On isoperimetric problems for domains with partly known boundaries

In the present paper, we discuss the isoperimetric problems for domains with partly known boundaries, i.e., the problem of determining a domain that minimizes the capacity functional in the class of plain double-connected domains having the same fixed area and outer boundary. The formulas for capacity variations obtained in this paper allows us to formulate necessary conditions.It is proved that the convexity of the fixed outer boundary implies the convexity of the inner boundary corresponding to an optimal domain. Then, we discuss the case where the fixed part of the boundary is a square.Further, we consider similar problems with more complicated functionals. We introduce the concept of a minimal function in the class of equimeasurable functions. This concept allows us to unify the approach to all of these problems. At the end, we produce a hypothesis that, if proved, would enable us to characterize the shape of the optimal domains in the isoperimetric problems mentioned above.The author wishes to express his appreciation to Dr. K. A. Lurie for his help and unceasing attention.     

基于跳-分形模型的美式看涨期权定价

假设股票变化过程服从跳一分形布朗运动,根据风险中性定价原理对股票发生跳跃次数的收益求条件期望现值推导出M次离散支付红利的美式看涨期权解析定价方程,并使用外推加速法求出当M趋于无穷时方程的二重、三重正态积分多项式表达,依此计算连续支付红利美式看涨期权价值.数值模拟表明通常仅需二重正态积分多项式能产生精确价值,而在极实值状态下则需三重正态积分多项式才能满足,结合两种多项式可以编出有效数字程序评价支付红利的美式看涨期权.     

T1 THEOREM FOR BESOV SPACES ON NONHOMOGENEOUS SPACES

Suppose μ is a Radon measure on Rd, which may be non doubling. The only condition assumed on μ is a growth condition, namely, there is a constant Co ＞ 0 such that for all x ∈ supp(μ) and r ＞ 0,μ(B(x,r)) ≤ Corn, where 0 ＜ n ≤ d. We prove T1 theorem for non doubling measures with weak kernel conditions. Our approach yields new results for kernels satisfying weakened regularity conditions, while recovering previously known Tolsa's results. We also prove T1 theorem for Besov spaces on nonhomogeneous spaces with weak kernel conditions given in [7].     

New thiazinediones and other components from Xanthium strumarium

Two new thiazinediones along with five known compounds were isolated from the fruits of Xanthium strumarium L. The structures of the two new compounds were determined to be 7-hydroxymethyl-8,8-dimethyl-4,8-dihydrobenzol[1,4]thiazine-3,5-dione-11-O-β-D-glucopyranoside (1) and 2-hydroxy-7-hydroxymethyl-8,8-dimethyl-4,8-dihydrobenzol[1,4]thiazine-3,5-dione-11-O-β-D-glucopyranoside (2). The five known compounds were identified as xanthiazone (3), chlorogenic acid (4), ferulic acid (5), formononetin (6), and ononin (7), respectively. Published in Khimiya Prirodnykh Soedinenii, No. 5, pp. 456–458, September–October, 2006.     

Analysis of Diquat by Ion Selective Elecrodes

Abstract

The calibration response of a diquat bis(tetra-4-chlorophenylborate) (DQT. 2T4C1PB) based ISE for DQT was stable for 55 days. The ISE calibration slope and minimum detectable activity a(min) of DQT were in the ranges (S.D. in parentheses) 30(0.6) to 28(1.7) mV/log a (DQT) and 4(3) × 10^?9M to 3(0.2) × 10^?6M, respectively.

The times for 100% response were 3 s at 1 mM and 25 s at 1 μM and the ISE was useable at pH 2 to 12 and over a sample temperature range of 2 to 50[ddot]C.

Samples (2.54–244 μM DQT) could be determined using the standard addition method with about a ?5% error and a precision of 7 to 8%. For comparison, DQT was also determined by titration with sodium tetraphenylborate (NaTPB) using DQT. 2TPB and TBA. TPB ISEs as TPB sensors. The errors were in the range of 12 to 20% for DQT analysis in deionized water, sodium chloride solution or simulated serum.     

Projection method for multiple criteria group decision making with incomplete weight information in linguistic setting

Multiple criteria group decision making (MCGDM) problems have become a very active research field over the last decade. Many practical problems are often characterized by MCGDM. The aim of this paper is to develop a new approach for MCGDM problems with incomplete weight information in linguistic setting based on the projection method. Firstly, to reflect the reality accurately, a method to determine the weights of decision makers in linguistic setting is proposed by calculating the degree of similarity between 2-tuple linguistic decision matrix given by each decision maker and the average 2-tuple linguistic decision matrix. By using the weights of decision makers, all individual 2-tuple linguistic decision matrices are aggregated into a collective one. Then, to determine the weight vector of criteria, we establish a non-linear optimization model based on the basic ideal of the projection method, i.e., the optimal alternative should have the largest projection on the 2-tuple linguistic positive ideal solution (TLPIS). Calculate the 2-tuple linguistic projection of each alternative on the TLPIS and rank all the alternatives according to the 2-tuple linguistic projection value. Finally, an illustrative example is given to demonstrate the calculation process of the proposed method, and the validity is verified by comparing the evaluation results of the proposed method with that of the technique for order preference by similarity to ideal solution (TOPSIS) method.     

A Chemometric Analysis of Compounds from Native New Zealand Medicinal Flora

Several hundred (396) compounds from New Zealand flora with medicinal properties were analyzed for their physicochemical properties. It was found that approximately 10 % fulfilled all the requirements to be considered to be lead‐like, over half of the compounds were deemed to be in the drug‐like space and ≈75 % were in the known drug space. These results indicate the presence of a significant proportion of compounds that are of particular interest to pursue as potential lead compounds or therapeutics. Additionally, compound classes were analyzed separately—most carbonyl‐containing compounds (aldehydes, ketones, esters and lactones), along with phenols were the most lead‐like compounds, which also displayed very good proportions in the drug‐like and known drug space. The information presented herein can be harnessed and utilized in future work, through focussing on the compounds and compound classes that exhibit high‐levels of lead‐likeness for further development.     

Analysis of Fenitrothion and Metabolites in Stored Wheat

Abstract

A simple and rapid method for the analysis of fenitrothion and its metabolites, fenitrooxon, S-methyl fenitrothion, demethyl fenitrothion, demethyl S-methyl fenitrothion, 3-methyl-4-nitrophenol, and dimethyl phosphorothioic acid in stored wheat has been developed. Simultaneous analysis of the extract was conducted using FPD-GLC after derivatization with diazoethane except for 3-methyl-4-nitrophenol which was analyzed directly by EC-GLC. Recoveries of all compounds from wheat fortified at the levels from 0.1 to 5.0 ppm were greater than 90%.

The developed method was used to quantitatively determine major metabolites found in grain treated with fenitrothion and stored at 20°C for 12 months. Demethyl fenitrothion, 3-methyl-4-nitrophenol, and dimethyl phosphorothioic acid were the major breakdown products of fenitrothion found in stored wheat. Confirmation of these metabolites was carried out by chemical derivatization plus FPD-GLC and by TLC.