iosr-Jm   Volume-12 ~ Issue-4 ~ Jul-Aug 2016

Abstract: The paper describes a special recurrence relation whose expansion involve with a typical sequence of plus (+) and minus (-) signs by a process of recursive substitution. The kind of a sign at any k-th place of the expansion depends on the powers of twos in the expression of k in binary scale.

Keywords: Recurrence; sequence; binomial coefficient; compositions; positive integer in binary scale.

[1]. Andrews G.E., The Theory of Partitions, Cambridge University Press, 1998, Chapter 4, p54.
[2]. Bera Soumendra, Relationships between Ordered Compositions and Fibonacci Numbers, Journal of Mathematics Research, CCSE,
Vol. 7, No. 3, 2015.
[3]. John Riordan, Combinatorial identities, R. E. Krie

Abstract:A linear stability analysis is carried out for triple diffusive convection in Oldroyd-B liquid. The expressions of Rayleigh number for stationary and oscillatory convection has been obtained. The neutral curvesforoscillatory mode for different values of stress relaxation parameter, strain retardation parameter, solute Rayleigh numbers, ratio of diffusivity of solutes and heat diffusivity and Prandtl number has been examined. It is found that the oscillatory triple diffusive convection sets in earlier in system with Oldroyd-B liquid as compared to Newtonian liquid system.
Keywords: Triple diffusive convection, viscoelastic liquid,Oldroyd-B liquid, oscillatory convection.

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Abstract:In the present paper, an efficient approach based on homotopy perturbation method by using natural transform is adopted to solve some linear and non-linear space-time fractional Fokker-Planck Equations (FPE) in closed form. The space and time fractional derivatives are considered in Caputo sense. The homotopy perturbation natural transform method is a combined form of natural transform, homotopy perturbation method and He's polynomials. The method gives an analytical solution in the form of a convergent series with easily computable components, requiring no linearization or small perturbation. The numerical result shows the effectiveness and good accuracy of the method.
Keywords: Fokker-Planck Equation, Caputo fractional derivative, Natural transform, Homotopy perturbation
method..

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Abstract: This research is an interdisciplinary study that aims to examine the cultural values of Bugisi Makassar which is involved in the interaction of the mathematics learning. This research was done at one of the schools in the city of Makassar by recording anecdotal for observing and analyzing the interactions that occur between teachers and students and also between students and students. The important recording is observing the cultural values of Bugisi Makassar that is involved in the interaction process. The result of this research shows that the dual concepts of the culture of bugis Makassar are siri' and pacce that is involved in the interaction of mathematics learning process between the interaction of teacher and students and also between students and students........
Keywords:Interactions, Siri', Pacce

[1]. Abdullah, Hamid.,1985., Manusia Bugis Makassar. Jakarta: Indti Idayu Press.
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[4]. Atweh, Bleicher & Cooper, 1998., The Construction of the Social Contex of Mathematics Classrooms: A Sosiolinguitics Analysis. Journal for Research in Mathematics Education. Volume 29, Number 1, January 1998 USA: NCTM, Inc
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Abstract: This study is conducted to compare two ratio estimators that use auxiliary information. The estimators are Olkin average ratio estimator and Kadilar-Cingi estimator. Efficiencies of the estimators are investigated theoretically and using data from Federal Inland Revenue Service Revenue House Store. The result shows Kadilar – Cingi estimator is more efficient than Olkin estimator..
Keywords: Auxiliary variable,Ratio Estimators,Efficiency, Comparison.

[1]. Abu-Dayyeh, W. A., Ahmed, M. S., Ahmed, R. A., and Muttlak, H. A. (2003) Some Estimators of finite population mean using
auxiliary information, Applied Mathematics and Computation, 139, 287–298.
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of Order 1 n
.Journal of Mathematics Sciences Vol. 19 No. 2 187-191.
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Journal of Statistical Planning and Inference, 60, 261–267.
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159-163.
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Statistical Society, XXXVIII Scientifi Meeting, Rimini, 9-13 April 1996, 119–126.

Abstract: The arithmetic operations on fuzzy number are basic content in fuzzy mathematics. But still the operations of fuzzy arithmetic operations are not established. There are some arithmetic operations for computing fuzzy number. Certain are analytical methods and furtherare approximation methods.In this paper we, compare the multiplication operation on triangular fuzzy number between 𝛼 −cut method and standard approximation method and give example and graphical representation supporting each examplee.
Keywords: Fuzzy number, Triangular Fuzzy number, 𝛼 −cut method, Standard approximation method. .

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[5]. Abeda Sultana, UtpalenduDev and NirmalKantimitra, Algebra of intervals, J. Math. and Math. Sci., Vol. 23, 2008, 49-62

Abstract:In this paper, the generalized analytic difference sequence space defined by Musielak-Orlicz function, are introduced, and some of their algebraic and topological properties are explored. Few inclusion relations involving the introduced spaces are also discussed
Keywords: Analytic Sequences, Difference Sequence Space, Entire Sequences, Musielak- Orlicz Function

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Abstract: In this paper, we introduce strongly soft 𝑔∗∗-closed sets and strongly soft 𝑔∗∗-open sets in soft Č𝑒𝑐𝑕 closure spaces, which are defined over an initial universe with a fixed set of parameters and studied some of their basic properties. Also, we show that every strongly soft 𝜕-close...........
Keywords: Soft set, Strongly soft g** -closed set, storngly soft g**-open set.

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Abstract: The aim of this paper is to obtain the decomposition of nano continuity in nano topological spaces. 2010 AMS Subject Classification: 54B05, 54C05.
Keywords: nano-open sets, nano continuity

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Abstract:In this paper an efficient modification of Adomian decomposition method is introduced for solving heat equation. Tested for some examples and the obtained results demonstrate efficiency of the proposed method. The results were presented in tables and figure using the MathCAD 12 and Matlab software package
Keywords: Modified decomposition method, Heat equation, Nonlocal problem.

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Abstract: In this study , we define the concepts of a higher bi-derivation , Jordan higher bi-derivation and Jordan triple higher bi-derivation on Г-rings and show that a Jordan higher bi-derivation on 2-torsion free prime Г-ring is a higher bi-derivation .
Keywords: ................

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Abstract: Many Combinatorial programming problems are NP-hard (Non Linear Polynomial), and we consider one of them called THREE DIMENSIONAL CONSTRAINED P-TSP. Let there be n cities and the distance/cost matrix D(i, j, k) is given from ith city to jth city in kth season. Each of P salesmen starts in first season from Headquarter city '1 'and visits few cities in that season then he enter into next season and visits some more cities in that season and reaches to Headquarter city on or before the last season ...........
Keywords: Lexi Search Algorithm, Pattern Recognition Technique ,Tour , Pattern,Season.

[1]. Ahuja,R.K.,J.B. Orlin, S. Pallottino, M.G.Scutella. Dynamic shortest paths minimizing travel times and costs. (2003) Networks 41 197-205.
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[4]. Balakrishna U. [a] Generalized Time Dependent Travelling Salesman Problem with Cyclic constraint [GTSP], [b] Generalized Time Dependent Travelling Salesman Problem (cluster constraint) [GTDTSP] models, (2009) PhD Thesis, S.V. University, Tirupati.

Abstract: In the present paper, the complex variable method is applied to derive exact expressions for Gaursat functions, for the first and second fundamental problems. Here, an infinite elastic plate weakened by a generalized curvilinear hole C is considered, in the two dimensional problems, in the theory of elasticity. The hole is conformally mapped outside the unit circle  by means of a generalized rational mapping function. In addition, when the hole is conformally mapped inside the unit circle, the Gaursat functions are discussed and obtained. Some applications are considered for the first and second fundamental problems. In addition, the
components of stress, in each application, are computed using Maple 9.5...........
Keywords: Gaursat functions, the first and second fundamental problems, conformal mapping, curvilinear hole, stress components.

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[2]. N. Noda, R. B. Hentarski, Y. Tanigowa, Thermal Stresses, Taylor and Francis, 2003
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Mech. of Mining sciences 39(2002) 905-916

Abstract: The negative numbers played an important role in daily life as well as in performing various arithmetic operations in computers. In a given data, most significant bit (MSB) is used for indicating the negative number and if it is equal to 1, the data is a negative number and if it is equal to 0, the given data is a positive number. Detailed discussions on negative numbers were made by considering an 8 bit data. The magic circle shows all positive and all negative numbers by moving through anti clock wise or clock wise direction respectively through outer circle. ...........
Keywords: Hexadecimal Numbers, Negative numbers, Data byte, Word, Most significant bit, 2's Compliment form, repeated addition and repeated Subtraction.

[1] Numerical Methods by E. Balaguru Swamy, Tata Mc grawhill Publishing Company Limited, New Delhi.
[2] Chapter 4, Computers, Numbers and Text: a thesis appeared on Internet Google search engine.
[3] Representing Signed integer numbers inside a computer, an article available in Google search engine.
[4] Signed Binary numbers and Binary codes by N.B. Dodge on 09/2015 at Erik Jonsson School of Engineering and Computer Science,
The University of Texas at Dallas (UTD).
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Publishing Company Limited, New Delhi.