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> en-US contact@journalarjom.com (Asian Research Journal of Mathematics) contact@journalarjom.com (Asian Research Journal of Mathematics) Sat, 18 Jan 2020 07:13:11 +0000 OJS 3.1.1.4 http://blogs.law.harvard.edu/tech/rss 60 The Existence of Random Attractor for Stochastic Suspension Bridge Equation http://journalarjom.com/index.php/ARJOM/article/view/30172 <p>This paper is aimed at an extensible suspension bridge equation with additive noise and linear&nbsp;memory. For the suspension bridge equations without additive noise and memory, there are&nbsp;many classical results. However, the extensible suspension bridge equations with both additive&nbsp;noise and linear memory were not studied before. The object of this paper is to provide a&nbsp;result on the random attractor to the above problem using compactness translation theorem and&nbsp;decomposition technique.</p> Xiao Bin Yao ##submission.copyrightStatement## http://journalarjom.com/index.php/ARJOM/article/view/30172 Sat, 18 Jan 2020 00:00:00 +0000 Certain Geometric Aspects of a Class of Almost Contact Structures on a Smooth Metric Manifold http://journalarjom.com/index.php/ARJOM/article/view/30173 <p>The classication of Smooth Geometrical Manifolds still remains an open problem. The concept of almost contact Riemannian manifolds provides neat descriptions and distinctions between classes of odd and even dimensional manifolds and their geometries. We construct an almost contact structure which is related to almost contact 3-structure carried on a smooth Riemannian manifold (M, gM) of dimension (5n + 4) such that gcd(2, n) = 1. Starting with the almost contact metric manifolds (N4n+3, gN) endowed with structure tensors (ϕi, ξj , ηk) such that 1 ≤ i, j, k ≤ 3 of types (1, 1), (1, 0), (0, 1) respectively, we establish that there exists a structure (ϕ4, ξ4, η4) on (N4n+3 ⊗ Rd) ≈ M; gcd(4, d) = 1, d|2n + 1, constructed as linear combinations of the three structures on (N4n+3, gN) . We study some algebraic properties of the tensors of the constructed almost contact structure and further explore the Geometry of the two manifolds (N4n+3⊗Rd) ≈ M and N4n+3 via a !submersion F : (N4n+3 ⊗Rd) ↩→ (N4n+3) and the metrics gM respective gN&nbsp;between them. This provides new forms of Gauss-Weigarten's equations, Gauss-Codazzi equations and the Ricci equations incorporating the submersion other than the First and second Fundamental coecients only. Fundamentally, this research has revealed that the structure (ϕ4, ξ4, η4) is constructible and it is carried on the hidden compartment of the manifold M∼=(N4n+3 ⊗ Rd) (d|2n + 1) which is related to the manifold (N4n+3).</p> Ojiema M. Onyango, Mengich Beatrice, Wafula A. Wanambisi ##submission.copyrightStatement## http://journalarjom.com/index.php/ARJOM/article/view/30173 Tue, 21 Jan 2020 00:00:00 +0000 The Coverage Issues in WSNs http://journalarjom.com/index.php/ARJOM/article/view/30171 <p><strong>Aim:</strong> Wireless Sensor Networks is one of the hot research topic in previous years due to its wide contribution in emerging industry that is Internet of Things. A wireless sensor network is a network of tiny devices, which can gather the information from surrounding and then successfully communicate it via wireless link. WSNs are widely used for monitoring targets in given field of interest. Most popular area of research in Wireless Sensor Networks is coverage. This paper focus on coverage issues in Wireless Sensor Networks.</p> <p><strong>Study Design: </strong>Various Issues in WSNs being studied and analyzed.</p> <p><strong>Place and Duration of Study: </strong>Swami Parmanand College Lalru, between May 2019 to December 2019.</p> <p><strong>Methodology: </strong>It included following steps:-</p> <ul> <li>Survey of the literature related to the proposed work.</li> <li>Comparison of different types of WSNs and challenges and issues related to them.</li> <li>Detailed study of coverage issue involved in implementation of WSN.</li> </ul> <p><strong>Results: </strong>Coverage selection depends on the system requirement. Each coverage has its own advantages and disadvantages related to its implementation.</p> <p>“Table 2: Comparison between Various WSN and challenges related to them” it discusses about various types of WSNs and the challenges related to each one of them.</p> <p><strong>Conclusion: </strong>Coverage in WSNs can be defined on how well the sensor nodes monitor the targets in given field of interest. Each application comes with different set of coverage requirements; hence, deployment strategies are chosen based on the requirements.</p> Jyoti Rani, Vishal Anand ##submission.copyrightStatement## http://journalarjom.com/index.php/ARJOM/article/view/30171 Sat, 18 Jan 2020 00:00:00 +0000