Discrete facility location with nonlinear diseconomies in fixed costs

A discrete facility location problem is formulated where the total fixed cost for establishing the facilities includes a component that is a nonlinear function of the number of facilities being established. Some theoretical properties of the solution are derived when this fixed cost is a convex nondecreasing function of the number of facilities. Based on these properties an efficient bisection heuristic is developed where at each iteration, the classical uncapacitated facility location and/or m-median subproblems are solved using available efficient heuristics.     

Pulsed double resonance in the pure quadrupole regime: off-resonant DRRF technique for detection of rare quadrupolar nuclei

A scheme for the detection of rare quadrupolar nuclei based on off-resonant pulse excitation of the abundant quadrupolar nuclei coupled to the rare ones in the sample has been outlined and demonstrated. Pure quadrupole resonance spectrum of ²³Na in poly-crystalline samples of sodium chlorate has been thus recorded at room temperature. The present double resonance scheme in the pure quadrupole regime is marked by a substantial reduction in spectrometer transmitter power and hardware requirements.     

On a nonstandard two-parametric quantum algebra and its connections withU p,q (gl(2)) andU p,q(gl(1/1))

A quantum algebraU _{p, q} (,H,X _±) associated with a nonstandardR-matrix with two deformation parameters (p, q) is studied and, in particular, its universal -matrix is derived using Reshetikhin's method. Explicit construction of the (p, q)-dependent nonstandardR-matrix is obtained through a coloured generalized boson realization of the universal -matrix of the standardU _{p, q}(gl(2)) corresponding to a nongeneric case. General finite dimensional coloured representation of the universal -matrix ofU _{p, q}(gl(2)) is also derived. This representation, in nongeneric cases, becomes a source for various (p, q)-dependent nonstandardR-matrices. Superization ofU _{p, q}(,H,X _±) leads to the super-Hopf algebraU _{p, q}(gl(1/1)). A contraction procedure then yields a (p, q)-deformed super-Heisenberg algebraU _{p, q}(sh(1)) and its universal -matrix.     

Reduced fluidity of dipalmitoyl phosphatidic acid membranes by salicylic acid

This paper presents DSC and NMR study of how the kerotolytic drug, salicylic acid (SA), affects the thermotropic and morphological behavior of a model membrane, dipalmitoyl phosphatidic acid (DPPA). The membrane-drug system has been studied in the multilamellar vesicular (MLV) and in the unilamellar vesicular (ULV) forms, for SA/DPPA molar ratios from 0 to 0.5. The mode of interaction of SA molecules with DPPA is similar in MLV and ULV. Chain-melting transition becomes sharper and shifts to higher temperatures in the presence of the drug, implying an enhanced co-operativity of the acyl chains. NMR and DSC data indicate that the drug molecules are located in the aqueous interfacial region neighboring the lipid headgroups. The membrane becomes more rigid in the presence of the drug molecules, due to a stronger interaction between the lipid headgroups leading to reduced permeability. ULVs are destroyed by even a short equilibration at room temperature, whereas prolonged equilibration of the MLV only leads to a slightly reduced interaction between the lipid headgroups due to sequestering of the drug molecules in the interfacial aqueous region.     

Polarographic reduction behaviour of copper in the presence of 1-amino-3-methoxypropane and 2-dimethylaminoethanol

1-Amino-3-methoxypropane (3MPA) and 2-dimethylaminoethanol (DMAE) are potential volatile amines for boiler water treatment and were investigated for their complexation behaviour with copper. Their pK_b values were 3.67 and 4.52 at 25°C and they formed coloured complexes with absorption in the region of 644 and 510 nm, respectively. In the pH range 10–11, the Cu-3MPA complex exhibited stepwise reduction and [Cu(3MPA)₂]⁺ was identified, with a stability constant of 10^9.52. In the pH range 8–10.5, the Cu-DMAE complex exhibited 2e^? reduction and the species [Cu(DMAE)₂(OH)₂] was identified, with a stability constant of 10^20.39. A correlation between visible and ESR spectra and reduction behaviour was established.     

Thermische Reaktionen mit 3-Phenyl-2H-azirinen; 1, 3-dipolare Cycloadditionen und En-Reaktionen

Benzonitrile p-nitrobenzylide ( 5 ) undergoes 1,3-dipolar cyclo-additions in the presence of 3-phenyl-2H-azirines ( 1 ), yielding in benzene at 0° 2-(p-nitrophenyl)-4,5-diphenyl-1,3-diazabicyclo[3.1.0]hex-3-enes ( 7 , scheme 2). Under the basic conditions of the reaction mixture, 7 a and 7 b are partially converted to 2-(p-nitrophenyl)-4,5-diphenyl-1,6-dihydropyrimidines ( 8a, b ) which are dehydrogenated by oxygen to the corresponding pyrimidines 9a and 9b , respectively. 3-Phenyl-2H-azirines ( 1 ) form, on heating at 145° in xylene in the presence of the azalactone 32 (2,4-diphenyl-Δ²-oxazolin-5-one), 4-(aziridin-2′-yl)-2,4-diphenyl-Δ²-oxazolin-5-ones ( 33 , scheme 11). 33 arises from an ene reaction of the enol form of 32 with 1 . Similar ene reactions are observed with the azirines 1 and dimedone ( 37 , scheme 12). Under the ene reaction conditions (xylene, 145°), the non-isolated intermediate primary adducts ( 38a and 38b ) undergo rearrangements of the vinylcyclopane-cyclopentene type to give 6,6-dimethyl-4-oxo-1,3-diphenyl-4, 5, 6, 7-tetrahydroisoindole ( 40 ) and 6, 6-dimethyl-4-oxo-3-phenyl-4, 5, 6, 7-tetrahedroindole ( 42 ), respectively.     

Finite-dimensional quantum mechanics of a particle

This paper analyzes the possible implications of interpreting the finitedimensional representations of canonically conjugate quantum mechanical position, and momentum operators of a particle consistent with Weyl's form of Heisenberg's commutation relation as the actual position, and momentum operators of the particle when it is confined to move within a finite spatial domain, and regarding the application of current quantum mechanical formalism based on Heisenberg's relation to such a situation as an asymptotic approximation. In the resulting quantum mechanical formalism the discrete and finite position and momentum spectra of a particle depend on its rest mass and the spatial domain of confinement. Such a finite-dimensional quantum mechanics may be very suitable for describing the physics of particles confined to move within very small regions of space.