Related papers: On the factorization formula for fundamental solut…
This paper introduces a multi-frequency factorization method for imaging a time-dependent source, specifically to recover its spatial support and the associated excitation instants. Using far-field data from two opposite directions, we…
We analyse the Gaussian wave packet transform. Based on the Fourier inversion formula and a partition of unity, which is formed by a collection of Gaussian basis functions, a new representation of square-integrable functions is presented.…
In this work, we propose an observation system based on the available data which solution is one-be-one mapping to the forward problem(with the unknown initial function) solution. It implies their solutions share the same linear structure…
Fourier and fractional-Fourier transformations are widely used in theoretical physics. In this paper we make quantum perspectives and generalization for the fractional Fourier transformation (FrFT). By virtue of quantum mechanical…
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…
This paper introduces Generalized Fourier transform (GFT) that is an extension or the generalization of the Fourier transform (FT). The Unilateral Laplace transform (LT) is observed to be the special case of GFT. GFT, as proposed in this…
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…
Fracture functions and their evolution equations are reviewed. Some phenomenological applications are briefly discussed.
We study incommensurate fractional variational problems in terms of a generalized fractional integral with Lagrangians depending on classical derivatives and generalized fractional integrals and derivatives. We obtain necessary optimality…
We use the periodicity properties of generalized Gauss sums to factor numbers. Moreover, we derive rules for finding the factors and illustrate this factorization scheme for various examples. This algorithm relies solely on interference and…
In the present paper we introduce the generalized inverse operators which have an interesting role in operator theory. We establish Douglas' factorization theorem type for Hilbert pro-$C^{\ast}$-module. We introduce the notion of atomic…
The Lambert W function has utility for solving various exponential and logarithmic equations arranged in the form of $g(x)e^{g(x)}$. Using the Lambert W function and tetration, a variety of categorized inversion formulas are presented.…
In recent years many efforts have been devoted to finding bidiagonal factorizations of nonsingular totally positive matrices, since their accurate computation allows to numerically solve several important algebraic problems with great…
The paper surveys recent progress in establishing uniqueness and developing inversion formulas and algorithms for the thermoacoustic tomography. In mathematical terms, one deals with a rather special inverse problem for the wave equation.…
In this paper we study generalized J-inner matrix valued functions which appear as resolvent matrices in various indefinite interpolation problems. Reproducing kernel indefinite inner product spaces associated with a generalized J-inner…
This work introduces a new inversion formula for analytical functions. It is simple, generally applicable and straightforward to use both in hand calculations and for symbolic machine processing. It is easier to apply than the traditional…
In this paper, we study both the direct and inverse random source problems associated with the multi-term time-fractional diffusion-wave equation driven by a fractional Brownian motion. Regarding the direct problem, the well-posedness is…
The main goal of this paper is to propose an approach to inverse spectral problems for functional-differential operators (FDO) with involution. For definiteness, we focus on the second-order FDO with involution-reflection. Our approach is…
We describe an algorithm for the application of the forward and inverse spherical harmonic transforms. It is based on a new method for rapidly computing the forward and inverse associated Legendre transforms by hierarchically applying the…
A novel factorization for the sum of two single-pair matrices is established as product of lower-triangular, tridiagonal, and upper-triangular matrices, leading to semi-closed-form formulas for tridiagonal matrix inversion. Subsequent…