Asian Research Journal of Mathematics http://journalarjom.com/index.php/ARJOM <p style="text-align: justify;"><strong>Asian Research Journal of Mathematics (ISSN: 2456-477X)</strong> aims to publish high-quality papers (<a href="/index.php/ARJOM/general-guideline-for-authors">Click here for Types of paper</a>) in all areas of ‘Mathematics and Computer Science’. By not excluding papers on the basis of novelty, this journal facilitates the research and wishes to publish papers as long as they are technically correct and scientifically motivated. The journal also encourages the submission of useful reports of negative results. This is a quality controlled, OPEN peer-reviewed, open access INTERNATIONAL journal.</p> SCIENCEDOMAIN international en-US Asian Research Journal of Mathematics 2456-477X Tetranacci and Tetranacci-Lucas Quaternions http://journalarjom.com/index.php/ARJOM/article/view/30137 <p>The quaternions form a 4-dimensional Cayley-Dickson algebra. In this paper, we introduce the Tetranacci and Tetranacci-Lucas quaternions. Furthermore, we present some properties of these quaternions and derive relationships between them. We present the generating functions, Binet's formulas and sums formulas of these quaternions. Moreover, we give matrix formulation of Tetranacci and Tetranacci-Lucas quaternions.</p> Yüksel Soykan ##submission.copyrightStatement## 2019-08-12 2019-08-12 1 24 10.9734/arjom/2019/v15i130137 Center Conditions for a Class of Rigid Quintic Systems http://journalarjom.com/index.php/ARJOM/article/view/30138 <p>The problem of determining necessary and sufficient conditions on P and Q for system.</p> <p><em>x = - y+P(x+y),y = x+Q(x+y)</em> to have a center at the origin is known as the Poincaré center-focus problem. So far, people has tried many ways to solve the problem of central focus. However, it is difficult to solve the center focus problem of higher order polynomial system. In this paper, we use the Poincaré and Alwash-Lloyd methods to study the center focus problem and derive the center conditions of the five periodic differential equation.</p> Fei Fei Lu ##submission.copyrightStatement## 2019-08-16 2019-08-16 1 8 10.9734/arjom/2019/v15i130138 A New and Simple Prime Sieving Technique for Generating Primes Ending with a Given Odd Digit http://journalarjom.com/index.php/ARJOM/article/view/30139 <p>The essence of this paper is to furnish a simple prime sieving technique which deletes composites from a nite list of natural numbers ending with any given odd digit with the exception of the digit 5, leaving behind prime numbers ending with the given digit. This technique is so much like the Eratosthenes' sieving technique.</p> Okoh Ufuoma ##submission.copyrightStatement## 2019-08-26 2019-08-26 1 11 10.9734/arjom/2019/v15i130139 Rosenzweig-Macaurther Model with Holling type II Predator Functional Response for Constant Delayed Migration http://journalarjom.com/index.php/ARJOM/article/view/30140 <p>Predator-prey models describe the interaction between two species, the prey which serves as a food source to the predator. The migration of the prey for safety reasons after a predator attack and the predator in search of food, from a patch to another may not be instantaneous. In this paper, a Rosenzweig-MacAurther model with a Holling-type II predator functional response and time delay in the migration of both species is developed&nbsp;and analysed. Stability analysis of the system shows that depending on the prey growth and prey migration rates either both species go to extinction or co-exist. Numerical simulations show that a longer delay in the migration of the species leads makes the model to stabilize at a slower rate compared to when the delay is shorter. Relevant agencies like<br>the Kenya Wildlife Service should address factors that slow down migration of species, for example, destruction of natural habitats for human settlement and activities, which may cause delay in migration.</p> Apima B. Samuel Lawi O. George Nthiiri J. Kagendo ##submission.copyrightStatement## 2019-08-29 2019-08-29 1 14 10.9734/arjom/2019/v15i130140