Outer Automorphisms of Lie Algebras related with Generic 2×2 Matrices

2010 Mathematics Subject Classification: 17B01, 17B30, 17B40, 16R30.Let Fm = Fm(var(sl2(K))) be the relatively free algebra of rank m in the variety of Lie algebras generated by the algebra sl2(K) over a field K of characteristic 0. Our results are more precise for m = 2 when F2 is isomorphic to the Lie algebra L generated by two generic traceless 2 × 2 matrices. We give a complete description of the group of outer automorphisms of the completion L^ of L with respect to the formal power series topology and of the related associative algebra W^. As a consequence we obtain similar results for the automorphisms of the relatively free algebra F2/F2^(c+1) = F2(var(sl2(K)) ∩ Nc) in the subvariety of var(sl2(K)) consisting of all nilpotent algebras of class at most c in var(sl2(K)) and for W/W^(c+1). We show that such automorphisms are Z2-graded, i.e., they map the linear combinations of elements of odd, respectively even degree to linear combinations of the same kind

Effect of shielding gas on microstructure and mechanical properties in AA6061-T6 alloy MIG welding

Due to its properties such as high strength/weight ratio, enhanced corrosion resistance, low density, AA6061-T6 aluminum alloy welding is widely used in structural, automotive and rail industry. In this study, AA6061-T6 alloy was welded with robotic metal inert gas technique using ER5356 filler wire. The effects of different shielding gas composition ratios (argon/helyum) on the macro / microstructre, mechanical properties (hardness, tensile strength) of the weld joint were investigated. Welding porosity decreased with the addition of helium gas to argon gas. Accordingly, the tensile strength of welded joints increased from 190 MPa to 221 MPa with the addition of helium gas. The strength of the welded joints (190-221 MPa) was obtained lower than that of the base material (290 MPa) due to the changes in the microstructure as a result of the weld thermal cycle and grain coarsening in the heat affected zone. Dentritic, columnar and coarse shaped grains were observed along the weld section, respectively in the weld bead, partially melted zone and heat affected zone. The differentiation of the shielding gas composition did not cause these regions to change, but the heat affected zone expanded with the increase in the helium content. The change in hardness of the cross section of welded joint has increased from around 60 HV to 90 HV from the welding area to the base material. 25% Argon-75% Helium gas mixtures provided optimum combination in terms of microstructure, mechanical properties and cost

The Nowicki Conjecture for free metabelian Lie algebras

Let $K[X_d]=K[x_1,\ldots,x_d]$ be the polynomial algebra in $d$ variables over a field $K$ of characteristic 0. The classical theorem of Weitzenb\"ock from 1932 states that for linear locally nilpotent derivations $\delta$ (known as Weitzenb\"ock derivations) the algebra of constants $K[X_{d}]^{\delta}$ is finitely generated. When the Weitzenb\"ock derivation $\delta$ acts on the polynomial algebra $K[X_d,Y_d]$ in $2d$ variables by $\delta(y_i)=x_i$, $\delta(x_i)=0$, $i=1,\ldots,d$, Nowicki conjectured that $K[X_d,Y_d]^{\delta}$ is generated by $X_d$ and $x_iy_j-y_ix_j$ for all $1\leq i<j\leq d$. There are several proofs based on different ideas confirming this conjecture. Considering arbitrary Weitzenb\"ock derivations of the free $d$-generated metabelian Lie algebra $F_d$, with few trivial exceptions, the algebra $F_d^{\delta}$ is not finitely generated. However, the vector subspace $(F_d')^{\delta}$ of the commutator ideal $F_d'$ of $F_d$ is finitely generated as a $K[X_d]^{\delta}$-module. In this paper we study an analogue of the Nowicki conjecture in the Lie algebra setting and give an explicit set of generators of the $K[X_d,Y_d]^{\delta}$-module $(F_{2d}')^{\delta}$.Comment: 8 page

Resources on the stage: A firm level analysis of the ICT adoption in Turkey

This study examines the impact of firm resources on ICT adoption by the Turkish business enterprises using firm level data. ICT adoption is measured at three levels: The first level is technology ownership. The second level is the presence of enterprise resource planning (ERP) and customer resource management (CRM), and the third level is the use of narrowband and broadband technologies. The effects of the three main features of each technology level, which are complementarity, specificity, and the complexity, are analyzed by using firm level data in Turkey. This study has three main conclusions. As for the complementarity, firm's resources play an important role in the adoption of technology while advancing from single technology to the multiple ones. Further, in the use of specific technologies such as ERP and CRM, firm resources generate differential effects between those technologies. Finally, the use of simple technologies does not require the same amount of firm resources as complex technologies

Intangible investment and technical efficiency: The case of software-intensive manufacturing firms in Turkey

This chapter analyzes the effect of intangible investment on firm efficiency with an emphasis on its software component. Stochastic production frontier approach is used to simultaneously estimate the production function and the determinants of technical efficiency in the software intensive manufacturing firms in Turkey for the period 2003-2007. Firms are classified based on the technology group. High technology and low technology firms are estimated separately in order to reveal differentials in their firm efficiency. The results show that the effect of software investment on firm efficiency is larger in high technology firms which operate in areas such as chemicals, electricity, and machinery as compared to that of the low technology firms which operate in areas such as textiles, food, paper, and unclassified manufacturing. Further, among the high technology firms, the effect of the software investment is smaller than the effect of research and development personnel expenditure. This result shows that the presence of R&D personnel is more important than the software investment for software intensive manufacturing firms in Turkey

First record of micrasema cinereum mosely (trichoptera, brachycentridae) in Turkey and a list of the caddisfly fauna in Arac Creek

Systematic studies on Trichoptera larvae in Turkey are very limited. The larval stage of the endemic species remains especially unknown. This study was carried out in Araç Creek between April and October 2013 and it is the first study to determine the caddisfly fauna in Araç Creek. Fourteen caddisflies taxa belonging to nine genera within eight different families (Brachycentridae, Hydropsychidae, Hydroptilidae, Lepidostomatidae, Leptoceridae, Limnephilidae, Psychomyiidae and Rhyacophilidae) were identified. Four of these taxa have previously been recorded from the creek and the other ten taxa are new records for the study area while Micrasema cinereum Mosely is the first record for the Trichoptera fauna of Turkey. As a result of the study, the number of caddisfly taxa in Turkey is now 501, with the addition of M. cinereum.Türkiye’de Trichoptera larvaları üzerindeki sistematik çalışmalar çok sınırlıdır ve özellikle endemik türlerin larva evresi bilinmemektedir. Çalışma Araç Çayı'nda 2013 yılı Nisan-Ekim ayları arasında gerçekleştirilmiştir ve Araç Çayı’nın Trichoptera faunasını belirleyen ilk çalışmadır. Sekiz farklı familyadan (Brachycentridae, Hydropsychidae, Hydroptilidae, Lepidostomatidae, Leptoceridae, Limnephilidae, Psychomyiidae ve Rhyacophilidae) 9 cinse ait 14 Trichoptera taksonu belirlenmiştir. Bu taksonlardan dördü daha önce Araç Çayı’ndan kaydedilmiş, diğer 10 takson ise Araç Çayı için yeni kayıttır. Buna ek olarak, Micrasema cinereum Mosely ise Türkiye Trichoptera faunası için ilk kayıttır. Çalışmanın sonucunda, Türkiye'deki Trichoptera takson sayısı yeni bir kayıtla birlikte 501 olmuştur

The aquatic oligochaetes (Annelida: Clitellata) of eight lakes in the A¸sa˘gı Fırat River Basin (Lower Euphrates, Turkey)

The A¸sa˘gı Fırat River is located in the south-eastern Anatolia, Turkey. The water quality of the A¸sa˘gı Fırat River basin has been degrading for some time, primarily as the result of pollutants associated with the discharges from numerous domestic and agricultural point sources. Aquatic macroinvertebrate samples were collected from eight lakes conducted by using both hand-nets and an Ekman-Birge grab sampler during the summer and autumn of 2014, focusing on the species composition and distribution of aquatic oligochaetes in eight lakes of the A¸sa˘gı Fırat River basin, and their relationships with physico-chemical parameters measured in those lakes using Principal Component Analysis. Results of analyses of all identified benthic macroinvertebrates clearly indicate the percent dominance of oligochaetes in benthic samples in the eight dam lakes that were sampled: Hacıhıdır lake (62.9%); Atat¨urk lake (49.6%); ¨U¸c¨oz lake (28.9%); Dumluca lake (22.01%); Seve lake (13.9%); C¸ at lake (8.5%); Karakaya lake (7.8%) and Birecik lake (5%). During this study, 1044 oligochaete specimens representing 10 species of two subfamilies within the family Naididae were identified. The most abundant taxa were Limnodrilus hoffmeisteri (48.94%), Potamothrix hammoniensis (19.3%), Tubifex tubifex (13.1%), Nais simplex (5.2%) and Nais communis (4.1%).This study was supported by the Ministry of Forestry and WaterManagement project [‘The establishment of our country Specific Water Quality Ecological Assessment System’]. We are grateful to the Ministry of Forestry and Water Management (Turkey) and DOKAY-C¸ED Environmental Engineering Ltd. Co. (Turkey)

Metal concentrations in surface sediments of beyler reservoir (Turkey)

The accumulation of metals (Iron, Aluminium, Zinc, Copper, Manganese, Boron, Chromium, Nickel, Cadmium, Lead) was seasonally (November 2009 to July 2010) measured in sediment samples taken from different areas of Beyler reservoir which is an important water source for irrigation in West Black Sea region (Turkey). Metals in sediment samples were analyzed by ICP-OES. The difference between the stations except for Zn metal (p\0.05) has not been considered as important and a statistical difference between seasons for Fe, Ni metals (p\0.01) and Cu metal (p\0.05) has been observed. The magnitude of metal concentrations in sediment was determined as Aluminium[ Iron[Manganese[Zinc[Chromium[Copper[ Boron[Nickel[Lead[Cadmium. Enrichment factor (EF) for all metals has been calculated (EF\1). In the evaluation done by considering the EF values, it is seen that the metal concentrations found in the Beyler Dam Lake sediment stem from the natural composition of the sediment.The authors are grateful for the financial support of the Scientific and Technological Council of Turkey, TUBITAK (Project No: 109Y013)

Incidental cutaneous microcystic/reticular schwannoma in pilonidal sinus

Schwannoma, a non-malign peripheral nerve sheath tumor, develops slowly and is usually clinically inapparent. It usually arises after the fourth decade of life in the subcutaneous tissue of the extremities and in the head and neck region of patients, with no gender bias. Microcystic/reticular schwannoma (MRS) is a rare histological form of schwannoma, first described in 2008 by Liegl et al. (1) MRS is a recent addition to this group of tumors, which shows predilection for visceral organs, without Antoni A and Antoni B areas or Verocay bodies (2,3). Cutaneous presentation of MRS is very unusual neoplasm which seven cases reported in the sources until to date (4). Here we report a case of incidental cutaneous MRS in a pilonidal sinus material

Kimyasal olarak sentezlenen poli(1,8-diaminonaftelen) ile çözeltilerden selenyum adsorpsiyonu

06.03.2018 tarihli ve 30352 sayılı Resmi Gazetede yayımlanan “Yükseköğretim Kanunu İle Bazı Kanun Ve Kanun Hükmünde Kararnamelerde Değişiklik Yapılması Hakkında Kanun” ile 18.06.2018 tarihli “Lisansüstü Tezlerin Elektronik Ortamda Toplanması, Düzenlenmesi ve Erişime Açılmasına İlişkin Yönerge” gereğince tam metin erişime açılmıştır.Bu çalışmada, asetonitril içinde 1,8-diaminonaftalen monomeri ve amonyumpersülfat arasındaki reaksiyon sonucu poli(1,8-diaminonaftalen) (poli(1,8-DAN)) sentezlenmiş ve sulu çözeltilerdeki selenite iyonlarının adsorpsiyonunda kullanılmıştır. 1,8-diaminonaftalenin (monomer) amonyum persülfata (oksidant) mol oranlarının 1/0,25; 1/0,5; 1/1; 1/2 ve 1/4 olduğu poli(1,8-diaminonaftalen) polimer numuneleri sentezlenmiştir. Adsorpsiyon çalışmalarında, farklı mol oranlarında hazırlanmış polimerler için asitlik etkisi ve başlangıç konsantrasyonunun etkisi incelenmiştir. Adsorpsiyona asitlik etkisinde en uygun olarak 6 M HCl konsantrasyonu, mol oranı olarak ise 1/0,5 ve 1/2 olduğu tespit edilmiştir. Adsorpsiyon çalışmaları ile elde edilen veriler Langmuir ve Freundlich adsorpsiyon izotermlerine uygulanmış ve 1/0,5 ve 1/2 mol oranları ile hazırlanan polimerlerin Se(IV) adsorpsiyon kapasiteleri sırasıyla 75,19 ve 45,05 mg Se/g bulunmuştur. Adsorpsiyon mekanizmasının iyonik etkileşim (>NH2+SeOCl3-) ve piazoselenol türü bağlanma ile yürüdüğü sonucuna varılmıştır.In the present work, poly(1,8-diaminonapthalene) ((poli(1,8-DAN)) was synthesized by the reaction of 1,8-diaminonapthalene monomer with ammonium persulfate in acetonitrile and it was used in the adsorption of selenite ions in aqueous phase. The polimer samples were synthesized at different mole ratios of 1,8-diaminonaphthalene (monomer) to ammonium persulfate (oxidant) which were 1/0.25; 1/0.5; 1/1; 1/2 ve 1/4.The effects of acidity and initial concentration on the adsorption of Se(IV) ions were examined for the polymer samples prepared at the different molar ratios. The optimum acidity was found to be 6 M HCl and the optimum molar ratios were found to be 1/0.5 and 1/2 for the adsorption. The data obtained from the adsorption studies at different initial concentrations were applied to the Langmuir and Freundlich isotherms. The maximum adsorption capacities of poli(1,8-DAN) samples at the 1/0.5 and 1/2 molar ratios were found to be 75.19 and 45.05 mg Se/g, respectively. It was concluded that the adsorption mechanisms were governed by ionic interaction (>NH2+SeOCl3-) and piazoselenol type binding (-N=Se=N-)