Approximate minimum-cost multicommodity flows in\tilde O(ɛ −2 KNM) timetime

We show that an ε-approximate solution of the cost-constrainedK-commodity flow problem on anN-nodeM-arc network,G can be computed by sequentially solving O(K(? ^?2+logGK) logGM log (G? ^?1 GK)) single-commodity minimum-cost flow problems on the same network. In particular, an approximate minimum-cost multicommodity flow can be computed in $\tilde O$ (G? ^?2 GKNM) running time, where the notation Õ(·) means “up to logarithmic factors”. This result improves the time bound mentioned by Grigoriadis and Khachiyan [4] by a factor ofM/N and that developed more recently by Karger and Plotkin [8] by a factor of? ^?1. We also provide a simple $\tilde O$ (NM)-time algorithm for single-commodity budget-constrained minimum-cost flows which is $\tilde O$ (? ^?3) times faster than the algorithm developed in the latter paper.     

Synthesis of new functional derivatives of pyrazolidine from 1-acetyl-3-methyl-5-nitromethyl-2-phenylpyrazolidine

3-Nitromethylpyrazolidine reacts with derivatives of unsaturated acids and reducing agents with the formation of polyfunctional compounds of the pyrazolidine nucleus. __________ Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 9, pp. 1365–1369, September, 2006.     

Analysis of cyanobacterial toxins (anatoxin-a, cylindrospermopsin, microcystin-LR) by capillary electrophoresis

Capillary zone electrophoresis (CZE) and micellar electrokinetic chromatography (MEKC) were applied to the simultaneous separation of cyanobacterial toxins (anatoxin-a, microcystin-LR, cylindrospermopsin). The analytical performance data of both methods, optimized for the three toxins, were similar with a precision of migration times smaller than 0.8 RSD% and a detection limit in the range of 1-4 microg/mL, using spectrophotometric detection at 230 nm. Both methods were applied to an analysis of cyanotoxins in water bloom samples and crude cyanobacterial extracts. The results obtained indicate that, for complex matrices, the sequential application of CZE and MEKC is necessary. It is recommended to use both CE techniques for the analysis of the same sample in order to confirm the results by an orthogonal approach.     

Conjugate-gradient method for computing the Moore-Penrose inverse and rank of a matrix

A conjugate-gradient method is developed for computing the Moore-Penrose generalized inverseA of a matrix and the associated projectors, by using the least-square characteristics of both the method and the inverseA . Two dual algorithms are introduced for computing the least-square and the minimum-norm generalized inverses, as well asA . It is shown that (i) these algorithms converge for any starting approximation; (ii) if they are started from the zero matrix, they converge toA ; and (iii) the trace of a sequence of approximations multiplied byA is a monotone increasing function converging to the rank ofA. A practical way of compensating the self-correcting feature in the computation ofA is devised by using the duality of the algorithms. Comparison with Ben-Israel's method is made through numerical examples. The conjugate-gradient method has an advantage over Ben-Israel's method.After having completed the present paper, the author received from Professor M. R. Hestenes his paper entitledPseudo Inverses and Conjugate Gradients. This paper treated the same subject and appeared in Communications of the ACM, Vol. 18, pp. 40–43, 1975.     

Kinetic parameters of the In(III)/In(I) electrode reaction in bromide medium

The electrode kinetic parameters of the In(III)/In(I) couple in acidic 4M bromide solution have been determined by means of the rotating disc electrode technique.

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Die elektrochemisch-kinetischen Parameter des In(III)/In(I)-Redoxsystems in Bromidlösung (Kurze Mitteilung)

Zusammenfassung Die elektrochemisch-kinetischen Parameter am In(III)/In(I)-Redoxsystem wurden in saurer 4-M-Bromidlösung mittels der rotierenden Scheibenelektrode bestimmt.

     

Monolayer adsorption isotherms and a disordered medium model

A model of disordered medium is proposed to describe the monolayer adsorption isotherm on heterogeneous surfaces. The model is based on the premise that adsorption medium consists of separate regions in each of which there is a permanent local equilibrium constant, the character of the changes of which is determined by the disorder parameter of the medium. __________ Translated from Teoreticheskaya i éksperimental’naya Khimiya, Vol. 42, No. 3, pp. 189–193, May–June, 2006.     

Electrostatic interaction between ion-penetrable membranes in a salt-free medium

A set of coupled equations is given which determines the distributions of the electric potential and counterions in a system of two interacting identical ion-penetrable membranes of thickness d at separation h immersed in a salt-free medium containing only counterions. The solution to these coupled equations also gives the electrostatic repulsive force between the membranes. It is shown that the interaction force remains finite at h-->0, unlike the case of the interaction between two planar charged surfaces (d-->0), and that the interaction force becomes independent of the membrane fixed charge and membrane thickness d at very large h. Finally, an approximate single transcendental equation giving the solution to the coupled equations is derived.     

An unequivocal synthesis of some substituted 1,2,4-triazolo[1,5-a]pyrimidines

An unequivocal synthesis of 5-chloro-7-methyl- (8) and 7-methyl-1,2,4-triazolo[1,5-a]pyrimidine (10) from 2-amino-4-chloro-6-methylpyrimidine (5) through the corresponding amidine6 and formamide oxime7 was developed. It was unambigously shown by comparison of the chemical shifts and the magnitude of coupling constants that the compounds obtained by condensation of 3-amino-1,2,4-triazole (12) and ethyl acetoacetate (13) and some further transformations are isomeric 5-methyl substituted 1,2,4-triazolo[1,5-a]pyrimidines1,9, and11.

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Eine eindeutige Synthese einiger substituierter 1,2,4-Triazolo[1,5-a]pyrimidine

Zusammenfassung Es wurde ein eindeutiger Syntheseweg für 5-Chlor-7-methyl- (8) und 7-Methyl-1,2,4-triazolo[1,5-a]pyrimidin (10) ausgehend von 2-Amino-4-chlor-6-methylpyrimidin (5) über das entsprechende Amidin6 und das Formamidoxim7 entwickelt. Durch Vergleich von chemischen Verschiebungen und Kopplungskonstanten konnte eindeutig gezeigt werden, daß die Verbindungen, die bei der Kondensation von 3-Amino-1,2,4-triazol (12) and Ethylacetoacetat (13), sowie einige weitere Transformationsprodukte, isomere 5-Methylsubstituierte 1,2,4-Triazolo[1,5-a]pyrimidine sind (1,9,11).

     

Preparation and Characteristics of Porous Silica Films by a Modified Base-Catalyzed Sol-Gel Process Containing PVA: II. Film Preparation

Porous SiO₂ films were successfully deposited on silicon substrates by a modified base-catalyzed Sol-Gel process (MBCP) containing polyvinyl alcohol (PVA). The process conditions, such as the gelation time, the synthesis temperature, the stabilizing agent of the precursor solution and the spin coating speed, the heat-treatment, the annealing temperature of the film on the microstructure and porosity of porous SiO₂ films were systematically investigated by SEM, XRD and ellipsometry techniques. This study provides a novel preparation technique for the porous SiO₂ film. Using this process, the resultant film can reach a thickness of 3.6 m for one layer, a porosity of 25–50%, a low thermal conductivity of 0.11 W/m·K. This film will be used as a low dielectric layer, an thermal-insulating layer and a low refractive index layer.