Inequalities for a unified family of Voigt functions in several variables

The classical Voigt functions occur frequently in a wide variety of problems in astrophysical spectroscopy, emission, absorption and transfer of radiation in heated atmosphere, and plasma dispersion, and indeed also in the theory of neutron reactions. Here, in the present paper, by applying several known upper bounds for the first-kind Bessel function J _ν (x) given recently by (for example) Landau, Olenko and Krasikov, sharp bounding inequalities are obtained for the unified multivariable Voigt function V _μ,ν (x; y) in terms of the confluent Fox-Wright function ₁ψ₀ and its incomplete variant ₁ψ₀. Connections of the unified multivariable Voigt function V _μ,ν (x; y) with other unifications and generalizations of the classical Voigt function are also briefly pointed out.     

Separation of Monovinyl and Divinyl Protochlorophyllides Using C30 Reverse Phase High Performance Liquid Chromatography Column: Analytical and Preparative Applications

A new, high performance liquid chromatography method has been developed for the separation of monovinyl- and divinyl-protochlorophyllides, using commercially available, C₃₀ reverse phase column and isocratic elution. This method can be used both for analytical applications and preparative scale purification of monovinyl- and divinyl-protochlorophyllides using the same column where submilimolar concentrations of the crude protochlorophyllide extract can be separated in one run. The purity of the obtained protochlorophyllides was demonstrated by spectroscopic methods, as well by the formation of aggregates in toluene.     

Temperature dependence of the iron hyperfine field distribution in amorphous Fe-rich Fe-Zr alloys

The temperature dependence of the iron hyperfine field distribution is reported in melt-quenched amorphous Fe-Zr alloys. The most remarkable feature is the compositinal change in the shape of the average hyperfine field versus temperature curves. The unusual increase in the average hyperfine field below about 85 K is a characteristic feature of the RSG systems; however, no anomaly is observed in the width of the hyperfine field distribution as a function of temperature. The results cannot be properly explained in the framework of the existing spin glass models.     

Thickness dependence of the magnetic anisotropy of Fe layers separated by Al

Magnetic multilayers of ⁵⁷Fe with nominal thickness, T _nom, between 0.4 and 1.0 nm separated by 3.0 nm Al spacer layers were prepared by alternate deposition of the constituents in high vacuum. The samples were investigated at 4.2 K in external magnetic field. A fraction of Fe atoms corresponding to about 0.3 nm equivalent Fe-thickness was found to mix into the Al spacer. The extremely strong magnetic anisotropy observed for T _nom < 0.8 nm is attributed to Fe layers of approximately two atomic planes thick. The anisotropy decreases considerably after the building up of the third Fe atomic layer starts at T _nom = 0.8 nm, but full saturation was not achieved even for T _nom = 1 nm and 3 T magnetic field applied perpendicularly to the sample plane.     

A combinatorial property of points and ellipsoids

For eachd1 there is a constantc _d>0 such that any finite setXR ^d contains a subsetYX, |Y|[1/4d(d+3)]+1 having the following property: ifEY is an ellipsoid, then |E X|c _d |X|.On leave from the Mathematical Institute of the Hungarian Academy of Sciences, 1364 Budapest, P.O. Box 127, Hungary. Supported by a research fellowship from the Science and Engineering Research Council, U.K., and by Hungarian National Foundation for Scientific Research Grant No. 1812.     

A fading effect in the X-ray diffraction contrast of dislocations

Fringes in the dislocation image in X-ray section topography are shown to fade away partially when unpolarized radiation is used. The fading effect is explained in terms of an analogy with the polarization beat in a wedge crystal. The polarization nature of the phenomenon is confirmed through numerical simulations of the contrast.Dedicated to Professor Dr. Ulrich Bonse on the occasion of his 60th birthday     

X-ray investigation of the role of the mixed emulsifier in the structure formation in o/w creams

The aim of this research work was to clarify the role of the mixed emulsifier in the structure formation and water binding mode in the case of o/w creams prepared with different surfactants. The swelling behavior of mixed emulsifiers was examined by means of direct investigation methods such as transmission electron microscopy (TEM) and X-ray diffraction. The detailed structure image of the creams was created with the help of the latter. The influence of the structure of the hydrophilic gel phase, and the structural changes during storage were studied with rheological methods. On the basis of the results, it can be stated that the investigated creams had different structures from those mentioned in the literature: surfactant did not create a mixed bilayer with the structure to furnish fatty amphiphile; instead, micelles were formed. These results correlated well with the results of the rheological tests.     

Origin of organic gaseous products formed in the thermal decomposition of formates

The gaseous products of the thermal decomposition of formates have been investigated and compared with the products of formaldehyde and synthesis gas transformation under analogous conditions in the presence of the solids formed in the thermal decomposition of particular formates. It was found that formaldehyde transformation leads to organic compounds identical to those obtained in the thermal decomposition of the respective formates, while synthesis gas does not react under such conditions. This fact substantiates the hypothesis that formaldehyde is a precursor of the organic compounds identified in the thermal decomposition of formates. The nature of the organic componds obtained in the thermal decomposition of formates indicates that the formaldehyde formed in the initial stages is then transformed in the Cannizzaro or Tishchenko reactions.

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Zusammenfassung Die gasförmigen Produkte der thermischen Zersetzung von Formiaten wurden untersucht und mit den Produkten verglichen, die bei der Umwandlung von Formaldehyd und Synthesegas unter analogen Bedingungen in Gegenwart von bei der thermischen Zersetzung von speziellen Formiaten gebildeten Feststoffen entstehen. Formaldehydumwandlungen führen zu organischen Verbindungen, die identisch mit denen sind, die bei der thermischen Zersetzung des betreffenden Formiats gebildet werden, während Synthesegas unter solchen Bedingungen nicht reagiert. Dies erhärtet die Hypothese, daß Formaldehyd eine Vorstufe der bei der thermischen Zersetzung von Formiaten identifizierten organischen Verbindungen ist. Die Natur der bei der thermischen Zersetzung von Formiaten auftretenden organischen Verbindungen weist darauf hin, daß das in den ersten Reaktionsschritten gebildete Formaldehyd nach der Cannizzaro-oder Tishchenko-Reaktion weiterreagiert.

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Preparation of Layer Structure-Controlled Ru-Sn-Al2O3 Catalysts and Their Reactivity

In order to achieve functional group selective hydrogenation, the layer structure of Ru-Sn-Al2O3 catalysts was controlled by using sol-gel, powder impregnation and combined sol-gel impregnation methods. The properties of the catalysts and effectiveness in hydrogenation of dimethyl terephthalate were examined. The surface Sn contents of the catalysts characterized by X-ray photoelectron spectroscopy depended on the preparation method, in spite of almost the same bulk Ru and Sn compositions measured by X-ray fluorescence analyses. TPR and CO adsorption of the catalysts also depended on the preparation method. With regard to the conversion rate of dimethyl terephthalate and the rate of product conversion from methyl 4-hydroxy methylbenzoate to p-xylene via methyl p-toluate, Ru impregnation catalysts had higher rates than the other catalysts.