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The Hill estimator is often used to infer the power behavior in tails of experimental distribution functions. This estimator is known to produce bad results in certain situations which have lead to the so-called Hill horror plots. In this brief note, we propose an improved estimator which is simple and coherent and often provides an efficient remedy in the bad situations, especially when the distribution is decreasing slowly, when the data is restricted by external cuts to lie within a finite domain, or even when the distribution is increasing. [ABSTRACT FROM AUTHOR]

Abstract: The version of the warp model that we proposed to explain the mass scale hierarchy has been extended by the introduction of one or more singularities in the metric. We restricted ourselves to a real massless scalar field supposed to propagate in a five-dimensional bulk with the extra dimension being compactified on a strip or on a circle. With the same emphasis on the hermiticity and commutativity properties of the Kaluza–Klein operators, we have established all the allowed boundary conditions to be imposed on the fields. From them, for given positions of the singularities, one can deduce either mass eigenvalues building up a Kaluza–Klein tower, or a tachyon, or a zero mass state. Assuming the Planck mass to be the high mass scale and by a choice, unique for all boundary conditions, of the major warp parameters, the low lying mass eigenvalues are of the order of the TeV, in this way explaining the mass scale hierarchy. In our model, the physical masses are related to the Kaluza–Klein eigenvalues, depending on the location of the physical brane which is an arbitrary parameter of the model. Illustrative numerical calculations are given to visualize the structure of Kaluza–Klein mass eigenvalue towers. Observation at high energy colliders like LHC of a mass tower with its characteristic structure would be the fingerprint of the model. [Copyright &y& Elsevier]

A specialp-form is a p-form which, in some orthonormal basis {eμ}, has components φμ1⋯μp = φ(eμ1,...,eμp) taking values in {-1, 0, 1}. We discuss graphs which characterize such forms. [ABSTRACT FROM AUTHOR]

We present generalizations of N-extended supersymmetry algebras in four dimensions, using Lorentz covariance and invariance under permutation of the N supercharges as selection criteria. © 2001 American Institute of Physics. [ABSTRACT FROM AUTHOR]

In this article all deformations of the general linear group, subject to certain restrictions which in particular ensure a smooth passage to the Lie group limit, are obtained. Representations are given in terms of certains sets of creation and annihilation operators. These creation and annihilation operators may belong to a generalization of the q-quark type or q-hadronic type with q-boson or q-fermion behavior. This leads to a natural definition of q-direct sums of q-algebras. [ABSTRACT FROM AUTHOR]

A general deformation of the Heisenberg algebra is introduced with two deformed operators instead of just one. This is generalized to many variables, and permits the simultaneous existence of coherent states, and the transposition of creation operators. [ABSTRACT FROM AUTHOR]

For each constant r-term Krichever–Novikov-type algebra, a minimal set of defining generators is given from which all the operators of the algebra can be constructed by sequential definitions. A finite system of polynomial conditions on the defining generators is given, guaranteeing the commutation relations of the full algebra. [ABSTRACT FROM AUTHOR]

The absolute minima for Landau potentials corresponding to one irreducible representation of SO(3) of spin up to 4 are computed together with their stability groups. For spin 4 the nonmaximal D4 stability group appears. This is a contribution to the literature about Michel’s conjecture. [ABSTRACT FROM AUTHOR]