An Enhancement of the Drezner—Wesolowsky Algorithm for Single-Facility Location with Maximin of Rectilinear Distance

In this note, we examine the algorithm of Drezner and Wesolowsky for locating a facility with maximin rectilinear distance to a given set of demand points. The concept of the closest-point constraint is introduced as a technique for increasing the efficiency of the algorithm. This potential increase in efficiency is demonstrated by an example.     

High-precision Monte Carlo test of the conformai-invariance predictions for two-dimensional mutually avoiding walks

Let _l be the critical exponent associated with the probability thatl independentN-step ordinary random walks, starting at nearby points, are mutually avoiding. Using Monte Carlo methods combined with a maximum-likelihood data analysis, we find that in two dimensions ₂=0.6240±0.0005±0.0011 and ₃=1.4575±0.0030±0.0052, where the first error bar represents systematic error due to corrections to scaling (subjective 95% confidence limits) and the second error bar represents statistical error (classical 95% confidence limits). These results are in good agreement with the conformal-invariance predictions ₂=5/8 and ₃=35/24.     

Pattern formation in diffusion-limited reactions

The conditions for macroscopic segregation ofA andB in a steady-stateA+B 0 reaction are studied in infinite systems. Segregation occurs in one and two dimensions and is marginal ford=3. We note the dependence of these results on the precise experimental conditions assumed in the theory. We also note the difference between these results and our earlier ones for finite systems where the critical dimension isd=2.     

Application of stir bar sorptive extraction for wine analysis

Stir bar sorptive extraction (SBSE) coupled with gas chromatography/mass spectrometry (GC/MS) was used to analyse wine samples for three applications: flavour and compositional analysis; 2,4,6-trichloroanisole (TCA), a common off-aroma in wine; and agrochemicals. SBSE was found to be orders of magnitude more sensitive than modern conventional methodology, allowing for lower detection and quantitation levels, and improved confirmation of identity; SBSE often gave better signal to noise in scan mode than other methods in selective ion monitoring (SIM) mode. With the help of their characteristic mass spectra all agrochemicals could be identified unambiguously at concentrations of 10 microg L(-1) in wine and a further 100 constituents were detected in a Cabernet Sauvignon sample. Thus it is now possible to analyse complex samples such as wine by scan mode, with better confirmation of identity, and without sacrificing sensitivity, where previously SIM methodology had to be used.     

Efficient synthesis of enynecarbamates and their ring-closing metathesis/[4 + 2] Diels-Alder cycloaddition: synthesis of hexahydroisoquinolines

Enynes 5a-g were prepared in moderate to good yields from 1-(triphenylphosphoranylideneaminoalkyl)benzotriazoles. Ring-closing metathesis of 5a-f afforded functionalized dienes 6a-f, respectively, which were used in a Diels-Alder cycloaddition reaction in the synthesis of the corresponding hexahydroisoquinoline derivatives 7a-f.     

Lithiation and electrophilic substitution of 8-chlorodibenz[b,f][1,4]-oxazepine-10-tert-butylcarbamate: The preparation of novel fused heterocyclic derivatives of 8-chlorodibenzoxazepine

Lithiation of 8-chlorodibenz[b,f][1,4]oxazepine-10-tert-butylcarbamate ( 1 ) is described. Electrophilic substitution of the resulting N-Boc dibenzoxazepine α- lithioamine 2 with ketones, aldehydes, nitriles, iso-cyanates and imines, followed by an in-situ cyclization, gave fused carbamates 5–26 , fused 2H-imidazol-2-ones 27–29 , fused hydantoins 30–32 , and fused ureas 33–35 , respectively, in 11–66% yield.     

Networks and chain coverings in partial orders and their products

For an arbitrary poset P, subposets {P _i : 1ik} form a transitive basis of P if P is the transitive closure of their union. Let u be the minimum size of a covering of P by chains within posets of the basis, s the maximum size of a family of elements with no pair comparable in any basis poset, and a the maximum size of an antichain in P. Define a dense covering to be a collection D of chains within basis posets such that each element belongs to a chain in D within each basis poset and is the top of at least k-1 chains and the bottom of at least k-1 chains in D. Dense coverings generalize ordinary chain coverings of poset. Let d=min {|D|–(k–1)|P|}. For an arbitrary poset and transitive basis, a convenient network model for dense coverings yields the following: Theorem 1: da, with equality iff P has a minimum chain decomposition in which every pair of consecutive elements on each chain are comparable in some basis poset. Theorem 2: usda. Theorem 3: s=d iff s=a. The most interesting special case is where the transitive basis expresses P as the product of two posets, in which case u and s measure the minimum and maximum sizes of unichain coverings and semiantichains.