than by an AGN. We also present multiple intriguing observational signatures suggesting that these galaxies may have substantial Lyman continuum (LyC) photon leakage, including weak [Sii]nebular emission lines. Our results imply that these galaxies may be captured in a short-lived phase of extrememore » | 2023-01-29T02:14:07 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 2, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6330127716064453, "perplexity": 7104.654594121751}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764499697.75/warc/CC-MAIN-20230129012420-20230129042420-00187.warc.gz"} |
https://nroer.gov.in/55ab34ff81fccb4f1d806025/file/58870873472d4a1fef8107d9 | ### Green Energy:
We all depend on fossil fuels for energy but there are other sources as well which are both renewable as well as non-polluting! These could be static, solar, friction, or biogas energy. This model was presented by a student at 38th JL Nehru National Science and Environment exhibition 2011. | 2021-10-27T09:34:19 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9592999815940857, "perplexity": 2559.4301794349726}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323588113.25/warc/CC-MAIN-20211027084718-20211027114718-00428.warc.gz"} |
http://pdglive.lbl.gov/Particle.action?init=0&node=M009&home=MXXX005 | LIGHT UNFLAVORED MESONS($\boldsymbol S$ = $\boldsymbol C$ = $\boldsymbol B$ = 0) For $\mathit I = 1$ (${{\mathit \pi}}$, ${{\mathit b}}$, ${{\mathit \rho}}$, ${{\mathit a}}$): ${\mathit {\mathit u}}$ ${\mathit {\overline{\mathit d}}}$, ( ${\mathit {\mathit u}}$ ${\mathit {\overline{\mathit u}}}−$ ${\mathit {\mathit d}}$ ${\mathit {\overline{\mathit d}}})/\sqrt {2 }$, ${\mathit {\mathit d}}$ ${\mathit {\overline{\mathit u}}}$;for $\mathit I = 0$ (${{\mathit \eta}}$, ${{\mathit \eta}^{\,'}}$, ${{\mathit h}}$, ${{\mathit h}^{\,'}}$, ${{\mathit \omega}}$, ${{\mathit \phi}}$, ${{\mathit f}}$, ${{\mathit f}^{\,'}}$): ${\mathit {\mathit c}}_{{\mathrm {1}}}$( ${{\mathit u}}{{\overline{\mathit u}}}$ $+$ ${{\mathit d}}{{\overline{\mathit d}}}$ ) $+$ ${\mathit {\mathit c}}_{{\mathrm {2}}}$( ${{\mathit s}}{{\overline{\mathit s}}}$ ) INSPIRE search
# ${{\boldsymbol \rho}{(770)}}$ $I^G(J^{PC})$ = $1^+(1^{- -})$
See related review: ${{\mathit \rho}{(770)}}$
${{\boldsymbol \rho}{(770)}}$ MASS
NEUTRAL ONLY, ${{\mathit e}^{+}}{{\mathit e}^{-}}$ $775.26 \pm0.25$ MeV
CHARGED ONLY, ${{\mathit \tau}}$ DECAYS and ${{\mathit e}^{+}}{{\mathit e}^{-}}$ $775.11 \pm0.34$ MeV
MIXED CHARGES, OTHER REACTIONS $763.0 \pm1.2$ MeV
CHARGED ONLY, HADROPRODUCED $766.5 \pm1.1$ MeV
NEUTRAL ONLY, PHOTOPRODUCED $769.0 \pm1.0$ MeV
NEUTRAL ONLY, OTHER REACTIONS $769.0 \pm0.9$ MeV (S = 1.4)
${\mathit m}_{{{\mathit \rho}{(770)}^{0}}}–{\mathit m}_{{{\mathit \rho}{(770)}^{\pm}}}$ $-0.7 \pm0.8$ MeV (S = 1.5)
${\mathit m}_{{{\mathit \rho}{(770)}^{+}}}–{\mathit m}_{{{\mathit \rho}{(770)}^{-}}}$
${{\mathit \rho}{(770)}}$ RANGE PARAMETER $5.3 {}^{+0.9}_{-0.7}$ GeV${}^{-1}$
${{\boldsymbol \rho}{(770)}}$ WIDTH
NEUTRAL ONLY, ${{\mathit e}^{+}}{{\mathit e}^{-}}$ $147.8 \pm0.9$ MeV (S = 2.0)
CHARGED ONLY, ${{\mathit \tau}}$ DECAYS and ${{\mathit e}^{+}}{{\mathit e}^{-}}$ $149.1 \pm0.8$ MeV
MIXED CHARGES, OTHER REACTIONS $149.5 \pm1.3$ MeV
CHARGED ONLY, HADROPRODUCED $150.2 \pm2.4$ MeV
NEUTRAL ONLY, PHOTOPRODUCED $151.7 \pm2.6$ MeV
NEUTRAL ONLY, OTHER REACTIONS $150.9 \pm1.7$ MeV (S = 1.1)
${\Gamma}_{{\mathit \rho}{(770)}^{0}}–{\Gamma}_{{\mathit \rho}{(770)}^{\pm}}$ $0.3 \pm1.3$ MeV (S = 1.4)
${\Gamma}_{{\mathit \rho}{(770)}^{+}}–{\Gamma}_{{\mathit \rho}{(770)}^{-}}$ $1.8 \pm2.1$
$\Gamma_{1}$ ${{\mathit \pi}}{{\mathit \pi}}$ $(\sim100)\%$ 363
constrained fit information | 2019-09-23T14:00:37 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9974702000617981, "perplexity": 3134.8349201839987}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-39/segments/1568514576965.71/warc/CC-MAIN-20190923125729-20190923151729-00020.warc.gz"} |
https://phys.libretexts.org/Bookshelves/College_Physics/Book%3A_Conceptual_Physics_(Crowell)/02._Conservation_of_Energy/2.4_Atomic_Phenomena | $$\require{cancel}$$
# 2.4 Atomic Phenomena
Variety is the spice of life, not of science. So far this chapter has focused on heat energy, kinetic energy, and gravitational energy, but it might seem that in addition to these there is a bewildering array of other forms of energy. Gasoline, chocolate bars, batteries, melting water --- in each case there seems to be a whole new type of energy. The physicist's psyche rebels against the prospect of a long laundry list of types of energy, each of which would require its own equations, concepts, notation, and terminology. The point at which we've arrived in the study of energy is analogous to the period in the 1960's when a half a dozen new subatomic particles were being discovered every year in particle accelerators. It was an embarrassment. Physicists began to speak of the “particle zoo,” and it seemed that the subatomic world was distressingly complex. The particle zoo was simplified by the realization that most of the new particles being whipped up were simply clusters of a previously unsuspected set of fundamental particles (which were whimsically dubbed quarks, a made-up word from a line of poetry by James Joyce, “Three quarks for Master Mark.”) The energy zoo can also be simplified, and it's the purpose of this section to demonstrate the hidden similarities between forms of energy as seemingly different as heat and motion.
### 2.4.1 Heat is kinetic energy.
What is heat really? Is it an invisible fluid that your bare feet soak up from a hot sidewalk? Can one ever remove all the heat from an object? Is there a maximum to the temperature scale?
The theory of heat as a fluid seemed to explain why colder objects absorbed heat from hotter ones, but once it became clear that heat was a form of energy, it began to seem unlikely that a material substance could transform itself into and out of all those other forms of energy like motion or light. For instance, a compost pile gets hot, and we describe this as a case where, through the action of bacteria, chemical energy stored in the plant cuttings is transformed into heat energy. The heating occurs even if there is no nearby warmer object that could have been leaking “heat fluid” into the pile.
An alternative interpretation of heat was suggested by the theory that matter is made of atoms. Since gases are thousands of times less dense than solids or liquids, the atoms (or clusters of atoms called molecules) in a gas must be far apart. In that case, what is keeping all the air molecules from settling into a thin film on the floor of the room in which you are reading this book? The simplest explanation is that they are moving very rapidly, continually ricocheting off of the floor, walls, and ceiling. Though bizarre, the cloud-of-bullets image of a gas did give a natural explanation for the surprising ability of something as tenuous as a gas to exert huge forces.
a / A vivid demonstration that heat is a form of motion. A small amount of boiling water is poured into the empty can, which rapidly fills up with hot steam. The can is then sealed tightly, and soon crumples.
The experiment shown in figure a, for instance, can be explained as follows. The high temperature of the steam is interpreted as a high average speed of random motions of its molecules. Before the lid was put on the can, the rapidly moving steam molecules pushed their way out of the can, forcing the slower air molecules out of the way. As the steam inside the can thinned out, a stable situation was soon achieved, in which the force from the less dense steam molecules moving at high speed balanced against the force from the more dense but slower air molecules outside. The cap was put on, and after a while the steam inside the can began to cool off. The force from the cooler, thin steam no longer matched the force from the cool, dense air outside, and the imbalance of forces crushed the can.
b / Random motion of atoms in a gas, a liquid, and a solid.
This type of observation leads naturally to the conclusion that hotter matter differs from colder in that its atoms' random motion is more rapid. In a liquid, the motion could be visualized as people in a milling crowd shoving past each other more quickly. In a solid, where the atoms are packed together, the motion is a random vibration of each atom as it knocks against its neighbors.
We thus achieve a great simplification in the theory of heat. Heat is simply a form of kinetic energy, the total kinetic energy of random motion of all the atoms in an object. With this new understanding, it becomes possible to answer at one stroke the questions posed at the beginning of the section. Yes, it is at least theoretically possible to remove all the heat from an object. The coldest possible temperature, known as absolute zero, is that at which all the atoms have zero velocity, so that their kinetic energies, $$K=(1/2)mv^2$$, are all zero. No, there is no maximum amount of heat that a certain quantity of matter can have, and no maximum to the temperature scale, since arbitrarily large values of $$v$$ can create arbitrarily large amounts of kinetic energy per atom.
The kinetic theory of heat also provides a simple explanation of the true nature of temperature. Temperature is a measure of the amount of energy per molecule, whereas heat is the total amount of energy possessed by all the molecules in an object.
There is an entire branch of physics, called thermodynamics, that deals with heat and temperature and forms the basis for technologies such as refrigeration. Thermodynamics is discussed in more detail in chapter 5, and I've provided here only a brief overview of the thermodynamic concepts that relate directly to energy.
### 2.4.2 All energy comes from particles moving or interacting.
If I stretch the spring in figure c and then release it, it snaps taut again. The creation of some kinetic energy shows that there must have been some other form of energy that was destroyed. What was it?
c / The spring's energy is really due to electrical interactions among atoms.
We could just invent a new type of energy called “spring energy,” study its behavior, and call it quits, but that would be ugly. Are we going to have to invent a new forms of energy like this, over and over? No: the title of this book doesn't lie, and physics really is fundamentally simple. As shown in figure d, when we bend or stretch an object, we're really changing the distances between the atoms, resulting in a change in electrical energy. Electrical energy isn't really our topic right now --- that's what most of the second half of this book is about --- but conceptually it's very similar to gravitational energy. Like gravitational energy, it depends on $$1/r$$, although there are some interesting new phenomena, such as the existence of both attraction and repulsion, which doesn't occur with gravity because gravitational mass can't be negative. The real point is that all the apparently dissimilar forms of energy in figure d turn out to be due to electrical interactions among atoms.
e / This figure looks similar to the previous ones, but the scale is a million times smaller. The little balls are the neutrons and protons that make up the tiny nucleus at the center of a uranium atom. When the nucleus splits (fissions), the source of the kinetic energy is partly electrical and partly nuclear.
Even if we wish to include nuclear reactions (figure e) in the picture, there still turn out to be only four fundamental types of energy:
• kinetic energy (including heat)
• gravitational energy
• electrical and magnetic energy
• nuclear energy
Astute students have often asked me how light fits into this picture. This is a very good question, and in fact it could be argued that it is the basic question that led to Einstein's theory of relativity as well as the modern quantum picture of nature. Since these are topics for the second half of the book, we'll have to be content with half an answer at this point. For now, we may think of light energy as a form of kinetic energy, but one calculated not according to $$(1/2)mv^2$$ but by some other equation. (We know that $$(1/2)mv^2$$ would not make sense, because light has no mass, and furthermore, high-energy beams of light do not differ in speed from low-energy ones.)
Example 21: Temperature during boiling
$$\triangleright$$ If you stick a thermometer in a pan of water, and watch the temperature as you bring the water to a boil, you'll notice an interesting fact. The temperature goes up until the boiling point is reached, but then stays at $$100°\text{C}$$ during the whole time the water is being boiled off. The temperature of the steam is also $$100°\text{C}$$. Why does the temperature “stick” like this? What's happening to all the energy that the stove's burner is putting into the pan?
d / All these energy transformations turn out at the atomic level to be due to changes in the distances between atoms that interact electrically.
$$\triangleright$$ As shown in figure d, boiling requires an increase in electrical energy, because the atoms coming out as gas are moving away from the other atoms, which attract them electrically. It is only this electrical energy that is increasing, not the atoms' kinetic energy, which is what the thermometer can measure.
Example 22: Diffusion
$$\triangleright$$ A drop of food coloring in a cup of water will gradually spread out, even if you don't do any mixing with a spoon. This is called diffusion. Why would this happen, and what effect would temperature have? What would happen with solids or gases?
$$\triangleright$$ Figure b shows that the atoms in a liquid mingle because of their random thermal motion. Diffusion is slow (typically on the order of a centimeter a minute), despite the high speeds of the atoms (typically hundreds of miles per hour). This is due to the randomness of the motion: a particular atom will take a long time to travel any significant distance, because it doesn't travel in a straight line.
Based on this picture, we expect that the speed of diffusion should increase as a function of temperature, and experiments show that this is true.
Diffusion also occurs in gases, which is why you can smell things even when the air is still. The speeds are much faster, because the typical distance between collisions is much longer than in a liquid.
We can see from figure b that diffusion won't occur in solids, because each atom vibrates around an equilibrium position.
##### Discussion Questions
◊ I'm not making this up. XS Energy Drink has ads that read like this: All the “Energy” ... Without the Sugar! Only 8 Calories!” Comment on this.”
### Contributors
Benjamin Crowell (Fullerton College). Conceptual Physics is copyrighted with a CC-BY-SA license. | 2019-01-18T20:46:06 | {"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": 0.6059584021568298, "perplexity": 468.14334369406214}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-04/segments/1547583660529.12/warc/CC-MAIN-20190118193139-20190118215139-00131.warc.gz"} |
https://pvpmc.sandia.gov/modeling-steps/dc-to-ac-conversion/driesse-et-al-2008-inverter-model/ | Driesse et al. 2008 presents an alternative inverter performance model to accurately express the effects of both power level and input voltage on PV inverter efficiency. Its accuracy was evaluated using CEC measurements on inverters of different sizes and designs.
The model is expressed by the following formula:
$\small&space;p_{loss}&space;=&space;\left&space;(b_{00}+b_{01}\left&space;(&space;v_{in}-1&space;\right&space;)&space;\right&space;)+$
$\small&space;\left&space;(b_{10}+b_{11}\left&space;(&space;v_{in}-1&space;\right&space;)&space;\right&space;)\cdot&space;p_{in}+$
$\small&space;\left&space;(b_{20}+b_{21}\left&space;(&space;v_{in}-1&space;\right&space;)&space;\right&space;)\cdot{p_{in}}^{2}$
where:
• $b$ is the set of empirical parameters whose values are determined by fitting to test data for each specific inverter model.
• $p_{in}$ is the normalized DC power, which is calculated as: $p_{in}=\frac{P_{dc}}{P_{nom}}$
• $v_{in}$ is the normalized DC voltage, which is calculated as: $v_{in}=\frac{V_{dc}}{V_{nom}}$
The nominal values that are used for the normalization are usually the maximum output power rating of the inverter and an input voltage identified as nominal by the manufacturer. The latter may correspond to the voltage where the highest efficiencies are achieved, but this is not a requirement
The Driesse inverter model differs in several ways from the Sandia inverter model:
• It is formulated to calculate power loss rather than efficiency or output power. This leads to smaller relative errors at higher power levels, where accuracy matters most.
• The three main terms of the equation represent measurable physical losses: 1) constant power consumption of auxiliary and drive circuits; 2) switching transition losses and voltage drops in semiconductor junctions; and 3) ohmic or resistive losses. Within each of the three terms the first parameter quantifies the loss when operating at the nominal voltage, and the second parameter specifies the voltage dependency, which is approximated as being linear.
• Normalized power and voltage values are used, which produces parameter values that usually lie in the same numeric range. This allows for meaningful comparison between parameter sets for different inverters, and even makes it possible to reuse parameter sets for inverters that are of the same basic design.
• The recommended form of the model given above uses 6 parameters, but it can be extended to 9 parameters to represent more complex voltage dependencies. On the other hand if no data on voltage dependencies is available it can be used with only 3 parameters. | 2019-12-11T02:41:03 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 8, "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": 0.9048948287963867, "perplexity": 908.7929352547145}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-51/segments/1575540529745.80/warc/CC-MAIN-20191211021635-20191211045635-00232.warc.gz"} |
https://pdglive.lbl.gov/DataBlock.action?node=S016CMR&home=sumtabB | # ${{\overline{\boldsymbol p}}}/{{\boldsymbol p}}$ CHARGE-TO-MASS RATIO, $\vert {\boldsymbol q_{{{\overline{\boldsymbol p}}}}\over {\boldsymbol m}_{{{\overline{\boldsymbol p}}}}}\vert /({\boldsymbol q_{{{\boldsymbol p}}}\over {\boldsymbol m}_{{{\boldsymbol p}}}}$) INSPIRE search
A test of $\mathit CPT$ invariance. Listed here are measurements involving the $\mathit inertial$ masses. For a discussion of what may be inferred about the ratio of ${{\overline{\mathit p}}}$ and ${{\mathit p}}$ $\mathit gravitational$ masses, see ERICSON 1990 ; they obtain an upper bound of $10^{-6}-10^{-7}$ for violation of the equivalence principle for ${{\overline{\mathit p}}}$'s.
VALUE DOCUMENT ID TECN COMMENT
$1.000000000001$ $\pm0.000000000069$
2015
TRAP Penning trap
• • • We do not use the following data for averages, fits, limits, etc. • • •
$0.99999999991$ $\pm0.00000000009$
1999
TRAP Penning trap
$1.0000000015$ $\pm0.0000000011$ 1
1995
TRAP Penning trap
$1.000000023$ $\pm0.000000042$ 2
1990
TRAP Penning trap
1 Equation (2) of GABRIELSE 1995 should read $\mathit M({{\overline{\mathit p}}})/\mathit M({{\mathit p}}$) = $0.999~999~995~$(11) (G.$~$Gabrielse, private communication).
2 GABRIELSE 1990 also measures ${\mathit m}_{{{\overline{\mathit p}}}}/{\mathit m}_{{{\mathit e}^{-}}}$ = $1836.152660$ $\pm0.000083$ and ${\mathit m}_{{{\mathit p}}}/{\mathit m}_{{{\mathit e}^{-}}}$ = $1836.152680$ $\pm0.000088$. Both are completely consistent with the 1986 CODATA (COHEN 1987 ) value for ${\mathit m}_{{{\mathit p}}}/{\mathit m}_{{{\mathit e}^{-}}}$ of $1836.152701$ $\pm0.000037$.
References:
ULMER 2015
NAT 524 196 High-Precision Comparison of the Antiproton-to-Proton Charge-to-Mass Ratio
GABRIELSE 1999
PRL 82 3198 Precision Mass Spectroscopy of the Antiproton and Proton Using Simultaneously Trapped Particles
GABRIELSE 1995
PRL 74 3544 Special Relativity and the Single Antiproton: Fortyfold Improved Comparison of ${{\overline{\mathit p}}}$ and ${{\mathit p}}$ Charge-to-Mass Ratios
GABRIELSE 1990
PRL 65 1317 A 1000 $−$ Fold Improvement in the Measured Antiproton Mass | 2021-03-02T20:57:59 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7136473655700684, "perplexity": 5655.078238979478}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178364764.57/warc/CC-MAIN-20210302190916-20210302220916-00591.warc.gz"} |
http://dlmf.nist.gov/25.16 | # §25.16 Mathematical Applications
## §25.16(i) Distribution of Primes
In studying the distribution of primes , Chebyshev (1851) introduced a function (not to be confused with the digamma function used elsewhere in this chapter), given by
25.16.1
which is related to the Riemann zeta function by
where the sum is taken over the nontrivial zeros of .
The prime number theorem (27.2.3) is equivalent to the statement
25.16.3.
The Riemann hypothesis is equivalent to the statement
25.16.4,
for every .
## §25.16(ii) Euler Sums
Euler sums have the form
where is given by (25.11.33).
is analytic for , and can be extended meromorphically into the half-plane for every positive integer by use of the relations
For integer (), can be evaluated in terms of the zeta function:
25.16.8
has a simple pole with residue () at each odd negative integer , .
is the special case of the function
which satisfies the reciprocity law
when both and are finite.
For further properties of see Apostol and Vu (1984). Related results are:
For further generalizations, see Flajolet and Salvy (1998). | 2013-05-18T16:19:23 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9903082251548767, "perplexity": 1154.141782735698}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368696382560/warc/CC-MAIN-20130516092622-00037-ip-10-60-113-184.ec2.internal.warc.gz"} |
http://dlmf.nist.gov/30.13 | # §30.13(i) Prolate Spheroidal Coordinates
Prolate spheroidal coordinates $\xi,\eta,\phi$ are related to Cartesian coordinates $x,y,z$ by
30.13.1 $\displaystyle x$ $\displaystyle=c\sqrt{(\xi^{2}-1)(1-\eta^{2})}\mathop{\cos\/}\nolimits\phi,$ $\displaystyle y$ $\displaystyle=c\sqrt{(\xi^{2}-1)(1-\eta^{2})}\mathop{\sin\/}\nolimits\phi,$ $\displaystyle z$ $\displaystyle=c\xi\eta,$ Symbols: $\mathop{\cos\/}\nolimits z$: cosine function, $\mathop{\sin\/}\nolimits z$: sine function, $z$: complex variable, $x$: real variable, $y$: real variable, $\xi$: prolate spheroidal coordinate, $\eta$: prolate spheroidal coordinate, $\phi$: prolate spheroidal coordinate and $c$: positive constant A&S Ref: 21.2.2 (in different form) Referenced by: §30.13(i) Permalink: http://dlmf.nist.gov/30.13.E1 Encodings: TeX, TeX, TeX, pMML, pMML, pMML, png, png, png
where $c$ is a positive constant. (On the use of the symbol $\theta$ in place of $\phi$ see §1.5(ii).) The $(x,y,z)$-space without the $z$-axis corresponds to
30.13.2 $\displaystyle 1$ $\displaystyle<\xi$ $\displaystyle<\infty,$ $\displaystyle-1$ $\displaystyle<\eta$ $\displaystyle<1,$ $\displaystyle 0$ $\displaystyle\leq\phi$ $\displaystyle<2\pi.$
The coordinate surfaces $\xi=\mbox{const}.$ are prolate ellipsoids of revolution with foci at $x=y=0$, $z=\pm c$. The coordinate surfaces $\eta=\mbox{const}.$ are sheets of two-sheeted hyperboloids of revolution with the same foci. The focal line is given by $\xi=1$, $-1\leq\eta\leq 1$, and the rays $\pm z\geq c$, $x=y=0$ are given by $\eta=\pm 1$, $\xi\geq 1$.
# §30.13(ii) Metric Coefficients
30.13.3 $\displaystyle h_{\xi}^{2}$ $\displaystyle=\left(\frac{\partial x}{\partial\xi}\right)^{2}+\left(\frac{% \partial y}{\partial\xi}\right)^{2}+\left(\frac{\partial z}{\partial\xi}\right% )^{2}$ $\displaystyle=\frac{c^{2}(\xi^{2}-\eta^{2})}{\xi^{2}-1},$ 30.13.4 $\displaystyle h_{\eta}^{2}$ $\displaystyle=\left(\frac{\partial x}{\partial\eta}\right)^{2}+\left(\frac{% \partial y}{\partial\eta}\right)^{2}+\left(\frac{\partial z}{\partial\eta}% \right)^{2}$ $\displaystyle=\frac{c^{2}(\xi^{2}-\eta^{2})}{1-\eta^{2}},$ 30.13.5 $\displaystyle h_{\phi}^{2}$ $\displaystyle=\left(\frac{\partial x}{\partial\phi}\right)^{2}+\left(\frac{% \partial y}{\partial\phi}\right)^{2}+\left(\frac{\partial z}{\partial\phi}% \right)^{2}$ $\displaystyle=c^{2}(\xi^{2}-1)(1-\eta^{2}).$
# §30.13(iii) Laplacian
30.13.6 $\nabla^{2}=\frac{1}{h_{\xi}h_{\eta}h_{\phi}}\left(\frac{\partial}{\partial\xi}% \left(\frac{h_{\eta}h_{\phi}}{h_{\xi}}\frac{\partial}{\partial\xi}\right)+% \frac{\partial}{\partial\eta}\left(\frac{h_{\xi}h_{\phi}}{h_{\eta}}\frac{% \partial}{\partial\eta}\right)+\frac{\partial}{\partial\phi}\left(\frac{h_{\xi% }h_{\eta}}{h_{\phi}}\frac{\partial}{\partial\phi}\right)\right)=\frac{1}{c^{2}% (\xi^{2}-\eta^{2})}\left(\frac{\partial}{\partial\xi}\left((\xi^{2}-1)\frac{% \partial}{\partial\xi}\right)+\frac{\partial}{\partial\eta}\left((1-\eta^{2})% \frac{\partial}{\partial\eta}\right)+\frac{\xi^{2}-\eta^{2}}{(\xi^{2}-1)(1-% \eta^{2})}\frac{{\partial}^{2}}{{\partial\phi}^{2}}\right).$
# §30.13(iv) Separation of Variables
The wave equation
30.13.7 $\nabla^{2}w+\kappa^{2}w=0,$ Symbols: $\kappa$: parameter and $w_{j}$: solution to DE Referenced by: §30.13(iv), §30.13(v), §30.14(iv), §30.14(iv), §30.14(v) Permalink: http://dlmf.nist.gov/30.13.E7 Encodings: TeX, pMML, png
transformed to prolate spheroidal coordinates $(\xi,\eta,\phi)$, admits solutions
30.13.8 $w(\xi,\eta,\phi)=w_{1}(\xi)w_{2}(\eta)w_{3}(\phi),$
where $w_{1}$, $w_{2}$, $w_{3}$ satisfy the differential equations
30.13.9 $\frac{d}{d\xi}\left((1-\xi^{2})\frac{dw_{1}}{d\xi}\right)+\left(\lambda+\gamma% ^{2}(1-\xi^{2})-\frac{\mu^{2}}{1-\xi^{2}}\right)w_{1}=0,$
30.13.10 $\frac{d}{d\eta}\left((1-\eta^{2})\frac{dw_{2}}{d\eta}\right)+\left(\lambda+% \gamma^{2}(1-\eta^{2})-\frac{\mu^{2}}{1-\eta^{2}}\right)w_{2}=0,$
30.13.11 $\frac{{d}^{2}w_{3}}{{d\phi}^{2}}+\mu^{2}w_{3}=0,$
with $\gamma^{2}=\kappa^{2}c^{2}\geq 0$ and separation constants $\lambda$ and $\mu^{2}$. Equations (30.13.9) and (30.13.10) agree with (30.2.1).
In most applications the solution $w$ has to be a single-valued function of $(x,y,z)$, which requires $\mu=m$ (a nonnegative integer) and
30.13.12 $w_{3}(\phi)=a_{3}\mathop{\cos\/}\nolimits\!\left(m\phi\right)+b_{3}\mathop{% \sin\/}\nolimits\!\left(m\phi\right).$
Moreover, $w$ has to be bounded along the $z$-axis away from the focal line: this requires $w_{2}(\eta)$ to be bounded when $-1<\eta<1$. Then $\lambda=\mathop{\lambda^{m}_{n}\/}\nolimits\!\left(\gamma^{2}\right)$ for some $n=m,m+1,m+2,\dots$, and the general solution of (30.13.10) is
30.13.13 $w_{2}(\eta)=a_{2}\mathop{\mathsf{Ps}^{m}_{n}\/}\nolimits\!\left(\eta,\gamma^{2% }\right)+b_{2}\mathop{\mathsf{Qs}^{m}_{n}\/}\nolimits\!\left(\eta,\gamma^{2}% \right).$
The solution of (30.13.9) with $\mu=m$ is
30.13.14 $w_{1}(\xi)=a_{1}\mathop{S^{m(1)}_{n}\/}\nolimits\!\left(\xi,\gamma\right)+b_{1% }\mathop{S^{m(2)}_{n}\/}\nolimits\!\left(\xi,\gamma\right).$
If $b_{1}=b_{2}=0$, then the function (30.13.8) is a twice-continuously differentiable solution of (30.13.7) in the entire $(x,y,z)$-space. If $b_{2}=0$, then this property holds outside the focal line.
# §30.13(v) The Interior Dirichlet Problem for Prolate Ellipsoids
Equation (30.13.7) for $\xi\leq\xi_{0}$, and subject to the boundary condition $w=0$ on the ellipsoid given by $\xi=\xi_{0}$, poses an eigenvalue problem with $\kappa^{2}$ as spectral parameter. The eigenvalues are given by $c^{2}\kappa^{2}=\gamma^{2}$, where $\gamma$ is determined from the condition
30.13.15 $\mathop{S^{m(1)}_{n}\/}\nolimits\!\left(\xi_{0},\gamma\right)=0.$
The corresponding eigenfunctions are given by (30.13.8), (30.13.14), (30.13.13), (30.13.12), with $b_{1}=b_{2}=0$. For the Dirichlet boundary-value problem of the region $\xi_{1}\leq\xi\leq\xi_{2}$ between two ellipsoids, the eigenvalues are determined from
30.13.16 $w_{1}(\xi_{1})=w_{1}(\xi_{2})=0,$ Symbols: $\xi$: prolate spheroidal coordinate and $w_{j}$: solution to DE Permalink: http://dlmf.nist.gov/30.13.E16 Encodings: TeX, pMML, png
with $w_{1}$ as in (30.13.14). The corresponding eigenfunctions are given as before with $b_{2}=0$.
For further applications see Meixner and Schäfke (1954), Meixner et al. (1980) and the references cited therein; also Ong (1986), Müller et al. (1994), and Xiao et al. (2001). | 2014-08-28T23:17:41 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 192, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.980468213558197, "perplexity": 1691.6224598902195}, "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-2014-35/segments/1408500831098.94/warc/CC-MAIN-20140820021351-00276-ip-10-180-136-8.ec2.internal.warc.gz"} |
https://gea.esac.esa.int/archive/documentation/GEDR3/Catalogue_consolidation/chap_cu9val/sec_cu9val_945/ssec_cu9val_945_subsets.html | # 8.5.4 Comparison with subsets
We also compared the 2D clustering in edr3int3 with its subsets. In particular, we consider the brightest ($bt11$), and the faintest ($ft20$) subsets. Figure 8.25 shows that in general, compared to the all sky dataset, there is more clustering in the brightest subset, and less clustering in the faintest subset, except for quantiles in faint: the nearly horizontal distribution of points is due to the flux quantiles, which because of ‘noise’ on the measurements at the faint end becomes more uniform, and less on the 1-to-1 line.
While in the bright subset, where there is more clustering in the full dataset, this is because for the bright subset, most stars have really small errors and hence, all fall in one bin, making the KLD very low. | 2022-01-19T03:43:16 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 2, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7997145652770996, "perplexity": 1347.7859634758415}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320301263.50/warc/CC-MAIN-20220119033421-20220119063421-00306.warc.gz"} |
http://lammps.sandia.gov/doc/dimension.html | # dimension command
## Syntax
dimension N
• N = 2 or 3
## Examples
dimension 2
## Description
Set the dimensionality of the simulation. By default LAMMPS runs 3d simulations. To run a 2d simulation, this command should be used prior to setting up a simulation box via the create_box or read_data commands. Restart files also store this setting.
See the discussion in Section 6 for additional instructions on how to run 2d simulations.
Note
Some models in LAMMPS treat particles as finite-size spheres or ellipsoids, as opposed to point particles. In 2d, the particles will still be spheres or ellipsoids, not circular disks or ellipses, meaning their moment of inertia will be the same as in 3d.
## Restrictions
This command must be used before the simulation box is defined by a read_data or create_box command.
## Default
dimension 3 | 2018-06-21T18:15:25 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.30432718992233276, "perplexity": 3101.3765491301815}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-26/segments/1529267864256.26/warc/CC-MAIN-20180621172638-20180621192638-00184.warc.gz"} |
Subsets and Splits