By filling in the missing data of the life variable, the complete-data likelihood function of Weibull distribution with multiple change points for truncated and censored data is obtained. The full conditional distributions of change-point positions, shape parameters, and scale parameters are studied. Gibbs samples of the parameters are obtaines by MCMC method of Gibbs sampling together with Metropolis-Hastings algorithm, and the means of Gibbs samples are taken as Bayesian estimations of the parameters. 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.

A finite T-IPH/Geo/1/N queue system is considered, where T-IPH denotes the discrete-time phase type distribution defined on a birth and death chain with countably many states. The queue model can be described by a quasi-birth-and-death (QBD) process with finite phases. The iterative formula to calculate nonzero values in the rate matrix of the QBD process is proved firstly. Furthermore, based on the obtained results, the stationary queue length and waiting time distribution of the T-IPH/Geo/1/N queue are given.

Let $X_t=\sum_{k=0}^\infty a_k \varepsilon_{t-k}$ be a long memory moving-average process, this paper achieves a general law of precise asymptotics for $X_t$. It can describe the relations among the boundary function, weighted function, convergence rate and limit value in studies of complete convergence.

Considering the factor of hospital cure, an SEIR epidemic model with nonlinear incidence and nonlinear recovery rate is investigated. It is shown that the model exhibits two equilibria, namely, the disease-free equilibrium and the endemic equilibrium. A backward bifurcation leading to bistability possibly occurs. The global stability of the model is further studied by using the Lyapunov function. The corresponding results in literatures are improved and extended.

The stability of epidemical model is analyzed, and the time-delay effect of infected person on susceptible person is considered. In the paper, firstly, the disease-free equilibrium is globally asymptotically stable by constructing Lyapunov functional when the basic reproductive number $R_{0}<1$. Furthermore, when $R_{0}>1$, the positive equilibrium that is locally asymptotically stable and permanent is proved.

This article is concerned with an optimal harvesting problem for a population model, which is based on expanded Leslie’s project matrix and incorporates an ecological balance and exploitation costs. By means of convex optimization method, the existence of optimal policies is shown and the harvesting ratio is specified. It is demonstrated that the optimal strategies are of two-staged form.

In the paper, one kind $p$-Laplacian-like equations with Neumann boundaries are first converted to the form of operator equation involving the maximal monotone operators. After being proved that the operator equation exists solution, the $p$-Laplacian-like equations with Neumann boundaries are shown to have non-trivial solution. Secondly, some iterative schemes are constructed to approximate strongly to the zeros of maximal monotone operators through the relative resolvent of the maximal monotone operators. Finally, the relation between the solution of $p$-Laplacian-like equations with Neumann boundaries and the zeros of maximal monotone operators is being set up and then the iterative approximate solution of the $p$-Laplacian-like equations is obtained. The work done in this paper extends and complements some previous corresponding work.

In this paper, the pointwise estimate for the sharp maximal function of the Toeplitz operators $T_{b}$ generalized by some singular integral whose kernel satisfied some variant $L^{r}$-Hormander condition and weighted Lipschitz function is established. The authors proved that $T_{b}$ is bounded from $L^{p}(w)$ to $L^{q}(w^{1-q})$. On the other hand, the pointwise estimate for the Toeplitz operator $T_{b}$ generalized by weighted \text{BMO} function and singular integral with a variant Lipschitz condition kernel is also established. Meanwhile the $(L^{p}(\mu),L^{q}(\nu))$-boundedness for $T_{b}$ is also proved.

Suppose that $\alpha>1$. Let $u$ be analytic in the unit disc $D$ and $\varphi$ be analytic map-self on $D$. In the paper, the authors give the simple necessary and sufficient condition of the weighted composition operator $uC_{\varphi}$ being compact from $\beta_{L}$ to $\beta_{\alpha}$ on $D$.

Berezin-type transform plays an important role in the study of the $(\alpha, \beta)$-hamonicity of the functions. The boundeness and the exact upper-norm and lower-norm of the Berezin-type transform on $L^p(1<p\leq\infty)$ space are given by using the hypergeometric function and Schur's test.

By the characteristic method, a new geometric flow-the hyperbolic gradient flow was studied. The necessary and sufficient conditions for the global existence of smooth solution were given. The uniqueness and decay estimates of solution were also discussed.

In this paper, the extensions of uninorms are studied. In bounded lattices, the concepts of retract, $(r, s)$-sublattice, retraction, and $e$-operator are introduced, the extensions of uninorms via retractions and $e$-operator on bounded lattices are presented, respectively. Also, the most properties of original uninorms are preserved by the extensions. Furthermore, the relationships between conjugate of uninorms and the extensions of uninorms are discussed.

It is important in the application to study the numerical computation for timefractional option pricing model (time-fractional Black-Scholes equation). Explicit-Implicit (E-I) scheme and Implicit-Explicit (I-E) scheme are constructed for solving time-fractional Black-Scholes equation. The stable, convergent, existence and uniqueness of solutions given by these schemes are discussed. Theoretical analysis demonstrates that E-I and I-E schemes are unconditional stability and convergent. They have the same calculation. Numerical experiments show that computational accuracy of E-I and I-E schemes is similar to the classic Crank-Nicolson (C-N) scheme, and their computational efficiency (computing time) is 30% higher than C-N scheme. Theoretical analysis and numerical experiments demonstrate the superiority of E-I and I-E schemes for solving time-fractional option pricing model, and affirm that time-fractional Black-Scholes equation is more in line with the actual financial market.

By taking advantage of the combinatorial features of Lyndon words, the global dimension and the Gelfand-Kirillov dimension of these algebras of which the set of obstructions consists of Lyndon words are characterized.