iosr-Jm   Volume-20 ~ Issue-1 ~ Jan. – Feb. 2024

Abstract : The need to improve the efficiency of industrial based materials and enhances its thermal conductivity has been on increase, this is as a result of the interest in increasing output. Thus, viscous non-Newtonian fluids conveying nanoparticles could serve as a material to meet the engineering and industrial demand for an enhanced productivity, this as apply in electronic gadgets, technology devices, biomedical sciences and others. As such, this study investigated mixed convective steady flow of Casson nanofluid in vertical porous plate with slip and temperature jump boundary conditions. The solution to the dimensionless formulated model is offered via shooting scheme.....

Keywords: Mixed convection; Casson nanofluid; Porous medium; Velocity slip; Temperature jump

[1]. Rafique, K., Anwar, M.I. And Misiran, M. (2019). Numerical Study On Micropolar Nanofluid Flow Over An Inclined Surface By Means Of Keller-Box. Asian J. Probab. Stat, 4,1-21.
[2]. Singh, J., Vishalakshi, A.B., Mahabaleshwar, U. S And Bognar, G (2022). Mhd Casson Fluid Flow With Navier's And Second Order Slip Due To A Perforated Stretching Orn Shrinking Sheet. Journal.Pone, 17(11): E0276870.
[3]. Radha, G., Reddy, N.B And Gangadhor, K (2017). Slip Flow Of Casson Fluid With Variable
[4]. Thermophysical Properties Along Exponentially Stretching Sheet Under Convective Heating. International Journal Of Mechanics And Solids. 12(2), (2017), Pp 235-256.
[5]. Arthur, E.M., Seini, I.Y. And Bortteir, L.B. (2015). Analysis Of Casson Fluid Flow Over A Vertical Porous Surface With Chemical Reaction In The Presence Of Magnetic Field. Journal Of Applied Mathematics And Physics, 3(2015), 713-723.

Abstract : According to some claims, using manipulatives helps pupils perform better while also enhancing their conceptual knowledge, problem-solving abilities, and attitudes toward mathematics. The purpose of this study was to determine whether or not first-year students at the University of Guyana, Turkeyen Campus, might improve their mathematical performance by using manipulatives as cognitive tools instead of lectures. Over ten weeks, the mathematical performance of two groups from the MTH1202 – Calculus 1 class was compared, and the.....

Key Words: First-Year Student, Concrete Materials; Effectiveness; Lecture Method; Manipulatives

[1]. Ball, D. (1992). Ball, D. L. (1992). "Magical Hopes: Manipulatives And The Reform Of Math Education", American Educator 16(2), 14-18, 46-47. Www.Sciepub.Com. Https://Www.Sciepub.Com/Reference/242763
[2]. Bellonio, J. (2012). 01.06.12: Multi-Sensory Manipulatives In Mathematics: Linking The Abstract To The Concrete. Teachersinstitute.Yale.Edu. Https://Teachersinstitute.Yale.Edu/Curriculum/Units/2001/6/01.06.12.X.Html
[3]. Cain-Caston, M. (1996). Manipulative Queen [Electronic Version]. Journal Of Instructional
a. Psychology 23(4), 270-274.
[4]. Carbonneau, K. J., & Marley, S. C. (2015). Instructional Guidance And Realism Of Manipulatives Influence Preschool Children's Mathematics Learning. The Journal Of Experimental Education, 83(4), 495–513. Https://Www.Jstor.Org/Stable/26594575
[5]. Clements, D. H., & Mcmillen, S. (1996). Rethinking Concrete Manipulatives. Teaching.

Abstract : The potency of disease transmission is hinged on contact with the infected or germs responsible for the disease and weak immunity of the uninfected person. In most cases, people with weak immunity are liable to be infected than those with strong immunity. In this paper, we formulated a tuberculosis mathematical model that in-cooperate weak immunity of latent infected and active tuberculosis to study their impact on the transmission of tuberculosis. We first, shown the properties of the model which captured that positivity of the solution and boundedness within a fixed domain.....

Key Words: Disease, Modeling, Tuberculosis TB, Sensitivity analysis, Lyapunov function.

[1] Abegye S. Y. And Shammah K. S. Sensitivity Analysis Of Mathematical Modeling Of Tuberculosis Dynamics With S Control Measure. African Journal Of Mathematics And Statistics Studies, 2023; 6 (3), 17 - 34.
[2] Akwafua, S. E., Abah, T And Oppong, J. R. Evaluation Of The Burden And Intervention Strategies Of Tb/HivCo-Infection In West Africa. Journal Of Infectious Diseases And Epidemiology, 2020; 6 (4), 1 - 11.
[3] Andrawus Et Al. A Mathematical Model Of Tuberculosis Transmission Dynamics Incorporating First And Second Treatment. J.Appl. Sci. Environ. Management , 2020; 24 (5), 915 - 922.
[4] Chukwuogo Et Al. Strategic Approach To Optimisation Of Tb Contact Investigation In Nigeria. The International Journal Of Tuberculosis And Lung Disease ,2023; 27 (2), 161 - 163.
[5] Diabaté A. B, Sangaré B, And Koutou O. Optimal Control Analysis Of A Covid-19 And Tuberculosis (Tb) Co-Infection Model With An Imperfect Vaccine For Covid-19. Sema Journal , 2023; 28 (5), 324 - 365.

Abstract : In this paper, we introduced the concept of generalized semi --topological group. Generalized semi --topological group is a group with a generalized-topology such that the multiplication mapping is generalized ----continuous . In this paper, we introduce the concept of generalized Semi --topological group and studied some of their theorem.

Key Words: 𝒢-𝑆𝛼-open,𝒢-𝑆𝛼𝖰-open, 𝒢-𝑆𝛼-Int, 𝒢-𝑆𝛼-Cl, 𝒢-𝛼𝛽-regular,𝒢𝑆𝛽−𝛼-topological group.

[1]. A.V.Arhangelskii ,M.Tkachenko , Topological Groups And Related Structures. Atlantis Studies In Mathematics,
Atlantis Press/ Word Scientific, Amsterdamparis, 1(2008).Https://Doi.Org/10.2991/978-94-91216-35- 0.
[2]. A.Csaszar, Generalized Topology,Generalized Continuity;Acta Math.Hungar.96(2002)351-357.
[3]. Csaszar, A.Generalized Open Sets In Generalized Topologies, Acta Mathematice Hungaria.106,2005,53-66.
[4]. A.Csaszar,Product Of Generalized Topologies,Acta Math.Hungar,123(2009),127-132.
[5]. Dylan Spivak. Introduction On Topological Groups,Math(4301).
[6]. H.Z.Ibrahim, On A Class Of 𝛼𝛾 -Open Sets In A Topological Space,Act Scientiarum. Technology, 35 (3) (2013),539-545.

Abstract : Fractional calculus has been mo re important in fields such as engineering, physics, economics, and more throughout the past 20 years. It results from the new opportunities fractional calculus opens up for problem modelling . The global nature and linearity of differintegrals are the key ideas. The tautochrone problem, one of the first instances of fractional calculus in action, will be covered in this essay. It shows how useful fractional calculus can be in solving certain kinds of integral equations.

Keywords: Differintegral, Caputo differintegral, TheMittage –Leffler function,The Tautochrone Problem

[1] Tareq Hamadneh; Amel Hioual; Rania Saadeh; Mohamed A. Abdoon; Dalal Khalid Almutairi; Thwiba A. Khalid; Adel Ouannas. General Methods To Synchronize Fractional Discrete Reaction–Diffusion
[2] Systems Applied To The Glycolysis Model. Fractal And Fractional 2023, 7, 828. Podlubn´ Y, Igor. Fractional Differential Equations. United States: Academic Pressc1999. 340 P. Isbn 0-12-558840-2.
[3] Kilbas, Anatoly A., Srivastava, Hari M., Trujillo, Juan J. Theory And Applications Of Fractional Differential Equations. John Van Mill. Netherlands: Elsevier, 2006. 523 P. Isbn 978-0-444-51832-3.
[4] Veit, Jan. Integr´Aln´I Transformace. 2. Vyd. Praha: Sntl, 1983. 120 P.Schumer, Rina, Et Al. Eulerian Derivation Of The Fractional Advection-Dispersion Equation. Journal Of Contaminant Hydrology. 2001, No. 48, P. 69-88.
[5] Benson, David Andrew. The Fractional Advection-Dispersion Equation: Develop- Ment And Application. 1998. 144 P. University Of Nevada, Reno. Ph.D. Thesis-545.

Abstract : We remedy the defect of our previous paper with respect to the insufficient argument of the necessary premises. To this end, based on the leftward extendedness of the px+q sequences, px+q infinite trees are built; based on the properties of the px+q infinite trees, the unprovability of the px+q sequences being noncircular sequences is revealed. Consequently, the proof of the 3x+1 problem in this paper is rigorous. Since the 3x+1 problem is equivalent to 3x+1 sequences, 3x+1 sequences are one kind of px+q sequences, and px+q sequences are one kind of mapping recurrent sequences. In this paper, we start with .....

Keywords: 3x+1 problem; 3x+1 sequence; px+q sequence; mapping recurrent sequence; px+q infinite tree

[1]. Ming Xian, Xunwei Zhou, Zi Xian, The Proof Of 3x+1 Problem, IOSR Journal Of Mathematics, Volume 17, Issue 2, Series 3, 05-12, 2021-545.