双分子水和氨气催化CF3OH分子裂解的理论研究

利用G3和CBS-QB3的理论方法研究CF₃OH分子裂解成FCFO和HF,并考虑大气中双分子和氨气对CF₃OH分子裂解的催化作用. 理论计算表明：由于在G3的理论水平下,计算的能垒为188.52 kJ/mol,所以CF₃OH分子在大气条件下不可能发生单分子裂解;当氨气和双分子水被加入时,能垒都被降到25.08 kJ/mol,起了强的催化作用. 除此之外,应用过渡态理论对速率常数进行了计算,计算结果表明：氨气催化CF₃OH分子的速率常数是单分子和双分子催化CF₃OH分子裂解速率常数的10⁹和10⁵倍. 考虑到大气中这些物质的浓度,计算结果预测了氨气催化CF₃OH分子裂解在大气中起到重要的作用.     

A fast dual proximal gradient algorithm for convex minimization and applications

We consider the convex composite problem of minimizing the sum of a strongly convex function and a general extended valued convex function. We present a dual-based proximal gradient scheme for solving this problem. We show that although the rate of convergence of the dual objective function sequence converges to the optimal value with the rate O(1/k²)$O(1/k^2)$, the rate of convergence of the primal sequence is of the order O(1/k)$O(1/k)$.     

Extending the applicability of Secant methods and nondiscrete induction

We use nondiscrete mathematical induction to extend the applicability of the Secant methods for solving equations in a Banach setting. Our approach has the following advantages over earlier works under the same information: weaker sufficient convergence conditions; tighter error bounds on the distances involved and more information on the location of the solution. Numerical examples where our results apply but earlier ones fail to solve nonlinear equation as well as tighter error bounds are also provided in this study.     

Approximation by Chlodowsky-Taylor polynomials

The subject of this paper is to study the problem of the approximation of function of two variables by means of Chlodowsky-Taylor polynomials in a rectangular domain.     

A family of minimax rates for density estimators in continuous time

In continuous time, rates of convergence of density estimators fluctuate with the nature of observed sample paths. In this paper, we give a family of rates reached by the kernel estimator and we show that these rates are minimax. Finally, we study applications of these results for specific classes of processes including the Gaussian ones     

Specific Deuteration in Patuletin and Related Flavonoids via Keto–Enol Tautomerism: Solvent‐ and Temperature‐Dependent 1H‐NMR Studies

An H/D exchange process in patuletin ( 1 ) and its derivatives in D‐donor solvents (e.g., CF₃COOD), which occurs regioselectively at C(8) was observed for the first time during NMR studies. The effect of substituents and temperature on the deuteration of various flavonoids (see Fig. 1) which include apigenin, chrysin, galangin, kaempferol, luteolin, morin, myricetin, patuletin, patulitrin, and quercetin, as well as derivatives of patuletin was examined extensively under NMR conditions. The rate constant of deuteration at C(8) of patuletin ( 1 ) and two flavones, luteolin ( 3 ) and apigenin ( 12 ), was also determined in CF₃COOD. The D‐atom was introduced into the flavonoids via a keto–enol tautomerism (Scheme 1). During these studies, monodeuterated patuletin was also obtained as a new compound. The examined flavonoids have been reported to possess significant pharmacological activities, and their deuterated derivatives would be of importance for the identification and quantification of these compounds in biological matrices.     

Uncertainty functions, a compact way of summarising or specifying the behaviour of analytical systems

Analytical chemists can advantageously use an uncertainty function to describe the performance of an analytical system in terms of the standard uncertainty or standard deviation as a function of the concentration of the analyte. This “characteristic function” is useful for estimating uncertainty at a new concentration. A similar function can be used to prescribe the uncertainty that is regarded as fit for purpose for a particular application. This “fitness function” is useful in setting standards of accuracy in proficiency tests and similar exercises without revealing the concentration of the analyte. In combination, these two functions provide a rational basis for method selection.     

X-ray calculations for a NLTE Ar plasma

A model is developed to calculate emission spectrum of non-local thermodynamic equilibrium(NLTE) plasmas. The Collisional-Radiative model is adopted for non-LTE population calculations. Configuration-averaged rate coefficients that needed in the rate equations are obtained based on the first order perturbation theory. The Hatree-Fock-Slater self-consistent-field method is used to calculate electron wave functions. The present model is applied to the calculation of emissivity from a Ar plasma. The features of the spectra are in good agreement with those calculated by other theoretical models, but the data of the integrated emissivity differ by a factor 2～8.     

The ‘Temperature Integral’ — Its use and abuse

This paper first reviews the history of the temperature dependence of reaction rate in reaction kinetics. The various equations which are in use today for expressing this dependence were delineated by van't Hoff almost one hundred years ago. Since an exponential form best describes this dependence for most thermal analysis reactions and, due to the fact that the simple Arrhenius equation (with a temperature-independent preexponential factor) has traditionally been used for this purpose, the mathematically intractable temperature integral often has become a necessary evil in the analysis of thermal analysis kinetics. Methods which avoid the temperature integral in kinetics analysis are discussed. The merits of various evaluations and approximations for the temperature integral are described and assessed in this paper.     

The rate of convergence of q-Bernstein polynomials for

In the note, we obtain the estimates for the rate of convergence for a sequence of q-Bernstein polynomials {B_n,q(f)} for 0<q<1 by the modulus of continuity of f, and the estimates are sharp with respect to the order for Lipschitz continuous functions. We also get the exact orders of convergence for a family of functions , and the orders do not depend on α, unlike the classical case.