Related papers: On one inverse problem relatively domain for the p…
Functional determinants on various domains of the sphere and flat space are presented for scalar and spinor fields.
We establish H\"older stability of an inverse hyperbolic obstacle problem. Mainly, we study the problem of reconstructing an unknown function defined on the boundary of the obstacle from two measurements taken on the boundary of a domain…
This note should clarify how the behavior of certain invariant objects reflects the geometric convexity of balanced domains.
In this article we deal with one-dimensional inverse problems concerning the Burgers equation and some related nonlinear systems (involving heat effects and/or variable density). In these problems, the goal is to find the size of the…
Let S be a subring of the ring R. We investigate the question of whether S intersected by U(R) is equal to U(S) holds for the units. In many situations our answer is positive. There is a special emphasis on the case when R is a full matrix…
It is known that inner functions exist on strongly pseudoconvex domains. In this paper we will show that they exist on a more general type of domains, including some domains of finite type.
We study the P versus NP problem through properties of functions and monoids, continuing the work of [3]. Here we consider inverse monoids whose properties and relationships determine whether P is different from NP, or whether injective…
We present the Boolean dimension of a graph, we relate it with the notions of inner, geometric and symplectic dimensions, and with the rank and minrank of a graph. We obtain an exact formula for the Boolean dimension of a tree in terms of a…
Several sets of quaternionic functions are described and studied. Residue current of the right inverse of a quaternionic function is introduced in particular cases.
We will prove that a function u(x,y) defined on a domain of RpxRq that is subharmonic in one variable and harmonic in the other is (jointly) subharmonic. This solves a long-standing open problem.
The property of isotonicity of a continuous convex function defined on the entire space or only on the positive cone is characterized via subdifferentials. Numerous examples illustrating the obtained results are included.
The purpose is to formulate a Fourier transformation for the space of functionals, as an infinitesimal meaning. We extend ${\bf R}$ to $ ^{\star}(^{\ast}{\bf R})$ under the base of nonstandard methods for the construction. The domain of a…
When considering fractional diffusion equation as model equation in analyzing anomalous diffusion processes, some important parameters in the model, for example, the orders of the fractional derivative or the source term, are often unknown,…
We study the local and global versions of the convexity, which is closely related to the problem of extending a convex function on a non-convex domain to a convex function on the convex hull of the domain and beyond the convex hull. We also…
This note treats several problems for the fractional perimeter or $s$-perimeter on the sphere. The spherical fractional isoperimetric inequality is established. It turns out that the equality cases are exactly the spherical caps.…
Paper is devoted to extremal problems in geometric function theory of complex variables associated with estimates of functionals defined on the systems of non-overlapping domains. In particular, we strengthen some known result in this…
In this paper, we study a partially overdetermined mixed boundary value problem in a half ball. We prove that a domain in which this partially overdetermined problem admits a solution if and only if the domain is a spherical cap…
For convex univalent functions we give instances where the sharp bound for various coefficient functionals are identical to those for the corresponding bound for the inverse function. We give instances where the sharp bounds differ and also…
In this work, a novel approach for the solution of the inverse conductivity problem from one and multiple boundary measurements has been developed on the basis of the implication of the framework of BV - functions. The space of the…
We study orthogonal polynomials for a weight function defined over a domain of revolution, where the domain is formed from rotating a two-dimensional region and goes beyond the quadratic domains. Explicit constructions of orthogonal bases…