整数的

Ifσ: I→C is an incidence coloring of G and |C|=k, k is a positive integer, then we say that G is k- incidence colorable andσis a k - incidence coloring of G; The minimum value of k such that G is k -incidence colorable is called the incidence chromatic number of G, and is denoted byχ_i, namelyχ_i = min {|C||σ: I→C is an incidence coloring of G}.

若σ：I(G→C是G的一个关联着色且|C|=k，k是一个正整数，则称G是k-可关联着色的，σ是G的一个k-关联着色；使得G是k-可关联着色的最小的k值称为G的关联色数，记为X_i，即X_i=min{|C||σ：I→C是G的关联着色}。

Suppose C is a Graph with k loops andf: G 梸- G is a continuous map with at least a peri- odic point. We prove the following three conditions are equivalent:(1) f is equicontinuous;(2) One of the following End + 2k + 1 conditions holds: in FJm.~0(E~+2L!= flJ1,m = l,2,挃,End J=1 + 2k; 1 0 = flf is a ioop on Gandf I~:0?- 0 is conjugate j=1 to a rational rotation;(3) One of the following End + 2k + 1 conditions holds: k m Lfl.m/~oE~(G+2i!~ is uniformly convergent, m = 1,2,,End+2k; n There is a poistive integer number n,~~~ is uniformly convergent.

假设G是含有k个圈的图，f是G到自身上的连续映射，并且至少有一个周期点，我们证明了下列三条陈述是等价的：（1）f是等度连续的；（2）下列End+2k+1个条件之一成立： m）F l）O=是G的一个圈，且fl_o：O→O共轭于一个有理旋转；（3）下列End+2k+1个条件之一成立： m）是一致收敛的，m=1，2，…，End+2k； l）存在某个正整数n，是一致收敛的。

In this paper, new classes of linear block codes over finite fields of the algebraicinteger ring of quadratic number fields Qd~(1/2 modulo irreducible elements with norm p or p~2 are presented. These codes can correct one error which takes from the cyclic subgroup of the multiplicative group of the finite fields. The results presented in this paper extend the corresponding results of previous papers.

在处理适用于二维信号的线性分组码时，我们考虑类数为1的有理数域二次扩域Qd~(1/2的代数整数环，利用范数为p或p~2的不可约元构造有限域，给出剩余类域的一组完全陪集代表元系，从而构造出一类有限域上的线性分组码，当错误取值于有限域乘法群的一个循环子群时，所得到的适用于二维信号的线性分组码可以纠单个错，推广了文[14-16]的结果。

Firstly, according to the difficulties in the optimization of chemical engineering and the intrinsic disadvantage of deterministic optimization algorithms, this work analyzed the importance and advantage of stochastic algorithms, and proposed some important aspects in research on them. Secondly, genetic algorithm was applied to two problems of data driven modeling, one of which was combination problem, the other was mixed integer nonlinear programming. Thirdly, systemic investigations were made on the basic structure, dynamic behavior and modifications of particle swarm optimization. Lastly, two kinds of proposed PSO algorithms were applied on calculation of phase equilibrium, which is nonconvex optimization.

本文首先根据化工优化中存在的困难和确定性优化算法内在的缺点，分析了随机优化算法的重要性，并提出研究随机优化算法应注意的问题；其次，将遗传算法应用于两个数据驱动建模问题，一为组合优化问题，一为混合整数优化问题；再次，从粒子群优化算法的基本结构、运动行为、改进方法做了系统的研究：最后，将提出的两种改进粒子群优化算法应用于相平衡计算问题，为非凸全局优化问题。

In 2000, F. LUCA proved that Fermat number are anti-sociable numbers, and in 2005, M. H. LE proved all powers of 2 are anti-sociable numbers. We have used the method of M. H. LE to obtain some new results of the anti-sociable numbers. For every integer n containing prime divisors that are 1 mod 4, let p mod 4 be an arbitrary prime divisor of n. There is at least one anti-sociable number in n^2, p^2n^2, p^4n^2, and p^6n^2. Therefore we can prove that anti-sociable numbers have positive density in perfect square numbers. We also give a method to find the exact anti-sociable numbers.

LUCA证明了Fermat数都是孤立数；2005年，乐茂华教授证明了2的方幂都是孤立数，用乐茂华教授的方法给出孤立数的一些新的结果：对于任意含有4w+1型素因子的正整数n，设p为n的任意一个4w+1型素因子，则在n^2，p^2n^2，p^4n^2，p^6n^2里至少有一个是孤立数，因此可以证明孤立数在完全平方数里有正密度，另外也给出求解确定孤立数的方法。

"Find wallet"and"buy horses"are one-degree indeterminate linear equations, which can be solved by removed parameter, making no significant impact in the history of development of the indeterminate linear equation. 3、the problem of remainder arises with divining number. In sum, indeterminate problem borrowed from the eastern countries is to show Fibonacci's mathematical charm. He did not make in-depth study of the problem, but it is fascinating to the later European scholars, because these issues are interesting, and Fibonacci's solution is creative.

本论文通过对散布在《计算之书》各个章节中的三类不定问题进行系统梳理之后发现：《计算之书》"买鸟问题"的解法是"合金法"，此方法是用来解答三种以上钱币配置问题整数解的情况；"捡钱包问题"和"买马问题"是一次不定方程组问题，解答过程相当于现今的一次方程组问题，通常通过"消参"即可解决，在历史上没有对不定分析问题的研究产生明显影响；而"剩余问题"是以占卜猜数问题的形式呈现计算过程，虽然斐波那契没有对不定问题进行深入研究，但正是因为这些问题的趣味性，以及斐波那契某些解法的独创性而引起以后欧洲学者对此类问题的兴趣，并由此将不定分析问题研究引入欧洲。

Paper puts forward the method of read DICOM field in term of sequence, reduces the time of read DICOM file in order to mend the arithmetic efficiency of read DICOM file information. Paper introduces two concept, slope and shift, reduces the linear interpolation function of VOI LUT (Value of Interest Look Up Table), and uses the way of make real number operation into integer operation to simplification the linear map function, thereby makes the image zoom speed up. Paper depicts the class and function of image measure and label particular at last, and analyses actualize step of the operation of measure and label.

论文提出严格按照顺序读取DICOM字段的做法，尽量减少访问DICOM文件的时间以加快读取DICOM文件信息的算法效率；论文中引入斜率和偏移量这两个概念，简化了VOI LUT转换的线性插值函数，并采用将实数乘除转化为整数运算的方法简化线性映射函数，从而加快了图像缩放的速度；论文最后详细描述了图像测量和标注用到的类和函数，并分析了具体的测量和标注操作的实现步骤。

Finishing in 3rd Place in the Men's Division was Gary Neal of Spartanburg, SC In 4th Place was Rusty Jackson III of Allensville, Ky. Tying for 5th Place in the Men's Division is Brian Belobradic of Whitby, Ontario, Canada and Eddie Little of Salisbury, NC Defending champion Michell Monk of Palm Bay, Fla. rounded out the top finishers in the Women's Division with a 3rd Place finish.

整理在第三位，在男性的分工是加里奥尼尔的斯帕坦堡，资深大律师在第四位，是生锈的杰克逊的第三艾伦斯维尔，肯塔基州并列第五位，在男性的分工是布赖恩belobradic的惠特， Ontario ，加拿大和埃迪小梳士巴利，数控卫冕冠军michell和尚棕榈湾，佛罗里达州的整数列顶端的优质买家询盘，在妇女的分工与第三的成绩。

No additional data for frequency tracking are need, but higher estimation accuracy and low computational complexity can be obtained. Finally, a kind of optimizing joint algorithm for symbol timing, frequency synchronization and channel estimation is proposed. The false alarm probability and miss detect probability of the symbol timing are derived. We proved that the time－frequency offset domain random sequence sliding in the frequency offset direction is orthogonal with the original random sequence, and proposed a new integer frequency offset estimation algorithm. The coarse estimation methods for fractional frequency offset both in AWGN and multipath channels are proposed too.

最后，提出了一种优化的符号同步、频偏估计和信道估计的联合算法，推导了符号同步方法的虚警概率和漏检概率，给出了随机序列在时间－频率偏移域沿频率偏移方向滑动后与原序列近似正交的证明，提出了一种新的在时间－频率偏移域沿频率偏移方向进行滑动相关估计整数频偏的方法，提出了在AWGN信道和多径信道下进行小数频偏粗估计的方法，给出了小数频偏细估计的ML估计结果和利用频域PN序列取值特性的简洁的信道估计结果。

Nyang and Song proposed a digital signature scheme based on quadratic residue problem.

对Shimada公钥密码体制进行推广，提出一种新的密码体制，这种新的公钥密码体制的安全性建立在一般形式的素因子分解问题之上，攻击这种新的密码体制等价于对一般形式的大整数进行素因子分解，并设计一种新的数字签名方案和新的认证加密方案。

I can not make it blossom and suits me

我不能让树为我开花

When temperatures are above approximately 80 °C discolouration of the raceways or rolling elements is a frequent feature.

当温度高于 80 °C 左右时，滚道或滚动元件褪色是很常见的特征。