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• Author or Editor: A. Zaharescu
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# Asymptotic behavior of the irrational factor

Acta Mathematica Hungarica
Authors: E. Alkan, A. Ledoan, and A. Zaharescu

## Abstract

We study the irrational factor function I(n) introduced by Atanassov and defined by
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$I(n) = \prod\nolimits_{\nu = 1}^k {p_\nu ^{1/\alpha _\nu } }$$ \end{document}
, where
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$n = \prod\nolimits_{\nu = 1}^k {p_\nu ^{\alpha _\nu } }$$ \end{document}
is the prime factorization of n. We show that the sequence {G(n)/n}n≧1, where G(n) = Πν=1 n I(ν)1/n, is convergent; this answers a question of Panaitopol. We also establish asymptotic formulas for averages of the function I(n).
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# Thermoanalytical study of the formation of compounds in the PbO−MO ( M =Ca, Sr, Ca+Sr) system

Journal of Thermal Analysis and Calorimetry
Authors: M. Zaharescu, A. Braileanu, and D. Crisan

## Abstract

In order to clarify the effect of PbO addition on the formation steps of the superconducting phases in the system Bi2O3−SrO−CaO−CuO, a study of solid-state reactions under non-isothermal conditions, in the PbO−MO (M=Ca, Sr, Ca+Sr) system has been carried out. Results suggest that the reactivity of the components in the system containing PbO and CaO is much higher than in the system containing SrO. The Ca2PbO4 compound is formed first even in the system whereM=Ca+Sr. It is confirmed that Ca2PbO4 systems containing PbO.

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# Ageing Effect on the SiO2-based Inorganic-Organic Hybrid Materials

Journal of Thermal Analysis and Calorimetry
Authors: M. Zaharescu, A. Jitianu, A. Braileanu, J. Madarász, and G. Pokol

## Abstract

It is well known that SiO2 -based inorganic-organic hybrid materials present significant differences due to the organic moieties bound to the inorganic network and to the preparation conditions. In the present work the ageing effect on the thermal stability of the SiO2 -based inorganic-organic hybrid materials prepared using tetraethoxysilan (TEOS), triethoxymethylsilan (MTEOS), triethoxyvinylsilan (VTEOS), tetramethoxysilan (TMOS), trimethoxymethylsilan (MTMOS) and trimethoxyvinylsilan (VTMOS) was studied. TG/DTA-MS was used to study the decomposition process of the materials. The structural modifications of the materials during ageing were studied using spectral methods. The gels obtained starting with more reactive alkoxides, of methoxy-type, present more complex structures and are less stable during ageing.

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# Phase Formation Study of Alkaline Earth-doped Lanthanum Chromites

Journal of Thermal Analysis and Calorimetry
Authors: A. Ianculescu, A. Braileanu, I. Pasuk, and M. Zaharescu

## Abstract

In this paper the influence of alkaline-earth admixtures on the synthesis of lanthanum chromites of La1–xMxCrO3 (x=0; 0.3; M=Ca, Sr, Ca+Sr) type was studied. The formation mechanism as well as the phase composition evolution, under non-isothermal and isothermal conditions, were investigated by thermal analysis and X-ray diffraction. The structure of the compounds and of the solid solutions formed depends on the solute type by means of the structural distortion induced. The crystallinity of the chromites obtained is obviously influenced by both the temperature and the thermal treatment plateau.

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# Solid State Phase Formation in the Bi2O3-PbO-CaO System

Journal of Thermal Analysis and Calorimetry
Authors: A. Brăileanu, M. Zaharescu, D. Crişan, and E. Segal

## Abstract

Following our previous research, this work is dedicated to the study of phase formation in the subsolidus domain of the Bi2O3-PbO-CaO system. Former investigations performed by DTA/TGA and XRD have pointed out that under non-isothermal conditions only the formation of binary compounds occurs. Under such conditions these compounds could be non-equilibrium phases. In order to establish the conditions of formation of equilibrium phases, a study of the Bi2O3-PbO-CaO system, in isothermal conditions, was carried out. The results obtained in isothermal conditions have confirmed the presence of Bi2O3-rich solid solutions and Ca2PbO4 as main equilibrium phases. An attempt to represent the phase relations of the mentioned system at 700C should be equally mentioned.

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# Formation and properties of some Nb-doped SrTiO3-based solid solutions

Journal of Thermal Analysis and Calorimetry
Authors: A. Ianculescu, A. Brăileanu, M. Zaharescu, S. Guillemet, I. Pasuk, J. Madarász, and G. Pokol
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# Composition and thermal stability of SiO2-based hybrid materials TEOS-MTEOS system

Journal of Thermal Analysis and Calorimetry
Authors: M. Zaharescu, A. Jitianu, A. Brăileanu, J. Madarász, CS. Novák, and G. Pokol
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# Phase Formation Study of The Substituted Lanthanum Manganites Solid Solutions

Journal of Thermal Analysis and Calorimetry
Authors: A. Ianculescu, A. Braileanu, M. Zaharescu, I. Pasuk, E. Chirtop, C. Popescu, and E. Segal

## Abstract

It is well known that the manganites-based solid solutions are interesting for their electric and magnetic properties. LaMnO3 exhibits a distorted perovskite structure due to Mn3+ ion, which determines the presence of the Jahn–Teller effect. Replacing La3+ host ions by cations of lower valence leads to the disappearance of this effect and changes the characteristics of these materials. Although the formation of manganites-based solid solutions has been intensively studied, there are some unelucidated aspects concerning their formation mechanism, depending both on the precursors used and on the thermal treatment applied in order to obtain suitable properties. In this work the formation mechanism of La0.7M0.3MnO3 (M=Ca, Sr, Ca+Sr in equimolecular mixture) solid solutions, in isothermal and non-isothermal conditions, was studied. For this purpose XRD, DTA/TG and spectral techniques were used. The solid solutions formation was found to be more dependent on the Mn-precursors type than the thermal treatment conditions.

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# Thermal Stability of SiO2-Based Inorganic-Organic Hybrid Materials

Journal of Thermal Analysis and Calorimetry
Authors: M. Zaharescu, A. Jitianu, A. Brãileanu, V. Bãdescu, G. Pokol, J. Madarász, and Cs. Novák

## Abstract

The hydrolysis-polycondensation of organically modified Si-alkoxides leads to the obtaining of inorganic-organic hybrid materials in which the organic moieties remain as permanent groups bonded to the inorganic network. The molecular species previously determinated by GC-MS during the gelation process have been significantly different according to the type of the alkoxide used. In the present work, thermal stability of SiO2-based inorganic-organic hybrid materials starting with TEOS (tetraethoxysilan), MTEOS (triethoxymethylsilan), VTEOS (triethoxyvinylsilan) and MTMOS (trimethoxymethylsilan) was studied. The molecular structure of the gels obtained determines differences in their thermal behaviour. Gels obtained starting with MTEOS show the highest thermal stability, while gels obtained using VTEOS the lowest, among the substituted alkoxides. A particular behaviour presents the gel obtained with MTMOS that decomposes in four steps. This could be explained by the presence in the gel of some prevalent types of molecular species with different thermal stability.

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# Composite SiO2—Iron Oxide Materials for Magnetically Intensified Adsorption

Journal of Radioanalytical and Nuclear Chemistry
Authors: I. Peleanu, M. Zaharescu, I. Rau, M. Crisan, A. Jitianu, and A. Meghea

## Abstract

Composite SiO2—iron oxide materials were prepared by three experimental procedures. In the first case, the iron oxides were precipitated during a sol-gel process. In the second case, a SiO2 matrix was initially obtained, and the iron oxides were formed by thermal treatment after impregnation of a soluble Fe2+ salt in the previously processed matrix. In the third method, ferrite powders, prepared by wet chemical method, were embedded into a SiO2 based sol-gel matrix. Materials with convenient porosity and nano-sized iron oxide content could be prepared using the mentioned methods. The prepared composite has been tested for arsenic(V) removal.

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