This paper considers some path pro~erties of real separable Gaussian processes ~ with parameter set an arbitrary interval. The following results are established, among others. At every fixed point the paths of ~ are continuous, or differentiable, with probability zero or one. If ~ is measurable, then with probability one its paths have essentially the same points of continuity and differentiabi...

The present paper investigates the sensitivity analysis, with respect to right-hand source term perturbations, of a scalar Tresca-type problem. This simplified, but nontrivial, model is inspired from (vectorial) Tresca friction problem found in contact mechanics. weak formulation considered leads variational inequality second kind depending on perturbation parameter. unique solution this then c...

In the paper compressible, stationary Navier-Stokes (N-S) equations are considered. The model is well-posed, there exist weak solutions in bounded domains, subject to inhomogeneous boundary conditions. The shape sensitivity analysis is performed for N-S boundary value problems, in the framework of small perturbations of the so-called approximate solutions. The approximate solutions are determin...

*Correspondence: [email protected] 1Department of Mathematical Sciences, UAE University, P.O. Box 15551, Al Ain, UAE Full list of author information is available at the end of the article Abstract In this paper we study linear and nonlinear fractional diffusion equations with the Caputo fractional derivative of non-singular kernel that has been launched recently (Caputo and Fabrizio in Prog....

We present some new relations between the pseudo-derivatives and parabolic epiderivatives recently introduced by Rockafellar, and also its infinite dimensional counterparts. Significant extensions of the most important known results are proven, which further clarify the range of applicability of this new theory.

We characterize some major algorithmic randomness notions via differentiability of effective functions. (1) We show that a real number z ∈ [0, 1] is computably random if and only if every nondecreasing computable function [0, 1] → R is differentiable at z. (2) A real number z ∈ [0, 1] is weakly 2-random if and only if every almost everywhere differentiable computable function [0, 1] → R is diff...

The traditional concept of smoothness concerns differentiability, and we consider a function to be smooth if it is k-times differentiable. This concept is important in many aspects of numerical analysis, and the quality of reconstructions of signals from certain given observations depend on this information. For instance, a k-times differentiable function on the unit cube [0, 1] can be approxim...