1. Amitsur in his paper on Finite Dimensional Central Division Algebras [l] has proved that in a division ring D with center C, (P: C) 5= ra2 < =o if and only if every primitive homomorphic image of a polynomial ring P[x] is a complete matrix ring Ah, h^n, over a division ring A. Equivalently speaking, a division ring is finite dimensional over its center if and only if the polynomial ring over...

This paper consists of three sections. In the first section an efficient method is used for decomposition of the canonical matrices associated with repetitive structures. to this end, cylindrical coordinate system, as well as a special numbering scheme were employed. In the second section, divide and conquer method have been used for eigensolution of these structures, where the matrices are in ...

tional challenges. For the harmonic oscillator, a particle is subjected to a force directed toward the origin and proportional to the distance between the particle and the origin. The resulting potential is V(x) = 1/2 x2, where is a constant. This system is quite thoroughly understood, and quantities of interest can be computed in closed form. Alternatively, the Ginzburg-Landau anharmonic poten...

The correlation clustering is an NP-hard problem, hence its solving methods do not scale well. The contraction method and its improvement enable us to construct a divide and conquer algorithm, which could help us to clustering bigger sets. In this article we present the contraction method and compare the effectiveness of this new new and our old methods.

Standard model-free deep reinforcement learning (RL) algorithms sample a new initial state for each trial, allowing them to optimize policies that can perform well even in highly stochastic environments. However, problems that exhibit considerable initial state variation typically produce high-variance gradient estimates for model-free RL, making direct policy or value function optimization cha...

The design and implementation of an interactive spot noise algorithm is presented. Spot noise is a technique which utilizes texture for the visualization of flow fields. Various design tradeoffs are discussed that allow an optimal implementation on a range of high end graphical workstations. Two applications are given: the steering of a smog prediction simulation and browsing a very large data ...