A Survey of the Differential Geometry of Discrete Curves

Discretization of curves is an ancient topic. Even discretization of curves with an eye toward differential geometry is over a century old. However there is no general theory or methodology in the literature, despite the ubiquitous use of discrete curves in mathematics and science. There are conflicting definitions of even basic concepts such as discrete curvature {\kappa}, discrete torsion {\tau}, or discrete Frenet frame.Comment: 19 pages, 16 figure

Financial Stress and Economic Activity

This paper briefly summarizes the results presented in Claessens, Köse and Terrones (2008a, 2008b) to provide a set of basic stylized facts about the linkages between macroeconomic and financial variables during recessions and episodes of financial stress, including the periods of credit crunches and asset (house and equity) price busts. The analysis employs a comprehensive database of key macroeconomic and financial variables for 21 OECD countries over the 1960-2007 period. The results indicate that recessions following periods of financial stress are often longer and deeper than other recessions are. The paper concludes with a short discussion of the implications of its findings for the current crisisFinancial Stress, Economic Activity, Business Cycles

Blood vitamin D levels in patients with fibromyalgia and the effectiveness of vitamin D treatment

Objective: The aim of this study was determination thelevel of vitamin D in patients diagnosed with fibromyalgiaand investigation the relationship with etiopathogenesisof the disease.Methods: In this study, between the months of Juneand December in 2012, Metin Sabancı Bone DiseasesTraining and Research Hospital, Physical Therapy OutpatientClinics, 141 patients diagnosed with fibromyalgiawere included. The patients were diagnosed accordingto American College of Rheumatology criteria. Levels ofC-reactive protein (CRP), serum calcium (Ca), phosphor(P), alkaline phosphatase (ALP), PTH, T3, T4, TSH, andvitamin D were analyzed in the blood of patients, for exclusionof a systemic illness. Deficiency of vitamin D isdetermined as ≤20 ng/ml and insufficiency of vitamin Dis determined 21-29 ng/ml. Normal level of vitamin D isaccepted as equal or ≥30 ng/ml.Results: The mean age of patients was found as45.70±14.10 years old. Mean vitamin D level was17.51±18.02 ng/ml. 76.6% (n=108) of all patients with fibromyalgiahad vitamin D deficiency and their mean vitaminD level was detected as 12.23±10.24 ng/ml. Twenty(14.2%) of all patients had vitamin D insufficiency andtheir mean vitamin D level was found as 23.83±2.76 ng/ml. The lower vitamin D level was seen in patients withage less than 45 years-old and their mean vitamin D levelwas 14.91±10.75 ng/ml.Conclusion: Vitamin D deficiency is frequently seen inpatients diagnosed with fibromyalgia and treatment withvitamin D may cause regression of the disease.Key words: D vitamin, fibromyalgia, calciu

Roman and Byzantine Church Structures Used As a Tekke in Istanbul

In this article, chronological information will be given about the takkas established in the church buildings in Istanbul. After the conquest of Istanbul in 1453 Mehmet II started to establish works of foundation in the city in order to reorganise the city and the statesmen were encouraged the creation of such charitable works. In order to provide the current needs in the city, some of the churches were converted into mosques, masjids, madrasah, lodges- takkas and public soup kitchens. Among these structures, there were double-function buildings serving both as a mosque and as a takka. Many of these mosques and masjids were used as a religious ceremony place/tevhidhane, suffering place/çilehane and training place. There are mosque and takkas were build on the grounds of many ruin churches, which could not be restored due to various reasons. In Istanbul, there were eighteen churches which were used as tevhidhane where the chanting of the tariqah was made on certain days of the week, and takkas were built in their places

Fikret Mualla ve Turgut Zaim kamyonetle birlikte satıldı

Taha Toros Arşivi, Dosya Adı: Fikret Muallaİstanbul Kalkınma Ajansı (TR10/14/YEN/0033) İstanbul Development Agency (TR10/14/YEN/0033

Haghia Sophia in Trabzon

Haghia Sophia is a small Church located to the North East of Turkey. Because of its dimensions when compared with Haghia Sophia in Istanbul it is called also “Small Haghia Sophia”. When Sultan Mehmet the Conqueror added Trabzon in the Ottoman Borders, He converted the main cathedral of city into a Mosque. However, he did not converted Haghia Sophia into a Mosque though it was the most beautiful building of Comnens. About one hundred years after the conquest, Haghia Sophia was converted into a mosque after it served as a church over 300 years and used as a mosque until the Russian occupation in 1916. The period of usage as a mosque was longer than that as a church. After the foundation of modern Turkish Republic, Haghia Sophia continued to be used as a mosque for a while, and all frescos during this time were under white wash except some cleaned by Russian Archeologist Uspensky during Russian Occupation. The most beautiful carvings of Haghia Sophia are placed on the southern narthex, the frizzes showing the creation of Adam and Eva. The Bell Tower about 200 years younger than the main complex also includes elaborate paintings in the small cell at the middle

Antineutrino Charm Production and Pentaquark Search in the CHORUS Experiment

During the years between 1994 and 1997, the emulsion target of the CHORUS experiment was exposed to the wide band neutrino beam of the CERN SPS of 27 GeV average energy collecting about 106 neutrino interactions. A measurement of induced charm production and search for anticharmed pentaquark (0 c ) have been performed by using the presence of a 6% component in the beam. By requiring a positive muon charge as determined by the CHORUS muon spectrometer, 46 -induced charm events were observed with an estimated background of 5:20:4 events. By using the data sample, anticharmed pentaquark ( 0 c ) have been searched and no evidence is found. Based on the null observation, the limit on the 0 c production is found as a function of di eren t possible 0 c lifetimes. The tightest bound is 0 c = < 0.039 at 90% C.L by assuming that 0 c lifetime is equal to 0.5 c D 0. (not complete