Prescriptions and Ingredients for Controlled CC Bond Formation with Organometallic Reagents. New synthetic methods (5)

Merits and drawbacks of known carbon-carbon linking procedures are outlined. Two novel methods are discussed in some detail: the copper-catalyzed alkylation of Grignard reagents and reactions with allylpotassium compounds. Both methods provide a very efficient access to saturated, unsaturated, as well as functionally substituted hydrocarbons and moreover permit an astonishing degree of regio- and stereoselective control of olefin synthesis.     

The structure of 1-formyl-3-phenyl-Δ-pyrazoline in the gas phase (DFT calculations), in solution (NMR) and in the solid state (X-ray crystallography)

The molecular structure of 1-formyl-3-phenyl-Δ²-pyrazoline was determined by X-ray crystallography (triclinic, P-1). The geometry thus obtained was compared with that obtained by DFT calculations. The GIAO method was used to calculate absolute shieldings, which agree conveniently with those measured by ¹³C and ¹⁵N NMR. The title compound appears to be an essentially planar molecule.     

In-capillary micro solid-phase extraction and capillary electrophoresis separation of heterocyclic aromatic amines with nanospray mass spectrometric detection

A miniaturised technique to analyse and detect heterocyclic aromatic amines (HAs) using micro solid-phase extraction (SPE) coupled on-line (in-capillary) to capillary electrophoresis (CE) separation with nanospray (nESI) mass spectrometry (MS) detection has been developed. HAs are mutagenic and carcinogenic compounds formed at low levels in protein-rich food during cooking. Due to the low concentrations of HAs and the high complexity of the matrix in which they exist, sensitive and selective analytical methods are required for quantification. SPE was performed on a packed bed of C₁₈ particles inside the CE capillary, which minimised the dead volume. The on-line coupling of SPE, CE and nESI-MS reduced the time for extraction and identification to less than half an hour, which will allow for screening of several samples per day. The new technique provides short analysis time, low sample and solvent consumption, and HAs in standard solutions were easily detected at 12–17 fmol injections, and in spiked urine samples at 750–810 fmol injections.     

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.     

Quadratically constrained least squares and quadratic problems

Summary We consider the following problem: Compute a vectorx such that Ax–b₂=min, subject to the constraint x₂=. A new approach to this problem based on Gauss quadrature is given. The method is especially well suited when the dimensions ofA are large and the matrix is sparse.It is also possible to extend this technique to a constrained quadratic form: For a symmetric matrixA we consider the minimization ofx ^T A x–2b ^T x subject to the constraint x₂=.Some numerical examples are given.This work was in part supported by the National Science Foundation under Grant DCR-8412314 and by the National Institute of Standards and Technology under Grant 60NANB9D0908.     

Differential calculus on quantized simple lie groups

Differential calculi, generalizations of Woronowicz's four-dimensional calculus on SU _q (2), are introduced for quantized classical simple Lie groups in a constructive way. For this purpose, the approach of Faddeev and his collaborators to quantum groups was used. An equivalence of Woronowicz's enveloping algebra generated by the dual space to the left-invariant differential forms and the corresponding quantized universal enveloping algebra, is obtained for our differential calculi. Real forms for q are also discussed.