Polyadic codes of prime power length

Polyadic codes constitute a special class of cyclic codes and are generalizations of quadratic residue codes, duadic codes, triadic codes, m-adic residue codes and split group codes, which have good error-correcting properties. In this paper, we give necessary and sufficient conditions for the existence of polyadic codes of prime power length. Examples of some good codes arising from the family of polyadic codes of prime power length are also given.     

Solving large-scale semidefinite programs in parallel

We describe an approach to the parallel and distributed solution of large-scale, block structured semidefinite programs using the spectral bundle method. Various elements of this approach (such as data distribution, an implicitly restarted Lanczos method tailored to handle block diagonal structure, a mixed polyhedral-semidefinite subdifferential model, and other aspects related to parallelism) are combined in an implementation called LAMBDA, which delivers faster solution times than previously possible, and acceptable parallel scalability on sufficiently large problems. This work was supported in part by NSF grants DMS-0215373 and DMS-0238008.     

Robust locally testable codes and products of codes

We continue the investigation of locally testable codes, i.e., error‐correcting codes for which membership of a given word in the code can be tested probabilistically by examining it in very few locations. We give two general results on local testability: First, motivated by the recently proposed notion of robust probabilistically checkable proofs, we introduce the notion of robust local testability of codes. We relate this notion to a product of codes introduced by Tanner and show a very simple composition lemma for this notion. Next, we show that codes built by tensor products can be tested robustly and somewhat locally by applying a variant of a test and proof technique introduced by Raz and Safra in the context of testing low‐degree multivariate polynomials (which are a special case of tensor codes). Combining these two results gives us a generic construction of codes of inverse polynomial rate that are testable with poly‐logarithmically many queries. We note that these locally testable tensor codes can be obtained from any linear error correcting code with good distance. Previous results on local testability, albeit much stronger quantitatively, rely heavily on algebraic properties of the underlying codes. © 2006 Wiley Periodicals, Inc. Random Struct. Alg., 2006     

Stereospecific approach to α,β-disubstituted nitroalkenes via coupling of α-bromonitroalkenes with boronic acids and terminal acetylenes

(Z)-α-Bromo-β-substituted nitroethylenes undergo facile Suzuki coupling with aryl, heteroaryl, and vinylboronic acids in the presence of Pd(PPh₃)₄ as catalyst to afford (E)-α,β-disubstituted nitroethylenes in high yield (up to 95%) and complete specificity. Similar coupling of α-bromonitroethylenes with terminal acetylenes (Sonogashira coupling) provides a novel route to (E)-nitroenynes. These Pd-catalyzed coupling methods offer a convenient and stereospecific entry into a diverse array of synthetically and biologically useful α,β-disubstituted nitroethylenes.     

Thermal decomposition study on nickel(ii) complexes of 1,2-(diimino-4’-antipyrinyl)ethane with varying counter ions

The phenomenological, kinetic and mechanistic aspects of the nitrate, chloride, bromide and iodide complexes of nickel(II) with1,2-(diimino-4’-antipyrinyl)ethane (GA) have been studied by TG and DTG techniques. The kinetic parameters like activation energy, pre-exponential factor and entropy of activation were computed. The rate controlling process in all stages of decomposition is random nucleation with one nucleus on each particle (Mampel model).     

Mechanism of ruthenium tetroxide-catalysed oxidation of aldoses by alkalineN-bromoacetamide

The kinetics of oxidation of three aldoses (glucose, mannose and galactose) byN-bromoacetamide (NBA) in the presence of an alkaline solution of RuO₄ as catalyst and Hg(OAc)₂ as co-catalyst and as a scavenger for bromide have been investigated. The main products of the oxidation are the corresponding aldonic acids. The reaction is zero order with respect to aldose and OH⁻. First order dependence of the reaction on both NBA and RuO₄ at low concentrations shifts to zero order at higher concentrations. Addition of acetamide decreases the reaction rate, while addition of Hg(OAc)₂ has the opposite effect. No significant effect of ionic strength was observed. OBr⁻ is postulated as the reactive oxidising species and a mechanism involving co-catalysis by RuO₄ and Hg^II is proposed. TMC 2588     

PHYTOENE AS A PROTECTIVE AGENT AGAINST SUNBURN (>280nm) RADIATION IN GUINEA PIGS

Abstract— Phytoene, the colorless triene precursor of β-carotene (17 mg/g body weight) or a placebo was given to guinea pigs by daily intraperitoneal injection for 14 days, after which the animals were exposed to radiation (> 280 nm). It was found that the animals receiving phytoene developed significantly less erythema to the radiation than did the animals receiving placebo.     

Magnetic enhancement and magnetic reduction in binary clusters of transition metal atoms

Electronic and magnetic properties of small binary clusters containing one or two transition metal atoms are investigated using ab initio calculations with a view to explain the experimentally observed magnetic enhancement/reduction in these systems. As the present investigations do not rely on spin-orbit effects, our results reveal the enhancement or reduction in the magnetic moment to depend on two main factors; namely geometry and, most importantly, the d-band filling. The results can be used as a guide in the experimental synthesis of high density magnetic grains.     

A stereoselective and atom-efficient approach to multifunctionalized five- and six-membered rings via a novel michael-initiated intramolecular Diels-Alder furan reaction

[reaction: see text] A variety of key precursors to the intramolecular Diels-Alder reaction of furan diene (IMDAF) have been prepared via a very facile 1,4-addition of O-, S-, N-, and C-centered nucleophiles possessing unsaturated tether to beta-furyl nitroethylene. Subsequent IMDAF reaction of the 1,4-adducts, carried out under thermal conditions, provided five- and six-membered carbocycles and heterocycles fused to an easily cleavable oxabicycloheptene moiety. The structure and stereochemistry of the cycloadducts were determined by 2D-NMR experiments and further confirmed by X-ray crystallography. The salient features of the strategy include high degree of stereoselectivity (>80:20) in the cycloaddition, atom and step economy, and generation of multiple chiral centers and functionalities. The feasibility of the cleavage of the oxa bridge in the cycloadducts to afford novel multifunctional molecules has also been demonstrated.     

Inhomogeneous minimum of indefinite quadratic forms in five variables of type (3,2) or (2,3): A conjecture of watson

LetQ(x,y,z,t,u) be a real indefinite quadratic form in five variables of type (3,2) or (2,3) and determinantD≠0. The given any real numbersx ₀,y ₀,z ₀,t ₀,u ₀ we can find integersx,y,z,t,u, satisfying $$|Q(x + x_0 ,y + y_0 ,z + z_0 ,t + t_0 ,u + u_0 )| \leqslant (\frac{1}{4}|D|)^{{\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 5}}\right.\kern-\nulldelimiterspace}\!\lower0.7ex\hbox{$5$}}} .$$ All the cases when the sign of equality holds are also determined.