iosr-Jm   Volume-18 ~ Issue-3 ~ May – Jun. 2022

Abstract: Based on the definition of a strongly 2-nil clean ring and the concept of fuzzy subring, we introduce a new structure that is a strongly 2-nil clean fuzzy ring. Some of characteristics of a strongly 2-nil clean fuzzy ring are as follows: (i) If R is a strongly 2-nil clean fuzzy ring then μ(1-x)=μ((p-q)+g) for two idempotent elements p,q and a nilpotent element g; (ii) μ(x-x^3 )=μ(z) for a nilpotent element z; (iii) μ(1-x-t)=μ(g) for a tripotent element t and a nilpotent element g; (iv) μ_t is a subring on R for t∈[0,μ(0)].

Key words: Ring; Strongly 2-nil clean ring; Fuzzy subring.

[1]. Chen H, Sheibani M. Strongly 2-nil clean rings. Journal of Algebra and Its Applications. 2017;16(9): 1750178.
[2]. Diesl AJ. Nil clean rings. Journal of Algebra. 2013;383: 197-211.
[3]. Koşan T, Wang Z, Zhou Y. Nil-clean and strongly nil-clean rings. Journal of Pure and Applied Algebra. 2016;220(2):633-646.
[4]. Liu WJ. Fuzzy invariant subgroups and fuzzy ideals. Fuzzy Sets and Systems. 1981;8:133-139.
[5]. Melliani S, Backhadach I, Chadli LS. Fuzzy rings and fuzzy polynomial rings. Springer Proceedings in Mathematics & Statistics. 2018;228: 89-98.

Abstract:In this paper we look at the critical edge detection problem (CEDP), which is the task of finding a set of K edges in a graph G whose removal reduces the number of connections between pairs of nodes in the residual graph. In particular, we mainly studied the case in which the given graph is a tree. We investigate the critical edge detection problem over trees in different situations of edge weights. We provide polynomial algorithms for the problems when all connections between pairs of nodes have unit cost.

Key words: Critical edge detection, Pairwise connectivity, Polynomial time algorithm

[1]. Albert.........

Abstract: Forecasting for a future has turned to be of practical importance in the world in many areas. Time series modeling has grown fundamental importance in forecasting to evaluate the said future events. Many important models have been proposed to improve the accuracy of the future prediction. Weather pattern have been changing due to global warming, which has brought a big challenge to the world in affecting economic and noneconomic activities. Global warming causes severe weather changes, which are characterized by precipitation and temperature. Rainfall prediction is one of the most important and challenging tasks in today's world. The objective of this study was to develop a Bayesian vector autoregressive model to forecast the rainfall pattern in Kenya. The Bayesian vector autoregressive model was developed after a diagnostic analysis of the rainfall data. The developed.....

Key words: Global Warming, Bayesian Vector Autoregressive. Forecasting

[1]. Bauer P., A. Thopre and G. Brunet, 2015: The quiet revolution of numerical weather prediction. Nature, 525:47–55.
[2]. Coumou, D. and S. Rahmstorf, 2012: A decade of weather extremes. Nature Climate Change, 2:491–49
[3]. Giannone D, Lenza M, Primiceri GE (2015). "Prior Selection for Vector Autoregressions." Review of Economics and Statistics, 97(2), 436–451
[4]. Jaynes, E. T. (2003). Probability theory: The logic of science. Cambridge university press.
[5]. Ji, M., A. Kumar and A. Leetmaa (2018): A multiseason climate forecast system at the National Meteorological Center. Bull. Amer. Meteo. Soc., 75:569–577

Abstract: This study investigated the effects of Math's kit instructional materials teaching approach on secondary school student's Retention in mathematics. The study was guided by three research questions and two null hypotheses. The study adopted the quasi-experimental research design. The population for the study was 2,526 students, comprising of 1,162 males and 1,364 females. Simple random sampling technique was adopted with a sample size of 135 students, consisting of 70 males and 65 females. Mathematics Retention Test (MRT) was the instrument used in collecting data for pre-test and post-test respectively. The reliability index of the instrument was 0.88%. The data.......

Key words: Math's Kit Instructional Materials, Conventional Method of Teaching Mathematics, Gender Issues, Retention Test.

[1]. Agwagah, U.N.V. & Ezeugo, N.C. (2000). Effects of concept mapping on students' Retention in algebra: Implication for secondary Mathematics education in 21st century. ABACUS. Journal Mathematical Association of Nigeria, 26 (1), 1-3.
[2]. Asante, K.O. (2010). Sex differences in mathematics performance among senior high students in Ghana. Retrieved from http://www.faqs.org/periodicals/201012/2187713381.html#ixzz1I5YvD0t3 American Journal of Education,110, 256-280.
[3]. Ayiego, E.M., Mang'are P.A., Ngome, C.K. & Mandilah, L. (2015). Analytical study of the extent of practices and implementation of ASEI-PDSI approach by teachers of Mathematics in vihiga country. American Research Journal of Mathematics Original Article, 1(1). Retrieved January 8, 2018, from www.arjonline.org 7
[4]. Azuka, B.F. (2013). Attitude of secondary school mathematics teachers towards the teaching of school mathematics in Nigeria. Journal Mathematical Sciences Education, 2(1), 181-191
[5]. CEMASTEA., (2014). Centre for Mathematics Science and Technology Education in Africa: Enhancing the practice of ASEI-PDSI in mathematics and science at primary school levels. Karen road- Bogani, Nairobi, Kenya..

Abstract: An analysis of unsteady turbulent magnetohydrodynamic (MHD) buoyancy driven fluid flow past an infinite vertical plate was developed. The study of magnetohydrodynamics is important due to its industrial and nonindustrial applications. Incompressible viscous dissipative fluid was impulsively started to flow in y-axis direction along the infinite vertical plate and flow problem analysed thereafter. A strong transverse uniform magnetic field is applied along horizontal z-axis normal to the infinite vertical plate in x-y plane. The fluid flow was modelled using laws of conservation of mass, momentum and energy. The model together with its boundary and initial conditions are then transformed to non-dimensional form to obtain non-linear partial dimensionless differential equations with non-dimensional flow parameters........

Key words: Buoyancy, Unsteady, Turbulent, Vertical plate, Finite difference and Magneto hydrodynamics

[1]. Chebos C., Sigey J.K., Okelo J.A., Okwoyo J.M. and Giterere K. (2016), Numerical investigation of unsteady MHD free convective flow past an oscillating free vertical plate with oscillatory heat flux, The Standard International Journal, 4(1), 2321-2403.
[2]. Chepkemoi E. and Mukuna W.O. (2021). Hydromagnetic free convection unsteady turbulent fluid flow over a vertical infinite heat absorbing plate. IOSR Journal of Mathematics, 17(3),42-48.
[3]. Falodun B.O. and Fadugba S.E. (2017). Effects of heat transfer on unsteady magneto hydrodynamics (MHD) boundary layer flow of an incompressible fluid flow of a chemically reacting fluid past a vertical plate. World scientific news 88(2), 118-137.
[4]. Júnior, S. V., Scalon, V. L., Oliveira, S. R., Mioralli, P. C., & Avellone, E. (2021). Dimensionless physical-mathematical modeling of turbulent natural convection. Revista de Engenharia Térmica, 20(3), 37-43.
[5]. Mukuna, W.O. (2021). MHD Turbulent free convection fluid flow over an infinite vertical heat generating cylinder. International Advance Research Journal in Science Engineering and Technology, 8(5), 39-49.

Abstract:Jump diffusion is a stochastic process that involves jumps and diffusion. A jump process is a type of stochastic process that has discrete movements, called jumps, with random arrival times, rather than continuous movement, typically modeled as a simple or compound Poisson process. In this paper we use jump diffusion process to model default risk and compare results of the traditional Merton and Moody's Kealhofer, McQuown, and Vasicek (MKMV) models. Results show that, jump diffusion models perform better than both the traditional
Merton and MKMV models.

Key words: Default Risk, Option Pricing, Jump Diffusion Model, Jump Process, Poisson Process.

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[5]. Itô K. On stochastic differential equations. American Mathematical Soc.; 1951.

Abstract: An eco-epidemic model with diseases in populations of plants is proposed and analysed in the present study, and pesticides are used as a control mechanism. Pesticides are assumed to be sprayed to populations of both susceptible and infected plant species. Linear responses between susceptible and infective, and between infective and pesticides are also considered. The positivity and boundedness of the system have been proven. The conditions for the existence of all possible equilibrium points and local stability have been carried out. The Routh-Hurwitz Criterion has been used to demonstrate the model's endemic equilibrium point. In order to address the analytical results, numerical simulations were finally conducted.

Key words: Eco- epidemic model, Pesticides, Jacobian matrix, Stability analysis, Routh-Hurwitz Criterion

[1]. Omotosho, L.O., Olayiwola M.O., Olaleye V.O. & Ozoh P. (2020). Simulation of Mathematical Model for Ecological Surveillance of Prey-Predator. Islamic University Multidisciplinary JournalIUMJ, vol. 7(1).
[2]. Kar, T.K. (2012). A Mathematical Study on the Dynamics of an Eco-Epidemiological Model in the Presence of Delay. Applications and Applied Mathematics: An International Journal (AAM), 7(1), 300 – 333.
[3]. Kapur. J.N. (1998). Mathematical modelling. New Age International (P) Limited, Publishers.
[4]. Hugo, A. & Simanjilo, E. (2019). Analysis of an Eco-Epidemiological Model under Optimal Control Measures for Infected Prey. Applications and Applied Mathematics: An International Journal (AAM), 14(10, 117-138.
[5]. Nandi, S.K, Mondal, P.K, Jana, S., Haldar, P. & Kar, T.K. (2015). Prey-Predator Model with Two-Stage Infection in Prey: Concerning Pest Control. Journal of Nonlinear Dynamics, Volume 2015, Article ID 948728, 13 pages.

Abstract: This article presents a review on Jacobsthal and Jacobsthal-Lucas numbers. Some basic properties of Jacobsthal numbers and Jacobsthal-Lucas numbers are given in this article. Except , all and are odd integers. The relations between Jacbsthal and Jacobsthal- Lucas numbers are mentioned in this article. These numbers can be represented by matrices. Fibonacci numbers can be expressed in terms of Jacobsthal numbers and vice versa. Also the identities satisfied by Jacobsthal numbers are discussed in this article.

Key words: Jacobsthal numbers, Jacobsthal- Lucas numbers, Fibonacci numbers, Pell numbers, Pell-Lucas numbers..

[1]. A.F.Horadam, Jacobsthal representation numbers, The Fibonacci Quarterly, Vol.43, No.1, pp.40-54, 1996.
[2]. F.Koken and D.Bozkurt, On the Jacobsthal numbers by matrix methods, International Journal of Contemporary Mathematical Sciences, Vol.3, No.13, pp.605-618, 2008.
[3]. Zvonko Cerin, Sums of squares and products of Jacobsthal numbers, Journal of Integer Sequences, Vol.10, Article 07.2.5, pp.1-15, 2007.
[4]. Ahmet Dasdemir, A study on the Jacobsthal and Jacobsthal-Lucas numbers, DUFEED, 3(1), pp.13-18, 2014.
[5]. Abdul Hamid Ganie and Mashael M. AlBaidani, Matrix structure of Jacobsthal numbers, Hindawi Journal of Function Spaces, Volume 2021, Article ID 2888840, 5 pages.

Abstract: Summary The comparative analysis of the effects of moving loads travelling on highly prestressed orthotropic rectangular plate resting on Pasternak foundation is investigated. When moving load traversing a structure is considered as a mass body, its effects are twofold: the gravitational effect of the moving load and the inertial effects of the load mass of the deformed structure. In this work, the two cases are presented. The motion of the plate is governed by a fourth-order partial differential equation for which the highest derivatives is multiplied by a small parameter. Such problem is amenable to singular perturbation. Of particular interest is the method of matched asymptotic expansions......

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[4]. Gbadeyan, J. A. and Oni, S. T. (1992): Dynamic response to moving concentrated masses of elastic plates on a non-Winkler elastic foundation. Journal of sound and vibration 154, 343 – 358.
[5]. Tolorunshagba J. M. (2022) Dynamic behaviour of highly prestressed orthotropic rectangular plate under a concentrated moving mass. Journal of physical sciences Accepted.