Related papers: Integer circulant determinants of order 16
We propose algorithms for efficient time integration of large systems of oscillatory second order ordinary differential equations (ODEs) whose solution can be expressed in terms of trigonometric matrix functions. Our algorithms are based on…
We construct solutions to the quintic nonlinear Schr\"odinger equation on the circle with initial conditions supported on arbitrarily many different resonant clusters. This is a sequel of a work of Beno\^it Gr\'ebert and the second author.
We consider equations that represent a constancy condition for a 2D Wronskian, mixed Wronskian-Casoratian and 2D Casoratian. These determinantal equations are shown to have the number of independent integrals equal to their order - this…
We present here necessary and sufficient conditions for the invertibility of circulant and symmetric matrices that depend on three parameters and moreover, we explicitly compute the inverse. The techniques we use are related with the…
We establish the local Lipschitz regularity for solutions to an orthotropic q-Laplacian-type equation within the Heisenberg group. Our approach is largely inspired by the works of X. Zhong, who investigated the q-Laplacian in the same…
In this paper we construct explicit solutions and calculate the corresponding $\tau$-function to the system of Schlesinger equations describing isomonodromy deformations of $2\times 2$ matrix linear ordinary differential equation whose…
We investigate the average order of the divisor function at values of totally reducible binary cubic forms and discuss some applications.
We consider a two-dimensional, incompressible fluid body, together with self-induced interactions. The body is perturbed by an external particle with small mass. The whole configuration rotates uniformly around the common center of mass. We…
The complexity of computing the Galois group of a linear differential equation is of general interest. In a recent work, Feng gave the first degree bound on Hrushovski's algorithm for computing the Galois group of a linear differential…
We establish new intrinsic Strichartz estimates for solutions of the Cauchy problem for a class of possibly degenerate Schr\"odinger equations with a real drift.
We present a finite-order system of recurrence relations for a permanent of circulant matrices containing a band of k any-value diagonals on top of a uniform matrix (for k = 1, 2, and 3) as well as the method for deriving such recurrence…
This work deals with the numerical solution of systems of oscillatory second-order differential equations which often arise from the semi-discretization in space of partial differential equations. Since these differential equations exhibit…
In this paper we consider a class of fourth order nonlinear integro-differential equations with Navier boundary conditions. By the reduction of the problem to operator equation we establish the existence and uniqueness of solution and…
The regular solutions to the Sch\"ordinger equation in the case of an electron experiencing a Coulomb force are well known. Being that the radial part of the differential equation to be solved is second order in derivatives, it will have…
Olkin [3] obtained a neat upper bound for the determinant of a correlation matrix. In this note, we present an extension and improvement of his result.
The purpose of this paper is to compute the asymptotics of determinants of finite sections of operators that are trace class perturbations of Toeplitz operators. For example, we consider the asymptotics in the case where the matrices are of…
The family of exactly solvable potentials for Newton's equation of motion in the one-dimensional system with quadratic drag force has been determined completely. The determination is based on the implicit inverse-function solution valid for…
Two known computation methods and one new computation method for matrix determinant over an integral domain are discussed. For each of the methods we evaluate the computation times for different rings and show that the new method is the…
We present a method to compute the inverse scattering transform (IST) for the famed Toda lattice by solving the associated Riemann--Hilbert (RH) problem numerically. Deformations for the RH problem are incorporated so that the IST can be…
These highly informal lecture notes aim at introducing and explaining several closely related problems on zeros of analytic functions defined by ordinary differential equations and systems of such equations. The main incentive for this…