A heterogeneous blocking system in a random environment

1996 ◽  
Vol 33 (01) ◽  
pp. 211-216 ◽  
Author(s):  
G. Falin
Keyword(s):  
Random Environment ◽  
Joint Distribution ◽  
Service System ◽  
External Environment ◽  
The State ◽  
Product Form ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Necessary And Sufficient

We obtain a necessary and sufficient condition for the interaction between a service system and an external environment under which the stationary joint distribution of the set of busy channels and the state of the external environment is given by a product-form formula.

A heterogeneous blocking system in a random environment

1996 ◽  
Vol 33 (1) ◽  
pp. 211-216 ◽  
Author(s):  
G. Falin
Keyword(s):  
Random Environment ◽  
Joint Distribution ◽  
Service System ◽  
External Environment ◽  
The State ◽  
Product Form ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Necessary And Sufficient

We obtain a necessary and sufficient condition for the interaction between a service system and an external environment under which the stationary joint distribution of the set of busy channels and the state of the external environment is given by a product-form formula.

The Power of Public Positions

2018 ◽  
Author(s):  
Thomas Sinclair
Keyword(s):  
Detailed Analysis ◽  
Political Authority ◽  
The State ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
State Institutions ◽  
State Of Nature ◽  
Necessary And Sufficient

The Kantian account of political authority holds that the state is a necessary and sufficient condition of our freedom. We cannot be free outside the state, Kantians argue, because any attempt to have the “acquired rights” necessary for our freedom implicates us in objectionable relations of dependence on private judgment. Only in the state can this problem be overcome. But it is not clear how mere institutions could make the necessary difference, and contemporary Kantians have not offered compelling explanations. A detailed analysis is presented of the problems Kantians identify with the state of nature and the objections they face in claiming that the state overcomes them. A response is sketched on behalf of Kantians. The key idea is that under state institutions, a person can make claims of acquired right without presupposing that she is by nature exceptional in her capacity to bind others.

scholarly journals DYNAMICAL STABILITY OF STRANGE QUARK STARS

2011 ◽  
Vol 20 (07) ◽  
pp. 1171-1182 ◽  
Author(s):  
P. S. NEGI
Keyword(s):  
Strange Quark ◽  
The State ◽  
Dynamical Stability ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Star Models ◽  
Quark Stars ◽  
Equilibrium Configurations ◽  
Necessary And Sufficient ◽  
R Relation

The necessary and sufficient condition for dynamical stability is worked out for the sequences of relativistic star models which correspond to the well-defined and causal values of adiabatic sound speed, [Formula: see text], at the center. On the basis of the conditions obtained in this study, we show that the mass–radius (M-R) relation corresponding to the MIT bag models of strange quark matter (SQM) and the models obtained by Dey et al. [Phys. Lett. B438 (1998) 123] does not provide the necessary and sufficient condition for dynamical stability for the equilibrium configurations. These findings will remain unaltered and can be extended to any other sequence of pure SQM. This study explicitly shows that though SQM may exist in the state of zero pressure and temperature, the models of pure strange quark "stars" cannot exist in the state of hydrostatic equilibrium. This study can affect the results which are claiming that various objects, like RX J1856.5-3754, SAX J1808.4-3658, 4U 1728-34 and PSR 0943+10, represent strange stars.

scholarly journals Finite-Time Set Reachability of Probabilistic Boolean Multiplex Control Networks

2022 ◽  
Vol 12 (2) ◽  
pp. 883
Author(s):  
Yuxin Cui ◽  
Shu Li ◽  
Yunxiao Shan ◽  
Fengqiu Liu
Keyword(s):  
Dynamical Systems ◽  
Finite Time ◽  
The State ◽  
Reconstruction Technique ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Control Networks ◽  
State Transfer ◽  
Necessary And Sufficient

This study focuses on the finite-time set reachability of probabilistic Boolean multiplex control networks (PBMCNs). Firstly, based on the state transfer graph (STG) reconstruction technique, the PBMCNs are extended to random logic dynamical systems. Then, a necessary and sufficient condition for the finite-time set reachability of PBMCNs is obtained. Finally, the obtained results are effectively illustrated by an example.

scholarly journals Controllability of generalised dynamical systems with constrained control

1988 ◽  
Vol 30 (1) ◽  
pp. 69-78
Author(s):  
Chen Zhaolin ◽  
Hong Huimin ◽  
Zhang Jifeng
Keyword(s):  
Dynamical Systems ◽  
Control Function ◽  
The State ◽  
Sufficient Condition ◽  
Constrained Control ◽  
Sense Of Control ◽  
Necessary And Sufficient Condition ◽  
Impulsive Behaviour ◽  
Necessary And Sufficient

AbstractThe state controllability for generalised dynamical systems with constrained control is discussed in this paper. The main results of the paper are the following:(1) a necessary and sufficient condition of the state controllability in the sense of control energy or amplitude constrained for generalised dynamical systems is obtained;(2) a control function u(t) is constructed such thata) u(t) satisfies constrained energy or amplitude condition,b) the state driven by u(t) moves from an arbitrary x(0−) = x0 to x(T(x0)) = 0,c) the trajectory driven by u(t) has no impulsive behaviour within (0, T(x0)].

THE ZAGREB INDICES OF RANDOM GRAPHS

2013 ◽  
Vol 27 (2) ◽  
pp. 247-260 ◽  
Author(s):  
Qunqiang Feng ◽  
Zhishui Hu ◽  
Chun Su
Keyword(s):  
Asymptotic Normality ◽  
Random Graphs ◽  
Joint Distribution ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Limit Laws ◽  
Zagreb Indices ◽  
Necessary And Sufficient

Several limit laws for the Zagreb indices of the classical Erdös–Rényi random graphs are investigated in this paper. We have obtained the necessary and sufficient condition for the asymptotic normality of the two Zagreb indices (suitably normalized), as well as the explicit values for the means and variances of both the indices. Besides, the limiting joint distribution of the numbers of paths of various lengths is also studied under several conditions.

scholarly journals On rational solution of the state equation of a finite automaton

1988 ◽  
Vol 11 (2) ◽  
pp. 355-364
Author(s):  
R. Chaudhuri ◽  
H. Höft
Keyword(s):  
Finite Automaton ◽  
Rational Solution ◽  
State Equation ◽  
The State ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Necessary And Sufficient

We prove that the necessary and sufficient condition for the state equation of a finite automatonMto have a rational solution is that the lexicographical Gödel numbers of the strings belonging to each of the end-sets ofMform an ultimately periodic set. A method of determining the existence of a rational solution of the state equation is also given.

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