Acta Mathematicae Applicatae Sinica, English Series最新文献

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].

In this paper, we consider the symmetric cone linear complementarity problem with the Cartesian P₀-property and present a regularization smoothing method with a nonmonotone line search to solve this problem. It has been demonstrated that the proposed method exhibits global convergence under the condition that the solution set of the complementarity problem is nonempty. This condition is less stringent than those that have appeared in some existing literature. We also show that the method has locally quadratic convergence under appropriate conditions. Some experimental results are reported to illustrate the efficiency of the proposed method.

This paper is concerned with the attraction-repulsion Keller-Segel model with volume filling effect. We consider this problem in a bounded domain Ω ⊂ ℝ³ under zero-flux boundary condition, and it is shown that the volume filling effect will prevent overcrowding behavior, and no blow up phenomenon happen. In fact, we show that for any initial datum, the problem admits a unique global-in-time classical solution, which is bounded uniformly. Previous findings for the chemotaxis model with volume filling effect were derived under the assumption 0 ≤ u₀(x) ≤ 1 with ρ(x,t) ≡ 1. However, when the maximum size of the aggregate is not a constant but rather a function ρ(x,t), ensuring the boundedness of the solutions becomes significantly challenging. This introduces a fundamental difficulty into the analysis.

In this paper, a new distribution named the Lindley-Weibull distribution which combines Lindley and Weibull distributions by using the method of T-X family is introduced. This distribution offers a more flexible model for lifetime data. We study its statistical properties include the shapes of density and hazard rate, residual and reversed residual lifetime, moment, moment generating functions, conditional moment, conditional moment generating, quantiles functions, mean deviations, Rényi entropy, Bonferroni and Loren curves. The distribution is capable of modeling increasing, decreasing, upside-down bathtub and decreasing-increasing-decreasing hazard rate functions. The method of maximum likelihood is adopted for estimating the model parameters. The potentiality of the new model is illustrated by means of one real data set.

In this paper, we discuss the long-time behavior of solutions to the nonclassical diffusion equation with fading memory when the nonlinear term f satisfies critical exponential growth and the external force g(x) ∈ L²(Ω). In the framework of time-dependent spaces, we verify the existence of absorbing sets and the asymptotic compactness of the process, then we obtain the existence of the time-dependent global attractor ({mathscr A}={{A_{t}}}_{tin{mathbb R}}) in ℳ_t. Furthermore, we achieve the regularity of ({mathscr A}), that is, A_t is bounded in ℳ ¹_t with a bound independent of t.

For a graph G of order n and a positive integer k, a k-weak cycle partition of G, called k-WCP, is a sequence of vertex disjoint subgraphs H₁, H₂, ⋯, H_k of G with (bigcupnolimits_{i=1}^{k} V(H_{i})=V(G)), where H_i is isomorphic to K₁, K₂ or a cycle. Let σ₂(G) = min{d(x) + d(y): xy ∉ E(G), x, y ∈ V(G)}. Hu and Li [Discrete Math. 307(2007)] proved that if G is a graph of order n ≥ k + 12 with a k-WCP and (sigma_{2}(G) geq {{2n+k-4} over 3}), then G contains a k-WCP with at most one subgraph isomorphic to K₂. In this paper, we generalize their result on the analogy of Fan-type condition that (max{{d(x),d(y)}} geq {{2n+k-4} over 6}) for each pair of nonadjacent vertices x, y ∈ V(G).