Let \(R=k[t^{n_{1}},\ldots ,t^{n_{s}}]=k[x_{1},\ldots ,x_{s}]/P\) be a numerical semigroup ring and let P(n) = PnRP ∩ R be the symbolic power of P and Rs(P) = ⊕i≥ 0P(n)tn the symbolic Rees ring of P. It is hard to determine symbolic powers of P; there are even non-Noetherian symbolic Rees rings for 3-generated semigroups. We determine the primary decomposition of powers of P for...

A problem of further generalization of generalized Choi maps Φ[a,b,c] acting on \(\mathbb M_{3}\) introduced by Cho, Kye, and Lee is discussed. Some necessary conditions for positivity of the generalized maps are provided as well as some sufficient conditions. Also, some sufficient conditions for decomposability of these maps are shown.

An element a of a group G is said to be anticentral in G if G ′ = {[g, a] : g ∈ G} and antisemicentral in G if {[g,a] : g ∈ G} contains a normal subgroup of G of finite index in G ′. We study such elements in various types of infinite soluble group.

We correct an error in the statement and proof of Theorem 1.4 of our paper in Acta Mathematica Vietnamica (2014) 39(4), 599-635.

This monograph is almost entirely devoted to the flexion structure generated by a flexion unit \(\boldsymbol {\mathfrak {E}}\) or the conjugate unit \(\boldsymbol {\mathfrak {O}}\), with special emphasis on the polar specialization of the units (“eupolar structure”). (i) We first state and prove the main facts (some of them new) about the central pairs of bisymmetrals pal∙/pil...

We study the global existence and decay rates of the Cauchy problem for the generalized Benjamin–Bona–Mahony equations in multi-dimensional spaces. By using Fourier analysis, frequency decomposition, pseudo-differential operators and the energy method, we obtain global existence and optimal L 2 convergence rates of the solution.

A smooth model of a system with diode nonlinearity following the ordinary differential equation with a large parameter K is proposed. It offers a convenient tool for numerical analysis using the advanced packages of the applied programs. The main result of this paper is presented in a theorem that gives the upper bound of the modeling error and shows that the model solution...