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In this paper, we discuss the cooperation behaviors of intelligent virtual agents with autonomous and cooperative ability .Based on the theory of fluent calculus, we have designed an agent reasoning model .In this model, intelligent virtual agent could automatically judge the next action in the action queue and constructs the dynamic environment quickly with limited information from sensor. Furthermore, a type of request/server cooperation function has been designed for the cooperation among virtual agents to solve the conflicts and to realize the joint goals. Experiment results obtained demonstrated that intelligent virtual agents could cooperate well by our reasoning model.

By using a modified approximation scheme to deal with the centrifugal term, we solve approximately the Schrödinger equation for the Eckart potential with the arbitrary angular momentum states. The bound state energy eigenvalues and the unnormalized radial wave functions are approximately obtained in a closed form by using the supersymmetric shape invariance approach and the function analysis method. The numerical experiments show that our analytical results are in better agreement with those obtained by using the numerical integration approach than the analytical results obtained by using the conventional approximation scheme to deal with the centrifugal term.

The (1+1)-dimensional Dirac equation with a PT-symmetric kink-like vector potential is investigated. By using the basic concepts of the supersymmetric WKB formalism and the function analysis method, we solve exactly the Dirac equation and obtain the bound-state energy levels and two-component spinor components. The PT-symmetric kink-like potential is not Hermitian and absent of bound states in the context of non-relativistic Schrodinger equation, but it possesses two sets of real discrete relativistic energy spectra in the context of the Dirac theory. When the PT symmetry is spontaneously broken, two sets of real energy spectra come into complex conjugate.

Solving Klein–Gordon equation with equal scalar and vector Rosen–Morse-type potentials, we obtain the exact energy equation for the s-wave bound states. It has been shown that the energy equations and corresponding wavefunctions for the standard Rosen–Morse well, Eckart potential and their PT-symmetric versions are included in those for Rosen–Morse-type potential as special cases.

We choose the five-parameter exponential-type potential model as input, and construct five trigonometric-type potentials via point canonical transformations. Their energy spectra and wavefunctions are obtained in a unified manner by using the expressions for the energy spectra and wavefunctions of the five-parameter exponential-type potential model.

Solving Klein–Gordon equation with equal five-parameter exponential-type scalar and vector potentials by the method of the supersymmetric quantum mechanics and shape invariance, we obtain the exact energy equation for the s-wave bound states. It has been shown that the energy equations for a large class of exponential-type potentials are included in the energy equation for the five-parameter exponential-type potential as special cases.

By employing the dissociation energy and the equilibrium bond length for a diatomic molecule as explicit parameters, we generate improved expressions for the well-known Rosen-Morse, Manning-Rosen, Tietz, and Frost-Musulin potential energy functions. It is found that the well-known Tietz potential function that is conventionally defined in terms of five parameters [T. Tietz, J. Chem. Phys. 38, 3036 (1963)] actually only has four independent parameters. It is shown exactly that the Wei [Phys. Rev. A 42, 2524 (1990)] and the well-known Tietz potential functions are the same solvable empirical function. When the parameter h in the Tietz potential function has the values 0, +1, and -1, the Tietz potential becomes the standard Morse, Rosen-Morse, and Manning-Rosen potentials, respectively.

The structure of Petri nets(PN) is too static to make the corresponding response to the system that the structure changes because of itself and the environment. When PN are running or the environment transforms, the change of the structure of Petri nets is considered, such as: place P, transition T, and flow relation F. Based on original PN, this paper develops one kind of Petri Nets with Systematized Changeable Structure (PN-SCS) that according to the certain mechanism (or actual need), the structure of Petri Nets (place, transition, flow relation and so on) may change for the running of PN (internal factor or home affair occurrence) and the change of the environment (exterior factor or some demands), and these changes are describing the variation of the element of actual system. This model will broaden the application of PN and the connection with other science, such as Nature Inspired Computation, Complex Networks and Automatic Control Theory. Finally, the modeled method of PN-SCS is introduced by an example that people browses web pages.

The original Hopfield neural networks model is adapted so that the weights of the resulting network are time varying. In this paper, the Discrete Hopfield neural networks with weight function matrix (DHNNWFM) the weight changes with time, are considered, and the stability of DHNNWFM is analyzed. Combined with the Lyapunov function, we obtain some important results that if weight function matrix (WFM) is weakly (or strongly) nonnegative definite function matrix, the DHNNWFM will converge to a stable state in serial (or parallel) model, and if WFM consisted of strongly nonnegative definite function matrix and column (or row) diagonally dominant function matrix, DHNNWFM will converge to a stable state in parallel model.

A great number of real network models exhibit the classical characteristics of networks: an exponential degree distribution, high clustering coefficient and a short average path length (APL). In order to construct more really network models, the process of adding edges is divided into two processes based on Wang Bing model that Wang Bing proposes a kind of Evolving scale-free network model with tunable clustering. One process increases the clustering coefficient. Another process reduces the APL. This article proposes a scale-free network model with tunable clustering and APL. Using continuum theory and rate equations method to calculate the degree distribution, the clustering coefficient and APL, the analytical result indicates that the degree distribution follows power law and the clustering coefficient and the APL can be tuned with tow parameters. The APL is estimated analytically, which increases at logarithmically, constantly or negative logarithmically with the time by tuning with tow parameters.

Most matrixes of Discrete Hopfield neural networks(DHNNs) and DHNNs with delay are constant matrixes. However, most weight matrixes of DHNNses are variable in many realistic systems. So, the weight matrix and the threshold vector with time factor are considered, and DHNNs with weight function matrix (DHNNWFM) is described. Moreover, the result that if weight function matrix and threshold function vector respectively converge to a constant matrix and a constant vector that the corresponding DHNNs is stable or the weight matrix function is a symmetric function matrix, then DHNNWFM is stable, is obtained by matrix analysis.

By using the basic concepts of the supersymmetric quantum mechanics formalism and the function analysis method, we solve the Dirac equation with vector and scalar potentials and obtain the bound-state solutions for the nuclei in the relativistic Poschl-Teller potential. All of the analyses are prepared under the conditions of the exact spin symmetry and pseudospin symmetry. The exact energy equation and corresponding two-component spinor wave functions for s -wave bound states are obtained analytically.

By employing an improved new approximation scheme to deal with the centrifugal term, we solve approximately the Klein–Gordon equation with equal scalar and vector generalized Poschl–Teller potentials for the arbitrary orbital angular momentum number l. The bound state energy equation and the unnormalized radial wave functions have been approximately obtained by using the supersymmetric shape invariance approach and the function analysis method. It is found that the present approximate analytical results are in better agreement with those obtained by using the numerical integration approach for small values of α than the approximate results obtained by using the conventional approximation to the centrifugal term.