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• Author or Editor: G. Ambrus
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# On iterative processes generating dense point sets

Periodica Mathematica Hungarica
Authors: G. Ambrus and A. Bezdek

## Summary

The central problem of this paper is the question of denseness of those planar point sets \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} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\mathcal{P}$$ \end{document}, not a subset of a line, which have the property that for every three noncollinear points in \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} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\mathcal{P}$$ \end{document}, a specific triangle center (incenter (IC), circumcenter (CC), orthocenter (OC) resp.) is also in the set \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} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\mathcal{P}$$ \end{document}. The IC and CC versions were settled before. First we generalize and solve the CC problem in higher dimensions. Then we solve the OC problem in the plane essentially proving that \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} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\mathcal{P}$$ \end{document} is either a dense point set of the plane or it is a subset of a rectangular hyperbola. In the latter case it is either a dense subset or it is a special discrete subset of a rectangular hyperbola.

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# A new lower bound on the surface area of a Voronoi polyhedron

Periodica Mathematica Hungarica
Authors: G. Ambrus and Ferenc Fodor

## Summary

We prove that the mininum surface area of a Voronoi cell in a unit ball packing in \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} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $${\mathbb E}^3$$ \end{document} is at least \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} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$16.1977$$ \end{document}. This result provides further support for the Strong Dodecahedral Conjecture according to which the minimum surface area of a Voronoi cell in a \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} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$3$$ \end{document}-dimensional unit ball packing is at least as large as the surface area of a regular dodecahedron of inradius \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} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$1$$ \end{document}, which is about \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} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$16.6508\ldots\,$$ \end{document}.

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# Physico-chemical characterization and dissolution properties of nifluminic acid-cyclodextrin-PVP ternary systems

Journal of Thermal Analysis and Calorimetry
Authors: R. Ambrus, Z. Aigner, L. Catenacci, G. Bettinetti, P. Szabó-Révész and M. Sorrenti

## Abstract

In view of the poor aqueous solubility of nifluminic acid (NIF), the aim of this article was to improve its solubility and dissolution rate through the preparation of formulations based on hydroxypropyl β-cyclodextrin (HPβCD) and polyvinylpyrrolidone K25 (PVP K25), a combination of carriers which has been advantageously used for a similar purpose with various hydrophobic drugs. Ternary systems of NIF, HPβCD, and PVP K25 were prepared in different drug to CD to PVP ratios by physical mixing, kneading, microwave irradiation, and co-evaporation. Differential scanning calorimetry, thermogravimetric analysis, hot stage microscopy, Fourier transform infrared spectroscopy, and X-ray powder diffractometry were used to investigate the resulting solid-state interactions. The results showed that the solid state of the drug in the amorphous or crystalline ternary combinations influenced both the solubility and the dissolution rate of NIF.

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# Genetic modification of cereals in the Agricultural Research Institute of the Hungarian Academy of Sciences

Acta Agronomica Hungarica
Authors: L. Sági, M. Rakszegi, T. Spitkó, K. Mészáros, B. Németh-Kisgyörgy, A. Soltész, F. Szira, H. Ambrus, A. Mészáros, G. Galiba, A. Vágújfalvi, B. Barnabás and L. Marton

Research with transgenic plants in the Agricultural Research Institute of the Hungarian Academy of Sciences is primarily related to applications that are essential for the genetic improvement of cereals. The two main directions are connected to wheat and maize breeding and are focused on improving agronomic and nutritional traits. This paper highlights experiments in these areas, which are conducted in national as well as international collaborations. The transparency of this work is ensured by the dissemination of information about approved confined field tests to the public via the internet.

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