Non-Uniformity and Generalised Sacks Splitting

We show that there do not exist computable functions f ₁(e, i), f ₂(e, i), g ₁(e, i), g ₂(e, i) such that for all e, i ∈ ω, (1) $ {\left( {W_{{f_{1} {\left( {e,i} \right)}}} - W_{{f_{2} {\left( {e,i} \right)}}} } \right)} \leqslant _{{\rm T}} {\left( {W_{e} - W_{i} } \right)}; $ (2) $ {\left( {W_{{g_{1} {\left( {e,i} \right)}}} - W_{{g_{2} {\left( {e,i} \right)}}} } \right)} \leqslant _{{\rm T}} {\left( {W_{e} - W_{i} } \right)}; $ (3) $ {\left( {W_{e} - W_{i} } \right)} \not\leqslant _{{\rm T}} {\left( {W_{{f_{1} {\left( {e,i} \right)}}} - W_{{f_{2} {\left( {e,i} \right)}}} } \right)} \oplus {\left( {W_{{g_{1} {\left( {e,i} \right)}}} - W_{{g_{2} {\left( {e,i} \right)}}} } \right)}; $ (4) $ {\left( {W_{e} - W_{i} } \right)} \not\leqslant _{{\rm T}} {\left( {W_{{f_{1} {\left( {e,i} \right)}}} - W_{{f_{2} {\left( {e,i} \right)}}} } \right)}{\text{unless}}{\left( {W_{e} - W_{i} } \right)} \leqslant _{{\rm T}} {\emptyset};{\text{and}} $ (5) $ {\left( {W_{e} - W_{i} } \right)} \leqslant _{{\rm T}} {\left( {W_{{g_{1} {\left( {e,i} \right)}}} - W_{{g_{2} {\left( {e,i} \right)}}} } \right)}{\text{unless}}{\left( {W_{e} - W_{i} } \right)} \leqslant _{{\rm T}} {\emptyset}. $ It follows that the splitting theorems of Sacks and Cooper cannot be combined uniformly.     

On a Conjecture of Kleene and Post

A proof is given that 0 ′ (the argest Turing degree containing a computably enumerable set) is definable in the structure of the degrees of unsolvability. This answers a long‐standing question of Kleene and Post, and has a number of corollaries including the definability of the jump operator.     

Ultra-thin film growth of titanium dioxide on W(1 0 0)

We have employed low energy electron diffraction (LEED) and X-ray photoelectron spectroscopy to follow the epitaxial growth of thin films of TiO₂ on W(1 0 0). The films were grown both by metal vapour deposition of titanium onto the substrate in UHV with subsequent annealing in a low partial pressure of oxygen, and by metal vapour deposition in a low partial pressure of oxygen. LEED patterns showed the characteristic patterns of (1 1 0) oriented rutile. A systematic spot splitting was observed and attributed to a stepped surface. The calculated step height was found to be in good agreement with that expected for rutile TiO₂(1 1 0), 3.3 Å. Titanium core level shifts were used to identify oxidation states as a function of film thickness allowing the interpretation in terms of a slightly sub-stoichiometric interface layer in contact with the substrate. In combination with the LEED patterns, the film structure is therefore determined to be (1 1 0) oriented rutile with a comparable level of stoichiometry to UHV prepared bulk crystals. The ordered step structure indicates considerable structural complexity of the surface.     

Palladium-catalyzed asymmetric allylic alkylation of meso- and dl-1,2-divinylethylene carbonate

The palladium-catalyzed asymmetric allylic alkylation of a 1:1 mixture of dl- and meso-1,2-divinylethylene carbonate is reported. For the first time, both the ionization and nucleophilic addition steps of the catalytic cycle act as enantiodiscriminating steps to give a single product in high enantiomeric excess. The reactions proceed in >98% ee to efficiently generate useful chiral building blocks from acrolein. The absolute and relative configurations of iso-cladospolide B and 11-epi-iso-cladospolide B were verified by total synthesis, solving an apparent discrepancy in the literature.     

Pd and Mo Catalyzed Asymmetric Allylic Alkylation

The ability to control the alkylation of organic substrates becomes ever more powerful by using metal catalysts. Among the major benefits of metal catalysis is the possibility to perform such processes asymmetrically using only catalytic amounts of the chiral inducing agent which is a ligand to the metal of the catalyst. A unique aspect of asymmetric metal catalyzed processes is the fact that many mechanisms exist for stereoinduction. Furthermore, using the same catalyst system, many types of bonds including but not limited to C-C, C-N, C-O, C-S, C-P, and C-H can be formed asymmetrically. An overview of this process using palladium and molybdenum based metals being developed in my laboratories and how they influence strategy in synthesizing bioactive molecular targets is presented.     

Synthesis of enantioenriched γ-quaternary cycloheptenones using a combined allylic alkylation/Stork-Danheiser approach: preparation of mono-, bi-, and tricyclic systems

A general method for the synthesis of β-substituted and unsubstituted cycloheptenones bearing enantioenriched all-carbon γ-quaternary stereocenters is reported. Hydride or organometallic addition to a seven-membered ring vinylogous ester followed by finely tuned quenching parameters achieves elimination to the corresponding cycloheptenone. The resulting enones are elaborated to bi- and tricyclic compounds with potential for the preparation of non-natural analogs and whose structures are embedded in a number of cycloheptanoid natural products.     

Synthesis of sterically hindered enamides via a Ti-mediated condensation of amides with aldehydes and ketones

The first TiCl(4)-mediated condensation of secondary amides with aldehydes and ketones has been achieved. The reaction proceeds at room temperature and is complete within 5 h in most cases. The optimized procedure used 5 equiv of an amine base hinting that the in situ activation of both the amide and the Lewis acid is required. The reaction affords polysubstituted (E)-enamides.     

Ionic radii for Group 1 halide crystals and ion-pairs

Internuclear separations calculated from empirical soft-sphere radii for seventeen crystalline Group 1 halides with rock-salt structures and from empirical hovering-sphere radii for fourteen gaseous Group 1 halide ion-pairs agree well with experimental measurements. Two lithium and four fluoride ion-pairs appear to be anomalous. Soft-sphere ionic radii are compared with atomic radii of noble gases.     

Highly efficient visible-light driven photochromism: developments towards a solid-state molecular switch operating through a triplet-sensitised pathway

We introduce a new highly efficient photochromic organometallic dithienylethene (DTE) complex, the first instance of a DTE core symmetrically modified by two Pt(II) chromophores [Pt(PEt(3))(2)(C≡C)(DTE)(C≡C)Pt(PEt(3))(2)Ph] (1), which undergoes ring-closure when activated by visible light in solvents of different polarity, in thin films and even in the solid state. Complex 1 has been synthesised and fully photophysically characterised by (resonance) Raman and transient absorption spectroscopy complemented by calculations. The ring-closing photoconversion in a single crystal of 1 has been followed by X-ray crystallography. This process occurs with the extremely high yield of 80%--considerably outperforming the other DTE derivatives. Remarkably, the photocyclisation of 1 occurs even under visible light (>400 nm), which is not absorbed by the non-metallated DTE core HC≡C(DTE)C≡CH (2) itself. This unusual behaviour and the high photocyclisation yields in solution are attributed to the presence of a heavy atom in 1 that enables a triplet-sensitised photocyclisation pathway, elucidated by transient absorption spectroscopy and DFT calculations. The results of resonance Raman investigation confirm the involvement of the alkynyl unit in the frontier orbitals of both closed and open forms of 1 in the photocyclisation process. The changes in the Raman spectra upon cyclisation have permitted the identification of Raman marker bands, which include the acetylide stretching vibration. Importantly, these bands occur in the spectral region unobstructed by other vibrations and can be used for non-destructive monitoring of photocyclisation/photoreversion processes and for optical readout in this type of efficiently photochromic thermally stable systems. This study indicates a strategy for generating efficient solid-state photoswitches in which modification of the Pt(II) units has the potential to tune absorption properties and hence operational wavelength across the visible range.     

High-resolution detection of adulteration of maize oil using multi-component compound-specific delta13C values of major and minor components and discriminant analysis

Maize oil commands a premium price and is thus a target for adulteration with cheaper vegetable oils. Detection of this activity presents a particular challenge to the analyst because of the natural variability in the fatty acid composition of maize oils and because of their high sterol and tocopherol contents. This paper describes a method that allows detection of adulteration at concentrations of just 5% (m/m), based on the Mahalanobis distances of the principal component scores of the delta(13)C values of major and minor vegetable oil components. The method makes use of a database consisting of delta(13)C values and relative abundances of the major fatty acyl components of over 150 vegetable oils. The sterols and tocopherols of 16 maize oils and 6 potential adulterant oils were found to be depleted in (13)C by a constant amount relative to the bulk oil. Moreover, since maize oil contains particularly high levels of sterols and tocopherols, their delta(13)C values were not significantly altered when groundnut oil was added up to 20% (m/m) and it is possible to use the values for the minor components to predict the values that would be expected in a pure oil; therefore, comparison of the predicted values with those obtained experimentally allows adulteration to be detected. A refinement involved performing a discriminant analysis on the delta(13)C values of the bulk oil and the major fatty acids (16:0, 18:1 and 18:2) and using the Mahalanobis distances to determine the percentage of adulterant oil present. This approach may be refined further by including the delta(13)C values of the minor components in the discriminant analysis thereby increasing the sensitivity of the approach to concentrations at which adulteration would not be attractive economically.