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Eggs in PG(4n−1,q), q even, containing a pseudo-pointed conic

Matthew R. Brown, Michel Lavrauw
2005 European journal of combinatorics (Print)  
We prove that an egg in PG(4n1, q), q even, contains a pseudo pointed conic, that is, a pseudo-oval arising from a pointed conic of PG(2, q n ), q even, if and only if the egg is elementary and the  ...  Thas [24] introduced the notion of pseudo-ovoids or eggs: a set of q 2n + 1 (n − 1)-spaces in PG(4n1, q), with the property that any three egg elements span a (3n − 1)-space and at every egg element  ...  Eggs in PG(4n1, q), q even, containing a pseudo pointed conic In this section we study the structure of TGQs whose corresponding egg contains a pseudo pointed conic.  ... 
doi:10.1016/j.ejc.2003.12.014 fatcat:mwzaaku6cnb7bbxouptpnjwlha

Characterizations and properties of good eggs in PG(4n-1,q), q odd

Michel Lavrauw
2005 Discrete Mathematics  
A. 96 (2) (2001) 303-315] we prove that a good egg of PG(4n1, q), q odd, is isomorphic to an ovoid of PG(3, q n ) seen over GF(q) if and only if there exists a (3n − 1)-space skew from the good element  ...  There are only three classes of known examples of eggs in PG(4n1, q), which are not elementary.  ...  For q even we refer to [2, 3] . Let F = GF(q n ), q odd and let E be a good egg of PG(4n1, q).  ... 
doi:10.1016/j.disc.2004.11.022 fatcat:jhqrkmpmdbbjjow7ajif5xz36m

Characterisations of elementary pseudo-caps and good eggs [article]

Sara Rottey, Geertrui Van de Voorde
2015 arXiv   pre-print
In this note, we use the theory of Desarguesian spreads to investigate good eggs. Thas showed that an egg in PG(4n-1, q), q odd, with two good elements is elementary.  ...  By a short combinatorial argument, we show that a similar statement holds for large pseudo-caps, in odd and even characteristic.  ...  The authors wish to thank Simeon Ball for suggesting the study of eggs in terms of the induced (partial) spreads.  ... 
arXiv:1502.01150v1 fatcat:6grnq6oeyfdofgrfh2qrs2xqey

Characterisations of Elementary Pseudo-Caps and Good Eggs

Sara Rottey, Geertrui Van de Voorde
2015 Electronic Journal of Combinatorics  
In this note, we use the theory of Desarguesian spreads to investigate good eggs. Thas showed that an egg in $PG(4n-1,q)$, $q$ odd, with two good elements is elementary.  ...  By a short combinatorial argument, we show that a similar statement holds for large pseudo-caps, in odd and even characteristic.  ...  Acknowledgements The authors wish to thank Simeon Ball for suggesting the study of eggs in terms of the induced (partial) spreads.  ... 
doi:10.37236/4913 fatcat:toylmqyp75hi3fp3zuzqbyi7lu

Subquadrangles of order s of generalized quadrangles of order (s,s2)

Koen Thas, Joseph Thas
2009 Innovations in Incidence Geometry Algebraic Topological and Combinatorial  
In this paper we consider the subquadrangles of order s for all known classes of generalized quadrangles of order (s, s 2 ).  ...  Let O = O(n, 2n, q), with q odd, be an egg in PG(4n1, q) which is good at π.  ...  For q even, one can use Theorem 6.2 and [25, Chapter 7] to show that if O = O(n, 2n, q) is an egg in PG(4n1, q) and T (O) contains a subGQ of order q n that is fixed pointwise by some nontrivial automorphism  ... 
doi:10.2140/iig.2009.10.133 fatcat:ddggc74uzvf2zkfavsxbrz6a34

Subquadrangles of order s of generalized quadrangles of order (s,s2), Part III

J.A. Thas, K. Thas
2006 Journal of combinatorial theory. Series A  
As a corollary we have: if O(n, 2n, q) is an egg in PG(4n1, q) for which the translation dual O * (n, 2n, q) is good at the tangent space of O(n, 2n, q) at its element π and if there is a pseudo-oval  ...  on O(n, 2n, q) not containing π , then O(n, 2n, q) is classical.  ...  Then O = {π 0 , π 1 , . . . , π q m } is a generalized oval of PG(3n − 1, q) for m = n, The tangent spaces of an egg O(n, 2n, q) in PG(4n1, q) form an egg O * (n, 2n, q) in the dual space of PG(4n −  ... 
doi:10.1016/j.jcta.2006.03.013 fatcat:6llexuywmvb5dchfz6gv32snrm

Transitive eggs

John Bamberg, Tim Penttila
2006 Innovations in Incidence Geometry Algebraic Topological and Combinatorial  
We prove that a pseudo-oval or pseudo-ovoid (that is not an oval or ovoid) admitting an insoluble transitive group of collineations is elementary and arises over an extension field from a conic, an elliptic  ...  quadric, or a Suzuki-Tits ovoid.  ...  Brown and Lavrauw [6] have shown that an egg of PG(4n1, q), q even, contains a pseudo-conic if and only if it is elementary and arises from an elliptic quadric. Recently, J. A. Thas and K.  ... 
doi:10.2140/iig.2006.4.1 fatcat:pzpqqo4ignd5bkxqugmcltjewm

Classification of 8-dimensional rank two commutative semifields [article]

Michel Lavrauw, Morgan Rodgers
2016 arXiv   pre-print
This is done using computational methods utilizing the connection to linear sets in PG(2,q^4).  ...  The implications of these results are detailed for other geometric structures such as semifield flocks, ovoids of parabolic quadrics, and eggs.  ...  If there exists an 11-space ρ containing an elementary pseudo-oval O q contained in E corresponding to a conic C of PG(2, q 4 ), and there is a tangent space intersecting ρ in a 7-space U whose associated  ... 
arXiv:1606.06151v2 fatcat:pdlefywj25cg5lxnnpc3metlbe

Page 1899 of Mathematical Reviews Vol. , Issue 2003C [page]

2003 Mathematical Reviews  
The egg O(n, 2n, q) = 0 of PG(4n1,q), ¢ even, is classical if and only if either O is good at some element and contains at least one pseudo- conic, or O contains at least two intersecting pseudo-conics  ...  is contained in exactly g + 1 elements of and each point of Q\ (U UV) is contained in exactly one element of @.  ... 

TRANSLATION GENERALIZED QUADRANGLES FOR WHICH THE TRANSLATION DUAL ARISES FROM A FLOCK

KOEN THAS
2003 Glasgow Mathematical Journal  
There are important consequences for the theory of generalized ovoids (or eggs) in PG(4n1, q), the study of span-symmetric generalized quadrangles, derivation of flocks of the quadratic cone in PG(3  ...  If p is a point and L is a line not incident with p, then there is a unique point-line pair (q, M) such that pIMIqIL. If s = t, then S is also said to be of order s.  ...  A. Thas for carefully reading the paper. The author is a research fellow supported by the Flemish Institute for the promotion of Scientific and Technological Research in Industry (IWT), grant no.  ... 
doi:10.1017/s0017089503001381 fatcat:lsj2jjwvobdc7g2aen4aogc62a

European Journal of Combinatorics Index, Volume 26

2005 European journal of combinatorics (Print)  
in PG(4n1, q), q even, containing a pseudo-pointed conic . . . . . . . . . . 117 CHEN, W.Y.C., DENG, E.Y.P. and DU, R.R.X., Reduction of m-regular noncrossing partitions . . . . . . . . . . .  ...  TANIGUCHI, H., On a family of dual hyperovals over GF(q) with q even . 195 TENT, K., A weak Moufang condition suffices . . . . . . . . 1207 TERWILLIGER, P. and WENG, C.  ... 
doi:10.1016/s0195-6698(05)00129-0 fatcat:vuytixhru5bupfpbxzzanswabu

Export Signals [chapter]

2008 Encyclopedia of Genetics, Genomics, Proteomics and Informatics  
Therefore, the probability that any two alleles of the population comes from the same individual is: 1 4N m þ 1 4N f ¼ 1 N e hence N e ¼ 4N m N f N m þN f : Fluctuations in population size from generation  ...  If a mutation from A to a is a regular event, the frequency of a may increase at the expense of A qn þ 1 ¼ qn þ mð1 À qnÞ f 1g where q = frequency of the recessive allele, and (1q) = frequency of the  ...  The conversion to log 2 from log 10 is carried out as follows: log 2 ½1024 ¼ log 10 ½1024ð1=log 10 ½2Þ ¼ 3:010299957 Â log 10 ð1=0:301029995Þ ¼ 3:010299957 Â 3:321928095 % 10 ▶growth curve Export Adaptor  ... 
doi:10.1007/978-1-4020-6754-9_5734 fatcat:6qstuftdi5dhnbuulcl4m6nfme

Ecology [chapter]

James C. Dunford, Louis A. Somma, David Serrano, C. Roxanne Rutledge, John L. Capinera, Guy Smagghe, Eli Shaaya, David G. Riley, John L. Capinera, Steve H. Dreistadt, Susanne D. Dyby, John B. Heppner (+24 others)
2008 Encyclopedia of Entomology  
Therefore, the probability that any two alleles of the population comes from the same individual is: 1 4N m þ 1 4N f ¼ 1 N e hence N e ¼ 4N m N f N m þN f : Fluctuations in population size from generation  ...  If a mutation from A to a is a regular event, the frequency of a may increase at the expense of A qn þ 1 ¼ qn þ mð1 À qnÞ f 1g where q = frequency of the recessive allele, and (1q) = frequency of the  ...  The conversion to log 2 from log 10 is carried out as follows: log 2 ½1024 ¼ log 10 ½1024ð1=log 10 ½2Þ ¼ 3:010299957 Â log 10 ð1=0:301029995Þ ¼ 3:010299957 Â 3:321928095 % 10 ▶growth curve Export Adaptor  ... 
doi:10.1007/978-1-4020-6359-6_3494 fatcat:zdm7o5n7jngerpge54q4mmczme

IETS 2006 abstracts

2006 Reproduction, Fertility and Development  
Even though many experimental findings indicate a pivotal role of IFNτ in the context of embryo-maternal communication in ruminants, a number of other systems may be involved.  ...  However, the transcripts of Oct-4 were mainly obtained in unspliced form at the earlier stage of culture (after Day 1 to Day 4 of culture), suggesting that a part of reprogramming processes by the egg  ...  Day 1 to Day 3  ... 
doi:10.1071/rdv18n2abs fatcat:gygnnsby3ra3tmfxlmrgrtlfwu

A Generic Method for the Production of Recombinant Proteins in Escherichia coli Using a Dual Hexahistidine-Maltose-Binding Protein Affinity Tag [chapter]

Joseph E. Tropea, Scott Cherry, Sreedevi Nallamsetty, Christophe Bignon, David S. Waugh
2007 Msphere  
A generic protocol that utilizes a dual hexahistidine-maltose-binding protein (His 6 -MBP) affinity tag has been developed for the production of recombinant proteins in Escherichia coli.  ...  In the final step, the unwanted byproducts of the digest are absorbed by a second round of IMAC, leaving nothing but the pure passenger protein in the flow-through fraction.  ...  The author would like to thank Anne Mason (University of Vermont) for help with Table 1 .  ... 
doi:10.1007/978-1-59745-209-0_1 pmid:17272834 fatcat:3ytri6xm45fztgo5nz7i2o4ssy
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