应用函数

Based on Bellman stochastic nonlinear dynamic programming, we develop an optimal control algorithm for the discrete stochastic system with conditional Markov structure.

基于Bellman随机非线性动态规划法，提出了具有条件马尔科夫跳变结构的离散随机系统的最优控制方法，应用随机变结构系统的性质对最优控制算法进行了简化处理，并将后验概率密度函数用条件高斯函数来逼近，针对一类具有条件马尔科夫跳变结构的线性离散随机系统，给出了其逼近最优控制算法。

The multi-index comprehensive evaluation model was established by artificial neural network BP algorithm. The evaluation index was described by adopting subordinative function of fuzzy mathematics. Sample-study pattern consists of the values of subordinative function on ends and on middle point.

利用人工神经网络BP算法建立了多指标综合评价模型，采用模糊数学的隶属函数对评价指标进行描述，由隶属函数的端点值和中间值组成学习样本模式，举例讨论了神经网络在多指标综合评价中的应用方法及应注意的一些问题。

A theorem for the summation of series expressed by function terms derived from function identities is established.

摘要建立了由函数恒等式所导出的函数项级数的求和定理，并给出了具体应用的实例。

And each symmetric function can be written into a linear combination of homogeneous symmetric functions.

这样，就可以把一个n元对称布尔函数转化为一个n+1维向量v_f =v_f (0， v_f (1)，…， v_f，其中v_f表示重量为i的函数值， 0≤i≤n，此向量v_f称为对称函数f的向量值，极大地减少了对存储空间的需求，并且在软件应用中发挥着重要作用。

Chapter 2 is devoted to study of exact solutions of the nonlinear evolution equations. Using solutions of a Bernoulli equation instead of tanh in tanh-function method we find some more general solutions of the KdV-Burgers-Kuramoto equation , and by using the nonlinear telegraph equation we show that there are many different choices on its balancing number m and the power n of the nonlinear term in Bernoulli equation by which we can recover the previously known solutions and also can derive new square root type solitary wave solutions. Exact solitary wave solutions for a surface wave equation are obtained by means of the homogeneous balance method. We also present an approach for constructing the solitary wave solutions and non-solitary wave solutions of the nonlinear evolution equations by using the homogeneous balance method directly, which is also used to find the steady state solutions, solitary wave solutions and the non-solitary wave solutions of the 2+1 dimensional dispersive long wave equations. The soliton-like solutions of the BLMP equation and the 2+1 dimensional breaking soliton equation are found by use of the symbolic-computation-based Method.

第二章中研究了非线性发展方程的精确解：用双曲正切函数法中的双曲正切函数换为Bernoulli方程的解的方法而给出KdV-Burgers-Kuramoto方程的精确解并用非线性电波方程为例说明了平衡数m和Bernoulli方程中非线性项的次数n有着多种选择的可能，它不但使我们能找到已知解而且也能找出新的根式孤立波解；用齐次平衡法给出一个曲面波方程的精确孤立波解，并提出直接用齐次平衡法寻找非线性发展方程的孤立波解、非孤立波解的方法，作为应用给出2+1维色散长波方程组等的定态解、孤立波解、非孤立波解等；用Symbolic-computation-basedMethod获得BLMP方程和2+1维破裂孤子方程的类孤子解；提出sine-Gordon型方程的直接求解方法，并获得sine-Gordon方程、双sine-Gordon方程、sinh-Gordon方程、MKdV-sine-Gordon方程和Born-Infeld方程等的精确孤立波解。

The tensor quality of energy density function, which contains coordinate vector, is mathematically proofed.

考虑到模型中能量密度函数含有坐标轴方向向量一项，该文对能量密度函数的张量性进行了严格的数学证明，并将VMIB模型初步应用到脆性材料的单轴受压破坏。

The purpose of this paper is to investigate the application of topology description function in material design.

研究了拓扑描述函数在材料设计中的应用，给出了一种基于拓扑描述函数的特定性能材料设计问题的提法和求解方法。

We also define two families of functions, named a torus height functionand an AdS-distance-squared function respectively, and use them to investigate thesingularities of the AdS-null surfaces and the torus Gauss images as applications ofsingularity theory of functions.

作为函数奇点理论的应用，利用这两个函数族来研究AdS-null曲面和环面高斯像的奇点。

Applied widely in the data encryption, pseudorandom sequences can be generated not only by hardware but also by trace function, and it is found that the sequences generated by trace function are much better than those generated by hardware, especially in the aspects of correlation properties.

摘要伪随机序列被广泛应用于数据加密，它既能利用硬件产生，也可以利用有限域上的迹函数来生成，并且由后者生成的序列的密码特性远远优于前者，特别是在相关函数方面更是如此。

The constructing process of the algorithms itself indicate that they are brevity and have definite geometric meaning, scientific iterative terminal criterions and no strict requirement to function. Finally, some digital experimentation is presented to indicate the algorithms application in solving the problem of maximum of function, transcendental equation,integer programming and so on. The results indicate that the algorithms have more global and more adaptability compared to traditional algorithms and have more calculating efficiency and more scientific iterative terminal criterions compared to some present popular artificial intelligence algorithms.

算法的构造过程本身表明了该算法简单明了、几何意义明确、迭代终止准则科学、对函数的要求较低；最后举了几个数值试验的例子以说明该类算法在求函数的最值，解超越方程以及整数规划等问题中的应用；数值试验的结果标明该算法比单纯由"微分"思想演化而来的传统算法有更好的全局性和对问题的更广泛的适应性，比现在流行的一些人工智能方法有更高的运算效率和更适当的迭代中止准则。

But we don't care about Battlegrounds.

但我们并不在乎沙场中的显露。

Ah! don't mention it, the butcher's shop is a horror.

啊！不用提了。提到肉，真是糟透了。