The Periodic Solutions of Partial Variables for An Class of Linear Periodic Systems

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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.     

一类广义Riccati方程的三个可积判据

考虑一类广义Riccati方程,通过函数变换,在所给条件下,将这类方程等价地化为变量分离方程,从而得到了该方程可积的三个充分性判据,并给出方程通解的参数表达形式,扩大了Riccati方程的可解性范围.     

关于一类广义Riccati方程三个可积判据的注记

通过变量变换的方法,将文[1]中一类广义Riccati方程的三个充分性判据统一起来,并加以推广.充分利用参数λ,κ的可变性揭示该结果与现有Riccati方程可积性间的关系,扩大了Riccati方程的可积性范围.     

Volterra系统全局稳定、扇形稳定及关联稳定的一些新判据

Stability of Volterra systems are discusses by subpositive definite matrix, and some new criterions for Volterra systems on overall situation stability, sector stability and connection stability are acquired. These results expand or improve some existing criterions.     

Numerical Methods for Non-Linear Black–Scholes Equations

Abstract

In recent years non-linear Black–Scholes models have been used to build transaction costs, market liquidity or volatility uncertainty into the classical Black–Scholes concept. In this article we discuss the applicability of implicit numerical schemes for the valuation of contingent claims in these models. It is possible to derive sufficient conditions, which are required to ensure the convergence of the backward differentiation formula (BDF) and Crank–Nicolson scheme (CN) scheme to the unique viscosity solution. These stability conditions can be checked a priori and convergent schemes can be constructed for a large class of non-linear models and payoff profiles. However, if these conditions are not satisfied we show that the schemes are not convergent or produce spurious solutions. We study the practical implications of the derived stability criterions on relevant numerical examples.     

具有特殊解结构的二阶线性微分方程的可积性判据

针对二阶线性微分方程y″+p(x)y′+q(x)y=0具有某种特殊解结构的情况下,进行可积性判据研究,利用降阶的思想,得到p(x),q(x)满足的关系式,找到了方程可积的充分条件.     

Input-to-state stability and stabilization for switched nonlinear positive systems

Input-to-state stability (ISS) analysis and stabilization are concerned in this paper for switched nonlinear positive systems (SNPS), where the deterministic and random switching are both included. For general SNPS, switched affine nonlinear positive systems (SANPS) and switched linear positive systems (SLPS) with deterministic and some kinds of random ”slow” switching, some criterions on ISS are provided. From the criterions for SANPS and SLPS, the ISS properties can be judged just by the differential, algebraic and switching characteristics of the systems. Further, based on the criterions for SANPS and SLPS, some state feedback controllers are designed such that the closed-loop systems be positive, ISS or ISS in some stochastic senses. Four simulation examples verify the validity of our results.     

A note on global solution to stochastic differential equation based on a semimartingale with spatial parameters

We give here some criterions for the existence and uniqueness of a global solution to a stochastic differential equation based on a semimartingale with spatial parameters of the form

控制系统实的第二标准型绝对稳定的显式准则

本文给出的非线性控制系统实的第二标准型绝对稳定的显式准则,包含并改进了文[1]所得到的判别准则。将本文准则应用于着名的飞机纵向运动方程,所得结果包含并改进了文[1,2,3,4]中所得到的相应结论。     

A new blowup criterion for strong solutions to the three‐dimensional compressible magnetohydrodynamic equations with vacuum in a bounded domain

In this paper, we establish a new blowup criterions for the strong solution to the Dirichlet problem of the three‐dimensional compressible MHD system with vacuum. Specifically, we obtain the blowup criterion in terms of the concentration of density in BMO norm or the concentration of the integrability of the magnetic field at the first singular time. The BMO‐type estimate for the Lam system 2.6 and a variant of the Brezis‐Waigner's inequality 2.3 play a critical role in the proof. Copyright © 2017 John Wiley & Sons, Ltd.     

Practical criteria for positive-definite matrix,M-matrix and Hurwitz matrix

All the conventional criterions to verify if a matrix is positive definite, Hurwitz or an M-matrix, such as Sylvester condition and Hurwitz theorem, require us to compute n determinants. This paper develops a new and simple criterion, based on a new type of Gaussian elimination process. In contrast to the traditional criterions, the new criterion only computes one determinate. Thus, the computing cost is greatly reduced. An illustrative example is given to show the application of the new criterion in the stability analysis of Hopfied-type neural networks with time delays.     

兼顾效益和成功率的区间数决策矩阵的一种综合排序方法

目前的区间数的决策矩阵排序方法都只根据效益型准则进行的,而没有考虑到方案实施的成功率这个重要准则。本文提出了区间数的可行度概念,在此基础上给出了基于可行度的区间数决策矩阵的排序方法;然后提出了一种兼顾效益和成功率的区间数决策矩阵排序的综合评价方法,该方法能融合多方面的决策信息。文中给出了一个实例说明本法的有效性和可行性。     

不定积分中的“积不出”问题

利用刘维尔(J.Liouville)定理讨论了几类不定积分是否初等函数的问题,并给出了相应的判定法则.     

Two novel synchronization criterions for a unified chaotic system

Two novel synchronization criterions are proposed in this paper. It includes drive–response synchronization and adaptive synchronization schemes. Moreover, these synchronization criterions can be applied to a large class of chaotic systems and are very useful for secure communication.     

On the equations defining monomial curves

Let C be a monomial curve in three dimensional projective space over an algebraically closed field K of characteristic zero . We give several necessary criterions for C to be set theoretic complete intersection. Using these criterions we get several restrictions concerning the form of the equations that define C set theoretically.     

Necessary and sufficient conditions for Lipschitz ergodicity and generalized ergodicity

In this paper, the Lipschitz ergodicity and generalized ergodicity are studied. Some criterions for a system to be Lipschitz ergodic or generalized ergodic are given.     

交错级数敛散性判别法

给出交错级数的几个判别法,它们可直接用以判别交错级数是绝对收敛,条件收敛还是发散.     

A remark on the Abel’s and Dirichlet’s criterions concerning generalizations to monotonicity

The Abel’s and Dirichlet’s criterions for convergence of series in analysis are very basic classical results and both require the monotonicity condition. In this note we show that the monotonicity condition in these criterions can be generalized to RBV condition, while cannot be generalized to quasimonotonicity.     

On L-functions of cyclotomic function fields

We study two criterions of cyclicity for divisor class groups of function fields, the first one involves Artin L-functions and the second one involves “affine” class groups. We show that, in general, these two criterions are not linked.