Related papers: Potential integrals on triangles
In this paper, we present a modular strategy which describes key properties of the absolute primary decomposition of an equidimensional polynomial ideal defined by polynomials with rational coefficients. The algorithm we design is based on…
The polarization of the $\Lambda$ particle offers the unique opportunity to study the hydrodynamic gradients in the Quark-Gluon Plasma formed in heavy-ion collisions. However, the theoretical formula commonly used to calculate polarization…
A method for the analytical evaluation of layer potentials arising in the collocation boundary element method for the Laplace and Helmholtz equation is developed for piecewise flat boundary elements with polynomial shape functions. The…
We present an effective method for computing parametric primary decomposition via comprehensive Gr\"obner systems. In general, it is very difficult to compute a parametric primary decomposition of a given ideal in the polynomial ring with…
The detection and estimation of quantum entanglement are the essential issues in the theory of quantum entanglement. We construct matrices based on the realignment of density matrices and the vectorization of the reduced density matrices,…
A triangulation of a polygon has an associated Stanley-Reisner ideal. We obtain a full algebraic and combinatorial understanding of these ideals, and describe their separated models. More generally we do this for stacked simplicial…
In this work, a new integral equation (IE) based formulation is proposed using vector and scalar potentials for electromagnetic scattering. The new integral equations feature decoupled vector and scalar potentials that satisfy Lorentz…
By defining two important terms called basic perturbation vectors and obtaining their linear bounds, we obtain the linear componentwise perturbation bounds for unitary factors and upper triangular factors of the generalized Schur…
We propose a method for transformating linear and nonlinear hypersingular integral equations into ordinary differential equations. Linear and nonlinear polyhypersingular integral equations are transformed into partial differential…
The purpose of this work is to introduce and analyze a numerical scheme to efficiently solve boundary value problems involving the spectral fractional Laplacian. The approach is based on a reformulation of the problem posed on a…
We calculate the fractional integral and derivative of the potential $1/r$ for all values of the fractional order $-1< \alpha \leq 0$ and $\alpha\geq 0$. We show that the result has the same form for all values of $\alpha$. Applications can…
Contour integrals of rational functions over ${\cal M}_{0,n}$, the moduli space of $n$-punctured spheres, have recently appeared at the core of the tree-level S-matrix of massless particles in arbitrary dimensions. The contour is determined…
We present a theoretical study of entanglement in ensembles consisting of an arbitrary number of particles. Multipartite entanglement criteria in terms of observables are formulated for a fixed number of particles as well as for systems…
The paper proposes an approximate expression for calculating very complex one-dimensional integrals depending on the parameter $a$. These integrals often occur in computational problems theory of magnetic solitons. The resulting analytical…
We introduce a framework for solving a class of parabolic partial differential equations on triangle mesh surfaces, including the Hamilton-Jacobi equation and the Fokker-Planck equation. PDE in this class often have nonlinear or stiff terms…
The existence of solutions of some nonlocal initial value problems for differential inclusions is established. The guiding potential method is used and the topological degree theory for admissible multivalued vector fields is applied. Some…
With ab initio codes that employ three-dimensional periodic boundary conditions, the slab-and-vacuum model has proven invaluable for the derivation of energetic, atomistic, and electronic properties of materials. Within this approach, polar…
A new algorithm for efficient exact maximum likelihood decoding of polar codes (which may be CRC augmented), transmitted over the binary erasure channel, is presented. The algorithm applies a matrix triangulation process on a sparse polar…
This paper investigates universal polar coding schemes. In particular, a notion of ordering (called convolutional path) is introduced between probability distributions to determine when a polar compression (or communication) scheme designed…
This paper presents a decomposition method for solving elliptic boundary value problems in one-dimension. The method is an improvement to an existing technique for approximating elliptic systems. It is demonstrated to be computationally…