On the convergence of multipoint Padé-type approximants and quadrature formulas associated with the unit circle

We study the convergence of rational interpolants with prescribed poles on the unit circle to the Herglotz-Riesz transform of a complex measure supported on [–, ]. As a consequence, quadrature formulas arise which integrate exactly certain rational functions. Estimates of the rate of convergence of these quadrature formulas are also included.This research was performed as part of the European project ROLLS under contract CHRX-CT93-0416.     

Alternating Sign Matrices and Some Deformations of Weyl's Denominator Formulas

An alternating sign matrix is a square matrix whose entries are 1, 0, or –1, and which satisfies certain conditions. Permutation matrices are alternating sign matrices. In this paper, we use the (generalized) Littlewood's formulas to expand the products and 2 as sums indexed by sets of alternating sign matrices invariant under a 180° rotation. If we put t = 1, these expansion formulas reduce to the Weyl's denominator formulas for the root systems of type B _n and C _n. A similar deformation of the denominator formula for type D _n is also given.     

Phenolic Compounds of Plants of the Scutellaria L. Genus. Distribution, Structure, and Properties

Information on flavones, flavanones, flavanonols, flavonols, chalcones, isoflavones, biflavonoids, lignoflavonoids, and lignane glycosides and stilbenes isolated from plants of the Scutellaria L. genus was systematized and reviewed. A list of 208 phenolic compounds was given according to flavonoid type with an indication of the plant sources, structures, and physicochemical properties and citations of the original articles.     

DETERMINATION OF DEGREE OF CRYSTALLINITY OF NYLON 1212 BY WIDE-ANGLE X-RAY DIFFRACTION

Based on the X-ray scattering intensity theory and using the approximate expression for the atomic scattering factor, the correction factors for three crystalline peaks and an amorphous peak of Nylon 1212 were calculated and the formula of degree of crystallinity of Nylon 1212 was derived by a graphic multipeak resolution method. The degree of crystallinity calculated from the WAXD method is compatible with those obtained by density and calorimetry methods.     

New Temperature Integral Approximate Formula for Non-isothermal Kinetic Analysis

A new approximate formula for temperature integral is proposed. The linear dependence of the new fomula on x has been established. Combining this linear dependence and integration-by-parts, new equation for the evaluation of kinetic parameters has been obtained from the above dependence. The validity of this equation has been tested with data from numerical calculating. And its deviation from the values calculated by Simpson's numerical integrating was discussed. Compared with several published approximate formulae, this new one is much superior to all other approximations and is the most suitable solution for the evaluation of kinetic parameters from TG experiments. This revised version was published online in August 2006 with corrections to the Cover Date.     

Unraveling the mystery of efficacy in Chinese medicine formula: New approaches and technologies for research on pharmacodynamic substances

Traditional Chinese medicine (TCM) is the key to unlock treasures of Chinese civilization. TCM and its compound play a beneficial role in medical activities to cure diseases, especially in major public health events such as novel coronavirus epidemics across the globe. The chemical composition in Chinese medicine formula is complex and diverse, but their effective substances resemble “mystery boxes”. Revealing their active ingredients and their mechanisms of action has become focal point and difficulty of research for herbalists. Although the existing research methods are numerous and constantly updated iteratively, there is remain a lack of prospective reviews. Hence, this paper provides a comprehensive account of existing new approaches and technologies based on previous studies with an in vitro to in vivo perspective. In addition, the bottlenecks of studies on Chinese medicine formula effective substances are also revealed. Especially, we look ahead to new perspectives, technologies and applications for its future development. This work reviews based on new perspectives to open horizons for the future research. Consequently, herbal compounding pharmaceutical substances study should carry on the essence of TCM while pursuing innovations in the field.     

Synthesis and Crystal Structure of 3,3‘—（Hexane—1,6—diyl）bis（1—acetyl—5,5—dimethylhydantoin）,a New Inducer of Differentiation

The title compound C20H30N4O6, Mr = 422.48)was synthesized and its crystal structure was determined by X-ray diffraction method. It crystallizes in the triclinic system, space group P ī with cell parameters: a = 8.330(2), b = 8.468(2), c = 16.017(3) A, α = 97.30(3), β = 92.33(3), γ = 103.94(3)o, V = 1084.7(4) A3, Dc = 1.294 g/cm3, Z = 2, F(000) = 452 and μ = 0.096 mm-1. The structure was refined to R = 0.0483 for 3732 observed reflections with I>2(I) and wR = 0.1335 for 4828 unique reflections. The hydantoin rings are planar and the two ring planes of one molecule are paralleled to each other.     

Synthesis and Asymmetric Enantioselective Addition of Chiral Polybinaphthyl and Polybinaphthol I.igands

Four chiral polymers P-1, P-2, P-3 and P-4 were synthesized by the polymerization of （S）-2,2＇-dioctoxy-1,1＇- binaphthyl-6,6＇-boronic acid （S-M-3） with （S）-6,6＇-dibromo-1,1＇-binaphthol （S-M-1）, （R）-6,6＇-dibromo-1,1＇- binaphthol （R-M-1）, （S）-3,3＇-diiodo-1,1＇-binaphthol （S-M-2） and （R）-3,3＇-diiodo-1,1＇-binaphthol （R-M-2） under Pd-catalyzed Suzuki reaction, respectively. All four polymers can show good solubility in some common solvents due to the nonplanarity of the polymers in the main chain backbone and flexible alkyl groups in the side chain. The analysis results indicate that specific rotation and circular dichroism （CD） spectral signals of the alternative S-S chiral polymers P-1 and P-3 are larger than those of S-R chiral polymers P-2 and P-4, but their UV-Vis and fluorescence spectra are almost similar. The results of asymmetric enantioselectivity of four polymers for diethylzinc addition to benzaldehyde indicate that catalytically active center is （R） or （S）-1, 1＇-binaphthol moieties.     

Study of spectral analytical data using fingerprints and scaled similarity measurements

A new chemoinformatic model has been developed for enlarging the differences between spectra and applied to differentiation of wines according to the criteria grape origin and variety and ageing process. The model is based on generation of fingerprints from normalised spectra, using empirical parameters and a set of 120 samples. After generation of the fingerprints, similarity matrixes were built on the basis of the Tanimoto similarity index between the fingerprints of the samples. Calculation of the Tanimoto index was modified to adapt the index to the characteristics of the analytical measurements. Thus, scaling factors taking into account pattern fingerprints generated from a group of samples with common characteristics were used. In addition, a modified expression for calculating the Tanimoto index was employed. Principal-components analysis (PCA) and soft independent modelling of class analogy (SIMCA) were applied to the similarity matrixes. The results obtained are discussed as a function of the normalisation method employed, the empirical factor used in generation of the fingerprints, and selection of samples for building the pattern fingerprint, etc. Finally, results from differentiation of wines are compared with those obtained by applying PCA to the unprocessed spectra as stated by the proposed model.     

1-烷（苯）氧基-3-（3，4-亚甲基二氧）苯基-2-丙醇的合成与生物活性研究

黄樟素氧化物与烷氧基钠和苯氧基钠反应，区域选择性地开环加成，生成1-烷 （苯）氧基-3-（3，4-亚甲基二氧）苯基-2-丙醇。该系列化合物具有诱导细胞凋 亡与分化的生物活性。