Efficiency of International Standard Serial Number Code as an Error Correcting Scheme
David Muriuki Gikunju,
Peter Waweru Kamaku,
Augustus Wali Nzomo
Issue:
Volume 10, Issue 1, February 2021
Pages:
1-8
Received:
30 July 2020
Accepted:
27 August 2020
Published:
10 February 2021
Abstract: Error correcting coding is an effective technique of detecting and correcting errors which may occur due to environmental interference or physical defects such as human errors in the communication channels. The International Standard Serial Number code is internationally used for identifying the title of serial publications. This paper analyzes the efficiency of the international standard serial number code as an error correcting scheme. Moreover, the paper explores on the factors which affect the efficiency of any error correcting scheme. The study utilizes weight checksum technique to detect and correct error(s) in a code word. It is clear that ISSN code is not an efficient error coding scheme. ISSN code is only reliable in error detection. ISSN code can detect any error in the code iff the weight checksum equation does not hold. However, the code does not detect silent errors. The study develops a new efficient and robust modified ISSN code that is efficient in error detection and correction capabilities. The code has dual mechanism for error detection and correction in a code word. If the weight checksum equation does not hold and secondly, if the conditions for the generating equation do not hold. Modified ISSN code can detect and correct silent errors in a code word. Modified ISSN code is an efficient error coding scheme for it is efficient in error detection and correction capabilities.
Abstract: Error correcting coding is an effective technique of detecting and correcting errors which may occur due to environmental interference or physical defects such as human errors in the communication channels. The International Standard Serial Number code is internationally used for identifying the title of serial publications. This paper analyzes the...
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Global Stability Analysis of the Role of Antiretroviral Therapy (ART) Abuse in HIV/AIDS Treatment Dynamics
Bassey Echeng Bassey,
Adagba Odey Henry
Issue:
Volume 10, Issue 1, February 2021
Pages:
9-31
Received:
24 December 2020
Accepted:
20 February 2021
Published:
4 March 2021
Abstract: Devastatingly, in spite of the long standing research works on HIV/AIDS infection and treatment dynamics, reviews of existing models clearly shown that the behavioral attitude to treatment consistency by those screened to become aware and those receiving treatment have not been given the desired attention. Moreso, the inconsistency following avoidable treatment truncation and later resumption of treatment by these classes of infectives, which could lead to colossal drug abuse is also not accorded the much expected consideration. Therefore, in this present study, we sought and formulated a nonlinear 6-Dimensional deterministic mathematical HIV/AIDS dynamic model that accounted for the global stability analysis of the role of antiretroviral therapy abuse for the treatment of HIV/AIDS epidemic. The model is structured upon dynamical interactions between 6-subpopulations and HI-virus under bilinear control functions with constant screening of the susceptible. It is assumed that the rate of resumption of ART upon truncation is less than initial ART truncation following the incorporation of HIV aware infectives not ready to receive ART treatment and HIV aware infectives with truncated treatment protocol The system mathematical well-posedness was investigated and model reproduction number determined for both off- treatment (with value ) and for onset-treatment (with value ). We considered the model for off-treatment and thereafter by incorporating LaSalle’s invariant principle into classical Lyapunov function method, we presented an approach for the global stability analysis of the role of ART abuse in HIV/AIDS treatment. Furthermore, the analysis and results of this paper presented a dynamic methodological application of bilinear control functions and an impeccable understanding of the fundamental mechanism in HIV/AIDS treatment in the presence of ART abuse. Using in-built Runge-Kutta of order of precision 4 in a Mathcad surface, numerical validity of model is conducted to investigate the study theoretical and analytical predictions. Results shows that application of onset-treatment functions with trend of ART abuse yield tremendous reduction in HIV/AIDS infection epidemic following the recovery rate of the susceptible population with value increasing from 0.5 cells/mm3 to 1.203 cells/mm3 within the first months and attained stability of 0.62 cells/mm3 through the time interval of 20- 30 months.
Abstract: Devastatingly, in spite of the long standing research works on HIV/AIDS infection and treatment dynamics, reviews of existing models clearly shown that the behavioral attitude to treatment consistency by those screened to become aware and those receiving treatment have not been given the desired attention. Moreso, the inconsistency following avoida...
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Second Refinement of Accelerated over Relaxation Method for the Solution of Linear System
Wondosen Lisanu Assefa,
Ashenafi Woldeselassie Teklehaymanot
Issue:
Volume 10, Issue 1, February 2021
Pages:
32-37
Received:
6 October 2020
Accepted:
3 November 2020
Published:
4 March 2021
Abstract: This paper describes a method for the numerical solution of linear system of equations. The main interest of refinement of accelerated over relaxation (RAOR) method is to minimize the spectral radius of the iteration matrix in order to increase the rate of convergence of the method comparing to the accelerated over relaxation (AOR) method. That is minimizing the spectral radius means increasing the rate of convergence of the method. This motivates us to refine the refinement of accelerated over relaxation method called second refinement of accelerated over relaxation method (SRAOR). In this paper, we proposed a second refinement of accelerated over relaxation method, which decreases the spectral radius of the iteration matrix significantly comparing to that of the refinement of accelerated over relaxation (RAOR) method. The method is a two-parameter generalization of the refinement of accelerated over relaxation methods and the optimal value of each parameter is derived. The third, fourth and in general the kth refinement of accelerated methods are also derived. The spectral radius of the iteration matrix and convergence criteria of the second refinement of accelerated over relaxation (SRAOR) are discussed. Finally a numerical example is given in order to see the efficiency of the proposed method comparing with that of the existing methods.
Abstract: This paper describes a method for the numerical solution of linear system of equations. The main interest of refinement of accelerated over relaxation (RAOR) method is to minimize the spectral radius of the iteration matrix in order to increase the rate of convergence of the method comparing to the accelerated over relaxation (AOR) method. That is ...
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