scholarly journals Ergodic automorphisms whose weak closure of off-diagonal measures consists of ergodic self-joinings

2008 ◽  
Vol 110 (1) ◽  
pp. 81-115 ◽  
Author(s):  
Y. Derriennic ◽  
K. Frączek ◽  
M. Lemańczyk ◽  
F. Parreau
Keyword(s):  
Weak Closure

Ergodic transformations conjugate to their inverses by involutions

1996 ◽  
Vol 16 (1) ◽  
pp. 97-124 ◽  
Author(s):  
Geoffrey R. Goodson ◽  
Andrés del Junco ◽  
Mariusz Lemańczyk ◽  
Daniel J. Rudolph
Keyword(s):  
Discrete Spectrum ◽  
Probability Space ◽  
Closure Property ◽  
Simple Spectrum ◽  
Ergodic Transformations ◽  
Ergodic Automorphism ◽  
Singular Spectrum ◽  
Weak Closure ◽  
Identity Automorphism ◽  
Borel Probability

AbstractLetTbe an ergodic automorphism defined on a standard Borel probability space for whichTandT−1are isomorphic. We investigate the form of the conjugating automorphism. It is well known that ifTis ergodic having a discrete spectrum andSis the conjugation betweenTandT−1, i.e.SsatisfiesTS=ST−1thenS2=Ithe identity automorphism. We show that this result remains true under the weaker assumption thatThas a simple spectrum. IfThas the weak closure property and is isomorphic to its inverse, it is shown that the conjugationSsatisfiesS4=I. Finally, we construct an example to show that the conjugation need not be an involution in this case. The example we construct, in addition to having the weak closure property, is of rank two, rigid and simple for all orders with a singular spectrum of multiplicity equal to two.

scholarly journals On weak closure of some diffusion equations

2019 ◽  
Vol 147 (9) ◽  
pp. 3803-3811
Author(s):  
Menglan Liao ◽  
Lianzhang Bao ◽  
Baisheng Yan
Keyword(s):  
Diffusion Equations ◽  
Weak Closure

scholarly journals The commutant is the weak closure of the powers, for rank-1 transformations

1986 ◽  
Vol 6 (3) ◽  
pp. 363-384 ◽  
Author(s):  
Jonathan King
Keyword(s):  
Weak Closure ◽  
Weak Isomorphism ◽  
Proper Factor

AbstractIn the class of rank-1 transformations, there is a strong dichotomy. For such a T, the commutant is either irivial, consisting only of the powers of T, or is uncountable. In addition, the commutant semigroup, C(T), is in fact a group. As a consequence, the notion of weak isomorphism between two transformations is equivalent to isomorphism, if at least one of the transformations is rank-1. In § 2, we show that any proper factor of a rank-1 must be rigid. Hence, neither Ornstein's rank-1 mixing nor Chacón's transformation, can be a factor of a rank-1.

scholarly journals Weak Closure Theorem fails for Z2-actions

2002 ◽  
Vol 153 (2) ◽  
pp. 115-125 ◽  
Author(s):  
T. Downarowicz ◽  
J. Kwiatkowski
Keyword(s):  
Closure Theorem ◽  
Weak Closure

scholarly journals Concept of „long centric"

2004 ◽  
Vol 132 (11-12) ◽  
pp. 441-447
Author(s):  
Zeljko Martinovic ◽  
Kosovka Obradovic-Djuricic ◽  
Nevenka Teodorovic ◽  
Rade Zivkovic
Keyword(s):  
Historical Perspective ◽  
Therapeutic Interventions ◽  
Therapeutic Modality ◽  
Anterior Portion ◽  
Occlusal Adjustment ◽  
Anterior Teeth ◽  
Lower Jaw ◽  
Weak Closure ◽  
Wedge Effect

The objective of this paper was to show the historical perspective of the ?long centric" occlusal concept and its importance in the modern dentistry, especially from the gnathological aspect. The ?long centric" concept represents therapeutic modality used in modern dentistry and occlusal adjustment in all patients showing differences in strong and weak closure of the lower jaw starting from the position of physiological rest/long centric" concept is applied only for anterior teeth and occlusal movements from rather than toward the center. Whenever the ?long centric" parameters are not adequate, occlusal disturbance, resulting from the ?wedge" effect during the initial closure of the lower jaw, is present. Different degrees of abrasion or hypermobility of the teeth are often the result of the above-mentioned occlusal disturbances and can potentially trigger bruxism and malfunction. Modus procedendi should be the regular approach of every dentist to any occlusion, because only the built-in ?long centric" efficiently contributes to the occlusal stability of the anterior portion of the dentition. All occlusions should be routinely tested regarding their need for ?long centric", especially when the extensive therapeutic interventions (conservative, prosthetics) of the occlusal complex are required.

Weak Closure of Infinite Actions of Rank 1, Joinings, and Spectrum

2019 ◽  
Vol 106 (5-6) ◽  
pp. 957-965
Author(s):  
V. V. Ryzhikov
Keyword(s):  
Weak Closure

scholarly journals Homomorphic Image and Inverse Image of Weak Closure Operations on Ideals of BCK-Algebras

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 567 ◽  
Author(s):  
Hashem Bordbar ◽  
Young Bae Jun ◽  
Seok-Zun Song
Keyword(s):  
Homomorphic Image ◽  
Inverse Image ◽  
Closure Operation ◽  
Weak Closure ◽  
Closure Operations ◽  
Epimorphic Image

We introduce the notions of meet, semi-prime, and prime weak closure operations. Using homomorphism of BCK-algebras φ : X → Y , we show that every epimorphic image of a non-zeromeet element is also non-zeromeet and, for mapping c l Y : I ( Y ) → I ( Y ) , we define a map c l Y ← on I ( X ) by A ↦ φ − 1 ( φ ( A ) c l Y ) . We prove that, if “ c l Y ” is a weak closure operation (respectively, semi-prime and meet) on I ( Y ) , then so is “ c l Y ← ” on I ( X ) . In addition, for mapping c l X : I ( X ) → I ( X ) , we define a map c l X → on I ( Y ) as follows: B ↦ φ ( φ − 1 ( B ) c l X ) . We show that, if “ c l X ” is a weak closure operation (respectively, semi-prime and meet) on I ( X ) , then so is “ c l X → ” on I ( Y ) .

Weak closure of the unitary orbit of contractions

1985 ◽  
Vol 46 (3-4) ◽  
pp. 255-263
Author(s):  
M. Kutkut
Keyword(s):  
Weak Closure ◽  
Unitary Orbit
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