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The complex-scaling method can be used to calculate molecular resonances within the Born-Oppenheimer approximation, assuming the electronic coordinates are dilated independently of the nuclear coordinates. With this method, one will…
A novel approach is introduced for deriving exact solutions to nonlinear systems of ordinary differential equations. This method consists of four parts. In the initial part, the examined nonlinear differential equation system is transformed…
We report on the calculation of multi-loop Feynman integrals for single-scale problems by means of difference equations in Mellin space. The solution to these difference equations in terms of harmonic sums can be constructed algorithmically…
For nonrelativistic Hamiltonians which are shape invariant, analytic expressions for the eigenvalues and eigenvectors can be derived using the well known method of supersymmetric quantum mechanics. Most of these Hamiltonians also possess…
When simulating partial differential equations, hybrid solvers combine coarse numerical solvers with learned correctors. They promise accelerated simulations while adhering to physical constraints. However, as shown in our theoretical…
Quantum computers have long been expected to efficiently solve complex classical differential equations. Most digital, fault-tolerant approaches use Carleman linearization to map nonlinear systems to linear ones and then apply quantum…
A first-order, Monte Carlo ensemble method has been recently introduced for solving parabolic equations with random coefficients in [26], which is a natural synthesis of the ensemble-based, Monte Carlo sampling algorithm and the…
We introduce a method for calculating individual elements of matrix functions. Our technique makes use of a novel series expansion for the action of matrix functions on basis vectors that is memory efficient even for very large matrices. We…
We develop a geometric version of the inverse problem of the calculus of variations for discrete mechanics and constrained discrete mechanics. The geometric approach consists of using suitable Lagrangian and isotropic submanifolds. We also…
We present a quantum algorithm that analyzes time series data simulated by a quantum differential equation solver. The proposed algorithm is a quantum version of the dynamic mode decomposition algorithm used in diverse fields such as fluid…
We present and analyze a methodology for numerical homogenization of spatial networks, modelling e.g. diffusion processes and deformation of mechanical structures. The aim is to construct an accurate coarse model of the network. By solving…
In this paper we propose an iterative method using alternating direction method of multipliers (ADMM) strategy to solve linear inverse problems in Hilbert spaces with general convex penalty term. When the data is given exactly, we give a…
The inclinations of exoplanets detected via radial velocity method are essentially unknown. We aim to provide estimations of the ranges of mutual inclinations that are compatible with the long-term stability of the system. Focusing on the…
The systems of nonlinear Volterra integral equations of the first kind with jump discontinuous kernels are studied. The iterative numerical method for such nonlinear systems is proposed. Proposed method employs the modified…
We present an exact version of the local bosonic algorithm for the simulation of dynamical quarks in lattice QCD. This version is based on a non-hermitian polynomial approximation of the inverse of the quark matrix. A Metropolis test…
We study numerical computation of conformal invariants of domains in the complex plane. In particular, we provide an algorithm for computing the conformal capacity of a condenser. The algorithm applies for wide kind of geometries: domains…
We propose a splitting algorithm for solving a system of composite monotone inclusions formulated in the form of the extended set of solutions in real Hilbert spaces. The resluting algorithm is a an extension of the algorithm in [4]. The…
Extending Eulerian polynomials and Faulhaber's formula 1, we study several combi-natorial aspects of harmonic sums and polylogarithms at non-positive multi-indices as well as their structure. Our techniques are based on the combinatorics of…
The calculation of physical quantities by lattice QCD simulations requires in some important cases the determination of the inverse of a very large matrix. In this article we describe how stochastic estimator methods can be applied to this…
For $b>1$ and $\alpha\beta$ a string of two digits in base $b$, let $K_1$ be the subsum of the harmonic series with only those integers having exactly one occurrence of $\alpha\beta$. We obtain a theoretical representation of such $K_1$…