If heterogeneity of the “inefficiency” term is disregarded, it will result in the incorrect estimate of this term in the stochastic frontier model. By combining the influence from characteristic differences of individuals with the time-varying property of variance, a dynamic heterogeneity stochastic frontier model is proposed. By the Gibbs sampling, the methodology for Bayesian analysis of the dynamic heterogeneity stochastic frontier model is given. For each model parameter, the posterior distribution is derived. A simulation study shows that under the criterion of minimizing the posterior mean square error, the Bayesian estimate is close to its true value for small and medium sized samples. From the Bayesian analysis based on the real electric power company generation data, it is evidenced that there exists the time-varying property for the variance of the logarithm “inefficiency” term.

In epidemiological studies, incidence of a disease is an important index which reflects the degree of the onset of a certain disease in the particular crowd. As a result, the structure of the confidence interval of it has important medical significance in judging disease extent. For some chronic diseases (such as cancer or cardiovascular, etc.), due to their long onset period and low incidence, Poisson sampling is in accord with the facts more than binomial sampling and inverse sampling. Four methods were used to study the construction of confidence interval for the incidence of chronic diseases under poisson distribution, and the performance properties of the four methods were compared through monte carlo simulation. Simulation results show that when higher incidence, pivot method did very well in both coverage and the interval length. When rates are relatively lower, pivot method is slightly inferior to Wald statistic method and the method of scoring on the interval length, but it did the best on the coverage. As a result, the overall performance of pivot method is very good.

In this paper, the causal relationships among variables of nonlinear structure vector autoregressive model are studied using graphical model method. The nonlinear structure vector autoregressive causal graph is presented, and a generalized likelihood ratio approach is developed to infer the causal relationships. The generalized likelihood ratio statistics of contemporaneous and lagged are presented respectively, and a bootstrap method is considered for determining the null distribution of the test statistic. The validity of the proposed method is confirmed by simulations analysis.

This paper deals with a class of Kirchhoff type equation involving the $p$-Laplacian-like operator. Base on sysmmetric mountain pass theorem, some sufficient conditions for the existence of multiplicity of solutions are obtained, which generalize and improve the existing ones.

A diffusive virus dynamics model with Beddington-DeAngelis incidence function is investigated. By constructing Lyapunov function, it is shown that the infection equilibrium is globally asymptotically stable.

By constructing the corresponding Green’s function and analysing the key properties with inequality technique, a high order fractional difference equation with boundary value conditions is studied in this paper. The existence of multiple positive solutions is obtained by using the fixed point index theory. Additionally, two examples are illustrated to guarantee the main results.

A class of the generalized disturbed nonlinear Schr¨odinger coupled system is studied. Using the specific technique relates to the approximate solutions, the corresponding linear system is first considered and its exact solution is obtained. Then, the functional asymptotic analytic solution of the nonlinear Schr¨odinger disturbed coupled model is found by using a valid method. The obtained asymptotic solution is an analytic expression, so it could also carry on analytic operations. These cannot happen to the simple simulate method.

This paper studies the weakly coupled beam-string system with boundary feedback control. First, under the appropriate hypothesis, it is proved that the well-posedness of the system by using the theory of linear operator semigroup. And then, it is showed that the energy of the weakly coupled beam-string system with boundary feedback control is uniform exponential decay by applying the frequence domain result on Hilbert space.

The two-weighted norm inequalities associated with the Hardy-Littlewood maximal operator on weighted Morrey spaces were discussed by Ye and Wang. These results of Ye and Wang were expanded into fractional maximal operator, and sufficient conditions for Ap type were also obtained.

In the sense of change of variables, separable solutions to the geometrical flows are constructed by invariant subspace method and ansatz-based method. Product separable solutions and generalized functional separable solutions are included. The behavior of these solutions are described.

In this paper, $H^{1}$-Galerkin mixed finite element method for Sobolev equation is studied. A new mixed finite element pattern is constructed using incomplete biquadratic element $Q_{2}^{-}$ and first order BDFM element. Through Bramble-Hilbert lemma, high precision results of interpolation operators corresponding to unit are proved. Further, the superclose properties for the primitive variables $u$ in $H^{1}$-norm and the intermediate variable $\vec{p}$ in $H(\text{div})$-norm are obtained respectively in semi-discrete and the backward Euler fully discrete schemes.

In this paper, necessary conditions are given for non-cosemisimple and pure noncosemisimple coalgebras being admissible, using block systems built for Hopf algebras through their coalgebra structure. The implications simplify the classification for Hopf algebras of dimension 45 and 105 and provide a new method for the finite dimensional Hopf algebras classification problem.

The problem of fuzzy filters in residuated lattices is deeply studied by using the principle and method of fuzzy sets. Three new notions of fuzzy prelinear, divisible and Glivenko filters are introduced in residuated lattices. Some of their properties and characterizations are given. Relations among these new fuzzy filters, fuzzy positive implicative filter, fuzzy Boolean filter, fuzzy MV filter, and fuzzy regular filter are discussed systematically. It is proved that a fuzzy filter is a fuzzy MV filter if and only if it is both a fuzzy regular filter and a fuzzy divisible filter.

Let $\varepsilon_{n}$ be the set of Eulerian graphs on $n$ vertices. In this paper, we discussed the properties of hyper-Wiener index of Eulerian graphs, characterized Eulerian graphs with smallest and greatest hyper-Wiener indices.