COMPOSITE LEGENDRE-LAGUERRE APPROXIMATION IN UNBOUNDED DOMAINS

1. IntroductionMany problems in science aam engineering are set in unbounded domains. There are severalways for their numerical simulatiolls. We may restrict calculations to some bounded domainswith certain artificial boundary conditions. But they induce errors. In particular, they ductshe wave Propagations in revolutionary problems. In opposite, if we use'spectral methods assorted with orthogonal systems of polynomials in Unbounded domains, then we could avoid tabstrouble, e.g., see Mad'ay,…     

Spectral methods for pantograph-type differential and integral equations with multiple delays

We analyze the convergence properties of the spectral method when used to approximate smooth solutions of delay differential or integral equations with two or more vanishing delays. It is shown that for the pantograph-type functional equations the spectral methods yield the familiar exponential order of convergence. Various numerical examples are used to illustrate these results.      

Approximations of spectra of Schrödinger operators with complex potentials on ℝd

We study spectral approximations of Schrödinger operators T = ?Δ+Q with complex potentials on Ω = ?^d, or exterior domains Ω??^d, by domain truncation. Our weak assumptions cover wide classes of potentials Q for which T has discrete spectrum, of approximating domains Ω_n, and of boundary conditions on ?Ω_n such as mixed Dirichlet/Robin type. In particular, Re Q need not be bounded from below and Q may be singular. We prove generalized norm resolvent convergence and spectral exactness, i.e. approximation of all eigenvalues of T by those of the truncated operators T_n without spectral pollution. Moreover, we estimate the eigenvalue convergence rate and prove convergence of pseudospectra. Numerical computations for several examples, such as complex harmonic and cubic oscillators for d = 1,2,3, illustrate our results.     

卡氏积图的Laplacian谱半径的上界

对近年来图的Laplacian谱半径上界的研究成果进行了简单梳理.利用2个图的卡氏积图的特征值,讨论了2个循环图的卡氏积图的Laplacian谱半径的上界问题,得到了几个上界,推广了已有文献的结论.     

一种基于特征分解的图像融合方法

一幅图像可以分解成几何特征不同的纹理部分和卡通部分,基于这两大特征提出了一种图像融合方法.利用卡通和纹理特征的差异,通过学习分别得到卡通字典和纹理字典.在融合过程中,分别利用特定的卡通和纹理字典对源图像的卡通和纹理部分进行融合,融合后的卡通和纹理部分经简单相加得到融合图像.实验结果表明,所提方法是有效的.     

磁场对含稀土铝锂合金断裂特征的影响

以含铈铝锂合金为研究对象，研究了磁场对含稀土铝锂合金时效过程的影响，从断裂特征及微观组织两方面分析了磁场作用规律。实验结果表明：未加磁场时，合金的断裂特征以理断裂为主；扁平晶粒厚度不匀，在磁场作用下，此合金的断裂特征与微观组织发生明显改观，随磁感应强度增强，合金主断裂面上准解理断裂特征减弱，同时二次裂纹增多，分层比较升高；扁平晶粒厚度变薄，尺寸趋于均匀。用少体物理理论，探讨了磁场对含稀土合金原子扩散过程的影响，为进一步研究稀土元素在磁场中的行为及其局域效应提供了一定的实验依据。     

New Diterpenoid Alkaloids from Delphinium Souliei Franch

Inourpreviouspapers'-',wehavereportedtheisolationandelucidationofaseriesofnewditerpenoidalkaloidsfromDelphinillnlsolllieiFranch.ContinuedphytochemcalinvestigationsontheconstituentsofthisplanthaveledtotheisolationoftwoothernewditerpenoidalkaloidssoulineE(l)andsoulineF(2).SoulineE(2.6mg)wasobtainedascolorlesscrystals,mpf77-78'C(fromethanol).[a]."8.0(c=0.05,CHCI;).itsmolecularformulaC,=H;,NO,wasderivedfromHkEIMS(M-f361.2613,cafe.361.2608).TheiHnmrspectrum(400MHz)exhibitedthefollowingsign…     

Reaction of Epichlorohydrin with 2-Aminobenzothiazole and Its Derivatives

We have shown that 2-aminobenzothiazoles when reacted with epichlorohydrin form 3-hydroxytetrahydropyrimido[2,1-b]benzothiazolium chlorides, while 2-iminobenzothiazolines form 2-(-chloro--hydroxypropyl)iminobenzothiazolines.     

Synthesis,characterization, density functional theory,X‐ray study,thermal stability,and biological and MOE relevance of metal complexes of griseofulvin

Metal(II) and metal(III) coordination compounds of griseofulvin (GFV) drug were synthesized. The structure of the ligand was determined on the basis of elemental analyses, infrared and ¹H NMR spectroscopies and thermal studies. GFV behaved as a neutral tridentate chelating agent and coordinated to metal ions through three oxygen atoms: two methoxy groups and oxygen atom of furan ring. Metal complexes were characterized by means of elemental analyses and molar conductance, spectral (infrared, electron spin resonance) and thermal studies. All the complexes showed molar conductance behaviour corresponding to an electrolytic nature. All the complexes showed octahedral geometry, except [Zn(GFV)Cl]Cl that showed tetrahedral geometry. Density functional theory (DFT) calculations were employed to understand and estimate the contribution of each interaction in the formation of the assembly using several theoretical models. The computed parameters from DFT calculations for structure optimizations and vibrational frequencies were in good agreement with the experimental data. Newly synthesized metal complexes in addition to GFV were examined against opportunistic pathogens. The biological applications of complexes were studied with two Gram‐positive bacteria (Bacillus subtilis and Staphylococcus aureus) and two Gram‐negative bacteria (Escherichia coli and Neisseria gonorrhoeae) as well as their antifungal activity against Candida albicans. Results suggested that metal complexes were more biologically sensitive than free ligand. The complexes showed a moderate inhibition of MCF7 breast cancer cell line growth. Molecular docking studies further helped in understanding the mode of action of the compounds through their various interactions with the crystal structures of: human serum albumin (PDB: 5FUO), Staphylococcus aureus nucleoside (PDB: 3Q8U), human acetylcholinesterase (PDB: 1B41) and the human DNA–Topo I complex (PDB: 1SC7).     

奥尔堡PBL模式对提升有机波谱分析教学效果的启示

概述了有机波谱分析课程教学中存在的主要问题,介绍了奥尔堡PBL模式的主要特点和优势,分析了将奥尔堡PBL模式用于有机波谱分析课程教学的必要性和可行性,并从课时分配、教学内容、教学方式和考核方式等4方面提出了教学改革方案,旨在提高教学效果。