Asian Journal of Mathematical Sciences(AJMS) <p>Mathematics in the Asian region has grown tremendously in recent years. There is a need to have a journal to unite such a development. The Asian Journal of Mathematical Sciences (AJMS) is a new journal that aims to stimulate mathematical research in the Asian region. It publishes original research papers and survey articles on all areas of pure mathematics and theoretical applied mathematics. High standards will be applied in evaluating submitted manuscripts, and the entire editorial board must approve the acceptance of any paper.</p> <p> </p> <p><strong>Asian Journal of Mathematical Sciences (AJMS) </strong>is an international Referred and Peer Reviewed Online Journal with E-ISSN: 2581-3463 published by B.R. Nahata Smriti Sansthan for the enhancement of Pure and Applied Mathematics, Mathematical Physics, Theoretical Mechanics, Probability and Mathematical Statistics, and Theoretical Biology. </p> <p>AJMS is an Open Access Online Journal that publishes full-length papers, reviews and short communications exploring and to promote diverse and integrated areas as Applied Mathematics and Modeling, Analysis and Its Applications, Applied Algebra and Its Applications, Geometry and Its Applications, Algebraic Statistics and Its Applications, Algebraic Topology and Its Applications.</p> <p><strong><u>SUBJECT CATEGORY </u></strong></p> <p>Papers reporting original research and innovative applications from all parts of the world are welcome.</p> <p><strong>Subject areas suitable for publication include, but are not limited to the following fields:</strong></p> <p><strong>Applied Mathematics and Modeling:</strong></p> <ul> <li>Computational Methods,</li> <li>Ordinary and partial Differential Equations,</li> <li>Mathematical Modeling and Optimization,</li> <li>Probability and Statistics Applications,</li> <li>Operations research,</li> <li>Model selection,</li> <li>Bio Mathematics,</li> <li>Data Analysis and related topics. </li> <li>Mathematical Finance,</li> <li>Numerical Solution of Stochastic Differential Equations,</li> <li>Stochastic Analysis and Modeling.</li> </ul> <p><strong>Analysis and Its Applications: </strong></p> <ul> <li>Approximation Theory and Its Applications,</li> <li>Ergodic Theory,</li> <li>Sequence Spaces and Summability,</li> <li>Fixed Point Theory,</li> <li>Functional Analysis and Its Applications and related topics.</li> </ul> <p><strong>Applied Algebra and Its Applications</strong>:</p> <ul> <li>Information Theory and Error Correcting Codes,</li> <li>Cryptography,</li> <li>Combinatorics and Its Applications,</li> <li>Cellular Automata,</li> <li>Fuzzy and Its Applications,</li> <li>Computational Algebra,</li> <li>Computational Group Theory and related topics</li> </ul> <p><strong>Geometry and Its Applications</strong>:</p> <ul> <li>Algebraic Geometry and Its Applications,</li> <li>Differential Geometry,</li> <li>Kinematics and related topics</li> </ul> <p><strong>Algebraic Statistics and Its Applications</strong>:</p> <ul> <li>Algebraic statistics and its applications</li> </ul> <p><strong>Algebraic Topology and Its Applications</strong>:</p> <ul> <li>Algebraic Topology and Its Applications,</li> <li>Knot Theory and related topics</li> </ul> <p><strong>Pure and Applied Mathematics and its Applications</strong>:</p> <ul> <li>Biology,</li> <li>Chemistry,</li> <li>Physics,</li> <li>Zoology,</li> <li>Health Science,</li> <li>Earth Science,</li> <li>Geology,</li> <li>Social Sciences,</li> <li>Industrial research,</li> <li>Computer Science,</li> <li>Agriculture and Forestry,</li> <li>Environmental Sciences,</li> <li>Statistics,</li> <li>Engineering,</li> <li>Natural Sciences,</li> <li>Political Sciences.</li> </ul> <p><strong><u>JOURNAL PARTICULARS</u></strong></p> <table> <tbody> <tr> <td width="281"> <p>Title</p> </td> <td width="517"> <p><strong>Asian Journal of Mathematical Sciences</strong></p> </td> </tr> <tr> <td width="281"> <p>Frequency</p> </td> <td width="517"> <p>Quarterly</p> </td> </tr> <tr> <td width="281"> <p>E- ISSN</p> </td> <td width="517"> <p><strong>2581-3463</strong></p> </td> </tr> <tr> <td width="281"> <p>P-ISSN</p> </td> <td width="517"> <p><strong>-</strong></p> </td> </tr> <tr> <td width="281"> <p>DOI</p> </td> <td width="517"> <p><strong></strong></p> </td> </tr> <tr> <td width="281"> <p>Publisher</p> </td> <td width="517"> <p><strong>Mr. Rahul Nahata</strong>, B.R. Nahata College of Pharmacy, Mhow-Neemuch Road, Mandsaur-458001, Madhya Pradesh</p> </td> </tr> <tr> <td width="281"> <p>Chief Editor</p> </td> <td width="517"> <p>Dr. M.A. Naidu</p> </td> </tr> <tr> <td width="281"> <p>Starting Year</p> </td> <td width="517"> <p>2017</p> </td> </tr> <tr> <td width="281"> <p>Subject</p> </td> <td width="517"> <p>Mathematics subjects</p> </td> </tr> <tr> <td width="281"> <p>Language</p> </td> <td width="517"> <p>English Language</p> </td> </tr> <tr> <td width="281"> <p>Publication Format</p> </td> <td width="517"> <p>Online</p> </td> </tr> <tr> <td width="281"> <p>Email Id</p> </td> <td width="517"> <p>,</p> </td> </tr> <tr> <td width="281"> <p>Mobile No.</p> </td> <td width="517"> <p>+91-7049737901</p> </td> </tr> <tr> <td width="281"> <p>Website</p> </td> <td width="517"> <p></p> </td> </tr> <tr> <td width="281"> <p>Address</p> </td> <td width="517"> <p>B.R. Nahata Smriti Sansthan, BRNSS PUBLICATION HUB, B.R. Nahata College of Pharmacy, Mhow-Neemuch Road, Mandsaur-458001, Madhya Pradesh</p> </td> </tr> </tbody> </table> <p> </p> BRNSS Publication Hub en-US Asian Journal of Mathematical Sciences(AJMS) <p>This is an Open Access article distributed under the terms of the Attribution-Noncommercial 4.0 International License [CC BY-NC 4.0], which requires that reusers give credit to the creator. It allows reusers to distribute, remix, adapt, and build upon the material in any medium or format, for noncommercial purposes only.</p> On Extension Theorems in Ordinary Differential Systems of Equations <p>Given the differential system x′ = f (t, x); f: J × M → Rn, we establish the Peano’s theorem on existence of the solution plus Picard Lindelof theorem on uniqueness of the solution. Using the two, we then worked on the extendibility of the solutions whose local existence is ensured by the above in a domain of open connected set producing the following results; If D is a domain of R × Rn and F: D → Rn is continuous and suppose that (t0, x0) is a point D and if the system has a solution x(t) defined on a finite interval (a, b) with t ∈ (a, b) and x(t0) = x0, then whenever f is bounded and D, the limits<br>xa<br>xtta+()=+lim()<br>xb<br>xttb−()=−lim()<br>Exists as finite vectors and if the point (a, x(a+)),(b, x(b-)) is in D then x(t) is extendable to the point t = a (t = b). In addition to this are other results as could be seen in major sections of this work.</p> Eziokwu, Chigozie Emmanuel Copyright (c) 2023 Eziokwu, Chigozie Emmanuel 2023-02-08 2023-02-08 6 3 10.22377/ajms.v6i3.444 Simulation of the Movement of Ground Water in a rectangular jumper with a screen <p>Within the frame work of planar steady-state filtration of incompressible fluid according to Darcy’s law, an exact analytical solution of the problem of flow in a rectangular cofferdam with a screen in the presence of evaporation from the free surface of groundwater is given. The limiting cases of the considered motion – filtration in unconfined reservoir to imperfect gallery, as well as the flow in the absence of evaporation – are noted.</p> E. N. Bereslavsky Copyright (c) 2023 E. N. Bereslavsky 2023-02-08 2023-02-08 6 3 10.22377/ajms.v6i3.445 On Application of the Newton-Raphson’s Fixed Point Iterative Method in the Solution of Chemical Equilibrum Problems <p>In this work, we discussed the solution of a chemical equilibrium problem aiming to obtain it’s fixed point. To do this, the preliminary and basic ideas introducing the fixed point theory were X-rayed and the Newton-Raphson’s iterative method for solving the system of non-linear equations discussed; then, the problem of the chemical equilibrium involving principal reactions in the production of synthesis gas by partial oxidation of methane with oxygen was stated. Using a computer program, the O reactant ratio that produces an adiabatic equilibrium temperature was obtained by developing a system of seven simultaneous non-linear equations that have the form which we now solve using the Newton-Raphson’s method described in section 2.2 and hence the desired fixed point of the chemical equilibrium problem.</p> Eziokwu C. Emmanuel Copyright (c) 2023 Eziokwu C. Emmanuel 2023-02-08 2023-02-08 6 3 10.22377/ajms.v6i3.443 Exploring the Methods of Cointegration Procedures in Dynamics of HIV/AIDS and Related Infections <p>Introduction: Cointegration has become an important property in contemporary time series analysis. Time series often have trends - either deterministic or stochastic. Material and Methods: This research work seeks to determine the inherent long run relationship between the human immunodeficiency virus (HIV) and other diseases and the circumstances when it is reasonable to expect that two or more diseases may be cointegrated. That is, if at least one of the processes is driving the other and if the diseases are being driven by the same underlying process. Result: The data (Prevalence of HIV/Acquired Immunodeficiency Syndrome [AIDS] Incidences) modeled in this study were obtained from the National Agency for the Control of AIDS. The stationarity characteristics of the study variables were investigated using Augmented Dickey-Fuller test, the long-run relationship between HIV and other two diseases was determined using Engle-Granger cointegration, Phillips-Ouliaris, and Johansen testing procedure while the Granger causality test was also performed to determine the short run relationship of the variables. Conclusion: Results showed that the series are integrated of order two; HIV, Hepatitis, and TB are found to be strongly and significantly positively correlated, the data series are considered to be stationary after the second differences. Furthermore, the Granger causality tests show that HIV “Granger causes” Tuberculosis and Hepatitis in Nigeria. However, Phillips-Ouliaris Test for Cointegration Determines the strongest cointegration level among HIV/AIDS and other infections. Hence, it is the most robust test for testing cointegration between HIV and tuberculosis, and HIV and Hepatitis disease.</p> S. A. Adeyemi Gidado Copyright (c) 2023 S. A. Adeyemi Gidado 2023-02-08 2023-02-08 6 3 10.22377/ajms.v6i3.446