Pure Mathematics
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Item Metadata only A class of Buekenhout unitals in the Hall plane(The Belgian Mathematical Society, 1996) Barwick, S.Let U be the classical unital in PG(2, q2) secant to ℓ∞. By deriving PG(2, q2) with respect to a derivation set disjoint from U we obtain a new unital U′ in the Hall plane of order q2. We show that this unital contains O'Nan configurations and is not isomorphic to the known unitals of the Hall plane, hence it forms a new class of unitals in the Hall plane.Item Metadata only A construction for multisecret threshold schemes(Springer Science and Business Media LLC, 1996) Jackson, W.A.; Martin, K.; O'Keefe, C.A multisecret threshold scheme is a system that protects a number of secrets (or keys) among a group of participants, as follows. Given a set of n participants, there is a secret sK associated with each k-subset K of these participants. The scheme ensures that sK can be reconstructed by any group of t participants in K (1 ≤ t ≤ k). A lower bound has been established on the amount of information that participants must hold in order to ensure that any set of up to w participants (0 ≤ w ≤ n - k + t - 1) cannot obtain any information about a secret with which they are not associated. In this paper, for parameters t = 2 and w = n - k + t - 1, we give a construction for multisecret threshold schemes that satisfy this bound. © 1996 Kluwer Academic Publishers.Item Metadata only A general approach to robust web metering(Kluwer Academic Publ, 2005) Barwick, S.; Jackson, W.; Martin, K.We consider the problem of metering access to web sites. Many services, such as web advertising, have a need for accurate counts of the number of visits to a web site. We consider the robust approach to web metering by looking at techniques that provide secure proofs of visit. We refine a number of previous models for metering schemes and provide a general construction for secure and efficient schemes that meter the interaction of a web site with a targeted audience. We generalise a technique for determining the minimum information that clients in the web site audience need to secure in order to supply proofs of visit. We also show how our metering schemes can be made robust against corrupt clients who attempt to prevent web servers constructing legitimate proofs of visit.Item Metadata only A general decomposition construction for incomplete secret sharing schemes(Springer Science and Business Media LLC, 1998) van Dijk, M.; Jackson, W.A.; Martin, K.A secret sharing scheme for an incomplete access structure (Γ, Δ) is a method of distributing information about a secret among a group of participants in such a way that sets of participants in Γ can reconstruct the secret and sets of participants in Δ can not obtain any new information about the secret. In this paper we present a more precise definition of secret sharing schemes in terms of information theory, and a new decomposition theorem. This theorem generalizes previous decomposition theorems and also works for a more general class of access structures. We demonstrate some applications of the theorem.Item Metadata only A geometrical construction of the oval(s) associated with an a-flock(Walter de Gruyter & Co., 2004) Brown, M.; Thas, J.; Brown, M.R.; Thas, J.A.It is known, via algebraic methods, that a flock of a quadratic cone in PG(3, q) gives rise to a family of q + 1 ovals of PG(2, q) and similarly that a flock of a cone over a translation oval that is not a conic gives rise to an oval of PG(2, q). In this paper we give a geometrical construction of these ovals and provide an elementary geometrical proof of the construction. Further we also give a geometrical construction of a spread of the GQ T 2(Ο) for Ο an oval corresponding to a flock of a translation oval cone in PG(3, q), previously constructed algebraically. © de Gruyter 2004.Item Metadata only A Nakai-Moishezon criterion for non-Kähler surfaces(Annales de L Institut Fourier, 2000) Buchdahl, N.Item Open Access A note on monopole moduli spaces(Amer Inst Physics, 2003) Murray, M.; Singer, M.We discuss the structure of the framed moduli space of Bogomolny monopoles for arbitrary symmetry breaking and extend the definition of its stratification to the case of arbitrary compact Lie groups. We show that each stratum is a union of submanifolds for which we conjecture that the natural L2 metric is hyper-Kähler. The dimensions of the strata and of these submanifolds are calculated, and it is found that for the latter, the dimension is always a multiple of four.Item Metadata only A note on the index bundle over the moduli space of monopoles(Springer-Verlag, 1995) Jones, J.; Murray, M.Donaldson has shown that the moduli space of monopoles Mk is diffeomorphic to the space Ratk of based rational maps from the two-sphere to itself. We use this diffeomorphism to give an explicit description of the bundle on Ratk obtained by pushing out the index bundle from Mk. This gives an alternative and more explicit proof of some earlier results of Cohen and Jones. © 1995 Springer-Verlag.Item Metadata only A unified construction of finite geometries associated with q-clans in characteristic 2(Walter de Gruyter GmbH & Co. KG, 2003) Cherowittzo, W.; O'Keefe, L.; Penttila, T.; Cherowitzo, W.E.; O'Keefe, C.M.; Penttila, T.Flocks of Laguerre planes, generalized quadrangles, translation planes, ovals, BLTsets, and the deep connections between them, are at the core of a developing theory in the area of geometry over finite fields. Examples are rare in the case of characteristic two, and it is the purpose of this paper to contribute a fifth infinite family. The approach taken leads to a unified construction of this new family with three of the previously known infinite families, namely those satisfying a symmetry hypothesis concerning cyclic subgroups of PGL(2, q). The calculation of the automorphisms of the associated generalized quadrangles is sufficient to show that these generalized quadrangles and the associated flocks and translation planes do not belong to any previously known family.Item Metadata only Abstract Cauchy problems: Three approaches(Chapman & Hall/CRC, 2001) Melnikova, I.; Filinkov, A.Item Metadata only Abstract hyperovals and Hadamard designs(1997) Polster, Burkard MichaelItem Metadata only Algebras like Clifford Algebras(Birkhauser, 2004) Eastwood, Michael George; School of Mathematical Sciences : Pure MathematicsItem Metadata only Almost everywhere convergence of Fourier-Laplace series(1995) Brown, Gavin; Wang, K-Y.; School of Mathematical Sciences : Pure MathematicsItem Metadata only An algorithm for efficient geometric secret sharing schemes(Utilitas Mathematica Pub., 1998) Jackson, W.A.; Martin, K.A secret sharing scheme is a method of distributing among a set of participants some information relating to a secret. A secret sharing scheme can be associated with two disjoint collections Γ, Δ of sets of participants. Sets of participants in Γ can use their information to reconstruct, the secret, whilst sets of participants in Δ cannot gain any knowledge of the secret from their information. Geometric secret sharing schemes form a wide class of secret sharing schemes with desirable properties. We present an algorithm for the construction of optimally efficient geometric secret sharing schemes. In order to do so, we first show that with the exception of degenerate cases, every geometric scheme can be obtained directly from its corresponding cumulative scheme (a generally inefficient secret sharing scheme which has a simple algorithmic construction). We analyse the complexity of our algorithm and discuss other published algorithms.Item Metadata only An optimal multisecret threshold scheme construction(Kluwer Academic Publ, 2005) Barwick, S.; Jackson, W.A multisecret threshold scheme is a system which protects a number of secret keys among a group of n participants. There is a secret sK associated with every subset K of k participants such that any t participants in K can reconstruct the secret sK, but a subset of w participants cannot get any information about a secret they are not associated with. This paper gives a construction for the parameters t = 2, k = 3 and for any n and w that is optimal in the sense that participants hold the minimal amount of information.Item Metadata only Analytic continuation of complex gauge fields(1998) Harris, A. G.Item Metadata only Analytic continuation of vector bundles with Lp-curvature(WORLD SCIENTIFIC PUBL CO PTE LTD, 2000) Harris, A. G.; Tonegawa, Y.Item Metadata only The André/Bruck and Bose representation of conics in Baer subplanes of PG(2,q2)(Birkhauser Verlag Ag, 2002) Quinn, Catherine T.The André/Bruck and Bose representation ([1], [5,6]) of PG(2,q 2) in PG(4,q) is a tool used by many authors in the proof of recent results. In this paper the André/Bruck and Bose representation of conics in Baer subplanes of PG(2,q 2) is determined. It is proved that a non-degenerate conic in a Baer subplane of PG(2,q 2) is a normal rational curve of order 2, 3, or 4 in the André/Bruck and Bose representation. Moreover the three possibilities (classes) are examined and we classify the conics in each classItem Metadata only Another integral transform in twistor theory(Marcel Dekker, 1995) Eastwood, Michael GeorgeItem Metadata only Approximating L2 invariants and the Atiyah conjecture(John Wiley & Sons Inc, 2003) Dodziuk, J.; Linnell, P.; Varghese, M.; Schick, T.; Yates, S.AbstractLet G be a torsion‐free discrete group, and let ℚ denote the field of algebraic numbers in ℂ. We prove that ℚG fulfills the Atiyah conjecture if G lies in a certain class of groups D, which contains in particular all groups that are residually torsion‐free elementary amenable or are residually free. This result implies that there are no nontrivial zero divisors in ℂG. The statement relies on new approximation results for L2‐Betti numbers over ℚG, which are the core of the work done in this paper. Another set of results in the paper is concerned with certain number‐theoretic properties of eigenvalues for the combinatorial Laplacian on L2‐cochains on any normal covering space of a finite CW complex. We establish the absence of eigenvalues that are transcendental numbers whenever the covering transformation group is either amenable or in the Linnell class 𝒞. We also establish the absence of eigenvalues that are Liouville transcendental numbers whenever the covering transformation group is either residually finite or more generally in a certain large bootstrap class 𝒢. © 2003 Wiley Periodicals, Inc.