共查询到20条相似文献,搜索用时 62 毫秒
1.
Mordecai J. Golin 《Discrete Mathematics》2010,310(4):792-803
Let T(G) be the number of spanning trees in graph G. In this note, we explore the asymptotics of T(G) when G is a circulant graph with given jumps.The circulant graph is the 2k-regular graph with n vertices labeled 0,1,2,…,n−1, where node i has the 2k neighbors i±s1,i±s2,…,i±sk where all the operations are . We give a closed formula for the asymptotic limit as a function of s1,s2,…,sk. We then extend this by permitting some of the jumps to be linear functions of n, i.e., letting si, di and ei be arbitrary integers, and examining
2.
Daqing Yang 《Discrete Mathematics》2009,309(13):4614-4623
Let be a directed graph. A transitive fraternal augmentation of is a directed graph with the same vertex set, including all the arcs of and such that for any vertices x,y,z,
- 1.
- if and then or (fraternity);
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- if and then (transitivity).
3.
L Foissy 《Bulletin des Sciences Mathématiques》2003,127(6):505-548
We introduce a functor from the category of braided spaces into the category of braided Hopf algebras which associates to a braided space V a braided Hopf algebra of planar rooted trees . We show that the Nichols algebra of V is a subquotient of . We construct a Hopf pairing between and , generalising one of the results of [Bull. Sci. Math. 126 (2002) 193-239]. When the braiding of c is given by c(vi⊗vj)=qi,jvj⊗vi, we obtain a quantification of the Hopf algebras introduced in [Bull. Sci. Math. 126 (2002) 193-239; 126 (2002) 249-288]. When qi,j=qai,j, with q an indeterminate and (ai,j)i,j the Cartan matrix of a semi-simple Lie algebra , then is a subquotient of . In this case, we construct the crossed product of with a torus and then the Drinfel'd quantum double of this Hopf algebra. We show that is a subquotient of . 相似文献
4.
José J. Ramón Marí 《Advances in Mathematics》2010,224(6):2237-2268
In this paper we give a detailed analysis of the interaction between homological self-correspondences of the general fibre Y/k(t) of the Lefschetz fibration of a Lefschetz pencil on a smooth projective variety X/k, and the Leray filtration of ρ. We derive the result that, if the standard conjecture B(Y) holds, then the operator is algebraic, where is defined as the inverse of L on LPn−1(X) and 0 on LkPj(X) for (1,n−1)≠(k,j); in the course of our proof we see that, under the above assumption, the Künneth projectors for i≠n−1,n,n+1 are algebraic. 相似文献
5.
We consider a process given by the SDE , t∈[0,T), with initial condition , where T∈(0,∞], α∈R, (Bt)t∈[0,T) is a standard Wiener process, b:[0,T)→R?{0} and σ:[0,T)→(0,∞) are continuously differentiable functions. Assuming , t∈[0,T), with some K∈R, we derive an explicit formula for the joint Laplace transform of and for all t∈[0,T) and for all α∈R. Our motivation is that the maximum likelihood estimator (MLE) of α can be expressed in terms of these random variables. As an application, we show that in case of α=K, K≠0,
6.
Stefan Gille 《Advances in Mathematics》2009,220(3):913-2058
Let k be a field with algebraic closure , G a semisimple algebraic k-group, and a maximal torus with character group X(T). Denote Λ the abstract weight lattice of the roots system of G, and by and the n-torsion subgroup of the Brauer group of k and G, respectively. We prove that if chark does not divide n and n is prime to the order of Λ/X(T) then the natural homomorphism is an isomorphism. 相似文献
7.
Jan O. Kleppe 《Journal of Pure and Applied Algebra》2011,215(7):1711-1725
A scheme X⊂Pn of codimension c is called standard determinantal if its homogeneous saturated ideal can be generated by the t×t minors of a homogeneous t×(t+c−1) matrix (fij). Given integers a0≤a1≤?≤at+c−2 and b1≤?≤bt, we denote by the stratum of standard determinantal schemes where fij are homogeneous polynomials of degrees aj−bi and is the Hilbert scheme (if n−c>0, resp. the postulation Hilbert scheme if n−c=0).Focusing mainly on zero and one dimensional determinantal schemes we determine the codimension of in and we show that is generically smooth along under certain conditions. For zero dimensional schemes (only) we find a counterexample to the conjectured value of appearing in Kleppe and Miró-Roig (2005) [25]. 相似文献
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9.
Nikola Kocei? Bilan 《Topology and its Applications》2010,157(5):894-901
The (pointed) coarse shape category Sh* (), having (pointed) topological spaces as objects and having the (pointed) shape category as a subcategory, was recently constructed. Its isomorphisms classify (pointed) topological spaces strictly coarser than the (pointed) shape type classification. In this paper we introduce a new algebraic coarse shape invariant which is an invariant of shape and homotopy, as well. For every pointed space (X,?) and for every k∈N0, the coarse shape group , having the standard shape group for its subgroup, is defined. Furthermore, a functor is constructed. The coarse shape and shape groups already differ on the class of polyhedra. An explicit formula for computing coarse shape groups of polyhedra is given. The coarse shape groups give us more information than the shape groups. Generally, does not imply (e.g. for solenoids), but from pro-πk(X,?)=0 follows . Moreover, for pointed metric compacta (X,?), the n-shape connectedness is characterized by , for every k?n. 相似文献
10.
Hongmei Xie 《Journal of multivariate analysis》2010,101(4):964-970
Let be generalized order statistics based on a continuous distribution function F with parameters k and (m1,…,mn−1). Chen and Hu (2007) [8] investigated the sufficient conditions on F and on the parameters k and mi’s such that , where , and is the Shaked-Shanthikumar multivariate dispersive order. Since the order does not possess the closure property under marginalization, one may naturally wonder whether the corresponding multivariate margins of the above random vectors are also ordered in the order . This is answered affirmatively in this paper. Some comparison results for generalized order statistics from two samples are presented. Potential applications are also mentioned. 相似文献
11.
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
12.
Let H be a Hilbert space and C be a nonempty closed convex subset of H, {Ti}i∈N be a family of nonexpansive mappings from C into H, Gi:C×C→R be a finite family of equilibrium functions (i∈{1,2,…,K}), A be a strongly positive bounded linear operator with a coefficient and -Lipschitzian, relaxed (μ,ν)-cocoercive map of C into H. Moreover, let , {αn} satisfy appropriate conditions and ; we introduce an explicit scheme which defines a suitable sequence as follows:
13.
Ke-Ang Fu 《Journal of Mathematical Analysis and Applications》2009,356(1):280-287
Let be a strictly stationary sequence of positively associated random variables with mean zero and finite variance. Set , Mn=maxk?n|Sk|, n?1. Suppose . In this paper, we study the exact convergence rates of a kind of weighted infinite series of , and as ε↘0, respectively. 相似文献
14.
Given a finite set of 2-dimensional points P⊆R2 and a positive real d, a unit disk graph, denoted by (P,d), is an undirected graph with vertex set P such that two vertices are adjacent if and only if the Euclidean distance between the pair is less than or equal to d. Given a pair of non-negative integers m and n, P(m,n) denotes a subset of 2-dimensional triangular lattice points defined by where . Let Tm,n(d) be a unit disk graph defined on a vertex set P(m,n) and a positive real d. Let be the kth power of Tm,n(1).In this paper, we show necessary and sufficient conditions that [ is perfect] and/or [ is perfect], respectively. These conditions imply polynomial time approximation algorithms for multicoloring (Tm,n(d),w) and . 相似文献
15.
Acyclic edge colouring of planar graphs without short cycles 总被引:1,自引:0,他引:1
Mieczys?aw Borowiecki 《Discrete Mathematics》2010,310(9):1445-2495
Let G=(V,E) be any finite graph. A mapping C:E→[k] is called an acyclic edgek-colouring of G, if any two adjacent edges have different colours and there are no bichromatic cycles in G. In other words, for every pair of distinct colours i and j, the subgraph induced in G by all the edges which have colour i or j, is acyclic. The smallest number k of colours, such that G has an acyclic edge k-colouring is called the acyclic chromatic index of G, denoted by .In 2001, Alon et al. conjectured that for any graph G it holds that ; here Δ(G) stands for the maximum degree of G.In this paper we prove this conjecture for planar graphs with girth at least 5 and for planar graphs not containing cycles of length 4,6,8 and 9. We also show that if G is planar with girth at least 6. Moreover, we find an upper bound for the acyclic chromatic index of planar graphs without cycles of length 4. Namely, we prove that if G is such a graph, then . 相似文献
16.
Agnieszka Görlich 《Discrete Mathematics》2010,310(4):681-686
Let TTn be a transitive tournament on n vertices. It is known Görlich, Pil?niak, Wo?niak, (2006) [3] that for any acyclic oriented graph of order n and size not greater than , two graphs isomorphic to are arc-disjoint subgraphs of TTn. In this paper, we consider the problem of embedding of acyclic oriented graphs into their complements in transitive tournaments. We show that any acyclic oriented graph of size at most is embeddable into all its complements in TTn. Moreover, this bound is generally the best possible. 相似文献
17.
Constantin Tudor 《Journal of Mathematical Analysis and Applications》2009,351(1):456-468
The domain of the Wiener integral with respect to a sub-fractional Brownian motion , , k≠0, is characterized. The set is a Hilbert space which contains the class of elementary functions as a dense subset. If , any element of is a function and if , the domain is a space of distributions. 相似文献
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19.
A k-dimensional box is the cartesian product R1×R2×?×Rk where each Ri is a closed interval on the real line. The boxicity of a graph G, denoted as box(G), is the minimum integer k such that G is the intersection graph of a collection of k-dimensional boxes. A unit cube in k-dimensional space or a k-cube is defined as the cartesian product R1×R2×?×Rk where each Ri is a closed interval on the real line of the form [ai,ai+1]. The cubicity of G, denoted as cub(G), is the minimum k such that G is the intersection graph of a collection of k-cubes. In this paper we show that cub(G)≤t+⌈log(n−t)⌉−1 and , where t is the cardinality of a minimum vertex cover of G and n is the number of vertices of G. We also show the tightness of these upper bounds.F.S. Roberts in his pioneering paper on boxicity and cubicity had shown that for a graph G, and , where n is the number of vertices of G, and these bounds are tight. We show that if G is a bipartite graph then and this bound is tight. We also show that if G is a bipartite graph then . We point out that there exist graphs of very high boxicity but with very low chromatic number. For example there exist bipartite (i.e., 2 colorable) graphs with boxicity equal to . Interestingly, if boxicity is very close to , then chromatic number also has to be very high. In particular, we show that if , s≥0, then , where χ(G) is the chromatic number of G. 相似文献
20.
Kui Liu 《Journal of Number Theory》2011,131(12):2247-2261
Let be the error term of the Riesz mean of the symmetric square L-function. We give the higher power moments of and show that if there exists a real number A0:=A0(ρ)>3 such that , then we can derive asymptotic formulas for , 3?h<A0, h∈N. Particularly, we get asymptotic formulas for , h=3,4,5 unconditionally. 相似文献