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Browsing by Author "Ersoy, Soley"

Browsing by Author "Ersoy, Soley"

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  • Algebraic Properties of Bihyperbolic Numbers 
    Bilgin, Merve; Ersoy, Soley (SPRINGER BASEL AG, 2020)
    In this paper, we study the four-dimensional real algebra of bihyperbolic numbers. Under consideration of the spectral representation of the bihyperbolic numbers, we give a partial order of bihyperbolic numbers which allows ...
  • Ball and Burmester points in Lorentzian sphere kinematics 
    Abdullah Inalcik; Ersoy, Soley (ACADEMIC PUBLICATION COUNCIL, 2015)
    In this work, we study Lorentzian spherical motion of rigid bodies by using instantaneous invariants and define Lorentzian inflection curve, Lorentzian circling points curve and Lorentzian cubic of twice stationary curve, ...
  • Beltrami-Meusnier formulas of generalized semi ruled surfaces in semi Euclidean space 
    Akyiğit, Mahmut; Ersoy, Soley; Tosun, Murat (ACADEMIC PUBLICATION COUNCIL, 2014)
    In this paper, we study the sectional curvatures of the generalized semi ruled surfaces in semi Euclidean space E-v(n+1). The first fundamental form and the metric coefficients of the generalized semi ruled surfaces are ...
  • Bobillier Formula for One Parameter Motions in the Complex Plane 
    Ersoy, Soley (ASME-AMER SOC MECHANICAL ENG, 2012)
    This is a brief note expanding on the aspect of Fayet (2002, "Bobillier Formula as a Fundamental Law in Planar Motion," Z. Angew. Math. Mech., 82(3), pp. 207-210), which investigates the Bobillier formula by considering ...
  • Bobillier Formula for the Elliptical Harmonic Motion 
    Furkan Semih Dundar; Ersoy, Soley; Nuno T. Sa Pereira (OVIDIUS UNIV PRESS, 2018)
    In this study, we have considered the elliptical harmonic motion which is the superposition of two simple harmonic motions in perpendicular directions with the same angular frequency and phase difference of pi/2. It is ...
  • Complex coupled dispersionless equations in Minkowski 3-space 
    Eren, Kemal; Ersoy, Soley (2022)
    In this study, we investigate the geometric and algebraic aspects of defocusing Complex Coupled Dispersionless (CCD) equations in Minkowski space. We give the conditions for obtaining CCD equations from moving spacelike ...
  • Dual Lorentzian spherical motions and dual Euler-Savary formula 
    Güngör, Mehmet Ali; Ersoy, Soley; Tosun, Murat (GAUTHIER-VILLARS/EDITIONS ELSEVIER, 2009)
    In this paper, defining one-parameter dual Lorentzian motion in three-dimensional dual Lorentzian space D(1)(3) and we have obtained the relations between the absolute, relative and sliding velocities of these motions. In ...
  • Elliptical Harmonic Motion and Euler-Savary Formula 
    Nuno T. Sa Pereira; Ersoy, Soley (SPRINGER BASEL AG, 2016)
    In this paper, we have introduced elliptical harmonic motion in terms of elliptical numbers. In addition, we have found the relationships between the absolute, the relative and the sliding velocities and accelerations of ...
  • En’de simetrik homotetik hareketler altında genelleştirilmiş regle yüzeylerin blaschke invaryantları 
    Ersoy, Soley (Sakarya Üniversitesi, 2004)
    ÖZET Anahtar Kelimeler: Öklid Uzayı, Regle Yüzey, Simetrik Homotetik Hareket, Blaschke İnvaryantı. Bu çalışma dört bölüm halinde düzenlenmiştir. Birinci bölümde E", «-boyutlu Öklid Uzayında 1 -parametreli hareketler ve 1 ...
  • Framed Curve Families Induced by Real and Complex Coupled Dispersionless-Type Equations 
    Popovic, Nikola; Eren, Kemal; Savic, Ana; Ersoy, Soley (MDPI, 2023)
    In this study, we investigate coupled real and complex dispersionless equations for curve families, even if they have singular points. Even though the connections with the differential equations and regular curves were ...
  • Fuzzy Mandelbrot sets 
    Ince, Ibrahim; Ersoy, Soley (2022)
    In this paper, we present a new approach to the Mandelbrot set via fuzzy set theory. We introduce and characterize the fuzzy Mandelbrot set by describing its membership function that determines the degrees of belonging of ...
  • GENERALIZED SPACELIKE BERTRAND CURVES IN MINKOWSKI 5-SPACE R-1(5) 
    Ersoy, Soley (NATL INQUIRY SERVICES CENTRE PTY LTD, 2014)
    In this paper, we give the definition of the generalization of spacelike Bertrand curves and obtain the characterization of these curves in Minkowski 5-space R-1(5). Moreover, we define three types special spacelike Bertrand ...
  • Generalized Timelike Mannheim Curves in Minkowski Space-Time E-1(4) 
    Özgür, İbrahim; Akyiğit, Mahmut; Ersoy, Soley; Tosun, Murat (HINDAWI PUBLISHING CORPORATION, 2011)
    We give the definition of generalized timelike Mannheim curve in Minkowski space-time E-1(4). The necessary and sufficient conditions for the generalized timelike Mannheim curve are obtained. We show some characterizations ...
  • Involute evolute curve family induced by the coupled dispersionless equations 
    Eren, Kemal; Yesmakhanova, Kuralay; Ersoy, Soley; Myrzakulov, Ratbay (2022)
    In this paper, we derive the coupled dispersionless (CD) equation from the motion of the involute evolute curve pairs, which provides a favourable interpretation for the integrability conditions. This nonlinear differential ...
  • IR",n-boyutlu Minkowski uzayında genelleştirilmiş regle yüzeylerin kesit eğrilikleri 
    Ersoy, Soley (Sakarya Üniversitesi, 2007)
    Anahtar Kelimeler: Minkowski uzayı, Regle yüzey, Kesit eğriliği, LorentzianBeltrami-Euler formülü, Lorentzian Beltrami-Meusnier formülü, Lorentzian Lamarleformülü.Bu tez bes bölümden olusmaktadır. Birinci bölüm giris kısmına ...
  • Lamarle formula in 3-dimensional Lorentz space 
    Ersoy, Soley; Tosun, Murat (UNIV OSIJEK, DEPT MATHEMATICS, 2011)
    The Lamarle Formula is known as a relationship between the Gaussian curvature and the distribution parameter (Drall) of a ruled surface in the surface theory, [12]. In R-1(3), the non-null ruled surfaces were investigated ...
  • On instantaneous invariants of hyperbolic planes 
    Abdullah Inalcik; Ersoy, Soley; Hellmuth Stachel (SAGE PUBLICATIONS LTD, 2017)
    In this study, we consider the kinematics of the hyperbolic plane and define the notions of inflection curve, circling-point curve, cubic of twice stationary curvature curve, and cubic of thrice stationary curve. We also ...
  • On simultaneous characterizations of partner-ruled surfaces in Minkowski 3-space 
    Li, Yanlin; Eren, Kemal; Ersoy, Soley (AMER INST MATHEMATICAL SCIENCES-AIMS, 2023)
    In this study, the partner-ruled surfaces in Minkowski 3-space, which are defined according to the Frenet vectors of non-null space curves, are introduced with extra conditions that guarantee the existence of definite ...
  • One-Parameter Homothetic Motion in the Hyperbolic Plane and Euler-Savary Formula 
    Ersoy, Soley; Akyiğit, Mahmut (SPRINGER BASEL AG, 2011)
    In [10] one-parameter planar motion was first introduced and the relations between absolute, relative, sliding velocities (and accelerations) in the Euclidean plane E-2 were obtained. Moreover, the relations between the ...
  • Revisiting Burmester theory with complex forms of Bottema's instantaneous invariants 
    K. Eren; Ersoy, Soley (TAYLOR & FRANCIS LTD, 2017)
    The objective of this study is to take advantage of using the concept of complex numbers for instantaneous geometric properties of planar motion of rigid bodies. We consider that both the fixed and the moving planes are ...