In this paper we study predimension inequalities in differential fields and define what it means for such an inequality to be adequate . Adequacy was informally introduced by Zilber, here give a precise definition quite general context. We also discuss the connection of problem definability derivations reducts differentially closed fields. The Ax-Schanuel exponential equation (proved Ax) its an...

The aim of this paper is to present strong maximum principles for infinite systems of parabolic differential-functional inequalities with nonstandard initial inequalities with sums in relatively arbitrary (n+1)-dimensional time-space sets more general than the cylindrical domain.

In this article, we establish some integral inequalities for function with two independent variables. Also we show applications of these inequalities for finding bounds of solutions to partial differential equations.

The aim of the present paper is to establish some variants integral inequalities in two independent variables. These integral inequalities given here can be applied as tools in the boundedness and uniquness of certain partial differential equations.

This is a survey article for Surveys in Differential Geometry series on the subject of Li-Yau-Hamilton type differential inequalities and related monotonicity formulae.

The purpose of this paper is to study the dynamical behavior of the sequence produced by a forward-backward algorithm, involving two random maximal monotone operators and a sequence of decreasing step sizes. Defining a mean monotone operator as an Aumann integral, and assuming that the sum of the two mean operators is maximal (sufficient maximality conditions are provided), it is shown that wit...

Since AES and PRESENT are two international standard block ciphers representing the most elegant design strategies for byteoriented and bit-oriented designs respectively, we regard AES and PRESENT the two most significant candidates to scrutinize with respect to related-key differential attack. In EUROCRYPT 2010 and CRYPTO 2013, the security of AES with respect to related-key differential attac...