Let{Xα}be a family of random variables following a certain type of distributions with finite expectation E[Xα]and finite variance Var(Xα),where α is a parameter.Motivated by the recent paper of Hollom and Portier(arXiv:2306.07811v1),we study the anti-concentration function(0,∞)∋ y →infα P |Xα-E[Xα]|≥y√Var(Xα)and find its explicit expression.We show that,for certain familiar families of distributions,including the uniform,exponential,non-degenerate Gaussian and student's t-distributions,the anti-concentration function is not identically zero,which means that the corresponding families of random variables have some sort of anti-concentration property;while for some other familiar families of distributions,including the binomial,Poisson,negative binomial,hypergeometric,Gamma,Pareto,Weibull,log-normal and Beta distributions,the anti-concentration function is identically zero.
Let be a σ -finite complete measure space and let Y be a subspace of a Banach space X . Let φ be a generalized Φ-function on . Denote by and the Musielak-Orlicz spaces whose functions take values in Y and X , respectively. Firstly, let , we characterize the distance of f from . Then, if Y is weakly -analytic and proximinal in X , we show that is proximinal in . Finally, we give the connection between the proximinality of in and the proximinality of in .
In this paper, two temporal discrete numerical schemes of the modified phase field crystal equation are presented by introducing a Lagrange multiplier U and two auxiliary functions ψ, W, which reduce the order of the original equation in time and space. For these schemes, we prove their mass conservation and energy stability. Error estimates of the BDF2 scheme are given. In the end, some numerical experiments are used to verify the correctness of our theoretical results.
In this paper we study the influences of the base points of cubic pencils on the Mordell-Weil groups.Specifically,we investigate and classify the cubic pencils with 8,7 and 6 base points in general position,and give some applications.
1.本刊为向国内外公开发行的学术季刊,主要刊登数学领域的学术论文. 2稿件应当包括题目、作者、作者单位、摘要、关键词、正文、参考文献等内容.如稿件正文为中文文本,请在中文关键词后依次提供题目、作者、作者单位、摘要及关键词准确的英文翻译;如正文内容为英文,则在英文关键词后依次提供题目、作者、作者单位、摘要及关键词准确的中文翻译.
设φ:Mn →Nn+p是一般外围流形中的n维紧致无边子流形.φ的第二基本型模长平方S、平均曲率模长平方H2 和迹零第二基本型模长平方ρ= S-nH2 等重要的低阶曲率分别刻画了全测地、极小、全脐等重要的几何性质.本文构造低阶曲率泛函L(I,n,F)(φ)= M F(S,H2)dv,L(II,n,F)(φ)= M F(ρ,H2)dv,其中F:[0,+∞)×[0,+∞)→R是一个抽象的充分光滑的双变量函数.这类泛函可刻画子流形与全测地子流形、极小子流形和全脐子流形的整体差异,将多类子流形泛函囊括在统一的框架之下,且与子流形中多类著名问题,如Willmore猜想,有着密切联系.本文将计算第一变分公式,在空间形式中构造临界点的一些例子,推导泛函临界点的积分不等式,并基于此对间隙现象进行讨论.
In this paper we investigate the necessary and sufficient conditions such that both a-Weyl's theorem and the property(WE)hold for a bounded linear operator,and study the stability of a-Weyl's theorem and the property(WE)under quasi-nilpotent or compact perturbations.As an application,the relative stability of special operators is studied.
Let G be a finite and simple graph.A walk S is called a segment of G if the endpoints(not necessarily distinct)of S are of degree 1 or at least 3,and each of the rest vertices is of degree 2 in G.In this paper,we determine the graphs that maximize the p-spectral radius for p>1 among trees,unicyclic and bicyclic graphs with given order and number of segments,respectively.
针对提升韧性系统在复杂赛博攻击下持续保障能力的需求,本文首先基于病毒的传播动力学原理构建赛博攻击类模型,模拟韧性系统面临的复杂赛博威胁环境,对其动力学特性进行深入研究?其次,构建一套赛博攻击下韧性系统的目标动态变化模型,利用中心流形定理及分岔理论对韧性系统的局部稳定性进行分析?最后,通过Matlab软件,以数值和图像的方式对赛博攻击的动力学传播过程和韧性系统的目标动态变化过程进行展现.
本文基于高精度填充算法,考虑低秩Toeplitz张量填充问题的求解,通过在每步迭代中将张量随机地按第n模展开并且对它的奇异值分解(Singular Value Decomposition,简记作SVD)进行修正,给出一种具有随机思想的高精度填充算法,并讨论其收敛性.通过对Toeplitz张量及Toeplitz均值张量的数值实验,结果表明新算法比低秩Toeplitz张量的高精度填充算法在计算代价上有明显改进.
In this paper we consider the gradient estimates on the positive solutions to the elliptic equation?v+vr-vs = 0,defined on a complete Riemannian manifold(M,g),where r and s are two real constants.When(M,g)satisfies Ric≥-(n-1)κ(where n≥2 is the dimension of M and κ is a nonnegative constant),we employ the Nash-Moser iteration technique to derive a Cheng-Yau type gradient estimate for the positive solutions to the above equation under some suitable geometric and analysis conditions.Moreover,it is shown that when the Ricci curvature of M is nonnegative,this elliptic equation does not admit any positive solutions except for v ≡ 1 if r
In this paper a kind of integral operator I α β f（z） related to the parameters α,β in an open unit disk is investigated.Firstly,the bi-univalent function classes h ∑ q α,β （λ;φ） and L（∑ q ） α,β （μ,λ;φ） involving this integral operator and the q-derivative operator are defined by applying the subordination principle of analytic functions.Then,the upper bounds of the first two coefficients a2 and a3 of the two classes of bi-univalent analytic functions are estimated,and the corresponding Fekete-Szeg? inequalites for these classes are obtained.
In this paper,the existence of positive periodic solutions for a sixth-order singular differential equation is proved by the properties of Green function of a sixth-order linear differential equation with variable coefficient coupled with the Schauder fixed point theorem.Our results contain both the attractive singularity case and the repulsive singularity case.
Let D(G)=(Di,j)be the distance matrix of a connected graph G,where Di,j equals the distance between the vertices vi and vj of G.Let η1(G)be the distance signless Laplacian spectral radius of G,i.e.,the largest eigenvalue of the distance signless Laplacian matrix Q(G)=Diag(Tr)+D(G),where Diag(Tr)is a diagonal matrix with Diag(Tr)ii=∑vivj∈E(G)'Di,j.In this paper,we investigate the relationships between the perfect matchings and the distance signless Laplacian spectral radius,and give sufficient conditions for the existence of perfect matchings in general graphs and bipartite graphs with respect to the distance signless Laplacian spectral radius,respectively.
In this paper, we discuss the long time behavior of strong solutions of semilinear reaction diffusion equations with fading memory. First of all, by the regularity of solutions and the control convergence principle,we prove that the semigroup of the solutions is an contractive semigroup on H 0 ~1（?） × L μ ~2（R; D（A））, which leads to the asymptotic compactness of the semigroup. Then, we show the existence and regularity of global attractor A on the product space. It is noteworthy that the nonlinearity f satisfies the polynomial growth of arbitrary order and A ? D（A） × L μ ~2（R; D（A））.
This paper investigates enterprises’ decision of the location, pricing and entry timing with asymmetric investment costs in a circular city. Using the option game theory, we construct the dynamic game model of duopoly enterprises with horizontal product differentiation in the circular market, analyze the existing sequential equilibrium and preemptive investment equilibrium, and depict the sub-game perfect equilibrium of the dynamic game under the Stackelberg Equilibrium. The study shows that the profit of enterprises increase with the increase of product differentiation; the enterprise with cost advantage always enters the market as a leader; when the cost asymmetry of two enterprises is less than the critical value, the leader’s entry timing is controlled by the threat of preemption, and the leader’s profits brought by cost advantage will be damaged; the entry timing of the follower is not affected by the degree of cost asymmetry.
In the resource scheduling network, the availability of resource scheduling is equivalent to the existence of the fractional factor in the corresponding network graph. The study on the existence of fractional factors in specific graph structure can help engineers design and construct the network with efficient use of resources. A graph G is called an all fractional (g, f, n', m)-critical deleted graph if after removing any n' vertices from G the remaining graph is still an all fractional (g, f, m)-deleted graph. In this paper, we present two binding number conditions for a graph to be an all fractional (g, f, n', m)-critical deleted graph, and illustrate the results are sharp with examples.
In this paper, we consider the elastic string equation with nonlinear damping and source terms. Following the ideas of Zhang and Miao [43] the blow up of the solutions with positive initial energy is investigated by the perturbed energy method.
For a simple graph G with edge set E（G）,the exponential inverse forgotten index of G is defined as e 1/F （G）=∑ nv∈E（G） e （1/d G ~2（u）+1/d G ~2（v）） ,where d G （u） is the degree of the vertex u in G.In this paper,firstly,we give the minimum value of exponential inverse forgotten index of a tree and determine its corresponding extremal graph.Then,we investigate the maximum value of the exponential inverse forgotten index and describe the structural characteristics of the extremal graph.
This paper is devoted to the nonparametric goodness-of-fit test for integrated diffusion processes. Firstly, a nonparametric test is constructed for testing whether the drift function of a integrated diffusion process is of a known parametric form with unknown parameters. Secondly, a test statistic for goodness-of-fit test is obtained by applying the empirical likelihood technique. And finally, the asymptotic distribution of the test statistic is established, and then the proposed test method is applied to an example to verify its effectiveness.
