iosr-Jm   Volume-13 ~ Issue-2 ~ Mar-Apr 2017

Abstract: In this paper, we have studied the Bézier variant of Chlodovsky-Durrmeyer operators 𝐷𝑚,𝜗 for function f measurable and locally bounded on the interval [0,∞). In this we improved the result given by Ibikl E. And Karsli H. [14]. We estimate the rate of pointwise convergence of 𝐷𝑚,𝜗𝑓 (𝑥) at those 𝑥>0 at which the one-sided limits 𝑓 𝑥+ ,𝑓(𝑥−) exist by using the Chanturia modulus of variation. In the special case 𝜗=1 the recent result of Ibikl E. And Karsli H. [14] concerning the Chlodowsky-Durrmeyer operators 𝐷𝑚 is essentially improved and extended to more general classes of functions.

Keywords: Rate of convergence, Chlodovsky-Durrmeyer operator, Bézier basis, Chanturia modulus of variation, p-th power variation

[1]. Agratini O., 2001, "An approximation process of Kantorovich type", Math. Notes (Miskolc), No. 1, pp. 3-10.
[2]. Albrycht J. and Radecki J., 1960, "On a generalization of the theorem of voronovskaya", Zeszyty Nauk. Uniw. Mickiewicza No. 25, pp. 3-7.
[3]. Aniol G. and Pych-Taberska P., 2001, "Some properties of the Bezier-Durremeyer type operators", Comment. Math. Prece Mat. 41, pp.1-11.
[4]. Bezier,P. 1972, "Numerical Control Mathematics and Applications", Wiley, London.
[5]. Butzer P. L. and Karsli H., 2009, "Voronovskaya-type theorems for derivatives of the Bernstein- Chlodovsky polynomials and the Szasz-Mirakyan operator", Comment Math. 49, No.1, pp. 33-57..

Abstract: At school level students learn about bisection of any arbitrary angle or repeated bisections if required with the help of straightedge and compass only. They do not come across about angle trisection or other higher multisections with the help of only these tools. In 1837 P. wantzel a French mathematician proved the impossibility of trisection of any arbitrary angle with only stranghtedge and compass except some specified angles. In my present work I have endeavored to demostrate methods for drawing very approximate multisections of any arbitrary angles lying between 0 to 900 with the help of only stranghtedge and compass.
I came to know about impossibility of angle trisection at my B.Sc. standard in 1970 through a mathematical journal and since then I was working on it. Thus my present work is the result of many years of dedicated efforts.

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Abstract: I propose as a research service learning project "A model of Implementation the Agro-tourism in Romanian Sea-side Area (Dobrodgea) on the basis of USA Experience", that I view as a part of teaching about globalization, and involving of mathematics in direct service to the community, which includes also the indirect service , that are preparation and reflection about the service experience.I choose that application for the following reasons:-at present, the tourism in Dobrodgea zone ensures 45% of the Romanian tourism, including almost all kinds of tourism developed in Romania, inclusively the agro-tourism (I mean the rural one) of relatively incipient forms

[1]. Stoica, Marcel and MaiferDemirbec. Case and practical applications concerning the economic forecast. , Ed. Matrix Rom, Bucharest, 2002, ISBN 973-685-418-3
[2]. Demirbec, Maifer. Prospects of developing in Dobrogean tourism. , Ed. Matrix Rom, Bucharest, 2003, ISBN 973-685-602-X
[3]. BMCC Service Learning Faculty Development, 24 February 2017, WORKSHOP

Abstract: This paper attempt to estimate and forecast the total cost of Marsland Aviation domestic services. The data were obtained from the Planning Directorate of Sudan Civil Aviation Authority, Air Transport Directorate and Marsland Aviation. The data were statistically analyzed the annual cost function of Marsland Aviation for the period from 2004 to 2013. The researcher study was to find out how the total cost (TC) behaves in relation to the domestic output, in revenue passenger (PAX), cargo/ freight (FRT), fuel cost (FC) and load factor (LF). The result shall lead us to estimate an airline cost function, by using Classical Normal Regression model (CNLRM) to analyze the data obtained for this research. The model is represented as follows...................

Keywords: Classical Linear Regression Model, Passenger, Freight, Fuel Price, Load Factor.

[1]. G.M. Marsland Airlines Statistics Section (2012), Khartoum, Sudan.
[2]. C.A.A., (2012). Sudan Civil Aviation Planning Directorate, Khartoum, Sudan.
[3]. Gujarati, D.N. and Porter, D.C. (2009). Basic Econometrics, Fifth Edition, Uni McGraw-Hill Companies.ted State Military Academy,West Point and University of Southern California.
[4]. Maddala, G.S. (1992). Introduction to Econometrics, Second Edition. University of Florida, Macmillan Publishing Company.
[5]. Greene, W.H. (1951). Econometric Analysis, Fifth Edition. New York University, Upper Saddle River, New Jersey

Abstract: This paper attempt to estimate and forecast the total cost of Badr Airlines domestic services. The data were obtained from the Planning Directorate of Sudan Civil Aviation Authority and Air Transport Directorate. The data were statistically analyzed the annual cost function of Badr Airlines for the period from 2004 to 2013. The researcher study was to find out how the total cost (TC) behaves in relation to the domestic output, in revenue passenger (PAX), cargo/ freight (FRT), fuel cost (FC) and load factor (LF). The result shall lead us to estimate an airline cost function, by using Classical Normal Regression model (CNLRM) to analyze the data obtained for this research. The model is represented as follows...............

Keywords: Classical Linear Regression Model, Passenger, Freight, Fuel Price, Load Factor.

[1]. S.C.A.A. (2012). Sudan Civil Aviation Integrated Statistics Centre, Khartoum, Sudan.
[2]. C.A.A., (2012). Sudan Civil Aviation Planning Directorate, Khartoum, Sudan.
[3]. Gujarati, D.N. and Porter, D.C. (2009). Basic Econometrics, Fifth Edition, Uni McGraw-Hill Companies.ted State Military Academy,West Point and University of Southern California.
[4]. Maddala, G.S. (1992). Introduction to Econometrics, Second Edition. University of Florida, Macmillan Publishing Company.
[5]. Greene, W.H. (1951). Econometric Analysis, Fifth Edition. New York University, Upper Saddle River, New Jersey.
[6]. Rawlings, J.O., Pantula, S.G. and Dickey D.A. (1932). Applied Regression Analysis: A Research Tool, Second Edition. North Carolina State University, Springer, USA

Abstract: In this paper we have calculated the electromagnetic field components in a skew uniform magnetic fields superimposed on Kerr Newman back ground geometry. The rotation axis of the Kerr Newman black hole makes an angle with the asymptotic magnetic field. We have compared the result with those of the corresponding Kerr black hole..

Keywords: Kerr Newman black hole, Electromagnetic field

[1]. Bicak,J and Janis,V. :Mon. Not. R. Astron. Soc. 1985 ,212, 899
[2]. Bicak.J and. Dvorak.L: Gen. Rel. Grav. 1976.7, 959
[3]. Chitre ,D.M and Vishveshwara,C.V .:1975, Phys. Rev. D12 ,153
[4]. King,A.R.:1976 ,Phys. Letters, 56A.339
[5]. King,A.R and Lasota.J.P.:1977Astron.Astrophy.58.175
[6]. Kinnersley,W.: J. Math. Phys. 10, 1195 (1969)

Abstract: In this paper we present an important result that a nil subnear-ring of a semiprime strictly left Goldie near-ring is nilpotent. It is to be noted that the essentiality of left near-ring subgroup here, arises as crucial from it's feeble nature. In contrast to such a result in ring theory, the crucial role played by substructures already mentioned appears here with very fascinating distinctiveness.

Keywords: Near-ring, semiprime, nil subring, nilpotent subring, sequentially nilpotent, Goldie near-ring

[1]. Chowdhury, K.C. : Goldie near-rings, bull. Cal. Math.soc.80(1988), no. 4,261-269
[2]. Goldie modules, IJPAM 19(7), 641-652, july 1988
[3]. Goldie M-group, Australian math. Soc.
[4]. Goldie theorem analogue for Goldie near-rings,IJPAM,20(2),141- 149,Feb,1989
[5]. A note on regular left Goldie near-ring, nat.acad. sci. letters,vol.12, no.(1989),433-435

Abstract: Using Nevanlinna value distribution theory, we study weighted sharing and uniqueness of entire functions concerning differential polynomials and obtain some results which improve the recent results due to Waghamore and Anand[1].

Keywords: Differential Polynomials, Entire Functions, Uniqueness, Value Distribution Theory, Weighted Sharing.

[1] H. P. Waghamore and S. Anand, Generalization of Uniqueness of Meromorphic Functions Sharing Fixed Point, Appl. Math., 2016, 7, pp. 939-952.
[2] W.K.Hayman,Meromorphic Functions, The Clarendon Press, Oxford (1964).
[3] I. Lahiri, Weighted value sharing and uniqueness of meromorphic functions, Complex Var. Theory Appl., 2001, 46, pp.241-253.
[4] M. L. Fang and X. H. Hua, Entire functions that share one value, J. Nanjing Univ. Math. Biquarterly, 1996, 13, pp. 44-48.
[5] M.L. Fang and W. Hong, A unicity theorem for entire functions concerning differential polynomials, Indian J. Pure Appl. Math., 2001, 32, pp.1343-1348.

Abstract: This paper deals with the key issue of management to improve the allocation capability, facilitating the optimization of the objective in minimizing the cost, with the accuracy in dynamic allocation of nearest customers to depot. A method has been proposed to solve the Multi Depot Vehicle Routing Problem (MDVRP) based on Ant Algorithm which is a modified version of the traditional Ant colony Optimization (ACO). Depending on the stochastic demand, distance between depot to customer and customer to customer, the solution to MDVRP is calculated with variant of Ant Algorithm..

Keywords: Ant Algorithm, customer demand, Multi Depot Vehicle Routing, Optimization, stochastic demand.

[1]. Tan, K.C., Lee, L.H., and Ou, K., : Artificial intelligence heuristics in solving vehicle routing problems with time window
constraints. Engineering Applications of Artificial Intelligence, vol. 14, 2001, 825-837
[2]. Dimitris J.Bertsimas.,: A vehicle routing problem with stochastic demand. Operations Research Society of America. vol 40, 1992, 3
[3]. Cheong, C.Y., Tan, K.C., Liu, D.K., Xu, J.X., : A multi objective evolutionary algorithm for solving vehicle routing problem with
stochastic demand. IEEE congress on Evolutionary Computation., 2006, 1370-1377
[4]. Nagalakshmi, M.R., Mukul Tripati., Nagesh Shukla., Tiwari, M.K., : Vehicle routing problem with stochastic demand (VRPSD):
optimization by neighbourhood search embedded adaptive ant algorithm (ns-AAA). Int. J. Computer Aided Engineering and
Technology, vol-1, No.3, 2009, 300- 321
[5]. Hjorring, C., : The Vehicle Routing Problem and Local Search Metaheuristics. Chapter 2. PhD thesis. Department of Engineering
Science, The University of Auckland. 1995.

Abstract: In this paper a class of sets called Nano generalized pre regular closed sets is introduced and its properties are studied. Further the notation of Nano pre regular 1/ 2 T space and Nano generalized pre regular continuity are discussed.

Keywords: Nano Generalized Pre Regular Closed sets, Nano Pre Regular 1/ 2 T spaces, Ngpr continuous, Ngpr irresolute.

[1] H. Maki ,J. Umehara and T. Noiri , "Every Topological space is pre- 1/ 2 T ", Mem. Fac. Sci. Kochi Univ. Ser.A . math., 17(1996),
33-42.
[2] K. Bhuvaneswari and K. Mythili Gnanapriya, "Nano Generalized pre Closed sets and Nano Pre Generalized Closed Sets in Nano
topological spaces", International Journal of Innovative Research in Science, Engineering And Technology. Volume 3 Issue 10, Oct
2014.
[3] K. Bhuvaneswari and K. Mythili Gnanapriya, "Nano Generalized Closed sets in Nano topological spaces", International Journal of
Scientific and Research Publications, Volume 4, Issue 5, May 2014 .
[4] M. Lellis Thivagar and Carmel Richard "Note on Nano topological spaces" – (communicated).
[5] M. Lellis Thivagar and Carmel Richard, "On Nano Continuity", Mathematical Theory and Modeling, Vol- 3, No. 7, 2013.
[6] Levine N. (1970), "Generalized closed sets in Topology", Rend. Circ. Math. Palermo, 19, 89-96.

Abstract: In this paper, we show that by a certain change of variables any equation of a particular type can be transported in to a canonical form which is associated with its type. In this, we refine our method in such a manner that the solutions retain their order and accuracy even in the vicinity of the singularity. Further, to solve some boundary value problems, we use iterative method, that is, the alternating group explicit
method to solve linear equation.

Keywords: Boundary value problem, Principal part, Partial differential equation, AGE method, Newton AGE method

[1]. JAIN, M.K., IYENGAR, S.R.K. AND JAIN, R.K.,(1993) numerical methods for scientific and engineering computation, 3rded: wiley eastern ltd..
[2]. EVANS, D. J., Group Explicit Methods for the Numerical Solution of Partial Differential Equations, Gordon and Breach Science Publishers.
[3]. EVANS, D. J. And AHMAD, A.R.,(1996). Comparison of SOR and AGE Methods for Solution of the Two-Point Boundary Value Problem, Advances in Engineering Software.
[4]. VARGA, R. S., (1962). Matrix Iterative Analysis, Prentice Hall, Englewood Cliffs, New Jersey.
[5]. KELLER, H. B.,(1968). Numerical Methods for Two Point Boundary Value Problem, Blaisdell Pub. Co.

Abstract: Let be a non-complete connected graph of order greater or equal to 3 with vertex set and edge set . An interior dominating set of is called a connected interior dominating set of if the subgraphs induced by is connected. The minimum cardinality of a connected interior dominating set of , denoted by , is called the connected interior domination number. A connected interior dominating set of cardinality is called a of . In this note, we revisit these concepts for some special graphs. Further, we characterize the connected interior dominating sets in the join and corona of two graphs and give some important results.

Keywords: Non-complete connected graphs, interior dominating set, connected interior dominating set, special graphs, join, corona

[1]. E. C. Castillano and R. A. L. Ugbinada, Secure domination in the joins of graphs, Applied Mathematical Sciences, Vol. 8, 2014, 5203-5211.
[2]. T. W. Haynes, S. T. Hedetniemi, and P. J. Slater, Fundamentals of domination in graphs, Marcel Dekker, New York, 1998.
[3]. E. J. Cockayne, and S. T. Hedetniemi, Towards a theory of domination in graph, Networks, 1977, 247-261.
[4]. O. Ore, Theory of graphs. Amer. Mathe Soc. Colloq. Publication (Amer. Soc., Providence, RI), 1962
[5]. J. Tarr, Domination in graphs, University of South Florida, 2010, 34-36.
[6]. E. Delavina, R. Pepper and B. Waller, Lower bounds for the domination number, Discussiones Mathematicae Graph Theory, January 2010

Abstract: The objective of the present paper is to analyze the heat and mass transfer effects on an unsteady MHD flow of a chemically reacting micropolar fluid past an infinite vertical porous plate through a porous media in the presence of thermal radiation with Hall current, viscoelastic and Soret effects by taking into account. The governing equations are transformed into dimensionless equations and then solved analytically using Perturbation technique. The expressions for the velocity, microrotation, temperature and concentration have been derived and its behavior is computationally discussed with reference to different pertinent flow parameters with the help of graphs. Also the influence of the various flow parameters on the skin friction coefficient, couples stress coefficient, Nusselt number, and Sherwood number are presented numerically in a tabular form.

Keywords: Micropolar fluid, Perturbation technique, Hall current and Soret effects, Chemical reaction, Porous medium, heat source

[1] A.C.Eringen, Theory of micropolar fluid, Journal of Mathematics and Mechanics,16, 1966, 1-18
[2] A.C.Eringen, Theory of thermomicrofluids, Journal of Mathematical Analysis and Applications, 38(2), 1972, 480–496.
[3] Ariman T, Turk MA, Sylvester ND, Microcontinuum fluid mechanics-a review. Int J Eng Sci, 11, 1973, 905–930.
[4] Prathap Kumar J, Umavathi JC, Chamkha Ali J, Pop I. Fully developed free convective flow of micropolar and viscous fluids in a vertical channel. Appl Math Model, 34, 2010, 1175–86.
[5] Srinivasacharya D, Ramana murthy JV, Venugopalam D, Unsteady stokes flow of micropolar fluid between two parallel porous plates, Int J Eng Sci, 39, 2001, 1557–63.