相关论文: Evaluation of inverse integral transforms for unde…

A general method for analytic inversion of geometric integral transforms is proposed

In this study, new master theorems and general formulas of integrals are presented and implemented to solve some complicated applications in different fields of science. The proposed theorems are considered to be generators of new problems,…

We derive an explicit inversion algorithm for the spherical Radon transform in odd dimensions with partial radial data. We prove that the reconstruction of the unknown function can be reduced to solving ordinary differential equations,…

This work aims to bridge the gap between pure and applied research on scalar, linear Volterra equations by examining five major classes: integral and integro-differential equations with completely monotone kernels, such as linear…

In the present article, the author uses Fourier theory of tempered distributions (generalized functions) in deriving a formula for Dirichlet-like integrals. The applied method is remarkably efficient and allows a solution in a few…

Fourier transforms are ubiquitous mathematical tools in basic and applied sciences. We here report classical and quantum optical realizations of the discrete fractional Fourier transform, a generalization of the Fourier transform. In the…

An integro-differential Dirac system with an integral term in the form of convolution is considered. We suppose that the convolution kernel is known a priori on a part of the interval, and recover it on the remaining part, using a part of…

We consider the inverse problem of the broken ray transform (sometimes also referred to as the V-line transform). Explicit image reconstruction formulas are derived and tested numerically. The obtained formulas are generalizations of the…

A new definition of a fractional derivative has recently been developed, making use of a fractional Dirac delta function as its integral kernel. This derivative allows for the definition of a distributional fractional derivative, and as…

The inverse Radon transform allows to obtain partonic double distributions from (extended) generalized parton distributions. We express the extension of generalized parton distributions by their dual parts, generalized distribution…

Inverse normal transformations applied to the partially overlapping samples t-tests by Derrick et.al. (2017) are considered for their Type I error robustness and power. The inverse normal transformation solutions proposed in this paper are…

This article handles in a short manner a few Laplace transform pairs and some extensions to the basic equations are developed. They can be applied to a wide variety of functions in order to find the Laplace transform or its inverse when…

We propose a novel numerical inversion algorithm for the coefficients of parabolic partial differential equations, based on model reduction. The study is motivated by the application of controlled source electromagnetic exploration, where…

Reciprocal transformations mix the role of the dependent and independent variables of (nonlinear partial) differential equations to achieve simpler versions or even linearized versions of them. These transformations help in the…

All integrals available in literature and books, that are related to Sinc(=sin x/x) function, are special cases of the general form of the integral given in the title. The evaluation of the integral is divided into two cases (i) $a$ and $b$…

Integral transforms are invaluable mathematical tools to map functions into spaces where they are easier to characterize. We introduce the hyperdimensional transform as a new kind of integral transform. It converts square-integrable…

The Dirac delta function is a standard mathematical tool used in multiple topical areas in the undergraduate physics curriculum. While Dirac delta functions are usually introduced in order to simplify a problem mathematically, students…

This revisit gives a survey on the analytical methods for the inverse exponential Radon transform which has been investigated in the past three decades from both mathematical interests and medical applications such as nuclear medicine…

Inverse optimization describes a process that is the "reverse" of traditional mathematical optimization. Unlike traditional optimization, which seeks to compute optimal decisions given an objective and constraints, inverse optimization…

The Dirac delta function is a standard mathematical tool that appears repeatedly in the undergraduate physics curriculum in multiple topical areas including electrostatics, and quantum mechanics. While Dirac delta functions are often…