Corresponding to R-smash products of associative algebras, a kind of Poisson structure construction for relative semiclassical limits is constructed. Going a step further, Poisson structures with a kind of braiding of tensor products are given, which contain the results of Poisson polynomial extensions and double Poisson-Ore extensions.

A kind of synchronization control problems of grid system connected high-power wind generators with nonlinear pulse disturbance was investigated in this paper. By using the Kirchhoff's law, a class of mathematical model of grid side converter system of wind generators was established. Meanwhile, an appropriate feedback synchronization controller was designed. By the theory of Lyapunov stability, the e?ectiveness of synchronous controller was validated. In order to restrain the nonlinear pulse disturbance in grid system connected with wind generators, make the current generated by wind generators synchronize the current in grid, an optimal algorithm was obtained. Finally, the theoretical results were demonstrated by the Simulink in Matlab.

In this paper, the aim is to study the singular nonlinear polyharmonic equations
of the following form $\Delta^{m}u=f(|x|,u, |\nabla u|)u^{-\beta}$. The su±cient and necessary condition for the
existence of positive radial symmetric entire solutions is proved, and some properties of the
solutions are obtained.

In this paper a class of boundary value problems of the singular perturbed semi-linear differential systems with discontinuous source term is discussed. The formal asymptotic expansion is constructed. Using Hartman-Nagumo inequality, the existence and uniqueness of the solution of the singular perturbed semi-linear differential systems is proved. Using Aumann intermediate theorem, the smoothness of the solution of the systems is obtained. And the uniformly valid estimation for the solution of the systems is obtained.

In this paper, the nonlinear two-dimensional Zakharov-Kuznetsov(ZK) equation under the external forcing in a potential vorticity equation which includes both the vertical and horizontal components of Coriolis parameter is derived by using multiscale and perturbation expation method in a weakly nonliear, long wave approximation near the equatorial Rossby waves. And then the periodic solution for the model is obtained with the help of Jacobi elliptic functions. It is show that the horizontal components of Coriolis parameter and external forcing play an important role in the structures of the Rossby waves.

In this paper, the growth and the distribution of zeros of solutions to some second order non-homogeneous differential equations $f''+A\text{e}^{az^n}f'+(B_1\text{e}^{bz^n}+B_0\text{e}^{dz^n})f=F(z)$ are investigated, where $F$ is a nonzero entire function with order less than $n$, $A, B_1, B_0$ are nonzero polynomials. Under an appropriate assumption on complex numbers $a, b, d$, the precise estimations on the hyper order and the hyper convergence exponent of zeros of solutions of such equation are obtained.

With the help of $EQ^{rot}_1$ element and zero order Raviart-Thomas(R-T) elements, a new nonconforming mixed finite elements approximation scheme is proposed for the extended Fisher-Kolmogorov equation(EFK). Firstly, a priori estimate of approximation solutions is proved and the existence and uniqueness are also derived for semi-discrete scheme. Based on the high accuracy analysis of two elements and the priori estimate of the finite element solutions, the superclose properties of order $O(h^{2})$ for the primitive solution $u$ and the intermediate variable $v=-\Delta u~$in~$H^{1}$-norm and flux $\vec{p}=\nabla u$ in $(L^{2})^{2}$-norm are obtained without the boundedness of numerical solution $u_{h}$ in $L^{\infty}$-norm, respectively. Meanwhile, the global superconvergent error estimates for above variables of order $O(h^{2})$ are proved through interpolated postprocessing technique. Secondly, a new linearized backward Euler full-discrete scheme is established, the existence and uniqueness of approximation scheme are proved. On the other hand, the superclose properties of order $O(h^{2}+\tau)$ for variable $u,v$ in $H^{1}$-norm and $\vec{p}$ in $(L^{2})^{2}$-norm are obtained respectively through a new splitting technique for consistent error estimate and nonlinear term, which have never been considered in the previous literature. Furthermore, the global superconvergent estimates for above variables are deduced by interpolated postprocessing technique.~Here,~$h,~\tau$~are parameters of the subdivision in space and time step, respectively. Finally, numerical results are provided to confirm the theoretical analysis.

Since the standard support vector machine model is a quadratic programming, the algorithm process will be more and more complicated with the increasing size of the data. In this article, a new model of a strictly convex quadratic programming is constructed which is based on the K-SVCR algorithm. The main feature of the present model is that it can transform the first-order optimality conditions into the variational inequality problems, and turn complementary problems into smooth equations by the use of the Fischer-Burmeister (FB) function. A more smooth and faster Newton algorithm is established. And this article expounds that the generated sequence by the algorithm is global convergent. After testing a standard data set, the efficiency of the algorithm was proposed. The algorithm has better performance on the training accuracy and run-time compared with the K-SVCR algorithm. The results of this experiment indicate that this algorithm was feasible and efficient.

For the problem of minimizing total completion time on single machine with unit processing time, an approximation algorithm with a performance ratio smaller than$\frac{9+\sqrt{3}}{6}\approx1.7817$ is given. The paper showed that there dose not exist any fully polynomial time approximation schedule unless $P=NP$, even if the total size of the jobs is smaller than 2.

Scheduling game is a kind of special scheduling problem used in Internet and cloud computing. Different from the traditional scheduling problem, each job is controlled by a selfish agent and it is only interested in choosing one machine to minimize its own cost. A scheduling game with hybrid coordination mechanisms is considered. There are $n$ selfish jobs and $m$ unrelated machines. The machine can choose WSPT policy or PS policy, and the social cost is the total weighted completion times of all jobs. A linear programming relaxation for this problem is designed firstly. Then by discussing the relationship between the linear programming and its dual, the main conclusion is given: The mixed Price of Anarchy (MPoA) of this scheduling game is exactly 4.

In 2012, Bang-Jensen and Huang (\emph{J. Combin. Theory Ser. B}. 2012, {\noindent\bf 102}: 701-714) proved that every $2$-arc-strong locally semicomplete digraph has two arc-disjoint strongly connected spanning subdigraphs, and conjectured that every $3$-strong local tournament has two arc-disjoint hamiltonian cycles. In this paper, the arc-disjoint hamiltonian paths and cycles in positive-round digraphs are discussed, and the following results are proved: every 3-arc-strong positive-round digraph contains two arc-disjoint hamiltonian cycles and every 4-arc-strong positive-round digraph contains one hamiltonian cycle and two hamiltonian paths, such that they are arc-disjoint pairwise. A round digraph must be positive-round, thus those conclusions on positive-round digraphs can be generalized to round digraphs. Since round digraphs form the subclass of local tournaments, Bang-Jensen and Huang's conjecture holds for round digraphs which is the subclass of local tournaments.

It is verified that the maximum likelihood estimation of the environment factor for the gamma distribution is biased, and that its bias is positive. Then an approximate unbiased estimation of the environment factor is derived. Using the Cornish-Fisher expansion, the generalized confidence interval of the environment factor is proposed. The bootstrap-$t$ confidence interval is also given. The performance of the proposed procedures is evaluated by using Monte Carlo simulation. The simulation results show that the proposed point estimation outperforms the MLE and that the coverage percentages of the proposed generalized confidence interval are quite close to the nominal coverage probabilities, even for small sample size and for small shape parameter.