iosr-Jm   Volume-12 ~ Issue-4 ~ Jul-Aug 2016

Abstract: The g-frame operator for g-frames in C* algebra is introduced. The results on g-frame operators are proved. Frame identities are shown. Result on direct sum of g-frame operators on direct sum of Hilbert Spaces is presented.

[1]. M.R.Abdollahpour ,M.H. Faroughi and A.Rahimi " PG-Frames in Banach spaces" Methods of Functional analysis and topology
[2]. Vol.13 no.3(2007),pp.201-210
[3]. R.Balan P.G.Casazza, D.Edidin and G.Kutynoik " Decomopostion of frames and a new frame identity " Wavelet XI (San
[4]. Diego),CA(2005) pp.379-388 SPIE Proc 5914 ,SPIE Bellinginam WA.
[5]. P.G.Casazza,, "The art of Frame theory" ,Taiwanese Journal of Mathematics Vol.4,No.2(2000) pp 129-201

Abstract: The ternary quadratic Diophantine equation given by 7(𝑥2+𝑦2)−13𝑥𝑦=27𝑧2 is analyzed for its patterns of non-zero distinct integral solutions. A few interesting relations between the solutions and special polygonal numbers are exhibited.

Keywords: Ternary quadratic, integral solutions, polygonal numbers.

[1] GopalanMA, Sangeethe G. On the Ternary Cubic Diophantine Equation 2 2 3 y  Dx  z Archimedes J.Math, 2011,1(1):7-14.
[2] GopalanMA,VijayashankarA,VidhyalakshmiS.Integral solutions of Ternary cubic Equation, 2 2 2 2 x  y  xy  2(x  y  2)  (k 3)z , Archimedes J.Math,2011;1(1):59-65.
[3] GopalanM.A,GeethaD,Lattice points on the Hyperboloid of two sheets 2 2 2 x 6xy  y 6x 2y 5  z 4 Impact J.Sci.Tech,2010,4,23-32.
[4] GopalanM.A,VidhyalakshmiS,KavithaA,Integral points on the Homogenous Cone 2 2 2 z  2x 7y ,The Diophantus J.Math,2012,1(2) 127-136.
[5] GopalanM.A,VidhyalakshmiS,SumathiG,Lattice points on the Hyperboloid of one sheet 2 2 2 4z  2x 3y 4 , The Diophantus J.Math,2012,1(2),109-115.

Abstract: The aim of this research paper is to derive some hypergeometric formulas of Laguerre polynomials of two, three and several variables. Also we apply this formulas to derive some integral formulas involving Laguerre polynomials of several variables.
Keywords: Generalized Lauricella function, Hypergeometric formulas, Integral formulas, Laguerre polynomials..

[1] A.A. Atash and A.M. Obad, Transformation formulas for some Exton's quadruple hypergeometric functions,
International Journal of Mathematical Analysis, 9(10) (2015), 483 – 492.
[2] S.K. Chatterjea, A note on Laguerre polynomials of two variables, Bull. Cal. Math.Sco. 82 (1991),263-266.
[3] H. Exton, Multiple hypergeometric functions and applications, Halsted Press, NewYork, 1976.
[4] H. Exton, Reducible double hypergeometric functions and associated integrals, AnFac. Ci. Univ. Porto, 63 (1982),137-143.
[5] M. A. Khan and A. K. Shukla, On Laguerre polynomials of several variables,Bull.Cal. Math. Soc. 89 (1997),155-164...

Abstract: Failure by teachers to meet students' expectations on desirable classroom instruction and assessment constitutes an assessment related problem in mathematics learning. The purpose of this study was to examine the relationship between students' expectation and mathematics teachers' exhibition of desirable classroom assessment behaviour. The study adopted a quantitative research approach and used the inferential survey design, which ensured close monitoring and supervision of both data collection and analysis and made interpretation easy. Using cluster sampling and systematic sampling techniques, the sample of 887 12th grade students was selected from the target population of all secondary school students in Liberia enrolled during the time of the study......

Key terms: student's expectation, desirable classroom assessment behaviour, effective instruction.

[1] Chilisa, B., &Preece, J. (2005). Research methods for adults in Africa: African perspectives on adult learning. Gaborone: Pearson.
[2] Coe, R., Aloisi, C., Higgins, S., & Major, L. E. (2014). What makes great teaching?Review of the underpinning research. Retrieved from http://www.suttontrust.com/wp-content/uploads/
[3] Creemers, B. P. M., &Kyriakides, L. (2006). Critical analysis of the current approaches to modelling educational effectiveness: The importance of establishing a dynamic model. School Effectiveness and School Improvement , 17, 347– 366. Retrieved from http://www.rug.nl/staff/b.p.m
[4] Creemers, B. P., &Kyriakides, L. (2011). Improving quality in education: dynamic approaches to school improvement . Routledge, Taylor & Francis Group.
[5] Gao, M. (2012). Classroom assessment in mathematics: High school students' perceptions. International Journal of Business and Social Sciences, 3 (2).

Abstract: We have established an integration by parts formula involving higher order Malliavin derivatives. This integration by parts formula can be used to extend the formulas in the work by Bally and Talay to include delay SDE's as well as ordinary SDE's. Keywords: Stochastic Differential Equations, Malliavin Calculus, Euler Scheme for delay SDE's, Integration by Parts, Densities of Distributions.

[1]. Ahmed, T.A. Stochastic Functional Differential Equations with Discontinuous Initial Data, M.Sc. Thesis, University of Khartoum, Khartoum, Sudan, (1983).
[2]. Bally, V. and Talay, D.: The law of Euler scheme for stochastic differential equations (I): Convergence rate of the distribution function. J. Probability Theory and related fields 104, 43-60 (1996)
[3]. Bally, V., Talay, D.: The law of Euler scheme for stochastic differential equations (II): Convergence rate of the density, Monte Carlo Methods and Appl., Vol.2, No.2, pp.93-128 (1996)
[4]. Elworthy, K.D., Stochastic Differential Equations on Manifolds, Cambridge University Press (1982).
[5]. Friedman, A., Stochastic Differential Equations and Applications, Academic press (1975).

Abstract: The steady mixed convection flow of a viscous incompressible micropolar fluid through porous medium towards a stagnation point over a vertical surface when the buoyancy force assists and opposes the flow has been investigated. The governing nonlinear partial differential equations are transformed into a system of ordinary differential equations and then solved by employing Runge–Kutta fourth order method along with shooting technique. The velocity, microrotation and temperature profiles for different governing parameters............

Keywords: Mixed convection, Micropolar fluid, Magnetohydrodynamic flows, Porous medium.

[1] A.C. Eringen, Theory of micropolar fluids, J.Math.Mech.16(1966), pp. 1-18.
[2] A.C. Eringen, Microcontinumm field theories. II: Fluent Media, Springer, Newyork, 2001.
[3] A.Ishak, R. Nazar, I. Pop, Moving vedge and flat plate in a micropolar fluid, Int.J.Eng.Sci.44(2006) 1225-1236.
[4] R.S.R.Gorla, Mixed convection in a micropolar fluid from a vertical surface with uniform heat flux, Int. J. Engi. Sci., 30, pp. 349–358, 1992.
[5] A.Ishak, R. Nazar, I. Pop, MHD flow of a micropolar fluid towards a stagnation point on a vertical surface, Computers and Mathematics with Applications 56(2008)3188-3194.

Abstract: This paper presents the possible effects of a temporary price discount offered by a supplier on a retailer's replenishment policy quadratic demand rate for the deteriorating items without salvage value. This model is developed by using the differential equation...............

Keywords: Inventory, Deterioration, Quadratic demand, perishable, Weibull distribution

[1] Covert, R. P. and Philip, G. C., (1973). An EOQ model for items with Weibull distributed deterioration. AIIE transactions, 5, 323-326.
[2] Buzacott, J. A., (1975). Economic order quantity with inflation, 1975, Operations research quarterly, Vol 26,553-558.
[3] Dave, U. and Patel, L.K., (1981). (T, Si) – policy for inventory model for deteriorating items with time proportional demand. Journal of Operational Research Society, 32, 137-142.
[4] Misra, R. B., (1975). Optimum production lot size model for a system with deteriorating inventory. International Journal of Production Research. 13,495-505.
[5] Goyal, S.K. and Giri, B.C 'Recent trends in modeling of deteriorating inventory' (2001) European Journal of Operations research, Vol.134, pp.1-16.

Abstract: The objective of this technical paper was to propose an approach for solving polynomials of degree higher than two. The main concepts were the decomposition of a polynomial of a higher degree to the product of two polynomials of lower degrees and the n-D Newton-Raphson method for a system of nonlinear equations. The coefficient of each term in an original polynomial of order m will be equated to the corresponding term from the collected-expanded product of the two polynomials of the lower degrees based on the concept of undetermined coefficients............

Keywords: Roots of a Polynomial of a High Degree, the n-D Newton-Raphson Method, Undetermined Coefficients, Jacobian of the Functions, Matrix Inversion

[1] R.B. King, Beyond the quartic equation (Boston-Basel-Berlin: Birkhäuser, 1996).
[2] R.G. Kulkarni, Unified methods for solving general polynomial equations of degree less than fives, Alabama Journal of Mathematics, (Spring/Fall), 2006, 1-17.
[3] R.G. Kulkarni, Solving certain quintics, Annales Mathematicae et Informaticae, 37(10), 2010, 193-197.
[4] M. A. Faggal and D. Lazard, Solving quintics and septics by radicals, International Journal of Scientific and Research Publications, 4(12), 2014, 1-10.
[5] C. Boswell and M.L. Glasser, Solvable sextic equations, Cornel University Library, Mathematical Physics, arXiv:math-ph/0504001v1,1 April, 2005, 1-7.

Abstract: General relativistic mechanics in gravitational fields exterior to homogenous spherically symmetric solution is developed using our coordinate displacement approach. In curved Schwarzschild spacetime, the coordinates provide a reference frame for an observer making measurements at an infinite distance from the gravitational source of the Schwarzschild spacetime. The Schwarzschild metric describes the spacetime surrounding a spherical non-rotating mass. However, physical quantities measured by arbitrary observers are not specified directly by these coordinates but rather are computed from the metric. It is well known that Newton's theory of gravity is an approximation to Einstein's theory when the curvature of space time is negligible............

Keywords: Gravitational field, General relativity, Schwarzschild spacetime, Newton's equations of motion

[1]. Anderson, J. L. (1967a). Solutions of the Einstein Equation. In: Principles of Relativity Physics. Academic Press, New York, 372 – 402.
[2]. Anderson, J. L. (1967b). Experimental Test of General Relativity. In: Principles of Relativity Physics. Academic Press, New York 403 – 421.
[3]. Belbruno, E. and Pretorius, F. (2011). A dynamical System's Approach to Schwarzschild null Geodesics. Classical and Quantum Gravity, 28(2011) 195007.
[4]. Bergamann, P. G. (1987). Introduction to the Theory of Relativity. Prentice Hall. 203 – 215.
[5]. Chifu E.N. (2010). Motion of Test Particles and Orbits Exterior to Static Homogenous Prolate Spheroidal Spacetime. The African Physical Review, Vol4, 113 – 118.

Abstract: I give here an electronic algorithm of the order O(n3) which is a generalization of the atomic algorithm found in [6] and allows us to find the optimal Hamiltonian cycles. If the atomic algorithm (see [6] and [5] ) was inspired by the movement of the particles in the atom, the electronic algorithm is inspired by the resistor in the electrical circuit

Keywords: Graph, Hamilton cycles, P=NP, the travelling salesman problem,

[1] Lizhi Du. A polynomial time algorithm for hamilton cycle. IMECS, I:17–19, March 2010. Hong Kong.
[2] L.Lovasz. Combinatorial problems and exercises. Noth-Holland, Amsterdam, 1979.
[3] D.S.Johnson M.R.Garey. Computers and intractability:a guid to the theory of np-completeness. Freeman,San Francisco, 1979.
[4] R.Diestel. Graph theory. Springer, New York, 2000.
[5] M. Sghiar. Algorithmes quantiques, cycles hamiltoniens et la k-coloration des graphes. Pioneer Journal of Mathematics and
Mathematical Sciences, 17-Issue 1:51–69, May 2016..

Abstract: In existing literature the inventory models are developed under the assumption of demand rate to be constant or linear or quadratic. In this paper, an inventory model is developed where demand rate is generalized as a polynomial of nth degree with constant deterioration rate. The holding cost is a linear function of time. Shortages are not allowed. A numerical example has been illustrated using MATLAB to describe the model and the sensitivity analysis of various parameters is carried out with graphical and tabular data.

Keywords: Constant deterioration; Demand rate is a polynomial of nth degree; Inflation; Inventory; Time dependent holding cost

[1]. Agrawal, R., Rajput, D., Varshney, N.K.,( 2009) "Integrated inventory system with the effect of inflation and credit period"
International Journal of Applied Engineering Research, Vol. 4, No. 11, pp. 2334-2348.
[2]. Amutha R. and Chandrasekaran E. (2013) "An Inventory Model for Constant Demand with Shortages under Permissible Delay
in Payments" in IOSR Journal of Mathematics (IOSR-JM) e-ISSN: 2278-5728,p-ISSN: 2319-765X, Volume 6, Issue 5
[3]. He, Y., Wang, S., and Lai, K. (2010) "An optimal production-inventory model for deteriorating items with multiple-market
demand" European Journal of Operational Research, 203(3), pp 593–600.
[4]. Hou, K.L., Lin, L.C., (2009) "A cash flow oriented EOQ model with deteriorating items under permissible delay in payments"
Journal of Applied Sciences, Vol. 9, No. 9, pp. 1791-1794.
[5]. Hung, K. (2011) "An inventory model with generalized type demand, deterioration and backorder rates" European Journal of
Operational Research, 208(3), pp 239–242.

Abstract: In this paper we introduce and study the new class of sets, namely Regular Mildly Generalized Open (briefly, RMG-open) sets, Regular Mildly Generalized neighborhoods (briefly, RMG-nhd), RMG-interior and RMG-closure in topological space and also some properties of new concept has been studied.

Keywords: RMG-closed sets, RMG-open sets, RMG-neighborhoods, RMG-interior, RMG-closure.

[1] D. Andrijevic, Semi-preopen sets, Mat. Vesnik, 38(1986), 24-32.
[2] S. S. Benchalli and R.S. Wali, On RW-closed sets in topological spaces, Bull.Malaysian.Math. Sci. Soc. (2) 30(2) (2007), 99-110.
[3] J. Dontchev and T. Noiri, Quasi-normal spaces and π-g-closed sets,Acta Math. Hungar.,89(3)(2000), 211-219.
[4] T.Kong, R. Kopperman and P. Meyer, A topological approach to digital topology,Amer. Math. Monthly, 98 (1991), 901-917.
[5] A.S. Mashhour, M.E. Abd. El-Monsef and S.N. El-Deeb, On pre continuous mappings and weak pre-continuous mappings, Proc Math, Phys. Soc. Egypt, 53(1982), 47-53.