A subset X of a finite group G is said to be prime-power-independent if each element in has prime power order and there no proper Y with 〈Y,Φ(G)〉=〈X,Φ(G)〉, where Φ(G) the Frattini subgroup G. Bpp all generating sets for have same cardinality. We prove that, Bpp, then solvable. Pivoting on some recent results Krempa Stocka (2014); (2020), this yields complete classification Bpp-groups.

We consider the notion of a Φ-zero divisor, where Φ is Young function, on discrete group. extend some results about p-divisors free groups by Linnell and Puls to divisors.

We find the best possible constant C in inequality‖φ‖Lrpr⩽C‖φ‖Lppr‖φ‖BMO1−pr for all values of parameters p and r such that 1⩽p<r<+∞. To solve problem, we define explicitly compute corresponding Bellman function. This function depends on three variables has a rather complicated structure. first problem an interval then transfer our results to circle line. also obtain explicit estimates several ...

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&gt;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.

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.