Limiting Empirical Singular Value Distribution of?Restrictions of?Discrete Fourier Transform Matrices

We determine the limiting empirical singular value distribution for discrete Fourier transform (DFT) matrices when a random set of columns and rows is removed.     

Obstructions to fibering a manifold

Given a map f : M → N of closed topological manifolds we define torsion obstructions whose vanishing is a necessary condition for f being homotopy equivalent to a projection of a locally trivial fiber bundle. If N = S ¹, these torsion obstructions are identified with the ones due to Farrell (Indiana Univ Math J 21:315–346, 1971/1972).     

Simulating cardiac electrophysiology using anisotropic mesh adaptivity

The simulation of cardiac electrophysiology requires small time steps and a fine mesh in order to resolve very sharp, but highly localized, wavefronts. The use of very high resolution meshes containing large numbers of nodes results in a high computational cost, both in terms of CPU hours and memory footprint. In this paper an anisotropic mesh adaptivity technique is implemented in the Chaste physiological simulation library in order to reduce the mesh resolution away from the depolarization front. Adapting the mesh results in a reduction in the number of degrees of freedom of the system to be solved by an order of magnitude during propagation and 2–3 orders of magnitude in the subsequent plateau phase. As a result, a computational speedup by a factor of between 5 and 12 has been obtained with no loss of accuracy, both in a slab-like geometry and for a realistic heart mesh with a spatial resolution of 0.125 mm.     

Preparation of ferrocene-containing phosphinamine ligands possessing central and planar chirality and their application in palladium-catalyzed asymmetric allylic alkylation

The preparation of [2-(S(p))-[(trans-(2R,5R)-2,5-dialkylpyrrolidinyl)methyl]]ferrocenyldiphenyl phosphines, new ferrocenylphosphinamine ligands possessing one site of planar and two stereogenic centers, is described. trans-(2R,5R)-2,5-Dialkyl-1-(ferrocenylmethyl)pyrrolidines were diastereoselectively lithiated and quenched with chlorodiphenylphosphine. For the dimethyl ligand, chemical yields of up to 65% and des of up to 90% were obtained whereas the diethyl ligand afforded lower chemical yields (10%) and des of 78%. Diastereomerically pure material was obtained in both cases after a single recrystallization from ethanol. (S)-Planar chirality was confirmed by X-ray crystallographic analysis of the dimethyl ligand. The palladium complexes of the new ligands were applied in the allylic alkylation of 1,3-diphenylprop-2-enyl acetate with reasonable chemical yields and moderate ees of up to 36% and 38% when dimethyl malonate and dimethyl methyl malonate were employed as nucleophiles, respectively. Importantly, it was found that the new ligands possessing the combination of planar and central chirality gave the opposite enantiomeric alkylation products compared to ligands which possess only the central chirality of the trans-2,5-dimethylpyrrolidinyl moiety. Solution NMR studies of the 1,3-diphenylallyl palladium complex of the dimethyl ligand revealed the presence of only the exo-configured allyl diastereomer.     

Effective index method for planar lightwave circuits containing directional couplers

A simple and intuitive effective index method for planar lightwave circuits containing directional couplers is proposed. The optimal cladding refractive index of the effective two-dimensional planar waveguide is found according to the coupling length of the directional coupler involved. Numerical examples indicate that this proposed effective index method gives accurate results while saving significant computation time in simulation and design of planar lightwave circuits containing directional couplers.     

Calibration method at the N K‐edge using interstitial nitrogen gas in solid‐state nitrogen‐containing inorganic compounds

The standard method of soft X‐ray beamline calibration at the N K‐edge uses the ν = 0 peak transition of gas‐phase N₂. Interstitial N₂ gas trapped or formed within widely available solid‐state ammonium‐ and amine‐containing salts can be used for this purpose, bypassing gas‐phase measurements. Evidence from non‐nitrogen‐containing compounds (KH₂PO₄) and from He‐purged ammonium salts suggest that production of N₂ gas is through beam‐induced decomposition. Compounds with nitrate or nitrite as anions produce coincident features and are not suitable for this calibration method.     

Spectroscopic analysis of single-walled carbon nanotubes and semiconjugated polymer composites

Interactions between arc discharge single-walled carbon nanotubes within polymer composites have been well documented. Here hybrid systems of the conjugated organic polymer poly(p-phenylene vinylene-co-2,5-dioctyloxy-m-phenylene vinylene) (PmPV) and HiPco SWNTs are explored using UV/vis/NIR and Raman spectroscopy at 514.5 and 632.8 nm to determine specific interactions. An examination of the radial breathing modes at 514.5 nm shows similar tube diameters of 1.28 and 1.35 nm selected for both the arc discharge and HiPco composites. The corresponding G lines of both composites show no specific type of tubes being selected. At 514.5 nm, the G line of the HiPco composite (1% mass fraction) shows contributions from semiconducing and metallic tubes, and the arc discharge composite (1% mass fraction) is dominated by semiconducting nanotubes. At 632.8 nm, the G line of the HiPco composite (1% mass fraction) is dominated by semiconducting tubes, and the arc discharge composite (1% mass fraction) shows strong contributions from metallic tubes. This finding is a strong indication that the selection process is dependent on tube diameter rather than backbone structure. The solubility limits of both composites are determined by investigating the G lines of both composites and have been found to be greater than 1% mass fraction by weight for the arc discharge composite and greater than 0.1% mass fraction by weight for the HiPco composite.     

Synthesis and characterization of a helical step‐ladder polyarylene

A helical step‐ladder polyarylene incorporating chiral (R)‐2,2′‐dioctoxy‐1,1′‐binaphthyl units was synthesized for the first time. The first step involved the preparation of a precursor poly(arylene ketone) via a palladium‐mediated Suzuki‐type cross‐coupling reaction with the aid of microwave heating. Two polymer‐analog reaction steps, the reduction of the keto groups to tertiary alcohol functionalities and subsequent intramolecular Friedel–Crafts cyclization, gave a step‐ladder polymer ( 6 ) in good yields with reasonable mean average molecular weights greater than 13,000. The regioselective cyclization pattern in the α position of the naphthalene core was confirmed by a comparison of the NMR data of the polymer with those of the corresponding model ladder oligomers, 12 and 13 , and also a single‐crystal structure of 13 . The optical spectra of the oligomers and polymers indicated that there was little electronic interaction across the binaphthyl units. The circular dichroism spectrum of 6 exhibited a strong bisignate Cotton effect in the π–π* absorption region of the planar chromophores, which reflected the strong exciton coupling within the helical polymer chain. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 5533–5545, 2006     

Synthesis,thermal reactivity,and kinetics of stabilized phosphorus ylides,part 2: [(Arylcarbamoyl)(cyano)methylene]triphenylphosphoranes and their thiocarbamoyl analogues

A series of five cyano(arylcarbamoyl) phosphorus ylides 2 and five cyano(arylthiocarbamoyl) phosphorus ylides 3 are prepared and fully characterized. Pyrolytic reaction products of a representative example of each type obtained by flash vacuum pyrolysis technique show that they undergo thermal extrusion of Ph₃PO or Ph₃PS. Kinetic study of the gas‐phase pyrolysis of each ylide by static method shows that these reactions are unimolecular and first order with no significant substituent effect, but the thiocarbamoyl ylides 3 react 40–65 times more rapidly than their carbamoyl analogues 2 . © 2006 Wiley Periodicals, Inc. Int J Chem Kinet 38: 496–502, 2006