Search

This paper presents a comprehensive study on developing a novel mathematical model of generalized thermoelasticity to investigate the transient phenomena for an infinite thermoelastic half-space under the action of ramp-type thermal loading and due to the influence of a gravitational field. The bounding plane of the half-space is subjected to rough and rigid foundation so that the rough surface prevents the vertical displacement. Due to the shortcomings of power-law distributions, some other forms of derivatives with few other kernel functions are proposed. The present analysis deals with the heat transport which involves the memory-dependent derivative (MDD) on a slipping interval in the context of Lord–Shulman model to describe the physical phenomena which is defined in the form of convolution with the kernels in the form of power functions. Employing the Laplace and the Fourier transform techniques as tools, the analytical expressions for different physical fields have been obtained on the transformed domain. The numerical inversion of the Fourier transforms have been performed analytically, whereas numerical inversion of the Laplace transform is carried out using the Riemann-sum approximation method. Excellent predictive capability is demonstrated due to the presence of MDD, delay time and gravitational field also. [ABSTRACT FROM AUTHOR]

This paper designs a general type time–frequency transform whose kernel function involves a nonlinear modulation and a frequency-varying dilation. The corresponding inversion formula is established. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the definitions of the Fourier transform and spherical Fourier transform on quaternionic Heisenberg group, then we present some of their properties, in particular, we will determine the spherical functions and the heat kernel of quaternionic Heisenberg group. Finally, we prove a qualitative uncertainty principle 'Donoho–Stark's uncertainty principle'. [ABSTRACT FROM AUTHOR]

New index transforms with Weber-type kernels, consisting of products of Bessel functions of the first and second kind, are investigated. Mapping properties and inversion formulas are established for these transforms in Lebesgue spaces. The results are applied to solve a boundary value problem on the wedge for a fourth-order partial differential equation. [ABSTRACT FROM PUBLISHER]

In their paper Barndorff-Nielsen et al. [4] employ so called ambit fields to model electricity spot-forward dynamics. We briefly introduce and discuss ambit fields, and introduce a novel method for approximating general ambit fields by a linear combination of ambit fields driven by exponential kernel functions (as has already been done in the null-spatial case of Lévy semistationary processes by Benth et al. [11]) by approximating the deterministic kernel function by a carefully selected finite sum. Moreover, we shall study examples, in the setting of modelling electricity forward markets, of ambit fields with singular kernel functions to illustrate the usefulness of our method for pricing purposes. [ABSTRACT FROM AUTHOR]

The adoption of a angular discretization scheme in the solution of the linear transport equation is introducing a wide range of distortions associated with the propagation of particles along discrete directions, usually called ray effects. These numerical artifacts and the consequent distortion of the physical description are observed in multidimensional configurations in steady-state and also in the one-dimensional case when the time-dependence is considered. Through the analysis of simplified configurations, this work aims at a characterization of the ray effect phenomenon. Steady-state and time-dependent problems are solved analytically and then compared to the results obtained by applying discrete ordinates, clearly isolating ray effects from other numerical effects and allowing the quantification of the physical distortion. The analysis of the transport kernel in the Fourier-transformed space permits the identification of a proper integral parameter, called ray effect indicator, to measure the distortion introduced in the transport model by the angular discretization. The efficiency of alternative schemes to the standard SN approach for the reduction of ray effects is also discussed. [ABSTRACT FROM AUTHOR]

In this paper, we generalize the theory of variation diminishing kernels introduced by Hirschman, Jr and van de Wetering for a class of singular second-order differential operators introduced by Chébli and Trimèche. We give a necessary and sufficient condition such that a function Λ is a variation diminishing convolution kernel. [ABSTRACT FROM PUBLISHER]

The Fourier exchange theorem is generalized to 𝒮′-convolvable kernels, i.e. temperate distributions K(x, y) ∈ 𝒮′(ℝ2n ) for which K(x − y, y) is semitemperate with respect to x and partially summable with respect to y. [ABSTRACT FROM AUTHOR]

We consider a class of polynomials related to the kernel Kiτ(x) of the Kontorovich-Lebedev transformation. Algebraic and differential properties are investigated and integral representations are derived. We draw a parallel and establish a relationship with the Bernoulli's and Euler's numbers and polynomials. Finally, as an application we invert a discrete transformation with the introduced polynomials as the kernel, basing it on a decomposition of Taylor's series in terms of the Kontorovich-Lebedev operator. [ABSTRACT FROM AUTHOR]

A class of pseudo-differential operators (p.d.o.'s) associated with the general Fourier kernel studied by Hardy and Titchmarsh is defined. A symbol class Tm is introduced. It is shown that the p.d.o.'s associated with the symbol are continuous linear mappings of the Braaksma and Schuitman space T(λ,μ) into itself. An integral representation of p.d.o. is obtained. Some special forms of the symbol are considered. It is shown that these p.d.o.'s and their products are bounded in certain Sobolev type space. [ABSTRACT FROM AUTHOR]

This article deals with a non-local problem for the harmonic function in a disc, when the value of the function on one part of its semi-circle and the relation of unknown function values on the semi-circles of concentrated circles on the other part of the circle are given. This problem is reduced to the integral equation with a periodical kernel. To solve it, the analogue of the Wiener–Hopf method for a discrete case is developed. Its use allows one to obtain the problem equivalent to the factorization problem which has a unique solution. An effective solution is constructed. [ABSTRACT FROM AUTHOR]

The problem of nonparametric regression is addressed, and a kernel smoothing estimator is proposed which has favorable asymptotic performance (bias, variance and mean squared error). The proposed class of kernels is characterized by a Fourier transform which is flat near the origin and infinitely differentiable. This property allows the bias of the estimate to decrease at the maximal rate without harming the rate at which the variance decreases, thus leading to a faster rate of convergence. [ABSTRACT FROM AUTHOR]