This paper presents and investigates a new class of equivalent-expenditure functions that is a generalization of the one that corresponds to exact (independent-of-base) equivalence scales. It provides less restrictive household demands, especially for children’s goods, and has associated equivalence scales that may depend on expenditure. We show that, under certain conditions, equivalent-expend...

Kengo Matsumoto has introduced λ-graph systems and strong shift equivalence of λ-graph systems [Doc.Math.4 (1999), 285-340]. We associate to a subshift of a subshift a λ-graph system. The strong shift equivalence class of the associated λ-graph system is an invariant of subsystem equivalence. Wolfgang Krieger and Kengo Matsumoto have introduced the λ-entropy of a λ-graph system and have shown i...

We establish new results and introduce new methods in the theory of measurable orbit equivalence, using bounded cohomology of group representations. Our rigidity statements hold for a wide (uncountable) class of groups arising from negative curvature geometry. Amongst our applications are (a) measurable Mostow-type rigidity theorems for products of negatively curved groups; (b) prime factorizat...

In this paper, we prove an integral theorem for the Cegrell class F(f) and use result to study F-equivalence relation.

The main goal of the present paper is to extend classical results from the measure theory and dynamical systems to the fuzzy subset setting. In this paper, the notion of  dynamic equivalence relation is introduced and then it is proved that this relation is an equivalence relation. Also, a new metric on the collection of all equivalence classes is introduced and it is proved that this metric is...

Divide the context-free languages into equivalence classes in the following way: L1 and L2 are in the same class if there are a-transducers M and M such that M(L1) ~ L~ and d~r(L,) = L1. Define L1 and L~ to be structurally similar if they are in the same class. Among the results given below are: (I) if L1 and L2 are structurally similar and L1 has a structurally similar set of (right) sententia...

We study a graph transformation (defined by Seidel) called switching which, given a graph G = ( V,E) and a subset W C Jf of its vertices, builds a new graph by exchanging the cocycle linking W to V\ W with its complement. Switching is an equivalence relation and the associated equivalence classes are called switching classes. A switching class is perfect if it contains only perfect graphs. We s...

In this article we survey the background and recent development on the Kequivalence relation among birational manifolds. The content is based on the author’s talk at ICCM-2001 at Taipei. I would like to dedicate this article to Professor Chern, Shiing-shen to celebrate his 90th birthday. For manifolds, K-equivalence is the same as c1-equivalence. In this sense, a major part of birational geomet...

We present a McCulloch-Pitts neural net to recognize even linear languages. The language class is studied in order to define the net topology. Finally, the equivalence between the language class and the languages recognized by the net is proved.

The existence of solutions belonging to the Karamata class of functions of a class of third order nonlinear differential equations is proved via some more general results on asymptotic equivalence.