Journal of Advances in Mathematics and Computer Science https://www.journaljamcs.com/index.php/JAMCS <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> en-US contact@journaljamcs.com (Journal of Advances in Mathematics and Computer Science) contact@journaljamcs.com (Journal of Advances in Mathematics and Computer Science) Mon, 13 Sep 2021 13:13:46 +0000 OJS 3.1.1.4 http://blogs.law.harvard.edu/tech/rss 60 On Relation between the Joint Essential Spectrum and the Joint Essential Numerical Range of Aluthge Transform https://www.journaljamcs.com/index.php/JAMCS/article/view/30386 <p>Associated with every commuting m-tuples of operators on a complex Hilbert space X is its Aluthge transform. In this paper we show that every commuting m-tuples of operators on a complex Hilbert space X and its Aluthge transform have the same joint essential spectrum. Further, it is shown that the joint essential spectrum of Aluthge transform is contained in the joint essential numerical range of Aluthge transform.</p> O. S. Cyprian ##submission.copyrightStatement## https://www.journaljamcs.com/index.php/JAMCS/article/view/30386 Mon, 13 Sep 2021 00:00:00 +0000 Nonexistence of Global Solutions to A Semilinear Wave Equation with Scale Invariant Damping https://www.journaljamcs.com/index.php/JAMCS/article/view/30387 <p>We obtain a blowup result for solutions to a semilinear wave equation with scale-invariant dissipation. We perform a change of variables that transforms our starting equation into a Generalized Tricomi equation, then apply Kato’s lemma, we can prove a blowup result for solutions to the transformed equation under some assumptions on the initial data. In the critical case, we use the fundamental solutions of the Generalized Tricomi equation to modify Kato’s lemma to deal with it.</p> Changwang Xiao ##submission.copyrightStatement## https://www.journaljamcs.com/index.php/JAMCS/article/view/30387 Thu, 16 Sep 2021 00:00:00 +0000 A New Approach to Detecting and Correcting Single and Multiple Errors in Wireless Sensor Networks https://www.journaljamcs.com/index.php/JAMCS/article/view/30388 <p>Transmission errors are commonplace in communication systems. Wireless sensor networks like many other communication systems are susceptible to various forms of errors arising from sheer noise, heat and interference in sensor circuitry and from other forms of distortions. Research efforts in WSN have attempted to guarantee reliable and accurate data transmission from a target environment in the midst of these unwanted exposures. Many techniques have appeared and employed over the years to deal with the issue of transmission errors in communication systems. In this paper we present a new approach for single and multiple error control in WSN relying on the inherent fault tolerant feature of the Redundant Residue Number System. As an off shoot of Residue Number System, RRNS's fault tolerant capabilities help in building robust systems required for reliable data transmission in WSN systems. The Chinese Remainder Theorem and the Manhattan Distance Heuristics are used during the integer recovery process when detecting and correcting error digit(s) in a transmitted data. The proposed method performs considerably better in terms of data retrieval time than similar approaches by needing a smaller number of iterations to recover an originally transmitted data from its erroneous form. The approach in this work is also less computationally intensive compared to recent techniques during the error correction steps. Evidence of utility of the technique is illustrated in numerical examples.</p> Yakubu Abdul-Wahab Nawusu, Alhassan Abdul-Barik, Salifu Abdul-Mumin ##submission.copyrightStatement## https://www.journaljamcs.com/index.php/JAMCS/article/view/30388 Wed, 22 Sep 2021 00:00:00 +0000 On Reflexivity of Certain Hyponormal Operators with Double Commutant Property https://www.journaljamcs.com/index.php/JAMCS/article/view/30391 <p>Sarason did pioneer work on the reflexivity and purpose of this paper is to discuss the reflexivity of different class of contractions. Among contractions it is now known that C<sub>11</sub> contractions with finite defect indices, C.<sub>o</sub> contractions with unequal defect indices and C<sub>1</sub>. contractions with at least one finite defect indices are reflexive. More over the characterization of reflexive operators among c<sub>o</sub> contractions and completely non unitary weak contractions with finite defect indices has been reduced to that of S (F), the compression of the shift on H<sup>2</sup> ⊖ F H<sup>2</sup>, F is inner. The present work is mainly focused on the reflexivity of contractions whose characteristic function is constant. This class of operator include many other isometries, co-isometries and their direct sum. We shall also discuss the reflexivity of hyponormal contractions, reflexivity of C<sub>1</sub>. contractions and weak contractions. It is already known that normal operators isometries, quasinormal and sub-normal operators are reflexive. We partially generalize these results by showing that certain hyponormal operators with double commutant property are reflexive. In addition, reflexivity of operators which are direct sum of a unitary operator and C.<sub>o</sub> contractions with unequal defect indices,is proved Each of this kind of operator is reflexive and satisfies the double commutant property with some restrictions.</p> Pradeep Kothiyal ##submission.copyrightStatement## https://www.journaljamcs.com/index.php/JAMCS/article/view/30391 Mon, 27 Sep 2021 00:00:00 +0000