Approximation of functions with linear positive operators which fix {1, φ} and {1, φ 2}

1 2 Κ ′ 2 ( Φ † Φ ′ ′ ) ( Φ ′ ′

We show how the nearly bi-maximal mixing scenario comes out naturally from gauged SO(3) F flavor symmetry via spontaneous symmetry breaking. An interesting relation between the neutrino mass-squared differences and the mixing angle, i.e., ∆m 2 µe /∆m 2 τ µ ≃ 2|U e3 | 2 is obtained. The smallness of the ratio (or |U e3 |) can also naturally be understood from an approximate permutation symmetry....

On the relation between Φ ( 1 , 2 ) and Φ ( 1 , 5 ) perturbed minimal models and unitarity

We consider the RSOS S–matrices of the Φ(1,5) perturbed minimal models which have recently been found in the companion paper [1]. These S–matrices have some interesting properties, in particular, unitarity may be broken in a stronger sense than seen before, while one of the three classes of Φ(1,5) perturbations (to be described) shares the same Thermodynamic Bethe Ansatz as a related Φ(1,2) per...

ON COMPOSITE n FOR WHICH φ ( n ) \ n - 1 , II

The problem of whether there exists a composite n for which φ(n) \ n — 1 (φ is Euler's function) was first posed by D. H. Lehmer in 1932 and still remains unsolved. In this paper we prove that the number of such n not exceeding x is O(x(logx)). We also prove that any such n with precisely K distinct prime factors is necessarily less than K. There are appropriate generalizations of these results...

φ-factorable operators and Weyl-Heisenberg frames on LCA groups

Φ-strongly Accretive Operators

Suppose that X is an arbitrary real Banach space and T : X → X is a Lipschitz continuous φ-strongly accretive operator or uniformly continuous φ-strongly accretive operator. We prove that under different conditions the three-step iteration methods with errors converge strongly to the solution of the equation Tx = f for a given f ∈ X.