定理

2By constructing a completely continuous operator in a functional space and employing the cone compression and expansion fixed point theorems, we obtain some sufficient conditions which guarantee the existence of positive periodic solutions for Eq.

通过在一个函数空间构造一个全连续算子，再利用锥压缩锥拉伸不动点定理，得到了一些保证方程(1)，(2)至少存在一个周期正解的充分条件，所得结论改进了文[1]和[6]中的结果。

Completeness Theorem showsthat syntactic and semantic consequences coincide in the case of the predicatelogic.

完全性定理表明一阶谓词逻辑的语法后承和语义后承是重合的，它标志着一阶逻辑的成熟。

Because Horn-clause logic theory is of significance in both respects of theory and application, We especially studied lattice-valued Horn-clause logic with truth-value in lattice implication algebra, and the soundness and completeness theorem have been proved.

经典逻辑中，Horn子句逻辑理论具有广泛的应用，因而，本文中特别建立了基于格蕴涵代数的格值-类Horn子句逻辑，并证明了可靠性和完备性定理，这为建立一类基于格值逻辑这种非经典逻辑的人工智能语言将产生重要的作用。

Compared with Plotkin's work, a reduction closed CPS language is defined in which all continuations are explicitly expressed as functional encodings and it is simpler to prove both the soundness and completeness directions of simulation theorem.

与Plotkin的工作比较，工作特点在于，给出了一个CPS归约闭语言，该语言中所有继续都可以用函数形式表达，且模拟定理的可靠性和完备性方向证明更为简单。

Algebraic semantics ; Barcan formula ; Kripke's relational semantics ; nested domains ; Kripke's special semantic ; completeness theorem

代数语义； Barcan－公式； Kripke的关系语义；嵌套论域；狭义Kripke语义；完全性定理

This paper studys the stability of nonlinear systems in two particular critical cases. In a case, the linear systems at the equilibrium point of interest is assumed to possess a simple zero eigenvalue. In the other case, it is assumed to possess a complex conjugate pair of simple pure imaginary eigenvalue.

本文基于中心流形定理研究了非线性系统在两种特殊临界情形下的稳定性问题，一种是与它相应的线性系统在平衡点仅有零特征根，另一种是与它相应的线性系统在平衡点仅有一对共轭的纯虚数特征根。

The central goal of this work is trying to generalize the above result to the Higgs version case, which should be helpful to the study of some question, say variants of the Kobayashi-Hitchin correspondence. The theorem to be proved here is the followingTheorem 02: Let M be a compact complex manifold of dimension m with a Hermitian standard metric g and let be a Higgs bundle over M.

本文的一个主要的目的是把上面的定理推广到E是—Higgs向量丛的情形；这一结果的意义在于在研究与Kobayashi-Hitchin correspondence相关的问题，如考虑Kobayashi-Hitchin correspondence的形变展现它的作用。

In this paper, we introduce the algorithm of Schoof-Elkies-Atkin to compute the order of elliptic curves over finite fields. We give out a fast algorithm to compute the division polynomial f〓 and a primitive point of order 2〓. This paper also gives an improved algorithm in computing elliptic curve scalar multiplication. Using the method of complex multiplication, we find good elliptic curves for use in cryptosystems, and implemented ElGamal public-key scheme based on elliptic curves. As a co-product, we also realized the algorithm to determine primes using Goldwasser-Kilian's theorem. Lastly, the elliptic curve method of integer factorization is discussed. By making some improvement and through properly selected parameters, we successfully factored an integer of 55 digits, which is the product of two 28-digit primes.

本文介绍了计算有限域上椭圆曲线群的阶的Schoof-Elkies-Atkin算法，在具体处理算法过程中，我们给出了计算除多项式f〓的快速算法和寻找2〓阶本原点的快速算法；标量乘法是有关椭圆曲线算法中的最基本运算，本文对[Koe96]中的椭圆曲线标量乘法作了改进，提高了其运算速度；椭圆曲线的参数的选择直接影向到椭圆曲线密码体的安全性，文中利用复乘方法构造了具有良好密码特性的椭圆曲线，并实现了椭圆曲线上ElGamal公钥体制；文中还给出了利用Goldwasser-Kilian定理和椭圆曲线的复乘方法进行素数的确定判别算法；最后讨论了利用椭圆曲线分解整数的方法并进行了某些改进，在PC机上分解了两个28位素数之积的55位整数。

In chapter 4, we give the definitions of almost spirallike mappings of type β and order α, spirallike mappings of type β and order α and strongly spirallike mappings of type β and order α, and obtain their growth and covering theorems on the unit ball in complex Banach spaces.

在第四章中，我们在复Banach空间中的单位球上定义了几类新的映射：α次的殆β型螺形映射，α次的β型螺形映射和α次的强β型螺形映射，并且证明了它们的增长掩盖定理。

Based on the higher mathematics method proved inequalities are summarized, and the proposed using the function extreme value and the monotonicity and concave and convex function sex, and mean value theorem, Taylor formula, integral these common higher mathematics method, combining with concrete examples of each kind of method to solve the problems for type, and the key problem of the specific steps, and points out that the inequality proof of higher mathematics method used properly, improve the difficult easy to ability to solve problems.

本文对不等式证明中的高等数学方法作了归纳总结，提出了利用函数的单调性，极值与最值，函数凹凸性，中值定理，泰勒公式，积分这些常用的高等数学方法，并结合具体实例阐述了每一种方法的适用类型、解决问题的关键和证明问题的具体步骤，指出在不等式证明中恰当地运用高等数学方法可以化难为易，提高解题能力。

We have no common name for a mime of Sophron or Xenarchus and a Socratic Conversation; and we should still be without one even if the imitation in the two instances were in trimeters or elegiacs or some other kind of verse--though it is the way with people to tack on 'poet' to the name of a metre, and talk of elegiac-poets and epic-poets, thinking that they call them poets not by reason of the imitative nature of their work, but indiscriminately by reason of the metre they write in.

索夫农 、森那库斯和苏格拉底式的对话采用的模仿没有一个公共的名称；三音步诗、挽歌体或其他类型的诗的模仿也没有——人们把&诗人&这一名词和格律名称结合到一起，称之为挽歌体诗人或者史诗诗人，他们被称为诗人，似乎只是因为遵守格律写作，而非他们作品的模仿本质。

The relationship between communicative competence and grammar teaching should be that of the ends and the means.

交际能力和语法的关系应该是目标与途径的关系。