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

Abstract:In this paper, we have studied fuzzy subspace, balanced fuzzy set, and absorbing fuzzy set over a
fuzzy vector space. We examine the properties of the balance fuzzy set, and absorbing fuzzy set, and established
some independent results, under the linear mapping from one fuzzy vector space to another fuzzy vector space.
Keywords: Fuzzy vector space, Fuzzy balanced set, Fuzzy absorbing set.

[1]. KANDEL,A and BAYATT,W.J.(1978)."Fuzzy sets, Fuzzy algebra and Fuzzy statistics."Proceeding of ILEE, Vol.66, and No.12
PP.1619-1639.
[2]. KATSARAS,A.K. and LIU,D.B.(1977)."Fuzzy vector spaces and Fuzzy topological vector spaces". J.Math.Anal.Appl.58, PP. 135 -
146.
[3]. LAKE,J.(1976)."Sets, Fuzzy sets, multisets, and Functions."Journal of London Mathematical Society, 12. PP.323 -326.
[4]. NAGUYEN,H.T.(1978)."A note on the extension principle for fuzzy sets."UCE/ERL MEMO M-611.UNIV.OF
CALIFORNIA,BERKELEY. [Also in J.Math.Anal.Appl.64,No.2,PP.369-380.]
[5]. RUDIN,W."Functional Analysis",MC Graw-Hill Book Company, New York,1973.
[6]. ZADEH,L.A. "Fuzzy sets"Inform.Control,8.(1965),PP. 338-353.

Abstract: The unsteady magnetohydrodynamic flow of an electrically conducting viscous, incompressible fluid between two parallel porous plates of a channel in the presence of a transverse magnetic field when the fluid is being withdrawn through both the walls of the channel at the same rate is discussed. An exact solution is obtained for all values of R (Suction Reynolds number) and M (Hartmann number). Expressions for the velocity components and the pressure are obtained. The graphs of axial and radial velocity profiles have been drawn for different values of M.

Key words: Unsteady flow, parallel porous plates, transverse magnetic field, suction Reynolds number, Hartmann number, pressure drop.

[1]. Aboul-Hassan, A.L and H.A. Attia (2002), "Unsteady hydromagnetic flow of a viscoelastic fluid with temperature dependent viscosity" Can. J. Phy. Rev. Can. Phys. 80: 1015-1024.
[2]. H.A. Attia and N.A. Kotb (1996), " MHD flow between two parallel plates with heat transfer" Acta Mechanica, 117: 215.
[3]. H.A. Attia (1999) " MHD flow and heat transfer between two parallel plates with temperature dependent viscosity" Mech. Res. Comm.,26: 115.

Abstract: Two Manpower planning models with different recruitment patterns are studied. During the operation time a machine produces random number of products. After the operation time, the sale time starts, and it has one among two distinct distributions depending on the magnitude of production is within or exceeding a random threshold magnitude. In this paper, the operation times have SCBZ property and the man power system, sales and recruitment have general distribution. Joint transforms of the variables, their means and covariance operation time and recruitment time with numerical results are presented. Mathematics Subject Classification: 91B70

Keywords: Departure and Recruitments, Failure and Repairs, Production and Sale times, Joint transform

[1]. Barthlomew. D.J,Statistical technique for manpower planning, John Wiley, Chichester(1979)
[2]. Esary.J.D, A.W. Marshall, F. Proschan, Shock models and wear processes, Ann. Probability, 1, No. 4 (1973), 627-649
[3]. Grinold.R.C,Marshall.K.T, Manpower Planning models, North Holl, Newyork (1977)
[4]. Hari Kumar.K, P.Sekar and R.Ramanarayanan, Stochastic Analysis of Manpower levels affecting business with varying
Recruitment rate, International Journal of Applied Mathematics, Vol.8,2014 no.29, 1421-1428.
[5]. Hari Kumar.K, Manpower System with Erlang departure and one by one Recruitment, International Journal of Mathematical
Archive-5(7),2014, 89-92.ISSN 2229-5046.
[6]. Lesson .G.W, Wastage and Promotion in desired Manpower Structures, J.Opl.Res.Soc.,33(1982)433-442.

Abstract:This study explores the relationship between government expenditure and foreign aid in Nigeria
using cointegration analysis and vector error correction model. Applying data for 43 years from 1970 to 2012,
the results of Johansen and Enger- Granger cointegration test suggest that there is positive and long run
relationship between foreign aid and government expenditure. We found also, that the coefficient estimate of the
foreign aid is not significant in the long run but, in the short run effect of increase in foreign aid is more
insignificant both in magnitude and level of significance. The study also finds that foreign direct investment and
real gross domestic product have positive impact on the government expenditures i.e. they provide important
information as determinants of government expenditure in Nigeria.
Keywords: Foreign Aid, Public Expenditure, Development, Nigeria

[1]. Asterio, D. & Price, S. (2007). Applied Econometrics', A Modern Approach. Basingstoke: Palgrave Macmillan.
[2]. Boone, P. (1996). Politics and the Effectiveness of Foreign Aid.EuropeanEconomic Review40 (2): 289–330.
[3]. Bruce,N.,andWaldman, M. (1991).Transfersin Kind: Why They Can Be Efficient andNon-Paternalistic.'American Economic Review81 (5): 1345–51.
[4]. Ekanayake, E.M. and Chatrna, D. (2007).The Effect of Foreign Aid on Economic Growth in Developing Countries.Journal of International Business and Cultural Studies.
[5]. Granger, C. W. J. &Newbold, P., (1974). Spurious regression in econometrics.Journal of Econometrics, 2, 111-120

Abstract:In this paper, evolution equations with two or more spatial variables, which may describe pseudospherical planes in higher dimensions, are considered. Necessary and sufficient conditions for equations of type to describe a 3-dimensionalpseudospherical plane of 5are given . Such equations are characterized. Keywords:Evolution equations, Pseudospherical surfaces, Riemannian manifold, Solitons and differential equations.

[1] Tenenblat K.," Backlund s theorems for submanifolds of space forms and a generalized wave equations", Bol. Soc. Bras. Mat. vol. 16 No. 2 (1985) 67-92. [2] Tenenblat. K, and D. Catalano Ferraioli" Fourth order evolution equations which describe pseudospherical surfaces " J. Differential equations. vol 275 (9), 3165- 3199 (2014). [3] Tenenblat K. and S.Chern, J.Results in Math. vol 60. (2011) 53- 101. [4] Beals R., Rahelo. M and K. Tenenblat, "Backlund transformations and inverse scattering solutions for some pseudospherical surfaces equations ",Stud. Appl. Mat. 81 (1989) 125-151. [5] Chern. S and Tenenblat. K," pseudospherical surfaces and soliton equations" Stud. Appl. Mat. 74 (1986) 55-83. [6] El-Sabbagh. M, "Sl(n,R) – structure and a possible model for higher dimensions solitons" J. Mat. Phys. Sci. vol. 18, No.4 (1984).127-138.

Abstract: In this paper we take a natural homomorphism f M : U  Hom R ( M , N ) → HomU ( U M , U N )
where U is an R-Algebra , R=CenU and M , N are any two R-modules.Here we have shown that

[1]. F. W. ANDERSON AND K. R. FULLER, Rings and Catagories of modules, New York Springer – Verlag Inc. 1973.
[2]. LOUIS HALLE ROWEN, Ring Theory.
[3]. T. Y. LAM, A first course in non commutative rings Springer – Verlag.
Proceedings Papers:
[4]. R. S. SINGH, Finitely presented modules, Proc. Math. Soc. , B. H. U. Vol 3 (1987)
[5]. R. S. SINGH AND BHUPENDRA, Tensor product of R-algebra and R- homomorphisms, Prog. of Math. Vol 37(nos 1 and 2) 2003.

Abstract:The objective of this paper to generalize certain Tauberian results proved by Gehring [3] for summability ( 𝐶, 𝑘; 𝛼) of sequences to functions. In [1] A. V. Boyd generalized the Tauberian theorem for 𝛼 convergence of Ces𝑎 ro means of sequences. In this paper ,we obtain some Tauberian theorems for (𝐶, 𝛼, 𝛽) convergence of Ces𝑎 ro means of order k of functions and investigate some of its properties .

Keywords: Tauberian theorem, Absolute and Cesàro summability , Lebesgue Integral, Convergence.

[1]. A.V. boyd, Some theorems on Summability, 1950.
[2]. J. M .Hyslop, A Tauberian theorem for absolute summability,J.London Math.Soc.Vol.12 (1937) pp.176-180.
[3]. F.W. Gehring, A study of 𝛼 − 𝑣𝑎𝑟𝑖𝑎𝑡𝑖𝑜𝑛 , I, Trans. Amer. Math.Soc.vol.76 (1954) pp.420-443.
[4]. O Szasz, On products of summability methods,Proc.Amer.Math.Soc.vol.3(1952) pp. 257-263.
[5]. G. H. Hardy, J. E.Littlewood,and Polya, Inequalities,1934.

Abstract: we have studied the numerical solutions for FitzHugh-Nagumo equation (FHN) using Finite Difference Methods (FDM) including explicit method, implicit (Crank-Nicholson) method, fully implicit method, Exponential method. A Comparison was made among all the methods by solving two numerical examples with different time steps.

Keywords: Fitz Hugh-Nagumo equation, explicit, implicit, fully implicit, Exponential methods.

[1]. L. Debnath (1997) , Nonlinear Partial Differential Equations for Scientists and Engineers, Birkhauser Boston.
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[4]. G. Hariharan, and K. Kannan, ,(2010), Haar wavelet method for solving FitzHugh-Nagumo equation, World Academy of Science, Engineering and Technology 43.
[5]. R. FitzHugh, , (1961), Impulse and physiological states in models of nerve membrane, Biophys. J. 1 445-466.
[6]. J.S. Nagumo, S. Arimoto, and S. Yoshizawa, (1962), An active pulse transmission line simulating nerve axon, Proc. IRE 50 2061-2071.