Pyridine N-alkylation by lithium, magnesium, and zinc alkyl reagents: synthetic, structural, and mechanistic studies on the bis(imino)pyridine system

The 2,6-bis(alpha-iminoalkyl)pyridines 2,6-[ArNC(CR(3))](2)C(5)H(3)N [R = H, D; Ar = 2,6-i-Pr(2)C(6)H(3) (DIPP), 2,6-Me(2)C(6)H(3) (DMP)] react with MeLi in Et(2)O to give a binary mixture of products: the pyridine N-methylated species 2,6-[ArNC(CR(3))](2)C(5)H(3)N(Me)Li(OEt(2)) and the deprotonated/dedeuterated species 2-[ArNC(CR(3))],6-[ArNC(=CR(2))]C(5)H(3)NLi(OEt(2)). For R = D, the product ratio is 2:1 in favor of the N-methylated product, while, for R = H, the deprotonated product is favored by 5:1, increasing to 8:1 in toluene solvent. Warming solutions of the N-methylated species leads to clean conversion to the thermodynamically preferred deprotonated species. Crossover experiments show that MeLi is re-formed and dissociates from the terdentate ligand before deprotonating the ketimine methyl unit. For MgR(2) (R = Et, i-Pr) and ZnR(2) (R = Et) reagents, N-alkylation products are formed exclusively, but derivatives containing bulky aryl substituents are found to undergo further rearrangement to 2-alkylated species, arising by migration of the alkyl group of the N-alkyl moiety to the adjacent ring carbon atom. The reversibility of the N-alkylation process has been probed using deuterio-labeled Mg alkyl reagents and mixed alkyl zinc species. A cationic zinc derivative is shown to undergo "reverse" alkyl migration, from the heterocycle nitrogen atom to the zinc center. EPR spectroscopy reveals a paramagnetic intermediate in which the unpaired electron is delocalized over the heterocycle and di-imine moieties of the ligand, indicating that the N-alkylation reactions proceed via single electron-transfer processes.     

Lower Bounds on the State Complexity of Geometric Goppa Codes

We reinterpret the state space dimension equations for geometric Goppa codes. An easy consequence is that if deg then the state complexity of is equal to the Wolf bound. For deg , we use Clifford's theorem to give a simple lower bound on the state complexity of . We then derive two further lower bounds on the state space dimensions of in terms of the gonality sequence of . (The gonality sequence is known for many of the function fields of interest for defining geometric Goppa codes.) One of the gonality bounds uses previous results on the generalised weight hierarchy of and one follows in a straightforward way from first principles; often they are equal. For Hermitian codes both gonality bounds are equal to the DLP lower bound on state space dimensions. We conclude by using these results to calculate the DLP lower bound on state complexity for Hermitian codes.     

A novel piezo-optical styrene sensor incorporating polymer-supported tribromide ion

Encapsulation of Amberlyst A-26 supported tribromide in a 10,000 MW polyethylene glycol matrix gives a robust colour-sensitive reagent matrix which can be deposited on indium-tin oxide coated polyvinylidene fluoride (PVDF) piezoelectric film for the detection of styrene (and other alkene) vapours.     

An early Chinese derivation of the volume of a pyramid: Liu Hui,third century A.D.

The Chiu-chang suan-shu (“Arithmetic in nine chapters”) is a mathematical book of the late first century A.D. It gives practical problems and states algorithms for their solution, with no explanation. A commentary attributed to Liu Hui, of the third century A.D., gives an explanation of each algorithm; these explanations satisfy many of the criteria for what we would call a proof. In this article Liu Hui's explanation of the formula for the volume of a particular kind of pyramid is translated and discussed.     

On the lax solution to the Hamilton-Jacobi equation. Part I

The review article of Crandall, Ishii, and Lions [Bull. AMS,27, No. 1, 1–67 (1992)] devoted to viscosity solutions of first- and second-order partial differential equations contains the exact Lax formula

Field and pressure response of Yb compounds close to a quantum critical point

YbCu_5−x Al _x provides the possibility to tune ground state properties by a change of the valence due to the Cu/Al substitution, by pressure as well as by the application of a magnetic field. Near to the critical concentration x _cr≈1.5 non-Fermi-liquid properties (NFL) are obvious, obeying hyperscaling. If magnetic order sets in for x>1.5, the application of moderate magnetic fields quenches order and again NFL features become evident. Hyperscaling in this case indicates strongly interacting spin fluctuations.     

In vivo study of the inflammatory modulating effects of low-level laser therapy on iNOS expression using bioluminescence imaging

This study was designed to demonstrate that bioluminescence imaging (BLI) can be used as a new tool to evaluate the effects of low-level laser therapy (LLLT) during in vivo inflammatory process. Here, the efficacy of LLLT in modulating inducible nitric oxide synthase (iNOS) expression using different therapeutic wavelengths was determined using transgenic animals with the luciferase gene under control of the iNOS gene expression. Thirty transgenic mice, FVB/N-Tg(iNOS-luc)Xen, were allocated randomly to one of four experimental groups treated with different wavelengths (lambda = 635, 785, 808 and 905 nm) or a control group (nontreated). Inflammation was induced by intra-articular injection of zymosan A in both knee joints. Laser treatment (25 mW cm(-2), 200 s, 5 J cm(-2)) was applied to the knees 15 min after inflammation induction. Measurements of iNOS expression were performed at various times (0, 3, 5, 7, 9 and 24 h) by measuring the bioluminescence signal using a highly sensitive charge-coupled device (CCD) camera. The results showed a significant increase in BLI signal after irradiation with 635 nm laser when compared to the nonirradiated animals and the other LLLT-treated groups, indicating wavelength dependence of LLLT effects on iNOS expression during the inflammatory process, and thus demonstrating an action spectrum of iNOS gene expression following LLLT in vivo that can be detected by BLI. Histological analysis was also performed and demonstrated the presence of fewer inflammatory cells in the synovial joints of mice irradiated with 635 nm compared with nonirradiated knee joints.