Related papers: Recurrence relations for four-electron integrals o…
One remaining problem of unitarity cut method for one-loop integral reduction is that tadpole coefficients can not be straightforward obtained through this way. In this paper, we reconsider the problem by applying differential operators…
A high-order quadrature scheme is constructed for the evaluation of Laplace single and double layer potentials and their normal derivatives on smooth surfaces in three dimensions. The construction begins with a harmonic approximation of the…
In many real-world applications we are interested in approximating costly functions that are analytically unknown, e.g. complex computer codes. An emulator provides a fast approximation of such functions relying on a limited number of…
We study the structure of analytic continuation of solutions of an even rank system of linear ordinary differential equations of Okubo normal form (ONF). We develop an adjustment of the method by using the Euler integral for evaluating the…
A set of recurrence relations for on-shell two-loop self-energy diagrams with one mass is presented, which allows to reduce the diagrams with arbitrary indices (powers of scalar propagators) to a set of the master integrals. The SHELL2…
We determine closed and compact expressions for the epsilon-expansion of certain Gaussian hypergeometric functions expanded around half-integer values by explicitly solving for their recurrence relations. This epsilon-expansion is…
We introduce a mixed density fitting scheme that uses both a Gaussian and a plane-wave fitting basis to accurately evaluate electron repulsion integrals in crystalline systems. We use this scheme to enable efficient all-electron Gaussian…
Recasting the $N$-point one loop scalar integral as a probabilistic problem, allows the derivation of integral recurrence relations as well as exact analytical expressions in the most common cases. $\epsilon$ expansions are derived by…
We present a novel approach to Gaussian Berezin correlation functions. A formula well known in the literature expresses these quantities in terms of submatrices of the inverse matrix appearing in the Gaussian action. By using a recently…
We calculate connected correlators in Gaussian orthogonal, unitary and symplectic random matrix ensembles by the replica method in the 1/N-expansion. We obtain averaged one-point Green's functions up to the next-to-leading order O(1/N) and…
An alternative methodology to evaluate two-electron-repulsion integrals based on numerical approximation is proposed. Computational chemistry has branched into two major fields with methodologies based on quantum mechanics and classical…
A set of fully numerical algorithms for evaluating the four-dimensional singular integrals arising from Galerkin surface integral equation methods over conforming quadrilateral meshes is presented. This work is an extension of DIRECTFN,…
This paper introduces an efficient algorithm for computing the general oscillatory matrix functions. These computations are crucial for solving second-order semi-linear initial value problems. The method is exploited using the scaling and…
Methods for electronic structure based on Gaussian and molecular orbital discretizations offer a well established, compact representation that forms much of the foundation of correlated quantum chemistry calculations on both classical and…
For over a century, extrapolation methods have provided a powerful tool to improve the convergence order of a numerical method. However, these tools are not well-suited to modern computer codes, where multiple continua are discretised and…
We present a novel construction of recursion operators for scalar second-order integrable multidimensional PDEs with isospectral Lax pairs written in terms of first-order scalar differential operators. Our approach is quite straightforward…
This revisit gives a survey on the analytical methods for the inverse exponential Radon transform which has been investigated in the past three decades from both mathematical interests and medical applications such as nuclear medicine…
The central idea of this article is to present a systematic approach to construct some recurrence relations for the solutions of the second-order linear difference equation of hypergeometric-type defined on the quadratic-type lattices. We…
The generalized spherical Radon transform associates the mean values over spherical tori to a function $f$ defined on $\mathbb{S}^3 \subset \mathbb{H}$, where the elements of $\mathbb{S}^3$ are considered as quaternions representing…
We use hexagonalization to compute four-point correlation functions of long BPS operators with special R-charge polarizations. We perform the computation at weak coupling and show that at any loop order our correlators can be expressed in…