The N = 1 supersymmetric extensions of two integrable systems,a special negative Kadomtsev–Petviashvili（NKP）system and a（2＋1）-dimensional modified Korteweg–de Vries（MKd V） system,are constructed from the Hiro...The N = 1 supersymmetric extensions of two integrable systems,a special negative Kadomtsev–Petviashvili（NKP）system and a（2＋1）-dimensional modified Korteweg–de Vries（MKd V） system,are constructed from the Hirota formalism in the superspace.The integrability of both systems in the sense of possessing infinitely many generalized symmetries are confirmed by extending the formal series symmetry approach to the supersymmetric framework.It is found that both systems admit a generalization of W∞type algebra and a Kac-Moody–Virasoro type subalgebra.Interestingly,the first one of the positive flow of the supersymmetric NKP system is another N = 1 supersymmetric extension of the（2＋1）-dimensional MKd V system.Based on our work,a hypothesis is put forward on a series of（2＋1）-dimensional supersymmetric integrable systems.It is hoped that our work may develop a straightforward way to obtain supersymmetric integrable systems in high dimensions.展开更多
Aristotle's Poetics exerts great influence upon literary critical theories.What he discussed in the Poetics has been direct or indirect sources for the later literary critical theories.Formalism Criticism,the firs...Aristotle's Poetics exerts great influence upon literary critical theories.What he discussed in the Poetics has been direct or indirect sources for the later literary critical theories.Formalism Criticism,the first contemporary literary critical theory,mainly takes linguistics as an approach to study literature and especially takes the form of literature as their research focus.This approach can be traced back to what Aristotle discussed about diction in Poetics.Aristotle's deliberate discussion about diction in Poetics,actually lays a foundation for Formalism Criticism.From diction to form shows the influence of Aristotle's poetics upon Formalism.展开更多
Automata theory has played an important role in computer science and engineering particularly modeling behavior of systems since last couple of decades. The algebraic automaton has emerged with several modern applicat...Automata theory has played an important role in computer science and engineering particularly modeling behavior of systems since last couple of decades. The algebraic automaton has emerged with several modern applications, for ex-ample, optimization of programs, design of model checkers, development of theorem provers because of having proper-ties and structures from algebraic theory of mathematics. Design of a complex system not only requires functionality but it also needs to model its control behavior. Z notation is an ideal one used for describing state space of a system and then defining operations over it. Consequently, an integration of algebraic automata and Z will be an effective computer tool which can be used for modeling of complex systems. In this paper, we have combined algebraic automata and Z notation defining a relationship between fundamentals of these approaches. At first, we have described algebraic automaton and its extended forms. Then homomorphism and its variants over strongly connected automata are speci-fied. Finally, monoid endomorphisms and group automorphisms are formalized, and formal proof of their equivalence is given under certain assumptions. The specification is analyzed and validated using Z/EVES tool.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11605102,11475052,11675055,and 11626140)
文摘The N = 1 supersymmetric extensions of two integrable systems,a special negative Kadomtsev–Petviashvili（NKP）system and a（2＋1）-dimensional modified Korteweg–de Vries（MKd V） system,are constructed from the Hirota formalism in the superspace.The integrability of both systems in the sense of possessing infinitely many generalized symmetries are confirmed by extending the formal series symmetry approach to the supersymmetric framework.It is found that both systems admit a generalization of W∞type algebra and a Kac-Moody–Virasoro type subalgebra.Interestingly,the first one of the positive flow of the supersymmetric NKP system is another N = 1 supersymmetric extension of the（2＋1）-dimensional MKd V system.Based on our work,a hypothesis is put forward on a series of（2＋1）-dimensional supersymmetric integrable systems.It is hoped that our work may develop a straightforward way to obtain supersymmetric integrable systems in high dimensions.
文摘Aristotle's Poetics exerts great influence upon literary critical theories.What he discussed in the Poetics has been direct or indirect sources for the later literary critical theories.Formalism Criticism,the first contemporary literary critical theory,mainly takes linguistics as an approach to study literature and especially takes the form of literature as their research focus.This approach can be traced back to what Aristotle discussed about diction in Poetics.Aristotle's deliberate discussion about diction in Poetics,actually lays a foundation for Formalism Criticism.From diction to form shows the influence of Aristotle's poetics upon Formalism.
文摘Automata theory has played an important role in computer science and engineering particularly modeling behavior of systems since last couple of decades. The algebraic automaton has emerged with several modern applications, for ex-ample, optimization of programs, design of model checkers, development of theorem provers because of having proper-ties and structures from algebraic theory of mathematics. Design of a complex system not only requires functionality but it also needs to model its control behavior. Z notation is an ideal one used for describing state space of a system and then defining operations over it. Consequently, an integration of algebraic automata and Z will be an effective computer tool which can be used for modeling of complex systems. In this paper, we have combined algebraic automata and Z notation defining a relationship between fundamentals of these approaches. At first, we have described algebraic automaton and its extended forms. Then homomorphism and its variants over strongly connected automata are speci-fied. Finally, monoid endomorphisms and group automorphisms are formalized, and formal proof of their equivalence is given under certain assumptions. The specification is analyzed and validated using Z/EVES tool.
