Search results for "Theorem"

Polydispersity Effects on Interpenetration in Compressed Brushes

2019

We study the effect of polydispersity on the compression and interpenetration properties of two opposing polymer brushes by numerical self-consistent field approach and by analytical theory. Polydispersity is represented by an experimentally relevant Schulz–Zimm chain-length distribution. We focus on three different polydispersities representing sharp, moderate, and extremely wide chain length distributions and derive approximate analytical expressions for the pressure–separation curves, Π(D). We study the brush interpenetration and quantify it in terms of the overlap integral, Γ, representing the number of interbrush contacts, and interpenetration length, δ. For the case of moderate densit…

Osmotic pressure, atomic pressure and the virial equation of state of polymer solutions: Monte Carlo simulations of a bead-spring model

1994

A recently introduced coarse-grained model of polymer chains is studied analyzing various contributions to the pressure as obtained from the virial theorem as a function of chain length N, temperature T and density ϕ. The off-lattice model of the polymer chains has anharmonic springs between the beads, but of finite extensibility, and the Morse-type interaction between beads is repulsive at very short distances and attractive at intermediate distances. Solvent molecules are not explicitly included. It is found that the covalent forces along the chain (modelled by the spring potentials) contribute a negative term to the pressure, irrespective of temperature, which vanishes linearly in ϕ as ϕ…

Stoïlow’s theorem revisited

2020

Stoilow's theorem from 1928 states that a continuous, open, and light map between surfaces is a discrete map with a discrete branch set. This result implies that such maps between orientable surfaces are locally modeled by power maps z -> z(k) and admit a holomorphic factorization. The purpose of this expository article is to give a proof of this classical theorem having readers in mind that are interested in continuous, open and discrete maps. (C) 2019 Elsevier GmbH. All rights reserved. Peer reviewed

Baum-Katz’s Type Theorems for Pairwise Independent Random Elements in Certain Metric Spaces

2020

In this study, some Baum-Katz’s type theorems for pairwise independent random elements are extended to a metric space endowed with a convex combination operation. Our results are considered in the cases of identically distributed and non-identically distributed random elements. Some illustrative examples are provided to sharpen the results. peerReviewed

Molecular phylogeny of the genus Chondrina (Gastropoda, Panpulmonata, Chondrinidae) in the Iberian Peninsula

2022

[EN] Chondrina Reichenbach, 1828 is a highly diverse genus of terrestrial molluscs currently including 44 species with about 28 subspecific taxa. It is distributed through North Africa, central and southern Europe, from Portugal in the West to the Caucasus and Asia Minor in the East. Approximately 70% of the species are endemic to the Iberian Peninsula constituting its main center of speciation with 34 species. This genus includes many micro endemic taxa, some of them not yet described, confined to limestone habitats (being strictly rock-dwelling species). They are distributed on rocky outcrops up to 2000 m.a.s.l. It is a genus of conical-fusiform snails that differ mainly in shell characte…

Orientation of the electric field gradient and ellipticity of the magnetic cycloid in multiferroic BiFeO3

2016

This work was supported by Uniwersytet Pedagogiczny.

Non-standard Problems in an Ordinary Differential Equations Course

2018

International audience; We report first results from a teaching intervention in an ordinary differential equations (ODEs) course for engineering students. Our aim is to challenge traditional approaches to teaching of Existence and Uniqueness Theorems (EUTs) through the design of problems that students cannot solve by applying well-rehearsed techniques or familiar methods. We analyse how the use of nonstandard problems contributes to the development of students' conceptual understanding of EUTs and ODEs.

Lipschitz Carnot-Carathéodory Structures and their Limits

2022

AbstractIn this paper we discuss the convergence of distances associated to converging structures of Lipschitz vector fields and continuously varying norms on a smooth manifold. We prove that, under a mild controllability assumption on the limit vector-fields structure, the distances associated to equi-Lipschitz vector-fields structures that converge uniformly on compact subsets, and to norms that converge uniformly on compact subsets, converge locally uniformly to the limit Carnot-Carathéodory distance. In the case in which the limit distance is boundedly compact, we show that the convergence of the distances is uniform on compact sets. We show an example in which the limit distance is not…

The historical role played by the work of Ulisse Dini on implicit function theory in the modern differential geometry foundations: the case of the st…

2012

On the spatial spread of a pattern

1980

A simple process is considered for the spread of a pattern in a spatially distributed population. Expressions are given for the stochastic means, variances and covariances. Central limit theorems are obtained for the number of individuals that have the pattern, and the time needed for the pattern to reach the n-th subpopulation.