GENERALIZED FIBONACCI NUMBERS OF THE FORM 11x² + 1

Ogut, Ummugulsum,Keskin, Refik The Honam Mathematical Society 2018 호남수학학술지 Vol.40 No.1

Let $P{\geq}3$ be an integer and let ($U_n$) denote generalized Fibonacci sequence defined by $U_0=0$, $U_1=1$ and $U_{n+1}=PU_n-U_{n-1}$ for $n{\geq}1$. In this study, when P is odd, we solve the equation $U_n=11x^2+1$. We show that only $U_1$ and $U_2$ may be of the form $11x^2+1$.

Experimental setup for testing climatic stress component in vegetation via AM: challenges and new opportunities

Ozge Ogut,Ole Emil Herrmann,Chao Gao,Nerantzia Julia Tzortzi,Chiara Bertolin 대한기계학회 2023 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.37 No.11

This study aims to analyze the challenges and the opportunities in developing an experimental setup to test climatic stress on vegetation using additive manufacturing (AM). Vegetation is unavoidable to analyze as species are the components of vertical green structures (VGS). These structures can increase the amount of green infrastructure in built environments optimizing space-related concerns. One benefit of VGS is to act as a thermal insulator by changing microclimate. It helps to stabilize temperature, and to reduce energy needs’ amount. To optimize these benefits, the vegetation selection must be done in an efficient way and each plant’s reaction to hygro-thermal variations should be evaluated quantitatively. AM offers opportunity to create reference object to study the effect of hygro-thermal modifications on leaves. In fact, AM-leaves used as reference shapes in comparison with real leaves’ shapes are not modifiable in the range of the experimental climate conditions and may help in detecting anomalies. The experimental procedure has still to be created and tested. This paper underlines the challenges met while developing such preliminary experimental setup and the initial tests which have offered solutions to the technical barriers.

GENERALIZED FIBONACCI NUMBERS OF THE FORM 11x^2 + 1

Ummugulsum Ogut,Refik Keskin 호남수학회 2018 호남수학학술지 Vol.40 No.1

Let P 3 be an integer and let (Un) denote generalizedFibonacci sequence de ned by U0 = 0;U1 = 1 and Un+1 = PUn Un 1 for n 1: In this study, when P is odd, we solve the equationUn = 11x2 + 1. We show that only U1 and U2 may be of the form11x2 + 1:

GENERALIZED FIBONACCI NUMBERS OF THE FORM 11x² + 1

( Ummugulsum Ogut ),( Refik Keskin ) 호남수학회 2018 호남수학학술지 Vol.40 No.1

Let P ≥ 3 be an integer and let (Un) denote generalized Fibonacci sequence defined by U0 = 0,U₁ = 1 and U_n+1 = PUn - U_n-1 for n ≥ 1, In this study, when P is odd, we solve the equation Un = 11x² + 1. We show that only U₁ and U₂ may be of the form 11x² + 1.

Evaluation of the morphology of the canalis sinuosus using cone-beam computed tomography in patients with maxillary impacted canines

Gurler, Gokhan,Delilbasi, Cagri,Ogut, Emine Esen,Aydin, Kader,Sakul, Ufuk Korean Academy of Oral and Maxillofacial Radiology 2017 Imaging Science in Dentistry Vol.47 No.2

Purpose: The nasopalatine canal is a well-known, important anatomical structure in the anterior maxilla, but this region contains many accessory canals. The canalis sinuosus (CS) is one of these canals; it contains the anterior superior alveolar nerve, along with veins and arteries. The purpose of this study was to evaluate the CS using cone-beam computed tomography (CBCT) in patients with maxillary impacted canines. Materials and Methods: A total of 111 patients admitted to the Istanbul Medipol University School of Dentistry for the exposure, orthodontic treatment, and/or extraction of an impacted canine were included in this study. CBCT images were obtained for these patients under standard conditions. Axial, coronal, and sagittal sections were evaluated to assess the prevalence of CS, the direction and diameter of the canal, its relation with the impacted canine, and its distance from the alveolar crest. Further, possible correlations with patient gender and age were analyzed. Results: The CS could be detected bilaterally in all the evaluated tomography images. The mean canal diameter was significantly larger in males than in females(P=.001). The CS ran significantly closer to the impacted canine when the canal was located horizontally (P=.03). Variations of the canal, such as accessory canals, were identified in 6 patients. Conclusion: CS is an anatomical entity that may resemble periapical lesions and other anatomical structures. Evaluation with CBCT prior to surgical procedures in the anterior maxilla will help to prevent overlooking such anatomical structures and to decrease possible surgical complications.

Evaluation of the morphology of the canalis sinuosus using cone-beam computed tomography in patients with maxillary impacted canines

Gokhan Gurler,Cagri Delilbasi,Emine Esen Ogut,Kader Aydin,Ufuk Sakul 대한영상치의학회 2017 Imaging Science in Dentistry Vol.47 No.2

Purpose: The nasopalatine canal is a well-known, important anatomical structure in the anterior maxilla, but this region contains many accessory canals. The canalis sinuosus (CS) is one of these canals; it contains the anteriorsuperior alveolar nerve, along with veins and arteries. The purpose of this study was to evaluate the CS using conebeam computed tomography (CBCT) in patients with maxillary impacted canines. Materials and Methods: A total of 111 patients admitted to the Istanbul Medipol University School of Dentistry for the exposure, orthodontic treatment, and/or extraction of an impacted canine were included in this study. CBCT images were obtained for these patients under standard conditions. Axial, coronal, and sagittal sections were evaluated to assess the prevalence of CS, the direction and diameter of the canal, its relation with the impacted canine, and its distance from the alveolar crest. Further, possible correlations with patient gender and age were analyzed. Results: The CS could be detected bilaterally in all the evaluated tomography images. The mean canal diameter was significantly larger in males than in females (P=.001). The CS ran significantly closer to the impacted canine when the canal was located horizontally (P=.03). Variations of the canal, such as accessory canals, were identified in 6 patients. Conclusion: CS is an anatomical entity that may resemble periapical lesions and other anatomical structures. Evaluation with CBCT prior to surgical procedures in the anterior maxilla will help to prevent overlooking such anatomical structures and to decrease possible surgical complications.

Electromyography-Guided Botulinum Toxin Injection Into the Cricothyroid Muscles in Bilateral Vocal Fold Abductor Paralysis

Mustafa Sahin,Ibrahim Aydogdu,Serdar Akyildiz,Munevver Erdinc,Kerem Ozturk,Fatih Ogut 대한이비인후과학회 2017 Clinical and Experimental Otorhinolaryngology Vol.10 No.2

Objectives. Bilateral vocal fold abductor paralysis (BVFAP) both deteriorates quality of life and may cause life-threatening respiratory problems. The aim of this study was to reduce respiratory symptoms in BVFAP patients using cricothyroid (CT) botulinum toxin (BTX) injection. Methods. Before and 2 weeks and 4 months after bilateral BTX injection into the CT muscles under electromyography; alterations in respiratory, acoustic, aerodynamic and quality of life parameters were evaluated in BVFAP patients with respiratory distress. For the respiratory evaluation modified Borg scale and spirometry, for the voice and aerodynamic evaluations Voice Handicap Index-30 (VHI-30), GRBAS, acoustic analysis (sound pressure level, F0, jitter%, shimmer%, noise-to-harmonic ratio) and maximum phonation time and for the quality of life assessment Short Form-36 (SF-36) form were used. Results. All patients were female with a mean age of 47±8.1 years. There was a mean time of 11.8±5.5 (minimum 2, maximum 23) months between BVFAP development and BTX injection. In all cases, other than one case with unknown aetiology, the cause of vocal fold paralysis was prior thyroid surgery. In total 18.6±3.1 units of BTX were applied to the CTs. In the preinjection period, and the 2nd week and 4th month after injection, the Borg dyspnea scale was 7.3/5.3/5.0, FIV1 (forced inspiratory volume in one second) was 1.7/1.7/1.8 L, peak expiratory flow (PEF) was 1.4/1.7/2.1 L/sec, maximum phonation time was 7.0/6.4/6.2 seconds and VHI-30 was 63.2/52.2/61.7 respectively. There was no significant alteration in acoustic analysis parameters. Many of the patients reported transient dysphagia within the first week. There were insignificant increases in SF-36 sub-scale values. Conclusion. After BTX injection, improvements in the mean Borg score, PEF and FIV1 values and SF-36 sub-scale scores showed the restricted success of this approach. This modality may be kept in mind as a transient treatment option for patients refused persistent tracheotomy or ablative airway surgeries.

The Evaluation of Exogenous Melatonin Administration in Supraspinatus Overuse Tendinopathy in an Experimental Rat Model

Onur Kocadal,Murad Pepe,Nalan Akyurek,Zafer Gunes,Hatice Surer,Ertugrul Aksahin,Betul Ogut,Cem Nuri Aktekin 대한견주관절학회 2019 대한견주관절학회지 Vol.22 No.2

Background: Increased oxidative stress and inflammation play a critical role in the etiopathogenesis of chronic tendinopathy. Melatonin is an endogenous molecule that exhibits antioxidant and anti-inflammatory activity. The aim of this study was to evaluate the biochemi-cal and histopathological effects of exogenous melatonin administrations in supraspinatus overuse tendinopathy.Methods: Fifty rats were divided into the following four groups: cage activity, melatonin treatment, corticosteriod therapy, and control. Melatonin (10 mg/kg, intraperitoneal; twice a day) and triamcinolone (0.3 mg/kg, subacromial; weekly) were administered to the treat-ment groups after the overuse period. Biochemical and histopathological evaluations were performed on serum samples and biopsies obtained from rats. Plasma inducible nitric oxide synthase (iNOS), vascular endothelial growth factor (VEGF), total antioxidant status (TAS), total oxidant status (TOS), and oxidative stress index (OSI) levels were evaluated biochemically. Results: The TAS, TOS, OSI, iNOS, and VEGF values were significantly lower than the pre-treatment levels in rats receiving exogenous melatonin treatment (3 or 6 weeks) (p<0.05). TOS, iNOS, VEGF, and OSI values after 3 weeks of triamcinolone administration, and TOS, VEGF, and OSI levels after 6 weeks of triamcinolone application, were significantly lower than the pre-treatment levels (p<0.05). Conclusions: Exogenous melatonin application in overuse tendinopathy reduces oxidative stress and inflammation. Melatonin might be an alternative potential molecule to corticosteroids in the treatment of chronic tendinopathy.