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131.
We give a very simple and elementary proof of the existence of a weakly compact family of probability measures {Pθ : θ∈θ} representing an important sublinear expectation- G-expectation E[·]. We also give a concrete approximation of a bounded continuous function X(ω) by an increasing sequence of cylinder functions Lip(Ω) in order to prove that Cb(Ω) belongs to the completion of Lip(Ω) under the natural norm E[|·|]. 相似文献
132.
Using Frobenius partitions we extend the main results of [4]. This leads to an infinite family of 4-way combinatorial identities. In some particular cases we get even 5-way combinatorial identities which give us four new combinatorial versions of Göllnitz-Gordon identities. 相似文献
133.
We present a randomized -approximation algorithm for the weighted maximum triangle packing problem, for any given ε>0. This is the first algorithm for this problem whose performance guarantee is better than . The algorithm also improves the best-known approximation bound for the maximum 2-edge path packing problem. 相似文献
134.
Motivated by the relation , holding for the -generalized Catalan numbers of type and , the connection between dominant regions of the -Shi arrangement of type and is investigated. More precisely, it is explicitly shown how copies of the set of dominant regions of the -Shi arrangement of type , biject onto the set of type such regions. This is achieved by exploiting two different viewpoints of the representative alcove of each region: the Shi tableau and the abacus diagram. In the same line of thought, a bijection between copies of the set of -Dyck paths of height
and the set of lattice paths inside an rectangle is provided. 相似文献
135.
For n even, a factorization of a complete graph Kn is a partition of the edges into n?1 perfect matchings, called the factors of the factorization. With respect to a factorization, a path is called rainbow if its edges are from distinct factors. A rainbow Hamiltonian path takes exactly one edge from each factor and is called orthogonal to the factorization. It is known that not all factorizations have orthogonal paths. Assisted by a simple edge‐switching algorithm, here we show that for n?8, the rotational factorization of Kn, GKn has orthogonal paths. We prove that this algorithm finds a rainbow path with at least (2n+1)/3 vertices in any factorization of Kn (in fact, in any proper coloring of Kn). We also give some problems and conjectures about the properties of the algorithm. © 2010 Wiley Periodicals, Inc. J Combin Designs 18: 167–176, 2010 相似文献
136.
In this paper, we study the vector invariants of the 2-dimensional indecomposable representation V2 of the cyclic group, Cp, of order p over a field F of characteristic p, FCp[mV2]. This ring of invariants was first studied by David Richman (1990) [20] who showed that the ring required a generator of degree m(p−1), thus demonstrating that the result of Noether in characteristic 0 (that the ring of invariants of a finite group is always generated in degrees less than or equal to the order of the group) does not extend to the modular case. He also conjectured that a certain set of invariants was a generating set with a proof in the case p=2. This conjecture was proved by Campbell and Hughes (1997) in [3]. Later, Shank and Wehlau (2002) in [24] determined which elements in Richman's generating set were redundant thereby producing a minimal generating set.We give a new proof of the result of Campbell and Hughes, Shank and Wehlau giving a minimal algebra generating set for the ring of invariants FCp[mV2]. In fact, our proof does much more. We show that our minimal generating set is also a SAGBI basis for FCp[mV2]. Further, our results provide a procedure for finding an explicit decomposition of F[mV2] into a direct sum of indecomposable Cp-modules. Finally, noting that our representation of Cp on V2 is as the p-Sylow subgroup of SL2(Fp), we describe a generating set for the ring of invariants F[mV2]SL2(Fp) and show that (p+m−2)(p−1) is an upper bound for the Noether number, for m>2. 相似文献
137.
We investigate bounds on the chromatic number of a graph G derived from the nonexistence of homomorphisms from some path \begin{eqnarray*}\vec{P}\end{eqnarray*} into some orientation \begin{eqnarray*}\vec{G}\end{eqnarray*} of G. The condition is often efficiently verifiable using boolean matrix multiplications. However, the bound associated to a path \begin{eqnarray*}\vec{P}\end{eqnarray*} depends on the relation between the “algebraic length” and “derived algebraic length” of \begin{eqnarray*}\vec{P}\end{eqnarray*}. This suggests that paths yielding efficient bounds may be exponentially large with respect to G, and the corresponding heuristic may not be constructive. © 2009 Wiley Periodicals, Inc. J Graph Theory 63: 198–209, 2010 相似文献
138.
W. Mader 《Journal of Graph Theory》2010,65(1):61-69
A result of G. Chartrand, A. Kaugars, and D. R. Lick [Proc Amer Math Soc 32 (1972), 63–68] says that every finite, k‐connected graph G of minimum degree at least ?3k/2? contains a vertex x such that G?x is still k‐connected. We generalize this result by proving that every finite, k‐connected graph G of minimum degree at least ?3k/2?+m?1 for a positive integer m contains a path P of length m?1 such that G?V(P) is still k‐connected. This has been conjectured in a weaker form by S. Fujita and K. Kawarabayashi [J Combin Theory Ser B 98 (2008), 805–811]. © 2009 Wiley Periodicals, Inc. J Graph Theory 65: 61–69, 2010. 相似文献
139.
Francesca D’Anna Camilla Zaira Lanza Salvatore Marullo Raffaella Spisani 《Tetrahedron》2010,66(29):5442-5450
By using a multi-parameter approach (a combination of Hammett/Ingold-Yukawa-Tsuno/Fujita-Nishioka free energy relationships) the mononuclear rearrangements of heterocycles (MRH) rates for five new ortho-substituted and ten new di-, tri-, or tetra-substituted (Z)-arylhydrazones of 5-amino-3-benzoyl-1,2,4-oxadiazole into the relevant (2-aryl-5-phenyl-2H-1,2,3-triazol-4-yl)ureas (in dioxane/water and in a large range of pS+ values) have been related to the electronic and proximity effects exerted by the present substituents, also considering previous results on some mono meta- and para-substituted (Z)-arylhydrazones. In every case, excellent correlation coefficients have been calculated (r2 or R2≥0.996). Once more the study of MRH has furnished an interesting panel of different reactivity (three pathways of reaction have been evidenced: general-base-catalyzed, uncatalyzed, and specific-acid-catalyzed) and this has been useful in enlightening how polysubstitution can differently affect the MRH rates. Moreover 2,6-disubstitution on the (Z)-arylhydrazono moiety causes a significant increase of the reactivity in all of the three studied pathways. All of the collected data appear useful for understanding structure-reactivity/activity relationships in polysubstituted compounds. 相似文献
140.
《Journal of Graph Theory》2018,88(3):402-410
We improve by an exponential factor the lower bound of Körner and Muzi for the cardinality of the largest family of Hamilton paths in a complete graph of n vertices in which the union of any two paths has maximum degree 4. The improvement is through an explicit construction while the previous bound was obtained by a greedy algorithm. We solve a similar problem for permutations up to an exponential factor. 相似文献