Planar functions are special functions from a finite field to itself that give rise to finite projective planes and other combinatorial objects. We consider polynomials over a finite field K that induce planar functions on infinitely many extensions of K; we call such polynomials exceptional planar. Exceptional planar monomials have been recently classified. In this paper we establish a partial...

We discuss some phenomenological aspects of an E6 inspired supersymmetric standard model with an extra U(1)N gauge symmetry under which right-handed neutrinos have zero charge, allowing a conventional see-saw mechanism. The μ problem is solved in a similar way to the NMSSM, but without the accompanying problems of singlet tadpoles or domain walls. The above exceptional supersymmetric standard m...

The Exceptional Child. By Maximilian P. E. Groszmann. New York: Charles Scribner's Sons, 1917. Pp. xxxiii+7G4. In the foreword Dr. Groszmann states that "the purpose of the book is to give a perspective of the entire situation, and to suggest ways and means of coping with the problem in its various aspects." Again he says, "It has been my endeavor to write the book in simple language and in a s...

Let M be an irreducible, compact, connected, orientable 3-manifold whose boundary is a torus. We show that if M is hyperbolic, then it admits at most six finite/cyclic fillings of maximal distance 5. Further, the distance of a finite/cyclic filling to a cyclic filling is at most 2. If M has a nonboundary-parallel, incompressible torus and is not a generalized 1-iterated torus knot complement, t...

The Dirichlet form given by the intrinsic gradient on Poisson space is associated with a Markov process consisting of a countable family of interacting diiusions. By considering each diiusion as a particle with unit mass, the randomly evolving connguration can be thought of as a Radon measure valued diiusion. The quasi-sure analysis of Dirichlet forms is used to nd exceptional sets for this Mar...

We study four-dimensional and five-dimensional exceptional quotient singularities.

The Dirichlet form given by the intrinsic gradient on Poisson space is associated with a Markov process consisting of a countable family of interacting diffusions. By considering each diffusion as a particle with unit mass, the randomly evolving configuration can be thought of as a Radon measure valued diffusion. The quasi-sure analysis of Dirichlet forms is used to find exceptional sets for th...

We study exceptional modes of both the Wilson and the clover action in order to understand why quenched clover spectroscopy suffers so severely from exceptional configurations. We show that a large clover coefficient can make the exceptional modes extremely localized and thus very sensitive to short distance fluctuations. We contrast this with the case of the Wilson action where exceptional mod...

The scalar multiplication of elliptic curve based cryptosystems (ECC) is computed by repeatedly calling the addition formula that calculates the elliptic curve addition of two points. The addition formula involves several exceptional procedures so that implementers have to carefully consider their treatments. In this paper we study the exceptional procedure attack, which reveals the secret scal...