The regular part of a semigroup of transformations with restricted range

2011 ◽  
Vol 83 (1) ◽  
pp. 134-146 ◽  
Author(s):  
Jintana Sanwong
Keyword(s):  
Regular Part ◽  
Restricted Range ◽  
Semigroup Of Transformations

scholarly journals Green’s Relations on a Semigroup of Transformations with Restricted Range that Preserves an Equivalence Relation and a Cross-Section

Mathematics ◽  
2018 ◽  
Vol 6 (8) ◽  
pp. 134
Author(s):  
Chollawat Pookpienlert ◽  
Preeyanuch Honyam ◽  
Jintana Sanwong
Keyword(s):  
Cross Section ◽  
Equivalence Relation ◽  
Nonempty Subset ◽  
Identity Relation ◽  
Green’S Relations ◽  
Restricted Range ◽  
Green's Relations ◽  
Semigroup Of Transformations

Let T(X,Y) be the semigroup consisting of all total transformations from X into a fixed nonempty subset Y of X. For an equivalence relation ρ on X, let ρ^ be the restriction of ρ on Y, R a cross-section of Y/ρ^ and define T(X,Y,ρ,R) to be the set of all total transformations α from X into Y such that α preserves both ρ (if (a,b)∈ρ, then (aα,bα)∈ρ) and R (if r∈R, then rα∈R). T(X,Y,ρ,R) is then a subsemigroup of T(X,Y). In this paper, we give descriptions of Green’s relations on T(X,Y,ρ,R), and these results extend the results on T(X,Y) and T(X,ρ,R) when taking ρ to be the identity relation and Y=X, respectively.

scholarly journals Regularity and Green's Relations on a Semigroup of Transformations with Restricted Range

2008 ◽  
Vol 2008 ◽  
pp. 1-11 ◽  
Author(s):  
Jintana Sanwong ◽  
Worachead Sommanee
Keyword(s):  
Nonempty Subset ◽  
Transformation Semigroup ◽  
Green’S Relations ◽  
Sufficient Condition ◽  
Restricted Range ◽  
Necessary And Sufficient Condition ◽  
Full Transformation ◽  
Green's Relations ◽  
Necessary And Sufficient ◽  
Semigroup Of Transformations

LetT(X)be the full transformation semigroup on the setXand letT(X,Y)={α∈T(X):Xα⊆Y}. ThenT(X,Y)is a sub-semigroup ofT(X)determined by a nonempty subsetYofX. In this paper, we give a necessary and sufficient condition forT(X,Y)to be regular. In the case thatT(X,Y)is not regular, the largest regular sub-semigroup is obtained and this sub-semigroup is shown to determine the Green's relations onT(X,Y). Also, a class of maximal inverse sub-semigroups ofT(X,Y)is obtained.

scholarly journals The Regular Part of a Semigroup of Full Transformations with Restricted Range: Maximal Inverse Subsemigroups and Maximal Regular Subsemigroups of Its Ideals

2018 ◽  
Vol 2018 ◽  
pp. 1-9
Author(s):  
Worachead Sommanee
Keyword(s):  
Nonempty Subset ◽  
Transformation Semigroup ◽  
Regular Part ◽  
Restricted Range ◽  
Full Transformation ◽  
Full Transformation Semigroup ◽  
Inverse Subsemigroups

Let TX be the full transformation semigroup on a set X. For a fixed nonempty subset Y of a set X, let TX,Y be the semigroup consisting of all full transformations from X into Y. In a paper published in 2008, Sanwong and Sommanee proved that the set FX,Y=α∈TX,Y:Xα=Yα is the largest regular subsemigroup of TX,Y. In this paper, we describe the maximal inverse subsemigroups of FX,Y and completely determine all the maximal regular subsemigroups of its ideals.

Ecology and biogeography in the introduction to “De bestiis marinis” by Georg Wilhelm Steller

2019 ◽  
Vol 46 (1) ◽  
pp. 63-74
Author(s):  
Stefano Mattioli
Keyword(s):  
Body Size ◽  
Phenotypic Plasticity ◽  
Geographical Distribution ◽  
Functional Traits ◽  
Marine Mammals ◽  
Main Part ◽  
Wide Distribution ◽  
Restricted Range ◽  
Direct Influence ◽  
Modern Biology

The rediscovery of the original, unedited Latin manuscript of Georg Wilhelm Steller's “De bestiis marinis” (“On marine mammals”), first published in 1751, calls for a new translation into English. The main part of the treatise contains detailed descriptions of four marine mammals, but the introduction is devoted to more general issues, including innovative speculation on morphology, ecology and biogeography, anticipating arguments and concepts of modern biology. Steller noted early that climate and food have a direct influence on body size, pelage and functional traits of mammals, potentially affecting reversible changes (phenotypic plasticity). Feeding and other behavioural habits have an impact on the geographical distribution of mammals. Species with a broad diet tend to have a wide distribution, whereas animals with a narrow diet more likely have only a restricted range. According to Steller, both sea and land then still concealed countless animals unknown to science.

Tweaking a Medieval Antecedent

2018 ◽  
Author(s):  
Theodore G. Van Raalte
Keyword(s):  
Early Modern ◽  
Regular Part ◽  
Swiss Cantons ◽  
University Training

Whereas disputations were a regular part of both elementary pedagogy and university training in the medieval and early-modern eras, not all disputations were of the same kind. This chapter explains the differences between the dialectic and scholastic disputations, of which Chandieu’s works belong to the latter. Further, it shows that Chandieu wrote his works “for the better practice of disputations,” and that his “theological and scholastic” treatises thus have an organic connection to the classroom. The use of disputations in the academies of the Swiss cantons more widely is also described. Comparisons to the structure of Thomas’s disputations occurs, as well as to that of an earlier Arabic philosopher.

On Semigroups of Orientation-preserving Transformations with Restricted Range

2015 ◽  
Vol 44 (1) ◽  
pp. 253-264 ◽  
Author(s):  
Vítor H. Fernandes ◽  
Preeyanuch Honyam ◽  
Teresa M. Quinteiro ◽  
Boorapa Singha
Keyword(s):  
Restricted Range

scholarly journals In what spaces is every closed normal cone regular?

1970 ◽  
Vol 17 (2) ◽  
pp. 121-125 ◽  
Author(s):  
C. W. McArthur
Keyword(s):  
Banach Space ◽  
Convex Space ◽  
Unconditional Basis ◽  
Normal Cone ◽  
Closed Subspace ◽  
Locally Convex Space ◽  
Regular Part ◽  
Fréchet Space ◽  
Sequential Completeness ◽  
Locally Convex

It is known (13, p. 92) that each closed normal cone in a weakly sequentially complete locally convex space is regular and fully regular. Part of the main theorem of this paper shows that a certain amount of weak sequential completeness is necessary in order that each closed normal cone be regular. Specifically, it is shown that each closed normal cone in a Fréchet space is regular if and only if each closed subspace with an unconditional basis is weakly sequentially complete. If E is a strongly separable conjugate of a Banach space it is shown that each closed normal cone in E is fully regular. If E is a Banach space with an unconditional basis it is shown that each closed normal cone in E is fully regular if and only if E is the conjugate of a Banach space.

Restricted-Range Boraginaceae Species Constitute Potential Sources of Valuable Fatty Acids

2013 ◽  
Vol 91 (2) ◽  
pp. 301-308 ◽  
Author(s):  
José Luis Guil-Guerrero ◽  
Francisco Gómez-Mercado ◽  
Rebeca Pilar Ramos-Bueno ◽  
Miguel Ángel Rincón-Cervera ◽  
Elena Venegas-Venegas
Keyword(s):  
Fatty Acids ◽  
Restricted Range ◽  
Potential Sources
Sign in / Sign up

Export Citation Format

Share Document