Related papers: A Consistency Condition for the Double Series Appr…
Two long-standing problems with the post-Newtonian approximation for isolated slowly-moving systems in general relativity are: (i) the appearance at high post-Newtonian orders of divergent Poisson integrals, casting a doubt on the soundness…
The Born-Oppenheimer approximation is widely used to investigate the properties of hydrogen-like systems and doubly heavy hadrons. However, the extent to which this approximation captures the features of such systems within potential models…
A technique is described for the detection and measurement of close binary systems whose images are unresolved. The method is based on analysis of the moment of inertia tensor of the image, from which the product of the binary flux ratio…
We propose a new boson expansion theory that does not premise the closed-algebra approximation, indispensable for formulation until now, as an extension of the conventional practical boson expansion methods that have tried to elucidate…
Based on the Green's function (GF) equation-of-motion formalism, we develop a method to expand the double time Green's function into Taylor series of the parameter $\lambda$ in the Hamiltonian $H=H_0 + \lambda H_1$. Here $H_0$ is the…
We discuss a simple singular system in one dimension, two heavy particles interacting with a light particle via an attractive contact interaction. It is natural to apply Born-Oppenheimer approximation to this problem. We present a detailed…
In this paper, we accomplish a unified convergence analysis of a second-order method of multipliers (i.e., a second-order augmented Lagrangian method) for solving the conventional nonlinear conic optimization problems.Specifically, the…
An important step in using observations of gravitational waves from bounded sources is to relate the observed waveforms far away from a source to the local dynamics and environment of the source. To isolate and identify different features…
There is a well-known series expansion (Neumann series) in functional analysis for perturbative inversion of specific operators on Banach spaces. However, operators that appear in signal processing (e.g. folding and convolution of…
Fourier series multiscale method, a concise and efficient analytical approach for multiscale computation, will be developed out of this series of papers. The second paper is concerned with simultaneous approximation to functions and their…
The extension of the singular perturbative approach to the second order is presented in this paper. The general expansion to the second order is derived. The second order expansion is considered as a small correction to the first order…
We discuss a simple singular system in two dimension, two heavy particles interacting with a light particle via an attractive contact interaction. Although intuitively clear the actual application of the Born-Oppenheimer approximation to…
In this paper we are concerned with convergence of solutions of the Poisson equation with Neumann boundary conditions in a two-dimensional thin domain exhibiting highly oscillatory behavior in part of its boundary. We deal with the resonant…
A polynomial homotopy is a family of polynomial systems, where the systems in the family depend on one parameter. If for one value of the parameter we know a regular solution, then what is the nearest value of the parameter for which the…
Much of the progress in the gravitational self-force problem has involved the use of singular perturbation techniques. Yet the formalism underlying these techniques is not widely known. I remedy this situation by explicating the foundations…
An iterative formula based on Newton Method alone is presented for the iterative solutions of equations that ensures convergence in cases where the traditional Newton Method may fail to converge to the desired root. In addition, the method…
This paper pursues a twofold goal. First, we introduce and study in detail a new notion of variational analysis called generalized metric subregularity, which is a far-going extension of the conventional metric subregularity conditions. Our…
The method of Taylor series expansion is used to develop a numerical solution to the reactor point kinetics equations. It is shown that taking a first order expansion of the neutron density and precursor concentrations at each time step…
This paper proposes an algorithm for deciding consistency of systems of Boolean equations in several variables with co-efficients in the two element Boolean algebra $B_{0}=\{0,1\}$ and find all satisfying assignments. The algorithm is based…
We present the construction of an exponentially accurate time-dependent Born-Oppenheimer approximation for molecular quantum mechanics. We study molecular systems whose electron masses are held fixed and whose nuclear masses are…