iosr-Jm   Volume-17 ~ Issue-4 ~ Jul. – Aug. 2021

Abstract: This article presents a short review on Calkin-Wilf Tree. This tree is named after the mathematicians Neil Calkin and Herbert S. Wilf. Some interesting properties of Calkin-Wilf tree are discussed in this article. The sequence of Fibonacci numbers &Lucas numbers, diagonals, continued fractions and paths in Calkin-Wilf tree are presented in this article. Trees like -Calkin-Wilf tree and - Calkin-Wilf tree, which are analogous to Calkin-wilf tree, are given in this article.

Key words: Calkin-Wilf tree, Fibonacci numbers, Lucas numbers, -Calkin-Wilf tree, - Calkin-Wilf tree, Diagonals.

[1]. Calkin Neil and Herbert S. Wilf, Recounting the rationals, The American Mathematical Monthly, Mathematical Association of America, Vol.107, No.4, pp. 360-363, April 2000.
[2]. Toufik Mansour and Bruce Bates, The - Calkin-Wilf tree, Journal of Combinatorial Theory Series A, pp.1-10, Jan.2011.
[3]. Sandie Han, Ariane M. Masuda, Satyanand Singh and Johann Theil, The - Calkin-Wilf forest, math . NT, pp.1-18, Oct. 2015.
[4]. K.Siddharth Choudhury and A. Satyanarayana Reddy, Calkin-Wilf tree, Resonance, Journal of Science Education, Vol.25, No.7, pp. 1001-1013, July 2020.
[5]. Kayla Javier, Exploring the Calkin-Wilf tree: subtrees and the birth of numbers, Honors Program Theses and Projects, Virtual Commons- Bridgewater State University, pp.1-17, Dec. 2015.

Abstract: Fighting any misdeed requires not only putting policies on ground but also the ability and will-power to implement them to the later. This research work intends to look critically at the establishment of Policy and Transparency unit as a mechanism for curbing Sexual Harassment and Corruption in the Nigeria Tertiary Institution. We however, use Kaduna Polytechnic as a case study being the first ever institution to set up the unit. Sexual harassment and corruption are two most devastating menace that affect the psychological and intellectual ability of most of the affect persons. In developed countries like USA one out of every eight graduates suffers the stigma of sexual harassment and only got better with the introduction of Title IX a policy put in place to curb the menace. The study collect data using......

Keywords: Sexual harassment, corruption, Transparency, exploitation and exploitation

[1]. Agardh A, Odberg-Pettersson K andOstergren P.O. (2011) Experience of Sexual Coercion and Risky Sexual Behaviour among Ugandan University Students. Journal of BMC Public Health;10:1471–2458.
[2]. Benson D and Thompson G. (1982) Sexual Harassment on a University Campus: The Confluence of Authority Relations, Sexual Interest and Gender Stratification. SocialProblems. 29(3):236–251.
[3]. Christofides C, Webster N, Jewkes R, Penn-Kekana L, Martin LJ, Abrahams N and Kim J. (2003) The state of sexual assault services: findings from a situation analysis of services in South Africa. The South African Gender-based Violence and Health Initiative report. Retrieved August 9, 2020, from http://www.mrc.ac.za/gender/sexualassault.pdf. Retrieved April 4, 2021
[4]. De Wet A. (2010.) Sexual Harassment of Learners in Secondary Schools: An Education Law Perspective. Thesis submitted in fulfilment of the requirements for the degree Philosophy Doctor in Education Law at the Potchefstroom Campus of the North-West University. Potchefstroom: North-West University;
[5]. Dziech B. W and Weiner L. (1994).The Lecherous Professor: Sexual Harassment on Campus. 2nd ed. Chicago: University of Illinois Press Champaign;.

Abstract: Mathematical modelling have and continuously provide insight on the dynamics of an infectious diseases such as HIV-1, Human Papilloma Virus, Tuberculosis etc. In this paper we develop an HIV-1 mathematical model having six parameters ( ). Effects of chemotherapy, time delay and immune response on Endemic Equilibrium Point (EEP) is studied both analytically and numerically. The analytic results shows that the EEP is stale whenever delay exceeds ten days, Chemotherapy below 72.3% efficacy and CD8+T-cells above 500. The analytic results were confirmed using Matlab dde23 solver..

Keywords : HIV, Reproduction Number, Time Delay, Stability, Endemic Equilibrium point, Chemotherapy, Immune Response, Efficacy.

[1]. Arruda, E. D. (2015). An Optimal Control Approach to HIV Immunology. Applied Mathematics, 1115-1130.
[2]. Bonhoeffer, R. M. (2013). Production of resistant HIV mutants during antiretroviral therapy. Journal of Apllied Mathematics.
[3]. Cherono, P., Kirui, W., Adicka, D. (2019). Modelling the Effects of Immune Response and time delay on HIV-1 In vivo Dynamics in the presence of chemotherapy. Mathematical modelling and Application, volume 4 no.2, 15-21.
[4]. Fisher, K. A. (2013). Stability conditions of HIV co-infection model using Next generation method. Journal of Applied Mathematics Science, 2815-2832.
[5]. Hatta, K. A. (2012). Optimal control of a Delayed HIV infection model with immune Response using an efficient Numerical method. Journal of ISRN Biomathematics, 1-7.