For a positive continuous function f satisfying some standard conditions, we study the f-moments of continuous-state branching processes with or without immigration. The main results give criteria for the existence of the f-moments. The characterization of the processes in terms of stochastic equations plays an essential role in the proofs.

Let X1, X2, ⋯, Xn, ⋯ be a sequence of i.i.d. random variables uniformly distributed on [0; 1], and denote by Ln the length of the longest increasing subsequences of X1, X2, ⋯, Xn. Consider the poissonized version H̃n based on Hammersley’s representation in the 2-dimensional space. A law of the iterated logarithm for H̃n is established using the well-known subsequence method and Borel-Cantelli lemma

This paper presents a novel genetic algorithm for globally solving un-constraint optimization problem. In this algorithm, a new real coded crossover operator is proposed firstly. Furthermore, for improving the convergence speed and the searching ability of our algorithm, the good point set theory rather than random selection is used to generate the initial population, and the chaotic search operator

By using a split argument due to [1], the transportation cost inequality is established on the free path space of Markov processes. The general result is applied to stochastic reaction diffusion equations with random initial values.

In this paper, we first consider the classical p-median location problem on a network in which the vertex weights and the distances between vertices are uncertain variables. The uncertainty distribution of the optimal objective value of the p-median problem is given and the concepts of the α-p-median, the most p-median and the expected p-median are introduced. Then, it is shown that the uncertain p-median

In this paper, we study the dispersive properties of multi-symplectic discretizations for the nonlinear Schrödinger equations. The numerical dispersion relation and group velocity are investigated. It is found that the numerical dispersion relation is relevant when resolving the nonlinear Schrödinger equations.

In this paper, we study the stochastic partial differential equation with two reflecting smooth walls h1 and h2, driven by a fractional noise, which is fractional in time and white in space. The large deviation principle for the law of the solution to this equation, will be established through developing a classical method. Furthermore, we obtain the Hölder continuity of the solution.

Riccati equation approach is used to look for exact travelling wave solutions of some nonlinear physical models. Solitary wave solutions are established for the modified KdV equation, the Boussinesq equation and the Zakharov-Kuznetsov equation. New generalized solitary wave solutions with some free parameters are derived. The obtained solutions, which includes some previously known solitary wave solutions

The vertex-arboricity a(G) of a graph G is the minimum number of colors required for a vertex coloring of G such that no cycle is monochromatic. The list vertex-arboricity al(G) is the list-coloring version of this concept. In this paper, we prove that every planar graph G without intersecting 5-cycles has al(G) ≤ 2. This extends a result by Raspaud and Wang [On the vertex-arboricity of planar graphs

Let xn, n ≥ 0} be a Markov chain with a countable state space S and let f(·) be a measurable function from S to ℝ and consider the functionals of the Markov chain yn:= f(xn). We construct a new type of self-normalized sums based on the random-block scheme and establish a Cramér-type moderate deviations for self-normalized sums of functionals of the Markov chain.

In this paper, by using an extension of Mawhin’s continuation theorem and some analysis methods, we study the existence of periodic solutions for the following prescribed mean curvature system $$\frac{d}{{dt}}\varphi \left( {x'} \right) + \nabla W\left( x \right) = p\left( t \right),$$ where x ∊ ℝn, W ∊ C1(ℝn, ℝ), p ∊ C(ℝ, ℝn) is T-periodic and $$\varphi \left( x \right)\frac{x}{{\sqrt {1 + |x{|^2}}

In this paper, nonconforming finite element methods (FEMs) are proposed for the constrained optimal control problems (OCPs) governed by the nonsmooth elliptic equations, in which the popular \(EQ_1^{rot}\) element is employed to approximate the state and adjoint state, and the piecewise constant element is used to approximate the control. Firstly, the convergence and superconvergence properties for

Let p be a prime, q be a power of p, and let Fq be the field of q elements. For any positive integer n, the Wenger graph Wn(q) is defined as follows: it is a bipartite graph with the vertex partitions being two copies of the (n+ 1)-dimensional vector space \(\mathbb{F}_q^{n+1}\), and two vertices p= (p(1),..., p(n+1)) and l = [l(1),...,l(n+1)] being adjacent if p+1(i) = p(1)l(1)i−1, for all i = 2,

In functional data analysis, the collected data are often assumed to be fully observed on the domain. However, in dealing with real data (for example, environmental pollution data), we are often faced with the scenario that some functional data are fully observed on dense lattice while others are incompletely observed. In this paper, we propose a method for testing equivalence of mean functions of

We combine the robust criterion with the lasso penalty together for the high-dimensional threshold model. It estimates regression coeffcients as well as the threshold parameter robustly that can be resistant to outliers or heavy-tailed noises and perform variable selection simultaneously. We illustrate our approach with the absolute loss, the Huber’s loss, and the Tukey’s loss, it can also be extended

In this paper, the modified projective synchronization between two fractional-order chaotic systems with different dimensions is investigated. The added-order scheme and the reduced-order scheme are proposed, respectively. Based on the Laplace transformation and feedback control theory, controllers are designed such that two chaotic systems with different dimensions could be synchronized asymptotically

In this paper, we study the periodic solutions to a type of differential delay equations with 2k − 1 lags. The 4k-periodic solutions are obtained by using the variational method and the method of Kaplan-Yorke coupling system. This is a new type of differential delay equations compared with all the previous researches. And this paper provides a theoretical basis for the study of differential delay equations

A robust and efficient shrinkage-type variable selection procedure for varying Coefficient models is proposed, selection consistency and oracle properties are established. Furthermore, a BIC-type criterion is suggested for shrinkage parameter selection and theoretical property is discussed. Numerical studies and real data analysis also are included to illustrate the finite sample performance of our

A new approach to modeling populations incorporating stochasticity, a random environment, and individual behavior is illustrated with a specific example of two interacting populations: rabbits and grass. The derivation of the system of stochastic partial differential equations (SPDEs) to show how the individual mechanisms of both populations are included. This model also has an unusual feature of a

This paper discusses robust nonparametric estimators of location regression function for errors-in-variables model with de-convolution kernel. The local constant smoother is used for the estimation of the nonparametric function, and the local linear smoother is proposed to deal with the boundary problem, as well as to improve the local constant smoother. We establish the asymptotic properties of the

In many statistical applications, data are collected over time, and they are likely correlated. In this paper, we investigate how to incorporate the correlation information into the local linear regression. Under the assumption that the error process is an auto-regressive process, a new estimation procedure is proposed for the nonparametric regression by using local linear regression method and the