Acta Mathematicae Applicatae Sinica, English Series最新文献

In this paper, we consider the regular s-level fractional factorial split-plot (FFSP) designs when the subplot (SP) factors are more important. The idea of general minimum lower-order confounding criterion is applied to such designs, and the general minimum lower-order confounding criterion of type SP (SP-GMC) is proposed. Using a finite projective geometric formulation, we derive explicit formulae connecting the key terms for the criterion with the complementary set. These results are applied to choose optimal FFSP designs under the SP-GMC criterion. Some two- and three-level SP-GMC FFSP designs are constructed.

We examine a quasilinear system of viscoelastic equations in this study that have fractional boundary conditions, dispersion, source, and variable-exponents. We discovered that the solution of the system is global and constrained under the right assumptions about the relaxation functions and initial conditions. After that, it is demonstrated that the blow-up has negative initial energy. Subsequently, the growth of solutions is demonstrated with positive initial energy, and the general decay result in the absence of the source term is achieved by using an integral inequality due to Komornik.

In this work, we consider the inverse scattering transform and multi-soliton solutions of the sextic nonlinear Schrödinger equation. The Jost functions of spectral problem are derived directly, and the scattering data with t = 0 are obtained accordingly to analyze the symmetry and other related properties of the Jost functions. Then we make use of translation transformation to get the relation between potential and kernel, and recover potential according to Gel’fand-Levitan-Marchenko (GLM) integral equations. Furthermore, the time evolution of scattering data is considered, on the basis of that, the multi-soliton solutions are derived. In addition, some solutions of the equation are analyzed and revealed its dynamic behavior via graphical analysis, which could enrich the nonlinear phenomena of the sextic nonlinear Schrödinger equation.

Given two non-empty graphs G, H and a positive integer k, the Gallai-Ramsey number gr_k(G: H) is defined as the minimum integer N such that for all n ≥ N, every exact k-edge-coloring of K_n contains either a rainbow copy of G or a monochromatic copy of H. Denote gr_k′(G: H) as the minimum integer N such that for all n ≥ N, every edge-coloring of K_n using at most k colors contains either a rainbow copy of G or a monochromatic copy of H. In this paper, we get some exact values or bounds for gr_k(P₅: H) and gr_k′(P₅: H), where H is a cycle or a book graph. In addition, our results support a conjecture of Li, Besse, Magnant, Wang and Watts in 2020.

A majority coloring of a directed graph is a vertex-coloring in which every vertex has the same color as at most half of its out-neighbors. Kreutzer et al. conjectured that every digraph is majority 3-colorable. For an integer k ≥ 2, ({1 over {k}})-majority coloring of a directed graph is a vertex-coloring in which every vertex v has the same color as at most ({1 over {k}}{d^{+}}(v)) of its out-neighbors. Girão et al. proved that every digraph admits a ({1 over {k}})-majority 2k-coloring. In this paper, we prove that Kreutzer’s conjecture is true for digraphs under some conditions, which improves Kreutzer’s results, also we obtained some results of ({1 over {k}})-majority coloring of digraphs. Moreover, we discuss the majority 3-coloring of random digraphs with some conditions.

Inspired by the idea of stochastic quantization proposed by Parisi and Wu, we reconstruct the transition probability function that has a central role in the renormalization group using a stochastic differential equation. From a probabilistic perspective, the renormalization procedure can be characterized by a discrete-time Markov chain. Therefore, we focus on this stochastic dynamic, and establish the local Poincaré inequality by calculating the Bakry-Émery curvature for two point functions. Finally, we choose an appropriate coupling relationship between parameters K and T to obtain the Poincaré inequality of two point functions for the limiting system. Our method extends the classic Bakry-Émery criterion, and the results provide a new perspective to characterize the renormalization procedure.

In this paper, we focus on the problem of nonparametric quantile regression with left-truncated and right-censored data. Based on Nadaraya-Watson (NW) Kernel smoother and the technique of local linear (LL) smoother, we construct the NW and LL estimators of the conditional quantile. Under strong mixing assumptions, we establish asymptotic representation and asymptotic normality of the estimators. Finite sample behavior of the estimators is investigated via simulation, and a real data example is used to illustrate the application of the proposed methods.

We study a multivariate linear Hawkes process with random marks. In this paper, we establish that a central limit theorem, a moderate deviation principle and an upper bound of large deviation for multivariate marked Hawkes processes hold.

In this paper, we focus on a control-constrained stochastic LQ optimal control problem via backward stochastic differential equation (BSDE in short) with deterministic coefficients. One of the significant features in this framework, in contrast to the classical LQ issue, embodies that the admissible control set needs to satisfy more than the square integrability. By introducing two kinds of new generalized Riccati equations, we are able to announce the explicit optimal control and the solution to the corresponding H-J-B equation. A linear quadratic recursive utility portfolio optimization problem in the financial engineering is discussed as an explicitly illustrated example of the main result with short-selling prohibited. Feasibility of the mean-variance portfolio selection problem via BSDE for a financial market is characterized, and associated efficient portfolios are given in a closed form.

In the present paper, we study uniqueness and nondegeneracy of positive solutions to the general Kirchhoff type equations

where M: [0, +∞) ↦ ℝ is a continuous function satisfying some suitable conditions and v ∈ H¹(ℝ^N). Applying our results to the case M(t) = at + b, a, b > 0, we make it clear all the positive solutions for all dimensions N ≥ 1. Our results can be viewed as a generalization of the corresponding results of Li et al. [JDE, 2020, 268, Section 1.2].