一类半线性椭圆方程爆破解的研究

文章讨论的是一类半线性椭圆方程,介绍了关于此类方程的解的存在性、唯一性的研究,以及其在边界附近的渐近性态.本文重点对方程中的函数满足的条件进行比较分析.     

关于半线性椭圆型方程和方程组的研究

研究半线性椭圆型方程和方程组。利用临界点理论和现代偏微分方程方法,对非线性椭圆型方程解的存在性、多解性和渐近性,得到了一系列有趣的结果。特别低,解决和部分解决了半线性椭圆方程中的2个公开问题。     

欧拉-泊松方程的周期解渐近性收敛加密

欧拉-泊松方程的椭圆函数周期解渐近性收敛模型是实现浮点数据模糊加密核心基础,广泛应用在通信编码和数据加密等领域。对浮点数据的模糊加密能有效保证网络中实时数据交互通信的安全,通过对浮点数据模糊加密稀疏集准确构造建模,提高加密性能。提出采用欧拉-泊松方程的椭圆函数周期解渐近性收敛数学建模的方法实现对浮点数据进行模糊加密,利用压缩映射原理来完成特征解分区处理,给出在控制单元的作用下对浮点数据进行密钥重整,求得欧拉-泊松方程椭圆函数在不定搜索下的三孤波解。通过数学推导证明了欧拉-泊松方程椭圆函数的周期解式渐进收敛性,实现对大数据库的数据加密,实验得出该加密数学模型的收敛性能较好,性能优越。     

自然科学总论

系统辩证论丰富和发展了辩证唯物主义；双指数跳跃扩散模型的McMC估计；查尔酮合酶超家族；正交异性板的三维渐近方程；一种路由器多操作系统平台的设计与实现。     

具有非线性边界耗散的四阶方程整体解的不存在性分析

物理学新现象的出现,在该领域内产生了对孤立子及混沌问题的探究,并出现了一些带有非线性耗散的方程,因此文中将具有非线性边界耗散的四阶方程作为研究对象,并对该方程的整体解进行不存在性分析。首先,运用变分法获取整体弱解的存在性,将Gronwall不等式与Galerkin方法和积分估计法结合进行恰当的先验预估计并研究解的渐近特性,通过积分不等式利用Sobolev嵌入定理和吸引子存在定理证明在内积空间中整体吸引子的存在性,同时得到了吸引子的存在条件;其次,引进位势井和井外集合,运用H?lder不等式与Galerkin方法结合给定初始能量条件,得到整体解存在的门槛结果,在该方程及给定的初始条件满足区间内单调递增条件时,利用反证法可证明方程解不存在整体解,即局部解可在限定时间内实现爆破。     

正态AR序列参数估计的Bahadur渐近有效性

我们只考虑带有正态噪声的自回归过程,并用Yule-Walker估计来估计模型参数。对相合估计给出了大偏差的渐近下界,达到这一下界的估计称为Bahadur渐近有效的。我们证明了在上述意义下,Yule-Walker估计是渐近有效的。     

高维Kramers系统尾部轨迹离出点的分布问题

该文运用奇摄动渐近展开的方法讨论了二维具变阻尼阵的Kramers系统尾部轨迹离出点的分布问题,得到了尾部轨迹所满足的随机动力系统;并给出了尾部轨迹离出点分布的渐近表达式。     

打通一矿渐近式揭穿8煤层的应用与研究

介绍了打通一矿采用“渐近式”揭煤方法,逐步安全揭穿8煤层的具体方案和实施方法,该方法的应用取得了良好效果。渐近式揭穿煤层方法可供类似矿井揭煤参考实施。     

非线性控制系统的一般形式及其稳定性

给出了SISO非线控制系统的点相对阶的概念,以此得出一般Brrnes Isidori标准形式。并对于具有最小相位非线性系统,给出了渐近稳定的充分条件;对于具有非最小相位系统,通过设计控制器来构建中心流形的方法,给出了其渐近稳定性的证明     

带连续接种和垂直传染的传染病模型的稳定性分析

研究了一类带连续接种和垂直传染的SEIV传染病模型,得到了系统的基本再生数R0,当R0〈1时,系统仅存在无病平衡点且全局渐近稳定;当R0〉1时,系统除存在不稳定的无病平衡点外,还存在唯一的地方病平衡点且局部渐近稳定。     

Construction of a Lyapunov function for a linear large-scale periodic system with possibly unstable subsystems

This article proposes an approach to construct a Lyapunov function for a linear large-scale periodic system. In this case, in contrast to various variants of small-gain stability conditions for large-scale systems, the presence of the asymptotic stability property of independent subsystems is not assumed. To analyze the asymptotic stability of a large-scale system, the direct Lyapunov method is used in combination with the discretization method and identities of the commutator calculus. The main results are illustrated by means of examples.     

Delay-independent stability conditions for a class of nonlinear difference systems

The paper addresses the asymptotic stability problem for a class of difference systems with nonlinearities of a sector type and time-delay. A new approach to Lyapunov–Krasovskii functionals constructing for considered systems is proposed. On the basis of the approach, delay-independent asymptotic stability conditions and estimates of the convergence rate of solutions are derived. In addition, stability of perturbed systems is investigated in the case where nonstationary perturbations admit zero mean values. Some examples are given to illustrate the obtained results.     

Further analysis of global robust stability of neural networks with multiple time delays

This paper deals with the problem of the global robust asymptotic stability of the class of dynamical neural networks with multiple time delays. We propose a new alternative sufficient condition for the existence, uniqueness and global asymptotic stability of the equilibrium point under parameter uncertainties of the neural system. We first prove the existence and uniqueness of the equilibrium point by using the Homomorphic mapping theorem. Then, by employing a new Lyapunov functional, the Lyapunov stability theorem is used to establish the sufficient condition for the asymptotic stability of the equilibrium point. The obtained condition is independent of time delays and relies on the network parameters of the neural system only. Therefore, the equilibrium and stability properties of the delayed neural network can be easily checked. We also make a detailed comparison between our result and the previous corresponding results derived in the previous literature. This comparison proves that our result is new and improves some of the previously reported robust stability results. Some illustrative numerical examples are given to show the applicability and advantages of our result.     

Stability in mean of partial variables for stochastic reaction–diffusion systems with Markovian switching

This paper is denoted to investigating stability in mean of partial variables for stochastic reaction–diffusion equations with Markovian switching (SRDEMS). By transforming the integral of the trajectory with respect to spatial variables as the solution of the stochastic ordinary differential equations with Markovian switching (SODEMS) and using Itô formula, sufficient criteria on uniform stability in mean, asymptotic stability in mean, uniformly asymptotic stability in mean, exponential stability in mean of partial variables for SRDEMS are first derived. An example is presented to illustrate the effectiveness and efficiency of the obtained results.     

Asymptotic stability of delayed fractional-order fuzzy neural networks with impulse effects

In this paper, we investigate the asymptotic stability of fractional-order fuzzy neural networks with fixed-time impulse and time delay. According to the fractional Barbalat’s lemma, Riemann–Liouville operator and Lyapunov stability theorem, some sufficient conditions are obtained to ensure the asymptotic stability of the fractional-order fuzzy neural networks. Two numerical examples are also given to illustrate the feasibility and effectiveness of the obtained results.     

Further mean-square asymptotic stability of impulsive discrete-time stochastic BAM neural networks with Markovian jumping and multiple time-varying delays

In this paper, the asymptotic stability analysis is investigated for a kind of discrete-time bidirectional associative memory (BAM) neural networks with the existence of perturbations namely, stochastic, Markovian jumping and impulses. Based on the theory of stability, a novel Lyapunov–Krasovskii function is constructed and by utilizing the concept of delay partitioning approach, a new linear-matrix-inequality (LMI) based criterion for the stability of such a system is proposed. Furthermore, the derived sufficient conditions are expressed in the structure of LMI, which can be easily verified by a known software package that guarantees the globally asymptotic stability of the equilibrium point. Eventually, a numerical example with simulation is given to demonstrate the effectiveness and applicability of the proposed method.     

A necessary and sufficient condition for delay-independent stability of linear time-varying neutral delay systems

In this paper, stability analysis of linear time-varying neutral delay systems is considered. A necessary and sufficient condition for delay-independent global asymptotic stability of such systems is derived. Eventually, two examples are given in order to show the results established.     

Impulsive control on the asymptotic stability of the solutions of a Solow model with endogenous labor growth

In this paper, the asymptotic behavior of a generalized Solow model with endogenous labor growth and impulsive perturbations at fixed moments of time is studied. By using the Lyapunov–Razumikhin method sufficient conditions for week uniform asymptotic stability of the solutions are obtained. We also show that the role of impulses in control the behavior of solutions of impulsive models is very important.     

Global asymptotic stability of switched boolean networks with missing data

This paper investigates the global asymptotic stability of a switched Boolean network (SBN) with missing data. Due to the physical constraints of the communication media, data loss often occurs during the transmission. In this paper, the data loss is described as a Bernoulli distribution sequence, and the switching signal sequence is determined by a logical system. Using a semi-tensor product, the dynamics of a SBN with missing data are converted to an algebraic form. Based on this, a necessary and sufficient condition for global asymptotic stability of SBNs with missing data and auxiliary theorems are provided. Two illustrative examples are presented to show the applicability of the developed theorems.     

Uniform asymptotic stability of linear time-varying singularly perturbed systems

An upper bound for the singular perturbation parameter is found for the uniform asymptotic stability of singularly perturbed linear time-varying systems.