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The refined theory of deep rectangular beams based on general solutions of elasticity

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Science China(Physics,Mechanics & Astronomy) 2006年第3期49卷 291-303页

The problem of deducing one-dimensional theory from two-dimensional the- ory for a homogeneous isotropic beam is investigated. Based on elasticity theory, the re- fined theory of rectangular beams is derived by using Papkovich-Neuber solution and Lur’e method without ad hoc assumptions. It is shown that the displacements and stresses of the beam can be represented by the angle of rotation and the deflection of the neutral surface. Based on the refined beam theory, the exact equations for the beam without transverse surface loadings are derived and consist of two governing differential equations: the fourth-order equation and the transcendental equation. The approximate equations for the beam under transverse loadings are derived directly from the refined beam theory and are almost the same as the governing equations of Timoshenko beam theory. In two ex- amples, it is shown that the new theory provides better results than Levinson’s beam the- ory when compared with those obtained from the linear theory of elasticity.

关键词： deep rectangular beams,the refined theory,Papkovich-Neuber solution,Lur'e method,governing equation

Collision free 4D path planning for multiple UAVs based on spatial refined voting mechanism and PSO approach

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Chinese Journal of Aeronautics 2019年第6期32卷 1504-1519页

作者： Yang LIU Xuejun ZHANG Yu ZHANG Xiangmin GUAN School of Information Science&Electric Engineering Shandong Jiaotong UniversityJinan 250357China School of Electronic&Information Engineering Beihang UniversityBeijing 100083China College of Air Traffic Control Civil Aviation University of ChinaTianjin 300350China College of Transportation Engineering Tongji UniversityShanghai 200092China School of General Aviation Civil Aviation Management Institute of ChinaBeijing 100102China

In this paper, a four-dimensional coordinated path planning algorithm for multiple UAVs is proposed, in which time variable is taken into account for each UAV as well as collision free and obstacle avoidance. A Spatial refined Voting Mechanism(SRVM) is designed for standard Particle Swarm Optimization(PSO) to overcome the defects of local optimal and slow *** each generation candidate particle positions are recorded and an adaptive cube is formed with own adaptive side length to indicate occupied regions. Then space voting begins and is sorted based on voting results, whose centers with bigger voting counts are seen as sub-optimal positions. The average of all particles of corresponding dimensions are calculated as the refined solutions. A time coordination method is developed by generating specified candidate paths for every UAV, making them arrive the same destination with the same time consumption. A spatial-temporal collision avoidance technique is introduced to make collision free. Distance to destination is constructed to improve the searching accuracy and velocity of particles. In addition, the objective function is redesigned by considering the obstacle and threat avoidance, Estimated Time of Arrival(ETA), separation maintenance and UAV self-constraints. Experimental results prove the effectiveness and efficiency of the algorithm.

关键词： 4D path planning Collision free Multiple UAVs Obstacle avoidance Particle swarm optimization Spatial refined voting mechanism

The refined theory of deep rectangular beams for symmetrical deformation

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Science China(Physics,Mechanics & Astronomy) 2009年第6期52卷 919-925页

作者： GAO Yang1 & WANG MinZhong2 1 College of Science, China Agricultural University, Beijing 100083, China 2 State Key Laboratory for Turbulence and Complex Systems and Department of Mechanics and Aerospace Engineering, Peking University, Beijing 100871, China College of Science China Agricultural University Beijing China State Key Laboratory for Turbulence and Complex Systems and Department of Mechanics and Aerospace Engineering Peking University Beijing China

Based on elasticity theory, various one-dimensional equations for symmetrical deformation have been deduced systematically and directly from the two-dimensional theory of deep rectangular beams by using the Papkovich-Neuber solution and the Lur'e method without ad hoc assumptions, and they construct the refined theory of beams for symmetrical deformation. It is shown that the displacements and stresses of the beam can be represented by the transverse normal strain and displacement of the mid-plane. In the case of homogeneous boundary conditions, the exact solutions for the beam are derived, and the exact equations consist of two governing differential equations: the second-order equation and the transcendental equation. In the case of non-homogeneous boundary conditions, the approximate governing differential equations and solutions for the beam under normal loadings only and shear loadings only are derived directly from the refined beam theory, respectively, and the correctness of the stress assumptions in classic extension or compression problems is revised. Meanwhile, as an example, explicit expressions of analytical solutions are obtained for beams subjected to an exponentially distributed load along the length of beams.

关键词： deep rectangular beams the refined theory symmetrical deformation the Papkovich-Neuber solution the Lur’e method

Operator Product Formulas in the Algebraic Approach of the refined Topological Vertex

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Chinese Physics Letters 2013年第2期30卷 37-40页

作者：蔡立强王丽芳吴可杨洁 School of Mathematical Sciences Capital Normal UniversityBeijing 100048

The refined topological vertex of Iqbal-Kozcaz-Vafa has been investigated from the viewpoint of the quantum algebra of type W1+∞by Awata,Feigin,and *** introduced the trivalent intertwining operator?which is normal ordered along with some *** manage to establish formulas from the infinite operator product of the vertex operators and the generalized ones to restore this prefactor,and obtain an explicit formula for the vertex realization of the topological vertex as well as the refined topological vertex.

关键词： vertex topological refined

Some theoretical comparisons of refined Ritz vectors and Ritz vectors

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Science China Mathematics 2004年第Z1期47卷 222-233页

作者： JIA Zhongxiao Department of Mathematical Sciences Tsinghua University Beijing 100084 China

refined projection methods proposed by the author have received attention internationally. We are concerned with a conventional projection method and its refined counterpart for computing approximations to a simple eigenpair (λ,x)of a large matrix A. Given a subspace w that contains anapproximation to x, these two methods compute approximations(μ(x~)) and (μ(x^)) to (λ,x),respectively. We establish three results. First, the refinedeigenvector approximation or simply the refined Ritz vector (x^) is unique as the deviation of x from w approaches zero if λ is simple. Second, interms of residual norm of the refined approximate eigenpair (μ,(x^)), we derive lower and upper bounds for the sine of the angle betweenthe Ritz vector (x~) and the refined eigenvector approximation (x^), and we prove that (x~)≠(x^) unless (x^)=x. Third, we establish relationships between theresidual norm ‖A(x~)-μ(x^)‖ of the conventionalmethods and the residual norm ‖A(x^)-μ(x^)‖ of therefined methods, and we show that the latter is always smallerthan the former if (μ,(x^)) is not an exact eigenpair ofA, indicating that the refined projection method is superiorto the corresponding conventional counterpart.

关键词： large matrix, conventional projection, refined projection, eigenvalue, eigenvector, Ritz value, Ritz vector,refined Ritz vector.

Analysis of the Effects on Self-Efficacy and Quality of Life of Patients Undergoing Coronary Intervention by Traditional Chinese Medicine Nursing Combined with refined Nursing

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World Journal of Integrated Traditional and Western Medicine 2019年第3期5卷 24-29页

作者：赵素云宋鸿 Department of Intervention Suzhou City HospitalSuzhou 234000 China

OBJECTIVE: To study the effects on self-efficacy and quality of life in patients undergoing coronary intervention, by traditional Chinese medicine nursing combined with refined nursing. METHODS: A total of 124 patients, who needed to undergo coronary intervention in our hospital, were randomly divided into the fine group and the combined group, with 62 patients in each group. The two groups of patients were enrolled in the PCI routine nursing procedure, in which the fine group was given refined nursing, and the joint group, based on that, added the traditional Chinese medicine nursing. The self-management (self-management scale of coronary heart disease), self-efficacy (self-efficacy scale of coronary heart disease), quality of life score (Seattle angina questionaire (SAQ), TCM symptom score] of the two groups were observed before and after treatment. The incidence of postoperative complications after nursing intervention was recorded. RESULTS: After nursing intervention, each score and total scores of the self-administration scale of the combined group were higher than those of the fine group (P refined nursing, can improve their quality of life, clinical symptoms and postoperative complications by improving their self-management and efficacy, which is conducive to the recovery of p

关键词： Coronary intervention Traditional Chinese medicine nursing refined

Research on refined Oil Distribution Plan Based on Dynamic Time Window

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Journal of Applied Mathematics and Physics 2017年第11期5卷 2104-2111页

作者： Qian Liu Lianhua Wang Le Yu Beijing Wuzi University Beijing China

Based on the analysis of the refined oil distribution plan which includes the various vehicles models-single oil-multiple gas stations. This paper puts forward the dynamic time window of oil supplementation based on every moment, and establishes the mathematical model of the refined oil distribution plan, using C language, taking various circumstances of the model into account to find the optimal solution through several operations. This process can make the refined oil distribution plan and the distribution route is more reasonable. At the same time, the distribution cost is lowest. Through the analysis of the experimental results, the validity and algorithm of the model are proved.

关键词： refined Oil Distribution Vehicle Scheduling Problem Time Window Optimized Model

Can regional economy influence China's water use intensity?:based on refined LMDI method

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Chinese Journal of Population,Resources and Environment 2014年第3期12卷 247-254页

作者： Chenjun Zhang Hengquan Zhang Simulation Laboratory of Project Management Business School of Hohai University

China experienced a decline of water use intensity in the 11th Five Year Plan,but the water use intensity actually increased in *** the best of our knowledge,the index decomposition analysis method was rarely used to analyze changes in water use,and no decomposition analysis has investigated the role of regional economy in the decline of water use *** this paper,we use logarithmic mean Divisia index(LMDI)techniques to decompose the change of water use intensity in the period *** find that the change of industrial water use intensity is confirmed as the dominant contributor to the decline in the overall water use intensity;the regional structure effect and the industrial structure effect is positive to the decline of overall water use intensity;the decline of China's water use intensity is mainly attributed to the effect of developed eastern provinces;meanwhile,the effect of central and undeveloped western is also positive to the decline of overall water use intensity;at least one out of three effects is positive to the decline of water use intensity in the different provinces;the intensity effect is positive and the industrial structure effect is positive to the declines of China's water use intensity based on chaining approach except the period 2008-2009,individually;and the deviation of regional structure effect and industrial structure effect between with regional economy and without regional economy in LMDI is 0.9 and2.3 m^3/10~4 RMB,respectively.

关键词： water use intensity decomposition refined LMDI method regional economy

New Features of Chinese Cross-Border E-Commerce: Branded, refined and Diversified

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China's Foreign Trade 2020年第2期 52-55页

作者： Lin Zhiyong the Business Research Institute of 100 EC

China’s cross-border e-commerce industry was dynamic in 2019,with pressing requirements being laid down on capital,technology and services,and the threshold and operation difficulty of this industry being raised to a higher *** traditional enterprises and brands began to move towards center stage,causing China’s cross-border e-commerce sector to become refined,branded,localized and *** can be said that the industry has entered a transitional period and has encountered a new situation where the driving force of development is called for.

关键词： Brand driving refined