Let 0 ≦ a1 < a2 < ⋯ be an infinite sequence of integers and let r1(A, n) = |(i;j): ai + aj = n, i ≦ j|. We show that if d > 0 is an integer, then there does not exist n0 such that d ≦ r1 (A, n) ≦ d + [√2d + ] for n > n0.
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.
This paper is connected with the fundamental work of E.S. Barnes and G.E. Wall  in which the authors defined the so-called Barnes-Wall lattice. We shall determine the number of minima of some special sublattices of dimension 2n-k of this lattice, where 1=k=n.
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.
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.
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.
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.