相关论文: The Newtonian kernel at the intersection of two di…

In this paper, we investigate the eigenvalue problem for a non-local dispersal operator defined on a bounded spatial domain with Neumann-type boundary conditions. Unlike the classical Laplacian, the non-local operator lacks compactness,…

We study a system of $N$ noninteracting spinless fermions in a confining, double-well potential in one dimension. When the Fermi energy is close to the value of the potential at its local maximum we show that physical properties, such as…

The quantum gravity problem of N point particles interacting with the gravitational field in 2+1 dimensions is approached working out the phase-space functional integral. The maximally slicing gauge is adopted for a non compact open…

Kernels are often developed and used as implicit mapping functions that show impressive predictive power due to their high-dimensional feature space representations. In this study, we gradually construct a series of simple feature maps that…

A scheme within density functional theory is proposed that provides a practical way to generalize to unrestricted geometries the method applied with some success to layered geometries [H. Rydberg, et al., Phys. Rev. Lett. 91, 126402…

The current capacity of computers makes it possible to perform simulations of small systems with portable, explicit-solvent potentials achieving high degree of accuracy. However, simplified models must be employed to exploit the behaviour…

The convolutional neural network (CNN) is one of the most commonly used architectures for computer vision tasks. The key building block of a CNN is the convolutional kernel that aggregates information from the pixel neighborhood and shares…

In this paper we develop a numerical scheme based on quadratures to approximate solutions of integro-differential equations involving convolution kernels, $\nu$, of diffusive type. In particular, we assume $\nu$ is symmetric and…

The success of deep convolutional neural network (CNN) in computer vision especially image classification problems requests a new information theory for function of image, instead of image itself. In this article, after establishing a deep…

We consider a semi-classical approximation to the dynamics of a point particle in a noncommutative space. In this approximation, the noncommutativity of space coordinates is described by a Poisson bracket. For linear Poisson brackets, the…

A basic building block in Classical Potential Theory is the fundamental solution of the Laplace equation in ${\mathbb R}^d$ (Newtonian kernel). The main goal of this article is to study the rates of nonlinear $n$-term approximation of…

We consider classical N-particle system with arbitrary central pair potential. Mechanical equilibrium condition in spherically-symmetric case leads to a nonlinear integro-differential equation for concentration n(r). For special state…

The "point mass singularity" inherent in Newton's law for gravitation represents a major difficulty in accurately determining the potential and forces inside continuous bodies. Here we report a simple and efficient analytical method to…

This work defines and studies one-dimensional convolution kernels that preserve nonnegativity. When the past dynamics of a process is integrated with a convolution kernel like in Stochastic Volterra Equations or in the jump intensity of…

We study nonlocal convolution-type operators with singular, possibly anisotropic kernels. Our main objective is to establish and quantify their nonlocal-to-local convergence to a local differential operator with natural boundary conditions,…

We study a non-relativistic particle subject to a three-dimensional spherical potential consisting of a finite well and a radial $\delta$-$\delta'$ contact interaction at the well edge. This contact potential is defined by appropriate…

Neural implicit functions have achieved impressive results for reconstructing 3D shapes from single images. However, the image features for describing 3D point samplings of implicit functions are less effective when significant variations…

We present a fast and accurate algorithm for the evaluation of nonlocal (long-range) Coulomb and dipole-dipole interactions in free space. The governing potential is simply the convolution of an interaction kernel $U(\bx)$ and a density…

Nearly a recent century of work is divided to Nucleon-Nucleon (NN) interaction issue. We review some overall perspectives of NN interaction with a brief discussion about deuteron, general structure and symmetries of NN Lagrangian as well as…

The challenge of explicitly evaluating, in elementary closed form, the weakly singular sixfold integrals for potentials and forces between two cubes has been taken up at various places in the mathematics and physics literature. It created…