网络安全产品研究

本文在研究了网络安全的国内外有关情况后对网络安全技术进行了探讨 ,介绍了一种简单而实用的网络安全产品 ,添补了这方面的空白 ,而且本文介绍的产品已经应用到了许多部门 ,为网络安全做出了贡献     

探究两个一次函数图像的对称规律

在学习了反比例函数后,老师带大家总结了两个点及函数图像的对称性.对于两个一次函数对称的情况,我自己进行了探索,发现了     

一种积分数据的函数重构及其误差估计

本文考虑了一种基于函数积分平均值的函数重构方法,在定义了一个插值算子之后建立了误差估计.从理论分析结果可以看出这种方法得到的解是适定的,因此我们不需要选择正则化参数,这样就简化了算法,而且最后一系列的数值结果很好的验证了这种方法的有效性.     

分数阶Chen-like系统混沌性态分析及控制

提出了一类Chen-like系统,研究了该系统奇点稳定性、混沌等动力学性态.讨论了Chen-like系中参数与阶数对系统混沌性态的影响,并给出了Chem-like系统出现混沌性态的阶次范围.与分数阶Chen系统相比,系统出现混沌性态的阶次范围增大了.根据分数阶系统稳定性理论及线性反馈控制,对系统进行了混沌控制,得出了混沌系统在平衡点处的稳定性条件.数值模拟验证了理论分析的正确性.     

对称阵的最小多项式及其应用

本文研究了对称阵的最小多项式的存在唯一性,利用对称阵的正交分解的基本思想,获得了对称阵的最小多项式的具体表示形式,改进了Hamilton-Caylay定理.并且给出了对称阵最小多项式的几个应用.     

数学教辅书中的一类极值问题解答错误及修正

指出了一些微积分教辅书中一类极值问题的解答错误,分析了产生错误的原因,仔细研究了变量之间的关系,从而给出了正确的答案.     

标准体系的使用期的模型与分析

本文提出了关于标准体系使用期的两个模型。首先定义了标准使用期,然后讨论了模型的合理性。通过模型讨论了标准使用期的性质,给出了数值示例。提出了需进一步研究的问题。     

分层教学的Bayes分析

对学校分层教学进行了初步探索 ,提出了分层分班的 Bayes决策 ,介绍了分层分班方法 ,获得了一些结论 ,并完成了对这些结论的证明 ,从理论上论述了分层教学是实施“因材施教”教育原则和素质教育的有效途径 ,给出了应用实例 .     

小鼠特征脑电波信号分离与相关性分析

基于生物的呼吸机理,建立了小鼠呼吸的闭环控制系统模型,并给出了呼吸脑电波的仿真曲线.结合相关性分析理论,得到了小鼠呼吸曲线和脑电波各自的自相关函数以及两者的互相关曲线与相关系数.利用功率谱估计方法重点研究了脑电波的频域特性并分析了能量比.设计了巴特沃斯数字滤波器和基于功率谱能量分布的脑电波分离算法,对脑电波进行了分离.并比较了分离结果与原始刺激之间的相关性.     

双层线性分式规划求顶点的算法

基于双层线性分式规划的性质,讨论了上层不带约束的双层线性分式规划模型,给出了求其所有顶点的算法.此算法为进一步进行双层线性分式规划的灵敏度分析打下了坚实的基础,通过例子对算法进行了检验,并利用结果进行了灵敏度分析.     

Active control of secondary resonances piezoelectric sandwich beams

Secondary resonances of piezoelectric/elastic/piezoelectric sandwich beams submitted to active control are studied in this paper. The proportional and derivative nonlinear potential feedback controls via piezoelectric sensor and actuator layers are used. The dynamics of the beam is modelled by a highly nonlinear ordinary-differential equation. The method of multiple scales is applied and approximate solutions are obtained for hard excitations. Analytical frequency and phase-amplitude relationships as well as the time response are explicitly given for various super- and subharmonic resonances. Static and dynamic stability criteria are elaborated and critical displacement and excitation amplitudes associated to the resulting unstable zones are analytically given. The feedback parameters effects on the subharmonic and superharmonic resonances and on their stability are investigated.     

Financial Risk Modelling and Econometric Inference

In finance, the explicit modelling of uncertainty takes on a particularly important role. The values of financial derivatives increase in the return volatility of the underlying security. This notion requires a concept of volatility and hence uncertainty. In addition, the choice between modelling in discrete and continuous time is not arbitrary, since it corresponds to a distinction between incomplete and complete markets, respectively, and this distinction matters for asset pricing, financial risk modelling, and inference. Risk and volatility are closely connected, and implied volatility, volatility forecasting, volatility in term structure models, stochastic volatility, and portfolio analysis are considered and related to a more general interplay between cross-sectional and dynamic aspects in finance. Stocks, bonds, and options are considered and placed in the context of efficiency and separation in inference.     

Remarks on classifications and adjunctions

Jon Barwise and Jerry Seligman introduced the category of classifications and infomorphisms to model information theoretical concepts and information flow processes. This is the dual category of the category of Chu spaces introduced by Michael Barr and Peter Chu and studied extensively by Vaughan Pratt, Gordon Plotkin and others at Stanford. It is also very closely related to the theory of institutions introduced in a different context by Joseph Goguen and Rod Burstall. Here some aspects of the theory are reviewed and some adjunctions between the category of classifications and other related categories are studied from a more abstract point of view.     

Latroids and their representation by codes over modules

It has been known for some time that there is a connection between linear codes over fields and matroids represented over fields. In fact a generator matrix for a linear code over a field is also a representation of a matroid over that field. There are intimately related operations of deletion, contraction, minors and duality on both the code and the matroid. The weight enumerator of the code is an evaluation of the Tutte polynomial of the matroid, and a standard identity relating the Tutte polynomials of dual matroids gives rise to a MacWilliams identity relating the weight enumerators of dual codes. More recently, codes over rings and modules have been considered, and MacWilliams type identities have been found in certain cases.

In this paper we consider codes over rings and modules with code duality based on a Morita duality of categories of modules. To these we associate latroids, defined here. We generalize notions of deletion, contraction, minors and duality, on both codes and latroids, and examine all natural relations among these.

We define generating functions associated with codes and latroids, and prove identities relating them, generalizing above-mentioned generating functions and identities.

     

Range的《微积分是什么?从简单代数到深入分析》

在于向中国读者介绍Michael Range的新书.他对导数及积分都进行了深入而又简练的分析.     

A system-theoretic model for cooperation, interaction and allocation

A system-theoretic approach to cooperation, interaction and allocation is presented that simplifies, unifies and extends the results on classical cooperative games and their generalizations. In particular, a general Weber theory of linear values is obtained and a new theory for local cooperation and general interaction indices is established. The model is dynamic and based on the notion of states of cooperation that change under actions of agents. Careful distinction between “local” states of cooperation and general “system” states leads to a notion of entropy for arbitrary non-negative and efficient allocations and thus to a new information-theoretic criterion for fairness of allocation mechanisms. Shapley allocations, for instance, are exhibited as arising from random walks with maximal entropy. For a large class of cooperation systems, a characterization of game symmetries in terms of λ-values is given. A concept for cores and Weber sets is proposed and it is shown that a Weber set of a game with selection structure always contains the core.     

Rectangularity and paramonotonicity of maximally monotone operators

Maximally monotone operators play a key role in modern optimization and variational analysis. Two useful subclasses are rectangular (also known as star monotone) and paramonotone operators, which were introduced by Brezis and Haraux, and by Censor, Iusem and Zenios, respectively. The former class has a useful range of properties while the latter class is of importance for interior point methods and duality theory. Both notions are automatic for subdifferential operators and known to coincide for certain matrices; however, more precise relationships between rectangularity and paramonotonicity were not known. Our aim is to provide new results and examples concerning these notions. It is shown that rectangularity and paramonotonicity are actually independent. Moreover, for linear relations, rectangularity implies paramonotonicity but the converse implication requires additional assumptions. We also consider continuous linear monotone operators, and we point out that in the Hilbert space both notions are automatic for certain displacement mappings.     

Some recurrence formulas for box splines and cone splines

A degree elevation formula for multivariate simplex splines was given by Micchelli and extended to hold ]or multivariate Dirichlet splines in [8]. We report similar formulae for multivariate cone splines and box splsplines andines. To this end, we utilize a relation due to Dahmen and Micchelli that connects box cone splines and a degree reduction formulagiven by Cohen, Lyche, and Riesenfeld in [2].     

资源禀赋视角下政府与企业互动行为演化分析

针对政府与企业资源的异质性,从资源禀赋的视角,对政府与企业互动的不同模式(随机合作型、政策驱动型、技术推动型、协作共赢型)的界定与分析,构建政府与企业互动行为的演化博弈模型,明确政府与企业在不同模式下的互动行为演化路径。研究结果表明:政府与企业不同互动模式存在显著差异,不同类型企业与政府之间的互动对应着某种互动模式;不同互动模式的产生和演化契合政企互动关系的发展历程;协作共赢型互动模式是政府与企业互动行为演化的高级阶段,有利于政府与企业形成紧密的合作,激发政府政策资源与企业技术资源的协同效应。