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EN
In order to investigate the chaos characteristics of corona discharge current pulse series in air, the statistical distributions of points (qn, ?tn+1) and points (qn, ?tn, qn+1) were plotted and compared under different experimental conditions including applied voltage value, gap distance and curvature radius of positive point, etc. To describe and study this phenomenon in view of non-linear dynamics, a 2-dimensional nonlinear discrete dynamic model was built. The equation forms and its specific coefficients of the model were obtained by fitting method. The basic dynamic characteristics including the Eigenvalue of the linear matrix- ? (Lyapunov exponent) and the attractors were calculated and analyzed. And then, the output q-t series of the model at three different modulus of Lyapunov exponent were simulated and discussed. As a conclusion, it was suggested that the randomness and statistical feasibility of corona discharge series were greatly influenced by external experiment conditions and the stochastic corona time series in limited time scope could be interpreted as a phenomenon driven by chaos.
PL
W artykule zaprezentowano nową metodę statystycznej charakterystyki wyładowań koronowych występujących seryjnie. Opracowany został dwuwymiarowy model dynamiczny zjawiska, na podstawie którego wyznaczono i poddano analizie charakterystyki dynamiczne oraz kryteria teorii chaosu dotyczące wyładowań koronowych.
2
Content available remote A generalizatio of injectivity for modules over a unitary ring
EN
In this note, we consider certain generalizations of injectivity and p-injectivity in connection with von Neumann regular rings, self-injective regular rings, I-regular rings, semi-simple Artinian and simple Artinian rings. A generalization of quasi-injective modules, noted SCS modules, is introduced. It is proved that A is a left self injective regular ring if, and only if, A is a left p-injective left non-singular left SCS ring. SCS rings are used to characterize simple Artinian rings. A generalization of p-injective modules, noted WGP-injective is used to study I-regular rings. If A is a right p.p. right WGP-injective ring, then A is I-regular. If A is a semi-prime ring whose simple left modules are either WGP-injective or projective, then the centre of A is von Neumann regular. Left Artinian rings are characterized as left Noetherian rings whose prime factor rings are left WGP-injective. Also, A is a left WGP-injective ring if and only if for any a is an element of A , there exists a positive integer n such that an A is a right anihilator. (Here an may be zero.)
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