We study the rapid stabilization of heat equation on 1-dimensional torus using backstepping method with a Fredholm transformation. This classical framework allows us to present transformations for Laplace operator in sharp functional setting, which is main objective this work. first prove that, under some assumptions control operator, two scalar controls are necessary and sufficient get control...

This paper studies a Laplace operator on semi-discrete surfaces. A semidiscrete surface is represented by a mapping into three-dimensional Euclidean space possessing one discrete and one continuous variable. It can be seen as a limit case of a quadrilateral mesh, or as a semi-discretization of a smooth surface. Laplace operators on both smooth and discrete surfaces have been an object of intere...

Motivation The identification of genetic variants influencing gene expression (known as expression quantitative trait loci or eQTLs) is important in unravelling the genetic basis of complex traits. Detecting multiple eQTLs simultaneously in a population based on paired DNA-seq and RNA-seq assays employs two competing types of models: models which rely on appropriate transformations of RNA-seq d...

‎Several modifications of the Laplace distribution have been introduced and applied in various fields up to this day‎. ‎In this paper‎,  ‎we introduce a modified symmetric version of the classical Laplace distribution‎.  ‎We provide a comprehensive theoretical description of this distribution‎. ‎In particular‎, ‎we derive the formulas for th...

this article is devoted to study of the autoconvolution equations and generalized mittag-leffler functions. these types of equations are given in terms of the laplace transform convolution of a function with itself. we state new classes of the autoconvolution equations of the first kind and show that the generalized mittag-leffler functions are solutions of these types of equations. in view of ...

In this paper we present the development of a rigorous approach for the solution of non-linear partial differential equations by use of the Laplace transformation — in particular, the convolution theorem for Laplace transforms. While the rigor of this new approach is general, our paper is devoted to the development, verification, and application of this method for the case of real gas flow in p...

This paper continues the study of metastable behaviour in disordered mean field models initiated in [2], [3]. We consider the generalized Hopfield model with finitely many independent patterns ξ1, . . . , ξP where the patterns have i.i.d. components and the components of patterns ξ1, . . . ξp have absolutely continuous distributions on [−1, 1] whereas the components of patterns ξp+1, . . . , ξP...

We introduce an improved second-order discretization method for the convection-reaction equation by combining analytical and numerical solutions. The method is derived from Godunov’s scheme, see [15] and [21], and uses analytical solutions to solve the one-dimensional convection-reaction equation. We can also generalize the second-order methods for discontinuous solutions, because of the analyt...