Unconventional model of neutrino masses

Gelmini and Roncadelli have proposed a model of neutrino masses in which B?L symmetry is spontaneously broken by a small vacuum expectation value of a Higgs triplet. We give an exegesis of this model. We show that the massive neutrinos in this model cannot be cosmologically relevant today and that conflicting analyses of double beta decay experiments can be reconciled.     

On fibering four- and five-manifolds

This paper studies the question of which manifolds fiber over the circle in dimensions four and five. Partially supported by an NSF Postdoctoral Fellowship.     

Optimal iterative processes for root-finding

Letf ₀(x) be a function of one variable with a simple zero atr ₀. An iteration scheme is said to be locally convergent if, for some initial approximationsx ₁, ...,x _s nearr ₀ and all functionsf which are sufficiently close (in a certain sense) tof ₀, the scheme generates a sequence {x _k} which lies nearr ₀ and converges to a zeror off. The order of convergence of the scheme is the infimum of the order of convergence of {x _k} for all such functionsf. We study iteration schemes which are locally convergent and use only evaluations off,f, ...,f ^[d] atx ₁, ...,x _k–1 to determinex _k, and we show that no such scheme has order greater thand+2. This bound is the best possible, for it is attained by certain schemes based on polynomial interpolation.This work was supported (in part) by the Office of Naval Research under contract numbers N0014-69-C-0023 and N0014-71-C-0112.     

Non-eikonal effects in high-energy scattering IV. Inelastic scattering

We calculate amplitudes of inelastically scattered high-energy projectiles. For the example of scattering on ¹²C (T_p = 1 GeV) we demonstrate sizeable non-eikonal corrections in diffraction extrema even for relatively small q². At least part of the anomaly in the 3-distribution may be due to these non-eikonal effects.     

A study of the van der Waerden conjecture and its generalizations

It Is shown here that a permanent of n× ndoubly stochastic matrix is not less than 1/ n!. The proof of this inequality follows from the study of a generalized van der Waerden problem on the set of doubly stochastic matrices.     

A characterization of transform absolute norms

Let 6x6 be a norm on Cⁿ. For A?M_n(C) denote by 6A6 the induced norm of A, by ?(A) the spectral radius of A. It is proved here that if inf_p6PAP^?16 = ?(A), then 6x6 is a transform absolute norm.     

Extremal eigenvalue problems defined for certain classes of functions

Archive for Rational Mechanics and Analysis -