Fundamentals of Computational Conformal Geometry

Computational conformal geometry is an inter-disciplinary field between mathematics and computer science. This work introduces the fundamentals of computational conformal geometry, including theoretic foundation, computational algorithms, and engineering applications. Two computational methodologies are emphasized, one is the holomorphic differentials based on Riemann surface theory and the other is surface Ricci flow from geometric analysis.     

Fixed points and exponential stability of mild solutions of stochastic partial differential equations with delays

The fixed-point theory is first used to consider the stability for stochastic partial differential equations with delays. Some conditions for the exponential stability in pth mean as well as in sample path of mild solutions are given. These conditions do not require the monotone decreasing behavior of the delays, which is necessary in [T. Caraballo, K. Liu, Exponential stability of mild solutions of stochastic partial differential equations with delays, Stoch. Anal. Appl. 17 (1999) 743-763; Ruhollan Jahanipur, Stability of stochastic delay evolution equations with monotone nonlinearity, Stoch. Anal. Appl. 21 (2003) 161-181]. Even in this special case, our results also improve the results in [T. Caraballo, K. Liu, Exponential stability of mild solutions of stochastic partial differential equations with delays, Stoch. Anal. Appl. 17 (1999) 743-763].     

LC–DAD–ESI-MS-MS for Characterization and Quantitative Analysis of Diterpenoids from Coleus forskohlii

Qualitative characterization and quantitative analysis of labdane diterpenoids from Coleus forskohlii have been achieved by liquid chromatography hyphenated with photodiode-array detection and tandem electrospray ionization mass spectrometry (LC–DAD–ESI-MSⁿ). By use of this method, thirteen forskolin-type diterpenoids were identified in the crude extract on the basis of their fragmentation mechanisms. Fragmentation rules were deduced from nine forskolin-type standards by ESI-MS in positive-ion mode. It was found that fragmentation behavior varied with the position and number of the substituents on the skeleton; this could be used for convenient identification of this type of compound. Six marker diterpenoids were also quantified, and the quality of both the cultivated and wild plants was evaluated.

     

On reinsurance and investment for large insurance portfolios

We consider a problem of optimal reinsurance and investment for an insurance company whose surplus is governed by a linear diffusion. The company’s risk (and simultaneously its potential profit) is reduced through reinsurance, while in addition the company invests its surplus in a financial market. Our main goal is to find an optimal reinsurance-investment policy which minimizes the probability of ruin. More specifically, in this paper we consider the case of proportional reinsurance, and investment in a Black-Scholes market with one risk-free asset (bond, or bank account) and one risky asset (stock). We apply stochastic control theory to solve this problem. It transpires that the qualitative nature of the solution depends significantly on the interplay between the exogenous parameters and the constraints that we impose on the investment, such as the presence or absence of shortselling and/or borrowing. In each case we solve the corresponding Hamilton-Jacobi-Bellman equation and find a closed-form expression for the minimal ruin probability as well as the optimal reinsurance-investment policy.     

Synthesis of ABCD 4‐Miktoarm star‐shaped quarterpolymers by combination of the “click” chemistry with multiple polymerization mechanism

Well‐defined ABCD 4‐Miktoarm star‐shaped quarterpolymers of [poly(styrene)‐poly(tert‐butyl acrylate)‐poly(ethylene oxide)‐poly(isoprene)] [star(PS‐PtBA‐PEO‐PI)] were successfully synthesized by the combination of the “click” chemistry and multiple polymerization mechanism. First, the poly(styryl)lithium (PS^?Li⁺) and the poly(isoprene)lithium (PI^?Li⁺) were capped by ethoxyethyl glycidyl ether (EEGE) to form the PS and PI with both an active ω‐hydroxyl group and an ω′‐ethoxyethyl‐protected hydroxyl group, respectively. After these two hydroxyl groups were selectively modified to propargyl and 2‐bromoisobutyryl group for PS, the resulted PS was used as macroinitiator for ATRP of tBA monomer and the diblock copolymer PS‐b‐PtBA with a propargyl group at the junction point was achieved. Then, using the functionalized PI as macroinitiator for ROP of EO monomer and bromoethane as blocking agent, the diblock copolymer PI‐b‐PEO with a protected hydroxyl group at the conjunction point was synthesized. After the hydrolysis, the recovered hydroxyl group of PI‐b‐PEO was modified to bromoacetyl and then azide group successively. Finally, the “click” chemistry between them was proceeded smoothly. The obtained star‐shaped quarterpolymers and intermediates were characterized by ¹H NMR, FT‐IR, and SEC in detail. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 2154–2166, 2008     

The electrochemical behavior of N-n-undecyl-N''-(sodium-p-amino-benzenesulfonate)thiourea and its interaction with bovine serum albumin

In pH 5.5 phosphate buffer solution,N-n-undecyl-N'-(sodium-p-amino-benzenesulfonate)thiourea(UPT)produced a pair of redox peaks on the bare glassy carbon electrode.At the multi-walled carbon nanotube(MWNT)modified electrode,the electrochemical behavior of UPT enhanced greatly.In the presence of bovine serum albumin (BSA),the peak currents of UPT decreased linearly due to the formation of a super-molecular complex.This method was successfully applied to the determination of BSA in a bovine serum sample.     

Typical Microstructures of Chinese Medicines with X-Ray Microscopy in Phase Contrast

Due to the low absorption contrast of plant tissues, traditional x-ray radiography has not been included in the microscopic techniques used in the identification of traditional Chinese medicines （TCMs）. With the development of x-ray phase contrast imaging （XPCI） in recent years, weakly absorbing materials could also be imaged by x- rays. Here we investigate microstructures of TCMs utilizing XPCI based on a nano-focus x-ray tube. The results demonstrated that XPCI is capable of revealing the microstructures of TCMs used as judging criteria in the identification of TCMs. The major advantages of the new method are nondestructivity, no special demand for sample preparation and suitability for thick samples.