Carbanion reactivity; studies of σ‐adduct formation from benzyltriflone anions and 4‐nitrobenzofurazan derivatives

¹H NMR studies in DMSO‐d₆ of the reaction of benzyltriflones, 2 , with 4,6‐dinitrobenzofuroxan, 4 , indicate the formation, with or without the presence of added base, of anionic σ‐adducts. Spectra obtained from solutions of 2 and 4‐nitrobenzofurazan, 6a , in the presence of triethylamine are consistent with products formed by the elimination of trifluoromethylsulfinic acid from σ‐adducts initially formed by carbanion attack at the 5‐position of 6a . Kinetic studies of the latter reaction in methanol allow the determination of rate constants for nucleophilic attack by the carbanions at the 5‐position. The low value of β for these reactions together with the failure to observe reaction with 1,3,5‐trinitrobenzene suggest that the benzyltriflone anions have unusually large steric requirements. Copyright © 2007 John Wiley & Sons, Ltd.     

Virtually semisimple modules and a generalization of the Wedderburn-Artin theorem

A widely used result of Wedderburn and Artin states that “every left ideal of a ring R is a direct summand of R if and only if R has a unique decomposition as a finite direct product of matrix rings over division rings.” Motivated by this, we call a module M virtually semisimple if every submodule of M is isomorphic to a direct summand of M and M is called completely virtually semisimple if every submodule of M is virtually semisimple. We show that the left R-module R is completely virtually semisimple if and only if R has a unique decomposition as a finite direct product of matrix rings over principal left ideal domains. This shows that R is completely virtually semisimple on both sides if and only if every finitely generated (left and right) R-module is a direct sum of a singular module and a projective virtually semisimple module. The Wedderburn-Artin theorem follows as a corollary from our result.     

广义Oldroyd-B流体作MHD旋转流动时的精确解

对充满多孔空间的广义Oldroyd-B流体,研究有滑移时磁流体动力学（MHD）的旋转流动．数学建模时采用了分式积分法．给出平板振荡和周期性压力梯度诱导的3个示例,并得到了每种情况下的精确解．比较了有滑移和没有滑移条件下两种情况的结果．曲线图表表明,滑移对速度分布的影响是巨大的．     

Curvature of the Determinant Line Bundle for the Noncommutative Two Torus

We compute the curvature of the determinant line bundle on a family of Dirac operators for a noncommutative two torus. Following Quillen’s original construction for Riemann surfaces and using zeta regularized determinant of Laplacians, one can endow the determinant line bundle with a natural Hermitian metric. By using an analogue of Kontsevich-Vishik canonical trace, defined on Connes’ algebra of classical pseudodifferential symbols for the noncommutative two torus, we compute the curvature form of the determinant line bundle by computing the second variation \(\delta _{w}\delta _{\bar {w}}\log \det ({\Delta })\).     

The methylsulfonylethoxymethyl (Msem) as a hydroxyl protecting group in oligosaccharide synthesis

The methylsulfonylethoxymethyl (Msem) is introduced as a base-labile, non-participating protecting group in carbohydrate chemistry. Conditions to introduce the Msem on primary and secondary alcohols are described. Removal of the Msem is best achieved using a catalytic amount of tetrabutylammonium fluoride (TBAF), with or without a nucleophilic scavenger. Applicability of the Msem group is illustrated in the assembly of an all 1,3-cis-linked mannotrioside.     

Carbofuran: analytical methods and its determination in natural water samples by flow injection DPA(III)–H2SO4 chemiluminescence

This study proposes, a simple, rapid and sensitive chemiluminescent (CL) method for determination of carbofuran based on diperiodatoargentate(III) (DPA)-sulfuric acid (H₂SO₄) reaction coupled with flow injection (FI) methodology. Under optimum conditions, a linear standard curve is achieved in the range of 0.001–8.0 mg L^–1 (R²= 0.9994 (n = 11) with relative standard deviation (RSD) of 1.4–3.7% (n = 4)), a limit of detection (LOD) 5.0 × 10^–4 mg L^–1 (S/N = 3) and injection throughput 180 h^–1. The proposed method was applied satisfactorily for the analysis of carbofuran in freshwater samples using solid phase extraction (SPE) technique with the recoveries of 94–110% (% RSD = 1.7–3.8, n = 4). A possible CL reaction mechanism has also been discussed briefly.     

Towards Multilayer QCA SISO Shift Register Based on Efficient D-FF Circuits

Quantum-dot Cellular Automata (QCA) is a new technology for replacing CMOS technology at nano-scale dimansion. Shift registers have commonly used circuit in the digital circuits design. In this paper, a new 3-bit Serial Input-Serial Output (SISO) QCA shift register is presented. The proposed circuit uses 3 novel D-Flip-Flops (D-FFs) that are developed in this paper. The proposed circuits are implemented by using QCADesigner tool version 2.0.3. The developed QCA SISO shift register has 120 cells and 0.03 μm² area. The results show that the developed circuits have advantages compared to other QCA circuits in terms of area.     

Approximate Noether symmetries of the geodesic equations for the charged-Kerr spacetime and rescaling of energy

Using approximate symmetry methods for differential equations we have investigated the exact and approximate symmetries of a Lagrangian for the geodesic equations in the Kerr spacetime. Taking Minkowski spacetime as the exact case, it is shown that the symmetry algebra of the Lagrangian is 17 dimensional. This algebra is related to the 15 dimensional Lie algebra of conformal isometries of Minkowski spacetime. First introducing spin angular momentum per unit mass as a small parameter we consider first-order approximate symmetries of the Kerr metric as a first perturbation of the Schwarzschild metric. We then consider the second-order approximate symmetries of the Kerr metric as a second perturbation of the Minkowski metric. The approximate symmetries are recovered for these spacetimes and there are no non- trivial approximate symmetries. A rescaling of the arc length parameter for consistency of the trivial second-order approximate symmetries of the geodesic equations indicates that the energy in the charged-Kerr metric has to be rescaled and the rescaling factor is r-dependent. This re-scaling factor is compared with that for the Reissner–Nordström metric.