scholarly journals A procedure for determining necessary and sufficient conditions for the existence of a solution to the multi-index problem

1974 ◽  
Vol 19 (3) ◽  
pp. 177-183
Author(s):  
Graham Smith
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Existence Of A Solution ◽  
Multi Index ◽  
Necessary And Sufficient ◽  
Index Problem

scholarly journals Eigenvalue assignment in fractional descriptor discrete-time linear systems

2017 ◽  
Vol 27 (1) ◽  
pp. 119-128
Author(s):  
Tadeusz Kaczorek ◽  
Kamil Borawski
Keyword(s):  
Linear Systems ◽  
Discrete Time ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Existence Of A Solution ◽  
Numerical Example ◽  
Necessary And Sufficient ◽  
Time Linear ◽  
Eigenvalue Assignment

Abstract The problem of eigenvalue assignment in fractional descriptor discrete-time linear systems is considered. Necessary and sufficient conditions for the existence of a solution to the problem are established. A procedure for computation of the gain matrices is given and illustrated by a numerical example.

scholarly journals Necessary and sufficient conditions for recurrence and transience of Markov chains, in terms of inequalities

1978 ◽  
Vol 15 (4) ◽  
pp. 848-851 ◽  
Author(s):  
Jean-François Mertens ◽  
Ester Samuel-Cahn ◽  
Shmuel Zamir
Keyword(s):  
Markov Chain ◽  
Markov Chains ◽  
State Space ◽  
Bounded Solution ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Existence Of A Solution ◽  
Necessary And Sufficient ◽  
Irreducible Markov Chain

For an aperiodic, irreducible Markov chain with the non-negative integers as state space it is shown that the existence of a solution to in which yi → ∞is necessary and sufficient for recurrence, and the existence of a bounded solution to the same inequalities, with yk < yo, · · ·, yN–1 for some k ≧ N, is necessary and sufficient for transience.

PLANAR ROUTING AROUND A RECTANGLE

1992 ◽  
Vol 02 (01) ◽  
pp. 27-38 ◽  
Author(s):  
RUEY-DER LOU ◽  
KUO-FENG LIAO ◽  
MAJID SARRAFZADEH
Keyword(s):  
Sufficient Conditions ◽  
Single Layer ◽  
Time Algorithm ◽  
Necessary And Sufficient Conditions ◽  
Minimum Area ◽  
Existence Of A Solution ◽  
Necessary And Sufficient

The problem of planar (single-layer) routing, of two- and multi-terminal nets, around a rectangle is considered. Necessary and sufficient conditions for the existence of a solution is presented. An O(n) time algorithm for obtaining a minimum-area planar routing, if one exists, is proposed, where n is the number of terminals.

scholarly journals Necessary and sufficient conditions for recurrence and transience of Markov chains, in terms of inequalities

1978 ◽  
Vol 15 (04) ◽  
pp. 848-851 ◽  
Author(s):  
Jean-François Mertens ◽  
Ester Samuel-Cahn ◽  
Shmuel Zamir
Keyword(s):  
Markov Chain ◽  
Markov Chains ◽  
State Space ◽  
Bounded Solution ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Existence Of A Solution ◽  
Necessary And Sufficient ◽  
Irreducible Markov Chain

For an aperiodic, irreducible Markov chain with the non-negative integers as state space it is shown that the existence of a solution to in which yi → ∞is necessary and sufficient for recurrence, and the existence of a bounded solution to the same inequalities, with yk &lt; y o, · · ·, yN –1 for some k ≧ N, is necessary and sufficient for transience.

scholarly journals Solutions to the System of Operator EquationsA1X=C1,XB2=C2, andA3XB3=C3on HilbertC*-Modules

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Xiaochun Fang ◽  
Enran Hou ◽  
Ge Dong
Keyword(s):  
General Solution ◽  
Positive Solution ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Operator Equations ◽  
Existence Of A Solution ◽  
Necessary And Sufficient

We study the solvability of the system of the adjointable operator equationsA1X=C1,XB2=C2, andA3XB3=C3over HilbertC*-modules. We give necessary and sufficient conditions for the existence of a solution and a positive solution of the system. We also derive representations for a general solution and a positive solution to this system. The above results generalize some recent results concerning the equations for operators with closed ranges.

scholarly journals A NOTE ON SOME SYSTEMS OF GENERALIZED SYLVESTER EQUATIONS

2021 ◽  
pp. 449
Author(s):  
Jovana Nikolov Radenković
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Operator Equations ◽  
Existence Of A Solution ◽  
Two Systems ◽  
Necessary And Sufficient

In this paper, we study two systems of generalized Sylvester operator equations. We derive necessary and sufficient conditions for the existence of a solution and provide the general form of a solution. We extend some recent results to more general settings.

The extinction time of a general birth and death process with catastrophes

1986 ◽  
Vol 23 (04) ◽  
pp. 851-858 ◽  
Author(s):  
P. J. Brockwell
Keyword(s):  
Laplace Transform ◽  
Size Distribution ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Death Process ◽  
Extinction Time ◽  
Birth And Death Process ◽  
Different Types ◽  
The Laplace Transform ◽  
Necessary And Sufficient

The Laplace transform of the extinction time is determined for a general birth and death process with arbitrary catastrophe rate and catastrophe size distribution. It is assumed only that the birth rates satisfyλ0= 0,λj&gt; 0 for eachj&gt; 0, and. Necessary and sufficient conditions for certain extinction of the population are derived. The results are applied to the linear birth and death process (λj=jλ, µj=jμ) with catastrophes of several different types.

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