Matematik ve Bilgisayar Bölümü / Department of Mathematics and Computer Science

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  • Publication
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    A Survey on the Theory of Integral and Related Operators in Geometric Function Theory
    (Springer, 2021) Ahuja, Om P.; ÇETİNKAYA, ASENA
    A brief tour of more than one hundred years of the historical development of some of the popular integral and related operators in Geometric Function Theory (GFT) is given in this article. The strengths and discovery of the methods used in these operators lie in their ability to unify a large number of diverse operators and results. We also address some of the q- analogues of the integral operators in GFT. Since there are several surveys and books in GFT, we present here only a selection of the results related to our precise objectives. © 2021, The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.
  • Publication
    Metadata only
    Unique Recovery of Unknown Spatial Load in Damped Euler-Bernoulli Beam Equation From Final Time Measured Output
    (IOP Publishing Ltd., 2021) Hasanov, Alemdar; Romanov, Vladimir; BAYSAL, ONUR
    In this paper we discuss the unique determination of unknown spatial load F(x) in the damped Euler-Bernoulli beam equation rho(x)u(tt)+mu u(t)+(r(x)u(xx))(xx)=F(x)G(t) 0, the damping coefficient mu > 0 and the temporal load G(t) > 0. As an alternative method we propose the adjoint problem approach (APA) and derive an explicit gradient formula for the Frechet derivative of the Tikhonov functional J(F)=parallel to u(.,T; F) - u(T)parallel to(2)(L2(0,l)). Comparative analysis of numerical algorithms based on SVE and APA methods are provided for the harmonic loading G(t) = cos(omega t), omega > 0, as a most common dynamic loading case. The results presented in this paper not only clearly demonstrate the key role of the damping term mu u (t) in the inverse problems arising in vibration and wave phenomena, but also allows us, firstly, to find admissible values of the final time T > 0, at which a final time measured output can be extracted, and secondly, to reconstruct the unknown spatial load F(x) in the damped Euler-Bernoulli beam equation from this measured output.
  • Publication
    Open Access
    On Ramsey Dynamical Model and Closed-Form Solutions
    (Springer Nature, 2021) POLAT, GÜLDEN GÜN; Özer, Teoman
    This study focuses on the analysis of Ramsey dynamical model with current Hamiltonian defining an optimal control problem in a neoclassical growth model by utilizing Lie group theory. Lie point symmetries of coupled nonlinear first-order ordinary differential equations corresponding to first-order conditions of maximum principle are analyzed and then first integrals and corresponding closed-form (analytical) solutions are determined by using Lie point symmetries in conjunction with Prelle-Singer and Jacobi last multiplier methods. Additionally, associated lambda-symmetries, adjoint symmetries, Darboux polynomials, and the properties of the model are represented.
  • Publication
    Restricted
    Univalent Functions Associated with the Symmetric Points and Cardioid-shaped Domain Involving (p,q)-Calculus
    (Kyungpook Natl Univ, Dept Mathematics, 2021) Ahuja, Om; Bohra, Nisha; ÇETİNKAYA, ASENA; Kumar, Sushil
    In this paper, we introduce new classes of post-quantum or (p, q)-starlike and convex functions with respect to symmetric points associated with a cardiod-shaped domain. We obtain (p,q)-Fekete-Szego inequalities for functions in these classes. We also obtain estimates of initial (p, q)-logarithmic coefficients. In addition, we get q-Bieberbachde-Branges type inequalities for the special case of our classes when p = 1. Moreover, we also discuss some special cases of the obtained results.
  • Publication
    Open Access
    Completely Monotonic Ratios of Basic and Ordinary Gamma Functions
    (Springer Basel AG, 2021) Berg, Christian; ÇETİNKAYA, ASENA; Karp, Dmitrii
    Objective: In this study, it was planned to examine fatigue, well-being and life habits in children with cancer. Methods: This cross-sectional analytical study was conducted between September 2019-January 2020. "24-Hour Child Fatigue Scale", "Child Well-being Assessment" and Child Life Habit Questionnaire (LIFE-H for Children 1.0)" were administered to 20 children with cancer aged 5-15 years. Pearson's correlation coefficient was used to determine the statistical relationship between life habits, fatigue and well-being. Statistical significance level was accepted as p<0.05. Results: There were significant relationships between fatigue and personal care, shelter and mobility parameters of life habits (r=-0.66, r=0.54, r=0.45, p<0.01, respectively) and there were significant relationships between fatigue and negative emotions (r=0.46), overall life satisfaction (r=-0.52), general happiness (r=-0.49) and positive emotions (r=-0.44 *) parameters of well-being assessment. Life habits scale was found to be related with nutrition, physical fitness and communication parameters of Child Life Habit Questionnaire were found to be most related with the meaning and purpose parameter of the well-being assessment (p<0.01). There were significant relationships between positive emotions and recreation (r=0.45, p=0.04); optimism and communication (r=-0.44, p=0.04); personal care (r=-0.49, p=0, 02), social life (r=-0.46, p=0.04) and autonomy; and mobility and negative emotions (r=-0.45, p=0.04). Conclusion: Considering the relationships determined in this study, the evaluation of the children with cancer and treatment approaches can be shaped. The fact that fatigue affects all aspects of children's life reveals the importance of dealing with fatigue. It is recommended to focus on the meaning and purpose and regain autonomy for children in order to rearrange the life habits of the children and ensure their well-being.