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Journal articles

Academic literature on the topic 'Representations of solutions'

Author: Grafiati

Published: 4 June 2021

Last updated: 17 February 2022

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Journal articles on the topic "Representations of solutions"

1

Guidotti, Patrick. "Semiclassical fundamental solutions." Abstract and Applied Analysis 2005, no. 1 (2005): 45–57. http://dx.doi.org/10.1155/aaa.2005.45.

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It is the aim of this paper to show how the classical theory, based on fundamental solutions and explicit representations, via special functions can be combined with the functional analytical approach to partial differential equations, to produce semiclassical representation formulae for the solution of equations in cylinder-like domains.

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2

Sarkar, Prabir, and Amaresh Chakrabarti. "The effect of representation of triggers on design outcomes." Artificial Intelligence for Engineering Design, Analysis and Manufacturing 22, no. 2 (2008): 101–16. http://dx.doi.org/10.1017/s0890060408000073.

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AbstractCreativity of designers can be enhanced by the application of appropriate triggers. The presence of triggers helps designers to search solution spaces. The searching of a solution space increases the possibility of finding creative solutions. Both representation and content of the triggers or stimulus to which the designers are exposed are believed to play a vital role in the representation and content of the outcome of the designers during problem solving. We studied the effect of representation of triggers on ideas generated by six design engineers while trying to solve a given probl

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3

Khutoryansky, Naum, and Horacio Sosa. "Construction of Dynamic Fundamental Solutions for Piezoelectric Solids." Applied Mechanics Reviews 48, no. 11S (1995): S222—S229. http://dx.doi.org/10.1115/1.3005076.

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Fundamental solutions are derived within the framework of transient dynamic, three-dimensional piezoelectricity. The purpose of the article is to show alternate integral representations for such solutions. Thus, a representation over the unit sphere in accordance to a methodology based on the plane wave decomposition is provided. It is shown, however, that more efficient representations from a computational point of view can be achieved through appropriate coordinate transformations. Hence, representations of the fundamental solutions over surfaces of slowness are provided as novel alternative

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4

BECK, J. CHRISTOPHER, TOM CARCHRAE, EUGENE C. FREUDER, and GEORG RINGWELSKI. "A SPACE-EFFICIENT BACKTRACK-FREE REPRESENTATION FOR CONSTRAINT SATISFACTION PROBLEMS." International Journal on Artificial Intelligence Tools 17, no. 04 (2008): 703–30. http://dx.doi.org/10.1142/s0218213008004114.

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In this paper we present a radical approach to obtaining a backtrack-free representation for a constraint satisfaction problem: remove values that lead to dead-ends. This technique does not require additional space but has the drawback of removing solutions. We investigate a number of variations on the basic algorithm including the use of seed solutions, consistency techniques, and a variety of pruning heuristics. Our experimental results indicate that a significant proportion of the solutions to the original problem can be retained especially when an optimization algorithm that specifically s

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5

Devert, Alexandre, Thomas Weise, and Ke Tang. "A Study on Scalable Representations for Evolutionary Optimization of Ground Structures." Evolutionary Computation 20, no. 3 (2012): 453–72. http://dx.doi.org/10.1162/evco_a_00054.

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This paper presents a comparative study of two indirect solution representations, a generative and an ontogenic one, on a set of well-known 2D truss design problems. The generative representation encodes the parameters of a trusses design as a mapping from a 2D space. The ontogenic representation encodes truss design parameters as a local truss transformation iterated several times, starting from a trivial initial truss. Both representations are tested with a naive evolution strategy based optimization scheme, as well as the state of the art HyperNEAT approach. We focus both on the best object

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6

Abian, Alexander, and Sergei Sverchkov. "Solutions and representations by iterated radicals." International Journal of Mathematical Education in Science and Technology 24, no. 3 (1993): 449–55. http://dx.doi.org/10.1080/0020739930240316.

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7

MAJID, SHAHN. "SOLUTIONS OF THE YANG-BAXTER EQUATIONS FROM BRAIDED-LIE ALGEBRAS AND BRAIDED GROUPS." Journal of Knot Theory and Its Ramifications 04, no. 04 (1995): 673–97. http://dx.doi.org/10.1142/s0218216595000284.

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We obtain an R-matrix or matrix representation of the Artin braid group acting in a canonical way on the vector space of every (super)-Lie algebra or braided-Lie algebra. The same result applies for every (super)-Hopf algebra or braided-Hopf algebra. We recover some known representations such as those associated to racks. We also obtain new representations such as a non-trivial one on the ring k[x] of polynomials in one variable, regarded as a braided-line. Representations of the extended Artin braid group for braids in the complement of S1 are also obtained by the same method.

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8

BRACKEN, A. J., M. D. GOULD, and R. B. ZHANG. "QUANTUM SUPERGROUPS AND SOLUTIONS OF THE YANG-BAXTER EQUATION." Modern Physics Letters A 05, no. 11 (1990): 831–40. http://dx.doi.org/10.1142/s0217732390000925.

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A method is developed for systematically constructing trigonometric and rational solutions of the Yang-Baxter equation using the representation theory of quantum supergroups. New quantum R-matrices are obtained by applying the method to the vector representations of quantum osp (1/2) and gl (m/n).

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9

Montgomery, James, Marcus Randall, and Tim Hendtlass. "Automated Selection of Appropriate Pheromone Representations in Ant Colony Optimization." Artificial Life 11, no. 3 (2005): 269–91. http://dx.doi.org/10.1162/1064546054407149.

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Ant colony optimization (ACO) is a constructive metaheuristic that uses an analogue of ant trail pheromones to learn about good features of solutions. Critically, the pheromone representation for a particular problem is usually chosen intuitively rather than by following any systematic process. In some representations, distinct solutions appear multiple times, increasing the effective size of the search space and potentially misleading ants as to the true learned value of those solutions. In this article, we present a novel system for automatically generating appropriate pheromone representati

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10

ZHANG, JIANMING, and SHUMING LI. "BIFURCATIONS OF TRAVELING WAVE SOLUTIONS AND EXACT SOLUTIONS FOR THE GENERALIZED SCHRÖDINGER EQUATION." International Journal of Bifurcation and Chaos 21, no. 09 (2011): 2623–28. http://dx.doi.org/10.1142/s0218127411029987.

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Using the method of dynamical systems for the generalized Schrödinger equation, the bright soliton solution, dark soliton solution, uncountably infinite many periodic wave solutions and breaking bounded wave solutions are obtained. Exact explicit parametric representations of the bounded traveling solutions are given. To guarantee the existence of the above solutions, all parameter conditions are determined.

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