用线性弱正算子逼近

用线性正算子的逼近理论飞速发展,但正性是一个较强的限制,孙永生,王仁宏等研究过减弱正性限制,作者研究用线性弱正算子逼近,推广Korovkin定理和Grundmann定理等等.     

依概率收敛与依分布收敛的关系

本文探讨了随机变量序列依概率收敛与依分布收敛的关系 ,并给出了一个依分布收敛能保证依概率收敛的最弱的条件 ,即 :设分布函数列 { Fn(x) }弱收敛于连续的分布函数 F(x) ,则存在随机变量序列{ξn}和随机变量ξ,它们分别以 { Fn(x) }和 F(x)为其对应的分布函数列和分布函数 ,且 {ξn}依概率收敛于ξ.     

Remarks on Multilevel Bases for Divergence-Free Finite Elements

The connection between the multilevel factorization method recently proposed by Sarin and Sameh for solving mixed discretizations of the Stokes equation using a divergence-free finite element formulation, and hierarchical basis preconditioners for the Poisson problem is established. For the 2D triangular Taylor–Hood element, a preconditioner is proposed that could be useful in fractional step methods.     

Approximation by Discrete GB-Splines

This paper addresses the definition and the study of discrete generalized splines. Discrete generalized splines are continuous piecewise defined functions which meet some smoothness conditions for the first and second divided differences at the knots. They provide a generalization both of smooth generalized splines and of the classical discrete cubic splines. Completely general configurations for steps in divided differences are considered. Direct algorithms are proposed for constructing discrete generalized splines and discrete generalized B-splines (discrete GB-splines for short). Explicit formulae and recurrence relations are obtained for discrete GB-splines. Properties of discrete GB-splines and their series are studied. It is shown that discrete GB-splines form weak Chebyshev systems and that series of discrete GB-splines have a variation diminishing property.     

First-order Fréedericksz transition at the threshold point for weak anchoring nematic liquid crystal cell under external electric and magnetic fields

Based on the modified formula of Rapini-Papoular, the equilibrium equation and boundary condition of the director have been obtained and the behaviour of the Fréedericksz transition at the threshold point has been studied for weak-anchoring nematic liquid crystal cells under external electric and magnetic fields with the methods of analytical derivation and numerical calculation. The results show that, except for the usual second-order transition, the first-order Fréedericksz transition can also be induced by a suitable surface anchoring technique for the liquid crystal cell given in the paper. The conditions for the existence of the first-order Fréedericksz transition are obtained. They are related to the material elastic coefficient k_{11}, k_{33} the thickness of the liquid crystal cell, the external electric field and the strength of surface anchoring, etc.     

The bifurcation threshold value of the chaos detection system for a weak signal＊

Recently, it has become an important problem to confirm the bifurcation threshold value of a chaos detectionsystem for a weak signal in the fields of chaos detection. It is directly related to whether the results of chaos detectionare correct or not. In this paper, the discrimination system for the dynamic behaviour of a chaos detection system fora weak signal is established by using the theory of linear differential equation with periodic coefficients and computingthe Lyapunov exponents of the chaos detection system; and then, the movement state of the chaos detection system isdefined. The simulation experiments show that this method can exactly confirm the bifurcation threshold value of thechaos detection svstem.     

A New Investigation of Mannich Reaction

Mannich reaction is widely used for the synthesis of many kinds of compounds1. In the synthesis of the derivatives of styryl ketonic Mannich bases, a one-pot method is used, in which ketone, secondary-amine hydrochloride, paraformaldehyde are refluxed together in alcohol2,3. In most cases the normal Mannich product MA is obtained. But when certain amine is used as the reactant, a side-product IM, instead of MA is obtained. MS and 1HNMR data indicate that compound IM is a new type of Man…     

Hydration of DNA Bases and Compounds Containing Small Rings—A Model for Interactions of the Ricin Toxin A-Chain. A Theoretical Ab Initio Study

Ab initio quantum chemical calculations were performed for four neutral gas phase adenine and four pterin tautomers along with guanine and formycin bases. The water complexes of the lowest energy tautomers of these bases have been studied to mimic their interaction with the ricin toxin A chain (RTA). The water molecules create a full first hydration shell around the bases. Full geometry optimizations without any constraints on the planarity of these hydrated complexes were carried out at the HF/6-31G(d,p) level. Single point calculations were also performed at the correlated MP2/6-31G(d,p)//HF/6-31G(d,p) level of theory. Hydration energies were corrected for the basis set superposition error. Hydration energies of adenine and formycin are predicted to be lower (in magnitude) than those for the pterin and guanine. Due to these properties, two pterin tautomers can be considered as potentially useful inhibitors of RTA.     

Addition of bromine to 2-methyl-2-azabicyclo[2.2.1]hept-5-ene

Addition of bromine to 2-methyl-2-azabicyclo[2.2.1]hept-5-ene was studied. Unexpectedly, 3-bromo-1-methyl-1-azoniatricyclo[2.2.1.0^2,6]heptane tribromide was isolated rather than the product of bromine addition to the double bond. The former reacted with the starting alkene in a polar solvent to form the corresponding monobromide.     

Synthesis of Pyrrolo[a]- and Pyrrolo[c]phenanthridine Derivatives and Indolinyl and Indolylsubstituted 6-Phenanthridines

The corresponding Mannich bases have been synthesized by the aminomethylation of 6-methyl-1H-pyrrolo[2,3-a]- and 4-methyl-3H-pyrrolo[3,2-c]phenanthridinium iodides. The interaction of 6-chloro-phenanthridine with indoline and with 5-amino-N-acetylindoline gave the corresponding derivatives of phenanthridine. 6-(1-Indolyl)phenanthridine has been obtained by the dehydrogenation of 6-(1-indolinyl)phenanthridine with manganese dioxide.