TR-Dizin İndeksli Yayınlar Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8652

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Citation - WoS: 2
Citation - Scopus: 3
Analysis of Mixed-Order Caputo Fractional System With Nonlocal Integral Boundary Condition
(Tubitak Scientific & Technological Research Council Turkey, 2018) Khodabakhshi, Neda; Baleanu, Dumitru; Akman Yildiz, Tugba
This paper deals with a mixed-order Caputo fractional system with nonlocal integral boundary conditions. This study can be considered as an extension of previous studies, since the orders of the equations lie on different intervals. We discuss the existence and uniqueness of the solution using fixed point methods. We enrich the study with an example.
Citation - WoS: 16
Citation - Scopus: 20
Common Fixed Point Theorems in Cone Banach Spaces
(Hacettepe Univ, Fac Sci, 2011) Abdeljawad, Thabet; Tas, Kenan; Karapınar, Erdal
Recently, E. Karapınar (Fixed Point Theorems in Cone Banach Spaces, Fixed Point Theory Applications, Article ID 609281, 9 pages, 2009) presented some fixed point theorems for self-mappings satisfying certain contraction principles on a cone Banach space. Here we will give some generalizations of this theorem.
Citation - WoS: 27
Citation - Scopus: 26
Completion of Cone Metric Spaces
(Hacettepe Univ, Fac Sci, 2010) Abdeljawad, Thabet
In this paper a completion theorem for cone metric spaces and a com- pletion theorem for cone normed spaces are proved. The completion spaces are defined by means of an equivalence relation obtained by convergence via the scalar norm of the Banach space E.
Citation - WoS: 8
Citation - Scopus: 11
The Diagnosis of Femoroacetabular Impingement Can Be Made on Pelvis Radiographs Using Deep Learning Methods
(Turkish Joint Diseases Foundation, 2023) Atalar, Ebru; Ureten, Kemal; Kanatli, Ulunay; Ciceklidag, Murat; Kaya, Ibrahim; Vural, Abdurrahman; Maras, Yuksel
Objectives: The aim of this study was to evaluate diagnostic ability of deep learning models, particularly convolutional neural network models used for image classification, for femoroacetabular impingement (FAI) using hip radiographs. Materials and methods: Between January 2010 and December 2020, pelvic radiographs of a total of 516 patients (270 males, 246 females; mean age: 39.1 +/- 3.8 years; range, 20 to 78 years) with hip pain were retrospectively analyzed. Based on inclusion and exclusion criteria, a total of 888 hip radiographs (308 diagnosed with FAI and 508 considered normal) were evaluated using deep learning methods. Pre-trained VGG-16, ResNet-101, MobileNetV2, and Inceptionv3 models were used for transfer learning. Results: As assessed by performance measures such as accuracy, sensitivity, specificity, precision, F-1 score, and area under the curve (AUC), the VGG-16 model outperformed other pre-trained networks in diagnosing FAI. With the pre-trained VGG-16 model, the results showed 86.6% accuracy, 82.5% sensitivity, 89.6% specificity, 85.5% precision, 83.9% F1 score, and 0.92 AUC. Conclusion: In patients with suspected FAI, pelvic radiography is the first imaging method to be applied, and deep learning methods can help in the diagnosis of this syndrome.
Citation - WoS: 11
Citation - Scopus: 11
Diagnosis of Osteoarthritic Changes, Loss of Cervical Lordosis, and Disc Space Narrowing on Cervical Radiographs With Deep Learning Methods
(Turkish Joint Diseases Foundation, 2022) Tokdemir, Gul; Ureten, Kemal; Atalar, Ebru; Duran, Semra; Maras, Hakan; Maras, Yuksel
Objectives: In this study, we aimed to differentiate normal cervical graphs and graphs of diseases that cause mechanical neck pain by using deep convolutional neural networks (DCNN) technology. Materials and methods: In this retrospective study, the convolutional neural networks were used and transfer learning method was applied with the pre-trained VGG-16, VGG-19, Resnet-101, and DenseNet-201 networks. Our data set consisted of 161 normal lateral cervical radiographs and 170 lateral cervical radiographs with osteoarthritis and cervical degenerative disc disease. Results: We compared the performances of the classification models in terms of performance metrics such as accuracy,
Citation - WoS: 2
Citation - Scopus: 6
Diamond Alpha Hardy-Copson Type Dynamic Inequalities
(Hacettepe Univ, Fac Sci, 2022) Kaymakcalan, Billur; Kayar, Zeynep
In this paper two kinds of dynamic Hardy-Copson type inequalities are derived via diamond alpha integrals. The first kind consists of twelve new integral inequalities which can be considered as mixed type in the sense that these inequalities contain delta, nabla and diamond alpha integrals together. The second kind involves another twelve new inequalities, which are composed of only diamond alpha integrals, unifying delta and nabla Hardy-Copson type inequalities. Our approach is quite new due to the fact that it uses time scale calculus rather than algebra. Therefore both kinds of our results unify some of the known delta and nabla Hardy-Copson type inequalities into one diamond alpha Hardy-Copson type inequalities and offer new Hardy-Copson type inequalities even for the special cases.
Diffraction of Waves by a Wedge With Phase Conjugate Faces
(2011) Umul, Yusuf Ziya
The scattering process of waves by a wedge with phase conjugate faces is investigated with the aid of the modified diffraction theory of Kirchhoff. The scattering integral is evaluated asymptotically. The uniform diffracted waves and geometrical optics fields are plotted and examined numerically.
Citation - WoS: 7
Citation - Scopus: 6
Dirac Systems With Regular and Singular Transmission Effects
(2017) Uğurlu, Ekin
In this paper, we investigate the spectral properties of singular eigenparameter dependent dissipative problems in Weyl s limit-circle case with finite transmission conditions. In particular, these transmission conditions are assumed to be regular and singular. To analyze these problems we construct suitable Hilbert spaces with special inner products and linear operators associated with these problems. Using the equivalence of the Lax Phillips scattering function and Sz-Nagy Foia¸s characteristic functions we prove that all root vectors of these dissipative operators are complete in Hilbert spaces.
Citation - WoS: 3
Citation - Scopus: 3
Dissipative Operator and Its Cayley Transform
(2017) Tas, Kenan; Uğurlu, Ekin
In this paper, we investigate the spectral properties of the maximal dissipative extension of the minimal symmetric differential operator generated by a second order differential expression and dissipative and eigenparameter dependent boundary conditions. For this purpose we use the characteristic function of the maximal dissipative operator and inverse operator. This investigation is done by the characteristic function of the Cayley transform of the maximal dissipative operator, which is a completely nonunitary contraction belonging to the class C0. Using Solomyak s method we also introduce the self-adjoint dilation of the maximal dissipative operator and incoming/outgoing eigenfunctions of the dilation. Moreover, we investigate other properties of the Cayley transform of the maximal dissipative operator.
Edelstein-Type Fixed Point Theorems in Compact Tvs-Cone Metric Spaces
(Hacettepe University, 2014) Abdeljawad, Thabet
In this paper we prove two fixed point theorems in compact cone metricspaces over normal cones. The first theorem generalizes Edelstein theorem [8] and is different from the generalization obtained in [11]. Thesecond theorem generalizes the main result in [10] and the first theorem.However, the two theorems fail in different categories. Moreover, different versions of the two theorems are proved in TVS-cone metric spacesby making use of the nonlinear scalarization function used very recentlyby Wei-Shih Du in [A note on cone metric fixed point theory and itsequivalence, Nonlinear Analysis,72(5),2259-2261 (2010).] to prove theequivalence of the Banach contraction principle in cone metric spacesand usual metric spaces.
Citation - Scopus: 4
Finite Groups All Whose Abelian Subgroups of Equal Order Are Conjugate
(2006) Sezer, Sezgin; Waall, Robert W. Van Der
In this paper we classify the finite groups whose abelian subgroups of equal order (B*-groups) are conjugate. The classification has been achieved by means of a lot of general structure properties of B*-groups, provided in the course of the paper.
Citation - WoS: 7
Citation - Scopus: 7
Fourth Order Differential Operators With Distributional Potentials
(Tubitak Scientific & Technological Research Council Turkey, 2020) Bairamov, Elgiz; Ugurlu, Ekin
In this paper, regular and singular fourth order differential operators with distributional potentials are investigated. In particular, existence and uniqueness of solutions of the fourth order differential equations are proved, deficiency indices theory of the corresponding minimal symmetric operators are studied. These symmetric operators are considered as acting on the single and direct sum Hilbert spaces. The latter one consists of three Hilbert spaces such that a squarely integrable space and two spaces of complex numbers. Moreover all maximal self-adjoint, maximal dissipative and maximal accumulative extensions of the minimal symmetric operators including direct sum operators are given in the single and direct sum Hilbert spaces.
Citation - WoS: 13
Citation - Scopus: 15
Hardy-Copson Type Inequalities for Nabla Time Scale Calculus
(Tubitak Scientific & Technological Research Council Turkey, 2021) Kaymakcalan, Billur; Kayar, Zeynep
This paper is devoted to the nabla unification of the discrete and continuous Hardy?Copson type inequalities. Some of the obtained inequalities are nabla counterparts of their delta versions while the others are new even for the discrete, continuous, and delta cases. Moreover, these dynamic inequalities not only generalize and unify the related ones in the literature but also improve them in the special cases.
Citation - WoS: 3
Citation - Scopus: 3
The Lebesgue Constants on Projective Spaces
(2021) Kushpel, Alexander
We give the solution of a classical problem of Approximation Theory on sharp asymptotic of the Lebesgueconstants or norms of the Fourier-Laplace projections on the real projective spaces Pd(R). In particular, these resultsextend sharp asymptotic found by Fejer [2] in the case of S1in 1910 and by Gronwall [4] in 1914 in the case of S2. Thecase of spheres, Sd, complex and quaternionic projective spaces, Pd(C), Pd(H) and the Cayley elliptic plane P16(Cay)was considered by Kushpel [8].
Citation - WoS: 3
Citation - Scopus: 3
Left-Definite Hamiltonian Systems and Corresponding Nested Circles
(Tubitak Scientific & Technological Research Council Turkey, 2023) Ugurlu, Ekin
This work aims to construct the Titchmarsh-Weyl M(A)-theory for an even-dimensional left-definite Hamiltonian system. For this purpose, we introduce a suitable Lagrange formula and selfadjoint boundary conditions including the spectral parameter A. Then we obtain circle equations having nesting properties. Using the intersection point belonging to all the circles we share a lower bound for the number of Dirichlet-integrable solutions of the system.
Citation - Scopus: 1
Linear Contrasts in One-Way Classification Ar(1) Model With Gamma Innovations
(Hacettepe Univ, Fac Sci, 2016) Senoglu, Birdal; Bayrak, Ozlem Turker
In this study, the explicit estimators of the model parameters in oneway classification AR(1) model with gamma innovations are derived by using modified maximum likelihood (MML) methodology. We also propose a new test statistic for testing linear contrasts. Monte Carlo simulation results show that the MML estimators have higher efficiencies than the traditional least squares (LS) estimators and the proposed test has much better power and robustness properties than the normal theory test.
Citation - WoS: 2
Citation - Scopus: 2
New Common Fixed Point Theorems of Greğus Type for R-Weakly Commuting Mappings in 2-Metric Spaces
(2009) Tas, Kenan; Murthy, P.p.
In this paper we extend and generalize a theorem of M.R. Singh, L. S. Singh and P.P. Murthy (Common fixed points of set valued mappings, Int. J. Math. Sci., 25 (6), 411–415, 2001) in a 2-metric space with a Gregu˘s type condition, and give some common fixed point theorems of set-valued maps in 2-metric spaces.
On a Fifth-Order Nonselfadjoint Boundary Value Problem
(Tubitak Scientific & Technological Research Council Turkey, 2021) Ugurlu, Ekin; Tas, Kenan
In this paper we aim to share a way to impose some nonselfadjoint boundary conditions for the solutions of a formally symmetric fifth-order differential equation. Constructing a dissipative operator related with the problem we obtain some informations on spectral properties of the problem. In particular, using coordinate-free approach we construct characteristic matrix-function related with the contraction which is obtained with the aid of the dissipative operator. In this paper we aim to share a way to impose some nonselfadjoint boundary conditions for the solutions of a formally symmetric fifth-order differential equation. Constructing a dissipative operator related with the problem we obtain some informations on spectral properties of the problem. In particular, using coordinate-free approach we construct characteristic matrix-function related with the contraction which is obtained with the aid of the dissipative
Citation - WoS: 5
Citation - Scopus: 5
On Some Fractional Operators Generated From Abel's Formula
(Tubitak Scientific & Technological Research Council Turkey, 2022) Ugurlu, Ekin
This work aims to share some fractional integrals and derivatives containing three real parameters. The main tool to introduce such operators is the corresponding Abel's equation. Solvability conditions for the Abel's equations are shared. Semigroup property for fractional integrals are introduced. Integration by parts rule is given. Moreover, mean value theorems and related results are shared. At the end of the paper, some directions for some fractional operators are given.
Citation - WoS: 10
Citation - Scopus: 9
On the Existence Interval for the Initial Value Problem of a Fractional Differential Equation
(Hacettepe Univ, Fac Sci, 2011) Mustafa, Octavian G.; Baleanu, Dumitru
We compute via a comparison function technique, a new bound for the existence interval of the initial value problem for a fractional differential equation given by means of Caputo derivatives. We improve in this way the estimate of the existence interval obtained very recently in the literature.

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