iosr-Jm   Volume-11 ~ Issue-6 ~ Nov-Dec 2015

Abstract: In this article we discuss some Geometric and Topological properties of the polyhedrons and reformulate Polyhedral Gauss Bonnet Theorem.

[1] Stephen Barr; Experiments in topology, Thomas Y. Crowell Company, New York (1964).

[2] Boltyanskii V. G., Efremovich V. A.; Intuitive Combinatorial Topology, translated from Russian addition, Springer Verlag, New York(1982).

[3] Karl Wirth, André S. Dreiding; Relations between edge lengths, dihedral and solid angles in tetrahedral,Math Chem (2014) 52, page1624–1638.
[4] Pressley, A.N.;Elementary Differential Geometry, Springer Undergraduate Mathematics Series(2010).

Abstract:In this paper, we consider the nonlocal Fredholm- Volterra integral equation of the second kind, with continuous kernels. We consider three different numerical methods,the Trapezoidal rule, Simpson rule and Collocation method to reduce the nonlocal F-VIE to a nonlocal algebraic system of equations. The algebraic system is computed numerically, when the historical memory of the problem (nonlocal function) takes three cases: when there is no memory, when the memory is linear and when the memory is nonlinear. Moreover, the estimate error, in each method and each case, is computed. Here, we deduce that, the error in the absence of memory is
larger than in the linear memory. Moreover, the error of the linear memory is larger than the nonlinear memory.

Keyword: nonlocal Fredholm-Volterra integral equation (nonlocal F-VIE), numerical methods, algebraic system (AS), the error estimate. MSC (2010): 45B05, 45G10, 60R.

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[4]. P .Schiavone ,C.Constanda and A. Mioduchowski , Integral Methods in Science and Engineering , Birkhauser Boston, 2002.
[5]. Peter Linz, Analytic and Numerical Methods for Volterra Equations, SIAM, Philadelphia, 1985 .
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Abstract: We consider a mixed boundary value problem in thermal stress in half space. The surface of the half space is heated by a time dependent source which produces temperature changes in the material. The resulting thermal stresses are our main focus in this study. We assume that the surface of the half space satisfies mixed boundary conditions. In the part of the boundary (𝑥<0) is stress free while in the remaining boundary (𝑥>0), the gradient of the stress vanishes. The determination of thermal stress is carried out using the Jones's modification of the so-called Wiener-Hopf technique.The solution in terms of the thermal stress in closed form is obtained. Keywords:Heat Conduction Equation, Thermal Stress, Mixed BoundaryProblem and Wiener-Hopf technique

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Abstract:The main objective of this paper is that to apply lifetime models on the fault of thermal electricity generation in Sudan to predict faults and failures during period of working and increase its lifetime to insure electricity production sustainability and reducing maintenance cost. Lifetimes data has been taken from Bahri Thermal Station for electricity generation, which is, belong to the National Electricity Authority in Sudan during the period (2011-2015). Through the lifetime models estimation fault distribution, reliability, hazard rate, availability and MTBF have been calculated for the five machines from analysis; it is clear that, fault time for all machines follow Weibull distribution with 2-parapmeters.

1. Honag Pham, System Software Reliability, The State University of New Jersey, USA, Springer, 2006.
2. Honag Pham, Handbook of Engineering Statistics, The State University of New Jersey, USA, Springer, 2006.
3. Adamantios Mellas & Wenbiao Zhao, Modeling and Analysis of Repairable System with Gerenral, Relia Soft Corporation, 2005.
4. Van Noortwijk, J.M. & Klatter, H.E., The use of Lifetime Distributions in Bridge Maintenance and Replacement Modeling, Computers and Structures, Vol. 82, 2004.
5. Saad Talib Hasson, The Building a Reliability model to Improve System Performance, Journal of Babylon University, Vol. 22, 2014.
6. Alicja Jokiel,Rokita,Ryszard Magiera, Selected Stochastic Models in Reliability, Wroclaw University of Technology, 2009.
7. J. A. M. van der Weide and Suyono and J. M. Van Noortwijk, Renewal Theory with Exponential and Hyperbolic Discounting, Probability in the Engineering and Informational Sciences, 53-74, 2008.

Abstract:Successful application of Adomian decomposition method (ADM) in solving problems in nonlinear ordinary and partial differential equations depend strictly on the Adomian polynomial. In this paper, we present a simple modified known Adomian polynomial for nonlinear polynomial functionals with index as integers. The simple modified Adomian polynomial was tested for nonlinear functional with index 3 and 4 respectively. The result shows remarkable exact results as that given by Adomian himself. Also, the modifed simple Adomian polynomial was further tested on concrete problems and the numerical results were exactly the same as the
exact solution. The large scale computation and evaluation was made possible by Maple software package.

Keywords - Adomian Polynomial, Adomian Decomposition Method.

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Applications, 135, 1988, 501 - 544.
[2]. J. Biazar, E. Babolian, A. Nouri, S. Islam, An Alternative Algorithm for Computing Adomian Polynomials in Special cases, Applied
Mathematics and Computation 138, 2003, 523 - 529.
[3]. A. M. Wazwaz, A new Algorithm for Calculating Adomian Polynomials for Nonlinear Operator, Applied Mathematics and
Computation, 111, 2000, 53 - 69.
[4]. G. Adomian and R. Rach, Polynomials Nonlinearity in Differential Equations, Journal of Mathematical Analysis and Application,
109(1), 1985
[5]. G. Adomian, Solving Frontier Problems of Physics: the Decomposition Method, Springer New York, 1993

Abstract: In real life, a person may observe that an object belongs and not belongs to a set to certain degree, but it is possible that he is not sure about it. In other words, there may be some hesitation or uncertainty about the membership and non-membership degree of an object belonging to a set. In fuzzy set theory there is no means to incorporate that hesitation in membership degree. A possible solution is to use vague sets and the concept of vague set was proposed by Gau and Buehrer [1993]. Distance measure between vague sets is one of the most important technologies in various application fields of vague sets. But these methods are unsuitable to deal with the similarity measures of IFSs.

[1]. Deng-Feng Li, Feng Shan, Chun-Tian Cheng, "On properties of four IFS operators", Fuzzy Sets and Systems, 154, 151-155, 2005.
[2]. Gau W. L, Buehrer D. J. "Vague sets", IEEE Transactions on Systems, Man, and Cybernetics, 23, 610-614, 1993.
[3]. Guo-Shun Huang, Yun-Sheng Liu, Xiang-Dong Wang, "Some new distance between intuitionistic fuzzy sets", Proceeding of
Fourth International Conference on Machine language and Cybernetics, 18-21 August 2005.
[4]. H. Bustince, P. Burillo, "Vague sets are intuitionistic fuzzy sets", Fuzzy Sets and Systems, 79, 403-405, 1996.

Abstract: The application of Laplace transformation in solving Initial value Problems (IVP's) of Ordinary Differential Equations (ODE's) of order 𝑛,𝑛 𝜖 ℤ+ is well known to scholars. The inversion of Laplace transformation in solving initial value problems of ODE's by the traditional algebraic method (i.e. through resolving into partial fraction and the use of Laplace Transforms table) can be very tedious and time consuming, especially when the Laplace transforms table is not readily available, thus renders the researcher handicapped. In this paper,

[1] Churchill R.V, Brown J.W and Verhey R.F (1974). Complex Variables and Applications, 3rd Edition, Mac Graw-hill book.co [2] Dass, H.K (2008). Advanced Engineering Mathematics, 21st Revised Edition, pg 927-931. S.Chand and Company Ltd. New Delhi. [3] Mark J. Ablowitz, Athanassios S. Fokas: Complex Variable; Introduction and Application.Cambridge University Press. ISBN 0-521-48523-1 [4] Sambo Dachollom, Abashi, Bulus Ayuba and Dongs, Dung Pam. (2015). Application of Cauchy Residue Theorem in the solution of Some Integrals, Proceeding of International Conference on Humanities, Science and Sustainable Development, Vol. 8, Number10, Pg 93-103.

Abstract:This paper compares the performance of regression diagnostics techniques based on Ordinary LeastSquares (OLS) estimators and four types of robust regression based on robust estimators todetect and identify outliers. It is known that OLS is not robust in the presence of multiple high leverage points.Thus severalrobust regression models are used as alternative and its approach is more reliable and appropriate method for solving this problem. The comparisonsaremadeviasimulationstudies.Our resultshaveshownthatinsomecases diagnostics basedonthe OLSandsome robustestimatorsgivesimilaroutcomes,they detectthesame percentage of correct outlier detection. And under small sample size OLS and M-estimation perform best for innovative outliers. The results also shows that Least Trimmed Square is the best among all its counterparts under large sample size.

[1] R. S. Tsay, Analysis Of Financial Time Series, pp. 1-448, 2002.
[2] S. S. S. Abd Mutalib, and K. Ibrahim, Identification Of Outliers: A Simulation Study, ARPN Journal of Engineering and Applied Sciences, Vol. 10, pp. 326-330, 2015.
[3] J. Lopez-de-Lacalle, tsoutliers R Package for Detection of Outliers in Time Series, pp. 1- 28, 2014.
[4] J. Xu,. B. Abraham and S. H. Steiner, Outlier Detection Methods in MultivariateRegression Models, pp. 1-27.
[5] E. Widodo, S. Guritno ands.Haryatmi, Response Surface Models with Data Outliersthrough a Case Study, Applied Mathematical Sciences, Vol. 9, pp. 1803 – 1812, 2015.
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Abstract:This paper presents an analytical method to describe the heat and mass transfer in the flow of an incompressible viscous fluid past an infinite horizontal wall. The governing equations account for the viscous dissipation effect and mass transfer with chemical reaction of constant reaction rate. The coupled partial differential equations describing the phenomenon have been solved analytically using variable seperation method and Fourier Sine transform. The results obtained are presented graphically. It is discovered that the
Schmidt number enhances the fluid velocity and decreases the fluid temperature. Lewis number and Eckert number enhance the fluid temperature while reaction rate number decreases the species concentration.

Keywords and phrases: Heat and mass transfer, incompressible fluid, viscous dissipation, chemical reaction, variable seperation method, fourier sine transform.

[1] Khair, K.R. and Bejan, A. (2012). Mass transfer to natural convection boundary layerflow driven heat transfer. Research Journal of
Mathematics and statistics,4(3): 63-69.
[2] Olajuwon, B.I.andDahimire, J.I. (2013). Unsteady free convection heat and mass transfer in an MHD micropolar fluid in the
presence of thermo diffusion and thermal radiation. International Journal of pure and applied mathematics,84(2): 15-37
http://www.ijpam.eu.

Abstract:Definition: Let v, k, and λ be positive integers such that v > k ≥ 2. A (v, k, λ)-balanced incomplete block
design (which we abbreviate to (v, k, λ)-BIBD) is a design (X,A) such that the following properties are
satisfied:
1. |X| = v,
2. Each block contains exactly k points, and
3. Every pair of distinct points is contained in exactly λ blocks.
Property 3 in the definition above is the "balance" property. A BIBD iscalled an incomplete block design
because k < v, and hence all its blocks are incomplete blocks.

[1]. Discrete and Combinatorial Mathematics "An Applied Introduction" 5th Edition, Ralph P. Grimaldi, B. V. Ramana.
[2]. Introduction to Number theory, Tom M. Apostal, Springer.
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[4]. "Existence of Semi Primitive root Mod pα" in IOSR Journal of Mathematics p-ISSN2319-765X, Vol.11, Issue2, ver. II (March- April
2015), PP14-17. By Dr.K.Vijayalakshmi

Abstract: Bipolar plates (BPs) are a key component of Proton Exchange Membrane (PEM) Fuel Cells with multifunctional character. They uniformly distribute fuel gas and air, conduct electrical current from cell to cell, remove heat from the active area, and prevent leakage of gases and coolant. Bi-Polar Plates also significantly contributes to the volume, weight and cost of Proton Exchange Membrane Fuel Cell stacks. Hence, there are vigorous efforts worldwide to find suitable materials for Bi-Polar Plates. The materials include non-porous graphite, coated metallic sheets, polymer composites, etc. This paper reviews various types of materials, in use and proposed, for Bi-Polar Plates and critically examines their physical and chemical properties.

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[3] Scha¨fer A, Heywood JB, Weiss MA. Future fuel cell and internal combustion engine automobile technologies: a 25-year life cycle and fleet impact assessment. Energy 2006; 31(12):2064–87.
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[5] Williams BD, Kurani KS. Commercializing light-duty plug-in/plug out hydrogen-fuel-cell vehicles: ''Mobile Electricity'' technology and opportunities. J Power Sources 2007;166(2): 549–66.