CHAOS FOR MIXING TRANSFORMATIONS

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Stochastic flows on the boundaries of SL(n,R)

Summary We study the asymptotic stability of the stochastic flows on a class of compact spaces induced by a diffusion process in SL(n, R) or GL(n, R). These compact spaces are called boundaries of SL(n, R), which include SO(n), the flag manifold, the sphereS ⁿ–1 and the Grassmannians. The one point motions of these flows are Brownian motions. For almost every, , we determine the set of stable points. This is a random open set whose complement has zero Lebesgue measure. The distance between any two points in the same component of this set tends to zero exponentially fast under the flow. The Lyapunov exponents at stable points are computed explicitly. We apply our results to a stochastic flow onS ⁿ–2 generated by a stochastic differential equation which exhibits some nice symmetry.Research supported in part by Hou Yin Dong Education Foundation of China On leave from Nankai University, Tianjin, China     

Dianion approach to chiral cyclopropene carboxylic acids

[reaction: see text] In this Letter, we describe a general method for preparing the dianions of cyclopropene carboxylic acids, and we show that their subsequent reactions with electrophiles provide a general means for selectively introducing diverse types of functional groups. This provides a general method for the synthesis of chiral 1,2-disubstituted cyclopropenes, and opens new avenues for the enantioselective preparation of cyclopropenes.     

The 4051-Angstroms band of C3 (A 1Piu-X 1Sigmag +, 000-000): perturbed low-J lines and lifetime measurements

Rotational analyses have been carried out at high resolution for the 000-000 and 000-100 bands of the A (1)Pi(u)-X (1)Sigma(g) (+) transition of supersonic jet-cooled C(3). Two different spectra have been recorded for each band, using time gatings of 20-150 and 800-2300 ns. At the shorter time delay the spectra show only the lines observed by many previous workers. At the longer time delay many extra lines appear, some of which have been observed previously by [McCall et al.Chem. Phys. Lett. 374, 583 (2003)] in cavity ring-down spectra of jet-cooled C(3). Detailed analysis of these extra lines shows that at least two long-lived states perturb the A (1)Pi(u), 000 state. One of these appears to be a (3)Sigma(u) (-) vibronic state, which may possibly be a high vibrational level of the b (3)Pi(g) state, and the other appears to be a P = 1 state with a low rotational constant B. Our spectra also confirm the reassignment by McCall et al. of the R(0) line of the 000-000 band, which is consistent with the spectra recorded towards a number of stars that indicate the presence of C(3) in the interstellar medium. Fluorescence lifetimes have been measured for a number of upper-state rotational levels. The rotational levels of the A (1)Pi(u) state have lifetimes in the range of 230-190 ns, decreasing slightly with J; the levels of the perturbing states have much longer lifetimes, with some of them showing biexponential decays. An improved value has been obtained for the nu(1) vibrational frequency of the ground state, nu(1) = 1224.4933 +/- 0.0029 cm(-1).     

Chemistry of O-Benzoquinones and Masked O-Benzoquinones IV. Synthesis of O-Spirodienonelactones from Unsymmetric Catechols

We describe the syntheses of 6, 8-di-tert-butyl-, 7, 9-di-tert-butyl., 6,7-di-n-propyl and 8, 9-di-n-propyl-O-spirodienonelactone from 3, 5-di-tert-butylcatechol and 3, 4-di-n-propylcatechol.     

掺铬铝酸钇红色颜料的合成、结构和性能表征

研究了高温固相合成制备掺铬铝酸钇红色颜料的方法，着重考察了灼烧温度（1000-1400℃）、灼烧时间（1-2h）、主要原料配比（Al／Y：1：0．5—1：1．5，Cr2O3％：0．3％-5％）等实验条件对产物结构和色泽的影响。XRD等方法对样品进行的相态分析表明，主相为铝酸钇石榴石相；运用反射光谱对红色颜料的色泽进行了反射峰位和相关强度的表征。当Y2O3：Al2O3摩尔比为1：1，掺杂3％的Cr2O3作显色剂，在少量矿化剂存在时，在1300℃下灼烧1 h，得到了色坐标为x=0．577，Y=0．401的红色陶瓷颜料。     

The First New Hydrogen-Bonded Heterohexanuclear Complex [(salen)Cu]4[(salen)Fe(H2O)2]2(ClO4)2: Molecular and Crystal Structure and Magnetic Properties

The preparation, magnetic properties, and crystal structure of [(salen)Cu]₄[(salen)Fe(H₂O)₂]₂(ClO₄)₂ via hydrogen bonding are described [salen=N,N-ethylenebis (salicylideneiminate)]. Crystals are triclinic, of space group , with cell constants a=12.853(3), b=13.921(3), c=14.251(3) Å, =68.68(3)°, =87.86(3)°, =86.82(3)°, and Z=1. The structure was solved and refined to R=0.064 and R=0.068. The structure comprises the hexanuclear units which result from the linking of four mononuclear fragments [(salen)Cu] and two mononuclear fragment [(salen)Fe(H₂O)]⁺, through Cu -O H -O -Fe -O -H O -Cu hydrogen bonds of coordinating H₂O. In this complex, Fe^III ions are in almost square-planar surroundings. The temperature dependences of the magnetic susceptibilities of the complex have been studied in the 4.2–300 K range, indicating the presence of an antiferromagnetic interactions between metal ions.     

特征线法在求解非线性液相吸附色谱模型中的应用

本文应用特征线法求解非线性液相吸附色谱分离过程模型，论述了特征线法的原理和步骤，讨论了时间步长和空间步长对模型数值解的影响，并用色谱分离甘露醇和山梨醇以及分离蔗糖和还原糖的实验进行验证，用特征线法计算的理论流出曲线与实验流出线吻合较好。本文还分折了模型中各个参数的灵敏度，结果表明：吸附等温方程Q＝Ci*／（ai＋biCi*）中参数ai比参数bi以及总传质系数ki有更高的灵敏度。