Platonic Riemann surfaces and Petrie polygons

Dört bölümden olusan bu tez çalısmasının ana konusu, Platonik Riemann yüzeylerine karsılık gelen düzgün figürlerin Petrie çokgenlerini ve bunların simetri gruplarını incelemektir. Birinci bölümde, tez konusu ve elde edilen sonuçlar kısaca tanıtılmıstır. ˙Ikinci bölümde, tezin ana konusu için gerekli olan temel bilgilere yer verilmistir. Üçüncü bölümde, Petrie çokgenleri ve bunlara karsılık gelen Petrie otomorfizmaları tanıtılmıstır. Bunlar, Petrie çokgenlerini kümesel olarak sabit tutan, ancak sabit noktası bulunmayan otomorfizmalardır. Ayrıca, Petrie otomorfizmalarının eslenik sınıfları belirlenmistir. Bir Petrie çokgeninin simetri grubunun dihedral oldu˘gu gösterilmistir. Daha sonra, bir düzgün figürün bütün Petrie çokgenlerinin sayısını veren bir formül ispatlanmıstır ve bu sayı için üst ve alt sınırlar bulunmustur. Cinsi 1 olan tüm yansımalı düzgün figürlerin Petrie otomorfizmalarının mertebeleri belirlenmistir. Hurwitz figürleri gibi iyi bilinen bazı düzgün figür ailelerinin, Petrie otomorfizmalarının mertebeleri ve bütün Petrie çokgenlerinin sayıları belirlenmistir. Ayrıca Petrie otomorfizmaları birim olan düzgün figürlerin sadece Wiman ve Accola-Maclachlan yüzeyleri üzerinde bulundu˘gu gösterilmistir. Son olarak, cinsi 15’e kadar olan yansımalı düzgün figürlerin Petrie otomorfizmalarının mertebeleri, bütün Petrie çokgenlerinin sayıları ve uzunlukları hesaplanmıstır. Dördüncü bölümde, elde edilen sonuçlar kısaca özetlenmistir.The main topic of this study, which consists of four chapters, is to investigate Petrie polygons and their symmetry groups corresponding to regular maps on Platonic Riemann surfaces. In the first chapter, the topic and the results of the thesis have been introduced. In the second chapter, basic concepts that are necessary for the main topic of the thesis have been included. In the third chapter, Petrie polygons and the corresponding Petrie automorphisms have been introduced. These are automorphisms that fix the Petrie polygons setwise but have no fixed points. Moreover, the conjugacy classes of Petrie automorphisms have been determined. It has been shown that the symmetry group of a Petrie polygon is dihedral. Then, a formula for the number of all Petrie polygons of a regular map has been proved, and upper and lower bounds have been found for this number. The orders of Petrie automorphisms of all reflexible regular maps of genus one have been determined. The orders of Petrie automorphisms and the numbers of all Petrie polygons of some well-known families of regular maps such as Hurwitz maps have been determined. It has also been shown that the regular maps with identity Petrie automorphisms can only exist on Wimann and Accola-Maclachlan surfaces. Finally, the orders of Petrie automorphisms, the numbers of all Petrie polygons and the lengths of Petrie polygons of all reflexible regular maps of genus up to 15 have been calculated. In the fourth chapter, the results of the thesis summarized briefly

Fixed curves on platonic Riemann surfaces

Yedi bölümden oluşan bu çalışmanın amacı platonik Riemann yüzeyleri üzerindeki sabit eğrileri ve bu eğrilerin bazı özelliklerini incelemektir. Birinci bölümde giriş kısmı verildi. İkinci bölümde tezin ana konusu için gerekli olan temel bilgilere yer verildi. Üçüncü bölümde kısaca hiperbolik geometri tanıtıldı. Dördüncü bölüm, Fuchs ve NEC (Non-Euclidean crystallographic) grupları ile Riemann yüzeylerine ayrıldı. Beşinci bölümde düzgün figürler tanıtılıp bunların sınıflandırılması yapıldı. Altıncı bölümde tezin ana konusu olan platonik Riemann yüzeyleri üzerindeki sabit eğrilerin desenleri tanıtıldı ve sınıflandırıldı. Ayrıca her sabit eğriye karşılık, birbirinin tersi olan, eğriyi ters yönlerde döndüren ve dönel otomorfizmalar olarak adlandırılan iki otomorfizma olduğu gösterildi. Son olarak bu otomorfizmalar yardımıyla cinsi 2 ve 3 olan platonik Riemann yüzeyleri üzerindeki sabit eğrilerin uzunlukları hesaplandı. Yedinci bölümde elde edilen sonuçlar verildi.The main topic of this study, which consists of seven chapters, is to investigate fixed curves on platonic Riemann surfaces and some properties of these curves. The first chapter is devoted to the introduction. In the second chapter, basic concepts, which are necessary for the main topic of the thesis, were given. In the third chapter, hyperbolic geometry has been shortly introduced. The fourth chapter is devoted to Fuchsian groups, NEC (Non-Euclidean crystallographic) groups and Riemann surfaces. In the fifth chapter, regular maps were introduced and classified. In the sixth chapter, the patterns of fixed curves on platonic Riemann surfaces, which are the main topic of the thesis, were introduced and classified. Furthermore, it has been shown that for each curve there exist two automorphisms so called rotary automorphisms. These are inverses of each other and they rotate the curve in opposite directions. Finally, with the aid of these automorphisms the lengths of fixed curves on platonic Riemann surfaces of genera two and three have been calculated. The seventh chapter involves the conclusion of study

Davranışsal finans kapsamında zihinsel muhasebe ve risk algısı: Marmara Üniversitesi’nde ampirik bir çalışma

With the prevalence of behavioral approaches to the consumption – and investment-based decisions of individuals, the mental coding of gains and losses employing the value function of prospect theory has been studied intensively by Thaler (2008), focusing on the process of mental accounting, the set of cognitive operations used by individuals and households to organize, evaluate, and keep track of financial activities. This study analyzes the behaviors of academicians in context of mental accounting and risk-based components. The sampling frame comprises academicians from the Faculty of Business Administration at Marmara University, Istanbul, and the findings show that mental accounting does, indeed, an impact on risk perception. However, the risk perceptions of academicians in terms of financial instruments differ with respect to demographic variables.Günümüzde, davranışsal tutum bireylerin tüketim ve yatırım kararlarına hâkim olmaya başladığından, Thaler (2008), Beklenti Teorisi’ndeki değer fonksiyonunu kullanarak kazanç ve kayıpların zihinsel kodlaması üzerinde yoğun olarak araştırmalar yapmıştır. Zihinsel muhasebe olarak isimlendirilen bu süreç, bireylerin ve hane halkının finansal aktivitelerini organize etmek, değerlendirmek ve takip etmek için kullandığı bir dizi bilişsel operasyondan oluşmaktadır. Bu çalışmanın amacı, zihinsel muhasebe ve risk bazlı bileşenler kapsamında akademisyenlerin davranışlarını analiz etmektir. Çalışmanın örneklemini Marmara Üniversitesi İşletme Fakültesi akademisyenleri oluşturmaktadır. Çalışmanın bulguları, zihinsel muhasebenin risk algısı üzerinde etkisi olduğunu ortaya çıkartmıştır. Ayrıca, akademisyenlerin, finansal araçlar üzerindeki risk algılarının demografik değişkenler arasında farklılık gösterdiği de görülmüştür.Publisher's Versio

A Sub-500 mu W Interface Electronics for Bionic Ears

This paper presents an ultra-low power current-mode circuit for a bionic ear interface. Piezoelectric (PZT) sensors at the system input transduce sound vibrations into multi-channel electrical signals, which are then processed by the proposed circuit to stimulate the auditory nerves consistently with the input amplitude level. The sensor outputs are first amplified and range-compressed through ultra-low power logarithmic amplifiers (LAs) into AC current waveforms, which are then rectified through custom current-mode circuits. The envelopes of the rectified signals are extracted, and are selectively sampled as reference for the stimulation current generator, armed with a 7-bit user-programmed DAC to enable patient fitting (calibration). Adjusted biphasic stimulation current is delivered to the nerves according to continuous inter-leaved sampling (CIS) stimulation strategy through a switch matrix. Each current pulse is optimized to have an exponentially decaying shape, which leads to reduced supply voltage, and hence similar to 20% lower stimulator power dissipation. The circuit has been designed and fabricated in 180nm high-voltage CMOS technology with up to 60 dB measured input dynamic range, and up to 1 mA average stimulation current. The 8-channel interface has been validated to be fully functional with 472 mu W power dissipation, which is the lowest value in the literature to date, when stimulated by a mimicked speech signal

Column generation algorithms for airline network revenue management problems

At the heart of the airline revenue management problem (ARM) lies the seat allocation problem, which has the ultimate aim of finding the right combination of passengers that will result in maximum profit. Due to the dynamic nature of the problem, optimal seat allocations can change continuously over the reservation period. In addition, widely used bid-price booking control policy which necessitates the dual information is obliged to be updated as the demand and capacity values adjust over the reservation period. Thus, in order to make changes in an interactive basis, it is crucial to solve the seat allocation problem in a small amount of time. This study embodies column generation algorithms applied to ARM problems. Networkbased ARM problems are computationally hard to solve even if the airline network is small. However, in this study we challenged ourselves with large-scale airline networks. For computational efficiency, the network is divided into subnetworks by means of date and time information. The overall network is decomposed to origin destination pairs, so that each pair is treated as a single-leg problem. The resulting seat allocation models (static, dynamic and deterministic linear programming) having a non-linear objective function are linearized by means of the transformation technique proposed by Dantzig which embodies a transformation only by means of additional decision variables. Since column generation can not cope with problems extending row-wise, Dantzigs formulation is the perfect fit. After applying column generation, the numerical results for the models is demonstrated

Investigating Conceptual Foundations of Design Ability: An Analysis through the Expressions of the Experiencing Mind

[EN] This paper aims to reveal conceptual foundations of design ability based on verbal expressions of students’ insights. This goal is based on two propositions. The first one is about categorizing abilities in order to make them meaningful, while the second one is about the disadvantages of explaining the designer based on linear levels. So that, a group, which consisted of industrial design students who were newly graduated or in their last semester, was interviewed individually. The interviews were based on their experiences and the evolution of skills during four years of undergraduate education. Semi-structured interviews were used as the main data collection method, resulting over ten hours of recording which turned to be over one hundred pages of transcriptions. Later, the gathered data was analyzed using thematic analysis. Chunks of data were coded and codes were categorized under themes in a reductionist manner within several iterations. Three conceptual themes were generated and interpreted. Themes’ reliability was ensured by using KALPHA in SPSS. Examples from four creative areas were given in order to broaden the field where the themes may be applied. As the final outcome, a model of fractal triangle simultaneously showing the findings is suggested. This model is claimed to indicate conceptual foundations which allow different states of design ability categories without being restricted to designer’s expertise levels. So that, without depending on the specified designer level, different levels of ability categories become possible.Ulusan, U.; Turan, A. (2016). Investigating Conceptual Foundations of Design Ability: An Analysis through the Expressions of the Experiencing Mind. En Systems&design:beyond processes and thinking. Editorial Universitat Politècnica de València. 449-465. https://doi.org/10.4995/IFDP.2015.3126OCS44946

Financing the preservation of historical buildings in Turkey

The aim of this paper is to trace the historical development of the state’s share in restoration of the immovable cultural heritage of the country

Retroperitoneal Malignant Fibrous Histiocytoma Can Mimic a Hydatid Cyst

Malignant fibrous histiocytoma is the second most common soft-tissue sarcoma in adults. After the extremities, the retroperitoneal space is the second most common site of this tumor. A 50-year-old man presented with a right retroperitoneal, thick-walled, cystic multilocular mass measuring 10 × 10 cm that was thought to be a type CE 5 hydatid cyst preoperatively. However, the postoperative histopathology did not agree with the radiological findings and instead showed a malignant fibrous histiocytoma. The computed tomography and ultrasound/Doppler ultrasound findings of this retroperitoneal mass mimicked a type CE 5 hydatid cyst. We present this case because the surgical management of these two lesions differs and misdiagnosis can be problematic