Acta Mathematicae Applicatae Sinica, English Series最新文献

The traditional simple random sampling (SRS) design method is ine cient in many cases. Statisticians proposed some new designs to increase e ciency. In this paper, as a variation of moving extremes ranked set sampling (MERSS), double MERSS (DMERSS) is proposed and its properties for estimating the population mean are considered. It turns out that, when the underlying distribution is symmetric, DMERSS gives unbiased estimators of the population mean. Also, it is found that DMERSS is more e cient than the SRS and MERSS methods for usual symmetric distributions (normal and uniform). For asymmetric distributions considered in this study, the DMERSS has a small bias and it is more e cient than SRS for usual asymmetric distribution (exponential) for small sample sizes.

The classical Archimedean approximation of π uses the semiperimeter or area of regular polygons inscribed in or circumscribed about a unit circle in ℝ² and it is well-known that by using linear combinations of these basic estimates, modern extrapolation techniques can greatly speed up the approximation process. Similarly, when n vertices are randomly selected on the circle, the semiperimeter and area of the corresponding random inscribed and circumscribing polygons are known to converge to π almost surely as n → ∞, and by further applying extrapolation processes, faster convergence rates can also be achieved through similar linear combinations of the semiperimeter and area of these random polygons. In this paper, we further develop nonlinear extrapolation methods for approximating π through certain nonlinear functions of the semiperimeter and area of such polygons. We focus on two types of extrapolation estimates of the forms ({{cal X}_n} = {cal S}_n^alpha {cal A}_n^beta ) and ({{cal Y}_n}(p) = {(alpha {cal S}_n^p + beta {cal A}_n^p)^{1/p}}) where α + β = 1, p ≠ 0, and ({{cal S}_n}) and ({{cal A}_n}) respectively represents the semiperimeter and area of a random n-gon inscribed in the unit circle in ℝ², and ({{cal X}_n}) may be viewed as the limit of ({{cal Y}_n}(p)) when p → 0. By deriving probabilistic asymptotic expansions with carefully controlled error estimates for ({{cal X}_n}) and ({{cal Y}_n}(p)), we show that the choice α = 4/3, β= −1/3 minimizes the approximation error in both cases, and their distributions are also asymptotically normal.

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}).

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.

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.