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.

[1]. Sakiadis BC. Boundary layer behaviour on continuous solid surfaces. Am Inst Chem Eng J 1961;7(2):221–5.
[2]. Crane LJ. Flow past a stretching plate. Z Angew Math Phys 1970;21:645–7.
[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.

[1]. Atanassov, K.T, Intuitionistic Fuzzy sets: Theory and applications, Studies in fuzziness and soft computing, Heidelberg, New York,
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.

Abstract: In this paper, we investigate the concept of completeness. We studied the concept whilst still attending college, but that wasfrom a mathematical perspective. In 2000, we got to have contact with The Logicians' understanding of the concept through the hands of one of the most important modern icons of Philosophy, Dr. Graham Priest. We recently mentioned his ways of applying the concept, and that was in our last paper with the APM journal. There seems to be a bit of discrepancy. Because of that, it is worth studying the subtleties involved. It seems that reserved words should not be recreated in meaning, so that if there is any chance The Logicians' completeness does not coincide with The Mathematicians' completeness, the sense that last appeared should be dropped in favour of coherence............

Keywords: Logic, priest, completeness, mathematics, gӧdel.

[1]. Pinheiro, M. R. (2015). Words for Science. Indian Journal of Applied Research, 5(5), 19–22. Retrieved from https://www.worldwidejournals.com/ijar/articles.php?val=NjQ0MQ==&b1=853&k=214
[2]. Pinheiro, M. R. (2016). Gödel and the Incompleteness of Arithmetic. Advances in Pure Mathematics, 6(8), 9. Retrieved from http://file.scirp.org/Html/4-5301134_68410.htm
[3]. Priest, G. (2001). An Introduction to Non-Classical Logic. Cambridge University Press.
[4]. Corcoran, J. (1999). Information-Theoretic Logic and Transformation-Theoretic Logic. Fragments of Science, 25–36. Retrieved from http://philpapers.org/archive/CORILA.pdf

Abstract: A finite element method involving collocation method with Quartic B-splines as basis functions has been developed to solve fourth order boundary value problems. The fourth order derivative for the dependent variable is approximated by the finite differences. The basis functions are redefined into a new set of basis functions which in number match with the number of collocated points selected in the space variable domain. The proposed method is tested on two linear and three non-linear boundary value problems. The solution to a nonlinear problem has been obtained as the limit of a sequence of solutions of linear problems generated by the quasilinearization technique. Numerical results obtained by the present method are in good agreement with the exact solutions available in the literature.

Keywords:Absolute error, Basis function, Collocation method, Fourth order boundary value problem, Quartic B-spline.

[1]. R.P. Agarwal, Boundary value problems for higher order differential Equations (Singapore, World Scientific, 1986).
[2]. Abdul-Majid waz waz, The numerical solution of special fourh-order boundary value problems by modified decomposition method,
International Journal of Computer Mathematics, 79(3), 2002, 345-356.
[3]. Waleed Al-Hayani and Luis casasus, Approximate anlytical solution of fourth order boundary value problems, Numerical
Algorithms, 40, 2005, 67-78.
[4]. Vedat suat Erturk and Shaher Momani, Comparing numerical methods for solving fourth-order boundary value problems, Applied
Mathematics and Computation, 188, 2007, 1963-1968.

Abstract: This paper presents an application of the novel modern Rao technique in attempt to solve integral equations of the second kind with variable limits of integration (i.e Volterra Equation of the second kind) when the kernel being linear in the arguments x and t. The numerical solution obtained by applying such technique has been compared with the exact solution that is obtained analytically. An algorithm for Rao-transform is contained here with an illustrative example, which has been solved by using MATLAB, is presented at the end of this paper............

Keywords:Volterra integral equations (VIE), linear kernel, Rao technique and Rao-Transform, ordinary differential equations.

[1]. Kanwal, R. R., "Linear Integral Equations: Theory and Technique", 2nd ed. Birkhauser Publisher, Boston, 1997.
[2]. Rao, M. S., "Rao Transforms a new Approach to integral and differential Equations", 2nd ed. Stony Brook, New York, 2007.
[3]. Masujima, M., "Applied Mathematical Methods in Theoretical Physics", WILEY-VCH Verlag Gmbh & Co. K. Ga. A. Weinheim, 2005.
[4]. Polyanin, A. D. and Manzhirov, A. V., "Handbook of integral equations", Boca Raton, FL:CRC Press, 1998.
[5]. King, A.C., Billingham, J. and Otto, S.R., "Differential Equations: Linear, Non-Linear, Ordinary, Partial", Cambridge University Press, New York, 2003..

Abstract: A simplified formula for the calculation of the curvature is suggested. This formula uses the velocity and acceleration, but avoids differentiation of the speed and the calculation of a functional determinant .

Keywords: Curves, curvature, simplified formula .

[1]. Smith, R., Minton, R. Calculus. Early Transcendental Functions. 3rd Ed., New York: McGraw Hill Higher Education; 2007.
[2]. Thomas, G., Weir, M., Hass, J. Thomas' Calculus: Early Transcendentals, 13th Ed., New York: Pearson; 2014..

Abstract: Decomposition of n! in terms of elementary symmetric polynomial of n of k integers: 1, …, k helps to find an expression that involves with all ordered compositions of the first n ordered natural numbers. The expression has a reduced version in terms of complete homogeneous symmetric polynomial of degree n in 1, 2, … , k; and thus there exists a relation between the polynomials of two kinds. In the context, we show an analogous pair of identities: one is a recurrence relation between Stirling numbers of both kinds and another one is a binomial coefficient identity.

Keywords: Recurrence; sequence; ordered composition; factorial; symmetric polynomials, Stirling number of kind 1 and Stiring number of kind 2.

[1]. G.E. Andrews, The Theory of Partitions, Cambridge University Press, 1998, Chapter 4, p54
[2]. H.S.Hall and S.R. Knight, Higher Algebra, Macmillan and Co, London 1967, pp164-165.

[3]. John F. Riordan. (1979). Combinatorial identities, R. E. Krieger Pub. Co

[4]. Khristo N. Boyadzhiev (2012). "Close encounters with the Stirling numbers of the second kind". Mathematics Magazine. 85 (4): pp.252–266.

[5]. M. Abramowitz, M. and I.A.Stegun (Eds.). "Stirling Numbers of the First kind and Second Kind." §24.1.3 and §24.1.4." in handbook of mathematical functions with formulas, graphs, mathemayicle Tables, 9the printing New York: Dover, pp. 824-825, 1972.

Abstract: In this paper we discuss 𝑝,𝑞 th order of an entire function in terms of central index and use it to estimate the growth of composite entire functions. AMS Subject Classification (2010): 30D20, 30D35

Keywords: Entire function, maximum term, central index, 𝑝,𝑞 th order, 𝑝,𝑞 th lower order ..

[1]. Chen, Z. X. and Yang, C.C.: Some further results on the zeros and growths of entire solutions of second order linear differential equations, Kodai Math J., Vol.22(1999), pp. 273-285.
[2]. He Y.Z. and Xiao X.Z.: Algebroid functions and ordinary differential equations. Science Press, Beijing, 1988.
[3]. Juneja, O. P. ; Kapoor, G. P. and Bajpai, S. K. : On the (p,q)-order and lower (p,q)-order of an entire function, J. Reine Angew. Math., Vol. 282(1976), pp. 53-67.
[4]. Sato, D. : On the rate of growth of entire functions of fast growth, Bull. Amer. Math. Soc., Vol. 69 (1963), pp. 411-414.
[5]. Valiron, G.: Lectures on the General Theory of Integral Functions, Chelsea Publishing Company, 1949.

Abstract: In this paper, it was proved that, if S is a Right regular semiring, then (S, +) is a band under the following cases. 1. If S is multiplicatively subidempotent semiring. 2. If S is an almost idempotent semiring.

Keywords: Periodic, rectangular band, Singular semigroup..

[1]. Kanchan Jana, "Quasi K-Ideals In K-Regular And Intra K-Regular Semirings", Pu. M.A.Vol. 22 (2011), No.1, PP. 65-74.
[2]. N.Kehayopulu, "On a characterization of regular duo le Semigroups", Maths. Balkonica 7 (1977), 181-186.
[3]. K.S.S.Nambooripad, "Structure of regular semigroups I fundamental regular semigroups", Semigroup Forum, Vol.9 (1975), 354-363.
[4]. M.Satyanarayana, "On the additive semigroup structure of semirings", Semigroup Forum, Vol.23 (1981), 7-14.
[5]. M.Satyanarayana, "On the additive semigroup of ordered semirings". Semigroup Forum, 31 (1985), 193-199..

Abstract: In this paper, the authors classified all solutions of the second order nonlinearneutral delay dynamic equations into four classes and obtained conditions for the existence/non-existence of solutions in these classes. Examples are included to illustrate the validation of the main results.

Keywords: second order, neutral dynamic equations, oscillatory solution, weakly oscillatory solution, asymptotic behavior, time scales.

[1]. S. Hilger, Analysis on measure chains: a unified approach to continuous and discrete calculus, Results.Math. 18 (1990), 18-56.
[2]. S. Panigrahi, and P. Rami Reddy, On oscillatory and asymptotic behavior of fourth order non-linearneutral delay dynamic equations, Comp. Math. Appl. 62 (2011), 4258-4271.
[3]. S. Panigrahi, and P. Rami Reddy, Oscillatory and asymptotic behavior of fourth order non-linear neutraldelaydynamic equations,Dynamics of Continuous, Discrete and Impulsive Systems Series A: Mathematical Analysis 20 (2013),143-163.
[4]. S. Panigrahi, J. R. Graef and P. R. Reddy, Oscillation Results for fourth order nonlinear neutral dynamicequations, Commu. Math. Anal., 15 (2013), 11-28.
[5]. J. R. Graef, S. Panigrahi, and P. Rami Reddy, On oscillatory and asymptotic behavior of fourth ordernonlinear neutral delay dynamic equations with positive and negative coefficients, Math. Slovaca, 64(2014), No. 2, 347-366.

Abstract: The purpose of this study is to investigate the solution of Diophantine equation. This study will be complete if we know more about the prime numbers of Mersenne. Besides that, this paper will discuss about Diophantine equation. It is about experiment with numbers and to discover patterns. Number theory plays an important role in the Diophantine equation. In this study, we consider Diophantine equation of the form: 2 2 2 x Dy  2z for any odd number D that is prime number. Using congruent method, this Diophantine equation could be solved.

Keywords: Diophantine, prime numbers, patterns, numbers, odd number

[1]. P. Novikov. 1948. A new solution of the indeterminate equation 2 2 2 ax by cz  0 .
[2]. Doklady Akad Nauk SSSR (N.S.) 61:205-206.
[3]. Barnes, E. S. 1953. On the Diophantine equation 2 2 x  y c  xyz . J. London Math.
[4]. Soc. 28:242-244.

Abstract: In this paper, we introduce the notion of cubic fuzzy H-ideals in BF-algebras and prove some interesting properties.

[1]. Biswas. R., Rosenfeld's fuzzy subgroups with interval valued membership function, Fuzzy Sets and Systems 1 (63) (1994), 87-90.
[2]. Jun. Y.B., Kim. C.S., and Yang. K.O., Cubic sets, Ann. Fuzzy Math. Inform, 4(1) (2012) 83- 98.
[3]. Jun. Y.B., Kim. C.S., and Kang. M.S., Cubic sub algebras and ideals of BCK/BCI algebras, Far East Journal of Mathematical
Sciences 44(2),(2010),239-250.
[4]. Neggers. J., Ahn. S.S and Kim. H.S., On BF-algebra, International Journal of Math. Sci. 27 (2001), 749-757.
[5]. Satyanarayana B., Bindu Madhavi U. and Durga Prasad R., On intuitionistic fuzzy H-ideals in BCK-algebras, International Journal
of Algebra, 4, (15)(2010), 743-749

Abstract: In this paper we develop solution procedure of fuzzy geometric programming based on Warner's approach for optimizing the design of plane truss structure with single objective subject to a specified constraint. In this optimum design formulation, the objective function is the weight of the truss; the design variables are the cross-sections of the truss members; the constraint is the stresses in member. A classical truss optimization example is presented here in to demonstrate the efficiency of this technique. The test problem includes a two-bar planar truss subjected to a single load condition. This single-objective structural optimization model is solved fuzzy geometric programming technique. Numerical example is given to illustrate our approach.

Keywords: Two-bar Truss Design, GeometricProgramming,Fuzzy Geometric Programming, Warner'sApproach, Max-additive Operator.

[1]. Zener, C. (1971).Engineering design by geometric programming, Wiley, New York.
[2]. Zimmermann, H.J. (1978).Fuzzy linear programming with several objective function .Fuzzy sets and systems, 1, 45-55.
[3]. Wang, G.Y. & Wang, W.Q. (1985).Fuzzy optimum design of structure. Engineering Optimization, 8, 291-300. [4]. Rao, S. S. (1987). Description and optimum design of fuzzy mechanical systems. Journal of Mechanisms, Transmissions, and Automation in Design, 109(1), 126-132.
[5]. Yeh, Y.C. & Hsu, D.S. (1990).Structural optimization with fuzzy parameters. Computer and Structure,37(6), 917–924.

Abstract: Semiring theory is one of the most developing branch of Mathematics with wide application in many disciplines such as Computer science, Coding theory, Topological space and many researchers studies different structure of semirings like Boolean like semirings, ternary semirings, complemented ternary semirings, gamma semirings, Complemented semirings etc . In this paper, we discuss some properties of Complemented semirings. We determine the additive and multiplicative structures of Complemented semirings by assuming different properties on the additive (multiplicative) structures.

Keywords: Band, left singular, right singular, multiplicatively sub idempotent, commutative, rectangular band.

[1] Arif Kaya and M. Satyanarayana – "Semi rings satisfying properties of distributive type". Proceeding of the American mathematical
society, volume 82, number 3, July 1981
[2] Jonathan S. Golan – "semirings and their applications".
[3] Jonathan S. Golan – "semirings and Affine Equations over Them: Theory and Applications". Kluwer Academic Publishers (1999).
[4] M. Satyanarayana – " On the additive semi group of ordered semirings", semi group forum vol.31(1985), 193-199
[5] M.P. Grillet – "subdivision rings of a semiring". Fund. Math., vol.67 (1970), 67-74.

Abstract: This research was a class action that begins with the development of learning tools. The subjects were students of class V SD Inpres Mallengkeri Makassar in the academic year 2015/2016, the number of students 45, there were 22 male students and 23 female students. The research was conducted in two (2) cycles. Each cycle consists of four phases: planning (planning), action (action), observations (observation) and reflection (reflection). The results of this research were to increase student learning thoroughness of the first cycle to the second cycle.............

Keywords: Type Cooperative Learning Outcomes and Numbered Head Together

[1]. Anita Lie. 2000. Cooperative Learning Mempraktikkan Cooperative Learning DiRuang-Ruang Kelas. Jakarta : Grasindo.
[2]. Ibrahim, R dan Syoadih, Nana. 1996. Perencanaan Pengajaran. Jakarta : Rineka. Cipta.
[3]. Ibrahim, Muslimin dkk. 2000. Pembelajaran Kooperatif. Surabaya : UNESA.
[4]. Muhsin, Arief. M. 2012. Pembelajaran Media Songs Base Learning Siswa Kelas Vii Smp Negeri 1 Sinjai Borong Kabupaten Sinjai. MEDIA, 1(2), 223-241.
[5]. Muhsin, Arief.M. 2016. The Effectiveness of Positive Feedback in Teaching Speaking Skill. Lingua Cultura, 10(1), 25-30.

Abstract: In this paper, we introduce and study some characterization and some properties of fuzzy continuous functions ( Fuzzy super continuous functions ) from fuzzy topological space into another fuzzy topological space has its bases on the notation of quasi-coincidence , quasi-neighborhood, fuzzy  -closure and - neighborhood

[1]. S.P. Arya and R. Gupta, on strongly continuous mapping, kyungpook Math. J. 14(2) (1974) 131 – 143 .
[2]. K.K. Azad, on fuzzy semi continuity, fuzzy almost continuity and fuzzy weakly continuity , J. Math. Anal. Appl. 82 (1) (1981) 14 – 32.

[3]. Casanovas J. Torrens, J., An axiomatic approach to fuzzy cardinalities of finite fuzzy sets , fuzzy sets and systems. 133 (2003), no.2, 193-209.
[4]. C.L. Chang, Fuzzy topological spaces , J. Math. Anal. Appl. 24 (1968) 182 – 190.
[5]. B. Hutton and I.L. Reilly, Separation axioms in fuzzy topological spaces, Fuzzy sets and systems 3 (1980) 127 – 141 .

Abstract: In this paperthe combined influence of chemical reaction, thermo diffusion and dissipation on convective heat and mass transfer flow of a Kuvshinski fluid past a vertical plate embedded in a porous medium is discussed. The equations governing the flow, heat and mass transfer have been solved by a regular perturbation technique. The effect of chemical reaction parameter (K), thermo-diffusion parameter (Sr), Eckert number (Ec), heat source parameter () and time (t) on the velocity, temperature and concentration distributions are discussed..............

Keywords: Kuvshinski fluid, MHD, Thermo-Diffusion, Chemical Reaction

[1]. Abdus-Sattar, M. D. and Hamid Kalim, M. D. :J. Math. Phys. Sci. 30 PP.25 - 37 (1996).
[2]. Cookey, C. I.; Ogulu, A. and Omubo-Pepple, V. M. Int. J. Heat Mass Transfer 46 PP.2305 -2311(2003).
[3]. Ganesan, P. and Loganathan, P. : Radiation and mass transfer effects on flow of an incompressible viscous fluidNpast a moving vertical cylinder, Int. J. of Heat and Mass Transfer 45 PP.4281- 4288(2002).
[4]. GireeshKumar.J&Ramakrishna.S , Effect of chemical reaction and mass transfer on radiation and MHD free convection flow of Kuvshinski fluid through porous medium, J.Pure& Appl.Phys.,Vol.22(3), pp.431-441(2010).
[5]. Hassanien, I. A. and Obied Allah, M. H. :Int. Comm. Heat mass transfer 29 (4) PP.567-575(2002).