Convergent and flexible approach to stereodefined polyhydroxylated fragments

Stereodefined acyclic polyhydroxylated fragments characteristic to polyketide natural products could be easily prepared in good yields and excellent diastereoisomeric ratios from common and simple enol carbamates. The reaction provides these fragments through a combined, one-pot sequence of metalation, carbamoyl transfer, aldol reaction, and finally Tishchenko reduction. This strategy assembles up to five consecutive stereogenic centers with exceptional stereocontrol. 2009 Elsevier Ltd. All rights reserved.     

Solution for Eshelby’s elliptic inclusion with polynomials distribution of the eigenstrains in plane elasticity

This paper provides a closed form solution for the Eshelby’s elliptic inclusion in plane elasticity with the polynomials distribution of the eigenstrains. The complex variable method and the conformal mapping technique are used. The continuity conditions for the traction and displacement along the interface in the physical plane are reduced to a similar condition along the unit circle of the mapping plane. From those continuity conditions, we can obtain two sets of the complex potentials for the region outside of the unit circle and for the ring region, respectively. Further, we can obtain the complex potentials in the physical plane, or z-plane (z = x + iy). The mapping function maps the ring region in the mapping plane into a finite elliptic region with a crack on the real axis in the physical plane. An exact form for the complex potentials defined in the ring region is studied and proposed. In addition, the stress distribution on the inclusion is evaluated. Those results are first obtained in the paper.     

A homothetic reference technology in data envelopment analysis

The assumption of a homothetic production function is often maintained in production economics. In this paper we explore the possibility of maintaining homotheticity within a nonparametric DEA framework. The main contribution of this paper is to use the approach suggested by Hanoch and Rothschild (1972) to define a homothetic reference technology. We focus on the largest subset of data points that is consistent with such a homothetic production function. We use the HR-approach to define a piecewise linear homothetic convex reference technology. We propose this reference technology with the purpose of adding structure to the flexible non-parametric BCC DEA estimator. Motivation for why such additional structure sometimes is warranted is provided. An estimation procedure derived from the BCC-model and from a maintained assumption of homotheticity is proposed. The performance of the estimator is analyzed using simulation.     

Reflection of an impulsive torsional wave by a moving boundary

Reflection of an impulsive torsional wave by a uniformly moving surface/boundary is discussed. Applying the Cagniard–de Hoop technique, the solution for the reflected wave is obtained in the closed form and a new wave that runs along the moving boundary has been found. Its wave front singularity is stronger than those of the incident and the regular reflected waves. This new wave has the cylindrical surface, but the shape of the disturbed region is a torus with a triangular-like cross section.     

A remark on the uniqueness of Silverstein extensions of symmetric Dirichlet forms

We prove the uniqueness of the Silverstein extension of symmetric Dirichlet forms under some condition on intrinsic metrics. As its application, we present some non‐local Dirichlet forms which possess the uniqueness of the Silverstein extension and generate non‐conservative Hunt processes.     

一类非线性磁流变系统局部分岔特性研究

讨论了一类基于磁流变阻尼器非线性系统的局部分岔与控制问题，建立了该系统的动力 学模型，运用中心流形定理和范式理论，得到该系统双零特征值问题的规范形及其普适开折， 进而探讨了此系统的分岔行为和稳定性；给出了分岔曲线、转迁集；并给出了此类非线性系 统的数值仿真结果.     

A FORM INVARIANCE OF CONSTRAINED BIRKHOFFIAN SYSTEM

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Global Bifurcations and Chaotic Dynamics in Nonlinear Nonplanar Oscillations of a Parametrically Excited Cantilever Beam

This paper presents the analysis of the global bifurcations and chaotic dynamics for the nonlinear nonplanar oscillations of a cantilever beam subjected to a harmonic axial excitation and transverse excitations at the free end. The governing nonlinear equations of nonplanar motion with parametric and external excitations are obtained. The Galerkin procedure is applied to the partial differential governing equation to obtain a two-degree-of-freedom nonlinear system with parametric and forcing excitations. The resonant case considered here is 2:1 internal resonance, principal parametric resonance-1/2 subharmonic resonance for the in-plane mode and fundamental parametric resonance–primary resonance for the out-of-plane mode. The parametrically and externally excited system is transformed to the averaged equations by using the method of multiple scales. From the averaged equation obtained here, the theory of normal form is applied to find the explicit formulas of normal forms associated with a double zero and a pair of pure imaginary eigenvalues. Based on the normal form obtained above, a global perturbation method is utilized to analyze the global bifurcations and chaotic dynamics in the nonlinear nonplanar oscillations of the cantilever beam. The global bifurcation analysis indicates that there exist the heteroclinic bifurcations and the Silnikov type single-pulse homoclinic orbit in the averaged equation for the nonlinear nonplanar oscillations of the cantilever beam. These results show that the chaotic motions can occur in the nonlinear nonplanar oscillations of the cantilever beam. Numerical simulations verify the analytical predictions.     

无限均质弹性体中圆片裂纹受均布载荷时的超奇异积分方程封闭解

本文运用一种特殊技巧将一个受均布压力作用的圆片裂纹超奇异积分方程化为Ａｂｅｌ积分形式，从而可获得超奇异积分方程中未知位移间断的封闭解。再利用这个封闭解和应力强度因子的定义，得到了一个无限弹性体中受均布载荷分布时圆片裂纹前沿Ｉ型应力强度因子的精确表达式。所得到的结果与现有解完全相同。     

LOCAL BIFURCATION ANALYSIS OF STRONGLY NONLINEAR DUFFING SYSTEM

ＬＯＣＡＬＢＩＦＵＲＣＡＴＩＯＮＡＮＡＬＹＳＩＳＯＦＳＴＲＯＮＧＬＹＮＯＮＬＩＮＥＡＲＤＵＦＦＩＮＧＳＹＳＴＥＭＢｉＱｉｎｓｈｅｎｇ（毕勤胜）；ＣｈｅｎＹｕｓｈｕ（陈予恕）；ＷｕＺｈｉｑｉａｎｇ（吴志强）Ａｂｓｔｒａｃｔ：Ｂｙｕｓｉｎｇｃｏｏｒｄｉｎ...