scholarly journals Minimal sets on tori

1984 ◽  
Vol 4 (4) ◽  
pp. 499-507 ◽  
Author(s):  
Daniel Berend
Keyword(s):  
Hausdorff Dimension ◽  
Commutative Semigroup ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Dimensional Torus ◽  
Minimal Set ◽  
Circle Group ◽  
Minimal Sets ◽  
Necessary And Sufficient

AbstractLet Σ be a commutative semigroup of continuous endomorphisms of the r-dimensional torus. Generalizing a result of Furstenberg dealing with the circle group, necessary and sufficient conditions are given here for Σ to possess the following property: Any Σ-minimal set consists of torsion elements. Semigroups not having this property are shown to admit minimal sets of positive Hausdorff dimension.

scholarly journals Minimal F2-flows

1985 ◽  
Vol 39 (2) ◽  
pp. 187-193
Author(s):  
Daniel Berend
Keyword(s):  
Hausdorff Dimension ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Affine Transformations ◽  
Dimensional Torus ◽  
Minimal Sets ◽  
Necessary And Sufficient

AbstractLet σ be an ergodic endomorphism of the r–dimensional torus and Π a semigroup generated by two affine transformations lying above σ. We show that the flow defined by Π admits minimal sets of positive Hausdorff dimension and we give necessary and sufficient conditions for this flow to be minimal.

Regular, Commutative, Maximal Semigroups of Quotients

1975 ◽  
Vol 18 (1) ◽  
pp. 99-104 ◽  
Author(s):  
Jurgen Rompke
Keyword(s):  
Commutative Semigroup ◽  
Regular Ring ◽  
Sufficient Conditions ◽  
Commutative Rings ◽  
Necessary And Sufficient Conditions ◽  
Natural Question ◽  
Commutative Case ◽  
Ring Of Quotients ◽  
Singular Ideal ◽  
Necessary And Sufficient

A well-known theorem which goes back to R. E. Johnson [4], asserts that if R is a ring then Q(R), its maximal ring of quotients is regular (in the sense of v. Neumann) if and only if the singular ideal of R vanishes. In the theory of semigroups a natural question is therefore the following: Do there exist properties which characterize those semigroups whose maximal semigroups of quotients are regular? Partial answers to this question have been given in [3], [7] and [8]. In this paper we completely solve the commutative case, i.e. we give necessary and sufficient conditions for a commutative semigroup S in order that Q(S), the maximal semigroup of quotients, is regular. These conditions reflect very closely the property of being semiprime, which in the theory of commutative rings characterizes those rings which have a regular ring of quotients.

On commutative semigroup algebras

1983 ◽  
Vol 93 (2) ◽  
pp. 237-246 ◽  
Author(s):  
W. D. Munn
Keyword(s):  
Commutative Semigroup ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Semigroup Algebras ◽  
Necessary And Sufficient

This paper is concerned with the problem of finding necessary and sufficient conditions on a commutative semigroup S for the algebra FS of S over a field F to be semiprimitive (Jacobson semisimple).

scholarly journals On the solvability of systems of linear equations on commutative semigroup

2010 ◽  
Vol 43 (4) ◽  
Author(s):  
Nguyen Thi Thu Huyen ◽  
Nguyen Minh Tuan
Keyword(s):  
Linear Operator ◽  
Linear Space ◽  
Commutative Semigroup ◽  
Linear Equations ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Operator Equations ◽  
Systems Of Linear Equations ◽  
Necessary And Sufficient ◽  
Linear Operator Equations

AbstractThis paper deals with the solvability of systems of linear operator equations in a linear space. Namely, the paper provides necessary and sufficient conditions for the operators under which certain kinds of systems of operator equations are solvable.

TWO-MACHINE FLOW-SHOP MINIMUM-LENGTH SCHEDULING WITH INTERVAL PROCESSING TIMES

2009 ◽  
Vol 26 (06) ◽  
pp. 715-734 ◽  
Author(s):  
C. T. NG ◽  
NATALJA M. MATSVEICHUK ◽  
YURI N. SOTSKOV ◽  
T. C. EDWIN CHENG
Keyword(s):  
Flow Shop ◽  
Probability Distributions ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Minimum Length ◽  
Lower And Upper Bounds ◽  
Minimal Set ◽  
Processing Times ◽  
Necessary And Sufficient ◽  
Two Machines

The flow-shop minimum-length scheduling problem with n jobs processed on two machines is addressed where processing times are uncertain: only lower and upper bounds of the random processing times are given before scheduling, but their probability distributions are unknown. For such a problem, there may not exist a dominant schedule that remains optimal for all possible realizations of the processing times and so we look for a minimal set of schedules that are dominant. We obtain necessary and sufficient conditions for the case when it is possible to fix the order of two jobs in a minimal set of dominant schedules. The necessary and sufficient conditions are proven for the case when one schedule dominates all the others. We characterize also the case where there does not exist non-trivial schedule domination. All the conditions proven may be tested in polynomial time of n.

scholarly journals Relations between Non-Compact Transformation Groups and Compact Transformation Groups

1971 ◽  
Vol 44 ◽  
pp. 97-117
Author(s):  
Hsin Chu
Keyword(s):  
Fundamental Group ◽  
Transformation Group ◽  
Fibre Bundle ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Transformation Groups ◽  
Almost Periodic ◽  
Minimal Set ◽  
Weakly Almost Periodic ◽  
Necessary And Sufficient

In this paper certain relations between non-compact transformation groups and compact transformation groups are studied. The notion of re-ducibility and separability of transformation groups is introduced, several necessary and sufficient conditions are established: (1) A separable transformation group to be locally weakly almost periodic, (2) A reducible and separable transformation group to be a minimal set and (3) A reducible and separable transformation group to be a fibre bundle. As applications we show, among other things, that (1) for certain reducible transformation groups its fundamental group is not trivial which is a generalization of a result in [4].

scholarly journals Maximal homomorphic images of commutative semigroups

1971 ◽  
Vol 12 (1) ◽  
pp. 12-17 ◽  
Author(s):  
D. B. McAlister ◽  
L. O'Carroll
Keyword(s):  
Homomorphic Image ◽  
Commutative Semigroup ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Commutative Semigroups ◽  
Necessary And Sufficient

In this paper we give necessary and sufficient conditions on a commutative semigroup in order that it should have a maximal homomorphic image of one of the following types: (1) groups, (2) semigroups which are unions of groups and (3) pseudoinvertible semigroups, i. e. semigroups having the property that some power of each element lies in a subgroup of the semigroup.

scholarly journals A characterization of the Morse minimal set up to topological conjugacy

2008 ◽  
Vol 28 (5) ◽  
pp. 1443-1451 ◽  
Author(s):  
ETHAN M. COVEN ◽  
MICHAEL KEANE ◽  
MICHELLE LEMASURIER
Keyword(s):  
Dynamical System ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Topological Conjugacy ◽  
Orbit Closure ◽  
Minimal Set ◽  
Set Up ◽  
Necessary And Sufficient

AbstractWe establish necessary and sufficient conditions for a dynamical system to be topologically conjugate to the Morse minimal set, the shift orbit closure of the Morse sequence. Conditions for topological conjugacy to the closely related Toeplitz minimal set are also derived.

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> 0 for eachj> 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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