Some necessary and sufficient conditions for admitting a continuous sphere order representation of two-dimensional space-times

2012 ◽  
Vol 53 (12) ◽  
pp. 122501 ◽  
Author(s):  
M. Vatandoost ◽  
Y. Bahrampour
Keyword(s):  
Dimensional Space ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Two Dimensional ◽  
Order Representation ◽  
Necessary And Sufficient

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.

Mean and variance of vacancy for distribution of k-dimensional spheres within k-dimensional space

1984 ◽  
Vol 21 (4) ◽  
pp. 738-752 ◽  
Author(s):  
Peter Hall
Keyword(s):  
Dimensional Space ◽  
Sufficient Conditions ◽  
Unit Cube ◽  
Necessary And Sufficient Conditions ◽  
Dimensional Sphere ◽  
Asymptotic Formulae ◽  
Dimensional Unit ◽  
Mean And Variance ◽  
The Mean ◽  
Necessary And Sufficient

Let n points be distributed independently within a k-dimensional unit cube according to density f. At each point, construct a k-dimensional sphere of content an. Let V denote the vacancy, or ‘volume' not covered by the spheres. We derive asymptotic formulae for the mean and variance of V, as n → ∞and an → 0. The formulae separate naturally into three cases, corresponding to nan → 0, nan → a (0 < a <∞) and nan →∞, respectively. We apply the formulae to derive necessary and sufficient conditions for V/E(V) → 1 in L2.

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.

A general canonical expression

1933 ◽  
Vol 29 (4) ◽  
pp. 465-469 ◽  
Author(s):  
J. Bronowski
Keyword(s):  
Linear Space ◽  
Dimensional Space ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
General Point ◽  
Linear Forms ◽  
Powers Of Linear Forms ◽  
Necessary And Sufficient

1. In a recent paper I established new conditions for a form φ of order n, homogeneous in r + 1 variables, to be expressible as the sum of nth powers of linear forms in these variables; and for this expression, if it exists, to be unique. These conditions, I further showed, may be stated as general theorems regarding the secant spaces of manifolds Mr in higher space, namely:Necessary and sufficient conditions that through a general point of a space N, of h (r + 1) − 1 dimensions, there passes (i) no, (ii) a unique (h − 1)-dimensional space containing h points of a manifold Mr lying in N are that(i) the space projecting a general point of Mr from the join of h − 1 general r-dimensional tangent spaces of Mr meets Mr in a curve, so that Mr cannot be so projected upon a linear space of r dimensions;(ii) the space projecting a general point of Mr from the join of h − 1 general r-dimensional tangent spaces of Mr does not meet Mr again, so that Mr can be so projected, birationally, upon a linear space of r dimensions..

scholarly journals Necessary and Sufficient Conditions for Circle Formations of Mobile Agents with Coupling Delay via Sampled-Data Control

2016 ◽  
Vol 2016 ◽  
pp. 1-8
Author(s):  
Jianwei Zhao ◽  
Hongxiang Hu ◽  
Chen Wang ◽  
Guangming Xie
Keyword(s):  
Mobile Agents ◽  
Dimensional Space ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Order System ◽  
Sampled Data ◽  
Coupling Delay ◽  
Data Control ◽  
Sampled Data Control ◽  
Necessary And Sufficient

A circle forming problem for a group of mobile agents governed by first-order system is investigated, where each agent can only sense the relative angular positions of its neighboring two agents with time delay and move on the one-dimensional space of a given circle. To solve this problem, a novel decentralized sampled-data control law is proposed. By combining algebraic graph theory with control theory, some necessary and sufficient conditions are established to guarantee that all the mobile agents form a pregiven circle formation asymptotically. Moreover, the ranges of the sampling period and the coupling delay are determined, respectively. Finally, the theoretical results are demonstrated by numerical simulations.

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.

scholarly journals Necessary and Sufficient Conditions for Complementary Stochastic Quadratic Operators of Finite-Dimensional Simplex

2017 ◽  
Vol 1 (1) ◽  
pp. 22 ◽  
Author(s):  
Rawad Abdulghafor ◽  
Sherzod Turaev ◽  
Akram Zeki
Keyword(s):  
Dimensional Space ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Finite Dimensional Space ◽  
Quadratic Operator ◽  
Dimensional Simplex ◽  
Quadratic Stochastic Operator ◽  
Finite Dimensional ◽  
Stochastic Operator ◽  
Necessary And Sufficient

We define a complementary stochastic quadratic operator on finite-dimensional space as a new sub-class of quadratic stochastic operator. We give necessary and sufficient conditions for complementary stochastic quadratic operator.  

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.

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