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  • Author or Editor: G. Horváth x
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Abstract  

Let 0 ≦ a 1 < a 2 < ⋯ be an infinite sequence of integers and let r 1(A, n) = |(i;j): a i + a j = n, ij|. We show that if d > 0 is an integer, then there does not exist n 0 such that dr 1 (A, n) ≦ d + [√2d + ] for n > n 0.

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Abstract  

Montgomery and Vaughan improved a theorem of Erdős and Fuchs for an arbitrary sequence. Srkzy extended this theorem of Erdős and Fuchs for two arbitrary sequences which are "near" in a certain sense. Using the idea of Jurkat (differentiation of the generating function), we will extend similarly the result of Montgomery and Vaughan for "sufficiently near" sequences.

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Albrechtsen, S. E.: Testing Methods for Seed-Transmitted Viruses: Principles and Protocols. CABI Publishing, Wallingford, UK, 2006. 268 pp. (US 100.00)

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This paper is connected with the fundamental work of E.S. Barnes and G.E. Wall [1] in which the authors defined the so-called Barnes-Wall lattice. We shall determine the number of minima of some special sublattices of dimension 2 n -k of this lattice, where 1=k=n.

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G. Loebenstein, P. H. Berger, A. A. Brunt and R. H. Lawson (eds): Virus and Virus-like Diseases of Potatoes and Production of Seed-Potatoes. Kluwer Academic Publ., Dordrecht (The Netherlands), 2001, 460 pp. László Nowinszky (ed.): The Handbook of Light Trapping. Savaria University Press, Szombathely, 2003.

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Abstract  

We prove that the tolerance lattice TolA of an algebra A from a congruence modular variety V is 0-1 modular and satisfies the general disjointness property. If V is congruence distributive, then the lattice Tol A is pseudocomplemented. If V admits a majority term, then Tol A is 0-modular.

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In this review results are summarized regarding the effect of virus infection on the physiological processes of weeds. Through several host-virus model relations the biomass and seed production, seed viability and germination, nutrient uptake, drought-resistance and photosynthetic pigment content of healthy and virus infected plants were compared. Because of their broad host range and high genetic variability viruses cannot be used for biological weed control. It was concluded that viruses unfavourably can influence physiological processes of weeds. Therefore, they may contribute indirectly to the reduction of competitive ability and population of weeds.

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The aim of our study was to investigate the susceptibility of some Chenopodium species (Chenopodium album, C. glaucum, C. berlandieri, C. ugandae) to six viruses (Alfalfa mosaic virus, Cucumber mosaic virus, Obuda pepper virus, Potato virus Y, Sowbane mosaic virus, Zucchini yellow mosaic virus). Fourteen plants of each species were mechanically inoculated and virus susceptibility was evaluated on the basis of symptoms and back inoculation. A series of new host-virus relations were determined.

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