Dimers from α-alkoxybenzyl radicals. An NMR study

meso and dl Dimers (ArCHOR)₂ where R is Me, Et, ⁱPr, ^tBu, cyclohexyl and 1-adamantyl may readily be differentiated by their NMR spectra; the benzylic protons of the meso isomer always absorb at a slightly higher field than those of the dl isomer in each of the solvents used. Differences in chemical shift are discussed in terms of preferences in conformer distribution. The formation of equal amounts of both dimers from the corresponding radical ArCHOR shows that steric and polar factors are not important in influencing the dimerization. Magnetic non-equivalence due to the presence of asymmetric centres was found in some of the compounds discussed above.     

Attojoule calorimetry of mesoscopic superconducting loops

We report the first experimental evidence of nontrivial thermal behavior of the simplest mesoscopic system--a superconducting loop. By measuring the specific heat C of an array of 450,000 noninteracting aluminum loops with very high accuracy of approximately 20 fJ/K, we show that the loops go through a periodic sequence of phase transitions (with a period of an integer number of magnetic flux quanta) as the magnetic flux threading each loop is increased. The transitions are well described by the Ginzburg-Landau theory and are accompanied by discontinuities of C of only several thousands of Boltzmann constants kB.     

A fast Fourier transform on multipoles (FFTM) algorithm for solving Helmholtz equation in acoustics analysis

This article presents a fast algorithm for the efficient solution of the Helmholtz equation. The method is based on the translation theory of the multipole expansions. Here, the speedup comes from the convolution nature of the translation operators, which can be evaluated rapidly using fast Fourier transform algorithms. Also, the computations of the translation operators are accelerated by using the recursive formulas developed recently by Gumerov and Duraiswami [SIAM J. Sci. Comput. 25, 1344-1381(2003)]. It is demonstrated that the algorithm can produce good accuracy with a relatively low order of expansion. Efficiency analyses of the algorithm reveal that it has computational complexities of O(Na), where a ranges from 1.05 to 1.24. However, this method requires substantially more memory to store the translation operators as compared to the fast multipole method. Hence, despite its simplicity in implementation, this memory requirement issue may limit the application of this algorithm to solving very large-scale problems.     

Banach space duality of absolute Schur algebras

Matrix Schur product is the entry-wise product of matrices of the same size. It was shown by P. Chaisuriya and S.-C. Ong [1] that (forr1) infinite matrices [a _jk ] such that [|a _jk | ^r ] B(l ² form a Banach algebra under the norm [a _jk ] _r =[|a _jk | ^r ]^1/r and the Schur product. In this paper we demonstrate the existence of Banach space duality within the class of these algebras which is analogous to the classical duality between the spaces of compact, trace class, and bounded operators onl ². Also we obtain a general functional calculus on these algebras, which is used to determine the spectrum and to justify the notion of -norm introduced in [1].This author's research was supported by a sabbatical leave and a Division grant from Colby College.This author's research was supported by a research professorship at Central Michigan University.This author's research was supported by a visiting professorship at Central Michigan University.     

Analysis of High-Resolution FTIR Spectrum of the nu6 Band of H13COOH

The FTIR spectrum of the nu6 band of H13COOH has been collected at a resolution of 0.004 cm-1 in the frequency range of 1030-1160 cm-1. The nu6 band was analyzed to be an A-B hybrid band and perturbed by the nearby nu8 band through a-, and b-Coriolis coupling terms. Using a Watson's A-reduced Hamiltonian in the Ir representation, with the inclusion of a- and b-Coriolis resonances, a total of 3004 IR transitions of nu6 have been analyzed to provide rovibrational constants for the v6 = 1 state with a standard deviation of 0.00047 cm-1. The nu6 band was found to be centered at 1095.40365 +/- 0.00003 cm-1. Copyright 1999 Academic Press.     

Heterocyclic benzothiazole-based liquid crystals: synthesis and mesomorphic properties

Two homologous series of 2-(4-alkanoyloxybenzylidenamino)benzothiazoles and 2-(2-hydroxy-4-alkanoyloxybenzylidenamino)benzothiazoles were synthesised and characterised. Their molecular structures differed wherein the latter comprised a lateral hydroxyl group, unlike the former. Spectroscopic techniques such as FT-IR, ¹H & ¹³C NMR and mass spectrometry together with elemental analysis were employed to elucidate the molecular structures. The transition temperatures and their mesophases were determined by differential scanning calorimetry, optical polarising microscopy and X-ray diffraction techniques. Members with decanoyloxy till hexadecanoloxy chain in the series without the lateral hydroxyl group each exhibited a smectic A phase, while those in the series with the lateral hydroxyl group were non-mesogenic. The mesomorphic properties of the present series were compared with other structurally related series to establish the chemical structure–mesomorphic properties relationship.     

Graphenes Prepared by Hummers,Staudenmaier and Hofmann Methods for Analysis of TNT‐Based Nitroaromatic Explosives in Seawater

The detection of TNT and related nitroaromatic compounds in seawater is of great interest. Electrochemical techniques can be applied for detection purposes since nitroaromatic compounds contain easily reducible nitro groups. In this study, we investigate the performance of thermally reduced graphenes prepared by three different oxidative methods: Hummers, Staudenmaier and Hofmann methods with consequent thermal exfoliation. The Hofmann method‐based graphene was found to exhibit the highest sensitivity in detecting TNT electrochemically. Extended study on the detection of TNT in seawater using the graphene material provided significant improvements in the detection sensitivity. These findings will have profound impacts on the detection of nitroaromatic explosives in seawater.     

Catalytic construction and reconstruction of guanidines: Ti-mediated guanylation of amines and transamination of guanidines

Bis(guanidinate) titanium imido complexes [{(Me2N)C(NiPr)2}2TiNAr'] (Ar' = 2,6-Me2C6H3 (1a); C6F5 (1b)) are competent catalysts for the guanylation of a variety of arylamines with carbodiimide. The reversible [2 + 2] addition of iPrN=C=NiPr to 1b is demonstrated and is proposed to be part of the catalytic cycle. Compounds 1a and 1b are also effective precatalysts for the transamination of trialkylguanidines with arylamines to yield aryldialkylguanidines.