共查询到20条相似文献,搜索用时 343 毫秒
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Mohammad Javaheri 《Journal of Mathematical Analysis and Applications》2010,361(2):332-337
Let γ:[0,1]→2[0,1] be a continuous curve such that γ(0)=(0,0), γ(1)=(1,1), and γ(t)∈2(0,1) for all t∈(0,1). We prove that, for each n∈N, there exists a sequence of points Ai, 0?i?n+1, on γ such that A0=(0,0), An+1=(1,1), and the sequences and , 0?i?n, are positive and the same up to order, where π1, π2 are projections on the axes. 相似文献
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Piotr Niemiec 《Topology and its Applications》2008,155(12):1323-1328
The aim of the paper is to generalize the notion of the Haar integral. For a compact semigroup S acting continuously on a Hausdorff compact space Ω, the algebra A(S)⊂C(Ω,R) of S-invariant functions and the linear space M(S) of S-invariant (real-valued) finite signed measures are considered. It is shown that if S has a left and right invariant measure, then the dual space of A(S) is isometrically lattice-isomorphic to M(S) and that there exists a unique linear operator (called the Haar integral) such that for each f∈A(S) and for any f∈C(Ω,R) and s∈S, , where . 相似文献
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Let N denote the set of positive integers. The asymptotic density of the set A⊆N is d(A)=limn→∞|A∩[1,n]|/n, if this limit exists. Let AD denote the set of all sets of positive integers that have asymptotic density, and let SN denote the set of all permutations of the positive integers N. The group L? consists of all permutations f∈SN such that A∈AD if and only if f(A)∈AD, and the group L* consists of all permutations f∈L? such that d(f(A))=d(A) for all A∈AD. Let be a one-to-one function such that d(f(N))=1 and, if A∈AD, then f(A)∈AD. It is proved that f must also preserve density, that is, d(f(A))=d(A) for all A∈AD. Thus, the groups L? and L* coincide. 相似文献
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Rostislav Caha 《Discrete Mathematics》2007,307(16):2053-2066
A set A of vertices of a hypercube is called balanced if . We prove that for every natural number n there exists a natural number π1(n) such that for every hypercube Q with dim(Q)?π1(n) there exists a family of pairwise vertex-disjoint paths Pi between Ai and Bi for i=1,2,…,n with if and only if {Ai,Bi∣i=1,2,…,n} is a balanced set. 相似文献
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B.P. Duggal 《Journal of Mathematical Analysis and Applications》2010,370(2):584-587
Let B(H) denote the algebra of operators on an infinite dimensional complex Hilbert space H, and let A○∈B(K) denote the Berberian extension of an operator A∈B(H). It is proved that the set theoretic function σ, the spectrum, is continuous on the set C(i)⊂B(Hi) of operators A for which σ(A)={0} implies A is nilpotent (possibly, the 0 operator) and at every non-zero λ∈σp(A○) for some operators X and B such that λ∉σp(B) and σ(A○)={λ}∪σ(B). If CS(m) denotes the set of upper triangular operator matrices , where Aii∈C(i) and Aii has SVEP for all 1?i?m, then σ is continuous on CS(m). It is observed that a considerably large number of the more commonly considered classes of Hilbert space operators constitute sets C(i) and have SVEP. 相似文献
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Sukumar Das Adhikari 《Journal of Combinatorial Theory, Series A》2008,115(1):178-184
Let G be a finite abelian group of order n and let A⊆Z be non-empty. Generalizing a well-known constant, we define the Davenport constant of G with weight A, denoted by DA(G), to be the least natural number k such that for any sequence (x1,…,xk) with xi∈G, there exists a non-empty subsequence (xj1,…,xjl) and a1,…,al∈A such that . Similarly, for any such set A, EA(G) is defined to be the least t∈N such that for all sequences (x1,…,xt) with xi∈G, there exist indices j1,…,jn∈N,1?j1<?<jn?t, and ?1,…,?n∈A with . In the present paper, we establish a relation between the constants DA(G) and EA(G) under certain conditions. Our definitions are compatible with the previous generalizations for the particular group G=Z/nZ and the relation we establish had been conjectured in that particular case. 相似文献
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Kyung Soo Kim 《Journal of Mathematical Analysis and Applications》2009,358(2):261-3419
Let S be a semitopological semigroup. Let C be a closed convex subset of a uniformly convex Banach space E whose norm is Fréchet differentiable and be a continuous representation of S as almost asymptotically nonexpansive type mapping of C into C such that the common fixed point set F(ℑ) of ℑ in C is nonempty. In this paper, we prove that if S is right reversible then for each x∈C, the closed convex set consists of at most one point. We also prove that if S is reversible, then the intersection is nonempty for each x∈C if and only if there exists a nonexpansive retraction P of C onto F(ℑ) such that PTt=TtP=P for all t∈S and Px is in the closed convex hull of for each x∈C. 相似文献
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Refael Hassin 《Operations Research Letters》2005,33(3):242-248
The input to the MAXIMUM SAVING PARTITION PROBLEM consists of a set V={1,…,n}, weights wi, a function f, and a family S of feasible subsets of V. The output is a partition (S1,…,Sl) such that Si∈S, and is maximized. We present a general -approximation algorithm, and improved algorithms for special cases of the function f. 相似文献
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Quoc-Phong Vu 《Journal of Mathematical Analysis and Applications》2007,334(1):487-501
We study properties of solutions of the evolution equation , where B is a closable operator on the space AP(R,H) of almost periodic functions with values in a Hilbert space H such that B commutes with translations. The operator B generates a family of closed operators on H such that (whenever eiλtx∈D(B)). For a closed subset Λ⊂R, we prove that the following properties (i) and (ii) are equivalent: (i) for every function f∈AP(R,H) such that σ(f)⊆Λ, there exists a unique mild solution u∈AP(R,H) of Eq. (∗) such that σ(u)⊆Λ; (ii) is invertible for all λ∈Λ and . 相似文献
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B.V. Subramanya Bharadwaj 《Discrete Mathematics》2009,309(4):834-1274
Let G=(V,E) be a finite, simple and undirected graph. For S⊆V, let δ(S,G)={(u,v)∈E:u∈S and v∈V−S} be the edge boundary of S. Given an integer i, 1≤i≤|V|, let the edge isoperimetric value of G at i be defined as be(i,G)=minS⊆V;|S|=i|δ(S,G)|. The edge isoperimetric peak of G is defined as be(G)=max1≤j≤|V|be(j,G). Let bv(G) denote the vertex isoperimetric peak defined in a corresponding way. The problem of determining a lower bound for the vertex isoperimetric peak in complete t-ary trees was recently considered in [Y. Otachi, K. Yamazaki, A lower bound for the vertex boundary-width of complete k-ary trees, Discrete Mathematics, in press (doi:10.1016/j.disc.2007.05.014)]. In this paper we provide bounds which improve those in the above cited paper. Our results can be generalized to arbitrary (rooted) trees.The depth d of a tree is the number of nodes on the longest path starting from the root and ending at a leaf. In this paper we show that for a complete binary tree of depth d (denoted as ), and where c1, c2 are constants. For a complete t-ary tree of depth d (denoted as ) and d≥clogt where c is a constant, we show that and where c1, c2 are constants. At the heart of our proof we have the following theorem which works for an arbitrary rooted tree and not just for a complete t-ary tree. Let T=(V,E,r) be a finite, connected and rooted tree — the root being the vertex r. Define a weight function w:V→N where the weight w(u) of a vertex u is the number of its successors (including itself) and let the weight index η(T) be defined as the number of distinct weights in the tree, i.e η(T)=|{w(u):u∈V}|. For a positive integer k, let ?(k)=|{i∈N:1≤i≤|V|,be(i,G)≤k}|. We show that . 相似文献
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Jie Xiao 《Journal of Differential Equations》2006,224(2):277-295
Let u(t,x) be the solution of the heat equation (∂t-Δx)u(t,x)=0 on subject to u(0,x)=f(x) on Rn. The main goal of this paper is to characterize such a nonnegative measure μ on that f(x)?u(t2,x) induces a bounded embedding from the Sobolev space , p∈[1,n) into the Lebesgue space , q∈(0,∞). 相似文献
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Peter Borg 《Discrete Mathematics》2009,309(14):4750-4753
Families A1,…,Ak of sets are said to be cross-intersecting if for any Ai∈Ai and Aj∈Aj, i≠j. A nice result of Hilton that generalises the Erd?s-Ko-Rado (EKR) Theorem says that if r≤n/2 and A1,…,Ak are cross-intersecting sub-families of , then
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Let ?n∈C∞(Rd?{0}) be a non-radial homogeneous distance function of degree n∈N satisfying ?n(tξ)=tn?n(ξ). For f∈S(Rd+1) and δ>0, we consider convolution operator associated with the smooth cone type multipliers defined by
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Let [n] denote the set of positive integers {1,2,…,n}. An r-partial permutation of [n] is a pair (A,f) where A⊆[n], |A|=r and f:A→[n] is an injective map. A set A of r-partial permutations is intersecting if for any (A,f), (B,g)∈A, there exists x∈A∩B such that f(x)=g(x). We prove that for any intersecting family A of r-partial permutations, we have .It seems rather hard to characterize the case of equality. For 8?r?n-3, we show that equality holds if and only if there exist x0 and ε0 such that A consists of all (A,f) for which x0∈A and f(x0)=ε0. 相似文献
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László Lovász 《Journal of Combinatorial Theory, Series A》2006,113(4):726-735
We prove the following theorem, which is an analog for discrete set functions of a geometric result of Lovász and Simonovits. Given two real-valued set functions f1,f2 defined on the subsets of a finite set S, satisfying for i∈{1,2}, there exists a positive multiplicative set function μ over S and two subsets A,B⊆S such that for i∈{1,2}μ(A)fi(A)+μ(B)fi(B)+μ(A∪B)fi(A∪B)+μ(A∩B)fi(A∩B)?0. The Ahlswede-Daykin four function theorem can be deduced easily from this. 相似文献