On a Sparre Andersen Risk Model with Time-Dependent Claim Sizes and Jump-Diffusion Perturbation

In this paper, we consider a Sparre Andersen risk model where the interclaim time and claim size follow some bivariate distribution. Assuming that the risk model is also perturbed by a jump-diffusion process, we study the Gerber?CShiu functions when ruin is due to a claim or the jump-diffusion process. By using a q-potential measure, we obtain some integral equations for the Gerber?CShiu functions, from which we derive the Laplace transforms and defective renewal equations. When the joint density of the interclaim time and claim size is a finite mixture of bivariate exponentials, we obtain the explicit expressions for the Gerber?CShiu functions.     

Molecular "light switch" for G-quadruplex DNA: cycling the switch on and off

We report a new G-quadruplex DNA "light switch", where the light switch can be cycled on and off through the successive introduction of G-quadruplex DNA and [Fe(CN)(6)](4-) ions.     

Enhanced brightness of organic light-emitting diodes based on Mg:Ag cathode using alkali metal chlorides as an electron injection layer

Different thicknesses of cesium chloride (CsCl) and various alkali metal chlorides were inserted into organic light-emitting diodes (OLEDs) as electron injection layers (EILs). The basic structure of OLED is indium tin oxide (ITO)/N,N′-diphenyl-N,N′-bis(1-napthyl-phenyl)-1.1′-biphenyl-4.4′-diamine (NPB)/tris-(8-hydroxyquinoline) aluminum (Alq₃)/Mg:Ag/Ag. The electroluminescent (EL) performance curves show that both the brightness and efficiency of the OLEDs can be obviously enhanced by using a thin alkali metal chloride layer as an EIL. The electron injection barrier height between the Alq₃ layer and Mg:Ag cathode is reduced by inserting a thin alkali metal chloride as an EIL, which results in enhanced electron injection and electron current. Therefore, a better balance of hole and electron currents at the emissive interface is achieved and consequently the brightness and efficiency of OLEDs are improved.     

Multi-spot focusing by using composite spiral zone plates

We present a flexible, simple, and cost effective approach for generating high-quality multiple focal spots in the far field using composite spiral zone plates (SZPs), which serve as a synthesis of two SZPs with different topological charges. By changing the topological charges of the SZPs can obtain different types of multiple focal spots. The numerical solution, fabrication method, and experimental results are presented to prove the capabilities of this approach.     

Global well-posedness for the microscopic FENE model with a sharp boundary condition

We prove global well-posedness for the microscopic FENE model under a sharp boundary requirement. The well-posedness of the FENE model that consists of the incompressible Navier–Stokes equation and the Fokker–Planck equation has been studied intensively, mostly with the zero flux boundary condition. In this article, we show that for the well-posedness of the microscopic FENE model ($b>2$) the least boundary requirement is that the distribution near boundary needs to approach zero faster than the distance function. Under this condition, it is shown that there exists a unique weak solution in a weighted Sobolev space. Moreover, such a condition still ensures that the distribution is a probability density. The sharpness of this boundary requirement is shown by a construction of infinitely many solutions when the distribution approaches zero no faster than the distance function.     

Feasibility study of hard-x-ray nanofocusing above 20 keV using compound photon sieves

Combining the advantages of photon sieves (PSs) and compound Fresnel zone plates (CZPs), we designed compound photon sieves (CPSs) for hard-x-ray nanofocusing. A CPS consists of an inner PS using the first-order diffraction surrounded by an outer zone plate using the third-order diffraction. A robust digital prolate spheroidal window was used as an apodization window for the inner PS, making CPSs more flexible than CZPs. CPSs can provide not only slightly better resolution compared to CZPs, but also it can significantly suppress the sidelobes, leading to a high signal-to-noise ratio. Further improvement of the high-aspect-ratio metal nanostructure process will allow CPSs to be a promising candidate for hard-x-ray nanofocusing in the high-energy region above 20 keV.     

Tailoring the liquid crystalline property via controlling the generation of dendronized polymers containing azobenzene mesogen

The first‐ and second‐generation dendronized polymers containing azobenzene mesogen were designed and successfully synthesized via free radical polymerization. The chemical structures of the monomers were confirmed by elemental analysis, ¹H NMR, and ¹³C NMR. The molecular characterizations of the polymers were performed with ¹H NMR and gel permeation chromatography. The phase structures and transition behaviors were studied using differential scanning calorimetry, polarized light microscopy, and small‐angle X‐ray scatter experiments. The experiment results revealed that the first‐generation dendronized polymer exhibited liquid crystalline behavior of the conventional side‐chain liquid crystalline polymer with azobenzene mesogen, that is, the polymer exhibited smectic phase structure at lower temperature and nematic phase structure at higher temperature. However, the second‐generation dendronized polymers exhibited more versatile intriguing liquid crystalline structures, namely smectic phase structure at lower temperature and columnar nematic phase structure at higher temperature, and moreover, the phase structure still remained before the decomposition temperature. © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 48: 1149–1159, 2010     

On Valuation of Derivative Securities: A Lie Group Analytical Approach

This paper proposes a Lie group analytical approach to tackle the problem of pricing derivative securities. By exploiting the infinitesimal symmetries of the Boundary Value Problem (BVP) satisfied by the price of a derivative security, our method provides an effective algorithm for obtaining its explicit solution. This work was supported by Research Grants Council of HKSAR (Project No. HKU 7239/04H) and the Small Project Funding Programme of HKU.