172 Matching Results

Search Results

Advanced search parameters have been applied.

in subjects: "Algebra"

open access

Basic linear algebra subprograms for FORTRAN usage. [BLAS, in FORTRAN and assembly language for IBM 360/67, CDC 6600 and 7600, and Univac 1108]

A package of 38 low-level subprograms for many of the basic operations of numerical linear algebra is presented. The package is intended to be used with FORTRAN. The operations in the package are dot products, elementary vector operations, Givens transformations, vector copy and swap, vector norms, vector scaling, and the indices of components of largest magnitude. The subprograms and a test driver are available in portable FORTRAN. Versions of the subprograms are also provided in assembly lang… more

Date: October 1, 1977

Creator: Lawson, C.L.; Hanson, R.J.; Kincaid, D.R. & Krogh, F.T.

Item Type: Report

Partner: UNT Libraries Government Documents Department

open access

Degenerate perturbation theory

The algebraic structure of degenerate Rayleigh-Schroedinger perturbation theory is reviewed. There are a number of different but equivalent algorithms which generate this perturbation series; we argue that the frequent need to carry out infinite-order partial summations selects one of these algorithms as the most efficient. Recent developments include coupled-cluster formulations for open shells, a new diagrammatic representation, and the concept of incomplete model subspaces. These subjects ar… more

Date: January 1, 1982

Creator: Brandow, B.

Item Type: Article

Partner: UNT Libraries Government Documents Department

open access

Algebraic calculation of stroboscopic maps of ordinary, nonlinear differential equations

The relation between the parameters of a differential equation and corresponding discrete maps are becoming increasingly important in the study of nonlinear dynamical systems. Maps are well adopted for numerical computation and several universal properties of them are known. Therefore some perturbation methods have been proposed to deduce them for physical systems, which can be modeled by an ordinary differential equation (ODE) with a small nonlinearity. A new iterative, rigorous algebraic meth… more

Date: July 25, 1991

Creator: Wackerbauer, R. (Max-Planck-Institut fuer Extraterrestrische Physik, Garching (Germany)); Huebler, A. (Illinois Univ., Urbana, IL (United States). Center for Complex Systems Research) & Mayer-Kress, G. (Los Alamos National Lab., NM (United States) California Univ., Santa Cruz, CA (United States). Dept. of Mathematics)

Item Type: Article

Partner: UNT Libraries Government Documents Department

open access

High energy behavior of fermion--meson and meson--meson scattering in a supersymmetric field theory

A review of the general methods of high energy calculations within the framework of field theory is given. These include Feynman parameter methods, the infinite momentum frame, and Mellin transform methods. A general discussion of supersymmetry is also presented. The basic aspects of the Wess-Zumino model are given. This includes a proof of renormalizability through one-loop, and a derivation of the Feynman rules. The general supersymmetry algebra is presented. The method of generating represen… more

Date: December 1, 1977

Creator: Opoien, J.W.

Item Type: Report

Partner: UNT Libraries Government Documents Department

open access

Dimensions, induces and congruence classes of representations of affine Kac-Moody algebras (with examples for affine E/sub 8/)

Affine generalizations of some familiar notions from the representation theory of semisimple Lie algebras/groups are introduced, described and illustrated. The multiplicity of a weight and the dimension congruence class, and indices of a representation are touched upon. Examples of the highest weight representations of affine E/sub 8/ are considered as a preview of far more extensive results of this type to appear.

Date: January 1, 1986

Creator: Kass, S.N. & Patera, J.

Item Type: Article

Partner: UNT Libraries Government Documents Department

open access

Meson dynamics in large-N limit

The large-N limit of QCD with matter fields present is considered in a Hamiltonian loop space approach. The semi-classical nature of the large-N limit is clarified where a valence approximation emerges naturally. A pseudospin algebra is introduced for handling fermions.

Date: January 1, 1983

Creator: Tan, C.I.

Item Type: Article

Partner: UNT Libraries Government Documents Department

open access

Algebraic approaches to nuclear structure

The concept and application of algebraic models to nuclear structure is surveyed with emphasis on interpretations in terms of traditional geometric models. Recent studies relating to the relationship between {beta} and {gamma} vibrations in deformed nuclei, to the rigidity or softness of axial asymmetry, to signature splitting in octupole excitations, to O(6) quantum numbers and multi-phonon excitations, and to pseudo-SU(3) are discussed. 31 refs., 9 figs.

Date: January 1, 1991

Creator: Casten, R.F. (Brookhaven National Lab., Upton, NY (USA) Koeln Univ. (Germany, F.R.). Inst. fuer Kernphysik)

Item Type: Article

Partner: UNT Libraries Government Documents Department

open access

LAPACK users' guide: Release 1. 0

LAPACK is a transportable library of Fortran 77 subroutines for solving the most common problems in numerical linear algebra: systems of linear equations, linear least squares problems, eigenvalue problems and singular value problems. LAPACK is designed to supersede LINPACK and EISPACK, principally by restructuring the software to achieve much greater efficiency on vector processors, high-performance superscalar'' workstations, and shared-memory multi-processors. LAPACK also adds extra function… more

Date: January 31, 1992

Creator: Anderson, E.; Bai, Z.; Bischof, C.; Demmel, J.; Dongarra, J.; Du Croz, J. et al.

Item Type: Report

Partner: UNT Libraries Government Documents Department

National Mathematics Advisory Panel

The U.S. Department of Education, in partnership with the Conference Board of Mathematical Sciences, hosted the first National Math Panel Forum on October 6-7, 2008. This page documents the Forum activities, which brought together various organizations and other interested parties.

Date: 2008

Creator: National Mathematics Advisory Panel

Item Type: Website

Partner: UNT Libraries Government Documents Department

open access

Mapping the geometry of the F4 group

In this paper, we present a construction of the compact form of the exceptional Lie group F4 by exponentiating the corresponding Lie algebra f4. We realize F4 as the automorphisms group of the exceptional Jordan algebra, whose elements are 3 x 3 Hermitian matrices with octonionic entries. We use a parametrization which generalizes the Euler angles for SU(2) and is based on the fibration of F4 via a Spin(9) subgroup as a fiber. This technique allows us to determine an explicit expression for the… more

Date: May 28, 2007

Creator: Bernardoni, Fabio; Cacciatori, Sergio L; Scotti, Antonio & Cerchiai, Bianca L.

Item Type: Article

Partner: UNT Libraries Government Documents Department

open access

Mapping the geometry of the E6 group

In this paper we present a construction for the compact form of the exceptional Lie group E{sub 6} by exponentiating the corresponding Lie algebra e{sub 6}, which we realize as the sum of f{sub 4}, the derivations of the exceptional Jordan algebra J{sub 3} of dimension 3 with octonionic entries, and the right multiplication by the elements of J{sub 3} with vanishing trace. Our parameterization is a generalization of the Euler angles for SU(2) and it is based on the fibration of E{sub 6} via a F… more

Date: October 1, 2007

Creator: Cerchiai , Bianca; Bernardoni, Fabio; Cacciatori, Sergio L.; Cerchiai, Bianca L. & Scotti, Antonio

Item Type: Article

Partner: UNT Libraries Government Documents Department

open access

Communication Requirements and Interconnect Optimization forHigh-End Scientific Applications

The path towards realizing peta-scale computing isincreasingly dependent on building supercomputers with unprecedentednumbers of processors. To prevent the interconnect from dominating theoverall cost of these ultra-scale systems, there is a critical need forhigh-performance network solutions whose costs scale linearly with systemsize. This work makes several unique contributions towards attaining thatgoal. First, we conduct one of the broadest studies to date of high-endapplication communicati… more

Date: November 12, 2007

Creator: Kamil, Shoaib; Oliker, Leonid; Pinar, Ali & Shalf, John

Item Type: Article

Partner: UNT Libraries Government Documents Department

open access

Soft Error Vulnerability of Iterative Linear Algebra Methods

Devices become increasingly vulnerable to soft errors as their feature sizes shrink. Previously, soft errors primarily caused problems for space and high-atmospheric computing applications. Modern architectures now use features so small at sufficiently low voltages that soft errors are becoming significant even at terrestrial altitudes. The soft error vulnerability of iterative linear algebra methods, which many scientific applications use, is a critical aspect of the overall application vulner… more

Date: December 15, 2007

Creator: Bronevetsky, G & de Supinski, B

Item Type: Article

Partner: UNT Libraries Government Documents Department

open access

EXTENSION OF THE 1D FOUR-GROUP ANALYTIC NODAL METHOD TO FULL MULTIGROUP

In the mid 80’s, a four-group/two-region, entirely analytical 1D nodal benchmark appeared. It was readily acknowledged that this special case was as far as one could go in terms of group number and still achieve an analytical solution. In this work, we show that by decomposing the solution to the multigroup diffusion equation into homogeneous and particular solutions, extension to any number of groups is a relatively straightforward exercise using the mathematics of linear algebra.

Date: September 1, 2008

Creator: Ganapol, B. D. & Nigg, D. W.

Item Type: Article

Partner: UNT Libraries Government Documents Department

open access

Deformed Matrix Models, Supersymmetric Lattice Twists and N=1/4 Supersymmetry

A manifestly supersymmetric nonperturbative matrix regularization for a twisted version of N = (8, 8) theory on a curved background (a two-sphere) is constructed. Both continuum and the matrix regularization respect four exact scalar supersymmetries under a twisted version of the supersymmetry algebra. We then discuss a succinct Q = 1 deformed matrix model regularization of N = 4 SYM in d = 4, which is equivalent to a non-commutative A*{sub 4} orbifold lattice formulation. Motivated by recent p… more

Date: September 24, 2008

Creator: Unsal, Mithat

Item Type: Article

Partner: UNT Libraries Government Documents Department

open access

Sensitivity technologies for large scale simulation.

Sensitivity analysis is critically important to numerous analysis algorithms, including large scale optimization, uncertainty quantification,reduced order modeling, and error estimation. Our research focused on developing tools, algorithms and standard interfaces to facilitate the implementation of sensitivity type analysis into existing code and equally important, the work was focused on ways to increase the visibility of sensitivity analysis. We attempt to accomplish the first objective throu… more

Date: January 1, 2005

Creator: Collis, Samuel Scott; Bartlett, Roscoe Ainsworth; Smith, Thomas Michael; Heinkenschloss, Matthias (Rice University, Houston, TX); Wilcox, Lucas C. (Brown University, Providence, RI); Hill, Judith C. (Carnegie Mellon University, Pittsburgh, PA) et al.

Item Type: Report

Partner: UNT Libraries Government Documents Department

open access

PERI - Auto-tuning Memory Intensive Kernels for Multicore

We present an auto-tuning approach to optimize application performance on emerging multicore architectures. The methodology extends the idea of search-based performance optimizations, popular in linear algebra and FFT libraries, to application-specific computational kernels. Our work applies this strategy to Sparse Matrix Vector Multiplication (SpMV), the explicit heat equation PDE on a regular grid (Stencil), and a lattice Boltzmann application (LBMHD). We explore one of the broadest sets of m… more

Date: June 24, 2008

Creator: Bailey, David H.; Williams, Samuel; Datta, Kaushik; Carter, Jonathan; Oliker, Leonid; Shalf, John et al.

Item Type: Article

Partner: UNT Libraries Government Documents Department

open access

Soft Error Vulnerability of Iterative Linear Algebra Methods

Devices are increasingly vulnerable to soft errors as their feature sizes shrink. Previously, soft error rates were significant primarily in space and high-atmospheric computing. Modern architectures now use features so small at sufficiently low voltages that soft errors are becoming important even at terrestrial altitudes. Due to their large number of components, supercomputers are particularly susceptible to soft errors. Since many large scale parallel scientific applications use iterative li… more

Date: January 19, 2008

Creator: Bronevetsky, G & de Supinski, B

Item Type: Article

Partner: UNT Libraries Government Documents Department

open access

Conformal Field Theories: From Old to New

In a short review of recent work, we discuss the general problem of constructing the actions of new conformal field theories from old conformal field theories. Such a construction follows when the old conformal field theory admits new conformal stress tensors in its chiral algebra, and it turns out that the new conformal field theory is generically a new spin-two gauge theory. As an example we discuss the new spin-two gauged sigma models which arise in this fashion from the general conformal no… more

Date: February 11, 1998

Creator: Halpern, M. B. & Schwartz, C.

Item Type: Article

Partner: UNT Libraries Government Documents Department

open access

Understanding Ultra-Scale Application CommunicationRequirements

As thermal constraints reduce the pace of CPU performance improvements, the cost and scalability of future HPC architectures will be increasingly dominated by the interconnect. In this work we perform an in-depth study of the communication requirements across a broad spectrum of important scientific applications, whose computational methods include: finite-difference, lattice-boltzmann, particle in cell, sparse linear algebra, particle mesh ewald, and FFT-based solvers. We use the IPM (integrat… more

Date: January 1, 2005

Creator: Shoaib, Kamil; Shalf, John; Oliker, Leonid & Skinner, David

Item Type: Article

Partner: UNT Libraries Government Documents Department

open access

LDRD final report on massively-parallel linear programming : the parPCx system.

This report summarizes the research and development performed from October 2002 to September 2004 at Sandia National Laboratories under the Laboratory-Directed Research and Development (LDRD) project ''Massively-Parallel Linear Programming''. We developed a linear programming (LP) solver designed to use a large number of processors. LP is the optimization of a linear objective function subject to linear constraints. Companies and universities have expended huge efforts over decades to produce f… more

Date: February 1, 2005

Creator: Parekh, Ojas (Emory University, Atlanta, GA); Phillips, Cynthia Ann & Boman, Erik Gunnar

Item Type: Report

Partner: UNT Libraries Government Documents Department

open access

New topological invariants for non-abelian antisymmetric tensor fields from extended BRS algebra

Extended non-linear BRS and Gauge transformations containing Lie algebra cocycles, and acting on non-abelian antisymmetric tensor fields are constructed in the context of free differential algebras. New topological invariants are given in this framework. 6 refs.

Date: September 1, 1988

Creator: Boukraa, S.; Maillet, J.M. & Nijhoff, F.

Item Type: Article

Partner: UNT Libraries Government Documents Department

open access

Dual spaces of differential lie algebras

No Description Available.

Date: January 1, 1981

Creator: Kupershmidt, B. A.

Item Type: Article

Partner: UNT Libraries Government Documents Department

open access

Toroidal compactification of closed bosonic strings

The boundary conditions of a free closed bosonic string propagating in a space where the compactified dimensions are toroidal limit the lattices defining the tori to be self dual, just as is required by modular invariance of the one-loop dual amplitudes. The spectra generated by the free-string oscillators for both Euclidean and Lorentzian lattice are described. 10 refs.

Date: January 1, 1986

Creator: Slansky, R.

Item Type: Article

Partner: UNT Libraries Government Documents Department