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

Abstract: The purpose of the study was to determine the students' error in learning trigonometry A total of 80 Senior Secondary 2 mathematics students randomly selected from two private schools in Zaria with a mean age of 17 constituted the sample size for the study. The Mathematics achievement tests (MAT) and Trigonometrical diagnostic test (TDT) were used as the instruments of this study that included two components: the use of formula and right-angled method. Diagnostic interview was also used to identify at which level students' errors occur in solving problems. The type of error is based on Newman Error Hierarchy Model that includes reading type error, comprehension, transformation............

Keywords: Trigonometry, Comprehension error, Transformation error, Process skill error

[1]. Brown, A.S. (2006). The trigonometric connection: students‟ understanding of sine and cosine. Proceedings 30th Conference of the International Group for the Psychology of Mathematics Education, 1, p.228. Prague: PME30.
[2]. Clements, M.A. & Ellerton, N.F. (1996).The Newman procedure for analysing errors on written mathematical tasks. Retrieved January12, 2010, from http://compasstech.com.au/ARNOLD/ PAGES/newman.htm
[3]. Delice, A. (2002). Recognizing, recalling and doing in the "simplification‟ of trigonometric expressions. The 26th Annual Conference of the International Group for the Psychology of Mathematics Education (PME26), the School of Education and Professional Development at the University of East Anglia, Norwich: England, 1, 247.
[4]. Fi, C. (2003). Preservice Secondary School Mathematics Teachers‟ Knowledge of Trigonometry: Subject Matter Content Knowledge, Pedagogical Content Knowledge and Envisioned Pedagogy. Unpublished PhD Thesis, University of Iowa: USA.
[5]. Gur, H.( 2009 ) Trigonometry Learning. New Horizons in Education, 57(1), 67- 80.

Abstract: This paper attempts to provide some insights on students' various approaches towards solving words problems in Mathematics. 15 students were randomly selected from SSIII students of Demonstration Secondary School, Azare Bauchi State. Three (3) visits were scheduled to the school for interview, questions administration on words problem and discussions, the findings revealed that the students lack necessary knowledge and skills to solve word problems. It is recommended that teachers should employ various heuristics when teaching words problem to enable the students develop necessary skills needed to solve words problems.mathematical journal and since then I was working on it. Thus my present work is the result of many years of dedicated efforts.

[1]. Adams T. L. (2003): Reading Mathematics: More than words can say; An understanding of Mathematical literacy draws on many of the same skills as print literacy. The reading teacher, vol. 56(8)
[2]. Adler, J. (2004): Research Inside Teacher Education: The QUANTUM Project, its context, some results and its implications. A paper presented at the AERA conference in San Diego, April, 2004
[3]. James, W. W. (2002): introduction to Problem Solving. File//A:/info.httm.
[4]. Luneta, K. (2008): The professional development model, evaluating and enhancing international year book on teacher education.Wheeling instructional effectiveness through collaborative research. Paper presented at the international council on education for teaching (ICET) 53rd World Assembly (July 14 - 17), Minho University, Broga, Portugal
[5]. Nancy, K. M. (1990): Learning Fractions with understanding; building on informal Knowledge. Journal for Research in Mathematics Education Vol. 21 No. 16 - 32

Abstract: The object of the present paper is to introduce the sequence spaces o (M,, P) defined by the sequence of fuzzy numbers and p = (pk) be any bounded sequence of positive real numbers. We study their different algebraic and topological properties. We also obtain some inclusion relations between these spaces.

Keywords: Fuzzy number, entire sequence spaces, completeness, convergence ,boundedness. This work is supported by UGC MRP(5647)

[1]. Ganapathy Iyer. V, On the space of integral functions, J.Indian. Math.Soc. 12(1948) 13-30.
[2]. Hemen Dutta On the sometric spaces of F F F o c c and  ,  ActaUniversitatis Apulensis No 19(2009)107-112.
[3]. Kamthan.P.K, Bases in a certain class of Frechet space, Tamkang.J. Ma th.7(1976)41-49.
[4]. Kavi Kumar.J Azme Bin Khamis and R.Kandasamy Fuzzy entire sequence spaces International journal of mathematics and
mathematical sciences 2007 article ID 58368
[5]. Maddox I.J. Elements of Functional Analysis Cambridge university press.

Abstract: We use Bayesian methods to fit a lognormal mixture model with two components to right censored survival data to estimate the survivor function. This is done using a simulation-based Bayesian framework employing a prior distribution of the Dirichlet process. The study provides an MCMC computational algorithm to obtaining the posterior distribution of a Dirichlet process mixture model (DPMM). In particular, Gibbs sampling through use of the WinBUGS package is used to generate random samples from the complex posterior distribution through direct successive simulations from the component conditional distributions. With these samples, a Dirichlet process mixture model with a lognormal kernel (DPLNMM) in the presence of censoring is implemented.

Keywords: Bayesian, Lognormal, Survivor Function, Finite Mixture models, Win BUGS

[1]. Escobar, M. and West, M. (1995). Bayesian density estimation and inference using mixtures. Journal of the American Statistical
Association, 90:577–588.
[2]. Farcomeni, A. and Nardi, A. (2010). A two-component Weibull mixture to model early and late mortality in a Bayesian framework.
Computational Statistics and Data Analysis, 54:416–428.
[3]. Ferguson, T. (1973). A bayesian analysis of some nonparametric problems. Annals of Statistics, 1(2):209–230.
[4]. Freireich, E. J., Gehan, E. A., and Frei, E. (1963). The effect of 6-mercaptopurine on the duration of steroid induced remissions in
acute leukemia: A model for evaluation of other potentially useful therapy. Blood, 1:699–716.
[5]. Giudici, P., Givens, G. H., and Mallick, B. K. (2009). Bayesian modeling using WinBUGS. John Wiley and sons, Inc., New Jersey.

Abstract: The concept of orthogonal polynomial matrices are introduced. Some properties and characterization for polynomial orthogonal matrices are obtained.

Keywords: Polynomial matrices, orthogonal matrices, symmetric matrices.

[1]. David W.Lewis, Matrix Theory (World Scientific Publishing Co.Pte.Ltd, 1991).
[2]. I. Gohberg,, P. Lancaster and L. Rodman, Invariant Subspaces of Matrices ith Applications (Wiley, New York, 1986 and SIAM,
Philadelphia, 2006).
[3]. G. Ramesh, P.N. Sudha, "On Polynomial Symmetric and Polynomial Skew Symmetric Matrices" IJSRD - International Journal for
Scientific Research & Development| Vol. 3, issue 06, 2015 | ISSN (online): 2321-0613
[4]. A.I.G. Vardulakis, Linear Multivariable Control (JohnWiley, Chichester, UK, 1991).
[5]. W.A. Wolovich, Linear Multivariable Systems (Springer Verlag, 1974).

Abstract: After defining, Bölcsföldi-Birkás prime numbers will be presented from 23 to 2327753. How many Bölcsföldi-Birkás prime numbers are there in the interval (10p-1, 10p) (where p is a prime number)? On the one hand, it has been counted by computer among the prime numbers with up to 13-digits. On the other hand, the function (1) gives the approximate number of Bölcsföldi-Birkás prime numbers in the interval (10p-1,10p). The function (2) gives the approximate number of Bölcsföldi-Birkás prime numbers where all digits are 3 or 7 in the interval (10p-1,10p). Near-proof reasonig has emerged from the conformity of Mills' prime numbers with..........

[1]. http://oeis.org/A019546
[2]. Freud, Robert – Gyarmati, Edit: Number theory (in Hungarian), Budapest, 2000
[3]. http://ac.inf.elte.hu → VOLUMES → VOLUME 44 (2015)→ VOLLPRIMZAHLENMENGE→FULL TEXT
[4]. http://primes.utm.edu/largest.html
[5]. http://mathworld.wolfram.com/SmarandacheSequences.html

Abstract: Prostate cancer is the most common men's cancer in the world. This study aimed to identify the predictive risk factors of prostate cancer incidence in order to set priorities for public heath interventions and to reduce the incidence of the disease. This study included patients with prostate cancer who were being treated at the National Center for Radiotherapy and Nuclear Medicine in Khartoum State, Sudan. 250 patients were chosen by interviews and from their medical history.............

Keywords: Incidence, PSA, Risk factor, Odds Ratio, Logistic.

[1]. https://www.pcrm.org/health/cancer-resources/diet-cancer/type/nutrition-and-prostate-health
[2]. http://globocan.iarc.fr/old/Factsheets/cancers/prostate-new.asp
[3]. F. Jacques, S. Isabelle, D. Rajesh, E. Sultan, M. Colin, R. Marise, P. Donald Maxwell, F. David, B. Freddie, Cancer incidence and mortality worldwide, Cancer International Journal of Cancer, 136(5), 2012, E359-E386.
[4]. Report of the Sudanese Federal Ministry of Health for 2016
[5]. http://training.seer.cancer.gov/prostate/intro/ [National cancer institute & SEER Training Modules]
[6]. Y. Chao, P. Joanne, L.L. Kuk & I.M. Gary, An Introduction to Logistic Regression Analysis and Reporting, The Journal of Educational Research, 96(1), 2002, 3-14

Abstract: In this paper, we give an explicit formula of the S-curvature of homogeneous Finsler space with special -metric and proved that a homogeneous Finsler space with almost isotropic S-curvature must have vanishing S-curvature. We also derived an explicit formula of the mean-Berwald curvature of homogeneous Finsler space.

Keywords: Finsler space, -metric, Homogeneous Finsler space, S-curvature, Mean-Berwald curvature.

[1]. P. L. Antonelli, R. S. Ingarden, and M. Matsumoto, The Theory of Sprays and insler Spaces with Applications in Physics and Biology, FTPH Vol. 58, Kluwer Academic Publishers, (1993).
[2]. S. Bacso, X. Cheng and Z. Shen., Curvature Properties of -metrics, Adv. Stud. Pure Math. Soc., Japan (2007).
[3]. S. S. Chern, Finsler geometry is just Riemannian geometry without the quadratic restriction, Notices Am. Math. Soc. 43(9), 959-963 (1996).
[4]. S.S. Chern, Z. Shen, RiemannFinsler Geometry, World Scientific Publishers, (2004).
[5]. X. Cheng and Z. Shen, A class of Finsler metrics with isotropic S-curvature, Israel J. Math. 169, 317-340, (2009), .

Abstract: Using the Hӧlder inequality, we establish several Lyapunov-type inequalities for quasilinear q-difference equation and q-difference systems.

Keywords: Lyapunov-type inequalities, q-difference equation, q-difference systems, Hӧlder inequality

[1]. A.Lyapunov,Probleme General de la Stabilite du Mouvement,in:Ann.Math.Studies,vol.17,Prin- ceton Univ.Press,1949,Reprinted
from Ann. Fac.Sci.Toulouse,9(1907)207-474, Translation of the original paper published in Comm.Soc.Math. Kharkow. 1892.
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[3]. D.Cakmak, Lyapunov-type integral inequalities for certain higher order differential equations, Appl. Math.Comp
216(2010)368-373.
[4]. A.Canada, J.A.Montero, S.Villegas,Lyapunov inequalities for partial differential equations, J. Funct. Anal. 237(2006)176-193.
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Abstract: The prime concept of this paper is to introduce further algebraic operations on some known sequences and hence derive some new sequences. It further regulates these sequence by introducing procedural routines like identifying nth term using recurrence relation, deriving its general form, introducing an operator matrix and its further exponential operations, and establishing Eigen values relation between them. During the work, we have observed that in some cases the traits of original sequences pursue in the extended work on generator matrices of the new sequences thus formed.

Keywords: Pell sequence, Fibonacci sequence, Jha sequence, Operator Matrix, and Eigen values.

[1]. T.Koshy, Fibonacci and Lucas Numbers with Applications (John Wiley, New York, 2001)
[2]. A. F. Horadam, Pell identities, Fibonacci Quart.,9(3) (1971),245-263.
[3]. V.A. Achesariya, Dr. P.J. Jha, "Set of Pythagorean Triplets", IOSR Journal of Mathematics (IOSR-JM); p-ISSN: 2319-7665X. vol-
11,pp51-60.
[4]. Kadiya S.S, Patel D.R. , Dr. P. J. Jha, " Matrix Operation on generator matrices of known sequences and important derivations"
International Journal of Applied Research 2016:2(7);p-ISSN: 2394-7500:pp933-938.
[5]. Patel D.R., Kadiya S.S., Patel C.K., Dr.P.J.Jha; "Member Triangles of Fermat Family and Geometric Inter-relationship with
Standard Sequences" ISBN.978-2-642-24819-9

Abstract: Unsteady naturally convective and thermally radiative micropolar fluid in presence of nano particle flow through a vertical porous plate with MHD has been studied. A flow model is established by employing the well-known boundary layer approximations. In order to obtain non-dimensional system of equations, different types of transformation is applied on the flow model. The coupled non-linear partial differential equations are solved by explicit finite difference method and the numerical results have been calculated by Compaq Visual 6.6a. The effects of various parameters entering into the problem on velocity, temperature and concentration are shown graphically.

Keywords: Micropolar Fluid, Nano Particle, Porous Plate, MHD, Thermal Radiation, Heat and Mass Transfer.

[1]. Kazimierz Rup and Konrad Nering (2014), Unsteady natural convection in micropolar nanofluids, archives of thermodynamics, 35:3, 155–170.
[2]. J. Buongiorno (2006). Convective Transport in Nanofluids, ASME J. Heat Transfer, 128, 240-250.
[3]. Abdul Rehman and S. Nadeem (2012), Mixed Convection Heat Transfer in Micropolar Nanofluid over a Vertical Slender Cylinder, CHIN. PHYS. LETT., 29:12, 1-5.
[4]. Kazimierz Rup and Konrad Nering (2016), Heat transfer enhancement in natural convection in micropolar nanofluids, Arch. Mech., 68:4,327–344.
[5]. Konrad Nering and Kazimierz Rup (2016), The effect of nanoparticles added to heated micropolar fluid, Superlattices and Microstructures, 98, 283-294.

Abstract:One of the problems that appear in reliability and survival analysis is how we choose the best distribution that fitted the data. Sometimes we see that the handle data have two fitted distributions. Both inverse Gaussian and Weibull distributions have been used among many well-known failure time distributions with positively skewed data. The problem of selecting between them is considered. We used the logarithm of maximum likelihood ratio as a test for discriminating between these two distributions. The test has been carried
out on some different data sets.

Keywords: Inverse Gaussian distribution, Weibull distribution, Ratio maximum likelihood, Discrimination.

[1]. Atkinson, A. (1969), "A Test of Discriminating between Models," Biometrica, 56, 337-341.
[ 1970 ) .[ 2 ), " A Method for Discriminating between Models" (with Discussion), Journal of Royal Statistical Society, Ser.
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[3]. Chhikara, R. S., and Folks, J. L. (1977), "The Inverse Gaussian Distribution as a Lifetime Model," Technometrics, 19, 461-468.
[ 1988 ) .[ 4 )," Inverse Gaussian Distribution: Theory, Methodology, and Applications" Marcel Dekker, Inc., New York.
[5]. Dumonceaux, R., Antle, C. E., and Hass, G. (1973),"Likelihood Ration Test for Discriminating between Two Models with
Unknown Location and Scale Parameters," Technometrics, 15, 19-31.

Abstract: Assignment problem is an important problem in mathematics and is also discuss in real physical world. In this paper we attempt to introduce a new proposed approach for solving assignment problem with algorithm and solution steps. We examine a numerical example by using new method and compute by existing two methods. Also we compare the optimal solutions among this new method and two existing methods. The proposed method isa systematic procedure, easy to apply for solving assignment problem.

Keywords: Assignment problem, Hungarian assignment method (HA-method), Matrix one's assignment method (MOA-method), Proposed method, Optimization.

[1]. D.F. Votaw, 1952, A. Orden, The perssonel assignment problem, Symposium on Linear Inequalities and Programming, SCOOP 10, US Air Force, pp. 155-163.
[2]. H.W. Kuhn, 1955, The Hungarian method for the assignment problem, Naval Research Logistics Quarterly 2 (1&2) 83-97 (original publication).
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Abstract: The present paper deals with the instabilities takes place in two immiscible phase flow through homogeneous porous media. If the flow of two immiscible fluids is considered unidirectional in a large medium, it can be investigated easily. Corresponding to the movement direction, if parameters like pressures, saturations, fluid speeds, etc. changes only in a single space direction then it can be easily investigated. Solution is obtained by finite difference method.

Keywords: Instabilities, Porous media, Immiscible, Finite difference method.

[1]. Scheidegrer ,A.E.(1960): The Physics of Flow through Porous Media , University of Toronto Press, Toronto, 201,216,229
[2]. Scheidegrer ,A.E.(1960): Geofishica Pura Appl., 41,47.
[3]. Scheidegger, A.E. and Johnson,E.F. (1961), Canadian Journal Of Physics, 39,329.
[4]. VermaA.P.:Statistical behavior of fingering in displacement process in heterogeneous porous medium with capillary pressure Canadian Journal of Physics, 1969, 47(3): 319-324, 10.1139/p69-042.
[5]. Cosse, R. (1993), Basics of Reservoir Engineering , Editions Technip , Paris.

Abstract: In this study the decay of temperature fluctuations in homogeneous turbulence before the final period is analyzed by using the correlation equations for fluctuating quantities at four point in the flow field. Throughout this work three- and four point- correlation equations are obtained. The correlation equations are converted into spectral form by their Fourier-transform. The set of equations are made to determinate by neglecting the quintuple correlations in comparison to the fourth- order correlation terms. Finally by integration of the energy spectrum over all wave numbers, we have obtained the decay of energy of temperature fluctuations for four point correlations.....................

Keywords: Deissler's method, Four-point correlation, Decay before the temperature fluctuations, final period.

[1]. G. I. Taylor, Statistical theory of turbulence. Proc. Roy. Soc. London. A 151 (1935), 421-454.
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(1951a), 435-449.
[3]. S. Corrsin, on spectrum of isotropic temperature fluctuations in isotropic turbulence, J. Apll. Phys, 22(1951b), 469-473.
[4]. R. G. Deissler, on the decay of homogeneous turbulence before the final period, Phys .Fluids 1(1958), 111-121.
[5]. R. G. Deissler, A theory of Decaying Homogeneous turbulence, Phys. Fluids 3(1960), 176-187.

Abstract: We established (in our theorem 3.2) a very simple but absolutely very strong and su_cient condition for a general weak topology to transmit discreteness property to its range spaces. An immediate consequence of this when applied to product topology (in _nite- or in_nite-dimensions) is that all its range spaces are discrete if a product topology is discrete. Elsewhere we also obtained the conditions for the extension of the coverse: namely, how a discrete range space may induce discreteness on a weak topology.

Keywords: Weak topological system, Product Topological System, Discrete Topology, Finite or In nite Dimensional Cartesian Product Sets Mathematics Subjects Classi_cation (MSC) 2010: 54 A5, 54 B10

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