Surface morphology and in vitro release performance of double-walled PLLA/PLGA microspheres entrapping a highly water-soluble drug

Double-walled microspheres trapping gentamicin sulphate were prepared from poly(l-lactic acid) (PLLA) and poly(l-lactic-co-glycolic acid) (PLGA) as a delivery system for highly hydrophilic antibiotics. The surface and cross-section morphology of the microspheres were characterized by SEM and FTIR. The diameters of the microspheres were ranging from about 50 μm to 700 μm. A low initial burst was achieved. The encapsulation efficiency was more than 70% and the cumulative drug release was about 40% for 30 days. The results indicated that the double-walled microspheres were able to achieve higher encapsulation efficiency and lower initial burst for highly water-soluble drugs.     

Vector-valued Littlewood-Paley-Stein theory for semigroups

We develop a generalized Littlewood-Paley theory for semigroups acting on L^p-spaces of functions with values in uniformly convex or smooth Banach spaces. We characterize, in the vector-valued setting, the validity of the one-sided inequalities concerning the generalized Littlewood-Paley-Stein g-function associated with a subordinated Poisson symmetric diffusion semigroup by the martingale cotype and type properties of the underlying Banach space. We show that in the case of the usual Poisson semigroup and the Poisson semigroup subordinated to the Ornstein-Uhlenbeck semigroup on Rⁿ, this general theory becomes more satisfactory (and easier to be handled) in virtue of the theory of vector-valued Calderón-Zygmund singular integral operators.     

On Some Exponential Diophantine Equations

 We apply a new, deep result of Bilu, Hanrot and Voutier to solve completely some exponential Diophantine equations of the type , where are given coprime positive integers, , and are unknown. (Received 29 May 2000; in revised form 21 September 2000)     

Modeling Photovoltaic Performances of BTBPD-PC61BM System via Density Functional Theory Calculations

Designing and fabricating high-performance photovoltaic devices have remained a major challenge in organic solar cell technologies.In this work,the photovoltaic performances of BTBPD-PC₆₁BM system were theoretically investigated by means of density functional theory calculations coupled with the Marcus charge transfer model in order to seek novel photovoltaic systems.Moreover,the hole-transfer properties of BTBPD thin-film were also studied by an amorphous cell with 100 BTBPD molecules.Results revealed that the BTBPDPC₆₁BM system possessed a middle-sized open-circuit voltage of 0.70 V,large short-circuit current density of 16.874 mA/cm²,large fill factor of 0.846,and high power conversion efficiency of 10%.With the Marcus model,the charge-dissociation rate constant was predicted to be as fast as 3.079×10¹³ s^-1 in the BTBPD-PC₆₁BM interface,which was as 3-5 orders of magnitude large as the decay (radiative and non-radiative) rate constant (10⁸-10¹⁰ s^-1),indicating very high charge-dissociation efficiency (～100%) in the BTBPD-PC₆₁BM system.Furthermore,by the molecular dynamics simulation,the hole mobility for BTBPD thin-film was predicted to be as high as 3.970×10^-3 cm²V^-1s^-1,which can be attributed to its tight packing in solid state.     

Scattering matrices of regular coverings of graphs

We give a decomposition formula for the determinant on the bond scattering matrix of a regular covering of G. Furthermore, we define an L-function of G, and give a determinant expression of it. As a corollary, we express the determinant on the bond scattering matrix of a regular covering of G by means of its L-functions.     

On binormality in non-separable Banach spaces

We study binormality, a separation property of the norm and weak topologies of a Banach space. We show that every Banach space which belongs to a P-class is binormal. We also show that the asplundness of a Banach space is equivalent to a related separation property of its dual space.     

An extended CEV model and the Legendre transform-dual-asymptotic solutions for annuity contracts

This paper develops an extended constant elasticity of variance (E-CEV) model to overcome the shortcomings of the general CEV model. Under the E-CEV model, we study the optimal investment strategy before and after retirement in a defined contribution pension plan where benefits are paid by annuity. By applying the Legendre transform, dual theory and an asymptotic expansion approach, we respectively derive two asymptotic strategies for a CRRA and CARA utility functions in two different periods. Furthermore, we find that each asymptotic strategy can be decomposed into an optimal zero-order strategy and a perturbation strategy. The optimal zero-order strategy denotes an investment strategy where the current volatility is just equal to the mean level of the volatility, whereas the perturbation strategy provides an approximation solution to hedge the slow varying nature of the current volatility deviating from mean level. Finally, we find that the optimal zero-order strategy under given conditions will reduce to the results of Devolder et al. (2003), Xiao et al. (2007) and Gao (2009), respectively.     

An optimal investment strategy for a stream of liabilities generated by a step process in a financial market driven by a Lévy process

In this paper we investigate an asset-liability management problem for a stream of liabilities written on liquid traded assets and non-traded sources of risk. We assume that the financial market consists of a risk-free asset and a risky asset which follows a geometric Lévy process. The non-tradeable factor (insurance risk or default risk) is driven by a step process with a stochastic intensity. Our framework allows us to consider financial risk, systematic and unsystematic insurance loss risk (including longevity risk), together with possible dependencies between them. An optimal investment strategy is derived by solving a quadratic optimization problem with a terminal objective and a running cost penalizing deviations of the insurer’s wealth from a specified profit-solvency target. Techniques of backward stochastic differential equations and the weak property of predictable representation are applied to obtain the optimal asset allocation.     

Constant elasticity of variance model for proportional reinsurance and investment strategies

In our model, the insurer is allowed to buy reinsurance and invest in a risk-free asset and a risky asset. The claim process is assumed to follow a Brownian motion with drift, while the price process of the risky asset is described by the constant elasticity of variance (CEV) model. The Hamilton-Jacobi-Bellman (HJB) equation associated with the optimal reinsurance and investment strategies is established, and solutions are found for insurers with CRRA or CARRA utility.     

Bifurcation of positive solutions to scalar reaction–diffusion equations with nonlinear boundary condition

The bifurcation of non-trivial steady state solutions of a scalar reaction–diffusion equation with nonlinear boundary conditions is considered using several new abstract bifurcation theorems. The existence and stability of positive steady state solutions are proved using a unified approach. The general results are applied to a Laplace equation with nonlinear boundary condition and bistable nonlinearity, and an elliptic equation with superlinear nonlinearity and sublinear boundary conditions.