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Finally,an effective graphical test is made for checking the robust stability of a polytope of neutral quasi-polynomials.

最后给出了检验中立型胞鲁棒稳定性的一个有效的图解法。

The synopses based Chebyshev polynomials can be efficiently used to estimate frequency distribution of attributes of a given database relation.

基于Chebyshev多项式的概要能有效估计数据库关系属性的频度分布。

In this thesis, we study some aspects in analytic combinatorics. The main contents can be summarized as follows. In Chapter 2, by classical umbral method, we obtain some properties and identities of invariant sequences. More generally, we study the self-inverse sequences related to sequences of polynomials of binomial type and the self-inverse sequences related to Sheffer sets, and give some interesting results of these sequences.

本文研究组合分析学中的若干问题，具体内容如下：第二章用经典哑运算方法研究了不变序列的性质及满足的恒等式，随后又推广到更一般的情形，即关于二项式型多项式序列的自反序列和关于Sheffer序列的自反序列。

The thesis mainly discuss the unimodality of independence polynomials of some graphs.

本文主要来讨论一些图的独立多项式的单峰型性质。

The third chapter further investigates the unimodality of independence polynomials of caterpillars and vertebrates.

第三章在Levit和Mandrescu所研究的蜈蚣树的基础上，进一步研究毛毛虫树、Vertebrate树的独立多项式的单峰型性质。

Newton inequality and Aissen-Schoenberg-Whitney theorem provide the basic link between the property of unimodality and polynomials having only real zeros.

Newton不等式和Aissen-Schoenberg-Whitney定理建立了实零点多项式与单峰型性质之间的联系。

The main academic productions of this thesis are:(1) the parallel algorithms of computing permanents and permanental polynomials of sparse matrices are designed and implemented;(2) an efficient balancing straggles of parallel load is proposed using the theory of scheduling;(3) valuable data for the research of the molecule structure of fullerenes are obtained;(4) the multi-dimensional stable marriage model and its numerical methods give a new path to solve the clustering problems.

本文的主要学术贡献是：(1)设计并实现了稀疏矩阵积和式与积和多项式的并行算法；(2)利用排序理论给出了有效的负载平衡策略；(3)为富勒烯分子结构的研究提供了有价值的数据支持；(4)多维稳定婚姻模型及计算方法，为聚类问题的求解提供了新途径。

These bases are produced by k-adic dilations and translates of integers of k-1 smooth functions which decay as polynomials.

这组基由k—1个具有多项式衰减速度的光滑函数经过k进伸缩与整数平移生成。

Real track isn't built out of 3rd order polynomials – it's built out of tangents, curves and easements.

真实的轨道并不是由三次多项式组成的–真实的轨道是由切线、弧线和介曲线。

Even if you're familiar with summations, integrals, polynomials, exponents, etc., if you see a thick nest of them your inclination is probably to skip right over that sucker as one atomic operation.

即使你熟悉累加，积分，多项式，指数，等等，如果你看到一堆符号堆彻的异常复杂时，你就把他实现的功能简单的当成一个原子操作好了，不要深究太多。

Now he worked in ajoint venture.

现在他在一家合资企业工作。

More troops in Afghanistan won't change any of the foregoing.

更多的在阿富汗的军队也不会改变之前的状况。