arXiv subjects
Publications and source records attributed to Yuan Gao.
In this paper, we consider the transition complexity of regular languages based on the incomplete deterministic finite automata. A number of results on Boolean operations have been obtained. It is shown that the transition complexity results for union and complementation are very different from the state complexity results for the same operations. However, for intersection, the transition complexity result is similar to that of state complexity.
This paper is a continuation of our research work on state complexity of combined operations. Motivated by applications, we study the state complexities of two particular combined operations: catenation combined with star and catenation combined with reversal. We show that the state complexities of both of these combined operations are considerably less than the compositions of the state complexities of their individual participating operations.
In this paper, we show that, due to the structural properties of the resulting automaton obtained from a prior operation, the state complexity of a combined operation may not be equal but close to the mathematical composition of the state complexities of its component operations. In particular, we provide two witness combined operations: reversal combined with catenation and star combined with catenation.
In this paper, we study the state complexities of union and intersection combined with star and reversal, respectively. We obtain the state complexities of these combined operations on regular languages and show that they are less than the mathematical composition of the state complexities of their individual participating operations.
In this paper, we introduce the new concept of state complexity approximation, which is a further development of state complexity estimation. We show that this new concept is useful in both of the following two cases: the exact state complexities are not known and the state complexities have been obtained but are in incomprehensible form.
An approximate homotopy symmetry method for nonlinear problems is proposed and applied to the six-order boussinesq equation. We summarize the general formulas for similarity reduction solutions and similarity reduction equations of different orders, educing the related homotopy series solutions. The convergence region of homotopy series solutions can be adjusted by the auxiliary parameter. Series solutions and similarity reduction equations from approximate symmetry method can be retrieved from approximate homotopy symmetry method.
Generally, natural scientific problems are so complicated that one has to establish some effective perturbation or nonperturbation theories with respect to some associated ideal models. In this Letter, a new theory that combines perturbation and nonperturbation is constructed. An artificial nonlinear homotopy parameter plays the role of a perturbation parameter, while other artificial nonlinear parameters, of which the original problems are independent, introduced in the nonlinear homotopy models are nonperturbatively determined by means of a principle minimal sensitivity. The method is demonstrated through several quantum anharmonic oscillators and a non-hermitian parity-time symmetric Hamiltonian system. In fact, the framework of the theory is rather general that can be applied to a broad range of natural phenomena. Possible applications to condensed matter physics, matter wave systems, and nonlinear optics are briefly discussed.
By using $ϕ$ -mapping method, we discuss the topological structure of the self-duality solution in Jackiw-Pi model in terms of gauge potential decomposition. We set up relationship between Chern-Simons vortices solution and topological number which is determined by Hopf index and and Brouwer degree. We also give the quantization of flux in the case. Then, we study the angular momentum of the vortex, it can be expressed in terms of the flux.
The density dependent relativistic hadron field theory(DDRH) is extended to inclusions of pentaquark $Θ^+$. We investigate In-medium properties of $Θ^+$ and nucleons. As well as the neutron and proton,the effective $Θ^+$ mass decreases as the baryon density increases,and remains larger than nucleons'. The effective mass of $Θ^+$ is calculated,$M^*_{Θ^+}\simeq0.71M_{Θ^+}$ at normal nuclear density with the fraction of $Θ^+$ 0.2. The effective masses of all baryon increase with the increasing fraction of $Θ^+$. The binding energy is also studied. We find the binding energy is much larger than it in nuclear matter without $Θ^+$,and then discuss the stability of the system with conclusions of pentaquark $Θ^+$. It is shown that the system becomes bounder added small fraction of $Θ^+$. Finally we discuss the condition when the system is the most stable and calculate the minimum of binding energy and the fractions of all baryons as functions of baryon density.