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.