The fluctuation-response relation is a fundamental relation that is applicable to systems near equilibrium. On the other hand, when a system is driven far from equilibrium, this relation is violated in general because the detailed-balance condition is not satisfied in nonequilibrium systems. Even in this case, it has been found that for a class of Langevin equations, there exists an equality be...

This paper is a contribution to the study of equality-free logic, that is, first-order logic without equality. We mainly devote ourselves to the study of algebraic characterizations of its relation of elementary equivalence by providing some Keisler-Shelah type ultrapower theorems and an Ehrenfeucht-Fraı̈ssé type theorem. We also give characterizations of elementary classes in equalityfree logic...

To establish the correctness of some software w.r.t. its formal speciication is widely recognized as a diicult task. A rst simpliication is obtained when the semantics of an algebraic speciication is deened as the class of all algebras which correspond to the correct realizations of the speciication. A software is then declared correct if it corresponds to some algebra of this class. We approac...

Silvers’s perfect set theorem says that every Π1 equivalence relation over a polish space either has countably many equivalence classes or has a perfect set of inequivalent elements. We prove an analog where the equivalence relation is replaced by a Π1 dependence relation, and the perfect set of inequivalent elements is replaced by a perfect independent set. The dependence relation should satis...

We prove an equality for the curvature function of a simple and closed curve on the plane. This equality leads to another proof of the four-vertex theorem in differential geometry. While examining the regularity assumption on the curve for the equality, we make comments on the relation between the boundary regularity of a Riemannmapping and two important subjects, the Schauder theory and the st...

Behavioural theories are a generalization of standard theories where the equality predicate is interpreted by an arbitrary (possibly partial) congruence relation, called behavioural equality. In this paper we first show how to reduce the behavioural theory of any class C of Σ-algebras to (a subset of) the standard theory of some corresponding class of algebras. Then we consider infinitary axiom...

In this paper two new concepts are introduced: the similarity and the (∗,δ)-equality of fuzzy choice functions. We investigate the manner the similarity and (∗,δ)-equality behave with respect to some fundamental concepts of fuzzy revealed preference theory. Keywords– Fuzzy choice function, Revealed preference, Similarity relation.

A generalized definition of the monogamy relation for entanglement measures is provided. equality rather than usual inequality presented based on weight, from which relations are given satisfied by ?th ( ? > 0 ) $(\alpha >0)$ power measures. Taking concurrence as an example, significance and advantages these further demonstrated. In addition, it shown that can be recovered considering multiple ...

A tree automaton with global tree equality and disequality constraints, TAGED for short, is an automaton on trees which allows to test (dis)equalities between subtrees which may be arbitrarily faraway. In particular, it is equipped with an (dis)equality relation on states, so that whenever two subtrees t and t′ evaluate (in an accepting run) to two states which are in the (dis)equality relation...

Steered molecular dynamics (SMD) permits efficient investigations of molecular processes by focusing on selected degrees of freedom. We explain how one can, in the framework of SMD, employ Jarzynski's equality (also known as the nonequilibrium work relation) to calculate potentials of mean force (PMF). We outline the theory that serves this purpose and connects nonequilibrium processes (such as...