VARIETIES OF LEFT RESTRICTION SEMIGROUPS

2018 ◽  
Vol 105 (2) ◽  
pp. 173-200 ◽  
Author(s):  
PETER R. JONES
Keyword(s):  
Inverse Semigroup ◽  
Identity Element ◽  
Unary Operation ◽  
Lattice Of Varieties ◽  
Simple Set ◽  
Restriction Semigroup ◽  
Almost All ◽  
Brandt Semigroups ◽  
Nonfinitely Based ◽  
Do So

Left restriction semigroups are the unary semigroups that abstractly characterize semigroups of partial maps on a set, where the unary operation associates to a map the identity element on its domain. They may be defined by a simple set of identities and the author initiated a study of the lattice of varieties of such semigroups, in parallel with the study of the lattice of varieties of two-sided restriction semigroups. In this work we study the subvariety $\mathbf{B}$ generated by Brandt semigroups and the subvarieties generated by the five-element Brandt inverse semigroup $B_{2}$, its four-element restriction subsemigroup $B_{0}$ and its three-element left restriction subsemigroup $D$. These have already been studied in the ‘plain’ semigroup context, in the inverse semigroup context (in the first two instances) and in the two-sided restriction semigroup context (in all but the last instance). The author has previously shown that in the last of these contexts, the behavior is pathological: ‘almost all’ finite restriction semigroups are inherently nonfinitely based. Here we show that this is not the case for left restriction semigroups, by exhibiting identities for the above varieties and for their joins with monoids (the analog of groups in this context). We do so by structural means involving subdirect decompositions into certain primitive semigroups. We also show that each identity has a simple structural interpretation.

THE LATTICE OF VARIETIES OF STRICT LEFT RESTRICTION SEMIGROUPS

2018 ◽  
Vol 106 (1) ◽  
pp. 31-55
Author(s):  
PETER R. JONES
Keyword(s):  
Identity Element ◽  
Unary Operation ◽  
Lattice Of Varieties ◽  
Restriction Semigroup ◽  
Specific Sense ◽  
Brandt Semigroups

Left restriction semigroups are the unary semigroups that abstractly characterize semigroups of partial maps on a set, where the unary operation associates to a map the identity element on its domain. This paper is the sequel to two recent papers by the author, melding the results of the first, on membership in the variety $\mathbf{B}$ of left restriction semigroups generated by Brandt semigroups and monoids, with the connection established in the second between subvarieties of the variety $\mathbf{B}_{R}$ of two-sided restriction semigroups similarly generated and varieties of categories, in the sense of Tilson. We show that the respective lattices ${\mathcal{L}}(\mathbf{B})$ and ${\mathcal{L}}(\mathbf{B}_{R})$ of subvarieties are almost isomorphic, in a very specific sense. With the exception of the members of the interval $[\mathbf{D},\mathbf{D}\vee \mathbf{M}]$, every subvariety of $\mathbf{B}$ is induced from a member of $\mathbf{B}_{R}$ and vice versa. Here $\mathbf{D}$ is generated by the three-element left restriction semigroup $D$ and $\mathbf{M}$ is the variety of monoids. The analogues hold for pseudovarieties.

THE SEMIGROUPS B2 AND B0 ARE INHERENTLY NONFINITELY BASED, AS RESTRICTION SEMIGROUPS

2013 ◽  
Vol 23 (06) ◽  
pp. 1289-1335 ◽  
Author(s):  
PETER R. JONES
Keyword(s):  
Finite Basis ◽  
Brandt Semigroup ◽  
Finitely Based ◽  
Natural Structure ◽  
Locally Finite ◽  
Locally Finite Variety ◽  
Restriction Semigroup ◽  
Inverse Operation ◽  
Brandt Semigroups ◽  
Nonfinitely Based

The five-element Brandt semigroup B2 and its four-element subsemigroup B0, obtained by omitting one nonidempotent, have played key roles in the study of varieties of semigroups. Regarded in that fashion, they have long been known to be finitely based. The semigroup B2 carries the natural structure of an inverse semigroup. Regarded as such, in the signature {⋅, -1}, it is also finitely based. It is perhaps surprising, then, that in the intermediate signature of restriction semigroups — essentially, "forgetting" the inverse operation x ↦ x-1 and retaining the induced operations x ↦ x+ = xx-1 and x ↦ x* = x-1x — it is not only nonfinitely based but inherently so (every locally finite variety that contains it is also nonfinitely based). The essence of the nonfinite behavior is actually exhibited in B0, which carries the natural structure of a restriction semigroup, inherited from B2. It is again inherently nonfinitely based, regarded in that fashion. It follows that any finite restriction semigroup on which the two unary operations do not coincide is nonfinitely based. Therefore for finite restriction semigroups, the existence of a finite basis is decidable "modulo monoids". These results are consequences of — and discovered as a result of — an analysis of varieties of "strict" restriction semigroups, namely those generated by Brandt semigroups and, more generally, of varieties of "completely r-semisimple" restriction semigroups: those semigroups in which no comparable projections are related under the generalized Green relation 𝔻. For example, explicit bases of identities are found for the varieties generated by B0 and B2.

scholarly journals Is it possible to register the ideas, concerns and expectations behind the reason for encounter as a means of classifying patient preferences with ICPC-2?

2017 ◽  
Vol 19 (01) ◽  
pp. 1-6 ◽  
Author(s):  
Diego Schrans ◽  
Pauline Boeckxstaens ◽  
An De Sutter ◽  
Sara Willems ◽  
Dirk Avonts ◽  
...  
Keyword(s):  
Primary Care ◽  
Patient Preferences ◽  
Time Frame ◽  
Specific Procedure ◽  
Reason For Encounter ◽  
Related Information ◽  
Almost All ◽  
Danger To Others ◽  
Do So

BackgroundFamily practice aims to recognize the health problems and needs expressed by the person rather than only focusing on the disease. Documenting person-related information will facilitate both the understanding and delivery of person-focused care.AimTo explore if the patients’ ideas, concerns and expectations (ICE) behind the reason for encounter (RFE) can be coded with the International Classification of Primary Care, version 2 (ICPC-2) and what kinds of codes are missing to be able to do so.MethodsIn total, 613 consultations were observed, and patients’ expressions of ICE were narratively recorded. These descriptions were consequently translated to ICPC codes by two researchers. Descriptions that could not be translated were qualitatively analysed in order to identify gaps in ICPC-2.ResultsIn all, 613 consultations yielded 672 ICE expressions. Within the 123 that could not be coded with ICPC-2, eight categories could be defined: concern about the duration/time frame; concern about the evolution/severity; concern of being contagious or a danger to others; patient has no concern, but others do; expects a confirmation of something; expects a solution for the symptoms without specification of what it should be; expects a specific procedure; and expects that something is not done.DiscussionAlthough many ICE can be registered with ICPC-2, adding eight new categories would capture almost all ICE.

The Municipal Map in Portugal

2019 ◽  
pp. 275-292
Author(s):  
Barbara Luize Iacovino Barreiros
Keyword(s):  
European Union ◽  
The European Union ◽  
Member States ◽  
Territorial Structure ◽  
Territorial Organization ◽  
Consequent Reduction ◽  
Almost All ◽  
Large Groups ◽  
Do So

The municipality is the basic territorial organization for almost all the Member States of the European Union and has approximately the same attributions in all these. Even so, the territorial structure of municipalities differs in each of the Member States, and it is possible to group them into two large groups: those that have implemented reforms with a consequent reduction in the number of these entities and those with a high number of municipalities. Although Spain is a neighbor of Portugal and Portugal gets some influences from France, in fact the territorial organization of municipalities corresponds to very different realities. Through this research you can see that Portugal did reform its municipalities while France and Spain failed to do so. However, they all recognize that there is a need to reform the territorial structure of municipalities.

Between willing and reluctant entrapment: CEE countries in NATO’s non-European missions

2013 ◽  
Vol 46 (3) ◽  
pp. 351-362 ◽  
Author(s):  
Péter Marton ◽  
Jan Eichler
Keyword(s):  
North Atlantic ◽  
Security Policy ◽  
Political Elites ◽  
Eastern European ◽  
Military Operations ◽  
Security Dilemma ◽  
Foreign Missions ◽  
The North ◽  
Simple Set ◽  
Do So

The article focuses on Central and Eastern European (CEE) countries’ experiences related to Afghanistan, Iraq and Libya, three non-European theatres of Western military operations, in predominantly Muslim lands, in the decade between 2001 and 2011. CEE countries readily became involved in two of these foreign missions (Afghanistan and Iraq) because of their deep ties to Western politico-economic structures, without direct security interests compelling them to do so, but not without normative convictions regarding what were seen by them as virtues of the two missions. In Libya, however, they were reluctant to join the Western intervention. In light of this, the article is interested in examining how political elites within the region relate to the generally constrained security policy agency that they have. A key argument advanced is that such agency may be located in how external hegemony is mediated in elite discourses of threat and legitimacy construction. This as well as the three case studies outlined in the article show that the seeming changes in CEE countries’ behaviour in fact boil down to a simple set of rules guiding their behaviour. Having identified this “algorithm” as an implicit pattern of CEE foreign policy behaviour, originating in the intra-alliance security dilemma within the North Atlantic Treaty Organisation (NATO), the article formulates its conclusions about the alliance policy of these countries largely within a neorealist framework.

JOINS OF INVERSE SEMIGROUP VARIETIES AND BAND VARIETIES

1991 ◽  
Vol 01 (03) ◽  
pp. 371-385 ◽  
Author(s):  
PETER R. JONES ◽  
PETER G. TROTTER
Keyword(s):  
Inverse Semigroup ◽  
Inverse Semigroups ◽  
Lattice Of Varieties ◽  
Orthodox Semigroups ◽  
Semigroup Varieties

The joins in the title are considered within two contexts: (I) the lattice of varieties of regular unary semigroups, and (II) the lattice of e-varieties (or bivarieties) of orthodox semigroups. It is shown that in each case the set of all such joins forms a proper sublattice of the respective join of the variety I of all inverse semigroups and the variety B of all bands; each member V of this sublattice is determined by V ∩ I and V ∩ B. All subvarieties of the join of I with the variety RB of regular bands are so determined. However, there exist uncountably many subvarieties (or sub-bivarieties) of the join I ∨ B, all of which contain I and all of whose bands are regular.

REPRODUCTIVE BEHAVIOUR AND PHYSIOLOGY OF TENEBRIO MOLITOR (COLEOPTERA: TENEBRIONIDAE): I. INITIATION OF MATING IN YOUNG ADULTS AND THE EFFECTS OF ADULT DENSITY

1973 ◽  
Vol 105 (5) ◽  
pp. 807-811 ◽  
Author(s):  
G. H. Gerber
Keyword(s):  
Young Adults ◽  
Mating Success ◽  
Tenebrio Molitor ◽  
Reproductive Behaviour ◽  
Adult Density ◽  
Young Males ◽  
Young Females ◽  
Almost All ◽  
Very High ◽  
Do So

AbstractAdults of Tenebrio molitor L. can copulate on the second day after eclosion, but the majority of them do not do so until after the third day. Almost all adults copulated at least once within the first 4 to 5 days. Young females initiated copulation at a slightly earlier age than young males. Crowding enhances mating success in young adults, for which there appears to be a critical minimum adult density. The initiation of copulation was not inhibited at very high densities; this suggests that there is not a critical maximum adult density for mating success.

Open Source Adoption Index

2010 ◽  
Vol 2 (3) ◽  
pp. 48-60 ◽  
Author(s):  
Sanjeev K. Saini ◽  
C. N. Krishnan ◽  
L. N. Rajaram
Keyword(s):  
Open Source ◽  
Quantitative Measure ◽  
Primary Data ◽  
Single Measure ◽  
The Status ◽  
Single Number ◽  
Almost All ◽  
Free Open Source ◽  
Do So

This paper reports the preliminary results of a study conducted to assess and quantify the adoption of Free/Open Source Software (FOSS) by organisations and enterprises. While almost all organisations use FOSS in some form today, there is a wide variation in the manner and extent to which they do so, and presently no quantitative measure exists that can capture the true picture. The present work has built a model with two sets of parameters that, when fed with relevant data about an organisation, generates a single number, the FOSS Adoption Index (FAI), for that organisation. The index is so defined that the higher its value for an organisation, the greater is the extent of FOSS adoption in that organisation. Beyond the single measure FAI that gives a coarse assessment, the model also allows drilling down to finer levels of granularity that provides deeper insights into the status and role of FOSS within a given organisation. Primary data collected for two classes of organisations through questionnaire based surveys and interviews have been used to demonstrate the working of the model as well as its potential usefulness for real world situations.

Are Thyroid Problems Really So Terrible? Recommendations for Therapists

2020 ◽  
pp. 42-48
Author(s):  
N. Demidov ◽  
O. Alipova ◽  
K. Soghomonyan ◽  
E. Zemskova
Keyword(s):  
General Practitioner ◽  
Primary Care Physicians ◽  
Sufficient Evidence ◽  
Huge Number ◽  
Simple Set ◽  
Excessive Load ◽  
Almost All ◽  
The Cost ◽  
Insufficient Knowledge

Patients with thyroid diseases often create difficulties in the practice of a therapist and general practitioner (GP). It usually occurs due to insufficient knowledge of primary care physicians regarding these diseases. But much more difficulties for the entire health care system are created by unreasonably high attention to these problems, and the desire to diagnose the state of the thyroid gland in almost all patients with any complaints. A huge number of diagnostic examinations, prescribed without sufficient evidence, create an excessive load on ultrasound and medical specialists, as well as increase the cost of laboratory tests, often not only not contributing, but even interfering with establishing the true cause of the patient’s condition. The article attempts to formulate a simple set of recommendations for a general practitioner (GP), aimed at reducing the number of unreasonable studies and reducing the burden on specialized professionals without compromising the quality of diagnosis.

Marketing and Marketing Plan for Information Services

2018 ◽  
pp. 5757-5766
Author(s):  
Sérgio Maravilhas
Keyword(s):  
Information Services ◽  
Marketing Plan ◽  
Economic Process ◽  
Almost All ◽  
Do So

Marketing is a social and economic process through which individuals and groups meet their needs and desires by creating and exchanging products among themselves. Initially, marketing was practiced by companies in selling sectors of products and services and did not seem to fit the non commercial side. In recent decades almost all types of organizations adopted the methods and practices of marketing, including information services. It is necessary to develop a program to properly plan all the actions and resources needed to achieve these objectives, and effectively control the deviations relative to them, allowing correcting the actions that do not get the expected results in order to constantly improve the system implemented. For this it is necessary to devise a marketing plan that focuses on the planning of all activities and objectives we want to achieve and the means necessary to do so. The Marketing Plan is a strategic document that will serve to identify the position occupied in the market. set goals and how they will be achieved, and expected results.

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