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1.
In the present paper, we define sensitive pairs via Furstenberg families and discuss the relation of three definitions: sensitivity, F -sensitivity and F -sensitive pairs, see Theorem 1. For transitive systems, we give some sufficient conditions to ensure the existence of F -sensitive pairs. In particular, each non-minimal E system (M system, P system) has positive lower density ( Fs , Fr resp.)-sensitive pairs almost everywhere. Moreover, each non-minimal M system is Fts -sensitive. Finally, by some examples we show that: (1) F -sensitivity can not imply the existence of F -sensitive pairs. That means there exists an F -sensitive system, which has no F -sensitive pairs. (2) There is no immediate relation between the existence of sensitive pairs and Li-Yorke chaos, i.e., there exists a system (X, f ) without Li-Yorke scrambled pairs, which has κ B -sensitive pairs almost everywhere. (3) If the system (G, f ) is sensitive, where G is a finite graph, then it has κ B -sensitive pairs almost everywhere.  相似文献   

2.
Furstenberg family and chaos   总被引:3,自引:0,他引:3  
A Furstenberg family F is a family,consisting of some subsets of the set of positive integers,which is hereditary upwards,i.e.A■B and A∈F imply B∈F.For a given system (i.e.,a pair of a complete metric space and a continuous self-map of the space) and for a Furstenberg family F, the definition of F-scrambled pairs of points in the space has been given,which brings the well-known scrambled pairs in Li-Yorke sense and the scrambled pairs in distribution sense to be F-scrambled pairs corresponding respectively to suitable Furstenberg family F.In the present paper we explore the basic properties of the set of F-scrambled pairs of a system.The generically F-chaotic system and the generically strongly F-chaotic system are defined.A criterion for a generically strongly F-chaotic system is showed.  相似文献   

3.
《数学学报》2023,(4):805-808
<正>On the Termination of Flips for Log Canonical Generalized Pairs Guo Du CHEN Nikolaos TSAKANIKAS Abstract We prove the termination of flips for pseudo-effective NQC log canonical generalized pairs of dimension 4.As main ingredients,we verify the termination of flips for 3-dimensional NQC log canonical generalized pairs,and show that the termination of flips for pseudo-effective NQC log canonical generalized pairs which admit NQC weak Zariski decompositions follows from the termination of...  相似文献   

4.
In this paper, the authors first introduce the concept of congruence pairs on the class of decomposable MS-algebras generalizing that for principal MS-algebras (see [13]). They show that every congruence relation θ on a decomposable MS-algebra L can be uniquely determined by a congruence pair (θ1, θ2), where θ1 is a congruence on the de Morgan subalgebra L?? of L and θ2 is a lattice congruence on the sublattice D(L) of L. They obtain certain congruence pairs of a decomposable MS-algebra L via central elements of L. Moreover, they characterize the permutability of congruences and the strong extensions of decomposable MS-algebras in terms of congruence pairs.  相似文献   

5.
An ordered pair (e, f) of idempotents of a regular semigroup is called a skew pair if ef is not idempotent whereas fe is idempotent. We have shown previously that there are four distinct types of skew pairs of idempotents. Here we investigate the ubiquity of such skew pairs in full transformation semigroups.  相似文献   

6.
The authors study the coincidence theory for pairs of maps from the Torus to the Klein bottle. Reidemeister classes and the Nielsen number are computed, and it is shown that any given pair of maps satisfies the Wecken property. The 1-parameter Wecken property is studied and a partial negative answer is derived. That is for all pairs of coincidence free maps a countable family of pairs of maps in the homotopy class is constructed such that no two members may be joined by a coincidence free homotopy.  相似文献   

7.
In general, the properties of modules over a triangular matrix ring T = (0ABU) are studied via modules over diagonal “small rings” A and B. However, we use model structures on the category of T-modules to characterize the stable categories GP(A), GP(B) of Gorenstein projective modules over A and B. To this end, we introduce two subcategories of Gorenstein T-modules, and obtain two corresponding complete cotorsion pairs. Moreover, cotorsion pairs of modules are lifted to T-complexes, and the equivalences and recollements of homotopy categories of complexes are studied. © 2022 Chinese Academy of Sciences. All rights reserved.  相似文献   

8.
A Riesz space K1 whose elements are pairs of convex-set collections is presented for the study on the calculus of generalized quasi-differentiable functions. The space K1 is constructed by introducing a well-defined equivalence relation among pairs of collections of convex sets. Some important properties on the norm and operations in K1 are given.  相似文献   

9.
<正>Fountain-Gould Left Orders for Associative Pairs A. ANQUELA Teresa CORTES Miguel GOMEZ LOZANO Mercedes SILES MOLINA Abstract In this paper, we introduce a notion of weak Fountain-Gould left order for associative pairs and give a Goldie-like theory of associative pairs which are weak Fountain-Gould left orders in semiprime pairs coinciding with their socles. Pointwise Convergence and Uniform Convergence of Wavelet Frame Series Zhi Hua ZHANG Abstract Pointwise convergence and uniform convergence for wavelet frame series is a new  相似文献   

10.
Let simple graph G=(V, E),V=n,E=m. If there exists a path containing i vertices connecting u and v in V, then property P_i(u,v) will be said to told.For 2≤i≤n, let S_i be the set of all unordered pairs of distinct u and v for which property P_i(u.v) holds, and Let S_1 be the set of all unordered pairs of vertices which are not connected by any path. A graph G satisfies property P_i if |S_i|=n(n-1)/2.  相似文献   

11.
Hsu-Riordan 阵/partial monoid   总被引:1,自引:0,他引:1       下载免费PDF全文
本文首先对Shapiro的Riordan群进行了推广。给出了Hsu-Riordan partial monoid的概念,然后在此框架内,对徐利治先生的两类扩展型广义Stirling数偶进行了统一处理;建立了Hsu-Wang转换定理。Brown-Sprugnoli转换公式,以及广义Brown转换引理-它揭示了一些不同类型的Hsu-Riordan阵之间转换的方法。由此可产生大量的恒等式。  相似文献   

12.
Motivated by its links to τ-tilting theory, we introduce left weak cotorsion pairs, as a generalization of cotorsion pairs in module categories. Such pairs are also linked to co-t-structures in corresponding triangulated categories, and to cotorsion pairs in certain extension closed (and hence extriangulated) subcategories, which we call two-term categories. We give a characterization of the (left) weak cotorsion pairs which come from two-term silting.  相似文献   

13.
In a recent article with Oleg Smirnov, we defined short Peirce (SP) graded Kantor pairs. For any such pair P, we defined a family, parameterized by the Weyl group of type BC2, consisting of SP-graded Kantor pairs called Weyl images of P. In this article, we classify finite dimensional simple SP-graded Kantor pairs over an algebraically closed field of characteristic 0 in terms of marked Dynkin diagrams, and we show how to compute Weyl images using these diagrams. The theory is particularly attractive for close-to-Jordan Kantor pairs (which are variations of Freudenthal triple systems), and we construct the reflections of such pairs (with nontrivial gradings) starting from Jordan pairs of matrices.  相似文献   

14.
On Iteration Semiring-Semimodule Pairs   总被引:3,自引:0,他引:3  
Conway semiring-module pairs and iteration semiring-semimodule pairs were shown to provide an axiomatic basis to automata on ω -words in [Bloom, Esik: Iteration Theories, Springer, 1993]. In this paper, we show that two natural classes of semiring-semimodule pairs, the complete and the bi-inductive semiring-semimodule pairs both give rise to iteration semiring-semimodule pairs. Complete semiring-semimodule pairs are defined by infinite sums and products, while a bi-inductive semiring-semimodule pair is an ordered semiring-semimodule pair possessing enough least pre-fixed points and greatest post-fixed points to solve linear inequations. Moreover, we show that when V is idempotent, then a semiring-semimodule pair equipped with a star and an omega operation satisfies the Conway equations (iteration semiring-semimodule pair equations, respectively) if and only if the quemiring associated with (S,V) embeds in a Conway semiring (iteration semiring, respectively).  相似文献   

15.
In the present paper, we define sensitive pairs via Furstenberg families and discuss the relation of three definitions: sensitivity, F -sensitivity and F -sensitive pairs, see Theorem 1. For transitive systems, we give some sufficient conditions to ensure the existence of F -sensitive pairs. In particular, each non-minimal E system (M system, P system) has positive lower density ( Fs , Fr resp.)-sensitive pairs almost everywhere. Moreover, each non-minimal M system is Fts -sensitive. Finally, by some exampl...  相似文献   

16.
Explicit Runge–Kutta pairs are known to provide efficient solutions to initial value differential equations with inexpensive derivative evaluations. Two criteria for selection are proposed with a view to deriving pairs of all orders 6(5) to 9(8) which minimize computation while achieving a user-specified accuracy. Coefficients of improved pairs, their stability regions and coefficients of appended optimal interpolatory Runge–Kutta formulas are provided on the author’s website (www.math.sfu.ca/~jverner). This note reports results of tests on these pairs to illustrate their effectiveness in solving nonstiff initial value problems. These pairs and interpolants may be used for implementation, or else to provide comparison targets for other new types of methods such as explicit general linear methods.  相似文献   

17.
Relative parametric canonical wreath homology and cohomology groups of an arbitrary metrizable space over pairs of copresheaves and presheaves are defined. Duality theorems are proved for these groups. Furthermore, based on epimorphisms of pairs of presheaves (copresheaves), exact and semi-exact cohomological (homological) sequences are constructed which estimate relative parametric canonical wreath cohomology (homology) groups over the pairs of presheaves (copresheaves) by means of relative parametric canonical wreath cohomology (homology) groups. __________ Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 41, Topology and Its Applications, 2006.  相似文献   

18.
本文将在两种特有的情形下研究谱与tilings之间的关系.首先,估计和比较谱与tilings关系中集合的Lebesgue测度,这包括一些不能直接用密度方法所得结果的推广,以及在正交对、填充对与覆盖对中集合的Lebesgue测度的比较.其次,明确了平移对(D,∧+Г)与(D+Г,∧)之间的一些谱与tilings关系.这里的研究是基于谱与tilings的基本性质,与共轭Fuglede猜想密切相关.  相似文献   

19.
We give a new proof for the existence and uniqueness (up to translation) of plane minimal pairs of convex bodies in a given equivalence class of the Hörmander-R»dström lattice, as well as a complete characterization of plane minimal pairs using surface area measures. Moreover, we introduce the so-called reduced pairs, which are special minimal pairs. For the plane case, we characterize reduced pairs as those pairs of convex bodies whose surface area measures are mutually singular. For higher dimensions, we give two sufficient conditions for the minimality of a pair of convex polytopes, as well as a necessary and sufficient criterion for a pair of convex polytopes to be reduced. We conclude by showing that a typical pair of convex bodies, in the sense of Baire category, is reduced, and hence the unique minimal pair in its equivalence class.  相似文献   

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