Laser fluorescence-absorption analysis of iodine-129 and nitrogen dioxide impurities in a special atmosphere

Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 56, No. 1, pp. 116–121, January, 1992.     

A note on differentiability of the cluster density for independent percolation in high dimensions

The cluster density function of independent percolation in ad-dimensional lattice is considered. For eachn, it is shown that(p) has finitenth leftderivative at critical probabilityp _c ifd is sufficiently large. This result agrees with the Bethe lattice approximation, where thenth one-sided derivative of(p) is bounded atp _c for alln.     

An Efficient Method for the Synthesis of Acyl-diazenes Using NaNO_2/NaHSO_4·H_2O

Azo compounds are widely utilized as analytic reagents and dyes1, they can also be used in material of non-linear optics, material of optics information storing in laser disks, and dyes with oil solubility in photochromy in modern technology2. Recently, many noteworthy studies have shown that some azo compounds possess excellent optical memory and photoelectric properties3,4. For example, polymer scaffolds bearing azobenzene-potential are useful for optical information storage, azo-dye doped…     

Molecular Recognition of Bridged Bis(β-cyclodextrin)s Linked by Phenylenediseleno Tether on the Primary or Secondary Side with Fluorescent Dyes

A Novel β-cyclodextrin dimer,2,2′-o-phenylenediseleno-bridgedbis(β-cyclodextrin)(2),has been synthesized by reaction ofmono-[2-O-(p-tolylsulfonyl)]-β-cyclodextrin and poly(o-phenylenediselenide).The complexation stability constants(K_s)and Gibbs free energy changes(-ΔG°)of dimer 2 with fourfluorescence dyes,that is,ammonium 8-anilino-1-naphthalene-sulfonate(ANS),sodium 6-(p-toluidino)-2-naphthalenesul-fonate(TNS),Acridine Red(AR)and Rhodamine B(RhB)have been determined in aqueous phosphate buffer solution(pH=7.2,0.1 mol·L~(-1)at 25℃ by means of fluorescence spec-     

Correlation functions of a Heisenberg ferromagnet in the paramagnetic region

Conclusions In the present paper, in the framework of the coupled-mode approximation for the second-order equations (2.6)–(2.9) we have obtained an approximate closed system of equations (2.10)–(2.14) for the spin correlation functions of a Heisenberg ferromagnet in a vanishing external magnetic field and at temperatures above the critical temperature ( _c )., In principle, Eqs. (2.10)–(2.14) make it possible to investigate the behavior of the correlation functions in the entire investigated temperature range, including the critical point. Equations (2.10)–(2.14) are very complicated, and a numerical calculation is needed to analyze them.In the fourth section, we obtained interpolation formulas that make it possible to describe in some detail the behavior of the spectral density at both high and low frequencies. It would be expedient to find first the solution, of the simplified system of equations obtained from (2.10)–(2.14) by replacement of the Green's function (2.10) and the spectral density (3.2) by their interpolation expressions (4.2) and (4.3). Substituting (4.3) in (3.3) and (3.4), we obtain equations for and , in terms of which all the remaining quantities can be expressed. The solution obtained from the simplified system can be used further as initial approximation in the solution of the system of equations (2.10)–(2.14). However, this problem goes beyond the framework of the given paper.V. A. Steklov Mathematics Institute, USSR Academy of Sciences. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 52, No. 1, pp. 147–160, July, 1982.     

Distribution of values of σ2 (n) in residue classes

IntegersN for which ₂ (n has weak uniform distribution (modN) are determined.     

p-adic zeta functions and Bernoulli numbers

One gives a new proof to the Leopoldt-Kubota-Iwasawa theorem regarding the possibility of the p-adic interpolation of the values of the Riemann zeta-function and of the Dirichlet L-functions at negative integral points. To this end, for each root ? ≠ 1 of unity one introduces and one investigates the numbers C_n(?) which arise in the expansion $$\frac{{\varepsilon - 1}}{{\varepsilon e^z - 1}} = \sum\limits_{n = 0}^\infty {\frac{{C_n (\varepsilon )}}{{n!}}Z^n }$$ One proves a generalization of the Kummer congruences for the Bernoulli numbers.     

Ein Algorithmus zur Lösung eines Verteilungsproblems

Zusammenfassung Bei der Lastverteilung eines Elektrizitätsversorgungsunternehmens besteht die Möglichkeit, durch eine Tonfrequenzrundsteueranlage die Last optimal aufzuteilen. Eine Zielsetzung besteht darin, durch Zu- und Wegschalten von Verbrauchergruppen die Lastspitze möglichst klein zu halten. Dabei muß allerdings jedem Verbraucher in einem gewissen Zeitraum eine gewisse Einschaltdauer garantiert sein. Der zur Lösung herangezogene Algorithmus basiert im wesentlichen auf dem Prinzip der dynamischen Optimierung und der Idee von Branch- and-Bound-Verfahren.

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Summary One aim of electric load management is to keep load peaks low by switching on and off water heaters of different groups of customers. There is a restriction that those heaters have to be switched on within a certain period of time for some fixed time. The optimal switching strategy for this distribution problem is computed using dynamic programming and the idea of branch and bound methods.

     

Density fluctuations in amorphous and semicrystalline polymers

Summary The small-angle scattering of amorphous and semicrystalline polymers contains an intensity component due to density fluctuations within the crystalline and amorphous domains.For amorphous polymers, the density fluctuations aboveT _g correspond to the theoretical value for a fluid system in thermodynamic equilibrium. BelowT _g , a temperature dependence proportional to T is observed over a range of about 50°. At lower temperatures, a linear relationship with a smaller slope has been found which extrapolates to a non-zero value at 0 °K. This value corresponds to the frozen-in disorder, the slope at low temperatures is related to thermal vibrations and can be evaluated in terms of photon-phonon scattering.Semicrystalline polymers show a temperature dependence of the density fluctuation similar to that of the amorphous polymers. At constant temperature the density fluctuations vary linearly with crystallinity.Natural rubber shows an increase of the density fluctuations with increasing cross-linking densities from which information on the density changes in the vicinity of a cross-link and on the statistics of the distribution of cross-linking can be obtained.

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Zusammenfassung Die Kleinwinkelstreuung amorpher und teilkristalliner Polymere besitzt eine Intensitätskomponente, die von Dichtefluktuationen innerhalb der kristallinen und amorphen Bezirke herrührt. Für amorphe Polymere entspricht die Dichtefluktuation oberhalb vonT _g dem theoretischen Wert für ein fluides System im thermodynamischen Gleichgewicht. UnterhalbT _g wird eine Temperaturabhängigkeit proportional zuT über einen Bereich von etwa 50° beobachtet. Bei tieferen Temperaturen wird eine lineare Beziehung mit einer geringeren Steigung gefunden, welche zu einem endlichen Wert bei 0 °K extrapoliert werden kann. Dieser Wert bezieht sich auf die eingefrorene Fehlordnung, die Steigung bei tiefen Temperaturen ist auf thermische Schwingungen zurückzuführen und kann als Photon-Phonon-Streuung ausgewertet werden.Teilkristalline Polymere zeigen eine Temperaturabhängigkeit der Dichtefluktuation, die der von amorphen Polymeren ähnlich ist. Bei konstanter Temperatur ändert sich die Dichtefluktuation linear mit der Kristallinität.Naturkautschuk zeigt eine mit der Vernetzungsdichte ansteigende Dichtefluktuation, aus der man Information über die Dichteänderung in der Umgebung eines Netzpunktes und die Statistik der Netzpunktverteilung erhalten kann.