On the Second Borel-Cantelli Lemma for α-mixing Sequences of Events

In this paper, we give some conditions on diverging rate of series of the probabilities and converging rate of series of the α-mixing coefficients for sequences of events, under which the conclusion of the Second Borel-Cantelli Lemma holds. As corollaries, some moment conditions are obtained, under which the strong law of large numbers holds for sequences of identically distributed random variables.

A Finite-Time Convergent Analysis of Continuous Action Iterated Dilemma

Dear Editor,In this letter, a finite-time convergent analysis of continuous action iterated dilemma(CAID) is proposed. In traditional evolutionary game theory, the strategy of the player is binary(cooperation or defection), which limits the number of strategies a player can choose from.

A generalization of Banach's lemma and its applications to perturbations of bounded linear operators

Let X be a Banach space and let P:X→X be a bounded linear operator.Using an algebraic inequality on the spectrum of P,we give a new sufficient condition that guarantees the existence of(I-P)^(-1) as a bounded linear operator on X,and a bound on its spectral radius is also obtained.This generalizes the classic Banach lemma.We apply the result to the perturbation analysis of general bounded linear operators on X with commutative perturbations.

THE BOUNDARY SCHWARZ LEMMA AND THE RIGIDITY THEOREM ON REINHARDT DOMAINS B_(p)^(n) OF C^(n)

By introducing the Carathéodory metric,we establish the Schwarz lemma at the boundary for holomorphic self-mappings on the unit p-ball B_(p)^(n) of C^(n).Furthermore,the boundary rigidity theorem for holomorphic self-mappings defined on B_(n)^(p) is obtained.These results cover the boundary Schwarz lemma and rigidity result for holomorphic self-mappings on the unit ball for p=2,and the unit polydisk for p=∞,respectively.

Rice AGL1 determines grain size and sterile lemma identity

The grass spikelet is a unique inflorescence structure that determines grain size.Although many genetic factors have been well characterized for grain size and glume development,the underlying molecular mechanisms in rice are far from established.Here,we isolated rice gene,AGL1 that controlled grain size and determines the fate of the sterile lemma.Loss of function of AGL1 produced larger grains and reduced the size of the sterile lemma.Larger grains in the agl1 mutant were caused by a larger number of cells that were longer and wider than in the wild type.The sterile lemma in the mutant spikelet was converted to a rudimentary glume-like organ.Our findings showed that the AGL1(also named LAX1)protein positively regulated G1 expression,and negatively regulated NSG1 expression,thereby affecting the fate of the sterile lemma.Taken together,our results revealed that AGL1 played a key role in negative regulation of grain size by controlling cell proliferation and expansion,and supported the opinion that rudimentary glume and sterile lemma in rice are homologous organs.

On the Weyl’s Lemma for Triharmonic Functions

In this paper,by choosing some appropriate test functions,we prove the Weyl’s lemma for triharmonic functions based on the new type of mean value formulas.

一类加权的Borel-Cantelli引理

本文给出了一类加权的第二Borel-Cantelli引理.这是对以前该引理的两种推广的一个补充.

National Security Dilemma in the Digital Era and the Building of a Community with a Shared Future in Cyberspace

A review of the history of human development shows that every major technological revolution brings new challenges to national security.With the advent of the information technology revolution represented by the Internet,cybersecurity has become an issue of paramount importance,and the digital intelligence revolution with digital technology innovations such as big data and cloud computing has further expanded the connotation and extension of cybersecurity.

A Proof of Brouwer’s Fixed Point Theorem Using Sperner’s Lemma

This article offers a simple but rigorous proof of Brouwer’s fixed point theorem using Sperner’s Lemma.The general method I have used so far in the proof is mainly to convert the n-dimensional shapes to the corresponding case under the Sperner’s Labeling and apply the Sperner’s Lemma to solve the question.

关于容度下Borel-Cantelli引理的一点注记(英文)

这个注记中我们证明了在没有两两独立假设条件下对容度的Borel-Cantelli引理,获得了容度对并事件的最优下界.这些结果推广了经典的Borel-Cantelli引理.

一类两阶段自适应鲁棒多目标规划的对偶性刻画

该文主要研究一类目标函数和约束函数均具有谱面不确定数据的两阶段自适应鲁棒多目标规划问题.首先,建立具有仿射自适应变量的两阶段自适应鲁棒多目标规划问题的Farkas引理.随后,引入该多目标规划问题的半定规划对偶问题.最后,借助该Farkas引理,刻画它们之间的对偶性质.

非对称性Goursat引理的推广

文章根据群与环上Goursat引理的非对称版本,得到了理想上的Goursat引理,并给出了计算3个三次交错群的直积的子群与Z_(2)×Z_(2)×Z_(2)的子环的一般步骤。另外,进一步考虑有限个群直积的一个子群K和任意子群G的积都有对应的Goursat分解下的性质,并给出了有限个环直积下的理想形式。

带导数非线性项的耦合Tricomi方程组解的破裂

在空间维数n≥2时,研究带导数非线性项的耦合Tricomi方程组的小初值问题。通过定义问题的能量解并构造适当的检验函数,得到关于解的积分泛函的不等式。根据非线性项指数的范围将解的性态研究分为次临界情形及临界情形。在次临界情形利用改进的Kato引理,在临界情形利用迭代方法,证明了问题的解会在有限时间破裂。同时,在次临界情形得到幂次形式解的生命跨度的上界估计,在临界情形得到指数形式解的生命跨度的上界估计,推广了现有文献的结论。

具有奇异性Duffing型p-Laplace方程的周期解

本文研究Duffing型p-Laplace方程(Φ_(p)(x′))′+g (x)=p(t)周期解的存在性。当g具有奇异性且满足单边非共振条件时,应用连续性引理和相平面分析的方法,证明了该方程周期解的存在性。

空间引力波探测无拖曳卫星有限频域抗扰控制器设计

在空间引力波探测任务中,有限测量频域约束以及高精度控制指标使双参考质量无拖曳卫星控制器设计面临诸多技术难题.基于此,本文提出了一种基于广义Kalman-Yakubovich-Popov(GKYP)引理的有限频域抗扰控制器设计方法.针对探测任务中指定频段内的性能约束,结合灵敏度和补灵敏度控制指标,在指定频段下构建了具有频率响应函数形式的有限频域控制性能指标.提出了具有固定阶数特性的输出反馈控制结构,并基于GKYP引理建立了控制器参数选取方法,构建了有限频域抗扰控制器设计方法.不同于现有的无拖曳控制器设计方法,该设计方法可以有效降低控制指标的保守性,同时在指定频段下实现了控制器的精确设计,从而降低控制器阶数.数值仿真表明,本文所提方法在复杂扰动和噪声影响下可以满足无拖曳系统各回路控制性能指标.

K-拟加测度空间上Borel-Cantelli引理的局部推广

基于K-拟加运算证明了集函数关于一般集合列满足次可数可加性,进而给出了K-拟加级数收敛的一个必要条件.其次,在K-拟加测度空间上获得了概率论中Borel-Cantelli引理的第一个结论,并通过构造子集合列方法对Borel-Cantelli引理进行了局部推广.

和优化问题的松弛型Farkas引理

利用共轭函数的上图性质,并引入2类新的约束规范条件,建立了和优化问题的松弛型Farkas引理.

一类拟线性薛定谔方程解的存在性

在R^(N)上探究形式为-Δu+V(x)u-Δ(u^(2))u=h(u)的拟线性薛定谔方程解的存在性,其中N≥3,V:R^(N)→R,h:R→R。运用变分法和山路引理,证明了当函数V和非线性项h分别满足一些适当条件时,该拟线性薛定谔方程存在一个非平凡正解。

适用于现场总线的无证书聚合签名方案

针对现场总线缺乏身份认证以及设备计算资源和网络带宽受限的缺点,提出一种适用于现场总线网络的无证书聚合签名方案,避免复杂的证书管理和密钥管理,在注册阶段使用中国剩余定理,提高假名分发的效率。在安全性证明部分,利用分叉引理对所提签名方案的不可伪造性进行证明。效率方面,签名生成和签名验证阶段避免计算量较大的双线性对运算,支持聚合签名,实现对签名的批量认证,适用于对实时性要求较高且计算资源受限的现场总线网络。实验结果表明,该方案相比于其它方案,计算开销和通信开销有显著降低。

The First Five Years of a Phase Theory for Complex Systems and Networks

In this paper,we review the development of a phase theory for systems and networks in its first five years,represented by a trilogy:Matrix phases and their properties;The MIMO LTI system phase response,its physical interpretations,the small phase theorem,and the sectored real lemma;The synchronization of a multi-agent network using phase alignment.Towards the end,we also summarize a list of ongoing research on the phase theory and speculate what will happen in the next five years.