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Soydan,Demirci,Cangul 장전수학회 2009 Advanced Studies in Contemporary Mathematics Vol.19 No.2
The object of this paper is to give a new proof of all the solutions of the Diophantine equation x² + 11m = yⁿ,in positive integers x; y with odd m > 1 and n ≥ 3.
On the additive structure of the set of quadratic residues modulo p
G. Soydan,N. Y. Ikikardes,M. Demirci,I. Cang?l 장전수학회 2007 Advanced Studies in Contemporary Mathematics Vol.14 No.2
It is well-known that the set of quadratic residues modulo p forms multiplicative group. But except for very special cases, there is no result on the sum of quadratic residues or non-residues. Here we study three different sums; the sum of two quadratic residues, the sum of two quadratic non-residues and the sum of a quadratic residue with a non-residue. Bachet elliptic curves are the curves of the form y2 = x3 + a3 where a is a fixed element of the underlying field. Studying the rational points on these curves depends on our knowledge of the sum of a variable x3 and a fixed value a. Therefore we study such sums as well.
İbrahim Damlar;Ahmet Altan;Berk Turgay;Soydan Kiliç 대한구강악안면외과학회 2016 대한구강악안면외과학회지 Vol.42 No.6
In this study, we present the surgical treatment of obstructive sleep apnea in a child with Treacher Collins syndrome. A 10-year-old girl with a past history of Treacher Collins syndrome presented to our clinic with her parents for respiratory distress and insomnia. The patient was referred to a sleep laboratory where she was diagnosed with obstructive sleep apnea, which was a consequence of her Treacher Collins syndrome. The patient underwent mandibular distraction osteogenesis under general anesthesia. The mandible was expanded by 15 mm using internal bilateral distractors. After distraction osteogenesis, the patient’s respiratory problems resolved, and she was able to sleep comfortably. Distraction osteogenesis was an effective method of advancing the mandible, increasing the upper airway space and ultimately preventing obstructive sleep apnea syndrome in patients with Treacher Collins syndrome.
Inam, Ilker,Soydan, Gokhan,Demirci, Musa,BiZim, Osman,Cangul, Ismail Naci Korean Mathematical Society 2007 대한수학회논문집 Vol.22 No.2
In this work, authors considered a result concerning elliptic curves $y^2=x^3+cx$ over $\mathbb{F}_p$ mod 8, given at [1]. They noticed that there should be a slight change at this result. They give counterexamples and the correct version of the result.
( Elif Kizildere ),( Gökhan Soydan ) 호남수학회 2020 호남수학학술지 Vol.42 No.1
Let p be a prime number with p > 3, p ≡ 3 (mod 4) and let n be a positive integer. In this paper, we prove that the Diophantine equation (5pn<sup>2</sup> - 1)<sup>x</sup> + (p(p - 5)n<sup>2</sup> + 1)<sup>y</sup> = (pn)<sup>z</sup> has only the positive integer solution (x; y; z) = (1; 1; 2) where pn ≡ ±1 (mod 5). As an another result, we show that the Diophantine equation (35n<sup>2</sup> - 1)<sup>x</sup> + (14n<sup>2</sup> + 1)<sup>y</sup> = (7n)<sup>z</sup> has only the positive integer solution (x, y, z) = (1, 1, 2) where n ≡ ±3 (mod 5) or 5 | n. On the proofs, we use the properties of Jacobi symbol and Baker's method.
Social Support and Quality of Life in Turkish Patients with Gynecologic Cancer
Nazik, Evsen,Nazik, Hakan,Ozdemir, Funda,Soydan, Selen Asian Pacific Journal of Cancer Prevention 2014 Asian Pacific journal of cancer prevention Vol.15 No.7
The aim of this study was to determine the level of social support and quality of life in Turkish patients with gynecologic cancer using a cross-sectional survey design. A total of 108 patients admitted to the gynecologic oncology clinic at a university hospital from September 2011 to January 2012 were included. Data were collected using patient information forms, the Multidimensional Scale of Perceived Social Support (MSPSS) and The Quality of Life-Cancer Survivors Instrument (QOL-CS). Average age was $54.5{\pm}10.8$ years and it was determined that 65.7% of patients had ovarian cancer and 19.4% had cervical cancer. The total QOL-CS mean score was $5.59{\pm}1.10$. Average score of total MSPSS was found to be $69.7{\pm}14.64$. Comparing socio-demographic and clinical characteristics of patients and average scores of QOL-CS and MSPSS, it was found that there was not a statisticaly significant corelation (p>0.05). Statistically significant relation was found between the average scores of QOL-CS and MSPSS. These results showed that quality of life was moderate and perceived social support was high in Turkish patients with gynecologic cancer.
Angioleiomyoma of the gingiva: a report of two cases
Osman Fatih Arpağ,Ibrahim Damlar,Soydan Kılıç,Ahmet Altan,Zeynel Abidin Taş,Tü,may Ö,zgü,r 대한구강악안면외과학회 2016 대한구강악안면외과학회지 Vol.42 No.2
Leiomyoma is a type of benign smooth muscle neoplasm that is a common neoplasm of the uterus and gastrointestinal tract but rarely affects the head and neck region and is especially unlikely to affect the oral cavity. The diagnosis of leiomyoma is mainly determined by histopathological studies due to variation in its clinical appearance and symptoms. In the present paper we report two rare cases of gingival angioleiomyoma in the posterior maxilla and mandible. After total excision, hematoxylin-eosin and smooth muscle actin staining confirmed the diagnosis of angioleimyoma.