共查询到20条相似文献,搜索用时 359 毫秒
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Jian Li 《Topology and its Applications》2011,158(16):2221-2231
Let (X,T) be a topological dynamical system and F be a Furstenberg family (a collection of subsets of Z+ with hereditary upward property). A point x∈X is called an F-transitive one if {n∈Z+:Tnx∈U}∈F for every non-empty open subset U of X; the system (X,T) is called F-point transitive if there exists some F-transitive point. In this paper, we aim to classify transitive systems by F-point transitivity. Among other things, it is shown that (X,T) is a weakly mixing E-system (resp. weakly mixing M-system, HY-system) if and only if it is {D-sets}-point transitive (resp. {central sets}-point transitive, {weakly thick sets}-point transitive).It is shown that every weakly mixing system is Fip-point transitive, while we construct an Fip-point transitive system which is not weakly mixing. As applications, we show that every transitive system with dense small periodic sets is disjoint from every totally minimal system and a system is Δ?(Fwt)-transitive if and only if it is weakly disjoint from every P-system. 相似文献
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Yossi Moshe 《Journal of Number Theory》2007,123(1):224-240
Let H(x) be a monic polynomial over a finite field F=GF(q). Denote by Na(n) the number of coefficients in Hn which are equal to an element a∈F, and by G the set of elements a∈F× such that Na(n)>0 for some n. We study the relationship between the numbers (Na(n))a∈G and the patterns in the base q representation of n. This enables us to prove that for “most” n's we have Na(n)≈Nb(n), a,b∈G. Considering the case H=x+1, we provide new results on Pascal's triangle modulo a prime. We also provide analogous results for the triangle of Stirling numbers of the first kind. 相似文献
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Marcin Bilski 《Indagationes Mathematicae》2009,20(1):23-41
Let X be an analytic subset of pure dimension n of an open set U ⊂ Cm and let E be a Nash subset of U such that E ⊂ X.Then for every a ∈ E there is an open neighborhood V of a in U and a sequence {Xv} of complex Nash subsets of V of pure dimension n converging to X ∩ V in the sense of holomorphic chains such that the following hold for every v ∈ N: E ∩ V ⊂ Xv and the multiplicity of Xv at x equals the multiplicity of X at x for every x in a dense open subset of E ⊂ V. 相似文献
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Assuming the absence of Q-points (which is consistent with ZFC) we prove that the free topological group F(X) over a Tychonov space X is o-bounded if and only if every continuous metrizable image T of X satisfies the selection principle fin?(O,Ω) (the latter means that for every sequence 〈un〉n∈ω of open covers of T there exists a sequence 〈vn〉n∈ω such that vn∈[un]<ω and for every F∈[X]<ω there exists n∈ω with F⊂?vn). This characterization gives a consistent answer to a problem posed by C. Hernándes, D. Robbie, and M. Tkachenko in 2000. 相似文献
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Let X be a Green domain in Rd, d?2, x∈X, and let Mx(P(X)) denote the compact convex set of all representing measures for x. Recently it has been proven that the set of harmonic measures , U open in X, x∈U, which is contained in the set of extreme points of Mx(P(X)), is dense in Mx(P(X)). In this paper, it is shown that Mx(P(X)) is not a simplex (and hence not a Poulsen simplex). This is achieved by constructing open neighborhoods U0, U1, U2, U3 of x such that the harmonic measures are pairwise different and . In fact, these measures form a square with respect to a natural L2-structure. Since the construction is mainly based on having certain symmetries, it can be carried out just as well for Riesz potentials, the Heisenberg group (or any stratified Lie algebra), and the heat equation (or more general parabolic situations). 相似文献
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P.D. Allenby 《Indagationes Mathematicae》2009,20(1):19-22
We prove that if X and Y are compact Hausdorff spaces, then every f ∈ C(X × Y)+, i.e. f(x, y) ≥ 0 for all (x, y) ∈ X × Y, can be approximated uniformly from below and above by elements of the form , where fi ∈ C(X)+ and gi ∈ C(Y)+ for i = 1, 2, …, n. The proof uses only elementary topology. We use this result, in conjuction with Kakutani's M-spaces representation theorem, to obtain an alternative proof for a known property of Fremlin's Riesz space tensor product of Archimedean Riesz spaces. 相似文献
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Jinghai Shao 《Bulletin des Sciences Mathématiques》2006,130(8):720-738
Let (X,ρ) be a Polish space endowed with a probability measure μ. Assume that we can do Malliavin Calculus on (X,μ). Let be a pseudo-distance. Consider QtF(x)=infy∈X{F(y)+d2(x,y)/2t}. We shall prove that QtF satisfies the Hamilton-Jacobi inequality under suitable conditions. This result will be applied to establish transportation cost inequalities on path groups and loop groups in the spirit of Bobkov, Gentil and Ledoux. 相似文献
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Let P and Q be non-zero integers. The Lucas sequence {Un(P,Q)} is defined by U0=0, U1=1, Un=PUn−1−QUn−2 (n?2). The question of when Un(P,Q) can be a perfect square has generated interest in the literature. We show that for n=2,…,7, Un is a square for infinitely many pairs (P,Q) with gcd(P,Q)=1; further, for n=8,…,12, the only non-degenerate sequences where gcd(P,Q)=1 and Un(P,Q)=□, are given by U8(1,−4)=212, U8(4,−17)=6202, and U12(1,−1)=122. 相似文献
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Enrique Llorens-Fuster Eva M. Mazcuñán-Navarro 《Nonlinear Analysis: Theory, Methods & Applications》2010,72(11):3984-34
In every inner product space H the Ptolemy inequality holds: the product of the diagonals of a quadrilateral is less than or equal to the sum of the products of the opposite sides. In other words, ‖x−y‖‖z−w‖≤‖x−z‖‖y−w‖+‖z−y‖‖x−w‖ for any points w,x,y,z in H. It is known that for each normed space (X,‖⋅‖), there exists a constant C such that for any w,x,y,z∈X, we have ‖x−y‖‖z−w‖≤C(‖x−z‖‖y−w‖+‖z−y‖‖x−w‖). The smallest such C is called the Ptolemy constant of X and is denoted by CP(X). We study the relationships between this constant and the geometry of the space X, and hence with metric fixed point theory. In particular, we relate the Ptolemy constant CP to the Zb?ganu constant CZ, and prove that if X is a Banach space with , then X has (uniform) normal structure and therefore the fixed point property for nonexpansive mappings. We derive general lower and upper bounds for both CP and CZ, and calculate the precise values of these two constants for several normed spaces. We also present a number of conjectures and open problems. 相似文献
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Let (a,b)∈Z2, where b≠0 and (a,b)≠(±2,−1). We prove that then there exist two positive relatively prime composite integers x1, x2 such that the sequence given by xn+1=axn+bxn−1, n=2,3,… , consists of composite terms only, i.e., |xn| is a composite integer for each n∈N. In the proof of this result we use certain covering systems, divisibility sequences and, for some special pairs (a,±1), computer calculations. The paper is motivated by a result of Graham who proved this theorem in the special case of the Fibonacci-like sequence, where (a,b)=(1,1). 相似文献
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Wanzhou Ye 《Discrete Mathematics》2011,(21):2437
Let Fk be a mapping from RZ to RZ, satisfying that for x∈RZ and n∈Z, Fk(x)(n) is the (k+1)th largest value (median value) of the 2k+1 numbers x(n−k),…,x(n),…,x(n+k). In [3] [W.Z. Ye, L. Wang, L.G. Xu, Properties of locally convergent sequences with respect to median filter, Discrete Mathematics 309 (2009) 2775–2781], we conjectured that for k∈{2,3}, if there exists n0∈Z such that x is locally finitely convergent with respect to Fk on {n0,…,n0+k−1}, then x is finitely convergent with respect to Fk. In this paper, we obtain some sufficient conditions for a sequence finitely converging with respect to median filters. Based on these results, we prove that the conjecture is true. 相似文献
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Kenjiro Ogawa 《Discrete Mathematics》2009,309(22):6353-6358
For a poset P=(X,≤P), the double bound graph (DB-graph) of P is the graph DB(P)=(X,EDB(P)), where xy∈EDB(P) if and only if x≠y and there exist n,m∈X such that n≤Px,y≤Pm. We obtain that for a subposet Q of a poset P,Q is an (n, m)-subposet of P if and only if DB(Q) is an induced subgraph DB(P). Using this result, we show some characterizations of split double bound graphs, threshold double bound graphs and difference double bound graphs in terms of (n, m)-subposets and double canonical posets. 相似文献
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We consider the linear nonautonomous system of difference equations xn+1−xn+P(n)xn−k=0, n=0,1,2,… , where k∈Z, P(n)∈Rrxr. We obtain sufficient conditions for the system to be oscillatory. The conditions based on the eigenvalues of the matrix coefficients of the system. 相似文献
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For any closed subset F of [1,∞] which is either finite or consists of the elements of an increasing sequence and its limit, a reflexive Banach space X with a 1-unconditional basis is constructed so that in each block subspace Y of X , ?p is finitely block represented in Y if and only if p∈F. In particular, this solves the question as to whether the stabilized Krivine set for a Banach space had to be connected. We also prove that for every infinite dimensional subspace Y of X there is a dense subset G of F such that the spreading models admitted by Y are exactly the ?p for p∈G. 相似文献
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Valentin Ferenczi 《Journal of Functional Analysis》2006,238(1):353-373
Let X be a Banach space with a Schauder basis (en)n∈N. The relation E0 is Borel reducible to permutative equivalence between normalized block-sequences of (en)n∈N or X is c0 or ?p saturated for some 1?p<+∞. If (en)n∈N is shrinking unconditional then either it is equivalent to the canonical basis of c0 or ?p, 1<p<+∞, or the relation E0 is Borel reducible to permutative equivalence between sequences of normalized disjoint blocks of X or of X∗. If (en)n∈N is unconditional, then either X is isomorphic to ?2, or X contains ω2 subspaces or ω2 quotients which are spanned by pairwise permutatively inequivalent normalized unconditional bases. 相似文献
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We study polynomial endomorphisms F of CN which are locally finite in the following sense: the vector space generated by r°Fn (n≥0) is finite dimensional for each r∈C[x1,…,xN]. We show that such endomorphisms exhibit similar features to linear endomorphisms: they satisfy the Jacobian Conjecture, have vanishing polynomials, admit suitably defined minimal and characteristic polynomials, and the invertible ones admit a Dunford decomposition into “semisimple” and “unipotent” constituents. We also explain a relationship with linear recurrent sequences and derivations. Finally, we give particular attention to the special cases where F is nilpotent and where N=2. 相似文献
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B.P. Duggal 《Journal of Mathematical Analysis and Applications》2008,340(1):366-373
A Banach space operator T∈B(X) is hereditarily polaroid, T∈HP, if every part of T is polaroid. HP operators have SVEP. It is proved that if T∈B(X) has SVEP and R∈B(X) is a Riesz operator which commutes with T, then T+R satisfies generalized a-Browder's theorem. If, in particular, R is a quasi-nilpotent operator Q, then both T+Q and T∗+Q∗ satisfy generalized a-Browder's theorem; furthermore, if Q is injective, then also T+Q satisfies Weyl's theorem. If A∈B(X) is an algebraic operator which commutes with the polynomially HP operator T, then T+N is polaroid and has SVEP, f(T+N) satisfies generalized Weyl's theorem for every function f which is analytic on a neighbourhood of σ(T+N), and f∗(T+N) satisfies generalized a-Weyl's theorem for every function f which is analytic on, and constant on no component of, a neighbourhood of σ(T+N). 相似文献
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Serguei V. Astashkin 《Journal of Functional Analysis》2005,226(1):173-192
Let X be a rearrangement invariant (r.i.) function space on [0,1]. We consider the Rademacher multiplicator space Λ(R,X) of measurable functions x such that xh∈X for every a.e. converging series h=∑anrn∈X, where (rn) are the Rademacher functions. We show that for a broad class of r.i. spaces X, the space Λ(R,X) is not r.i. In this case, we identify the symmetric kernel of the Rademacher multiplicator space and study when reduces to L∞. In the opposite direction, we find new examples of r.i. spaces for which Λ(R,X) is r.i. We consider in detail the case when X is a Marcinkiewicz or an exponential Orlicz space. 相似文献