Related papers: Higher-Order Singular-Value Derivatives of Rectang…
The Taylor expansion of wave fields with respect to shape parameters has a wide range of applications in wave scattering problems, including inverse scattering, optimal design, and uncertainty quantification. However, deriving the high…
Given a Hilbert space operator $T$, the level sets of function $\Psi_T(z)=\|(T-z)^{-1}\|^{-1}$ determine the so-called pseudospectra of $T$. We set $\Psi_T$ to be zero on the spectrum of $T$. After giving some elementary properties of…
The goal of this paper is to construct a nonlinear Fourier transformation on the space of symbols of compact Hankel operators on the circle. This transformation allows to solve a general inverse spectral problem involving singular values of…
We construct new, efficient, and accurate high-order finite differencing operators which satisfy summation by parts. Since these operators are not uniquely defined, we consider several optimization criteria: minimizing the bandwidth, the…
We study Hadamard variation of eigenvalues of Laplacian with respect to general domain perturbations. We show their existence up to the second order rigorously and characterize the derivatives, using associated eigenvalue problems in finite…
A new approach to multi-dimensional quantum scattering by the infinite order discrete variable representation is presented. Determining the expansion coefficients of the wave function at the asymptotic regions by the solution of the…
We analyze a certain class of integral equations related to Marchenko equations and Gel'fand-Levitan equations associated with various systems of ordinary differential operators. When the integral operator is perturbed by a finite-rank…
We address the problem of complementing higher-order patterns without repetitions of existential variables. Differently from the first-order case, the complement of a pattern cannot, in general, be described by a pattern, or even by a…
Scientific studies often require the precise calculation of derivatives. In many cases an analytical calculation is not feasible and one resorts to evaluating derivatives numerically. These are error-prone, especially for higher-order…
We propose an asymptotic expansion formula for matrix integrals, including oscillatory terms (derivatives of theta-functions) to all orders. This formula is heuristically derived from the analogy between matrix integrals, and formal matrix…
In this paper, we propose a novel recovery based finite element method for the Cahn-Hilliard equation. One distinguishing feature of the method is that we discretize the fourth-order differential operator in a standard $C^0$ linear finite…
The complex scaling method, which consists in continuing spatial coordinates into the complex plane, is a well-established method that allows to compute resonant eigenfunctions of the time-independent Schroedinger operator. Whenever it is…
Motivated by the occurrence of "shattering" mass-loss observed in purely continuous fragmentation models, this work concerns the development and the mathematical analysis of a new class of hybrid discrete--continuous fragmentation models.…
We introduce real vector spaces composed of set-valued maps on an open set. They are also complete metric spaces, lattices, commutative rings. The set of differentiable functions is a dense subset of these spaces and the classical gradient…
To be able to solve operator equations numerically a discretization of those operators is necessary. In the Galerkin approach bases are used to achieve discretized versions of operators. In a more general set-up, frames can be used to…
In this paper we construct the spectral expansion for the non-self-adjoint differential operators generated in the space of vektor functions by the ordinary differential expression of arbitrary order with the periodic matrix coefficients by…
In this paper we develop a new approach for studying differential operators of an isolated singularity graded hypersurface ring $R$ defining a surface in affine three-space over a field of characteristic zero. With this method, we construct…
We consider non-self-adjoint electromagnetic Schr\"odinger operators on arbitrary open sets with complex scalar potentials whose real part is not necessarily bounded from below. Under a suitable sufficient condition on the electromagnetic…
Tree tensor networks (TTNs) provide a compact and structured representation of high-dimensional data, making them valuable in various areas of computational mathematics and physics. In this paper, we present a rigorous mathematical…
We analyse a new notion of total anisotropic higher-order variation which, differently from the Total Generalized Variation by Bredies et al., quantifies for possibly non-symmetric tensor fields their variations at arbitrary order weighted…