Asymptotic and exponential decay in mean square for delay geometric Brownian motion

Applications of Mathematics - We derive sufficient conditions for asymptotic and monotone exponential decay in mean square of solutions of the geometric Brownian motion with delay. The conditions...     

Polarographische Bestimmung des Pyridoxols in pharmazeutischen Präparaten

Zusammenfassung Es wird eine neue polarographische Methode zur direkten Bestimmung des Pyridoxols in Injektionspräparaten und Tabletten beschrieben. Die ausgearbeitete Methode beruht auf der polarographischen Reduktion des Pyridoxolmoleküls im Milieu von Ammoniak-Ammoniumchlorid-Puffern und weiter auf der Bildung einer katalytischen Stufe des Pyridoxols in Veronalpuffern. Die polarographische Methode ist rascher und in manchen Fällen genauer und empfindlicher als die bisher in Gebrauch stehenden Methoden. Die Anwesenheit der in den Präparaten laufend vorkommenden Begleitstoffe des Pyridoxols stört nicht die polarographische Bestimmung. Die Methode kann auch zur Bestimmung des 3-Hydroxy-4-methoxymethyl-5-oxymethyl-2-methylpyridins benutzt werden, das ein Zwischenprodukt bei der Pyridoxolerzeugung ist.

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Summary A new polarographic method is described for the direct determination of pyridoxol in injection preparations and tablets. This method is based on the polarographic reduction of the pyridoxol in ammonia-ammonium chloride buffer medium and also on the formation of a catalytic stage of the pyridoxol in veronal buffers. The polarographic method is faster and in many cases more accurate and more sensitive than the methods now in use. The presence of the materials which always accompany the pyridoxol in the preparations does not interfere with the polarographic determination. The method can likewise be used for determining 3-hydroxy-4-methoxymethyl-5-oxymethyl-2-methylpyridine, which is an intermediate product in the manufacture of pyridoxol.

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Résumé On décrit une nouvelle méthode polarographique pour le dosage direct du pyridoxol dans les préparations pour injections et dans les comprimés. La méthode élaborée repose sur la réduction polarographique de la molécule de pyridoxol dans le milieu tampon ammoniaque-chlorure d'ammonium, et, en outre, sur la formation d'une phase catalytique du pyridoxol dans les tampons au véronal. La méthode polarographique est plus rapide et dans de nombreux cas plus exacte et plus sensible que les méthodes utilisées jusqu'ici. La présence d'impuretés existant couramment dans les préparations à côté du pyridoxol ne gêne pas le dosage polarographique. On peut aussi utiliser la méthode pour le dosage de l'hydroxy-3 méthoxyméthyl-4 oxyméthyl-5 méthyl-2 pyridine, substance intermédiaire dans la préparation du pyridoxol.

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Herrn Dr.P. Zuman danken wit für Ratsehläge bei der Abfassung dieser Arbeit.     

Tight upper bounds for the discrepancy of half-spaces

We show that the discrepancy of anyn-point setP in the Euclideand-space with respect to half-spaces is bounded byC _d n ^1/2−1/2d , that is, a mapping χ:P→{−1,1} exists such that, for any half-space γ, γ, |Σ _p∈P⋂γ χ(p)|≤C _d n ^1/2-1/2d . In fact, the result holds for arbitrary set systems as long as theprimal shatter function isO(m ^d ). This matches known lower bounds, improving previous upper bounds by a factor. Part of this research was done at the Third Israeli Computational Geometry Workshop in Ramot and during a visit at Tel Aviv University in December 1993. Also supported in part by Charles University Grant No. 351 and Czech Republic Grant GAČR 201/93/2167.     

Kneser-type oscillation criteria for self-adjoint two-term differential equations

It is proved that the even-order equationy ⁽²ⁿ⁾ +p(t)y=0 is (n,n) oscillatory at if

Encapsulation of magnetite in vesicles

The encapsulation of fine magnetite particles of 10 nm size and marker ANS within asolectin vesicles has been made by sonication of the mixture in water. For the proof of encapsulation of magnetite in vesicles the electron microscope and spectrofluoriphotometer technique were used. The theory for the calculation of the magnetic force acting on the system consisted of non-capsulated magnetic particles dispersed in water and magnetic vesicles was developed.This work was supported by the Slovak Academy of Sciences within the framework of Project GAV No. 1361.     

Effect of nuclear structure on the single particle β− transitions in deformed nuclei

In the framework of the Nilsson model the calculations of the so called shape factor for the first forbidden ^– transitions 5/2^{+ 241}Pu 5/2^{– 241}Am and 7/2^{+ 177}Lu 7/2^{– 177}Hf are carried out. The dependence on the Nilsson potential parameters is studied. It turns out that for the transitions considered the calculated shape factor depends linearly on the electron energy and its slope is 10^–3 per 20 keV. This can affect the analysis of electron spectra if the endpoint energy is sufficiently large.     

The SO(3,3) group as a common basis for Dirac's and Proca's equations

Dirac's and Proca's equations are unified in the sense that the algebras of Dirac -matrices and Duffin-Kemmer-matrices are shown to furnish two distinct matrix representations of the Lie algebra of the SO(3,3)-group. This fact is then interpreted as evidence for the classical picture of particles described by the above-mentioned equations to be a relativistic top. It is also argued that the shape of the top is rod-like.     

Individual extraction constants of some dicarbollylcobaltate anions in the water-nitrobenzene system

Individual extraction constants of nine dicarbollylcobaltate anions in the two-phase water-nitrobenzene system were determined radiometrically assuming that the changes of Gibbs energy of the transfer of the tetraphenylarsonium cation, Ph₄As⁺, and of the tetraphenylborate anion, BPh ₄ ^– , from the aqueous into the nitrobenzene phase are equal. The constants obtained by this method were correlated with Hansch's constants of hydrophobity.     

Structural phase transitions in ‘hcp’ C70 single-crystals

The thermal expansion of vapor-grownC ₇₀ single crystals ahs been investigated using high-resolution capacitance dilatometry from 5–380 K. Measurements were made both parallel and perpendicular to the hexagonalc-axis. Three first-order phase transitions which we associate with the consecutive disordering of theC ₇₀ molecules are observed upon heating at 280 K (long-axis spinning), 300 K (long-axis precession) and 355 K (quasi-free rotation), respectively. The highest-temperature transition exhibits a very large (50 K) thermal hysteresis. Powder and single-crystal X-ray diffraction show that the crystals are predominantly hexagonal-close-packed (HCP) with an idealc/a1.63 above 360 K andc/a1.84 at 295 K.     

Topologically nontrivial field configurations in noncommutative geometry

In the framework of noncommutative geometry we describe spinor fields with nonvanishing winding number on a truncated (fuzzy) sphere. The corresponding field theory actions conserve all basic symmetries of the standard commutative version (space isometries and global chiral symmetry), but due to the noncommutativity of the space the fields are regularized and they contain only a finite number of modes.Part of the Project P8916-PHY of the Fonds zur Förderung der wissenschaftlichen Forschung in Österreich.