let $r$ be an infinite ring. here we prove that if $0_r$ belongs to ${x_1x_2cdots x_n ;|; x_1,x_2,dots,x_nin x}$ for every infinite subset $x$ of $r$, then $r$ satisfies the polynomial identity $x^n=0$. also we prove that if $0_r$ belongs to ${x_1x_2cdots x_n-x_{n+1} ;|; x_1,x_2,dots,x_n,x_{n+1}in x}$ for every infinite subset $x$ of $r$, then $x^n=x$ for all $xin r$.

‎linear semi-infinite programming problem is an important class of optimization problems which deals with infinite constraints‎. ‎in this paper‎, ‎to solve this problem‎, ‎we combine a discretization method and a neural network method‎. ‎by a simple discretization of the infinite constraints,we convert the linear semi-infinite programming problem into linear programming problem‎. ‎then‎, ‎we use...

Line and load transients are step functions that inject disturbances into the power supply. A load transient injects disturbance into the output by stepping the load current, and a line transient does so by stepping the line voltage. The supply’s output response demonstrates its ability to attenuate the various frequency components of a line or load step. The following discussion describes thes...

Vapor-deposition techniques are emerging as an economical and flexible way of fabricating multiphase materials with spatially varying architectures. The aim of this work is to design architectures that exploit the concept of functional grading. We consider two basic problems; the first is the computation of the response of an infinite plate with a circular hole to a remote symmetric radial load...

in this paper, power system restoration in the presence of svc and tcsc in partial outage conditions is considered and a new method for maximum load restoration using different control variables is presented. control variables are tap of transformers, generation rescheduling and operating points of facts devices. objective function is restored load (to be maximized) and constraints are voltage ...

A prediction method of the thickness, resonant space and frequency for the two cases of an ultra-thin layer and the narrow-band frequency spectra has been developed without the appearance of the resonance/anti-resonance. Using the characteristic of straight line and the period of  of the layer phase shift obtained from the measured data, the relations of the line slope with time of flight and ...

In this study, dynamic behavior of a mooring line in a floating system is analyzed by probability approaches. In dynamics, most researches have shown the system model and environments by mathematical expression. We called this process as the forward dynamics. However, there is a limit to define the exact environments because of uncertainty. To consider uncertainty, we introduce the redundancy i...