A function J defined on a family C of stationary processes is finitely observable if there is a sequence of functions sn such that sn(x1 . . . xn) → J(X ) in probability for every process X =(xn) ∈ C. Recently, Ornstein and Weiss proved the striking result that if C is the class of aperiodic ergodic finite valued processes, then the only finitely observable isomorphism invariant defined on C is...

Abstract In this paper, we introduce and study Golden-like statistical manifolds. We obtain some basic inequalities for curvature invariants of submanifolds in Also, support our definition, provide a couple examples.

A macroscopic model describing elastic-plastic solids is derived in a special case of the internal specific energy taken in separable form: it is the sum of a hydrodynamic part depending only on the density and entropy, and a shear part depending on other invariants of the Finger tensor. In particular, the relaxation terms are constructed compatible with the von Mises yield criteria. In additio...

Chaotic saddles are nonattracting dynamical invariant sets that physically lead to transient chaos. As a system parameter changes, chaotic saddles can evolve via an infinite number of homoclinic or heteroclinic tangencies of their stable and unstable manifolds. Based on previous numerical evidence and a rigorous analysis of a class of representative models, we show that dynamical invariants suc...

Tied links and the tied braid monoid were introduced recently by authors used to define new invariants for classical links. Here, we give a version purely algebraic–combinatoric of With this prove that has decomposition like semi–direct group product. By using reprove Alexander Markov theorem links; also, introduce singular knots, certain families Homflypt type these are five–variables polynomi...

Proxies are a common technique to virtualize objects in object-oriented languages. A proxy is a placeholder object that emulates or wraps another target object. Both the proxy’s representation and behavior may differ substantially from that of its target object. In many OO languages, objects may have language-enforced invariants associated with them. For instance, an object may declare immutabl...