On functions derived from 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...

study of hash functions based on chaotic maps

توابع درهم نقش بسیار مهم در سیستم های رمزنگاری و پروتکل های امنیتی دارند. در سیستم های رمزنگاری برای دستیابی به احراز درستی و اصالت داده دو روش مورد استفاده قرار می گیرند که عبارتند از توابع رمزنگاری کلیددار و توابع درهم ساز. توابع درهم ساز، توابعی هستند که هر متن با طول دلخواه را به دنباله ای با طول ثابت تبدیل می کنند. از جمله پرکاربردترین و معروف ترین توابع درهم می توان توابع درهم ساز md4, md...

Derived From Multivariate Generating Functions

Very Slowly Varying Functions

A real-valued function f of a real variable is said to be (p-slowly varying ((p-s .v.) if limn_ . rp (x) [ f (x + a) f (x)] = 0 for each a. It is said to be uniformly 9-slowly varying (u . (P-s .v .) if limn-. . sup, e r rp(x) ; f (x-a) f (x)I =0 for every bounded interval I. It is supposed throughout that rp is positive and increasing . It is proved that if w increases rapidly enough, then eve...

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...