iosr-Jm   Volume-16 ~ Issue-3 ~ may – june 2020

Abstract: Relativistic techniques [3,4] have made it possible to give the conjectures of Goldbach and De Polignac new and hitherto unknown versions. Relativistic techniques have also made it possible to demonstrate
them in their new versions. This shows the importance of the theory of mathematical relativity in the theory of numbers and that the mathematical community must finally admit......

Keywords: La relativité, conjecture de Goldbach , conjecture de De Polignac, nombres premiers jumeaux

[1]. Andrew Wiles, Modular elliptic curves and Fermat's last Théorème, Annal of mathematics, 142, 443-551, 1995.
[2]. M. Sghiar, Des applications génératrices des nombres premiers et cinq preuves de l'hypothèse de Riemann, Pioneer Journal of Algebra,
Number Theory and its Application, Volume 10, Numbers1-2, 2015, Pages 1-31. http://www.pspchv.com/content_PJNTA-vol-10- issues-1-2.html
[3]. M. Sghiar, La relativité et la théorie des nombres (déposé au Hal : 01174146) : https://hal.archives-ouvertes.fr/hal- 01174146v4/document
[4]. M. Sghiar, Une preuve relativiste du Théorème de Fermat-Wiles , IOSR Journal of Mathematics (IOSR-JM) , e-ISSN: 2278-5728, p- ISSN: 2319-765X. Volume 12, Issue 5 Ver. VI (Sep.-Oct.2016), PP 35-36 .
[5]. Y. Zhang, « Bounded gaps between primes », Ann. Math., 179, 2014 , p. 1121-1174

Abstract: From the ancient civilizations of Egyptians pharaohs andGreeks, Theyknew the shape of circle and used it on their temples and tombs. They described circles by using diameters and after that, manytrials have done to find the relation between area of circles and diameters by using π, which results from the division area of circle over its radius square. Unfortunately, All chords have been neglected because there is no specific description for circles by using chordsas well as there is no a real explanation for the ratio result from division area of circle over square of any chords because it change from chord to another. In this paper, we managed to make a new description for circles by chords (golden description)in addition to proving a ratio can deal with all chords and diameters to determine the area of circle and called it (twin ratio).

Keywords: Twin ratio; golden theta; golden chord; golden description

[1]. Lennart Berggren, Jonathan Borwein, Peter Borwein (1997), Pi: A source Book, 2nd edition, Springer-Verlag Ney York Berlin
Heidelberg SPIN 10746250The joy of pi.
[2]. Alfred S. Posamentier& Ingmar Lehmann (2004), A Biography of the World's Most Mysterious Number, Page. 25 prometheus
Books, New York 14228-2197π Biography of the world's most mysterious number
[3]. David Blatner, The Joy of Pi (Walker/Bloomsbury, 1997)

Abstract: One of the most frequent decisions faced by operations managers is "how much" or "how many" items are they to make or buy in order to satisfy external or internal requirements for the item. Replenishment in many cases is made using the economic order quantity (EOQ) model. The model considers the tradeoff between ordering cost and storage cost in choosing the quantity to use in replenishing items in inventories. This paper demonstrates an approach to optimize the EOQ of an item under a periodic review inventory system with stochastic demand using value iteration. The objective is to determine in each period of the planning horizon, an optimal decision so that the long.......

KEYWORDS: Markov decision process, inventory management, optimization, EOQ, Markov chain, stochastic process, value iteration.

[1]. Broekmeullen, R., Van Donselaar, K, Van Woensel T and Fransoo J.C. (2006). Inventory control for perishables in supermarket. Int. J. Prod. Econ. 104(2), 462–472.
[2]. Cheung, R., and Powell,W. (1996). Models and algorithms for distribution problems with uncertainty demands. Trans. Sci. 30, 43–59.
[3]. Eynan, A., and Kropp, D. (1998). Periodic review and joint replenishment in stochastic demand environments. IIE Trans. 30(11).
[4]. Kallen, M.J., van Noortwijk, J.M. (2006), "Optimal periodic inspection of a deterioration process with sequential condition states," International Journal of Pressure Vessels and Piping, vol. 83, no. 4, pp. 249-255.
[5]. Mubiru K.P. and Bernard K.B (2017). The joint location inventory replenishment problem at a supermarket chain under stochastic demand. Journal of Industrial Engineering and Management Science, 1,161–178.

Abstract: One of the most frequent decisions faced by operations managers is "how much" or "how many" items are they to make or buy in order to satisfy external or internal requirements for the item. Replenishment in many cases is made using the economic order quantity (EOQ) model. The model considers the tradeoff between ordering cost and storage cost in choosing the quantity to use in replenishing items in inventories. This paper demonstrates an approach to optimize the EOQ of an item under a periodic review inventory system with stochastic demand.The objective is to determine in each period of the planning horizon, an optimal EOQ so that the long run profits are maximized for a given state of demands. Using dynamic programming over a finite planning horizon with equal intervals, the decision of how much.....

Keywords: Dynamic programming, inventory management, optimization, EOQ, Markov chain, stochastic process.

[1]. Berman O and Perry D (2006) Two control policies for stochastic EOQ- type models, Probability in the Engineering
andInformation sciences. 20(2), 151-163.
[2]. Broekmeullen, R., Van Donselaar, K, Van Woensel T and Fransoo J.C. (2006). Inventory control for perishables in supermarket.
Int. J. Prod. Econ. 104(2), 462–472.
[3]. Borodin A.I. and Nataliya N.S (2018). The model of stochastic optimization of production under uncertainty and risk. Asian social
science,14(5).
[4]. Cheung, R., and Powell,W. (1996). Models and algorithms for distribution problems with uncertainty demands. Trans. Sci. 30, 43–
59.
[5]. Eynan,A., and Kropp, D. (1998). Periodic review and joint replenishment in stochastic demand environments. IIE Trans. 30(11).

Abstract: In the present article a study is made of the characteristics of the coronavirus, its transformation into a pandemic and its aggressiveness towards the life of the man; reference is made to a set of certain diseases that have historically turned into epidemics due to the speed with which they were transmitted among the population; in addition, in most cases, this occurs due to the delay in reacting to control the disease. We applied the generalized logistic model to model this process and conclusions are drawn regarding the development of the coronavirus until it becomes a pandemic.

Keywords: Model, epidemic, disease, transmission

[1]. Chaveco, A. I. R. And others. Modeling of Various Processes. Curitiba: Appris, 2018, v.1. p.320.
[2]. Chaveco, A. I. R. Andothers. Applications of Differential Equations in Mathematical Modeling. Curitiba: CRV, 2016, v.Um. p.196.
[3]. Del Sol G. Y."The interferon that treats covid-19". www.granma.cu. 2020.
[4]. Earn D. J. D., Rohani P., Bolker B. M., and Grenfell B. T., A simple model for complex dynamical transitions in epidemics, Science, 287 (2000), pp. 667–670.
[5]. Esteva L. and Vargas C., Analysis of a dengue disease transmission model, Math.Biosci.,150 (1998), pp. 131–151.

Abstract: In this paper the Transportation problem with mixed constraints having all parameters as integer intervals is considered. Here we solve the fully integer interval transportation problem without converting it to
the crisp transportation problem. Numerical example is illustrated to validate the argument and the results are compared with the existing methods.

Keywords: Interval numbers, Interval Transportation problem, ranking methods

[1]. Akilbasha .A, Natarajan.G and Pandian .P ," Finding an optimal solution of the interval integer transportation problem with rough
nature by split and separation method", In.J.of Pure and Applied Math, 2016.
[2]. AtanuSengupta and Tapan Kumar Pal, Theory and Methodology: On comparing interval numbers, European Journal of Operational
Research, 27 (2000), 28 - 43.
[3]. Das S.K, Goswami. A. and Alam S.S.,"Multiobjective transportation problem with interval cost, source and destination
parameters", European Journal of Operational Research, volume 117 , pages 100 – 112,1999.
[4]. Dinesh et al ,"Trisectional fuzzy trapezoidal approach to optimize interval data based transportation problem",Journal of King saud University – Science,2018.
[5]. Juman, Z. A. M. S., and M. A. Hoque. A Heuristic Solution Technique to Attain the Minimal Total Cost Bounds of Transporting a Homogeneous Product with Varying Demands and Supplies, European Journal of Operational Research , volume 239 , pages 146–156,2014.

Abstract: The world is speedily becoming a global village and that makes it even more imperative that individuals have a better understanding and appreciation of mathematical procedures and methods of reasoning to be carried along.Mathematical knowledge indeed equips individuals with the skill to solve a wide range of practical tasks and problems they may encounter in life.This research work focused on assessing Impact ofMathematicscourses though at National Diploma in Federal Polytechnics of North Eastern state of Nigeria. Samples of Students from four (4) Federal Polytechnics were drawn and information on the subject matter were collected using questionnaires. The data collected were analyzed using Chi-square test. The output of the analysis indicates that all the Polytechnic are doing well in relation to students' performance in ND Mathematics courses. Findingsof the analysis may serve as search light to stakeholders to determine the level of Students performance in ND Mathematics examinations in our various Institutions.Appropriate recommendations were made based on the result of the research.

Keywords: Categorical Data Analysis,Chi-square Test, ND Mathematics Courses and Students Performance

[1]. Adeoti, V. (2012); Challenges of Nigeria's Education System. Retrieved from http://www.thetidenewsonline.com/2012 /09/09/challenges-of-nigeria's-education-system/.
[2]. Ajayi, I. A, Ekundayo H. T. (2010); Contemporary Issues in Educational Management. Ikeja Lagos: Bolabay.
[3]. Ale, S. O. and Adetula, L. O. (2010). The National Mathematical Centre and the Mathematics Improvement Project in Nation Building. Journal of Mathematical Sciences Education. Volume 1, pp1-19
[4]. Aremu, A. O. andSokan, B. O.(2003); A Multi-causal Evaluation of Academic Performance of Nigerian Learners: Issues and Implications for National Development. Department of Guidance of Counselling, University of Ibadan.
[5]. Bakare, C.G.M.(1994); Mass Failure in Public Examinations: Some Psychological Perspectives. Monograph. Department of Guidance of Counselling, University of Ibadan..

Abstract: This work focuses on the application of Newton's divided difference interpolation formula to obtain numerical solutions to certain parabolic, hyperbolic and elliptic partial differential equations at non-nodal points in a discretized domain. The finite difference method (FDM) is first applied to solve the initial boundary value problems (IBVPs) to obtain non-nodal point solutions. Interpolating polynomials 𝑃𝑖,𝑗(𝑠) are constructed using the nodal points solutions, which are later used to obtain the non-nodal point solutions. The non-nodal point solutions obtained are found to be accurate to one decimal place for the parabolic PDE, two decimal places for the hyperbolic PDE and exact for the elliptic PDE. The numerical results obtained show that this procedure is significantly efficient and accurate. A general interpolating polynomial is also obtained for computation at any other time level t greater than zero.

Keywords: non-nodal, partial differential equations, boundary conditions, finite difference method, numerical approximation

[1]. Bhrawy, A.H, Doha, A.H, Ezz-Eldien, S.S & Van-Gorder, R.A. (2014). A new Jacobi spectral collocation method for solving 1+1 fractional Schrodinger equations and fractional coupled Schrodinger systems. The European Physical Journal Plus, 129: 1-12.
[2]. Iyenga, S.R. & Jain, R. K, (2009). Numerical methods. New Delhi: New Age International (p) Limited Publishers.
[3]. Sakar, S. (2006). Quantum phase diagram of a super conducting quantum dots array. EPL (Europhysics letters).
[4]. Burden, R.L. & Douglass, J.F. (2011). Numerical analysis. New York: Richard Straton.
[5]. Davis, M. (2010). Finite difference methods. London: Department of Mathematics, Imperial College.