We survey some recent advances in computational tools for determining estimates of the parameters of algebraic geometry codes. We show how the Weierstrass semigroup and its minimal generating set may be used to find the pure gap set as well as floors and ceilings of certain divisors. The code parameter estimates obtained are at least as good as the bounds given by Goppa and in many cases are an...

The main purpose of this paper is to establish a relation between universality of certain P-compactifications of a semitopological semigroup and their corresponding enveloping semigroups. In particular, we show that if we take P to be the property that the enveloping semigroup of a compactification of a semitopological semigroup s is left simple, a group, or the trivial singleton semigroup, t...

For a set X , an equivalence relation ρ on X , and a cross-section R of the partition X/ρ induced by ρ, consider the semigroup T (X, ρ, R) consisting of all mappings a from X to X such that a preserves both ρ (if (x, y) ∈ ρ then (xa, ya) ∈ ρ) and R (if r ∈ R then ra ∈ R). The semigroup T (X, ρ, R) is the centralizer of the idempotent transformation with kernel ρ and imageR. We determine the str...

If R is a 2-sided fir (free ideal ring) with no non-trivial right invariant elements, we shall find that the non-zero 2-sided ideals of R, under the usual multiplication of ideals, form a free semigroup with 1. In particular, this holds when R is a free associative algebra over a field. (We also consider the operations of multiplying right ideals by 2-sided ideals to get right ideals, 2-sided i...

We study semigroup C*-algebras of ax + b-semigroups over integral domains. The goal is to generalize several results about C*-algebras of ax + bsemigroups over rings of algebraic integers. We prove results concerning K-theory and structural properties like the ideal structure or pure infiniteness. Our methods allow us to treat ax+b-semigroups over a large class of integral domains containing al...

In this paper we study commuting families of holomorphic mappings in Cn which form abelian semigroups with respect to their real parameter. Linearization models for holomorphic mappings are been used in the spirit of Schröder’s classical functional equation. The one-dimensional linearization models for holomorphic mappings and semigroups, based on Schröder’s and Abel’s functional equation have ...

This paper presents several characterizations of a local α-times integrated C-semigroup {T(t); 0 ≤ t < τ} by means of functional equation, subgenerator, and well-posedness of an associated abstract Cauchy problem.We also discuss properties concerning the nondegeneracy of T(·), the injectivity of C, the closability of subgenerators, the commutativity of T(·), and extension of solutions of the as...

Originally, fuzzy logic was proposed to describe human reasoning. Lately, it turned out that fuzzy logic is also a convenient approximation tool, and that moreover, sometimes a better approximation can be obtained if we use real values outside the interval 0; 1]; it is therefore necessary to describe possible extension of t-norms and t-conorms to such new values. It is reasonable to require tha...

We consider continuous semigroups of analytic functions {Φt}t≥0 in the so-called Gordon-Hedenmalm class G, that is, family Φ:C+→C+ giving rise to bounded composition operators Hardy space Dirichlet series H2. show there is a one-to-one correspondence between G and strongly {Tt}t≥0, where Tt(f)=f∘Φt, f∈H2. extend these results for range p∈[1,∞). For case p=∞, we prove no non-trivial semigroup H∞...

the product σ-algebra. Let A : E × E → E be A(x1, x2) = x1 + x2. For ν1, ν2 ∈ P(E), the convolution of ν1 and ν2 is the pushforward of the product measure ν1 × ν2 by A: ν1 ∗ ν2 = A∗(ν1 × ν2). The convolution ν1 ∗ ν2 is an element of P(E). Let I = R≥0. A convolution semigroup is a family (νt)t∈I of elements of P(E) such that for s, t ∈ I, νs+t = νs ∗ νt. From this, it turns out that μ0 = δ0. 2 A...