A pseudo-hyperoval of a projective space PG(3n− 1, q), q even, is a set of q +2 subspaces of dimension n − 1 such that any three span the whole space. We prove that a pseudo-hyperoval with an irreducible transitive stabiliser is elementary. We then deduce from this result a classification of the thick generalised quadrangles Q that admit a point-primitive, line-transitive automorphism group wit...

In [Z1] S. Zelditch introduced an equivariant version of a pseudo-differential calculus on a hyperbolic Riemann surface. We recast his construction in terms of trilinear invariant functionals on irreducible unitary representations of PGL2(R). This allows us to use certain properties of these functionals in the study of the action of pseudodifferential operators on eigenfunctions of the Laplacia...

The Random Oracle Model and the Ideal Cipher Model are two well known idealised models of computation for proving the security of cryptosystems. At Crypto 2005, Coron et al. showed that security in the random oracle model implies security in the ideal cipher model; namely they showed that a random oracle can be replaced by a block cipher-based construction, and the resulting scheme remains secu...

A. We give upper bounds on the numbers of various classes of polynomials reducible over Z and over Z/pZ, and on the number of matrices in SL(n),GL(n) and Sp(2n) with reducible characteristic polynomials, and on polynomials with non-generic Galois groups. We use our result to show that a random (in the appropriate sense) element of the mapping class group of a closed surface is pseudo-Ano...

The paper applies the pseudo-linear algebra to unify the results on reducibility, reduction and transfer equivalence for continuousand discrete-time nonlinear control systems. The necessary and sufficient condition for reducibility of nonlinear input-output equation is presented in terms of the greatest common left factor of two polynomials describing the behaviour of the ‘tangent linearized sy...

The Random Oracle Model and the Ideal Cipher Model are two well known idealised models of computation for proving the security of cryptosystems. At Crypto 2005, Coron et al. showed that security in the random oracle model implies security in the ideal cipher model; namely they showed that a random oracle can be replaced by a block cipher-based construction, and the resulting scheme remains secu...

Let arithmetic pseudo-NCk denote the problems that can be solved by log space uniform arithmetic circuits over the finite prime field Fp of depth O(log(n + p)) and size (n + p)O(1). We show that the problem of constructing an irreducible polynomial of specified degree over Fp belongs to pseudo-NC2.5. We prove that the problem of constructing an irreducible polynomial of specified degree over Fp...

Recall that a commutative ring R is said to be a pseudo-valuation ring if every prime ideal of R is strongly prime. We define a completely pseudovaluation ring. Let R be a ring (not necessarily commutative). We say that R is a completely pseudo-valuation ring if every prime ideal of R is completely prime. With this we prove that if R is a commutative Noetherian ring, which is also an algebra ov...