Uniform and 𝐿-Convergence of Logarithmic Means of Double Walsh–Fourier Series

2005 ◽  
Vol 12 (1) ◽  
pp. 75-88
Author(s):  
György Gát ◽  
Ushangi Goginava
Keyword(s):  
Fourier Series ◽  
Function Space ◽  
Modulus Of Continuity ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Two Dimensional ◽  
Logarithmic Means ◽  
Convergence And Divergence ◽  
Necessary And Sufficient ◽  
Series Of Functions

Abstract We discuss some convergence and divergence properties of twodimensional (Nörlund) logarithmic means of two-dimensional Walsh–Fourier series of functions both in the uniform and in the Lebesgue norm. We give necessary and sufficient conditions for the convergence regarding the modulus of continuity of the function, and also the function space.

ON THE TEMPLATES CORRESPONDING TO CYCLE-SYMMETRIC CONNECTIVITY IN CELLULAR NEURAL NETWORKS

2002 ◽  
Vol 12 (12) ◽  
pp. 2957-2966 ◽  
Author(s):  
CHIH-WEN SHIH ◽  
CHIH-WEN WENG
Keyword(s):  
Neural Networks ◽  
Dimensional Space ◽  
Sufficient Conditions ◽  
Cellular Neural Networks ◽  
Necessary And Sufficient Conditions ◽  
Local Interaction ◽  
Two Dimensional ◽  
Linear Coupling ◽  
Symmetric Connectivity ◽  
Necessary And Sufficient

In the architecture of cellular neural networks (CNN), connections among cells are built on linear coupling laws. These laws are characterized by the so-called templates which express the local interaction weights among cells. Recently, the complete stability for CNN has been extended from symmetric connections to cycle-symmetric connections. In this presentation, we investigate a class of two-dimensional space-invariant templates. We find necessary and sufficient conditions for the class of templates to have cycle-symmetric connections. Complete stability for CNN with several interesting templates is thus concluded.

scholarly journals A note on the norm convergence by Vilenkin–Fejér means

2014 ◽  
Vol 21 (4) ◽  
Author(s):  
George Tephnadze
Keyword(s):  
Modulus Of Continuity ◽  
Hardy Spaces ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Norm Convergence ◽  
Fejér Means ◽  
Necessary And Sufficient

AbstractThe main aim of this paper is to find necessary and sufficient conditions for the convergence of Fejér means in terms of the modulus of continuity on the Hardy spaces

scholarly journals STRUCTURE-REVERSIBILITY OF A TWO-DIMENSIONAL REFLECTING RANDOM WALK AND ITS APPLICATION TO QUEUEING NETWORK

2014 ◽  
Vol 29 (1) ◽  
pp. 1-25 ◽  
Author(s):  
Masahiro Kobayashi ◽  
Masakiyo Miyazawa ◽  
Hiroshi Shimizu
Keyword(s):  
Random Walk ◽  
Stationary Distribution ◽  
Sufficient Conditions ◽  
Queueing Network ◽  
Necessary And Sufficient Conditions ◽  
Negative Integer ◽  
Product Form ◽  
Two Dimensional ◽  
Necessary And Sufficient

We consider a two-dimensional reflecting random walk on the non-negative integer quadrant. It is assumed that this reflecting random walk has skip-free transitions. We are concerned with its time-reversed process assuming that the stationary distribution exists. In general, the time-reversed process may not be a reflecting random walk. In this paper, we derive necessary and sufficient conditions for the time-reversed process also to be a reflecting random walk. These conditions are different from but closely related to the product form of the stationary distribution.

Geometric Ergodicity of the ALOHA-system and a Coupled Processors Model

1991 ◽  
Vol 5 (1) ◽  
pp. 15-42 ◽  
Author(s):  
F. M. Spieksma
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Geometric Ergodicity ◽  
Two Dimensional ◽  
Necessary And Sufficient ◽  
Stieltjes Transforms ◽  
Coupled Processors

μ-Geometric ergodicity of two-dimensional versions of the ALOHA and coupled processors models is verified by checking μ-geometric recurrence. Ergodicity and convergence of the Laplace-Stieltjes transforms in a neighborhood of 0 are necessary and sufficient conditions for the first model. The second model is exponential, for which ergodicity suffices to establish the required results.

Stability and Bifurcations in 2D Spatiotemporal Discrete Systems

2018 ◽  
Vol 28 (08) ◽  
pp. 1830026
Author(s):  
Mohamed Lamine Sahari ◽  
Abdel-Kaddous Taha ◽  
Louis Randriamihamison
Keyword(s):  
Asymptotic Stability ◽  
Current Literature ◽  
Sufficient Conditions ◽  
Discrete Systems ◽  
Necessary And Sufficient Conditions ◽  
Two Dimensional ◽  
Local Bifurcations ◽  
Stability And Bifurcations ◽  
Necessary And Sufficient

This paper deals with stability and local bifurcations of two-dimensional (2D) spatiotemporal discrete systems. Necessary and sufficient conditions for asymptotic stability of the systems are obtained. They prove to be more accurate than those in the current literature. Some definitions for the bifurcations of 2D spatiotemporal discrete systems are also given, and an illustrative example is provided to explain the new results.

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