Dynamic mechanical analysis (DMA), 13c solid state nmr and micro-thermomechanical studies of historical parchment

DMA and solid state ¹³C NMR techniques were used to measure historical parchment samples within the framework of the project (MAP) Micro Analysis of Parchment (EC contract No. SMT4-96-2101) in collaboration with the School of Conservation in Copenhagen. DMA was used in both thermal scan and creep modes. Thermal scans provided information on the transitions associated with the collagen polymer. Microthermal analysis was also used to obtain information on the topography and thermal conductivity of sample areas of 100 μm. Localised heating enabled measurements of softening transitions in the sample. This behaviour is influenced by the chemical composition of parchment. 13C NMR provided information on the carbon atoms associated with the polypeptide chains of the collagen in parchment. The behaviour of samples immersed in water and measured in DMA creep mode was used to measure the shrinkage behaviour of the parchment samples. The different but complementary techniques provided a means for characterising the physicochemical state of parchment samples. This revised version was published online in July 2006 with corrections to the Cover Date.     

Complete 1H and 13C NMR assignments of two phytosterols from roots of Piper nigrum

Using modern NMR techniques, including DQF-COSY, NOESY, HETCOR and HMBC, the full assignments of all 1H and 13C chemical shifts were made for stigmastane-3,6-dione and stigmast-4-ene-3,6-dione, isolated from the roots of Piper nigrum (Piperaceae). Their stereochemistry was resolved by a combination of 2D NOESY data and analysis of coupling constants. The two compounds were isolated from the genus Piper for the first time.     

The tert-butyl-NNO-azoxy group in the synthesis of 1,2,4-benzotriazin-3(4H)-one 1-oxides

Treatment of 2-(tert-butyl-NNO-azoxy)anilines with phosgene at 20 °C was proposed as a novel route to 1,2,4-benzotriazin-3(4H )-one 1-oxides. This method involves a new reaction, viz., an intramolecular interaction of the tert-butyl-NNO-azoxy group with a C-electrophile (leading to the formation of the N(2)—C(3) bond of the triazine ring) followed by elimination of the tert-butyl group. Complete assignment of the signals in the ¹H and ¹³C NMR spectra of the compounds obtained was performed. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 8, pp. 1507–1509, August, 2007.     

Implementation of a general multireference configuration interaction procedure with analytic gradients in a semiempirical context using the graphical unitary group approach

The graphical unitary group approach has been applied in an efficient implementation of a general multireference configuration interaction (MRCI) method for use with small active molecular orbital spaces in a semiempirical framework. Gradients can be computed analytically for molecular orbitals from a closed-shell or a half-electron open-shell Hartree-Fock calculation. CPU times for single point energy and gradient calculations are reported. The code allows MRCI geometry optimizations of large molecules, as illustrated for the singlet ground state and the four lowest triplet states of fullerene C(76).     

Solvent-induced electronic spectral shifts: Benzene·Arn revisited

Just what can be learned about cluster dynamics (and, more generally, about solvation dynamics) from spectral studies of small clusters that have been doped with a chromophore is still an open question. In the present work we suggest a novel procedure for calculating the shift in the electronic absorption spectrum of a chromophore deriving from the attachment to or the incorporation in a cluster. The particular system of interest here is benzene·Ar _n , for which experimental results are readily available although their interpretation has been a point of controversy. In addition, since the present formalism is equally applicable to a chromophore isolated in a bulk phase (either liquid or solid), we are able to venture an explanation for the apparent observation that the spectral shift of cluster-isolated benzene does not approach the asymptotic values characteristic of the bulk-isolated species.     

Orthmodular lattices whose MacNeille completions are not orthomodular

The only known example of an orthomodular lattice (abbreviated: OML) whose MacNeille completion is not an OML has been noted independently by several authors, see Adams [1], and is based on a theorem of Ameniya and Araki [2]. This theorem states that for an inner product space V, if we consider the ortholattice ?(V,⊥) = {A \( \subseteq \) V: A = A ^⊥⊥} where A ^⊥ is the set of elements orthogonal to A, then ?(V,⊥) is an OML if and only if V is complete. Taking the orthomodular lattice L of finite or confinite dimensional subspaces of an incomplete inner product space V, the ortholattice ?(V,⊥) is a MacNeille completion of L which is not orthomodular. This does not answer the longstanding question Can every OML be embedded into a complete OML? as L can be embedded into the complete OML ?(V,⊥), where V is the completion of the inner product space V. Although the power of the Ameniya-Araki theorem makes the preceding example elegant to present, the ability to picture the situation is lost. In this paper, I present a simpler method to construct OMLs whose Macneille completions are not orthomodular. No use is made of the Ameniya-Araki theorem. Instead, this method is based on a construction introduced by Kalmbach [7] in which the Boolean algebras generated by the chains of a lattice are glued together to form an OML. A simple method to complete these OMLs is also given. The final section of this paper briefly covers some elementary properties of the Kalmbach construction. I have included this section because I feel that this construction may be quite useful for many purposes and virtually no literature has been written on it.     

Search

This paper reviews the theory of search. The main viewpoint is statistical but considerable space is spent on connections with other fields such as logic and optimisation. Three primitive ideas dominate: consistency, entropy, and Bayes' methods. The theory of screening provides one of the central examples and there is a section on nonsequential random search deriving from the work of Renyi. The game of Bulls and Cows provides a motivating example for both sequential and nonsequential algorithms.     

A geometric construction of local representations of local Lie groups

Local transformation groups acting on a manifold X define a natural action of on a space D(X), of functions on X. The natural action induces a local representation of on a Hilbert subspace of the space of distributions on D(X).     

Chromatic number of Hasse diagrams,eyebrows and dimension

We construct posets of dimension 2 with highly chromatic Hasse diagrams. This solves a previous problem by Nesetril and Trotter.