Ising model

SearchAdvancedHelp

(0.001 seconds)

11—20 of 20 matching pages

11: Foreword

… ►The provision of standard reference data of this type is a core function of NIST. … ►The new printed volume, the NIST Handbook of Mathematical Functions, serves a similar function as the original A&S, though it is heavily updated and extended. …The DLMF may well serve as a model for the effective presentation of highly mathematical reference material on the Web. … ►Their unfailing dedication is acknowledged deeply and gratefully. Particular attention is called to the generous support of the National Science Foundation, which made possible the participation of experts from academia and research institutes worldwide. …

12: Ian J. Thompson

… ► 1953 in New Zealand) has been since 2006 a Theoretical Nuclear Physicist in the Nuclear Theory and Modeling Group of the Lawrence Livermore National Laboratory, Livermore, California. … ►Thompson is a Fellow of the U. … ►Thompson is author of the following DLMF Chapter …

13: 5.20 Physical Applications

… ►

Solvable Models of Statistical Mechanics

►Suppose the potential energy of a gas of $n$ point charges with positions $x_1,x_2,\mathrm{\dots },x_n$ and free to move on the infinite line , is given by …The probability density of the positions when the gas is in thermodynamic equilibrium is: …where $k$ is the Boltzmann constant, $T$ the temperature and $C$ a constant. … ►and the partition function is given by …

14: Daniel W. Lozier

… ►He is currently a Research Associate at NIST and a General Editor for the DLMF project. … ►Then he transferred to NIST (then known as the National Bureau of Standards), where he collaborated for several years with the Building and Fire Research Laboratory developing and applying finite-difference and spectral methods to differential equation models of fire growth. …

15: 19.33 Triaxial Ellipsoids

… ►The potential is …and the electric capacity $C=Q/V(0)$ is given by … ►A conducting elliptic disk is included as the case $c=0$. … ►Ellipsoidal distributions of charge or mass are used to model certain atomic nuclei and some elliptical galaxies. …In suitable units the self-energy of the distribution is given by …

16: Bibliography M

… ►

Two-point quasi-fractional approximations to the Airy function $\mathrm{Ai}(x)$ . J. Comput. Phys. 99 (2), pp. 337–340.

ⓘ

Notes:

There is an error in Eq. (5): the second term in parentheses needs to be multiplied by $x$.

External Links:

ISSN 0021-9991, Document, MathReview Entry, ZentralBlatt

Referenced by:

1st item.

Encodings:

BibTeX

… ►

Spectral functions for the Tomonaga-Luttinger model. Phys. Rev. B 46 (24), pp. 15753–15760.

ⓘ

External Links:

Document

Referenced by:

§13.28(iii).

Encodings:

BibTeX

… ►

Calculation of the complete elliptic integrals with complex modulus. Numer. Math. 29 (2), pp. 233–236.

ⓘ

Notes:

An Algol procedure for calculating the complete elliptic integrals of the first and the second kind with complex modulus $k$ is included.

External Links:

ISSN 0029-599X, Document, MathReview (H. E. Fettis), ZentralBlatt

Referenced by:

§19.36(ii), §19.39(ii).

Encodings:

BibTeX

… ►

Further improvements of some double inequalities for bounding the gamma function. Math. Comput. Modelling 57 (5-6), pp. 1360–1363.

ⓘ

External Links:

ISSN 0895-7177, Document, FullText, MathReview (Emil C. Popa)

Referenced by:

§5.6(i).

Encodings:

BibTeX

… ►

ⓘ

Notes:

MPFR is a C library for multiple-precision floating-point computations with correct rounding. The main goal of MPFR is to provide a library for multiple-precision floating-point computation which is both efficient and has well-defined semantics. MPFR includes most of the elementary functions. It also implements the gamma function, and more special functions are planned in the future.

External Links:

MPFR

Referenced by:

§ ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index.

Encodings:

BibTeX

…

17: 31.17 Physical Applications

… ►The problem of adding three quantum spins $𝐬$, $𝐭$, and $𝐮$ can be solved by the method of separation of variables, and the solution is given in terms of a product of two Heun functions. … ►for the common eigenfunction $\mathrm{\Psi }(𝐱)=\mathrm{\Psi }(x_s,x_t,x_u)$, where $a$ is the coupling parameter of interacting spins. … ►For application of biconfluent Heun functions in a model of an equatorially trapped Rossby wave in a shear flow in the ocean or atmosphere see Boyd and Natarov (1998). …

18: Bibliography L

… ►

Exact computation of the $3$-$j$ and $6$-$j$ symbols. Comput. Phys. Comm. 61 (3), pp. 350–360.

ⓘ

Notes:

A Fortran program is included.

External Links:

Document, ZentralBlatt

Referenced by:

§34.15.

Encodings:

BibTeX

… ►

Exact operator solution of the Calogero-Sutherland model. Comm. Math. Phys. 178 (2), pp. 425–452.

ⓘ

Notes:

For a Maple implementation of the algorithm given in this paper for Jack and zonal polynomials see Zeilberger (website).

External Links:

ISSN 0010-3616, Link, MathReview (Kazuhiro Hikami), ZentralBlatt

Referenced by:

§35.12.

Encodings:

BibTeX

… ►

Well-posedness and blow-up solutions for an integrable nonlinearly dispersive model wave equation. J. Differential Equations 162 (1), pp. 27–63.

ⓘ

External Links:

ISSN 0022-0396, Document, MathReview (John Albert), ZentralBlatt

Referenced by:

§22.19(iii).

Encodings:

BibTeX

…

19: Bibliography C

… ►

Analytical solution of a model for complex food webs. Phys. Rev. E 65 (3), pp. (030901–1)–(030901–4).

ⓘ

External Links:

Document

Referenced by:

§8.24(i).

Encodings:

BibTeX

… ►

Reduction theorems for elliptic integrands with the square root of two quadratic factors. J. Comput. Appl. Math. 118 (1-2), pp. 71–85.

ⓘ

Notes:

Code written by the second author to compute symmetric elliptic integrals numerically in the Derive computer algebra system is available.

External Links:

ISSN 0377-0427, Document, Code, MathReview, ZentralBlatt

Referenced by:

§19.29(ii), §19.36(i), §19.36(i), §19.39(iv).

Encodings:

BibTeX

… ►

Toward symbolic integration of elliptic integrals. J. Symbolic Comput. 28 (6), pp. 739–753.

ⓘ

Notes:

Code written by J. FitzSimons to generate reduction tables for elliptic integrals symbolically in the Derive computer algebra system is available.

External Links:

ISSN 0747-7171, Document, Code, MathReview (Axel Riese), ZentralBlatt

Referenced by:

§19.29(i), §19.29(ii), §19.29(ii), §19.29(ii), §19.29(ii).

Encodings:

BibTeX

…

20: Bibliography S

… ►

An Introduction to the Operations with Series. 2nd edition, Chelsea Publishing Co., New York.

ⓘ

Notes:

This is a reprint, with corrections, of the first edition [University of Pennsylvania Press, Philadelphia, Pa., 1924].

External Links:

MathReview, ZentralBlatt

Referenced by:

§24.1, §24.6.

Encodings:

BibTeX

… ►

Parabolic Cylinder Functions and their Application in Symmetric Two-centre Shell Model. In Proceedings of the Conference on Mathematical Analysis and its Applications (Inst. Engrs., Mysore, 1977), Matscience Rep., Vol. 91, Aarhus, pp. P81–P89.

ⓘ

External Links:

MathReview

Referenced by:

§12.17.

Encodings:

BibTeX

… ►

ⓘ

Notes:

The SLATEC Common Math Library is a large general purpose mathematical software library with broad coverage of elementary and special functions. Implementations in both single and double precision are provided. Developed by a consortium of US national laboratories. See Buzbee (1984).

External Links:

GAMS (package SLATEC)

Referenced by:

§ ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index.

Encodings:

BibTeX

… ►

Some comments on Fourier analysis, uncertainty and modeling. SIAM Rev. 25 (3), pp. 379–393.

ⓘ

External Links:

ISSN 0036-1445, Document, MathReview (H. Vincent Poor), ZentralBlatt

Referenced by:

§30.15(ii), §30.15(iii), §30.15(iv), §30.15(v), §30.15(v).

Encodings:

BibTeX

… ►

Numerical Methods Based on Sinc and Analytic Functions. Springer Series in Computational Mathematics, Vol. 20, Springer-Verlag, New York.

ⓘ

Notes:

Sinc-Pack, a set of 480 Matlab programs with a 470-page tutorial, is available for purchase from SINC, LLC by contacting Frank Stenger.

External Links:

ISBN 0-387-94008-1, MathReview (B. Boyanov), ZentralBlatt

Referenced by:

§3.3(vi), §3.4(i), §3.5(i).

Encodings:

BibTeX

…