FeBr_3-catalyzed dibromination of alkenes and alkynes

The dibromination of alkenes and alkynes with bromosuccinimide and sodium bromide catalyzed by FeBr₃ under mild conditions has been developed.The trans-dibromo compounds were exclusively obtained with excellent yields.     

Translocation versus cyclisation in radicals derived from N-3-alkenyl trichloroacetamides

Under radical reaction conditions, two different and competitive reaction pathways were observed for N-(α-methylbenzyl)trichloroacetamides with a N-3-cyclohexenyl substituent: 1,4-hydrogen translocation and radical addition to a double bond. However, for radicals with an acyclic alkenyl side chain, the direct cyclisation process was exclusively observed. The dichotomy between translocation and direct radical cyclisation in these substrates has been theoretically studied using density functional theory (DFT) methods at the B3LYP/6-31G** computational level.     

Computational study of FOX‐7 synthesis in a solvated reaction system

Ethene and two kinds of nitrating reagents (HNO₃ and N₂O₅) in a variety of solvents were included in respective molecular systems, and each underwent a two‐stage electrophilic and free radical nitro‐substitution reaction to obtain the corresponding nitroethene compounds. Subsequent halogenation (using Cl₂ and Br₂) and amination (using NH₃) were then performed in solvents, also by electrophilic and radical substitution, to produce the desired 1,1‐diamino‐2,2‐dinitroethene (FOX‐7) derivatives. The reaction energy barrier in the nitration stage for obtaining each kind of mononitro ethene exhibited a stepwise decreasing trend when the reaction was carried out in H₂O‐solvated and CH₃OH‐solvated systems, no matter what nitrating agent was used. Related energy barrier data showed that the nitration reaction is more feasible in an H₂O‐solvated than a CH₃OH‐solvated system. The modeling results suggested that N₂O₅ is the better agent for nitration to proceed in water, bromine is suitable for halogenation, and the bromine derivatives are convenient for further amination in an H₂O‐solvated system. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Structure-property relations in crystalline L-leucine obtained from calorimetry, X-rays, neutron and Raman scattering

We have studied the amino acid L-leucine (LEU) using inelastic neutron scattering, X-rays and neutron diffraction, calorimetry and Raman scattering as a function of temperature, focusing on the relationship between the local dynamics of the NH(3), CH(3), CH(2) and CO(2) moieties and the molecular structure of LEU. Calorimetric and diffraction data evidenced two novel phase transitions at about 150 K (T(1)) and 275 K (T(2)). The dynamical susceptibility function, obtained from the inelastic neutron scattering results, shows a re-distribution of the intensity of the vibrational bands that can be directly correlated with the phase transitions observed at T(1) and T(2), as well as with the already reported phase transition at T(3) = 353 K. Through the analysis of the Raman modes, the new structural arrangement observed below T(1) was related to conformational modifications of the CH and CH(3) groups, while the behavior of the N-H stretching vibration, ν(NH(3)), gave insight into the intermolecular N-H…O interactions. The observation of changes in the translational symmetry in the crystalline lattice, as well as anharmonic dynamics, allows for localized motions in LEU.     

On the numerical solution of large-scale sparse discrete-time Riccati equations

We discuss the numerical solution of large-scale discrete-time algebraic Riccati equations (DAREs) as they arise, e.g., in fully discretized linear-quadratic optimal control problems for parabolic partial differential equations (PDEs). We employ variants of Newton??s method that allow to compute an approximate low-rank factor of the solution of the DARE. The principal computation in the Newton iteration is the numerical solution of a Stein (aka discrete Lyapunov) equation in each step. For this purpose, we present a low-rank Smith method as well as a low-rank alternating-direction-implicit (ADI) iteration to compute low-rank approximations to solutions of Stein equations arising in this context. Numerical results are given to verify the efficiency and accuracy of the proposed algorithms.     

Approximation of the Fractional Schrödinger Propagator on Compact Manifolds

Let L be a second order positive, elliptic differential operator that is self-adjoint with respect to some C~∞ density dx on a compact connected manifold M. We proved that if 0 α 1,α/2 s α and f ∈ H~s(M) then the fractional Schr?dinger propagator e~(it Lα/2) on M satisfies e~(it Lα/2) f(x)-f(x) = o(t~(s/α-ε)) almost everywhere as t → 0~+, for any ε 0.     

Contribution of UV light to the decomposition of toluene in dielectric barrier discharge plasma/photocatalysis system

The contribution of UV light from plasma and an external UV lamp to the decomposition of toluene in a dielectric barrier discharge (DBD) plasma/UV system, as well as in a plasma/photocatalysis system was investigated. It was found that UV light from the DBD reactor was very weak. Its contribution to the removal of toluene in the plasma/photocatalysis system could be ignored. Whereas, the introduction of external UV light to the plasma significantly improves the removal efficiency of toluene by 20%. The removal efficiency of toluene in the plasma/photocatalysis system increased about 22% and 16% when compared with a plasma only system and plasma driven photocatalyst system, respectively. The increased toluene removal efficiency was mostly attributed to the contribution of the synergy between plasma and UV light, but not to the synergy between plasma and photocatalysis. The synergetic effect between plasma and photocatalysis was not significant.     

直线上函数的Banach空间的Poincaré型不等式的变分公式

基于研究对数Sobolev,Nash和其它泛函不等式的需要,将Poincare不等式 的变分公式拓广到一大类直线上函数的Banach(Orlicz)空间.给出了这些不等式成立 与否的显式判准和显式估计. 作为典型应用,仔细考察了对数Sobolev常数.