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Critical points with discrete Morse theory
ACM SIGGRAPH 2015 Posters, 2015In this work, we present some of the unexpected observations resulted from our recent research. We, recently, needed to identify a small number of important critical points, i.e. minimum, maximum and saddle points, on a given manifold mesh surface. All critical points on a manifold triangular mesh can be identified using discrete Gaussian curvature ...
Peihong Guo +4 more
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Disjunctive Optimization: Critical Point Theory
Journal of Optimization Theory and Applications, 1997zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jongen, H. T. +2 more
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2019
Critical point theory deals with variational problems and so it can be argued that it is as old as calculus. Nevertheless, in its modern form, critical point theory has its roots in the so-called “Dirichlet principle”.
Nikolaos S. Papageorgiou +2 more
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Critical point theory deals with variational problems and so it can be argued that it is as old as calculus. Nevertheless, in its modern form, critical point theory has its roots in the so-called “Dirichlet principle”.
Nikolaos S. Papageorgiou +2 more
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1993
In the study of nonminimum critical points, a basic method is the so-called minimax principle. In this chapter we study the connections between Morse theory and a variety of concrete versions of the minimax principle. We point out that the minimax principle for relative homology classes is particularly suitable for Morse theory because certain critical
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In the study of nonminimum critical points, a basic method is the so-called minimax principle. In this chapter we study the connections between Morse theory and a variety of concrete versions of the minimax principle. We point out that the minimax principle for relative homology classes is particularly suitable for Morse theory because certain critical
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The Minimax Approach to the Critical Point Theory
1995Note for the reader. Looking at the many applications of the Ekeland Variational Principle, some 2 years ago we met the Mountain Pass Theorem of Ambrosetti—Rabinowitz. This stimulated us to know more about Critical Point Theory, and to better understand the fascinating interplay between the topological and differential ideas of the minimax approach.
CONTI, MONICA, LUCCHETTI, ROBERTO
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Theory of the Critical Point of 4He
1990We do not have yet a microscopic global theory of the thermodynamic properties of 4He in the normal phase, inclusive of the region of the critical point. At a very simple level the effect of the attractive part of the interatomic forces has been considered1 in a perturbative way starting from the properties of quantum hard spheres.
A. Meroni, L. Reatto, K. J. Runge
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1999
Many nonlinear problems can be reduced to the form Many nonlinear problems can be reduced to the form $$G'(u) = 0,$$ (1.1.1) where G is a C1-functional on a Banach space E. In this case the problems can be attacked by specialized, important techniques which can produce results where other methods fail.
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Many nonlinear problems can be reduced to the form Many nonlinear problems can be reduced to the form $$G'(u) = 0,$$ (1.1.1) where G is a C1-functional on a Banach space E. In this case the problems can be attacked by specialized, important techniques which can produce results where other methods fail.
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The Critical Point: Theory and Experiment
High Temperature, 2001It is demonstrated that the Gibbs concept of the critical state and the equations for the critical point formulated by him make it possible to provide a complete description the peculiarities of the behavior and properties of matter at the critical point.
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Some remarks on nonsmooth critical point theory
Journal of Global Optimization, 2006zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Livrea, Roberto, Bisci, Giovanni Molica
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Critical Points and Morse Theory
1997In this chapter we introduce Morse theory, a systematic way of studying certain features of smooth functions on manifolds. We will primarily consider surfaces and three-manifolds, because the main applications of Morse theory in computer geometry are concentrated in these dimensions.
Anatolij T. Fomenko, Tosiyasu L. Kinii
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