Fairness in Scheduling

On-line machine scheduling has been studied extensively, but the fundamental issue of fairness in scheduling is still mostly open. In this paper we explore the issue in settings where there are long-lived processes which should be repeatedly scheduled for various tasks throughout the lifetime of a system. For any such instance we develop a notion ofdesiredload of a process, which is a function of the tasks it participates in. Theunfairnessof a system is the maximum, taken over all processes, of the difference between the desired load and the actual load.An example of such a setting is thecarpool problemsuggested by Fagin and Williams [IBM Journal of Research and Development27(2) (1983), 133–139]. In this problem, a set ofnpeople form a carpool. On each day a subset of the people arrive and one of them is designated as the driver. A scheduling rule is required so that the driver will be determined in a “fair” way.We investigate this problem under various assumptions on the input distribution. We also show that the carpool problems can capture several other problems of fairness in scheduling.     

Determination of radiostrontium in soil samples using a crown ether

A simple and rapid method has been developed for the separation and determination of total radiostrontium in soil. The method consists of three basic steps: oxalate precipitation to remove bulk potassium, chromatographic separation of strontium from most inactive and radioactive interferences utilizing a crown ether (Sr. Spec, EIChroM Industries, Il. USA) and oxalate precipitation of strontium to evaluate the chemical yield. Radiostrontium is then determined by liquid scintillation counting of the dissolved precipitate. When 10 g samples of soil are used, the sensitivity of the method is about 10 Bq/kg. The chemical yield is about 80%. The separation and determination of radiostrontium can be carried out in about 8 hours.     

Electron diffraction studies of the molecular structures of iron(II) chloride and iron(II) bromide. Evidence on the structure of dimeric species Fe2Br4

An expression for the extreme values of mean-square amplitudes of vibrations in polyatomic molecules has been derived which permits estimation of the mean-square amplitude without solving the vibrational problem. This expression can be improved for the stretching and scissoring modes when the assignment of frequencies is known. In turn, the corresponding vibrational frequency may be estimated from the experimental value of the mean-square amplitude. The mean-square amplitudes of the butadiene-1,3 molecule are considered as an example.     

Improved sample preparation method for environmental plutonium analysis by ICP-SFMS and alpha-spectrometry

A rapid and simple sample preparation method for plutonium determination in environmental samples by inductively coupled plasma sector field mass spectrometry (ICP-SFMS) and alpha-spectrometry is described. The developed procedure involves a selective CaF₂ co-precipitation for preconcentration followed by extraction chromatographic separation. The proposed method effectively eliminates the possible interferences in mass spectrometric analysis and also removes interfering radionuclides that may disturb alpha-spectrometric measurement. For ²³⁹Pu, ²⁴⁰Pu and ²⁴¹Pu limits of detection of 9.0 fg·g⁻¹ (0.021 mBq), 1.7 fg·g⁻¹ (0.014 mBq) and 3.1 fg·g⁻¹ (11.9 mBq) were achieved by ICP-SFMS, respectively, and 0.02 mBq by alpha-spectrometry. Results of certified reference materials agreed well with the recommended values.     

Synthesis,Spectral and Magnetic Properties,and Crystal Structures of Copper(II) Pyridinecarboxylate Adducts with N‐Heterocyclic Ligands

Synthesis and characterization of seven new complexes [Cu(2‐MeSnic)₂(CH₃OH)]₂ (where 2‐MeSnic is 2‐methylthionicotinate), [Cu(2‐MeSnic)₂L₂]₂ (where L is pyridine — py, ethylnicotinate — Etnic and butylnicotinate — Bunic), [Cu(2‐MeSnic)₂L₂(H₂O)₂] (where L is py and nicotinamide — nia) and [Cu(2‐MeSnic)₂(N‐Menia)₂(H₂O)₂]·2H₂O (where N‐Menia is N‐methylnicotinamide) are reported. The characterization were based on elemental analysis, infrared, electronic and EPR spectra, and magnetic susceptibility measurements over a temperature range of 1.8 — 300 K or 70 — 300 K. Three complexes of different type were studied by X‐ray analysis. The molecule of [Cu(2‐MeSnic)₂(CH₃OH)]₂ has dimeric paddle‐wheel cage structure with a tetragonal pyramidal arrangement around Cu^II. The dimer results from the fact that carboxyl groups of four 2‐MeSnic anions function as bridging in a syn‐syn arrangement. On the other hand [Cu(2‐MeSnic)₂(py)₂]₂ forms dimers with hexacoordinated Cu^II atoms in highly distorted coordination octahedra, each with two oxygen atoms of bridging carboxyl groups in an anti‐anti arrangement of two 2‐MeSnic anions, with two oxygen atoms of one asymmetrically chelating 2‐MeSnic anion and with two nitrogen atoms of two pyridine ligands. The temperature independent EPR spectrum for this complex exhibits an axial signal which corresponds to almost isolated S = ¹/₂ magnetic ions. Magnetic data for the dimer show a weak antiferromagnetic interaction between the two metal ions with J = —0.65 cm^—1. The Cu^II atom in complex [Cu(2‐MeSnic)₂(py)₂(H₂O)₂] is hexacoordinated in an elongated centrosymmetrical tetragonal‐bipyramidal arrangement (4 + 2). Based on the molecular structure the electronic, infrared, electron paramagnetic resonance spectra and magnetic properties are discussed and stereochemistry as well as the mode of ligand coordination in new solid complexes under study have been determined.     

Line absorption of matrix elements as a background correction error in atomic absorption spectrometry

Accurate measurement of weak atomic absorption signals is only possible after exact background correction. If the accompanying elements in excess have their own resonance lines in the immediate vicinity of the resonance line of the element to be determined,and these fall within the spectral band transmitted by the monochromator, then the value the measured apparent background absorbance is higher than the true one. The error may usually be diminished by choosing an appropriate spectral bandwidth. Tables of such bandwidths for a large number of pairs of elements are given.     

Sr and stable strontium in bones of wild, herbivorous animals from Poland

Activity concentration of ⁹⁰ Sr and stable strontium concentration was analysed in 42 samples of animal (deer, roe-deer, elk and boar) bones, which mostly originated from north-eastern Poland. Strontium separation was performed by extraction chromatography. Determination of chemical yield was controlled by means of stable Sr determination using atomic spectrometry at the beginning and at the end of the separation procedure. Equilibrated ⁹⁰ Sr and ⁹⁰ Y activity was measured using a liquid scintillator spectrometer. Stable strontium range was from 55.4±1.7 ppm to 91.8±4.5 ppm, the mean was 71.84 ppm with a standard deviation (SD) of 9.31 ppm. The mean recovery of strontium was 26.7% with SD = 16.1%. The maximum activity of ⁹⁰ Sr, equal to 629±13 Bq/kg (ash) was found for a deer sample from Augustów Primeval Forest. In average, deer show the highest radiostrontium level, followed by roe-deer, elk and the lowest level were observed for boar. Differences between boar and deer or roe-deer are significant in terms of Kruskal-Wallis statistical test. Animal bones from north-eastern Poland showed about twice the mean concentration of ⁹⁰ Sr, compared to those of south-central Poland, but the difference was found not significant. Activities observed in roe-deer bones suggest the deposition of a concentration of 1.9 to 3.5 kBq/m² in the average of Chernobyl-origin ⁹⁰ Sr in 1986 in north-eastern Poland.     

Identifiability classes in reaction kinetics

Some difficulties of eliciting reliable rate constants from experimental data are considered. Different classes of ill-posed estimation problems are given and demonstrated by simple examples.

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