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• Author or Editor: P. Erdős
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# On the residues of products of prime numbers

Authors: P. Erdős, A. M. Odlyzko and A. Sárközy
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# On chagnes of signs in infinite series

Authors: I. Borosh, C. K. Chui and P. Erdós

Доказана теорема. Пус ть {аn} — последовате льность положительн ых чисел, монотонно стре мящаяся к нулю, причем Σa n=∞. Тогда найд ется такая последовательность знаковε(п)=±1 (п=1,2, ...), что для каждого натураль ного т и любого целого b с условием 0≦b≦m−1 выполнено равен ство

\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} $$\mathop \sum \limits_{n \equiv b(mod m)} \varepsilon (n)a_n = 0$$ \end{document}
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# Generation of alternating groups by pairs of conjugates

Authors: L. Beasley, J. Brenner, P. Erdős, M. Szalay and A. Williamson
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# Book reviews

Authors: E. Molnár, P. Erdős, A. Ádám, Gy. Béda and Zs. Páles
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# On the existence of triangulated spheres in 3-graphs, and related problems

Authors: V. T. Sós, P. Erdős and W. G. Brown
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# Some extremal properties concerning transitivity in graphs

Authors: R. C. Entringer, P. Erdős and C. C. Harner
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# The size Ramsey number

Authors: P. Erdős, R. J. Faudree, C. C. Rousseau and R. H. Schelp

Let denote the class of all graphsG which satisfyG→(G 1,G 2). As a way of measuring minimality for members of, we define thesize Ramsey number ř(G 1,G 2) by.

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# A test of naturalness indicator values to evaluate success in grassland restoration

Authors: P. Sengl, M. Magnes, L. Erdős and C. Berg

How should the somewhat vague term of restoration success be measured? This is a critical question rooted in European law, where in fact the creation of proper replacement habitats is a prerequisite for permitting projects that trigger a loss of species or habitats. Previous studies have used indices that relied on a comparison to reference sites, for example the number of a predefined pool of target species or compositional similarity. However, since restoration sites have rarely the same biotic and abiotic conditions as reference sites, plant communities in restored sites will not perfectly match the reference sites. Furthermore, such indices fail when reference sites are lacking or degraded. Hence, there is a need for an alternative approach that evaluates the conservation value of a restored site independently from reference sites. We propose that naturalness indicator values can be an option to measure restoration success. The approach of using naturalness indicator values makes use of the fact that plants are able to indicate environmental parameters, including degradation and regeneration. We compared and measured the restoration success of three well-established methods for grassland restoration (sod transplantation, hay transfer, seeding) with three commonly used indices (diversity, number of target species, similarity to reference sites). The results verified earlier studies and showed that sod transplantation led to the highest restoration success followed by hay transfer and seeding of sitespecific seed mixtures. Further, we used those well-established indices for an evaluation of novel, naturalness-based indices (unweighted and cover-weighted mean naturalness indicator values, the sum of naturalness indicator values). While calculating the means of naturalness indicator values failed to offer conclusive information on restoration success, we could show that the sum of naturalness indicator values was highly correlated with the number of target species and compositional similarity to reference sites. Thus, our case study demonstrated that naturalness indices can be an excellent option to estimate success in grassland restoration.

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# Factors affecting the structure of bee assemblages in extensively and intensively grazed grasslands in Hungary

Authors: M. Sárospataki, A. Báldi, P. Batáry, Z. Józan, S. Erdős and T. Rédei

Bees are the most important pollinators in Europe. We studied bee assemblages on 7 pairs of extensively and intensively grazed sites in three lowland grassland types in Hungary. No chemicals were applied on the grasslands. The bees were collected using sweep net surveys and 1 m wide transect surveys in 2003. We mapped land-use types (grasslands; arable fields; forests; built-up areas; marshy habitat and open water) based on aerial photographs within a 500 m radius of each study site. We captured 483 individuals of 124 Apoidea species in total. This shows very diverse and species rich bee assemblages in these semi-natural grassland areas. Both diversity and percentage of rare species were the highest on the Kiskunság alkali area. The dominance of honey bee ( Apis mellifera ) was very low at each site. Neither species richness nor abundances differed between extensively and intensively grazed sampling sites, among regions, and between edge and interior of sites. However, both species richness and abundance of bees correlated positively with species richness and cover of flowering plants, indicating the important role of food sources. From the landscape parameters wet areas were preferred by small species, while large species tended to avoid build-up areas.

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