Research Article
BibTex RIS Cite

PLANE KINEMATICS IN LORENTZIAN HOMOTHETIC MULTIPLICATIVE CALCULUS

Year 2024, , 64 - 74, 31.07.2024
https://doi.org/10.33773/jum.1411844

Abstract

In this study, Lorentzian plane homothetic multiplicative calculus kinematics is discussed.
Lorentzian plane homothetic multiplicative calculus movement, the pole points of a point X relative to
the moving and fixed plane are discussed. In this motion, the velocities and accelerations of a point
X are obtained. In this motion, the relations between the velocities and accelerations of a point X are
obtained. In addition, new theorems and results are given.

References

  • V. Volterra, B. Hostinsky, Operations Innitesimales Lineares. Herman, Paris (1938).
  • D. Aniszewska, Multiplicative Runge-Kutta Methods. Nonlinear Dynamics Vol.50, pp.262-272 (2007).
  • W. Kasprzak, B. Lysik, M. Rybaczuk, Dimensions, Invariants Models and Fractals, Ukrainian Society on Fracture Mechanics, Spolom, Wroclaw-Lviv, Poland (2004).
  • M. Rybaczuk, A. Kedzia, W. Zielinski, The concepts of physical and fractional dimensions 2. The differential calculus in dimensional spaces, Chaos Solitons Fractals Vol.12, pp.2537-2552 (2001).
  • M. Grossman, R. Katz, Non-Newtonian Calculus, Lee Press, Piegon Cove, Massachusetts (1972).
  • D. Stanley, A multiplicative calculus, Primus IX, Vol.4, pp.310-326 (1999).
  • A. E. Bashirov, E. M. Kurpınar, A. Ozyapici, Multiplicative Calculus and its applications, J. Math. Anal. Appl. Vol.337, pp.36-48 (2008).
  • S. Aslan, M. Bekar, Y. Yaylı, Geometric 3-space and multiplicative quaternions, International Journal 1 of Geometric Methods in Modern Physics, Vol.20, No.9 (2023).
  • S. Nurkan, K., I. Gürgil, M. K., Karacan, Vector properties of geometric calculus, Math. Meth. Appl. Sci., pp.1-20 (2023).
  • H. Es, On The 1-Parameter Motions With Multiplicative Calculus, Journal of Science and Arts, Vol.2, No.59 (2022).
  • A. E. Bashirov, M. Rıza, On Complex multiplicative differentiation, TWMS J. App. Eng. Math. Vol.1, No.1, pp.75-85 (2011).
  • A. E. Bashirov, E. Mısırlı, Y. Tandoğdu, A. Ozyapıcı, On modeling with multiplicative differential equations, Appl. Math. J. Chinese Univ. Vol.26, No.4, pp.425-438 (2011).
  • A. E. Bashirov, E. M. Kurpınar, A. Ozyapici, Multiplicative Calculus and its applications, J. Math. Anal. Appl. Vol.337, pp.36-48 (2008).
  • K. Boruah and B. Hazarika, Application of Geometric Calculus in Numerical Analysis and Difference Sequence Spaces, arXiv:1603.09479v1 (2016).
  • K. Boruah and B. Hazarika, Some basic properties of G-Calculus and its applications in numerical analysis, arXiv:1607.07749v1(2016).
  • A. F. Çakmak, F. Başar, On Classical sequence spaces and non-Newtonian calculus, J. Inequal. Appl. 2012, Art. ID 932734, 12 pages (2012).
  • E. Misirli and Y. Gurefe, Multiplicative Adams BashfortMoulton methods, Numer Algor, Vol.57, pp.425-439(2011).
  • A. F. Çakmak, F. Başar, Some sequence spaces and matrix transformations in multiplicative sense, TWMS J. Pure Appl. Math. Vol.6, No.1, pp.27-37 (2015).
  • D. Campbell, Multiplicative Calculus and Student Projects, Vol.9, No.4, pp.327-333 (1999)
  • M. Coco, Multiplicative Calculus, Lynchburg College, Vol.9, No.4, pp.327-333 (2009).
  • M. Grossman, Bigeometric Calculus: A System with a scale-Free Derivative, Archimedes Foundation, Massachusetts (1983).
  • M. Grossman, An Introduction to non-Newtonian calculus, Int. J. Math. Educ. Sci. Technol., Vol.10, No.4, pp.525-528 (1979).
  • J. Grossman, M. Grossman, R. Katz, The First Systems of Weighted Differential and Integral Calculus, University of Michigan (1981).
  • J. Grossman, Meta-Calculus: Differential and Integral, University of Michigan (1981).
  • Y. Gurefe, Multiplicative Differential Equations and Its Applications, Ph.D. in Department of Mathematics (2013).
  • W. F. Samuelson, S.G. Mark, Managerial Economics, Seventh Edition (2012).
  • S. Tekin, F. Başar, Certain Sequence spaces over the non-Newtonian complexeld, Abstr. Appl. Anal. Article ID 739319, 11 pages (2013).
  • C. Türkmen and F. Başar, Some Basic Results on the sets of Sequences with Geometric Calculus, Commun. Fac. Fci. Univ. Ank. Series A1., Vol.61, No.2, pp.17-34 (2012).
  • A. Uzer, Multiplicative type Complex Calculus as an alternative to the classical calculus, Comput. Math. Appl. Vol.60, pp.2725-2737 (2010).
  • K. Boruah and B. Hazarika, G-Calculus, TWMS J. App. Eng. Math., Vol.8, No.1, pp.94-105 (2018)
Year 2024, , 64 - 74, 31.07.2024
https://doi.org/10.33773/jum.1411844

Abstract

References

  • V. Volterra, B. Hostinsky, Operations Innitesimales Lineares. Herman, Paris (1938).
  • D. Aniszewska, Multiplicative Runge-Kutta Methods. Nonlinear Dynamics Vol.50, pp.262-272 (2007).
  • W. Kasprzak, B. Lysik, M. Rybaczuk, Dimensions, Invariants Models and Fractals, Ukrainian Society on Fracture Mechanics, Spolom, Wroclaw-Lviv, Poland (2004).
  • M. Rybaczuk, A. Kedzia, W. Zielinski, The concepts of physical and fractional dimensions 2. The differential calculus in dimensional spaces, Chaos Solitons Fractals Vol.12, pp.2537-2552 (2001).
  • M. Grossman, R. Katz, Non-Newtonian Calculus, Lee Press, Piegon Cove, Massachusetts (1972).
  • D. Stanley, A multiplicative calculus, Primus IX, Vol.4, pp.310-326 (1999).
  • A. E. Bashirov, E. M. Kurpınar, A. Ozyapici, Multiplicative Calculus and its applications, J. Math. Anal. Appl. Vol.337, pp.36-48 (2008).
  • S. Aslan, M. Bekar, Y. Yaylı, Geometric 3-space and multiplicative quaternions, International Journal 1 of Geometric Methods in Modern Physics, Vol.20, No.9 (2023).
  • S. Nurkan, K., I. Gürgil, M. K., Karacan, Vector properties of geometric calculus, Math. Meth. Appl. Sci., pp.1-20 (2023).
  • H. Es, On The 1-Parameter Motions With Multiplicative Calculus, Journal of Science and Arts, Vol.2, No.59 (2022).
  • A. E. Bashirov, M. Rıza, On Complex multiplicative differentiation, TWMS J. App. Eng. Math. Vol.1, No.1, pp.75-85 (2011).
  • A. E. Bashirov, E. Mısırlı, Y. Tandoğdu, A. Ozyapıcı, On modeling with multiplicative differential equations, Appl. Math. J. Chinese Univ. Vol.26, No.4, pp.425-438 (2011).
  • A. E. Bashirov, E. M. Kurpınar, A. Ozyapici, Multiplicative Calculus and its applications, J. Math. Anal. Appl. Vol.337, pp.36-48 (2008).
  • K. Boruah and B. Hazarika, Application of Geometric Calculus in Numerical Analysis and Difference Sequence Spaces, arXiv:1603.09479v1 (2016).
  • K. Boruah and B. Hazarika, Some basic properties of G-Calculus and its applications in numerical analysis, arXiv:1607.07749v1(2016).
  • A. F. Çakmak, F. Başar, On Classical sequence spaces and non-Newtonian calculus, J. Inequal. Appl. 2012, Art. ID 932734, 12 pages (2012).
  • E. Misirli and Y. Gurefe, Multiplicative Adams BashfortMoulton methods, Numer Algor, Vol.57, pp.425-439(2011).
  • A. F. Çakmak, F. Başar, Some sequence spaces and matrix transformations in multiplicative sense, TWMS J. Pure Appl. Math. Vol.6, No.1, pp.27-37 (2015).
  • D. Campbell, Multiplicative Calculus and Student Projects, Vol.9, No.4, pp.327-333 (1999)
  • M. Coco, Multiplicative Calculus, Lynchburg College, Vol.9, No.4, pp.327-333 (2009).
  • M. Grossman, Bigeometric Calculus: A System with a scale-Free Derivative, Archimedes Foundation, Massachusetts (1983).
  • M. Grossman, An Introduction to non-Newtonian calculus, Int. J. Math. Educ. Sci. Technol., Vol.10, No.4, pp.525-528 (1979).
  • J. Grossman, M. Grossman, R. Katz, The First Systems of Weighted Differential and Integral Calculus, University of Michigan (1981).
  • J. Grossman, Meta-Calculus: Differential and Integral, University of Michigan (1981).
  • Y. Gurefe, Multiplicative Differential Equations and Its Applications, Ph.D. in Department of Mathematics (2013).
  • W. F. Samuelson, S.G. Mark, Managerial Economics, Seventh Edition (2012).
  • S. Tekin, F. Başar, Certain Sequence spaces over the non-Newtonian complexeld, Abstr. Appl. Anal. Article ID 739319, 11 pages (2013).
  • C. Türkmen and F. Başar, Some Basic Results on the sets of Sequences with Geometric Calculus, Commun. Fac. Fci. Univ. Ank. Series A1., Vol.61, No.2, pp.17-34 (2012).
  • A. Uzer, Multiplicative type Complex Calculus as an alternative to the classical calculus, Comput. Math. Appl. Vol.60, pp.2725-2737 (2010).
  • K. Boruah and B. Hazarika, G-Calculus, TWMS J. App. Eng. Math., Vol.8, No.1, pp.94-105 (2018)
There are 30 citations in total.

Details

Primary Language English
Subjects Algebraic and Differential Geometry, Operator Algebras and Functional Analysis
Journal Section Research Article
Authors

Hasan Es 0000-0002-7732-8173

Publication Date July 31, 2024
Submission Date December 29, 2023
Acceptance Date January 31, 2024
Published in Issue Year 2024

Cite

APA Es, H. (2024). PLANE KINEMATICS IN LORENTZIAN HOMOTHETIC MULTIPLICATIVE CALCULUS. Journal of Universal Mathematics, 7(2), 64-74. https://doi.org/10.33773/jum.1411844
AMA Es H. PLANE KINEMATICS IN LORENTZIAN HOMOTHETIC MULTIPLICATIVE CALCULUS. JUM. July 2024;7(2):64-74. doi:10.33773/jum.1411844
Chicago Es, Hasan. “PLANE KINEMATICS IN LORENTZIAN HOMOTHETIC MULTIPLICATIVE CALCULUS”. Journal of Universal Mathematics 7, no. 2 (July 2024): 64-74. https://doi.org/10.33773/jum.1411844.
EndNote Es H (July 1, 2024) PLANE KINEMATICS IN LORENTZIAN HOMOTHETIC MULTIPLICATIVE CALCULUS. Journal of Universal Mathematics 7 2 64–74.
IEEE H. Es, “PLANE KINEMATICS IN LORENTZIAN HOMOTHETIC MULTIPLICATIVE CALCULUS”, JUM, vol. 7, no. 2, pp. 64–74, 2024, doi: 10.33773/jum.1411844.
ISNAD Es, Hasan. “PLANE KINEMATICS IN LORENTZIAN HOMOTHETIC MULTIPLICATIVE CALCULUS”. Journal of Universal Mathematics 7/2 (July 2024), 64-74. https://doi.org/10.33773/jum.1411844.
JAMA Es H. PLANE KINEMATICS IN LORENTZIAN HOMOTHETIC MULTIPLICATIVE CALCULUS. JUM. 2024;7:64–74.
MLA Es, Hasan. “PLANE KINEMATICS IN LORENTZIAN HOMOTHETIC MULTIPLICATIVE CALCULUS”. Journal of Universal Mathematics, vol. 7, no. 2, 2024, pp. 64-74, doi:10.33773/jum.1411844.
Vancouver Es H. PLANE KINEMATICS IN LORENTZIAN HOMOTHETIC MULTIPLICATIVE CALCULUS. JUM. 2024;7(2):64-7.