iosr-Jm   Volume-11 ~ Issue-1 ~ Jan-Feb 2015

Abstract: Descriptor dynamic control system application plays an important role in modern science and mathematics. This paper focuses on an approximate solution to some kind of descriptor dynamic control system with constant coefficient . The non-classical variational approach is developed for this purpose to obtain a very suitable approximate solution with a high degree of accuracy, and freedom. Some illustrations have been provided to show the effectiveness of this approach.

Keywords: consistent initial condition, Drazin inverse, linear descriptor systems, non-classical variational approach.

[1] k.E.Brenan, S.L. Campblle, Numerical solution of initial value problem in differential-algebraic equations ( Elsevier, new York,1989). [2] S.L.Campblle, Singular system of differential equations I ( Pitman Advanced Publishing Program1980).

[3] S.L. Campbell , Singular systems of differential equations II ( Pitman Advanced Publishing Program 1982).

[4] S.L.Campbell, C.D. Mayer, Applications of the Drazin inverse to Linear System of Differential Equation with Singular Constant Coefficients, Siam J.Appl., 31(1976):411.425.

[5] G.R.Duan, Analysis and Design of Descriptor Linear System, Advances in Mechanics and mathematics ( Sipinger, 2010).

[6] G.Denk , R. Winkler , Modeling and simulation of transient noise in circuit simulation, international journal of mathematical and computational modeling of dynamical systems ,13(4),(2007),pp.383-394

Abstract: The paper shows that Discriminant analysis as a general research technique can be very useful in the investigation of various aspects of a multi-variate research problem. It is sometimes preferable than logistic regression especially when the sample size is very small and the assumptions are met. Application of it to the failed industry in Nigeria shows that the derived model appeared outperform previous model build since the model can exhibit true ex ante predictive ability for a period of about 3 years subsequent.
Keywords: Factor Analysis, Multiple Discriminant Analysis, Multicollinearity

[1]. Alexakos, C. E.(1966). Predictive efficiency of two multivariate statistical techniques in comparison with clinical predictions.
Journal of Educational Psychology, 57, 297-306.
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of discriminant functions. American Educational Research Journal, No. 6, 315-328
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Abstract: The research was an experimental study carried out to determine the efficacy of Problem-Based Learning on senior secondary school students' achievement in trigonometry. A sample of 365 out of 4162 senior secondary school two students from four secondary schools in Northern educational zone of cross River State was used. The items of the instrument were validated by two mathematics educators, two experts in measurement and evaluation and one mathematics teacher. Mean and standard deviation were used to answer the research questions while ANCOVA was employed to test the hypotheses at .05 level of significance. The result was analyzed to verify whether any significant difference existed in the achievement of problem-based learning group and conventional group, as well as significant gender difference in their achievement. The study revealed that there existed a significant difference between the experimental and control groups in favour of the experimental class.

[1]. Abakpa, B.O. (2011). Effects of mastery learning approach on senior secondary school students' achievements and interest in geometry. Unpublished Ph.D Thesis. University of Agriculture, Makurdi.
[2]. Abdullah, N.I., Tarmizi, R.A. & Abu, R. (2010). The effects of problem-based learning on mathematics performance and effective attributes in learning statistics at form four secondary level. ELSEVIER science direct, procedural social and behaviour sciences 8, 370-376. Retrieved on5/6/2012 from www.simedirect.com
[3]. Achuonye, K.A. (2004). The effect of problem-based learning strategy on higher cognitive skills performance in biology at the senior secondary school level. An unpublished Ph.D Thesis. University of Port Harcourt, Port Harcourt.
[4]. Chire, S.T.C. & Akem, J.A. (2010). Mathematics for everyday living: implication for tertiary education. CAPS Journal of Multi-disciplinary 1(1), 222-228.
[5]. Elliot, S.N; Kratochwill, T.R, Cook, J.I. & Travers, T.P. (2002). Educational psychology: Effective teaching, effective learning (3rd eds). Boston: McGraw-Hill.
[6]. Etukudo, U.E. (2000). The effect of improvised instructional materials on students' performance in mathematics. Proceedings of the 41st annual conference of STAN, Pg. 228-232.

Abstract: We have defined a new polynomial on the interval [0,1+𝑟𝑛 ] for Lebesgue integral in𝐿1norm as

[1]. A. Habib, "On the degree of approximation of functions by certain new Bernstein typePolynomials," Indian J. pure Math., vol. 7, pp. 882-888, 1981.
[2]. A Habib , S Umar and H H Khan , " On the Degree of Approximation by Bernstein type Operators"
[3]. Communications , de la Fac. Des Sc. De L‟Univ. d‟Ankara, Tom 33 Annee 1984 pp.121-136
[4]. A. Habib & S. Al Shehri(2012) "On Generalized Polynomials I " International Journal of Engineering Research and Development e-ISSN:2278-067X, 2278-800X, Volume 5, Issue 4 ,December 2012 , pp.18-26
[5]. E. Cheney and A. Sharma, "On a generalization of Bernstein polynomials," Rev. Mat. Univ. Parma, vol. 2, pp. 77-84, 1964.

Abstract: Under the assumption that there exist a subject whose performance, observed value or score may be regarded as an average or standard value or score to be used as reference, standard, average value or score for comparison with the performance or score of other subjects on a condition in a population, this paper developed what is here referred to as metric distance measured in terms of the number of subjects to determine how many subjects' performance or scores a randomly selected subject is above (better, worse), the same or lower (worse, better), than their own relative to the standard with respect to a condition of research interest in a population. The farther away the so-called metric distance, expressed in terms of number of subjects, a randomly selected subject is from the average or standard subjects' performance value or score, the better or less serious (the worse or more serious) than that subjects' condition relative to, that is in comparison with the average, reference or standard subjects' condition relative to, the average, reference or standard subjects' condition, that is in comparison with the conditions of some other subjects in the study population. Test statistics are developed for use in testing the statistical significance of the metric distance of a randomly selected subject as well as the statistical significance of the difference between the metric distances of any two randomly selected subjects in the population. The proposed method is illustrated with some sample data.

Keywords: Metric Distance, Score, Relative, Standard value distance, Measure.

[1]. Siegel S. (1956): Nonparametric Statistics for the Behavioral Sciences. McGraw Hill Kogakusha Ltd. Tokyo.
[2]. Mahalanobis, P.C. (1936), "On the Generalized Distance in Statistics". Proceedings of the National Institute of Sciences of India 2(1):49-55.
[3]. Machlachlan, G.J. (1992) Discriminant Analysis and Statistical Pattern Recognition. Wiley Intersciences.
[4]. Dodge, Y. (2003): Oxford Dictionary of Statistical Terms, Oxford University Press.

Abstract: The goal of the paper is to examine the concentration of the longitudinal dispersion phenomenon arising in fluid flow through porous media. The solution of the Burger's equation for the dispersion problem is presented by approach to Sumudu transformation. The solution is obtained by using suitable conditions and is more simplified under the standard assumptions.

Keywords: Longitudinal Dispersion phenomenon, porous media, Sumudu transform.

[1]. Kilicman, V. G. Gupta and B. Shrma, On the solution of fractional Maxwell equations by Sumudu transform, J. of Math Research 2(4) (2010) 147-151.
[2]. E. Hopf, The Partial Differential Equation ut+uux=μuxx comm, Pure Appl. Math. 3 (1950) 201-230.
[3]. F. B. M. Belgacem, A. A. Karabali and S. L. Kalla, Analytical investigations of the Sumudu transform and applications to integral production equations, Math. Prob. In Engg. 3 (2003) 103-118.
[4]. G. K. Watugala, Sumudu transform: a new integral transform to solve differential equations and control engineering problems, Int. J. of Math. Edu. In Sci. and Tech. 24(1) (1993) 35-43.
[5]. H. Eltayeb, A. Kilicman and B. Fisher, A new integral transform and associated distributions, Int. Tr. and Sp. Fn.21(5-6) (2010) 367-379.

Abstract: An analysis is performed to study the effect of Thermal radiation and first order Chemical reaction on unsteady natural Convective flow of a viscous incompressible Conducting fluid past over an infinite isothermal vertical oscillating plate in Porous medium. The dimensionless governing equations are solved using the Laplace transform technique. The velocity, temperature and concentration are studied for different parameters like the magnetic field parameter, radiation parameter, chemical reaction parameter, thermal Grashof number, Schmidt number, phase angle and time. It is observed that the velocity increases with decreasing magnetic field parameter or radiation parameter. It is also observed that the velocity increases with decreasing magnetic field parameter, radiation parameter and phase angle.

Keywords: Chemical reaction, magnetic field, oscillating vertical plate, porous medium, radiation.

[1]. Soundalgekar V. M. : Free convection effects on the Flow Past a Vertical Oscillating Plate, Astrophysics Space Science, 66(1979), 165-172.
[2]. Soundalgekar V. M. and Akolkar S. P. : Effects of free convection and mass transfer on flow past a vertical oscillating plate, Astrophysics and Space Science, 89(1983), 241-254.
[3]. Das U. N., Deka R. K. and Soundalgekar V. M. : Effects of mass transfer on flow past an impulsively started vertical infinite plate with constant heat flux and chemical reaction, Forschung in Ingenieurwesen, 60(1994), 284-287.
[4]. MHD Flow Past a Vertical Oscillating Plate with Radiation and chemical Reaction in Porous Medium
[5]. Das U.N., Deka R.K. and Soundalgekar V.M. : Transient free convection flow past an infinite vertical plate with periodic temperature variation, Journal of Heat Transfer, Trans. ASME, 121(1999), 1091-1094.

Abstract: The n -path graph PG (G) n of a graph G is a graph having the same vertex set as G and 2 vertices u and v in PG (G) n are adjacent if and only if there exist a path of length n between u and v in G . In this paper we find n -path graph of some standard graphs. Bounds are given for the degree of a vertex in PG (G) n . We further characterise graphs G with PG (G) = G 2 , PG (G) = G 2 and n PG (G) = K 2
Keyword: n -path , distance, diameter. AMS subject classification: 05C76

[1]. S. Arumugam, S. Velammal, Edge Domination in Graphs, Taiwanese Journal of mathematics, 2(2)(1998), 173-179.
[2]. F.Harary, Graph Theory, Addison Wesley, Reading,Mass, 1972.

Abstract: Analogous to Maxwell stress tensor in electric and magnetic fields, a stress tensor is defined in a vorticity field. Thus by treating vortices as physical structures, it is possible to study the forces on a surface element in it. Based on this the force between vortex lines, the pressure and the shearing stress that deform the volume element can also be defined.

Keywords: Enstrophy, Maxwell stress tensor, static pressure, vorticity equation, vorticity stress tensor.

[1]. Casperson, L. W. Forces on permeable conductors in magnetic fields. Am. J. Phys, 70(2), 2002,163-168.
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Abstract: This work described the determination of energy involved in a stepwise size reduction of maize, using a numerical approach. It adopts an implicit one-step third-derivative method of the form;

[1]. Bond, F. C. 1952. The third theory of comminution. Transactions of the AIME 193(2): 484
[2]. Famurewa J.A.V(2007). The Development and Evaluation of Four Roller Flour Mill with Parallelogram Configuration, Intenational Journal of Food Engineering. 3(6): 1-7.
[3]. Famurewa O K E and Olorunsola S. A (2013). The effect of involving more derivative properties on the accuracy of an implicit one – step method. Asian Journal of Natural and Applied Sciences . 2 (3): 142-157.
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Abstract: This paper uses the DEA models to rank the efficiency of Indian non-life insurance firms over the period 2008-2013 with Expenses, Capital, Premium and Investment income variables in the modelling. These basic DEA models identify adequately the inefficient firms, but are weak in discriminating among those found to be efficient. To improve the discrimination, we used the Cross-Efficiency and the Super-Efficiency DEA models.

Keywords: Efficiency, Data Envelopment Analysis(DEA),Non-life Insurance Firms

[1]. Charnes, A., Cooper, W. W. and Rhodes, E. (1981) "Measuring the Efficiency of Decision-Making Units", European Journal of Operations Research, 2: 429-444.
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Abstract: The present paper deals with the different geometrical properties of an unified contact Riemannian manifold [7] equipped with semi-symmetric metric S -connection. Also the form of curvature tensor R  of the manifold relative to this connection has been derived.

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Abstract: In this paper, we considered the role of penalty when the higher-order conjugate gradient method (HCGM) was used as a computational scheme for the minimization of penalised cost functions for optimal control problems described by linear systems and integral quadratic costs. For this family of commonly encountered problems, we find out that the conventional penalty methods require very large penalty constants for good constants satisfaction. Numerical results shows that, as the penalty constant tend to infinity, the convergence rate of the method becomes poor. To circumvent the poor convergence rate of the penalty method, the HCGM was often considered as a good substitute to accelerate the convergence.

Keywords: Conjugate Gradient Method, Optimal Control, Non-linear Systems, Positive Definite Matrix, Unconstrained Problems.

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Abstract: This is an extension of the co-operative advertising model developed earlier by the authors. We develop a manufacturer-retailer channel co ordination where the demand is modeled as a multiplicative effect of price and an additive sales response function. We change the form of demand here as an extension to earlier model developed by the authors .We use isoelastic form of the price dependent demand instead of the linear form to observe changes in the model if any. We develop both sequential and simultaneous moves non co-operative game structures where both retailer and manufacturer act simultaneously and independently and compare them through propositions. Finally we develop a cooperative model and discuss the optimality of pareto efficient scheme.

Keywords: Cooperative advertising, Game theory, Nash equilibrium, Stackelberg equilibrium, Supply chain coordination

[1]. Kuehn, A.A., (1962): How advertising performance depends upon other marketing Factors, Journal of Advertising Research, 2 (1), 2–10.
[2]. Thompson, G.L., Teng, J., (1984): Optimal pricing and advertising policies for new product oligopoly models, Marketing Science, 3 (3), 148–168.
[3]. Jorgensen, S., Zaccour, G., (1999): Equilibrium pricing and advertising strategies in a marketing channel, Journal of Optimization Theory and Applications, 102 (1), 111–125.
[4]. Jorgensen, S., Zaccour, G.,( 2003a): Channel coordination over time: Incentiveequilibria and credibility, Journal of Economic Dynamics and Control, 27 (5), 801–822.
[5]. Jorgensen, S., Zaccour, G., (2003b): A differential game of retailer promotions, Automatica, 39 (7), 1145–1155.

Abstract: We consider an extension of the co-operative advertising model developed earlier by the authors. We consider a manufacturer-retailer channel co-ordination where the demand is modeled as a multiplicative effect of price and an additive sales response function. We develop both sequential and simultaneous moves non co-operative game structures where both retailer and manufacturer act simultaneously and independently and compare them through propositions. Finally we develop a cooperative model and discuss the optimality of pareto efficient scheme.

Keywords: Cooperative advertising, Game theory, Nash equilibrium, Stackelberg equilibrium, Supply chain coordination

[1]. Buzzell, R.D., Quelch, J.A., Salmon, W.J., 1990. The costly bargain of trade promotion. Harvard business Review 141-149.
[2]. Fulop, C., 1988. The role of advertising in the retail marketing mix. International Journal of Advertising 7, 99-117.
[3]. Solanki Krishna, Gor Ravi, (2013): A Game theoretic model on cooperative advertising where demand is dependent on price and advertising expenditures, Journal of data and information processing, volume I, iss 2, 28-33.
[4]. Kuehn, A.A., (1962): How advertising performance depends upon other marketing Factors, Journal of Advertising Research, 2 (1), 2–10.
[5]. Thompson, G.L., Teng, J., (1984): Optimal pricing and advertising policies for new product oligopoly models, Marketing Science, 3 (3), 148–168.
[6]. Jorgensen, S., Zaccour, G., (1999): Equilibrium pricing and advertising strategies in a marketing channel, Journal of Optimization Theory and Applications, 102 (1), 111–125.

Abstract: We consider a manufacturer retailer channel co ordination in a scenario where the demand is dependent on the price and the advertising expenditures by the manufacturer and the retailer, the channel members. We extend a previous model developed by the authors to a non cooperative simultaneous move nash game frame work. We also derive pareto efficient schemes in case of a cooperative problem.

Keywords- Cooperative advertising, Game theory, Nash equilibrium, Stackelberg equilibrium, Supply chain coordination

[1]. Kuehn, A.A., (1962): How advertising performance depends upon other marketing Factors, Journal of Advertising Research, 2 (1), 2–10.
[2]. Thompson, G.L., Teng, J., (1984): Optimal pricing and advertising policies for new product oligopoly models, Marketing Science, 3 (3), 148– 168.
[3]. Jorgensen, S., Zaccour, G., (1999): Equilibrium pricing and advertising strategies in a marketing channel, Journal of Optimization Theory and Applications, 102 (1), 111–125.
[4]. orgensen, S., Zaccour, G.,( 2003a): Channel coordination over time: Incentiveequilibria and credibility, Journal of Economic Dynamics and Control, 27 (5), 801–822.
[5]. Jorgensen, S., Zaccour, G., (2003b): A differential game of retailer promotions, Automatica, 39 (7), 1145–1155.

Abstract: In this paper we introduce and study about pseudo symmetric ideals and P-pseudo symmetric ideals in ternary semi rings. It is proved that (1) every completely P-Semiprime ideal A in a ternary semi ring T is a Ppseudo symmetric ideal, (2) If A is a P-pseudo symmetric ideal of a ternary semi ring T then (i) A2 = {x : xn ∈ A for some odd natural number n∈ N} is a minimal completely P-Semiprime ideal of T, (ii) A4 = {x : < x >n  A for some odd natural number n} is the minimal P-Semiprime ideal of T containing A, (3) Every P-prime ideal Q minimal relative to containing a P-pseudo symmetric ideal A in a ternary semi ring T is completely P-prime,
and (4) Let A be an ideal of a ternary semi ring T. Then A is completely P-prime iff A is P-prime and P-pseudo symmetric. Further we introduced the terms pseudo symmetric ternary semi ring and P-pseudo symmetric ternary semi ring. It is proved that (1) Every commutative ternary semi ring is a pseudo symmetric ternary semi ring, (2) Every commutative ternary semi ring is a P-pseudo symmetric ternary semi ring, (3) Every pseudo commutative ternary semi ring is a P-pseudo symmetric ternary semi ring and (4) If T is a ternary semiring in which every element is a midunit then T is a P-pseudo symmetric ternary semiring. Mathematical Subject Classification: 16Y30, 16Y99.

Key Words: Pseudo Symmetric ideal, P-pseudo symmetric ideal, P-Prime, Completely P-Prime, P-Semiprime, Completely P-Semiprime, Pseudo Commutative, mid unit.

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Algebra and Related Topics, World Scienti¯c, New Jersey, 2003, 3IV3{355.
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2(2012), 89-93.
[3]. Dutta, T.K. and Kar, S., A note on regular ternary semirings, Kyung-pook Math. J., IV6 (2006), 357{365.
[4]. Kar, S., On quasi-ideals and bi- ideals in ternary semirings, Int. J. Math.Math.Sc., 18 (2005), 3015{3023.
[5]. Lehmer. D. H., A ternary analogue of abelian groups, Amer. J. Math., 59(1932), 329-338.
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[7]. Madhusudhana Rao. D,Anjaneyoulu. A and Gangadhara Rao. A., Pseudo Symmetric Γ-ideals in Γ- Semigroups-Internationla
eJournals of Mathematics and Engineering, 116(2011), 1074-1081.

Abstract: Let G = (V, E) be a simple graph. A set S of vertices in a graph G is said to be a total dominating set if every vertex v  V is adjacent to an element of S. A total dominating set S of G is called a connected total dominating set if the induced subgraph <S> is connected. In this paper, we study the concept of connected total domination polynomials of the star graph Sn and wheel graph Wn. The connected total domination polynomial of a graph G of order n is the polynomial.

[1]. Alikhani. S and peng. Y.H, 2009, Introduction to Domination polynomial of a Grpah, ar Xiv : 0905 .225[v] [math.co] 14
may.
[2]. Alikhani. S and Peng. Y. H, 2008, Dominating sets and Domination polynomials of cycles, Global Journal of Pure and
Applied Mathematics, Vol.4, No.2.
[3]. Haynes. T.W, Hedetniemi. S.T, Slater. P.J, 1998, Fundamentals of Domination in Graphs, Marcel Dekker, Newyork.
[4]. Sahib Shayyal Kahat, Abdul Jalil. M, Khalaf, Roslan Hasni, 2014, Dominating sets and Domination polynomials of stars ,
Asian Journal of Basic and Applied Sciences, 8(6).
[5]. Shahib.Sh.Kahat, Abdul Jalil M.Khalaf and Roslan Hasni,2014, Dominating sets and Domination polynomials of
wheels, Asian Journal of Applied Sciences, Vol.2, Issue 03.