The X-Shooter Spectral Library (XSL) contains more than 800 spectra of stars across the color-magnitude diagram, that extend from near-UV to near-IR wavelengths (320-2450 nm). We summarize properties of the spectra of O-rich Long Period Variables in the XSL, such as phase-related features, and we confront the data with synthetic spectra based on static and dynamical stellar atmosphere models. We discuss successes and remaining discrepancies, keeping in mind the applications to population synthesis modeling that XSL is designed for.

In this paper, a Chebyshev-collocation spectral method is developed for Volterra integral equations (VIEs) of second kind with weakly singular kernel. We first change the equation into an equivalent VIE so that the solution of the new equation possesses better regularity. The integral term in the resulting VIE is approximated by Gauss quadrature formulas using the Chebyshev collocation points. The convergence analysis of this method is based on the Lebesgue constant for the Lagrange interpolation polynomials, approximation theory for orthogonal polynomials, and the operator theory. The spectral rate of convergence for the proposed method is established in the L ∞-norm and weighted L 2-norm. Numerical results are presented to demonstrate the effectiveness of the proposed method.

It is a challenging task to discover information from a large amount of data in an open domain. 1 In this paper, an event network framework is proposed to address this challenge. It is in fact an empirical construct for exploring open information, composed of three steps: document event detection, event network construction and event network analysis. First, documents are clustered into document events for reducing the impact of noisy and heterogeneous resources. Secondly, linguistic units (e.g., named entities or entity relations) are extracted from each document event and combined into an event network, which enables content-oriented retrieval. Then, in the final step, techniques such as social network or complex network can be applied to analyze the event network for exploring open information. In the implementation section, we provide examples of exploring open information via event network.

In this paper, we consider an optimal control problem governed by Stokes equations with H 1-norm state constraint. The control problem is approximated by spectral method, which provides very accurate approximation with a relatively small number of unknowns. Choosing appropriate basis functions leads to discrete system with sparse matrices. We first present the optimality conditions of the exact and the discrete optimal control systems, then derive both a priori and a posteriori error estimates. Finally, an illustrative numerical experiment indicates that the proposed method is competitive, and the estimator can indicate the errors very well.

In the paper, we present an efficient two-grid method for the approximation of two-dimensional nonlinear reaction-diffusion equations using a expanded mixed finite-element method. We transfer the nonlinear reaction diffusion equation into first order nonlinear equations. The solution of the nonlinear system on the fine space is reduced to the solutions of two small (one linear and one non-linear) systems on the coarse space and a linear system on the fine space. Moreover, we obtain the error estimation for the two-grid algorithm. It is showed that coarse space can be extremely coarse and achieve asymptotically optimal approximation as long as the mesh sizes satisfy . An numerical example is also given to illustrate the effectiveness of the algorithm.

In this paper, we study the numerical solution of singularly perturbed time-dependent convection-diffusion problems. To solve these problems, the backward Euler method is first applied to discretize the time derivative on a uniform mesh, and the classical upwind finite difference scheme is used to approximate the spatial derivative on an arbitrary nonuniform grid. Then, in order to obtain an adaptive grid for all temporal levels, we construct a positive monitor function, which is similar to the arc-length monitor function. Furthermore, the ε-uniform convergence of the fully discrete scheme is derived for the numerical solution. Finally, some numerical results are given to support our theoretical results.

A spectral Jacobi-collocation approximation is proposed for Volterra delay integro-differential equations with weakly singular kernels. In this paper, we consider the special case that the underlying solutions of equations are sufficiently smooth. We provide a rigorous error analysis for the proposed method, which shows that both the errors of approximate solutions and the errors of approximate derivatives decay exponentially in L∞ norm and weighted L2 norm. Finally, two numerical examples are presented to demonstrate our error analysis.

The miscible displacement of one incompressible fluid by another in a porous medium is governed by a system of two equations. One is elliptic form equation for the pressure and the other is parabolic form equation for the concentration of one of the fluids. Since only the velocity and not the pressure appears explicitly in the concentration equation, we use a mixed finite element method for the approximation of the pressure equation and mixed finite element method with characteristics for the concentration equation. To linearize the mixed-method equations, we use a two-grid algorithm based on the Newton iteration method for this full discrete scheme problems. First, we solve the original nonlinear equations on the coarse grid, then, we solve the linearized problem on the fine grid used Newton iteration once. It is shown that the coarse grid can be much coarser than the fine grid and achieve asymptotically optimal approximation as long as the mesh sizes satisfy h = H2 in this paper. Finally, numerical experiment indicates that two-grid algorithm is very effective.

In this paper, we investigate the Galerkin spectral approximation for elliptic control problems with integral control and state constraints. Firstly, an a posteriori error estimator is established,which can be acted as the equivalent indicatorwith explicit expression. Secondly, appropriate base functions of the discrete spacesmake it is probable to solve the discrete system. Numerical test indicates the reliability and efficiency of the estimator, and shows the proposed method is competitive for this class of control problems. These discussions can certainly be extended to two- and three-dimensional cases.

The Chinese black honey bee is a distinct honey bee subspecies distributed in the Xinjiang, Heilongjiang and Jilin Provinces of China. We conducted a study to investigate the genetic origin and the parasite/pathogen profile on Chinese black honeybees. The phylogenetic analysis indicated that Chinese black honeybees were two distinct groups: one group of bees formed a distinct clade that was most similar to Apis mellifera mellifera and the other group was a hybrid of the subspecies, Apis mellifera carnica, Apis mellifera anatolica and Apis mellifera caucasica. This suggests that the beekeeping practices might have promoted gene flow between different subspecies. Screening for pathogens and parasites showed that Varroa destructor and viruses were detected at low prevalence in Chinese black honeybees, compared with Italian bees. Further, a population of pure breeding black honeybees, A. m. mellifera, displayed a high degree of resistance to Varroa. No Varroa mites or Deformed wing virus could be detected in any examined bee colonies. This finding suggests that a population of pure breeding Chinese black honeybees possess some natural resistance to Varroa and indicated the need or importance for the conservation of the black honeybees in China.

Our main purpose in this paper is to propose the piecewise Legendre spectral-collocation method to solve Volterra integro-differential equations. We provide convergence analysis to show that the numerical errors in our method decay in $h^{m}N^{-m}$ -version rate. These results are better than the piecewise polynomial collocation method and the global Legendre spectral-collocation method. The provided numerical examples confirm these theoretical results.

In this paper, we consider a singularly perturbed convection-diffusion problem. The problem involves two small parameters that gives rise to two boundary layers at two endpoints of the domain. For this problem, a non-monotone finite element methods is used. A priori error bound in the maximum norm is obtained. Based on the a priori error bound, we show that there exists Bakhvalov-type mesh that gives optimal error bound of (N−2) which is robust with respect to the two perturbation parameters. Numerical results are given that confirm the theoretical result.

A posteriori error estimates of semidiscrete mixed finite element methods for quadratic optimal control problems involving linear parabolic equations are developed. The state and co-state are discretised by Raviart-Thomas mixed finite element spaces of order k, and the control is approximated by piecewise polynomials of order k (k ≥ 0). We derive our a posteriori error estimates for the state and the control approximations via a mixed elliptic reconstruction method. These estimates seem to be unavailable elsewhere in the literature, although they represent an important step towards developing reliable adaptive mixed finite element approximation schemes for the control problem.

A Legendre-collocation method is proposed to solve the nonlinear Volterra integral equations of the second kind. We provide a rigorous error analysis for the proposed method, which indicate that the numerical errors in L2-norm and L∞-norm will decay exponentially provided that the kernel function is sufficiently smooth. Numerical results are presented, which confirm the theoretical prediction of the exponential rate of convergence.

In this paper, we study an efficient scheme for nonlinear reaction-diffusion equations discretized by mixed finite element methods. We mainly concern the case when pressure coefficients and source terms are nonlinear. To linearize the nonlinear mixed equations, we use the two-grid algorithm. We first solve the nonlinear equations on the coarse grid, then, on the fine mesh, we solve a linearized problem using Newton iteration once. It is shown that the algorithm can achieve asymptotically optimal approximation as long as the mesh sizes satisfy H = O(h1/2). As a result, solving such a large class of nonlinear equations will not be much more difficult than getting solutions of one linearized system.

Mesoporous Fe3O4 nanoparticles coated with ZnO nanocrystals were successfully synthesized by a simple solution method at low temperature. The transmission electron microscopy analysis indicates that the mesoporous Fe3O4 nanoparticles are monodispersed with a mean diameter of 160 nm and the thickness of ZnO layer is 15 nm approximately. The porosity of the products was further substantiated by the nitrogen (N2) sorption measurement. The N2 adsorption-desorption isotherm curve can be identified as type IV, which is a characteristic of mesopores. Electromagnetic (EM) wave absorption properties of the as-prepared Fe3O4@ZnO mesoporous spheres-wax composites were investigated at a room temperature in the frequency range of 0.5∼18 GHz. Interestingly, the Fe3O4@ZnO mesoporous spheres exhibit an enhanced EM wave absorption due to the mesoporous structure. The multiple absorbing mechanisms result from the interface polarization induced by the special core/shell and mesoporous structures as well as dipole polarization of both Fe3O4 and ZnO. The results demonstrate that the Fe3O4@ZnO mesoporous spheres are attractive candidates for a new kind of EM wave absorption materials with wide absorption frequency band.

In this paper, we will investigate the error estimates and the superconvergence property of mixed finite element methods for a semilinear elliptic control problem with an integral constraint on control. The state and co-state are approximated by the lowest order Raviart-Thomas mixed finite element and the control variable is approximated by piecewise constant functions. We derive some superconvergence properties for the control variable and the state variables. Moreover, we derive L∞- and H−1 -error estimates both for the control variable and the state variables. Finally, a numerical example is given to demonstrate the theoretical results.