The standard approaches to solving overdetermined linear systems Ax ≈ b construct minimal corrections to the vector b and/or the matrix A such that the corrected system is compatible. In ordinary least squares (LS) the correction is restricted to b, while in data least squares (DLS) it is restricted to A. In scaled total least squares (Scaled TLS) [15], corrections to both b and A are allowed, ...

The physical basis behind the Ostwald ripening process for two-phase mixture has been reviewed in detail, using the various theories developed to describe this process. The Ostwald ripening, also termed second phase coarsening, is generally thought to be slow, diffusion-controlled process which occurs subsequent to phase separation under extremely small under-saturation levels. The major advanc...

Self{scaled barrier functions are fundamental objects in the theory of interior{point methods for linear optimization over symmetric cones, of which linear and semideenite programming are special cases. We are classifying all self{scaled barriers over irreducible symmetric cones and show that these functions are merely homothetic transformations of the universal barrier function. Together with ...

According to the Quantum de Finetti Theorem, locally normal infinite particle states with Bose-Einstein symmetry can be represented as mixtures of infinite tensor powers of vector states. This note presents examples of infinite-particle states with Bose-Einstein symmetry that arise as limits of Gibbs ensembles on finite dimensional spaces, and displays their de Finetti representations. We consi...

We study the dynamics of a quantum particle governed by a linear Schrödinger equation with a scaled Gaussian potential. In the weak coupling limit the average dynamics of such a particle can be described by a linear Boltzmann equation. In this work we prove a bound for the rate at which the average dynamics of the quantum particle approach linear Boltzmann equation dynamics. For the so called s...

Self–scaled barrier functions are fundamental objects in the theory of interior–point methods for linear optimization over symmetric cones, of which linear and semidefinite programming are special cases. We are classifying all self–scaled barriers over irreducible symmetric cones and show that these functions are merely homothetic transformations of the universal barrier function. Together with...

astrophysics is becoming now an integral part of general physics. considering the black hole theory ,which is a new and exciting branch of relativistic astrophysics, we see many connections between elementary particle physics and astrophysics. in this article we attempt to explain the development of star physics ,in an easy ,understandable manner. previous knowledge of relativistic theory or cl...