iosr-Jm   Volume-13 ~ Issue-3 ~ May-June 2017

Abstract: In this article a four point boundary value problem associated with a second order differential equation involving directional derivative boundary conditions is proposed. Then its solution is developed with the help of the Green's function associated with the homogeneous equation. Using this idea and an Iteration method is proposed to solve the corresponding nonlinear problem.

Key words: Green's function, Schauder fixed point theorem, Vitali's convergence theorem.

[1] Al-Hayan, W. (2007). A domain Decomposition method with Green's functions for solving Twelfth-order of boundary value
problems. Applied Mathematical sciences, Vol. 9, 2015, no. 8, 353 – 368.
[2] Bender, C. M. and S. A. Orzag (1999). Advanced mathematical methods for scientists and Engineers; Asymptotic methods and
perturbation theory, ACM30020.
[3] Benchohra, M. et al Second-Order boundary value problem with integral boundary conditions. Boundary value problems article ID
260309 vol. 2011
[4] Dr. Raisinghania, M. D. (2013), Integral equations and boundary value problems sixth edition; S. Chand & Company PVT. LTD.
[5] Greengard, L. and V. Kokhlin (1991). On the numerical solution of two-point boundary value problems. Communications on pure
and applied mathematics vol. XLIV, 419-452(1991)

Abstract: The concept of a Bipolar intuitionistic M fuzzy group is a new algebraic structure of a bipolar intuitionistic M fuzzy subgroup of a M fuzzy group and anti M fuzzy group are defined and some related properties are investigated. The purpose of the study is to implement the fuzzy set theory and group theory of bipolar intuitionistic M fuzzy subgroup of a M fuzzy group and anti M fuzzy group. The relation between of a bipolar intuitionistic M fuzzy group and bipolar intuitionistic anti M fuzzy group are established.

Keywords: M fuzzy group, anti M fuzzy group, bipolar intuitionistic fuzzy set, bipolar intuitionistic M fuzzy group, bipolar intuitionistic anti M fuzzy group.

[1]. K. Chakrabarthy, Biswas R. Nanda, A note on union and intersection of intuitionistic fuzzy sets, Notes on intuitionistic fuzzy sets,
3(4), 1997.
[2]. P.S. Das, Fuzzy groups and level subgroups, Journal of Mathematical Analysis and its Application, 84, 1981, 264-269.
[3]. V.N. Dixit., A. Rajeshkumar, Naseem Ajmal , Level subgroups and union of fuzzy subgroups, Fuzzy sets and systems, 37,
1990, 359-371.
[4]. Krassimir T. Atanassov, Intuitionistic fuzzy sets :Theory and Application ( Physica-verlag, A springer – verlag company).
[5]. K.. M. Lee, Bipolar valued fuzzy sets and their operations, proceeding of International conference on Intelligent
Technologies, Bangkok, Thailand, 2000, 307-312.

Abstract: A study of operations research (OR) applications to issues of health care systems are made in this article. Operations Research (OR) is picking up importance in public health mediations and projects progressively both broadly and globally. The concentration of these research techniques is to always manage the program execution to achieve best results it adjusts information sources and procedures required in the program cycle and endeavor to create ideal picks up in accomplishing targets and objectives. Using the incomprehensible scope of subjective and quantitative apparatuses, this research has created critical results worth applying and testing in the genuine field..........

Keywords: Operations research, health care systems, importance, public health, programmes, implementation, achieve, improvements.

[1] H Morohosi (2008) A case study of optimal ambulance location problems. The 7th International Symposium on Operations Research and Its Applications pp. 125-130.
[2] T Hanne, T Melo, S Nickel (2009) Bringing robustness to patient flow management through optimized patient transports in hospitals. Interfaces 39: 241-255.
[3] N Litvak, Marleen Van Rijsbergen, RJ Boucherie, Mark Van Houdenhoven (2008) Managing the overflow of intensive care patients. European Journal of Operational Research 185: 998-1010
[4] Z Zhang, Mengyang Liu, Andrew Lim (2015) A memetic algorithm for the patient transportation problem. Omega 54: 60-71.
[5] K Knyazkov, Ivan Derevitsky, Leonid Mednikov, Alexey Yakovlev (2015) Evaluation of Dynamic Ambulance Routing for the Transportation of Patients with Acute Coronary Syndrome in Saint-petersburg. Procedia Computer Science 66: 419-428.

Abstract: In this paper an inventory model is developed with seasonal quadratic demand and time proportional deterioration. Shortages are considered and are partially backlogged. At the start of shortage period price discount is declared on unit selling price for backordered quantity so as to enhance the demand and to reduce the lost sales which in turn maximizes the total profit per unit time. Numerical illustration and sensitivity analysis of the optimal solution with respect to various parameters is carried out to describe the model.

Kew Words: Deterioration, Partial backlogging, Seasonal demand, Price discounting.

[1] Ardalan, A. (1994): Optimal prices & Order quantities when temporary price discounts result on increase in demand, European
Journal of Operational Research, 72(1), 52-61.
[2] Bhunia et al (2009): An application of tournament genetic algorithm in a marketing, oriented economic production lot size model
for deteriorating items, Int.J. Production Economics, 119,112-121.
[3] Cardenas-Barron, L.E, Smith, N.R. and Goyal, S.K. (2010): Optimal Order size to take advantage of a one-time discount offer with
allowed backorders, Applied Mathematical Modeling, 34, 1642-1652.
[4] Chakarbarty et al (1998): An EOQ modal for items with weibull distribution deterioration shortage and trended demand, Computers
and Operation Research,25,649-657
[5] Chang, H. J. and Dye, C. Y. (1999): An EOQ model for deteriorating items with time varying demand and partial backlogging,
Journal of the Operational Research Society, 50, 1176-1182.

Abstract: Difference equations are difficult problems, and rarely can an analytic formula be found for the solution. The problems of difference equations are those of existence, uniqueness and stability of solutions subject to various types of initial two – point or multipoint boundary conditions. Other problems include the behavior of solution with constant and variable coefficients, the stability and instability of linear and non-linear difference equations. This study was designed to evaluate ordinary differential equations and to test the stability of solutions to difference equation using difference methods..............

Kew Words: Differential equations, difference methods, Stability, ordinary, homogenous.

[1]. Anes, W.F. (1977).numerical methods for partial differential equations. Academic press, New York.
[2]. Grewal, B.S. (1998). Numerical methods in engineering and science. Khanna publishers, India.
[3]. Gupta.(2004). Mathematical physics.mc Graw hill, Boston.
[4]. Kreyszig, E. (1999).advance engineering mathematics (8th edition). John Wiley and sons, New York.
[5]. Mathews, J. H., Fink, K. D. (2004). Numerical methods using MATLAB (4th Edition) Prentice-hall, New York USA.

Abstract: We show the Concept of a Series on a Hardy-Sobolev space and give its atomic decomposition. As an application of a Series functions we shown a div-curl lemma

[1]. R. A. Adams, Sobolev Spaces, Academic Press, New York, 1975.
[2]. P. Auscher, E. Russ and Ph. Tchamitchian, Hardy Sobolev spaces on strongly Lipschitz domains of Rn, J. Funct. Anal., 218 (2005), 54-109.
[3]. R. Coifman,A real variable characterization ofHp, Studia Math., 51 (1974), 269-274.
[4]. R. Coifman, P. L. Lions, Y. Meyer and S. Semmes, Compensated compactness and Hardy spaces, J. Math. Pures and Appl., 72 (1993), 247-286.
[5]. R. Coifman, Y. Meyer and E. M. Stein, Some new function spaces and their application to harmonic analysis, J. Funct. Anal., 62 (1985), 304-335.

Abstract: A skew edge coloring of a graph G is defined to be a set of two edge colorings such that no two edges are assigned the same unordered pair of colors. The skew chromatic index s(G) is the minimum number of colors required for a skew edge coloring of G. In this paper, skew edge coloring of certain classes of graphs are determined. Furthermore, the skew chromatic index of those graphs is obtained in polynomial time.

Kew Words: NP- complete, skew chromatic index, skew edge coloring..

[1] S. Fiorini, R.J. Wilson, Edge-colorings of graphs (Pitman, London, 1977).
[2] I. Holyer, The NP-completeness of edge-coloring, SIAM. I. Comput.,10, 1981, 718-720.
[3] V. G. Vizing, On an estimate of the chromatic class of a p-graph(Russian), Diskret Analiz. 3, 1964, 25-30.
[4] D. R. Stinson, The spectrum of skew room squares, J. Australi. Math. Soc. 31(A),1981, 475-480.
[5] M. F. Foregger, The skew chromatic index of a graph, Discrete Mathematics, 49, 1984, 27-39.

Abstract: Till now 174 geometrical methods have supported that the Cosmic Pi equal to (14 – root 2) / 4 = 3.14644660941… is the true value, exact value and an algebraic number. And this Pi number also squared a circle. This is yet another method, in which, a sole line segment proves that Cosmic Pi is the real Pi

Kew Words: Circle, Diameter, Line segment, Square, Pi

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Abstract: The object of this paper is to establish continued fraction for the ratio of two 4 3  series by the application of some known transformation formula in basic hyper geometric series.

Kew Words:Basic hyper geometric series, Continued fractions and some known results in basic hyper geometric series.

[1]. Andrews, G.E., Askey R. and Roy, Ranjan. Special Functions, Cambridge University Press, Cambridge, 1999.
[2]. Agarwal, R.P. (1996): Resonance of Ramanujan's Mathematics, vol.II, New Age International (P) Limited, New Delhi.
[3]. A.M. Mathai and R.K. Saxena, Generalized Hypergeometric Functions with Applications in Statistics and Physical Sciences.
Springer-Verlag, Berlin (1973).
[4]. Andrews, G.E. and Berndt, B.C. (2005): Ramanujan's Lost Notebook,Part1,Springer, New York
[5]. Gasper, G. and Rahman, M. (1990): Basic hyper geometric series, Cambridge University Press, Cambridge.

Abstract: Usually, the length of the diagonal of square is obtained with the help of Pythogorean theorem. In this paper the circumference of an inscribed circle finds the length of the diagonal of its superscribed square .

Kew Words: Circle, Circumference, Square, Side, Diagonal, Pi

[1] Pi of the Circle (6 volumes) , R.D.SarvaJagannadha Reddy.
[2] A History of Pi, Petr Beckmann.
[3] Journey through Genius, William Dunham

Abstract: In this paper an inventory model for deteriorating and repairable items is developed with linear demand. An Exponential distribution is used to represent the distribution of time for deterioration. In the model considered here, shortages are allowed to occur and defective items can be repaired. The model is solved analytically to obtain the optimal solution of the problem. The derived model is illustrated by a numerical example and its sensitivity analysis is carried out.

[1] Bhojak, A., Gothi, U.B. A note on an order-level model for a system with constant rate of deterioration. International Journal of Management and Social Science Research Review, 1(2), 2016, 85–98p. [2] Chen S. J., Chen S. P., and Liu X. B., A production inventory model for deteriorating items, Journal of Zhaoqing University, Vol. 23, No. 2, 2002, pp. 66–68.
[3] Chatterji, D. A. and Gothi, U. B., Three-parametric Weibully deteriorated EOQ model with price dependent demand and shortages under fully backlogged condition, International Journal of Innovative Research in Science, Engineering and Technology, Vol. 4, Issue 12, 2015, 12710-12720.
[4] Datta, T. K. and Pal, A. K. Order level inventory system with power demand pattern for items with variable rate of deterioration. Ind Journal of Pure & Applied. Maths, 19 (11), 1988, 1043-1053.
[5] Ghare, P. M., and Schrader, G.F., A model for an exponentially decaying inventory, Journal of Industrial Engineering, 14, pp. 1963, 238 – 243.

Abstract:Supplier selection is a problem of determining the optimal supplier(s) which are capable to supply a product (raw material) in order to meet the demand so that the total procurement cost is minimal. When the supplier selection problem involving some uncertain parameter, an appropriate optimization method will be necessary. In this paper, we formulate a mathematical model in a probabilistic integer quadratic optimization to solve a multi-product and multi-period supplier selection problem with uncertain demand. The demand is considered as a random variable with some probability distribution. The constraints of the model are covering supplier capacity, inventory management, quality level management and budgetary constraint. To determine the optimal decision,.................

Keywords: Supplier selection, probabilistic integer quadratic programming, probabilistic demand

[1]. S. H. Ghodsypour C. O'Brien, "A decision support system for supplier selection using an integrated analytic hierarchy process and
linear programming," International Journal of Production Economics, Vols. 56-57, pp. 199-212, 1998.
[2]. C.X. Feng, J. Wang, & J.S. Wang, "An optimization model for concurrent selection of tolerances and suppliers," Computers &
Industrial Engineering, vol. 40, pp. 15-33, 2001.
[3]. S.H. Ghodsypour & C. O'Brien, "The total cost of logistics in supplier selection, under conditions of multiple sourcing, multiple
criteria and capacity constraint," International Journal of Production Economics , vol. 73, pp. 15-27, 2001.
[4]. H. Ding, L. Benyoucef, & X. Xie, "A simulation optimization methodology for supplier selection problem," International Journal of
Computer Integrated Manufacturing, vol. 18, no. 2-3, pp. 210-224, 2005.
[5]. Nilesh R. Ware, S.P. Singh, & D.K. Banwet, "A mixed-integer non-linear program to model dynamic supplier selection problem,"
Expert Systems with Applications, vol. 41, pp. 671-678, 2014.P. M., and Schrader, G.F., A model for an exponentially decaying inventory, Journal of Industrial Engineering, 14, pp. 1963, 238 – 243.

Abstract: An attempt is made in this analysis to study the flow of blood through a uniform rigid artery with an axial velocity slip condition at vessel wall has been considered by assuming blood a power fluid. It has been observed that the effect of the Hartmann number and the Reynolds number on the velocity field as well as on the wall shear stress is very prominent and when the Hartmann number and Reynolds number increases, the fluid velocity decreases. It also includes Poiseuille fluid models of blood for both slip and no-slip at a wall and one-layered power fluid model and no slip at tube wall as its special cases. The role of slip in influencing the flow variables and physiological implications of this theoretical modeling are discussed in brief................

Keywords: Power fluid model, stenosed vessels, Magnetic effect, Reynolds number, Hartmann number Blood flow

[1]. Barnothy, M.F. (ed.), Biological effects of Magnetic field, Vol-I & II, Plenum Press (1969).
[2]. Bhuyan, B.C and Hazarika, G.C, Bio-science Research Bulletin, Vol.17(2), PP.105-112(2001).
[3]. Bhuyan, B.C and Hazarika. G.C, proc. National conference on applied Mathematics, 212-217(2001).
[4]. Bhuyan B.C. and Hazarika G.C., Blood flow in channels of varying cross section with permeable boundaries in presence of transverse of magnetic field, Bio science Research Bulletin, Vol. 18 (No. 1), (2002)
[5]. Boyd, W., Text Book of Pathology: Structure and Functions in Diseases, Lea and Febigar, Philadelphia (1963).
[6]. Biswas, D and Nath , J., Oscillating Blood flow through a uniform Artery with wall slip, Journal of Assam University, 4(1), pp. 142-154(1999)..