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1.
Valdis Laan 《Periodica Mathematica Hungarica》2010,60(1):81-94
Two semigroups are called strongly Morita equivalent if they are contained in a Morita context with unitary bi-acts and surjective
mappings. We consider the notion of context equivalence which is obtained from the notion of strong Morita equivalence by
dropping the requirement of unitariness. We show that context equivalence is an equivalence relation on the class of factorisable
semigroups and describe factorisable semigroups that are context equivalent to monoids or groups, and semigroups with weak
local units that are context equivalent to inverse semigroups, orthodox semigroups or semilattices. 相似文献
2.
David Fried 《Commentarii Mathematici Helvetici》1982,57(1):237-259
We analyze the dynamics of diffeomorphisms in terms of their suspension flows. For many Axion A diffeomorphisms we find simplest
representatives in their flow equivalence class and so reduce flow equivalence to conjugacy. The zeta functions of maps in
a flow equivalence class are correlated with a zeta function ζ
H
for their suspended flow. This zeta function is defined for any flow with only finitely many closed orbits in each homology
class, and is proven rational for Axiom A flows. The flow equivalence of Anosov diffeomorphisms is used to relate the spectrum
of the induced map on first homology to the existence of fixed points. For Morse-Smale maps, we extend a result of Asimov
on the geometric index.
Partially supported by MCS 76-08795. 相似文献
3.
Scot Adams 《Israel Journal of Mathematics》1988,64(3):362-380
We define rigorously a “treed” equivalence relation, which, intuitively, is an equivalence relation together with a measurably
varying tree structure on each equivalence class. We show, in the nonamenable, ergodic, measure-preserving case, that a treed
equivalence relation cannot be stably isomorphic to a direct product of two ergodic equivalence relations. 相似文献
4.
R. N. Gumerov 《Proceedings of the American Mathematical Society》2005,133(9):2771-2778
We study limit mappings from a solenoid onto itself. It is shown that each equivalence class of finite-sheeted covering mappings from connected topological spaces onto a solenoid is determined by a limit mapping. Properties of periodic points of limit mappings are also studied.
5.
6.
Zbigniew Le?niak 《Journal of Mathematical Analysis and Applications》2010,366(1):310-373
We present a method for finding continuous (and consequently homeomorphic) orientation preserving iterative roots of a Brouwer homeomorphism which is embeddable in a flow. To obtain the roots we use a countable family of maximal parallelizable regions of the flow which is a cover of the plane. The maximal parallelizable regions are unions of equivalence classes of an appropriate equivalence relation. We show that if an equivalence class is invariant under the nth iterate of a Brouwer homeomorphism g, then it is invariant under g. We use this fact to prove that each maximal parallelizable region of the flow must be invariant under all homeomorphic orientation preserving iterative roots of the given Brouwer homeomorphism. 相似文献
7.
Andrzej Ehrenfeucht David Haussler Grzegorz Rozenberg Paul Zeiger 《Semigroup Forum》1984,29(1):123-148
Roughly speaking,DOS systems formalize the notion of generatively deterministic context free grammars. We explore the containment relationships
among the class of languages generated byDOS systems and other subclasses of the class of context free languages. Leaving the axiom of aDOS system unspecified yields aDOS scheme, which defines a mapping from words to languages over a given alphabet. We explore the algebraic properties ofDOS mappings and obtain an algebraic characterization of a fundamental subclass of theDOS mappings generated byDOS schemes which are propagating (non erasing) and have no cycles of derivability among letters of the alphabet. We apply this
characterization to show that the mapping equivalence problem for propagatingDOS schemes is decidable. 相似文献
8.
K. J. Horadam 《组合设计杂志》2000,8(5):330-346
A semiregular relative difference set (RDS) in a finite group E which avoids a central subgroup C is equivalent to a cocycle which satisfies an additional condition, called orthogonality. However the basic equivalence relation, cohomology, on cocycles, does not preserve orthogonality, leading to the perception that orthogonality is essentially a combinatorial property. We show this perception is false by discovering a natural atomic structure within cohomology classes, which discriminates between orthogonal and non‐orthogonal cocycles. This atomic structure is determined by an action we term the shift action of the group G = E/C on cocycles, which defines a stronger equivalence relation on cocycles than cohomology. We prove that for each triple (C, E, G), the set of equivalence classes of semiregular RDS in E relative to C is in one to one correspondence with the set of shift‐orbits of the (Aut(C) × Aut(G))‐orbits of orthogonal cocycles. This determines a new algorithm for detecting and classifying central semiregular RDS. We demonstrate it, and propose a 7‐parameter classification scheme for equivalence classes of central semiregular relative difference sets. © 2000 John Wiley & Sons, Inc. J Combin Designs 8: 330–346, 2000 相似文献
9.
V. A. Zorich 《Mathematical Notes》1971,10(4):662-666
We determine the widest class of topological mappings for which a correspondence of boundaries is describable in terms of prime ends in the sense of Caratheodory. Relying on a concept of relative distance, we explain why the class so determined is the widest possible, and using a characteristic property of mappings of this class we prove a generalized theorem of Koebe on correspondence of accessible points and we establish its logical equivalence to a fundamental theorem of the Caratheodory theory.Translated from Matematicheskie Zametki, Vol. 10, No. 4, 399–406, October, 1971. 相似文献
10.
Werner Seier 《Journal of Geometry》1973,3(2):165-178
Incidencestructures with an equivalence relation on the set of blocks or lines, satisfying the euclidean axiom of parallelism, are called generalised parallel structures, if on each line are at least two points and if through two different points passes at most one line. In this paper we give a coordinatization for a class of generalised parallel structures. Isomorphisms of desarguesian affine spaces induce in a well known manner regular semilinear mappings of the corresponding vector spaces. We prove an analogous theorem for generalised parallel structures and the corresponding algebraic structures. 相似文献
11.
Kenny De Commer Paweł Kasprzak Adam Skalski Piotr M. Sołtan 《Israel Journal of Mathematics》2018,226(1):475-503
To any action of a compact quantum group on a von Neumann algebra which is a direct sum of factors we associate an equivalence relation corresponding to the partition of a space into orbits of the action. We show that in case all factors are finite-dimensional (i.e., when the action is on a discrete quantum space) the relation has finite orbits. We then apply this to generalize the classical theory of Clifford, concerning the restrictions of representations to normal subgroups, to the framework of quantum subgroups of discrete quantum groups, itself extending the context of closed normal quantum subgroups of compact quantum groups. Finally, a link is made between our equivalence relation in question and another equivalence relation defined by R. Vergnioux. 相似文献
12.
In this paper, we investigate a class of nonlinear complementarity problems arising from the discretization of the free boundary problem, which was recently studied by Sun and Zeng [Z. Sun, J. Zeng, A monotone semismooth Newton type method for a class of complementarity problems, J. Comput. Appl. Math. 235 (5) (2011) 1261–1274]. We propose a new non-interior continuation algorithm for solving this class of problems, where the full-Newton step is used in each iteration. We show that the algorithm is globally convergent, where the iteration sequence of the variable converges monotonically. We also prove that the algorithm is globally linearly and locally superlinearly convergent without any additional assumption, and locally quadratically convergent under suitable assumptions. The preliminary numerical results demonstrate the effectiveness of the proposed algorithm. 相似文献
13.
We continue the study of minimal singular surfaces obtained by a minimization of a weighted energy functional in the spirit
of J. Douglas’s approach to the Plateau problem. Modeling soap films spanning wire frames, a singular surface is the union
of three disk-type surfaces meeting along a curve which we call the free boundary. We obtain an a priori regularity result
concerning the real analyticity of the free boundary curve. Using the free boundary regularity of the harmonic map, we construct
local harmonic isothermal coordinates for the minimal singular surface in a neighborhood of a point on the free boundary.
Applications of the local uniformization are discussed in relation to H. Lewy’s real analytic extension of minimal surfaces. 相似文献
14.
We investigate properties of dynamical systems associated with the approximation of pseudotrajectories of a dynamical system
by its trajectories. According to modern terminology, a property of this sort is called the “property of tracing pseudotrajectories”
(also known in the English literature as the “shadowing property”). We prove that dynamical systems given by mappings of a
compact set into itself and possessing this property are systems with stable prolongation of orbits. We construct examples
of mappings of an interval into itself that prove that the inverse statement is not true, i.e., that dynamical systems with
stable prolongation of orbits may not possess the property of tracing pseudotrajectories.
Institute of Mathematics, Ukrainian Academy of Sciences, Kiev. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 49,
No. 8, pp. 1016–1024, August, 1997. 相似文献
15.
Pólya's enumeration theorem is generalized in the following way. We have sets R and D, and a group G acting (by means of representations) on R and D simultaneously. This induces an equivalence relation in the set of all mappings (or of all one-to-one mappings) of R into D. The number of equivalence classes is determined for both cases. The example of types of mappings of a set into itself is treated in detail. 相似文献
16.
Damien Gaboriau 《Inventiones Mathematicae》2000,139(1):41-98
We study a new dynamical invariant for dicrete groups: the cost. It is a real number in {1−1/n}∪[1,∞], bounded by the number of generators of the group, and it is well behaved with respect to finite index subgroups.
Namely, the quantities 1 minus the cost are related by multiplying by the index. The cost of every infinite amenable group
equals 1. We compute it in some other situations, including free products, free products with amalgamation and HNN-extensions
over amenable groups and for direct product situations. For instance, the cost of the free group on n generators equals n. We prove that each possible finite value of the cost is achieved by a finitely generated group. It is dynamical because
it relies on measure preserving free actions on probability Borel spaces. In most cases, groups have fixed price, which implies that two freely acting groups which define the same orbit partition must have the same cost. It enables us
to distinguish the orbit partitions of probability-preserving free actions of free groups of different ranks. At the end of
the paper, we give a mercuriale, i.e. a list of costs of different groups. The cost is in fact an invariant of ergodic measure-preserving equivalence relations
and is defined using graphings. A treeing is a measurable way to provide every equivalence class (=orbit) with the structure of a simplicial tree, this an example
of graphing. Not every relation admits a treeing: we prove that every free action of a cost 1 non-amenable group is not treeable,
but we prove that subrelations of treeable relations are treeable. We give examples of relations which cannot be produced
by an action of any finitely generated group. The cost of a relation which can be decomposed as a direct product is shown
to be 1. We define the notion for a relation to be a free product or an HNN-extension and compute the cost for the resulting
relation from the costs of the building blocks. The cost is also an invariant of the pairs von Neumann algebra/Cartan subalgebra.
Oblatum 27-I-1999 & 4-IV-1999 / Published online: 22 September 1999 相似文献
17.
Zhenyu Huang 《Journal of Mathematical Analysis and Applications》2007,329(2):935-947
In this paper, the equivalence of the strong convergence between the modified Mann and Ishikawa iterations with errors in two different schemes by Xu [Y.G. Xu, Ishikawa and Mann iteration process with errors for nonlinear strongly accretive operator equations, J. Math. Anal. Appl. 224 (1998) 91-101] and Liu [L.S. Liu, Ishikawa and Mann iterative process with errors for nonlinear strongly accretive mappings in Banach spaces, J. Math. Anal. Appl. 194 (1995) 114-125] respectively is proven for the generalized strongly successively Φ-pseudocontractive mappings without Lipschitzian assumption. Our results generalize the recent results of the papers [Zhenyu Huang, F. Bu, The equivalence between the convergence of Ishikawa and Mann iterations with errors for strongly successively pseudocontractive mappings without Lipschitzian assumption, J. Math. Anal. Appl. 325 (1) (2007) 586-594; B.E. Rhoades, S.M. Soltuz, The equivalence between the convergences of Ishikawa and Mann iterations for an asymptotically nonexpansive in the intermediate sense and strongly successively pseudocontractive maps, J. Math. Anal. Appl. 289 (2004) 266-278; B.E. Rhoades, S.M. Soltuz, The equivalence between Mann-Ishikawa iterations and multi-step iteration, Nonlinear Anal. 58 (2004) 219-228] by extending to the most general class of the generalized strongly successively Φ-pseudocontractive mappings and hence improve the corresponding results of all the references given in this paper by providing the equivalence of convergence between all of these iteration schemes for any initial points u1, x1 in uniformly smooth Banach spaces. 相似文献
18.
The authors consider proper holomorphic mappings between smoothly bounded pseudoconvex regions in complex 2-space, where the
domain is of finite type and admits a transverse circle action. The main result is that the closure of each irreducible component
of the branch locus of such a map intersects the boundary of the domain in the union of finitely many orbits of the group
action. 相似文献
19.
The authors consider proper holomorphic mappings between smoothly bounded pseudoconvex regions in complex 2-space,where the domain is of finite type and admits a transverse circle action.The main result is that the closure of each irreducible component of the branch locus of such a map intersects the boundary of the domain in the union of finitely many orbits of the group action. 相似文献
20.
Philibert Nang 《Comptes Rendus Mathematique》2004,338(2):139-144
We classify regular holonomic -modules whose characteristic variety is contained in the union of conormal bundles to the orbits of the group of invertible matrices. The main result is an equivalence between the category of such -modules and the one of graded modules of finite type over a Weyl algebra. To cite this article: P. Nang, C. R. Acad. Sci. Paris, Ser. I 338 (2004). 相似文献