We prove rigorously that the one-particle density matrix of three dimensional interacting Bose systems with a short-scale repulsive pair interaction converges to the solution of the cubic nonlinear Schrödinger equation in a suitable scaling limit. The result is extended to k-particle density matrices for all positive integer k. AMS Classification Number (2000): 35Q55, 81Q15, 81T18, 81V70. Runni...

7. While Salmon discusses the satellite line of the cubic at some length he fails to give its equation. The symbolical expression for this important covariant has been supplied by Morley. In the present paper Professor Winger derives the explicit equation of the satellite, both for the rational and general cubic, in canonical forms, and discusses associated loci. Several chain theorems are obta...

It is shown that the collective nonlinear interactions between intense neutrino or anti-neutrino fluxes and a dense neutrino plasma are governed by a multidimensional coupled cubic Schrödinger equation in which the interaction potential is positive or negative depending on the neutrino type. The cubic Schrödinger equation describes the splitting and focusing of intense neutrino beams due to the...

This paper presents a simple and fast recurrence equation-based method for solving the cubic spline interpolation problem. The computational complexity of the method is O(n), where n is the number of measurements. The recurrence equation-based method is illustrated by an example that estimates the movement of a moving object. The paper also describes a MATLAB implementation of the new method an...

We will prove that we can specialize the indeterminate α in a linear differential α-resolvent of a univariate polynomial over a differential field of characteristic zero to an integer q to obtain a q-resolvent. We use this idea to obtain a formula, known as the powersum formula, for the terms of theα-resolvent. Finally, we use the powersum formula to rediscover Cockle’s differential resolvent o...

We study the stability of traveling waves of nonlinear Schrödinger equation with nonzero condition at infinity obtained via a constrained variational approach. Two important physical models are Gross-Pitaevskii (GP) equation and cubic-quintic equation. First, under a non-degeneracy condition we prove a sharp instability criterion for 3D traveling waves of (GP), which had been conjectured in the...

In this paper we unify the two subjects of implicitization and parametrization of nonsingular cubic surfaces. Beginning with a cubic parametrization with six basepoints, we first form a three by four Hilbert–Burch matrix, and then a three by three matrix of linear forms whose determinant is the implicit equation. Beginning with an implicit equation, we show how to construct a three by three mat...

The high-pressure behaviour of PbS was investigated by angular dispersive X-ray powder diffraction up to pressures of 6.8 GPa. Experiments were accompanied by first principles calculations at the density functional theory level. By combining both methods reliable data for the elastic properties of rock-salt type αand high-pressure β-PbS could be obtained. β-PbS could be determined to crystallis...

Let $X$ be a vector space over a field $K$ of real or complex numbers. We will prove the superstability of the following Go{l}c{a}b-Schinzel type equation$$f(x+g(x)y)=f(x)f(y), x,yin X,$$where $f,g:Xrightarrow K$ are unknown functions (satisfying some assumptions). Then we generalize the superstability result for this equation with values in the field of complex numbers to the case of an arbitr...

We study controllability of 2D defocusing cubic Schroedinger equation under periodic boundary conditions and control applied via source term (additively). The source term is a linear combination of few complex exponentials (modes) with time-variant coefficients controls. We manage to prove that controlling just 4 modes one can achieve controllability of this equation in any finite-dimensional p...