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  • 1
    ISSN: 1573-7586
    Keywords: Baer subplane ; flag-transitive affine plane ; linearized polynomials
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract The classification of perfectBaer subplane partitions of PG(2, q2) is equivalentto the classification of 3-dimensional flag-transitive planeswhose translation complements contain a linear cyclic group actingregularly on the line at infinity. Since all known flag-transitiveplanes admit a translation complement containing a linear cyclicsubgroup which either acts regularly on the points of the lineat infinity or has two orbits of equal size on these points,such a classification would be a significant step towards theclassification of all 3-dimensional flag-transitive planes. Usinglinearized polynomials, a parametric enumeration of all perfectBaer subplane partitions for odd q is described.Moreover, a cyclotomic conjecture is given, verified by computerfor odd prime powers q 〈 200, whose truth would implythat all perfect Baer subplane partitions arise from a constructionof Kantor and hence the corresponding flag-transitive planesare all known.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Designs, codes and cryptography 8 (1996), S. 79-89 
    ISSN: 1573-7586
    Keywords: Regulus ; spread ; flag-transitive
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract An old conjecture of Bruck and Bose is that every spreadof Σ = PG(3,q) could be obtained by startingwith a regular spread and reversing reguli. Although it was quicklyrealized that this conjecture is false, at least for qeven, there still remains a gap in the spaces for which it isknown that there are spreads which are regulus-free. In severalpapers Denniston, Bruen, and Bruen and Hirschfeld constructedspreads which were regulus–free, but none of these dealtwith the case when q is a prime congruent to onemodulo three. This paper closes that gap by showing that forany odd prime power q, spreads of PG(3,q) yielding nondesarguesian flag-transitive planes are regulus–free.The arguments are interesting in that they are based on elementarylinear algebra and the arithmetic of finite fields.
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Designs, codes and cryptography 8 (1996), S. 79-89 
    ISSN: 1573-7586
    Keywords: Regulus ; spread ; flag-transitive
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract An old conjecture of Bruck and Bose is that every spread of Σ =PG(3,q) could be obtained by starting with a regular spread and reversing reguli. Although it was quickly realized that this conjecture is false, at least forq even, there still remains a gap in the spaces for which it is known that there are spreads which are regulus-free. In several papers Denniston, Bruen, and Bruen and Hirschfeld constructed spreads which were regulus-free, but none of these dealt with the case whenq is a prime congruent to one modulo three. This paper closes that gap by showing that for any odd prime powerq, spreads ofPG(3,q) yielding nondesarguesian flag-transitive planes are regulus-free. The arguments are interesting in that they are based on elementary linear algebra and the arithmetic of finite fields.
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    Geometriae dedicata 27 (1988), S. 9-14 
    ISSN: 1572-9168
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract An affine plane is called flag-transitive if it admits a collineation group which acts transitively on the incident point-line pairs. It has been shown that finite flag-transitive planes are necessarily translation planes, and much work has been devoted to this class of translation planes in recent years. All flag-transitive groups of finite affine planes have been determined, and an infinite family of non-Desarguesian flag-transitive planes has been found. In this paper a method is given for constructing all two-dimensional flag-transitive planes of odd order, subsuming the infinite family mentioned above.
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  • 5
    Electronic Resource
    Electronic Resource
    Springer
    Designs, codes and cryptography 4 (1994), S. 307-312 
    ISSN: 1573-7586
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract The one-to-one correspondence between the class of two-dimensional translation planes of orderq 2 and the collection of spreads ofPG(3,q) has long provided a natural context for describing new planes. The method often used for constructing “interesting” spreads is to start with a regular spread, corresponding to a desarguesian plane, and then replace some “nice” subset of lines by another partial spread covering the same set of points. Indeed the first approach was replacing the lines of a regulus by the lines of its opposite regulus, or doing this process for a set of disjoint reguli. Nontrivial generalizations of this idea include thechains of Bruen and thenests of Baker and Ebert. In this paper we construct a replaceable subset of a regular spread ofPG (3, 19) which is the union of 11 reguli double covering the lines in their union, hence is a chain in the terminology of Bruen or a 11-nest in the Baker-Ebert terminology.
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  • 6
    ISSN: 1439-6912
    Keywords: 06 C 10 ; 15 A 06 ; 11 T 99
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract LetA be a nonsingularn byn matrix over the finite fieldGF q ,k=⌊n/2⌋,q=p a ,a≥1, wherep is prime. LetP(A,q) denote the number of vectorsx in (GF q ) n such that bothx andAx have no zero component. We prove that forn≥2, and $$q 〉 2\left( {\begin{array}{*{20}c} {2n} \\ 3 \\ \end{array} } \right)$$ ,P(A,q)≥[(q−1)(q−3)] k (q−2) n−2k and describe all matricesA for which the equality holds. We also prove that the result conjectured in [1], namely thatP(A,q)≥1, is true for allq≥n+2≥3 orq≥n+1≥4.
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  • 7
    Electronic Resource
    Electronic Resource
    Springer
    Geometriae dedicata 63 (1996), S. 1-15 
    ISSN: 1572-9168
    Keywords: 51A40 ; 51E15 ; Flag-transitive ; translation plane ; two-dimensional ; enumeration
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper shows that the odd order two-dimensional flag-transitive planes constructed by Kantor-Suetake constitute the same family of planes as those constructed by Baker-Ebert. Moreover, for orders satisfying a modest number theoretical assumption this family consists of all possible such planes of that order. In particular, it is shown that the number of isomorphism classes of (non-Desarguesian) two-dimensional flag-transitive affine planes of order q 2 is precisely (q−1)/2 when q is an odd prime and precisely (q−1)/2e when q=p e is an odd prime power with exponent e that is a power of 2. An enumeration is given in other cases that uses the Möbius inversion formula.
    Type of Medium: Electronic Resource
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  • 8
    ISSN: 1420-9071
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Medicine
    Notes: Zusammenfassung Der Transport desL-Methionins durch die Rattendarmwand wurde in vitro untersucht. Die Transportgeschwindigkeit im Verlaufe von 1 h ist am höchsten im unteren Jejunum und im oberen Ileum (Abschnitte 4, 5 und 6). DNP-verursachte Hemmung ist in diesen Darmabschnitten am stärksten, was das Verschwinden des Maximums bewirkt.
    Type of Medium: Electronic Resource
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  • 9
    ISSN: 1365-2494
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Notes: In a trial lasting 3 years at Jealott's Hill and 2 years at Ravenscroft Hall, a total of 73 January- March-calving Friesian x Holstein cows and heifers were given a diet consisting almost exclusively of ensiled and grazed ryegrass for an entire lactation to establish the level of milk production which grass alone can support. From calving to turnout in April/May (average duration 87 days), the animals were given high digestibility (DOMD = 678g kg-1 DM) ryegrass silage ad libitum. After turnout, they grazed ryegrass swards until housing in autumn. Thereafter, the cattle were given ryegrass silage of lower digestibility (DOMD = 600–620 g kg-1 DM) for the remainder of the lactation and during the dry period.Mean silage dry matter intakes from calving to turnout were 13–2 kg day-1 at Jealott's Hill and 11·5 kg day-1 at Ravenscroft Hall. Average milk yields were 21-1 kg day-1 for cows and 16-1 kg day-1 for heifers with 39-2g fat kg-1, 29-6g protein kg-1 and 47–9 g lactose kg-1. Over the complete lactation, average milk yields were 4680 kg and 4006 kg for the cows and heifers, respectively, with 39-4 g fat kg-1, 31·4 g protein kg-1 and 46·9 g lactose kg-1. Animal health and fertility were satisfactory. The results demonstrated the value of high quality grazed and ensiled ryegrass and provided a measure of milk production from grass only.
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  • 10
    Electronic Resource
    Electronic Resource
    Oxford, UK : Blackwell Publishing Ltd
    Grass and forage science 20 (1965), S. 0 
    ISSN: 1365-2494
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Notes: Survey data collected during a grassland-recording investigation showed a strong positive correlation between nitrogen input and the output of utilized starch equivalent per acre. At the levels of output covered, sward type was not very important in relation to total yield. Herbage species were important for other reasons and the choice of seeds mixtures should be determined by factors such as earliness and lateness of growth and resistance to disease and drought. The survey showed that well-managed ley and permanent pasture are both capable of producing at a high level. A disturbing feature of the results was the low production of most spring resowings, primarily as a result of poor management. Although the records were obtained from an above-average group of farms, the results have general application. Potential responses to fertilizers may be even greater on less intensive farms, especially with regard to phosphate and potash. However, the level of production of a field will always depend finally on the level of management exercised by the farmer himself.
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