FOLDING TRANSFORMATIONS AND HKY MAPPINGS

We present a new method for the derivation of mappings of HKY type. These are second-order mappings which do not have a biquadratic invariant like the QRT mappings, but rather an invariant of degree higher than two in at least one of the variables. Our method is based on folding transformations which exist for some discrete Painlevé equations. They are transformations which relate the variable of a discrete Painlevé equation to the square of the variable of some other one. By considering the autonomous limit of these relations we derive folding-like transformations which relate QRT mappings to HKY ones. We construct the invariants of the latter mappings and show how they can be extended beyond the ones given by the strict application of the folding transformation.     

Synthesis of N-heterocyclic diols by diastereoselective pinacol coupling reactions

A series of 5-8 membered N-heterocyclic diols have been prepared from acyclic dicarbonyls via diastereoselective pinacol reactions whereby cis- or trans-diol stereoselectivity is controlled by the choice of low-valent metal reagent used.     

Synthesis of the first pentaethynylferrocene derivatives

Starting from a bisprotected ferrocene-1,2,3-triscarbaldehyde, Ohira-alkynylation and Pd-catalyzed protection of the free alkyne with 4-iodotoluene leads to a ferrocene in which one Cp-ring is 1,2,3-substituted by two acetal rings (1,2-position) and an internal alkyne. Metalation of the ferrocene nucleus with sec-BuLi, workup with DMF and reduction with LiAlH₄ leads to a 1,2,3,4-tetrasubstituted ferrocene carrying a hydroxymethyl group. The acetal groups are removed by para-toluenesulfonic acid and the aldehyde groups are converted into arylalkynes. A second metalation followed by workup with DMF furnishes a 1,2,3,4,5-pentasubstituted ferrocenecarbaldehyde. The aldehyde is transformed into an alkyne by the Ohira method and converted to an internal alkyne by Pd-catalyzed reaction with 4-iodotoluene. The sequence gives a 1,2,3,4,5-pentasubstituted ferrocene derivative with four alkyne groups and one hydroxymethyl group. Airless Marko oxidation of the alcohol is followed by another Ohira alkynylation. Pd-catalyzed arylation finishes the reaction sequence to give the symmetrical 1,2,3,4,5-pentakis(4′-tolylethynyl)ferrocene, the first pentaethynylferrocene derivative. A second, similar route was explored that furnished 1,2,3,4,5-pentakis(4′-butylphenylethynyl)ferrocene and its butadiyne-bridged dimer.     

Probing the N(5)-H bond of the isoalloxazine moiety of flavin radicals by X- and W-band pulsed electron-nuclear double resonance.

An X- (9.7 GHz and W-band (94 GHz) pulsed electron-nuclear double resonance (ENDOR) study of the flavin cofactor of Escherichia coli DNA photolyase in its neutral radical form is presented. Through proton and deuteron ENDOR measurements at T = 80 K, we detect and characterize the full anisotropy of the hyperfine coupling (hfc) tensor of the proton or deuteron bound to N(5) of the isoalloxazine ring. Scaling of the anisotropic proton hfc components by multiplication with the quotient of the magnetogyric ratio of a deuteron and a proton, chiD/chiH, reveals subtle differences compared to the respective deuteron couplings obtained by 95-GHz deuterium ENDOR spectroscopy on an H-->D buffer-exchanged sample. These differences can be attributed to the different lengths of N(5)-H and N(5)-D bonds arising from the different masses of protons and deuterons. From the R(-3) dependence of the dipolar hyperfine splitting, we estimated that the N(5)-D bond is about 2.5% shorter than the respective N(5)-H bond. That such subtle bond-length differences can be resolved by pulsed ENDOR spectroscopy suggests that this method may be favorably used to probe the geometry of hydrogen bonds between the H(5) of the paramagnetic flavin and the protein backbone. Such information is only obtained with difficulty by other types of spectroscopy.     

McMurry reactions of (η-acetylcyclopentadienyl) cobalt-(η-tetraphenylcyclobutadiene) with benzophenone: ketone couplings and a pinacol/pinacolone rearrangement

The reaction of (η⁴-C₄Ph₄) Co[η⁵-C₅H₄-C(O)Me], 5, with benzophenone under McMurry conditions (TiCl₄/Zn/THF) gives the hetero-coupled product (η⁴-C₄Ph₄)Co[η⁵-C₅H₄-C(Me)CPh₂], 7, together with the dicobalt species: trans-(η⁴-C₄Ph₄)Co[(η⁵-C₅H₄-C(Me)C(Me)-η⁵-C₅H₄₋)] Co(η⁴-C₄Ph₄), 9, and the pinacolone Me[(η⁴-C₄Ph₄)Co(η⁵-C₅H₄)]₂C-C(O)Me, 10. The latter is apparently formed from the pinacol by migration of an (η⁴-C₄Ph₄)Co[(η⁵-C₅H₄) group. Preferential migration of the cobalt sandwich moiety rather than a methyl group is rationalized in terms of a favored transition state involving a metal-stabilized cation. The products 7, 9 and 10, and also the ketone (η⁴-C₄Ph₄)Co[η⁵- C₅H₄-C(O)Et], 6, were all characterized by X-ray crystallography.     

Fluorine–Fluorine Interactions: NMR and AIM Analysis

The structure of a number of compounds that show experimental FsF coupling constants across the space has been studied using HF-DFT methods (B3LYP) and Atoms in Molecules (AIM) methodologies. For all the cases with strong coupling constants a bond critical point and the corresponding bond path between the fluorine atoms involved has been found in the electron density map. In an attempt to predict NMR properties, new compounds for which no experimental F-F coupling constants are available, but with the same characteristics in the electron density maps, have been calculated.     

Characterization of polyphenols from plant materials through their silylation and 29Si NMR spectroscopy-line assignment through 29Si, 13C spin-spin couplings

The lines in (29)Si NMR spectra of silylated polyphenols and some other compounds are difficult to assign owing to the absence of couplings with protons outside the silyl group. The assignment can be derived through small (n)J((29)Si, (13)C) couplings (n > 1). Using a previously described method for measurements of these couplings, the assignment procedure is demonstrated here on three examples of trimethylsilylated phenols: 7-hydroxyflavone, ferulic acid, and quercetin. In some cases the procedure can be used to identify carbon atoms to which the siloxy groups are attached.     

Measurement of PV asymmetry in(→n)+p→d+γ and (→γ)+d→n+p

The measurement of parity-violating(PV)observables in few-nucleon system can shed light on our current understanding of the week interaction between nucleons.Theoretical models describe the nucleonnucleon weak interaction at low energies use a series of undetermined parameters.Two parity violating measurements have been considered: the capture of polarized slow neutrons on hydrogen((n)+p→d+γ)at Los Alamos National Laboratory for first phase and Oka Ridge National Laboratory for second phase and the helicity dependence of the deuteron photodisintegration cross section using circularly polarized photons((γ)+d→n+p*)at Shanghai Institute of Applied Physics.The goal of both experiments is to constraint the weak meson-nucleon couplings to a precision of 1 × 10-8.The introduction of both experiments is presented.     

What non-linear methods offered to linear problems? The Fokas transform method

In 1750 D’ Alembert demonstrated how a linear partial differential equation can be solved via separation of variables, a method that decomposes a PDE into a set of ODEs. This method was the basis for the development of many branches of contemporary analysis, from function spaces to spectral analysis of operators and the theory of special functions. A condition for the method of separation of variables to work is the existence of a coordinate system that fits the boundary of the fundamental domain and at the same time it separates the PDE. It is remarkable that two and a half centuries later a generalization is introduced that has its origin in the analysis of non-linear integrable equations. In the present work, this promising new transform method is outlined and applied to particular boundary value problems. A crucial part of the method is the introduction of a global relation which, if properly used, can provide the missing boundary data in a very elegant and effective way. We show how this can be used to generate separable solutions of partial differential equations even when no system, that fits the geometry of the fundamental domain, is available. This is shown for the case of the Dirichlet problem for the modified Helmholtz equation in the interior of an equilateral triangle. Furthermore, the connection of the Fokas method to the classical moment problem is investigated. It is shown that, in this case, the global relation is decomposed into a sequence of global relations, directly associated with the Fourier coefficients of the Dirichlet and Neumann boundary values.