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algebraic method‑Based Point‑to‑Point Trajectory Planning of an Under‑Constrained Cable‑Suspended Parallel Robot with Variable Angle and Height Cable Mast

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Chinese Journal of Mechanical Engineering 2020年第4期33卷 45-62页

作者： Tao Zhao Bin Zi Sen Qian Jiahao Zhao School of Mechanical Engineering Hefei University of TechnologyHefei 230009China Chemical Science and Engineering College North Minzu UniversityYinchuan 750021China

To avoid impacts and vibrations during the processes of acceleration and deceleration while possessing flexible working ways for cable-suspended parallel robots(CSPRs),point-to-point trajectory planning demands an under-constrained cable-suspended parallel robot(UCPR)with variable angle and height cable mast as described in this paper.The end-effector of the UCPR with three cables can achieve three translational degrees of freedom(DOFs).The inverse kinematic and dynamic modeling of the UCPR considering the angle and height of cable mast are completed.The motion trajectory of the end-effector comprising six segments is given.The connection points of the trajectory segments(except for point P3 in the X direction)are devised to have zero instantaneous velocities,which ensure that the acceleration has continuity and the planned acceleration curve achieves smooth transition.The trajectory is respectively planned using three algebraic methods,including fifth degree polynomial,cycloid trajectory,and double-S velocity curve.The results indicate that the trajectory planned by fifth degree polynomial method is much closer to the given trajectory of the end-effector.Numerical simulation and experiments are accomplished for the given trajectory based on fifth degree polynomial planning.At the points where the velocity suddenly changes,the length and tension variation curves of the planned and unplanned three cables are compared and analyzed.The OptiTrack motion capture system is adopted to track the end-effector of the UCPR during the experiment.The effectiveness and feasibility of fifth degree polynomial planning are validated.

关键词： Under-constrained cable-suspended parallel robot Variable angle and height cable mast Inverse kinematic and dynamic modeling algebraic method Point-to-point trajectory planning

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Extended Fan's algebraic method and Its Application to KdV and Variant Boussinesq Equations

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Communications in Theoretical Physics 2007年第7期48卷 1-6页

作者： YANG Xian-Lin TANG Jia-Shi College of Mechanics and Aerospace,Hunan University,Changsha 410082,China2 Department of Computer Science,Hunan Radio and Television University,Changsha 410004,China College of Mechanics and Aerospace Hunan University Changsha 410082 China Department of Computer Science Hunan Radio and Television University Changsha 410004 China

An extended Fan's algebraic method is used for constructing exact traveling wave solution of nonlinearpartial differential equations.The key idea of this method is to introduce an auxiliary ordinary differential equationwhich is regarded as an extended elliptic equation and whose degree Υ is expanded to the case of r>4.The efficiency ofthe method is demonstrated by the KdV equation and the variant Boussinesq equations.The results indicate that themethod not only offers all solutions obtained by using Fu's and Fan's methods,but also some new solutions.

关键词： algebraic method KdV equation variant boussinesq equations polynomial complete discrimination system

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Analytical analysis of hollow CORC cable under thermo-mechanical loads

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Superconductivity 2023年第1期5卷 26-39页

作者： Xianhao Li Yuejin Tang Ying Xu Li Ren State Key Laboratory of Advanced Electromagnetic Engineering and Technology Wuhan 430074China School of Electrical and Electronic Engineering Huazhong University of Science and TechnologyWuhan 430074China

According to engineering experience,the axial shrinkage caused by the refrigerant seriously endangers the performance of long‐distance conductor on round core(CORC)cables.Since outage maintenance of high‐temperature superconducting(HTS)cables is inevitable,providing appropriate compensation for cyclic temperature is one of the key technologies in the actual application of power cables.Therefore,this paper presents an analytical solution for hollow CORC cables under thermo‐mechanical loads.First,regarded as an axisymmetric composite structure,the radial temperature distribution of CORC cable under Dirichlet boundary or mixed boundary conditions was calculated.Then,assuming cable ends were axially fixed,a recursive method without variables is used to evaluate its displacement,strains,and stresses.Then,an algebraic method with axial strain as a variable is developed to analyze the mechanical behavior of the CORC cable more directly.Finally,concluded from the above derivation,a matrix equation is constructed based on continuity equations and boundary conditions,which applies to isotropic and orthotropic materials with orientations.Calculation results show that the analytical solution agrees with finite element method(FEM)results.Compared to the trial results of a 360 m CORC cable,the calculation error of axial shrinkage is within 1.63 cm,and the relative error is within 6.1%.In addition,the recursive method is the fastest to calculate axial strain,while the matrix method has a significant efficiency advantage in calculating the stresses and strains of each layer.

关键词： CORC cable Analytical solution Thermo‐mechanical loads Axial shrinkage Recursive method algebraic method

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Accurate studies of dissociation energies and vibrational energies on alkali metals

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Chinese Physics B 2008年第6期17卷 2048-2061页

作者：刘秀英孙卫国樊群超 Institute of Physics Sichuan University

This paper studies full vibrational spectra {Ev} and molecular dissociation energies De by using conventional least-squares （LS） fitting and an algebraic method （AM） proposed recently for 10 diatomic electronic states of ^7Li2, Na2, NaK and NaLi molecules based on some known experimental vibrational energies in a subset [Ev^expt] respectively. Studies show that：（1） although both the full AM spectrum {Ev^AM} and the LS spectrum {Ev^LS} can reproduce the known experimental energies in [Ev^expt], the {EAM} is superior to the {Ev^LS} in that the high-lying AM vibrational energies which may not be available experimentally have better or much better accuracy than those LS counterparts in {Ev^LS}, and so is the AM dissociation energy De^AM; （2） the main source of the errors in the data obtained by using the LS fitting is that the fitting which is just a pure mathematical process does not use any physical criteria that must be satisfied by the full vibrational spectrum, while the AM method does. This study suggests that when fitting or solving a physical equation using a set of source data, it is important not only to apply a proper mathematical tool, but also to use correct physical criteria which measure the physical properties of the data, kick out those data having bigger errors, and impose conditional convergence on the numerical process.

关键词： least-squares method algebraic method vibrational energy dissociation energy

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Accurate studies on the full vibrational energy spectra and molecular dissociation energies for some electronic states of halogen molecule

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Chinese Physics B 2011年第2期20卷 209-215页

作者：吕建良任维义徐平川陈太红 Institute of Theoretical Physics China West Normal University

This paper obtains accurate vibrational spectroscopic constants and full vibrational energy spectrum by the al- gebraic method （AM） for some electronic states of halogen diatomic molecules. Motivated by the recent success of obtaining the dissociation energies of Li2 molecule by using a new analytical formula, it further extends the formula to study the dissociation energies of halogen diatomic molecules. The results show that the AM spectrum and the theoretical dissociation energies agree well with RKR data and experimental data respectively.

关键词： vibrational energy dissociation energy halogen molecule algebraic method

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Investigation of analytical potential energy function, harmonic frequency and vibrational levels for the X~2Σ~+ and A~2Π states of CN radical

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Chinese Physics B 2008年第8期17卷 2919-2924页

作者：王建坤吴振森 School of Science Xidian University

This paper calculates the equilibrium structure and the potential energy functions of the ground state (X 2 Σ + ) and the low lying excited electronic state (A 2 Π ) of CN radical are calculated by using CASSCF method. The potential energy curves are obtained by a least square fitting to the modified Murrell–Sorbie function. On the basis of physical theory of potential energy function, harmonic frequency (ω e ) and other spectroscopic constants (ω e χ e , β e and α e ) are calculated by employing the Rydberg–Klein–Rees method. The theoretical calculation results are in excellent agreement with the experimental and other complicated theoretical calculation data. In addition, the eigenvalues of vibrational levels have been calculated by solving the radial one-dimensional Schro¨dinger equation of nuclear motion using the algebraic method based on the analytical potential energy function.

关键词： potential energy function harmonic frequency vibrational levels algebraic method

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Empirical Research on the Application of a Structure-Based Software Reliability Model

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IEEE/CAA Journal of Automatica Sinica 2021年第6期8卷 1153-1162页

作者： Jie Zhang Yang Lu Ke Shi Chong Xu School of Computer and Information Anhui Normal UniversityWuhu 241003China School of Computer Science and Information Engineering Hefei University of TechnologyHefei 230601China

Reliability engineering implemented early in the development process has a significant impact on improving software quality.It can assist in the design of architecture and guide later testing,which is beyond the scope of traditional reliability analysis methods.Structural reliability models work for this,but most of them remain tested in only simulation case studies due to lack of actual data.Here we use software metrics for reliability modeling which are collected from source codes of post versions.Through the proposed strategy,redundant metric elements are filtered out and the rest are aggregated to represent the module reliability.We further propose a framework to automatically apply the module value and calculate overall reliability by introducing formal methods.The experimental results from an actual project show that reliability analysis at the design and development stage can be close to the validity of analysis at the test stage through reasonable application of metric data.The study also demonstrates that the proposed methods have good applicability.

关键词： algebraic method reliability evaluation software metrics software reliability

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Cryptanalysis of dragon scheme

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The Journal of China Universities of Posts and Telecommunications 2010年第4期17卷 80-87页

作者： YUAN Feng HU Yu-pu WANG Yan OU Hai-wen Key Laboratory of Computer Networks and Information Security Ministry of Education Xidian University Xi'an 710071 China School of Science Xi'an University of Architecture and Technology Xi'an 710055 China Key Laboratory of Information Security Beijing Electronic Science and Technology Institute Beijing 100070 China

Patarin proposed the dragon scheme, pointed out the insecurity of the dragon algorithm with one hidden monomial and suggested a candidate dragon signature algorithm with a complicated function. This paper presents an algebraic method to attack the candidate dragon signature algorithm. The attack borrows the basic idea of the attack due to Kipnis and Shamir, and utilizes the underlying algebraic structure of the candidate dragon signature algorithm over the extension field to derive a way to enable the variable Y be viewed as a fixed value. The attack recovers the private keys efficiently when the parameters are n≤2s and D=[logq^d]≤3.

关键词： cryptography public key cryptography polynomials mapping multivariate dragon scheme algebraic method cryptanalysis

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A Series of Exact Solutions of (2+1)-Dimensional CDGKS Equation

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Communications in Theoretical Physics 2006年第11期46卷 807-811页

作者： YANG Zong-Hang Department of Mathematics, City University of Hong Kong, Hong Kong, China Department of Mathematics City University of Hong Kong Hong Kong China

An algebraic method with symbolic computation is devised to uniformly construct a series of exact solutions of the (2+1)-dimensional Caudrey Dodd-Gibbon Kotera-Sawda equation. The solutions obtained in this paper include solitary wave solutions, rational solutions, triangular periodic solutions, Jacobi and Weierstrass doubly periodic solutions. Among them, the Jacobi periodic solutions exactly degenerate to the solutions at a certain limit condition. Compared with most existing tanh method, the method used here can give new and more general solutions. More importantly, this method provides a guideline to classify the various types of the solution according to some parameters.

关键词： CDGKS equations solitary wave solution Jacobi and Weierstrass periodic wave solution algebraic method

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Analysis on an SEIR Epidemic Model with Logistic Death Rate of Virus Mutation

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Journal of Mathematical Research with Applications 2019年第3期39卷 259-268页

作者： Jianzhong GAO Tailei ZHANG School of Science Chang’an University

In this paper, we propose an SEIR epidemic model with Logistic death rate of virus mutation. By means of the direct Lyapunov method and the LaSalle’s Invariance Principle, the global stability of the disease-free equilibrium is proved. Using algebraic method to construct Lyapunov function, the global stability of the endemic equilibrium is proved. In addition, numerical simulations are done and the influence of parameters in the model on disease transmission is analyzed.

关键词： virus mutation logistic death rate global stability algebraic method

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