Fourier regularization for a backward heat equation

In this paper a simple and convenient new regularization method for solving backward heat equation—Fourier regularization method is given. Meanwhile, some quite sharp error estimates between the approximate solution and exact solution are provided. A numerical example also shows that the method works effectively.     

Results of the maximum genus of graphs

In this paper,we provide a new class of up-embeddable graphs,and obtain a tight lower bound on the maximum genus of a class of 2-connected pseudographs of diameter 2 and of a class of diameter 4 multi-graphs.This extends a result of Skoviera.     

Covalent functionalization of multi-walled carbon nanotubes by lipase

Lipase from Candida rugosa was covalently anchored onto acid-treated multi-walled carbon nanotubes (MWNTs) through a self-catalytic mechanism. A variety of characterization techniques including FTIR, Raman spectroscopy, and XPS were employed to demonstrate the formation of the ester linkage between lipase and MWNTs. The MWNTs-lipase biocomposites showed significantly increased solubility in some common-used organic solvents, such as THF, DMF and chloroform. This study may offer a novel and facile route for covalent modification of carbon nanotubes, and expand the potential utilization of both lipases and MWNTs in the fields of biocatalyst and biosensor.     

炉液倾动重心近似计算的数学分析

为给转炉设计提供依据,需要计算炉液倾动的重心.利用数学方法将实际问题进行简化,通过分析炉液倾动过程中变量间的相互关系,来确定每个倾动角度对应情况下的液面位置.利用数学中三重积分的有关应用,进一步得出转炉在每个倾动角度为α∈(0,π2)时的重心计算方法及相关结论,在理论上为工程计算重心的方法提供参考.     

Sobolev空间H~s(R~n)上矩阵伸缩的多尺度分析特征刻画

本文对高维Sobolev空间Hs(Rn)上具有矩阵伸缩的多尺度分析特征进行了 刻划,特别给出了稠密性特征的一个充分必要条件,从而解决了文献[4]中提出的一个 问题.所得结果覆盖了这方面的已知结论.     

A study of ion exchange selectivity coefficient by cyclic voltammetric measurement

An equation to express ion exchange selectivity coefficient was derived and used for calculating that of PPY film with the results obtained by cyclic voltammetric measurement. PPY film was synthesized by electrochemical method in aqueous solution using K₄Fe(CN)₆ as supporting electrolyte, and the anions were doped into the film. Ion exchange behaviour of doped Fe (CN)₆^3-/4- in the PPY film with Cl^?, NO₃^? or F^? ions in solution has been studied, and the corresponding ion exchange selectivity coefficients were determined.     

Validation of a method for predicting the precision, limit of detection and range of quantitation in competitive ELISA.

The mathematical model for predicting the precision, limit of detection (LOD) and range of quantitation (ROQ) in a competitive enzyme-linked immunosorbent assay (ELISA) proposed by Hayashi et al. (Anal. Chem., 2004, 76, 1295) was validated. The model describes the relative standard deviation (RSD) of concentration estimates by the RSDs of pipetting volumes of analyte, enzyme-conjugated antigen, antibody and substrate solutions, and the standard deviation (SD) of inherent absorbances between the wells in an ELISA plate. For 6 kinds of direct competitive ELISA kits, the LOD and ROQ predicted by the model agreed well with those obtained by experiments with real samples. It was also confirmed that the model is applicable to the prediction of uncertainty that depends on the pipetting error of the viscous antiserum solution. The model was demonstrated to be useful for estimating the LOD and ROQ of competitive ELISA.     

On the Bounded Complex of an Affine Oriented Matroid

We prove that the bounded complex of an affine oriented matroid is pure and collapsible. We also generalize Zaslavsky's central decomposition theorem for hyperplane arrangements to affine oriented matroids.     

Integrability of det▽u and Evolutionary Wente''s Problem Associated to Heat Operator

In this note, the authors resolve an evolutionary Wente's problem associated to heat equation, where the special integrability of det▽u for u ∈ H1(R2,R2) is used.