Skew-t-normal distribution is one of the most important statistical tools to analyze the obvious peak and fat tail data. A linear mixture joint location and scale model with skew-t-normal data is proposed in this paper. The maximum likelihood estimation of the unknown parameters of this model is investigated based on Expectation Maximization (EM) algorithm and Newton-Raphson method. Furthermore, the proposed procedure works satisfactorily through Monte Carlo experiments. Finally, a real example shows that both this model and method are useful and effective.

A method of calculating price of European options is obtained via Fourier-Cosine expansions approach when the underlying asset price follows a very general state-dependent regime-switching Levy process. Furthermore, in order to improve accurate of the Fourier-Cosine expansions, a modified Fourier-Cosine expansions is developed. The method is then applied to option pricing for European options in Black-Scholes model, Merton jump diffusion model and CGMY Levy model, all with Markov regime switching. Numerical results illustrate that although the convergence rate of method modified Fourier-Cosine expansions is slower than that of Fourier-Cosine expansions, accuracy of method of modified Fourier-Cosine expansions is greatly improved. In particular for case of CGMY Levy model, the improvement is significant.

In this paper, the author studies the $(\alpha,\beta)$-mixing sequences which are stochastically dominated. Some results on the strong stability for $(\alpha,\beta)$-mixing sequences are presented.

By filling in some missing data of the life variable, the relatively simple likelihood function of failure rate model with a change point for truncated and censored data is obtained. The probability distribution and random sampling method of the missing data variable fillled in are discussed. All the unknown parameters are iterated by MCEM algorithm. The parameters are sampled from their full conditional distributions by Gibbs sampler together with Metropolis-Hastings algorithm, and are estimated based on Gibbs sample. The implementation steps of MCMC method are introduced in detail. The random simulation test results show that Bayesian estimations of the parameters are fairly accurate.

In this paper, a class of inertial Cohen-Grossberg neural networks with time delays in leakage terms is investigated. By constructing the appropriate Lyapunov functional, sufficient conditions are obtained for the global exponential stability of the equilibrium. By analyzing the corresponding characteristic equation, the local stability of the equilibrium and the existence of Hopf bifurcation are established. Numerical simulations are carried out to illustrate the main results.

This paper studied the dynamic complexity of a class of discrete population model by computer simulation. The autonomous predator-prey system model is established through theoretical derivation, which has Allee effect and Holling II functional effect. The growth states of discrete-time populations are simulated to explore the influence of the parameters’changes to its population size by MATLAB. It also illustrated the importance of Allee effect and Holling II functional in the model of interaction among populations. The research results show that the larger the processing time, the bigger parameter region for stable coexistence population when the processing time is within the effective range. The introduction of Allee effect makes dynamic behavior of the population more complicated, thus increase the extinction risk of predator population. The population appears bifurcation in advance when predator-prey system strongly affected by Allee effect. It will lead to population extinction, if Allee effect increasingly raises. The strong Allee effect is more prone to population extinction. The conclusion of this paper not only enriches the theory of ecology, but also puts forward important basis of conservation ecology.

In this paper, the properties of SLE hull in the strip region are discussed by using the properties of strip SLE and Schwarz reflection principe. The relation between $\mathbb{R}$-symmetric conformal mappings and hulls in the strip region is given. The relationship between the set which consists of a pair of disjoint hulls and Loewner conformal mappings is obtained. It is derived that the lift of a $\mathbb{R}$-symmetric conformal mapping is continuous in the space of hulls in the strip region, and that some related mappings are continuous in the corresponding space of hulls, too. This generalizes the related properties of SLE hull in the upper half-plane to the case of strip region.

Based on some results for finite posets and the specialization order of a topology, as well as relationships between topologies and orderings, we calculate the total number of $T_0 $-topologies on a 5-element set, which is 4231. We also calculate the total number of different topologies on a 5-element set, which is 6942.

This paper proposes some new methods for generating fuzzy implications. Some new fuzzy operations can be generated by using some selected fuzzy implications through multiple iterations. According to different iterative methods, all of the new fuzzy operations have been proved to be fuzzy implications. Furthermore, when the selected fuzzy implications satisfied some important properties, whether multiple fuzzy implications still keep these properties or not is also discussed. Two important cases have been investigated: the selected implications are (S, N)-implications or R-implications. This work provides some new possible selections of fuzzy implications for some applied fields such as fuzzy control and fuzzy decision making.

The quasistatic elastic problem is formulated as an elliptic system for the displacements coupled with a parabolic equation for the damage field. The corresponding inverse problem is reformulated as an optimal control problem to find a stable traction, by a given observation data. Firstly, a convex functional is constructed with Tikhonov regularization, and a stable approximation of surface traction is obtained by minimizing it. Then a finite element discretization of the inverse elastic problem is analyzed. Moreover, the error estimation of the numerical solutions is deduced. At last, a numerical algorithm is detailed and three examples illustrate the efficiency of the algorithm.

By using the general framework introduced in Arnod et al. and the new method dealting with the nonlinear convection term, the error estimates of three-step implicit-explicit hpLDG method for nonlinear convection diffusion problems are obtained. The numerical example for the nonlinear Burgers equation is presented in the paper. The numerical results verify the theoretical results obtained in this paper.