The orienteering problem with stochastic travel and service times

In this paper, we introduce a variant of the orienteering problem in which travel and service times are stochastic. If a delivery commitment is made to a customer and is completed by the end of the day, a reward is received, but if a commitment is made and not completed, a penalty is incurred. This problem reflects the challenges of a company who, on a given day, may have more customers than it can serve. In this paper, we discuss special cases of the problem that we can solve exactly and heuristics for general problem instances. We present computational results for a variety of parameter settings and discuss characteristics of the solution structure.     

Formal synthesis of dictyostatin and synthesis of two dictyostatin analogues

A formal convergent synthesis of dictyostatin from (R)-Roche ester is described. Synthetic highlights include a Ni-catalyzed Nozaki-Hiyama-Kishi coupling between an aldehyde and a Z vinyl iodide to assemble the two main fragments, a diastereoselective Myers alkylation, a stereoselective Evans aldolization, two asymmetric Duthaler crotyltitanations, and a stereoselective Pd-catalyzed Marshall allenylindium addition to install the stereogenic centers of dictyostatin. The synthesis of (9R)-epi-dictyostatin and a new ring-contracted dictyostatin isomer were also achieved.     

Rate constants for O(3P) recombination and association with N(4S)

It is shown that N(⁴S) and O(³P) atom quenching effects upon chemiluminescence from NO(B²π) (θ = 0) are of importance when this emissio Values of k₂ = (1.74 ± 0.13) × 10⁹ and (4.05 ± 0.17) × 10⁹ &² mole^-2 sec^-1 are found at 298 and 196°K respectiv     

The determination of sulphate in fertilizers by atomic absorption spectrometry

Methods are described for the determination of sulphate in superphosphate fertilizers. Barium sulphate precipitated from an acidified EDTA solution is filtered onto a membrane filter and redissolved in ammoniacal EDTA, and the barium equivalent to the sulphate is determined by atomic absorption spectrometry. Alternatively, after precipitation of calcium as oxalate during sample solution preparation, and by following a similar sulphate precipitation technique, excess of barium is determined in the filtrate. No interferences were encountered when a nitrous oxide—acetylene flame was used with a potassium ionization buffer.     

Radionuclide emitters for high-temperature measurements on metals using positron annihilation

The fabrication of⁶⁸Ge and⁴⁴Ti positron sources which can withstand temperatures up to 1000°C is described. The sources are designed for use in the measurement of thermally-generated vacancy concentrations by the positron trapping technique. Measurements of positron lifetimes and Doppler-broadened annihilation photon lineshapes indicate that if suitable corrections are made the contribution of source matrix annihilations to experimental data can be reduced to less than 0.5% of the total annihilation events.     

Surface entropy of rare-gas clusters

Abundances of ArN+ and XeN+ clusters produced in a supersonic expansion source are inverted to find relative dissociation energies. The values around the shell and subshell closings at N=55, 71, and 147 differ from theoretical values derived from ground-state energies of Lennard-Jones clusters. A significant part of the difference can be accounted for by the conformational entropies of surface atoms and vacancies.     

Algebraic computing and the Newman-Penrose formalism in general relativity

The curvature tensor of space-time can be described most concisely by giving the components of the Weyl and Ricci tensors relative to a complex null tetrad. The Newman-Penrose equations provide a simple and direct algorithm for calculating these components. This paper describes a computer program, written in the symbolic manipulation language CAMAL, which performs this calculation. Comparisons are made with the classical tensorial method of calculation, and some applications are discussed.