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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.

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): Farid Messelmi1
1Department of Mathematics and LDMM Laboratory, Universite of Djelfa, Algeria.
Abstract:

The purpose of this paper is to apply the concept of \(log -\)series in order to determine the sum of certain power series, where the n-th terms involves the factorial mapping, the generalized harmonic numbers and the reciprocals of factorial sums.

Author(s): Mogoi N. Evans1, Robert Obogi2
1Department of Pure and Applied Mathematics Jaramogi Oginga Odinga University of Science and Technology, Kenya.
2Department of mathematics and actuarial science Kisii University, Kenya.
Abstract:

This paper investigates the geometry and norm-attainability of operators within various operator ideals, with a particular focus on the role of singular values and compactness. We explore the behavior of norm-attainable operators in the context of classical operator ideals, such as trace-class and Hilbert-Schmidt operators, and examine how their geometric and algebraic properties are influenced by membership in these ideals. A key result of this study is the connection between the singular values of trace-class operators and their operator norm, establishing a foundational relationship for understanding norm-attainment. Additionally, we explore the conditions under which weakly compact and compact operators can attain their operator norm, providing further insights into the structural properties that govern norm-attainability in operator theory. The findings contribute to a deeper understanding of the interplay between operator ideals and norm-attainability, with potential applications in functional analysis and related fields.

Author(s): Ahmed Chana1, Abdellatif Akhlidj1, Zakaria Sadik1
1Laboratory of Fundamental and Applied Mathematics, Department of Mathematics and Informatics, Faculty of Sciences Ain Chock, University of Hassan II, B.P 5366 Maarif, Casablanca, Morocco
Abstract:

The primary objective of this paper is to introduce a novel integral transform, referred to as the Hartley-Bessel-Stockwell transform, and to establish several fundamental results associated with it. Specifically, we derive generalized versions of Parseval’s identity, Plancherel’s theorem, the inversion formula, and Calderon’s reproducing formula for this transform. Furthermore, we investigate the concentration properties of the Hartley-Bessel-Stockwell transform on sets of finite measure and present an uncertainty principle for orthonormal sequences. Finally, leveraging the theory of reproducing kernels and best approximation methods, we examine the extremal functions associated with this transform. We provide their integral representations and derive optimal estimates for these functions within weighted Sobolev spaces.

Author(s): Bitrus Sambo1, Timothy Oloyede Opoola2
1Department of Mathematics , Gombe State University , P.M.B. 127, Gombe , Nigeria.
2Department of Mathematics , University of Ilorin , P.M.B. 1515 , Ilorin , Nigeria.
Abstract:

In this research, we utilize the Opoola differential operator to define new subclasses of starlike and convex functions within the unit disk \(U\): \(S^{m,t}_{\beta,\mu}(\alpha,\eta,\gamma)\), \(K^{m,t}_{\beta,\mu}(\alpha,\eta,\gamma)\), \(T^{m,t}_{\beta,\mu}(\alpha,\eta,\gamma)\), and \(C^{m,t}_{\beta,\mu}(\alpha,\eta,\gamma)\), characterized by parameters \(\alpha\), \(\eta\), and \(\gamma\), which denote their order and type. We investigate various geometric properties of these functions, including characterization properties, growth and distortion theorems, arithmetic mean, and radius of convexity. The results obtained generalize many existing findings, forming a foundation for further research in the theory of geometric functions. Additionally, we present several corollaries and remarks to illustrate extensions of our results.

Author(s): Sumayah Ghaleb Othma1, Yahya Qaid Hasa2
1Department of Mathematics, University of Aden, Taiz University, Yemen
2Department of Mathematics, University of Sheba Region , Yemen
Abstract:

This paper proposes a new creative modification to the well-known standard Adomian decomposition method (ADM) in order to investigate various types of initial-value problems (IVPs) involving distinct kinds of fourth order ordinary differential equations (ODEs). We demonstrate that the singular point at \(x=0,\) therefore the form factor, could show up in several equations terms. Some non-linear numerical applications that have been studied and explained this method have confirmed its effectiveness and ability to find appropriate solutions for such equations. The outcomes we arrive at with this operator are reliable and converge faster than the exact solution.

Author(s): Tristram de Piro1
1Flat 3, Redesdale House, 85 The Park, Cheltenham, GL50 2RP.
Abstract:

We consider non oscillatory functions and prove an everywhere Fourier Inversion Theorem for functions of very moderate decrease. The proofs rely on some ideas in nonstandard analysis.

Author(s): M. A. Ramadan1, M.M. A. Mansour2, N. M. El-Shazly1, H. S. Osheba1
1Mathematics and Computer Science Department, Faculty of Science, Menoufia University, Egypt.
2Department of basic science, Modern Academy of Computer Science and Management Technology in Maadi, Egypt.
Abstract:

To solve the approximate analytic solutions of the quadratic Riccati differential equations, this study introduces a hybrid method that combines an accelerated variant of the Adomian decomposition method (AADM) proposed by I. El-Kalla with the Ramadan Group transform (RGT). This hybrid technique produces accurate and dependable results, outperforming the regular Adomian decomposition method (RADM) and the Newton- Raphson version of Adomian polynomials in terms of accuracy. Three examples are provided here to demonstrate good accuracy and fast convergence when compared to the exact solution and other recent analytical methods using Shifted Chebyshev polynomials, Variation of Parameters Method (VPM), Bezier polynomials, homotopy analysis method (HAM), and Newton – Raphson based modified Laplace Adomian decomposition method.

Author(s): E. Bwayo1,2, W. K. Njoroge1, J. Okumu1, D. Mukiibi3
1Department of Physics, School of Physical and Applied Sciences, Kenyatta University, P. O. Box 43844-00100, Nairobi-Kenya.
2Department of Physics, Faculty of Science, Muni University, P. O. Box 725, Arua-Uganda.
3Department of Physics, School of Physical Sciences, College of Natural Sciences, Makerere University, P. O. Box 7062, Kampala- Uganda.
Abstract:

The performance of an antireflection coating entirely depends on the proportion of light energy transmitted or reflected by the coating material. To enhance the transmittance of an antireflection coating, evaluation of the amount of the light energy transmitted to generate charge carriers is very critical. Thus, in this paper, we demonstrate the effect of sputtering power and gas flow rate on the optical transmittance of aluminium oxide (Al\(_{2}\)O\(_{3}\)) and copper-doped zinc sulphide (ZnS:Cu) antireflection nanostructures. To this end, radiofrequency sputtering was used for the deposition of ZnS:Cu, using the ZnS:Cu target (94/6.0%) using argon (99.9% pure), and direct current sputtering was used for the deposition of Al\(_{2}\)O\(_{3}\) using the aluminium target (99.99% purity) and oxygen (99.9% pure). The gas flow rates of 40 to 100 sccm were used. The sputtering power values of 70 W to 140 W were used at a low process pressure of \(6.5 \times 10^{-3}\). The transmittance was observed to decrease with an increase in sputter power and deposition time. However, the transmittance of single-layer nanofilms was lower than that of the double-layer nanostructures. For photovoltaic applications, the Al\(_{2}\)O\(_{3}\)/ZnS:Cu(112.1 nm) nanostructure exhibited the highest transmittance of 96.9% at \(\lambda=780\) nm. The reflectance of the nanostructures increased with an increase in coating time and sputtering power, with the lowest value of 3.03% recorded at 360 nm. The nanostructures are crystalline, smooth, and dense but the crystallite sizes decreased from 0.02508 to 0.02071 \(\text{\AA}\) with an increase in gas flow rate. This decrease in crystallinity was due to the reduced adatom migration on the substrate. The optimal gas flow rate was 100 sccm, in which the Al\(_{2}\)O\(_{3}\)/ZnS:Cu(117 nm) had the highest transmittance of 97.7% at \(\lambda=741\) nm. The results demonstrate the potential use of Al\(_{2}\)O\(_{3}\)/ZnS:Cu nanostructures as antireflection materials for photovoltaic solar cells.

Author(s): Sikander Ali1, Furqan Ahmad1, Muhammad Kamran Jamil1
1Department of Mathematics, Riphah International University, Lahore, Pakistan
Abstract:

In this paper, we introduce a new resolvability parameter named as the local edge partition dimension \((LEPD)\) of graphs. The local edge partition dimension \((LEPD)\) makes a specialty of partitioning the vertex set of a graph into awesome instructions based totally on localized resolving properties. Our findings offer a fresh angle on graph resolvability, offering capability insights for optimizing network overall performance and structural analysis. Let \(G=(V, E)\) be a connected graph with vertex set \(V\) and edge set \(E\). A partition set \({R}_{p}=\{{R}_{p1},{R}_{p2},{R}_{p3}\dots,{R}_{pn}\}\) contain subsets of vertices of \(G\). If for every pair of adjacent edges \(p\) and \(q\) in \(G\), then \(d(p,{R}_{p})\neq d(q,{R}_{p})\) and if \(p\) and \(q\) are non-adjacent then not necessary \(d(p,{R}_{p})\neq d(q,{R}_{p})\) then \({R}_{p}\) is called a local edge resolving partition set and minimum cardinality of such set is called local edge partition dimension. We discussed local metric, local edge metric, metric, edge metric dimension, local partition, local edge partition, partition dimension, and edge partition dimension of the Petersen graph.

Author(s): David Allen1, Jose La Luz2, Guarionex Salivia3, Jonathan Hardwick4
1 Department of Mathematics BMCC, CUNY, New York, New York 10007
2Departmento de Matem\’aticas, Universidad de Puerto Rico, Industrial Minillas 170 Carr 174, Bayam\’on, PR, 00959-1919
3Department of Mathematics, Computer Science and Statistics, Gustavus Adolphus College, 800 West College Avenue Saint Peter, MN 56082
4Department of Computer Information Science, Minnesota state University, Mankato, South Rd and Ellis Ave, Mankato, MN 56001
Abstract:

In this paper we construct families of bit sequences using combinatorial methods. Each sequence is derived by converting a collection of numbers encoding certain combinatorial numerics from objects exhibiting symmetry in various dimensions. Using the algorithms first described in [1] we show that the NIST testing suite described in publication 800-22 does not detect these symmetries hidden within these sequences.

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