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  • Author or Editor: Katalin Gyarmati x
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C. Mauduit conjectured that C 2 (E)C N 3(E N) ?? Nc always holds with some constant 1/2< c = 1. This will be proved for c=2/3, more exactly if for a sequence E N =C {-1,+1}N we have C 2 (E N) << N 2/3 then  C 3 (E N) ??  N 1/2. Indeed, a more general theorem is proved, involving correlation measures.

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In the applications it may occur that our initial pseudorandom binary sequence is not long enough, thus we have to take the concatenation of it with another pseudorandom binary sequences. Here we will consider concatenation of Legendre symbol sequences so that the resulting longer sequence has strong pseudorandom properties.

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Abstract

Hubert, Mauduit and Sárközy introduced the pseudorandom measure of order of binary lattices. This measure studies the pseudorandomness only on box lattices of very special type. In certain applications one may need measures covering a more general situation. In this paper the line measure and the convex measure are introduced.

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Abstract  

Using the discrete logarithm in [7] and [9] a large family of pseudorandom binary sequences was constructed. Here we extend this construction. An interesting feature of this extension is that in certain special cases we get sequences involving points on elliptic curves.

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Summary  

We study the pseudorandom properties of the power generator (which includes as special cases the RSA generator and the Blum--Blum--Shub generator). In order to estimate the pseudorandom measures character sums with exponential functions are used.

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Abstract  

In the applications it may occur that our initial pseudorandom binary sequence turns out to be not long enough, thus we have to take the concatenation or merging of it with other pseudorandom binary sequences. Here our goal is study when we can form the concatenation of several pseudorandom binary sequences belonging to a given family? We introduce and study new measures which can be used for answering this question.

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Abstract  

Ahlswede, Khachatrian, Mauduit and A. Sárközy introduced the notion of family-complexity of families of binary sequences. They estimated the family-complexity of a large family related to Legendre symbol introduced by Goubin, Mauduit and Sárközy. Here their result is improved, and apart from the constant factor the best lower bound is given for the family-complexity.

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Authors: T. Tauber, Brigitta Berta, Anna Székely, I. Gyarmati, Katalin Kékesi, K. Márialigeti and Erika Tóth

The aim of the present work was to compare the microbial communities of a mesophilic and a thermophilic pilot scale anaerobe sludge digester. For studying the communities cultivation independent chemotaxonomical methods (RQ and PLFA analyses) and T-RFLP were applied. Microbial communities of the mesophilic and thermophilic pilot digesters showed considerable differences, both concerning the species present, and their abundance. A Methanosarcina sp. dominated the thermophilic, while a Methanosaeta sp. the mesophilic digester among Archaea. Species diversity of Bacteria was reduced in the thermophilic digester. Based on the quinone patterns in both digesters the dominance of sulphate reducing respiratory bacteria could be detected. The PLFA profiles of the digester communities were similar though in minor components characteristic differences were shown. Level of branched chain fatty acids is slightly lower in the thermophilic digester that reports less Gram positive bacteria. The relative ratio of fatty acids characteristic to Enterobacteriaceae, Bacteroidetes and Clostridia shows differences between the two digesters: their importance generally decreased under thermophilic conditions. The sulphate reducer marker (15:1 and 17:1) fatty acids are present in low quantity in both digesters.

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