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In addition, by utilizing Jacobi two square numbers theorem and Lagrange four square numbers theorem and some theta function identities, we also prove the known results of number theory: two triangular number theorem, four triangular number theorem, and the number of representations of a positive integer by various quadratic forms in terms of divisor functions

包括Jacobi二平方数定理，Lagrange四平方数定理等，然后利用这些结果结合几个theta函数恒等式，我们获得了把任意一个正整数表示成两个三角数或四个三角数的和以及其他的二次形式的方法数，这些方法数都是用因子函数来表示的。

The dynamic measuring method of alignment parameters based on the Satisfaction Criterion Model is presented in this paper. Using the quadratic regression crosscut combination method to organize the experiment, the mapping relationship between side force of slippage and camber angle and toe-in of the testing vehicles is obtained by regressing the experiment data. In this experiment, side force and slippage are testing objects, camber and toe-in value are testing factors.

本文提出了基于满意准则数学模型的车轮定位参数智能化动态测量方法，运用二次回归正交组合设计方法组织和安排试验，以车轮外倾角和前束值作为试验因素，侧向力和侧滑量作为试验目标，通过对试验数据的回归处理得到了试验车辆的侧滑量或侧滑量同车轮外倾角以及前束值之间的映射关系。

An optimization design scheme is crucial for torpedo, however, there has been no any such method recognized so far. This paper presents a method for torpedo lineshape optimization design based on the iSIGHT. In this method, the optimization strategies of simulated annealing algorithm and continuous quadratic planning method are adopted, and the fluid analysis software Fluent is integrated to calculate the fluid parameters of torpedo body lineshape. The comparison of the optimization results obtained by both the presented and the traditional methods shows that the torpedo lineshape optimization method based on the iSIGHT is satisfactory and feasible.

寻找最优设计方案是鱼雷设计的重中之重，针对目前鱼雷优化设计领域还没有一套公认的优化设计方法这一现状，提出了一套基于iSIGHT的工程设计优化方法，将这款商业软件应用于鱼雷线形优化设计中，采用了模拟退火算法+连续二次规划法的优化策略，集成流体分析软件Fluent对雷体线形的流体参数进行了计算，并与传统优化方法结果相比较，结果表明，基于iSIGHT的优化设计方法在鱼雷线形优化设计中是可行的，能够得到令设计人员满意的鱼雷线形优化方案。

The nonlinear dynamic system with quadratic and cubic nonlinearities is obtained by applying mathematical transformation to the equation.

基於Karman方程的动态比拟，运用Galerkin法，选用合适的正交函数将控制薄板振动的偏微分方程离散化为常微分方程，得到一带有平方和立方非线性的参数激励和外激励联合作用的非线性动力学系统。

Show that the coefficient a of the quadratic term changes sign at the BCS transition point, while b and c are positive.

证明系数a的四次项在BCS跃迁点上变号，而b及 c 均是正的。

In this paper,we give a sufficient and necessary condition for the level surface s with respect to non-degenerate quadratic functions by the usage of the Hessian metric and of a transversal vector field.

本文利用Hessian度量和横截向量场，给出了非退化二次函数的水平曲面的一个充要条件。

The trigonometric polynomial curves retain the main superiority of the quadratic Bézier curves.

给出了二次三角多项式形式的Bézier曲线，基函数由一组带形状参数的二次三角多项式组成。

Necessary and sufficient conditions for equalities between a 2 y′y and minimum norm quadratic unbiased estimator of variance under the general linear model, where a 2 is a known positive number, are derived.

给出了一般线性模型下方差的最小范数二次无偏估计相等的充要条件，并且当高斯马尔可夫估计与最小二乘估计相等时，获得了一个相对简单的条件，最后给出此条件应用于抽样调查的一个例子。

In this paper, using the method of the Lagrangian dual, an unconstraint but nondifferentiable optimal problem in input space is proposed as the dual of the quadratic programm...

证明了该分片二次函数的极小点对应原二次规划的ε最优解，而用此极小点可直接算出支持向量和最优超平面。

Since the lengths of the line segments and the angles between line segments are treated as representation parameters, it is convenient to construct energy function and to deal with displacement and length constraints. Based on this advantage, a parametrical model for human body is proposed, which can easily produce human body models with different feature sizes. The above method is just suitable for polylines. Therefore, a generic deformation method for both discrete curves and surfaces is presented. The energy function is constructed by analyzing the relationship of the points before and after deformation. Together with the displacement constraints, the deformation problem is converted to a convex quadratic programming. A necessary condition for constraint points and a sufficient condition for the uniqueness of solution are given. The proposed method can be combined with skeleton-driven animation to control the deformation.

将线段长度与线段之间的角度作为表示参数，既有利于能量函数的构造，又便于处理位移约束和长度内蕴约束条件，利用这一优势，将其应用于三维人体的参数化建模，可以方便地产生具有不同特征尺寸参数的人体模型，由于这种方法只适用于折线变形，具有较大局限性，因此，本文进一步提出一种较通用的离散曲线曲面变形方法，通过分析变形前后的位置关系来构造能量函数，再加上位移约束条件，将变形问题转化为一个凸二次规划问题，并且给出了约束点应满足的必要条件及模型解唯一的充分条件，这种方法还可以与骨架驱动变形的思想相结合，能更好的控制变形。

Article 144 The Government of the Hong Kong Special Administrative Region shall maintain the policy previously practised in Hong Kong in respect of subventions for non-governmental organizations in fields such as education, medicine and health, culture, art, recreation, sports, social welfare and social

第一百四十四条香港特别行政区政府保持原在香港实行的对教育、医疗卫生、文化、艺术、康乐、体育、社会福利、社会工作等方面的民间团体机构的资助政策。原在香港各资助机构任职的人员均可根据原有制度继续受聘。

Small wonder, then, that the Chinese spend more in the shop than any other group of foreign visitors do .

这样的小惊喜，使中国顾客比任何国家的人消费得更多。