The job-shop problem and immediate selection

The job-shop problem is one of the most difficult NP-hard scheduling problems. A 10×10-problem published in 1963 has been solved only recently by Carlier and Pinson using a branch and bound method. Other branch and bound algorithms have been developed recently. The efficiency of all these branch and bound methods relies on the concept of immediate selection which allows to introduce order relations on the setI of all operations to be processed on the same machine before branching. We present new algorithms for immediate selection. Among them are

1. anO(max {n logn,f})-algorithm for fixing all disjunctions induced by cliques;
2. anO(n ²)-algorithm based on concepts which are different from those used by Carlier and Pinson.

Here,n is the number of operations inI andf is the number of induced order relations.     

On the interpretation of random forces derived by projection operators

We study the derivation of a Langevin equation from a microscopic basis in order to elucidate the nature of the random force. We arrive at the conclusion that the consistent interpretation of the microscopic Langevin equation in terms of a stochastic differential equation (SDE) is according to I o rules. In addition, the random force is in general not Gaussian, and it is hence not completely characterized by its second moments.     

Radiometric titration based on colloidal and slow precipitate formation

Fluoride ions and, in about 0.005M concentration, tungstate ions form gelatinous precipitates, poorly soluble in water, with calcium ions. The radiometric determinations of the above ions are based on these reactions. Accurate radiometric determination can be carried out only if the gelatinous precipitate formed during titration can be properly separated from the solution. It has been found that in the case of fluoride ions the application of crystalline, easily filtrable Ca(COO)₂·H₂O or CaCO₃, and in the case of tungstate ions the application of CaWO₄ precipitate improves the filtration properties of⁴⁵CaF₂ and⁴⁵CaWO₄, respectively, formed during titration, whereby the radiometric determinations of the above ions become possible. Titrations were carried out with 0.05M and 0.005M CaCl₂ solutions, labelled with⁴⁵Ca.     

Elimination of 1,3-Dioxolan-2-yliden from cyclic ethylene ketals

The structural prerequisites for an elimination of :C(OCH₂)₂ from the molecular ions of ethylene ketals of cyclic ketones are discussed.     

Analysis of aerosols at the bosporus bridge of Istanbul

Air samples collected at the second Bosporus bridge of Istanbul which carries a heavy traffic load between Asia and Europe, were analyzed for 22 elements by the INAA method. Pb, Cd and Fe concentrations in the samples were determined by AAS. Iron concentrations were used as a cross check between the two methods. In order to define the enrichment factors for the elements in the bridge area, a sample collected from our university campus which can be considered as a rural site, was also analyzed. Differences were observed especially for Br, Al, Mg, Ti, Cu and Na between the two sites. Based on the results of the samples from the bridge, we got a value of 0.58(16) for the Br/Pb-ratio.     

On the construction of least favourable pairs of distributions

Summary Convex programming techniques were used by Witting and Krafft in [4] in order to reduce a testing problem for composite hypotheses to one for simple hypotheses. This is realized in terms of least favourable pairs of distributions, which represent the solution of the dual of a suitable program. Without further assumptions on the hypotheses, however, the results, derived that way (cf. Baumann [1], Österreicher [6] and Kusolitsch and Österreicher [5]), are of less practical impact. This is due to the fact that in this case the least favourable pairs depend on the level of the testing problem. Conditions avoiding this, were given by Huber and Strassen in [3]. These conditions make use of 2-alternating capacities in the sense of Choquet. The present paper offers a rather general principle of constructing the least favourable distribution in the case, when one of the two hypotheses is simple. This method works also for the local variation model and the Prohorov neighbourhood model in the case of monotone likelyhood ratio. For simple cases—subsuming the gross error model and the total variation model, for which the solution was given by Huber in [2]—a least favourable pair is obtained by using the mentioned technique of construction two times successively.     

Selective LC Determination of Cabergoline in the Bulk Drug and in Tablets: In Vitro Dissolution Studies

Cabergoline (CAB) is an ergot alkaloid derivative with dopamine agonist activity. A novel, simple, and rapid stability-indicating high-performance liquid chromatographic (HPLC) method for assay of CAB in tablets has been developed and validated. Chromatography was performed on a 4.6 mm i.d. × 250 mm, 5 μm particle, cyano column with acetonitrile–10 mM phosphoric acid, 35:65 (v/v), containing 0.04% triethylamine, as mobile phase, at a flow rate of 1.0 mL min^?1, and UV detection at 280 nm. Response was a linear function of concentration in the range 0.1–4 μg mL^?1 (r ² = 0.9999). The recovery of the method was good (99.45%) and RSD values for intra-day and inter-day precision were 0.24–0.88% and 0.66–1.19%, respectively. The method can be used for quality-control assay of CAB in tablets, for stability studies, and for in vitro dissolution studies.     

Investigation of the NMR enhancement factor in CuMn spin glasses

The NMR enhancement factor of a frozenCuMn spin glass has been measured at a temperatureT?T _g /5. The measurements were performed as function of static magnetic fields of different directions. A two component model of a spin glass has been outlined. One component being a “system of single spins” and the other one being a “subsystem of clusters”. Both components were attributed to different kinds of interaction being RKKY and dipole interaction respectively. The effective anisotropy field of the single spin system consists of two unidirectional contributionsH _a ^s andH _a ^c , which have been measured for different conditions. A second anisotropy fieldH _d binds the cluster system to the system of single spins. All anisotropy fields depend on the annealing temperature of the alloys.