关键词： 最优分解   贪心算法   数学归纳法  

摘要： 任何贪心算法必须有数学上的正确性证明.虽然最优分解问题有很多算法介绍,但是没有看到算法的正确性证明.本文用数学归纳法给出最优分解问题贪心算法的正确性证明.同时,最优分解问题也是一个贪心选择性质和最优子结构性质不能独立证明的很好的例子.

关键词： 公钥加密   大数分解   离散对数   最短格矢问题   子集和问题  

摘要： 基于数学难解问题的公钥体制加密算法面临着计算机计算能力进步的挑战,如何优化现有公钥加密理论基础、从数学角度分析验证抗量子密码的安全性与实用性,进而推进密码学加密技术的进步,一直是密码学与计算机科学的主要攻坚方向。本文通过回顾大数分解、对数难解等数学难题分析公钥密码的数学基础,同时结合科研动态从数学理论出发验证抗量子公钥密码体制的可靠性。这对有效应对即将到来的量子计算对公钥密码体制的威胁具有现实意义。

关键词： crossover of variable lengths   optimization model   EPANET solver   constraint satisfaction model  

摘要： This research proposes a genetic algorithm that provides a solution to the problem of deficient distribution of drinking water via the current hydraulic network in the neighborhood "Fraccionamiento Real Montecasino" (FRM), in Huitzilac, Morelos, Mexico. The proposed solution is the addition of new elements to the FRM network. The new elements include storage tanks, pipes, and pressure-reducing valves. To evaluate the constraint satisfaction model of mass and energy conservation, the hydraulic EPANET solver (HES) is used with an optimization model to minimize the total cost of changes in the network (new pipes, tanks, and valves). A genetic algorithm was used to evaluate the optimization model. The analysis of the results obtained by the genetic algorithm for the FRM network shows that adequate and balanced pressures were obtained by means of small modifications to the existing network, which entailed minimal costs. Simulations were performed for an extended period, which means that the pressure was obtained by simulation with HSE at one-hour intervals, during the algorithm execution, to verify adequate pressure at a specific point in the system, or to make corrections to ensure proper distribution, this with the aim of having a final optimized network design.

关键词： 聚合物驱油   数学模型   数值求解   软件测试  

摘要： 计算机数值模拟计算已被广泛在社会各个行业,在一定程度上通过理论计算,代替了实际实验过程,在初期模拟分析过程,能有效的降低工作难度、缩短研究周期、降低资金成本。在油田开发领域,提高采收率一直是研究的热门课题,利用聚合物驱进行三次采油近年来取得了较大的进展。设计聚合驱采油模拟软件,对该技术工艺的实施具有较大的实践价值。通过优化数值模拟方程及改进算法,设计了聚合物驱模拟软件,实际测试应用表明与实际情况较为吻合。

关键词： 机载激光雷达   点云数据   数据滤波  

摘要： 机载激光雷达系统获取被测目标的三维坐标数据,是一系列空间分布不均匀的离散点云,点云数据滤波算法是当前的研究热点.通过介绍常用的数学形态学、迭代最小二乘线性内插、基于地形坡度、移动曲面拟合等滤波算法,设置不同滤波窗口大小和阈值得到不同地面点,比较各种方法滤波效果,从而选出较好的滤波方法.

关键词： 小学数学   运算方法   多元思维  

摘要： “鼓励学生算法多样化”是数学新课程的一个重要理念，它是实现不同的人在数学学习上得到不同发展的有效途径，新课程理念引导下的课堂，以学生的学为主，小学数学教学中更注重培养学生“一题多解”的多元思维，算法的多样化和优化成了师生教与学的难点和关键。

关键词： binary data   accuracy class   internal recycling   forward propagation   algorithms   Neural network   Algebra   Network  

摘要： The concept of an -weakly regular problem is introduced. On the basis of the Zhuravlev operator approach combined with the neural network paradigm, it is shown that, for each such problem, a correct algorithm and a six-level spatial neural network reproducing the computations executed by this algorithm can be constructed. Moreover, the set of -weakly regular problems includes the set of -regular problems. It turns out that a three-level spatial network (-block) is a forward propagation network whose inner loop under estimation of the class membership for each test object consists of a single iteration. As a result, the amount of computations required for the six-level network is reduced noticeably.

摘要： We develop a surface hopping algorithm based on frozen Gaussian approximation for semiclassical matrix Schrodinger equations, in the spirit of Tully's fewest switches surface hopping method. The algorithm is asymptotically derived from the Schrodinger equation with rigorous approximation error analysis. The resulting algorithm can be viewed as a path integral stochastic representation of the semiclassical matrix Schrodinger equations. Our results provide mathematical understanding to and shed new light on the important class of surface hopping methods in theoretical and computational chemistry.