PSR Press – Mission Statement

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.

Open Journal of Mathematical Science (OMS)

ISSN: 2523-0212 (online) 2616-4906 (Print)

Open Journal of Mathematical Analysis (OMA)

ISSN: 2616-8111 (online) 2616-8103 (Print)

Open Journal of Discrete Applied Mathematics (ODAM)

ISSN: 2617-9687 (online) 2617-9679 (Print)

Ptolemy Journal of Chemistry (PJC)

ISSN: 2618-0758 (online) 2618-074X (Print)

Engineering and Applied Science Letters (EASL)

ISSN: 2617-9709 (online) 2617-9695 (Print)

Trends in Clinical and Medical Sciences (TCMS)

ISSN: 2791-0814 (online) 2791-0806 (Print)

Our Journals

Open Journal of Mathematical Science (OMS)

ISSN: 2523-0212 (online) 2616-4906 (Print)

Open Journal of Mathematical Analysis (OMA)

ISSN: 2616-8111 (online) 2616-8103 (Print)

Open Journal of Discrete Applied Mathematics (ODAM)

ISSN: 2617-9687 (online) 2617-9679 (Print)

Ptolemy Journal of Chemistry (PJC)

ISSN: 2618-0758 (online) 2618-074X (Print)

Engineering and Applied Science Letters (EASL)

ISSN: 2617-9709 (online) 2617-9695 (Print)

Trends in Clinical and Medical Sciences (TCMS)

ISSN: 2791-0814 (online) 2791-0806 (Print)

Latest in Press

Author(s): Silvia Foschi1, Daniele Ritelli2
1Liceo Oriani Ravenna, Italy.
2Dipartimento di Scienze Statitiche, University of Bologna, Italy.
Abstract:

One of the problems on which a great deal of focus is being placed today, is how to teach Calculus in the presence of the massive diffusion of Computer Algebra tools and online resources among students. The essence of the problem lies in the fact that, during the problem solving activities, almost all undergraduates can be exposed to certain “new” functions, not typically treated at their level. This, without being prepared to handle them or, in some cases, even knowing the meaning of the answer provided by the computer system used. One of these functions is Lambert’s \(W\) function, undoubtedly due to the elementary nature of its definition. In this article we introduce \(W\), in a way that is easy to grasp for first year undergraduate students and we provide some general results concerning polynomial-exponential and polynomial-logarithmic equations. Among the many possible examples of its applications, we will see how \(W\) comes into play in epidemiology in the SIR model. In the second part, using more advanced concepts, we motivate the importance of the Implicit Function Theorem, using it to obtain the power series expansion of the Lambert function around the origin. Based on this approach, we therefore also provide a way to obtain the power series expansion of the inverse of a given smooth function \(f(y)\), when it is assumed that \(f(0)=0,\,f'(0)\neq0\), aided by the computational power of Mathematica®. Basically, in this way, we present an alternative approach to the Lagrange Bürman Inversion Theorem, although in a particular but relevant case, since the general approach is not at an undergraduate level. A number of good references are [1, pp. 23-28] and [2], where the Lambert function is applied. Finally, these skills are used to take into consideration the particular quintic equation in the unknown \(y\) presented by F. Beukers [3]. Namely, we consider \(x(1+y)^5-y=0\) as an example of an equation for which the power series representation of one of its real solutions is known, calculating, with the same method used for the Lambert function, the first terms of its power series representation.

Author(s): U. K. Qureshi1, A. A. Shaikhi2, F. K. Shaikh2, S. K. Hazarewal2, T. A. Laghari2
1Department of Business Administration, Shaheed Benazir Bhutto University, Sanghar, Sindh, Pakistan.
2Department of Basic Sciences and Related Studies, Mehran University of Engineering and Technology Jamshoro, Sindh, Pakistan.
Abstract:

Finding root of a nonlinear equation is one of the most important problems in the real world, which arises in the applied sciences and engineering. The researchers developed many numerical methods for estimating roots of nonlinear equations. The this paper, we proposed a new Simpson type method with the help of Simpson 1/3rd rule. It has been proved that the convergence order of the proposed method is two. Some numerical examples are solved to validate the proposed method by using C++/MATLAB and EXCEL. The performance of proposed method is better than the existing ones.

Author(s): Huan You1
1School of Mathematics and Statistics, Nanjing University of Information Science & Technology, Nanjing, Jiangsu Province, China
Abstract:

The purpose of this study is to explore the influence of factors on patients with chronic kidney disease (CKD) and to establish predictive models using machine learning methods. Data were collected from the Affiliated Hospital of Nanjing University of Chinese Medicine between January 2016 and December 2017, including 69 CKD patients and 155 healthy subjects. This study found that carotid intima-media thickness (cIMT) is the most important indicator among the top 9 important features of each model. In order to find the best model to diagnosis CKD, extreme gradient boosting (XGBoost), support vector machine (SVM) and logistic regression are established and XGBoost is the most suitable model for this study (accuracy, 0.93; specificity, 0.89; sensitivity, 0.94; F1 score, 0.91; AUC, 0.99).

Author(s): S. O. Ehikhuenmen1, E. E. Ikponmwosa1, F. A. Falade1
1Civil and Environmental Engineering Department, Faculty of Engineering, University of Lagos, Lagos, Nigeria.
Abstract:

Out of the top ten current global issues, climate change and pollution top the list. These issues have brought about adverse effects on our climate, health and communities. This study aims to investigate the structural performance of sawdust ash blended steel slag aggregate concrete and modelling their structural properties using a multivariate interpolation method. In order to achieve this, the physical properties, physio-chemical, chemical composition, mechanical properties tests were conducted. The result revealed that sawdust ash is classified as a class C type pozzolan having a total of 61.59% combined percentage masses of silica, alumina and ferric oxides, while steel slag aggregate is classified as poorly graded. The composite concrete recorded higher density, compressive and split tensile strengths when compared with normal concrete cured in potable water. The results revealed that normal concrete with normal aggregate is more durable than sawdust ash blended steel slag aggregate (composite) concrete when cured in an aggressive environment. The developed models were found to agree strongly with the experimental data, with an outstanding correlation level. This research has led to the creation of high strength pozzolan blended steel slag aggregate concrete, thus improving waste management, reduction in environmental pollution and \(CO_2\) gas emission.

Author(s): Mawia Osman1, Zengtai Gong2, Altyeb Mohammed Mustafa1,3
1College of Mathematics and Statistics, Northwest Normal University, Lanzhou, Gansu, P.R. China.
2College of Mathematics and Statistics, Northwest Normal University, Lanzhou, Gansu, P.R. China
3Department of Applied Mathematics, Faculty of Mathematical Science, University of Khartoum, Khartoum, Sudan.
Abstract:

In this paper, the reduced differential transform method (RDTM) is applied to solve fuzzy nonlinear partial differential equations (PDEs). The solutions are considered as infinite series expansions which converge rapidly to the solutions. Some examples are solved to illustrate the proposed method.

Author(s): Tersoo Luga1, Sunday Simon Isah2, Vershima Benjamin Iyorter3
1Department of Mathematics/Statistics/Computer Science, College of Science, Federal University of Agriculture, Makurdi, Nigeria.
2Department of Mathematics/Statistics/Computer Science, College of Science, Federal University of Agriculture, Makurdi, Nigeria
3Department of Mathematics/Computer Science, College of Natural and Applied Sciences, University of Mkar, Mkar, Nigeria.
Abstract:

Collocation methods are efficient approximate methods developed by utilizing suitable set of functions known as trial or basis functions. These methods are used for solving differential equations, integral equations and integro-differential equations, etc. In this study, the Laguerre polynomial of degree 10 is used as a basis function to propose a collocation method for solving higher order linear ordinary differential equations. Four examples on \(4th\), \(6th\), \(8th\) and \(10th\) order ordinary differential equations are selected to illustrate the effectiveness of the method. The numerical results show that the proposed collocation method is easy and straightforward to implement, nevertheless, it is very accurate.

Author(s): Helmut Prodinger1
1Department of Mathematical Sciences, Stellenbosch University, 7602 Stellenbosch, South Africa.
Abstract:

A variation of Dyck paths allows for down-steps of arbitrary length, not just one. Credits for this invention are given to Emeric Deutsch. Surprisingly, the enumeration of them is somewhat akin to the analysis of Motzkin-paths; the last section contains a bijection.

Author(s): Timilehin Gideon Shaba1
1Department of Mathematics, University of Ilorin, P. M. B. 1515, Ilorin, Nigeria.
Abstract:

In this current study, we introduced and investigated two new subclasses of the bi-univalent functions associated with \(q\)-derivative operator; both \(f\) and \(f^{-1}\) are \(m\)-fold symmetric holomorphic functions in the open unit disk. Among other results, upper bounds for the coefficients \(|\rho_{m+1}|\) and \(|\rho_{2m+1}|\) are found in this study. Also certain special cases are indicated.

Author(s): Taieb Hamaizia1
1Laboratory of Dynamical Systems and Control, Department of Mathematics and Informatics, Oum El Bouaghi University, 04000, Algeria.
Abstract:

The purpose of this paper is to prove a fixed point theorem for \(C\)-class functions in complete \(b\)-metric spaces. Moreover, the solution of the integral equation is obtained using our main result.

Author(s): Ahmed Ali Al-Gonah1, Waleed Khadher Mohammed1
1Department of Mathematics, Aden University, Aden, Yemen.
Abstract:

In this paper, a new forms of extended hypergeometric functions are introduced. Some functional relations, integral representations and transformation formulas for these functions are derived.

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