丢番图方程；正整数解；同余；递归序列。
Diophantine equation; Positive integer solution; congruence; Recurrent sequence.
丢番图方程；素数；整数解；勒让德符号；同余。
Diophantine equation; prime; integer solution; Legendre symbol; congruence.
应用复变函数论的方法，简洁地给出了的一切有理数解和一切整数解公式。
In this paper, the general rational solutions and the general integer solutions of are given.
从理论上讲，只有模糊度的成功率才是评价模糊度整数解正确性的严密尺度。
Theoretically speaking, only ambiguity success rate is a severe approach to evaluate the rightness of ambiguity integer solution.
提出的算法对整数变量进行搜索，并采用合并调度规则来求解整数解对应的调度子问题。
This scatter search approach interactively USES a combined dispatching rule to solve a scheduling sub-problem corresponding to each integer solution visited in the search process.
实例试算表明这两种方法有着不同的执行过程，但有着相同的模糊度整数解和相当的搜索效率。
It is shown by an example that though these two approaches have different performance process, but they have the same integer ambiguity solution and the equivalent search efficiency.
本文给出一个不定方程非负整数解的组数的组合计数公式，说明了它在求解一类与数字有关的古典概率方面的应用。
This paper introduces the problems of some identical equation solved by the numerical characters of the classic probability and stochastic variable.
佩雷尔曼的定理远远超过证明这些“不存在”的断言，正如怀尔斯证明的定理所告诉你的东西要多于一类方程不存在整数解这个结论。
Perelman's theorem goes far beyond proving this "non-existence" claim, just as Wiles' theorem tells you much more than non-existence of integer solutions of certain equations.
电力系统机组组合问题是一个典型的大规模混合整数的非线性组合优化问题，很难得到理论上的最优解。
Power system unit commitment, a problem of nonlinear commitment optimization with typical large-scale hybrid integers, is difficult to get an optimal solution in theory.
本文对其做适当改进，用于解凸整数规划问题。
In this paper it is improved appropriately and applied to the convex integer programming problems.
整数规划是NP困难的经典问题之一，将传统的二分搜索方法推广应用到整数规划的解空间中，提出一种求解整数规划的新算法。
Integer Programming is a famous NP hard problem. This paper presents a new algorithm, in which the method of similar dimidiate is adopted.
研究了一个特殊的整数瓶颈问题并给出了两个求最优解的多项式算法程序。
In this paper, we consider a special integer bottleneck problem, and present two polynomial algorithms.
“分支”为整数规划最优解的出现创造了条件，而“定界”则可以提高搜索的效率。
"Branching step" has created the condition for the integer linear programming appearance, but "bounding step" may enhance the search the efficiency.
本文给出了用代理约束选取混合整数线性规划问题初始可行解的一种方法。
In this paper, a method using surrogate constraint to select an initial feasible solution of a mixed integer linear programming problem is presented.
HEWC问题第一次被归结为一个整数线性规划问题，并且利用LP的放松问题和有界启发得到一个近似解。
The HEWC problem was formulated as an integer linear program, and an approximation solution was obtained by using LP-relation and rounding heuristic.
给出了一类整数规划问题有唯一最优解的充要条件。
The number of the most optimal solutions of this integer programming is determined.
提出了一种新的解整数可分离凹规划问题的分支定界算法，并证明了其收敛性。
In this paper, a new branch and its bound algorithm for solving integer separable concave programming problems is proposed, and the convergence of the algorithm is proved.
该结构优化问题的决策变量采用了向量表示方法，建立0-1整数非线性规划模型，给出了可行解存在性的判定方法。
Expressing decision variables of the structure optimization problem in the form of vector, a 0-1 integer nonlinear programming model is presented.
对以第一种网络为基础的DCPM问题，本文首先介绍了三条简化法则，然后建立了一个求最优解的新整数规划模型；
Three rules are put forward for simplifying the DCPM problem based on the first decision network, and a new integer programming model is developed for solving the problem.
在通过对任一正整数提出另外一种唯一分解式的基础上，利用初等方法得到了关于立方补数的几个有趣的渐近公式。
On the basis of requesting another factorization of an integer in only one way, two interesting asymptotic formulas on cub complements are obtained through the elementary method.
利用单纯形法求解该线性规划问题，便可得到整数规划的最优解。
By using simplex method to solve the LP, the optimal solution of ILP can be obtained.
线材的合理利用问题是一类很有代表性的整数规划问题。本文对线材下料问题决策的方案选择、模型的建立、解的分析进行了系统的分析和研究。
The problem of preparation of linear materials is a typical integer programing. In this paper, the selection of decision schemes, modeling, the analysis of solution are studied.
证明了连续正整数的立方和为素数或素数方幂仅有惟一解。
On the prime powers in sums of squares of three consecutive positive integers;
在解决各类整数规划问题时，分支-切割法是一个非常成功的方法，并且它能保证给出一个最优解。
In this paper, we analyze the methods from two aspects, cutting planes and branching on the basis of branch-and-cut algorithms.
这个同解模型是整数规划问题，作者指出了解法。
After Simplification, the author finds that the model is an integer programming problem, and gives the method.
与现有方法相比，新方法可采用单频gps数据实现中长基线GPS网络rtk的整数模糊度快速解算。
Compared with the existing methods, the improved method can solve the ambiguities of the medium-long baseline GPS network RTK only using L1-frequency GPS data.
研究了一个特殊的整数瓶颈问题并给出了两个求最优解的多项式算法程序。
A polynomial time algorithm for the scheduling problem of identical coupled-task jobs is presented in.
研究了一个特殊的整数瓶颈问题并给出了两个求最优解的多项式算法程序。
A polynomial time algorithm for the scheduling problem of identical coupled-task jobs is presented in.
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