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22,897
Similarity solution of the Boussinesq equation
"... Similarity transforms of the Boussinesq equation in a semiinfinite medium are available when the boundary conditions are a power of time. The Boussinesq equation is reduced from a partial dierential equation to a boundaryvalue problem. Chen et al. [Trans Porous Media 1995;18:15–36] use a hodograph ..."
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Similarity transforms of the Boussinesq equation in a semiinfinite medium are available when the boundary conditions are a power of time. The Boussinesq equation is reduced from a partial dierential equation to a boundaryvalue problem. Chen et al. [Trans Porous Media 1995;18:15–36] use a
Similarity Solutions for Reactive Shock Hydrodynamics
, 2011
"... Abstract The method of Lie group invariance is used to obtain a class of selfsimilar solutions for a onedimensional, timedependent problem in shock hydrodynamics, with a chemical reaction taking place behind the shock. The forms of the initial specific volume v 0 and the reaction rate Q, for whi ..."
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Abstract The method of Lie group invariance is used to obtain a class of selfsimilar solutions for a onedimensional, timedependent problem in shock hydrodynamics, with a chemical reaction taking place behind the shock. The forms of the initial specific volume v 0 and the reaction rate Q
Similarity Solutions for Granular Flows in Hoppers
 IN PROCEEDINGS OF THE SIAM/AMS CONFERENCE ON NONLINEAR PDES, DYNAMICS AND CONTINUUM PHYSICS
, 1998
"... Similarity solutions for the steady state equations governing flow of granular materials under gravity in a conical or wedgeshaped hopper are constructed. Such solutions can be considered for various plasticity models. Results obtained under the classical MohrCoulomb yield condition are compared ..."
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Cited by 2 (2 self)
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Similarity solutions for the steady state equations governing flow of granular materials under gravity in a conical or wedgeshaped hopper are constructed. Such solutions can be considered for various plasticity models. Results obtained under the classical MohrCoulomb yield condition are compared
A solution to Plato’s problem: The latent semantic analysis theory of acquisition, induction, and representation of knowledge
 PSYCHOLOGICAL REVIEW
, 1997
"... How do people know as much as they do with as little information as they get? The problem takes many forms; learning vocabulary from text is an especially dramatic and convenient case for research. A new general theory of acquired similarity and knowledge representation, latent semantic analysis (LS ..."
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Cited by 1816 (10 self)
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How do people know as much as they do with as little information as they get? The problem takes many forms; learning vocabulary from text is an especially dramatic and convenient case for research. A new general theory of acquired similarity and knowledge representation, latent semantic analysis
SelfSimilar Solutions for NavierStokes Equations in R³
"... We construct selfsimilar solutions for threedimensional incompressible NavierStokes equations, providing some examples of functional spaces where this can be done. We apply our results to a particular case of L² initial data. ..."
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Cited by 44 (7 self)
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We construct selfsimilar solutions for threedimensional incompressible NavierStokes equations, providing some examples of functional spaces where this can be done. We apply our results to a particular case of L² initial data.
Knowledgebased Analysis of Microarray Gene Expression Data By Using Support Vector Machines
, 2000
"... We introduce a method of functionally classifying genes by using gene expression data from DNA microarray hybridization experiments. The method is based on the theory of support vector machines (SVMs). SVMs are considered a supervised computer learning method because they exploit prior knowledge of ..."
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Cited by 520 (8 self)
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analysis, including their exibility in choosing a similarity function, sparseness of solution when dealing with large data sets, the ability t...
The empirical case for two systems of reasoning
, 1996
"... Distinctions have been proposed between systems of reasoning for centuries. This article distills properties shared by many of these distinctions and characterizes the resulting systems in light of recent findings and theoretical developments. One system is associative because its computations ref ..."
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Cited by 669 (4 self)
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reflect similarity structure and relations of temporal contiguity. The other is “rule based” because it operates on symbolic structures that have logical content and variables and because its computations have the properties that are normally assigned to rules. The systems serve complementary functions
SIMILARITY SOLUTIONS OF THE GROSSPITAEVSKII EQUATION
, 2000
"... We propose a novel method to analyze a generalized GrossPitaevskii equation in D space dimensions with the nonlinearity of order n. We show that the selfsimilar behavior of the solutions can only be observed for Dn = 2. The relevance of this result to the dynamics of Bose condensates in two dimens ..."
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We propose a novel method to analyze a generalized GrossPitaevskii equation in D space dimensions with the nonlinearity of order n. We show that the selfsimilar behavior of the solutions can only be observed for Dn = 2. The relevance of this result to the dynamics of Bose condensates in two
Results 1  10
of
22,897