COMPONENTS OF V (ρ) ⊗ V (ρ)

1 v 2 5 J an 1 99 9 THE ρ ± − ρ 0 MASS SPLITTING PROBLEM

It is discussed the problem of the ρ ± − ρ 0 mass splitting. It is suggested to use the φ → ρπ → 3π decay to measure the ρ ± − ρ 0 mass splitting.

– 1– the Ρ(1450) and the Ρ(1700)

In our 1988 edition, we replaced the ρ(1600) entry with two new ones, the ρ(1450) and the ρ(1700), because there was emerging evidence that the 1600-MeV region actually contains two ρ-like resonances. Erkal [1] had pointed out this possibility with a theoretical analysis on the consistency of 2π and 4π electromagnetic form factors and the ππ scattering length. Donnachie [2], with a full analysi...

(φ,ρ)-monotonicity and Generalized (φ,ρ)-monotonicity

In this paper, new concepts of monotonicity, namely (Φ, ρ)-monotonicity, (Φ, ρ)-pseudo-monotonicity and (Φ, ρ)-quasi-monotonicityare introduced for functions defined in Banach spaces. Series of necessary conditions are also given that relate (Φ, ρ)-invexity and generalized (Φ, ρ)-invexity of the function with (Φ, ρ)monotonicity and generalized (Φ, ρ)-monotonicity of its gradient.

Simulation Methods of the Processes B → π + π − V Including ρ 0 − ω Mixing Effects

Additive ρ-functional inequalities

In this paper, we solve the additive ρ-functional inequalities ‖f(x+ y)− f(x)− f(y)‖ ≤ ∥∥∥∥ρ(2f (x+ y 2 ) − f(x)− f(y) )∥∥∥∥ , (1) ∥∥∥∥2f (x+ y 2 ) − f(x)− f(y) ∥∥∥∥ ≤ ‖ρ (f(x+ y)− f(x)− f(y))‖ , (2) where ρ is a fixed non-Archimedean number with |ρ| < 1 or ρ is a fixed complex number with |ρ| < 1. Using the direct method, we prove the Hyers-Ulam stability of the additive ρ-functional inequalit...