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Annamalai’s Computing Model for Algorithmic Geometric Series and Its Mathematical Structures
Issue:
Volume 3, Issue 1, January 2018
Pages:
1-6
Received:
6 October 2017
Accepted:
24 October 2017
Published:
20 December 2017
Abstract: This paper presents a new mathematical model for formation as well as computation of geometric series and summability in step-by-step procedures. Also, it provides mathematical structures for geometric series-ordered terms. The novel mathematical model uses Annamalai’s computing method of geometric series and summability, which provided a technique to establish the algorithmic geometric series and its formulae in an earlier paper, for further improvement in the scientific research study. This mathematical/computational models of geometric series are widely used in the fields of physics, engineering, biology, medicine, economics, computer science, queueing theory, finance, and management for the purpose of research and development meeting today’s challenges. In an earlier research article, the geometric series along with exponential decay model were used to determine effective medicine dosage. Few specific mathematical formulae had also been discovered by using Annamalai’s algorithmic geometric series and summability. This could be very interesting and informative for current students and researchers.
Abstract: This paper presents a new mathematical model for formation as well as computation of geometric series and summability in step-by-step procedures. Also, it provides mathematical structures for geometric series-ordered terms. The novel mathematical model uses Annamalai’s computing method of geometric series and summability, which provided a technique...
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A Research Approximation to Generalized Riemann Derivatives by Integral Operator Families
Issue:
Volume 3, Issue 1, January 2018
Pages:
7-12
Received:
23 November 2017
Accepted:
4 December 2017
Published:
19 January 2018
Abstract: Approximation theory has very important applications of polynomial approximation in various areas of functional analysis, Harmonic analysis, Fourier analysis, application mathematic, operator theory in the field generalized derivatives and numerical solutions of differential and integral equations, etc. Integral operators is very important in Harmonic and Fourier analysis. The study of approximation theory is a well-established area of research which deals with the problem of approximating a function f by means of a sequence Ln of positive linear operators. Generalized derivatives (Riemann, Peano and Taylor derivative) are more general than ordinary derivative. Approximation theory is very important for mathematical world. Nowadays, many mathematicians are working in this field.
Abstract: Approximation theory has very important applications of polynomial approximation in various areas of functional analysis, Harmonic analysis, Fourier analysis, application mathematic, operator theory in the field generalized derivatives and numerical solutions of differential and integral equations, etc. Integral operators is very important in Harmo...
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Handling and Stability Analysis of Vehicle Plane Motion
Verbitskii Vladimir Grigorievich,
Bezverhyi Anatoliy Igorevich,
Tatievskyi Dmitry Nikolayevich
Issue:
Volume 3, Issue 1, January 2018
Pages:
13-22
Received:
19 January 2018
Accepted:
2 February 2018
Published:
23 February 2018
Abstract: The work analyzes the properties of handling and bicycle vehicle model motion stationary states manifold stability taking into account drift force nonlinear characteristics. Determining single two-axle vehicle nonlinear model stationary states and analyzing their stability were based on a graphical method (Y. M. Pevzner, H. Pacejka). It has its disadvantages: the absence of evident analytical stability criteria for the entire wheeled vehicle circular stationary states manifold. And also the absence of global stability threshold characteristics in the controlled parameter space. The task part suggests developing methods for building bifurcation manifold or critical parameters manifold (longitudinal velocity and wheel turning angle) with which the divergent loss of stability occurs. Known H. Troger, K. Zeman and Fabio Della Rossaa, GiampieroMastinub, Carlo Piccardia results are based on parameter continuation numerical methods which makes the quality analysis of drift force nonlinear characteristics impact on the entire stationary states manifold stability conditions more difficult. A compelling grapho-analytic approach towards bifurcation manifold building and getting circular stationary states analytical stability conditions based on moving from nonlinear drift forces on axles dependencies to their inverse dependence is developed in the suggested work. This methodology allows defining dangerous/safe stability threshold conditions in the control parameters space.
Abstract: The work analyzes the properties of handling and bicycle vehicle model motion stationary states manifold stability taking into account drift force nonlinear characteristics. Determining single two-axle vehicle nonlinear model stationary states and analyzing their stability were based on a graphical method (Y. M. Pevzner, H. Pacejka). It has its dis...
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Some New Traveling Wave Solutions of Modified Camassa Holm Equation by the Improved G'/G Expansion Method
Rida Tassew Redi,
Akalu Abriham Anulo
Issue:
Volume 3, Issue 1, January 2018
Pages:
23-45
Received:
17 January 2018
Accepted:
16 February 2018
Published:
9 April 2018
Abstract: In this article, the improved G'/G-expansion method has been implemented to generate travelling wave solutions, where G(ŋ) satisfies the second order nonlinear ordinary differential equation. To show the advantages of the method, the Simplified Modified Camassa Holm (SMCH) equation has been investigated. Nonlinear partial differential equations have many potential applications in mathematical physics and engineering sciences. Some of our solutions are in good agreement with already published results for a special case and others are new. The solutions in this work may express a variety of new features of waves. Furthermore, these solutions can be valuable in the theoretical and numerical studies of the considered equation.
Abstract: In this article, the improved G'/G-expansion method has been implemented to generate travelling wave solutions, where G(ŋ) satisfies the second order nonlinear ordinary differential equation. To show the advantages of the method, the Simplified Modified Camassa Holm (SMCH) equation has been investigated. Nonlinear partial differential equations ha...
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