一类具有修正Leslie-Gower和Holling-type Ⅲ型的时滞食饵捕食模型的周期解与持久性（英文）

本文研究了一类具有修正的Leslie-Gower和Holling-typeⅢ型时滞食饵捕食模型.运用重合度理论和比较定理,得到系统正周期解和持久性的充分条件.结论拓展和完善了已有的结论.最后,从例子可以看到结论是容易验证的.     

含混合时滞和脉冲的Cohen-Grossberg神经网络的全局指数稳定性

本文讨论了含混合时滞和脉冲的Cohen-Grossberg神经网络的稳定性.通过应用M矩阵理论和不等式技巧,得到了含混合时滞的Cohen-Grossberg神经网络平衡态的全局指数稳定性的充分条件.相比以前同类文献,本文减弱了部分条件,推广了部分结论,并在文末给出了两个示例.本文结论对于设计和应用神经网络有一定实用价值.     

基于降维思想的客观组合评价模型

为了解决多方法评价结论的非一致性问题,产生了组合评价方法.最大限度地利用多评价结论的信息是组合评价的关键.为此提出了一个基于降维思想的客观组合评价模型,它能够最大程度地保留多评价结论所包含的评价信息,充分地整合多评价结论中的共性信息.鉴于该模型求解属复杂非线性优化问题,常规方法难以直接处理,建立了微粒群改进算法,进行全局寻优.最后,通过实例说明了模型的可操作性和实用性.     

多类复高阶q-平移差分方程组的解

利用亚纯函数的Nevanlinna值分布理论,研究了多类复高阶q-平移差分方程组的解的存在问题,得到了一些结果.推广和改进了一些文献的结论.例子表明作者的结论精确.     

一类预条件AOR迭代法的比较定理(英文)

本文研究了当线性方程组的系数矩阵是严格对角占优L-矩阵时带有预条件子P1→kα的预条件AOR迭代方法.利用矩阵分裂的相关理论,获得了预条件AOR迭代法的收敛性结论以及参数α和k对收敛速度影响的比较定理.结果表明当α和k取值较大时这类预条件方法更加有效.文中的结论推广了Li等人关于预条件Gauss-Seidel迭代法的相关结论.最后,用数值例子进一步验证了这些结果.     

中国证券市场价格及波动率长记忆性实证研究

证券市场股价运动是否存在长记性,近年来的实证研究结论不一.其中重要原因是数据选择的局限和检验方法的不统一.通过自相关函数、修正的R/S和GPH方法对中国证券市场的日和五分钟数据进行了递进检验,得出了一些与众不同的结论.     

锥度量空间中Picard迭代的T-稳定性

研究了锥度量空间中关于压缩映射和扩张映射的Picard迭代的T-稳定性,并且列举了一些例子验证了其结论.同时通过应用这些结论,获得了一类常见的带有边值条件的微分方程的正解公式.     

含p-Laplace算子的Sturm-Liouville边值问题正解的性质

研究了含p-Laplace算子的Sturm-Liouville边值问题正解的性质.利用p-Laplace算子的性质,使用L’Hpital(洛必达)法则和闭区间上连续函数的最值性定理,研究了含p-Laplace算子的Sturm-Liouville边值问题,得到了其正解存在的两个必要条件.最后给出了主要结论的应用.结论丰富了边值问题研究领域的内容,为利用计算机使用迭代技术求这类边值问题的近似解提供了新的渠道,推广了一些文献的结论.     

β混合随机变量序列加权和的收敛性

本文研究了混合随机变量序列加权和的收敛性.利用Utev, S.和Peligrad, M不等式得到了混合随机变量序列加权和的收敛性定理及Hajeck-Rènyi型不等式,推广和改进了W.F,Stout,吴群英,J.Hajeck和A.Rènyi.的相应结论.     

加权和线性过程的渐近正态性

本文建立了α-混合序列情形的加权和平稳线性过程的渐近正态性.获得的结论基于最少的权条件.所得结论将Abadir等[Econometric Theory,2014,30(1):252-284]中的结论推广至α-混合序列情形.     

Duality for Multiobjective Optimization via Nonlinear Lagrangian Functions

In this paper, a strong nonlinear Lagrangian duality result is established for an inequality constrained multiobjective optimization problem. This duality result improves and unifies existing strong nonlinear Lagrangian duality results in the literature. As a direct consequence, a strong nonlinear Lagrangian duality result for an inequality constrained scalar optimization problem is obtained. Also, a variant set of conditions is used to derive another version of the strong duality result via nonlinear Lagrangian for an inequality constrained multiobjective optimization problem.     

Well-posedness and stability for a mixed order system arising in thin film equations with surfactant

The objective of the present work is to provide a well-posedness result for a capillary driven thin film equation with insoluble surfactant. The resulting parabolic system of evolution equations is not only strongly coupled and degenerated, but also of mixed orders. To the best of our knowledge the only well-posedness result for a capillary driven thin film with surfactant is provided in [4] by the same author, where a severe smallness condition on the surfactant concentration is assumed to prove the result. Thus, in spite of an intensive analytical study of thin film equations with surfactant during the last decade, a proper well-posedness result is still missing in the literature. It is the aim of the present paper to fill this gap. Furthermore, we apply a recently established result on asymptotic stability in interpolation spaces [15] to prove that the flat equilibrium of our system is asymptotically stable.     

Addendum to “Distribution of points on the circle” [J. Number Theory 127 (1) (2007) 127-135]

In an earlier paper we gave a result relating the value of an exponential sum with the distribution of summands in the arcs of the unit circle in the complex plane. In a marginal case, this result is superseded by a result of Lev. In this addendum we use an idea of Lev to give a new proof of our earlier result and to improve upon the marginal result.     

Mazur-Ulam定理的一个注记

本文的主要结论是给出了一个更广泛形式的Mazur-Ulam定理.讨论的对象是实的赋准范空间,满等距算子被减弱成其像空间构成一个加法子群的算子.最后给出的推论推广了Skof的一个结果.     

Analysis of Topological Structure in Transiently Chaotic Neural Networks

Under the condition that the damping factor is between zero and one, chaotic dynamics is proved to exist in one-dimensional transiently chaotic neural networks by Li-Misiurewicz theorem. This result extends the previous result which is done under the condition that the damping factor is zero. Because the value of damping factor affects the speed of dynamical process of transiently chaotic neural networks, this result provides more complete theoretical basis for applications. Finally, two examples by numerical simulation are given to reinforce and illustrate this result.     

Minkowski空间中具有常值支持函数的子流形

在Mlinkowski空间中证明了完备连通且具有常值支持函数的子流形必为Finsler球面或者为一个平面．利用支持函数研究的两类子流形是Euclid空间中结果的推广，同时优化了Euclid空间中子流形的相应结果．     

基于小波神经网络与ARIMA组合模型在股票预测中的应用

为了实现对股票价格变化的短期预测,提出了一种基于小波神经网络(WNN)与自回归积分滑动平均模型(ARIMA)的组合预测模型.将股票的收盘价序列数据划分为线性以及非线性(误差项)两个部分,分别利用统计学中ARIMA模型和小波神经网络分别对两部分数据进行预测并得到结果,将两部分结果组合相加合成为整个股票价格的预测结果.实验结果表明该组合模型在预测精度方面有提高,是一种比较有效的预测模型.     

Representing polyhedra: faces are better than vertices

This paper investigates the reconstruction of planar-faced polyhedra given their spherical dual representation. The spherical dual representation for any genus 0 polyhedron is shown to be unambiguous and to be uniquely reconstructible in polynomial time. It is also shown that when the degree of the spherical dual representation is at most four, the representation is unambiguous for polyhedra of any genus. The first result extends, in the case of planar-faced polyhedra, the well known result that a vertex or face connectivity graph represents a polyhedron unambiguously when the graph is triconnected and planar. The second result shows that when each face of a polyhedron of arbitrary genus has at most four edges, the polyhedron can be reconstructed uniquely. This extends the previous result that a polyhedron can be uniquely reconstructed when each face of the polyhedron is triangular. As a consequence of this result, faces are a more powerful representation than vertices for polyhedra whose faces have three or four edges. A result of the reconstruction algorithm is that high level features of the polyhedron are naturally extracted. Both results explicitly use the fact that the faces of the polyhedron are planar. It is conjectured that the spherical dual representation is unambiguous for polyhedra of any genus.     

On results of Czubiak-Gundersen and Osgood-Yang

This paper studies the problem of uniqueness of entire functions that share real zeros and real ones. An example is provided to show that a result of Czubiak and Gundersen is not completely correct. Results in this paper correct the result of Czubiak and Gundersen, and also correct a result of Osgood and Yang.

     

Homogenization and corrector for the wave equation with discontinuous coefficients in time

In this paper we analyze the homogenization of the wave equation with bounded variation coefficients in time, generalizing the classical result, which assumes Lipschitz-continuity. We start showing a general existence and uniqueness result for a general sort of hyperbolic equations. Then, we obtain our homogenization result comparing the solution of a sequence of wave equations to the solution of a sequence of elliptic ones. We conclude the paper making an analysis of the corrector. Firstly, we obtain a corrector result assuming that the derivative of the coefficients in the time variable is equicontinuous. This result was known for non-time dependent coefficients. After, we show, with a counterexample, that the regularity hypothesis for the corrector theorem is optimal in the sense that it does not hold if the time derivative of the coefficients is just bounded.