This paper is devoted to the study of geometric structures modeled on homogeneous spaces G/P , where G is a real or complex semisimple Lie group and P ⊂ G is a parabolic subgroup. We use methods from differential geometry and very elementary finite–dimensional representation theory to construct sequences of invariant differential operators for such geometries, both in the smooth and the holomor...

Establishing unambiguously the existence of speculative bubbles is an ongoing controversy complicated by the need of defining a model of fundamental prices. Here, we present a novel empirical method which bypasses all the difficulties of the previous approaches by monitoring external indicators of an anomalously growing interest in the public at times of bubbles. From the definition of a bubble...

We prove that every key exchange protocol in the random oracle model in which the honest users make at most n queries to the oracle can be broken by an adversary making O(n) queries to the oracle. This improves on the previous Ω̃(n) query attack given by Impagliazzo and Rudich (STOC’ 89). Our bound is optimal up to a constant factor since Merkle (CACM ’78) gave an n query key exchange protocol i...

We classify integral rootless lattices which are sums of pairs of EE8-lattices (lattices isometric to √ 2 times the E8-lattice) and which define dihedral groups of orders less than or equal to 12. Most of these may be seen in the Leech lattice. Our classification may help understand Miyamoto involutions on lattice type vertex operator algebras and give a context for the dihedral groups which oc...

The results of numerical experiments on the structure of chaotic attrac-tors in the Khalatnikov-Kroyter model of two freedoms are presented. This model was developed for a qualitative description of the wave turbulence of the second sound in helium. The attractor dimension, size, and the maximal Lyapunov exponent in dependence on the single dimensionless parameter F of the model are found and d...

I have been asked to review the history of the formation of the Standard Model. It is natural to tell this story as a sequence of brilliant ideas and experiments, but here I will also talk about some of the misunderstandings and false starts that went along with this progress, and why some steps were not taken until long after they became possible. The study of what was not understood by scient...

7 he photoelsctrons emrrgmg from unpoldrlzed CO* and N20 molecules exposed to circularly polarrzed s> nchrctron radlarmn dre spm polarlzcd After a brlcf dcscrlprlon of the apparatus the polarxzations measured at the lomzatlon threshold are prcscntcd and compared. In the case of COz, with a calculated. m an ab mlflo theory obrdmed value Usmg the SPUI densit) nutrl\ fornlahsnl .I gcncral c\prcssl...

A " Master " gauge theory is constructed in 2+1-dimensions through which various gauge invariant and gauge non-invariant theories can be studied. In particular, Maxwell-Chern-Simons, Maxwell-Proca and Maxwell-Chern-Simons-Proca models are considered here. The Master theory in an enlarged phase space is constructed both in Lagrangian (Stuckelberg) and Hamiltonian (Batalin-Tyutin) frameworks, the...

A Brody curve, a.k.a. normal curve, is a holomorphic map f from the complex line C to the complex projective space P such that the family of its translations {z 7→ f(z + a) : a ∈ C} is normal. We prove that Brody curves omitting n hyperplanes in general position have growth order at most one, normal type. This generalizes a result of Clunie and Hayman who proved it for n =

The diffractive dissociation of virtual photons, γ * p → Xp, has been studied in ep interactions at HERA with the H1 and ZEUS detectors. The data are presented in terms of the diffractive structure function F D 2 and of the diffractive cross sections dσ/dt and dσ/dMX. The t-dependence of the cross section is measured. The Pomeron intercepts extracted from diffractive and inclusive ep interactio...