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Öğe Spline based sparseness and smoothness for partially nonlinear model via c-fused lasso(American Institute of Mathematical Sciences, 2025) Taylan, Pakize; Özkurt, Fatma Yerlikaya; Tez, MüjganOne of the most beneficial and widely used models for data analysis are partially nonlinear models (PNLRM), which consists of parametric and nonparametric components. Since the model includes the coefficients of both the parametric and nonparametric parts, the complexity of the model will be high and its interpretation will be very difficult. In this study, we propose a procedure that not only achieves sparseness, but also smoothness for PNLRM to obtain a simpler model that better explains the relationship between the response and covariates. Thus, the fused Lasso problem is taken into account where nonparametric components are expressed as a spline basis function, and then the Fused Lasso estimation problem is built and expressed in terms of conic quadratic programming. Applications are conducted to evaluate the performance of the proposed method by considering commonly utilized measures. Promising results are obtained, especially in the data with nonlinearly correlated variables.Öğe Clairaut semi-invariant riemannian maps to kähler manifolds(Birkhauser, 2024) Polat, Murat; Meena, KiranIn this paper, first, we recall the notion of Clairaut Riemannian map (CRM) F using a geodesic curve on the base manifold and give the Ricci equation. We also show that if base manifold of CRM is space form then leaves of (kerF∗)⊥ become space forms and symmetric as well. Secondly, we define Clairaut semi-invariant Riemannian map (CSIRM) from a Riemannian manifold (M,gM) to a Kähler manifold (N,gN,P) with a non-trivial example. We find necessary and sufficient conditions for a curve on the base manifold of semi-invariant Riemannian map (SIRM) to be geodesic. Further, we obtain necessary and sufficient conditions for a SIRM to be CSIRM. Moreover, we find necessary and sufficient condition for CSIRM to be harmonic and totally geodesic. In addition, we find necessary and sufficient condition for the distributions D1¯ and D2¯ of (kerF∗)⊥ (which are arisen from the definition of CSIRM) to define totally geodesic foliations. Finally, we obtain necessary and sufficient conditions for (kerF∗)⊥ and base manifold to be locally product manifold D1¯×D2¯ and (rangeF∗)×(rangeF∗)⊥, respectively.Öğe Some m-fold symmetric bi-univalent function classes and their associated Taylor-Maclaurin coefficient bounds(Springer Nature, 2024) Srivastava, Hari Mohan; Sabır, Pishtiwan Othman; Eker, Sevtap Sümer; Wanas, Abbas Kareem; Mohammed, Pshtiwan Othman; Chorfi, Nejmeddine; Baleanu, DumitruThe Ruscheweyh derivative operator is used in this paper to introduce and investigate interesting general subclasses of the function class ?m of m-fold symmetric bi-univalent analytic functions. Estimates of the initial Taylor-Maclaurin coefficients |am+1| and |a2m+1| are obtained for functions of the subclasses introduced in this study, and the consequences of the results are discussed. Additionally, the Fekete-Szegö inequalities for these classes are investigated. The results presented could generalize and improve some recent and earlier works. In some cases, our estimates are better than the existing coefficient bounds. Furthermore, within the engineering domain, the utilization of the Ruscheweyh derivative operator can encompass a broad spectrum of engineering applications, including the robotic manipulation control, optimizing optical systems, antenna array signal processing, image compression, and control system filter design. It emphasizes the potential for innovative solutions that can significantly enhance the reliability and effectiveness of engineering applications.Öğe B. Y. Chen-Ricci inequalities for anti-invariant Riemannian submersions in Kenmotsu space forms(Springer Heidelberg, 2024) Polat, MuratThe aim of the present paper is to analyze sharp type inequalities including the scalar and Ricci curvatures of anti-invariant Riemannian submersions in Kenmotsu space forms K-s(epsilon). We give non-trivial examples for anti-invariant Riemannian submersions, investigate some curvature relations between the total space and fibres according to vertical and horizontal cases of xi. Moreover, we acquire Chen-Ricci inequalities on the ker theta(*) and (ker theta(*))(perpendicular to) distributions for anti-invariant Riemannian submersions from Kenmotsu space forms according to vertical and horizontal cases of xi.Öğe CG-lasso estimator for multivariate adaptive regression spline(Springer International Publishing Ag, 2019) Taylan, Pakize; Weber, Gerhard Wilhelm[Abstract Not Available]Öğe New integral operator for analytic functions(Hindawi Limited, 2024) Güney, Hatun Özlem; Owa, Shigeyoshi; Attiya, Adel A.Let Apn be the class of functions fz given by fz=zp+ap+nzp+n+ap+n+1zp+n+1+⋯ which are analytic in the open unit disk U. For fz∈Apn, new integral operators O-jfz and Ojfzj=0,1,2,⋯. are considered. The operators O-jfz and Ojfz satisfy OjO-jfz=O-jOjfz=fz and O-j∗Ojfz=Oj∗O-jfz=f∗fz for the convolution ∗ of O-jfz and Ojfz. In the present paper, the dominants for both operators O-jfz and Ojfz and subordinations for O-jfz and Ojfz are discussed. Also, new subclass Tpγm,δ,ρ;m,j concerning with m different boundary points is defined and discussed. Moreover, some interesting problems of Tpγm,δ,ρ;m,j associated with Ojfz are obtained. Furthermore, some interesting examples for our results are considered.Öğe New computational methods for classification problems in the existence of outliers based on conic quadratic optimization(Taylor and Francis Inc., 2020) Özkurt, Fatma Yerlikaya; Taylan, PakizeMost of the statistical research involves classification which is a procedure utilized to establish prediction models to set apart and classify new observations in the dataset from every fields of science, technology, and economics. However, these models may give misclassification results when dataset contains outliers (extreme data points). Therefore, we dealt with outliers in classification problem: firstly, by combining robustness of mean-shift outlier model and then stability of Tikhonov regularization based on continuous optimization method called Conic Quadratic Programming. These new methodologies are performed on classification dataset within the existence of outliers, and the results are compared with parametric model by using well-known performance measures.Öğe On global solutions for the Cauchy problem of a Boussinesq-type equation(2012) Taşkesen, Hatice; Polat, Necat; Ertaş, AbdulkadirWe will give conditions which will guarantee the existence of global weak solutions of the Boussinesq-type equation with power-type nonlinearity γ|u| p and supercritical initial energy. By defining new functionals and using potential well method, we readdressed the initial value problem of the Boussinesq-type equation for the supercritical initial energy case.Öğe Estimation in the partially nonlinear model by continuous optimization(Taylor and Francis Ltd., 2021) Özkurt, Fatma Yerlikaya; Taylan, Pakize; Tez, MüjganA useful model for data analysis is the partially nonlinear model where response variable is represented as the sum of a nonparametric and a parametric component. In this study, we propose a new procedure for estimating the parameters in the partially nonlinear models. Therefore, we consider penalized profile nonlinear least square problem where nonparametric components are expressed as a B-spline basis function, and then estimation problem is expressed in terms of conic quadratic programming which is a continuous optimization problem and solved interior point method. An application study is conducted to evaluate the performance of the proposed method by considering some well-known performance measures. The results are compared against parametric nonlinear model.Öğe On ?-pseudo bi-starlike functions related with Fibonacci numbers(Episciences, 2024) Vijaya, Kaliyappan; Murugusundaramoorthy, Gangadharan; Güney, Hatun ÖzlemIn this paper we define a new subclass λ-bi-pseudo-starlike functions of Σ related to shell-like curves connected with Fibonacci numbers and determine the initial Taylor-Maclaurin coefficients |a2| and |a3| for f. Further we determine the Fekete-Szegö result for the function class and for special cases, corollaries are stated which some of them are new and have not been studied so far.Öğe Coefficient bounds and Fekete–Szegö Inequality for a new family of bi-univalent functions defined by Horadam polynomials(Springer Science and Business Media Deutschland GmbH, 2022) Wanas, Abbas Kareem; Güney, Hatun ÖzlemIn the current article, we introduce and investigate a new family KΣ(δ, λ, x) of analytic and bi-univalent functions by using the Horadam polynomials defined in the open unit disk U. We determine upper bounds for the initial Taylor–Maclaurin coefficients. Further we obtain the Fekete–Szegö inequality of functions belonging to this family. We also point out several certain special cases for our results.Öğe A strong-form meshfree computational method for plane elastostatic equations of anisotropic functionally graded materials via multiple-scale Pascal polynomials(Elsevier Ltd., 2023) Oruç, ÖmerA strong-form meshfree method is proposed for solving plane elastostatic equations of anisotropic functionally graded materials. Any general function may be the grading function and it is changing smoothly from location to location in the material. The proposed method is based on Pascal polynomial basis and multiple-scale technique and it is a genuinely meshfree method since no numerical integrations over domains and meshing processes are required for considered problems. Implementation of the proposed method is straightforward and the method gives very accurate results. Stability of the solutions are examined numerically in occurrence of random noise. Some certain test problems with known exact solutions are solved both on regular and irregular geometries. Acquired solutions by the suggested method are compared with the exact solutions as well as with solutions of some existing numerical techniques in literature, such as boundary element, meshless local Petrov–Galerkin and radial basis function based meshless methods, to show accuracy of the proposed method.Öğe Arf numerical semigroups(TUBITAK, 2017) İlhan, Sedat; Karakaş, Hali̇l İbrahi̇mThe aim of this work is to exhibit the relationship between the Arf closure of a numerical semigroup S and its Lipman semigroup L(S). This relationship is then used to give direct proofs of some characterizations of Arf numerical semigroups through their Lipman sequences of semigroups. We also give an algorithmic construction of the Arf closure of a numerical semigroup via its Lipman sequence of semigroups.Öğe Counting components of an integral lamination(Springer New York LLC, 2017) Yurttaş, S. Öykü; Hall, TobyWe present an efficient algorithm for calculating the number of components of an integral lamination on an n-punctured disk, given its Dynnikov coordinates. The algorithm requires O(n2M) arithmetic operations, where M is the sum of the absolute values of the Dynnikov coordinates.Öğe The second hankel determinant of logarithmic coefficients for Strongly Ozaki close-to-convex functions(Springer, 2023) Eker, Sevtap Sümer; Lecko, Adam; Çekiç, Bilal; Şeker, BilalThe aim of this paper is to determine sharp bound for the second Hankel determinant of logarithmic coefficients H2 , 1(Ff/ 2) of strongly Ozaki close-to-convex functions in the open unit disk. Furthermore, sharp bound of H2,1(Ff-1/2) , where f- 1 is the inverse function of f, is also computed. The results show an invariance property of the second Hankel determinants of logarithmic coefficients H2 , 1(Ff/ 2) and H2,1(Ff-1/2) for strongly convex functions.Öğe Sonlu noktası çıkarılmış disk üzerindeki örgüler(Bitlis Eren Üniversitesi, 2020) Meral, Alev; Demirtaş, MeryemÖrgüler, düğüm teorisi, düşük boyutlu topoloji, sayı teorisi, cebirsel geometri, geometrik grup teorisi, cebirsel topoloji ve matematiksel fizik gibi birçok alanda önemli bir rol oynamaktadır. Örgü grupları ayrıca, kriptoloji, robotik, akışkan dinamikleri ve moleküler biyoloji gibi çoğu uygulamalı alanda çok geniş bir role sahiptir. Bu çalışmada geometrik örgü grup yapısı ele alınmıştır. Sonlu noktası çıkarılmış bir disk üzerindeki yön koruyan homeomorfizmaların izotopi sınıfları örgülerle temsil edilmektedir. Çalışmada amaç geometrik örgülerle ilgili genel özellikleri vermek, okuyucuya geometrik örgülerin grup yapısı, izotopi sınıfları ve disk üzerindeki bir geometrik örgünün bir Gönderim Sınıf Grubu (MCG)’na nasıl doğal olarak izomorfik olduğunu açıklamaktır.Öğe Blow-up phenomena and stability of solitary waves for a generalized Dullin-Gottwald-Holm equation(Springer, 2013) Dündar, Nurhan; Polat, NecatIn this work, we consider the Cauchy problem of the generalized Dullin-Gottwald-Holm equation. We establish a blow-up result for the generalized Dullin-Gottwald-Holm equation. In addition to this, we investigate the stability of solitary wave solutions of the equation.Öğe On a new subclass of bi-univalent functions defined by using Salagean operator(TUBITAK, 2018) Şeker, BilalIn this manuscript, by using the Salagean operator, new subclasses of bi-univalent functions in the open unit disk are defined. Moreover, for functions belonging to these new subclasses, upper bounds for the second and third coefficients are found.Öğe Clairaut pointwise slant submersions from locally product riemannian manifolds(DergiPark, 2023) Polat, MuratIn this paper, we consider pointwise slant submersions from locally product Riemannian manifolds. We first give a necessary and sufficient condition for a curve on the total manifold to be a geodesic and then focus investigate new Clairaut conditions for considered submersion. In a main theorem, we find a new necessary and sufficient condition for a pointwise slant submersion to be Clairaut in case of its total manifold is locally product Riemannian manifold. Finally, we present an illustrative example for this kind of submersion which satisfies Clairaut condition.Öğe Clairaut semi invariant submersions from locally product Riemannian manifolds(Erzincan Binali Yıldırım Üniversitesi, Fen Bilimleri Enstitüsü, 2023) Polat, MuratThe purpose of this article is to analyze geometric features of Clairaut semi-invariant Riemannian submersions whose total manifolds are locally product Riemannian manifold and investigate fundamental results on such submersion. We also ensure an explicit example of Clairaut semi-invariant Riemannian submersion.
