数控编程常见工艺问题剖析及解决方法

对数控编程中容易忽视的一些数控加工工艺问题进行了分析归纳 ,并各自相应提出了解决方法和原则。     

一类具有可修复储备部件的人-机系统解的谱特征

针对一个具有2个运行部件和1个储备部件,故障修复时间服从一般分布的人-机模型,利用算子半群理论研究了与此模型对应的线性算子生成的C0半群所对应的预解式的谱特征.     

一类隐预解动力系统解的存在性

文章建立了Hilbert空间中一类与广义集值拟变分包含问题有关的隐预解动力系统,并给出了这类隐预解动力系统解的存在性定理,这些结果改进、推广和统一了文献[1-8]的相应结果。     

二阶变系数线性非齐次微分方程求解的"预解法"

为了更多地得到理论上和应用上占有重要地位的二阶线性非齐次微分方程的通解，用不同于前人的方法研究了二阶线性非齐次微分方程的解法。对这类方程引入预解方程和特征常数的概念，得到了一个新的、实用的可积判据及相应的通解积分表达式，从而提出了二阶线性非齐次微分方程的一个新的解略——预解法。实例证明该方法是可行的。     

基于粒语义推理的粒归结研究

粒归结方法和粒语义推理均是针对粒计算与逻辑推理相互融合研究的成果.粒语义推理能否作为粒归结方法的推理基础,或粒归结方法是否为粒语义推理的另一种形式是值得探究的问题.研究表明,粒归结方法中的粒归结序列是粒语义推理的充分条件.但对粒归结方法推广后,所得到的特殊粒归结序列是粒语义推理的充分必要条件.于是粒归结方法具有了推理的基础,粒语义推理也存在了其它的形式.这样粒归结方法与粒语义推理便具有相互支撑的紧密关系.     

Spectral analysis for a degenerate tree and applications

The energy in network of strings subject to the feedback in a root is decreasing to zero if the network is non-degenerate and this decrease is never exponential. We study in this paper the case of degenerate network (i.e. the ratio of two lengths of strings is a rational number) with a feedback in the root of the network. Under this assumption, we determine the energy limit and we identify the best rate of decay with the spectral abscissa of the underlying semi-group generator. We identify the spectral abscissa as in terms of the largest modulus of the roots of a polynomial.     

Approximate controllability of a semi‐linear neutral evolution system with infinite delay

In this work, we study the approximate controllability for a class of neutral control systems governed by semi‐linear neutral equations with infinite delay in Hilbert space. Sufficient conditions for approximate controllability are established by constructing fundamental solutions and using resolvent condition and techniques of fractional power operators. An example is also provided to illustrate the applications of the obtained results. Copyright © 2016 John Wiley & Sons, Ltd.     

Existence and Controllability Results for a New Class of Impulsive Stochastic Partial Integro‐Differential Inclusions with State‐Dependent Delay

In this paper, we study a new class of impulsive stochastic partial integro‐differential inclusions with state‐dependent delay in separable Hilbert spaces. Firstly, by using stochastic analysis theory, analytic resolvent operators, fractional powers of closed operators and suitable fixed point theorems, we prove the existence of mild and extremal mild solutions for these systems in the α‐norm. Secondly, we establish the controllability of the controlled stochastic partial integro‐differential inclusions with not instantaneous impulses. The results are obtained under the mixed Lipschitz and Carathéodory conditions. Finally, an example is provided to show the application of our results.     

非线性动力学方程的李级数解法及其应用

分别从推广的微分方程幂级数解的理论和线性算子半群理论等不同的角度研究了非线性动力学方程的求解问题,得到了所谓的李级数解法．并进一步讨论了算法的具体实施过程,它可以用于构造非线性动力学方程任意高阶的显式积分格式．最后,把李级数解法应用于求解广义Hamilton系统,它能保持广义Hamilton系统真解的典则性．数值算例显示该方法是有效的。     

线性偏微分方程问题的微分算子解

用微分算子法给出了线性扩散方程和波动方程的通解及初值以及边值相关问题的算子解,特别是对非齐次方程和非齐次边界问题处理尤其简捷适用.同时,此法也很好地克服了行波法、分离变量法与积分变换法等方法计算的繁锁,成为一种简便易记计算十分简单的解决问题的方法.