Journal of Advances in Mathematics and Computer Science <p style="text-align: justify;"><strong>Journal of Advances in Mathematics and Computer Science (ISSN:&nbsp;2456-9968) </strong>aims to publish original research articles, review articles and short communications, in all areas of mathematics and computer science. Subject matters cover pure and applied mathematics, mathematical foundations, statistics and game theory, use of mathematics in natural science, engineering, medicine, and the social sciences, theoretical computer science, algorithms and data structures, computer elements and system architecture, programming languages and compilers, concurrent, parallel and distributed systems, telecommunication and networking, software engineering, computer graphics, scientific computing, database management, computational science, artificial Intelligence, human-computer interactions, etc. This is a quality controlled, OPEN peer reviewed, open access INTERNATIONAL journal.</p> SCIENCEDOMAIN international en-US Journal of Advances in Mathematics and Computer Science 2456-9968 Solution of Two-Point Linear and Nonlinear Boundary Value Problems with Neumann Boundary Conditions Using a New Modified Adomian Decomposition Method <p><span class="fontstyle0">In this paper, we present the New Modified Adomian Decomposition Method which is a&nbsp;modification of the Modified Adomian Decomposition Method. The new method incorporates&nbsp;the inverse linear operator theorem into the modified Adomian decomposition method for the&nbsp;calculation of </span><span class="fontstyle2">u</span><span class="fontstyle3">0</span><span class="fontstyle0">. Six linear and nonlinear boundary value problems with Neumann conditions&nbsp;are solved in order to test the method. The results show that the method is effective.</span> </p> Justina Mulenga Patrick Azere Phiri ##submission.copyrightStatement## 2020-09-26 2020-09-26 49 60 10.9734/jamcs/2020/v35i730303 Simulation of a Deterministic Model of HIV Transmission between Two Closed Patches <p>Numerical simulation of a deterministic model of HIV transmission between major cities in Kenya is carried out. The model considered two closed patches connected by the commuter movements of truck drivers being the agents of HIV transmission. The transmission kernel being the function of distance between the patches is ignored. The numerical algorithms are applied in the solution of a nonlinear first-order differential equations. The algorithms are implemented with the aid of MATLAB solver which has an in- built mechanism of Runge Kutta method of fourth order. Numerical simulation indicated the population dynamics of the patches, effect of migration on female sex workers and model reproduction number. The findings of the study were that the migration of the truck drivers between two closed patches contributed significantly to the spread of HIV. In this regard, it was recommended that, stakeholders should target the truck driving population and towns along the transport corridors to mitigate the growing HIV infections and integrate the truck drivers in the national health strategy</p> James Khobocha Mirgichan Cyrus Gitonga Ngari Stephen Karanja ##submission.copyrightStatement## 2020-09-08 2020-09-08 1 11 10.9734/jamcs/2020/v35i730298 A Theoretical Model of Corruption Using Modified Lotka Volterra Model: A Perspective of Interactions between Staff and Students <p>Corruption is the misuse of power or resources for private gain. This undermines economic development, political stability, and government legitimacy, the society fabric, allocation of resources to sectors crucial for development, and encourages and perpetuates other illegal opportunities. Despite Mathematical modeling being a powerful tool in describing real life phenomena it still remains unexploited in the fight of corruption menace. This study uses Lotka Volterra, predator-prey equations to develop a model to describe corruption in institutions of higher learning, use the developed model to determine its equilibria, determine the condition for stability of the equilibria and finally carry out the simulation. The corrupt students and staff act as predators while their non-corrupt counterparts act as prey in the paper. Theory of ordinary differential equations was used to determine steady states and their stability. Mathematica was used for algebraic analysis and Matlab was used for numerical analysis and simulation. Analytical result suggested multiple steady state however numerical result confirmed that the model has four steady states. Numerical bifurcation analysis suggests the possibility of backward of corrupt staff when &nbsp;is about 39. Numerical simulation points to an increasing trend on corrupt staff and decrease trend on corrupt student. This study concludes that more focus should be put to staff than students in curbing the spread of corruption. Future study should strive to fit this model in real data.</p> Mercy Kawira Cyrus Gitonga Ngari Stephen Karanja ##submission.copyrightStatement## 2020-09-08 2020-09-08 12 25 10.9734/jamcs/2020/v35i730299 Some Exact Solutions of Compressible and Incompressible Euler Equations <p><span class="fontstyle0">In this paper, we use a surprised system to construct some exact solutions of compressible Euler equations with two and three dimension. Furthermore, we also give other exact solutions of three dimension incompressible Euler equations.</span></p> Rulv Li Zhihui Ye Yunnan Minzu ##submission.copyrightStatement## 2020-09-09 2020-09-09 26 37 10.9734/jamcs/2020/v35i730300 A Mathematical Modeling of Tuberculosis Dynamics with Hygiene Consciousness as a Control Strategy <p><span class="fontstyle0">Tuberculosis, an airborne infectious disease, remains a major threat to public health in Kenya.&nbsp;In this study, we derived a system of non-linear ordinary differential equations from the SLICR&nbsp;mathematical model of TB to study the effects of hygiene consciousness as a control strategy&nbsp;against TB in Kenya. The effective basic reproduction number (</span><span class="fontstyle2">R</span><span class="fontstyle3">0</span><span class="fontstyle0">) of the model was determined&nbsp;by the next generation matrix approach. We established and analyzed the equilibrium points.&nbsp;Using the Routh-Hurwitz criterion for local stability analysis and comparison theorem for global&nbsp;stability analysis, the disease-free equilibrium (DFE) was found to be locally asymptotically stable&nbsp;given that </span><span class="fontstyle2">R</span><span class="fontstyle3">0 </span><span class="fontstyle2">&lt; </span><span class="fontstyle0">1.</span>&nbsp;&nbsp;<span class="fontstyle0">Also by using the Routh-Hurwitz criterion for local stability analysis and Lyapunov function and&nbsp;LaSalle’s invariance principle for global stability analysis, the endemic equilibrium (EE) point&nbsp;was found to be locally asymptotically stable given that </span><span class="fontstyle2">R</span><span class="fontstyle3">0 </span><span class="fontstyle2">&gt; </span><span class="fontstyle0">1. Using MATLAB </span><span class="fontstyle4">ode45 </span><span class="fontstyle0">solver,&nbsp;we simulated the model numerically and the results suggest that hygiene consciousness can help<br>in controlling TB disease if incorporated effectively.</span> </p> Phineas Z. Mawira David M. Malonza ##submission.copyrightStatement## 2020-09-14 2020-09-14 38 48 10.9734/jamcs/2020/v35i730302 Meta-Heuristic Solutions to a Student Grouping Optimization Problem faced in Higher Education Institutions <p><span class="fontstyle0">Combinatorial problems which have been proven to be NP-hard are faced in Higher Education Institutions and researches have extensively investigated some of the well-known combinatorial&nbsp;problems such as the timetabling and student project allocation problems. However, NP-hard&nbsp;problems faced in Higher Education Institutions are not only confined to these categories of&nbsp;combinatorial problems. The majority of NP-hard problems faced in institutions involve grouping&nbsp;students and/or resources, albeit with each problem having its own unique set of constraints.&nbsp;Thus, it can be argued that techniques to solve NP-hard problems in Higher Education Institutions&nbsp;can be transferred across the different problem categories. As no method is guaranteed to<br>outperform all others in all problems, it is necessary to investigate heuristic techniques for&nbsp;solving lesser-known problems in order to guide stakeholders or software developers to the most&nbsp;appropriate algorithm for each unique class of NP-hard problems faced in Higher Education</span>&nbsp;<span class="fontstyle0">Institutions. To this end, this study described an optimization problem faced in a real university&nbsp;that involved grouping students for the presentation of semester results. Ordering based&nbsp;heuristics, genetic algorithm and the ant colony optimization algorithm implemented in Python&nbsp;programming language were used to find feasible solutions to this problem, with the ant colony&nbsp;optimization algorithm performing better or equal in 75% of the test instances and the genetic&nbsp;algorithm producing better or equal results in 38% of the test instances.</span> </p> Kenekayoro Patrick Biralatei Fawei ##submission.copyrightStatement## 2020-10-01 2020-10-01 61 74 10.9734/jamcs/2020/v35i730304 Ideally Statistical Convergence in n-normed Space <p><span class="fontstyle0">The aim of the article is to extend the concept of Ideally statistical convergence from 2 normed&nbsp;spaces to n-normed space. We have also study and prove some important algebraic and&nbsp;topological properties of </span><span class="fontstyle2">I</span><span class="fontstyle3">deally</span><span class="fontstyle0">-statistical convergence of real sequences in n-normed space. In&nbsp;the last part of this article we obtain a criterion for </span><span class="fontstyle2">I</span><span class="fontstyle0">-statistically Cauchy sequence in n-normed&nbsp;space to be </span><span class="fontstyle2">I</span><span class="fontstyle0">-statistically Cauchy with respect to </span><span class="fontstyle2">∥</span><span class="fontstyle3">.</span><span class="fontstyle2">∥</span><span class="fontstyle4">∞</span><span class="fontstyle0">.</span> </p> Nazneen Khan Amani Shatarah ##submission.copyrightStatement## 2020-10-03 2020-10-03 75 84 10.9734/jamcs/2020/v35i730305 The Fornberg-Whitham Equation Solved by the Differential Transform Method <p><span class="fontstyle0">The Differential Transform Method is a powerful analytical method that can solve nonlinear&nbsp;partial differential equations. Yet, the method cannot be used to solve time-dependent partial&nbsp;differential equations that involve more than one partial derivative with respect to the temporal&nbsp;variable </span><span class="fontstyle2">t </span><span class="fontstyle0">when they are of the same order, as in the case of the Fornberg-Whitham type&nbsp;equations. In this paper, a new theorem is devised to overcome the aforementioned problem of<br>the method, and it has been successfully applied to solve the Fornberg-Whitham equation. The&nbsp;other equations belonging to this group of equations, such as the Camassa-Holm equation and&nbsp;the Degasperi-Procesi equation, may also be solved by this approach.</span> </p> Helena Nayar Patrick Azere Phiri ##submission.copyrightStatement## 2020-10-13 2020-10-13 85 95 10.9734/jamcs/2020/v35i730306 Fractal Properties of Pore Distribution of Electrospun Nanofiber Membrane <p>Due to the complex and chaotic characteristics of elecrtospun nanofiber membrane, fractal theory is a suitable mathematical framework. Using the fractal theory, Matlab and other computer software in Mathematics, the fractal properties of pore distribution of elecrtospun nanofiber membrane and the relationship between the fractal dimension and the physical properties of nonwovens are studied. Thirty samples were produced by using polyvinyl alcohol (PVA)on the DXES-01 automatic electrostatic spinning machine; BMP images of 30 samples were obtained by TM-1000 table scanning electron microscope; The scanning electron micro-scope images were grayed by digital image processing technology, and the average pore width of the samples was further calculated by Matlab software from the gray value matrix; G-P algorithm is used to calculate the fractal dimension of pore width distribution; The relationship between air flow resistance and the fractal dimension of pore width distribution of electrospun nanofiber membrane was analyzed. Finally, the correlation fractal dimension of the average pore width of electrospun nanofiber membrane has a quadratic function relation with the air flow resistance; The correlation fractal dimension of the average pore width obtained is consistent with the fractal dimension of porosity obtained by Ting Wang under the meaning of the relative error less than 10%is the same.</p> Bai Chun- yu Chen Ying Liu Yong Shi Luo- yi Chen Ru- dong ##submission.copyrightStatement## 2020-10-15 2020-10-15 96 105 10.9734/jamcs/2020/v35i730307 Eigenvalues and Eigenvectors for 3×3 Symmetric Matrices: An Analytical Approach <p>Research problems are often modeled using sets of linear equations and presented as matrix equations. Eigenvalues and eigenvectors of those coupling matrices provide vital information about the dynamics/flow of the problems and so needs to be calculated accurately. Analytical solutions are advantageous over numerical solutions because numerical solutions are approximate in nature, whereas analytical solutions are exact. In many engineering problems, the dimension of the problem matrix is 3 and the matrix is symmetric. In this paper, the theory behind finding eigenvalues and eigenvectors for order 3×3 symmetric matrices is presented. This is followed by the development of analytical solutions for the eigenvalues and eigenvectors, depending on patterns of the sparsity of the matrix. The developed solutions are tested against some examples with numerical solutions.</p> Abu Bakar Siddique Tariq A. Khraishi ##submission.copyrightStatement## 2020-10-21 2020-10-21 106 118 10.9734/jamcs/2020/v35i730308