相关论文: Applications of integral transforms composition me…

Although being powerful, the differential transform method yet suffers from a drawback which is how to compute the differential transform of nonlinear non-autonomous functions that can limit its applicability. In order to overcome this…

Functional group replacement is a pivotal approach in cheminformatics to enable the design of novel chemical compounds with tailored properties. Traditional methods for functional group removal and replacement often rely on rule-based…

In this paper, Bernstein piecewise polynomials are used to solve the integral equations numerically. A matrix formulation is given for a non-singular linear Fredholm Integral Equation by the technique of Galerkin method. In the Galerkin…

It is known that the unified transform method may be used to solve any well-posed initial-boundary value problem for a linear constant-coefficient evolution equation on the finite interval or the half-line. In contrast, classical methods…

Classical trellis-coded modulation (TCM) as introduced by Ungerboeck in 1976/1983 uses a signal constellation of twice the cardinality compared to an uncoded transmission with one bit of redundancy per PAM symbol, i.e., application of codes…

This paper introduces a waveform design method using Multi-Tone Feedback Frequency Modulation (MT-FFM), a generalization of the single oscillator feedback FM method developed by [Tomisawa, 1981]. The MT-FFM utilizes a collection of $K$…

This article addresses linear hyperbolic partial differential equations and pseudodifferential equations with strongly singular coefficients and data, modelled as members of algebras of generalised functions. We employ the recently…

Some general remarks about integral transform approaches to response functions are made. Their advantage for calculating cross sections at energies in the continuum is stressed. In particular we discuss the class of kernels that allow…

We present a collection of well-conditioned integral equation methods for the solution of electrostatic, acoustic or electromagnetic scattering problems involving anisotropic, inhomogeneous media. In the electromagnetic case, our approach…

The use of orthonormal wavelet basis functions for solving singular integral scattering equations is investigated. It is shown that these basis functions lead to sparse matrix equations which can be solved by iterative techniques. The…

Performing analog computations with metastructures is an emerging wave-based paradigm for solving mathematical problems. For such devices, one major challenge is their reconfigurability, especially without the need for a priori mathematical…

The main content of this book is composed from two doctoral theses: by V.\,V.~Katrakhov (1989) and by S.\,M.~Sitnik (2016). In our work, for the first time in the format of a monograph, we systematically expound the theory of transmutation…

In the paper, we utilize the fractional differential transformation (FDT) to solving singular initial value problem of fractional Emden-Fowler type differential equations. The solutions of our model equations are calculated in the form of…

We consider mapping properties of the iterated Stieltjes transform, establishing its new relations with the iterated Hilbert transform (a singular integral) on the half-axis and proving the corresponding convolution and Titchmarsh's type…

In this paper, approximate analytical solutions of nonlinear Emden-Fowler type equations are obtained by the differential transform method (DTM). The DTM is a numerical as well as analytical method for solving integral equations, ordinary…

Novel analytic solutions are derived for integrals that involve the generalized Marcum Q-function, exponential functions and arbitrary powers. Simple closed-form expressions are also derived for the specific cases of the generic integrals.…

For the calculation of multi-loop Feynman integrals, a novel numerical method, the Direct Computation Method (DCM) is developed. It is a combination of a numerical integration and a series extrapolation. In principle, DCM can handle…

In this paper we provide a unified approach to a family of integrals of Mellin--Barnes type using distribution theory and Fourier transforms. Interesting features arise in many of the cases which call for the application of pull-backs of…

In this paper we formulate a general method for building completely integrable quantum systems. The method is based on the use of the so-called multi-parameter spectral equations, i.e. equations with several spectral parameters. We show…

We present a numerically stable re-formulization of the transfer matrix method (TMM). The iteration form of the traditional TMM is transformed into solving a set of linear equations. Our method gains the new ability of calculating accurate…