Planar D-bar integral equation is one of the inverse scattering solution methods for complex problems including inverse conductivity considered in applications such as Electrical impedance tomography (EIT). Recently two different methodologies are considered for the numerical solution of D-bar integrals equation, namely product integrals and multigrid. The first one involves high computational ...

A multiple-parameter convolution integral is used to define and generate waveforms that quantitatively and qualitatively resemble the experimentally observed behavior of episodic endocrine signals. Our formulation of the convolution integral in terms of multiple distinct parameters with statistically bounded values allows investigators to quantitatively model variations in the duration, amplitu...

Analytical expressions for the non-relativistic and relativistic Sunyaev-Zel'dovich effect (SZE) are derived by means of suitable convolution in-tegrals. The establishment of these expressions is based on the fact that the SZE disturbed spectrum, at high frequencies, possesses the form of a Laplace transform of the single line distortion profile (structure factor). Implications of this descript...

Notions of orthogonality and convolution are explored with the use Kontorovich–Lebedev transform its convolution. New classes corresponding orthogonal polynomials functions investigated. Integral representations, relations explicit expressions established.

The Fourier transform is considered as a Henstock–Kurzweil integral. Sufficient conditions are given for the existence of the Fourier transform and necessary and sufficient conditions are given for it to be continuous. The Riemann–Lebesgue lemma fails: Henstock– Kurzweil Fourier transforms can have arbitrarily large point-wise growth. Convolution and inversion theorems are established. An appen...

where f(t) -=I0 for 0 :::;; t :::;; t* and is zero otherwise. Response x(t) can be simply calculated for any given f(t) using convolution integral-see, e.g., textbook [1J, where several examples for various specific forms off(t) are presented. In this note an explicit expression for x (t), t ~ t* is derived for an arbitrary f(t), in terms of its Fourier transform. This expression has important ...

Three types of integral representations for the cumulative distribution functions of convolutions of Γp(αk,Σk,∆k)–distributions with non–centrality matrices ∆k are given by integration of products of simple complex functions over the p–cube (−π, π]. In particular, the joint distribution of the diagonal elements of a generalized quadratic form XAX ′ with n independentNp(μk,Σ)–distributed columns...

We present a method for image-based visualization of flow fields on unstructured grids. For interactive exploration of flow data from CFD simulations, we combine GPU-accelerated surface extraction methods and line integral convolution (LIC) in a multi-pass algorithm. In contrast to other highly efficient methods, computation of stream lines is performed directly on the unstructured grid, where ...

This paper presents a numerical method for solving the Volterra integral equation with a convolution kernel. The integral equation was first converted to an algebraic equation using the Laplace transform, after which its numerical inversion was determined by power series. The Padé approximants were effectively used to improve the convergence rate and accuracy of the computed series. The method ...

The initial-value problem for the focusing nonlinear Schrödinger (NLS) equation is solved numerically by following the various steps of the inverse scattering transform. Starting from the initial value of the solution, a Volterra integral equation is solved followed by three FFT to arrive at the reflection coefficient and initial Marchenko kernel. By convolution these initial data are propagate...