整数

The sum of two positive integers is 29, find the minimum value of the sum of their squares.

两个正整数之和为29，求此两数平方和的最小值。

Several have integral, mark and 0; have; of sheer number, relative number, average to plus, negative, reciprocal,; also includes rational number, surd; median of even number, odd, decimal;, mode, logarithm,, these are maths the basiccest in kingdom indispensable, it is scientific domain enumerated foundation.

数有整数、分数和零；有绝对数、相对数、平均数；有正数、负数、倒数、；也包含有理数、无理数；偶数、奇数、小数；中位数、众数、对数、指数、函数等等，这些都是数学王国里最基本的不可缺少的，是科学领域计数的基础。

Wavelet transform is done in image space directly. The multiplication number of the method is rough 25% less than the conventional implementation based on 1-D tensor product, so the memory usage is also reduced.

该方法进行小波变换时直接在图像空间进行2维分解，其乘法运算次数比传统的基于1维张量积的2维提升整数小波变换减少约25％，从而也减少了存储空间。

All the angles whose terminal edges are the same as the terminal of an angle α form the set S=｛β｜β＝α＋k·360°,k∈Z｝,i.e.,any angle whose terminal edge is the same of αcan always be represented by αplus intergral number of perigons .

所有与角α终边相同的角，连同角α在内，可构成一个集合S＝｛β｜β＝α＋k·360°，k∈Z｝，即任一与角α终边相同的角，都可以表示成角α与整数个周角的和。

By using the transfer matrix method of multibody system, the hard problem of computation of the vibration characteristics of LRMLRS coupled with rigid bodies and elastic bodies is solved which is very difficult to the ordinary dynamic methods, and the vibration characteristics of LRMLRS which is varied when the number of rockets in the launch device is varied, is obtained conveniently. By developing augmented eigenvectors of the LRMLRS and its orthogonality conditions, the nonorthogonality problem of the multibody system including rigid bodies and elastic bodies is solved and the exact analysis of the dynamics response of the LRMLRS including rigid bodies and elastic bodies is realized. By using the random integer programming method, the hard optimization problem which contains continuous variables, discrete variables and random variables at the same time is solved. This method provides a technology for optimum design with random variables and discrete variables. The dynamic optimum design is realized to decrease the number of rockets consumption in the LRMLRS test. The simulation system of dispersion of fire is established by using the maximum entropy method to estimate dispersion of fire.

通过应用多体系统传递矩阵法，解决了刚弹耦合远程多管火箭多体系统振动特性这一通常力学方法不便于解决的计算难题，方便地获得了远程多管火箭振动特性及其随发射架上火箭弹个数变化而变化的情况；通过构造增广特征矢量及其正交性条件，解决了刚弹耦合多体系统特征矢量不具有通常意义下的正交性的难题，实现了对刚弹耦合远程多管火箭动力响应的精确分析；应用随机整数规划法，解决了同时考虑连续、离散和随机变量等多种设计变量的优化设计难题，为含随机和离散变量的优化设计提供了手段，实现了减少远程多管火箭试验用弹量的动态优化设计；建立了应用最大熵法估计的密集度仿真系统，优化射序和射击间隔，实现了提高远程多管火箭射击密集度的动态优化。

This mapping can introduce sampling inaccuracies at texel boundaries.

得到的纹理地址被舍入到最近的整数，这种映射方法在texel边界会产生取样误差。

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。

If there are two such numbers, then the one that is closest to positive infinity is returned.

如果有两个同样接近的整数，则返回最接近于正无穷的那个。

According to the reuse of the expressway network toll data, the toll amount prediction by car type amount, the classification to fraud toll collectors and solve the integer linear programming problem of toll collector job scheduling are the three application solution examples.

在高速公路联网收费数据的再利用中，根据分车型车流量预测收费额、对收费员进行作弊分类和求解收费员排班这个整数线性规划问题是遗传规划的三个应用算例。

In 2004 Zhang Zhongfu presented the concept ofadjacent vertex distinguishing total coloring whose content is: Let G be a connectedsimple graph with order at least 2, k be a positive integer and f be a mappling fromV∪E to {1,2,...,k}. Let C={f}∪{f|uv∈E,v∈V}for all u∈V. If (1) for any uv, vw∈E,u≠w, we have f≠f;(2) for any uv∈E, we have f≠f, f≠f, f≠f,then f is called a k-proper total coloring of graph G.

第三章和第四章主要研究了两种联图的邻点可区别全染色，邻点可区别全染色的定义是张忠辅在2004年提出来的，其内容为：设G是阶至少为2的简单连通图，k是正整数，f是V∪E到{1，2，…，k}的映射，对任意u∈V，记C={f}∪{f|uv∈E，v∈V}。

Breath, muscle contraction of the buttocks; arch body, as far as possible to hold his head, right leg straight towards the ceiling (peg-leg knee in order to avoid muscle tension).

呼气，收缩臀部肌肉；拱起身体，尽量抬起头来，右腿伸直朝向天花板（膝微屈，以避免肌肉紧张）。

The cost of moving grain food products was unchanged from May, but year over year are up 8%.

粮食产品的运输费用与5月份相比没有变化，但却比去年同期高8％。