共查询到20条相似文献,搜索用时 15 毫秒
1.
Ruifeng ZHANG 《Frontiers of Mathematics in China》2022,17(6):1169
We introduce the notion of measurable n-sensitivity for measure preserving systems, and study the relation between measurable n-sensitivity and the maximal pattern entropy. We prove that, if (X, B, µ, T) is ergodic, then (X, B, µ, T) is measurable n-sensitive but not measurable (n+1)-sensitive if and only if hµ*(T) = log n, where hµ* (T) is the maximal pattern entropy of T. 相似文献
2.
On the Characterization of Maximal Planar Graphs with a Given Signed Cycle Domination Number
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Xiao Ming Pi 《数学学报(英文版)》2018,34(5):911-920
Let G =(V, E) be a simple graph. A function f : E → {+1,-1} is called a signed cycle domination function(SCDF) of G if ∑_(e∈E(C))f(e) ≥ 1 for every induced cycle C of G. The signed cycle domination number of G is defined as γ'_(sc)(G) = min{∑_(e∈E)f(e)| f is an SCDF of G}. This paper will characterize all maximal planar graphs G with order n ≥ 6 and γ'_(sc)(G) = n. 相似文献
3.
A graph G with n vertices is said to be embeddable (in its complement) if there is an automorphism φ of Kn such that E(G) ∩ E(φ(G))=. It is known that all trees T with n (≥2) vertices and T K1,n−1 are embeddable. We say that G is 1-embeddable if, for every edge e, there is an automorphism φ of Kn such that E(G) ∩ E(φ(G))={e};and that it is 2-embeddable if,for every pair e1, e2 of edges, there is an automorphism φ of Kn such that E(G) ∩ E(φ(G))={e1, e2}. We prove here that all trees with n (3) vertices are 1-embeddable; and that all trees T with n (4) vertices and T K1,n−1 are 2-embeddable. In a certain sense, this result is sharp. 相似文献
4.
Homogenization of Elliptic Problems with Neumann Boundary Conditions in Non-smooth Domains
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Jun Geng 《数学学报(英文版)》2018,34(4):612-628
We consider a family of second-order elliptic operators {L_ε} in divergence form with rapidly oscillating and periodic coefficients in Lipschitz and convex domains in R~n. We are able to show that the uniform W~(1,p) estimate of second order elliptic systems holds for 2n/(n+1)-δ p 2n/(n-1)+ δ where δ 0 is independent of ε and the ranges are sharp for n = 2, 3. And for elliptic equations in Lipschitz domains, the W~(1,p) estimate is true for 3/2-δ p 3 + δ if n ≥ 4, similar estimate was extended to convex domains for 1 p ∞. 相似文献
5.
Let a(n)be the Fourier coefficients of a holomorphic cusp form of weightκ=2n≥12 for the full modular group and A(x)=∑_(n≤x)a(n).In this paper,we establish an asymptotic formula of the fourth power moment of A(x)and prove that ∫T1A~4(x)dx=3/(64κπ~4)s_4;2()T~(2κ)+O(T~(2κ-δ_4+ε))with δ_4=1/8,which improves the previous result. 相似文献
6.
Let G be a k-regular vertex transitive graph with connectivity κ(G)=k and let mk(G) be the number of vertex cuts with k vertices. Define m(n,k)=min{mk(G): GTn,k}, where Tn,k denotes the set of all k-regular vertex transitive graphs on n vertices with κ(G)=k. In this paper, we determine the exact values of m(n,k). 相似文献
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8.
In a simple digraph, a star of degree t is a union of t edges with a common tail. The k-domination number γk(G) of digraph G is the minimum number of stars of degree at most k needed to cover the vertex set. We prove that γk(T)=n/(k+1) when T is a tournament with n14k lg k vertices. This improves a result of Chen, Lu and West. We also give a short direct proof of the result of E. Szekeres and G. Szekeres that every n-vertex tournament is dominated by at most lg n−lglg n+2 vertices. 相似文献
9.
Given graph G=(V,E) on n vertices, the profile minimization problem is to find a one-to-one function f:V→{1,2,…,n} such that ∑vV(G){f(v)−minxN[v] f(x)} is as small as possible, where N[v]={v}{x: x is adjacent to v} is the closed neighborhood of v in G. The trangulated triangle Tl is the graph whose vertices are the triples of non-negative integers summing to l, with an edge connecting two triples if they agree in one coordinate and differ by 1 in the other two coordinates. This paper provides a polynomial time algorithm to solve the profile minimization problem for trangulated triangles Tl with side-length l. 相似文献
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11.
We study the number of solutions N(B,F) of the diophantine equation n_1n_2 = n_3 n_4,where 1 ≤ n_1 ≤ B,1 ≤ n_3 ≤ B,n_2,n_4 ∈ F and F[1,B] is a factor closed set.We study more particularly the case when F={m = p_1~(ε1)···p_k~(εk),ε_j∈{0,1},1 ≤ j ≤ k},p_1,...,p_k being distinct prime numbers. 相似文献
12.
On partial regularity of suitable weak solutions to the stationary fractional Navier–Stokes equations in dimension four and five
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In this paper, we investigate the partial regularity of suitable weak solutions to the multidimensional stationary Navier Stokes equations with fractional power of the Laplacian (-△)~α 1 and α≠ 1/2). It is shown that the n + 2-6α(3 ≤ n ≤ 5) dimensional Hausdorff measure of the set of the possible singular points of suitable weak solutions to the system is zero, which extends a recent result of Tang and Yu [19] to four and five dimension. Moreover, the pressure in e-regularity criteria is an improvement of corresponding results in [1, 13, 18, 20]. 相似文献
13.
In this paper, we prove that for-1/2 ≤β≤0.suppose M is an invariant subspaces of the Hardy Sobolev spaces H_β~2(D) for T_z~β, then M() zM is a generating wandering subspace of M, that is,M=[MzM]_T_z~β Moreover, any non-trivial invariant subspace M of H_β~2(D) is also generated by the quasi-wandering subspace P_MT_z~βM~⊥ that is,M=[P_MT_z~βM~⊥]_(T_z~β). 相似文献
14.
Let(X, ω) be a compact Hermitian manifold of complex dimension n. In this article,we first survey recent progress towards Grauert–Riemenschneider type criteria. Secondly, we give a simplified proof of Boucksom's conjecture given by the author under the assumption that the Hermitian metric ω satisfies ?■ω~l= for all l, i.e., if T is a closed positive current on X such that ∫_XT_(ac)~n 0, then the class {T } is big and X is Kahler. Finally, as an easy observation, we point out that Nguyen's result can be generalized as follows: if ?■ω = 0, and T is a closed positive current with analytic singularities,such that ∫_XT_(ac)~n 0, then the class {T} is big and X is Kahler. 相似文献
15.
Bipartite dimensions and bipartite degrees of graphs 总被引:2,自引:0,他引:2
A cover (bipartite) of a graph G is a family of complete bipartite subgraphs of G whose edges cover G's edges. G'sbipartite dimension d(G) is the minimum cardinality of a cover, and its bipartite degree η(G) is the minimum over all covers of the maximum number of covering members incident to a vertex. We prove that d(G) equals the Boolean interval dimension of the irreflexive complement of G, identify the 21 minimal forbidden induced subgraphs for d 2, and investigate the forbidden graphs for d n that have the fewest vertices. We note that for complete graphs, d(Kn) = [log2n], η(Kn) = d(Kn) for n 16, and η(Kn) is unbounded. The list of minimal forbidden induced subgraphs for η 2 is infinite. We identify two infinite families in this list along with all members that have fewer than seven vertices. 相似文献
16.
We study the Dirichlet problem of the n-dimensional complex Monge–Ampère equation det(uij) = F/|z|~(2α), where 0 α n. This equation comes from La Nave–Tian's continuity approach to the Analytic Minimal Model Program. 相似文献
17.
Xuding Zhu 《Discrete Mathematics》1998,190(1-3):215-222
Suppose G is a graph. The chromatic Ramsey number rc(G) of G is the least integer m such that there exists a graph F of chromatic number m for which the following is true: for any 2-colouring of the edges of F there is a monochromatic subgraph isomorphic to G. Let Mn = min[rc(G): χ(G) = n]. It was conjectured by Burr et al. (1976) that Mn = (n − 1)2 + 1. This conjecture has been confirmed previously for n 4. In this paper, we shall prove that the conjecture is true for n = 5. We shall also improve the upper bounds for M6 and M7. 相似文献
18.
Tomasz Rybicki 《数学学报(英文版)》2017,33(8):1061-1072
The notion of n-transitivity can be carried over from groups of diffeomorphisms on a manifold M to groups of bisections of a Lie groupoid over M. The main theorem states that the n-transitivity is fulfilled for all n ∈ N by an arbitrary group of Cr-bisections of a Lie groupoid Γ of class Cr, where 1 ≤ r ≤ ω, under mild conditions. For instance, the group of all bisections of any Lie groupoid and the group of all Lagrangian bisections of any symplectic groupoid are n-transitive in the sense of this theorem. In particular, if Γ is source connected for any arrow γ ∈ Γ, there is a bisection passing through γ. 相似文献
19.
Let G be a graph of order n, and let a and b be integers such that 1a<b. Let δ(G) be the minimum degree of G. Then we prove that if δ(G)(k−1)a, n(a+b)(k(a+b)−2)/b, and |NG(x1)NG(x2)NG(xk)|an/(a+b) for any independent subset {x1,x2,…,xk} of V(G), where k2, then G has an [a,b]-factor. This result is best possible in some sense. 相似文献
20.
A. V. Ivashchenko 《Discrete Mathematics》1993,120(1-3):107-114
Every graph can be represented as the intersection graph on a family of closed unit cubes in Euclidean space En. Cube vertices have integer coordinates. The coordinate matrix, A(G)={vnk} of a graph G is defined by the set of cube coordinates. The imbedded dimension of a graph, Bp(G), is a number of columns in matrix A(G) such that each of them has at least two distinct elements vnk≠vpk. We show that Bp(G)=cub(G) for some graphs, and Bp(G)n−2 for any graph G on n vertices. The coordinate matrix uses to obtain the graph U of radius 1 with 3n−2 vertices that contains as an induced subgraph a copy of any graph on n vertices. 相似文献