2,6-Di-O-pentyl-3-O-propionyl-γ-cyclodextrin as an enantiomeric stationary phase for capillary gas chromatography

Summary 2,6-Di-O-pentyl-3-O-propionyl--cyclodextrin has been synthesized and used for enantiomer separation in capillary gas chromatography. Experimental results showed that the stationary phase has good enantiomer selectivity toward amino acids, amines, alcohols, diols, epoxides, and lactones,etc. 2,6-Di-O-pentyl-3-O-propionyl--cyclodextrin has good thermal stability: the highest recommended temperature isca 170°C.     

Global existence and blow‐up of the solutions for the multidimensional generalized Boussinesq equation

In this paper, the existence and the uniqueness of the global solution for the Cauchy problem of the multidimensional generalized Boussinesq equation are obtained. Furthermore, the blow‐up of the solution for the Cauchy problem of the generalized Boussinesq equation is proved. Copyright © 2007 John Wiley & Sons, Ltd.     

Long-term morpho-dynamics in special type of estuary

Thousands of rocky hills and islands scattered in the Pearl River delta plain and the adjacent coastal waters in South China have been or will be acted as deposition nucleus during the evolution process of the delta. The Huangmaohai estuarine complex consists of two of the eight major outlets of the Pearl River estuarine system. Since sea level reached the present level approximately 6000 years ago, especially in the last 250 years, the Huangmaohai estuarine complex has progressed to the sea by filling up the sea inlets formed between these rocky islands and between mainland and islands. This 'filling up' process left deep imprints on the long-term mor-pho-dynamic equilibrium in the estuaries. The present paper reveals that the long-term mor-pho-dynamic relation originating from this 'filling up' process in the Huangmaohai estuarine complex is different from that in many coastal plain estuaries in several aspects: (1) longitudinal variation of estuary width, (2) longitudinal variation of tidal range, (3)     

Blow up for a Cauchy viscoelastic problem with a nonlinear dissipation of cubic convolution type

In this paper, we consider a Cauchy viscoelastic problem with a nonlinear source of polynomial type and a nonlinear dissipation of cubic convolution type involving a singular kernel. Under suitable conditions on the initial data and the relaxation functions, it is proved that the solution of this particular problem blows up in finite time. Copyright © 2009 John Wiley & Sons, Ltd.     

On the total operating costs up to default in a renewal risk model

The paper proposes a new approach to study a general class of ruin-related quantities in the context of a renewal risk model. While the classical approaches in Sparre Andersen models have their own merits, the approach presented in this paper has its advantages from the following perspectives. (1) The underlying surplus process has the flexibility to reflect a broad range of scenarios for surplus growth including dividend policies and interest returns. (2) The solution method provides a general framework to unify a great variety of existing ruin-related quantities such as Gerber–Shiu functions and the expected present value of dividends paid up to ruin, and facilitates derivations of new ruin-related quantities such as the expected present value of total claim costs up to ruin, etc. In the end, many specific examples are explored to demonstrate its application in renewal risk models.     

Critical extinction and blow‐up exponents for fast diffusive p‐Laplacian with sources

We discuss and determine the critical extinction and blow‐up exponents for the homogeneous Dirichlet boundary value problem of the fast diffusive p‐Laplacian with sources. Copyright © 2007 John Wiley & Sons, Ltd.     

A sharp form of trace Moser–Trudinger inequality on compact Riemannian surface with boundary

In this paper, a sharp form of trace Moser–Trudinger inequality is established on the boundary of compact Riemannian surface, and the existence of extremal function is proved via the method of blowing up analysis.     

Smoothness of transition maps in singular perturbation problems with one fast variable

This paper deals with the smoothness of the transition map between two sections transverse to the fast flow of a singularly perturbed vector field (one fast, multiple slow directions). Orbits connecting both sections are canard orbits, i.e. they first move rapidly towards the attracting part of a critical surface, then travel a distance near this critical surface, even beyond the point where the orbit enters the repelling part of the critical surface, and finally repel away from the surface. We prove that the transition map is smooth. In a transcritical situation however, where orbits from an attracting part of one critical manifold follow the repelling part of another critical manifold, the smoothness of the transition map may be limited, due to resonance phenomena that are revealed by blowing up the turning point! We present a polynomial example in R³.     

Studies on electron cloud instability in BEPCⅡ

Electron Cloud Instability has been studied in the operation of BEPC. The BEPCⅡ began the commissioning in November 2006 and the positron beam current has reached 500 mA. Because of such a high beam current, some instabilities such as ECI, bunch lengthening et al, have appeared during the operation. The experimental investigation on ECI during the commissioning of BEPCⅡ will be reported in this paper.