Some Decision Problems for Extended Modular Groups

In this paper we investigate solvability of the word problem for Extended Modular groups, Extended Hecke groups and Picard groups in terms of complete rewriting systems. At the final part of the paper we examine the other important decision problem (conjugacy problem) for only Extended Modular groups

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]

Subgross and macroscopic investigation of the coeliac artery in the chinchilla (chinchilla lanigera)

The knowledge of branching and variations of the coeliac artery is clinicallyimportant, especially in the surgical operations and non-surgical treatments.Moreover, the chinchillas abdominal region have been used as a model in somesurgical experimental researches. In this frame, we have aimed to explain thebranching of this artery in the chinchillas detailedly. A total of 10 adult, healthy,male chinchillas (chinchilla lanigera) were used to investigate the origin and thecourse of the coeliac artery and its branches. Coloured latex was injected intothe carotid arteries, following conventional anatomical applications. The resultsindicated that the coeliac artery was divided into 4 branches such as left gastricartery, hepatic artery, splenic artery and gastrolienal artery. The left gastric arterywas a continuity of the coeliac artery and the main vessel of the stomach. Thehepatic artery was divided into the left lateral branch, the left medial branch andthe right branch. The splenic artery was covered by the pancreas tissue and sentbranches to the pancreas. The gastrolienal artery was supplying the fundus ofthe stomach and the dorsal extremity of the spleen. We believe that the findingswill be of help to the researchers interested in the anatomical area, surgeons andexperimental researches

Two N-terminal regions of the Sendai virus L RNA polymerase protein participate in oligomerization

AbstractThe RNA dependent RNA polymerase of Sendai virus consists of a complex of the large (L) and phosphoprotein (P) subunits where L is thought to be responsible for all the catalytic activities necessary for viral RNA synthesis. We previously showed that the L protein forms an oligomer [Smallwood, S., Cevik, B., Moyer, S.A., 2002. Intragenic complementation and oligomerization of the L subunit of the Sendai virus RNA polymerase. Virology 304, 235–245] and mapped the L oligomerization domain between amino acids 1 and 174 of the protein [Çevik, B., Smallwood, S., Moyer, S.A., 2003. The oligomerization domain resides at the very N-terminus of the Sendai virus L RNA polymerase protein. Virology 313, 525–536]. An internal deletion encompassing amino acids 20 to 178 of the L protein lost polymerase activity but still formed an L–L oligomer. The first 25 amino acids of paramyxovirus L proteins are highly conserved and site-directed mutagenesis within this region eliminated the biological activity of the L protein but did not have any effect on P–L or L–L interactions. Moreover deletion of amino acids 2–18 in L abolished biological activity, but again the L–L binding was normal demonstrating that the oligomerization domain of L protein resides in two N-terminal regions of the protein. Therefore, sequences between both aa 2–19 and aa 20–178 can independently mediate Sendai L oligomerization, however, both are required for the activity of the protein

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

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

On the first Zagreb index and multiplicative Zagreb coindices of graphs

For a (molecular) graph G with vertex set V (G) and edge set E(G), the first Zagreb index of G is defined as M-1(G) = Sigma v(i is an element of V(G))d(C)(v(i))(2), where d(G) (v(i)) is the degree of vertex v(i), in G. Recently Xu et al. introduced two graphical invariants (Pi) over bar (1) (G) = Pi v(i)v(j is an element of E(G)) (dG (v(i))+dG (v(j))) and (Pi) over bar (2)(G) = Pi(vivj is an element of E(G)) (dG (v(i))+dG (v(j))) named as first multiplicative Zagreb coindex and second multiplicative Zagreb coindex, respectively. The Narumi-Katayama index of a graph G, denoted by NK(G), is equal to the product of the degrees of the vertices of G, that is, NK(G) = Pi(n)(i=1) d(G) (v(i)). The irregularity index t(G) of G is defined as the num=1 ber of distinct terms in the degree sequence of G. In this paper, we give some lower and upper bounds on the first Zagreb index M-1(G) of graphs and trees in terms of number of vertices, irregularity index, maximum degree, and characterize the extremal graphs. Moreover, we obtain some lower and upper bounds on the (first and second) multiplicative Zagreb coindices of graphs and characterize the extremal graphs. Finally, we present some relations between first Zagreb index and NarumiKatayama index, and (first and second) multiplicative Zagreb index and coindices of graphs.Korean Government - 2013R1A1A2009341Necmettin Erbakan ÜniversitesiSelçuk Üniversites

Effect of Expanded Glass Lightweight Aggregate on the Performance of Geopolymer Mortar at Elevated Temperatures

The greenhouse gas emissions associated with conventional concrete as a result of the cement industry have prompted scientists to search for eco-friendly alternatives. Among these promising alternatives is geopolymer concrete or mortar. This work studies the impact of using polyvinyl alcohol (PVA) fibers and lightweight expanded glass (EG) aggregate on the mechanical behaviour of lightweight geopolymer mortar (LWGM) at various temperatures (room temperature, 250 °C, and 500 °C). EG was utilized to partially replace the sand by 10 and 20%. Limited studies dealt with geopolymer mortar based on such composition at high temperatures. The geopolymer mortar was created using slag as the main precursor activated by a mixed solution of sodium hydroxide and sodium silicate. Various combinations were produced, and their behaviour was observed at room and high temperatures. Several tests such as workability, compressive and flexural strengths, density, stress-strain relationship, load-displacement behaviour, and uniaxial tensile strength were performed. The findings of the study indicate that the density and compressive strength of geopolymer mortar reduced with increasing the replacement level by the EG. However, the utilization of 10% EG can produce a lightweight mortar with a compressive strength of 17.9 at 28 days. Moreover, the use of 1% PVA significantly improves the mechanical performance. Furthermore, the mechanical characteristics of the materials were considerably altered when subjected to extreme temperatures of 500 °C as observed from experimental data