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Exploiting the similarities between the Helmholtz wave equation and the Klein-Gordon equation, the former is linearized using the Feschbach-Villars procedure used for linearizing the Klein-Gordon equation. Then the Foldy-Wouthuysen…
A class of exact infinitesimal renormalization group transformations is proposed and studied. These transformations are pure changes of variables (i.e., no integration or elimination of some degrees of freedom is required) such that a…
In this paper, we demonstrate a polynomial convergence rate for homogenization of Hamilton-Jacobi equations with quasi-periodic potentials. We establish a connection between the convergence rate of homogenization and the regularity of the…
The generalized perturbative approach is an all purpose variant of Stein's method used to obtain rates of normal approximation. Originally developed for functions of independent random variables this method is here extended to functions of…
In this paper we develop a plane wave type method for discretization of homogeneous Helmholtz equations with variable wave numbers. In the proposed method, local basis functions (on each element) are constructed by the geometric optics…
We propose an efficient and flexible method for solving Abel integral equation of the first kind, frequently appearing in many fields of astrophysics, physics, chemistry, and applied sciences. This equation represents an ill-posed problem,…
The Bohr-Sommerfeld approximation to the eigenvalues of a one-dimensional quantum Hamiltonian is derived through order $\hbar^2$ (i.e., including the first correction term beyond the usual result) by means of the Moyal star product. The…
Exact numerical diagonalization is carried out for the Bohr Hamiltonian with a beta-soft, axially stabilized potential. Wave function and observable properties are found to be dominated by strong beta-gamma coupling effects. The validity of…
The focus of this article is the approximation of functions which are analytic on a compact interval except at the endpoints. Typical numerical methods for approximating such functions depend upon the use of particular conformal maps from…
Using the scattering transform for $n^{th}$ order linear scalar operators, the Poisson bracket found by Gel'fand and Dikii, which generalizes the Gardner Poisson bracket for the KdV hierarchy, is computed on the scattering side.…
We present a method for constructing global analytical expressions that approximate a function over its entire range. These approximations not only mirror the original function as accurately as desired, but are purposefully created to…
We provide a simple explicit estimator for discretely observed Barndorff-Nielsen and Shephard models, prove rigorously consistency and asymptotic normality based on the single assumption that all moments of the stationary distribution of…
We calculate a certain mean-value of meromorphic functions by using specific ergodic transformations, which we call affine Boolean transformations. We use Birkhoff's ergodic theorem to transform the mean-value into a computable integral…
Using the Hamilton-Jacobi method, we solve chemical Fokker-Planck equations within the Gaussian approximation and obtain a simple and compact formula for a conditional probability distribution. The formula holds in general transient…
The paper introduces a new adaptive version of the Frank-Wolfe algorithm for relatively smooth convex functions. It is proposed to use the Bregman divergence other than half the square of the Euclidean norm in the formula for step-size.…
Starting from a constrained real $BF$-type action for general relativity that includes both the Immirzi parameter and the cosmological constant, we obtain the Ashtekar-Barbero variables used in the canonical approach to the quantization of…
The study of self-gravitating stellar systems has provided important hints to develop tools of analytical mechanics. In the present contribution we review how to exploit detuned resonant normal forms to extract information on several…
Found all equivalence classes for electromagnetic potentials and space-time metrics of Stackel spaces, provided that the equations of motion of the classical charged test particles are integrated by the method of complete separation of…
Employing a suitable nonlinear Lagrange functional, we derive generalized Hamilton-Jacobi equations for dynamical systems subject to linear velocity constraints. As long as a solution of the generalized Hamilton-Jacobi equation exists, the…
Many data-driven algorithms in dynamical systems rely on ergodic averages that converge painfully slowly. One simple idea changes this: taper the ends. Weighted Birkhoff averages can converge much faster (sometimes superpolynomially, even…