定理

Owing to the importance of Disquisitiones Arithmeticae in histoiy of number theory and the core position of the congruent theory in elementary number theory, this paper is to focus on the following two topics: the origin and development of Fermats little theorem and the quadratic reciprocity law which was hailed as golden by Gauss.

鉴于《算术研究》在数论发展史上的重要性以及同余理论在初等数论中的核心地位，本文重点研究费马小定理和被高斯誉为"黄金定律"的二次互反律的起源和发展。

According to the fUndamental theorem of coniC In projective geometry any five points can decide one conic section .

在射影几何中，二次曲线定理告诉我们任意五点可以决定一条二次曲线。

This article takes the teaching of conic sections as an example. By designing worksheets, teachers can introduce the historical material about conic sections to students. By way of using Apollonius' definition of parabola, ellipse and hyperbola, teachers can introduce the geometric aspect of "conic section" to students. By using the concept of " latus rectum " in Conics , we can connect "conic sections"-- representation of geometrical aspect, with "the equation of conic sections"-- representation of algebraic aspect to improving insufficiency of text books.

同时本文也试著从历史文本中寻找材料，简单举例说明数学教师可以如何应用这些史料在几何单元教学上，例如三角函数的正余弦定理，最后再以圆锥曲线的正焦弦为例，说明如何利用数学史料於此单元的教学，尤其是阿波罗尼斯的《锥线论》中对圆锥曲线的3个命题，将此3个命题的内容与意涵，尤其是正焦弦在圆锥曲线的几何意义上所扮演的角色，将其适当地融入教学中，将可使学生真正学习圆锥曲线的几何知识，而不再只是代数形式的几何知识。

Generalized strong vector variational-like inequalities; Minty's lemma; KKM mapping; pseudomonotone; Ky Fan lemma; open mapping theorem; complete; the second category; conjugate; proper convex lower semicontinuous function; linear mapping; closedness

基础科学，数学，数学分析广义强向量似变分不等式； Minty引理； KKM映象；伪单调； Ky Fan引理；开映射定理；完备；第二纲；共轭；真凸下半连续函数；线性映射；闭性

In the third, we hit the variational principle, orthogonal decomposition, orthonormal base, Riesz representation theorem and the conjugate operators in the Hilbert space.

第三部分，Hilbert空间的变分原理、正交分解、完备标准正交系的存在性、Riesz表现定理和共扼算子等。

Chapter 4 establishes the theory of convex fuzzy mappings: The concepts, such as Jensen's inequality, positively homogeneous, infimal convolution, right scalar multiplication and convex hull are introduced. The corresponding theorems are demonstrated by using the parametric representations of fuzzy numbers. In anti-fuzzy number space, the conjugate mapping of convex fuzzy mapping is concerned, and convexities of conjugate set and conjugate mapping of convex fuzzy mapping are proved. The notions of subgradient, subdifferential, differential with respect to convex fuzzy mappings are investigated, which provides the basis of the theory of fuzzy extremum problems.

在第4章中，建立了有关凸模糊映射的理论：建立了关于凸模糊映射的Jensen不等式、模糊正齐次映射、凸模糊映射的下卷积、右数乘和凸包等概念，利用模糊数的参数化表示，给出了相应的定理；在反模糊数空间，对凸模糊映射的共轭也作了探讨，证明了凸模糊映射的共轭集合和共轭映射都是凸的；最后对凸模糊映射的次梯度、次微分和微分等概念进行了研究，为模糊极值理论打下了基础。

We give strong continuity of an operator connected with fractional power space and obtain existence of optimal controls.

得到了分数指数空间一算子的强连续性和最优控制的存在性定理。

The discovery of strange particles lead to a generalization of the law of nucleon conservation .

奇异粒子的发现导致了核子守恒定理的推广。

Considering enough first integrals,such as conservation of energy and angular momentum,the system is integrable by Liouville's theorem.

利用能量积分，根据惠特克定理对系统的动力学方程进行降阶，并根据旋转数给出系统作周期或准周期运动的判别条件。

Key words: theorem of kinetic energy; conservation law of mechanical energy; reference frame

动能定理，机械能守恒定律应用

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。