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

[1]. M. S. Bartlett-Some evolutionary stochastic processes. Journal of Royal StatisticalSociety vol. B no. 11: 211 – 229. 1928.
[2]. F.Carrat, E.Vergu,N. Ferguson M.,Lemaitre, S.Cauchemez, S. Leach andA. Valleron.Timeline of infection and disease in human influenza: a review of volunteerchallenge studies. American Journal of Epidemiology 167.7: 775-785. 2008.
[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.
[4]. Knoeman.com -Nigeria Birth and Death Rates, 1950 – 2021. RetrievedFebruary 12, 2022 from https//knoema.com.

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.

[1]. A.F.Horadam, Applications of modified Pell numbers to representations, Ulam Quart. , Vol.3, pp. 34-53, 1994.
[2]. N. Bicknell, A primer on the Pell sequence and related sequence, Fibonacci Quart., Vol.13, No.4, pp. 345-349, 1975.
[3]. Ahmet Dasdemir , On the Pell, Pell-Lucas and modified Pell numbers by matrix method, Vol.5, No.64, pp.3173-3181, 2011.
[4]. J.Ercolano, Matrix generator of Pell sequence, Fibonacci Quart., Vol.17, No.1, pp.71-77, 1979.
[5]. Naresh Patel and Punit Shrivastava, Pell and Pell-Lucas identities, Global Journal of Mathematical Sciences: Theory and Practical, Vol.5, No.4, pp.229-236, 2013.
[6]. S.F.Santana and J.L. Diaz-Barrero, Some properties of sums involving Pell numbers, Missouri Journal of mathematical Sciences, doi.10.35834/2006/1801033, Vol.18, No.1, 2006.

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Abstract : In this paper Δ𝑥 is considered as an equal length (constant length) of each rectangles and triangles under a closed curve define by a function.

Key Word: Definite Integral, Area under a curve by summation

[1]. Calculus and Analytic geometry, George B. Thomas, Jr. Massachusetts institute of Technology. Ross L. Finney with the collaboration of Maurice D. Weir, Naval Postgraduate School. 9th Edition.
[2]. Mathematical Analysis (Four Edition),S.C. Malik, Savita Arora.

Abstract : In this paper, a mathematical model is prepared for solvingoptimal mix of two or more products to maximize the contributionof linear programming problemusing graphical method. An optimization is founded by solving LPP both by manually and technically as an excel solver software. We get the basic feasible solution of LPP and trying to maximize the production with limited time hourand limited contribution.For Linear programming based optimization problems, Solver makes Linear programming very easy. It can forget difficult Simplex methods and Graphical methods. Solver takes care of the Mathematical programs of the Linear programming problem to be able to use solver we need to ensure to solver has been installed. Number of techniques can be used but an excel solver is readily available in any windows platform with easy to use with accuracy result.

Key Word: Linear programming, Graphical methods, excel solver, LPP.

[1]. Adukia, K. L., Agrawal, B. (2022). OPTIMAL SOLUTION OF ASSIGNMENT PROBLEM WITH THE HELP OF LEAST VALUE ALGORITHM. International Journal of Research and Analytical Reviews, 9(4), pp.335-341. http://ijrar.org/viewfull.php?&p_id=IJRAR22D2981 DOI (Digital Object Identifier) - http://doi.one/10.1729/Journal.32536 [2]. Adukia, K. L., Agrawal, B. (2022). Optimal solution of fuzzy linear programming problems for trapezoidal number by using method of matrix inversion. ©IJEDR 2022, 10(4), pp.80-84.https://www.ijedr.org/archive.php?vol=10&issue=4#IJEDR2204012
[3]. Agrawal, B., Kumar, S., & Sharma, G. OPTIMUM SOLUTION OF A TRANSPORTATION PROBLEM WITH AN EXCEL SOLVER. International Journal of Research and Analytical Reviews, 9(3), pp.892-901. http://ijrar.org/viewfull.php?&p_id=IJRAR22C1598 DOI (Digital Object Identifier) - http://doi.one/10.1729/Journal.33184
[4]. Agrawal, B., Kumar, P. (2022). AN APPROACH OF L.P.P METHOD-GAME PROBLEM USING SIMPLEX METHOD. International Journal of Research and Analytical Reviews, 9(4), pp.927-935.http://ijrar.org/viewfull.php?&p_id=IJRAR22D2939 DOI (Digital Object Identifier) - :http://doi.one/10.1729/Journal.33185
[5]. Agrawal, B., Singh, P. (2022). LINEAR PROGRAMMING IN AN OPERATION RESEARCH FOR OPTIMUM BEST SOLUTION IN REAL WORLD PROBLEM USING EXCEL SOLVER. International Journal of Research and Analytical Reviews, 9(4), pp.34-40. http://ijrar.org/viewfull.php?&p_id=IJRAR22D1602 DOI (Digital Object Identifier) - http://doi.one/10.1729/Journal.33183

Abstract : Here in this work we consider and introduce different type of matrices in fuzzy soft set theory. Then we define some important operations on fuzzy soft matrices. Using these operations we established new results on fuzzy soft matrices. Finally, using a suitable algorithm, a real world problem on decision making theory is solved and presented in detail in this pape

Keywords: Fuzzy Soft Set, Fuzzy Soft Matrix, Production Matrix..

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[3]. T. Mitra Basu, N.K Mahapatra, S.K Mondal, Matrices in Soft Set Theory And Their Applications in Decision Making Problems, S. Asia. J. Math. Vol. 2 No. 2 (2012), 126-143.
[4]. Petroudi et. al., Some new results on Fuzzy soft matrices,TJFS,Vol 8, No.1, (2017),052-062.
[5]. D. Chen, E.C.C.Tang, D. S. Yeung, X. wang, The parameterization Reduction of Soft Set and it's Application, Comput Math Appl., 49(2005), 757-763