iosr-Jm   Volume-12 ~ Issue-3 ~ May-June 2016

Abstract: This paper extends the concept of measure to a finite matrix set. Concrete constructions of measurable functions for finite matrix set are presented and their properties identified. In the process some theorems emerged.

Keywords: measure, matrix set, measurable function, sigma algebra.

[1]. Bogachev, V. I. (2006), Measure theory, Berlin: Springer, ISBN 978-3540345138
[2]. Hohn F. E. (1958) Elementary matrix algebra; New York: The Macmillan Company. Library of congress card number 58-8469
[3]. Keith C. (2000) Computing the norm of matrix. www.math.uconn.ed/ (30/4/2015).

Abstract: In the literature of inventory after the development of classical economic order quantity (EOQ) model researchers extensively studied several aspects of inventory modeling by assuming constant demand rate. But in a real market demand of a product is always dynamic state due to the variability of time, price or even of the instantaneous level of inventory displayed in retail shop. This impressed researchers and marketing practitioners to think about the variability of demand rate
Keywords: Ramp Type demand, Present worth Ordering Cost, Present worth Deterioration Cost

[1]. Deng, P.S., Lin, R.H.J., Chu, P. (2007). "A note on the inventory models for deteriorating items with ramp type demand", European Journal of Operational Research; 178: 112-120.
[2]. Goyal, S.K., Giri, B.C. (2001). "Recent trends in modeling of deteriorating inventory", European Journal of Operational Research; 134(1): 1-16.
[3]. Bansal, K.K. (2016), "A supply chain model with shortages under inflationary environment", Uncertain Supply Chain Management 4(2016) 1-10
[4]. Kumar, A., Bansal, K.K. (2014) "An Optimal Production Model or Deteriorating Item with Stocks and Price Sensitive Demand Rate", International Journal of Education & Science Research Review " 1(4) 79-83

Abstract: Inventory models in which the demand rate depends on the inventory level are based on the common real-life observation that greater product availability tends to stimulate more sales. In this model we discussed a selling price dependent demand rate with a time varying holding cost and shortages are not allowed. The holding cost per unit of the item per unit time is assumed to be an increasing function of the time spent in storage. At the end of the paper, numerical examples are provided to illustrate the problem and sensitivity analyses have been carried out for showing the effect of variation in the parameters.
Keywords: Constant Deterioration, Selling price dependent demand, Time varying holding cost.

[1]. R. Amutha and E. Chandrasekaran, "An EOQ Model for Deteriorating Items with Quadratic Demand and Time Dependent Holding Cost," International Journal of Emerging Science and Engineering, Vol. 1, No. 5, 2013, pp. 5-6.
[2]. Burwell T. H., Dave D. S., Fitzpatrick K. E. and Roy M. R. (1997), Economic lot size model for price-dependent demand under quantity and freight discounts, International Journal of Production Economics, 48(2) 141-155.
[3]. Burwell T. H., Dave D. S., Fitzpatrick K. E. and Roy M. R. (1997), Economic lot size model for price-dependent demand under quantity and freight discounts, International Journal ofProduction Economics, 48(2) 141-155.
[4]. Ghare, P.M., and Schrader, G.F., "An inventory model for exponentially deteriorating items,"journal of industrial engineering,14(1963),238-243.
[5]. S. K. Goyal and B. C. Giri, "Recent Trends in Modeling of Deteriorating Inventory," European Journal of Operational Re- search, Vol. 134, No.1, 2001, pp. 1-16.

Abstract:A new model of asset management for a business organization is proposed based on the uncertainty theory in which the capital assets are managed. Here, a continuous-time utility portfolio problem with the assumption of Hyperbolic Absolute Risk Aversion (HARA) utility function is examined from an investor whose income is generated by return and capital gains on investments in risky tangible assets with price and return on assets assumed to satisfy the Liu uncertain process. Thus, the problem is solved and the optimal controls are obtained.
Keywords: Optimal control, uncertainty theory, uncertain process, optimality, asset management

[1]. Arthur, D. K. (1995). An optimal control model for analyzing human postural balance. IEEE Transaction on Biomedical Engineering.
42(1), 87-101.
[2]. Bamigbola, O. M. and Aderinto, Y. O. (2009). The characterization of optimal control model of electric power power generating
system. International Journal of Physical science. 4(1), 104-115.
[3]. Cairns, A. (2000). Some Notes on the Dynamics and Optimal Control of Stochastic Pension Fund Models in Continuous Time. ASTIN
Bulletin. 30(1), 19-50.
[4]. Deng, L. and Zhu, Y. (2012). An uncertain optimal control model with n jumps and application. ComSIS 9(4), 1453-1468.
[5]. Dixit, A. K. and Pindych, R. S. (1994). Investment under Uncertainty. Princeton: Princeton University Press.

Abstract:In this paper, we propose a new technique, namely homotopy perturbation natural transform method (HPNTM) for solving fractional physical models. It consists of coupling the natural transform methodand the homotopy perturbation method.This technique yields an analytical solution in terms of a rapidly convergent infinite power series with easily computable terms. The fractional derivatives are described in the Caputo sense. The resultsobtained reveal the efficiency, simplicity and applicability of the proposed method for solving other fractional physical models.
Keywords: Natural transform, Homotopy perturbation natural transformmethod (HPNTM),Fractional Jaulent– Miodeksystem.

[1]. H. T. Ozer, S. Salihoglu, Nonlinear Schrödinger equations and n=1 super conformal algebra, Chao Soliton. Fract, 33(2007),1417–
1423.
[2]. S. Y. Lou, A direct perturbation method: nonlinear Schrodinger equation withloss,Chin.Phys.Lett,16 (1999),659–661.
[3]. A. Atangana, D. Baleanu, Nonlinear fractional Jaulent-Miodek and Whitham-Broer-Kaup equations with Sumudu transform, Abstr.
Appl. Anal, 8(2013), ID160681.
[4]. A. M. Wazwaz, Partial differential equations and solitary waves theory, Higher Education Press, Beijing and Springer-Verlag
,Berlin,(2009).
[5]. L. Debnath, Nonlinear partial differential equations for scientists and engineers Birkhauser, Springer, NewYork,(2012).

Abstract:This paper considers two special cases of correlation matrices, when k repeated observation on each of the p – variatewere collected from entity j at time t(t = 1, 2, …, k; p = 1,2,3; j = 1, 2, …, ni; i = 1,2)have equal correlation and auto correlation. Case 1 assumed constant equi-correlation matrix for all variables of both populations with a common variance covariance matrix while case 2 assumed auto correlation matrix. Two discriminant procedures (Regression Discriminant and elongated data discriminant) were employed in constructing the sampled based discriminant function.Systolic and diastolic blood pressures and heart rate were........
Keywords: Disciriminant Function, Elongated Data Discriminant, Regression Discriminant, Equicorrelation, Autocoreelation

[1]. Basu. P. A and Odell, P. L (1974). Effect of IntraclasssCorrelationAmongh Training Samples on Misclassification Probabilities of
Bayes Procedure. Pattern Recognition. Vol. 6. Pg. 13-16.
[2]. Choi, S. C. (1972). Classification of Multiple Observed Data. Biometrika, Vol. 14 pg. 8- 11.
[3]. Gupta, K. A. (1980).On a Multivariate Classification Model.in Multivariate Statistical Analysis, R. A. Gupta (Ed) Amsterdam.
North Holland. Pg 83 -93.
[4]. Gupta A. K. (1986). On Classification Rule for Multiple Measurements. Computer Mathematics Applicltion. Vol, 12a Pg.301 –
308.
[5]. Mclachlan, G. J. (1976). The Bias of Apperent Error in DiscrimirnantAnalyses. Biometrika. Vol. 63. Pg.239 – 244.

Abstract: Theory of matrices is an integral part of algebra as well as Theory of equations. Matrices plays an important role in every branch of Physics, Computer Graphics and are also used in representing the real world's data and there are so many applications of matrices ,for this reason we thought of studying bicomplex matrices. Bicomplex matrix has a number of applications in various fields of science as well as real world but it has captured less attention what it deserves.........
Keywords: Bicomplex matrices, Bicomplex polynomial, eigen value, Fundamental Theorem of Bicomplex Algebra.

[1] Anjali, "Certain Results on bicomplex matrices."M.Phil,Desertation Dr. B.R. AmbedkarUniversity, Agra (2011)
[2] Futagawa, M, "On the theory of functions of a quaternary variable." Tohoku. Math. J,29(1928), 175-222. Kumar, Prabhat, "Certain study of bicomplex matrices and a new composition ofbicomplex matrices."M.Phil,
[3] Desertation Dr. B.R. Ambedkar University (2011-12)
[4] Price, G.B. "An introduction to multicomplex spaces & functions."Marcel Dekker Inc., NewYork (1991).
[5] Riley, J.D; "Contribution to the theory of functions of a bicomplex variable."TohokuMath , J,2ed series 5 (1953),132-165.

Abstract:In this paper, we obtain a Presic type fixed point theorem for two pairs of jointly 2k -weakly compatible maps in complex valued b -metric spaces.We also give an example to illustrate our main theorem
Keywords: B -metric spaces, Jointly 2k -weakly compatible pairs,Presic type theorem.

[1]. S.B.Presic, Sur une classe d inequations aux differences finite et sur la convergence de certaines suites, Pub de 1 l inst. Math. Belgrade, 5(19), (1965), 75-78.
[2]. Lj.B.Ciric and S.B. Presic, On Presic type generalization of Banach contraction mapping principle, Acta. Math. Univ. Comenianae, LXXVI (2), (2007), 143-147.
[3]. K.P.R.Rao, G.N.V.Kishore and Md.Mustaq Ali, Generalization of Banach contraction principle of Presic type for three maps, Math.Sci. 3(3), (2009), 273 - 280.
[4]. K.P.R.Rao, Md.Mustaq Ali and B.Fisher, Some Presic type generalization of Banach contraction principle, Math.Moravica 15(2011), 41 - 47.

Abstract:The purpose of this paper is to prove the existence of generalized solution of quasilinear differential elliptic equations in Sobolev space 1 ( , ) p l l W R dx . To achieve our goal, we used the following scheme: we introduced new type of differential form in
p L that is generated by quasilinear differential elliptic equations; that form generate nonlinear operator 1 1 : ( , ) ( , ) p p l l p l l A W R dx W R dx   and we study its properties; we use Galerkin method to show that a given equations has a solution in 1 ( , ) p l l W R dx space.
Keywords: Galerkin method, elliptic equations, nonlinear operator

[1]. Вишик М.Й. О сильно эллиптических системах дифференциальных уравнений / М.Й. Вишик // Матем. сб. - 1951. - Т.
29(71), №3. - С. 615-676.
[2]. Kato T. Perturbation theory for linear operators / T. Kato. – Berlin-Heidelberg-New York: Springer-Verlag, 1980. – 578 p.
[3]. Kato T. Non-linear semigroups and evolution equations / T. Kato // J. Math. Soc. Japan. – 1967. – V. 19. – P. 508 – 520.
[4]. Komura Y. Differentiability of nonlinear semigroups / Y. Komura // J. Math. Soc. Japan. –1969. – V. 21. – P. 375–402.
[5]. Komura Y. Nonlinear semi-groups in Hilbert space / Y. Komura // J. Math. Soc. Japan. – 1967. – V. 19. – P. 493 – 507.

Abstract: In this paper, we define three different types of fuzzy path connectedness on fuzzy Banach manifold and we show that these fuzzy path connectedness forms an equivalence relations on fuzzy Banach manifold. Further, we show that the image of fuzzy path connected fuzzy Banach manifold under smooth fuzzy map is fuzzy path connected and also we study some of its properties.
Keywords: Locally fuzzy path connectedness, Internally fuzzy path connectedness, Maximally fuzzy path connectedness, Smooth fuzzy network structure

[1] A. K. Katsaras, D. B. Liu, Fuzzy Vector Space and Fuzzy Topological Vector Spaces, Journal of Mathematical Analysis and Application 58, 135-146(1977).
[2] C. L. Chang, Fuzzy Topological Spaces, Journal of Mathematical Analysis and Application, 24, 182-190(1968).
[3] C. Y. Zheng, Fuzzy path and fuzzy connectedness, Fuzzy sets and Systems, 14, 273-280(1984).
[4] D. M. Ali, On fuzzy path connectedness, BUSEFAL, 26-33(1987).
[5] Erdal Guner, THE TANGENT BUNDLE ON 𝐶1 FUZZY MANIFOLD, Commun. Fac. Sci. Uni. Ank. Series AI, 52, 29-34(2003).

Abstract: After classifyingprimes into forms 8n + k for k = 1, 3, 5 and 7, their abundance in these forms is compared.For each block of 1–10n,for 1 ≤ n ≤ 12, the first & last prime in them are determined.Minimum number of primes in blocks, their minimum occurrence frequency, first and last minimum prime containing blocks are given. Similar analysis for maximum number of primes in blocks is also carried out. 2010 Mathematics Subject Classification:11A41, 11N05, 11N25
Keywords: Arithmetical progressions, block-wise distribution, prime, prime density

[1] Euclid (of Alexandria), Elements, Book IX(300 BC).
[2] Ivan Niven, Herbert S. Zuckerman, Hugh L. Montgomery, An Introduction to the Theory of Numbers, 5th Edition (John Wiley & Sons Inc., 2008).
[3] Neeraj Anant Pande, Analysis of Twin Primes less that a Trillion, Journal of Science and Arts, Communicated, 2016.
[4] Benjamin Fine, Gerhard Rosenberg, Number Theory : An Introduction via the Distribution of Primes(Birkhauser, 2007).
[5] Neeraj Anant Pande, Analysis of Primes in Arithmetical Progressions 3n + k up to a Trillion, IOSR Journal of Mathematics, Volume 11, Issue 3 Ver. IV, pp. 72-85, 2015.

Abstract: The present study deals with unsteady two-dimensional hydro magnetic free convective boundary layer flow of an incompressible and electrically-conducting fluid along an infinite vertical plate embedded in the porous medium with heat and mass transfer is analyzed, by taking into account the effect of Radiation, Chemical Reaction, viscous dissipation, heat source and Hall current.........
Keywords: Radiation, Chemical Reaction, MHD, heat and mass transfer, free convection flow, porous medium, viscous dissipation

[1]. S. J. Kim, K. Vafai, Analysis of natural convection about a vertical plate embedded in porous medium, Int. J. Heat Mass Transfer,
32, 665-677, 1989. (New 1 Green)
[2]. S. D. Harris, D. B. Ingham, I. Pop, Free convection from a vertical platein a porous medium subject to a sudden change in surface
heat flux, Transport in Porous Media, 26, 207-226, 1997. (New Green)
[3]. Takhar et al. 2006, Unsteady free convection flow over an infinite vertical porous plate due to the combined effects of thermal and
mass diffusion, magnetic field and hall current,. Heat Mass Transfer 39, 823-834.
[4]. Hossain & Mondal. 1985, Mass transfer effects on the unsteady hydromagnetic free convection flow past an accelerated vertical
porous plate,. J. Phys. D: Appl. Phys 18, 163-169.
[5]. Israel-Cookey. & Sigalo. 2003, Unsteady MHD free convection and Mass Transfer flow past an infinite heated porous vertical plate with time suction., ASME Modelling B 72(3), 25.

Abstract: One of the most interesting themes of the mathematical ecology is the description of population biology and human epidemic models, which are almost nonlinear dynamic equations. In this communication we described the population biology by the logistic differential equation and applied an unconditionally stable nonstandard finite difference method through the methodology of Mickens. It has been proved that the Mickens scheme is dynamically consistent with the original differential equation regardless of the step sizes used in numerical simulations, in comparison with the standard finite difference methods.
Keywords: Logistic differential equation; Standard finite difference scheme; Non-standard finite difference method; Stability analysis

[1]. L. Edelstein-Keshe .Mathematical Models in Biology.McGraw-Hill, 1988.
[2]. L. J. S. Allen. Some discrete-time SI, SIR, and SIS epidemic models MathematicalBiosciences, 124: 83-105, 1994.
[3]. Mickens R.E.2005, Advances in the applications of nonstandard finite difference schemes edited by Ronald E.Mickens.2005, pp.823-847.
[4]. H. Al-Kahby, F. Dannan, and S. Elaydi. Non-standard discretization methods for somebiological models. In R. Mickens, editor, Applications of Nonstandard Finite Difference Schemes, chapter 4, pages 155-180. World Scientific, New Jersey, 2000.
[5]. C.W. Chi, S.-B. Hsu, and L.-I. Wu. On the asymmetric May-Leonard model of threecompeting species. SIAM J. Appl.Math., 58(1): 211-226, 1998.