基于正交性条件识别机械结构结合面参数方法的改进

本文在文献［１］所提出的基于正交性条件识别机械结构结合面阻尼参数方法的基础上，进一步提出采用正交条件式中虚部方程识别结合面动力学参数的方法。理论和算例分析表明这种改进方法能大大降低机械结构的物理参数（即质量、阻尼和刚度）矩阵和结构系统测试振型二者的误差对结合面参数识别精度的不利影响，从而使这种方法更具有可行性。

正交各向异性矩形薄板振动的一种半解析方法

使用半解析的多项康氏法分析对边简支、对边固定和对边固定-简支的正交各向异性矩形薄板振动问题。选择多个梁特征函数作为试函数,精确满足对边所有边界条件。通过Gakerkin积分将偏微分振动方程转化为常微分方程组并整理为状态方程形式。强迫满足另一对边的边界条件,获得频率方程,确定固有频率。文献结果比较不仅证实了该方法的有效性,而且揭示通过该方法获得的对边简支板的解是精确解。最后,研究了不同长宽比下试函数项数对无量纲固有频率的影响。

三维Wilson立方体元插值的各向异性

证明了著名的三维Wilson立方体元具有各向异性插值特征,因而可用于任意窄边立方体剖分,并得到了窄边立方体元Wilson元的插值误差。

环上矩阵的Moore-Penrose逆的注记

讨论带有对合反自同构的环上矩阵的广义逆，给出了矩阵存在Mooore－Penrose逆的条件及Moore－Penrose逆的一些性质和显式．

Extraction,Physiochemical Properties and Antibacterial Activities of Polysaccharides from Auricularia auricular

[Objective] To explore the optimal conditions for extracting polysaccharide from Auricularia auricular, and to study its physiochemical properties and antibacterial activities. [ Method] The extraction conditions for Auricularia auricular polysaccharides were optimized by orthogonal test, and its physiochemical characteristics and antagonistic activities on bacteria and molds were tested. I-Result] The optimized condition was with sample to liquid ratio of 1 ： 50, temperature of 90 ℃ and extraction time of 2.5 h. Under the optimized condition, the yield of pelysaccharide was 7.3%, with polysaccharide content of 77.81%. Containing aldose and amylase, the polysaccharides of Auncu/aria auricular was soluble in water. The inhibitory effect on bacteria was significantly stronger than on molds that the minimum diameter of inhibition zone for bacteria is 12.7 mm, while 7.9 mm for the molds. [ Conclusion] This study provides scientific basis for the development and utilization of Auricularia auricular polysaccharides.

Comparison of Flow Characteristics Around Refractive and Right-angled Groins in Barotropic and Baroclinic Conditions

Groins are employed to prevent nearshore areas from erosion and to control the direction of flow. However, the groin structure and its associated flow characteristics are the main causes of local erosion. In this study, we investigate the flow patterns around refractive and right-angle groins. In particular, we analytically compare the flow characteristics around a refractive groin and study the degree of accuracy that can be achieved by using a right-angle groin of various projected lengths. To compare the flow characteristics, we replaced the right-angle groin with an approximation of a refractive groin. This replacement had the least effect on the maximum velocity of flow in the channel. Moreover, we investigated the distribution of the density variables of temperature and salinity, and their effects on the flow characteristics around the right-angle groin. A comparison of the flow analysis results in baroclinic and barotropic conditions reveals that the flow characteristic values are very similar for both the refractive and right-angle groins. The geometry of the groin, i.e., right-angle or refractive, has little effect on the maximum speed to relative average speed. Apart from the angular separation, the arm length of the groin in downstream refractive groins has less effect on other flow characteristics than do upstream refractive groins. We also correlated a number of non-dimensional variables with respect to various flow characteristics and groin geometry. These comparisons indicate that the correlation between the thalweg height and width of the channel and groin arm＇s length to projection length have been approximated using linear and nonlinear formulas regardless of inner velocity in the subcritical flow.

A state space solution for the bending problem of thick laminated piezoelectric open cylindrical shells

Based on the theories of three-dimensional elasticity and piezoelectricity, and by assuming appropriate boundary functions, we established a state equation of piezoelectric cylindrical shells. By using the transfer matrix method, we presented an analytical solution that satisfies all the arbitrary boundary conditions at boundary edges, as well as on upper and bottom surfaces. Our solution takes into account all the independent elastic and piezoelectric constants for a piezoelectric orthotropy, and satisfies continuity conditions between plies of the laminates. The principle of the present method and corresponding results can be widely used in many engineering fields and be applied to assess the effectiveness of various approximate and numerical models.

A Quadrature Approach for N-Collinear Crack Problem in an Orthotropic Strip

This study presents the determination of the stress intensity factors （SIFs） at the edges of the cracks in an elastic strip weakened by N-collinear cracks. The problem of an orthotropic elastic strip is reduced to a system of Cauchy type singular integral equations. The system of singular integral equations is approached by a Quadrature technique. Under two different loading conditions, the results are obtained for the different cases of crack numbers. The resistance of the strip is examined by considering the orthotropic properties of the strip material. Finally, the crack interactions are clarified during the analysis.

Retakh's Conditions (M_0) and Weakly (Sequentially) Compact Regularity

Weakly (sequentially) compactly regular inductive limits and convex weakly (sequentially) compactly regular inductive limits are investigated. (LF)-spaces satisfying Retakh's condition (M0) are convex weakly (sequentially) compactly regular but need not be weakly (sequentially) compactly regular. For countable inductive limits of weakly sequentially complete Frechet spaces, Retakh's condition (M0) implies weakly (sequentially) compact regularity. Particularly for Kothe (LF)-sequence spaces Ep(1 ≤ p < ∞), Retakh's condition (M0) is equivalent to weakly (sequentially) compact regularity. For those spaces, the characterizations of weakly (sequentially) compact regularity are given by using the related results of Vogt.

ＱＵＡＤＲＩＬＡＴＥＲＡＬ ＭＥＳＨ

Several quadrilateral shape regular mesh conditions commonly used in the finite element method are proven to be equivalent. Their influence on the finite element interpolation error and the consistency error committed by nonconforming finite elements are investigated. The effect of the Bi-Section Condition and its extended version (1+α)-Section Condition on the degenerate mesh conditions is also checked. The necessity of the Bi-Section Condition in finite elements is underpinned by means of counterexamples.

A linear varying coefficient ARCH-M model with a latent variable

Motivated by the psychological factor of time-varying risk-return relationship, this paper studies a linear varying coefficient ARCH-M model with a latent variable. Due to the unobservable property of the latent variable, a corrected likelihood method is employed for parametric estimation. Estimators are proved to be consistent and asymptotically normal under certain regularity conditions. A simple test statistic is also proposed for testing latent variable effect. Simulation results confirm that the proposed estimators and test perform well.The model is further applied to examine whether the risk-return relationship depends on investor's sentiment in American Market and some explainable results are obtained.

Analysis of thin plates by the weak form quadrature element method

The recently proposed weak form quadrature element method （QEM） is applied to flexural and vibrational analysis of thin plates The integrals involved in the variational description of a thin plate are evaluated by an efficient numerical scheme and the par- tial derivatives at the integration sampling points are then approximated using differential quadrature analogs. Neither the grid pattern nor the number of nodes is fixed, being adjustable according to convergence need. The C~ continuity conditions char- acterizing the thin plate theory are discussed and the robustness of the weak form quadrature element for thin plates against shape distortion is examined. Examples are presented and comparisons with analytical solutions and the results of the finite element method are made to demonstrate the convergence and computational efficiency of the weak form quadrature element method. It is shown that the present formulation is applicable to thin plates with varying thickness as well as uniform plates.

NEUMANN PROBLEM OF ELLIPTIC EQUATIONS WITH LIMIT NONLINIEARITY IN BOUNDARY CONDITION

This paper deals with a problem proposed by H. Brezis on the existence of positive solutionsto the equation An + u(rt+2)/(n--2) + f(x,u) = 0 under the Neumann boundaly collditionD.u = un/(rt--z), where f(x, u) is a lower order perturbation of u(n+2)/(n--2) at infinity.

Darboux Transformation and N-soliton Solution for Extended Form of Modified Kadomtsev–Petviashvili Equation with Variable-Coefficient

The extended form of modified Kadomtsev–Petviashvili equation with variable-coefficient is investigated in the framework of Painlevé analysis. The Lax pairs are obtained by analysing two Painlevé branches of this equation.Starting with the Lax pair, the N-times Darboux transformation is constructed and the N-soliton solution formula is given, which contains 2n free parameters and two arbitrary functions. Furthermore, with different combinations of the parameters, several types of soliton solutions are calculated from the first order to the third order. The regularity conditions are discussed in order to avoid the singularity of the solutions. Moreover, we construct the generalized Darboux transformation matrix by considering a special limiting process and find a rational-type solution for this equation.

Asymptotically efficient parameter estimation for ordinary differential equations

Parameter estimation for ordinary differential equations arises in many fields of science and engineering. To be the best of our knowledge, traditional methods are often either computationally intensive or inaccurate for statistical inference. Ramsay et al.(2007) proposed a generalized profiling procedure. It is easily implementable and has been demonstrated to have encouraging numerical performance. However, little is known about statistical properties of this procedure. In this paper, we provide a theoretical justification of the generalized profiling procedure. Under some regularity conditions, the procedure is shown to be consistent for a broad range of tuning parameters. When the tuning parameters are sufficiently large, the procedure can be further shown to be asymptotically normal and efficient.

Self-consistency of a Modification Method Based on Membrane Model with Minimal Length Considered

By adopting a result from generalized uncertainty principles (GUP), we modify the inner bound of the membrane model to a physical fixed value and get the cut-offs naturally rather than by hand, which are both in brickwall model and membrane model, and the semi-classical quantization condition could always be valid as well. We also calculate the entropies of Schwarzschild-de Sitter black hole and find the GUP we choose qualitatively shows that the requirement of mass in this method is the same as the natural requirement of the Schwarzschild-de Sitter black hole,which means the method might be self-consistent.

DYNAMICAL PROPERTIES OF A STOCHASTIC TWO-SPECIES SCHOENER＇S COMPETITIVE MODEL

A stochastic two-species Schoener＇s competitive model is proposed and investigated. Sufficient conditions for the existence of global positive solutions, boundedness~ uniform continuity, global attractivity stochastic permanence and extinction are obtained. More- over, the upper-growth rate and the average in time of the sample paths of solutions are also estimated. Finally, some figures are introduced to illustrate the main results.