The Efficiency of the Semi-Direct Products of Free Abelian Monoid with Rank n by the Infinite Cyclic Monoid

In this paper we give necessary and sufficient conditions for the efficiency of the semi-direct product of free abelian monoid with rank n by the infinite cyclic monoid

Conjugacy for Free Groups under Split Extensions

At the present paper we show that conjugacy is preserved and reflected by the natural homomorphism defined from a semigroup S to a group G, where G defines split extensions of some free groups. The main idea in the proofs is based on a geometrical structure as applied in the paper [8]

Finite derivation type for graph products of monoids

Bu çalışma, 08-11, Ağustos 2014 tarihlerinde Gyeongju[Güney Kore]’de düzenlenen 22. International Conference on Finite and Infinite Dimensional Complex Analysis and Applications (ICFIDCAA) Kongresi‘nde bildiri olarak sunulmuştur.The aim of this paper is to show that the class of monoids of finite derivation type is closed under graph products.Balıkesir Üniversitesi - 2014/95, 2015/4

The next step of the word problem over monoids

It is known that a group presentation P can be regarded as a 2-complex with a single 0-cell. Thus we can consider a 3-complex with a single 0-cell which is known as a 3-presentation. Similarly, we can also consider 3-presentations for monoids. In this paper, by using spher- ical monoid pictures, we show that there exists a finite 3-monoid-presentation which has unsolvable ‘‘generalized identity problem’’ that can be thought as the next step (or one- dimension higher) of the word problem for monoids. We note that the method used in this paper has chemical and physical applications

Reguler and pi-Inverse Monoids under Schützenberger Products

In this paper we give a partial answer to the problem which is about the regularity of Schützenberger product in semigroups asked by Gallagher in his thesis [4, Problem 6.1.6]. Furthermore, we determine necessary and sufficient conditions for the new version of the Schützenberger product of monoids which was firstly defined in [1] to be regular and strongly pi-inverse

Updated-extended molecular time and molecular phylogeny of Gundelia species native to Turkey

Generally, Gundelia tournefortii is considered as the sole representative of the genus and the other species of Gundelia as synonyms. Recent studies suggest that the genus is rich with 22 species. Off these, thirteen are endemic to Turkey. To date, no comprehensive molecular study dealing with speciation exists in the genus. To address the speciation at the molecular level, fresh leaves from 57 samples representing 15 species from their natural ranges in Turkey were obtained by sampling over several years and studied with respect to nrDNA (ITS) and the cpDNA (ndhF) gene regions. Molecular data from cpDNA and nrDNA revealed that there were two major clades. One of these clades consists of G. anatolica, G. glabra and G. asperrima when the ndhF data were used (or just G. anatolica based on ITS data) while the other major clade included the remaining species with subclades. Divergence time and geographical phylogenetic reconstruction analysis indicated that there may be 3 major ancestral associations existing in the studied Gundelia species. Based on ndhF data, the oldest ancestral group included G. anatolica, G. glabra and G. asperrima with the divergence time about 21.27 MYA, while G. tournefortii var. tenuisecta and G. dersim were the most recently diverged group (about 4.66 MYA). Ancestral history of diversity analysis suggested that the dispersal and vicariance events involved in the speciation in the genus Gundelia with complex events of natural hybridization, introgression, geographical isolations or some other weak isolation mechanisms

Updated-extended molecular time and molecular phylogeny of Gundelia species native to Turkey

Generally, Gundelia tournefortii is considered as the sole representative of the genus and the other species of Gundelia as synonyms. Recent studies suggest that the genus is rich with 22 species. Off these, thirteen are endemic to Turkey. To date, no comprehensive molecular study dealing with speciation exists in the genus. To address the speciation at the molecular level, fresh leaves from 57 samples representing 15 species from their natural ranges in Turkey were obtained by sampling over several years and studied with respect to nrDNA (ITS) and the cpDNA (ndhF) gene regions. Molecular data from cpDNA and nrDNA revealed that there were two major clades. One of these clades consists of G. anatolica, G. glabra and G. asperrima when the ndhF data were used (or just G. anatolica based on ITS data) while the other major clade included the remaining species with subclades. Divergence time and geographical phylogenetic reconstruction analysis indicated that there may be 3 major ancestral associations existing in the studied Gundelia species. Based on ndhF data, the oldest ancestral group included G. anatolica, G. glabra and G. asperrima with the divergence time about 21.27 MYA, while G. tournefortii var. tenuisecta and G. dersim were the most recently diverged group (about 4.66 MYA). Ancestral history of diversity analysis suggested that the dispersal and vicariance events involved in the speciation in the genus Gundelia with complex events of natural hybridization, introgression, geographical isolations or some other weak isolation mechanisms. © 2021, The Author(s), under exclusive licence to Springer-Verlag GmbH Austria, part of Springer Nature