Equivalence classes of regularly varying functions

An Extension of the Class of Regularly Varying Functions

We define a new class of positive and Lebesgue measurable functions in termsof their asymptotic behavior, which includes the class of regularly varying functions.We also characterize it by transformations, corresponding to generalized momentswhen these functions are random variables. We study the properties of this new classand discuss their applications to Extreme Value The...

Equivalence classes of functions between finite groups

Two types of equivalence relation are used to classify functions between finite groups into classes which preserve combinatorial and algebraic properties important for a wide range of applications. However, it is very difficult to tell when functions equivalent under the coarser (“graph”) equivalence are inequivalent under the finer (“bundle”) equivalence. Here we relate graphs to transversals ...

Regularly varying probability densities

The convolution of regularly varying probability densities is proved asymptotic to their sum, and hence is also regularly varying. Extensions to rapid variation, O-regular variation, and other types of asymptotic decay are also given. Regularly varying distribution functions have long been used in probability theory; see e.g. Feller [7, VIII.8], Bingham, Goldie and Teugels [5, Ch. 8]. This note...

The graph of equivalence classes and Isoclinism of groups

‎Let $G$ be a non-abelian group and let $Gamma(G)$ be the non-commuting graph of $G$‎. ‎In this paper we define an equivalence relation $sim$ on the set of $V(Gamma(G))=Gsetminus Z(G)$ by taking $xsim y$ if and only if $N(x)=N(y)$‎, ‎where $ N(x)={uin G | x textrm{ and } u textrm{ are adjacent in }Gamma(G)}$ is the open neighborhood of $x$ in $Gamma(G)$‎. ‎We introduce a new graph determined ...

Some equivalence classes of operators on B(H)