Journal of Progressive Research in Mathematics http://scitecresearch.com/journals/index.php/jprm Journal of Progressive Research in Mathematics en-US jprmeditor@scitecresearch.com (Managing Editor) jprmeditor@scitecresearch.com (JPRM Support Team) Mon, 04 Jul 2022 15:55:24 +0000 OJS 3.1.1.2 http://blogs.law.harvard.edu/tech/rss 60 Traveling wave solutions and numerical solutions for a mBBM equation http://scitecresearch.com/journals/index.php/jprm/article/view/2145 <p>In this paper, some exact meromorphic solutions and generalized trigonometric solutions of the space-time fractional modified Benjamin-Bona-Mahony (mBBM) equation are established by a new transformation and reliable methods. Moreover, some numerical solutions are obtained by using the optimal decomposition method (ODM), and their accuracy is shown in tables and images.</p> Wei Ni, Yezhou Li ##submission.copyrightStatement## http://creativecommons.org/licenses/by-nc/4.0 http://scitecresearch.com/journals/index.php/jprm/article/view/2145 Mon, 04 Jul 2022 15:54:54 +0000 Exact Ordering http://scitecresearch.com/journals/index.php/jprm/article/view/2153 <p>&nbsp;Ordering is an important subject of learning; it has so many applications in day -to - day life. Hence, in this paper exact and general exact ordering methods are reviewed giving sample applications for them.</p> <p>Firstly, the exact ordering method is introduced and few theorems are given to assign the conditions needed to locate the position of a required object among a class of objects to be ordered in a certain manner in three classes.</p> <p>Secondly, the exact ordering method is generalized to any odd number of classes &nbsp;In both cases and if the required object class is put in the middle of other classes, then the required object will be located exactly in the middle of all objects provided that we arrange the objects orderly in three classes in the first case and in ones in the second general case and where certain defined steps are to be followed.In general &nbsp;steps are required to determine the required object exactly and where &nbsp;is the odd number of classes.</p> <p>Making the subject more interesting, deeper, and handled in a sophisticated manner, through the introduction of exact ordering operators, is then exposed to.</p> <p>Finally, few different applications are suggested in physics, operational research, criminal investigation and in sorting files and postal mailing. A practical demonstration with playing cards is also mentioned.</p> Reem A. Abdulali, Muna I. Bnis, Asmaa A. Altayib, Ali M. Awin ##submission.copyrightStatement## http://creativecommons.org/licenses/by-nc/4.0 http://scitecresearch.com/journals/index.php/jprm/article/view/2153 Mon, 08 Aug 2022 00:00:00 +0000 Two Classes of Optimal Fourth-Order Iterative Methods Free from Second Derivative for Solving Nonlinear Equations http://scitecresearch.com/journals/index.php/jprm/article/view/2158 <p>This work proposes new fourth-order iterative methods to solve non-linear equations <em>&nbsp;</em> . The iterative methods proposed here are presented by modifications of a third-order iterative method to be two classes of optimal fourth order. Convergence analysis was done for the iterative methods proposed in this paper. Multiple numerical examples were taken to explain the accuracy and efficiency of the proposed iterative methods.</p> Laila A. Alnaser ##submission.copyrightStatement## http://creativecommons.org/licenses/by-nc/4.0 http://scitecresearch.com/journals/index.php/jprm/article/view/2158 Mon, 08 Aug 2022 01:45:09 +0000 Idempotent Structures Of Semigroup Of Singular - Regular Matrices http://scitecresearch.com/journals/index.php/jprm/article/view/2150 <p>Let S be a semigroup of singular matrices over a subset of the set of integers. The idempotent<br>elements of S are classified into tridempotent, fractional idempotent and skew idempotent<br>elements. Matrices are generally known to be non-commutative but an example of commutative<br>matrices is established in this work. Matrix multiplication and its axioms are employed<br>to establish the results. Regularity was first established and the condition for regularity of<br>each idempotent structure obtained is discussed. Some of the structures obtained are used to<br>establish bands of regular elements. The fractional component of S is obtained combinatorially<br>by choosing a number with its sign for every row of each matrix. There are m values of<br>matrices with first and second rows being equal, which are removed from the set since their<br>multiplication gives zero. The satisfaction of the condition for commutativity implies that all<br>the matrices have the same characteristic equation and all are of a specified order n. This is<br>evident in the fact that the product of the principal diagonal, D1 of matrix A is the same as<br>the product of the principal diagonal D2 of matrix B. Also, the product of the off- diagonal of<br>matrices A and B are the same.</p> Adenike Olusola Adeniji ##submission.copyrightStatement## http://creativecommons.org/licenses/by-nc/4.0 http://scitecresearch.com/journals/index.php/jprm/article/view/2150 Thu, 27 Oct 2022 16:38:00 +0000 On the Solutions of Systems of Rational Difference Equations http://scitecresearch.com/journals/index.php/jprm/article/view/2166 <p>In this paper we study the form of the solutions of the following systems of difference equations</p> <p>w_{n+1}=\frac{s_{n}(w_{n-3}+s_{n-4})}{s_{n-4}+w_{n-3} -s_{n}} ,&nbsp; &nbsp;s_{n+1}=\frac{w_{n-2}(w_{n-2}+s_{n-3})}{2*w_{n-2}+s_{n-3}}.</p> <p>w_{n+1}=\frac{(s_{n-4} - w_{n-3})s_{n}}{s_{n-4} -w_{n-3} +s_{n}} ,&nbsp; &nbsp;s_{n+1}=\frac{(s_{n-3} - w_{n-2})w_{n-2}}{s_{n-3}}.</p> <p>With nonzero real numbers initial conditions.</p> E. M. Elsayed, J. G. Al-Juaid, H. Malaikah ##submission.copyrightStatement## http://creativecommons.org/licenses/by-nc/4.0 http://scitecresearch.com/journals/index.php/jprm/article/view/2166 Tue, 01 Nov 2022 00:00:00 +0000 Mathematical Modelling of Cholera Incorporating The Dynamics of The Induced Achlorhydria Condition And Treatment http://scitecresearch.com/journals/index.php/jprm/article/view/2168 <p><span dir="ltr" style="left: 162.16px; top: 487.149px; font-size: 16.6043px; font-family: sans-serif; transform: scaleX(0.926152);" role="presentation">Cholera is an infectious disease caused by the bacterium</span> <span dir="ltr" style="left: 557.035px; top: 487.149px; font-size: 16.6043px; font-family: sans-serif; transform: scaleX(0.948747);" role="presentation">Vibrio cholerae</span> <span dir="ltr" style="left: 667.767px; top: 487.149px; font-size: 16.6043px; font-family: sans-serif; transform: scaleX(0.934212);" role="presentation">rampant in countries with inadequate&nbsp;</span><span dir="ltr" style="left: 70.8667px; top: 507.075px; font-size: 16.6043px; font-family: sans-serif; transform: scaleX(0.931663);" role="presentation">access to clean water and proper sanitation. In this work a mathematical model for cholera incorporating the dynamics of the&nbsp;</span><span dir="ltr" style="left: 70.8667px; top: 527px; font-size: 16.6043px; font-family: sans-serif; transform: scaleX(0.915958);" role="presentation">induced achlorhydria condition and treatment is analysed. Michaelis-menten equation in microbiology is used to show variation&nbsp;</span><span dir="ltr" style="left: 70.8667px; top: 546.925px; font-size: 16.6043px; font-family: sans-serif; transform: scaleX(0.929886);" role="presentation">in pH level of the hydrochloric acid in the digestive system.</span> <span dir="ltr" style="left: 477.17px; top: 546.925px; font-size: 16.6043px; font-family: sans-serif; transform: scaleX(0.936118);" role="presentation">Vibrio cholerae</span> <span dir="ltr" style="left: 585.13px; top: 546.925px; font-size: 16.6043px; font-family: sans-serif; transform: scaleX(0.93402);" role="presentation">are acid labile and thrive well in alkaline medium.</span><br role="presentation"><span dir="ltr" style="left: 70.8667px; top: 566.85px; font-size: 16.6043px; font-family: sans-serif; transform: scaleX(0.914937);" role="presentation">Once the gastric pH is raised by factors like antacid drugs or surgery the stomach medium become suitable for</span> <span dir="ltr" style="left: 817.758px; top: 566.85px; font-size: 16.6043px; font-family: sans-serif; transform: scaleX(0.93717);" role="presentation">Vibrio cholerae&nbsp;</span><span dir="ltr" style="left: 70.8667px; top: 586.775px; font-size: 16.6043px; font-family: sans-serif; transform: scaleX(0.931697);" role="presentation">to thrive and multiply very fast than healthy people. This lead to cholera transmission as the infected individuals with induced&nbsp;</span><span dir="ltr" style="left: 70.8667px; top: 606.7px; font-size: 16.6043px; font-family: sans-serif; transform: scaleX(0.943932);" role="presentation">achlorhydria condition shed more folds of</span> <span dir="ltr" style="left: 362.123px; top: 606.7px; font-size: 16.6043px; font-family: sans-serif; transform: scaleX(0.944688);" role="presentation">Vibrio cholerae</span> <span dir="ltr" style="left: 471.967px; top: 606.7px; font-size: 16.6043px; font-family: sans-serif; transform: scaleX(0.962126);" role="presentation">to the environment. If individuals with achlorhydria condition are&nbsp;</span><span dir="ltr" style="left: 70.8667px; top: 626.627px; font-size: 16.6043px; font-family: sans-serif; transform: scaleX(0.908085);" role="presentation">treated, the effect of cholera outbreak is reduced. The existence and stability of the equilibrium points is established. Analysis of&nbsp;</span><span dir="ltr" style="left: 70.8667px; top: 646.552px; font-size: 16.6043px; font-family: sans-serif; transform: scaleX(0.920536);" role="presentation">the model show that the disease free equilibrium is both locally and globally asymptotically stable when the basic reproduction&nbsp;</span><span dir="ltr" style="left: 70.8667px; top: 666.477px; font-size: 16.6043px; font-family: sans-serif; transform: scaleX(0.906407);" role="presentation">number is less than unity, while the endemic equilibrium is locally asymptotically stable when the reproduction number is greater</span><br role="presentation"><span dir="ltr" style="left: 70.8667px; top: 686.402px; font-size: 16.6043px; font-family: sans-serif; transform: scaleX(0.929829);" role="presentation">than unity. Numerical simulations is done using MATLAB software to show the effect of the induced achlorhydria condition on&nbsp;</span><span dir="ltr" style="left: 70.8667px; top: 706.327px; font-size: 16.6043px; font-family: sans-serif; transform: scaleX(0.914195);" role="presentation">the spread of cholera and individuals with this condition suffer severe infection during cholera outbreak</span>.</p> Charles Wanjohi Ngari, Cyrus Gitonga Ngari, Mark Okongo, Jimrise Ochwach ##submission.copyrightStatement## http://creativecommons.org/licenses/by-nc/4.0 http://scitecresearch.com/journals/index.php/jprm/article/view/2168 Wed, 02 Nov 2022 16:21:37 +0000 Graph Applications Using Graphviz in Drainage System: The Case in Madiun City, Indonesia http://scitecresearch.com/journals/index.php/jprm/article/view/2157 <p>There is a need for a drainage system in an area so that the potential for inundation or flooding during rainfall can be predicted to enable anticipatory steps to be taken. One way to present the drainage system is to use graphs. A graph is defined as a set of pairs (𝑉, 𝐸), which in this case 𝑉 is a finite non-empty set whose elements are called vertices and 𝐸 is a set (possibly empty) of unsorted pairs connecting a pair of vertices called sides. In this study, a drainage system in Madiun City, Indonesia, will be presented in a graph using the Graphviz application. Graphviz is software that can be used to create a visualization of structured data such as network images.</p> Gregoria Ariyanti, Ana Easti Rahayu Maya Sari ##submission.copyrightStatement## http://creativecommons.org/licenses/by-nc/4.0 http://scitecresearch.com/journals/index.php/jprm/article/view/2157 Mon, 08 Aug 2022 01:44:37 +0000