i-manager's Journal on Mathematics (JMAT)


Volume 10 Issue 1 January - June 2021

Research Paper

Reduced Order Anti-Synchronization: A Comparison of Simulation between Mathematica and Matlab

Mohammad *
Nizwa College of Applied Sciences, University of Technology & Applied Sciences, Salalah, Oman.
Shahzad, M. (2021). Reduced Order Anti-Synchronization: A Comparison of Simulation between Mathematica and Matlab. i-manager's Journal on Mathematics, 10(1), 1-9. https://doi.org/10.26634/jmat.10.1.17980

Abstract

The present study is based on the anti-synchronization of chaotic systems of different orders. The author studied the reduced-order anti-synchronization (ROAS) in order to observe the variations between the computational studies on Mathematica and Matlab. For demo purpose, circular restricted three body problem (CRTBP) and Lorenz chaotic systems of different orders are chosen. The study of ROAS has been carried out via a robust generalized active control technique under the effect of both unknown model uncertainties and external disturbances. In order to see the variations between the computational studies, a parallel simulation is carried out on Mathematica and Matlab at the same values of the parameters and initial conditions.

Research Paper

Numerical Treatment of Casson Micropolar Fluid Past a Stretching Sheet with the Impact of Slip Velocity and Viscous Dissipation

K. Kranthi Kumar * , Ch. Baby Rani **, A. V. Papa Rao ***
* Department of Mathematics, Jawaharlal Nehru Technological University, Kakinada, Andhra Pradesh, India.
** Department of Mathematics, V. R. Sidhartha Engineering College, Vijayawada, Andhra Pradesh, India.
*** Department of Mathematics, Jawaharlal Nehru Technological University College of Engineering, Vizianagaram, Andhra Pradesh, India.
Kumar, K. K., Rani, C. B., and Rao, A. V. P. (2021). Numerical Treatment of Casson Micropolar Fluid Past a Stretching Sheet with the Impact of Slip Velocity and Viscous Dissipation. i-manager's Journal on Mathematics, 10(1), 10-21. https://doi.org/10.26634/jmat.10.1.18003

Abstract

The flow of convective Casson micropolar fluid is studied numerically using stretching sheet. The domain is influenced by second order velocity slip and viscous dissipation. The conservative governing X-momentum, micro-rotational momentum and energy equations are abbreviated to ordinary differential equations using similarity transformation technique. The transformed equations are reformed into first order ordinary differential equations and the resultant system of differential equations is solved with help of 4th order Runge-Kutta scheme along with shooting method.

Research Paper

Some Topological Properties of the Spectrum of Prime D-Filters of Distributive Lattices

A. P. Phaneendra Kumar * , M. Sambasiva Rao **, K. Sobhan Babu ***
* Department of Mathematics, Vignan's Institute of Engineering for Women, Vishakapatnam, Andhra Pradesh, India.
** Department of Mathematics, MVGR College of Engineering, Vizianagaram, Andhra Pradesh, India.
*** Department of Mathematics, JNTU-K University College of Engineering, Guntur, Andhra Pradesh, India.
Kumar, A. P. P., Rao, M. S., and Babu, K. S. (2021). Some Topological Properties of the Spectrum of Prime D-Filters of Distributive Lattices. i-manager's Journal on Mathematics, 10(1), 22-31. https://doi.org/10.26634/jmat.10.1.18165

Abstract

Some properties of prime D-filters of distributive lattices are studied with respect to the direct products and set-theoretic intersection. Properties of minimal prime D-filters of distributive lattices are studied. Some topological properties of the space of all minimal prime D-filters of a distributive lattice are studied. Finally, it is showed that the space of all minimal prime D-filters of a distributive lattice is a Hausdorff space.

Research Paper

Orbits in Dynamical Systems Defined by Groups

Volety V. S. Ramachandram*
Department of Humanities and Basic Sciences, Dadi Institute of Engineering and Technology, Anakapalle, Visakhapatnam District, Andhra Pradesh, India.
Ramachandram, V. V. S. (2021). Orbits in Dynamical Systems Defined by Groups. i-manager's Journal on Mathematics, 10(1), 32-36. https://doi.org/10.26634/jmat.10.1.18197

Abstract

The aim of this paper is to study some basic properties of the orbits of elements in dynamical systems defined by groups. The relation between orbit of an element and the orbit of its inverse element has been established. The nature of the orbit of the identity element in the dynamical system has been studied and a singleton set containing the identity element itself has been obtained. It is observed that the set of all fixed points in the dynamical system is strongly invariant (Sinvariant) and is a closed subgroup of the group. By using the topological conjugacy between dynamical systems defined by groups, a relation between the orbit of an element and the orbit of its image element in the other dynamical system has been obtained. Finally, we obtained that if an element is in the kernel of the homomorphism, then it must be eventually fixed at the identity element of the group.

Research Paper

A Subclass of Generalized Harmonic Univalent Functions

Sitavani Venkata * , V. Srinivas **
* Department of Mathematics, Nalla Malla Reddy Engineering College, Hyderabad, Telangana, India.
** Department of Mathematics, Dr. B. R. Ambedkar Open University, Hyderabad, Telangana, India.
Sitavani, K. V., and Srinivas, V. (2021). A Subclass of Generalized Harmonic Univalent Functions. i-manager's Journal on Mathematics, 10(1), 37-44. https://doi.org/10.26634/jmat.10.1.18272

Abstract

The main contribution of this article is to define a certain subclass of generalized harmonic univalent rational functions. Complex-valued harmonic functions that are univalent and sense preserving in the unit disk U can be written in the form f=h+g ̅, where h and g are analytic in U. In the study of harmonic functions geometric properties of certain subclasses were discussed. Conditions of characterization involving bounds on the coefficients lead to various external properties. We further define a new subclass of harmonic rational functions and also find their coefficient characterization and certain geometric properties such as star-likeness, convexity and growth and distortion bounds for the functions of the subclass. Convolution property and extreme points of the subclass has been discussed.