Finite difference reaction–diffusion equations with nonlinear diffusion coefficients

Summary. A monotone iterative method for numerical solutions of a class of finite difference reaction-diffusion equations with nonlinear diffusion coefficient is presented. It is shown that by using an upper solution or a lower solution as the initial iteration the corresponding sequence converges monotonically to a unique solution of the finite difference system. It is also shown that the solution of the finite difference system converges to the solution of the continuous equation as the mesh size decreases to zero. Received February 18, 1998 / Revised version received April 21, 1999 / Published online February 17, 2000     

Quantification of Gut Microbiota Dysbiosis-Related Organic Acids in Human Urine Using LC-MS/MS

Urine organic acid contains water-soluble metabolites and/or metabolites—derived from sugars, amino acids, lipids, vitamins, and drugs—which can reveal a human’s physiological condition. These urine organic acids—hippuric acid, benzoic acid, phenylacetic acid, phenylpropionic acid, 4-hydroxybenzoic acid, 4-hydroxyphenyl acetic acid, 3-hydroxyphenylpropionic acid, 3,4-dihydroxyphenyl propionic acid, and 3-indoleacetic acid—were the eligible candidates for the dysbiosis of gut microbiota. The aim of this proposal was to develop and to validate a liquid chromatography–tandem mass spectrometry (LC-MS/MS) bioanalysis method for the nine organic acids in human urine. Stable-labeled isotope standard (creatinine-d₃) and acetonitrile were added to the urine sample. The supernatant was diluted with deionized water and injected into LC-MS/MS. This method was validated with high selectivity for the urine sample, a low limit of quantification (10–40 ng/mL), good linearity (r > 0.995), high accuracy (85.8–109.7%), and high precision (1.4–13.3%). This method simultaneously analyzed creatinine in urine, which calibrates metabolic rate between different individuals. Validation has been completed for this method; as such, it could possibly be applied to the study of gut microbiota clinically.     

A Review of the Influence of Various Extraction Techniques and the Biological Effects of the Xanthones from Mangosteen (Garcinia mangostana L.) Pericarps

Xanthones are significant bioactive compounds and secondary metabolites in mangosteen pericarps. A xanthone is a phenolic compound and versatile scaffold that consists of a tricyclic xanthene-9-one structure. A xanthone may exist in glycosides, aglycones, monomers or polymers. It is well known that xanthones possess a multitude of beneficial properties, including antioxidant activity, anti-inflammatory activity, and antimicrobial properties. Additionally, xanthones can be used as raw material and/or an ingredient in many food, pharmaceutical, and cosmetic applications. Although xanthones can be used in various therapeutic and functional applications, their properties and stability are determined by their extraction procedures. Extracting high-quality xanthones from mangosteen with effective therapeutic effects could be challenging if the extraction method is insufficient. Although several extraction processes are in use today, their efficiency has not yet been rigorously evaluated. Therefore, selecting an appropriate extraction procedure is imperative to recover substantial yields of xanthones with enhanced functionality from mangosteens. Hence, the present review will assist in establishing a precise scenario for finding the most appropriate extraction method for xanthones from mangosteen pericarp by critically analyzing various conventional and unconventional extraction methods and their ability to preserve the stability and biological effects of xanthones.     

Electrodeposition of copper on a Pt(111) electrode in sulfuric acid containing poly(ethylene glycol) and chloride ions as probed by in situ STM

This study employed real-time in situ STM imaging to examine the adsorption of PEG molecules on Pt(111) modified by a monolayer of copper adatoms and the subsequent bulk Cu deposition in 1 M H(2)SO(4) + 1 mM CuSO(4)+ 1 mM KCl + 88 μM PEG. At the end of Cu underpotential deposition (~0.35 V vs Ag/AgCl), a highly ordered Pt(111)-(√3 × √7)-Cu + HSO(4)(-) structure was observed in 1 M H(2)SO(4) + 1 mM CuSO(4). This adlattice restructured upon the introduction of poly(ethylene glycol) (PEG, molecular weight 200) and chloride anions. At the onset potential for bulk Cu deposition (~0 V), a Pt(111)-(√3 × √3)R30°-Cu + Cl(-) structure was imaged with a tunneling current of 0.5 nA and a bias voltage of 100 mV. Lowering the tunneling current to 0.2 nA yielded a (4 × 4) structure, presumably because of adsorbed PEG200 molecules. The subsequent nucleation and deposition processes of Cu in solution containing PEG and Cl(-) were examined, revealing the nucleation of 2- to 3-nm-wide CuCl clusters on an atomically smooth Pt(111) surface at overpotentials of less than 50 mV. With larger overpotential (η > 150 mV), Cu deposition seemed to bypass the production of CuCl species, leading to layered Cu deposition, starting preferentially at step defects, followed by lateral growth to cover the entire Pt electrode surface. These processes were observed with both PEG200 and 4000, although the former tended to produce more CuCl nanoclusters. Raising [H(2)SO(4)] to 1 M substantiates the suppressing effect of PEG on Cu deposition. This STM study provided atomic- or molecular-level insight into the effect of PEG additives on the deposition of Cu.     

On the uniqueness problem of differential equations in normed spaces †

Simple direct proofs of some recent results by Kalla, Conde, and Hubbell for a generalized elliptic type integral [Appl. Anal., 22 (1986), pp. 273-287] are presented. Furthermore, a new single term asymptotic approximation for this function is derived, which is superior to the two term approximation given by these authors     

Aromatic Heterocycles Used as Terminal Groups of Calamitic Liquid Crystals

Three series of compounds 1 ‐ 21 were prepared by using 2‐, 3‐, and 4‐pyridinemethanol as terminal group of calamitic liquid crystals. These compounds have some similarities in their phase behavior. They all exhibit SmA phase. A tilt smectic phase, SmC, will be formed when their flexible alkoxy chain is longer than hexoxy group. The profound difference between them is that the compounds 15 ‐ 17 possess a short temperature range of N phase. The compounds 3 and 6 have the widest SmA phase, up to 94 °C, and SmC phase, up to 46 °C, respectively.     

近红外光谱的不同产地柑橘无损鉴别方法

柑橘是世界第一大水果。不同产地的柑橘内部品质和价格有所不同,但其外观差别较小,外行人较难通过肉眼实现准确鉴别分析。DNA标记法与仪器分析操作复杂、成本较高,且对样品具有破坏性,无法实现快速无损分析,影响了产品的二次销售。近红外光谱技术是一种快速无损的新型检测手段,可以用于不同产地农产品的鉴别分析。由于柑橘皮对光谱的干扰较大,导致现阶段柑橘产地无损鉴别研究匮乏。此外柑橘体积较大,因此需要对光谱采样点进行优化。为此,基于近红外光谱技术与化学计量学方法,提出了一种用于不同产地柑橘无损鉴别的新方法。使用近红外光谱仪得到了120个来自云南、湖南、广西武鸣、广西来宾的沃柑漫反射光谱数据。采用单一和组合光谱预处理方式以消除光谱中的多种干扰;采用主成分分析方法对数据进行降维处理,并以此作为输入值结合Fisher线性判别分析方法构建柑橘产地鉴别模型,并与主成分分析模型进行对比。此外,考察了不同光谱采样位置（赤道线4个采集点、果梗部以及果顶部）对结果的影响。结果表明：主成分分析方法结合优化光谱预处理的方法不能实现不同产地柑橘的准确鉴别分析,最优鉴别率仅为5%;而采用主成分分析-Fisher线性判别分析方法,利用赤道线4个点的平均光谱结合去偏置校正或多元散射校正预处理方法可实现不同产地柑橘的100%鉴别分析;采用主成分分析-Fisher线性判别分析对6个点的平均光谱数据进行处理时,采用原始光谱便可实现不同产地柑橘的100%鉴别分析。为此,通过对光谱预处理方法以及光谱采集点的优化,利用主成分分析-Fisher线性判别分析方法即可建立准确的柑橘产地鉴别模型,为不同产地柑橘的快速鉴别提供了新途径,为后续各种柑橘类水果的鉴别分析提供了参考。     

Computationally efficient learning of multivariate <Emphasis Type="Italic">t</Emphasis> mixture models with missing information

A finite mixture model using the multivariate t distribution has been well recognized as a robust extension of Gaussian mixtures. This paper presents an efficient PX-EM algorithm for supervised learning of multivariate t mixture models in the presence of missing values. To simplify the development of new theoretic results and facilitate the implementation of the PX-EM algorithm, two auxiliary indicator matrices are incorporated into the model and shown to be effective. The proposed methodology is a flexible mixture analyzer that allows practitioners to handle real-world multivariate data sets with complex missing patterns in a more efficient manner. The performance of computational aspects is investigated through a simulation study and the procedure is also applied to the analysis of real data with varying proportions of synthetic missing values.     

Ionic Liquid-Based Ultrasonic/Microwave-Assisted Extraction Combined with UPLC for the Determination of Anthraquinones in Rhubarb

Ionic liquid-based ultrasonic/microwave-assisted extraction (IL-UMAE) of five anthraquinones (physcion, chrysophanol, emodin, rhein, and aloe-emodin) from rhubarb was first studied. Several parameters of UMAE were optimized, and the results were compared with of the heat-reflux extraction (HRE), ultrasound, and microwave-assisted extraction (MAE and UAE). The optimal UMAE conditions were as follows: the solvent was 2.0 mol L^?1 1-butyl-3-methylimidazolium bromide [bmim]Br solution, the ration of solid/liquid (g mL^?1) was 1:15, time was 2 min, and microwave power was 500 W. Under these UMAE conditions, total content of five anthraquinones was 28.00 mg g^?1. Compared with the conventional HRE, regular MAE and UAE techniques, the proposed approach exhibited higher efficiency (18.90?C24.40% enhanced) and shorter extraction time (from 6 h to 2 min). The anthraquinones were then determined by ultra performance liquid chromatography (UPLC). Based on optimized conditions, contents of physcion, chrysophanol, emodin, rhein and aloe-emodin in rhubarb collected from different cultivated areas were 0.68?C2.99, 5.03?C15.40, 0.48?C4.34, 0.025?C3.93 and 0.26?C2.56 mg g^?1, respectively. This study suggests that IL-UMAE was an efficient, rapid, simple and green preparation technique.