Loop-space hamiltonians and numerical methods for large-N gauge theories (II)

We generalize our numerical loop-space methods to consider the full large-N Yang-Mills problem. First we study the weak-coupling phase in loop space and derive the equation obeyed by spacelike Wilson loops. We then consider the problem of topological reduction and derive the effective potential for topologically distinct loops. In connection with numerical computations we discuss the issues of truncation of the system. We present an initial numerical result for a simplest truncation of the full (2+1)-dimensional Yang-Mills theory.     

Differential Line Broadening in the Presence of Quadrupolar–CSA Interference

The formalism for calculating the lineshape of a spin 1/2J-coupled to a high-spin nucleus undergoing quadrupolar and chemical shift anisotropy (CSA) relaxations is derived in the case where the tensors of both interactions are noncoincident and nonaxial. The expressions show that the CSA–quadrupolar interference term which is responsible for the asymmetry of lines involves a term depending on tensorial parameters. The effect of this term on the lineshapes is discussed with respect to three cases, namely coincident–axially symmetric, noncoincident–axially symmetric, and general noncoincident quadrupolar and CSA tensors. These cases are considered in the analysis of the lineshape of the¹H-decoupled spectra of the³¹P nucleusJ-coupled to the⁵⁹Co nucleus encountered in the tetrahedral cluster HFeCo₃(CO)₁₁PPh₂H.     

Comparison between optical interconnection processors: folded perfect-shuffle versus three-dimensional butterfly

The differences between folded perfect shuffle and three-dimensional (3-D) multi-channel butterfly optical interconnection architectures are quantified. The three-dimensional butterfly network, in particular, is used to implement Hartley transform operation.     

Microwave Photonic Link with Carrier Suppression for Increased Dynamic Range

Theoretical analysis and experimental investigation of microwave photonic links with bias-shifted Mach-Zehnder modulators are presented. An optical amplifier is used to increase link gain and reduce noise figure. The combination of modulator bias shift away from quadrature and optical amplification reduces the link noise figure by more than 15 dB. For modulation frequencies from 2 to 18 GHz, the third-order limited spurious-free dynamic range (SFDR3) of these links is greater than 120 dB, normalized to a 1-Hz bandwidth. Conventional links based on Mach-Zehnder modulators are limited to SFDR3 values of approximately 110 dB, normalized to a 1-Hz bandwidth. This level of performance is achieved without electronic or optical linearization.     

Conformational analysis by HRMAS NMR spectroscopy of resin-bound homo-peptides from C(alpha)-methyl-leucine

A series of [L-(alphaMe)Leu]n (n = 1-5) homo-peptides have been covalently linked to Tentagel and POEPOP resins and submitted to a conformational study using HRMAS NMR spectroscopy. Whereas the mono- and dipeptide are mainly fully-extended, stable 3(10)-helical structures are formed beginning from the trimer.     

Hydrogen bonded H3O, H2O, HF, F in fluoride metalates (Al, Cr, Fe, Zr, Ta) templated with tren (tris-(2-aminoethyl)amine)

The environment of H₃O⁺, H₂O, HF and F⁻ species (non-bonded to metals) is considered in fluoride metalates which crystallise from the (Al(OH)₃, Cr(OH)₃, FeF₃, ZrF₄, Ta₂O₅)-tren-HF_aq·-ethanol systems (microwave heating at 190 °C during 1 h). The presence of (H₃O)(H₂O)₆⁺ clusters or H₃O⁺ cations, of isolated or associated H₂O molecules, of (HF₂)⁻ and F⁻ anions is evidenced. The thermal stability of the solids depends strongly on the nature of the hydrogen-bonded species associated with the preceding cations or anions and on the formation of water ribbons or layers.     

Etude des interferences spectrophotometriques par utilisation d'une matrice d'experiences factorielle

(Use of a factorial design to study interferences in spectrophotometry.) Ozonation of aqueous solutions leads to the formation of hydrogen peroxide and oxalic acid. Hydrogen peroxide is determined spectrophotometrically by the classical method in which TiO·H₂O₂²⁺ is formed, but oxalic acid interferes by forming a complex with titanium. The interference is studied by using a simple factorial design. The results, calculated by linear regression, show the existence of both translational and rotational effects on the absorbance signals.     

A facile one‐pot synthesis of novel substituted 1,2,3,4‐tetrahydropyrimidines

A facile one‐pot synthesis of 5‐benzoyl‐6‐methylthio‐1,2,3,4‐tetrahydropyrimidines in good yields is reported.     

Regio- and diastereoselective synthesis of 2-alkylidenetetrahydrofurans by domino SN/SN' and SN/SN reactions of 1,3-dicarbonyl dianions

The domino C,O-cyclodialkylation reaction of dilithiated 1,3-dicarbonyl compounds with 1,4-dibromo-2-butene resulted in regio- and diastereoselective formation of 2-alkylidene-5-vinyltetrahydrofurans. The cyclization of 1,3-dicarbonyl dianions with 1-bromo-2-chloroethane regio- and diastereoselectively afforded 2-alkylidenetetrahydrofurans under thermodynamic reaction control.