scholarly journals The determination of necessary and sufficient conditions for the existence of a solution to the $3\times3\times3$ multi-index problem

1979 ◽  
Vol 24 (3) ◽  
pp. 201-208
Author(s):  
Graham Smith ◽  
Jeremy Dawson
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Existence Of A Solution ◽  
Multi Index ◽  
Necessary And Sufficient ◽  
Index Problem

Arithmetical Semigroup Rings

1980 ◽  
Vol 32 (6) ◽  
pp. 1361-1371 ◽  
Author(s):  
Bonnie R. Hardy ◽  
Thomas S. Shores
Keyword(s):  
Principal Ideal ◽  
Sufficient Conditions ◽  
Forthcoming Paper ◽  
Semigroup Ring ◽  
Necessary And Sufficient Conditions ◽  
Semigroup Rings ◽  
Principal Ideal Ring ◽  
Arithmetical Semigroup ◽  
Necessary And Sufficient

Throughout this paper the ring R and the semigroup S are commutative with identity; moreover, it is assumed that S is cancellative, i.e., that S can be embedded in a group. The aim of this note is to determine necessary and sufficient conditions on R and S that the semigroup ring R[S] should be one of the following types of rings: principal ideal ring (PIR), ZPI-ring, Bezout, semihereditary or arithmetical. These results shed some light on the structure of semigroup rings and provide a source of examples of the rings listed above. They also play a key role in the determination of all commutative reduced arithmetical semigroup rings (without the cancellative hypothesis on S) which will appear in a forthcoming paper by Leo Chouinard and the authors [4].

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.

On the Hausdorff and Trigonometric Moment Problems

1961 ◽  
Vol 13 ◽  
pp. 454-461
Author(s):  
P. G. Rooney
Keyword(s):  
Moment Problem ◽  
Closed Interval ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Functions Of Bounded Variation ◽  
Moment Problems ◽  
Image Position ◽  
Necessary And Sufficient ◽  
Hausdorff Moment Problem

Let K be a subset of BV(0, 1)—the space of functions of bounded variation on the closed interval [0, 1]. By the Hausdorff moment problem for K we shall mean the determination of necessary and sufficient conditions that corresponding to a given sequence μ = {μn|n = 0, 1, 2, …} there should be a function α ∈ K so that(1)For various collections K this problem has been solved—see (3, Chapter III)By the trigonometric moment problem for K we shall mean the determination of necessary and sufficient conditions that corresponding to a sequence c = {cn|n = 0, ± 1, ± 2, …} there should be a function α ∈ K so that(2)For various collections K this problem has also been solved—see, for example (4, Chapter IV, § 4). It is noteworthy that these two problems have been solved for essentially the same collections K.

scholarly journals The Determination of Jupiter's Mass from Large Perturbations on Cometary Orbits in Jupiter's Sphere of Action

1972 ◽  
Vol 45 ◽  
pp. 227-232 ◽  
Author(s):  
E. I. Kazimirchak-Polonskaya
Keyword(s):  
Electronic Computer ◽  
Sufficient Conditions ◽  
Great Accuracy ◽  
Necessary And Sufficient Conditions ◽  
Necessary And Sufficient

Necessary and sufficient conditions are formulated for determining the mass of Jupiter from large perturbations induced in cometary orbits in the sphere of action of Jupiter. A procedure for the investigation has been developed and programmed for an electronic computer. Comparison of heliocentric and jovicentric computations shows that the perturbations on P/Wolf could be determined with great accuracy when this comet passed through Jupiter's sphere of action in 1922. The first attempt has been made to determine the mass of Jupiter using this passage and the observations of the comet in 1925. The resulting value for the reciprocal mass is 1047.345.

scholarly journals Existence and determination of the set of Metzler matrices for given stable polynomials

2012 ◽  
Vol 22 (2) ◽  
pp. 389-399 ◽  
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Numerical Examples ◽  
Stable Polynomials ◽  
Necessary And Sufficient

Existence and determination of the set of Metzler matrices for given stable polynomialsThe problem of the existence and determination of the set of Metzler matrices for given stable polynomials is formulated and solved. Necessary and sufficient conditions are established for the existence of the set of Metzler matrices for given stable polynomials. A procedure for finding the set of Metzler matrices for given stable polynomials is proposed and illustrated with numerical examples.

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