iosr-Jm   Volume-17 ~ Issue-3 ~ May – June 2021

Abstract: This theoretical analysis investigates the unsteady convective flow of nanofluid using Blasius-Rayleigh-Stokes variable with slip effect. The non-Newtonian fluid problem is examined mathematically via a system of governing partial differential equations to determine the effect of moving slot parameter, thermal Grashof number and mass Grashof number on the flow. A suitable similarity variable is employed to transform these equations into the corresponding ordinary differential equations and then solved using the method of Newton's Finite differences adopted from MAPLE 18.0 software. From the graphical representations derived, an overview of the effects of some physical parameters on the velocity, temperature and the concentration profiles is then presented.

Keywords – Blasius-Rayleigh-Stokes variable, moving slot, thermal Grashof number, slip velocity, mass Grashof number..

[1]. Pop, I., Ingham, D.B.: (2001) convective heat transfer: Mathematical and computational modeling of viscous fluids and Porous media pergamon. Oxford.
[2]. Vafai, K.: (2010) Porous media: Applications in biological systems and biotechnology. CRC press
[3]. Sobamowo, M.G., Akinshilo, A.T., Yinusa, A.A.: (2018) Thermo-Magneto-Solutal squeezing flow of nanofluid between two Parallel disk embedded in a porous medium: Effects of nanoparticule geometry, slip and temperature jump conditions. Modelling and Simulation in Engineering, Volume 2018, Articule ID 7364634, 18 pages https://doi.org/10.1155/2018/7364634
[4]. Sravan Kumar, T and Rushi Kumar, B.: (2019) Effect of homogeneous-heterogeneous reactions in MHD stagnation point nanofluid flow toward a cylinder with nonuniform heat source or sink. Applied Mathematics and Computing, Trends in Mathematics, https://doi.org/10.1007/978-3-030-01123-9_29

Abstract: We currently have a variety of price indexes, the most popular of which are the Paasche's price index, the Laspeyres' price index and the Fisher's price index. But there is no such price index yet that satisfies all the four tests of adequacy. The most successful price index of all time is Fisher's ideal price index, which satisfies three of the four tests of adequacy —unit test, factor reversal test, and time reversal test. But it fails to complete circular test. We present a new price index which will be called real price index. This price index satisfies all the four tests of adequacy - unit test, factor reversal test, time reversal test and Circular test. Real price index is a generalized measure......

Keywords: Real Price Index, Perfect Price Index, Fisher's Price Index, Geometric and Summative Parts of Real Price Index, Proportional cum Exponential Weighting Method, Commodities, Adequacy Tests.

[1]. Dr. V. K. Nigam, Dr. Ankita Gupta, Dr. Anamika Chaudhary, Dr. Monika Malhotra, Dr. S. V. Rawat, Pro. A. P. Sen ( Hindi Editition April 2016), Quantative Methods, Directorate Study and Publications, Uttarakhand Open University, Haldwani, Nainital, Uttarakhand, India
[2]. Dr.V. C. Sinha, Dr. B. N. Gupta (Revised Hindi Editition 2012) Economics, S.B. P.D. Publications, 3/20B, Agra-Mathura Bypass Road, Near Tulsi Cinema, Agra, Uttar Pradesh, India

Abstract: The demand for observation and forecast of wind shear and other troubling weather phenomena in the aviation industry has been on the increase in this period of climate change and its associated impacts. Nigeria and other countries in the tropical region greatly experience wind shear, hence the need for accurate wind shear forecast. The study mathematically modeled the relationship between wind shear and flight diversions, delays and cancellations at Murtala Mohammed and Port Harcourt International Airports, Nigeria. The annual time series secondary data used for this study were sourced from Nigerian Airspace Management Agency (NAMA) at Murtala Mohammed and Port Harcourt International Airports and Nigerian Meteorological Agency (NIMET). The data were compiled and presented in tables for easy understanding and further analysis. The statistical estimation (or analysis) techniques employed in......

Keywords: Wind Shear; Mathematical Modeling; Aircraft Operations; Relationship; Aviation Industry

[1]. Ajie, U. E., & Dienye, A. (2014). Spatial data analysis of solid waste management system in Port Harcourt Metropolis after 100 years of its existence. FIG Congress, Kuala Lumpur, Malaysia.
[2]. Azad, K. A. (2011). Effect of wind shear on wind velocity at coastal sites of Bangladesh. Proceedings of the international conference on Mechanical Engineering. Dhaka, Bangladesh.
[3]. Building Nigeria's Response to Climate Change Project (BNRCC) (2012). Towards a Lagos State climate change adaptation strategy. Report prepared for the Honourable Commissioner of Environment, Lagos State.
[4]. Demographia (2016). Demographia World Urban Areas.
[5]. Enete, I. C., Ajator, U., & Nwoko, K. C. (2015). Impacts of thunderstorm on flight operations in Port-Harcourt International Airport, Omagwa, Rivers State, Nigeria. International Journal of Weather, Climate Change and Conservation Research, 1(1), 1 – 10..

Abstract: Optimization has become a common phenomenon in almost all organizations and establishments. In developed, countries managerial decisions are mostly based on the use of optimization techniques the objective of this research work was to apply linear programming for profit maximization of raw material in water production. Viclibo Venturs (VILA), Zango, Lokoja, Kogi State was used as our case study. The decision variables in this research work are the three different sizes of water (Sachet bag of water, 50cl pack of water, and 75cl pack of water) produced by Viclibo Venturs. The researcher focused mainly on three raw materials (production cost, production time and Demand or Sales) used in the production and the amount of raw material required of each variable (water size). The result shows that 600 unit of a bag of sachet water, 150 unit of a pack of 50cl water 100 unit of a pack of 75cl of water respectively which will give a maximum profit of ₦40,000.00.

Keywords: Optimization, Water, Production, Linear Programming, Excel Solver

[1]. Anieting, A.E., Ezugwu, V. O and OLOGUN .S. (2013) Application of linear programming Technique in the Determination of Optimum Production Capacity: IOSR Journal of mathematics (IOSR-JM) 2278-5728. Vol 5, Is 6, pp 62-65
[2]. Ezema, B.I. and Amakon. U. (2012) Optimizing profit with the linear programming Model: A case on Boldem plastic industry limited enugu Inter Disciplinary Journal of Research in Business Vol 4 Is 2 pp 37-49
[3]. Fagoyinbo, I. S. and Ajibode, I. A (2010) Application of linear programming move Techinque in one effective use of resources for staff training
[4]. Frizzone J. et al (1997) linear programming model to optimize the water resource use in irrigation i. Inter disciplinary Journal of Research in Business Vol 1 Pg 136-148
[5]. Khan, I. U., Bajuri, N.H. and Jadom I. A (2011) Optimal production levels for the different products manufactures at ICL a multinational Company in Pakistan

Abstract: Analysis of hydromagnetic free convection turbulent fluid flow over an infinite vertical plate was carried out. The fluid flow was modeled using conservation equations of energy and momentum. The governing equations were then non-dimensionalised which gave rise to non-dimensional parameters.The approximate numerical solution for the non-linear partial differential equations were determined by use of the finite difference method and solved using MATLAB computer software. The various non-dimensional parameters were thereafter examined of their effects on the velocities and temperature profiles. Thereafter the solutions presented in graphs and an analysis of the results......

Keywords: Unsteady, Hydromagnetic, Turbulent, Free convection, Vertical plate, Finite difference

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Abstract: The aim of this article is to solve a problem opened more than 2 millennia ago (300 BC) : There is no odd perfect number.} Résumé : Le but de cet article est de résoudre un problème ouvert il y' a plus de 2 millénaires (300 av. J.-C) à savoir qu'il n'existe aucun nombre parfait impair.

Key words: perfect number, number theory.

[1]. Science-et-vie, https://www.science-et-vie.com/science-et-culture/maths-une-des-plus-anciennes-enigmes-sur-les-nombres-resisteencore-
58692 : une des plus anciennes énigmes sur les nombres résiste encore , 17 sept 2020 .
[2]. Pace Nielsen, Odd, spoof perfect factorizations, https://arxiv.org/abs/2006.10697 , 18 Jun 2020 .
[3]. Wikipedia, https://fr.wikipedia.org/wiki/Nombre_parfait

Abstract: The present work is a study of the properties of the product rough approximation space determined by two rough approximation spaces. It is found that the projection functions are continuous with respect to the induced topologies on the product space and the individual spaces. Further, the product rough topology is defined as the topology of rough sets generated by the family of the products of the rough open sets in the rough topologies on the individual spaces. As in the case of general topological spaces, the product rough topology is found to be the smallest topology which makes the projection functions rough continuous. The rough interior and rough closure with respect to the rough product topology are also presented

Key words: Approximation space; Product Topology; Rough Set; Topology; Rough Topology

[1]. M. E. Abd El-Monsef, O. A. Embaby and M. K. El-Bably,Comparison between Rough Set Approximations Based on Different Topologies, International Journal of Granular Computing, Rough Sets and Intelligent Systems, 2014;3(4);292-305.
[2]. K. Anitha, Rough Set Theory on Topological Spaces, Rough Sets and Knowledge Technology LNAI 8818, Springer 2014;69-74.
[3]. M. J. Iqlan, M. S. Marouf and M. S. Shulaq, Approximations of Sets in Topological Spaces, International Research Journal of Pure Algebra, 2014;4(12);636-643.
[4]. T. B. Iwinski, Algebraic Approach to Rough Sets, Bulletin of the Polish Academy of Science and Mathematics, 1987;35;673-683.
[5]. J. Jarvinen, The Ordered Structure of Rough Sets. in RSCTC 2004, LNAI 3066, eds S. Tsumoto et al., Springer- Verlag, Berlin, 2004; 49–58.

Abstract: In this communication it is shown that a function of the Laplace operator acting on an arbitrary function can be transformed to a three-dimensional integral. The cases of the exponential function and of an arbitrary function expressible as a power series, are treated. Two special cases of radial functions are presented based on elementary observations made here. 1
Mathematical Classification Mathematics Subject Classification: 34A05, 34A12, 34A55, 34A30, 34C20, 34L40, 35J05, 35J91

Key words:Laplace operator, function of Laplace, wave equation, three-dimensional differential Equations

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[5]. Stenlund, H.: On the Basics of Linear Diffusion, IOSR Journal of Mathematics (IOSR-JM) e-ISSN: 2278-5728, p-ISSN: 2319-765X. Volume 16, Issue 2 Ser. III (Mar. { Apr. 2020), PP 44-49 www.iosrjournals.org