iosr-Jm   Volume-10 ~ Issue-5 ~ Sep-Oct 2014

Abstract: In the present paper, after defining an integrated contact metric structure manifold [3] I have
defined n M
and nearly n M
manifold. It has been shown that n M
is integrable. Several useful theorems on
these manifolds have also been derived.
Mathematics Subject Classification: 53
Keywords : and Phrases: C -manifold, integrated contact structure, integrated contact metric structure,
Riemannian metric, Riemannian connection.

[1] K. Matsumoto., On Lorentzian Paracontact manifolds, Bull. Yamogata Univ. Nat. Sci., 12 , 1989,151-156.
[2] S. D. Singh and D. Singh., Tensor of the type (0, 4) in an almost Norden contact metric manifold, Acta Cincia Indica, India, 18
M(1), 1997, 11-16.
[3] Shalini Singh, Holomorphic sectional curvature on an integrated contact metric structure manifold, Ultra scientist of physical
sciences, 21 (3)M, 2009, 655-658.
[4] T. Adati and K. Matsumoto, On almost paracontact Riemannian manifold, T.R.U. Maths.,13(2), 1977, 22-39.

Abstract: This paper presents numerical solutions of first order linear fuzzy differential equations using Leapfrog method. The obtained discrete solutions are compared with single-term Haar wavelet series (STHWS) method [1]. Error graphs and error calculation tables are presented to highlight the efficiency of the Leapfrog method. This method can be implemented in the digital computers and take any time of solutions.
Keywords: Fuzzy differential equations, Fuzzy initial value problems, Haar wavelet series, Leapfrog method, Single-term Haar wavelet series method.

[1] S.Sekar and S.Senthilkumar, Single-term Haar wavelet series for fuzzy differential equations, International Journal of Mathematics Trends and Technology, 4(9), 2013, 181 – 188

[2] S. Abbasbandy and T. Allahviranloo, Numerical solutions of fuzzy differential equations by Taylor method, Journal of Computational Methods in Applied Mathematics. 2, 2002, 113-124.

[3] S. S. L. Chang and L. A. Zadeh, On fuzzy mapping and control, IEEE Transactions on Systems, Man, and Cybernetics, 2, 1972, 30–34.

[4] D. Dubois and H. Prade, Towards fuzzy differential calculus.III. Differentiation, Fuzzy Sets and Systems, 8( 3), 1982, 225–233.

[5] M. L. Puri and D. A. Ralescu, Differentials of fuzzy functions, Journal of Mathematical Analysis and Applications, 91(2), 1983, 552–558

Abstract: Dengue fever is an infectious disease in tropical regions, where its spread is transmitted by Aedesaegypti mosquito. Modeling the spread of dengue disease will facilitate in understanding the dynamics of the spread of disease in a population. There have been several mathematical models of the spread of dengue, in this paper will be modified a model that considering the incubation period. At its transmission in both humans and mosquitoes, viruses undergo an incubation period before the virus can move from mosquitoes to humans and vice versa humans to mosquitoes. In this paper will discuss the transmission of dengue in SIR model involving the incubation of virus in humans it called Intrinsic Incubation Period and model involving virus incubation period in humans and in mosquitoes. The virus incubation period in mosquitos it called Extrinsic Incubation Period. The fixed points were determined on this paper on both models, there were two fixed point namely free disease fixed point and endemic fixed point. Stability analysis performed on both models and numerical approach also performed. It was found that model with intrinsic incubation oscillates towards a stable value, and model with the effect of intrinsic and extrinsic incubation oscillates cyclically.

Keywords: dengue fever, incubation, mathematical model, SIR model, stability

[1] P Pongsumpun, Transmission Model For Dengue Disease With And Without The Effect Of Extrinsic Incubation Period, KMITL Sci. Tech. J. Vol. 6 No. 2, 2006.
[2] M Derouich, A Boutayeb, EH Twizell, A Model of Dengue Fever, BioMedical Engineering OnLine 4 (2003):1-10.

[3] Esteva L, Dynamics of Dengue Disease, Mexico :Cinvestav-Ipv ,1998.

[4] DJ Gubler, Dengue and Dengue Hemorhagic Fever, Clinical Microbiology Review 11 :450-496, 1998.

[5] P Van Den Driesscheand J Watmough, Chapter 6: Further Notes on the Basic Reproduction Number, In: Brauer, F, Van Den Driessche P, Wu J (Eds.), Mathematical Epidemiology, Vol. 1945. Lecture Notes in Mathematics, Springer 159–178, 2008.

Abstract: This paper provided the preliminary test single stage shrinkage estimator for estimating the parameters of simple linear regression model, when a prior estimate of these parameters are available. This prior estimate has been referred in statistical literatures as guess point about the parameters. The expressions for Bias, Mean Squared Error (MSE) and Relative Efficiency of the proposed estimators are obtained. Numerical results are provided when the proposed estimators are estimators of level of significance .Comparisons with the usual estimator (O.L.S.) and existing estimators were made to show the usefulness of the proposed estimators in the sense of Relative Efficiency and Mean Squared Error.
Keywords: Simple Linear Regression Model, Least Square Estimator, Single Stage Shrinkage Estimator, Bias Ratio,Mean Squared Error, Relative Efficiency.

[1] Z.A. Al-Hemyari, A. Khurshid, and A. N. Al-Joboori, On Thompson Type Estimators for the Mean of Normal Distribution , Revista Investigación Operacional , 30(2),2009, 109-116.
[2] A.N. Al-Joboori, Preliminary Test Single Stage Shrunken Estimator for the Parameters of Simple Linear Regression Model, Ibn Al-Haitham Journal for Pure and Applied Science,13(3), 2000, 65-73.
[3] A.N. Al-Joboori, On Shrunken Estimators for the Parameters of Simple Linear Regression Model, Ibn Al-Haitham Journal for Pure and Applied Science, 15(4A), 2002, 60-67.
[4] A.N. Al-Joboori, Pre-Test Single and Double Stage Shrunken Estimators for the Mean of Normal Distribution with Known Variance, Baghdad Journal for Science,7(4), 2010,1432-1441.
[5] A.N. Al-Joboori, On Significance Test Estimator for the Shape Parameter of Generalized Rayleigh Distribution, AL-Qadesyia Journal for Computer and Mathematics Sciences ,3(2),2011,390-399.

Abstract: This research work is an exhaustic survey of some basic results and ideas in the theory of one dimensional dynamical systems. We have looked at the eventual behaviour of the iterates of the quadratic family f(x) = x (1-x), where  is parameter value, 0 < x < 1 and 1 < μ< 3. In contrast to the graphical approach outlined in Devaney, we gave an analytical approach as means of justifying the convergence of the sequence of iterates to the fixed points.

Keywords: Quadratic Map, Dynamic Systems, Quadratic Family and Fixed Points

[1]. Devaney, R. L. (1986). Introduction to chaotic Dynamics. Benjamin Cummings.
[2]. USA 159.
[3]. May, R. M (1976). Simple Mathematical Models with very complicated Dynamics. Nature, 261, 459 – 466.
[4]. Yuguda, KB. (1998). Contrasts and Analogues in Iteration theory and Dynamical Systems. Ph. D Thesis Unpublished, Unijos.

Abstract: In this paper we have found that if a Kenmotsu manifold with a Killing vector field satisfies gradient Ricci soliton equation then the smooth function 𝑓 is either constant or 𝛻𝑓 is orthogonal to the Killing vector field. Mathematics Subject classification 2000: Primary 53C44 ; Secondary 53D10, 53C25.

Keywords: Ricci flow, Ricci soliton, Kenmotsu manifold.

[1]. R. Hamilton, Three manifold with positive Ricci curvature, J. Differential Geom.17(2),(1982),256-306.
[2]. R. Hamilton, Four - manifolds with positive curvature operator, J.Differential Geom. 24(2),(1986),153-179.
[3]. G. Perelman, The entropy formula for the Ricci flow and its geometric applications,arxiv.org/abs/math/0211159v1.
[4]. G. Perelman, Ricci flow with surgery on three manifolds,arxiv.org/abs/math/0303109.
[5]. R. Hamilton, The Ricci flow on surfaces, Mathematics and general relativity, Contemp. math., 71,(1988),237-261.
[6]. B. Barua, U. C. De, Characterizations of a Riemannian manifold admitting Ricci solitons, Facta Universitatis (Nis), Ser. Math. Inform., 28(2013), no. 2, 127-132.

Abstract: The purpose of this paper is to introduce and study the concepts of intuitionistic fuzzy 𝜋 generalized semi connectedness in intuitionistic fuzzy topological space. Some of their properties are explored.

Keywords: Intuitionistic fuzzy topology, Intuitionistic fuzzy 𝜋 generalized semi closed set, Intuitionistic fuzzy 𝜋 generalized semi continuous mapping, Intuitionistic fuzzy almost 𝜋 generalized semi continuous mapping, Intuitionistic fuzzy 𝜋 generalized semi connectedness. 2010 AMS Classification: 54A40, 03E72

[1] Atanassov, K., Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20 (1986), 87-96.
[2] C.L.Chang, Fuzzy topological spaces, J.Math.Anal.Appl, 24(1968), 182-190.
[3] D.Coker, An introduction to intuitionistic fuzzy topological spaces, Fuzzy sets and systems, 88(1997), 81-89.
[4] Joung Kon Jeon, Young Bae Jun and Jin Han Park, Intuitionistic fuzzy alpha continuity and intuitionistic fuzzy pre continuity, International journal of Mathematics and Mathematical Sciences, (2005), 3091-3101.
[5] S.Maragathavalli and K.Ramesh, Intuitionistic fuzzy π- generalized semi closed sets, Advances in Theoretical and Applied Sciences, 1 (2012), 33-42.
[6] S.Maragathavalli and K.Ramesh, Intuitionistic fuzzy - generalized semi irresolute mappings, International journal of mathematical Archive, 3 (2012), 1-7.

Abstract: In this paper, we study some coupled fixed point theorems in a dislocated quasi-metric space which improve and extend some existing results.

Keywords: dislocated quasi-metric space: coupled fixed point

[1]. P. Hitzler and A. K. Seda. Dislocated topologies. J. Elect. Eng., 51:3:7, 2000.
[2]. S. G. Matthews. Metric Domains for completeness. Ph.d., thesis, 1986.
[3]. C. Alaca. Coupled Fixed Point Theorems in Dislocated Quasi-metric Spaces, 2013Modern Science Publishers
[4]. R. Shrivastava, Z. K. Ansari, and M. Sharma. Some results on fixed points in dislocated quasi-metric spaces. Journal of Advanced Studies in Topology, 3(1):25:31, 2012.
[5]. F. M. Zeyada, M. R. Moubarak, and A. H. Soliman. A generalization of generalized banach fixed-point theorem in a weak left small self-distance space. Miskolc Mathematical Notes, 8:99:105, 2007.

Abstract: In this paper we introduce and investigate the notions of gr*-closed set, gr*-open set, gr*- continuous, gr*-neighbourhood, gr*O-connected spaces, pairwise gr*O-compact spaces in Bitopological Spaces.
Keywords: (i,j) gr*-closed sets, (i,j) gr*-open sets, Dr *(i,j)- σk-continuous, (τi,τj)-gr*-neighbourhood, pairwise gr*O-connected, pairwise gr* open cover, pairwise gr*O-compact

[1] I. Arokiarani. Studies on generalizations of generalised closed sets and maps in topological spaces. Ph.D. Thesis, Bharathiar University, Coimbatore-1997.

[2] T.Fukutake. On generalized closed sets in bitopological spaces. Bull. Fukuoka Univ. Ed. Part-III, 35:19:28(1985).

[3] T. Fukutake, P. Sundaram, and N. Nagaveni. On weakly generalized closed sets and weakly generalized continuous in topological spaces. Bull. Fukuoda Univ. Ed. Part, 48:33:40 (1999).

[4] T. Fukutake, P.Sundaram, and M. Sheik John. W-closed sets, W-open sets and W-continuity in bitoplogical spaces. Bull. Fukuoka Univ. Ed. Part III, 51:1:9(2002).

[5] K. Indirani, P. Sathishmohan and V. Rajendran, On gr*-Closed Sets in a Topological Spaces, Int. Jr. of Math. Trends and Technology, 6(2)(2014).

Abstract: In this paper, we consider a continuous review perishable inventory system with Markovian demand. The operating policies are (s, S) and (0,M). The life time of an item has an exponential distribution. The ordered items are received after a random time which is assumed to be exponential distribution. The demands that occur directly to the distribution centre are called direct demands. The arrival process for the direct demand follows Poisson process. The demand process to the retailer node is independent to the direct demand process and follows Poisson process. The demands that occur during stock out period are enter into the orbit of finite size. These orbiting demands retry for their demand after a random time, which is assumed to be exponential distribution. The joint probability distribution of the inventory level at lower echelon, higher echelon and the number of customer in the orbit is obtained in the steady state case. Various system performance measures in the steady state are derived and the long run total expected cost rate is calculated.
Keywords: Two-echelon Inventory system, Perishable Inventory, Retrial demand, Direct demand

[1] Clark, A. J. and H. Scarf, 1960. Optimal Policies for a Multi- Echelon Inventory Problem. Management Science, 6(4): 475-490.

[2] Hadley, G and Whitin, T. M., (1963), Analysis of inventory systems, Prentice- Hall, Englewood Cliff, New Jersey.

[3] Cinlar, E. Introduction to Stochastic Processes. Prentice Hall, Englewood Cliffs, NJ, 1975.

[4] Nahimas, S. 1982. Perishable inventory theory. A review. Operations Research, 30, 680-708.

[5] Kalpakam, S and Arivarignan, G. 1988. A Continuous review Perishable Inventory Model, Statistics 19, 3, 389-398.

[6] Svoronos, Antony and Paul Zipkin, 1991. Evaluation of One-for-One Replenishment Policies for Multiechelon Inventory Systems, Management Science, 37(1): 68-83

Abstract: The aim of this paper is to study the ultra contra continuous multifunction.

Keywords : and Phrases: ultra upper contra continuous and ultra lower contra continuous multifunction.

[1]. M.C.Dutta., Contribution to theory of bitopological spaces, Ph.D Thesis, Pilani, 1971.
[2]. J.C.Kelli., Bitopological Spaces, Pro.London Math.Soc,13(1963),71- 89.
[3]. M.Lellis Thivagar., Generalization of (1,2)-continuous functions, Pure and Applied Mathematika Sciences 33 (1991),55-63.
[4]. G.Navalagi, M.Lellis Thivagar and R.RajaRajeswari., (1,2)- Hy- perconnected spaces, International Journal of Mathematics and Anal- ysis, Vol.3 (2006), 120 -129.
[5]. G.Navalagi, M.Leelis Thivagar and R.RajaRajeswari., On ultra multifunctios in bitopological spaces, International Journal of Mathe- matics, Computer Science and Information Technology Vol.1,No.1(2008),69- 74.
[6] V.Popa., A note on weakly and almost continuous multifunc- tions,Univ.u Novom sadu, Zb.Rad.Priorod. - Mat.Fak.Ser.Mat.21, 2(1991), 31-38.

Abstract: Given the sets of flights and aircrafts of an airline, the fleet assignment problem consists of assigning the most profitable aircraft in every flight. In this paper, the model of fleet assignment is set up using the data from the airline company which has the largest market in Indonesia, i.e. Lion Air. It's involved the runway constraints in the model to result more realistic scenarios, where three scenarios of the fleet assignment have been analyzed. The aim of the first scenario is to assign the most appropriate fleet type to flights while minimizing the cost. The second scenario is to see what is the minimum number of aircraft required to cover all flights. The aim of the third scenario is to assign the most appropriate fleet type to flights while minimizing not only the cost but also the number of aircraft for all flights. Models have been set up under constraints of all airline operations and formulated in term of an integer linear programming. The solution of these problems generates a minimum daily cost of fleet assignment and the minimum number of aircraft for all flights.

Keywords: Cost minimization, fleet assignment, integer linear programming, lion air, number of aircraft

[1] J. Abara, Applying integer linear programming to the fleet assignment problem, Interfaces, 19(4), 1989, 20-28.
[2] [ACRP] Airport Cooperative Research Program, Federal Aviation Administration, Improved models for risk assessment of runway safety areas (Washington DC, Transportation Research Board, 2011).
[3] C. Barnhart, P.P. Belobaba, and A.R. Odoni, Applications of operations research in the air transport industry, Transportation Science, 37 (4), 2003, 368-391.
[4] M. Bazargan, Airline operations and scheduling. 2nd ed (United States, Ashgate, 2004).
[5] P. Belobaba, A. Odoni, and C. Barnhart, The global airline industry (United States, Wiley, 2009).
[6] C.A. Hane, C. Barnhart, E.L. Johnson, R.E. Marsten, G.L. Nemhauser, and G. Sigismondi, The fleet assignment problem: solving a large-scale integer program, Mathematical Programming, 70, 1995, 211-232.

Abstract: The Research paper throws light on the processes involved in Dynamic pricing in attracting the customers in balancing the price sensitive and time sensitive issues. It examined the how market volatility constrained in maximising the benefits and measures strategized in optimising the profits with the paramount importance to the customer satisfaction in terms of price and services. It also critically located the practices of a few players in manipulation in the pricing at certain times in maximising the utility of services with relative profits and customer satisfaction......

Keywords: Profit-making, Paramount, Analysis, Capacity, Dynamic pricing, Customer satisfaction, Revenue management, price sensitive, refinement, Operation research.

[1]. An econometric analysis of hotel-motel room nights a New Zealand with strochastic seasonality, International Journal of Revenue Management, Vol 5, Issue 1, February, 2011, pp. 63-83,
[2]. Brotherton, B. and Mooney, S. (1992), "Revenue Management Progress and Prospects", International Journal of Hospitality Management, Vol. 11 No. 1. pp 23-32.
[3]. Burgess, C. and Bryant, K. (2001). "Revenue Management the Contribution of the Finance Function to Profitability", International Journal of Contemporary Hospitality Managementt, 13/3.pp. 144-150.
[4]. Jauncey, S., Mitchell, 1. and Slamet P. (1995). "The Meaning and Management of Revenue is Hotels". International Journal of Contemporary Hospitality Management, Vol. 7, No. 4, pp. 23. 26.
[5]. Jones, C. and Val, P. (1993). Accommodation Management, UK: Redwood Books