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.     

Evidence of a phase transition of RbHCO3 from high-resolution solid-state 13C and 87Rb NMR by comparison with KHCO3

A variable-temperature high-resolution 13C and 87Rb solid-state NMR study of powder rubidium hydrogencarbonate, RbHCO3, is presented for the first time. At ambient temperature, RbHCO3 is formed by centrosymmetric dimers linked by hydrogen bonds, but almost no information is available on this compound concerning proton disorder and the low-temperature phase. However, potassium hydrogencarbonate, KHCO3, which has an isomorphic structure for the high temperature phase, was well studied: it undergoes a non-ferroic, non-ferroelectric phase transition at Tc = 318 K between two monoclinic structures. The protons are disordered in an asymmetric double-well potential in the low-temperature phase, and the double-well potential becomes symmetric in the high-temperature phase. By comparison with recent solid-state NMR experimental results on KHCO3, we show that RbHCO3 undergoes a phase transition at Tc approximately 245 K, and give evidence that the proton dynamic disorder in both compounds is very similar.     

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.     

Relationships among Preparative Technique,Phase Composition and Bending Strength of Bauxite Porcelain

1 INTRODUCTION Bauxite porcelain is a novel “K2O–Al2O3–SiO2” system ceramic by using sintered bauxite, clay and potash feldspar and albite as the main raw materials with the Al2O3’s content of 50%～60(massfraction). Compared to the traditional“K2O–Al2O3–SiO2” feldspar porcelain by using quartz, bolus alb and potash feldspar and albite as the main raw materials, the bauxite porcelain possesses such advantages as high mechanical strength, excellent electrical insula- tion prop…     

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, Structure and Geometrical Calculation of a Novel Co-crystal of {[4-Bromo-2-(benzimidazol-2-yl)phenolato][2- (1-butylbenzimidazol-2-yl)phenolato]zinc(Ⅱ)] and Bis[μ-2- (1- butylbenzimidazol-2-yl)phenolato]- 1κN3: 2κO; 1κO:2κN3-bis{[2-(1-butylbenzimidazol-2-yl)phenolato-κ2N3,O]zinc(Ⅱ)}

The title compound has been synthesized and characterized crystallographically. It is a co-crystal consisting of two different neutral zinc(Ⅱ) complexes with Hbpbm (Hbpbm = 4-bromo-2-(benzimidazol-2-yl)phenol) and Hnpbm (Hnpbm = 2-(1-butylbenzimidazol-2-yl)phenol).One is a monomeric mixed-ligand complex of [Zn(bpbm)(npbm)] 1 and the other a dimer of[Zn2(npbm)4] 2 with their ratio of 2:1. Thus the overall formula for the title compound is 21·2.Adjacent 1 and 2 are connected to each other by intermolecular hydrogen bonding interactions in the lattice. The crystal data: monoclinic, space group P21/c, a= 15.0141(12), b = 20.9941(17), c =18.4686(15) (A), β = 97.445(2)°, V= 5772.4(8) (A)3, Mr= 2429.68, Z = 2, Dc = 1.398 g/cm3,μ = 1.579mm-1, F(000) = 2504, R = 0.0637 and wR = 0.1771 for 6464 observed reflections (I＞ 2σ(Ⅰ)). The geometrical structure for 1 has also been theoretically optimized and compared with the experimental one.     

Influence of the particle size distribution on the CRTA curves for the solid-state reactions of interface shrinkage type

The kinetic curves at infinite temperature for the solid-state reactions of the interface shrinkage type were drawn theoretically by taking account the particle size distribution in the sample mixture. The CRTA curves for the reactions with the particle size distribution can be drawn by utilizing the universal kinetic curves at infinite temperature. The proper kinetic treatment for the CRTA curves with the particle size distribution is discussed in connection with the property of the kinetic equation with respect to the particle size distribution. The present kinetic consideration is taken as a simulation for the reactions with a certain distribution in among the reactant particles, produced preferably by the mass and heat transfer phenomena during the thermoanalytical measurements. The merit of the rate jump method by a single cyclic CRTA curve is also discussed on the basis of the present results.