In this paper, we concern the Klein-Gordon-Maxwell system with steep potential well $$\left\{{\matrix{{- {\rm{\Delta u +}}\left({\lambda a\left(x \right) + 1} \right)u - \left({2\omega + \phi} \right)\phi u = f\left({x,u} \right),} \hfill & {{\rm{in}}\,{\mathbb{R}^3},} \hfill \cr {- {\rm{\Delta}}\phi {\rm{=}} - \left({\omega + \phi} \right){u^2},} \hfill & {{\rm{in}}\,{\mathbb{R}^3}.} \hfill \cr}}

Stochastic gradient descent (SGD) is one of the most common optimization algorithms used in pattern recognition and machine learning. This algorithm and its variants are the preferred algorithm while optimizing parameters of deep neural network for their advantages of low storage space requirement and fast computation speed. Previous studies on convergence of these algorithms were based on some traditional

In this paper, we propose a new nonmonotone trust region Barzilai-Borwein (BB for short) method for solving unconstrained optimization problems. The proposed method is given by a novel combination of a modified Metropolis criterion, BB-stepsize and trust region method. The new method uses the reciprocal of BB-stepsize to approximate the Hessian matrix of the objective function in the trust region subproblems

A matching M of a graph G is an induced matching if no two edges in M are joined by an edge of G. Let iz(G) denote the total number of induced matchings of G, named iz-index. It is well known that the Hosoya index of a graph is the total number of matchings and the Hosoya index of a path can be calculated by the Fibonacci sequence. In this paper, we investigate the iz-index of graphs by using the Fibonacci-Narayana

for graphs F and G, let F → (G, G) denote that any red/blue edge coloring of F contains a monochromatic G. De ne Folkman number f(G; t) to be the smallest order of a graph F such that F → (G, G) and ω(F) ≤ t. It is shown that f(G; t) ≤ cn for p-arrangeable graphs with n vertices, where p ≥ 1, c = c(p) and t = t(p) are positive constants.

In epidemiological and clinical studies, the restricted mean lifetime is often of direct interest quantity. The differences of this quantity can be used as a basis of comparing several treatment groups with respect to their survival times. When the factor of interest is not randomized and lifetimes are subject to both dependent and independent censoring, the imbalances in confounding factors need to

The admissibility of the initial-boundary data, which characterizes the existence of solution for the initial-boundary value problem, is important. Based on the Fokas method and the inverse scattering transformation, an approach is developed to solve the initial-boundary value problem of the nonlinear Schrödinger equation on a finite interval. A necessary and sufficient condition for the admissibility

We investigate a hyperbolic system of one-dimensional isothermal fluid with liquid-vapor phase transition. The refraction-reflection phenomena are intensively analyzed when elementary waves travel across the two-phase interface. We apply the characteristic method and hodograph transform of Riemann to reduce the nonlinear PDEs to a concise form. Specially for the case of incident rarefaction wave, reduced

Cost effective sampling design is a problem of major concern in some experiments especially when the measurement of the characteristic of interest is costly or painful or time consuming. In the current paper, a modification of ranked set sampling (RSS) called moving extremes RSS (MERSS) is considered for the estimation of the location parameter for location family. A maximum likelihood estimator (MLE)

The paper is devoted to the homogenization of elliptic systems in divergence form. We obtain uniform interior as well as boundary Lipschitz estimates in a bounded C1, γ domain when the coefficients are Dini continuous, inhomogeneous terms are divergence of Dini continuous functions and the boundary functions have Dini continuous derivatives. The results extend Avellaneda and Lin’s work [Comm. Pure

Identity by descent (IBD) sharing is a very important genomic feature in population genetics which can be used to reconstruct recent demographic history. In this paper we provide a framework to estimate IBD sharing for a demographic model called two-population model with migration. We adopt the structured coalescent theory and use a continuous-time Markov jump process {X(t), t ≥ 0} to describe the

In this paper, we assume that the pest population is divided into susceptible pests and infected pests, and only susceptible pests do harm to crops. Considering the two methods of spraying pesticides and releasing infected pests and natural enemies to control susceptible pests (the former is applied more frequently), and assuming that only susceptible pests develop resistance to pesticides, a pest

An m × k matrix is said to be a d-row (column) antimagic matrix if its row-sums (column-sums) form an arithmetic progression with a difference d. The goal of this paper is to obtain the existence theorems and construction methods of some d-row (column) antimagic matrices. Using these results we give the necessary and sufficient condition for the existence of an (m, d)-partition of [1, mk].

This paper deals with an initial boundary value problem for a class of nonlinear wave equation with nonlinear damping and source terms whose solution may blow up in finite time. An explicit lower bound for blow up time is determined by means of a differential inequality argument if blow up occurs.

In this paper, we explore two conjectures about Rademacher sequences. Let (εi) be a Rademacher sequence, i.e., a sequence of independent {−1, 1}-valued symmetric random variables. Set Sn = a1ε1 + … + anεn for a = (a1, …, an) ∈ ℝn. The rst conjecture says that P (|Sn| ≤ ‖a‖) ≥ \({\mathbb{R}^n}\) for all a ∈ ℝn and n ∈ \(\mathbb{N}\). The second conjecture says that P (|Sn| ≥ ‖a‖) ≥ \({\mathbb{R}^n}\)

A nonincreasing sequence π = (d1,…,dn) of nonnegative integers is a graphic sequence if it is realizable by a simple graph G on n vertices. In this case, G is referred to as a realization of π. Given a graph H, a graphic sequence π is potentially H-graphic if π has a realization containing H as a subgraph. For graphs G1 and G2, the potential-Ramsey number rpot(G1, G2) is the smallest integer k such

In the paper, we characterize a necessary and sufficient condition which ensures the continuities of the non-centered Hardy-Littlewood maximal function Mf and the centered Hardy-Littlewood maximal function Mcf on ℝn. As two applications, we can easily deduce that Mcf and Mf are continuous if f is continuous, and Mf is continuous if f is of local bounded variation on ℝ.

In present note, we apply the Leibniz formula with the nabla operator in discrete fractional calculus (DFC) due to obtain the discrete fractional solutions of a class of associated Bessel equations (ABEs) and a class of associated Legendre equations (ALEs), respectively. Thus, we exhibit a new solution method for such second order linear ordinary differential equations with singular points.

We consider a nonlocal boundary value problem for a viscoelastic equation with a Bessel operator and a weighted integral condition and we prove a general decay result. We also give an example to show that our general result gives the optimal decay rate for ceratin polynomially decaying relaxation functions. This result improves some other results in the literature.

A path in an edge-colored graph G is called a rainbow path if no two edges of the path are colored the same color. The minimum number of colors required to color the edges of G such that every pair of vertices are connected by at least k internally vertex-disjoint rainbow paths is called the rainbow k-connectivity of the graph G, denoted by rck(G). For the random graph G(n,p), He and Liang got a sharp

An orbit code is a special constant dimension subspace code, which is an orbit of a subgroup of a general linear group acting on the set of all subspaces in the given ambient space. This paper presents some methods of constructing new orbit codes from known orbit codes. Firstly, we introduce the sum operation, intersection operation and union operation of subspace codes, and then we give some methods

The paper gives a new method to identify significant effects in two-level factorial experiments, and compares the new method with the exiting methods using Monte Carlo simulation. The existing methods only perform well under the assumption of effect sparsity, but the new method performs well without effect sparsity.

In this paper, we consider the existence and uniqueness of the mild solutions for a class of fractional non-autonomous evolution equations with delay and Caputo’s fractional derivatives. By using the measure of noncompactness, β-resolvent family, fixed point theorems and Banach contraction mapping principle, we improve and generalizes some related results on this topic. At last, we give an example

An n × n matrix A consisting of nonnegative integers is a general magic square of order n if the sum of elements in each row, column, and main diagonal is the same. A general magic square A of order n is called a magic square, denoted by MS(n), if the entries of A are distinct. A magic square A of order n is normal if the entries of A are n2 consecutive integers. Let A*d denote the matrix obtained

In this paper, we study a nonlinear Petrovsky type equation with nonlinear weak damping, a superlinear source and time-dependent coefficients $${u_{tt}} + {{\rm{\Delta }}^2}u + {k_1}\left(t \right){\left| {{u_t}} \right|^{m - 2}}{u_t} = {k_2}\left(t \right){\left| u \right|^{p - 2}}u,\,\,\,\,\,\,\,\,\,\,x \in {\rm{\Omega,}}\,\,\,{\rm{t > 0,}}$$ where Ω is a bounded domain in Rn. Under certain conditions

A new kind of tangent derivative, M-derivative, for set-valued function is introduced with help of a modified Dubovitskij-Miljutin cone. Several generalized pseudoconvex set-valued functions are introduced. When both the objective function and constraint function are M-derivative, under the assumption of near conesubconvexlikeness, by applying properties of the set of strictly efficient points and

In this paper we investigate the existence of the periodic solutions of a nonlinear differential equation with a general piecewise constant argument, in short DEPCAG, that is, the argument is a general step function. We consider the critical case, when associated linear homogeneous system admits nontrivial periodic solutions. Criteria of existence of periodic solutions of such equations are obtained

In this paper, we give a Gröbner-Shirshov basis of quantum group of type ℂ3 by using the Ringel-Hall algebra approach. For this, first we compute all skew-commutator relations between the isoclasses of indecomposable reprersentations of Ringel-Hall algebras of type ℂ3 by using an “inductive” method. Precisely, we do not use the traditional way of computing the skew-commutative relations, that is first

In this paper we prove that every compact invariant subset \(\mathscr{A}\) associated with the semigroup Sn,k(t)t≥0 generated by wave equations with variable damping, either in the interior or on the boundary of the domain where Ω ⊂ ℝ3 is a smooth bounded domain, in H 10 (Ω) × L2(Ω) is in fact bounded in D(B0) × H 10 (Ω). As an application of our results, we obtain the upper-semicontinuity for global

In the paper, we establish some exponential inequalities for non-identically distributed negatively orthant dependent (NOD, for short) random variables. In addition, we also establish some exponential inequalities for the partial sum and the maximal partial sum of identically distributed NOD random variables. As an application, the Kolmogorov strong law of large numbers for identically distributed

The frequentist model averaging (FMA) and the focus information criterion (FIC) under a local framework have been extensively studied in the likelihood and regression setting since the seminal work of Hjort and Claeskens in 2003. One inconvenience, however, of the existing works is that they usually require the involved criterion function to be twice differentiable which thus prevents a direct application

This paper considers a competing risks model for right-censored and length-biased survival data from prevalent sampling. We propose a nonparametric quantile inference procedure for cause-specific residual life distribution with competing risks data. We also derive the asymptotic properties of the proposed estimators of this quantile function. Simulation studies and the unemployment data demonstrate

In recent years, there has been a large amount of literature on missing data. Most of them focus on situations where there is only missingness in response or covariate. In this paper, we consider the adequacy check for the linear regression model with the response and covariates missing simultaneously. We apply model adjustment and inverse probability weighting methods to deal with the missingness

Let a, b and k be nonnegative integers with a ≥ 2 and b ≥ a(k + 1) + 2. A graph G is called a k-Hamiltonian graph if after deleting any k vertices of G the remaining graph of G has a Hamiltonian cycle. A graph G is said to have a k-Hamiltonian [a, b]-factor if after deleting any k vertices of G the remaining graph of G admits a Hamiltonian [a, b]-factor. Let G is a k-Hamiltonian graph of order n with

In this paper, we deduced an iteration formula for the computation of central composite discrepancy. By using the iteration formula, the computational complexity of uniform design construction in flexible region can be greatly reduced. And we also made a refinement to threshold accepting algorithm to accelerate the algorithm’s convergence rate. Examples show that the refined algorithm can converge

This paper evaluates the performance of the FW-test for testing part of p-regression coefficients in linear panel data model when p is divergent. The asymptotic power of the FW-statistic is obtained under some regular conditions. The theoretical development are challenging since the number of covariates increases as the sample size increases. It is worth noting that the inference approach does not

Two interesting sequences arose in the study of the series expansions of the complete elliptic integrals, which are called the Catalan-Larcombe-French sequence {Pn}n≥0 and the Fennessey-Larcombe-French sequence {Vn}n>0 respectively. In this paper, we first establish some criteria for determining log-behavior of a sequence based on its three-term recurrence. Then we prove the log-convexity of {V2n −

Under the framework of sub-linear expectation initiated by Peng, motivated by the concept of extended negative dependence, we establish a law of logarithm for arrays of row-wise extended negatively dependent random variables under weak conditions. Besides, the law of logarithm for independent and identically distributed arrays is derived more precisely and the sufficient and necessary conditions for

A graph is outer-1-planar if it can be drawn in the plane so that all vertices are on the outer face and each edge is crossed at most once. It is known that the list edge chromatic number Χ′l(G) of any outer-1-planar graph G with maximum degree Δ(G) ≥ 5 is exactly its maximum degree. In this paper, we prove Χ′l(G) = Δ(G) for outer-1-planar graphs G with Δ(G) = 4 and with the crossing distance being

In this paper, we present a QP-free algorithm without a penalty function or a filter for nonlinear semideflnite programming. At each iteration, two systems of linear equations with the same coefficient matrix are solved to determine search direction; the nonmonotone line search ensures that the objective function or constraint violation function is sufficiently reduced. There is no feasibility restoration

In survival analysis, data are frequently collected by some complex sampling schemes, e.g., length biased sampling, case-cohort sampling and so on. In this paper, we consider the additive hazards model for the general biased survival data. A simple and unified estimating equation method is developed to estimate the regression parameters and baseline hazard function. The asymptotic properties of the

Published auxiliary information can be helpful in conducting statistical inference in a new study. In this paper, we synthesize the auxiliary information with semiparametric likelihood-based inference for censoring data with the total sample size is available. We express the auxiliary information as constraints on the regression coefficients and the covariate distribution, then use empirical likelihood

A proper edge coloring of a graph G is acyclic if there is no 2-colored cycle in G. The acyclic chromatic index of G is the least number of colors such that G has an acyclic edge coloring and denoted by Χ′a(G). An IC-plane graph is a topological graph where every edge is crossed at most once and no two crossed edges share a vertex. In this paper, it is proved that Χ′a(G) ≤ Δ(G) + 10, if G is an IC-planar

In this paper, we present a primal-dual interior point algorithm for semidefinite optimization problems based on a new class of kernel functions. These functions constitute a combination of the classic kernel function and a barrier term. We derive the complexity bounds for large and small-update methods respectively. We show that the best result of iteration bounds for large and small-update methods

Let H = (V, E) be an n-balanced k-partite k-graph with partition classes V1,…, Vk. Suppose for every legal (k − l)-tuple f contained in V V1 and for every legal (k − 1)-tuple g contained in V Vk. such that f ∪ g ∉ E(H), we have d(f) + d(g) ≥ n + 1. In this paper, we prove that under this condition {tiH} must have a perfect matching. Another result of this paper is about the perfect matching in 3-uniform

Hartsfield and Ringel conjectured that every connected graph other than K2 is antimagic. Since then, many classes of graphs have been proved to be antimagic. But few is known about the antimagicness of lexicographic product graphs. In this paper, via the construction of a directed Eulerian circuit, the Siamese method, and some modification on graph labeling, the antimagicness of lexicographic product

In this paper, we make use of stochastic theta method to study the existence of the numerical approximation of random periodic solution. We prove that the error between the exact random periodic solution and the approximated one is at the \({1 \over 4}\) order time step in mean sense when the initial time tends to ∞.

Matching is a routinely used technique to balance covariates and thereby alleviate confounding bias in causal inference with observational data. Most of the matching literatures involve the estimating of propensity score with parametric model, which heavily depends on the model specification. In this paper, we employ machine learning and matching techniques to learn the average causal effect. By comparing

This paper is concerned with the existence and stability of steady state solutions for the SKT biological competition model with cross-diffusion. By applying the detailed spectral analysis and in virtue of the bifurcating direction to the limiting system as the cross diffusion rate tends to infinity, it is proved the stability/instability of the nontrivial positive steady states with some special bifurcating

In this paper, Wang’s Harnack and shift Harnack inequality for a class of stochastic differential equations driven by G-Brownian motion are established. The results generalize the ones in the linear expectation setting. Moreover, some applications are also given.

In 2005, Flandrin et al. proved that if G is a k-connected graph of order n and V(G) = X1 ∪X2 ∪ ⋯ UXfc such that d(x) + d(y) ≥ n for each pair of nonadjacent vertices x, y ∈ Xi and each i with i = 1, 2, ⋯, k, then G is hamiltonian. In order to get more sufficient conditions for hamiltonicity of graphs, Zhu, Li and Deng proposed the definitions of two kinds of implicit degree of a vertex v, denoted

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