Related papers: A new generalized integral transform and applicati…
The transformations of the sum identities for generalized harmonic and oscillatory numbers, obtained earlier in our recent report [1], enable us to derive the new identities expressed in terms of the corresponding square roots of x. At…
The initial value problem is introduced after a thorough review of the essential geometry. The initial value equations are put into elliptic form using both conformal transformations and a treatment of the extrinsic curvature introduced…
In this article we give a totally new proof of the integral localization formula for equivariantly closed differential forms (Theorem 7.11 in [BGV]). We restate it here as Theorem 2. This localization formula is very well known, but the…
The goal of this paper is to introduce the notion of polyconvolution for Fourier-cosine, Laplace integral operators, and its applications. The structure of this polyconvolution operator and associated integral transforms are investigated in…
A new class of affine scaling matrices for the interior point Newton-type methods is considered to solve the nonlinear systems with simple bounds. We review the essential properties of a scaling matrix and consider several well-known…
Integral transformations are useful mathematical tool to work out signals and wave-packets in electronic devices. They may be used in software protocols. Necessary knowledge may come from quantum field theory, in particular from quantum…
The Fourier transform is typically seen as closely related to the additive group of real numbers, its characters and its Haar measure. In this paper, we propose an alternative viewpoint; the Fourier transform can be uniquely characterized…
In this PhD thesis we introduce a generalized fractional calculus of variations. We consider variational problems containing generalized fractional integrals and derivatives, and study them using standard (indirect) and direct methods. In…
We consider a class of generalized binomials emerging in fractional calculus. After establishing some general properties, we focus on a particular yet relevant case, for which we provide several ready-for-use combinatorial identities,…
In [Trace identities and $\bf {Z}/2\bf {Z}$-graded invariants, {\it Trans. Amer. Math. Soc. \bf309} (1988), 581--589] we generalized the first and second fundamental theorems of invariant theory from the general linear group to the general…
This paper presents invariants under gamma correction and similarity transformations. The invariants are local features based on differentials which are implemented using derivatives of the Gaussian. The use of the proposed invariant…
An overview of some of the recent developments in the theory of valuations on convex sets and its generalizations to manifolds is given. The exposition is focused towards applications to integral geometry; several of such applications are…
The paper studies coincidence points of parameterized set-valued mappings (multifunctions), which provide an extended framework to cover several important topics in variational analysis and optimization that include the existence of…
We propose a novel definition of Fourier transform, with the property that the transform of a real function is again a real function (without doubling the number of real components). We prove the inversion theorem for the novel definition,…
In a variety of scientific applications we wish to characterize a physical system using measurements or observations. This often requires us to solve an inverse problem, which usually has non-unique solutions so uncertainty must be…
We introduce a new type of reduction of inversive difference polynomials that is associated with a partition of the basic set of automorphisms $\sigma$ and uses a generalization of the concept of effective order of a difference polynomial.…
The axiomatic theory of ordinary differential equations, owing to its simplicity, can provide a useful framework to describe various generalizations of dynamical systems. In this study, we consider how dynamical properties can be…
Some new survival distributions are introduced based on a generalised exponential function. This class of distributions includes heavy-tailed generalisations of exponential, Weibull and gamma distributions. Properties of the distributions…
We propose a discrete fractional random transform based on a generalization of the discrete fractional Fourier transform with an intrinsic randomness. Such discrete fractional random transform inheres excellent mathematical properties of…
This paper provides new sufficient and necessary conditions for the frame property of generalized translation-invariant systems. The conditions are formulated in the Fourier domain and consists of estimates involving the upper and lower…