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.     

A review ofL=λW and extensions

A fundamental principle of queueing theory isL=W (Little's law), which states that the time-average or expected time-stationary number of customers in a system is equal to the product of the arrival rate and the customer-average or expected customer-stationary time each customer spends in the system. This principle is now well known and frequently applied. However, in recent years there have been extensions, such as H=G and the continuous, distributional, ordinal and central-limit-theorem versions, which show that theL=W relation, when viewed properly, has much more power than was previously realized. Moreover, connections have been established between H=G and other fundamental relations, such as the rate conservation law and PASTA (Poisson arrivals see time averages), which show that there is a much greater unity in the overall theory than was previously realized. This paper provides a review.This paper is dedicated to the memory of our colleague Professor Peter Franken (1937–1989), who contributed greatly to the subject of this paper and to queueing theory more generally.     

Wiener distributions and white noise analysis

The paper describes the structure of a new space of generalized Wiener functionals, , called the Wiener algebra, or space of Wiener distributions, and demonstrates its use in the white noise analysis. The concepts of derivatives and integrals for multi-time parameter generalized stochastic process:^N are introduced, and a derivative version of Itô's lemma is proved. The algebraic structure of and its lattice of subspaces is elaborated, and within this framework a generalized version of the Malliavin calculus is presented.     

Root determination by use of Padé approximants

In this paper we describe a new technique for generating iteration formulas — of arbitrary order — for determining a zero (assumed simple) of a functionf, assumed analytic in a region containing the zero. The 1/p Padé Approximant (p0) to the functiong(t)f(z) is formed wherez=w+t, using the Taylor series forf at the pointw, an approxination to the zero off. The value oft for which the 1/p Padé Approximant vanishes provides the basis of iteration formulas of orderp+2.Some known iteration formulas, e.g., Newton-Raphson's, Halley's and Kiss's of order of convergence two, three and four, are directly obtained by settingp=0,1 and 2, respectively.     

Kibble–Slepian formula and generating functions for 2D polynomials

We prove a generalization of the Kibble–Slepian formula (for Hermite polynomials) and its unitary analogue involving the 2D Hermite polynomials recently proved in [16]. We derive integral representations for the 2D Hermite polynomials which are of independent interest. Several new generating functions for 2D q-Hermite polynomials will also be given.     

Euler–MacLaurin formulas via differential operators

Recently there has been a renewed interest in asymptotic Euler–MacLaurin formulas, because of their applications to spectral theory of differential operators. Using elementary means, we recover such formulas for compactly supported smooth functions on intervals, polygons, and three-dimensional polytopes, where the coefficients in the asymptotic expansion are sums of differential operators involving only derivatives of the function in directions normal to the faces of the polytope. Our formulas apply to wedges of any dimension.     

Approximating exponential and logarithmic functions using polynomial interpolation

This article takes a closer look at the problem of approximating the exponential and logarithmic functions using polynomials. Either as an alternative to or a precursor to Taylor polynomial approximations at the precalculus level, interpolating polynomials are considered. A measure of error is given and the behaviour of the error function is analysed. The results of interpolating polynomials are compared with those of Taylor polynomials.     

一种分解指数算符的简洁方法

提出一种新的分解指数算符的方法,这种方法不仅简单易懂,而且有助于找到更多的算符恒等式.