具有边界控制的线性Timoshenko型系统的指数稳定性

研究多孔弹性材料在实际应用中的稳定性问题.多孔物体的动力学行为由线性Timoshenko型方程描述,这样的系统一般只是渐近稳定但不指数稳定,假定系统在一端简单支撑,另一端自由,在自由端对系统施加边界反馈控制,讨论闭环系统的适定性和指数稳定性.首先,证明了由闭环系统决定的算子A是预解紧的耗散算子、生成C0压缩半群,从而得到了系统的适定性.进一步通过对系统算子A的本征值的渐近值估计,得到算子谱分布在一个带域,相互分离的,模充分大的本征值都是A的简单本征值.通过引入一个辅助算子A0,利用算子A0的谱性质以及算子A与A0之间的关系,得到了A的广义本征向量的完整性以及Riesz基性质.最后利用Riesz基性质和谱分布得到闭环系统的指数稳定性.     

Lq(Ω)空间中C0-半群的一些结果

设T（t）是Lq（1＜q＜∞）空间上的C0-半群,A为其无穷小生成元．本文证明若T（t）是弱LP稳定的,则其生成元的谱界是负的。由LotzWeis最近得到的关于Lq（Ω）空间中正C0半群的增长界等于生成元的谱界这一结果得出,Lq（Ω）空间中正C0半群弱Lp稳定与指数稳定等价．     

可修复人机系统的指数稳定性

研究了两相同部件温储备可修的人机系统,运用C_0半群的相关理论,对系统主算子的谱界进行估值.估算系统的算子产生的半群的增长界,然后运用了共尾的概念及相关的理论,得到了系统算子A+B的谱界与系统算子产生的半群的增长界相同.进而运用相关代数知识证得,0为系统算子的简单本征值,并分析了系统算子的谱分布,得到系统的指数稳定性.并研究了系统算子预解式的特性.对任意给定的δ0,γ=a+bi,-μ+δa_1≤a≤a_2,得到lim|b|→∞‖R(γ;A+B)‖=0.进而得到在~sRγ≥a_1的右半平面内相应于系统算子A+B的谱点由有限个本征值组成.     

On χ2-test of goodness-of-fit for a class of discrete multivariate models

A model for an n-dimensional random vector which is the sum of v i.i.d. random variables with an exponential family distribution is considered. It is shown that the exact test can be approximated by a χ²-test as v → ∞. As an example a goodness-of-fit test for Poisson-distribution based on observed frequencies is derived.     

A new generalized linear exponential distribution and its applications

A new generalized linear exponential distribution （NCLED） is considered in this paper which can be deemed as a new and more flexible extension of linear exponential distribution. Some statistical properties for the NGLED such as the hazard rate function, moments, quantiles are given. The maximum likelihood estimations （MLE） of unknown parameters are also discussed. A simulation study and two real data analyzes are carried out to illustrate that the new distribution is more flexible and effective than other popular distributions in modeling lifetime data.     

一个二元丢番图不等式

本文证明了如果1相似文献   

更一般高阶非完整系统的指数调节

研究了一类更具有一般性的强漂移高阶非完整系统的指数调节问题.首先通过指数形式的input-state-scaling不连续变换将原x子系统的指数调节问题转化为变换后z子系统的镇定问题,并有效克服x子系统在控制输入u₀=0时不能控的问题.然后基于"加幂积分器"反推方法设计鲁棒控制器,在新的切换策略下,使闭环系统状态指数收敛到零点.仿真例子验证了所提方法的有效性.     

微分方程的指数稳定性

比较系统地研究了It方程解的指数稳定性.给出了随机指数稳定性、指数P-稳定性、几乎必然指数稳定性的比较准则,这些比较准则推广了Nevel’son和Has’minskiǐ的相应结果.     

Approximation of the linear combination of $\varphi$-functions using the block shift-and-invert Krylov subspace method

In this paper, we develop an algorithm in which the block shift-and-invert Krylov subspace method can be employed for approximating the linear combination of the matrix exponential and related exponential-type functions. Such evaluation plays a major role in a class of numerical methods known as exponential integrators. We derive a low-dimensional matrix exponential to approximate the objective function based on the block shift-and-invert Krylov subspace methods. We obtain the error expansion of the approximation, and show that the variants of its first term can be used as reliable a posteriori error estimates and correctors. Numerical experiments illustrate that the error estimates are efficient and the proposed algorithm is worthy of further study.     

关于(a,a,b)类型的三维除数问题

本文研究了(a,a,b)类型的三维除数问题.当a＜b≤2a时,我们利用指数和的新估计得到了余项△(a,a,b;x)的较好估计.     

汉明距离矩阵的研究

汉明距离矩阵Ds是由测量定义在F_s~q：={0,1,…,q-1}^s上的码字的汉明距离的元素构成.汉明距离矩阵Ds可以由递归的形式表示出来.利用汉明距离矩阵Ds的递归公式求得了矩阵D_s所有特征根以及特征向量.在文章的最后还得出-cDs的Schur指数形的所有特征根.如果c〉0的话,-cDs的Schur指数形的所有特征根都大于零,从而-cDs的Schur指数形是正定的.     

Groups of Exponential Algebras

In this paper we study groups corresponding a free exponential algebra, a free product of exponential algebras and a HNN-extension of exponential algebras over a field F of characteristic 0.     

Exponential stability of a mildly dissipative viscoelastic plate equation with variable density

This paper is concerned with a viscoelastic Kirchhoff plate featuring variable material density. It is modeled by the equation defined in a bounded domain of , where ? = |u_t|^ρ accounts for a velocity‐dependent material density. It is known that its analogue second‐order wave equation can be exponentially stabilized with the sole dissipation given by the memory term. However, for the plate equation, exponential stability was only shown with an additional strong damping ?Δu_t. Our objective is to show the exponential stability of the present system by exploring only the memory term.     

Euler-Bernoulli梁边界反馈控制系统的Riesz基生成问题

本文用基扰动的方法,证明了由速度和角速度组成的边界反馈Ｅｕｌｅｒ－Ｂｅｒｎｏｕｌｌｉ梁振动系统的广义本征元生成状态空间Ｈ的Ｒｉｅｓｚ基,从而给出了振动系统最优指数衰减率的计算公式,     

GLOBAL EXISTENCE, UNIFORM DECAY AND EXPONENTIAL GROWTH FOR A CLASS OF SEMI-LINEAR WAVE EQUATION WITH STRONG DAMPING

In this paper, we consider the nonlinearly damped semi-linear wave equation associated with initial and Dirichlet boundary conditions. We prove the existence of a local weak solution and introduce a family of potential wells and discuss the invariants and vacuum isolating behavior of solutions. Furthermore, we prove the global existence of solutions in both cases which are polynomial and exponential decay in the energy space respectively, and the asymptotic behavior of solutions for the cases of potential well family with 0相似文献   

Lyapunov’s coefficient of regularity and nonuniform hyperbolicity

For a nonautonomous dynamics with discrete time defined by a sequence of matrices, we obtain sharp lower and upper bounds for the Lyapunov coefficient of regularity. This has the advantage of avoiding considering the adjoint dynamics (in contrast to what happens with the regularity coefficients considered by Perron and Grobman). We also show that the dynamics can always be reduced to one defined by upper triangular matrices with the additional properties that the canonical basis is normal and ordered. Moreover, we show in a simpler manner that the Lyapunov coefficient of regularity is related to the notion of nonuniform hyperbolicity, more precisely to the nonuniform part of a nonuniform exponential contraction or a nonuniform exponential dichotomy. Finally, as an application of this relation, we show that from the point of view of ergodic theory, for almost all trajectories with negative Lyapunov exponents the nonuniformity can be made arbitrarily small.     

Dynamics of Hodgkin–Huxley systems revisited

We consider the singularly perturbed Hodgkin–Huxley system subject to Neumann boundary conditions. We construct a family of exponential attractors {?_ε} which is continuous at ε = 0, ε being the parameter of perturbation. Moreover, this continuity result is obtained with respect to a metric independent of ε, compared with all previous results where the metric always depends on ε. In the latter case, one needs to consider more regular function spaces and more smoother absorbing sets. Our results show that we can construct and analyse the stability of exponential attractors in a natural phase-space as it is known for the global attractor. Also, a new proof of the upper semicontinuity of the global attractor 𝒜_ε at ε = 0 is given.     

A State Space Model for Software Reliability

In this paper, we propose a non-Gaussion state space model to apply in software reliability. This model assumes an exponential distribution for the failure time in every test-debugging stage, conditionally on the state parameter — the number of faults in the program. It is a generalized JM model which can be applied to the imperfect debugging situation as well as in evolving programs. By examining a set of data on evolving program failures, the effect of evolving program model is amply proved.     

具有热储备的并行可修复系统指数稳定性分析

应用泛函分析的方法讨论了有两个相同部件和一个热储备的并行可修复系统的指数稳定性.我们通过分析系统算子生成C0半群的本质谱增长阶,证明了该半群是拟紧的.此外,该半群还是不可约的.于是作为半群拟紧性和不可约性的直接结果,得到了系统的时间依赖解指数收敛到其静态解,并且该静态解即为系统算子简单特征值0对应的正的特征向量.     

Stability analysis of a stochastic Gilpin–Ayala model driven by Lévy noise

A stochastic one-dimensional Gilpin–Ayala model driven by Lévy noise is presented in this paper. Firstly, we show that this model has a unique global positive solution under certain conditions. Then sufficient conditions for the almost sure exponential stability and moment exponential stability of the trivial solution are established. Results show that the jump noise can make the trivial solution stable under some conditions. Numerical example is introduced to illustrate the results.