Using semi-tensor product of matrices, the controllability and stabilizability of finite automata are investigated. By expressing the states, inputs, and outputs in vector forms, the transition and output functions ar...Using semi-tensor product of matrices, the controllability and stabilizability of finite automata are investigated. By expressing the states, inputs, and outputs in vector forms, the transition and output functions are represented in matrix forms.Based on this algebraic description, a necessary and sufficient condition is proposed for checking whether a state is controllable to another one. By this condition, an algorithm is established to find all the control sequences of an arbitrary length. Moreover, the stabilizability of finite automata is considered, and a necessary and sufficient condition is presented to examine whether some states can be stabilized. Finally, the study of illustrative examples verifies the correctness of the presented results/algorithms.展开更多
In this paper,a stepwise coupled-mode model with the use of the direct global matrix approach is proposed.This method is capable of handling two-dimensional problems with either a point source in cylindrical geometry ...In this paper,a stepwise coupled-mode model with the use of the direct global matrix approach is proposed.This method is capable of handling two-dimensional problems with either a point source in cylindrical geometry or a line source in plane geometry.With the use of the direct global matrix approach,this method is numerically stable.In addition,by introducing appropriately normalized range solutions,this model is free from the numerical overflow problem.Furthermore,we put forward source conditions appropriate for the line-source problem in plane geometry.As a result,this method is capable of addressing the scenario with a line source on top of a sloping bottom.Closed-form expressions for coupling matrices are derived and applied in this paper for handling problems with pressure-release boundaries and a homogeneous water column.The numerical simulations indicate that the proposed model is accurate,efficient,and numerically stable.Consequently,this model can serve as a benchmark model in range-dependent propagation modeling.Although this method is verified by an ideal wedge problem in this paper,the formulation applies to realistic problems as well.展开更多
This paper investigates the transition function and the reachability conditions of finite automata by using a semitensor product of matrices, which is a new powerful matrix analysis tool. The states and input symbols ...This paper investigates the transition function and the reachability conditions of finite automata by using a semitensor product of matrices, which is a new powerful matrix analysis tool. The states and input symbols are first expressed in vector forms, then the transition function is described in an algebraic form. Using this algebraic representation, a sufficient and necessary condition of the reachability of any two states is proposed, based on which an algorithm is developed for discovering all the paths from one state to another. Furthermore, a mechanism is established to recognize the language acceptable by a finite automaton. Finally, illustrative examples show that the results/algorithms presented in this paper are suitable for both deterministic finite automata （DFA） and nondeterministic finite automata （NFA）.展开更多
This paper aims to develop a direct approach,namely,the Cauchy matrix approach,to non-isospectral integrable systems.In the Cauchy matrix approach,the Sylvester equation plays a central role,which defines a dressed Ca...This paper aims to develop a direct approach,namely,the Cauchy matrix approach,to non-isospectral integrable systems.In the Cauchy matrix approach,the Sylvester equation plays a central role,which defines a dressed Cauchy matrix to provideτfunctions for the investigated equations.In this paper,using the Cauchy matrix approach,we derive three non-isospectral nonlinear Schrödinger equations and their explicit solutions.These equations are generically related to the time-dependent spectral parameter in the Zakharov–Shabat–Ablowitz–Kaup–Newell–Segur spectral problem.Their solutions are obtained from the solutions of unreduced non-isospectral nonlinear Schrödinger equations through complex reduction.These solutions are analyzed and illustrated to show the non-isospectral effects in dynamics of solitons.展开更多
Polymer matrix composites(PMC)are extensively been used in many engineering applications.Various natural fibers have emerged as potential replacements to synthetic fibers as reinforcing materials composites owing to t...Polymer matrix composites(PMC)are extensively been used in many engineering applications.Various natural fibers have emerged as potential replacements to synthetic fibers as reinforcing materials composites owing to their fairly better mechanical properties,low cost,environment friendliness and biodegradability.Selection of appropriate constituents of composites for a particular application is a tedious task for a designer/engineer.Impact loading has emerged as the serious threat for the composites used in structural or secondary structural application and demands the usage of appropriate fiber and matrix combination to enhance the energy absorption and mitigate the failure.The objective of the present review is to explore the composite with various fiber and matrix combination used for impact applications,identify the gap in the literature and suggest the potential naturally available fiber and matrix combination of composites for future work in the field of impact loading.The novelty of the present study lies in exploring the combination of naturally available fiber and matrix combination which can help in better energy absorption and mitigate the failure when subjected to impact loading.In addition,the application of multi attributes decision making(MADM)tools is demonstrated for selection of fiber and matrix materials which can serve as a benchmark study for the researchers in future.展开更多
The semi-tensor product （STP） of matrices was used in the article, as a new matrix analysis tool, to investigate the problem of verification of self-verifying automata （SVA）. SVA is a special variant of finite aut...The semi-tensor product （STP） of matrices was used in the article, as a new matrix analysis tool, to investigate the problem of verification of self-verifying automata （SVA）. SVA is a special variant of finite automata which is essential to nondeterministic communication with a limited number of advice bits. The status, input and output symbols are expressed in vector forms, the dynamic behaviour of SVA is modelled as matrix product is STP. By such algebraic formulation, three an algebraic equation of the states and inputs, in which the necessary and sufficient conditions are presented for the verification problem, by which three algorithms are established to find out all the strings which are accepted, rejected, or unrecognized by a SVA. Testing examples show the correctness of the results.展开更多
基金supported by the National Natural Science Foundation of China(61174094)the Tianjin Natural Science Foundation of China(13JCYBJC1740014JCYBJC18700)
文摘Using semi-tensor product of matrices, the controllability and stabilizability of finite automata are investigated. By expressing the states, inputs, and outputs in vector forms, the transition and output functions are represented in matrix forms.Based on this algebraic description, a necessary and sufficient condition is proposed for checking whether a state is controllable to another one. By this condition, an algorithm is established to find all the control sequences of an arbitrary length. Moreover, the stabilizability of finite automata is considered, and a necessary and sufficient condition is presented to examine whether some states can be stabilized. Finally, the study of illustrative examples verifies the correctness of the presented results/algorithms.
基金supported by the National Natural Science Foundation of China (Grant Nos. 10734100 and 11125420)the Knowledge Innovation Program of Chinese Academy of Sciences
文摘In this paper,a stepwise coupled-mode model with the use of the direct global matrix approach is proposed.This method is capable of handling two-dimensional problems with either a point source in cylindrical geometry or a line source in plane geometry.With the use of the direct global matrix approach,this method is numerically stable.In addition,by introducing appropriately normalized range solutions,this model is free from the numerical overflow problem.Furthermore,we put forward source conditions appropriate for the line-source problem in plane geometry.As a result,this method is capable of addressing the scenario with a line source on top of a sloping bottom.Closed-form expressions for coupling matrices are derived and applied in this paper for handling problems with pressure-release boundaries and a homogeneous water column.The numerical simulations indicate that the proposed model is accurate,efficient,and numerically stable.Consequently,this model can serve as a benchmark model in range-dependent propagation modeling.Although this method is verified by an ideal wedge problem in this paper,the formulation applies to realistic problems as well.
基金Acknowledgements This work was supported by the National Natural Science Foundation of China （Grant No. 61174094）, and the Tianjin Natural Science Foundation of China under （14JCYBJC18700 and 13JCY- BJC17400）.
文摘This paper investigates the transition function and the reachability conditions of finite automata by using a semitensor product of matrices, which is a new powerful matrix analysis tool. The states and input symbols are first expressed in vector forms, then the transition function is described in an algebraic form. Using this algebraic representation, a sufficient and necessary condition of the reachability of any two states is proposed, based on which an algorithm is developed for discovering all the paths from one state to another. Furthermore, a mechanism is established to recognize the language acceptable by a finite automaton. Finally, illustrative examples show that the results/algorithms presented in this paper are suitable for both deterministic finite automata （DFA） and nondeterministic finite automata （NFA）.
基金supported by the National Natural Science Foundation of China(No.12271334).
文摘This paper aims to develop a direct approach,namely,the Cauchy matrix approach,to non-isospectral integrable systems.In the Cauchy matrix approach,the Sylvester equation plays a central role,which defines a dressed Cauchy matrix to provideτfunctions for the investigated equations.In this paper,using the Cauchy matrix approach,we derive three non-isospectral nonlinear Schrödinger equations and their explicit solutions.These equations are generically related to the time-dependent spectral parameter in the Zakharov–Shabat–Ablowitz–Kaup–Newell–Segur spectral problem.Their solutions are obtained from the solutions of unreduced non-isospectral nonlinear Schrödinger equations through complex reduction.These solutions are analyzed and illustrated to show the non-isospectral effects in dynamics of solitons.
文摘Polymer matrix composites(PMC)are extensively been used in many engineering applications.Various natural fibers have emerged as potential replacements to synthetic fibers as reinforcing materials composites owing to their fairly better mechanical properties,low cost,environment friendliness and biodegradability.Selection of appropriate constituents of composites for a particular application is a tedious task for a designer/engineer.Impact loading has emerged as the serious threat for the composites used in structural or secondary structural application and demands the usage of appropriate fiber and matrix combination to enhance the energy absorption and mitigate the failure.The objective of the present review is to explore the composite with various fiber and matrix combination used for impact applications,identify the gap in the literature and suggest the potential naturally available fiber and matrix combination of composites for future work in the field of impact loading.The novelty of the present study lies in exploring the combination of naturally available fiber and matrix combination which can help in better energy absorption and mitigate the failure when subjected to impact loading.In addition,the application of multi attributes decision making(MADM)tools is demonstrated for selection of fiber and matrix materials which can serve as a benchmark study for the researchers in future.
基金supported by the National Natural Science Foundation of China (61174094)the Tianjin Natural Science Foundation of China (14JCYBJC18700, 13JCYBJC17400)
文摘The semi-tensor product （STP） of matrices was used in the article, as a new matrix analysis tool, to investigate the problem of verification of self-verifying automata （SVA）. SVA is a special variant of finite automata which is essential to nondeterministic communication with a limited number of advice bits. The status, input and output symbols are expressed in vector forms, the dynamic behaviour of SVA is modelled as matrix product is STP. By such algebraic formulation, three an algebraic equation of the states and inputs, in which the necessary and sufficient conditions are presented for the verification problem, by which three algorithms are established to find out all the strings which are accepted, rejected, or unrecognized by a SVA. Testing examples show the correctness of the results.
