This paper is concerned with an optimal model averaging estimation for linear regression model with right censored data. The weights for model averaging are picked up via minimizing the Mallows criterion. Under some mild conditions, it is shown that the identified weights possess the property of asymptotic optimality, that is, the model averaging estimator corresponding to these weights achieves the lowest squared error asymptotically. Some numerical studies are conducted to evaluate the finite-sample performance of our method and make comparisons with its intuitive competitors, while an application to the PBC dataset is provided to serve as an illustration.

The UK is the most important partner of the EU in terms of economic and other fields due to the geographical proximity. It was one of the largest economies in the EU and its per capita income is higher than the EU average, so it is a net contributor to the EU. With UKs membership of the EU ended on 31 January 2019, there are concerns that the Brexit may have a significant impact on the EU, resulting in social, economic, political, and institutional changes, etc. in EU. While the impact of Brexit on the UK has always been the subject of considerable scholarly interest in recent years, there is relatively little literature on the impact of Brexit on the EU. This paper focuses on the evaluation of the impact of Brexit on the EU economy and other relevant aspects along three dimensions: GDP, PPP, Quarterly GDP growth. Employing powerful quantitative analysis technology that includes vector autoregression model, multivariate time series model with intervention variables, and autoregression integrated moving average, this paper obtains the important and novel evidence about the potential impact of Brexit on the EU economy, pointing out that Brexit is of far-reaching significance to the EU. This analysis uses several statistical models to screen out several key influencing factors, which can be used to predict the total GDP of EU in the next five years. The results show that EU economy will react negatively to "no-deal" Brexit, and its growth rate of economy will slow down significantly in next 5 years. Finally, we put forward relevant policy suggestions on how to deal with the negative impact of Brexit on EU.

In this paper, we consider the initial value problem of a class of fractional differential equations. Firstly, we obtain the existence and uniqueness of the solutions by using Picard’s method of successive approximation. Then we discuss the dependence of the solutions on the initial value.

The traditional approaches to false discovery rate (FDR) control in multiple hypothesis testing are usually based on the null distribution of a test statistic. However, all types of null distributions, including the theoretical, permutation-based and empirical ones, have some inherent drawbacks. For example, the theoretical null might fail because of improper assumptions on the sample distribution. Here, we propose a null distribution-free approach to FDR control for multiple hypothesis testing in the case-control study. This approach, named target-decoy procedure, simply builds on the ordering of tests by some statistic or score, the null distribution of which is not required to be known. Competitive decoy tests are constructed from permutations of original samples and are used to estimate the false target discoveries. We prove that this approach controls the FDR when the score function is symmetric and the scores are independent between different tests. Simulation demonstrates that it is more stable and powerful than two popular traditional approaches, even in the existence of dependency. Evaluation is also made on two real datasets, including an arabidopsis genomics dataset and a COVID-19 proteomics dataset.

As biological studies become more expensive to conduct, it is a frequently encountered question that how to take advantage of the available auxiliary covariate information when the exposure variable is not measured. In this paper, we propose an induced cure rate mean residual life time regression model to accommodate the survival data with cure fraction and auxiliary covariate, in which the exposure variable is only assessed in a validation set, but a corresponding continuous auxiliary covariate is ascertained for all subjects in the study cohort. Simulation studies elucidate the practical performance of the proposed method under finite samples. As an illustration, we apply the proposed method to a heart disease data from the Study of Left Ventricular Dysfunction.

Frequentist model averaging has received much attention from econometricians and statisticians in recent years. A key problem with frequentist model average estimators is the choice of weights. This paper develops a new approach of choosing weights based on an approximation of generalized cross validation. The resultant least squares model average estimators are proved to be asymptotically optimal in the sense of achieving the lowest possible squared errors. Especially, the optimality is built under both discrete and continuous weigh sets. Compared with the existing approach based on Mallows criterion, the conditions required for the asymptotic optimality of the proposed method are more reasonable. Simulation studies and real data application show good performance of the proposed estimators.

In this short note we present a new Harnack expression for the Gaussian curvature flow, which is modeled from the shrinking self similiar solutions. As applications we give alternate proofs of Chow's Harnack inequality and entropy estimate.

In this paper, we derive a time-dependent Ginzburg-Landau model for liquid ⁴He coupling with an applied magnetic field basing on the Le Châtlier principle.
We also obtain the existence and uniqueness of global weak solution for this model. In addition, by utilizing the regularity estimates for linear semigroup, we prove that the model possesses a global classical solution.

Space-filling designs are widely used in various fields because of their nice space-filling properties. Uniform designs are one of space-filling designs, which desires the experimental points to scatter uniformly over the experimental area. For practical need, the construction and their properties of nine-level uniform designs are discussed via two code mappings in this paper. Firstly, the algorithm of constructing nine-level uniform designs is presented from an initial three-level design by the Type-I code mapping and tripling technique. Secondly, the algorithm of constructing nine-level uniform designs is presented from a three-level base design by the Type-II code mapping and generalized orthogonal arrays. Moreover, relative properties are discussed based on the two code mappings. Finally, some numerical examples are given out for supporting our theoretical results.

The authors present some new criteria for oscillation and asymptotic behavior of solutions of third-order nonlinear differential equations with a sublinear neutral term of the form $$\left(r(t)(z''(t))^{\alpha}\right)'+\int^{d}_{c}q(t,\xi)f\left(x\left(\sigma(t,\xi)\right)\right)d\xi=0, \qquad t\geq t_{0}$$ where $z(t)=x(t)+\int^{b}_{a}p(t,\xi)x^{\gamma}\left(\tau(t,\xi)\right)d\xi,~0<\gamma\leq1.$ Under the conditions $\int^{\infty}_{t_{0}}r^{-\frac{1}{\alpha}}(t)dt=\infty$ or $\int^{\infty}_{t_{0}}r^{-\frac{1}{\alpha}}(t)dt<\infty.$ The results obtained here extend, improve and complement to some known results in the literature. Examples are provided to illustrate the theorems.

A graph is 1-planar if it can be drawn on the Euclidean plane so that each edge is crossed by at most one other edge. A proper vertex k-coloring of a graph G is defined as a vertex coloring from a set of k colors such that no two adjacent vertices have the same color. A graph that can be assigned a proper k-coloring is k-colorable. A cycle is a path of edges and vertices wherein a vertex is reachable from itself. A cycle contains k vertices and k edges is a k-cycle. In this paper, it is proved that 1-planar graphs without 4-cycles or 5-cycles are 5-colorable.

This paper proposes an approximate analytical solution method to calculate counterparty credit risk exposures. Compared with the Standard Approach for measuring Counterparty Credit Risk and the Internal Modeling Method provided by Basel Committee, the proposed method significantly improves the calculation efficiency based on sacrificing a little accuracy. Taking Forward Rate Agreement as an example, this article derives the exact expression for Expected Exposure. By approximating the distribution of Forward Rate Agreement’s future value to a normal distribution, the approximate analytical expression for Potential Future Exposure is derived. Numerical results show that this method is reliable and is robust under different parameters.

A tournament is an orientation of the complete graph. Tournaments form perhaps the most interesting class of digraphs and it has a great potential for application. Tournaments provide a model of the statistical technique called the method of paired comparisons and they have also been studied in connection with sociometric relations in small groups. In this paper, we investigate disjoint cycles of the same length in tournaments. In 2010, Lichiardopol conjectured that for given integers l ≥ 3 and k ≥ 1, any tournament with minimum out-degree at least (l - 1)k - 1 contains k disjoint l-cycles, where an l-cycle is a cycle of order l. Bang-Jensen et al. verified the conjecture for l = 3 and Ma et al. proved that it also holds for l ≥ 10. This paper provides a proof of the conjecture for the case of 9 ≥ l ≥ 4

Consider a two-dimensional renewal risk model, in which the claim sizes {X_k; k ≥ 1} form a sequence of i.i.d. copies of a non-negative random vector whose two components are dependent. Suppose that the claim sizes and inter-arrival times form a sequence of i.i.d. random pairs, with each pair obeying a dependence structure via the conditional distribution of the inter-arrival time given the subsequent claim size being large. Then a precise large-deviation formula of the aggregate amount of claims is obtained.

With applications in communication networks, the minimum stretch spanning tree problem is to find a spanning tree T of a graph G such that the maximum distance in T between two adjacent vertices is minimized. The problem has been proved NP-hard and fixed-parameter polynomial algorithms have been obtained for some special families of graphs. In this paper, we concentrate on the optimality characterizations for typical classes of graphs. We determine the exact formulae for the complete k-partite graphs, split graphs, generalized convex graphs, and several planar grids, including rectangular grids, triangular grids, and triangulated-rectangular grids.

The Hosoya index of a graph is the total number of matchings in it. And the Merrifield-Simmons index is the total number of independent sets in it. They are typical examples of graph invariants used in mathematical chemistry for quantifying relevant details of molecular structure. In this paper, we obtain explicit analytical expressions for the expectations of the Hosoya index and the Merrifield-Simmons index of a random polyphenyl chain.

This paper studies the trading behavior of an irrational insider and its influence on the market equilibrium in the presence of market regulation. We find that the market with only one insider with private information is almost close to a strong efficient market, under the condition of market regulation. In the equilibrium, the probability of the insider being caught trading with private information is zero, which shows that the reasonable behavior of the regulator is to essentially give up regulation. But the market efficiency and the irrational trader’s trading intensity all greatly improve because of the existence of the market regulation.

Let G be a simple connected graph with order n. Let L(G) and Q(G) be the normalized Laplacian and normalized signless Laplacian matrices of G, respectively. Let λ_k(G) be the k-th smallest normalized Laplacian eigenvalue of G. Denote by ρ(A) the spectral radius of the matrix A. In this paper, we study the behaviors of λ₂(G) and ρ(L(G)) when the graph is perturbed by three operations. We also study the properties of ρ(L(G)) and X for the connected bipartite graphs, where X is a unit eigenvector of L(G) corresponding to ρ(L(G)). Meanwhile we characterize all the simple connected graphs with ρ(L(G)) = ρ(Q(G)).

So far there have been few results presented on the exponential stability for time-changed stochastic differential equations. The main aim of this work is to fill this gap. By making use of general Lyapunov methods and time-changed Itô formula, we establish the exponential stability and almost sure exponential stability of solution to time-changed SDEs. Finally, we construct some examples to illustrate the effectiveness of our established theory.

A graph G is called a fractional [a, b]-covered graph if for each e ∈ E(G), G contains a fractional [a,b]-factor covering e. A graph G is called a fractional (a,b,k)-critical covered graph if for any W ⊆ V (G) with |W| = k, G - W is fractional [a, b]-covered, which was first defined and investigated by Zhou, Xu and Sun [S. Zhou, Y. Xu, Z. Sun, Degree conditions for fractional (a,b,k)-critical covered graphs, Information Processing Letters 152(2019)105838]. In this work, we proceed to study fractional (a,b,k)-critical covered graphs and derive a result on fractional (a,b,k)-critical covered graphs depending on minimum degree and neighborhoods of independent sets.

In this paper, we investigate dual problems for nonconvex set-valued vector optimization via abstract subdifferential. We first introduce a generalized augmented Lagrangian function induced by a coupling vector-valued function for set-valued vector optimization problem and construct related set-valued dual map and dual optimization problem on the basic of weak efficiency, which used by the concepts of supremum and infimum of a set. We then establish the weak and strong duality results under this augmented Lagrangian and present sufficient conditions for exact penalization via an abstract subdifferential of the object map. Finally, we define the sub-optimal path related to the dual problem and show that every cluster point of this sub-optimal path is a primal optimal solution of the object optimization problem. In addition, we consider a generalized vector variational inequality as an application of abstract subdifferential.

n this paper, we deal with the nonlinear second-order differential equation with damped vibration term involving p-Laplacian operator. Of particular interest is the resolution of an open problem. An interesting outcome from our result is that we can obtain the fast homoclinic solution with general superlinear growth assumption in suitable Sobolev space. To our knowledge, our theorems appear to be the first such result about damped vibration problem with p-Laplacian operator.

A graphic sequence π=(d₁, d₂, ..., d_n) is said to be forcibly k-edge-connected if every realization of π is k-edge-connected. In this paper, we obtain a new sufficient degree condition for π to be forcibly k-edge-connected. We also show that this new sufficient degree condition implies a strongest monotone degree condition for π to be forcibly 2-edge-connected and a conjecture about a strongest monotone degree condition for π to be forcibly 3-edge-connected due to Bauer et al. (Networks, 54(2) (2009) 95-98), and also implies a strongest monotone degree condition for π to be forcibly 4-edge-connected.

In this paper, we consider the one dimensional third order p-Laplacian equation (Φ_p(u"))'+ h(t)f(t, u(t))=0 with integral boundary conditions u(0)-αu'(0)= ∫t₀¹g₁(s)u(s)ds, u(1)+β u'(1)= ∫t₀¹g₂(s)u(s)ds, u"(0)=0. By using kernel functions and the Avery-Peterson fixed point theorem, we establish the existence of at least three positive solutions.

We investigate a diffusive, stage-structured epidemic model with the maturation delay and freelymoving delay. Choosing delays and diffusive rates as bifurcation parameters, the only possible way to destabilize the endemic equilibrium is through Hopf bifurcation. The normal forms of Hopf bifurcations on the center manifold are calculated, and explicit formulae determining the criticality of bifurcations are derived. There are two different kinds of stable oscillations near the first bifurcation: on one hand, we theoretically prove that when the diffusion rate of infected immature individuals is sufficiently small or sufficiently large, the first branch of Hopf bifurcating solutions is always spatially homogeneous; on the other, fixing this diffusion rate at an appropriate size, stable oscillations with different spatial profiles are observed, and the conditions to guarantee the existence of such solutions are given by calculating the corresponding eigenfunction of the Laplacian at the first Hopf bifurcation point. These bifurcation behaviors indicate that spatial diffusion in the epidemic model may lead to spatially inhomogeneous distribution of individuals.

A matching is extendable in a graph G if G has a perfect matching containing it. A distance q matching is a matching such that the distance between any two distinct matching edges is at least q. In this paper, we prove that any distance 2k-3 matching is extendable in a connected and locally (k-1)-connected K_{1, k}-free graph of even order. Furthermore, we also prove that any distance q matching M in an r-connected and locally (k-1)-connected K_{1, k}-free graph of even order is extendable provided that M is bounded by a function on r, k and q. Our results improve some results in [J. Graph Theory 93 (2020), 5-C20].

Several tests for multivariate mean vector have been proposed in the recent literature. Generally, these tests are directly concerned with the mean vector of a high-dimensional distribution. The paper presents two new test procedures for testing mean vector in large dimension and small samples. We do not focus on the mean vector directly, which is a different framework from the existing choices. The first test procedure is based on the asymptotic distribution of the test statistic, where the dimension increases with the sample size. The second test procedure is based on the permutation distribution of the test statistic, where the sample size is fixed and the dimension grows to infinity. Simulations are carried out to examine the finite-sample performance of the tests and to compare them with some popular nonparametric tests available in the literature.

A class of fractional stochastic neutral functional differential equation is analyzed in this paper. With the utilization of the fractional calculations, semigroup theory, fixed point technique and stochastic analysis theory, a sufficient condition of the existence for p-mean almost periodic solution is obtained, which are supported by two examples.

In this work, we study the approximate controllability for a class of semilinear second-order control systems with finite delay. Sufficient conditions for approximate controllability are established by constructing fundamental solutions and using the resolvent condition and techniques on cosine family of linear operators. To illustrate the applications of the obtained results, an example is provided in the end.

In this paper we propose the Gini correlation screening (GCS) method to select the important variables with ultrahigh dimensional data. The new procedure is based on the Gini correlation coefficient via the covariance between the response and the rank of the predictor variables rather than the Pearson correlation and the Kendall τ correlation coefficient. The new method does not require imposing a specific model structure on regression functions and only needs the condition which the predictors and response have continuous distribution function. We demonstrate that, with the number of predictors growing at an exponential rate of the sample size, the proposed procedure possesses consistency in ranking, which is both useful in its own right and can lead to consistency in selection. The procedure is computationally efficient and simple, and exhibits a competent empirical performance in our intensive simulations and real data analysis.

Anomalous diffusion is a widespread physical phenomenon, and numerical methods of fractional diffusion models are of important scientific significance and engineering application value. For time fractional diffusion-wave equation with damping, a difference (ASC-N, alternating segment Crank-Nicolson) scheme with intrinsic parallelism is proposed. Based on alternating technology, the ASC-N scheme is constructed with four kinds of Saul’yev asymmetric schemes and Crank-Nicolson (C-N) scheme. The unconditional stability and convergence are rigorously analyzed. The theoretical analysis and numerical experiments show that the ASC-N scheme is effective for solving time fractional diffusion-wave equation.

The effectiveness of this paper lies in the influence of the discretization step on the asymptotic stability of the positive two-dimensional fractional linear systems. It aims at investigating whether, how and when this step affects the asymptotically stable two-dimensional positive fractional linear continuous-discrete systems. To accomplish this study, a new test was outlined and used so that the asymptotic stability of the system was measured both before and after being exposed to the sampling step. Furthermore, the conditions of that stability were assessed. As a result, the outcome of the approximation shows that the stability is preserved under a particular set of conditions. On this basis, the newly proposed approach is recommended for testing the intended stability of such systems. A numerical example is tested to show the accuracy and the applicability of the proposed tests.

In this paper, we study the existence of positive solution for the $p$-Laplacian equations with fractional critical nonlinearity \[ \begin{cases} (-\Delta)^{s}_{p}u+V(x)|u|^{p-2}u=K(x)f(u)+P(x)|u|^{p^{*}_{s}-2}u, \qquad x\in \mathbb{R}^{N}, \\ u\in \mathcal {D}^{s,p}(\mathbb{R}^{N}), \end{cases} \] where $s\in(0,1), \ p^{*}_{s}=\frac{Np}{N-sp}, \ N>sp, \ p>1$ and $ V(x),K(x)$ are positive continuous functions which vanish at infinity, $f$ is a function with a subcritical growth, and $P(x)$ is bounded, nonnegative continuous function. By using variational method in the weighted spaces, we prove the above problem has at least one positive solution.

In this paper, we study the well-posedness and the asymptotic stability of a one-dimensional thermoelastic microbeam system, where the heat conduction is given by Gurtin-Pipkin thermal law. We first establish the well-posedness of the system by using the semigroup arguments and Lumer-Phillips theorem. We then obtain an explicit and general formula for the energy decay rates through perturbed energy method and some properties of the convex functions.

In this paper, we investigate a delayed HIV infection model that considers the homeostatic proliferation of CD4⁺ T cells. The existence and stability of uninfected equilibrium and infected equilibria (smaller and larger ones) are studied by analyzing the characteristic equation of the system. The intracellular delay does not affect the stability of uninfected equilibrium, but it can change the stability of larger positive equilibrium and Hopf bifurcation appears inducing stable limit cycles. Furthermore, direction and stability of Hopf bifurcation are well investigated by using the central manifold theorem and the normal form theory. The numerical simulation results show that the stability region of larger positive equilibrium becomes smaller as the increase of time delay. Moreover, when the maximum homeostatic growth rate is very small, the larger positive equilibrium is always stable. On the contrary, when the rate of supply of T cells is very small, the larger positive equilibrium is always unstable.

In this paper we first establish the uniform regularity of smooth solutions with respect to the viscosity coefficients to the isentropic compressible magnetohydrodynamic system in a periodic domain $\mathbb{T}^n$. We then apply our result to obtain the isentropic compressible magnetohydrodynamic system with zero viscosity.

Let $m$, $t$, $r$ and $k_i$ $(1\leq i\leq m)$ be positive integers with $k_i\geq\frac{(t+3)r}{2}$, and $G$ be a digraph with vertex set $V(G)$ and arc set $E(G)$. Let $H_1,H_2,\cdots,H_t$ be $t$ vertex-disjoint subdigraphs of $G$ with $mr$ arcs. In this article, it is verified that every $[0,k_1+k_2+\cdots+k_m-(m-1)r]$-digraph $G$ has a $[0,k_i]_1^{m}$-factorization $r$-orthogonal to every $H_i$ for $1\leq i\leq t$.

This paper investigates the stabilization and synchronization of two fractional chaotic maps proposed recently, namely the 2D fractional Hénon map and the 3D fractional generalized Hénon map. We show that although these maps have non–identical dimensions, their synchronization is still possible. The proposed controllers are evaluated experimentally in the case of non–identical orders or time–varying orders. Numerical methods are used to illustrate the results.

In this paper, we focus on the immiscible compressible two-phase flow described by the coupled compressible Navier-Stokes system and the modified Allen-Cahn equations. The generalized Navier boundary condition and the relaxation boundary condition are established in order to solve the problem of moving contact lines on the solid boundary by using the principle of minimum energy dissipation. The existence and uniqueness for local strong solution in three dimensional bounded domain for this type of boundary value problem is obtained by the elementary energy method and the maximum principle.

The Turán number of a k-uniform hypergraph H, denoted by ex_k (n; H), is the maximum number of edges in any k-uniform hypergraph F on n vertices which does not contain H as a subgraph. Let C_e^(k) denote the family of all k-uniform minimal cycles of length e, S(e₁, ..., e_r) denote the family of hypergraphs consisting of unions of r vertex disjoint minimal cycles of length e₁, ..., e_r, respectively, and C_e^(k) denote a k-uniform linear cycle of length e. We determine precisely ex_k(n; S(e₁, ..., e_r)) and ex_k(n; C_e1^(k), ..., C_er^(k)) for sufficiently large n. Our results extend recent results of Füredi and Jiang who determined the Turán numbers for single k-uniform minimal cycles and linear cycles.