Computer Algebra Systems have been extensively used in higher education. The reasons are many e.g., visualize mathematical problems, correlate real-world problems on a conceptual level, are flexible, simple to use, ac...Computer Algebra Systems have been extensively used in higher education. The reasons are many e.g., visualize mathematical problems, correlate real-world problems on a conceptual level, are flexible, simple to use, accessible from anywhere, etc. However, there is still room for improvement. Computer algebra system (CAS) optimization is the set of best practices and techniques to keep the CAS running optimally. Best practices are related to how to carry out a mathematical task or configure your system. In this paper, we are going to examine these techniques. The documentation sheets of CASs are the source of data that we used to compare them and examine their characteristics. The research results reveal that there are many tips that we can follow to accelerate performance.展开更多
This paper explores the algebraic essence of universal logic functions(ULFs)from an algebraic perspective.Under the framework of semi-tensor product of matrices,the“sequential nature”of ULFs is revealed.Utilizing th...This paper explores the algebraic essence of universal logic functions(ULFs)from an algebraic perspective.Under the framework of semi-tensor product of matrices,the“sequential nature”of ULFs is revealed.Utilizing the nature,a technique called universal transformation method is proposed,by which any ULF can be transformed into an equivalent expression with desired features that facilitate achieving specific objectives,such as modeling,analyzing and synthesizing universal logical systems.Furthermore,several useful logical operators are constructed in a mixed-dimensional situation,including power-raising operator,power-descending operator,erasure operator,and appending operator.Finally,these results are applied to model and analyze finite state machines and their networks,which demonstrate the practical value of the method and operators.展开更多
This article deals with a class of numerical methods for retarded differential algebraic systems with time-variable delay. The methods can be viewed as a combination of Runge-Kutta methods and Lagrange interpolation. ...This article deals with a class of numerical methods for retarded differential algebraic systems with time-variable delay. The methods can be viewed as a combination of Runge-Kutta methods and Lagrange interpolation. A new convergence concept, called DA-convergence, is introduced. The DA-convergence result for the methods is derived. At the end, a numerical example is given to verify the computational effectiveness and the theoretical result.展开更多
The robust stability test of time-delay systems with interval parameters can be concluded into the robust stability of the interval quasipolynomials. It has been revealed that the robust stability of the quasipolynomi...The robust stability test of time-delay systems with interval parameters can be concluded into the robust stability of the interval quasipolynomials. It has been revealed that the robust stability of the quasipolynomials depends on that of their edge polynomials. This paper transforms the interval quasipolynomials into two-dimensional （2-D） interval polynomials （2-D s-z hybrid polynomials）, proves that the robust stability of interval 2-D polynomials are sufficient for the stability of given quasipolynomials. Thus, the stability test of interval quasipolynomials can be completed in 2-D s-z domain instead of classical 1-D s domain. The 2-D s-z hybrid polynomials should have different forms under the time delay properties of given quasipolynomials. The stability test proposed by the paper constructs an edge test set from Kharitonov vertex polynomials to reduce the number of testing edge polynomials. The 2-D algebraic tests are provided for the stability test of vertex 2-D polynomials and edge 2-D polynomials family. To verify the results of the paper to be correct and valid, the simulations based on proposed results and comparison with other presented results are given.展开更多
A discrete event system is a dynamical system whose state evolves in time by the occurrence of events at possibly irregular time intervals. Timed Petri nets are a graphical and mathematical modeling tool applicable to...A discrete event system is a dynamical system whose state evolves in time by the occurrence of events at possibly irregular time intervals. Timed Petri nets are a graphical and mathematical modeling tool applicable to discrete event systems in order to represent its states evolution where the timing at which the state changes is taken into consideration. One of the most important performance issues to be considered in a discrete event system is its stability. Lyapunov theory provides the required tools needed to aboard the stability and stabilization problems for discrete event systems modeled with timed Petri nets whose mathematical model is given in terms of difference equations. By proving stability one guarantees a bound on the discrete event systems state dynamics. When the system is unstable, a sufficient condition to stabilize the system is given. It is shown that it is possible to restrict the discrete event systems state space in such a way that boundedness is achieved. However, the restriction is not numerically precisely known. This inconvenience is overcome by considering a specific recurrence equation, in the max-plus algebra, which is assigned to the timed Petri net graphical model.展开更多
This paper is concerned with the order of the solutions of systems of high-order complex algebraic differential equations.By means of Zalcman Lemma,the systems of equations of[1]is extended to more general form.
The algebraic structure and Poisson＇s integral theory of mechanico-electrical systems are studied. The Hamilton canonical equations and generalized Hamilton canonical equations and their the contravariant algebraic f...The algebraic structure and Poisson＇s integral theory of mechanico-electrical systems are studied. The Hamilton canonical equations and generalized Hamilton canonical equations and their the contravariant algebraic forms for mechanico-electrical systems are obtained. The Lie algebraic structure and the Poisson＇s integral theory of Lagrange mechanico-electrical systems are derived. The Lie algebraic structure admitted and Poisson＇s integral theory of the Lagrange-Maxwell mechanico-electrical systems are presented. Two examples are presented to illustrate these results.展开更多
Presents the meshing analysis based on the Computer Algebra System to make it easier to deduce complex formulas while the expression of more complicated surface equations are visualized, by which, the contact line, me...Presents the meshing analysis based on the Computer Algebra System to make it easier to deduce complex formulas while the expression of more complicated surface equations are visualized, by which, the contact line, meshing bordlines and undercut bordlines of toroidal drive are deduced, and the results obtained are consistent with the results discussed in literature [1] , and concludes that the absolute value of the induced normal curvature is usually smaller (less than 0.12, for example), and it increases as parameters φ 2, V and R increase, decreases as parameter r increases, and hardly varies with W 2, and the variation with a, i 21 is not definite.展开更多
Lie symmetry algebra of linear nonconservative dynamical systems is studied in this paper. By using 1-1 mapping, the Lie point and Lie contact symmetry algebras are obtained from two independent solutions of the one-d...Lie symmetry algebra of linear nonconservative dynamical systems is studied in this paper. By using 1-1 mapping, the Lie point and Lie contact symmetry algebras are obtained from two independent solutions of the one-dimensional linear equations of motion.展开更多
The algebraic structures of the dynamical equations for the rotational relativistic systems are studied. It is found that the dynamical equations of holonomic conservative rotational relativistic systems and the speci...The algebraic structures of the dynamical equations for the rotational relativistic systems are studied. It is found that the dynamical equations of holonomic conservative rotational relativistic systems and the special nonholonomic rotational relativistic systems have Lie's algebraic structure, and the dynamical equations of the general holonomic rotational relativistic systems and the general nonholonomic rotational relativistic systems have Lie admitted algebraic structure. At last the Poisson integrals of the dynamical equations for the rotational relativistic systems are given.展开更多
In this work, we study superintegrable quantum systems in two-dimensional Euclidean space and on a complex twosphere with second-order constants of motion. We show that these constants of motion satisfy the deformed o...In this work, we study superintegrable quantum systems in two-dimensional Euclidean space and on a complex twosphere with second-order constants of motion. We show that these constants of motion satisfy the deformed oscillator algebra. Then, we easily calculate the energy eigenvalues in an algebraic way by solving of a system of two equations satisfied by its structure function. The results are in agreement to the ones obtained from the solution of the relevant Schroedinger equation.展开更多
In this paper, a real-time computation method for the control problems in differential-algebraic systems is presented. The errors of the method are estimated, and the relation between the sampling stepsize and the con...In this paper, a real-time computation method for the control problems in differential-algebraic systems is presented. The errors of the method are estimated, and the relation between the sampling stepsize and the controlled errors is analyzed. The stability analysis is done for a model problem, and the stability region is ploted which gives the range of the sampling stepsizes with which the stability of control process is guaranteed.展开更多
文摘Computer Algebra Systems have been extensively used in higher education. The reasons are many e.g., visualize mathematical problems, correlate real-world problems on a conceptual level, are flexible, simple to use, accessible from anywhere, etc. However, there is still room for improvement. Computer algebra system (CAS) optimization is the set of best practices and techniques to keep the CAS running optimally. Best practices are related to how to carry out a mathematical task or configure your system. In this paper, we are going to examine these techniques. The documentation sheets of CASs are the source of data that we used to compare them and examine their characteristics. The research results reveal that there are many tips that we can follow to accelerate performance.
基金supported in part by the National Natural Science Foundation of China under Grants 62073124 and U1804150.
文摘This paper explores the algebraic essence of universal logic functions(ULFs)from an algebraic perspective.Under the framework of semi-tensor product of matrices,the“sequential nature”of ULFs is revealed.Utilizing the nature,a technique called universal transformation method is proposed,by which any ULF can be transformed into an equivalent expression with desired features that facilitate achieving specific objectives,such as modeling,analyzing and synthesizing universal logical systems.Furthermore,several useful logical operators are constructed in a mixed-dimensional situation,including power-raising operator,power-descending operator,erasure operator,and appending operator.Finally,these results are applied to model and analyze finite state machines and their networks,which demonstrate the practical value of the method and operators.
文摘This article deals with a class of numerical methods for retarded differential algebraic systems with time-variable delay. The methods can be viewed as a combination of Runge-Kutta methods and Lagrange interpolation. A new convergence concept, called DA-convergence, is introduced. The DA-convergence result for the methods is derived. At the end, a numerical example is given to verify the computational effectiveness and the theoretical result.
基金This project was supported by the National Science Foundation of China (60572093).
文摘The robust stability test of time-delay systems with interval parameters can be concluded into the robust stability of the interval quasipolynomials. It has been revealed that the robust stability of the quasipolynomials depends on that of their edge polynomials. This paper transforms the interval quasipolynomials into two-dimensional （2-D） interval polynomials （2-D s-z hybrid polynomials）, proves that the robust stability of interval 2-D polynomials are sufficient for the stability of given quasipolynomials. Thus, the stability test of interval quasipolynomials can be completed in 2-D s-z domain instead of classical 1-D s domain. The 2-D s-z hybrid polynomials should have different forms under the time delay properties of given quasipolynomials. The stability test proposed by the paper constructs an edge test set from Kharitonov vertex polynomials to reduce the number of testing edge polynomials. The 2-D algebraic tests are provided for the stability test of vertex 2-D polynomials and edge 2-D polynomials family. To verify the results of the paper to be correct and valid, the simulations based on proposed results and comparison with other presented results are given.
文摘A discrete event system is a dynamical system whose state evolves in time by the occurrence of events at possibly irregular time intervals. Timed Petri nets are a graphical and mathematical modeling tool applicable to discrete event systems in order to represent its states evolution where the timing at which the state changes is taken into consideration. One of the most important performance issues to be considered in a discrete event system is its stability. Lyapunov theory provides the required tools needed to aboard the stability and stabilization problems for discrete event systems modeled with timed Petri nets whose mathematical model is given in terms of difference equations. By proving stability one guarantees a bound on the discrete event systems state dynamics. When the system is unstable, a sufficient condition to stabilize the system is given. It is shown that it is possible to restrict the discrete event systems state space in such a way that boundedness is achieved. However, the restriction is not numerically precisely known. This inconvenience is overcome by considering a specific recurrence equation, in the max-plus algebra, which is assigned to the timed Petri net graphical model.
基金Supported by the Natural Science Foundation of Guangdong Province（04010474） Supported by the Foundation of the Education Department of Anhui Province for Outstanding Young Teachers in University（2011SQRL172）
文摘This paper is concerned with the order of the solutions of systems of high-order complex algebraic differential equations.By means of Zalcman Lemma,the systems of equations of[1]is extended to more general form.
基金Project supported by the State Key Laboratory of Scientific and Engineering Computing, Chinese Academy of Sciences and the National Natural Science Foundation of China （Grant Nos 10471145 and 10372053） and the Natural Science Foundation of Henan Provincial Government of China （Grant Nos 0311011400 and 0511022200）.
文摘The algebraic structure and Poisson＇s integral theory of mechanico-electrical systems are studied. The Hamilton canonical equations and generalized Hamilton canonical equations and their the contravariant algebraic forms for mechanico-electrical systems are obtained. The Lie algebraic structure and the Poisson＇s integral theory of Lagrange mechanico-electrical systems are derived. The Lie algebraic structure admitted and Poisson＇s integral theory of the Lagrange-Maxwell mechanico-electrical systems are presented. Two examples are presented to illustrate these results.
文摘Presents the meshing analysis based on the Computer Algebra System to make it easier to deduce complex formulas while the expression of more complicated surface equations are visualized, by which, the contact line, meshing bordlines and undercut bordlines of toroidal drive are deduced, and the results obtained are consistent with the results discussed in literature [1] , and concludes that the absolute value of the induced normal curvature is usually smaller (less than 0.12, for example), and it increases as parameters φ 2, V and R increase, decreases as parameter r increases, and hardly varies with W 2, and the variation with a, i 21 is not definite.
基金Project supported by the National Natural Science Foundation of China （Grant No 10672143） and the Natural Science Foundation of Henan Provinces China （（]rant Nos 0511022200 and 072300440220）.
文摘Lie symmetry algebra of linear nonconservative dynamical systems is studied in this paper. By using 1-1 mapping, the Lie point and Lie contact symmetry algebras are obtained from two independent solutions of the one-dimensional linear equations of motion.
文摘The algebraic structures of the dynamical equations for the rotational relativistic systems are studied. It is found that the dynamical equations of holonomic conservative rotational relativistic systems and the special nonholonomic rotational relativistic systems have Lie's algebraic structure, and the dynamical equations of the general holonomic rotational relativistic systems and the general nonholonomic rotational relativistic systems have Lie admitted algebraic structure. At last the Poisson integrals of the dynamical equations for the rotational relativistic systems are given.
文摘In this work, we study superintegrable quantum systems in two-dimensional Euclidean space and on a complex twosphere with second-order constants of motion. We show that these constants of motion satisfy the deformed oscillator algebra. Then, we easily calculate the energy eigenvalues in an algebraic way by solving of a system of two equations satisfied by its structure function. The results are in agreement to the ones obtained from the solution of the relevant Schroedinger equation.
文摘In this paper, a real-time computation method for the control problems in differential-algebraic systems is presented. The errors of the method are estimated, and the relation between the sampling stepsize and the controlled errors is analyzed. The stability analysis is done for a model problem, and the stability region is ploted which gives the range of the sampling stepsizes with which the stability of control process is guaranteed.
