一类分数阶神经网络模型的稳定性与Hopf分支分析

分析了一类分数阶神经网络的稳定性与Hopf分支问题.基于分数阶稳定性判据,得到了分数阶神经网络模型局部渐近稳定的条件.并以q为分支参数,得到了分数阶系统产生Hopf的条件.最后数值仿真证明了我们的结论.     

一类不确定分数阶多混沌系统的终端滑模同步控制

根据分数阶系统理论利用终端滑模方法研究了分数阶不确定多混沌系统同步问题,获得了整数阶分数阶两种情形下多混沌系统取得滑模同步的充分性条件,最终结论说明设计合适的控制律和切换函数,分数阶多混沌系统取得滑模同步.     

Lipschitz条件下一致分数阶Ostrowski型不等式的一个拓展

考虑满足一致分数阶Lipschitz条件的函数,用普通数学分析的方法,建立了涉及一致分数阶积分的Ostrowski型不等式,拓展了一致分数阶可微函数的Ostrowski型不等式.     

分数阶不确定多混沌系统的自适应滑模同步

研究分数阶不确定多混沌系统的自适应滑模同步,通过构造滑模面,设计控制器和适应规则,能够满足滑模面的稳定性与到达性,进而得到分数阶不确定多混沌系统取得自适应滑模同步的充分性条件,研究表明:分数阶不确定多混沌系统满足在一定条件下能够取得自适应滑模同步.     

一个新的分数阶比较定理

研究了Caputo和Riemann-Liouville两型分数阶微分方程的比较定理.首先,讨论了一类线性分数阶微分不等式解得非负性.其次,引入单边Lipschitz条件,将微分方程解的比较问题化为线性微分不等式非负解问题,通过线性分数阶微分方程的求解,得到分数阶比较定理.最后,为进一步说明结论,给出了两个数值仿真例子.     

一类具有分数阶积分条件的分数阶微分方程组边值问题的可解性

研究一类具有Riemann-Liouville分数阶积分条件的分数阶微分方程组边值问题,将该问题转化为等价的积分方程组,应用Leray-Schauder不动点定理和Banach压缩映像原理,结合一个分数阶形式的新不等式,获得了该问题解的存在性和唯一性结果,并给出一个应用实例.     

带脉冲的有序分数阶微分方程边值问题解的存在性（英文）

本文研究带脉冲的有序分数阶微分方程边值问题解的存在性的问题.利用Banach压缩映像原理和Krasnoselskii不动点定理的方法,获得带脉冲的有序分数阶微分方程边值问题解的存在性结果,推广了有序分数阶微分方程带脉冲边值条件的一些结果.     

空间分数阶Schr?dinger方程调制不稳定性的数值研究

调制不稳定性在数学和物理等学科中应用十分广泛.本文主要通过分裂谱方法对空间分数阶薛定谔方程进行数值计算,并根据Benjamin-Feir-Lighthill准则推导了非线性薛定谔方程的调制不稳定条件.文中分别研究了空间分数阶薛定谔方程在不同初值条件下的不稳定行为,并与整数阶薛定谔方程的不稳定性行为作比较,通过数值比较分析,发现整数阶薛定谔方程的这种不稳定行为对于空间分数阶薛定谔方程同样存在.     

一类分数阶微分方程组积分边值问题的正解

利用锥拉伸和压缩不动点定理,研究了一类具有Riemann-Liouvile分数阶积分条件的分数阶微分方程组边值问题.结合该问题相应Green函数的性质,获得了其正解的存在性条件,并给出了一些应用实例.     

含有离散时滞及分布时滞分数阶神经网络的渐近稳定性分析

研究了含有离散时滞及分布时滞的分数阶神经网络在Caputo导数意义下的渐近稳定性问题.通过构造Lyapunov函数和利用分数阶Razumikhin定理给出了含有离散时滞和分布时滞的分数阶神经网络渐近稳定性的充分条件,并给出4个例子验证了定理条件的有效性.     

Algorithms for approximation of invariant measures for IFS

We prove convergence of two algorithms approximating invariant measures to iterated function systems numerically. We consider IFSs with finitely many continuous and injective non-overlapping maps on the unit interval. The first algorithm is a version of the Ulam algorithm for IFSs introduced by Strichartz et al. [16]. We obtain convergence in the supremum metric for distribution functions of the approximating eigen-measures to a unique invariant measure for the IFS. We have to make some modifications of the usual way of treating the Ulam algorithm due to a problem concerning approximate eigenvalues, which is part of our more general situation with weights not necessarily being related to the maps of the IFS. The second algorithm is a new recursive algorithm which is an analogue of forward step algorithms in the approximation theory of ODEs. It produces a sequence of approximating measures that converges to a unique invariant measure with geometric rate in the supremum metric. The main advantage of the recursive algorithm is that it runs much faster on a computer (using Maple) than the Ulam algorithm.Mathematics Subject Classification (2000): 37A30, 37C30, 37M25, 47A58Acknowledgement I would like to express my deep gratitude to Andreas Strömbergsson and to the anonymous referee. The referee had several very enlightening comments, which Andreas helped me to deal with. Section 4 is essentially due to Andreas and he also came up with the new Proposition 3 and helped me to improve Lemma 1. Thanks also to Svante Janson, Anders Johansson, Sten Kaijser, Robert Strichartz and Hans Wallin.     

Equations for coefficients of tactical decomposition matrices for t-designs

Equations for coefficients of tactical decomposition matrices for 2-designs are well-known and they have been used for constructions of many examples of 2-designs. In this paper, we generalize these equations and propose an explicit equation system for coefficients of tactical decomposition matrices for \(t\text{-}(v,k,\lambda _t)\) designs, for any integer value of \(t.\)      

Rates of Convergence for a Class of Rank Tests for Independence

An almost optimal rate of convergence estimate is obtained for a large class of rank statistics for testing independence, including Gini's and Spearman's rank correlation coefficients as well as Spearman's footrule. Bibliography: 18 titles.     

Equivalence of conditions for convergence of iterative methods for singular equations

Equivalence is shown between different conditions for convergence of iterative methods for consistent singular systems of linear equations on Banach spaces. These systems appear in many applications, such as Markov chains and Markov processes. The conditions considered relate the range and null spaces of different operators.     

积分中值定理中间点比较及有关平均不等式

中值定理中间点是区间端点的平均.设f (x)、g(x)在同一区间[a,b]内严格单调并可积,p(x)、q(x)恒正可积,按积分中值定理各有唯一的中间点ξf ,p(a,b)和ξg,q(a,b) .当f递增(减)且f (g- 1)凸(凹)时,有ξg,p(a,b) <ξf,p(a,b) ;当p(x)q(x) 递增(减)且q(x) ∫bap(x) dx >( <) 0时,有ξf,q(a,b) <ξf ,p(a,b) .由此可证明和发现一系列有关平均的不等式.     

Error estimates for a Galerkin method for a class of model equations for long waves

The Galerkin method, together with a second order time discretization, is applied to the periodic initial value problem for $$\frac{\partial }{{\partial t}}(u - (a(x)u_x )_x ) + (f(x,u))_x = 0$$ . Heref(x, ·) may be highly nonlinear, but a certain cancellation effect is assumed for∫f(x, u) _x u. Optimal order error estimates inL ₂,H ₁, andL _∞ are derived for a general class of piecewise polynomial spaces.     

带有Gilbert阻尼项的Landau-Lifshitz铁磁链方程解的最佳衰减率

主要研究带有Gilbert阻尼项的Landau-Lifshitz铁磁链方程的柯西问题.当初值的一阶导数适当小时,基于加权能量估计,证明了强解的整体存在性并且给出了解的最优的L2和L∞衰减估计.     

Bounds for the number of moduli for irregular varieties of general type

LetX be a minimal surface of general type and M (X) the set of equivalence classes of complex structures on the differentiable manifold underlyingX; denoting byM _x the dimension of M(X) at [X], the point corresponding to the complex structure ofX we consider the problem of finding an upper bound forM _x in terms of the basic numerical invariants ofX. The main result is the Castelunovo's bound:M _xP_g(X)+2q(X) for certain irregular surfaces. We also generalize the above bound to an arbitrary dimension.