iosr-Jm   Volume-19 ~ Issue-6 ~ Nov. – Dec. 2023

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Abstract : In the present paper we investigated the heat and mass transfer in the MHD micropolar Jeffery fluid flow over stretching sheet in the presence of porous medium. By using suitable similarity transformations, we get non-linear ordinary differential equations with the help of governing partial differential equations. We used DTM method for finding the analytical solution from the nonlinear ordinary differential equations. Obtained DTM solution is explored by bvp4c numerical solver built in MATLAB and effect of porosity parameter, Deborah number, magnetic field parameter, Jeffery fluid parameter etc. on velocity profile, temperature distribution, microrotation and concentration profile are explained by graphs. It is found that that as porosity parameter increases velocity decreases while increases in Prandtl number decreases the temperature profile distributions.

Key words: Micropolar fluid, Jeffery Fluid, MHD, Thermal Radiation, Porous Medium, Heat Transfer, Mass Transfer.

[1]. Eringen, A.C., Simple micropolar fluid, Int. J. Engg. Sci., 2, 205-217 (1964).
[2]. Eringen, A.C., Theory of micropolar fluids, J. Math. Mech., 16, 1-18 (1966).
[3]. Wilson, A.J., Basic flows of micropolar fluids, Appl. Sci. Res., 20, 338-355 (1969).
[4]. Kilne, K.A., A spin vorticity relation for unidirectional plane flows of micropolar fluids, Int. J. Engg. Sci., 15, 131-134 (1977).
[5]. Gorla, R.S.R. and Takhar, H. S., Free convection boundary layer flow of a micropolar fluid past a cylinder bodies, Int. J. Engg. Sci., 25, 949-962 (1987).

Abstract : This analysis explores the consequences of flow and heat transfer by the process of free convection inside a triangular cavity, which contains heat source/sink at the bottom wall. The entire cavity has been filled with Al2O3 -Cu water based hybrid nanofluid. Finite element method has been applied for descretization the governing equations of the present problem numerically. A fixed Prandtl number (Pr = 0.71) has been used for the numerical solution. The impact of relevant parameters such as Rayleigh number(Ra), heat generation(Q), Hartmann number...

Key Word: Triangular Cavity, Nusselt Number, Hybrid Nanofluid, Rayleigh Number.

[1]. Rashad AM, Chamkha AJ, Ismael MA, Salah Taha. MHD natural convection in a triangular cavity filled with a Cu-Al2O3/water hybrid nanofluid with localized heating from below and internal heat generation. J. of Heat Transfer. 2018, pp. 1-23 (doi:10.1115/1.4039213).
[2]. Dogonchi AS , Ismael MA and Chamkha AJ. Numerical analysis of natural convection of Cu- water nanofluid filling triangular cavity with semicircular bottom wall. J Therm Anal calorim . 2019; 135, 3485-3497.
[3]. Mahmoudi A, Pop I and Shahi M . Effect of magnetic field on natural convection in a triangular enclosure filled with nanofluid. Int. J. Therm. Sci. 2012, 59, 126–140.
[4]. Chamkha and Ismael . Magnetic field effect on mixed convection in LID-driven trapezoidal cavities filled with a Copper–Water nanofluid with an aiding or opposing side wall. J Thermal Sci .Engg. App. 2016, 8, pp-031009 - 1 .
[5]. Angirasa D. Analysis of hybrid nanofluid behavior in a triangular cavity along with heat source consideringthe effect of Magnetic force. Fluid Dynamics Research . 2000, vol.26. pp.219-233

Abstract : MOOCs have great impact in education for the different stakeholders as they offer an opportunity to learners to enhance their higher education and the faculty to hone their competence and professional development. Although there exist vast literature relating to the benefits of using MOOCs among the learners and the faculty in mathematics, there is paucity of information focusing on the Middle East. The purpose of this qualitative descriptive study was exploration of the use of MOOCs for the professional development and training of mathematics faculty at higher...

Key Word: MOOCs, Mathematics Faculty, Technology, Self-efficacy, STEM

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Abstract : Scientists and academicians are always fascinated by the human brain because it is an intricately structured and sophisticated organ. In the discipline of neuroscience, the study of brain networks has become more popular because it provides insight into the interactions and contributions of distinct brain regions to various cognitive activities. Graph theory, a mathematical framework that has proven invaluable in helping to uncover the complexities of brain connectivity, is at the center of this investigation. This article will explore the fundamental role that graph theory plays in comprehending brain networks, from its historical foundations to its modern uses in mental mapping.

Key Word: Brain network; Graph; Centrality measure

[1]. F. V. Farahani, W. Karwowski, N. R. Lighthall, Application Of Graph Theory For Identifying Connectivity Patterns In Human Brain Networks: A Systematic Review, Frontiers In Neuroscience, 2019, Doi: 10.3389/Fnins.2019.00585.
[2]. A. Schuster, Y. Yamaguchi, Application Of Game Theory To Neuronal Networks, Advances In Artificial Intelligence, Volume 2010, Article Id 521606, 12 Pages, Doi:10.1155/2010/521606.
[3]. K. Friston, Causal Modelling And Brain Connectivity In Functional Magnetic Resonance Imaging. Plos Biol. 7:E33, Doi: 10.1371/Journal.Pbio.1000033(2009
)[4]. M. London, M. Hausser, Dendritic Computation, Annual Review Of Neuroscience, Vol. 28, Pp. 503–532, 2005
[5]. O. Sporns, G. Tononi, R. Kötter, The Human Connectome: A Structural Description Of The Human Brain. Plos Comput. Biol. 1:E42, Doi: 10.1371/Journal.Pcbi.0010042 (2005)

Abstract : In this study, a modified three-parameter Weibull distribution was proposed and its properties are derived, including the probability density function (PDF), cumulative density function (CDF), quantile function, mean, variance, and estimation of parameters. The maximum likelihood method was used to estimate the parameters of the proposed distribution using a simulated data set. The theoretical properties of the proposed distribution were compared with the existing Weibull (1951) distribution. Results show that the proposed distribution has a unique expression for......

Keywords: Weibull distribution, Modified distribution, Maximum likelihood estimation, Probability density function, Parameter estimation

[1]. Aslam, M., Guo, X., & Jiang, R. (2016). Reliability evaluation of mechanical systems using the three-parameter Weibull distribution. Quality and Reliability Engineering International, 32(8), 2991-3003.
[2]. Batten, J. A., & Szilagyi, P. G. (2011). Modelling stock return distributions with a three-parameter Weibull distribution. Applied Economics Letters, 18(5), 401-404.
[3]. Cheng, Y., & Jiang, R. (2019). Exponentiated generalized Weibull-Poisson distribution: Properties and applications. Communications in Statistics-Simulation and Computation, 48(2), 570-584.
[4]. Cox, D. R. (1972). Regression models and life-tables. Journal of the Royal Statistical Society. Series B (Methodological), 34(2), 187-220.
[5]. Crowder, M. J. (2001). Classical competing risks. Chapman and Hall/CRC

Abstract : The convection-diffusion equation is a very important branch of partial differential equations, with wide applications in many fields such as fluid mechanics and gas dynamics. Since it is difficult to obtain analytical solutions for the convection-diffusion equation, solving the equation and its eigenvalue problems using various numerical methods has great value in numerical analysis and is currently a hot topic in computational mathematics. This paper studies the local discontinuous Galerkin (LDG) method for convection-diffusion eigenvalue problems, provides both a priori and a posteriori error estimates, analyzes the reliability of eigenvalue estimates, and conducts adaptive experiments. Combining theoretical analysis, it is demonstrated that our method achieves optimal convergence rates.

Key Word: eigenvalues of convection-diffusion; local discontinuous Galerkin method; a posteriori error; adaptive

[1]. 曾晓艳，陈建业，孙乐林，对流扩散方程的一种新型差分格式[J]数学杂志，2003,23(1):37-42
[2]. 由同顺.对流-扩散方程的hp-局部间断Galerkin有限元方法的最优L~∞(H~1)误差估计[J]. 高校应用数学 学报A 辑,2020,v.35(01):40-48.
[3]. Li Y, Bi H, Yang Y. The a Priori and a Posteriori Error Estimates of DG Method for the Steklov Eigenvalue Problem in Inverse Scattering[J]. Journal of Scientific Computing, 2022, 91(1): 20.
[4]. Babuska I,Rheinboldt W C.Error estimates for adaptive finite element computations [J]. SIAM Journal on Numerical Analysis ,1978,15(4):736-754.
[5]. 杜莹玉，韩家宇.对流扩散特征值问题的Crouzeix-Raviart元二网格离散方案.贵州师范大学学报(自然科学版)，2021, 39(6): 8-12.

Abstract : In this work, we developed a multi-objective chance constrained programming model involving Gumbel distributed random variables. It also applies the fuzzy goal program- ming technique in solving multi-objective chance constrained problems. We employed the quantitative research method following a descriptive approach to solve a multi-objective chance constrained problem where the right hand side parameter of the constraints are considered as triangular fuzzy numbers. The deterministic equivalence of the probabilistic problem was obtained and solved by the fuzzy programming approach to obtain the best and worst values of......

Keywords: Fuzzy programming, triangular fuzzy numbers, chance constrained programming, Gumbel random variables, membership function

[1]. Abou-El-Enien, T. H. M. (2000). A Mixed Algorithm For Stochastic Multiple Objective Programming Problems Using MATLAB Program. Computer Reviews Journal, 8:14 – 19.
[2]. Archarya, S., Belay, B., And Mishra, R. (2021). Solving Multi Objective Chance Constrained Pro- Gramming Problem Involving Three Parameters Log Normal Distribution. International Journal Of Mathematics In Operations Research, 18(2):236 – 253.
[3]. Atalay, K. D., Perkin, T. S., And Apaydin, A. (2021). A New Methodology For Solving Multi-Objective Chance Constrained Problems: An Application On IOT Systems. Mathematical Problems In Engi- Neering, 2021.
[4]. Barik, S. K. (2015). Probabilistic Fuzzy Goal Programming Problems Involving Pareto Distribution: Some Additive Approaches. Fuzzy Information And Engineering, 7.
[5]. Bhargava, A. K., Singh, S. R., And Bansal, D. (2014). Multi-Objective Fuzzy Chance Constrained Fuzzy Goal Programming For Capacitated Transportatrion Problem. International Journal Of Computer Applications, 107(3).