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

2005
*
European journal of combinatorics (Print)
*

We prove that an

doi:10.1016/j.ejc.2003.12.014
fatcat:mwzaaku6cnb7bbxouptpnjwlha
*egg**in**PG*(*4n*−*1*,*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*(*4n*−*1*,*q*), with the property that any three*egg*elements span*a*(3n −*1*)-space and at every*egg*element ...*Eggs**in**PG*(*4n*−*1*,*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*. ...##
###
Characterizations and properties of good eggs in PG(4n-1,q), q odd

2005
*
Discrete Mathematics
*

*A*. 96 (2) (2001) 303-315] we prove that

*a*good

*egg*of

*PG*(

*4n*−

*1*,

*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*(

*4n*−

*1*,

*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*(

*4n*−

*1*,

*q*). ...

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

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. ...

##
###
Characterisations of Elementary Pseudo-Caps and Good Eggs

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. ...

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

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*(

*4n*−

*1*,

*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*(

*4n*−

*1*,

*q*) and T (O)

*contains*

*a*subGQ of order

*q*n that is fixed pointwise by some nontrivial automorphism ...

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

2006
*
Journal of combinatorial theory. Series A
*

As

doi:10.1016/j.jcta.2006.03.013
fatcat:6llexuywmvb5dchfz6gv32snrm
*a*corollary we have: if O(n, 2n,*q*) is an*egg**in**PG*(*4n*−*1*,*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*(*4n*−*1*,*q*) form an*egg*O * (n, 2n,*q*)*in*the dual space of*PG*(*4n*− ...##
###
Transitive eggs

2006
*
Innovations in Incidence Geometry Algebraic Topological and Combinatorial
*

We prove that

doi:10.2140/iig.2006.4.1
fatcat:pzpqqo4ignd5bkxqugmcltjewm
*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*(*4n*−*1*,*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. ...##
###
Classification of 8-dimensional rank two commutative semifields
[article]

2016
*
arXiv
*
pre-print

This is done using computational methods utilizing the connection to linear sets

arXiv:1606.06151v2
fatcat:pdlefywj25cg5lxnnpc3metlbe
*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 ...##
###
Page 1899 of Mathematical Reviews Vol. , Issue 2003C
[page]

2003
*
Mathematical Reviews
*

The

*egg*O(n, 2n,*q*) = 0 of*PG*(*4n*—*1*,*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

2003
*
Glasgow Mathematical Journal
*

There are important consequences for the theory of generalized ovoids (or

doi:10.1017/s0017089503001381
fatcat:lsj2jjwvobdc7g2aen4aogc62a
*eggs*)*in**PG*(*4n*−*1*,*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. ...##
###
European Journal of Combinatorics Index, Volume 26

2005
*
European journal of combinatorics (Print)
*

*in*

*PG*(

*4n*−

*1*,

*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. ...

##
###
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:

doi:10.1007/978-1-4020-6754-9_5734
fatcat:6qstuftdi5dhnbuulcl4m6nfme
*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 (*1*−*q*) = 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 ...##
###
Ecology
[chapter]

2008
*
Encyclopedia of Entomology
*

Therefore, the probability that any two alleles of the population comes from the same individual is:

doi:10.1007/978-1-4020-6359-6_3494
fatcat:zdm7o5n7jngerpge54q4mmczme
*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 (*1*−*q*) = 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 ...##
###
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 ...

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

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*. ...

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