Existence of positive solutions for three-point boundary value problems at resonance

With the help of the theorem of a fixed point index for A-proper semilinear operators established by Cremins, we get a existence theorem concerning the existence of positive solution for the second order ordinary differential equation of three-point boundary value problems at resonance.     

Lanthanide Complexes for Oligomerization of Phenyl Isocyanate

IntroductionThestudyonthereactivitiesoflanthanidecomplexesto wardisocyanateshasattractedmuchattention .Ithasbeenre portedthatlanthanidealkoxides,1anddivalentdiaza pentadi enyllanthanidecomplexes2 canbeusedasthesinglecompo nentinitiatorsforisocyanatespolymerization .Recentlyourre searchgrouphasalsofoundthatlanthanoceneamide ,3diva lentaryloxideofsamarium4 ,5anddivalentsamarocene6 areallactivefortheoligomerizationofphenylisocyanate,andtheactivespeciesforthesethreesystemswereallsuccessfullyisolat…     

Henry Reaction in Aqueous Media：Chemoselective Addition of Aldehydes

The chemoselective addition of aldehydes in aquoues medium was obtained under mild condition using improved Henry reaction.     

Synthesis,and Antimycobacterial and Cytotoxic Evaluation of Certain Fluoroquinolone Derivatives

Certain 1‐ethyl‐ and 1‐aryl‐6‐fluoro‐1,4‐dihydroquinol‐4‐one derivatives were synthesized and evaluated for antimycobacterial and cytotoxic activities. Preliminary results indicated that, for 1‐aryl‐6‐fluoroquinolones, both 7‐(piperazin‐1‐yl)‐ and 7‐(4‐methylpiperazin‐1‐yl) derivatives, 9b and 11a , are able to completely inhibit the growth of M. tuberculosis at a concentration of 6.25 μg/ml, while the 7‐[4‐(2‐oxo‐2‐phenylethyl)piperazin‐1‐yl] derivative 13 exhibits only 31% growth inhibition at the same concentration. For 1‐ethyl‐6‐fluoroquinolones, both 7‐[4‐(2‐oxopropyl)piperazin‐1‐yl]‐ and 7‐[4‐(2‐oxo‐2‐phenylethyl)piperazin‐1‐yl]‐derivatives, 2a and 2b , respectively, show complete inhibition, while their 2‐iminoethyl and substituted phenyl counterparts 3a and 2c are less active. In addition, the 6,8‐difluoro derivative was a more‐favorable inhibitor than its 6‐fluoro counterpart ( 2b vs. 2d ). These results deserve full attention especially because 2a, 2b, 9b , and 11a are non‐cytotoxic at a concentration of 100 μM . Furthermore, compound 9b proved to be a potent anti‐TB agent with selective index (SI)>40 and an EC₉₀ value of 5.75 μg/ml.     

Probabilistic and Average Linear Widths of Sobolev Space with Gaussian Measure in L \infty-Norm

In this paper we investigate the probabilistic linear $(n,\delta)$-widths and $p$-average linear $n$-widths of the Sobolev space $W^r_2$ equipped with the Gaussian measure $\mu$ in the $L_{\infty}$-norm, and determine the asymptotic equalities \begin{eqnarray*} \lambda_{n,\delta}(W^r_2,\mu,L_{\infty}) &\asymp&\frac{\sqrt{\ln (n/\delta)}}{n^{r+(s-1)/2}},\\[3pt] \lambda^{(a)}_n(W^r_2,\mu,L_{\infty})_p &\asymp&\frac{\sqrt{\ln n}}{n^{r+(s-1)/2}}, \qquad 0 < p < \infty. \end{eqnarray*}     

Partial Differential Equations in Conformal Geometry

In this paper we present our recent work on conformally compact Einstein 4-manifolds. We present our discovery of a conformal compactification by positive eigenfunctions and many interesting consequences of this compactification in the study of topology of conformally compact Einstein 4-manifolds.     

Preparation of nanometer MgO by sol-gel auto-combustion

Nanometer MgO was prepared via a sol-gel auto-combustion technique using magnesium nitrate as raw material and citric acid as chelating agent. IR spectra of the dried gel were used to investigate the structure of the precursors. By studying the different TG curves of magnesium citrate gel prepared by different methods, we found that a combustion process occurred and the nitrate ions acted as an oxidant in the combustion process. TEM photographs of synthesized powders from the sol-gel auto-combustion showed that the crystallites were uniform in size. In addition, the XRD pattern of this sample showed that the particle size was 8.9 nm. The BET curves, in turn, showed that the specific surface of the sample was 26.34 m²/g. The mechanism of the frothing process in restraining agglomeration is discussed. __________ Translated from Journal of East China Normal University (Natural Science), 2007, (2): 52–57 [译自: 华东师范大学学报(自然科学版)]     

Na离子和Cl离子引起He原子直接多重电离过程的研究

利用2～8 MeV的Naq+、Clq+(q=2,3,4,5)轰击氦原子,对碰撞的直接多重电离过程进行研究.实验采用反冲离子-散射离子飞行时间符合技术,通过反冲离子飞行时间谱区分不同价态反冲离子;利用静电偏转和位置灵敏探测技术区分不同电荷态散射离子;结合CAMAC-PC多参数获取系统得到一定价态散射离子所对应的反冲离子电荷态分布谱;经分析该谱得到直接多重电离截面与直接单电离截面之比R21.讨论了R21随入射离子速度和电荷态的变化关系.     

Rough隶属函数关于集合并与交的一种高精度计算方法

近些年来，许多处理近似问题的方法陆续被提出，其中利用Rough集理论计算两个集合的并和交的Rough隶属函数方法是被用较多的一种方法，但毕竟该方法精度较差。为此，介绍了一种精度较高的计算两个集合的并和交的Rough隶属函数方法，它克服了前者利用Rough集理论计算Rough隶属函数的复杂性，而迎来了简单和高精度的特点。     

Ultrasonic investigation of amorphous carbon in various frequencies at low temperatures from 2.1 to 300 K

Using pulse echo overlap measurement, the elastic behavior of amorphous carbon has been studied at ambient and low temperatures. The smaller ratio B/G of the bulk modulus to shear modulus and smaller Poisson's ratio σ at room temperature indicate that there is an intrinsic stiffening of transverse acoustic phonons in the amorphous carbon. The acoustic velocity and attenuation for longitudinal modes have been measured between 2.1 and 300 K at three frequencies of 7, 21 and 35 MHz, respectively. Their frequency and temperature dependence are observed. The elastic constant C₁₁ increases with decreasing temperature and show enhanced stiffening at low temperatures. In the 130-220 K region, the abnormal change and effect of longitudinal velocity and attenuation with temperature and frequency, and a phase transition associated with structure relaxations are discussed.