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Combinatorial Resolution of Systems of Differential Equations. IV. Separation of Variables
[chapter]

1988
*
Annals of Discrete Mathematics
*

In the context

doi:10.1016/s0167-5060(08)70790-8
fatcat:xvabar4jwvgypemkohxnmoxova
*of*the*combinatorial*theory*of*ordinary*differential**equations*recently introduced by the authors, a concrete interpretation is given to the classical method*of**separation**of**variables*. ... This approach is then extended to more general*equations*and applied to*systems**of**differential**equations*with forcing terms. ... this work was developed, the Natural Sciences and Engineering Research Council*of*Canada for financial assistance, and the organizers*of*the First Japan Conference on Graph Theory and Applications for ...##
###
Combinatorial resolution of systems of differential equations. IV. separation of variables

1988
*
Discrete Mathematics
*

In the context

doi:10.1016/0012-365x(88)90213-0
fatcat:qjmkl53odfawpoegzktk67a5ma
*of*the*combinatorial*theory*of*ordinary*differential**equations*recently introduced by the authors, a concrete interpretation is given to the classical method*of**separation**of**variables*. ... This approach is then extended to more general*equations*and applied to*systems**of**differential**equations*with forcing terms. ... this work was developed, the Natural Sciences and Engineering Research Council*of*Canada for financial assistance, and the organizers*of*the First Japan Conference on Graph Theory and Applications for ...##
###
Page 6398 of Mathematical Reviews Vol. , Issue 91M
[page]

1991
*
Mathematical Reviews
*

(F-BORD)

*Combinatorial**resolution**of**systems**of**differential**equations*.*IV*.*Separation**of**variables*. Proceedings*of*the First Japan Conference on Graph Theory and Applications (Hakone, 1986). ... {For the entire collection see MR 91m:05005.} 91m:05010 OSAI5 13F25 26A06 34A25 Bergeron, Francois (3-PQ); Reutenauer, Christophe (3-PQ)*Combinatorial**resolution**of**systems**of**differential**equations*. ...##
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Page 5 of Mathematical Reviews Vol. , Issue 96a
[page]

1996
*
Mathematical Reviews
*

Mamedov, On the lattice

*of*interpretability types*of*varieties (187-189); I. Mirchev,*Separable*and dominating sets*of**variables*for functions (191-198); J. ... [Xiang Zhang*], Boundary value problems for vec- tor integral*differential**equations**of*singularly perturbed Volterra type (297-308); Ai Long Zheng and Fu Jun Wang, Stability and periodic bifurcation due ...##
###
Author index

1988
*
Discrete Mathematics
*

Viennot,

doi:10.1016/0012-365x(88)90234-8
fatcat:eslxmu3e3ne2tboojeam7psxti
*Combinatorial**resolution**of**systems**of**differential**equations*.*IV*.*Separation**of**variables*Lim, C.-K., see C.-L. Deng Loupekine, F. and J.J. ... Jr., Chromatic polynomials*of*generalized trees (72) 385-390 (72) 251-256 (72) 391-393 (72) 299-310 (72) 395-404 hexagonal*systems*(72) 405-415 (72) 225-236 (72) 35-47 (72) 163-166 (72 ...##
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Diagnosis of Breast Cancer using a Combination of Genetic Algorithm and Artificial Neural Network in Medical Infrared Thermal Imaging

2013
*
Iranian Journal of Medical Physics
*

Then these 8 parameters are used as input

doi:10.22038/ijmp.2013.470
doaj:622c25df1d524e7c8cd7fc56ad3ec531
fatcat:gdtromqokvgoldu62aei7x5xh4
*of*our proposed*combinatorial*model which is formed using artificial neural network and genetic algorithm. ... The results indicate that the proposed*combinatorial*model produces optimum and efficacious parameters in comparison to other parameters and can improve the capability and power*of*globalizing the artificial ... The manager and staff*of*vasei hospital*of*sabzevar are also greatly appreciated for their efficient support regarding this study. ...##
###
Relaxation and metastability in a local search procedure for the random satisfiability problem

2003
*
Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
*

For alpha > alpha_d, the

doi:10.1103/physreve.67.066103
pmid:16241300
fatcat:s2nmosr6hfaifaubb4q74ei7hu
*system*is trapped in some metastable state, and*resolution*occurs from escape from this state through crossing*of*a large barrier. ... Depending on the ratio alpha*of*constraints per*variable*,*resolution*takes a time T_res growing linearly (T_res \sim tau(alpha) N, alpha < alpha_d) or exponentially (T_res \sim exp(N zeta(alpha)), alpha ... A3͒ The set*of*Kϩ1 linear coupled*differential*͑A1͒ reduces to a partial*differential**equation*on ⌽(x,t): ץ⌽ ץt ͑ x,t ͒ϭϪ1ϩxϩ␣K͑ xϪ1 ͒⌽͑ x,t ͒ϩ␣͑ 1Ϫx 2 ͒ ץ⌽ ץx ͑ x,t ͒. ͑ ...##
###
Dynamic Optimization Strategies for Three-Dimensional Conflict Resolution of Multiple Aircraft

2004
*
Journal of Guidance Control and Dynamics
*

*differential*, algebraic, and control

*variables*

*of*the individual aircraft in that order, g., are the algebraic equalities, and gine are

*separation*constraints between different pairs

*of*aircraft. ... ., A“, AY), we obtain a candidate step by solving the following

*system*

*of*

*equations*: H(w) Vic(w) —! | Vi c(w)? ...

##
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String Topology: Background and Present State
[article]

2007
*
arXiv
*
pre-print

The sum over all surface types

arXiv:0710.4141v1
fatcat:6d7u4xsmyvgjbmp63ztvgaoadm
*of*the top pseudomanifold chain yields a chain X satisfying the master*equation*dX + X*X = 0 where * is the sum over all gluings. ... The data*of*a "2D field theory with a closed string compactification" is an equivariant chain level action*of*a cell decomposition*of*the union*of*all moduli spaces*of*punctured Riemann surfaces with each ... Actually, we think*of*such a master*equation*as a presentation*of*a free*differential*algebra generated by the X α with the*differential*on the generators defined by the master*equation*. ...##
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Page 729 of Mathematical Reviews Vol. , Issue 2001B
[page]

2001
*
Mathematical Reviews
*

Yurik],

*Separation**of**variables*and construction*of*exact solutions*of*nonlinear wave*equations*(73-82); Leonid F. Barannyk [L. F. ... Wiltshire, Symmetries*of**systems**of*nonlinear reaction-diffusion*equations*(47-59); M. B. Abd-el-Malek, I. A. El-Awadi and S. M. A. ...##
###
Effective Coefficient Asymptotics of Multivariate Rational Functions via Semi-Numerical Algorithms for Polynomial Systems
[article]

2020
*
arXiv
*
pre-print

To our knowledge, this is the first completely automatic treatment and complexity analysis for the asymptotic enumeration

arXiv:1905.04187v2
fatcat:urrhplwdzng2tj4abeeufccvby
*of*rational functions in an arbitrary number*of**variables*. ... Their diagonal coefficient sequences enjoy nice arithmetic and asymptotic properties, and the field*of*analytic combinatorics in several*variables*(ACSV) makes it possible to compute asymptotic expansions ... Acknowledgments The authors would like to thank Mohab Safey El Din and Éric Schost for several discussions during the preparation*of*this work, and the anonymous referees for their close readings and helpful ...##
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Low power and massively parallel simulation of oscillatory biochemical networks on FPGA

2019
*
2019 IEEE Biomedical Circuits and Systems Conference (BioCAS)
*

In order to reverse engineer networks and map their design space, dynamics needs to be simulated for many different parameters and topologies, leading to a

doi:10.1109/biocas.2019.8919020
dblp:conf/biocas/ThanhLKBFGL19
fatcat:mvu2woqcs5agrl7lqcilhea7fe
*combinatorial*explosion that requires heavy computational ... It is crucial to compute the dynamics*of*a biochemical network from its kinetics and topology. ... ACKNOWLEDGMENT We would like to thank the MITI*of*CNRS (project DNA2 in Biomimetisme 2019). ...##
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Combinatorial Koszul Homology: Computations and Applications
[article]

2008
*
arXiv
*
pre-print

*of*monomial ideals and apply it to describe the structure

*of*monomial ideals. ... Describe algorithms to perform efficient computations

*of*the homological invariants

*of*monomial ideals. ... To obtain the prolongation R 2

*of*our

*equation*, we have to formally

*differentiate*the two

*equations*

*of*the

*system*4. 3 with respect to all the

*variables*and add the result to R 1 . ...

##
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The Piecewise Smooth Mumford–Shah Functional on an Arbitrary Graph

2009
*
IEEE Transactions on Image Processing
*

In contrast to traditional optimization methods, use

doi:10.1109/tip.2009.2028258
pmid:19635698
fatcat:inyuw77aj5arbntnya2rtoimfe
*of*these*combinatorial*techniques necessitates consideration*of*the reconstructed image outside*of*its usual boundary, requiring additionally the inclusion ... In order to reduce these problems, we reformulate the corresponding Mumford-Shah functional on an arbitrary graph and apply the techniques*of**combinatorial*optimization to produce a fast, lowenergy solution ...*equation*by solving the*system*L R * f R * = −B T f R * . (16) In summary, the optimum for f R * and f R * may be produced by solving sparse, positive definite*systems**of*linear*equations*for which many ...##
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Smooth curve extraction by mean field annealing

1995
*
Annals of Mathematics and Artificial Intelligence
*

Moreover, this cost function fits the constraints

doi:10.1007/bf01530832
fatcat:emf6htp6aff5pmcknopbmf6oiy
*of*a interacting spin*system*which in turn is a well suited physical model to solve hard*combinatorial*optimization problems. ... In this paper we attack the figure-ground discrimination problem from a*combinatorial*optimization perspective. ... Instead, the solution for the vector µ = [µ 1 , · · · , µ N ] may well be the stationary solution*of*the following*system**of*N*differential**equations*: τ dµ i dt = tanh N j=1 J ij µ j + δ i T − µ i (15) ...
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