Generalizations of warped product manifolds with Spin(7) holonomy

Riemann holonomi grupları teorisinde ayrıcalıklı iki grup yer almaktadır. Bunlar 7-boyutlu manifoldlar üzerinde G2 ve 8-boyutlu manifoldlar üzerinde Spin(7) holonomi gruplarıdır. Bu çalışmada, holonomi grubu Spin(7)'nin bir alt grubu olan Riemann manifoldlarının yapısı, özel bir durum için incelenmiştir.  Spin(7) holonomisine sahip manifoldlar, Bonan formu olarak adlandırılan bir 4-formun varlığı ile karakterize edilir. Bonan formu Hodge anlamında kendine eş,  Spin(7) invaryant ve kapalı bir    4-formdur. Çalışmada öncelikli olarak Bonan formunun oktonion çarpımı kullanılarak elde edilme yolu verilmiştir. Daha sonra, çoklu warped çarpım metriklerinin genellemeleri tartışılmış ve özel bir hal olan (3+3+2) warped-benzeri çarpım metriği tanım-lanmıştır. Bu metrik, literatürde Yasui-Ootsuka tarafından verilen Spin(7)manifoldu üzerindeki metriğin bir soyutlaması olarak düşünülmüş olup, warped çarpımların lif-taban dekompozisyonunu korumakta, ancak lif uzayındaki metriğin blok köşegen olmadığı durumu da içermektedir. Çalışmada elde edilen ana sonuç, 2 boyutlu bir taban üzerinde, 3 boyutlu, tam, bağlantılı ve basit bağlantılı liflerden oluşan (3+3+2) warped-benzeri bir çarpım manifoldunda, eğer Yasui-Ootsuka çalışmasında kullanılan Bonan formu kapalı ise, liflerin  S3’e isometrik olması gerektiğidir. Buradan, Yasui-Ootsuka çöz ümünün (3+3+2) warped-benzeri metrikler sınıfında, yukarıda belirlenmiş olan Bonan formuna karşılık gelen  Spin(7)yapıları içerisinde tek olduğunu göstermektedir. Anahtar Kelimeler: Holonomi, Spin(7) holonomi manifoldu, warped ve çoklu warped çarpım manifoldları, warped-benzeri çarpım manifoldu.The holonomy group of a Riemannian manifold was defined by Elie Cartan in 1923 and proved to be an efficient tool in the study of Riemannian manifolds (Kobayashi and Nomizu, 1969). Later, Berger (Berger, 1955) gave a list of the possible holonomy groups of irreducible, simply-connected and non-symmetric Riemannian manifolds. Berger's list (refined later by Alekseevski (1968) and Gray-Brown (1972)) includes the groups SO(n) in n-dimensions, U(n),SU(n) in 2n-dimensions, Sp(n),Sp(n)Sp(1) in 4n-dimensions and two exceptional cases, the holonomy group G2 in 7-dimensions and the holonomy group Spin(7) in 8-dimensions. After Berger introduced his classi-fication list, the existence of manifolds with the specified holonomy groups was an open problem. The existence of manifolds with exceptional holonomy was first demonstrated by Bryant (1987), complete examples were given by Bryant and Salamon (1989) and the first compact examples were found by Joyce (1996). The study of manifolds with exceptional holonomy and the construction of explicit examples is still an active research area in mathematics and physics. In the present work, we investigate the structure of Riemannian manifolds whose holonomy group is a subgroup of Spin(7), for a special case. Manifolds with Spin(7)  holonomy are characterized by the existence of a globally defined 4-form, called the Bonan form (Bonan, 1966) with the following properties i- self-duality in the Hodge sense, ii- Spin(7)  invariance, iii- closedness. We review the structure of the Bonan form and its explicit construction using the structure constants of the octonionic algebra. The starting  point of the present   research was an explicit example of  Spin(7) metric on S3 x S3 x R2 given by Yasui and Ootsuka (2001). We looked whether one could obtain other solutions by relaxing some of their assumptions, in particular without requiring the three dimensional submanifolds to be S3  The method used in (Yasui and Ootsuka, 2001) is based on the notion of "volume-preserving vector fields" and a specific tensor formula called the "2-vector condition". The construction of a metric with Spin(7) holonomy starts with an ansatz for an orthonormal frame which is shown to satisfy the conditions given in (Yasui and Ootsuka, 2001), provided that certain first order differential equations are satisfied. Then the solution of these equations gives a metric with Spin(7) holonomy on S3 x S3 x R2 that we call the "Yasui-Ootsuka solution". Inspired by the metric ansatz of Yasui-Ootsuka, we discuss a generalization of warped product metrics (O'Neil, 1983), by allowing the fiber metric to be non block diagonal in a multiply-warped product (Flores and Sanchez, 2002). We work with a spesific case that we call (3+3+2) warped-like product manifold M = F1 x F2 x B and a specific Spin(7) structure. We prove that, when  the base B is two  dimensional, the fibre F is a 6-manifold of the form   F = F1 x F2  such that Fi 's (i=1,2) are complete, connected and simply connected 3-manifolds and the metric is given by the (3+3+2) warped-like product, then the connection of the fibers is completely determined by the requirement that the Bonan 4-form given in the work by Yasui and Ootsuka (2001) be closed. With the global assumptions given above, it is concluded that the fibers (Fi,i = 1,2) are isometric to S3. It follows that the Yasui-Ootsuka solution is unique in the class of (3+3+2) warped-like product metrics admitting the Spin(7) structure determined by the Bonan form given in the work by Yasui-Ootsuka (2001). As the Bonan form  is a 4-form, then closedness of the Bonan form  gives 56 equations involving exterior derivatives of the basis 1-forms. In the case of the (3+3+2) warped-like product metric, there are 9 parameters on each 3-manifolds (Fi,i = 1,2). Hence there are totally 18 parameters and 56 equations mentioned above. Under some special conditions, it is not surprising to obtain a unique solution. Keywords: Holonomy, Spin(7) holonomy manifold, warped and multiply warped product manifolds, warped-like product manifolds

Naiv hepatit C enfeksiyonlu hastaların on-altı yıllık prognozu

Objectives: In this study, we aimed to evaluate the clinical course of treatment-naive patients infected with hepatitis C virus (HCV) who were followed up in various centers in Turkey. Materials and Methods: This was a retrospective study performed with the participation of 15 centers. Patients aged 18 years and older with HCV infection were included. Results: A total of 391 treatment-naive patients infected with HCV were included in this study. During the follow-up period, the final values of alanine aminotransferase, aspartate transaminase, and total protein were significantly decreased when compared to the initial values (p<0.001, p<0.001, and p=0.005, respectively). In the study group, 19.2% of the patients underwent liver biopsy and 4.1% underwent transient elastography (FibroScan). An increased histological activity index (HAI) score and fibrosis in the second biopsy were observed in one patient, only increased HAI in two patients and increased fibrosis in one patient, as shown on the FibroScan. In the 16 years of the study period, cirrhosis was radiologically detected in only one patient. Conclusion: Even if rapid progression is not observed, close monitoring of the clinical findings related to liver failure and fibrosis with invasive or non-invasive methods may be useful.Amaç: Bu çalışmada ülkemizin çeşitli merkezlerinde takip edilen naiv hepatit C virüs (HCV) ile enfekte hastaların klinik seyrini değerlendirmeyi amaçladık. Gereç ve Yöntemler: Bu çalışma retrospektif olarak 15 merkezin katılımıyla gerçekleştirilmiştir. Çalışmaya 18 yaş üstü, HCV enfeksiyonu olan hastalar dahil edilmiştir. Bulgular: Çalışmada 391 tedavi-naiv HCV enfeksiyonlu hasta yer almıştır. Hastaların takip süresinde son alanine aminotransferase, aspartate transaminase ve total protein değerleri ilk düzeyine göre önemli düzeyde azalmıştır (sırasıyla p<0,001, p<0,001, p=0,005). Çalışma grubunda hastaların %19,2’sine karaciğer biyopsisi, %4,1’ine elastografi (FibroScan) uygulanmıştır. Takip esnasında bir hastada ikinci biyopside histolojik aktivite indeksi (HAI) ve fibroziste artma, iki hastada sadece HAI’da artma, birinde FibroScan ile fibrozis değerinde artma olduğu gözlenmiştir. Bir hastada 16 yıl içinde radyolojik olarak siroz saptanmıştır. Sonuç: Hızlı progresyon gözlenmemekle birlikte hastaların izleminde karaciğer yetmezliği ile ilgili klinik bulguların ve invaziv veya noninvaziv yöntemlerle fibrozisin yakın takibi yararlı olabilir

Çay olarak da tüketilen bazı bitkilerdeki ağır metal içeriğinin ASS ile tayini

TEZ 581/UĞUçKaynakça: 76-82 ss.[Özet Yok

Stuttering in children: A comprehensive study

Kekemeliğin sebebi bilinmemekle birlikte genetik, psikososyal stres etmenlerine maruz kalma, obsesif, özgüveni yetersiz kişilik özelliğine sahip olma, merkezi sinir sistemi anomalileri, ailenin ilk çocuğu olma risk etmenleri olarak bildirilmektedir. Bu çalışmada, kekemeliği olan çocuk ve ergenlerin sosyodemografık özelliklerini, psikososyal stres etmenlerini belirlemek, düzeleri ve düzelmeyen kekeme gruplar arasındaki sosyodemografik faklılıkları saptamak hedeflenmiştir. Çocuk ve ergen psikiyatri polikliniğine başvuran 188 çocuk ve ergen kekeme olgusu çalışmaya alındı. 83'üne ulaşılarak muayeneleri yeniden yapıldı: 43 olguda son 6 aydır kekemelik yoktu (Grup 1). 40 olguda kekemelik değişen sıklıkta devam ediyordu (Grup 2). Grup 1' deki olgular polikliniğe daha erken yaşta başvurmuştu ve üç kelimeli cümle kurmaya Grup 2'deki olgulara göre daha erken başlamışlardı. Grup 1'deki olgularda daha fazla stres faktörü saptandı.Although the cause of stuttering is unknown, genetic, psychosocial stress factors, having obsessive personality or low-selfesteem, central nervous system anomalities, being first child in family are risk factors. In this study we aimed; first, to under-stand sociodemographic pattern of the patients with stuttering, second, to evaluate the features o f psychosocial stress factors and to find the sociodemographic differences between recovered and unrecovered groups. 188 children/adolescents with stuttering referred to the departments of child and adolescent psychiatry were enrolled this study. 83 of all children with stuttering were interviewed again, and 43 of this have not have stuttering for 6 months (Group 1). 40 of this cases have stuttering (Group 2). Group 1 was earlier referral at department of child and adoles-cent psychiatry than Group 2. The onset time of starting speak with sentences using three words was earlier in Group 1. There was much more stress factors before begining of stuttering in Group L

Determination of Some Heavy Metal Concentrations of Sage Tea with FAAS

Herbal teas are blends based on the plant's roots, root hairs, branch shoots, aromatic parts of leaves, flowers, shells, fruits, or seeds that are prepared by drying aromatic parts in the boiling water. Although the plant teas are known with many benefits in terms of health, they are an important threat for people’s life if they are exposed to some contamination due to the misuse or overuse or uncontrolled production. The living environment of the plants is polluted with many harmful substances which arise from the various sources. The factors such as the development of industry and increasing traffic, pesticides, industrial and household waste increase the heavy metal pollution. In this study, the sage teas were collected from the different localities (markets, market place, herbalist) within the province, Karaman (Turkey). The samples were taken in the sufficient quantities and analyzed by the appropriate drying, milling and dissolution processes. The samples were prepared as 2 parallels for each sample and were solved by the wet burning method. The concentrations of the examined elements were determined by Flame Atomic Absorption Spectrometry. According to the results, the amounts of Co, Ni, Cu, Zn, Cd, Mn, Mg, Fe and Ca were determined in all of the samples. Cr was not designated in the samples. Co and Cd exceeded the limits which are accepted in Europe and in Turkey. It should be noted that these foods can easily be contaminated due to the factors such as the physical and chemical structure of the soil, agricultural activities, storage and packaging conditions

New asymmetric bisthiocarbohydrazones and their mixed ligand nickel(II) complexes: Synthesis, characterization, crystal structure, electrochemical-spectroelectrochemical property, antimicrobial and antioxidant activity

New asymmetric isatin bisthiocarbohydrazone ligands were synthesized by the condensation of 3,5-dibromosalicylaldehyde, 3,5-dichlorosalicylaldehyde and 3-bromo-5-chlorosalicylaldehyde with isatin monothiocarbohydrazone. New mixed ligand Ni(II) complexes were synthesized from these ligands using triphenylphosphine (PPh3) as a secondary ligand. The synthesized ligands and complexes were characterized by elemental analysis, FT-IR, H-1 NMR, UV-Vis spectroscopy and mass spectrometry techniques, along with conductivity measurements. The ligands bind to the Ni(II) ion as ONS donors. The fourth coordination site is completed by the secondary ligand PPh3. The single crystal structures of one ligand and one complex were also resolved by X-ray crystallography. The electrochemical responses of the ligands and their complexes were determined and the results were evaluated to illustrate the influence of the substitution of different groups on the ligands. While the free ligands only give one oxidation peak, two oxidation peaks are observed for the Ni(II) complexes. Complexation of the ligands with the Ni(II) ion considerably affected the in-situ spectroelectrochemical responses of the ligands. Finally, the in vitro antioxidant and antimicrobial activities of the synthesized compounds were determined

Sakarya Nehri ve Değirmenderesi'nde alkilfenol kirliliği ve nonilfenolün alabalıklar (Onchoryncus mykiss) üzerine etkileri

TÜBİTAK YDABAG15.09.2005Bu çalışmada, Değirmenderesi ve Sakarya Nehri üzerinde belirlenen istasyonlardan alınan su ve sedim örneklerinde ve bu bölgelerden tutulan balıkların dokularında alkilfenol kirliliği metanol özütlemesi ve ardından HPLC yöntemi ile ölçülmüştür. Her iki nehirde de, su örneklerinde alkilfenof'e rastlanmazken, Değirmenderesi'nin en kirli bölgesinden alınan sedim örneklerinde 4,45 ug /g NP ve 1,68 ug /g BP belirlenmiştir. Sakarya Nehrinin en kirli yerinde ise, yine sedim örneklerinde 3,15 ug/g BP ölçülmüştür. Bu istasyonlardan toplanan balık örneklerinde NP ve alkilfenol ilintili bir madde varlığı tespit edilmiştir. Ayrıca bu çalışmada, laboratuvarda NP verilmiş alabalıklarda NP'nin karaciğer glutatyon S-transferaz üzerine etkileri incelendi ve maruziyet süresine ve doza bağımlı değişken bir etki gözlendi. Bu balıkların karaciğerlerinde yapılan sitolojik incelemelerde, 17-estradıol benzeri yağlanma etkileri görüldü. Karaciğer dokusundaki moleküler düzeydeki değişiklikler FTIR spektrofotometresinde belirlendi. Estrojenik etkinin belirteci kabul edilen karaciğerde vitellogenin üretimindeki artışlar immünolojik yöntemlerle saptandı