iosr-Jm   Volume-11 ~ Issue-3 ~ May-June 2015

Abstract: The objective of the present paper is to study the effects of chemical reaction on a three dimensional MHD mass transfer flow past a vertical plate in presence of heat source. The governing non dimensional equations relevant to the problem are solved by regular perturbation technique. Under certain assumptions, the solutions for velocity field, temperature distribution and species concentration are obtained. The expressions for skin-friction, Nusselt number and Sherwood number are performed. The influences of various parameters on the velocity field, temperature field, concentration field, skin-friction, Nusselt number and Sherwood number are studied graphically. The obtained results have shown that the chemical reaction effect has a great influence in the study of flow and heat transfer process in the presence of magnetic field of some types of fluids considered.

Keywords: MHD, chemical reaction, mass transfer, perturbation.

[1]. Ahmed, N. and Sarma, D. "Three dimensional free convective flow and heat transfer through a porous medium." Indian J. Pure and
Appl. Maths, 26 (10), 1345 (1997)
[2]. Ahmed, N. and Goswami, J.K. "Mixed convection on a three dimensional MHD mass transfer flow past a vertical plate with
thermal diffusion in presence of a heat source." Bull. Cal. Math. Soc., 103(1), 71-92 (2011).
[3]. Chamkha, A J. "MHD flow of a numerical of uniformly stretched vertical permeable surface in the presence of heat
generation/absorption and a chemical reaction." International Communication in heat mass transfer, 30, (413-422), (2003).
[4]. Choudhury,R.C. and Chand, T. "Three dimensional flow and heat transfer through porous medium." Int. J. Appl. Mech.
Engineering, 7(4), 1141.
[5]. Cramer, K.P. and Pai, S.I. "Magneto Fluid dynamics for Engineers and applied physics." Mc Graw-Hill Book Co, New York
(1973).

Abstract: The study determined the effect of geogebra on senior secondary school students' interest and achievement in statistics. The study was carried out in Makurdi local government area of Benue state. A sample size of two hundred and forty two (242) senior secondary one students was used. The study was a quasi-experimental design. Data were collected from the subjects using two (2) instruments namely: Statistics Achievement Test (SAT) and Statistics Interest Inventory (SII). The SAT and SII had reliabilities of 0.62 and 0.71 using Kuder-Richardson formula 20 and Cronbach Alpha coefficient respectively. Four research questions and four research hypotheses were formulated to guide the study. The research questions were answered using mean and standard deviation while the hypotheses were tested at 5% level of significance using a 2-way analysis of covariance (ANCOVA). Results from the study revealed that students taught statistics using the geogebra teaching method achieved higher and also showed greater interest in learning statistics than those taught with conventional teaching approach. The study also revealed that both male and female students in experimental group achieved the same and also showed similar interest in statistics. The study recommended among others that teacher education institutions should be encouraged to include geogebra as a method in teaching secondary school statistics.

Keywords: Geogebra, Senior Secondary School Students, Interest, Achievement, Benue state.

[1]. Abiam, P.O. & Odok, J.K. (2006). Factors in Students' achievement in different branches of secondary school Mathematics. Journal of Education and Technology 1(1), 161 – 168.
[2]. Abimbade, J. (1995). School quality factors and secondary school students' achievement in mathematics in south-western and north-central Nigeria. The african symposium: an online journal of the African educational research network 11(1) 1-10.
[3]. Agwagah, U. N. V. (1993). Instructions in mathematics reading as a factor in students' achievement and interest in word problem-solving. Unpublished doctoral thesis, University of Nigeria, Nsukka.
[4]. Ahmad, F.M. & Rohani,A.T. (2010). Graphing calculator strategy in teaching and learning of Mathematics: Effects on Conceptual And Procedural Knowledge Performance and Instructional Efficiency Retrieved from http://65.54.113.26/Publication/13742028/graphing-calculator-strategy-in-teaching-and-learning-of-mathematics.

Abstract: In this paper the Geo/Geo/1/k queuing model with controllable arrival rates, single server with identical service rates and feedback is considered. The steady state solution and system characteristics are derived for this model. The analytical results are numerically illustrated, the effect of the nodal parameters on the system characteristics are studied and relevant conclusion is presented. Keywords: Single server, Controllable arrival rates, Bivariate Bernoulli feedback, Finite capacity ,System characteristics. AMS 2000 Subject Classification Primary 60K25; Secondary 68M20.90B22

[1]. Goswami, V. and Gupta, U.C. (2002) Distribution of the Number of Customers Served During a Busy Period in a Discrete Time Geom/Geom/1 Queue, Indian J. Pure Appl. Maths., 33(9), 1405-1408.
[2]. Kalyanaraman, R. and Renganathan, N. (1996) A Single Server Instantaneous Bernoulli Feedback Queue with Multiple Vacation, Optimization, 37(1), 87-96.
[3]. Kalyanaraman, R. and Sumathy, S. (2009) A Feedback Queue with Multiple Servers and Batch Service, International Review of Pure and Applied Mathematics, 5(1), 23-27.
[4]. Rani, G. and Srinivasan, A. (2013) Geo/Geo/c/k Interdependent Queueing Model with Controllable Arrival Rates and Feedback, International Journal of Computational Science and Mathematics, 5(2), 33-42, ISSN: 0974-3189.
[5]. Rani, G. and Srinivasan, A. (2013) M/M/c/k Loss and Delay Interdependent Queueing Model with Controllable Arrival Rates, No Passing and Feedback, International Journal of Mathematical Sciences and Engineering Applications, 7(IV), 403-419, ISSN 0973-9424.

Abstract: Proper randomness of the numbers generated by L.H.C Tippett has been examined. By B.K. Sarmah and D. Chakrabarty in Dec.. 2014, IJESRT Vol-3, issue 12, by applying the Chi-square test for testing the significance of difference between observed frequency of each of the digit in the table and the corresponding theoretical (expected) frequency. In this paper, the randomness of the digits have been tested by applying t-test for amount of deviation of the observed number of occurrences and the theoretical(expected) number of occurrences of the respective digits and hence the numbers.

[1]. Cochran, W.G. (1940): "Sample survey", Cambridge University press.
[2]. Chakrabarty, D. (2004): "A theoretical definition of probability based on common sense", Bulletin of pure and applied sciences, 23 E-2, 343-349.
[3]. Chakrabarty, D. (2005): "Probability;Link between classical definition and Empirical definition", J. Ass. Sc. Soc., 45,13-18.
[4]. Chakrabarty, D. (2006): "Non equally likely outcomes: The classical definition of probability", Bulletin of pure and applied sciences, 25, E-2, 471-481.
[5]. Chakrabarty, D. (2007): "Empirical definition of probability : Special case of its Theoretical definations". Int. J. Agricult. Stats. Sci., 3(1), 261-267.
[6]. Chakrabarty, D. (2008): "Bernolli‟s definition of probability: Special case of its Chakrabarty definition", Int. J. . Agricult. Stats. Sci., 4(1), 23-267.

Abstract: Motivated by some results on Orthogonal Generalized Derivations ofSemiprime Rings, in [2], the authors defined the notion of derivations and generalized derivations on semirings and investigated some results on the derivations in semirings. In this paper, we also introduce the notion of orthogonal generalized derivations of Semiprimesemirings and derived some interesting results.

keywords: Semirings, Derivations, Orthogonal derivations, Generalized orthogonalderivations, Centralizer

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[2]. Chandramouleeswaran, Thiruveni, On Derivations of Semirings, Advances in Algebra, 3(1) (2010), 123-131
[3]. Chandramouleeswaran, Revathy, Orthogonal Derivations on Semirings, M.Phil. Dissertation submitted to Madurai Kamaraj University (2012), 20-47
[4]. Jonathan S.Golan, Semirings and their Applications, Kluwer Academic Press(1969).
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Abstract: In thispaper we will derive Bäcklund transformations and conservation laws based on geometrical properities of evolution equations with more than two independent variables that describe pseudospherical surfaces.

Keywords: Evolution equations, Pseudospherical surfaces, Bäcklund transformations, conservation laws andSolitons.

[1]. Chern. S.S and Tenenblat. K," pseudospherical surfaces and soliton equations" Stud. Appl. Mat. 74, 55-83 (1986).
[2]. El-Sabbagh. M and K.R.Abdo, "Pseudospherical surfaces and evolution equations in higher dimensions "IJSET. Math. vol (4) Issue No.3, 165-171 (2015).
[3]. El-Sabbagh. M and K.R.Abdo, "Pseudospherical planes and evolution equations in higher dimensions II" IOSR-JM. Math. vol(11) Issue No.2, Ver. I, 102-111(2015).
[4]. El-Sabbagh. M and K.R.Abdo, "Pseudospherical 3- Planes In ℝ5and Evolution Equations Of Type utt=ψ u,ux,……..,∂ku∂ xk ,uy,………,∂kʹu∂ ykʹ ,ut " IOSR-JM. Math. Vol (11) Issue No.2, Ver. PP 28-38(2015).
[5]. J. A. Cavalcante and K. Tenenblat, "Conservation laws for nonlinear evolution equations" Stud. Appl. Math. 74, 1. 1044-1049(1988).

Abstract: Discrete-time linear systems with perturbed initial state are considered. A disturbance that infects the initial state is said to be 𝜖-tolerable if the corresponding output signal is relatively insensitive to their effects. In this paper, we will define a new set that characterize each gain matrix 𝐾 and the associated feedback control law 𝑢𝑖=𝐾𝑥𝑖, this set will be called the 𝜖-capacity of the gain matrix 𝐾. The set of all possible gain matrix that makes the system insensitive to all disturbances is noted 𝛷. The characterization of 𝛷 is investigated, and we propose an algorithmic approach that allows to determine if a control law is belongs to 𝛷 or not. Numerical simulations are given.

Index Terms: discrete-time, linear system, 𝜖-capacity, 𝜖-tolerable, disturbances, perturbed initial state, admissible set.

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[4]. Kunisch, K. (1988). A review of some recent results on the output least squares formulation of parameter estimation problems. Automatica, 24(4), 531-539.

Abstract: The concept of Serendipity fixed point was initiated by Powar&Sahu in "Powar P. L. and Sahu G. R. K., (2013), Serendipity fixed point, International Journal of Mathematics and Computer Applications Research (IJMCAR) ISSN: 2249-6955: Vol. 3, Issue 3, 65-78". Recently, Wardowskihas investigated the existence & uniqueness of fixed point in view of the new concept of contraction viz. F-Contraction in "Wardowski D., (2012), Fixed Points of a new type of contractive mappings in complete Metric Spaces, Fixed Point Theory and Applications, 2012:94". Considering these two new ideas, in the present paper authors have established the existence and uniqueness of Serendipity fixed point with respect to the F-Contraction map. The definition of Serendipity fixed point has been emerged from the concept of weak completeness criterion.

[1]. Alber, YaI, Guerre-Delabriere, S. (1997), Principles of weakly contractive maps in Hilbert spaces. Oper. Theory. Adv. Appl. 98, 7-22.
[2]. Babu, G.V.R. and Shaik, Ismail (2001), A fixed point theorem by altering distances, Bull Cal. Math Soc, 93(5), 393-398.
[3]. Babu, G.V.R. (2004), Generalization of fixed point theorems relating to the diameter of orbits by using a control function, Tamkang J. Math, 35(2), 159-168.
[4]. Banach, S. (1922), Surles operations dans les ensembles abstraitsetleur application aux equationsitegrales, Fund. Math., 3, 133-181.
[5]. Brouwer, L.E.J. (1912), Uberabbidungenvommannigfaltikeiten, Math., Ann. 71, 97-115.
[6]. Choudhury, B.S. (2005), A common unique fixed point result in metric spaces involving generalized altering distances, Math. Commun. 10, 105-110.

Abstract: In this paper some certain results of r-Riemann-Liouville fractional integration and differentiation of k-Wright function are established. A new transform Elzaki transform of k-Wright function and r-Riemann-Liouville fractional integral are also obtained. Corollaries of the main theorems have also been derived.

Keywords: r-Riemann-Liouville fractional integral and differential operators, k-Wright function, Elzaki transform

[1] Diaz R. and Pariguan E. On hypergeometric functions and k- Pochhammer symbol, Div. Math. 15(2), 2007, 179-192.
[2] Dorrego G.A. and Cerutti R. A. , The k-Mittag Leffler function, Int. J. Contemp. Math. Sci. , 7(15), 2012, 705-716.
[3] Mubeem, S. and Habibullah, G. M., k-fractional integral and application, Int. J. Contemp. Math. Sci. , 7(2), 2012, 89-94.
[4] Romero L. G. and Cerutti R. A. , Fractional calculus of a k-wright type function, Int. J. Contemp. Math. Sci. , 7(31), 2012, 1547-1557.

Abstract: Prime numbers are highly irregularly distributed. Every integer fits in unique form 3n+k. In this paper, distribution of primes in arithmetical progressions 3n+k is analyzed in the range of 1 to 1 trillion. As the decimal number system has the base 10, the distribution trends of the primes in the blocks of all powers of 10 are also presented.

Keywords –Block-wise distribution, prime density, prime numbers, prime spacing.

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