Removability of the wave singularities in the plane.
We prove a stochastic formula for the Gaussian relative entropy in the spirit of Borell’s formula for the Laplace transform. As an application, we give simple proofs of a number of functional inequalities.
Strengthened forms of Ling's representation theorem concerning a class of continuous associative functions are given: Firstly the monotonicity condition is removed. Then the associativity condition is replaced by the power associativity.
Separation is a famous principle and separation properties are important for optimization theory and various applications. In practice, input data are rarely known exactly and it is advisable to deal with parameters. In this article, we are concerned with the basic characteristics (existence, description, stability etc.) of separating hyperplanes of two convex polyhedral sets depending on parameters. We study the case, when parameters are situated in one column of the constraint matrix from the...