Succession of one-soliton pulses in the zero-dispersion region of silica optical fibres: The role of the phase difference between the adjacent pulses

Some features of the propagation of one-soliton successions in the third order dispersion region are presented for the case where the phase difference between adjacent pulses is rads. We show that this considerably improves the stability of the pulses in the zero-dispersion region. Walk-off can be diminished by increasing the number of pulses in the succession. These features may help optimize the bandwidth of non-linear fibre communication links.     

Reliable evaluation of temperature-independent parameters in correlation of vapour–liquid equilibrium data

A new algorithm/program has been elaborated for simultaneous processing of different sets of vapour–liquid equilibrium data. The program was tested with six binary hexane + isomeric pentanol systems, each of them measured at three different isobaric conditions and one isothermal system of tert-butyl-methyl-ether + 2-methyl-2-propanol measured at three different temperatures. The correlation uses the maximum likelihood method, taking into account real behaviour of vapour phase. The parameters obtained are valid within the whole temperature range of the data, and are consistent in comparison with those obtained from individual correlations of isobars or isotherms. Results are presented for the Wilson and NRTL equations.     

Formation of spanning water networks on protein surfaces via 2D percolation transition

The formation of spanning hydrogen-bonded water networks on protein surfaces by a percolation transition is closely connected with the onset of their biological activity. To analyze the structure of the hydration water at this important threshold, we performed the first computer simulation study of the percolation transition of water in a model protein powder and on the surface of a single protein molecule. The formation of an infinite water network in the protein powder occurs as a 2D percolation transition at a critical hydration level, which is close to the values observed experimentally. The formation of a spanning 2D water network on a single rigid protein molecule can be described by adapting the cluster analysis of conventional percolation studies to the characterization of the connectivity of the hydration water on the surface of finite objects. Strong fluctuations of the surface water network are observed close to the percolation threshold. Our simulations also furnish a microscopic picture for understanding the specific values of the experimentally observed hydration levels, where different steps of increasing mobility in the hydrated powder are observed.     

Extremal hexagonal chains

Some extremal properties of the linear chainL _h ofh hexagons are pointed out. In the class of all hexagonal chains withh hexagons,L _h has minimumK,Z andx ₁ values, as well as maximum W and values;K = number of perfect matchings,Z = number of independent edge sets (Hosoya index),x ₁ = largest graph eigenvalue,W = Wiener index, = number of independent vertex sets (Merrifield-Simmons index). The extremality ofL _h with respect toZ, andx ₁ is demonstrated here for the first time.Dedicated to Frank Harary, teacher, inspirer and friend, pioneer, champion and proprietor of graph theory, on the occasion of his 70th birthday.     

On the mechanism of THF catalyzed vinylic lithiation of allylamine derivatives: structural studies using 2-D and diffusion-ordered NMR spectroscopy

N-Lithio-N-(trialkylsilyl)allylamines can be deprotonated in the presence of ethereal solvents exclusively at the cis-vinylic position to yield 3,N-dilithio-N-(trialkylsilyl)allylamines under mild conditions. Low temperature (1)H and (7)Li NMR ((1)H NOESY, TOCSY, (1)H/(7)Li HSQC, and DO-NMR) studies on the solution structure of 3,N-dilithio-N-(tert-butyldimethylsilyl)allylamine identified three major aggregates in THF (monomer, dimer and tetramer), but the aggregate structures failed to explain the solvent dependence and regiochemical outcome of the reaction. Low temperature (1)H NMR (NOESY, TOCSY, DO-NMR) studies on the solution structure of N-lithio-N-(tert-butyldimethylsilyl)allylamine in the presence of nBuLi identified amide/nBuLi mixed aggregates in both the ethereal solvent THF (1:1 dimer) and the hydrocarbon solvent toluene (1:3 tetramer). Addition of 2 equiv of THF to toluene solutions induces the formation of the same THF solvated 1:1 dimer as observed in neat THF. NMR evidence suggests that in THF the mixed aggregate has close contact between the olefin and the beta-CH(2) of nBuLi, while in the absence of THF, the allyl chain appears to be pointed away from the nearest nBuLi residues.     

Transition metal methylene complexes : III. Methylene (CH2), a carbonyl analogous ligand; crystal structure of μ-methylenebis(carbonyl-η5-cyclopentadienylrhodium)(Rh—Rh

μ-Carbonylbis(carbonyl-ν⁵-cycopentadienylrhodium)(Rh—Rh) reacts with N-methyl-and N-ethyl-N-nitrosourea in boiling benzene to yield the dinuclear, diamagnetic, neutral rhodium complexes μ-methylene- (A) and μ-ethylidenebis(carbonyl-η⁵-cyclopentadienylrhodium)(Rh—Rh) (B), respectively. Deuterium labelled experiments prove the origin of the metal-stabilized methylene ligand to be the alkyl group of the organic precursor. This new method of preparation of transition metal—methylene complexes may be used as an alternative to the commonly used diazo method; the latter method was shown to work with diazodiethylmalonate and dicarbonyl-η⁵-cyclopentadienylrhodium, the reaction yielding μ-bis(ethoxycarbonyl)methylenebis(carbonyl-η⁵-cyclopentadienylrhodium)(Rh—Rh).Compound A crystallizes in the triclinic system, P$\text{1}$, and with cell constants of a 803.42(5), b 909.98(6), c 938.81(2) pm, α 74.402(3), β81.923(3), and γ 83.685(6)°. The unit cell volume and the calculated density are 651.6 ų and 2.069 g cm^-3, for one molecule in the asymmetric unit. The molecular geometry of μ-CH₂[η⁵-C₅H₅Rh(CO)]₂ was established from 2718 unique reflections collected with a computer-controlled diffractometer and refined to a final R(F) = 0.0379. The molecular parameters derived from the single-crystal X-ray study conform to a remarkable degree with those found for μ-CO[η⁵-C₅H₅Rh(CO)]₂. Thus, the bridging ligands CH₂ and CO seem to be analogous in their effects on the structural characteristics of the molecular framework of the two molecules.     

2-Oxocephems. Synthesis and Properties of 7-Acylamino-2-oxocephem-4-carboxylic Acids

A synthesis of (6 R, 7 R)-7-acylamino-2-oxocephem-4-carboxylic acids from penicillins is reported based on the formation of the 2-oxocephem system in an intramolecular Wittig condensation. An interesting steric effect of the acylamino grouping on the course of this key step was used to advantage. Some physical and biological properties of this new type of Δ³-cephem are described.     

Solid state and solution conformation of 2-pyridinecarboxylic acid hydrazides: a new structural motif for foldamers

X-Ray crystallography and NMR show a strong preference for trans conformers of N′-phenyl or N′-(2-pyridyl) 2-pyridinecarboxylic acid hydrazides, stabilized by an NHN_pyr. intramolecular hydrogen bond both in the solid state and in solution. This allows us to extrapolate that oligomers of this unit should adopt extended linear conformations.