scholarly journals The natural pseudo-distance as a quotient pseudo-metric, and applications

2015 ◽  
Vol 27 (3) ◽  
Author(s):  
Francesca Cagliari ◽  
Barbara Di Fabio ◽  
Claudia Landi
Keyword(s):  
Uniform Convergence ◽  
Similarity Measure ◽  
Compact Manifold ◽  
Continuous Functions ◽  
Point Of View ◽  
Space Of Continuous Functions ◽  
Morse Functions

AbstractThe natural pseudo-distance is a similarity measure conceived for the purpose of comparing shapes. In this paper we revisit this pseudo-metric from the point of view of quotients. In particular, we show that the natural pseudo-distance coincides with the quotient pseudo-metric on the space of continuous functions on a compact manifold, endowed with the uniform convergence metric, modulo self-homeomorphisms of the manifold. As applications of this result, the natural pseudo-distance is shown to be actually a metric on a number of function subspaces such as the space of topological embeddings, of isometries, and of simple Morse functions on surfaces.

scholarly journals Characterization of pseudocompactness by the topology of uniform convergence on function spaces

1978 ◽  
Vol 26 (2) ◽  
pp. 251-256 ◽  
Author(s):  
R. A. McCoy
Keyword(s):  
Uniform Convergence ◽  
Continuous Functions ◽  
Function Spaces ◽  
Metrizable Space ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Space Of Continuous Functions ◽  
Tychonoff Space ◽  
Necessary And Sufficient

AbstractIt is shown that a Tychonoff space X is pseudocompact if and only if for every metrizable space Y, all uniformities on Y induce the same topology on the space of continuous functions from X into Y. Also for certain pairs of spaces X and Y, a necessary and sufficient condition is established in order that all uniformities on Y induce the same topology on the space of continuous functions from X into Y.

scholarly journals Analytic semigroups generated by Dirichlet-to-Neumann operators on manifolds

2021 ◽  
Author(s):  
Tim Binz
Keyword(s):  
Boundary Conditions ◽  
Elliptic Operator ◽  
Compact Manifold ◽  
Analytic Semigroup ◽  
Continuous Functions ◽  
Analytic Semigroups ◽  
Abstract Theory ◽  
Neumann Operator ◽  
Wentzell Boundary Conditions ◽  
Dirichlet To Neumann Operator

AbstractWe consider the Dirichlet-to-Neumann operator associated to a strictly elliptic operator on the space $$\mathrm {C}(\partial M)$$ C ( ∂ M ) of continuous functions on the boundary $$\partial M$$ ∂ M of a compact manifold $$\overline{M}$$ M ¯ with boundary. We prove that it generates an analytic semigroup of angle $$\frac{\pi }{2}$$ π 2 , generalizing and improving a result of Escher with a new proof. Combined with the abstract theory of operators with Wentzell boundary conditions developed by Engel and the author, this yields that the corresponding strictly elliptic operator with Wentzell boundary conditions generates a compact and analytic semigroups of angle $$\frac{\pi }{2}$$ π 2 on the space $$\mathrm {C}(\overline{M})$$ C ( M ¯ ) .

Periodic solutions to functional differential equations

1985 ◽  
Vol 101 (3-4) ◽  
pp. 253-271 ◽  
Author(s):  
O. A. Arino ◽  
T. A. Burton ◽  
J. R. Haddock
Keyword(s):  
Differential Equations ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Uniform Boundedness ◽  
Continuous Functions ◽  
Ultimate Boundedness ◽  
Space Of Continuous Functions ◽  
Uniform Ultimate Boundedness ◽  
Functional Differential ◽  
Image Position

SynopsisWe consider a system of functional differential equationswhere G: R × B → Rn is T periodic in t and B is a certain phase space of continuous functions that map (−∞, 0[ into Rn. The concepts of B-uniform boundedness and B-uniform ultimate boundedness are introduced, and sufficient conditions are given for the existence of a T-periodic solution to (1.1). Several examples are given to illustrate the main theorem.

SURVEY Towards a global view of dynamical systems, for the C1-topology

2011 ◽  
Vol 31 (4) ◽  
pp. 959-993 ◽  
Author(s):  
C. BONATTI
Keyword(s):  
Dynamical Systems ◽  
Compact Manifold ◽  
Global Structure ◽  
Point Of View ◽  
List Type ◽  
Global View ◽  
Local Phenomenon ◽  
Generic Dynamics

AbstractThis paper suggests a program for getting a global view of the dynamics of diffeomorphisms, from the point of view of the C1-topology. More precisely, given any compact manifold M, one splits Diff1(M) into disjoint C1-open regions whose union is C1-dense, and conjectures state that each of these open sets and their complements is characterized by the presence of: •either a robust local phenomenon;•or a global structure forbidding this local phenomenon. Other conjectures state that some of these regions are empty. This set of conjectures draws a global view of the dynamics, putting in evidence the coherence of the numerous recent results on C1-generic dynamics.

Multi-criteria Decision-making Applications Based on Set Valued Generalized Neutrosophic Quadruple Sets for Law

2021 ◽  
pp. 41-60
Author(s):  
Necmiye Merve Sahin ◽  
◽  
◽  
Merve Sena Uz
Keyword(s):  
Decision Making ◽  
Similarity Measure ◽  
Point Of View ◽  
Multi Criteria Decision Making ◽  
Legal Decisions ◽  
The Law ◽  
Made In

In this article, an algorithm has been introduced that enables judges to see the decisions that should be made in a way that is closest to the conscience and the law, without transferring the cases to the higher authorities, without anyone objecting to their decisions. This algorithm has been introduced depending on the generalized set-valued neutrosophic quadruple numbers and the Euclidean similarity measure in sets, what the decision is made by considering all the situations, regardless of which case the defendants come before the judge, how similar these decisions are to the legal decisions that should be made. In this way, we can easily see the decisions given to the accused in all kinds of cases, and we can arrange the decisions according to the similarity value. The closer the similarity value is to 1, the more correct the judge's decision from a legal point of view.

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