It is possible to associate with every atom or molecule in a liquid its own atomic stress tensor. These atomic stress tensors can be used to describe liquids' structures and to investigate the connection between structural and dynamic properties. In particular, atomic stresses allow to address atomic scale correlations relevant to the Green-Kubo expression for viscosity. Previously correlations...

In this paper, we first define the notion of finitely-cosmall quotient (singly-cosmall quotient) morphisms. Then give a characterization new concept. We show that an epimorphism p:Y→U is if and only for any right R-module Z morphism g:Z→Y such pg finitely-copartial isomorphism (singly-copartial isomorphism) from to Y with codomain U finitely (singly) split epimorphism. also investigate relation...

Abstract We give a syntax independent formulation of finitely presented generalized algebraic theories as initial objects in categories with families (cwfs) extra structure. To this end, we simultaneously define the notion presentation Σ theory and associated category CwF small cwfs Σ-structure cwf-morphisms that preserve on nose. Our definition refers to purely semantic uniform family contexts...

Providing appropriate cues to users when interacting with objects in immersive virtual environments (IVEs) is a difficult task. In addition to individual user differences, environmental factors, and task-specific requirements, the technological complexity of the current state of the art in haptic feedback further increases the difficulty. Though the technology continues to improve, we are still...

M. Gromov has shown that any two finitely generated groups Γ and Λ are quasi-isometric if and only if they admit a topological coupling, i.e., a commuting pair of proper continuous cocompact actions Γ y X x Λ on a locally compact Hausdorff space. This result is extended here to all (compactly generated) locally compact second-countable groups. In his seminal monograph on geometric group theory ...

This paper develops a theory for completely random measures in the framework of free probability. A general existence result is established, and analogy to classical work Kingman it proved that such can be decomposed into sum purely atomic part (freely) infinitely divisible part. The latter (termed Lévy basis) studied detail terms Lévy-Khintchine representation parallel Rajput Rosiński develope...