Presentations for monoids of finite partial isometries

In this paper we give presentations for the monoid $\mathcal{DP}_n$ of all partial isometries on $\{1,\ldots,n\}$ and for its submonoid $\mathcal{ODP}_n$ of all order-preserving partial isometries.Comment: 11 pages, submitte

The Relationships in Marketing: Contribution of a Historical Perspective

This paper presents an historical analysis of relationship marketing. We discuss the roots and the directions of relationship marketing that are considered relevant: their origins, the Industrial Marketing and Purchasing group (IMP) approach to business relationships, the Nordic approach to services relationships and, the managerial and Customer Relationship Management (CRM) approach of relationship marketing. The paper highlights that the boundaries of relationship marketing as defined in contemporary literature have been permeable and elastic. Relationship marketing consists of a fragmented collection of different approaches, partly independent partly overlapping, inspired by different theories, with a multitude of aggregation levels and several units of analysis. We clarify the scope of this domain and we present a number of critical issues that remain unresolved. Is the concept of relationship marketing ubiquitous and can it be applied to every context? Are relationships alike whatever the market considered? Do they describe the same phenomena or are they different phenomena resulting from different contexts? We present a historical analysis of relationships marketing that could contribute to a better understanding of what relationships are in marketing.relationships, business-to-business relationships, relationship marketing, CRM

On semigroups of endomorphisms of a chain with restricted range

Let $X$ be a finite or infinite chain and let $O(X)$ be the monoid of all endomorphisms of $X$. In this paper, we describe the largest regular subsemigroup of $O(X)$ and Green's relations on $O(X)$. In fact, more generally, if $Y$ is a nonempty subset of $X$ and $O(X,Y)$ the subsemigroup of $O(X)$ of all elements with range contained in $Y$, we characterize the largest regular subsemigroup of $O(X,Y)$ and Green's relations on $O(X,Y)$. Moreover, for finite chains, we determine when two semigroups of the type $O(X,Y)$ are isomorphic and calculate their ranks.Comment: To appear in Semigroup Foru

Perfil literário das pessoas com 65 e mais anos com actividade económica

A partir da década de sessenta, surgiram modificações nos padrões de morbilidade e mortalidade da população devido aos processos de transição demográfica e epidemiológica repercutindo-se, principalmente, na estrutura populacional de alguns países1. No seguimento dos processos de transição, uma das consequências resultantes é, naturalmente, o envelhecimento populacional. Este processo é um dos objectos de estudo da Gerontologia, em interdisciplinaridade com outras áreas do saber2, entre as quais a educação. A literacia é sem dúvida uma das competências essenciais para a actividade do quotidiano3, tornando-se, ainda mais necessária em actividades específicas, nomeadamente a actividade económica

Interaction between innovation in small firms and their environments: an exploratory study

Small food firms make up an important sector in the European economy and are particularly significant in rural areas where they are potential sources of employment and growth. Despite this, their behaviour as regards innovation has been relatively little studied to date. This exploratory investigation finds different types of innovative behaviours among small agro-food firms in peripheral regions and identifies some of the factors with which they are associated. The research reported here is based on a sample of 323 small and very small food and drink (hereafter “food”) firms drawn from 11 regions in six European countries. The food industry is generally regarded as a mature, low-technology industry, but this study identifies different clusters of small food firms according to innovative behaviours. It finds that, although a substantial number of firms may be defined as non-innovators, by far the largest cluster of food firms is involved in multiple forms of innovative activity. Recent studies have demonstrated the complexity of the determinants of technological progress. This may be modelled as a learning process in which small innovative firms tend to draw on internal and external sources of expertise and are both influenced by and influence the broader socio-economic environment in which they operate. This study uses cluster analyses to identify four types of innovative behaviours and examines the factors influencing these. It takes first steps to incorporate both measures of innovative capacity at the firm level as well as of the local development environment in order to explore links between the innovative capacity of small food firms and the characteristics of their regional contexts

Presentations for three remarkable submonoids of the dihedral inverse monoid on a finite set

In this paper we consider the submonoids $\mathcal{OPDI}_n$, $\mathcal{MDI}_n$ and $\mathcal{ODI}_n$ of the dihedral inverse monoid $\mathcal{DI}_n$ of all orientation-preserving, monotone and order-preserving transformations, respectively. Our goal is to exhibit presentations for each of these three monoids.Comment: arXiv admin note: text overlap with arXiv:2205.0219

On monoids of endomorphisms of a cycle graph

In this paper we consider endomorphisms of an undirected cycle graph from Semigroup Theory perspective. Our main aim is to present a process to determine sets of generators with minimal cardinality for the monoids $wEnd(C_n)$ and $End(C_n)$ of all weak endomorphisms and all endomorphisms of an undirected cycle graph $C_n$ with $n$ vertices. We also describe Green's relations and regularity of these monoids and calculate their cardinalities