iosr-Jm   Volume-19 ~ Issue-2 ~ Mar. – Apr. 2023

Abstract : This paper is an improvement of the analysis undertaken in the paper of Deng, Lin, and Chu that was published in the European Journal of Operational Research. It shows that the lengthy computations can be replaced by a more elegant one that yields the generalization of the targeted system. We generalize their model from ramp-type demand to arbitrary demand while theoretically discovering a fascinating phenomenon: the optimal solution is actually independent of the demand. This study provides a justification that a form of abstract generalization sometimes has the capability of solving the inventory model in a much more efficient manner..

Key Word: Inventory model; Deteriorating item

[1]. Deng, P.S., (2005) Improved inventory models with ramp type demand and Weibull deterioration.International Journal of
Information and Management Sciences, 16 (4), 79-86.
[2]. Deng, P.S., Lin, R., and Peter Chu, P. (2007) A note on the inventory models for deteriorating items with ramp type demand rate.
European Journal of Operational Research, 178, 112-120.
[3]. Giri, B.C., Jalan, A.K., and Chaudhuri, K.S. (2003) Economic Order Quantity model with Weibull deterioration distribution,
shortage and ramp-type demand.International Journal of Systems Science 34 (4), 237-243.
[4]. Hill, R.M., (1995) Inventory models for increasing demand followed by level demand.Journal of the Operational Research
Society, 46 (10), 1250-1259.
[5]. Mandal, B. and Pal, A.K. (1998) Order level inventory system with ramp type demand rate for deteriorating items. Journal of
Interdisciplinary Mathematics, 1, 49-66.

Abstract : In many tropical countries, influenza epidemic has remained a health concern. Allocating resources for its treatment and control has always targeted certain period of the year when its incidence is believed to be highest. In this study, we have used the stochastic rates of changes insix classes of the population N(t) to find suitable Markov jump process from which a stochastic differential equation was obtained for the symptomatic infectious class and solved by Ito's formula. Analysis of the sample path of the infectives shows that influenza is endemic in Nigeria throughout the year with occasional change in epidemic size..

Keywords: Infectives, Poisson process, Brownian motion, Stochastic process

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[3]. P. E. Greenwood. and L. F. Gordillo -Stochastic epidemic modeling. Mathematical and Statistical Estimation Approaches in
Epidemology, Springer, Dordrecht, 2020 31 – 52, 2009. Retrieved Aug. 15, 2021 from https://doi.or/10.1007/978-90-481-2313-1_2.
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Abstract : The synchronization problem of memristive high-order competitive neural networks with two types of time varying delays is studied. By using Lyapunov function method and inequality method, some sufficient conditions for asymptotic synchronization of high order memory competitive neural networks are given. Finally, a numerical example is shown to verify the correctness and validity of the theoretical result

Keywords: memristive high-order competitive neural neural network; Lyapunov function; synchronization

[1]. Y. Liu, S.H. Zhang, W. Ding, Fixed-time synchronization for fuzzy Cellular neuralnetworks with time-varying coefficients and delays,
Pure Mathematics 11(7) (2021) 1369-1378.
[2]. Z.B. Liu, Z.H. Guang, D.S. Yang, Adaptive synchronization of a class of chaotic neural net- works with mixed time-varying delays,
Journal of Northeastern University (Natural Science Edition) 30(4) (2009) 475-478.
[3]. X.L. Li, J.H. Han, J.G. Jiang, Stability dynamic behavior analysis of Hopfield neural net- work, Journal of Hefei University of
Technology (Natural Science Edition) 21(2) (1998) 14-17.
[4]. L.M.Wang,H.B.He, Z.G. Zeng, Intermittent stabilization of fuzzy competitive neural networks with reaction diff usions, IEEE
Transactions on Fuzzy Systems doi.10.1109/TFUZZ.2020.2999041.
[5]. M.A. Cohen, S. Grossberg, Absolute stability of global pattern formation and parallel memory storage by competitive neural networks,
IEEE Transactions on Systems Man and Cybernetics 42 (1983) 288-308

Abstract : In this paper, we have presented few properties of Pell and Pell-Lucas numbers. Then the matrices related to these numbers are given in this paper. Next some identities satisfied by these numbers with proofs are discussed in this paper..

Key Word: Recurrence relation, Pell numbers, Pell-Lucas numbers, Binet formula.

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[3]. Ahmet Dasdemir , On the Pell, Pell-Lucas and modified Pell numbers by matrix method, Vol.5, No.64, pp.3173-3181, 2011.
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