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Computer Algebra Systems [chapter]

Michael Dewar, Johannes Grabmeier, Stephen Watt, Bernhard Kutzler, John Cannon, Bill Unger, Wolfgang Windsteiger, Jürgen Gerhard, Andreas Sorgatz, Herbert Melenk, Sebastien Veigneau, David P. Jacobs (+91 others)
2003 Computer Algebra Handbook  
Through the use of an adequate coordinate system objects are described by equations as simple as possible, geometric transformations by matrices.  ...  Computer Algebra Systems -Old Wine in New Bottles?  ... 
doi:10.1007/978-3-642-55826-9_4 fatcat:3imemzg6zbd6zalw5xtq6zlktq

Das Fehlertolerante System Tandem T16 [chapter]

Alfred Schulz
1984 Software-Fehlertoleranz und -Zuverlässigkeit  
Zhejiang Universität, College of Computer Science: Hangzhou, China, p 1 12.Dosch W, Magnussen S (2002) Lübeck Transformation System: A Trans- formation System for Equational Higher-Order Algebraic Specifications  ...  Heriot-Watt Universität: Edinburgh, pp 63-78 26.Magnussen S (2003) Mechanizing the Transformation of Higher-Order Alge- braic Specification for the Development of Software Systems.  ...  Ferner werden die im Rahmen von TESE-ICSI erhobenen histologischen Daten im Hinblick u. a. auf ihren prognostischen Wert und auf die Sicherheit bei der Beurteilung eines Sertoli-Zell-Only-Syndroms ausgewertet  ... 
doi:10.1007/978-3-642-69705-0_18 dblp:conf/icftcs/Schulz84 fatcat:mcbxefmt25ajljtzk6nh5vudqq

Universality classes in nonequilibrium lattice systems

Géza Ódor
2004 Reviews of Modern Physics  
The main body of this work is given in section four where genuine, dynamical universality classes specific to nonequilibrium systems are introduced.  ...  In the second section I briefly address the question of scaling behavior at first order phase transitions.  ...  IV.A.3͒, and in models described by field theory with higher-order terms like 3 ͑x , t͒ or ٌ 4 ͑x , t͒, which are irrelevant under the RG transformation.  ... 
doi:10.1103/revmodphys.76.663 fatcat:ijrp6opmkvef3a7aj5efc7ts3m

HAsP—Heterogeneous associative processing

R.F. Freund, J.L. Potter
1992 Computing Systems in Engineering  
The of vectorizing compilers might be a first step, but same algorithm may be in two or three different they emphasize transforming code designed for one forms; one for each type of machine in the system  ...  with vectors of a specific size, which is and t the resultant throughput; then the better machine for execution?  ...  The next specific circumstances.  ... 
doi:10.1016/0956-0521(92)90091-v fatcat:u27tlpwq2jdinjsbcst23ke5ha

Functional significance of complex fluctuations in brain activity: from resting state to cognitive neuroscience

David Papo
2014 Frontiers in Systems Neuroscience  
Here, we analyze the meanings of scaling properties and the significance of their task-related modulations for cognitive neuroscience.  ...  It is proposed that cognitive processes can be framed in terms of complex generic properties of brain activity at rest and, ultimately, of functional equations, limiting distributions, symmetries, and  ...  For the linear diffusion equation, the solution is a time-evolving spatial Gaussian probability function maximizing the Shannon entropy.  ... 
doi:10.3389/fnsys.2014.00112 pmid:24966818 pmcid:PMC4052734 fatcat:mjpt6r45zjhl5b7fiagdzbo4ee

Perspectives for process systems engineering—Personal views from academia and industry

Karsten-Ulrich Klatt, Wolfgang Marquardt
2009 Computers and Chemical Engineering  
Process systems engineering (PSE) has been an active research field for almost 50 years.  ...  MSO technologies have become a commodity, they are not a distinguishing feature of the PSE field any more. Consequently, PSE has to reassess and to reposition its future research agenda.  ...  Simulations with models comprising some 100,000 to even 1,000,000 algebraic or even differential-algebraic equations, some 10 partial differential-algebraic equations in two space dimensions or a few such  ... 
doi:10.1016/j.compchemeng.2008.09.002 fatcat:i3bqe52p7rbwllvs75t6kwlt4u

Crossover scaling in the Domany–Kinzel cellular automaton

S Lübeck
2006 Journal of Statistical Mechanics: Theory and Experiment  
Our results are compared to those of a recently performed field theoretical approach. In particular, the value of the crossover exponent phi=2 is confirmed.  ...  We consider numerically the crossover scaling behavior from the directed percolation universality class to the compact directed percolation universality class within the one-dimensional Domany-Kinzel cellular  ...  For example, the steady state order parameter scales (up to higher orders) as ρ a ∝ τ β (3) for τ > 0.  ... 
doi:10.1088/1742-5468/2006/09/p09009 fatcat:dkoypi6dgrhmjaxjsho23nkvba

Fraction-free algorithm for the computation of diagonal forms matrices over Ore domains using Gröbner bases

Viktor Levandovskyy, Kristina Schindelar
2012 Journal of symbolic computation  
The fraction-free approach gives us more information on the system of linear functional equations and its solutions, than the classical setup of an operator algebra with rational functions coefficients  ...  We discuss the relation of this lifting with the solutions of the original system of equations. Moreover, we prove some new results concerning normal forms of matrices over non-simple domains.  ...  Many thanks to Moulay Barkatou and Sergey Abramov for explanations of their algorithms for linear functional systems.  ... 
doi:10.1016/j.jsc.2011.12.042 fatcat:4zen36t7zba7pch4obkl5s7al4

Classification of phase transitions in reaction-diffusion models

Vlad Elgart, Alex Kamenev
2006 Physical Review E  
Treatment of non-equilibrium systems requires doubling of degrees of freedom, which may be often interpreted as a transition from the "coordinate" to the "phase" space representation.  ...  As a result, one has to deal with the Hamiltonian formulation of the field theory instead of the Lagrangian one.  ...  DMR-0405212 and by the A. P. Sloan Foundation.  ... 
doi:10.1103/physreve.74.041101 pmid:17155016 fatcat:7iudeobjgzdhbm3fe6nlylck2i

A semi-analytical approach for the characterization of ordered 3D nanostructures using grazing-incidence X-ray fluorescence

K. V. Nikolaev, V. Soltwisch, P. Hönicke, F. Scholze, J. de la Rie, S. N. Yakunin, I. A. Makhotkin, R. W. E. van de Kruijs, F. Bijkerk
2020 Journal of Synchrotron Radiation  
The computational scheme is based on the dynamical diffraction theory in many-beam approximation, which allows a semi-analytical solution to the Sherman equation to be derived in a linear-algebraic form  ...  structures, this work presents a new computational scheme for the simulation of the angular-dependent fluorescence intensities from such periodic 2D and 3D nanoscale structures.  ...  Funding information This project has received funding from the Electronic Component Systems for European Leadership Joint Undertaking under grant agreement No 826589 -MADEin4.  ... 
doi:10.1107/s1600577519016345 pmid:32153277 pmcid:PMC7064098 fatcat:q5pudxbolbdphihoz5f77445ra

HPFBench: a high performance Fortran benchmark suite

Y. Charlie Hu, Guohua Jin, S. Lennart Johnsson, Dimitris Kehagias, Nadia Shalaby
2000 ACM Transactions on Mathematical Software  
We also provide a benchmark guide to aid the choice of subsets of the benchmarks for evaluating particular aspects of an HPF compiler.  ...  The High Performance Fortran (HPF) benchmark suite HPFBench is designed for evaluating the HPF language and compilers on scalable architectures.  ...  This benchmark solves dense linear systems of equations using Householder transformations [Dahlquist et al. 1974; Golub and van Loan 1989] .  ... 
doi:10.1145/347837.347872 fatcat:uufmly6xovc7zegukmtpgfhmzy

Non-equilibrium phase transitions

Haye Hinrichsen
2006 Physica A: Statistical Mechanics and its Applications  
The first one discusses the universality class of directed percolation, which plays a similar role as the Ising model in equilibrium statistical physics.  ...  These lecture notes give a basic introduction to the physics of phase transitions under non-equilibrium conditions.  ...  system of differential equations.  ... 
doi:10.1016/j.physa.2006.04.007 fatcat:lwcz2dvxwvbnvkp5rm4utmfppy

Topological quantum field theories from Hecke algebras [article]

Vladimir Fock, Valdo Tatitscheff, Alexander Thomas
2021 arXiv   pre-print
We construct two-dimensional non-commutative topological quantum field theories (TQFTs), one for each Hecke algebra corresponding to a finite Coxeter system.  ...  We give explicit formulas in terms of the Schur elements of the Hecke algebra and prove positivity properties for the invariants when the Coxeter group is of classical type, or one of the exceptional types  ...  We write Hecke algebra for an Iwahori–Hecke algebra for a finite Coxeter system.  ... 
arXiv:2105.09622v3 fatcat:duijta7gdbhgxdupnrtm5yfume

Estimates of products of inner radii of non-overlapping domains in the complex plane

I. V. Denega, Ya. V. Zabolotnii
2017 Complex Variables and Elliptic Equations  
Thus, for such systems, we must "directly" integrate the main equation of dynamics.  ...  The Lie algebras that are generated depend but on singularity classes, and the same, obviously, holds for the nilpotency orders. Those orders can by effectively written down (and computed) [4] .  ...  Then a rational function I on the manifold J k we call a projective invariant of order ≤ k, if X (k) (I) = 0, for all vector fields X ∈ sl 2 (C).  ... 
doi:10.1080/17476933.2016.1265952 fatcat:2xawrm3jqvh3dg4kwpkk24n73i

A lower bound for quantifying overlap effects: An empirical approach

Federico Bassetti
2000 Computers & electrical engineering  
Acknowledgments Many thanks to Olaf Lubeck, Yong Luo, and Harvey Wasserman for their precious suggestions and comments.  ...  Many thanks also to the Parallel Architecture Team at Los Alamos National Lab, and in particular to Michele Benzi, Jeffrey Hammes, and Adolfy Hoisie for the careful readings and critiques.  ...  Equation (2) was derived by transforming (l), and incorporating the overlap in the stall component.  ... 
doi:10.1016/s0045-7906(99)00044-0 fatcat:s6oci2fr4zd5fkicgrrv7shgpe
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