A Novel and Efficient Synthesis of 2,3-Dichloroquinoline

2,3-Dichloroquinoline was prepared in three steps in good overall yield from commercial 3-bromoquinoline via N-oxide formation and rearrangement to 3-bromocarbostyril, followed by a one-pot conversion to 3-bromo-2-chloroquinoline and halogen exchange to the title compound.     

Intramolecular Baylis-Hillman Reaction: A Pathway to Substituted Coumarins

The acrylate ester of salicylaldehyde, in the presence of DABCO, affords a crystalline coumarin salt. Formation of this derivative confirms a vital intermediate in the mechanism of the reaction. Salicylaldehyde, suitably protected, reacts with methyl acrylate to afford a novel coumarin not unlike the vasodilator chromonar.     

Spatial updating, spatial transients, and regularities of a complex automaton with nonperiodic architecture

We study the dynamics of patterns exhibited by rule 52, a totalistic cellular automaton displaying intricate behaviors and wide regions of active/inactive synchronization patches. Systematic computer simulations involving 2(30) initial configurations reveal that all complexity in this automaton originates from random juxtaposition of a very small number of interfaces delimiting active/inactive patches. Such interfaces are studied with a sidewise spatial updating algorithm. This novel tool allows us to prove that the interfaces found empirically are the only interfaces possible for these periods, independently of the size of the automata. The spatial updating algorithm provides an alternative way to determine the dynamics of automata of arbitrary size, a way of taking into account the complexity of the connections in the lattice.     

Numerical rheometry of bulk materials using a power law fluid and the lattice Boltzmann method

In the present study, the flow of bulk materials is characterised as a non-Newtonian fluid and modelled using the lattice Boltzmann method. A power law and a Bingham model is implemented in the LBM, which is hydrodynamically coupled to the discrete element method (DEM) for structural interaction. The performance of both non-Newtonian models is assessed, both qualitatively and quantitatively, in benchmark problems. The validated, non-Newtonian LBM–DEM framework is then applied to the geometry of a cylindrical Couette rheometer to numerically determine the constitutive response of a sample of Leighton Buzzard sand. The numerical results, which employ the power law, are compared with experimental data, and a number of other synthetic soil samples are defined using the presented process of numerical rheometry. Finally, the numerical stress–strain rate response of the synthetic soil samples is interpreted within the context of a regularised Bingham model, and the similarities discussed.     

Values of games without side payments

A value forn-person games without side payments is given which coincides with theShapley value for games with side payments, and with theNash value for two-person games.     

A class of loss functions of catenary form

The catenary form of loss function is considered in the framework of Bayesian decision theory. The mathematical tractability of this form seems to be unrecognized; it contains quadratic loss as a limiting case. For various probability distributions expressions are given for posterior analysis, and limiting properties are investigated.     

Optimal threat strategies of bimatrix games

A bi-matrix threat game is defined as a triple (A,B,S) whereA andB arem×n payoff matrices, andS is a closed convex subset of the plane, with (a _ij,B _ij) εS for eachi,j. Given (threat) mixed strategiesx andy,Nash's model suggests that the eventual outcome will be that point (u, v) εS which maximizes the product (u ?xAy ^t) (v ?xBy ^t) subject tou ≥xAy ^t,v ≥xBy ^t. Optimality of the threat strategies is then defined in the obvious way. A constructive proof of existence of optimal threat strategies is given; in particular, it is shown that they are optimal strategies for the matrix gameA-kB, wherek is to be determined. In this paper,k is approximated by aNewton-Raphson technique. Two examples are solved in detail.     

Infrared spectra and molecular conformation of butyronitrile and methyl thioacetonitrile

The infrared absorption spectra of two related compounds, butyronitrile (CH₃CH₂-CH₂CN) and methylthioacetonitrile (CH₃SCH₂CN) have been examined in the liquid and solid phases. Vapour phase spectra of butyronitrile have also been recorded. Evidence is given for the existence of two rotational isomers trans and gauche, for both compounds. In both cases the energy difference between the two rotamers appears to be small with the gauche form identified as the low energy conformer for butyronitrile. For methylthioacetonitrile it was not possible to determine the more stable rotational isomer.