Acta Mathematicae Applicatae Sinica, English Series最新文献

This paper considers a linear regression model involving both quantitative and qualitative factors and an m-dimensional response variable y. The main purpose of this paper is to investigate D-optimal designs when the levels of the qualitative factors interact with the levels of the quantitative factors. Under a general covariance structure of the response vector y, here we establish that the determinant of the information matrix of a product design can be separated into two parts corresponding to the two marginal designs. Moreover, it is also proved that D-optimal designs do not depend on the covariance structure if we assume hierarchically ordered system of regression models.

We are concerned with singularity formation of strong solutions to the two-dimensional (2D) full compressible magnetohydrodynamic equations with zero resistivity in a bounded domain. By energy method and critical Sobolev inequalities of logarithmic type, we show that the strong solution exists globally if the temporal integral of the maximum norm of the deformation tensor is bounded. Our result is the same as Ponce’s criterion for 3D incompressible Euler equations. In particular, it is independent of the magnetic field and temperature. Additionally, the initial vacuum states are allowed.

In this paper we deal with the initial-boundary value problem for the coupled Keller-Segel-Stokes system with rotational flux, which is corresponding to the case that the chemical is produced instead of consumed,

subject to the boundary conditions (∇n − nS(x, n, c)∇c) · ν = ∇c · ν = 0 and u = 0, and suitably regular initial data (n₀(x), c₀(x), u₀(x)), where Ω ⊂ ℝ³ is a bounded domain with smooth boundary ∂Ω. Here S is a chemotactic sensitivity satisfying ∣S(x, n, c)∣ ≤ C_S(1 + n)^−α with some C_S > 0 and α > 0. The greatest contribution of this paper is to consider the large time behavior of solutions for the system (KSS), which is still open even in the 2D case. We can prove that the corresponding solution of the system (KSS) decays to (({1 over {|Omega |}}int_Omega {{n_0}} ), ({1 over {|Omega |}}int_Omega {{n_0}} ), 0) exponentially, if the coefficient of chemotactic sensitivity is appropriately small. As a precondition to consider the asymptotic behavior, we also show the global existence and boundedness of the corresponding initial-boundary problem KSS with a simplified method. We find a new phenomenon that the suitably small coefficient C_S of chemotactic sensitivity could benefit the global existence and boundedness of solutions to the model KSS.

An independent set in a graph G is a set of pairwise non-adjacent vertices. The independence polynomial of G is the polynomial (sumlimits_A {{x^{|A|}}} ), where the sum is over all independent sets A of G. In 1987, Alavi, Malde, Schwenk and Erdős conjectured that the independence polynomial of any tree or forest is unimodal. Although this unimodality conjecture has attracted many researchers’ attention, it is still open. Recently, Basit and Galvin even asked a much stronger question whether the independence polynomial of every tree is ordered log-concave. Note that if a polynomial has only negative real zeros then it is ordered log-concave and unimodal. In this paper, we observe real-rootedness of independence polynomials of rooted products of graphs. We find some trees whose rooted product preserves real-rootedness of independence polynomials. In consequence, starting from any graph whose independence polynomial has only real zeros, we can obtain an infinite family of graphs whose independence polynomials have only real zeros. In particular, applying it to trees or forests, we obtain that their independence polynomials are unimodal and ordered log-concave.

In this paper, we are concerned with the the Schrödinger-Newton system with L²-constraint. Precisely, we prove that there cannot exist multi-peak normalized solutions concentrating at k different critical points of V(x) under certain assumptions on asymptotic behavior of V(x) and its first derivatives near these points. Especially, the critical points of V(x) in this paper must be degenerate.

The main tools are a local Pohozaev type of identity and the blow-up analysis. Our results also show that the asymptotic behavior of concentrated points to Schrödinger-Newton problem is quite different from the classical Schrödinger equations, which is mainly caused by the nonlocal term.

This paper considers a multi-state repairable system that is composed of two classes of components, one of which has a priority for repair. First, we investigate the well-posedenss of the system by applying the operator semigroup theory. Then, using Greiner’s idea and the spectral properties of the corresponding operator, we obtain that the time-dependent solution of the system converges strongly to its steady-state solution.

Given a graph G, the adjacency matrix and degree diagonal matrix of G are denoted by A(G) and D(G), respectively. In 2017, Nikiforov^[24] proposed the A_α-matrix: A_α(G) = αD(G) + (1 − α)A(G), where α ∈ [0, 1]. The largest eigenvalue of this novel matrix is called the A_α-index of G. In this paper, we characterize the graphs with minimum A_α-index among n-vertex graphs with independence number i for α ∈ [0, 1), where (i = 1,,,leftlfloor {{n over 2}} rightrfloor,leftlceil {{n over 2}} rightrceil,,leftlfloor {{n over 2}} rightrfloor + 1,n - 3,n - 2,n - 1), whereas for i = 2 we consider the same problem for (alpha in [0,{3 over 4}]). Furthermore, we determine the unique graph (resp. tree) on n vertices with given independence number having the maximum A_α-index with α ∈ [0, 1), whereas for the n-vertex bipartite graphs with given independence number, we characterize the unique graph having the maximum A_α-index with (alpha in [{1 over 2},1)).

This paper introduces two local conditional dependence matrices based on Spearman’s ρ and Kendall’s τ given the condition that the underlying random variables belong to the intervals determined by their quantiles. The robustness is studied by means of the influence functions of conditional Spearman’s ρ and Kendall’s τ. Using the two matrices, we construct the corresponding test statistics of local conditional dependence and derive their limit behavior including consistency, null and alternative asymptotic distributions. Simulation studies illustrate a superior power performance of the proposed Kendall-based test. Real data analysis with proposed methods provides a precise description and explanation of some financial phenomena in terms of mathematical statistics.

We prove that the weak Morrey space WM ^p_q is contained in the Morrey space (M_{{q_1}}^p) for 1 ≤ q₁ < q ≤ p < ∞. As applications, we show that if the commutator [b, T] is bounded from L^p to L^p,∞ for some p ∈ (1, ∞), then b ∈ BMO, where T is a Calderón-Zygmund operator. Also, for 1 < p ≤ q < ∞, b ∈ BMO if and only if [6, T] is bounded from M ^p_q to WM ^p_q . For b belonging to Lipschitz class, we obtain similar results.

Let p, q be two positive integers. The 3-graph F(p, q) is obtained from the complete 3-graph K ³_p by adding q new vertices and (p(_2^q)) new edges of the form vxy for which v ∈ V(K ³_p ) and {x, y} are new vertices. It frequently appears in many literatures on the Turán number or Turán density of hypergraphs. In this paper, we first construct a new class of r-graphs which can be regarded as a generalization of the 3-graph F(p, q), and prove that these r-graphs have the same Turán density under some situations. Moreover, we investigate the Turán density of the F(p, q) for small p, q and obtain some new bounds on their Turán densities.