Suppose that Q is a positive defined n×n matrix, and Q[x̲]=x̲TQx̲ with x̲∈Zn. The Epstein zeta-function ζ(s;Q), s=σ+it, defined, for σ>n2, by the series ζ(s;Q)=∑x̲∈Zn∖{0̲}(Q[x̲])−s, it has meromorphic continuation to whole complex plane. Let n⩾4 be even, while φ(t) an increasing differentiable function continuous monotonic bounded derivative φ′(t) such φ(2t)(φ′(t))−1≪t, sequence {aφ(k)} uniformly d...

We use QCD sum-rules to study the decays φ → ηγ and φ → η′γ, obtaining B(φ → ηγ) = (1.15±0.2) 10−2 and B(φ → η′γ) = (1.18±0.4) 10−4, in very good agreement with existing experimental data. We also discuss the issue of η−η′ mixing, predicting the η and η′ decay constants in a mixing scheme in the quark-flavour basis.

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.

and Applied Analysis 3 As application, we consider the holomorphic case and we prove the following result: Theorem 1.3. We suppose that P is aC0-contraction holomorphic semigroup on B and β be a Bochner subordinator satisfying ∫1 0 1 s βt ds < ∞, t > 0. 1.9 Then each zero-integrable P-exit law ψ is subordinated to a unique P-exit law φ. Moreover, φ is given by φt ( q a ) PtVq ( ψ ) − bAPtVq(ψ) ...

Given an unbounded non-decreasing positive function φ, we studied what the relations are between growth order of any solution a complex linear differential–difference equation whose coefficients entire or meromorphic functions finite φ-order. Our findings extend some earlier well-known results.