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.

Abstract: This paper discusses the development of the Economic Ordering Quantity (EOQ) model in the form of a deterministic inventory for single-item by adding a tolerance value for perishable goods. The tolerance value given is called when an order is placed and when the item is stored, assuming that . The model in this paper is able to minimize the damage or shrinkage which is controlled from the start, especially for fish, fruit, vegetables and meat. The EOQ model by adding a tolerance value is able to minimize the total inventory cost by increasing the order cycle and controlling the lifetime for each product.

Key words: EOQ; inventory management; perishable goods; tolerance value

[1]. T. Bramorski, Determining discounts for perishable inventory, Journal of Business & Economics Research, 6 (2008), 51-58.
[2]. J. M. Cargal, The EOQ inventory formula, http://www.cargalmathbooks.com. Web. Accessed in 6th July 2020 time 02.00.
[3]. J. M. Chen, An inventory model for deteriorating items with time proportional demand and shortages under inflation and time discounting, International Journal of Production Economics, 55 (1998), 21-30.
[4]. P. H. Hsu, Optimal ordering policy for fast deteriorating items, African Journal of Business Management, 6 (2012), 8837-8852.
[5]. H. C. Iwu, C.J. Ogbonna, O. Jude, and K.G. Onuma, Application of inventory model in determining stock control in an organization, American Journal of Applied Mathematics and Statistics, 2 (2014), 307-317.

Abstract: In this paper, a new method for the numerical inversion of the Sumudu Transform is proposed. Using the Laplace-Sumudu duality, a method of series expansion is presented in which the expansion is done in terms of the Legendre polynomials.

Key words: Sumudu Transform; Inverse Sumudu Transform; numerical inversion; Legendre Polynomials; Laplace-Sumudu duality.

[1]. Watugala, G. K. (1993). Sumudu Transform: A new integral transform to solve differential equations and control engineering problems. International Journal of Mathematical Education in Science and Technology, 24(1), 35-43
[2]. Weerakoon, S. (1998). Complex inversion formula for Sumudu transform. International Journal of Mathematical Education in Science and Technology, 29(4), 618-620.
[3]. Belgacem, F. B. M., and Karaballi, A. A. (2006). Sumudu transform fundamental properties investigations and applications. International Journal of Applied mathematics and Stochastic Analysis, 2006.
[4]. A. M. Cohen. Numerical Methods for Laplace Transform Inversion, Springer, 2007

Abstract: The article analyzes the properties of the sequences 3k – 1 and 3k + 1 at their separate and joint use in iterative processes. The Collatz problem is considered as a special case of the problem of determining the optimal iterative process using both sequences 3k – 1 and 3k +1, which achieves 1 in the minimum number of steps (iterations). It is proved that the process P2, using the sequence 3k + 1, cannot diverge or go in loops, so it always reaches 1, but in general this requires a large number of iterations. Process P1, using the sequence 3k – 1, cannot diverge, but can go in loops. An estimate is obtained for the number of iterations required to establish the absence of divergence of the processes P1 and P2.

Keywords and phrases: Collatz problem, problem of representation of integers, iterative process, optimal algorithm.

[1]. Romanov V.N. Study of fundamental problems of number theory. Saint Petersburg, Publishing house "Asterion", 2015 (in Russian).
[2]. Romanov V.N. Fermat quadratic equation and prime numbers. IOSR Journal of Mathematics, V. 15, Issue I (Ser. II), 2019, pp. 19 – 23.

Abstract: Background: Though Mathematics is an important and major subject taught in schools, the performance in the subject has been very poor. Learner's Self-efficacy on the topic of probability may determine their ability to tackle questions. There is insufficient empirical data on the influence of learners' self-efficacy on academic performance in the topic of Probability in Meru County. This study therefore sought to establish the relationship between teacher's influence on learner's self-efficacy and performance in the topic of Probability. in teaching. Material and methods: Data collection instruments were survey questionnaire and an interview guide. A pilot study was conducted to check on validity and reliability of the instruments. Data analysis utilized statistical measures of central tendency and dispersion. Simple regression analysis was used to determine the statistical relationship (y=a+bx......

Keywords Teacher, Probability, Self-Efficacy

[3]. Alexander, J., Nuchols, B., Bloom, J., & Lee, S. (2010). Organizational demography and turnover: An examination of multiform and nonlinear heterogeneity. Human Relations, 48(12), 1455- 1480.doi: 10.1177/001872679504801204
[4]. Benson, A. D., & Whitworth, A. (2014). Research on course management systems in higher education. North Carolina: Information Age Publishing.
[5]. Bray, B., &McClaskey, K. (2015). Make learning personal: The what, who, where, and why. Indiana: Corwin.
[6]. Burt, A. (April 01, 2010). Perspective: Sex, Recombination, And The Efficacy Of Selection & Mdash;Was Weismann Right?. Evolution, 54, 2, 337-351.
[7]. Busato, V. V., Prins, F. J., Elshout, J. J., & Hamaker, C. (January 01, 2010). Intellectual ability, learning style, personality, achievement motivation and academic success of psychology students in higher education. Personality and Individual Differences, 29, 6, 1057-1068.