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Inverse kinematic deriving and actuator control of Delta robot using symbolic computation technology
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作者 冯李航 张为公 +2 位作者 林国余 龚宗洋 陈刚 《Journal of Southeast University(English Edition)》 EI CAS 2014年第1期51-56,共6页
In order to effectively derive the inverse kinematic solution of the Delta robot and realize actuator control a description of the linear graph principle for automatically generating kinematic equations in a mechanica... In order to effectively derive the inverse kinematic solution of the Delta robot and realize actuator control a description of the linear graph principle for automatically generating kinematic equations in a mechanical system as well as the symbolic computation implementation of this procedure is reviewed and projected into the Delta robot. Based on the established linear graph representation the explicit symbolic expression of constraint equations and inverse kinematic solutions are obtained successfully using a symbolic computation engine Maple so that actuator control and trajectory tracking can be directly realized.Two practical motions the circular path and Adept motion are simulated for the validation of symbolic solutions respectively.Results indicate that the simulation satisfies the requirement of the quick motion within an acceptable threshold. Thus the precision of kinematic response can be confirmed and the correctness of inverse solution is verified. 展开更多
关键词 delta robot SYMBOLIC COMPUTATION inverse kinematic problems linear graph theory
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Improvement of Fuzzy Inference Mechanism in FuzzyJ Toolkit
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作者 吴沁奕 陈英 《Journal of Beijing Institute of Technology》 EI CAS 2002年第4期414-417,共4页
By applying the aggregation operator γ-operator and introducing a new method for global data contribution, the problems of information loss and the decrease of running efficiency in FuzzyJ Toolkit, an expert system s... By applying the aggregation operator γ-operator and introducing a new method for global data contribution, the problems of information loss and the decrease of running efficiency in FuzzyJ Toolkit, an expert system shell, can be effectively solved. The example shows that the approach can overcome imprecision of max-operator and min-operator used during the process of fuzzy reasoning. Therefore, the information accuracy and the system performance can be effectively improved, which promotes the usability of FuzzyJ Toolkit. 展开更多
关键词 FuzzyJ Toolkit γ-operator DEFUZZIFICATION global data contribution
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A note on the Marcinkiewicz integral operators on F_p^(α,q) 被引量:3
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作者 ZHANG Chun-jie QIAN Rui-rui 《Journal of Zhejiang University-Science A(Applied Physics & Engineering)》 SCIE EI CAS CSCD 2007年第12期2037-2040,共4页
In this paper, we shall prove that the Marcinkiewicz integral operator #n, when its kernel Ω satisfies the L^1-Dini condition, is bounded on the Triehel-Lizorkin spaces. It is well known that the Triehel-Lizorkin spa... In this paper, we shall prove that the Marcinkiewicz integral operator #n, when its kernel Ω satisfies the L^1-Dini condition, is bounded on the Triehel-Lizorkin spaces. It is well known that the Triehel-Lizorkin spaces are generalizations of many familiar spaces such as the Lehesgue spaces and the Soholev spaces. Therefore, our result extends many known theorems on the Marcinkiewicz integral operator. Our method is to regard the Marcinkiewicz integral operator as a vector valued singular integral. We also use another characterization of the Triehel-Lizorkin space which makes our approach more clear. 展开更多
关键词 Marcinkiewicz integral Triebel-Lizorkin spaces Fourier transtforms
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Constraints and Soliton Solutions for KdV Hierarchy and AKNS Hierarchy 被引量:2
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作者 李年华 李玉奇 《Communications in Theoretical Physics》 SCIE CAS CSCD 2011年第10期605-610,共6页
It is well-known that the finite-gap solutions of the KdV equation can be generated by its recursion operator. We generalize the result to a special form of Lax pair,from which a method to constrain the integrable sys... It is well-known that the finite-gap solutions of the KdV equation can be generated by its recursion operator. We generalize the result to a special form of Lax pair,from which a method to constrain the integrable system to a lower-dimensional or fewer variable integrable system is proposed.A direct result is that the n-soliton solutions of the KdV hierarchy can be completely depicted by a series of ordinary differential equations(ODEs),which may be gotten by a simple but unfamiliar Lax pair.Furthermore the AKNS hierarchy is constrained to a series of univariate integrable hierarchies.The key is a special form of Lax pair for the AKNS hierarchy.It is proved that under the constraints all equations of the AKNS hierarchy are linearizable. 展开更多
关键词 KdV hierarchy AKNS hierarchy soliton constraint
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Using Symbolic Computation to Exactly Solve the Integrable Broer-Kaup Equations in (2+1)-Dimensional Spaces 被引量:19
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作者 CHENJing XIEFu-Ding LüZhuo-Sheng 《Communications in Theoretical Physics》 SCIE CAS CSCD 2005年第4期585-590,共6页
The extended tanh method is further improved by generalizing the Riccati equation and introducing its twenty seven new solutions. As its application, the (2+ 1)-dimensional Broer-Kaup equation is investigated and then... The extended tanh method is further improved by generalizing the Riccati equation and introducing its twenty seven new solutions. As its application, the (2+ 1)-dimensional Broer-Kaup equation is investigated and then its fifty four non-travelling wave solutions have been obtained. The results reported in this paper show that this method is more powerful than those, such as tanh method, extended tanh method, modified extended tanh method and Riccati equation expansion method introduced in previous literatures. 展开更多
关键词 BK equations symbolic computation non-travelling wave solution
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Multiverse and the Time State 被引量:2
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作者 Khaled (Moh'd Khalaf) Suleiman Alnobani 《Journal of Energy and Power Engineering》 2017年第3期160-163,共4页
This article is not inspired by any religion or quantum many-worlds interpretation. The mathematics of multiverse is presented here. The mass operator was introduced earlier by Alnobani. This operator is used here to ... This article is not inspired by any religion or quantum many-worlds interpretation. The mathematics of multiverse is presented here. The mass operator was introduced earlier by Alnobani. This operator is used here to deduce the time state. It is found that time has four states and those four states are orthogonal. Time is the constitution of any verse. Time has direction. Every orthogonal direction of time belongs to a verse. Past and future belong to opposite directions of time and they are arbitrary. Other verses are there by their own and not a probabilities of any other verse and if any similarity it is only a coincidence. Among applications of this thesis is travelling through groups of galaxies, or more or less. 展开更多
关键词 TIME MASS multiverse.
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On New Invariant Solutions of Generalized Fokker-Planck Equation 被引量:1
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作者 YAORuo-Xia LIZhi-Bin 《Communications in Theoretical Physics》 SCIE CAS CSCD 2004年第5期665-668,共4页
The generalized one-dimensional Fokker-Planck equation is analyzed via potential symmetry method and the invariant solutions under potential symmetries are obtained. Among those solutions, some are new and first repor... The generalized one-dimensional Fokker-Planck equation is analyzed via potential symmetry method and the invariant solutions under potential symmetries are obtained. Among those solutions, some are new and first reported. 展开更多
关键词 Fokker-Planck equation potential symmetry invariant solutions symbolic computation
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Finite Operators
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作者 Hadia Messaoudene 《Journal of Mathematics and System Science》 2013年第4期190-194,共5页
Let H be a separable infinite dimensional complex Hilbert space, and L(H) the algebra of all bounded linear operators on 3-t'. The class of finite operators is the class of operators for which the distance of the i... Let H be a separable infinite dimensional complex Hilbert space, and L(H) the algebra of all bounded linear operators on 3-t'. The class of finite operators is the class of operators for which the distance of the identity operator I and the derivation range is maximal; where the derivation range of the operator A is defined by δA;δA : L(H) -L(H) X- AX - XA. In this paper we present some properties of finite operators and give some classes of operators which are in the class of finite operators, and find for witch condition A ~ W is a finite operator in L(2-H H), and gave a g6neralisation of Stampflli theorem. 展开更多
关键词 Finite operator IDENTITY class R1 reduced approximate point spectrum.
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New Convenient Way for Disentangling Exponential Operator Composed of Angular Momentum Operators
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作者 李洪奇 徐兴磊 范洪义 《Communications in Theoretical Physics》 SCIE CAS CSCD 2011年第5期787-789,共3页
In the preceding paper (Commun. Theor. Phys. 51 (2009) 321) we have recommended a convenient method for disentangling exponential operators. In this work we use this method for disentangling exponential operators ... In the preceding paper (Commun. Theor. Phys. 51 (2009) 321) we have recommended a convenient method for disentangling exponential operators. In this work we use this method for disentangling exponential operators composed of angular momentum operators. We mainly desentangle the form of exp[2hJz + g J+ + kJ_] as the ordering exp(... J+)exp(... Jz)exp(... J_), we employ the Schwinger Bose realization J_ = bta, J+ = atb, Jz=(ata - btb)/2 to fulfil this task, without appealing to Lie algebra method. Note that this operator's desentanglng is different from its decomposition in normal ordering. 展开更多
关键词 exponential operator angular momentum
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New Weierstrass Semi-rational Expansion Method to Doubly Periodic Solutions of Soliton Equations
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作者 YANZhen-Ya 《Communications in Theoretical Physics》 SCIE CAS CSCD 2005年第3期391-396,共6页
Based on the Weierstrass elliptic function equation, a new Weierstrass semi-rational expansion method and its algorithm are presented. The main idea of the method changes the problem solving soliton equations into ano... Based on the Weierstrass elliptic function equation, a new Weierstrass semi-rational expansion method and its algorithm are presented. The main idea of the method changes the problem solving soliton equations into another one solving the corresponding set of nonlinear algebraic equations. With the aid of Maple, we choose the modified KdV equation, (2+ 1)-dimensional KP equation, and (3+1)-dimensional Jimbo-Miwa equation to illustrate our algorithm. As a consequence, many types of new doubly periodic solutions are obtained in terms of the Weierstrass elliptic function.Moreover the corresponding new Jacobi elliptic function solutions and solitary wave solutions are also presented as simple limits of doubly periodic solutions. 展开更多
关键词 soliton equations Weierstrass elliptic function doubly periodic solution symbolic computation
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New Families of Rational Form Solitary Wave Solutions to (2+1)-Dimensional Broer-Kaup-Kupershmidt System*
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作者 WANGQi CHENYong +1 位作者 LIBiao ZHANGHong-Qing 《Communications in Theoretical Physics》 SCIE CAS CSCD 2005年第5期769-774,共6页
Taking the (2+1)-dimensional Broer-Kaup-Kupershmidt system as a simple example, some families of rational form solitary wave solutions, triangular periodic wave solutions, and rational wave solutions are constructed b... Taking the (2+1)-dimensional Broer-Kaup-Kupershmidt system as a simple example, some families of rational form solitary wave solutions, triangular periodic wave solutions, and rational wave solutions are constructed by using the Riccati equation rational expansion method presented by us. The method can also be applied to solve more nonlinear partial differential equation or equations. 展开更多
关键词 Riccati equation rational expansion method (2+1) -dimensional Broer-Kaup-Kupershmidt system symbolic computation rational form solitary wave solutions
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HBFTrans2: A Maple Package to Construct Hirota Bilinear Form for Nonlinear Equations
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作者 杨旭尔 阮航宇 《Communications in Theoretical Physics》 SCIE CAS CSCD 2011年第5期747-752,共6页
An improved algorithm for symbolic computation of Hirota bilinear form of nonlinear equations by a logarithm transformation is presented. The improved algorithm is more efficient by using the property of Hirota-D oper... An improved algorithm for symbolic computation of Hirota bilinear form of nonlinear equations by a logarithm transformation is presented. The improved algorithm is more efficient by using the property of Hirota-D operator. The software package HBFTrans2 is written in Maple and its running efficiency is tested by a variety of soliton equations. 展开更多
关键词 Hirota bilinear form nonlinear equation symbolic computation
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Operators on the orthogonal complement of the Dirichlet space (Ⅱ) 被引量:2
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作者 YU Tao 《Science China Mathematics》 SCIE 2011年第9期2005-2012,共8页
In this paper we first prove that a dual Hankel operator Rφ on the orthogonal complement of the Dirichlet space is compact for φ ∈ W^1,∞(D), and then that a semicommutator of two Toeplitz operators on the Dirich... In this paper we first prove that a dual Hankel operator Rφ on the orthogonal complement of the Dirichlet space is compact for φ ∈ W^1,∞(D), and then that a semicommutator of two Toeplitz operators on the Dirichlet space or two dual Toeplitz operators on the orthogonal complement of the Dirichlet space in Sobolev space is compact. We also prove that a dual Hankel operator Re with φ ∈ W^1,∞(D) is of finite rank if and only if Be is orthogonal to the Dirichlet space for some finite Blaschke product B, and give a sufficient and necessary condition for the semicommutator of two dual Toeplitz operators to be of finite rank. 展开更多
关键词 Sobolev space Dirichlet space dual Toeplitz operator dual Hankel operator Toeplitz operator
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Chebfun and numerical quadrature 被引量:1
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作者 HALE Nicholas TREFETHEN Lloyd N 《Science China Mathematics》 SCIE 2012年第9期1749-1760,共12页
Chebfun is a Matlab-based software system that overloads Matlab's discrete operations for vectors and matrices to analogous continuous operations for functions and operators.We begin by describing Chebfun's fa... Chebfun is a Matlab-based software system that overloads Matlab's discrete operations for vectors and matrices to analogous continuous operations for functions and operators.We begin by describing Chebfun's fast capabilities for Clenshaw-Curtis and also Gauss-Legendre,-Jacobi,-Hermite,and-Laguerre quadrature,based on algorithms of Waldvogel and Glaser,Liu and Rokhlin.Then we consider how such methods can be applied to quadrature problems including 2D integrals over rectangles,fractional derivatives and integrals,functions defined on unbounded intervals,and the fast computation of weights for barycentric interpolation. 展开更多
关键词 Chebfun Clenshaw-Curtis quadrature Gauss quadrature barycentric interpolation formula Riemann-Liouville integral fractional calculus
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On the bilinear square Fourier multiplier operators and related multilinear square functions 被引量:1
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作者 SI ZengYan XUE QingYing YABUTA Kz 《Science China Mathematics》 SCIE CSCD 2017年第8期1477-1502,共26页
Let n 1 and Tm be the bilinear square Fourier multiplier operator associated with a symbol m,which is defined by Tm(f1, f2)(x) =(∫0^∞︱∫(Rn)^2)e^2πix·(ξ1+ξ2))m(tξ1, tξ2)f1(ξ1)f2(ξ2)d... Let n 1 and Tm be the bilinear square Fourier multiplier operator associated with a symbol m,which is defined by Tm(f1, f2)(x) =(∫0^∞︱∫(Rn)^2)e^2πix·(ξ1+ξ2))m(tξ1, tξ2)f1(ξ1)f2(ξ2)dξ1dξ2︱^2dt/t)^1/2.Let s be an integer with s ∈ [n + 1, 2n] and p0 be a number satisfying 2n/s p0 2. Suppose that νω=∏i^2=1ω^i^p/p) and each ωi is a nonnegative function on Rn. In this paper, we show that under some condition on m, Tm is bounded from L^p1(ω1) × L^p2(ω2) to L^p(νω) if p0 〈 p1, p2 〈 ∞ with 1/p = 1/p1 + 1/p2. Moreover,if p0 〉 2n/s and p1 = p0 or p2 = p0, then Tm is bounded from L^p1(ω1) × L^p2(ω2) to L^p,∞(νω). The weighted end-point L log L type estimate and strong estimate for the commutators of Tm are also given. These were done by considering the boundedness of some related multilinear square functions associated with mild regularity kernels and essentially improving some basic lemmas which have been used before. 展开更多
关键词 multilinear square functions Fourier multiplier operator multiple weights COMMUTATORS
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Von Neumann algebras generated by multiplication operators on the weighted Bergman space:A function-theory view into operator theory 被引量:1
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作者 HUANG HanSong 《Science China Mathematics》 SCIE 2013年第4期811-822,共12页
Recently,a class of Type Ⅱ factors has been constructed,arising from holomorphic coverings of bounded planar domains.Those operators in Type Ⅱ factors act on the Bergman space.In this paper,we develop new techniques... Recently,a class of Type Ⅱ factors has been constructed,arising from holomorphic coverings of bounded planar domains.Those operators in Type Ⅱ factors act on the Bergman space.In this paper,we develop new techniques to generalize those results to the case of the weighted Bergman spaces.In addition,a class of group-like von Neumann algebras are constructed,which are shown to be-isomorphic to the group von Neumann algebras. 展开更多
关键词 weighted Bergman space holomorphic covering map the fundamental group yon Neumann algebra Type factor
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Similarity invariants of operators on a class of Gowers-Maurey spaces 被引量:1
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作者 LIN LiQiong ZHONG HuaiJie ZHANG YunNan 《Science China Mathematics》 SCIE 2013年第4期803-810,共8页
This paper studies the similarity invariants of operators on a class of Gowers-Maurey spaces, ∑dc spaces, where an infinite dimensional Banach space X is called a ∑dc space if for every bounded linear operator on X ... This paper studies the similarity invariants of operators on a class of Gowers-Maurey spaces, ∑dc spaces, where an infinite dimensional Banach space X is called a ∑dc space if for every bounded linear operator on X the spectrum is disconnected unless it is a singleton. It shows that two strongly irreducible operators T1 and T2 on a ∑dc space are similar if and only if theK0-group of the commutant algebra of the direct sum T1 GT2 is isomorphic to the group of integers Z. On a ∑dc space X, it uses the semigroups of the commutant algebras of operators to give a condition that an operator is similar to some operator in (∑SI)(X), it further gives a necessary and sufficient condition that two operators in (∑SI)(X) are similar by using the ordered K0-groups. It also proves that every operator in (∑SI)(X) has a unique (SI) decomposition up to similarity on a ∑dc space X, where (∑SI)(X) denotes the class of operators which can be written as a direct sum of finitely many strongly irreducible operators. 展开更多
关键词 Gowers-Maurey spaces strongly irreducible operators K0-groups commutant algebras
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New fundamental quantum mechanical operator-ordering identities for the coordinate and momentum operators 被引量:4
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作者 FAN HongYi 《Science China(Physics,Mechanics & Astronomy)》 SCIE EI CAS 2012年第5期762-766,共5页
In quantum mechanics theory one of the basic operator orderings is Q-P and P-Q ordering,where Q and P are the coordinate operator and the momentum operator,respectively.We derive some new fundamental operator identiti... In quantum mechanics theory one of the basic operator orderings is Q-P and P-Q ordering,where Q and P are the coordinate operator and the momentum operator,respectively.We derive some new fundamental operator identities about their mutual reordering.The technique of integration within Q-P ordering and P-Q ordering is introduced.The Q-P ordered and P-Q ordered formulas of the Wigner operator are also deduced which makes arranging the operators in either Q-P or P-Q ordering much more convenient. 展开更多
关键词 Q-ordering and B-ordering IWOP technique operator-ordering identities Wigner operator
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K_0-group and similarity of operator weighted shifts
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作者 LIJueXian 《Science China Mathematics》 SCIE 2012年第7期1441-1448,共8页
By using simultaneous triangularization technique, similarity for operator weighted shifts with finite multiplicity is characterized in terms of K0-group of commutant algebra. The result supports the conjecture posed ... By using simultaneous triangularization technique, similarity for operator weighted shifts with finite multiplicity is characterized in terms of K0-group of commutant algebra. The result supports the conjecture posed by Cao et al. in 1999. Moreover, we discuss the relations between similarity and quasi-similarity for operator weighted shifts. 展开更多
关键词 operator weighted shift strongly irreducible operator K0-group Lie algebra
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Recursion Operators for Dispersionless KP Hierarchy
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作者 程秋盛 贺劲松 《Communications in Theoretical Physics》 SCIE CAS CSCD 2012年第11期631-638,共8页
Based on the corresponding theorem between dispersionless KP (dKP) hierarchy and h-dependent KP (hKP) hierarchy, a general formal representation of the recursion operators for dKP hierarchy under n-reduction is gi... Based on the corresponding theorem between dispersionless KP (dKP) hierarchy and h-dependent KP (hKP) hierarchy, a general formal representation of the recursion operators for dKP hierarchy under n-reduction is given in a systematical way from the corresponding hKP hierarchy. To illustrate this method, the recursion operators for dKP hierarchy under 2-reduction and 3-reduction are calculated in detail. 展开更多
关键词 dispersionless KP hierarchy h dependent KP hierarchy recursion operators
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