iosr-Jm   Volume-10 ~ Issue-5 ~ Sep-Oct 2014

Abstract: In the Present paper effect of angle of incidence on pitching derivatives of a delta wing with Straight leading edges for attached shock case in Supersonic Flow has been studied. A Strip theory is used in which strips at different span wise location are independent. This combines with similitude to give a piston theory. From the results it is seen that with the increase in the Mach number, there is a decrement of stiffness as well as the damping derivatives in pitch for all the Mach number tested, however, the magnitude of decrement for different inertia level will differ. It is seen that with the increase in the angle of attack both stiffness and damping derivatives increase linearly, nevertheless, this linear behavior limit themselves for different Mach numbers. For Mach number M = 2, this limiting value of validity is fifteen degrees, for Mach 2.5 & 3, it is twenty five degrees, whereas, for Mach 3.5 & 4 it becomes thirty five degrees. When these stability derivatives were considered at various pivot positions, namely h = 0.0, 0.2, 0.4, 0.6, 0.8, and 1.0. After scanning the results it was observed that with the shift of the pivot position from the leading edge to the trailing edge, the magnitude of both the stability derivatives were decreasing progressively with the pivot position. Results have been obtained for supersonic flow of perfect gases over a wide range of angle of attack and Mach number. The effect of real gas, leading edge bluntness of the wing, and secondary wave reflections are neglected.

Keywords: angle of incidence, delta wing, Pitching derivatives, Supersonic Flow, Straight leading edge

[1] Pike. J, "The pressure on flat and anhydral delta wings with attached shock waves", The Aeronautical Quarterly, November 1972, XXIII, Part 4, pp. 253-262.

[2] Hui, W.H., "Stability of Oscillating Wedges and Caret Wings in Hypersonic and Supersonic Flows", AIAA Journal, Vol. 7, Aug. 1969, pp.1524-1530.

[3] Carrier, G.F. 1949, "The oscillating Wedge in Supersonic stream", Journal of Aeronautical Sciences, Vol. 16, No. 3, pp. 150-152, March.

[4] Hui, W. H., "Supersonic/hypersonic flow past on oscillating flat plate at high angles of attack", ZAMP, Vol. 29, 1978, pp. 414-427. [5] Hui, W. H., "Supersonic and hypersonic flow with attached shock waves over delta wings", Proc of Royal Society, London, 1971, A. 325, pp. 251-268

Abstract: This paper proposes, develops and presents a method that may be used to adjust and correct sample estimates of the usual spearman rank correlation coefficient for the possible presence of tied observation in the sampled populations. Without these adjustments the sums of squares of ranks in the denominator of the usual expression for the estimation of spearman rank correlation coefficients are often over estimated if there are ties in the populations and no effort is made to correct and adjust for them especially if these ties are not few, resulting in inefficient, unreliable and often misleading estimates. The proposed method is shows to be easily modified and applied to estimate ties adjusted spearman partial rank correlation coefficient between any two populations holding observations from a third population at constant levels with all the populations adjusted for the possible presence of tied observations. The usual statistical tests for significance are also easily modified using the ties adjusted rank correlation coefficients in place of the unadjusted and usual rank correlation coefficients. The proposed method is illustrated with some sample data and shows to produce more efficient estimates than the usual ties unadjusted uncorrected spearman rank correlation coefficients.

Keywords: Rank, Ties, Adjusted, Correlation, Partial, Efficient, Ordinal

[1]. Gibbons, J. D. (1971): Non parametric Statistical Interference. McGraw-Hill Book Company, New York.
[2]. Siegel S. (1956): Nonparametric Statistics for the Behavioural Sciences. McGraw-Hill Kogakusha, Ltd. Tokyo
[3]. Maritz, J. S. (1981): Distribution-Free Statistical Methods. Chapman and Hall.
[4]. Kendall, M. G. (1970): Rank Correlation Methods (4th Edition). London: Griffin.
[5]. Hollander M, Wolfe D. A. (1973): Nonparametric Statistical Methods. New York; Wiley.

Abstract: A study on atomic separation axioms on atomic measure space (𝑅𝑛, τ, Σ, 𝜇𝐴) has been introduced in this paper. The key feature of this study is that, the atomic separation axioms like A𝑇2, AR are not only invariant under homeomorphism but they are invariant under measure invariant transformation on an atomic measure space (𝑅𝑛, τ, Σ, 𝜇𝐴 ).

Keywords: Atomic measure space, Atomic separation axioms, Measure atlas, Measure chart, Measure invariant transformation, Measure manifold, Measure space.

[1]. S. C. P. Halakatti and H. G. Haloli, "Introducing the Concept of Measure Manifold (M,Σ1,τ1, μ1)", IOSR Journal of Mathematics(IOSR-JM), Volume10, Issue 3 Ver. II, 01-11(2014)
[2]. John K Hunter, "Measure Theory Lecture notes", University of California at davis(2011)
[3]. C. W. Patty, "Foundations of Topology", Jones and Bartlett Publications Inc., First Indian edition(2010)
[4]. M. M. Rao, "Measure Theory and Integration", Second Edition, Marcel Dekkar, INC., New York-Basel(2004)
[5]. R. K. Singh and T. Veluchamy, "Atomic Measure Space and Essential Normal Composition Operators", Bull Austral Math, Soc., Vol. 27(1983).

Abstract: The aim of this paper is to elaborate the study of some nearly- open sets as p-open, s-open, α-open
& β-open sets & the associated strongly continuity as well as compactness. Also the inter relationship of these
nearly open sets has been discussed.
Keywords: p- open set, s-open set, α-open set, β-open set.

[1]. Andrijevic, D., : semi-pre open sets, Mat. Vesnik, 38, no.1, 24-32(1986).
[2]. Balachandran, K., Sundaram, P. and Mack, H., : On generalized continuous maps in topological spaces, Mem. Fac. Sci., Kochi Univ. Ser. A, Math., 12, 5-13(1991).
[3]. Njastad,O.; On Some Class Of Nearly Open Sets, Pacific J.Math., (15)(1965), 961-970 ,
[4]. Devi,R. and Bhuwaneshwari, K., : α-weekly generalized closed sets in bitopological spaces, Acta ciencia Indica, Vol .30, 2004 pp, 167-172.
[5]. Devi, R., Mack, H. & Balachandran, K., : Semi-generalized closed maps and generalized semi closed maps, Mem. Fac. Sci., Kochi Univ. Ser. A, Math, 14, 41-54(1993).
[6]. EI-Deeb, S.N., M.E.abd EI-Monsef & Mahmoud,R.A., : β-open sets and β-continuous mappings , Bull. Fac. Sci. Assiut. Univ., 12, 77-90(1983)

Abstract: In this paper, the unsteady viscous flow produced by a sudden coincidence of the axes of a disk and the fluid at infinity rotating with the uniform angular velocity Ω has been studied. The exact solution of the governing equation has been obtained using Laplace transform technique. The velocity field and the shear stress components that rare related to the force components in the x and y –directions exerted by the fluid on the disk are discussed. The exact solutions are also verified by another solution obtained and that is valid at small times instants. The fluid motions are depicted through graphs using MATLAB.

Key Words: viscous fluid, rotating disk, angular velocity, Laplace transform

[1]. Abramowitz, M., and Stegun, I.A., Handbook of Mathematical Functions, Dover Publications, NewYork, 1965.
[2]. Berker, R., \An Exact Solution of the Navier-Stokes Equation: The Vortex with Curvilinear Axis", Int.J. Eng. Sci., 20, 217-230, 1982.

[3]. Coirier, J., \Rotations non Coaxiales d'un Disque etd'un Fluide _a L'in_ni", J. M_ecanique, 11, 317-340,1972.
[4]. Erdo_gan, M.E., \Flow due to Eccentric Rotating a Porous Disk and a Fluid at In_nity", J. Appl. Mech. - T. ASME,43E, 203-204, 1976a.
[5]. Erdo_gan, M.E., \Non-Newtonian Flow due to Noncoaxially Rotations of a Disk and a Fluid at In_nity", Z. Angew.Math. Mech., 56, 141-146, 1976b

Abstract: In this paper we introduce the notion of weakly Ricci 𝜑-symmetric𝜀-trans-Sasakian manifolds and study characteristic properties of locally 𝜑-Ricci symmetric and 𝜑-recurrent spaces. Finally, local symmetry of a generalized recurrent weakly symmetric𝜀-trans-Sasakian manifolds is discussed.

Keyword: 𝜀-trans-Sasakian manifolds, Weakly symmetric 𝜀-trans-Sasakian manifolds.

[1]. A. Benjancu and K. L. Duggal., Real hypersurface of indefinite Kaehler manifold. Int. J. math.and Sci., 16 no. 3(1993), 545-556.
[2]. X. Xufeng and C. Xiaolic., Two theorems on (ε)-Sasakian manifolds, Int. J. Math. and Math. Sci., Vol.21 No. 2(1998), 249-245.
[3]. R. Kumar, R. Raani and R.K. Nagaich., On sectional curvature of ε-Sasakian manifolds. Int. J. Math., Math. Sci. (2007), Art ID 93562, pp 8.
[4]. K.L. Duggal., Space time manifold and contact structures, Int. J. math. and math. Sci., 13 no. 3(1990), 345-553.
[5]. U.C. De and AvijitSarkar, On (ε)-Kenmotsu manifolds, Hadronic Journal 32(2009), 231-242.
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Abstract: We study a series of new energy sources of the Gaussian energy group SU(6), SU(12), SU(24), ….etc. called intelligences which created consciousness and which are responsible for the creation of everything of this universe. The effective quantity and quality of the consciousness of the earth-like planet where living elements were found depends on environment and place of position within the galaxy or cluster or super cluster etc. & mechanical structure of the planet. The said energy sources created consciousness within the living cell and also controlled the whole universe with the symmetry breaking of the energy group SU(11) [ SU(6)  SU(5)  U(1)]; SU(23); SU(47);…… etc. In the living body, generally consciousness controlled by the self gravitational force of the energy group SU(6) and plays with biological revolution. But consciousness level of any living body including human group and also inanimate objects is particularly controlled by SU(12), SU(24), ….etc. We examine the quantum measurement, using the Wheeler DeWitt wave equation over the complex space-time R + iRI of (4+D) dimensions, where D is an extra dimensions. We know that the quantum super-positions will continually be reaching the Di𝑜 si-Penrose (DP) threshold for Objective Reduction in non-biological settings as well as in biological ones, and usually take place in the purely random environment of a quantum system under measurement through the symmetry breaking of the Generalized Gaussian Energy Group from infinity i.e. from Big-Rip singularity when RI →∞.

[1]. Everett, H. (1957). Relative state formulation of quantum mechanics. In Quantum Theory and Measurement, Wheeler, J.A., and zurek,W.H., (eds) Princeton University Press, 1983; Originally in Reviews of Modern Physics, 29, 454.
[2]. Engel, G.S., Calhoun, T.R., Read, E.L., Ahn, T-K., Mancal, T., Cheng, Y-C., Blankenship, R.E., Fleming, G.R., (2007). Evidence for wave-like energy transfer through quantum coherence in photo synthetic systems. Nature 446: 782.
[3]. Bhadra N.K(2012):The complex Model of the Universe, IOSR-JM, ISSN: 2278-5728, vol.2, 4, pp-20; and The complex model of the quantum universe, ISSN: 2278-5728. IOSR Journal of Mathematics (IOSR-JM) vol.4, Iss. 1 (Nov. - Dec 2012), pp-20. "The Complex Quantum-State of Black-Hole and Thermostatistics‟ (IOSR-JM: e-ISSN: 2278-3008, p-ISSN: 2319-7676. Volume 8, Issue 5 (Nov. – Dec. 2013), PP 01-19)].
[4]. Bhadra NK; THE COMPLEX QUANTUM AND CLASSICAL PSEUDO-TACHYONIC UNIVERSE; (IOSR-JM) e-ISSN: 2278-5728,p-ISSN: 2319-765X, Volume 8, Issue 3 (Sep. - Oct. 2013), PP 15
[5]. Einstein, A. de-Sitter, W. (1932): On the relation between the expansion and mean density of the universe. Proc. Natl. Acad. Sci.,(USA), 18,213. Hawking S.W(1984): The quantum state of the universe, Nucl. Phys. B239.257.

Abstract: Let M and M' be two prime -rings and n,n be two higher homomorphism of a -ring M, for all n  N in the present paper we show that under certain conditions of M, every Jordan (,)-higher homomorphism of a -Ring M into a prime  '-Ring M 'is either (,)-higher homomorphism or (,)-anti-higher homomorphism.

Key Words: prime -ring , homomorphism,Jordan homomorphism. Mathematics Subject Classication : 16N60; 16U80

[1] W.E.Barnes, "On The -Rings of Nobusawa", Pacific J.Math., Vol.18 (1966), pp.411-422.
[2] Y.Ceven and M.A.Ozturk, "On Jordan Generalized Derivations in Gamma Rings", Hocet type J.of Mathematics and Statistics,
Vol.33 (2004), pp.11-14.
[3] K.K.Dey, A.C.Paul and I.S.Rakhimov, " Generalized Derivations in Semiprime Gama Rings", International Journal of Mathematics
and Mathematical Sciences, Vol.(2012), 14 pages.
[4] A.K.Halder and A.C.Paul, "On Two Torsion Free Prime Gamma Ring with Jordan Left Derivations", Journal of Math., Vol.46(1)
(2014), pp.59-66.
[5] M.F.Hoque and A.C.Paul, "On Generalized Derivations on Semiprime Gamma Ring with Involution", Palestine Journal of Math.,
Vol.3(2) (2014),pp. 235-239.

Abstract: In this paper some results concerning to right reverse derivation on prime -rings are presented if M be a prime -ring with non-zero right reverse derivation d and U be the ideal of M, then M is commutative. Mathematics Subject Classification: 16A70, 16N60, 16W25

Keywords: prime -ring, derivation,reverse derivation

[1] W.E.Barnes, 1966, "on the gamma rings of Nobusawa ",pacific .J. math 18, 411-422.

[2] M.Bresar and J.Vukman ,on some additive mapping in rings with involution, equation math, 38(1989), 178-185.

[3] K.K.Dey ,A.C.Paul, I.S.Rakhimove "Semiprim Gamma Rings With Orthogonal Reverse Derivations", International Journal Of Pure and Applied Mathematics, vol.83, No.2, 2013, 233-245.

[4] C.J.S.Reddy and K.Hemavathi, "right reverse derivation on prime rings", International Journal of Research in Engineering and Tec , vol.2, Issue 3, 2014, 141-144.

[5] N.Nobusawa, 1964, "on a generalization of the ring theory " Osaka J. Math.1, 81-89.

[6] M.Samman and N.Alyamani, "Derivation and reverse derivations in semiprim rings", International Mathematical forum2 , No.39, (2007), 1895-1902.

Abstract: In this paper we investigate of multi-server retrial queue system .Server provides two stages of homogeneous service in succession. The customer has to complete first service from first server then to the second server of the service. After completion of the second service, the second server takes Bernoulli vacation. On arriving customer on finding a free for the first server enters into service immediately, and goes for the second server; otherwise the customer enters into an orbit of infinite service. An orbiting customer competes for the service by sending signals at random times until a free server is captured. Using the above concept we obtain steady state behaviour of multiserver.

Keywords: M/M/2 Retrial, Steady state equation, Bernoulli vacation

[1]. Abramowitz, M and Stegun, I.A (1972) Hand book of Mathematical functions. Dover, New York.
[2]. Artalejo, J.R (1993) Explicit formulae for the characteristics of the M/H2/I retrial queue. Operate Res.soc.44,(309-313).
[3]. Artalejo, J.R and Falin, G.I (1994), Stochastic decomposition for retrial queues top2, 329-342.
[4]. Cooper, R.B (1990) .Queuing theory .In Heyman, D.P., Sobel, M.J.eds stochastic Models Amsterdam: North-Holland (Elsevier),pp 469-518.
[5]. Falin, G.I.(1980) An M/M/1 queue with repeated calls in the presence of persistence function: Paper 1606-80.All-Union Institute for scientific and Technical information ,Moscow.
[6]. Falin,G.I.(1984) An Double channel queuing system with repeated calls :Paper 4221-84.All-Union Institute for scientific and Technical information ,Moscow

Abstract: The present work is to investigate the magnetohydrodynamic behaviour of two dimensional Poiseuille flow under the influence of an inclined magnetic field and constant pressure gradient for a viscous, incompressible and electrically conducting fluid between two infinite parallel plates of which the lower plate is taken to be porous. The solution of the fluid flow governing equation has been obtained by analytical method and expressed in terms of Hartmann number. The fluid flow profiles are represented through graphs for different values of Hartmann number with different angles of inclination for injection/suction. The effects of the other parameters such as pressure gradient, inclined magnetic field and suction/injection on the flow are also studied graphically. The resulting equation of motion has preferably been solved by the method of variation of parameters.

Key words: Poiseuille flow; Porous plate; Conducting fluid; Pressure gradient; Inclined magnetic field; Hartmann number.

[1]. H.Alfve´n. Existence of electromagnetic hydrodynamic waves, Nature, 150, No.3805 (1942), 405-406.
[2]. J.Bear, Dynamics of fluids in porous media, Dover (1988).
[3]. Richard Bronson & Gabriel B Costa, Differential Equations,Thirdedition, Tata McGraw-Hill Education Private Limited, New Delhi .
[4]. P.A.Davidson, An Introduction to Magnetohydrodynamics, First edition, Cambridge University Press, UK (2001).
[5]. S.Ganesh and S. Krishnambal, Unsteady MHD Stokes flow of viscous fluid between two parallel porous plates, J.Appl.Sci. 7(2007), 374-379.
[6]. U.Kazuyuki, Inertia effects on two- dimensional magnetohydrodynamic channel flow under traveling sine wave magnetic field, Phys.Fluids A, 3 No.12 (1991), 3107-3116.

Abstract: Let G = (V,E) be the IFG and D be set of vertices, then D is said to be Intuitionistic point set dominating set of G if for every S⊆ V- D there exists a node d ∈ D such that the Intuitionistic fuzzy sub graph < S∪{d} > induced by S∪{d} is a connected Intuitionistic fuzzy graph. In this paper we study some results on Intuitionistic Point set dominating set and its number of IFGs. Also we establish some theorems and bound of Intuitionistic psd-sets in purely semi-complete IFGs.

Keywords: Point set domination set of IFG, Set domination set of IFG, Semi complete IFG. 2010Mathematics Subject Classification: 03E72, 03F55, 05C69, 05C72.

[1]. Atanassov KT. Intuitionistic fuzzy sets: theory and applications. Physica, New York, 1999.
[2]. Harary,F., Graph Theory, Addition Wesley, Third Printing, October 1972.
[3]. Nagoor Gani. A and Shajitha Begum.S, Degree, Order and Size in Intuitionistic Fuzzy Graphs, International Journal of Algorithms, Computing and Mathematics,(3)3 (2010).
[4]. Parvathi, R. and Karunambigai, M.G., Intuitionistic Fuzzy Graphs, Computational Intelligence, Theory and applications, International Conference in Germany, Sept 18 -20, 2006.
[5]. Parvathi,R., and Thamizhendhi, G. Domination in Intuitionistic fuzzy graphs, Fourteenth Int. conf. on IFGs, Sofia, NIFS Vol.16, 2, 39-49, 15-16 May 2010.
[6]. Kulli,V.R., Theory of domination in graph, Vishwa International Publications, 2010.
[7]. Sampathkumar. E., and Pushpa Latha. L., Point set domination number of a Graph, Indian J. pure appl. Math.,24(4); 225-229, April 1993.

Abstract: In this paper we will introduced soft disjoint sets, soft separated sets ,soft connected space , soft disconnected space ,and study the relation between soft disjoint sets and soft separated sets, define soft hereditary property and study soft hereditary property on soft connected spaces , study the product of two soft disconnected spaces and the product of soft connected with soft disconnected

[1] A.Aygunoglu and H.Aygun, "Some notes on soft topological paces" ,Neural Comput and Applic, (2011).
[2] D. Molodtsov, "Soft Set Theory-First Results", Computers and Mathematics with Applications, Vol. 37, p.p 19–31,(1999).
[3] Dariusz Wardowski,"On a Soft Mapping and its Fixed Points",fixed point theory and application springer open journal , Vol. 182 , p.p.1-11 ,(2013).
[4] E.Peyghan , B.Samadi , A.Tayebi, " About soft topological spaces ", journal of new results in science , No.2, p.p 60-75(2013).
[5] E.Peyghan , B.Samadi, A.Tayebi ,"on soft connectedness ",arXiv:1202.1668v1 [math.GN]8Feb(2012).
[6] Gnanambal Hango,Mrudula Ravindran ,"On soft pre open sets in soft topological spaces", international journal of mathematics research, Vol.5,No.4,p.p.399-409,(2013).