A note on global solution to stochastic differential equation based on a semimartingale with spatial parameters

We give here some criterions for the existence and uniqueness of a global solution to a stochastic differential equation based on a semimartingale with spatial parameters of the form

The generally useful estimate of solvent systems method facilitates off-line two-dimensional countercurrent chromatography for isolating compositions from Siraitia grosvenorii roots

Solvent system selection is a crucial and the most time-consuming step for successful countercurrent chromatography separation. A thin-layer chromatography-based generally useful estimate of solvent systems method has been developed to simplify the solvent system selection. We herein utilized the method to select a solvent system for off-line two-dimensional countercurrent chromatography to separate chemical compositions from a complex fraction of the Siraitia grosvenorii root extract. The first-dimensional countercurrent separation using chloroform/methanol/water (10:5.5:4.5, v/v/v) yielded four compounds with high purity and three mixture fractions (Fr I, III, and VII). The second-dimensional countercurrent separation conducted on Fr I, III, and VII using the hexane/ethyl acetate/methanol/water (4:6:6:4, 3:7:3:7, v/v/v) and chloroform/methanol/water (10:9:6, v/v/v) solvent systems, respectively, produced another four compounds. Four triterpenoids and four lignans were finally isolated, including two novel compounds. Hence, the generally useful estimate of solvent systems method is a feasible and efficient approach for selecting an applicable solvent system for separating complex samples. In addition, the off-line two-dimensional countercurrent chromatography method can improve both the peak resolution and the capacity of countercurrent chromatography.     

Silica sulfuric acid-catalyzed expeditious environment-friendly hydrolysis of carboxylic acid esters under microwave irradiation

Silica sulfuric acid was found to be an efficient, recoverable, reusable and environment-friendly catalyst for the fast hydrolysis of various carboxylic acid esters in high conversions and selectivities under microwave irradiation conditions. This protocol has the advantages of no corrosion, no environmental pollution, high reaction rate, high yield, and simple work-up procedure.     

An asymptotic property of the number of spanning trees of double fixed step loop networks

Let T(C(p,1,q))be tbe number of spanning trees of circulant graph C(p,1,q). In this note we show that T(C(p 1,1,q))/T(C(p,1,q))→2,p→ ∞.     

关于“蝴蝶”图的“DNICP”性质

本文证明了“蝴蝶”图且有“DNICP”性质,并给出了相应的分解式,最后将此结果推广到“锯形”图。     

Laccase-Catalyzed Oxidative Polymerization of Phenolic Compounds

Enzymatic polymerization of phenolic compounds (catechol, resorcinol, and hydroquinone) was carried out using laccase. The mechanism of polymerization and the structures of the polymers were evaluated in terms of UV–Vis and Fourier transform infrared spectroscopy. The molecular weights of the produced polyphenols were determined with GPC. The results showed that the phenolic monomers firstly turned into quinone intermediates by laccase catalysis. Through further oxidation, the intermediates formed covalent bonds. Finally, catechol units were linked together with ether bonds, and both resorcinol and hydroquinone units were linked together with C-C bonds. The number-average molecular weights of the polyphenols ranged from 1,000 to 1,400 Da (corresponding to the degree of polymerization that varied from 10 to 12) with a lower polydispersity value of about 1.10, showing selective polymerization of phenolic compounds catalyzed by laccase.     

Synthesis and biological activity of kalkitoxin and its analogues

Total syntheses of kalkitoxin, isolated from the Caribbean Lyngbya majuscula, and its analogues, 3-epi-, 7-epi-, 8-epi-, 10-epi-, 10-nor-, and 16-nor-kalkitoxin, were achieved via oxazolidinone-based diastereoselective 1,4-addition reaction of a methyl group and efficient TiCl(4)-mediated thiazoline ring formation as the key steps. The biological activities of synthetic kalkitoxin and its analogues were evaluated with brine shrimp.     

高效液相色谱-串联质谱法同时检测化妆品中6种禁用着色剂

建立了高效液相色谱-串联质谱(HPLC-MS/MS)同时测定膏状和粉状化妆品中苏丹红IV、酸性紫49、苏丹蓝2、溶剂红49、碱性紫1和颜料橙5等6种禁用着色剂的检测方法。样品经乙醇-乙腈(3:2, v/v)超声振荡提取20 min、离心净化及氮吹浓缩后,在Luna C18色谱柱(150 mm×2.1 mm, 5 μm)上进行反相液相色谱分离,以甲醇和10 mmol/L乙酸铵溶液为流动相进行梯度洗脱,采用多反应监测(MRM)模式进行质谱测定。根据保留时间及质谱图上特征离子的相对丰度比进行定性,外标法定量。结果表明: 6种着色剂的定量限(信噪比为10计)为0.1～10 μg/kg,回收率为86.67%～98.22%,相对标准偏差(RSD)为4.01%～7.01%。该方法简便、快速、灵敏度高且重现性好,适合于化妆品中禁用着色剂的定性与定量。     

On estimation and inference in a partially linear hazard model with varying coefficients

We study estimation and inference in a marginal proportional hazards model that can handle (1) linear effects, (2) non-linear effects and (3) interactions between covariates. The model under consideration is an amalgamation of three existing marginal proportional hazards models studied in the literature. Developing an estimation and inference procedure with desirable properties for the amalgamated model is rather challenging due to the co-existence of all three effects listed above. Much of the existing literature has avoided the problem by considering narrow versions of the model. The object of this paper is to show that an estimation and inference procedure that accommodates all three effects is within reach. We present a profile partial-likelihood approach for estimating the unknowns in the amalgamated model with the resultant estimators of the unknown parameters being root- \(n\) consistent and the estimated functions achieving optimal convergence rates. Asymptotic normality is also established for the estimators.     

The adapted solution and comparison theorem for backward stochastic differential equations with Poisson jumps and applications

This paper deals with a class of backward stochastic differential equations with Poisson jumps and with random terminal times. We prove the existence and uniqueness result of adapted solution for such a BSDE under the assumption of non-Lipschitzian coefficient. We also derive two comparison theorems by applying a general Girsanov theorem and the linearized technique on the coefficient. By these we first show the existence and uniqueness of minimal solution for one-dimensional BSDE with jumps when its coefficient is continuous and has a linear growth. Then we give a general Feynman-Kac formula for a class of parabolic types of second-order partial differential and integral equations (PDIEs) by using the solution of corresponding BSDE with jumps. Finally, we exploit above Feynman-Kac formula and related comparison theorem to provide a probabilistic formula for the viscosity solution of a quasi-linear PDIE of parabolic type.