Related papers: New lower bounds for the integration of periodic f…
In this paper, we give new explicit representations of the Hilbert scheme of $\mu$ points in $\PP^{r}$ as a projective subvariety of a Grassmanniann variety. This new explicit description of the Hilbert scheme is simpler than the previous…
In this paper we propose a product space reformulation to transform monotone inclusions described by finitely many operators on a Hilbert space into equivalent two-operator problems. Our approach relies on Pierra's classical reformulation…
Computing accurate periodic responses in strongly nonlinear or even non-smooth vibration systems remains a fundamental challenge in nonlinear dynamics. Existing numerical methods, such as the Harmonic Balance Method (HBM) and the Shooting…
The evaluation of the error to be attributed to cut efficiencies is a common question in the practice of experimental particle physics. Specifically, the need to evaluate the efficiency of the cuts for background removal, when they are…
In this work, we consider an initial-boundary value problem for a time-fractional biharmonic equation in a bounded polygonal domain with a Lipschitz continuous boundary in $\mathbb{R}^2$ with clamped boundary conditions. After establishing…
We investigate an extended version of Hilbert space of analytic functions called Hilbert space of complex-valued harmonic functions. It is found that functions in Hilbert space of complex-valued harmonic functions exhibit many properties…
We first present an abstract principle for the interchange of infimization and integration over spaces of mappings taking values in topological spaces. New conditions on the underlying space and the integrand are then introduced to convert…
This article considers Hamiltonian mechanical systems with potential functions admitting jump discontinuities. The focus is on accurate and efficient numerical approximations of their solutions, which will be defined via the laws of…
We consider the problem of finding the shortest possible period for an exactly periodic solution to some given autonomous ordinary differential equation. We show that, given a pair of Lyapunov-like observable functions defined over the…
We investigate an extension of classical empirical risk minimization, where the hypothesis space consists of a random subspace within a given Hilbert space. Specifically, we examine the Nystr\"om method where the subspaces are defined by a…
This paper describes a trapezoidal quadrature method for the discretization of weakly singular, singular and hypersingular boundary integral operators with complex symmetric quadratic forms. Such integral operators naturally arise when…
We investigate the function $L(h,p,q)$, called here the threshold function, related to periodicity of partial words (words with holes). The value $L(h,p,q)$ is defined as the minimum length threshold which guarantees that a natural…
We analyze, mainly using bifurcation methods, an elliptic superlinear problem in one-dimension with periodic boundary conditions. One of the main novelties is that we follow for the first time a bifurcation approach, relying on a…
We derive a residual-based $hp$-a posteriori error estimator for hybrid high-order (HHO) methods on simplicial meshes applied to the biharmonic problem posed on two- and three-dimensional polytopal Lipschitz domains. The a posteriori error…
By exploiting the Fueter theorem, we give new formulas to compute zonal harmonic functions in any dimension. We first give a representation of them as a result of a suitable ladder operator acting on the constant function equal to one.…
The present paper is devoted to construction of an optimal quadrature formula for approximation of Fourier integrals in the Hilbert space $W_2^{(1,0)}[a,b]$ of non-periodic, complex valued functions. Here the quadrature sum consists of…
We introduce a new type of cubature formula for the evaluation of an integral over the disk with respect to a weight function. The method is based on an analysis of the Fourier series of the weight function and a reduction of the bivariate…
We lay down the preliminary work to apply the Functional Analytic Approach to quasi-periodic boundary value problems for the Helmholtz equation. This consists in introducing a quasi-periodic fundamental solution and the related layer…
Many applications require multi-dimensional numerical integration, often in the form of a cubature formula. These cubature formulas are desired to be positive and exact for certain finite-dimensional function spaces (and weight functions).…
Error bounds are central objects in optimization theory and its applications. They were for a long time restricted only to the theory before becoming over the course of time a field of itself. This paper is devoted to the study of error…