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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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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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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 2n-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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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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After a short explanatory Introduction, an immunotherapy protocol is presented for glioblastoma multiforme (GBM). GBM is considered to be an incurable tumor; tumor-free survival over 2 to 3 years is so rare that when it happens the original diagnosis is questioned. It is known that the type of the genetic mutation that a given GBM tumor harbors strongly influences the length of survival. However, most patients with GBM are receiving treatment without the preparation of a microarray gene map of their tumors. It is possible that the reason for a rare and exceptional long survival was not the treatment that the patient received, but the type of gene mutations that the tumor was exposed to. It is recognized that any therapeutic approach should ideally be evaluated against the background of all prognostic factors of each individual case, prominent among them the microarray gene map of the tumor. In practice, this is not easily achieved, while the patient is in need of, and is expecting, prompt therapy. Insurance companies do not reimburse the patient, or the clinical investigators, or their institutions for investigational diagnostic tests, or such treatment modalities. A temporary compromise is possible. The emergence of empirically administered treatment modalities with extraordinary efficacy has occasionally been recorded in the history of medical oncology. In some of these rare clinical trials, the control groups were discontinued (to the dismay of the statisticians), and the control patients were enrolled in the treatment groups so to escape doom and share the benefit of the unfolding high remission inductions experienced in the treatment group. Chemo-radiotherapy of Hodgkin's disease and cisplatin therapy of certain testicular carcinomas provided the first éclat examples. More recently, the rapidly approved and marketed imitanib mesylate for Ph-chromosome-positive chronic myelogenous leukemia and the anti-HER2/neu monoclonal antibody trastuzumab, and the not yet marketed double tyrosine kinase (ErbB1/2) inhibitor lapatinib (Tykerb, GlaxoSmithKline) for a subgroup of breast carcinoma patients excelled. Thus, a clinical trial for GBM, but without precise pre-identification of all its prognostic factors, however with a great deal of evidence-based empirical expectations of benefits, for patients with rapid advancement toward a fatal outcome, implying an element of urgency, appears to be justified.

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A questionnaire study was performed involving 76 farms with a total of 380,207 pigs to assess the welfare of pigs kept in Hungary based on the animal welfare legislation of the European Union. Most significant deficiencies were found in the fulfilment of the provisions relating to space requirements, the stall microclimate and the behavioural needs of the animals.

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