关于极限理论的学习经验

分析极限理论在数学分析学习中的重要性，介绍学习极限理论的三点经验与体会，即充分理解基本内容；加强基本功训练；试着多问自己一些问题，学会举出各种各样的例子。     

Nonstandard Finite Difference Schemes for Differential Equations

This paper gives an introduction to nonstandard finite difference methods useful for the construction of discrete models of differential equations when numerical solutions are required. While the general rules for such schemes are not precisely known at the present time, several important criterion have been found. We provide an explanation of their significance and apply them to several model ordinary and partial differential equations. The paper ends with a discussion of several outstanding problems in this area and other related issues.     

Synthese et Etude Structurale D'acides Alkylphosphoniques a Longue Chaine Hydrocarbonee

Long-chain dialkyl alkylphosphonates were synthesized by radical addition of dialkyl hydrogenphosphonates onto alkenes in presence of di(t-butyl) peroxide. This synthetic route leads to high yields between 94 and 97%. We performed chemical modifications of these phosphonates in order to obtain acidic derivatives. The structure of these compounds was characterized by NMR analyses and mass spectroscopy. We also studied their thermal behaviour and various crystalline phases were put in evidence by differential scanning calorimetry and optical microscopy. The thermal stability of these compounds was compared by thermogravimetric analyses.     

Orthogonal Wavelets Analysis of Electroanalytical Signals

ABSTRACT

A signal processing technique based on orthogonal wavelet analysis is applied to process various simulated electroanalytical signals. The results indicate that if the scale parameters are selected, the orthogonal wavelet processing method (OWPM) can remove high-frequency noise. Experimental signal was recorded by computer and used to test the OWPM procedure. After processing with OWPM, the processed data was used to analyze the mechanism of the electrode reactions. Processed results of the experimental data are also satisfactory.     

On Felbin-type Fuzzy 2-normed Spaces and Its Fuzzy Ⅰ-topologies

In this paper using the concept of Felbin-type fuzzy 2-norm ‖.,.‖ on a vector space,two Ⅰ-topologies τ‖.,.‖ and τ*‖.,.‖ is constructed.After making our elementary observations on this fuzzy Ⅰ-topologie...     

Discriminant Analysis of Selected Organics Evaluated as Corrosion Inhibitors in 0.5 M HCL

Abstract

Discriminant analysis can be used to (1) find criteria to separate observations into groups and (2) to optimally assign a new observation to its correct group. It is rather exploratory in nature especially when causal relationships are not known. Twenty four selected organics were tested as corrosion inhibitors and both physical and structural features were encoded as criteria for discrimination. In addition, a narrower set of twelve nitrogen containing compounds was also studied. In both cases the carbon chain length was an important uncoded criterion. The physical factors such as boiling point, molecular weight, pKa, and molecular area were not as important as some of the structural parameters.     

Controllability of Nonsmooth Discrete Systems with Delay

This paper is concerned with a study of local controllability to discrete inclusions with delay. The sufficient conditions for relative and complete local controllability are obtained on the base of using Mordukhovich's nonsmooth constructions.     

Structure of the Polymer Obtained from Bisphenol-A and Cl 2 P(O)CH 3

Using the step-by-step build-up approach, the possible conformations of compound PhOP(O)(Me)OPh(Me) 2 Ph were constructed and geometrically optimized. Among the obtained structures 32 conformations belonging to low, comparable energy levels were used to construct the most stable dimers and tetramers of the title polymer. The results allowed us to estimate the geometrical structure of the polymer.     

EFFECT OF MAGNESIUM COMPLEXATION ON THE 31P MIDDLE-GROUP CHEMICAL SHIFTS OF CHAIN AND RING PHOSPHATES

Abstract

For pure sodium polyphosphates, Na _{n + 2}P _n O_{3n + 1}, exhibiting 3 through 6 phosphorus atoms per molecule, the ³¹P chemical shift of the middle group phosphorus atoms as measured in aqueous solution (0.1 M in P) at pH 7 was seen to increase with increasing magnesium ion concentration until there was one Mg atom per polyphosphate molecule, after which the chemical shift decreased. Finally the rate of decrease diminishes and precipitation occurs. For the longer-chain phosphates, Na _{n + 2}P _n O_{3n + 1} with n = 8, 9, 10, or an average of 100, as well as for the ring phosphates, Na _n P _n O_3n for n ranging from 3 through 10, an increase in magnesium concentration simply leads to a decrease in chemical shift which diminishes at the higher concentrations. These data lend additional support to the concept that polymerized phosphate anions in solution exist in preferred conformations which depend on the nature of the counteraction.