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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): Gee-Choon Lau1, Sin-Min Lee2, Wai Chee Shiu3,4
1Faculty of Computer & Mathematical Sciences, Universiti Teknologi MARA (Segamat Campus), 85000 Johor, Malaysia.
21304, North First Avenue, Upland, CA 91786 USA
3Department of Mathematics, The Chinese University of Hong Kong, Shatin, Hong Kong.
4College of Global Talents, Beijing Institute of Technology, Zhuhai, China.
Abstract:

Let \(G= G(V,E)\) be a \((p,q)\)-graph. A bijection \(f: E\to\{1,2,3,\ldots,q \}\) is called an edge-prime labeling if for each edge \(uv\) in \(E\), we have \(GCD(f^+(u),f^+(v))=1\) where \(f^+(u) = \sum_{uw\in E} f(uw)\). A graph that admits an edge-prime labeling is called an edge-prime graph. In this paper we obtained some sufficient conditions for graphs with regular component(s) to admit or not admit an edge-prime labeling. Consequently, we proved that if \(G\) is a cubic graph with every component is of order \(4, 6\) or \(8\), then \(G\) is edge-prime if and only if \(G\not\cong K_4\) or \(nK(3,3)\), \(n\equiv2,3\pmod{4}\). We conjectured that a connected cubic graph \(G\) is not edge-prime if and only if \(G\cong K_4\).

Author(s): Abdualrazaq Sanbo1,2, Elsayed M. Elsayed1,3
1Mathematics Department, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia.
2General studies department, Jeddah College of Telecom and Electronics, TVTC, B.P. 2816, Jeddah 21461, Saudi Arabia.
3Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt.
Abstract:

In this article, we study some properties of the solutions of the following difference equation: \(x_{n+1}=a x_{n}+\dfrac{b x_{n} x_{n-4}}{cx_{n-3}+dx_{n-4}},\quad n=0,1,…\) where the initial conditions \(x_{-4},x_{-3}, x_{-2}, x_{-1}, x_0\) are arbitrary positive real numbers and \(a, b, c, d\) are positive constants. Also, we give specific form of the solutions of four special cases of this equation.

Author(s): Shamsuddeen Ibrahim1,2, Nicholas Kwasi-Do Ohene Opoku2, Hamenyimana Emanuel GervasORIC ID
1Inspire Paradigm Academy Army Barracks Road, Jimeta, Yola North, Adamawa State, Nigeria.
2African Institute for Mathematical Sciences, Ghana.
Abstract:

A deterministic model for the transmission dynamics of two-strains Herpes Simplex Virus (HSV) is developed and analyzed. Following the qualitative analysis of the model, reveals a globally asymptotically stable disease free equilibrium whenever a certain epidemiological threshold known as the reproduction number (\(\mathcal{R}_0\)), is less than unity and the disease persist in the population whenever this threshold exceed unity. However, it was shown that the endemic equilibrium is globally asymptotically stable for a special case. Numerical simulation of the model reveals that whenever \(\mathcal{R}_1<1<\mathcal{R}_2\), strain 2 drives strain 1 to extinction (competitive exclusion) but when \(\mathcal{R}_2<1<\mathcal{R}_1\), strain 1 does not drive strain 2 to extinction. Finally, it was shown numerically that super-infection increases the spread of HSV-2 in the model.

Author(s): Elmetwally M. Elabbasy1, Ethiraju Thandapani2, Osama Moaaz1, Omar Bazighifan3
1Department of Mathematics, Faculty of Science, Mansoura University, 35516 Mansoura, Egypt
2University of Madras Ramanujan Institute for Advanced Study in Mathematics Chennai, 600005, India
3Department of Mathematics; Faculty of Science; Hadhramout University; Hadhramout 50512, Yemen.
Abstract:

This work is concerned with the oscillatory behavior of fourth-order delay differential equation with middle term. By using the generalized Riccati transformations and new comparison principles, we establish new oscillation results for this equation. An example illustrating the results is also given.

Author(s): Muhammad Awais Umar1, Noshad Ali2, Afshan Tabassum2, Basharat Rehman Ali3
1Government Degree College (B), Sharaqpur Shareef, Pakistan
2Department of Mathematics, NCBA\&E, DHA Campus, Lahore, Pakistan
3Abdus Salam School of Mathematical Sciences, GC University, Lahore.
Abstract:

Let \(G=(V,E)\) be a finite simple graph with \(v =|V(G)|\) vertices and \(e=|E(G)|\) edges. Further suppose that \(\mathbb{H}:=\{H_1, H_2, \dots, H_t\}\) is a family of subgraphs of \(G\). In case, each edge of \(E(G)\) belongs to at least one of the subgraphs \(H_i\) from the family \(\mathbb{H}\), we say \(G\) admits an edge-covering. When every subgraph \(H_i\) in \(\mathbb{H}\) is isomorphic to a~given graph \(H\), then the graph \(G\) admits an \(H\)-covering. A graph \(G\) admitting \(H\) covering is called an \((a,d)-H\)-antimagic if there is a bijection \(\eta:V\cup E \to \{1,2,\dots, v+e \}\) such that for each subgraph \(H’\) of \(G\) isomorphic to \(H\), the sum of labels of all the edges and vertices belongs to \(H’\) constitutes an arithmetic progression with the initial term \(a\) and the common difference \(d\). For \(\eta(V)= \{ 1,2,3,\dots,v\}\), the graph \(G\) is said to be super \((a,d)-H\)-antimagic and for \(d=0\) it is called \(H\)-supermagic. When the given graph \(H\) is a cycle \(C_m\) then \(H\)-covering is called \(C_m\)-covering and super \((a,d)-H\)-antimagic labeling becomes super \((a,d)-C_m\)-antimagic labeling. In this paper, we investigate the existence of super \((a,d)-C_m\)-antimagic labeling of book graphs \(B_n\), for \(m=4,\ n\geq2\) and for differences \(d=1, 2, 3, \dots,13\).

Author(s): Muhammad Athar Abbasi1,2, Seong-Hui Eo1, Aziz- ur- Rehman2, Sabahat Zahra Siddiqui2, Yohan Han1, Seon-Mi Yu1, Song Ja Kim1, Mubashir Hassan1, Hussain Raza1, Syed Anan Ali Shah3, Sung-Yum Seo1
1College of Natural Sciences, Department of Biological Sciences, Kongju National University, Gongju, 32588, South Korea.
2Department of Chemistry, Government College University, Lahore-54000, Pakistan.
3Faculty of Pharmacy and Atta-ur-Rahman Institute for Natural Products Discovery (AuRIns), Level 9, FF3, Universiti Teknologi MARA, Puncak Alam Campus, 42300 Bandar Puncak Alam, Selangor Darul Ehsan, Malaysia.
Abstract:

Matrix metalloproteinases-2 and -9 (MMP-2/-9) are key tissue remodeling enzymes that have multiple overlapping activities critical for wound healing and tumor progression. In search of new anti-tumor agents, indole-oxadiazole containing butanamides (1-5) were evaluated with B16F10 mouse melanoma cells in this study. The results showed that compounds 1, 2 and 3 inhibited the cell proliferation in a considerable manner at concentrations ranging from 0-44M. The possible migration inhibitory effects of these melanoma cells were further evaluated through gelatinolytic activity of MMP-2 and MMP-9 secreted from B16F10 cells and it was inferred that compounds 1, 2 and 3 affected the expression and activity of these enzymes in a dose dependent manner while compound 1 can be regarded as promising anti-tumor agent.

Author(s): Aisha Shamim1, Zaheer Ahmad1, Sajid Mahmood2, Umair Ali2, Tariq Mahmood3, Zamir Ahmad Nizami4
1Department of Chemistry, University of Wah, Wah Cantt 47040, Pakistan.
2Department of Chemistry, Division of Science and Technology, University of Education, Township Campus, Lahore, Pakistan.
3Nano Sciences and Technology Department, National Centre for Physics, QAU, Islamabad 45320, Pakistan.
4Department of Chemistry, University of Sargodha,Sub Campus Bhakkar, Pakistan.
Abstract:

The under consideration study focuses on synthesis and characterization of Nickel oxide (NiO) nanoparticles. Nanosized Nickel oxide powder was successfully synthesized using a simple and low cast sol-gel method. This method is environment friendly requiring no expensive chemicals and is time saving. The sol-gel method was accompanied by the formation of precipitates which were dried and calcined at 550\(^{o}\)C to get nickel oxide nanoparticles. The synthesized nanopowder was characterized by X-ray diffraction (XRD), Scanning Electron Microscopy (SEM), and Energy Dispersive Spectroscopy (EDX).

Author(s): Farman ullah Khan1, Sajid Mahmood2, Zaheer Ahmad1, Tariq Mahmood3, Zamir Ahmad Nizami4
1Department of Chemistry, University of Wah, Wah Cantt 47040, Pakistan.
2Department of Chemistry , Division of Science and Technology, University of Education, Lahore 54000, Pakistan.
3Nano Sciences and Technology Department, National Centre for Physics, QAU, Islamabad 45320, Pakistan.
4Department of Chemistry, University of Sargodha,Sub Campus Bhakkar, Pakistan.
Abstract:

The graphene and graphene oxide are latest and advanced materials with wide applications in environment, medical applications, industries, defense applications. We have synthesized graphene oxide from graphite flakes by modifying Hummer method in which we used NaNO\(_{2}\) instead of NaNO\(_{3}\). Then we characterized our samples with X-Ray Diffractometry (XRD), Scanning-Electron Microscopy (SEM) and Fourier-Transform Infrared-Spectroscopy (FT-IR). These results confirmed the formation of graphene oxide also through this process. This graphene oxide can further be used for future applications in wastewater treatment and biomedical applications.

Author(s): Aziz- Ur- Rehman1, Muhammad Athar Abbasi1, Sabahat Zahra Siddiqui1, Shahid Rasool1, Sadia Jabeen1, Amar Masood Joyia1, Asma Salah-Ud-Din Gondal1
1Department of Chemistry, Government College University, Lahore-54000, Pakistan.
Abstract:

Sulfonamides are considered to be biologically active and an important class of pharmaceutical compounds. These constitute an important class of antimicrobials, antidiabetics, anticancer and diuretics. These were the first chemotherapeutic drugs introduced to the world but their rapidly developed resistance decreased their use. In the present work, N-(2/4-substitutedphenyl)-4-(substituted)benzenesulfonamide (3a-d) and N-(tetrahydrofuran-2-ylmethyl)-4-methylbenzenesulfonamide 3e were synthesized by the reaction of substituted aniline (1a-c) and tetrahydrofuran-2-ylmethanamine (1d) with substituted benzenesulfonyl chloride (2a-d) using 10% aqueous \(Na_{2}CO_{3}\) solution as a reaction medium. In the second step, the synthesized molecules 3a-e were allowed to react different alkyl/aralkyl halides (4a-j) to synthesize the target N-substituted compounds, 5a-z,aa,bb, using lithium hydride as an activator and N,N-dimethylformamide (DMF) as a reaction medium. All the synthesized compounds were characterized by using spectral techniques such as \(^{1}\)H-NMR, IR and EI-MS; and further examined for their anti-bacterial activities.

Author(s): Azzeddine El Baraka1, Mohamed Toumlilin1
1University Sidi Mohamed Ben Abdellah, FST Fes-Saiss, Laboratory AAFA Department of Mathematics, B.P 2202 Route Immouzer Fes 30000 Morocco.
Abstract:

In this paper, we study the Cauchy problem of the fractional Navier-Stokes equations with Coriolis force in critical Fourier-Besov-Morrey spaces. By using the Fourier localization argument and the Littlewood-Paley theory, we get a local well-posedness results and global well-posedness results with small initial data belonging to the critical Fourier-Besov-Morrey spaces. Moreover; we prove that the corresponding global solution decays to zero as time goes to infinity, and we give the stability result for global solutions.

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