关键词： Structural systems   Dynamics   Control algorithm   Full mathematical implementation   Non-linear response  

摘要： The paper falls within the framework of dynamic control of existing structures exhibiting non-linear behaviour. On the basis of some previous research developed by the authors, it specifically focuses on the analytical setup and development of a control algorithm for mitigating in an improved way the response of non-linear spatial structures, made of masonry. The presented setup does not involve the gross simplifications of the structural model behaviour that are usually adopted in these cases;on the contrary it proposes a more appropriate full mathematical formulation, which is, nevertheless, made still manageable for numerical purposes and significantly more reliable than alternative approaches.

关键词： system of linear inequalities   algebraic programming   software verification   canonical form   linear semialgebraic formula  

摘要： The results of testing formula simplification tools are presented in the first part of this paper. In the second part, an algorithm for constructing canonical forms of linear semi-algebraic formulas is described. The main result of the study is the definition of the canonical form of a linear semi-algebraic formula that has the property of uniqueness and other useful properties. An algorithm for constructing such a formula is described.

关键词： framed-tube building   outrigger-braced system   lateral loadings   interstory drift   optimum design   genetic algorithm  

摘要： In this paper, the analysis of optimal locations of framed-tube structures with outriggers is conducted with the uniform and nonuniform core and peripheral columns using genetic algorithm, aiming to minimize the interstory drift. Also, comparison and difference of the results between the uniform and nonuniform structures are carried out and discussed. Besides, several parameters which influence the behavior of the structure are identified and analyzed, such as different objective functions, segments of outriggers, thickness of core wall, stiffness of outriggers, and grade of concrete strength. In addition, a Matlab program is written to perform the parameter analysis of optimal location of outriggers. Take a 260-m high-rise building as a target building, the optimal locations of one to two sets of outriggers subjected to three kinds of horizontal loadings (uniform, parabolic, and triangular) are obtained and can be utilized for the structural preliminary design of tall buildings.

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.