Search results for "topological [model]"
showing 10 items of 88 documents
Semiflexible Polymers in Spherical Confinement: Bipolar Orientational Order Versus Tennis Ball States
2017
Densely packed semiflexible polymers with contour length L confined in spheres with radius R of the same order as L cannot exhibit uniform nematic order. Depending on the chain stiffness (which we vary over a wide range), highly distorted structures form with topological defects on the sphere surface. These structures are completely different from previously observed ones of very long chains winding around the inner surface of spheres and from nematic droplets. At high densities, a thin shell of polymers close to the sphere surface exhibits a tennis ball texture due to the confinement-induced gradual bending of polymer bonds. In contrast, when the contour length of the chains is significant…
On Słowikowski, Raíkov and De Wilde Closed Graph Theorems
1986
Publisher Summary This chapter focuses on the Slowikowski, Raikov and De Wilde closed graph theorems. The vector spaces used in the chapter, are defined over the field Ղ of real or complex numbers. The term, “space” means separated topological vector space, unless the contrary is specifically stated. If Ω is a non-empty open subset of the n -dimensional euclidean space, then the Schwartz space ҟ′(Ω) endowed with the strong topology belongs to this class. The chapter also studies the classes of spaces related with this conjecture. The class of Slowikowski spaces contains the F-spaces and it is stable with respect to the operations that include: countable topological direct sums, closed subsp…
Noetherian type in topological products
2010
The cardinal invariant "Noetherian type" of a topological space $X$ (Nt(X)) was introduced by Peregudov in 1997 to deal with base properties that were studied by the Russian School as early as 1976. We study its behavior in products and box-products of topological spaces. We prove in Section 2: 1) There are spaces $X$ and $Y$ such that $Nt(X \times Y) < \min\{Nt(X), Nt(Y)\}$. 2) In several classes of compact spaces, the Noetherian type is preserved by the operations of forming a square and of passing to a dense subspace. The Noetherian type of the Cantor Cube of weight $\aleph_\omega$ with the countable box topology, $(2^{\aleph_\omega})_\delta$, is shown in Section 3 to be closely related …
A topological model for Oersted-Amp�re's law
1973
A geometrical description of Oersted-Ampere's law ∮H ds=(4π/c)I can be given in terms of an appropriate topological manifold. More precisely: It will be shown that Oersted-Ampere's law can be related to the topological invariantH 1(S 1), i.e. de Rham's first cohomology group on the differentiable manifoldS 1={(x,y) ∈ ℝ2∶x 2+y 2}
Localification of variable-basis topological systems
2011
The paper provides another approach to the notion of variable-basis topological system generalizing the fixed-basis concept of S. Vickers, considers functorial relationships between the categories of modified variable-basis topological systems and variable-basis fuzzy topological spaces in the sense of S.E. Rodabaugh and shows that the procedure of localification is possible in the new setting. Quaestiones Mathematicae 33(2010), 11–33
Volume-convergent sequences of Haken 3-manifolds
2003
Abstract Let M be a closed orientable 3-manifold and let Vol(M) denote its Gromov simplicial volume. This paper is devoted to the study of sequences of non-zero degree maps f i :M→N i to Haken manifolds. We prove that any sequence of Haken manifolds (Ni,fi), satisfying limi→∞deg(fi)×Vol(Ni)=Vol(M) is finite up to homeomorphism. As an application, we deduce from this fact that any closed orientable 3-manifold with zero Gromov simplicial volume and in particular any graph manifold dominates at most finitely many Haken 3-manifolds. To cite this article: P. Derbez, C. R. Acad. Sci. Paris, Ser. I 336 (2003).
Convergence and applications of vector rational approximations
1992
The Padé approximants and their generalizations are for many years the matter of intense researchs .Yet , many theoritical problems stay in suspense : problems of exitence and unicity , problems of convergence and acceleration of convergence .The purpose of the present work vas to give answers to such questions .In the first section we take an in terest in vector Padé approximants of matrix series .Conditions of existence and unicity ,results of convergence are given ,as also the link with the theory of Lanczos method for the resolution of linear Systems . We utilize also the vector Padé approximants to provide a simultaneous approximation of a function and its derivative .In the second sec…
Convergence Rates for Persistence Diagram Estimation in Topological Data Analysis
2014
International audience; Computational topology has recently seen an important development toward data analysis, giving birth to the field of topological data analysis. Topological persistence, or persistent homology, appears as a fundamental tool in this field. In this paper, we study topological persistence in general metric spaces, with a statistical approach. We show that the use of persistent homology can be naturally considered in general statistical frameworks and that persistence diagrams can be used as statistics with interesting convergence properties. Some numerical experiments are performed in various contexts to illustrate our results.
Topological ranks reveal functional knowledge encoded in biological networks: a comparative analysis
2022
Abstract Motivation Biological networks topology yields important insights into biological function, occurrence of diseases and drug design. In the last few years, different types of topological measures have been introduced and applied to infer the biological relevance of network components/interactions, according to their position within the network structure. Although comparisons of such measures have been previously proposed, to what extent the topology per se may lead to the extraction of novel biological knowledge has never been critically examined nor formalized in the literature. Results We present a comparative analysis of nine outstanding topological measures, based on compact vie…
Ordering, phase behavior, and correlations of semiflexible polymers in confinement.
2021
Semiflexible polymers are ubiquitous in biological systems, e.g., as building blocks of the cytoskeleton, and they also play an important role in various materials due to their ability to form liquid-crystalline order. These rigid macromolecules are characterized by numerous (hierarchical) length-scales that define their static and dynamic properties. Confinement can promote uniform order, e.g., through capillary nematization in narrow slits, but it can also introduce long-ranged disruptions of the nematic ordering field through (unavoidable) topological defects in spherical containers. This Perspective concentrates on the theoretical description and computational modeling of such confined …