Báo cáo toán học: "A Beurling-Lax theorem for the Lie group U(m,n) which contains most classical interpolation theory " pot
Báo cáo toán học: " Weak convergence theorem for the three-step iterations of non-Lipschitzian nonself mappings in Banach spaces" pptx
... (2004)doi:10.1186/1687-1812-2011-106Cite this article as: Zhu et al.: Weak convergence theorem for the three-step iterations of non-Lipschitzian nonself mappings in Banach spaces. Fixed Point Theory and Applications 2011 2011:106.Submit ... Shahzad, N: Convergence theorems for a common fixed point of finite family of nonself nonexpansive mappings. Fixed Point Theory Appl. 2005,1–9 (2005)15. Shahzad, N: Approximating fixed points of non-self ... 225002, ChinaAbstract In this article, we introduce a new three-step iterative scheme for the mappings which are asymptotically nonexpansive in the intermediate sense in Banach spaces. Weak convergence...
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Báo cáo toán học: "A LOWER BOUND FOR THE NUMBER OF EDGES IN A GRAPH CONTAINING NO TWO CYCLES OF THE SAME LENGTH" pptx
... v(G) denote the number of vertices, and (G) denote the number of edges. In thispaper, we construct a graph G having no two cycles with the same length which leads to the following result.Theorem. ... Chunhui Lai, On the size of graphs with all cycle having distinct length, DiscreteMath. 122(1993) 363-364.[6] Chunhui Lai, The edges in a graph in which no two cycles have the same length, J.Zhangzhou ... Acknowledgment The author thanks Prof. Yair Caro and Raphael Yuster for sending reference [7]. The author also thanks Prof. Cheng Zhao for his advice.References[1] J .A. Bondy and U.S.R....
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Báo cáo toán học: "A reciprocity theorem for domino tilings" pptx
... extended to T(m,n) for all m.It is worth remarking that the reciprocity theorem satisfied by the Laurent polynomialsM((m,n)) is a bit more complicated than the reciprocity theorem satisfied by ... is worth mentioning here that Cohn has proved a different reciprocity theorem for domino tilings [1]; it is unclear to me whether his Theorem 1 is related to the result treated here.It is also ... sign-factorεm,n, there is also a monomial factor involving the vari-ables. A comprehensive reciprocity theorem for domino tilings of rectangles would take thisinto account. I intend to write a longer...
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Báo cáo toán học: "A simple proof for the existence of exponentially balanced Gray codes" ppsx
... is the number of times the integer i occurs in the sequence T . Note that the sum of all b(i), 1 ≤ i ≤ n,isequaltol, the length of T .3 A simple proof for the existence of exponentially balanced ... two, or are two successive powers of two. A proof for the existence of exponentially balanced Gray codes is derived. The proof is much sim-pler than an earlier proof presented by van Zanten and ... A simple proof for the existence of exponentially balanced Gray codesI Nengah Suparta∗Department of Applied MathematicsFaculty of Electrical Engineering, Mathematics and Computer...
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Báo cáo toán học: "An addition theorem on the cyclic group Zpαqβ" pptx
... A1+ A2+ ···+ Ak, the electronic journal of combinatorics 13 (2006), #N9 2 An addition theorem on the cyclic group ZpαqβHui-Qin CaoDepartment of Applied MathematicsNanjing Audit ... Proof of Theorem 1For any subset A of an abelian group G let H(A) denote the maximal subgroup of G suchthat A + H(A)=A. What we state below is a classical theorem of Kneser [3].Kneser’s Theorem ... denote the maximal multiplicity of the terms of S.In 1961, Erd˝os-Ginzburg-Ziv [1] proved the following theorem. EGZ Theorem If S is a sequence of elements from Znof length 2n− 1, then 0 ∈nS.The...
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Báo cáo toán học: "A sharp bound for the reconstruction of partitions" ppt
... agree above row r and to the left of column c (and the definitions of r and c) we see that the only possibility for /à is (r, c), completing the proof of this case and the theorem.Acknowledgements. ... 308, 9 (2008), 1524–1530. the electronic journal of combinatorics 15 (2008), #N23 4 A sharp bound for the reconstruction of partitionsVincent VatterDepartment of MathematicsDartmouth CollegeHanover, ... ).Finally, recall that the conjugate of a partition λ is the partition λobtained by flipping the diagram of λ across the NW-SE axis; it follows that λicounts the number of entries of λ which are...
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Báo cáo toán học: "A closed formula for the number of convex permutominoes" pot
... interpretation of the closed formula (10) for the number of con-vex permutominoes. We remark that the expression of fnresembles the expression(1) for the number cn of convex polyominoes of semi-perimeter ... : the uppermost cell of the rightmost column of the polyomino has the maximalordinate among all the cells of the polyomino;U2 : the lowest cell of the rightmost column of the polyomino has the ... parameters, using the simple remark that the number fn of convex permutominoes of size n is given by the number of objects at level n of the generatingtree of Ω, n ≥ 1, assuming without loss of generality...
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Báo cáo toán học: "A natural series for the natural logarithm" pot
... that those formulae yield interesting power series expansions for the logarithm function. This generalizes an infinite series of Lehmer for the natural logarithm of 4.1 The abelian case: the Mahler ... fundamental group of the knot complement. For a square matrixM with entries in CG the trace trCG(M) denotes the coefficient of the unit element in the sum of the diagonal elements. The matrix A∗= ... a)2j=n≥11nnj=0nj−1k2jjl=02j2j − 2l, l, l,where the terms in the inner most sum are multinomial coefficients. the electronic journal of combinatorics 15 (2008), #N5 4 A natural series for the natural logarithmOliver...
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Báo cáo toán học: "A normalization formula for the Jack polynomials in superspace and an identity on partitions" pps
... bi in P[k]j,i. the electronic journal of combinatorics 16 (2009), #R70 18 A normalization formula for the Jack polynomials in superspace and an identity on partitionsLuc Lapointe∗Instituto ... where σj and ∂jare respectively the interchang e and divided difference operators on the variables aj and aj+1(see for instance [6]). The main step in this approach is to the electronic journal ... P[k],+j−1,i−1 The first equality comes from Lemma 12, the second by induction on i for ∆[k],+j,i−1 and by the induction hypothesis for ∆[k−1],+j−1,i−1. We then recognize P[k+1]j,i on the right hand...
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Báo cáo toán học: "A Colorful Involution for the Generating Function for Signed Stirling Numbers of the First Kind" pps
... Beissinger, who was the first to explore [1]combinatorial proofs using colored permutations, for their assistance.References[1] Janet Beissinger. Colorful proofs of generating function identities. ... follows for (π, f ) ∈ Sn,A: If R(π,f)= ∅, let φ((π, f)) = (π, f).Otherwise, let (i, j) ∈ R(π,f)be minimal under the lexicographic ordering of R(π,f). Let˜π = (i, j) ◦ π, the product of the ... of CambridgeStudies in Advanced Mathematics. Cambridge University Press, Cambridge, 1997.With a foreword by Gian-Carlo Rota, Corrected reprint of the 1986 original. the electronic journal of...
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Báo cáo toán học: "A recurrence relation for the “inv” analogue of q-Eulerian polynomials" ppsx
... A recurrence relation for the “inv” analogue of q-Eulerian polynomialsChak-On ChowDepartment of Mathematics and Information Technology,Hong Kong Institute of Education,10 Lo ... relation algebraically. In the final section, we givea combinatorial proof of this recurrence relation. 2 The recurrence relation We derive in the present section the recurrence relation by algebraic ... denote, resp ectively, the descent number and inversion number of σ in the symmetric group Sn of degree n. We give an algebraic proof and acombinatorial proof of the recurrence relation. 1 IntroductionLet...
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Báo cáo toán học: "A Combinatorial Formula for the Hilbert Series of bigraded Sn-modules" ppsx
... t). The basic idea of the proof of Theorem 3.1 is to show Fà(q, t) and Gà(q, t) satisfy the same recursion in the hook case.Proof. We first note the Garsia-Haiman recursion for the Hilbert series ... to the product of the weights of each of its entries, here the weight of entry s in T is taken to be the weight of the corner square containing s in the pa rt itio nobtained from the shape of ... is the the number of columns of height equal to the height of the column of iin the tableau obtained by removing all the entries j > i from T , and bj(T ) is the number of cells in the...
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Báo cáo toán học: "A Decomposition Algorithm for the Oriented Adjacency Graph of the Triangulations of a Bordered Surface with Marked Point" potx
... is a signed adjacency matrix associated to an ideal triangulation of a bordered surface with marked points (S, M), and G is a quiver. If B(G) = B, we sayG is the oriented adjacency graph associated ... class of an adjacency matrix associated to a triangulation of a bordered surface with marked points is finite (Corollary 12.2 in [2]). It is also proved in [2] that an integer matrix B isan adjacency ... II:Triangle IIIa:Infork IIIb:Outfork IV:D ia mond V:SquareTable 1: Blocks The algorithm also helps to retrieve the triangulations and surfaces that a decompos-able graph G is associated with. ...
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Báo cáo toán học: "A short proof for the number of permutations containing pattern 321 exactly once" ppt
... a short proof for the result of Noonan [3] that the number of permutations of length n containing exactly one occurence of pattern 321 is3n2nn−3.(To be precise, Noonan considered permutations ... A short proof for the number of permutations containing pattern 321 exactly onceAlexander BursteinDepartment of MathematicsHoward UniversityWashington, ... Published: Sep 2, 2011Mathematics Subject Classification: 05A05, 05A15AbstractWe give a short proof for J. Noonan’s result on the number of permutations containing pattern 321 exactly once.In this...
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