Probabilistic information theory determines fundamental limits in the topics of data compression channel capacity thermodynamics statistical estimation prediction hypothesis testing and related topics Moreover information theory provides an illuminating perspective on the limit the orems of probability Beginning with some identities and inequalities for relative entropy followed by their use in...

In this paper we investigate common xed point theorems for contraction mapping in fuzzy metric space introduced by Gregori and Sapena [V. Gregori, A. Sapena, On xed-point the- orems in fuzzy metric spaces, Fuzzy Sets and Systems, 125 (2002), 245-252].

in this paper we investigate common xed point theorems for contraction mapping in fuzzy metric space introduced by gregori and sapena [v. gregori, a. sapena, on xed-point the- orems in fuzzy metric spaces, fuzzy sets and systems, 125 (2002), 245-252].

Gödel: The Completeness and Incompleteness Theorems Kurt Gödel (1906–1978) 1930-The completeness of first-order logic 1931-On formally undecidable statements of Principia Mathematica and related systems I Gödel's first paper proves the completeness of the axioms and rules of first-order logic, essentially as given in Hilbert and Ackermann. There has been much discussion as to why Skolem (or Her...

Influence diagram is a graphical representa­ tion of belief networks with uncertainty. This article studies the structural properties of a probabilistic model in an influence diagram. In particular, structural controllability the­ orems and structural observability theorems are developed and algorithms are formulated. Controllability and observability are funda­ mental concepts in dynamic syste...

An extension of the classical van der Waerden and Szemerédi the-orems is proved for commuting operators whose exponents are polynomials.As a consequence, for example, one obtains the following result: Let S ⊆ Zlbe a set of positive upper Banach density, let p1(n), . . . , pk(n) be polynomialswith rational coefficients taking integer values on the integers and satisfyingpi(0)...