Acta Mathematicae Applicatae Sinica, English Series最新文献

An acyclic edge coloring of a graph G is a proper edge coloring such that there are no bichromatic cycles in G. The acyclic chromatic index (cal{X}_{alpha}^{prime}(G)) of G is the smallest k such that G has an acyclic edge coloring using k colors. It was conjectured that every simple graph G with maximum degree Δ has (cal{X}_{alpha}^{prime}(G)leDelta+2). A 1-planar graph is a graph that can be drawn in the plane so that each edge is crossed by at most one other edge. In this paper, we show that every 1-planar graph G without 4-cycles has (cal{X}_{alpha}^{prime}(G)leDelta+22).

In this paper, we consider the clustering of bivariate functional data where each random surface consists of a set of curves recorded repeatedly for each subject. The k-centres surface clustering method based on marginal functional principal component analysis is proposed for the bivariate functional data, and a novel clustering criterion is presented where both the random surface and its partial derivative function in two directions are considered. In addition, we also consider two other clustering methods, k-centres surface clustering methods based on product functional principal component analysis or double functional principal component analysis. Simulation results indicate that the proposed methods have a nice performance in terms of both the correct classification rate and the adjusted rand index. The approaches are further illustrated through empirical analysis of human mortality data.

In this paper, the insurance company considers venture capital and risk-free investment in a constant proportion. The surplus process is perturbed by diffusion. At first, the integro-differential equations satisfied by the expected discounted dividend payments and the Gerber-Shiu function are derived. Then, the approximate solutions of the integro-differential equations are obtained through the sinc method. Finally, the numerical examples are given when the claim sizes follow different distributions. Furthermore, the errors between the explicit solution and the numerical solution are discussed in a special case.

A neighbor sum distinguishing (NSD) total coloring ϕ of G is a proper total coloring of G such that (sumlimits_{z in {E_G}(u) cup {u}} {phi (z) ne} sumlimits_{z in {E_G}(v) cup {v}} {phi (z)} ) for each edge uv ∈ E(G), where EG(u) is the set of edges incident with a vertex u. In 2015, Pilśniak and Woźniak conjectured that every graph with maximum degree Δ has an NSD total (Δ + 3)-coloring. Recently, Yang et al. proved that the conjecture holds for planar graphs with Δ ≥ 10, and Qu et al. proved that the list version of the conjecture also holds for planar graphs with Δ ≥ 13. In this paper, we improve their results and prove that the list version of the conjecture holds for planar graphs with Δ ≥ 10.

We consider the relation between the direction of the vorticity and the global regularity of 3D shear thickening fluids. It is showed that a weak solution to the non-Newtonian incompressible fluid in the whole space is strong if the direction of the vorticity is ({{11 - 5p} over 2})-Hölder continuous with respect to the space variables when (2 < p < {{11} over 5}).

In this paper, we have introduced the concepts of pseudomonotonicity properties for nonlinear transformations defined on Euclidean Jordan algebras. The implications between this property and other P-properties have been studied. More importantly, we have solved the solvability problem of the nonlinear pseudomonotone complementarity problems over symmetric cones.

In this paper, we study a global zero-relaxation limit problem of the electro-diffusion model arising in electro-hydrodynamics which is the coupled Planck-Nernst-Poisson and Navier-Stokes equations. That is, the paper deals with a singular limit problem of

involving with a positive, large parameter ϵ. The present work show a case that (u^ϵ, n^ϵ, c^ϵ) stabilizes to (u^∞, n^∞, c^∞):= (u, n, c) uniformly with respect to the time variable as ϵ → + ∞ with respect to the strong topology in a certain Fourier-Herz space.

Let G be a simple graph and G^σ be the oriented graph with G as its underlying graph and orientation σ. The rank of the adjacency matrix of G is called the rank of G and is denoted by r(G). The rank of the skew-adjacency matrix of G^σ is called the skew-rank of G^σ and is denoted by sr(G^σ). Let V(G) be the vertex set and E(G) be the edge set of G. The cyclomatic number of G, denoted by c(G), is equal to ∣E(G)∣ − ∣V(G)∣+ ω(G), where ω(G) is the number of the components of G. It is proved for any oriented graph G^σ that −2c(G) ⩽ sr(G^σ) − r(G) ⩽ 2c(G). In this paper, we prove that there is no oriented graph G^σ with sr(G^σ) − r(G) = 2c(G)−1, and in addition, there are in nitely many oriented graphs G^σ with connected underlying graphs such that c(G) = k and sr(G^σ)−r(G) = 2c(G)−ℓ for every integers k, ℓ satisfying 0 ⩽ ℓ ⩽ 4k and ℓ≠ 1.

For an integer r ≥ 2 and bipartite graphs H_i, where 1≤ i ≤ r the bipartite Ramsey number br(H₁, H₂, …, H_r) is the minimum integer N such that any r-edge coloring of the complete bipartite graph K_N,N contains a monochromatic subgraph isomorphic to H_i in color i for some 1 ≤ i ≤ r. We show that if (r ge 3,{alpha _1},{alpha _2} > 0,{alpha _{j + 2}} ge [(j + 2)! - 1]sumlimits_{i = 1}^{j + 1} {{alpha _i}} ) for j = 1, 2, …, r −2, then (br({C_{2leftlfloor {{alpha _1},n} rightrfloor }},{C_{2leftlfloor {{alpha _2},n} rightrfloor }}, cdots ,{C_{2leftlfloor {{alpha _r},n} rightrfloor }}) = (sumlimits_{j = 1}^r {{alpha _j} + o(1))n} ).

Given two graphs G and H, the Ramsey number R(G,H) is the minimum integer N such that any two-coloring of the edges of K_N in red or blue yields a red G or a blue H. Let v(G) be the number of vertices of G and χ(G) be the chromatic number of G. Let s(G) denote the chromatic surplus of G, the number of vertices in a minimum color class among all proper χ(G)-colorings of G. Burr showed that (R(G,H) ge (v(G) - 1)(chi (H) - 1) + s(H)) if G is connected and (v(G) ge s(H)). A connected graph G is H-good if (R(G,H) = (v(G) - 1)(chi (H) - 1) + s(H)). Let tH denote the disjoint union of t copies of graph H, and let (G vee H) denote the join of G and H. Denote a complete graph on n vertices by K_n, and a tree on n vertices by T_n. Denote a book with n pages by B_n, i.e., the join ({K_2} vee overline {{K_n}} ). Erdős, Faudree, Rousseau and Schelp proved that T_n is B_m-good if (n ge 3m - 3). In this paper, we obtain the exact Ramsey number of T_n versus 2B₂- Our result implies that T_n is 2B₂-good if n ≥ 5.