iosr-Jm   Volume-6 ~ Issue-1

Abstract: A unified approach is attempted to bring the descriptive statistics in to a more refined frame work. Different measure of central tendencies such as arithmetic mean, median, mode, geometric mean and harmonic mean are derived from a generalized notion of a measure of central tendency developed through an optimality criteria. This generalized notion is extended to introduce the concept of an interval of central tendency. Retaining the spirit of this notion, measure of central tendency may be called point of central tendency. The same notion is further extended to obtain confidence interval for population mean in a finite population model and confidence interval for probability of success in Bernoulli population.

Key words: Point of central tendency, Interval of central tendency, Metric space, Confidence coefficient.

[1]. G. Casella, and Berger R.L. (1990), Statistical inference, Wadsworth Group ,California.
[2]. Berger J.O, (1985), Statistical Decision theory and Bayesian Analysis 2nd edition-Springer-verlag, New York.
[3]. Serfling R.J,(1980),Approximation theorem in mathematical statistics, Wiley ,New York.
[4]. Tukey,John.W. (1977),Exploratory data analysis ,Addison Wesley..
[5]. Croxton,F.E.D, J.Cowden and S.Klein (1967: 178-182), Applied general Statistics 3rd edition ,Prentice-Hall,Englewoodcliff,New Jersey.

Abstract: In this action research study, where the subjects are our undergraduate grade mathematics students, w e try to investigate the impact of direct 'inquisition' instruction on their communication and achievement. We will strategically implement the addition of 'replication' study into each concept of limit over a four-month time period and thus conclusion can be making for the rest of the Mathemat ics . The students practiced using inquiry in verbal discussions, review activities, and in mathematical problem explanations. We discovered that a majority of students improved their overall understanding of mathematical concepts based on an analysis of the data we collected. We also found that in general, students felt that knowing the definition of mathematical words are important and that it increased their achievement when they understood the concept as a whole. In addition, students will be more exact in their communication after receiving inquiry instructions. As a result of this research, we plan to continue to implement inquisition into daily lessons and keep replication communication as a focus of the mathematics class.

Keywords: Concept of Limits,   definition of Limit

[1]. Chris Rasmussen: An inquiry oriented Approach to undergraduate mathematics. The Journal ofMathematical Behavior, Vol. 26,
Nov.3, (2007).
[2]. Borasi, R. & Rose, B. (1989). Journal writing and mathematics instruction. EducationalStudies in Mathematics, 20(4), 347-365.
[3]. Zaslavsky, O. & Shir, K. (2005). Students' conceptions of a mathematical definition.Journal for Research in Mathematics
Education, 36(4), 317-346.
[4]. Zimmerman, C. (1997). Do reading and interactive vocabulary instruction make a difference? An empirical study. TESOL
Quarterly, 31(1), 121-140.

Abstract: The problem of Rayleigh-Bénard convection in a ferromagnetic fluid saturated porous medium with the Maxwell-Cattaneo law is studied by the method of small perturbation. Modified Darcy-Brinkman model is used to describe the fluid motion. The horizontal porous layer is cooled from the upper boundary, while an isothermal boundary condition is imposed at the lower boundary. The non-classical Maxwell-Cattaneo heat flux law involves a wave type heat transport and does not suffer from the physically unacceptable drawback of infinite heat propagation speed. The resulting eigenvalue problem is solved exactly for simplified boundary conditions and the thresholds for the marginal stability are determined. Some of the known cases are derived as special cases. The influence of porous, magnetic, and non-magnetic parameters on the onset of ferroconvection has been analyzed. It is found that the Bénard problem for a Maxwell-Cattaneo ferromagnetic fluid is always less stable than the classical ferroconvection problem. It is shown that the destabilizing influence of the Cattaneo number is not attenuated by that of magnetic forces and vice versa, and that the aspect ratio of the convection cells changes when the parameters involved in the study vary with the porous structure bringing out considerable influence.

Keywords - Darcy-Brinkman porous layer, Ferromagnetic fluid, Magnetization, Second sound, Stability.

[1] V.G. Bashtovoy, B.M. Berkovsky and A.N. Vislovich, Introduction to thermomechanics of magnetic fluids (Washington D.C.:
Hemisphere, 1987).
[2] B.A. Finlayson, Convective instability of ferromagnetic fluids, J. Fluid Mech., 40(4), 1970, 753-767.
[3] M.D. Gupta and A.S. Gupta, Convective instability of a layer of a ferromagnetic fluid rotating about a vertical axis, Int. J. Engg.
Sci., 17(3), 1979, 271-277.
[4] K. Gotoh and M. Yamada, Thermal convection in a horizontal layer of magnetic fluids, J. Phys. Soc. Japan, 51(9), 1982,
3042-3048.
[5] E. Blums, Free convection in an isothermic magnetic fluid caused by magnetophoretic transport of particles in the presence of a
non-uniform magnetic field, JMMM, 65(2-3),1987, 343-346.
[6] P.J. Stiles and M. Kagan, Thermoconvective instability of a horizontal layer of ferrofluid in a strong vertical magnetic field, JMMM,
85(1-3), 1990, 196-198.
[7] S. Odenbach, Convection driven by forced diffusion in magnetic fluids under the influence of strong magnetic field gradients, JMMM, 149(1-2), 1995, 116-118.

[8] S. Aniss, M. Belhaq and M. Souhar, Effects of magnetic modulation on the stability of a magnetic liquid layer heated from above, J. Heat Transfer, 123(3), 2001, 428-433.

[9] A. Abraham, Rayleigh-Bénard convection in a micropolar ferromagnetic fluid, Int. J. Engg. Sci., 40(4), 2002, 449-460.

[10] S. Maruthamanik

Abstract: In this paper we studied m-projectively flat, m-projectively conservative, 𝜑-m-projectively flat LP-Sasakian manifold. It has also been proved that quasi m- projectively flat LP-Sasakian manifold is locally isometric to the unit sphere 𝑆𝑛(1) if and only if �𝑛 is m-projectively flat.

Keywords – Einstein manifold, m-projectively flat, m-projectively conservative, quasi m-projectively flat, 𝜑-m-projectively flat

[1] D. E. Blair, Contact manifolds on Riemannian geometry, Lecture Notes in Mathematics, Vol.509, Spinger-Verlag, Berlin, 1976.

[2] U. C. De, K. Matsumoto and A. A. Shaikh, On Lorentzian para-Sasakian manifolds, Rendicontidel Seminario Mathematico di Messina, Series ΙΙ, Supplemento al 3 (1999), 149-158.

[3] K. Matsumoto, On Lorentzian para-contact manifolds, Bull. Of Yamagata Univ. Nat. Sci., 12 (1989), 151-156.

[4] K. Matsumoto, I. Mihai, On certain transformation in a Lorentzian para-Sasakian manifold, Tensor N.S., 47 (1988), 189-197.

[5] R. H. Ojha, A notes on the m-projective curvature tensor, Indian J. Pure Applied Math., 8 (1975), No. 12, 1531-1534.

[6] R. H. Ojha, On Sasakian manifold, Kyungpook Math. J., 13 (1973), 211-215.

[7] G. P. Pokhariyal and R. S. Mishra, Curvature tensor and their relativistic significance ΙΙ, Yokohama Mathematical Journal, 19 (1971), 97-103.

[8] S. Prasad and R. H. Ojha, Lorentzian para contact submanifolds, Publ. Math. Debrecen, 44/3-4 (1994), 215-223.

[9] A. A. Shaikh and U. C. De, On 3-dimensional LP-Sasakian manifolds, Soochow J. of Math., 26 (4) (2000), 359-368.

[10] J. P. Singh, On an Einstein m-projective P-Sasakian manifolds, (2008) (to appear in Bull. Cal. Math. Soc.).

Abstract: Inventory management decisions are an integral aspect of organisations. This research addresses the inventory management systems that are evident in the manufacturing industry being inventory postponement and inventory speculation. Inventory postponement as argued by Bucklin (1965) is where a firm deliberately delays the purchase and the physical possession of inventory items until demand or usage requirements are known with certainty. This is an effective supply chain strategy adopted by most manufacturing organisations by reducing the inventory, and in turn reducing the cost of obsolete stock. This research investigates Unilever Nigeria with respect to inventory management decisions, and identifies factors that lead the manufacturing organisation to adopt inventory postponement over inventory speculation. This research also examines the relative importance of the inventory management decisions made by the organisation, and the implications these decisions have on the consumer. There have been 13 key qualities investigated with respect to inventory management decisions with the effect these have on the consumer. These qualities are customer satisfaction, on time delivery, strong communication with client, strong communication with customers, order fulfilment, adequate inventory levels, rapid inventory replenishment, adequate warehouse storage, accurate forecasting, reliable service providers, safety stock, reliable stock quality, and warranty. This research has shown that the three key qualities that are essential in inventory management decisions for manufacturing organisation from the perspective of the third party logistics provider are customer satisfaction, on time delivery and order fulfillment.

Key words: inventory, Food

[1]. Andel, Tom, and Daniel A. Kind. "Flow It, Don't Stow It." Transportation and Distribution May 1996.
[2]. Bergin, Sarah. "Make Your Warehouse Deliver: New Developments in Warehouse Management Systems Inspire New Productivity in Needy Operations." Transportation and Distribution. February 1997.
[3]. Billington, C., Callioni, G., Crane, B., Ruark, J.D. (2004) "Accelerating the Profitability of Hewlett-Packard's Supply Chains". Interfaces. Linthicum: Jan/Feb 2004.
[4]. Breugelmans, E., Campob, K., Gijsbrechts (2006), "Opportunities for active stock-out management inonline stores: The impact of the stock-out policy on online stock-out reactions 2006 NewYork University. Published by Elsevier Inc.
[5]. Bucklin, L.P. (1965), "Postponement, speculation, and the structure of distribution channels", Journalof Marketing Research, Vol. 2 No. 1, pp. 26-32 Byoungho, J., (2004) "Achieving an Optimal Global Versus Domestic Sourcing Balance under Demand Uncertainty". International. Journal of Operations and Production Management.Bradford. Vol.24, Iss 11/12, p.1292
[6]. Chan, L.M.A., Muriel, A., Shen, Z-J.M., Simchi-Levi, D. and Teo C-P.(2002) "Effectivezeroinventory-ordering policies for the single-warehouse multiretailer problem with piecewise linear cost structures".Management Science. Linthicum: Vol.48, Iss. 11; pg.
[7]. 1446, 15 pgs
[8]. Eisenhardt, Kathleen M. (1989), "Building Theories from Case Study Research," Academy of Management Review. Vol. 14, No. 4, pp. 532-550.
[9]. Ellram, Lisa M. (1996), "The Use of the Case Study Method in Logistics Research," Journal of Business Logistics. Vol. 17, No. 2, pp. 93-139.
[10]. Fleischmann, M., van Nunen, J.A.E.E., and Grave, B., (2003) "Integrating Closed-Loop Supply Chains and Spare-Parts Management at IBM" Interfaces. Linthicum: Vol.33, Iss. 6; pg. 44

Abstract: Production of rubber in Tripura is the second largest after Kerala. But a less quantity is locally utilized compare to other rubber producing states. A large quantity of rubber is transported to different parts of the country. But transportation costs at present is not so much favourable for the firms or agencies due to frequent price hike of petroleum. Bangladesh is the neighbouring country of Tripura. Bilateral trading now a days is functioning smoothly. Industrialization in rubber sector in Bangladesh needs a sizable quantity of rubber. For exportation of rubber from Tripura to Bangladesh, a transhipment model is considered to minimize the transportation costs.

Keywords: Transhipment model, Vogel's Approximation Method, Optimal Solution etc.

1 A. Jarzemskis, Assumptions of small scale intermodal transport, Transport 2008; 23(1), 16-20.

2 C. Perng and, Z.P. Ho, Receiving and Shipping Management in a Transhipment Centre, Asian Journal of Management and Humanity Sciences 2007; 1(4), 514-522.

3 G.B. Dantzig, Linear Programming and Extensions, Princeton, N.J.: Princeton University 1963 .

4 H.A. Taha (). Operation Research: An Introduction, Prentice Hall, 7th Edition, USA 1996.

5 J. Reeb and, S. Leavengood, Transportation Problem: A special case for Linear Programming Problems, Performance Excellence in the Wood Products Industry, EM 8779, Oregon State University, USA 2002.

6 K. Yamashita, Y. Karuno And M. Lu, An Inapproximability of Transhipment Problems with Per mutable Transit Vectors, Journal of the Operations Research Society of Japan 2010; 53(3), 220-234.

7 N. Sen, T. Som And B. Sinha, A study of Transportation Problem for an Essential Item of Southern Part of North Eastern Region of India as an OR Model and Use of Object Oriented Programming, International Journal of Computer Sciences and Networking Security 2010; 10(4), 78-86.

8 S. Kikuchi, J. Rhee And D. Teodorvic, Applicability of an Agent based Modeling Concept to Modeling of Transportation Phenomena, Yugoslav Journal of Operation Research 2002; 12(2), 141-156.

9 T. Imam , G. Elsharawy, M. Gomah and I. Samy, Solving Transportation Problem Using Object-Oriented Model, International Journal of Computer Science and Network Security 2009; 9(2), 353-361.

10 V. Adlakha and, H. Arsham, Managing Cost Uncertainties in Transportation and Assignment Problems, Journal of Applied Mathematics and Decision Sciences 1998; 2(1), 65-104.

Abstract: In this paper, we have discussed about a steady state solution of the ordered queuing problem with balking and reneging. Here we have taken the waiting line is of chi-square queue with Poisson balking probability which depend not only on the number of customers in the system, but also the rate of services in the system.

Keywords: Balk Queue, Renege, Rate of Service, Steady state.

[1] D.Y.Barrer,Queueing with impatient customers and indifferent clerks,Operation Research,Vol.5,No.5.1957.

[2] E.Koenigsberg,Queueing with special service, Operation Research,Vol.4,213-220, 1956.

[3] R.G.Miller,A contribution to the theory of balk queues,J.Roy Statist.Soc.,Vol.21,No.2,320-337,1959.

[4] G.G.O,Brien, The solution of some queuing problems,J.Soc.Ind.Appl.Math.,Vol.2,133-142,1954.

Abstract: In this paper we define Scheduling, Batch Scheduling, Coloring, Subcoloring, Hypocoloring, Chromatic number, Subchromatic number, and Hypochromatic number for a given graph. A batch Scheduling problem has been obtained by using the above discussed concepts.An exponential algorithm has been developed for triangle free graphs. The solution is obtained by introducing COCA - 'Contract or Connect" Principle. The Subchromatic and Hypochromatic number for shell graphs has been illustrated. A Hypocoloring model for personnel assignment problem has been briefly discussed.

Keywords: Exponential algorithm, Hypochromatic number, Shell graphs, Subchromatic number

[1] De Werra D., Demange M.., Monnot J. and Paschos V.T., Discrete Applied Mathematics', 146, 2005, 3-26.

[2] Bodlaender H.L., Jansen K. and Woe ginger G.J., "Scheduling with incompatible jobs‟,Discrete Applied Mathematics 55, 1994, 219-232.

[3] Albertson M.O., Jamison R.E., Hedetniemi S.C. and Locke S.C. , "The Subchromaticnumber of a graph‟, Discrete Mathematics, 74, 1989 33-49.

[4] Sethuraman G. and Dhavamani R., "Graceful Numbering of an Edge -gluing of Shell graphs‟ Discrete Mathematics 218,2000,283-287.

[5] Brown J.L. and Corneil D.G., "On generalized graph colorings‟, Journal Graph theory, 11, 1987, 87-99.

Abstract: Some optimality criteria used in estimations of parameters in finite dimensional space has been extended to a separable Hilbert space. Different optimality criteria and their equivalence are established for estimating sequence rather than estimator. An illustrious example is provided with the estimation of the mean of a Gaussian process

Key words: sieves, Gaussian process, reproducing kernel Hilbert space , MVUE , estimating sequence

[1]. Anilkumar, p. (1994)on estimating the mean function of a Gaussian process. Statistics and prob. Letters 19 (1994) 77-84
[2]. Ash, R.B. and Gardner, M.F(1975) Topics in Stochastic process, Academic press , New York
[3]. Basavu, I.V, Prakasa Rao,B.L.V (1987) Statistical inference for stochastic process .Academic press, New York
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[5]. Beder, J. H. (1988) A Sieve estimator for the covariance of a Gaussian process. Ann statist 16 No: 2,648-660
[6]. Chatterji,S.P. and Handrekar,V.(1978) equivalence and singularity of a Gaussian measure and applications. In probabilistic analysis and related topics. Vol.1 Ed. Bharucha – Reid A.T
[7]. Geman and Hwang, C.R (1982) Non – Parametric Maximum Likelihood Estimation by the method of sieves Annals. Statist. 10,401-414
[8]. Grenander,U (1981) Abstract inference John wiley and sons
[9]. Kale, B.K. (1999) A First Course on Parametric Inference Narosa Publishing House, Delhi
[10]. Leskow,J and Rozanski (1989) Histogram maximum likelihood estimation for the multiplicative intencity models. Stochastic process and their applications, 31, 151-159

Abstract: The purpose of this work is to extend and generalize some common fixed point theorems for Expansive type mappings in complete cone metric spaces. We are attempting to generalize the several well- known recent results. Mathematical subject classification; 54H25, 47H10

Key word: Complete cone metric space, common fixed point, expansive type mapping.

[1] D.Jlic and V.Rakocevic, Quasi-Contraction on a cone metric space, Appl.Lett., 22,(5),(2009),728-731.

[2] D . Turkoglu and M .Abuloha and Tt .Abdeljawad, KKM mapping in cone metric spaces and some fixed point theorems, Nonlinear Analysis Theory ,Methods and Applications, 72 (2010) 348-353,.

[3] Huang Long – Guang, Zhang Xian, Cone metric spaces and Fixed Point Theorems of Contractive mappings. J.math.Anal.Appl.332 (2007)1468-1476.

[4] Sh. Rezapour, R. Hamal barani, some notes on the paper "Cone metric spaces and Fixed Point Theorems of Contractive mappings. J.math.Anal.Appl.345 (2), (2008) 719-724.

[5] J.O.Olaleru, some generalizations of fixed point theorems in cone metric spaces, Fixed point theory and Apllications (2009), Article ID 65791

[6] C.T. AAGE & J.N. Salunke, On common Fixed Points for Contractive Type Mapping in cone metric spaces. Bulletin of Mathematical Analysis and application. 13 (2009) 10-13.

[7] G.E Hardy. & T. D Rogers., A generalization of fixed point theorem of Reich canad, math. Bull. 16, (1973) 201-206.

[8] I. Sahin and M. Telci, Fixed point of contractive mappings on complete cone metric spaces, Hcettepe journal of mathematicsa and stastics, 38 ,( 2009) 59-67.

[9] Shobha jain, Shishir jain,Lal bahadur, compatibility and weak compatibility for four self maps in a cone metric space.Bulletin of Mathematical Analysis and Application 2,1,(2010) 15-24.

[10] Erdal Karapinar Fixed point Theorems in cone Banach space , fixed point theory and Applications Vol 2009 ,Article ID 609281..

Abstract: A congruence  of a lattice L is said to be isoform, if any two congruence classes of  are isomorphic as lattices. The lattice L is said to be isoform, if all congruence's of L are isoform. We prove that every finite distributive lattice D can be represented as the congruence lattice of a finite isoform lattice.

[1]. G.Gratzer, H.Lakser, and E.T.Schmidt, Congruence lattices of small planar lattices. Proc. Amer. Math. Soc. 123(1995), 2619-2623.
[2]. G.Gratzer, General Lattice Theory, Second edition, Birkhauser Verlag, Basel, 2010.
[3]. G.Gratzer and E.T.Schmidt, Congruence-preserving extensions of finite lattices into sectionally complemented lattice, Proc. Amer.Math.Soc.127(1999), 1903-1915.
[4]. .Gratzer and F.Wehrung, Proper congruence-preserving extensions of lattices, Acta Math. Hungar. 85(1999),175-185.
[5]. G.Gratzer and E.T.Schmidt, Regular congruence-preserving extensions. Algebra Universalis 46(2008), 119-130.
[6]. G.Gratzer and E.T.Schmidt, Finite lattices with isoform congruences. Tatra.Mt.Math.Publ 27(2009), 111-124.
[7]. G.Gratzer and E.T.Schmidt, Finite lattices and congruences. Algebra Universalis.
[8]. R.Freese-UACALC program-Sec:http://WWW. Math. hawaii. edu/ ralph/UACALC/.

Abstract: The Canonical Cosine transform, which is a generalization of the linear canonical transform, has many applications in several areas, including signal processing and optics. In this paper we have introduced convolution theorem, linearity property, derivative property, modulation property and Parseval's identity for the generalized canonical cosine transform.

Keywords: Fractional Fourier Transform, Linear Canonical Transform, Convolution.

[1] Almeida L B (1997): Product and convolution theorems for the fractional Fourier transform. IEEE Signal Processing Letters,4(1):
Page No.15—17
[2] Gudadhe A. S., Joshi A.V. (2013): On Generalized Half Canonical Cosine Transform, IOSR-JM Volume X, Issue X.
[3] Pie S. C., Ding J. J.( 2002): Fractional cosine, sine and Hartley transform; trans. On signal processing, Vo. 50, No. 7, P. 1661-1680,
pub.
[4] Zayed A. I., (1998): A convolution and product theorem for the fractional Fourier transform, IEEE Sig. Proc. Letters, Vol. 5, No. 4,
101-103.
[5] Zemanian A. H., (1965): Distribution Theory and Transform Analysis, Mc. Graw Hill, New York.

Abstract: Padmanabhan and Ganeshan have obtained some results on Hadamard product of univalent functions with negative coefficients of the type f (z) z a z , a 0. 2n n 1 2n 2n       In this paper we have obtained coefficient bounds and convolution results of p-valent function.

Keywords: Hadamard (convolution) product, p-Valent function, Cauchy-Schwarz inequality. Mathematics Subject Classification (2000): 30C45, 30C50

[1]. A.W.Goodman ,Univalent functions,Vol I , II, Polygonal Publishing House, Washington,N.J.,1983
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[4]. S.M.Khairnar and Meena More, Convolution properties of univalent functions with Missing Second Coefficient of Alternating Series,Int.J.Of Math Analysis,Vol.2,2008, No.12,569-580.
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