Related papers: The Distribution Relation and Inverse Function The…

The aim of this note is to prove the inversion formula, which can be used to compute the Levi measure of an infinitely divisible distribution from its characteristic function. Obtained formula is similar to the well-known inversion formula…

The paper is devoted to differential geometry of singular distributions (i.e., of varying dimension) on a Riemannian manifold. Such distributions are defined as images of the tangent bundle under smooth endomorphisms. We prove the novel…

We construct C-algebras for a class of surfaces that are inverse images of certain polynomials of arbitrary degree. By using the directed graph associated to a matrix, the representation theory can be understood in terms of ``loop'' and…

We first introduce new algebras of generalized functions containing Gevrey ultradistributions and then develop a Gevrey microlocal analysis suitable for these algebras. Finally, we give an application through an extension of the well-known…

Using a new technique involving integration it is possible to find the exact roots of simple functions. In this case, simple functions are defined as smooth functions having an inverse, and that inverse having an antiderivative. This…

Gowers norms have been studied extensively both in the direct sense, starting with a function and understanding the associated norm, and in the inverse sense, starting with the norm and deducing properties of the function. Instead of…

We discuss a recent line of research investigating inverse theorems with respect to general k-wise correlations, and explain how such correlations arise in different contexts in mathematics. We outline some of the results that were…

In distributed optimization and distributed numerical linear algebra, we often encounter an inversion bias: if we want to compute a quantity that depends on the inverse of a sum of distributed matrices, then the sum of the inverses does not…

This work studies slice functions over finite-dimensional division algebras. Their zero sets are studied in detail along with their multiplicative inverses, for which some unexpected phenomena are discovered. The results are applied to…

We continue to study the problem of modeling of substitution of production factors motivated by the need for computable mathematical models of economics that could be used as a basis in applied developments. This problem has been studied…

Recently, there has been an increasing interest in employing rotational motion measurements for seismic source inversion, structural imaging and ambient noise analysis. We derive reciprocity and representation theorems for rotational…

The Bertrand's theorem can be formulated as the solution of an inverse problem for a classical unidimensional motion. We show that the solutions of these problems, if restricted to a given class, can be obtained by solving a numerical…

We extend the construction of [19] by introducing spaces of generalized tensor fields on smooth manifolds that possess optimal embedding and consistency properties with spaces of tensor distributions in the sense of L. Schwartz. We thereby…

The usual formulation of efficient division uses Newton iteration to compute an inverse in a related domain where multiplicative inverses exist. On one hand, Newton iteration allows quotients to be calculated using an efficient…

The division between two vectors belonging to the same vector space is obtained by elementary procedures of vector algebra and is defined by a matrix. This representation is obtained for two and three dimensional vector spaces. A new vector…

In this paper we will survey some recent developments in the last decade or so on variation of Geometric Invariant Theory and its applications to Birational Geometry such as the weak Factorization Theorems of nonsingular projective…

In two previous papers the author introduced a multiplication of distributions in one dimension and he proved that two one-dimensional Dirac delta functions and their derivatives can be multiplied, at least under certain conditions. Here,…

We study the joint distribution of descents and inverse descents over the set of permutations of n letters. Gessel conjectured that the two-variable generating function of this distribution can be expanded in a given basis with nonnegative…

In this note we provide a quick proof of the Sklar's Theorem on the existence of copulas by using the generalized inverse functions as in the one dimensional case, but a little more sophisticated.

This is a brief overview of our work on the theory of group invariant solutions to differential equations. The motivations and applications of this work stem from problems in differential geometry and relativistic field theory. The key…