ON THE p-ADIC VALUATION OF GENERALIZED HARMONIC NUMBERS

Cagatay Altuntas 대한수학회 2023 대한수학회보 Vol.60 No.4

For any prime number $p$, let $J(p)$ be the set of positive integers $n$ such that the numerator of the $n^{th}$ harmonic number in the lowest terms is divisible by this prime number $p$. We consider an extension of this set to the generalized harmonic numbers, which are a natural extension of the harmonic numbers. Then, we present an upper bound for the number of elements in this set. Moreover, we state an explicit condition to show the finiteness of our set, together with relations to Bernoulli and Euler numbers.

Anterior Herniation of Partially Calcified and Degenerated Cervical Disc Causing Dysphagia

Cagatay Ozdol,Cezmi Cagri Turk,Ali Erdem Yildirim,Ali Dalgic 대한척추외과학회 2015 Asian Spine Journal Vol.9 No.4

We report a rare case of anterior cervical disc herniation associated with dysphagia. A 32-year-old man presented with complaints of dysphagia and concomitant pain in the right arm resistant to conservative therapy. On physical examination with respect to the muscle strength, the right shoulder abduction and flexion of the forearm were 3/5. Lateral X-ray revealed calcified osteophytes at the anterior C4–5 level. Magnetic resonance imaging showed soft disc herniation involving the right C6 root at the C5–6 level and anterior herniation of the C4–5 cervical disc. Anterior discectomies for C4–5 and C5–6 levels stabilized and ameliorated the dysphagia and pain. Cervical disc herniation usually presents with radicular findings. However, dysphagia may be an uncommon presentation. Anterior cervical disc herniation should be considered in a patient presenting with dysphagia.

Optimum design of prestressed concrete beams by a modified grid search method

Cagatay, Ismail H.,Dundar, Cengiz,Aksogan, Orhan Techno-Press 2003 Structural Engineering and Mechanics, An Int'l Jou Vol.15 No.1

A computer program has been developed for the optimum design of prestressed concrete beams under flexure. Optimum values of prestressing force, tendon configuration, and cross-sectional dimensions are determined subject to constraints on the design variables and stresses. 28 constraints have been used including flexural stresses, cover requirement, the aspect ratios for top and bottom flanges and web part of a beam and ultimate moment. The objective function contains cost of concrete, prestressing force and formwork. Using this function, it is possible to obtain minimum cost design, minimum weight or cross-sectional area of concrete design and minimum prestressing force design. Besides the idealized I-shaped cross-section, which is widely used in literature, a general I-shaped cross-section with eight geometrical design variables are used here. Four examples, one of which is available in the literature and the others are modified form of it, have been solved for minimum cost and minimum cross-sectional area designs and the results are compared. The computer program, which employs modified grid search optimization method, can assist a designer in producing efficient designs rapidly and easily. Considerable savings in computational work are thus made possible.

THE DIFFERENCE OF HYPERHARMONIC NUMBERS VIA GEOMETRIC AND ANALYTIC METHODS

Altuntas, Cagatay,Goral, Haydar,Sertbas, Doga Can Korean Mathematical Society 2022 대한수학회지 Vol.59 No.6

Our motivation in this note is to find equal hyperharmonic numbers of different orders. In particular, we deal with the integerness property of the difference of hyperharmonic numbers. Inspired by finiteness results from arithmetic geometry, we see that, under some extra assumption, there are only finitely many pairs of orders for two hyperharmonic numbers of fixed indices to have a certain rational difference. Moreover, using analytic techniques, we get that almost all differences are not integers. On the contrary, we also obtain that there are infinitely many order values where the corresponding differences are integers.

Serum S100B Protein Levels in Patients with Panic Disorder: Effect of Treatment with Selective Serotonine Reuptake Inhibitors

Berna Cagatay Kaya,Hasan Karadag,Ozgur Oner,Aysegul Kart,Mehmet Hakan Turkcapar 대한신경정신의학회 2015 PSYCHIATRY INVESTIGATION Vol.12 No.2

ObjectiveaaAltered serum S100B protein levels have been shown in several psychiatric disorders. Our aim was to investigate whether plasma S100B is different in patients with panic disorder (PD) when compared with controls. Our second aim was to investigate whether treatment with SSRIs have an effect on S100B levels in patients with PD. MethodsaaThe sample included 32 patients diagnosed with PD (21 women, 11 men) per DSM-IV criteria and 21 healthy controls (11 women, 10 men). S100B levels were measured with BioVendor Human S100B ELISA (Enzyme Linked Immunosorbent Assay) kit. Resultsaa14 patients were not on drug treatment (43.8%) while 18 patients were taking various SSRIs. Median S100B value was 151.7 pg/mL (minimum-maximum: 120.4–164.7 pg/mL) in the control group, 147.4 pg/mL (minimum-maximum: 138.8–154.1 pg/mL) in the drug free group and 153.0 pg/mL (minimum-maximum: 137.9–164.7 pg/mL) in the treatment group. Kruskal-Wallis analysis showed a significant diffrerence among the three groups (z=9.9, df=2, p=0.007). Follow up Mann-Whitney-U tests indicated that while the control and the patients with treatment were not significantly different (z=-0.05, p=0.96), there were significant differences between the control group and untreated patients (z=-2.6, p=0.009) and treated and untreated patients (z=-3.0, p=0.003). ConclusionaaOur results suggested that, serum S100B protein level might be decreased in untreated PD patients and that patients who were treated with SSRIs had similar S100B level to healthy controls.

Modeling of concrete containing steel fibers: toughness and mechanical properties

Ismail H. Cagatay,Riza Dincer 사단법인 한국계산역학회 2011 Computers and Concrete, An International Journal Vol.8 No.3

In this study, effect of steel fibers on toughness and some mechanical properties of concrete were investigated. Hooked-end steel fibers were used in concrete samples with three volume fractions (vf) of 0.5%, 0.75% and 1% and for two aspect ratios (l/d) of 45 and 65. Compressive and flexural tensile strength and modulus of elasticity of concrete were determined for cylindrical, cubic and prismatic samples at the age of 7 and 28 days. The stress-strain curves of standard cylindrical specimens were studied to determine the effect of steel fibers on toughness of steel-fiber-reinforced concrete (SFRC). In addition, the relationship between compressive strength and the flexural tensile strength of SFRC were reported. Finally, a simple model was proposed to generate the stress-strain curves for SFRC based on strains corresponding to the peak compressive strength and 60% of peak compressive stress. The proposed model was shown to provide results in good correlation with the experimental results.

The System Dynamics Modelling for Container Capacity & Transportation Planning Policies

Bahadir Mehmet Cagatay,Akdag Hatice Camgoz 한국해운물류학회 2019 The Asian journal of shipping and Logistics Vol.35 No.4

The aim of the paper is to develop a system dynamics model for hub & spoke container network’s capacity & transportation planning policy selection of which objective is to maximize the long term earnings. The system dynamic modelling approaches are used to compare the policies associated with some performance indicators including capacity utilization, service level, return on investment. The main contribution of the study is to compare the policies by including the interactions of container system processes from a broad perspective for balancing capacity utilization and market share with the proposed approaches with system dynamic modelling approaches.

Investigation of short column effect of RC buildings: failure and prevention

Ismail H. Cagatay,Caner Beklen,Khalid M. Mosalam 한국계산역학회 2010 Computers and Concrete, An International Journal Vol.7 No.6

If an infill wall in a reinforced concrete frame is shorter than the column height and there is no initial gap between the column and the infill wall, the short column effect can occur during an earthquake shaking. This form of damage is frequently observed in many earthquake-damaged buildings all around the world and especially in Turkey. In this study, an effective method, which consists of placing additional infill wall segments surrounding the short column, to prevent this type of failure is examined. The influence of adding infill wall in the reduction of the shear force in the short column is also investigated. A parametric study is carried out for one-storey infilled frames with one to five bays using the percentage of the additional infill wall surrounding the short column and the number of spans as the parameters. Then the investigation is extended to a case of a multistorey building damaged due to short column effect during the 1998 Adana-Ceyhan earthquake in Turkey. The results show that the addition of the infill walls around the potential short columns is an effective way to significantly reduce the shear force.

Argon Green Laser for Valsalva Retinopathy Treatment and Longterm Follow-up of the Internal Limiting Membrane Changes in Optical Coherence Tomography

Hakan Tirhis,Cagatay Caglar,Pelin Yilmazbas,Mustafa Alparslan Anayol,Mehmet Ali Şekeroğlu 대한안과학회 2015 Korean Journal of Ophthalmology Vol.29 No.6

Experimental investigation on CFRP-to-concrete bonded joints across crack

Ozgur Anil,Cagatay M. Belgin,M. Emin Kara 국제구조공학회 2010 Structural Engineering and Mechanics, An Int'l Jou Vol.35 No.1

Bonding of carbon fiber reinforced polymer (CFRP) composites has become a popular technique for strengthening concrete structures in recent years. The bond stress between concrete and CFRP is the main factor determining the strength, rigidity, failure mode and behavior of a reinforced concrete member strengthened with CFRP. The accurate evaluation of the strain is required for analytical calculations and design processes. In this study, the strain between concrete and bonded CFRP sheets across the notch is tested. In this paper, indirect axial tension is applied to CFRP bonded test specimen by a four point bending tests. The variables studied in this research are CFRP sheet width, bond length and the concrete compression strength. Furthermore, the effect of a crack- modeled as a notch- on the strain distribution is studied. It is observed that the strain in the CFRP to concrete interface reaches its maximum values near the crack tips. It is also observed that extending the CFRP sheet more than to a certain length does not affect the strength and the strain distribution of the bonding. The stress distribution obtained from experiments are compared to Chen and Teng’s (2001) analytical model.