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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

One method towards the trisection of the angle

OMS-Vol. 4 (2020), Issue 1, pp. 23 – 26 Open Access Full-Text PDF
Gerasimos T. Soldatos
Abstract: This article maintains that the impossibility of trisection is based on a cubic polynomial whose trigonometric content is not clear; or, the impossibility may be referring to one particular trisection method even if the cubic equation does constitute the equation of trisection. It next proceeds to trisection “indirectly” by attempting bto construct one of the two trisectors on the basis of reductio ad absurdum.
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The Hadamard product and recursively defined sequences

ODAM-Vol. 3 (2020), Issue 1, pp. 20 – 24 Open Access Full-Text PDF
Sergei Dmitrievich Kazenas
Abstract: In this paper, the approach to obtaining nontrivial formulas for some recursively defined sequences is illustrated. The most interesting result in the paper is the formula for the solution of quadratic map-like recurrence. Also, some formulas for the solutions of linear difference equations with variable coefficients are obtained. At the end of the paper, some integer sequences associated with a quadratic map are considered.
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Dynamic analysis of non-homogenous varying thickness rectangular plates resting on Pasternak and Winkler foundations

EASL-Vol. 3 (2020), Issue 1, pp. 1 – 20 Open Access Full-Text PDF
S. A. Salawu, M. G. Sobamowo, O. M. Sadiq
Abstract: Modern day technological advancement has resulted in manufacturing industries intensify the use and application of thin plates in their productions thereby, resulting in increased research awareness in the study of dynamic behavior of thin plates. This research analyzes the free vibration dynamic behavior of thin rectangular plates resting on elastic Winkler and Pasternak foundations using two-dimensional differential transformation method. The reliability of the obtained analytical solutions are validated with results presented in cited literature and confirmed very precise. However, the analytical solutions obtained are used to investigate the influence of elastic foundations, homogeneity and thickness variation on the dynamic behavior of the plates under clamped and condition. From the results obtained, it is realized that increase in non-homogenous material results in corresponding increase in natural frequency of the plates. Also, increase in Winkler, Pasternak and combine Winkler and Pasternak foundations stiffness leads to increase in natural frequency of the plates. Increase in thickness results to natural frequency increases. The findings will serve as benchmark for further study of plate vibration research.
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Walk counting and Nikiforov’s problem

ODAM-Vol. 3 (2020), Issue 1, pp. 11 – 19 Open Access Full-Text PDF
Lihua Feng, Lu Lu, Dragan Stevanović
Abstract: For a given graph, let \(w_k\) denote the number of its walks with \(k\) vertices and let \(\lambda_1\) denote the spectral radius of its adjacency matrix. Nikiforov asked in [Linear Algebra Appl 418 (2006), 257–268] whether it is true in a connected bipartite graph that \(\lambda_1^r\geq\frac{w_{s+r}}{w_s}\) for every even \(s\geq 2\) and even \(r\geq 2\)? We construct here several infinite sequences of connected bipartite graphs with two main eigenvalues for which the ratio \(\frac{w_{s+r}}{\lambda_1^r w_s}\) is larger than~1 for every even \(s,r\geq 2\), and thus provide a negative answer to the above problem.
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Extremal total eccentricity of \(k\)-apex trees

ODAM-Vol. 3 (2020), Issue 1, pp. 8 – 10 Open Access Full-Text PDF
Naveed Akhter, Hafiza Iqra Yasin
Abstract: In a simple connected graph \(G\), eccentricity of a vertex is one of the first, distance-based invariants. The eccentricity of a vertex \(v\) in a connected graph \(G\) is the maximum distance of the vertex \(v\) to any other vertex \(u\). The total eccentricity of the graph \(G\) is the sum of the all vertex eccentricities. A graph \(G\) is called an apex tree if it has a vertex \(x\) such that \(G-x\) is a tree. In this work we have found the graph having extremal total eccentricity of \(k\)-apex trees.
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Antimagicness of subdivided fans

OMS-Vol. 4 (2020), Issue 1, pp. 18 – 22 Open Access Full-Text PDF
Afshan Tabassum, Muhammad Awais Umar, Muzamil Perveen, Abdul Raheem
Abstract: A graph \(\Gamma\) (simple, finite, undirected) with an \(\Omega\)-covering has an \((\alpha,\delta)\)-\(\Omega\)-antimagic labeling if the weights of all subgraphs \(\Omega\) of graph \(\Gamma\) constitute an arithmetic progression with the common difference \(\delta\). Such a~graph is called super \((\alpha,\delta)\)-\(\Omega\)-antimagic if \(\nu(V(\Gamma))= \{ 1,2,3,\dots,|V(\Gamma)|\}\). In the present paper, the cycle coverings of subdivision of fan graphs has been considered and results are proved for several differences.
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BOOK-foundations-of-mathematical-analysis-and-semigroups-theory
BOOK - NULL CONTROLLABILITY OF DEGENERATE AND NON-DEGENERATE SINGULAR PARABOLIC