We study the periodic boundary value problem for semilinear fractional differential equations in an ordered Banach space. The method of upper and lower solutions is then extended. The results on the existence of minimal and maximal mild solutions are obtained by using the characteristics of positive operators semigroup and the monotone iterative scheme. The results are illustrated by means of a...

The Archimedean components of triangular norms (which turn the closed unit interval into an abelian, totally ordered semigroup with neutral element 1) are studied, in particular their extension to triangular norms, and some construction methods for Archimedean components are given. The triangular norms which are uniquely determined by their Archimedean components are characterized. Using ordina...

We study continuity in extensive measurement which is related to the existence of continuous additive utility functions on semigroups. In the particular case of groups we obtain a continuous version of the classical Ho lder's theorem on Archimedeaness, and in the general case we introduce some conditions that guarantee additive representability, and then we analyze when they are good enough to ...

It has been well known that the band of idempotents of a naturally ordered orthodox semigroup satisfying the “strong Dubreil-Jacotin condition” forms a normal band. In the literature, the naturally ordered orthodox semigroups satisfying the strong Dubreil-Jacotin condition were first considered by Blyth and Almeida Santos in 1992. Based on the name “epigroup” in the paper of Blyth and Almeida S...

An argument is made for a double implicational associative information frame, 〈S, , , →, ←〉 being a relevant structure insofar as the specification of the information gain from inference (IGfI) is concerned. A strong informational pluralism is adopted throughout. The rejection of the structural rules K, K′, W, WI, C and CI is justified on the basis of the identification, frequency, and order ...

We introduce the concept of δ-sequence. A δ-sequence ∆ generates a well-ordered semigroup S in Z or R. We show how to construct (and compute parameters) for the dual code of any evaluation code associated with a weight function defined by ∆ from the polynomial ring in two indeterminates to a semigroup S as above. We prove that this is a simple procedure which can be understood by considering a ...

We introduce the concept of δ-sequence. A δ-sequence ∆ generates a well-ordered semigroup S in Z or R. We show how to construct (and compute parameters) for the dual code of any evaluation code associated with a weight function defined by ∆ from the polynomial ring in two indeterminates to a semigroup S as above. We prove that this is a simple procedure which can be understood by considering a ...

By an ordered commutative semigroup of the first kind (abbreviated "o.c.s.I") we mean a system 5(o, <) consisting of a set 5 endowed with a binary operation o and a binary relation < such that the following axioms are satisfied. I. S is a commutative semigroup with respect to o, i.e. the associative law, a o (b o c) = (a o b)o c, and the commutative law, a o b = b o a, hold (a, b, c in S). II. ...

The contribution aims to create hypergroups of linear first-order partial differential operators with proximities, one of which creates a tolerance semigroup on the power set of the mentioned differential operators. Constructions of investigated hypergroups are based on the so called “Ends-Lemma” applied on ordered groups of differnetial operators. Moreover, there is also obtained a regularly p...

We give a necessary and sufficient condition on a given family A of finite subsets of integers for the Cauchy-Davenport inequality |A+ B| ≥ |A|+ |B| − 1, to hold for any family B of finite subsets of integers. We also describe the extremal families for this inequality. We prove this result in the general context of acyclic semigroups, which contain also the semigroup of sequences of elements in...