Now showing items 1-20 of 23

    • On the eigenvalues and eigenvectors of a lorentzian rotation matrix by using split quaternions 

      Özdemir, Mustafa; Erdoğdu, Melek; Şimşek, Hakan (Advances in Applied Clifford Algebras, 2014)
      In this paper, we examine eigenvalue problem of a rotation matrix in Minkowski 3 space by using split quaternions. We express the eigenvalues and the eigenvectors of a rotation matrix in term of the coefficients of the ...
    • Similar and self-similar curves in minkowski n-space 

      Şimşek, Hakan; Özdemir, Mustafa (Bulletin of Korean Mathematical Society, 2015)
      In this paper, we investigate the similarity transformations in the Minkowski n-space. We study the geometric invariants of nonnull curves under the similarity transformations. Besides, we extend the fundamental theorem ...
    • Generating hyperbolical rotation matrix for a given hyperboloid 

      Şimşek, Hakan; Özdemir, Mustafa (Linear Algebra and Its Applications, 2016)
      Hyperbolic rotation is hyperbolically the motion of a smooth object on general hyperboloids given by −a1x2+a2y2+a3z2=±λ, λ ∈R+. In this paper, we investigate the hyperbolical rotation matrices in order to get the motion ...
    • On conformal curves in 2-dimensional de sitter space 

      Şimşek, Hakan; Özdemir, Mustafa (Advances in Applied Clifford Algebras, 2016)
      In this paper, we examine the pseudo-spherical curves, which are equivalent to each other under the conformal maps preserving a fixed point in the de Sitter 2-space, by using the Clifford algebra Cl 2,1. Also, we find the ...
    • Bäcklund’s theorem for n dimensional lorentzian submanifold in the minkowski space 𝔼21𝑛−1 

      Şimşek, Hakan; Özdemir, Mustafa (Results in Mathematics, 2016)
      In this paper, Bäcklund’s Theorem is introduced on the Lorentzian n-submanifold of the Minkowski space 𝔼2𝑛−11 by using the method of moving frames. Also, we prove the Integrability Theorem for the Lorentzian n-submanifold ...
    • On focal curves of null Cartan curves 

      Şimşek, Hakan (Turkish Journal of Mathematics, 2017)
      The focal curve, which is determined as the locus of centers of osculating pseudo-spheres of a null Cartan curve, is investigated in Minkowski (n+2)-space Mn+2. Moreover, a curve called acceleration focal curve of a null ...
    • Rotations on a lightcone in minkowski 3-Space 

      Şimşek, Hakan; Özdemir, Mustafa (Advances in Applied Clifford Algebras, Springer, 2017)
      In this paper the generalization of the rotations on any lightcone in Minkowski 3-space ℝ1,2𝑔 is given. The rotation motion on the lightcone is examined by means of a bilinear form and Lorentzian notions. We use the ...
    • Shape curvatures of the Lorentzian plane curves 

      Şimşek, Hakan; Özdemir, Mustafa (Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 2017)
      In this paper, we examine the Lorentzian similar plane curvesusing the hyperbolic structure and spherical arc length parameter. We classifyall self-similar Lorentzian plane curves and give formulas for pseudo shapecurvatures ...
    • Computational bifurcation analysis to find dynamic transitions of the corticotroph model 

      Şengül Ayan, Sevgi; Kurt, Ahmet (Ankara University Faculty of Sciences, 2018)
      The corticotroph model is a 7th order nonlinear differential equation system derived for representing the action potential dynamics of corticotrophs; one of the endocrine cells that are responsible for stress regulation. ...
    • Some results on p-shape curvatures of non-lightlike space curves 

      Şimşek, Hakan; Özdemir, Mustafa (International Electronic Journal of Geometry, 2018)
      In this paper, we obtain some findings for a non-null curve parameterized by spherical arc length. We investigate the relationship between a non-null curve with p-shape curvatures and pseudospherical curves on S21 and ...
    • A cost-effective framework for the optimal placement of drones in smart cities 

      Ülgen, Semail; Al-Turjman, Fadi; Daboul, Reda; Zahmatkesh, Hadi (CRC Press, 2019)
      This chapter presents the existing studies related to the use of unmanned aerial vehicles in the internet of things era. It outlines problem description and the proposed framework. The chapter discusses the performance ...
    • Investigation of the effects of IMPULS Maturity model with a simulation-based analysis 

      Altan, Cansu; Başarır, Ali Cem; Aydemir, Erdal (10th International Symposium onIntelligent Manufacturing and Service Systems, 2019)
      Industry 4.0 enables to produce products that are complex in production in a short time and in high quality by entering factories and making our production environments smarter. Industry 4.0 is defined as the digitization ...
    • Modeling and analyzing Ca2+ channel dynamics during cardiac action potential 

      Şengül Ayan, Sevgi; Sırcan, Ahmet K.; Kurt, Ahmet; Özdoğan, Hasan (International Conference on Applied Analysis and Mathematical Modeling, 2019)
      We have studied the cardiac action potential model which consists of 26 nonlinear first-order differential equations in a detailed manner computationally. Later, it has been discussed what is the role of the Ca2+ ion channel ...
    • Effects of neuronal noise on neural communication 

      Gençağa, Deniz; Şengül Ayan, Sevgi (Proceedings, 2019)
      In this work, we propose an approach to better understand the effects of neuronal noise on neural communication systems. Here, we extend the fundamental Hodgkin-Huxley (HH) model by adding synaptic couplings to represent ...
    • Analysis of parameter changes of a neuronal network model using transfer entropy 

      Şengül Ayan, Sevgi; Gençağa, Deniz (International Advanced Researches and Engineering Journal, 2020)
      Understanding the dynamics of coupled neurons is one of the fundamental problems in the analysis of neuronal model dynamics. The transfer entropy (TE) method is one of the primary analyses to explore the information flow ...
    • Mathematical model of the ventricular action potential and effects of isoproterenol-induced cardiac hypertrophy in rats 

      Şengül Ayan, Sevgi; Sırcan, Ahmet K.; Abewa, Mohamedou; Kurt, Ahmet; Dalaman, Uğur; Yaraş, Nazmi (European Biophysics Journal, 2020)
      Mathematical action potential (AP) modeling is a well-established but still-developing area of research to better understand physiological and pathological processes. In particular, changes in AP mechanisms in the isoproterenol ...
    • Mazeret/telafi sınavı çizelgeleme problemi için bir hedef programlama modeli 

      Saraç, Tuğba; Özçelik, Feristah; Erdoğan, Hatice (Pamukkale Üniversitesi Mühendislik Bilimleri Dergisi, 2020)
      In the universities and other educational institutions, make-up/compensation examinations are made for students who cannot take the exam at the scheduled exam periods due to examinations, health problems and so on. Especially ...
    • Statistical approaches for the analysis of dependency among neurons under noise 

      Gençağa, Deniz; Şengül Ayan, Sevgi; Farnoudkia, Hajar; Okuyucu, Serdar (MDPI, 2020)
      Neuronal noise is a major factor affecting the communication between coupled neurons. In this work, we propose a statistical toolset to infer the coupling between two neurons under noise. We estimate these statistical ...
    • Quantitative roles of ion channel dynamics on ventricular action potential 

      Sırcan, Ahmet Kürşad; Şengül Ayan, Sevgi (Channels, 2021)
      Mathematical models for the action potential (AP) generation of the electrically excitable cells including the heart are involved different mechanisms including the voltage-dependent currents with nonlinear time- and ...
    • Analysis of public transportation for efficiency 

      Özgün, Kamer; Günay, Melih; Başaran, Barış Doruk; Bulut, Batuhan; Yürüten, Ege; Baysan, Fatih; Kalemsiz, Melisa (Springer, 2021)
      Transit authorities have been searching for the indicators to measure transit service quality and the key factors to attract citizens who do not prefer public transport. The recent advent of data collection technologies ...