Function-valued Padé-type approximant via the formal orthogonal polynomials and its applications in solving integral equations

A kind of function-valued Padé-type approximant via the formal orthogonal polynomials (FPTAVOP) is introduced on the polynomial space and an algorithm is sketched by means of the formal orthogonal polynomials. This method can be applied to approximate characteristic values and the corresponding characteristic function of Fredholm integral equation of the second kind. Moreover, theoretical analyses show that FPTAVOP method is the most effective one for accelerating the convergence of a sequence of functions. In addition, a typical numerical example is presented to illustrate when the estimates of characteristic value and characteristic function by using this new method are more accurate than other methods.     

Characteristic polynomials of linear polyacenes and their subspectrality

Coefficients of characteristic polynomials (CP) of linear polyacenes (LP) have been shown to be obtainable from Pascal’s triangle by using a graph factorisation and squaring technique. Strong subspectrality existing among the members of the linear polyacene series has been shown from the derivation of the CP’s. Thus it has been shown that the entire eigenspectrum of ann-ring LP is included in that of (2n + 1)-ring LP. Correspondence between the eigenspectra of linear chains and LP’s is brought out by a recently developed vertex-alternation and squaring algorithm.     

Details of Structure Formation During the Induction Period of Spinodal-Type Polymer Crystallization

An unexpected type of primary crystal nucleation is described, involving spinodal decomposition (SD) type microphase separation due to the orientation fluctuations of rigid segments prior to crystal nucleation. This type of mechanism was found by the present authors about 10 years ago, and recently, it was theoretically revealed by Olmsted et al. to be one of three types of primary crystal nucleation: the well-known homogeneous crystal nucleation directly from the liquid–crystal coexistence domain, which occurs at higher temperatures above the binodal temperature T _b , crystal nucleation after binodal microphase separation between T _b and spinodal temperature T _s , and that after SD below T _s . The detailed experimental results for the spinodal-type crystal nucleation, especially the temperature dependence of characteristic wavelength in SD, are explained as well.     

A note on iterative roots of PM functions

In this paper we study iterative roots of PM functions, a special class of non-monotone functions. Problem 2 in [W. Zhang, PM functions, their characteristic intervals and iterative roots, Ann. Polon. Math. LXV (1997) 119-128] is solved partly and Theorem 4 in that paper is generalized.     

Periodic solutions for planar autonomous systems with nonsmooth periodic perturbations

In this paper we consider a class of planar autonomous systems having an isolated limit cycle x₀ of smallest period T>0 such that the associated linearized system around it has only one characteristic multiplier with absolute value 1. We consider two functions, defined by means of the eigenfunctions of the adjoint of the linearized system, and we formulate conditions in terms of them in order to have the existence of two geometrically distinct families of T-periodic solutions of the autonomous system when it is perturbed by nonsmooth T-periodic nonlinear terms of small amplitude. We also show the convergence of these periodic solutions to x₀ as the perturbation disappears and we provide an estimation of the rate of convergence. The employed methods are mainly based on the theory of topological degree and its properties that allow less regularity on the data than that required by the approach, commonly employed in the existing literature on this subject, based on various versions of the implicit function theorem.     

Structural modeling of beams on elastic foundations with elasticity couplings

A new simplified structural model and its governing equations for beams on elastic foundations with elastic coupling are proposed. This modeling system is simple but appropriate for the initial structural design of large-scale submerged floating-beam structures moored by tension legs spaced at uniform interval along the beam. The model is actually for beam on discrete elastic supports rather than on continuous elastic foundations. Therefore, the governing equations are based on finite difference calculus and solutions for beams on discrete elastic supports with elasticity coupling are also proposed. To clarify the applicability limit of the proposed model, the equivalence between a beam on discrete elastic supports and that on continuous elastic foundation is investigated by comparisons of characteristic solutions.     

蜂蜜中果糖和葡萄糖近红外检测的差异性分析及优化研究

采集了来自全国20种单植物源和其它多植物源的101份的蜂蜜样品,分别运用傅立叶型近红外光谱仪采用光纤透反射(800～2500nm,2mm光程)和透射(800～1370nm,20mm光程)采集方式获得近红外光谱,来预测蜂蜜中结构和含量都很相近的果糖和葡萄糖含量。结果发现,两种测量方式下果糖、葡萄糖的预测准确度存在着较大的差异。为了分析这种差异产生的原因,采用支持向量机分析其非线性信息,采用遗传算法分析其特征波长,结果表明:这种差异主要来自两种糖分特征波长分布不同所导致。通过对两种糖分的检测方案进行优化,得出在利用近红外光谱技术检测蜂蜜中葡萄糖成分含量时应尽量采集短波区、长光程的光谱,或者对全谱区、短光程的光谱,进行特征波长的提取,避开水分的干扰,从而提高其预测精度;而对于果糖,则应尽量采集全谱区、短光程的光谱;采用常用线性定量建模方法PLSR就可以得到很好的预测模型,非线性的支持向量机模型未能明显提升模型性能。     

Fast computation of wideband RCS using characteristic basis function method and asymptotic waveform evaluation technique

The Asymptotic Waveform Evaluation (AWE) technique is an extrapolation method that provides a reduced-order model of linear system and has already been successfully used to analyze wideband electromagnetic scattering problems. As the number of unknowns increases, the size of Method Of Moments (MOM) impedance matrix grows very rapidly, so it is a prohibitive task for the computation of wideband Radar Cross Section (RCS) from electrically large object or multi-objects using the traditional AWE technique that needs to solve directly matrix inversion. In this paper, an AWE technique based on the Characteristic Basis Function (CBF) method, which can reduce the matrix size to a manageable size for direct matrix inversion, is proposed to analyze electromagnetic scattering from multi-objects over a given frequency band. Numerical examples are presented to illustrate the computational accuracy and efficiency of the proposed method.     

Artificial boundary conditions for the numerical solution of the Euler equations by the discontinuous galerkin method

We present artificial boundary conditions for the numerical simulation of compressible flows using high-order accurate discretizations with the discontinuous Galerkin (DG) finite element method. The construction of the proposed boundary conditions is based on characteristic analysis and applied for boundaries with arbitrary shape and orientation. Numerical experiments demonstrate that the proposed boundary treatment enables to convect out of the computational domain complex flow features with little distortion. In addition, it is shown that small-amplitude acoustic disturbances could be convected out of the computational domain, with no significant deterioration of the overall accuracy of the method. Furthermore, it was found that application of the proposed boundary treatment for viscous flow over a cylinder yields superior performance compared to simple extrapolation methods.     

Positivity preserving semi-Lagrangian discontinuous Galerkin formulation: Theoretical analysis and application to the Vlasov–Poisson system

Semi-Lagrangian (SL) methods have been very popular in the Vlasov simulation community , , , , , ,  and . In this paper, we propose a new Strang split SL discontinuous Galerkin (DG) method for solving the Vlasov equation. Specifically, we apply the Strang splitting for the Vlasov equation [6], as a way to decouple the nonlinear Vlasov system into a sequence of 1-D advection equations, each of which has an advection velocity that only depends on coordinates that are transverse to the direction of propagation. To evolve the decoupled linear equations, we propose to couple the SL framework with the semi-discrete DG formulation. The proposed SL DG method is free of time step restriction compared with the Runge–Kutta DG method, which is known to suffer from numerical time step limitation with relatively small CFL numbers according to linear stability analysis. We apply the recently developed positivity preserving (PP) limiter [37], which is a low-cost black box procedure, to our scheme to ensure the positivity of the unknown probability density function without affecting the high order accuracy of the base SL DG scheme. We analyze the stability and accuracy properties of the SL DG scheme by establishing its connection with the direct and weak formulations of the characteristics/Lagrangian Galerkin method [23]. The quality of the proposed method is demonstrated via basic test problems, such as linear advection and rigid body rotation, and via classical plasma problems, such as Landau damping and the two stream instability.