关键词： 塑料模具   模具使用寿命   塑料材料   材料科学   数学模型分析   生产流程   模具温度场   使用效能  

摘要： 随着材料科学的发展,材料的组织结构、性质、生产流程和使用效能不断完善。塑料材料具备较强的可塑性和丰富的功能性,在生产生活中应用广泛。工业转型升级背景下,塑料模具工业得到发展,但与国外顶尖工艺相比,部分塑料模具厂依然存在制造水平低下问题,如模具制造工期过长、修模次数过多、模具使用寿命不长等。

关键词： 中国科学技术大学   数学算法   潘建伟   量子计算   超级计算机   恐惧症   优越性  

摘要： 2020年12月4日,中国科学技术大学宣布该校潘建伟等人成功构達76个光子的量子计算原型机“九章”,求解数学算法高斯玻色取样只需200秒,而目前世界最快的超级计算机“富岳”要用6亿年。这一突破使我国成为继美国之后全球第二个实现“量子优越性”的国家。从早期的“算力不足恐惧症”。

关键词： 科技与经济   数学建模   影响因子   处理过程   相互关系   深入挖掘  

摘要： 科技经济,简单的来说,就是科技的进步有助于经济的增长,或者科技的发展依赖经济的支撑。因此科技经济问题,总的来说,就是处理好科技与经济之间的相互关系的问题,需要在不同的阶段,意识到科技与经济的主导关系。其中科技经济问题在具体的处理过程中,可以运用数量关系进行简化,从而深入挖掘出核心的影响因子。

关键词： gravitational search algorithm   hybrid meta‐   heuristic algorithm   pipeline scheduling problem   simulated annealing   variable neighborhood search  

摘要： The system under investigation contains a single refinery, a unique distribution center, and a multiproduct pipeline. The basic aim is to plan the optimal sequence for pumping products to achieve financial benefit and satisfy the customers with on-time delivery. In this study, some restrictions (such as batch sizing, discharging rate, forbidden sequences, and settling periods) are considered and the problem is formulated as a MILP model. Although the multiproduct pipeline scheduling problem has high time complexity, meta-heuristic algorithms have been used rarely in the literature. Another contribution of this work is to develop several meta-heuristic algorithms to solve the proposed MILP effectively. Therefore, as a novelty, some classical meta-heuristics like population-based simulated annealing and population-based variable neighborhood search are hybridized by the gravitational search algorithm for obtaining better performance. Parameters of the algorithms are tuned by an optimization problem and then all algorithms are compared by numerical examples. The achieved results demonstrate the validity of the model and the efficient performance of the proposed algorithms against exact methods. These algorithms also lead to better solutions in much lower computational time. Among them, the hybrid algorithm obtained by combining the SA and GSA meta-heuristics are superior to the other algorithms.

关键词： Full configuration interaction   Thermodynamic functions   Feynman diagrams   Power series   Perturbation theory   Slater determinant   Statistical thermodynamics  

摘要： A comprehensive and detailed account is presented for the finite-temperature many-body perturbation theory for electrons that expands in power series all thermodynamic functions on an equal footing. Algebraic recursions in the style of the Rayleigh-Schrodinger perturbation theory are derived for the grand potential, chemical potential, internal energy, and entropy in the grand canonical ensemble and for the Helmholtz energy, internal energy, and entropy in the canonical ensemble, leading to their sum-over-states analytical formulas at any arbitrary order. For the grand canonical ensemble, these sum-over-states formulas are systematically transformed to sum-over-orbitals reduced analytical formulas by the quantum-field-theoretical techniques of normal-ordered second quantization and Feynman diagrams extended to finite temperature. It is found that the perturbation corrections to energies entering the recursions have to be treated as a nondiagonal matrix, whose off-diagonal elements are generally nonzero within a subspace spanned by degenerate Slater determinants. They give rise to a unique set of linked diagrams-renormalization diagrams-whose resolvent lines are displaced upward, which are distinct from the well-known anomalous diagrams of which one or more resolvent lines are erased. A linked-diagram theorem is introduced that proves the size-consistency of the finite-temperature many-body perturbation theory at any order. General-order algorithms implementing the recursions establish the convergence of the perturbation series toward the finite-temperature full-configuration-interaction limit unless the series diverges. The normal-ordered Hamiltonian at finite temperature sheds light on the relationship between the finite-temperature Hartree-Fock and first-order many-body perturbation theories.

关键词： 并行计算机   量子计算机   超级计算机   工程技术研究中心   中国科学技术大学   数学算法   潘建伟   研究团队  

摘要： 中国科学技术大学潘建伟研究团队与中科院上海微系统所、国家并行计算机工程技术研究中心合作,成功研制出量子计算原型机“九章”,它求解数学算法高斯玻色取样只需200秒,比目前最快的超级计算机快一百万亿倍。这一突破使我国成为全球第二个实现“量子优越性”的国家。那量子计算机是什么?这一突破又意味着什么呢?

关键词： 数学算法   计算机编程   程序语言  

摘要： 在计算机程序设计中,充分利用数理逻辑算法规则的性质,可以完美地总结和梳理疑难问题,并在此基础上进行规律化、规范化的计算操作,将复杂问题作为一个整体,可以大大简化和表达基础法则。计算机程序设计正是因为这种科学技术与程序设计语言的组织和实现有关,所以说根据我国计算机程序设计的现状,对计算机程序设计的综合基础科学研究和结构分析具有重要意义。

关键词： 计算机随机信号   量化   数学模型   控制组合   功率谱密度  

摘要： 随着信息技术的快速发展,个人计算机得到广泛使用。计算机输出的数字信号不能直接使用,需经过相关处理。传统随机信号处理的数学模型精准度不高,易造成信号失真。采用数学建模的研究方法,将控制组合算法与数学模型相结合,并且在数学模型中引入了功率谱密度函数。结果显示,控制组合算法显著提升了随机信号的控制精度和实时性。相比于传统模型,控制组合数学模型实现了对计算机随机信号的快速收敛,提高了计算机的控制效率,该控制组合数学模型算法对相关技术领域的发展有较高的研究价值和指导意义。

关键词： 小学数学   高年级   算理   算法  

摘要： 算理理解是小学数学运算教学的重要目标。随着新课改的深入,广大一线教师对算理教学的重视程度不断提升。“说理”教学作为一种重要的启发式教学手段,不仅促进学生在课堂中充分发挥主观能动性,还促进深度学习的实现。文章聚焦小学高年级数学算理课堂,在分析算理教学现状的基础上提升算理教学优化策略,以期为广大教师提供一些算理教学参考。

关键词： direction-of-arrival estimation   geometric algebra   ESPRIT algorithm   electromagnetic vector-sensor array  

摘要： Direction-of-arrival (DOA) estimation plays an important role in array signal processing, and the Estimating Signal Parameter via Rotational Invariance Techniques (ESPRIT) algorithm is one of the typical super resolution algorithms for direction finding in an electromagnetic vector-sensor (EMVS) array;however, existing ESPRIT algorithms treat the output of the EMVS array either as a "long vector", which will inevitably lead to loss of the orthogonality of the signal components, or a quaternion matrix, which may result in some missing information. In this paper, we propose a novel ESPRIT algorithm based on Geometric Algebra (GA-ESPRIT) to estimate 2D-DOA with double parallel uniform linear arrays. The algorithm combines GA with the principle of ESPRIT, which models the multi-dimensional signals in a holistic way, and then the direction angles can be calculated by different GA matrix operations to keep the correlations among multiple components of the EMVS. Experimental results demonstrate that the proposed GA-ESPRIT algorithm is robust to model errors and achieves less time complexity and smaller memory requirements.