Probabilistic Analysis of Condition Numbers for Linear Programming

In this paper, we provide bounds for the expected value of the log of the condition number C(A) of a linear feasibility problem given by a n × m matrix A (Ref. 1). We show that this expected value is O(min{n, m log n}) if n > m and is O(log n) otherwise. A similar bound applies for the log of the condition number C _R(A) introduced by Renegar (Ref. 2).     

Synthesis of polysiltrimethylenes with trimethylsilyl groups in the branch of the main chain

The thermally initiated and platinum-catalyzed polymerization of 1-silacyclobutanes with substitutents containing a trimethylsilyl group was carried out. Soluble, high-molecular-weight, heterochain siltrimethylene polymers were obtained, containing trimethylsilyl groups removed from the main chain by various bridges.A. V. Topchiev Institute of Petrochemical Synthesis, Russian Academy of Sciences, 117912 Moscow. Translated from Izvestiya Akademii Nauk, Seriya Khimicheskaya, No. 1, pp. 223–225, January, 1992.     

Application of microwave digestion to the preparation of sediment samples for arsenic speciation

Several extraction procedures are described allowing arsenic speciation in sediments. The extraction of organometallic compounds such as dimethylarsinic acid or monomethylarsonic acid is quite simple since these compounds are stable in the different extraction media (HCl/ HNO₃, H₃PO₄, ammonium oxalate) and are easily released independent of the extraction mode (magnetic stirring or microwave solubilization). Extraction yields are higher than 96% for these two arsenic forms. An HCl/HNO₃ microwave solubilization procedure allows the quantitative solubilization of mineral arsenic, but the differentiation between the two oxidation states is not possible owing to the oxidation of As(III) to As(V). Extractions with orthophosphoric acid or ammonium oxalate allow the solubilization of mineral arsenic with extraction yields ranging from 90 to 95% and the differentiation between As(III) and As(V). Nevertheless, the amount of As(III) is underestimated owing to its partial oxidation. The usefulness and advantages of microwave solubilization compared with conventional extraction procedures are discussed. Received: 17 May 1996 / Revised: 19 September 1996 / Accepted: 25 September 1996     

Geometrical restrictions of water diffusion in aqueous protein systems. A study using NMR field-gradient techniques

Geometrical restrictions of water diffusion in different aqueous protein systems were studied using two versions of the NMR field gradient technique. The samples were aqueous systems of bovine serum albumin, gelatin and horse myoglobin at concentrations ranging from diluted solutions to almost dry powders being only partly hydrated. Hydrated protein aerogels were produced by the aid of a special preparation procedure and studied in addition. The experiments referred to the, temperature and concentration dependences of the water diffusion coefficient above and below the free-water freezing temperature. The diffusion coefficient within clusters of overlapping hydration shells is reduced by one order of magnitude compared with that of bulk water. Geometrical restrictions manifest themselves (a) by the obstruction effect observed at low protein concentrations, (b) by the topologically two-dimensional diffusion in the network of overlapping hydration shells, (c) by the percolation threshold appearing at about 15%_b.w. water and (d) by the anomalous diffusion behaviour concluded from the protein aerogel study.     

Growth properties of Sobolev space functions over unbounded domains

Summary We study Sobolev space functions with prescribed growth properties on large spheres. In particular, we prove a weighted Poincaré type inequality for such functions. An extension to weighted Sobolev spaces is sketched.

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Sunto Si studiano funzioni che appartengono a certi spazi di Sobolev e che hanno crescita assegnata su sfere di grande raggio. Per tali funzioni si dimostra una disuguaglianza di tipo Poincaré con peso. Si indica inoltre anche una estensione di tale risultato a funzioni in spazi di Sobolev con peso.

     

Ablation of an optically homogeneous absorbing medium by scattered pulsed laser radiation

We have studied the ablation of an aqueous CuCl₂ solution in a pulsed Nd:YAG laser field featuring a speckle-patterned structure characterized by spatial radiation energy fluence fluctuations. This leads to a nonuniform distribution of the energy absorbed in the bulk of the sample being irradiated and causes local overheating centers to form, wherein ablation is observed to take place at laser energy fluences below the threshold value found in experiments with a homogeneous laser beam. This effect should be manifest in the laser irradiation of biotissues which, as a rule, scatter light strongly.     

Regioorientation in the reaction of side chain activated alkylpyridines with electrophiles

X-ray structural data has shown that condensation of sym-3-nitrocollidine with benzaldehyde occurs at the 6-methyl group. The presence of an acceptor group in the side chain of 2,6-dimethyl-4-cyanomethyl-3-nitropyridine causes condensation to occur at the activated methylene group in the 4-position.M. V. Lomonosov State University, Moscow 119899. A. N. Nesmeyanov Institute of Organoelemental Compounds, Moscow 117813. Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 11. pp. 1543–1550, November, 1995. Original article submitted June 10, 1995.     

Matrix effects in the determination of butyltin compounds in environmental samples by GC AA after hydride generation

Experiments for the determination of mono-, di and tri-butyltin (MBT, DBT and TBT) by hydride generation/gas chromatography/atomic absorption spectrometry in various matrices (sediment, suspended matter, mussel, algae and water) have revealed that poor butyltin recoveries are obtained in sediments displaying high sulphur and hydrocarbon contents; very poor recoveries were also observed for TBT in sediments with high chlorophyll pigment contents as well as in algal samples. It was however not clear whether the hydride generatin was inhibited by these infering compounds, as was previously assumed in the case of hydrocarbons, or whether interferences affected the atomization rate. Further studies were performed to solve this problem in order to validate this method in the case of analyses of, for example, oil-contaminated sediment and algae. This paper presents the results obtained. It is concluded here that the poor recoveries were due to an inhibition of hydride generation rather than to interference at the atomization stage.