Random iterated function systems (IFSs) is discussed, which is one of the methods for fractal drawing. A certain figure can be reconstructed by a random IFS. One approach is presented to determine a new random IFS, th...Random iterated function systems (IFSs) is discussed, which is one of the methods for fractal drawing. A certain figure can be reconstructed by a random IFS. One approach is presented to determine a new random IFS, that the figure reconstructed by the new random IFS is the image of the origin figure reconstructed by old IFS under a given affine transformation. Two particular examples are used to show this approach.展开更多
It was proved that velocity-dependent infinitesima l symmetry transformations of nonholonomic systems have a characteristic functio nal structure, which could be formulated by means of an auxiliary symmetry tra nsform...It was proved that velocity-dependent infinitesima l symmetry transformations of nonholonomic systems have a characteristic functio nal structure, which could be formulated by means of an auxiliary symmetry tra nsformation function and is manifestly dependent upon constants of motion of th e system. An example was given to illustrate the applicability of the results.展开更多
The key notions in Halliday's Systematic Grammar and Functional Grammar are first summarized, and then contrasted with Chomsky's Transformational-Generative Grammar. Results show that Systematic-Functional Gra...The key notions in Halliday's Systematic Grammar and Functional Grammar are first summarized, and then contrasted with Chomsky's Transformational-Generative Grammar. Results show that Systematic-Functional Grammar could be viewed as complementa ry to Transformational-Generative Grammar. They combine to reveal the whole picture of language.展开更多
The theory of time scales,which unifies continuous and discrete analysis,provides a powerful mathematical tool for the study of complex dynamic systems.It enables us to understand more clearly the essential problems o...The theory of time scales,which unifies continuous and discrete analysis,provides a powerful mathematical tool for the study of complex dynamic systems.It enables us to understand more clearly the essential problems of continuous systems and discrete systems as well as other complex systems.In this paper,the theory of generalized canonical transformation for second-order Birkhoffian systems on time scales is proposed and studied,which extends the canonical transformation theory of Hamilton canonical equations.First,the condition of generalized canonical transformation for the second-order Birkhoffian system on time scales is established.Second,based on this condition,six basic forms of generalized canonical transformation for the second-order Birkhoffian system on time scales are given.Also,the relationships between new variables and old variables for each of these cases are derived.In the end,an example is given to show the application of the results.展开更多
This paper deals with mathematical modelling of impulse waveforms and impulse switching functions used in electrical engineering. Impulse switching functions are later investigated using direct and inverse z-transform...This paper deals with mathematical modelling of impulse waveforms and impulse switching functions used in electrical engineering. Impulse switching functions are later investigated using direct and inverse z-transformation. The results make possible to present those functions as infinite series expressed in pure numerical, exponential or trigonometric forms. The main advantage of used approach is the possibility to calculate investigated variables directly in any instant of time;dynamic state can be solved with the step of sequences (T/6, T/12) that means very fast. Theoretically derived waveforms are compared with simulation worked-out results as well as results of circuit emulator LT spice which are given in the paper.展开更多
This paper describes a prototype power delivery system developed for high voltage electronic current transformer （ECT） that uses laser light to transfer power to and communicates with the primary converter. The desi...This paper describes a prototype power delivery system developed for high voltage electronic current transformer （ECT） that uses laser light to transfer power to and communicates with the primary converter. The design is based on optical-to-electrical power converters, solid-state diode lasers and optical fibers. Command signals are transmitted via the same up-fiber used to send power from secondary power supply to primary converter. The upward data transmission is completed during the brief interruption of power delivery without affecting steady power-supply. A simple comparator added to the primary converter can take the command data. Experimental results show that the fibers can provide reliable up-link for data transmission at 200 kb/s from the secondary to the primary converter. Based on the delivery system, the secondary converter can control three auxiliary channels to provide additional information. These monitoring channels are used in a time-multiplexing mode to provide information about the operation temperature, voltage and current at the remote unit for monitoring the ECT. This preventive maintenance or built-in test can increase reliability by giving early warning for necessary maintenance request.展开更多
This paper gives the definition of fractal affine transformation and presents a specific method for its realization and its corresponding mathematical equations which are essential in fractal image construction.
In this paper, we study the linear thermo-visco-elastic system in one-dimensional space variable. The mathematical model is a hyperbolic-parabolic partial differential system. The solutions of the system show some dec...In this paper, we study the linear thermo-visco-elastic system in one-dimensional space variable. The mathematical model is a hyperbolic-parabolic partial differential system. The solutions of the system show some decay property due to the parabolicity. Based on detailed analysis on the Green function of the system, the pointwise estimates of the solutions are obtained, from which the generalized Huygens’ principle is shown.展开更多
Quantum-classical correspondence is affirmed via performing Wigner function and a classical-quantum chaotic system containing random variables.The classical-quantum system is transformed into a Kolmogorov model for fo...Quantum-classical correspondence is affirmed via performing Wigner function and a classical-quantum chaotic system containing random variables.The classical-quantum system is transformed into a Kolmogorov model for force and energy analysis.Combining different forces,the system is divided into two categories:conservative and non-conservative,revealing the mechanical characteristic of the classical-quantum system.The Casimir power,an analysis tool,is employed to find the key factors governing the orbital trajectory and the energy cycle of the system.Detailed analyses using the Casimir power and an energy transformation uncover the causes of the different dynamic behaviors,especially chaos.For the corresponding classical Hamiltonian system when Planck’s constant h→0,the supremum bound of the system is derived analytically.Difference between the classical-quantum system and the classical Hamiltonian system is displayed through trajectories and energies.Quantum-classical correspondences are further demonstrated by comparing phase portrait,kinetic,potential and Casimir energies of the two systems.展开更多
文摘Random iterated function systems (IFSs) is discussed, which is one of the methods for fractal drawing. A certain figure can be reconstructed by a random IFS. One approach is presented to determine a new random IFS, that the figure reconstructed by the new random IFS is the image of the origin figure reconstructed by old IFS under a given affine transformation. Two particular examples are used to show this approach.
文摘It was proved that velocity-dependent infinitesima l symmetry transformations of nonholonomic systems have a characteristic functio nal structure, which could be formulated by means of an auxiliary symmetry tra nsformation function and is manifestly dependent upon constants of motion of th e system. An example was given to illustrate the applicability of the results.
文摘The key notions in Halliday's Systematic Grammar and Functional Grammar are first summarized, and then contrasted with Chomsky's Transformational-Generative Grammar. Results show that Systematic-Functional Grammar could be viewed as complementa ry to Transformational-Generative Grammar. They combine to reveal the whole picture of language.
基金supported by the National Natural Science Foundation of China(Grants 11972241 and 11572212)
文摘The theory of time scales,which unifies continuous and discrete analysis,provides a powerful mathematical tool for the study of complex dynamic systems.It enables us to understand more clearly the essential problems of continuous systems and discrete systems as well as other complex systems.In this paper,the theory of generalized canonical transformation for second-order Birkhoffian systems on time scales is proposed and studied,which extends the canonical transformation theory of Hamilton canonical equations.First,the condition of generalized canonical transformation for the second-order Birkhoffian system on time scales is established.Second,based on this condition,six basic forms of generalized canonical transformation for the second-order Birkhoffian system on time scales are given.Also,the relationships between new variables and old variables for each of these cases are derived.In the end,an example is given to show the application of the results.
文摘This paper deals with mathematical modelling of impulse waveforms and impulse switching functions used in electrical engineering. Impulse switching functions are later investigated using direct and inverse z-transformation. The results make possible to present those functions as infinite series expressed in pure numerical, exponential or trigonometric forms. The main advantage of used approach is the possibility to calculate investigated variables directly in any instant of time;dynamic state can be solved with the step of sequences (T/6, T/12) that means very fast. Theoretically derived waveforms are compared with simulation worked-out results as well as results of circuit emulator LT spice which are given in the paper.
基金Project supported by the National Natural Science Foundation of China （Grant No.50447006）
文摘This paper describes a prototype power delivery system developed for high voltage electronic current transformer （ECT） that uses laser light to transfer power to and communicates with the primary converter. The design is based on optical-to-electrical power converters, solid-state diode lasers and optical fibers. Command signals are transmitted via the same up-fiber used to send power from secondary power supply to primary converter. The upward data transmission is completed during the brief interruption of power delivery without affecting steady power-supply. A simple comparator added to the primary converter can take the command data. Experimental results show that the fibers can provide reliable up-link for data transmission at 200 kb/s from the secondary to the primary converter. Based on the delivery system, the secondary converter can control three auxiliary channels to provide additional information. These monitoring channels are used in a time-multiplexing mode to provide information about the operation temperature, voltage and current at the remote unit for monitoring the ECT. This preventive maintenance or built-in test can increase reliability by giving early warning for necessary maintenance request.
文摘This paper gives the definition of fractal affine transformation and presents a specific method for its realization and its corresponding mathematical equations which are essential in fractal image construction.
基金Xingwen Hao's research was supported in part by National Natural Science Foundation of China (10571120 and 10971135)Shanghai Shuguang Project (06SG11)+1 种基金the Program for New Century Excellent Talents of Chinese Ministry of Education (NCET-07-0546) Doctorial Foundation of Weifang University (2011BS11)
文摘In this paper, we study the linear thermo-visco-elastic system in one-dimensional space variable. The mathematical model is a hyperbolic-parabolic partial differential system. The solutions of the system show some decay property due to the parabolicity. Based on detailed analysis on the Green function of the system, the pointwise estimates of the solutions are obtained, from which the generalized Huygens’ principle is shown.
基金Supported by National Natural Science Foundation of China （61079001, 61273006）, National High Technology Research and Development Program of China （863 Program） （2011AA110301）, and Specialized Research Fund for the Doctoral Program of Higher Education of China （20111103110017）
基金Project supported by the National Natural Science Foundation of China(Grant Nos.61873186 and 11902220)the Natural Science Foundation of Tianjin City of China(Grant No.17JCZDJC38300)+1 种基金the Provincial Foundation for Excellent Young Talents of Colleges and Universities of Anhui Province of China(Grant No.GXYQ2017014)the Anhui University Humanities and Social Sciences Research Project of China(Grant No.SK2019A0116).
文摘Quantum-classical correspondence is affirmed via performing Wigner function and a classical-quantum chaotic system containing random variables.The classical-quantum system is transformed into a Kolmogorov model for force and energy analysis.Combining different forces,the system is divided into two categories:conservative and non-conservative,revealing the mechanical characteristic of the classical-quantum system.The Casimir power,an analysis tool,is employed to find the key factors governing the orbital trajectory and the energy cycle of the system.Detailed analyses using the Casimir power and an energy transformation uncover the causes of the different dynamic behaviors,especially chaos.For the corresponding classical Hamiltonian system when Planck’s constant h→0,the supremum bound of the system is derived analytically.Difference between the classical-quantum system and the classical Hamiltonian system is displayed through trajectories and energies.Quantum-classical correspondences are further demonstrated by comparing phase portrait,kinetic,potential and Casimir energies of the two systems.
