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## Filters

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Computer Algebra Systems
[chapter]

2003
*
Computer Algebra Handbook
*

Through

doi:10.1007/978-3-642-55826-9_4
fatcat:3imemzg6zbd6zalw5xtq6zlktq
*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? ...##
###
Das Fehlertolerante System Tandem T16
[chapter]

1984
*
Software-Fehlertoleranz und -Zuverlässigkeit
*

Zhejiang Universität, College of Computer Science: Hangzhou,
China, p 1
12.Dosch W, Magnussen S (2002)

doi:10.1007/978-3-642-69705-0_18
dblp:conf/icftcs/Schulz84
fatcat:mcbxefmt25ajljtzk6nh5vudqq
*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 ...##
###
Universality classes in nonequilibrium lattice systems

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*. ...

##
###
HAsP—Heterogeneous associative processing

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. ...

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

2014
*
Frontiers in Systems Neuroscience
*

Here, we analyze

doi:10.3389/fnsys.2014.00112
pmid:24966818
pmcid:PMC4052734
fatcat:mjpt6r45zjhl5b7fiagdzbo4ee
*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. ...##
###
Perspectives for process systems engineering—Personal views from academia and industry

2009
*
Computers and Chemical Engineering
*

Process

doi:10.1016/j.compchemeng.2008.09.002
fatcat:i3bqe52p7rbwllvs75t6kwlt4u
*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 ...##
###
Crossover scaling in the Domany–Kinzel cellular automaton

2006
*
Journal of Statistical Mechanics: Theory and Experiment
*

Our results are compared to those of

doi:10.1088/1742-5468/2006/09/p09009
fatcat:dkoypi6dgrhmjaxjsho23nkvba
*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. ...##
###
Fraction-free algorithm for the computation of diagonal forms matrices over Ore domains using Gröbner bases

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*. ...

##
###
Classification of phase transitions in reaction-diffusion models

2006
*
Physical Review E
*

Treatment of non-equilibrium

doi:10.1103/physreve.74.041101
pmid:17155016
fatcat:7iudeobjgzdhbm3fe6nlylck2i
*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. ...##
###
A semi-analytical approach for the characterization of ordered 3D nanostructures using grazing-incidence X-ray fluorescence

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. ...

##
###
HPFBench: a high performance Fortran benchmark suite

2000
*
ACM Transactions on Mathematical Software
*

We also provide

doi:10.1145/347837.347872
fatcat:uufmly6xovc7zegukmtpgfhmzy
*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] . ...##
###
Non-equilibrium phase transitions

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*. ...

##
###
Topological quantum field theories from Hecke algebras
[article]

2021
*
arXiv
*
pre-print

We construct two-dimensional non-commutative topological quantum field theories (TQFTs), one

arXiv:2105.09622v3
fatcat:duijta7gdbhgxdupnrtm5yfume
*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*. ...##
###
Estimates of products of inner radii of non-overlapping domains in the complex plane

2017
*
Complex Variables and Elliptic Equations
*

Thus,

doi:10.1080/17476933.2016.1265952
fatcat:2xawrm3jqvh3dg4kwpkk24n73i
*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). ...##
###
A lower bound for quantifying overlap effects: An empirical approach

2000
*
Computers & electrical engineering
*

Acknowledgments Many thanks to Olaf

doi:10.1016/s0045-7906(99)00044-0
fatcat:s6oci2fr4zd5fkicgrrv7shgpe
*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. ...
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