A scaling method for obtaining kinetic equations from the BBGKY hierarchy

Kinetic equations for the one-particle distribution function of dilute gases and plasmas and evolution equations for the variance of their fluctuations are obtained from the BBGKY hierarchy equations by using Mori's scaling method in an extended form.     

Solvable lattice models related to the vector representation of classical simple Lie algebras

A series of solvable lattice models with face interaction are introduced on the basis of the affine Lie algebraX _n ⁽¹⁾ =A _n ⁽¹⁾ ,B _n ⁽¹⁾ ,C _n ⁽¹⁾ ,D _n ⁽¹⁾ . The local states taken on by the fluctuation variables are the dominant integral weights ofX _n ⁽¹⁾ of a fixed level. Adjacent local states are subject to a condition related to the vector representation ofX _n . The Boltzmann weights are parametrized by elliptic theta functions and solve the star-triangle relation.     

Invar effects on some iron-base amorphous alloys

The thermal expansion and magnetic properties of Fe-B and Fe-P amorphous alloys prepared from melts have been investigated. These amorphous alloys show distinct Invar characteristics. heir magnetic properties are also very similar to those of Fe-Ni crystalline Invar alloys; that is, the high-field susceptability and forced-volume magnetostriction are remarkably large, the magnetic moment per Fe atom does not increase linearly, the Curie temperature decreases with a decrease in concentration of B or P, and their reduced their magnetization curves are much flatter than those of crystalline pure Fe.     

Determination of nitrate in natural waters by flow-injection analysis

Summary Nitrate was determined in natural water samples by flow-injection spectrophotometry. It was reduced to nitrite with copperized cadmium and the nitrite thus produced reacted with p-aminoacetophenone and m-phenylenediamine. The limit of detection was about 1.5 g l^–1 for sample injections of 650 l. The sampling rate was about 40 samples h^–1 and the relative standard deviation was above 1% for 0.1–0.3 mg l^–1 nitratenitrogen. Nitrite present in the sample was determined separately and subtracted.

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Nitratbestimmung in natürlichen Wässern mit Hilfe der Fließinjektions-Analyse

Zusammenfassung Nitrat wird bei dieser Methode mit Hilfe einer Cu/Cd-Reduktionssäule zu Nitrit reduziert, das mit p-Aminoacetophenon und m-Phenylendiamin zur Reaktion gebracht wird. Die gebildete Verbindung wird spektral-photometrisch gemessen. Die Nachweisgrenze beträgt etwa 1,5 g/l bei injizierten Probevolumina von 650 l. Der Probendurchsatz beträgt 40/h. Die relative Standardabweichung liegt über 1% bei 0,1–0,3 mg/l Nitrat-Stickstoff. Vorhandenes Nitrit wird gesondert bestimmt und abgezogen.

     

Determination of sulphate in natural water by flow-injection analysis

Summary Sulphate was determined in natural water samples by flow-injection analysis using dimethylsulphonazo-III as reagent. The interference by Ca was eliminated by a cation-exchanger column inserted directly after the sample injection valve. In order to ensure high sensitivity and reproducibility it was necessary to saturate the carrier solution with barium sulphate and to fill the reaction coil with ethanol-water (11) when not in use. Standard deviations were 0.94–1.2% for 6–10mg/l sulphate. The limit of detection was about 0.2mg/l. The calibration graph was linear up to 14mg/l Mg²⁺, NH ₄ ⁺ , Na⁺, K⁺, Cl^–, NO ₃ ^– , PO ₄ ^3– , HCO ₃ ^– and SiO ₃ ^2– did not interfere in the normally occurring concentrations.

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Sulfatbestimmung in natürlichem Wasser durch Flow-Injection-Analyse

Zusammenfassung Als Reagens dient Dimethylsulfonazo-III. Die Störung durch Calcium bei dieser Bestimmung wird durch eine Kationenaustauschersäule eliminiert, die direkt nach dem Probeinjektions-Ventil angeordnet ist. Zur Erhöhung der Empfindlichkeit und Reproduzierbarkeit ist es notwendig, die Trägerlösung mit Bariumsulfat zu sättigen sowie bei Nichtbenutzung des Systems den Reaktionsteil mit Ethanol-Wasser (11) zu füllen. Mit dem so modifizierten Verfahren ergaben sich Standardabweichungen von 0,94–1,2% für 6–10 mg/l Sulfat, die Nachweisgrenze liegt bei 0,2 mg/l. Die Eichkurve ist bis 14 mg/l linear. Mg²⁺, NH ₄ ⁺ , Na⁺, K⁺, Cl^–, NO ₃ ^– , PO ₄ ^3– , HCO ₃ ^– und SiO ₃ ^2– stören in den normalerweise vorkommenden Konzentrationen nicht.

     

Chemistry of the phenoxathiins and isosterically related heterocycles. XIX.. The crystal and molecular structure of 1-N,N-dimethylamino-2,3-diazaphenoxathiin: An interesting product isolated from the reaction of o-mercaptophenol with 3,4,5-trichloropyridazine in N,N-dimethylformamide

The isolation of 1-N,N-dimethylamino-2,3-diazaphenoxathiin and its molecular structure as determined by X-ray crystallography are described. The existence of a potential non-bonded interaction between the lone pair of electrons of the dimethylamino group nitrogen and sulfur atom are also discussed.     

Structural modeling in a class of systems using fuzzy sets theory

On the basis of fuzzy sets theory, we propose a method for structuring hierarchy for the several complex problems, and call it Fuzzy Structural Modeling (FSM) method. An important requirement for structural modeling of complex systems is that the necessary data is acquired and organized into a form such that a structural model can be developed. The main purpose of this method is to describe and illustrate a formal procedure for constructing the graphic presentation of the hierarchical arrangement given the necessary information concerning the relation of each element to each other element. The procedure permits an automatic development of the graphic structure that portrays the hierarchy.