A semi-analysis method of differential equations with variable coefficients under complicated boundary conditions

IntroductionInthemostcases,asfarasthesolutiontothedifferentialequationwithvariablecoefficientsisconcerned ,therehasbeennoanysatisfactoryanswer.Forthisreason ,thescholarsbothathomeandabroadhavedonesomeresearchjustasindicatedinRefs.[1 ] ,[2 ]and [3 ] ,etc.Theauthorsinthispaperhaveusedthefiniteelementmodelandthemetricfunctiontheoryincombinationwithadjustableparametermodelwithvariablecoefficientstosimplifythesolutiontothedifferentialequationwithvariablecoefficientsintothefeaturevalueaswellasthefea…     

Unfolding of multiparameter equivariant bifurcation problems with two groups of state variables under left-right equivalent group

Introduction Intheunfoldingtheoryofbifurcationproblems,Refs.[1-6]providedvariousversionsof theversalunfoldingtheorem.Itispointedoutthattheequivalentrelationadoptedintheabove mentionedreferencesiscontactequivalencederivedfromthesingularitytheoryofsmoothmap…     

Computational model for short-fiber composites with eigenstrain formulation of boundary integral equations

A computational model is proposed for short-fiber reinforced materials with the eigenstrain formulation of the boundary integral equations （BIE） and solved with the newly developed boundary point method （BPM）. The model is closely derived from the concept of the equivalent inclusion Of Eshelby tensors. Eigenstrains are iteratively determined for each short-fiber embedded in the matrix with various properties via the Eshelby tensors, which can be readily obtained beforehand either through analytical or numerical means. As unknown variables appear only on the boundary of the solution domain, the solution scale of the inhomogeneity problem with the model is greatly reduced. This feature is considered significant because such a traditionally time-consuming problem with inhomogeneity can be solved most cost-effectively compared with existing numerical models of the FEM or the BEM. The numerical examples are presented to compute the overall elastic properties for various short-fiber reinforced composites over a representative volume element （RVE）, showing the validity and the effectiveness of the proposed computational modal and the solution procedure.     

Spin coupling in shake-up processes

The treatment of spin coupling in calculations of shake-up states in core photoelectron processes is reviewed and the problems arising when the equivalent core approximation is used to model the core hole are discussed. A method for approximating the intensity of the triplet-coupled doublet state in semiempirical calculations is proposed. The intensities of the triplet-coupled doublet states in N₂, formaldehyde, and aniline core ionization spectra are calculated. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 63: 189–196, 1997     

Treatment of multibody interactions in molecular simulations of systems with general bond networks

One of the most formidable difficulties in the computer programming of molecular simulations is the sometimes complicated bookkeeping required for keeping track of internal coordinates and their derivatives. A completely general method for keeping track of stretch (two-body), bend (three-body), and torsion, wag, and other four-body interactions for ANY bond network is presented. Computer code using this method for calculating internal coordinates and their derivatives can be used for completely different types of bond networks, no matter how complex, with little or no modification. The method is designed to incorporate recent improved formulas for calculating internal coordinates and their derivatives to ensure the most optimal calculation sequence. © 1997 John Wiley & Sons, Inc. J Comput Chem 18 : 1513–1522, 1997     

Comparison of Different Extraction Solvents for Characterization of Antioxidant Potential and Polyphenolic Composition in Boletus edulis and Cantharellus cibarius Mushrooms from Romania

Edible mushrooms are well-known for their nutritional benefits and low energy density. In addition, mushroom extracts contain various bioactive compounds that account for their antioxidant activity; the applied extraction conditions influence the extraction efficiency of such compounds. Therefore, this study investigates the effects of four extractants on the content of polyphenols and antioxidant properties of Boletus edulis and Cantharellus cibarius mushrooms, aiming to optimize the extraction process. Powders of B. edulis and C. cibarius mushrooms were subjected to extraction with acidic water (10% CH₃COOH), ethanol/water/acetic acid (15:76.5:8.5, v/v/v), hexane, and diethyl ether to measure their total phenolic content (TPC), total flavonoid content (TFC), and Trolox equivalent antioxidant capacity (TEAC). Furthermore, the level of individual polyphenolic compounds in these extracts was quantified using an HPLC-DAD-ESI-MS method. Results showed that the type of solvent significantly influenced the TPC and TEAC of mushroom powder but insignificantly influenced the TFC. A very strong positive correlation was found between TPC and TEAC, but no correlation was found between TFC and TEAC or TPC and TFC. Acidic water extracted the highest amount of polyphenolic compounds from these mushroom powders. Therefore, the aqueous extract showed the highest TPC and strongest antioxidant activity. Thus, acidic water is recommended for polyphenol analysis in B. edulis and C. cibarius mushrooms.     

硬脂酸二茂铁酯L-B膜修饰SnO2电极的阻抗研究

测定了二茂铁衍生物——硬脂酸二茂铁酯L-B膜修饰SnO₂电极在Fe(CN)₆^3-/4-溶液中的阻抗性能,用单纯形法求出了等效电路中的元件参数值,计算了电极反应速度常数K_s。从分析SnO₂电极修饰不同层的硬脂酸二茂铁酯L-B膜的界面阻抗和电极反应的动力学性能,表明与在固相中研究的硬脂酸二茂铁酯L-B膜的阻抗性能明显不同,在Fe(CN)₆^3-/4-溶液中表现了电活性分子修饰电极的界面阻抗行为,进一步证实了修饰在SnO₂电极上的硬脂酸二茂铁酯L-B膜在Fe(CN)₆^3-/4-的氧化还原电极反应过程中,起电荷传递的中介作用。     

The linearization of certain class of nonlinear simultaneous equation set containing amplitude and phase frequency characteristics and application

A class of complex function of rational fraction type is frequently used to describe the dynamical properties of systems. It is however quite difficult to establish a mathematical model of this type on the basis of amplitude and phase frequency data collected from experiments conducted on the related physical system. Since the erection of mathematical model G(j) would involve the solution of a set of nonlinear simultaneous equations with the unknown coefficients a_is and b_is(i=0, 1, ..., m, ..., n) in G(j). Up to now, these nonlinear equations have been considered to be very difficult to solve directly. In spite of the fact there are special computer programmes in certain software packages available to tackle this problem, it is by no means an easy task due to the complex procedures involved in picking up a set of initial values that should be close enough to the exact solutions. This paper proposes a simplified method of linearizing these nonlinear equations set so that direct solution is possible. The method can also be applied to systems with factors of (j) andej0 in G(j). An illustration by a workable example is furnished at the end of this paper to show its versatility.     

一个-4齐次核的Hilbert型积分不等式

通过引入双参数及应用权函数的方法,建立一个核为-4齐次的Hilbert型积分不等式及等价式,并证明其常数因子为最佳值．作为应用,给出其逆向形式及一些特殊结果．     

The nonlinear propagation of acoustic waves in a viscoelastic medium containing cylindrical micropores

Based on an equivalent medium approach, this paper presents a model describing the nonlinear propagation of acoustic waves in a viscoelastic medium containing cylindrical micropores. The influences of pores' nonlinear oscillations on sound attenuation, sound dispersion and an equivalent acoustic nonlinearity parameter are discussed. The calculated results show that the attenuation increases with an increasing volume fraction of micropores. The peak of sound velocity and attenuation occurs at the resonant frequency of the micropores while the peak of the equivalent acoustic nonlinearity parameter occurs at the half of the resonant frequency of the micropores. Furthermore, multiple scattering has been taken into account, which leads to a modification to the effective wave number in the equivalent medium approach. We find that these linear and nonlinear acoustic parameters need to be corrected when the volume fraction of micropores is larger than 0.1%.