Potential non-steroidal estrogens and antiestrogens,IV Organic azides in heterocyclic synthesis,part 13: Synthesis of aza- and diazacoumestrols via azido derivatives

Summary 4-Chloro-3-aryl-coumarins and quinolones2 a–e undergo thermolytic ring closure by reaction with sodium azide in refluxing dimethyl formamide to yield indolo[3,2-c]coumarins and indolo[3,2-c]quinolin-6(5H)-ones6 a–e. In the case of the coumarin2 a the azido coumarin5 can be isolated. The mono- and diazacoumestrol-dimethylethers6 a–c are converted into the coumestrol analogues7 a–c and their diacetyl derivatives8 a–c.

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Potentielle nichtsteroidale Östrogene und Antiöstrogene, 4. Mitt.: Organische Azide in der Heterocyclensynthese, Teil 13: Synthese von Aza- und Diazacumöstrolen über Azidzwischenstufen

Zusammenfassung 4-Chlor-3-arylcumarine und-chinolone2 a–e reagieren thermolytisch mit Natriumazid in siedendem Dimethylfomamid unter Ringschluß zu Indolo[3,2-c]cumarinen und Indolo[3,2-c]chinolin-6(5H)-onen6 a–e. Nur aus dem Cumarinderivat2 a kann das zwischenzeitlich gebildete Azidocumarin5 isoliert werden. Die so erhaltenen Mono- und Diazacumöstroldimethylether6 a–c werden in die entsprechenden Cumöstrole7 a–c und ihre Diacetylderivate8 a–c umgewandelt.

     

Monolayer adsorption isotherms and a disordered medium model

A model of disordered medium is proposed to describe the monolayer adsorption isotherm on heterogeneous surfaces. The model is based on the premise that adsorption medium consists of separate regions in each of which there is a permanent local equilibrium constant, the character of the changes of which is determined by the disorder parameter of the medium. __________ Translated from Teoreticheskaya i éksperimental’naya Khimiya, Vol. 42, No. 3, pp. 189–193, May–June, 2006.     

无穷积分余项与其被积函数比值的收敛阶

对一类函数的无穷积分余项与该函数的比值得到当x趋于无穷大时的收敛阶,这类函数是幂函数与指数函数的乘积函数,并将其应用到Mittag-Leffler函数.同时考虑了对应的级数情形.     

On the two methods of kinetic theory of ECRM

The kinetic theory based on the expansion of local field in the guiding center coordinate system, presented by paper[1]–[3], has successfully developed into a theoretical system. The mathematical background and physical explanation of setting up the guiding center coordinate system is expounded in the paper. By using the methods of the guiding center and waveguide coordinate systems respectively, the same dispersion equations for interaction of an axially symmetrical single momentum electron beam with TE_mn field in the circular waveguide are rigorously derived. A number of mistakes in paper[4] are indicated as well.     

一类多维的非线性Schrdinger方程组的初边值问题

本文考虑一类具有耗散与磁场效应的多维非线性Schrdinger型方程组的初边值问题。使用积分估计(包括L~p—L~q估计)证明了整体解的存在性。     

Bernoulli泛函空间中广义计数算子的表示

得到离散时间正规鞅平方可积泛函空间L^{\mathrm{2}}(M)中广义计数算子N_h的5种表示：（1）量子Bernoulli噪声（quantum Bernoulli noises,QBN）\{{?}_k,{?}_k^{\mathrm{*}};k\ge \mathrm{0}\}的加权表示;（2）N_h的谱表示,广义计数算子N_h以h-计数测度{\#}_h的值域为其点谱;（3）N_h的“对角化”表示,N_h可表示为L^{\mathrm{2}}(M)的标准正交基\{Z_{\sigma };\sigma \in \mathrm{\Gamma }\}所生成的一维对角化正交投影算子的加权极限;（4）广义Skorohod积分-广义随机梯度表示,N_h可表示为互共轭算子{\delta }_h和{?}_h的复合算子;（5）对\mathbf{N}上的任意非负函数h,可构造一列有界广义计数算子,N_h恰为该有界广义计数算子的强极限,当h可和时,N_h为该有界广义计数算子的一致极限。     

A fast directional algorithm for high-frequency electromagnetic scattering

This paper is concerned with the fast solution of high-frequency electromagnetic scattering problems using the boundary integral formulation. We extend the O(N log N) directional multilevel algorithm previously proposed for the acoustic scattering case to the vector electromagnetic case. We also detail how to incorporate the curl operator of the magnetic field integral equation into the algorithm. When combined with a standard iterative method, this results in an almost linear complexity solver for the combined field integral equations. In addition, the butterfly algorithm is utilized to compute the far field pattern and radar cross section with O(N log N) complexity.     

Limit Cycles Bifurcating from a k-dimensional Isochronous Center Contained in ?n with k ? n

The goal of this paper is double. First, we illustrate a method for studying the bifurcation of limit cycles from the continuum periodic orbits of a k-dimensional isochronous center contained in ℝ ⁿ with n ⩾ k, when we perturb it in a class of differential systems. The method is based in the averaging theory. Second, we consider a particular polynomial differential system in the plane having a center and a non-rational first integral. Then we study the bifurcation of limit cycles from the periodic orbits of this center when we perturb it in the class of all polynomial differential systems of a given degree. As far as we know this is one of the first examples that this study can be made for a polynomial differential system having a center and a non-rational first integral. The first and third authors are partially supported by a MCYT/FEDER grant MTM2005-06098-C01, and by a CIRIT grant number 2005SGR-00550. The second author is partially supported by a FAPESP–BRAZIL grant 10246-2. The first two authors are also supported by the joint project CAPES–MECD grant HBP2003-0017.     

非线性耗散对亚稳态系统量子衰变速率的影响

发展了一种快速傅里叶变换路径积分方法，研究非线性耗散系统的量子衰变速率，得到了Bounce轨道的作用量S_B，即衰变速率的指数因子.在系统与环境存在非线性耦合f(x)=tanh［λ(x-x_b)］的情形下，发现其对衰变速率具有抑制作用.指数因子随温度T的关系不再满足S_B=a［1-b(T/T_c)²］法则；与通常的线性耗散情形相比，跨越温度T_c回升，即系统更早地进入穿透区域. 关键词： 量子衰变 非线性耦合 路径积分 快速傅里叶变换