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    Generalızatıons Of Bernoullı Polynomıals And Fıbo-Bernoullı Matrıces

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    Bu tezde, Bernoulli F−polinomları için yeni bir F−üstel üreteç fonksiyon ve Bernoulli F−polinomlarının çesitli özellikleri elde edildi. Euler-Fibonacci sayıları ve polinomları tanımlanarak, bu polinomların F−üstel üreteçleri bulundu. Ayrıca Euler-Fibonacci sayılarının ve polinomlarının Bernoulli F−polinomları ile iliskisi gösterildi. Ardından harmonik tabanlı F−üstel fonksiyon tanımlandı. Bernoulli F−polinomları, Euler-Fibonacci sayıları, Euler-Fibonacci polinomları ve Bernoulli-Fibonacci sayılarının harmonik tabanlı F−üstel üreteçleri tanımlandı ve bu polinomların harmonik Fibonacci sayıları ve polinomları ile iliskisi gösterildi. Bernoulli F−polinomlarından yararlanarak Fibo-Bernoulli matrisi tanımlandı. Genellestirilmis Fibo-Pascal matrisinin fibonomial katsayılı özel bir matris ile çarpanlaması yapılarak Fibo-Bernoulli matris elde edildi. Ayrıca Fibo-Bernoulli matrisinin tersi bulundu. Son olarak Fibo-Euler matrisi tanımlanarak, bu matrisin Fibo-Bernoulli matrisi ile iliskisi gösterildiIn this thesis, a new F-exponential generating function for Bernoulli F−polynomials and various properties of Bernoulli F−polynomials are obtained. By identifying Euler-Fibonacci numbers and polynomials, F-exponential generating function of these polynomials are found. In addition, the relationship of Euler-Fibonacci numbers and polynomials with Bernoulli F−polynomials is shown. Then, harmonic based F-exponential function is defined. Harmonic based F-exponential generating function is defined for Bernoulli F−polynomials, Euler-Fibonacci numbers, Euler-Fibonacci polynomials and Bernoulli-Fibonacci numbers, and their relations are shown with harmonic Fibonacci numbers and polynomials. The Fibo-Bernoulli matrix is defined using Bernoulli F−polynomials. The generalized Fibo-Pascal matrix is multiplied by a special matrix with fibonomial coefficient to obtain the Fibo-Bernoulli matrix. Also the inverse of the Fibo-Bernoulli matrix is found. Finally, Fibo-Euler matrices are defined and their relation with Fibo-Bernoulli matrix is shown

    Ultrastructural Features Of Dıgestıve, Excretory, Female And Male Reproductıve Systems Of Isophya Nervosa Ramme, 1931 (Orthoptera: Tettıgonııdae

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    Bu çalışma, Isophya nervosa Ramme, 1931 (Orthoptera, Tettigoniidae)'nin sindirim sistemi, boşaltım sistemi, dişi ve erkek üreme sisteminin ışık mikroskobu (IM), taramalı elektron mikroskobu (SEM) ve geçirmeli elektron mikroskobu (TEM) ile gözlemlenen ultrastrüktürel ayrıntıları ortaya koymaktadır. I. nervosa, Orthoptera takımına ait bir türdür ve Ankara, Eskişehir ve Nevşehir illerinde yayılım göstermektedir. I. nervosa üzerinde birçok sistematik ve taksonomik çalışma olmasına rağmen, bu türün iç organlarının morfolojisi ve histolojisi ile ilgili bir çalışmaya rastlanmamıştır. Bu amaçla, I. nervosa'nın yetişkin bireyleri 2017 ve 2018 yıllarında Ankara Kızılcahamam'da toplanmıştır. Disekte edilen sistemler ışık mikroskobu çalışmaları için Formaldehit, elektron mikroskobu çalışmaları için gluteraldehit içinde tespit edilmişlerdir. Dehidrasyon, bloklama, kesit alma ve boyama işlemleri tamamlandıktan sonra incelenmiş ve fotoğraflanmıştır. Genel morfoloji ve ultrastrüktür, araştırılan diğer böcek takımları ve Orthoptera takımına ait diğer türler ile karşılaştırıldı. Yapıda küçük farklılıklar gözlense de, elde edilen veriler neredeyse benzerdir. Bu çalışmada sunulan verilerin gelecekteki çalışmalara katkı sağlayacağı gösterilmiştir.The present study reveals ultrastructural details observed by light microscope (LM), scanning electron microscope (SEM) and transmission electron microscope (TEM) of the digestive system, excretory system, female and male reproductive system of Isophya nervosa Ramme, 1931 (Orthoptera, Tettigoniidae). I. nervosa is a species that belongs to Orthoptera order and spreads in Ankara, Eskişehir and Nevşehir provinces. Although there are many systematic and taxonomic studies on I. nervosa, no study on the morphology and histology of internal organs of this species, has been encountered. For this purpose, adult individuals of I. nervosa were collected in Kızılcahamam, Ankara in 2017 and 2018. Dissected systems were fixed in Formaldehyde for light microscopy, in glutaraldehyde for electron microscopes. They were examined and photographed after dehydration, blocking, sectioning and staining processes were completed. General morphology and ultrastructure were compared to the other species belonging to Orthoptera order and other insect orders, which were analyzed. Although small differences were observed in the structure, obtained data are almost similar. It is shown that the data which present with this study, will contribute to the future studies

    Evaluation of the effects of the hybrid Pendulum in comparison with the conventional Pendulum appliance

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    Objective: To evaluate the anchorage control and distalization of maxillary molars with the hybrid Pendulum appliance and to compare the results with a conventional Pendulum appliance. Materials and Methods: This study was carried out on the pre-(T0) and post-(T1) treatment lateral cephalograms and dental casts of 43 patients with Angle Class II molar relationships who were treated with conventional or hybrid Pendulum appliances. The hybrid Pendulum (HP) group consisted of 22 patients (14 females; eight males; mean age 14.3 +/- 2.43 years) and treatment results were compared with a conventional Pendulum appliance (CP) group, which consisted of 21 patients (15 females; six males; mean age 14.6 +/- 3.39 years). Intragroup comparisons were made with Wilcoxon test and intergroup comparisons were made with MannWhitney U- test (P <.05). Results: The mean distalization duration was 0.70 +/- 0.25 years in the HP group and 0.83 +/- 0.4 years in the CP group. Maxillary first molars showed significant distal movement and tipping of 4.25 mm and 9.09 degrees in the HP group, and 3.21 mm and 9.86 degrees in the CP group. Loss of anchorage at the first premolars was significantly smaller in the HP appliance group compared to CP group. The second premolars distalized spontaneously in the HP group while they mesialized significantly in the CP group. Proclination and protrusion of maxillary incisors were greater with the CP appliance compared to the HP appliance. Conclusions: Maxillary molar distalization was achieved with both appliances. Mesialization of the anchorage unit was controlled successfully with the hybrid Pendulum; however, the conventional Pendulum appliance caused anchorage loss

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