iosr-Jm   Volume-10 ~ Issue-6 ~ Nov-Dec 2014

Abstract: In this paper an inventory model for deteriorating and repairable item developed with linear demand. It extends a lot size inventory model with inventory-level dependent demand. Shortages are partially backordered and defective product can be repaired. Optimal lot size with minimum total cost is derived using Taylor and calculus analysis. The business strategies, technological change and free market economy is forcing organizations to reconsider their planning for maintaining competitive advantage. The most effective way of sustaining competitive advantage in modern economy, besides producing quality and innovative products, is to make products that can be repaired at minimal cost. Making products that can be repaired will help environment as well as save cost.
Keywords: deteriorating items, repairable product, linear demand, Taylor analysis.

[1]. Covert, R.P., and Philip, G.C. An EOQ Model for Item with Weibull Distribution Deterioration, AIIE Transactions, 5, (4), 323-
326, 1973
[2]. Dat ta, T. K. and Pal , A. K. (1988) Order level inventory system with power demand pattern for items with variable rate
of deterioration. Ind Jour of Pure & Appl . Maths, 19 (11) : 1043-1053
[3]. Dave, U. On A Discrete-In-Time Order-Lever Inventory Model for Deterioration Items, Operations Research, 30, (4), 349-354,
1979
[4]. Elsayed, E.A., and Teresi, C. Analysis of Inventory Systems with Deteriorating Item, International Journal of Production Research,
21, (4), 449-460, 1983
[5]. Ghare, P.M., and Schrader, G.F. A Model for An Exponentially Decaying Inventory, The Journal of Industrial Engineering, 14, (5), 238-243, 1963.

Abstract: Let G = (V, E) be a simple graph. A set S  E(G) is a edge-vertex dominating set of G (or simply an ev - dominating set), if for all vertices vV(G), there exists an edge eS such that e dominates v. Let  ,  ev n D P i denote the family of all ev - dominating sets of n P with cardinality i. Let  ,   ,  ev n ev n d P i  D P i . In this paper, we obtain a recursive formula for  ,  ev n d P i . Using this recursive formula, we construct the polynomial,     4 , , n i ev n n ev n i D P x   d P i x       , which we call ev - domination polynomial of n P and obtain some properties of this polynomial.
Keywords: ev - Domination Set, ev - Domination Number, ev - Domination Polynomials.

[1]. S. Alikhani and Y.-H. Peng, "Introduction to Domination Polynomial of a Graph," arXiv:0905.2251v1[math.co], 2009.
[2]. S. Alikhani and Y.-H. Peng, "Dominating Sets and Domination Polynomials of Paths," International Journal of Mathematics and
Mathematical Sciences, Vol. 2009, 2009, Article ID: 542040.
[3]. G. Chartand and P. Zhang, "Introduction to Graph Theory," McGraw-Hill, Boston, 2005.
[4]. A. Vijayan and K. Lal Gipson, "Dominating sets and Domination polynomials of square of paths", Open Journal of Discrete
Mathematics, 3, 60 – 69, January-2013, USA.
[5]. E. SampathKumar and S.S. Kamath, "Mixed Domination in Graphs," Sankhya: The Indian Journal of Statistics, special volume54,
pp. 399 – 402, 1992.

Abstract: The aim of this paper to develop a theory for generic representation of 2-D shape, where structural descriptions are derived from the shocks (singularities) of a curve evolution process, acting on bounding contours. The shocks are organized into a directed, acyclic shock graph and complexity is managed by attending to the most significant (central) shape components first. The space of all such graphs is highly structured and can be characterized by the rules of a shock graph grammar which permits a reduction of a shock graph to a unique rooted shock tree. A novel tree matching algorithm which finds the best set of corresponding nodes between two shock trees in polynomial time.
Keywords: shape matching, shock graph, shock graph grammar, subgraph isomorphism.

[1]. Alizadeh, F. 1995. Interior point methods in semidefinite programming with applications to combinatorial optimization.SIAM J.Optim., 5(1):13–51.
[2]. Alvarez, L., Lions, P.L., and Morel, J.M. 1992. Image selective smoothing and edge detection by nonlinear diffusion.SIAM J. Numer. Anal., 29:845–866.
[3]. Arnold, V. 1991. The Theory of Singularities and Its Applications.LezioniFermiane, Piza, Italy.
[4]. Basri, R., Costa, L., Geiger, D., and Jacobs, D. 1995. Determining the similarity of deformable shapes.In Proc. ICCV Workshop on Physics-Based Modeling in Computer Vision, pp. 135–143.
[5]. Basri, R. and Ullman, S. 1988. The alignment of objects with smooth surfaces.In Second International Conference on Computer Vision (Tampa, FL, December 5–8, 1988), Computer Society Press: Washington, DC, pp. 482–488.

Abstract: The purpose of this paper is to introduce and study the intuitionistic fuzzy 𝑇2–spaces. We investigate some relations amongthem. We also investigate the relationship between intuitionistic fuzzy topological spaces and intuitionistic topological spaces.
Keywords: Intuitionistic set,Intuitionistic fuzzy set,Intuitionistic topological space, Intuitionistic fuzzytopological space, Intuitionistic fuzzy 𝑇2–spaces

[1]. D. Coker, A note on intuitionistic sets and intuitionistic points, TU J. Math. 20(3)1996, 343-351.
[2]. D. Coker, An introduction to intuitionistic topological space, BUSEFAL 81(2000), 51-56.
[3]. K.T. Atanassov, Intuitionistic fuzzy sets, Fuzzy sets and Systems20 (1986), 87 - 96.
[4]. D. Coker, An introduction to intuitionistic fuzzy topological space, Fuzzy sets and Systems, 88(1997), 81-89.
[5]. S. Bayhan and D. Coker, OnT1 and T2 separation axioms in intuitionistic fuzzy topological space, J.Fuzzy Mathematics 11(3) 2003, 581-592.

Abstract: We investigate line graceful labeling for the spliting graph, total graph, shadow graph and mirror graph of cycle. Moreover we prove that the graphs obtained by duplication of each edge of cycle by a vertex and duplication of each vertex of cycle by an edge admit line graceful labeling.
Keywords: Graceful labeing, edge graceful labeling, line graceful labeling, total graph, spliting graph, shadow graph.
AMS Subject Classification (2010): 05C78, 05C38, 05C76.

[1] N. Lakshmi Prasanna K. Sravanthi and Nagalla Sudhakar, Applications of Graph Labeling in Communication Networks, Oriental
Journal of Computer science & Technology, 7(1), 2014, 139-145.
[2] V. Yegnanaryanan and P. Vaidhyanathan, Some Interesting Applications of Graph Labelings, J. Math. Comput. Sci., 2(5), 2012,
1522-1531.
[3] J. A. Gallian, A dynamic survey of graph labeling, The Electronic Journal of Combinatorics, 16(2013), #DS6.
[4] D. B. West, Introduction to Graph Theory (2/e, Prentice-Hall of India, 2003, New Delhi).
[5] A. Rosa, On certain valuations of the vertices of a graph, in Theory of Graphs, International Symposium Rome, (July 1966),
Gordon and Breach), N.Y. and Dunod Paris, 1967, 349-355.

Abstract: Given a graph G, the dominator coloring problem seeks a proper coloring of G with the additional property that every vertex in the graph dominates an entire color class. In this paper, as an extension of Dominator coloring some standard results for the middle graph of path and cycle has been discussed.

Keywords: Coloring, Domination, Dominator Coloring, Middle Graph

[1]. Ralucca Michelle Gera, On Dominator Colorings in Graphs, Department of Applied Mathematics, Naval Postgraduate School, Monterey, CA 93943, USA
[2]. E.Cockayne, S. Hedetniemi, and S. Hedetniemi, Dominating partitions of graphs, tech. rep., 1979, unpublished manuscript
[3]. S. M. Hedetniemi, S. T. Hedetniemi, and A. A. McRae, Dominator colorings of graphs (2006) In preparation
[4]. T. W. Haynes, S. T. Hedetniemi, and P. J. Slater, Domination in Graphs: Advanced Topics, Marcel Dekker, New York, 1998
[5]. Marcel Dekker, Fundamentals of Domination in Graphs, New York, 1998.

Abstract:A large eddy simulation of a plane turbulent channel flow is performed by using the third order Low- Storage Runge-Kutta method in time and second order Finite Difference formulation in space with staggered grid at a Reynolds number 590 based on the channel half width and wall shear velocity. The computation is performed in a domain where streamwise and spanwise directions are periodic with 32×64×32 grid points. Standard Smagorinsky model is used for subgrid scale modeling. Turbulence statistics of this simulation are compared with Direct Numerical Simulation (DNS) data. The behavior of the flow structures in the computed
flow field have also been discussed.

Keywords: Large eddy simulation, staggered grid, turbulent channel flow.

[1]. J. Kim, P. Moin, and R. Moser, Turbulence statistics in fully developed channel flow at low Reynolds number, Journal of Fluid
Mechanics, 177, 1987, 133-166.
[2]. R. D. Moser, J. Kim, and N. N. Mansour, Direct numrical simulation of turbulent channel flow up to Reτ = 590, Physics of Fluids,
11(4), 1999, 943-945.
[3]. J. W. Deardorff, A Numerical study of three-dimensional turbulent channel flow at large Reynolds numbers, Journal of Fluid
Mechanics, 41,1970, 453-465.
[4]. P. Moin, and J. Kim, Numerical Investigation of Turbulent Channel Flow, Journal of Fluid Mechanics, 118, 1982, 341-377.
[5]. F. Yang, H. Q. Zhang, C. K. Chan, and X. L. Wang, Large Eddy Simulation of Turbulent Channel Flow with 3D Roughness Using a
Roughness Element Model, Chinese Physics Letters, 25 (1), 2008, 191-194.
[6]. U. Piomelli, P. Moin, and J. E. Ferziger, Model Consistency in Large Eddy Simulation of Turbulent Channel Flows, Physics of
Fluids, 31, 1988, 1884-1891.

Abstract:The object of this paper is to evaluate an integral involving Bessel polynomial and I-function of several variables and employ it to obtain a particular solution of the general solution derived in this paper of the classical problem known as the, "Time-domain Synthesis Problem", occurring in electrical network theory.
Keywords: Time-domain Synthesis Problem, electrical network theory,Bessel polynomial,I-Function of several variables.

[1]. Ahmad, S. S.: A Study of Hypergeometric Functions, Ph.D. Thesis, A.P.S. University, Rewa (M.P.), 1992.
[2]. Exton, H. On Orthogonal of Bessel Polynomials. Rev. Mat. Univ. parma (4) 12 (1986), 213-215.
[3]. Erdelyi, A.: A Table of Integral Transform, Vol.I, McGraw-Hill, New York, 1954.
[4]. Erdelyi, A. et. al. Higher Transcendental Functions, Vol. 1 McGraw-Hill, New York, 1953.
[5]. Exton, H. Handbook of Hypergeometric Integrals, Ellis Horwood Ltd., Chichester, 1978.

Abstract: Studies in the evolutionary biology of cancer research require good estimates of the intrinsic growth rate of the tumour coefficient. A Gompertzian model is a classical continuous model useful in describing population dynamics; in particular, it is a very efficient mathematical modelto describe tumour growth in humans and animals. The Gompertz survival model of a tumour growth is the interest of many investigators in experimental biology and the evolutionary biology of ageing. Standard parameter estimation techniques, such as regression and maximum likelihood analysis, require knowledge of actual lifespan for parameter estimation to be successful. In this paper we introduce an alternative algorithm for estimating this parameter. And we examine maximum life span predictions through the Gompertz tumour growth model for large number of tumour cells at particular time.

Keywords: Asymptotic, Gompertz model, Maximum lifetime of tumour cells, Tumour doubling time. AMS classiffication code: 92B05,35A02.

[1]. Al-Dweri,F.M.O., Guirado,D., Lallena,A. M., and Pedraza,V. E_ect on tumour control of time interval between surgery and postoperative radiotherapy: an empirical approach using Monte Carlo simulation, Phys. Med. Biol., Vol.49, p.2827-2839, (2004).
[2]. Anna Kane Laird. Dynamics of Tumour Growth, Br. J. Cancer., Vol.18(3), p.490-502, (September 1964).
[3]. Anna Kane Laird. Dynamics of Tumour Growth: Comparisons of growth rates and extrapolation of growth curve to one cell, Br J Cancer., Vol. 19, p.278-291, (1965).
[4]. Araujo,R.P., and McElwain,L.S. A History of the Study of Solid Tumor Growth: The Contribution of Mathematical Modeling, Bulletin of Mathematical Biology, Vol.66, p.1039-1091, (2004).
[5]. Bass,L., Green,H.S., and Boxenbaum,H. Gompertzian mortality derivedfrom competitionbetween cell-types: congenial, toxicologic and biometric determinants of longevity, J.Theor.Biol., Vol.140, p.263-278, (1989).

Abstract:In this paper we have introduced the new concept of RAM finite hyperbolic transforms. Transform of some standard functions are obtained and some properties are proved.
Keywords: Generalized Transform, Finite transform, RAM Finite hyperbolic transform, Transform of some standard functions.

[1]. Chandrasenkharan K., Classical Fourier Transform, Springer-Verlag, New York (1989).
[2]. Debnath L.and Thomas J., On Finite Laplace Transformation with Application, Z.Angrew.Math.und meth.56(1976),559-593.
[3]. S.B.Chavan, V.C.Borkar., "Canonical Sine transform and their Unitary Representation", Int. J. Contemp. Math. Science, Vol.7,
2012, No. 15,717-725.
[4]. S.B.Chavan, V.C.Borkar., "Operation Calculus of Canonical Cosine transform", IAENG International Journal of Applied
Mathematics, 2012.
[5]. S.B.Chavan, V.C.Borkar., "Some aspect of Canonical Cosine transform of generalised function", Bulletin of Pure and Applied
Sciences.Vol.29E(No.1),2010.

Abstract: This study is aimed at designing CUSUM and EWMA control chart and comparing their performances. The data used in this paper are records of outbreak of some diseases collected from Edo State Civil service Hospital, Benin City and are therefore secondary data. The data covered the period, January 2006 to December 2010. Cumulative Sum (CUSUM ) and Exponentially Weighted Moving Average (EWMA) control charts scheme were designed and used to study the rate of outbreak of some diseaes. Finally, the performances of the two designed control chart schemes were compared. Both CUSUM and EWMA were capable of detecting shifts in diseases data. EWMA charts tended to be slightly slower in providing alarms, but were much easier to set up. Overall CUSUM charts are more efficient to use. Use of these techniques could allow detection of changes in time to mitigate the recurrent pattern of the outbreak of epidemics.

[1]. Barnard, G.A. (1959). "Control charts and stochastic processes". Journal of the Royal Statistical Society.
[2]. Bower, K.M. (October 2000), Using Exponentially Weighted Moving Average (EWMA) Charts, Asia Pacific Process Engineer.
[3]. Cembrowski G.S, Westgard J.O, Eggert A.A, Toren E.C, Jr. (1975): Trend detection in control data, optimization and interpretation of Trigg's technique for trend analysis.
[4]. Crowder S.V (1987): A simple method for studying run-lengths of exponentially weighted moving average control charts. Technometrics; 29:401-407.
[5]. Crowder S.V (1989): Design of exponentially weighted moving average schemes. J Qual Technology; 21:155-162.