iosr-Jm   Volume-12 ~ Issue-5 ~ Sep-Oct 2016

Abstract: It is well know that in order to improve the efficiencies of the estimates probability sampling is preferred over non probability sampling. If the difference in the size of the units is large enough to affect the study, we make use of PPS sampling where the probability of selecting a unit is proportional to the size measure of the unit. Sometimes we may be confronted with situations where information on a character closely related to the main variable is available from a previous study or other secondary sources. Various authors have utilized this auxiliary information by taking the initial probability of selection equal to the size measure of the auxiliary information............

Keywords: Coefficient of mean deviation, probability of selection, relative efficiency, sampling strategy, sampling design

[1]. Chaudhuri, A. (1974): On some properties of the sampling scheme due to Midzuno, Bull. Cal. Stat. Assoc., 18 ,1-24.
[2]. Horvitz, D.G. and Thompson, D.J. (1952): A generalisation of sampling without replacement from a finite universe. Jour. Amer. Stat. Assoc., 47, 663-85.
[3]. Jessen,R. J. (1969): Some methods of probability non-replacement sampling. Jour. Amer. Stat. Assoc.
[4]. Midzuno,H. (1952): On the sampling system with probability proportional to sum of sizes. Ann. Inst. Stat. Math, 3, 99-107.
[5]. Mukhopadhyay, P (1974): πps sampling schemes to base HTE. Cal. Stat. Assoc. Bull, 23 ,21-44.

Abstract: This research paper, in the first part, introduces two new sequences- 'CDS' sequence and Pell+sequence. These sequences, in order, introduced are identified and derived as a result of identifying recurrence relation in fundamental geometric properties of right triangles of Fermat family and as an attempt of locating such Pythagorean triplets whose middle term itself is a square of an integer. In addition to this, some algebraic properties related to these sequences are also established. These sequences have established their importance when we extended our work on operator matrices on Fermat family triplets of Right triangles. Immediate application of the operator matrices and their algebraic properties, like Eigen values of different exponents will be best summarized by the terms of these new sequences.

Keywords: CDS Sequence, Fermat Family, Generator Matrices, Pell Sequence, Pell + Sequence.

[1]. Ahmet Dasdemir, On the Pell, Pell-Lucas and Modified Pell Numbers By Matrix Method, Applied Mathematical Science, Vol. 5(64) (2011), 3173-3181.
[2]. Paula Catarino, On Generating Matrices of the k-Pell, k-Pell-Lucas and Modified k-Pell Sequences, Pure Mathematical Science, Vol. 3(2) (2014), 71-77
[3]. A.F Horadam, Pell identities, The Fibonacci Quarterly, Vol. 9(3) (1971), 245-263
[4]. J. Ercolano, Matrix generator of Pell sequence, The Fibonacci Quarterly, Vol. 17(1) (1979), 71-77

Abstract: In this paper, we have studied the effects of heat and mass transfer on the free convective flow of stratified fluid through a porous medium past a vertical porous isothermal plate fluctuating with time dependent suction velocity. An analytical solution is obtained for the velocity field, temperature field and concentration using regular perturbation method. The effects of various physical quantities on the Velocity field, Temperature field, Concentration, Nusselt number and Skin friction have been discussed through graphs in detail..........

Keywords: MHD flows, Heat and mass transfer, stratified flows, Vertical plates.

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[3]. Sharidan S, Mahmood T, Pop I. Similarity solutions for the unsteady boundary layer flow and heat transfer due to a stretching sheet.
Int J Appl Mech Eng 2006;11(3):647–54.
[4]. Carragher P, Crane LJ. Heat transfer on continuous stretching surface. ZAMM 1982;62:564–77.
[5]. Gupta PS, Gupta AS. Heat and mass transfer on a stretching sheet with suction or blowing. Can J Chem Eng 2009;55:744–6.

Abstract: In this paper, we introduce the notion of intuitionistic fuzzy graph structure 𝐺 = (A, B1, B2,......,Bk and discuss some analogs of fuzzy graph structure theoretical concepts. We also discuss some properties of intuitionistic fuzzy Bi- tree and intuitionistic fuzzy Bi-forests.

Keywords: Intuitionistic fuzzy graph structure (IFGS), tree, forest, edge, path.

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Physica-Verlag, 1999.
[2]. Dinesh T. and Ramakrishnan T. V., On Generalised Intuitionistic fuzzy Graph Structures, Applied Mathematical Sciences, Vol. 5,
no. 4, 2011, 173 – 180.
[3]. Mordeson John N., Nair Premchand S., Fuzzy Mathematics: An Introduction for Engineers and Scientists, Springer- Verlag
Company, 2001.
[4]. Mordeson, J.N. & Nair, P.S., Fuzzy Graphs and Fuzzy Hypergraphs, Physica-verlag, 2000.
[5]. Parvathi R, Karunambigai M. G., Intuitionistic fuzzy Graphs, Journal of Computational Intelligence, Theory and Applications, 20,
2006, 139-150.