iosr-Jm   Volume-11 ~ Issue-2 ~ Mar-Apr 2015

Abstract: A factorization procedure for matrices that satisfy the without row or column exchange condition (WRC) is introduced. The strategy is to reduce a column to corresponding column of the identity matrix. Factors so obtained are triangular matrices with same entries in a row or column. These factors and their inverse with simple structures can be constructed using the entries of a given non-zero vector without any computations among the entries. The advantage is that n2+2n flops associated with conventional Gaussian elimination (GE) or Neville elimination (NE) can be saved using the present approach in solving n x n nonhomogeneous linear system. The benefits of applying this procedure for decomposing symmetric indefinite matrices are discussed by introducing a tridiagonal reduction procedure. Results on numerical experiments are provided to demonstrate that entries are much less perturbed than GE for typical problems considered here using the proposed approach. AMS classifications: 15A04, 15A23
Keywords: Symmetric Indefinite matrices; Matrix Factorization; Linear Transformations; Tridiagonal Reduction.

[1]. B.N. PARLETT AND J.K. REID, On the Solution of a System of Linear Equations Whose Matrix is Symmetric but not Definite, BIT Numerical Mathematics, Vol.10, 1970, pp 386-397
[2]. J.O. AASEN, On the Reduction of a Symmetric Matrix to Tridiagonal Form, BIT Numerical Mathematics, Vol.11, 1971,pp 233-242.
[3]. G.H GOLUB AND CHARLES. F VAN LOAN, Matrix Computations, 4th Edition, The John Hpokins University Press, 1985.
[4]. PURUSHOTHAMAN NAIR R, A Simple and Effective Factorization Procedure for Matrices, International Journal of Maths, Game Theory Algebra, 18(2009), No.2, 145-160.
[5]. N.J. HIGHAM, Accuracy and Stability of Numerical Algorithms, 2nd edition, SIAM, Philadelphia, 2002.

Abstract: In this paper we study Radon measure on compact topological measurable space, particularly on measurable regular space, second countable measurable space and e-normal space.
Key words: Regular measurable space, Regular measure space, second countable measurable space, e-normal space.

[1]. Bogachev V. I. "Measures on Topological Spaces", Journal of Mathematical Sciences, Volume 91, No. 4, (1998)
[2]. Bogachev V. I. "Measure theory", Volume II, Springer, (2006).
[3]. Dorlas T. C. "Remainder Notes for the Course on Measure on Topological Spaces", Dublin Institute for Advanced Studies, School of theoretical Physics , 10, Dublin 4, Ireland , (2010).
[4]. William Arveson, "Notes on Measure and Integration in Locally Compact Spaces", Department of Mathematics, University of California, Berkeley, (1996).
[5]. C. Wayne Patty (2012), "Foundations of Topology", Second Edition, Jones and Bartlett India. Pvt. Ltd New Delhi, Canada, London.

Abstract:In this paper, Z = 3 tx y z  type plane gravitational waves is studied with source Cosmic cloud strings coupled with Electromagnetic fields in Rosen'sbimetric theory of relativity.It is shown that there is nil contribution either from Cosmic cloud orfrom Maxwell'sfield andalso for cosmic cloud strings coupled with Maxwell's field in this theory.Only vacuum model can be constructed.
Keywords: Plane gravitational waves, Cosmic cloud strings, Maxwell's field, Bimetric Relativity.

[1]. Bondi H.;Pirani, F.A.E. and Robinson, I.(1959). Gravitational waves in general relativity III.Exact plane waves. Proc. Roy.Soc.Lond.A23, 25, 519-533
[2]. Deo S.D. and Suple S.R. (2013)Plane gravitational waves with cosmic strings in BimetricRelativity.Asian Journal of current Engineering and Maths 2: 2 March – April 131 - 133.
[3]. Deo S.D. and Suple S.R.(2013)Plane gravitational waves with cosmic strings in BimetricRelativity.MathematicaAeterna, Vol. 3, , no. 6, 489 - 496
[4]. Deo S.D. and Suple S.R. (2014)Plane gravitational waves with Macro and Micro Matter fields inBimetric Relativity.International Journal of Mathematics Trends and Technology – Volume 8 Number 1,51-5
[5]. Goldman I. (1978). "Plane waves in bimetric gravitation theory."Gen.Relativity.Grav.,7(11),895-901

Abstract: The paper discusses the relevance of statistics in technological advancement with emphasis on the contribution of all sectors of the economy and their roles in contributing to the technological advancement. To achieve a sound advancement in terms of technology the areas to be developed includes the applications of statistics in the sectors such as Educational Development, the need for an efficient information system for Data Analysis and Information Dissemination. Development of a good Statistical System backed up by a well developed act to provide a reliable data base to network with. There is need to map out strategic plans, set up by machinery for execution of plans and monitor the implementation process, so that the nations of the world especially can appreciate the beauty of statistical data.
Keywords: National Accounts, Millennium Electronic Devices, Genuine, Stock-Exchange, Sale Registers, Matrix, Astrology, Probability theory, Least Squares, Permutations.

[1]. Adamu, S.O. (1978). The Nigerian Statistical System Ibadan University Press, Shangodoyin D.K and Agunbiade D.A (1999). Fundamentals of Statistics and Database Management: Ransmed Publications, ISBN 978-34610-5-2.
[2]. Central Office of Statistics (2008). 2003 Poverty Datum Line for Botswana.
[3]. Ward, M. (2004). Qualifying the world: UN ideas and Statistics, United Nations intellectual History Project Series. Indiana University Press, USA.
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Abstract: The aim of this paper, is to study the integro-differential equations with a bulge function, to find the exact solution we use Elzaki transform, inverse Elzaki transform and the convolution theorem. This method is more efficient and easy to handle such partial differential equations and integro-differential equations with a bulge function in comparison to other methods. The result showed the efficiency, accuracy and validation of Elzaki transform method.
Keywords: Elzaki transform, Integro-differential equations, convolution theorem.

[1]. J. Biazar, H. Ghazvini, He's variational iteration method for solving linear and non-linear systems of ordinary differential equations, Appl. Math. Comput. 191 (2007) 287–297.
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[3]. J.H. He, Variational iteration method—a kind of non-linear analytical technique: some examples, Int. J. Nonlinear Mech. 34 (1999) 699–708.
[4]. J.H. He, Variational iteration method for autonomous ordinary differential systems, Appl. Math. Comput. 114 (2000) 115–123.
[5]. J.H. He, X.H. Wu, Variational iteration method: new development and applications, Comput. Math. Appl. 54 (2007) 881–894.

Abstract: In this paper, the problem of time to recruitment is studied using a univariate policy of recruitment involving two thresholds for a single grade manpower system with attrition generated by its policy decisions. Assuming that the policy decisions and exits occur at different epochs, a stochastic model is constructed and the variance of the time to recruitment is obtained when the inter-policy decision times form a geometric process and inter- exit times form an ordinary renewal process. The analytical results are numerically illustrated with relevant findings by assuming specific distributions.
Keywords: Single grade manpower system; decision and exit epochs; geometric process; ordinary renewal process; univariate policy of recruitment with two thresholds and variance of the time to recruitment.

[1]. D. J. Bartholomew, Stochastic model for social processes, ( John Wiley and Sons, New York, 1973 ).
[2]. D. J. Bartholomew and F. Andrew Forbes, Statistical techniques for manpower planning, ( John Wiley and Sons, New York, 1979 ).
[3]. R. C. Grinold and K.T. Marshall, Manpower planning models, ( North-Holland, New York, 1977 ).
[4]. A. Muthaiyan, A study on stochastic models in manpower planning, doctoral diss., Bharathidasan University, Tiruchirappalli, 2010.
[5]. K. P. Uma, A study on manpower models with univariate and bivariate policies of recruitment, doctoral diss., Avinashilingam University for Women,Coimbatore, 2010.

Abstract:Insect herbivores are hypothesized to be major factors affecting the ecology and evolution of plants. Earlier, plant-herbivore models were phrased in terms of total vegetation biomass and total herbivore population. Allee effect is an important dynamics phenomenon believed to be manifested in several population process, notably extinction and invasion. In this paper, a discrete-time plant-herbivore model with mating induced Allee effect is investigated. We obtain asymptotically stable conditions of the equilibrium points which are subject to the Allee effect. The Allee effect which occurs on plant population is discussed by stability and numerical analysis. This study suggests that Allee effect has stabilizing effect on Plant-Herbivore system.
Keywords: Plant-herbivore system, Mating, Allee effect, Stability analysis, Equilibrium points.

[1]. Allee, W.C., 1931.Animal Aggregations: A study in General Sociology. University of Chicago Press, Chicago.
[2]. Amarasekare, P., 1998. Interactions between local dynamics and dispersal: insights from single species models. Theor. Popul. Biol. 53, 44-59.
[3]. Andrew M. Kramer, Brain Dennis, Andrew M. Liebhold, John M.Drake., 2009. The evidence for Allee effects.Popul.Ecol.51:341-354.
[4]. Birkhead, T.R., 1977.The effect of habitat and density on breeding success in the common guillemot (Uria aagle).J.Anim.Ecol.46, 751-764.
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Abstract: In this paper, a prey-predator model with infectious disease in predator population involving Holling type II functional response is proposed and studied. The existence, uniqueness and boundedness of the solution of the system are studied. The existence of all possible equilibrium points is discussed. The local stability analysis of each equilibrium point is investigated. Finally further investigations for the global dynamics of the proposed system are carried out with the help of numerical simulations.

Keywords: eco-epidemiological model, SIS epidemic disease, prey-predator model, stability analysis, Holling type II functional response.

[1]. Murray, J.D.2002. Mathematical biology an introduction. Third edition. Springer-Verlag. Berlin Heidelberg.
[2]. Smith, J.M. 1974. Models in ecology. Cambridge university press. Great Britain.
[3]. May, R.M. 1974. Stability and complexity in model ecosystems.Princeton University Press. New Jersey.
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[7]. Sci. 314, pp. 533-570.
[8]. Haque, M., Zhen, J., and Venturino, E. 2009. Rich dynamics of Lotka-Volterra type predator-prey model system with viral disease
in prey species. Mathematical Methods in the Applied Sciences, 32, pp: 875-898.
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eco-epidemiological system. Mathematical Medicine and Biology, 24,pp: 301-326.

Abstract: In this paper on the most known and popular subject, our efforts are to establish many algebraic properties of Pythagoras Triplets and associate them with different branches of mathematics. Some new methods of generating Pythagoras triplets and number of primitive triplets to a given integer, if it exists, have been elaborated. In this paper and many following papers, classification of Pythagorean triplets into three families—Plato's, Pythagoras', and Fermat's, will play important role showing inter connectivity between the different branches –Number theory, matrices, abstract algebra, graph theory and some more.
Keywords: Primitive Triplets, Hypotenuse, pro-addition, pro-multiplication, Plato, Pythagoras and Fermat family.

[1]. Stifel,Michael, (1544), Arithmetica Integra(http:// mathdl.maa.org/math DL/46/?pa=content&sa=view document & nodeld=2591& body Id=3752
[2]. Ozanem,Jacques(1844)Science and natural philosophy: Dr. Huttons‟ Translation of Montucla‟s edition of Ozanam, revised by Edward Riddle, Thomas Tegg,London,Read online- Cornell University
[3]. Theoretical properties of the Pythagorean triples and connection to geometry
[4]. (http://www.math.rutger.edu/ ~erowland/pythagoreantriples.html)
[5]. Generating Pythagorean Triples Using Arithmetic Progressions
[6]. (http:// people.wcsu.edu/sandifere/Academics/2007Spring/Mat342/ PythagTrip02.pdf)
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Abstract: A number of methods are available to find the root of function. The study is aimed to compare Bisection method, Newton-Raphson method and Secant method in term of time, iteration needed to get root in a desire level of error. A mathematical polynomial equation for beam deflection developed and the point at which maximum deflection occurs find by Bisection method, Newton-Raphson method and Secant method. We compare these root finding methods by using the software "MATLAB R2008a". It would seem obvious that Newton's method is faster, since it converges more quickly. However, to compare performance, we must consider both cost and speed of convergence [1]. From the above observation it is seen that the Bisection method converge at 25th iteration while Newton-Raphson method and Secant method converge at 3rd and 4th iteration respectively. In Newton-Raphson method two functions evaluate per iteration and in Secant method only a single function (from 2nd) evaluate per iteration. Then it was conclude that among three methods Secant method is converge faster than others. And it is most effective method.

Keywords: Mathematical model, Algorithm, Root, Iteration, Function, Beam deflection, Bisection method, Newton-Raphson method and Secant method, Execution time, Flops.

[1]. Ron, Amos (2010), Lecture notes on CS412: Solving Equations and Polynomial Interpolation.
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Abstract: The aim of this paper, is study the non-homogeneous second order differential equation of the Heaviside step function with a bulge function. Elzaki transform, inverse Elzaki transform and Power series expansion are mentioned to obtain the solution of differential equation of the Heaviside step function with a bulge function.
Keywords: Elzaki transform, Heaviside step function, Bulge function.

[1]. Tarig M. Elzaki, (2011), The New Integral Transform "Elzaki Transform" Global Journal of Pure and Applied Mathematics, ISSN 0973-1768, Number 1, pp. 57-64.
[2]. Tarig M. Elzaki & Salih M. Elzaki, (2011), Application of New Transform "Elzaki Transform" to Partial Differential Equations, Global Journal of Pure and Applied Mathematics, ISSN 0973-1768, Number 1, pp. 65-70.
[3]. Tarig M. Elzaki & Salih M. Elzaki, (2011), On the Connections between Laplace and Elzaki transforms, Advances in Theoretical and Applied Mathematics, ISSN 0973-4554 Volume 6, Number 1, pp. 1-11.
[4]. Tarig M. Elzaki & Salih M. Elzaki, (2011), On the Elzaki Transform and Ordinary Differential Equation With Variable Coefficients, Advances in Theoretical and Applied Mathematics. ISSN 0973-4554 Volume 6, Number 1, pp. 13-18.
[5]. Lokenath Debnath and D. Bhatta. (2006), Integral transform and their Application second Edition, Chapman & Hall /CRC.
[6]. A. Kilicman and H. E. Gadain. (2009), An application of double Laplace transform and Sumudu transform, Lobachevskii J. Math.30 (3), pp. 214-223.

Abstract: In this paper I introduce intuitionistic fuzzy perfectly alpha continuous mappings and their properties are studied.

Key words and phrases: Intuitionistic fuzzy topology, intuitionistic fuzzy alpha generalized closed set, intuitionistic fuzzy alpha generalized continuous mappings and intuitionistic fuzzy perfectly alpha continuous mappings.

[1] Atanassov, K., Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20 (1986), 87-96.
[2] Chang, C., Fuzzy topological spaces, J. Math. Anal. Appl., 24 (1968), 182-190.
[3] Coker, D., An introduction to fuzzy topological space, Fuzzy sets and systems, 88 (1997), 81-89.
[4] Gurcay, H., Coker. D., and Haydar, A., On fuzzy continuity in intuitionistic fuzzy topological spaces, jour. of fuzzy math., 5 (1997), 365-378.
[5] Hanafy. I. M, Intuitionistic fuzzy  continuity, Canad. Math. Bull. XX (2009), 1-11.
[6] 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, 19 (2005), 3091-3101.
[7] Rajarajeswari, P. and Krishna Moorthy, R., Intuitionistic fuzzy weekly generalized continuous mappings, Far East Journal of Mathematical Sciences, 66 (2012), 153-170.
[8] Sakthivel. K., Intuitionistic fuzzy alpha generalized continuous mappings and intuitionistic fuzzy alpha generalized irresolute mappings, Applied Mathematical Sciences, 4 (2010), 1831 -1842.

Abstract: In this paper, the notions of pairwise 𝛿𝐼-semi-open functions, pairwise 𝛿𝐼-semi-closed functions, pairwise 𝛿𝐼-semi-homeomorphism and pairwise 𝛿𝐼∗-semi-homeomorphism are introduced and investigated some characterizations of these functions in ideal bitopological spaces.

Keywords and Phrases: pairwise 𝛿𝐼-semi-open functions, pairwise 𝛿𝐼-semi-closed functions, pairwise 𝛿𝐼-semi-homeomorphism, pairwise 𝛿𝐼∗-semi-homeomorphism.

[1]. V.Inthumathi and A.Anis Fathima, On i,j -δI- semi-open sets (Submitted).
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