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**排序方式：**共有233条查询结果，搜索用时 24 毫秒

1.

Maomao Cai 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(13):4581-4588

An explicit integro-differential equation formulation is derived for surface ocean waves with finite depth. The equation involves only 2D surface variables. For this equation, we establish the stability and existence of solutions, and explain the effect of depth on surface wave properties. 相似文献

2.

Pawe? Pra?at 《Graphs and Combinatorics》2011,27(4):567-584

A model for

*cleaning*a graph with brushes was recently introduced. Let*α*= (*v*_{1},*v*_{2}, . . . ,*v*_{ n }) be a permutation of the vertices of*G*; for each vertex*v*_{ i }let ${N^+(v_i)=\{j: v_j v_i \in E {\rm and} j>\,i\}}${N^+(v_i)=\{j: v_j v_i \in E {\rm and} j>\,i\}} and*N*^{-}(*v*_{i})={*j*:*v*_{j}*v*_{i}?*E*and*j*<*i*}{N^-(v_i)=\{j: v_j v_i \in E {\rm and} j<\,i\}} ; finally let*b*_{a}(*G*)=?_{i=1}^{n}max{|*N*^{+}(*v*_{i})|-|*N*^{-}(*v*_{i})|,0}{b_{\alpha}(G)=\sum_{i=1}^n {\rm max}\{|N^+(v_i)|-|N^-(v_i)|,0\}}. The*Broom*number is given by*B*(*G*) = max_{ α }*b*_{ α }(*G*). We consider the Broom number of*d*-regular graphs, focusing on the asymptotic number for random*d*-regular graphs. Various lower and upper bounds are proposed. To get an asymptotically almost sure lower bound we use a degree-greedy algorithm to clean a random*d*-regular graph on*n*vertices (with*dn*even) and analyze it using the differential equations method (for fixed*d*). We further show that for any*d*-regular graph on*n*vertices there is a cleaning sequence such at least*n*(*d*+ 1)/4 brushes are needed to clean a graph using this sequence. For an asymptotically almost sure upper bound, the pairing model is used to show that at most*n*(*d*+2?{*d*ln2})/4{n(d+2\sqrt{d \ln 2})/4} brushes can be used when a random*d*-regular graph is cleaned. This implies that for fixed large*d*, the Broom number of a random*d*-regular graph on*n*vertices is asymptotically almost surely \frac*n*4(*d*+Q(?*d*)){\frac{n}{4}(d+\Theta(\sqrt{d}))}. 相似文献3.

The single 2 dilation wavelet multipliers in one-dimensional case and single

*A*-dilation (where*A*is any expansive matrix with integer entries and |det*A*| = 2) wavelet multipliers in twodimensional case were completely characterized by Wutam Consortium (1998) and Li Z., et al. (2010). But there exist no results on multivariate wavelet multipliers corresponding to integer expansive dilation matrix with the absolute value of determinant not 2 in*L*^{2}(ℝ^{2}). In this paper, we choose $2I_2 = \left( {{*{20}c} 2 & 0 \\ 0 & 2 \\ } \right)$2I_2 = \left( {\begin{array}{*{20}c} 2 & 0 \\ 0 & 2 \\ \end{array} } \right) as the dilation matrix and consider the 2*I*_{2}-dilation multivariate wavelet Φ = {*ψ*_{1},*ψ*_{2},*ψ*_{3}}(which is called a dyadic bivariate wavelet) multipliers. Here we call a measurable function family*f*= {*f*_{1},*f*_{2},*f*_{3}} a dyadic bivariate wavelet multiplier if Y_{1}= {*F*^{ - 1}(*f*_{1}[^(y_{1})] ),*F*^{ - 1}(*f*_{2}[^(y_{2})] ),*F*^{ - 1}(*f*_{3}[^(y_{3})] ) }\Psi _1 = \left\{ {\mathcal{F}^{ - 1} \left( {f_1 \widehat{\psi _1 }} \right),\mathcal{F}^{ - 1} \left( {f_2 \widehat{\psi _2 }} \right),\mathcal{F}^{ - 1} \left( {f_3 \widehat{\psi _3 }} \right)} \right\} is a dyadic bivariate wavelet for any dyadic bivariate wavelet Φ = {*ψ*_{1},*ψ*_{2},*ψ*_{3}}, where [^(*f*)]\hat f and*F*^{−1}denote the Fourier transform and the inverse transform of function*f*respectively. We study dyadic bivariate wavelet multipliers, and give some conditions for dyadic bivariate wavelet multipliers. We also give concrete forms of linear phases of dyadic MRA bivariate wavelets. 相似文献4.

It was conjectured by A. Bouchet that every bidirected graph which admits a nowhere-zero

*k*-flow admits a nowhere-zero 6-flow. He proved that the conjecture is true when 6 is replaced by 216. O. Zyka improved the result with 6 replaced by 30. R. Xu and C. Q. Zhang showed that the conjecture is true for 6-edge-connected graph, which is further improved by A. Raspaud and X. Zhu for 4-edge-connected graphs. The main result of this paper improves Zyka’s theorem by showing the existence of a nowhere-zero 25-flow for all 3-edge-connected graphs. 相似文献5.

With graphs considered as natural models for many network design problems, edge connectivity

*κ*′(*G*) and maximum number of edge-disjoint spanning trees*τ*(*G*) of a graph*G*have been used as measures for reliability and strength in communication networks modeled as graph*G*(see Cunningham, in J ACM 32:549–561, 1985; Matula, in Proceedings of 28th Symposium Foundations of Computer Science, pp 249–251, 1987, among others). Mader (Math Ann 191:21–28, 1971) and Matula (J Appl Math 22:459–480, 1972) introduced the maximum subgraph edge connectivity \({\overline{\kappa'}(G) = {\rm max} \{\kappa'(H) : H {\rm is} \, {\rm a} \, {\rm subgraph} \, {\rm of} G \}}\) . Motivated by their applications in network design and by the established inequalities $$\overline{\kappa'}(G) \ge \kappa'(G) \ge \tau(G),$$ we present the following in this paper:- For each integer
*k*> 0, a characterization for graphs*G*with the property that \({\overline{\kappa'}(G) \le k}\) but for any edge*e*not in*G*, \({\overline{\kappa'}(G + e) \ge k+1}\) . - For any integer
*n*> 0, a characterization for graphs*G*with |*V*(*G*)| =*n*such that*κ*′(*G*) =*τ*(*G*) with |*E*(*G*)| minimized.

6.

A non-increasing sequence \({\pi = (d_1, d_2, \ldots, d_n)}\) of non-negative integers is said to be

*graphic*if it is the degree sequence of a simple graph*G*on*n*vertices. Let*A*be an (additive) abelian group. An extremal problem for a graphic sequence to have an*A*-connected realization is considered as follows: determine the smallest even integer \({\sigma (A, n)}\) such that each graphic sequence \({\pi = (d_1, d_2, \ldots, d_n)}\) with*d*_{ n }≥ 2 and \({\sigma (\pi) = d_1 + d_2 + \cdots +d_n \ge \sigma (A, n)}\) has an*A*-connected realization. In this paper, we determine \({\sigma (A, n)}\) for |*A*| ≥ 5 and*n*≥ 3. 相似文献7.

Tutte introduced the theory of nowhere zero flows and showed that a plane graph

*G*has a face*k*-coloring if and only if*G*has a nowhere zero*A*-flow, for any Abelian group*A*with |*A*|≥*k*. In 1992, Jaeger et al. [9] extended nowhere zero flows to group connectivity of graphs: given an orientation*D*of a graph*G*, if for any*b*:*V*(*G*)?*A*with ∑_{v∈V(G)}*b*(*v*)=0, there always exists a map*f*:*E*(*G*)?*A*−{0}, such that at each*v*∈*V*(*G*), in*A*, then*G*is*A*-connected. Let*Z*_{3}denote the cyclic group of order 3. In [9], Jaeger et al. (1992) conjectured that every 5-edge-connected graph is*Z*_{3}-connected. In this paper, we proved the following.(i) Every 5-edge-connected graph is *Z*_{3}-connected if and only if every 5-edge-connected line graph is*Z*_{3}-connected.(ii) Every 6-edge-connected triangular line graph is *Z*_{3}-connected.(iii) Every 7-edge-connected triangular claw-free graph is *Z*_{3}-connected.

8.

**Abstract.**Subdivision with finitely supported masks is an efficient method to create discrete multiscale representations of smooth surfaces for CAGD applications. Recently a new subdivision scheme for triangular meshes, called

*subdivision*, has been studied. In comparison to dyadic subdivision, which is based on the dilation matrix

*2I*,

*M*with det

*M=3*. This has certain advantages, for example, a slower growth for the number of control points. This paper concerns the problem of achieving maximal sum rule orders for stationary

*2n*in

**Z**

^{ 2 }, and obtain exact formulas for the maximal sum rule order for arbitrary

*n*. For approximating schemes, the solution is simple, and schemes with maximal sum rule order are realized by an explicit family of schemes based on repeated averaging [15]. In the interpolating case, we use properties of multivariate Lagrange polynomial interpolation to prove the existence of interpolating schemes with maximal sum rule orders. These can be found by solving a linear system which can be reduced in size by using symmetries. From this, we construct some new examples of smooth (

*C*

^{ 2 }

*,C*

^{ 3 }) interpolating

9.

Tutte conjectured that every 4-edge-connected graph admits a nowhere-zero

*Z*_{3}-flow and Jaeger et al. [Group connectivity of graphs–a nonhomogeneous analogue of nowhere-zero flow properties, J. Combin. Theory Ser. B 56 (1992) 165-182] further conjectured that every 5-edge-connected graph is*Z*_{3}-connected. These two conjectures are in general open and few results are known so far. A weaker version of Tutte’s conjecture states that every 4-edge-connected graph with each edge contained in a circuit of length at most 3 admits a nowhere-zero*Z*_{3}-flow. Devos proposed a stronger version problem by asking if every such graph is*Z*_{3}-connected. In this paper, we first answer this later question in negative and get an infinite family of such graphs which are not*Z*_{3}-connected. Moreover, motivated by these graphs, we prove that every 6-edge-connected graph whose edge set is an edge disjoint union of circuits of length at most 3 is*Z*_{3}-connected. It is a partial result to Jaeger’s*Z*_{3}-connectivity conjecture. Received: May 23, 2006. Final version received: January 13, 2008 相似文献10.

The Berge-Fulkerson Conjecture states that

*every cubic bridgeless graph has six perfect matchings such that every edge of the graph is contained in exactly two of these perfect matchings*. In this paper, a useful technical lemma is proved that*a cubic graph**G**admits a Berge-Fulkerson coloring*if and only if*the graph**G**contains a pair of edge-disjoint matchings**M*_{1}*and**M*_{2}such that (i)*M*_{1}∪*M*_{2}*induces a*2-*regular subgraph of**G*and (ii)*the suppressed graph*,*the graph obtained from**G*?*M*_{i}*by suppressing all degree*-2-*vertices, is*3-*edge-colorable for each**i*=1,2. This lemma is further applied in the verification of Berge-Fulkerson Conjecture for some families of non-3-edge-colorable cubic graphs (such as,*Goldberg snarks, flower snarks*). 相似文献