The XYZ model is an integrable spin chain which has infinite set of conserved charges, but it lacks a global U(1) U(1) -symmetry. We consider the current ope...

A retrospective evaluation of attitudinal, behavioural and knowledge change among diverse stakeholder groups was conducted in Limpopo Province of South Africa to assess the effectiveness of a series of values clarification (VC) interventions. Telephone and face-to-face interview (193) results revealed that over two-thirds (70.2%) reported behavioural changes and 93.2% reported increased compass...

p 1−f(p) p diverges then the limit in (1.1) exists, and equals 0 = Θ(f,∞). Wirsing’s result settled an old conjecture of P. Erdős and Wintner that every multiplicative function f with −1 ≤ f(n) ≤ 1 had a mean-value. The situation for complex valued multiplicative functions is more delicate. For example, the function f(n) = n (0 6= α ∈ R) does not have a mean-value because 1 x ∑ n≤x n iα ∼ x 1+i...