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Ptolemy Scientific Research Press (PSR Press)is a highly regarded publisher of scientific literature dedicated to bringing the latest research and findings to a broader audience. With a focus on cutting-edge research and technology, Ptolemy Scientific Research Press offers a range of publications catering to professionals, researchers, and student’s needs. Whether looking for information on the latest breakthroughs in physics, biology, engineering, or computer science, you can trust Ptolemy Scientific Research Press to deliver insightful, accurate, and engaging content. With its commitment to quality, accessibility, and innovation, Ptolemy Scientific Research Press is an essential resource for anyone interested in science and technology.

Latest Published Articles

Minimum degree polynomial of graphs obtained by some graph operators

ODAM-Vol. 2 (2019), Issue 2, pp. 1–18 Open Access Full-Text PDF
Bommanahal Basavanagoud, Praveen Jakkannavar
Abstract: The minimum degree matrix \(MD(G)\) of a graph \(G\) of order \(n\) is an \(n\times n\) symmetric matrix whose \((i,j)^{th}\) entry is \(min\{d_i,d_j\}\) whenever \(i\neq j\), and zero otherwise, where \(d_i\) and \(d_j\) are the degrees of the \(i^{th}\) and \(j^{th}\) vertices of \(G\), respectively. In the present work, we obtain the minimum degree polynomial of the graphs obtained by some graph operators (generalized \(xyz\)-point-line transformation graphs).
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Analysis of the qualitative behaviour of an eighth-order fractional difference equation

ODAM-Vol. 2 (2019), Issue 1, pp. 41–47 Open Access Full-Text PDF
Mohammed Bakheet Almatrafi, Marwa Mohammed Alzubaidi
Abstract: The exact solutions of most nonlinear difference equations cannot be obtained theoretically sometimes. Therefore, a massive number of researchers predict the long behaviour of most difference equations by investigating some qualitative behaviours of these equations from the governing equations. In this article, we aim to analyze the asymptotic stability, global stability, periodicity of the solution of an eighth-order difference equation. Moreover, a theoretical solution of a special case equation will be presented in this paper.
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Fractional frequency Laplace transform by inverse difference operator with shift value

OMS-Vol. 3 (2019), Issue 1, pp. 121–128 Open Access Full-Text PDF
Sandra Pinelas, Meganathan Murugesan, Britto Antony Xavier Gnanaprakasam
Abstract: In this paper, we study the outcome of fractional Laplace transform using inverse difference operator with shift value. By the definition of convolution product, the properties of fractional transformation, the relation between convolution product and fractional frequency Laplace transform with shift value have been discussed. Further, the connection between usual Laplace transform and fractional frequency Laplace transform with shift value are also presented. Numerical examples with graphs are verified and generated by MATLAB.
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Flow of viscous fluid over an infinite plate with Caputo-Fabrizio derivatives

OMS-Vol. 3 (2019), Issue 1, pp. 115–120 Open Access Full-Text PDF
M. Umar Farooq, M. Saqib Khan, Ahmad Hajizadeh
Abstract: This paper presents Caputo-Fabrizio fractional derivatives approach to analysis of a viscous fluid over an infinite flat plate together with general boundary motion. Closed form exact general solutions of the fluid velocity are obtained by means of the Laplace transform. The solutions of ordinary viscous fluids corresponding to time-derivatives of integer order is obtained as particular cases of the present solutions. Several special cases are also discussed. Numerical computations and graphical illustrations are used in order to study the effects of the Caputo-Fabrizio time-fractional parameter \(\alpha\) and Reynolds number on velocity field.
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Synchronous and a-synchronous machines (SAASMs): rotor and stator faults

EASL-Vol. 2 (2019), Issue 2, pp. 01–09 Open Access Full-Text PDF
Babar Azeem, Zahid Ullah, Faisal Rehman, Sahibzada Muhammad Ali, Bilal Arif, Aun Haider
Abstract: This paper investigates the rotor and stator faults of synchronous and asynchronous machine. We studied major and minor faults and failures in synchronous and asynchronous machines (SAASMs) to avoid excessive downtime, maintaining quality of service, and minimum revenue losses to smart grid (SG) operators and planners. Further, faults detection, faults diagnosis, major causes of faults, and fault remedial measures are discussed with state-of-the-art work for: (a) transformers, (b) stator, and (c) rotor. Our work presents detailed taxonomy of rotor and stator faults, electrical and mechanical stress, and faults diagnosis schemes for stable SG operation. We believe that our research contribution is more versatile covering every aspect of SAASMs faults and failures, compared to prior works.
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Modified Abbasbandy’s method free from second derivative for solving nonlinear equations

OMS-Vol. 3 (2019), Issue 1, pp. 109–114 Open Access Full-Text PDF
Sahar Saba, Amir Naseem, Muhammad Irfan Saleem
Abstract: The boundary value problems in Kinetic theory of gases, elasticity and other applied areas are mostly reduced in solving single variable nonlinear equations. Hence, the problem of approximating a solution of the nonlinear equations is important. The numerical methods for finding roots of such equations are called iterative methods. There are two type of iterative methods in literature: involving higher derivatives and free from higher derivatives. The methods which do not require higher derivatives have less order of convergence and the methods having high convergence order require higher derivatives. The aim of present report is to develop an iterative method having high order of convergence but not involving higher derivatives. We propose three new methods to solve nonlinear equations and solve text examples to check validity and efficiency of our iterative methods.
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BOOK-foundations-of-mathematical-analysis-and-semigroups-theory
BOOK - NULL CONTROLLABILITY OF DEGENERATE AND NON-DEGENERATE SINGULAR PARABOLIC