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.
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.
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.
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.
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.
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.