iosr-Jm   Volume-14 ~ Issue-6 ~ Nov-Dec 2018

Abstract: In order to solve certain problems in calculating probabilities, such as Markov chains or conditional specification of discrete distributions, the use of matrix and vector treatment of conditioned probabilities and of vectors of marginal probabilities is common. Following these ideas, the present study obtains matrix forms of some elementary results of probability theory, such as the total probability and Bayes theorems. These results and methodology are applied to the matrix study of results of diagnostic tests, allowing an immediate generalization to tests with more than two results. In addition,we propose safety and validity measures of a test based on matrix rules, which in some cases are related to the well-known Youden index.

Key Word: Conditioned Probabilities, BayesTheorem, Matrix, Diagnostic Tests

[1]. Berman A. Plemmons R.J. (1994) Nonnegative Matrices in the Mathematical Sciences. SIAM.
Piladelphia
[2]. Isaacson D.L. y Madsen R.W. (1976) Markov Chain: Theory and aplications. John Wiley and Sons. New
York.
[3]. Arnold B.C. Press S. J. (1989) Compatible conditional distributions. Journal of the American Statistical
Association. 84, 152-156
[4]. ] Gordis, L. (2014) Epidemiology. 5ª edición. Elsevier Saunders Philadelphia
[5]. Schott J.R.(1997) Matrix Analysis for Statistics John Wiley and sons New York.

Abstract: This study aims to determine the ability of students in the ability literacy and interpret the graphs and data from an environmental event in everyday life. The study was conducted in state junior high school 1 of Braja Selebah. The number of students who become the sample of research is 25 people who are sitting in Class 8, the class 8A. The research instrument uses Test of Graphing in Science (TOGS). In reading and interpreting the graphs and data the students have average percentages below 50% for correct answers and the Minimum Criteria Completion (KKM) in Class 8A is 3.5% complete, and 96.5% remedial. From the results of TOGS diagnostic test tests that students can not read the chart well and found that students have difficulty in interpreting graphs and data. This problem is caused by the lack of students' knowledge, explanation and practical activities of the teacher regarding the presentation of graphs and data.

Keywords: literacy, interpretation, data, graphics, TOGS.

[1] Ambelu, T., Gebregziabher. (2011). The Effects of Student-Centered Approach in Improving Students' Graphical Interpretation Skills and Conceptual Understanding of Kinematical Motion. Lat. Am. J. Phys. Educ. Vol. 5, No. 2.
[2] Carlos M & Janet A. (2007). Investigating The Interpretation of Media Graphs Among Student Teachers. Vol. 2, No. 3. IEJME.
[3] McKenzie, D. L., & Padilla, M. J. (1986). The construction and validation of the test of graphing in science (TOGS). Journal of Research in Science Teaching, 23(7), 571-579.
Books:
[4] A. Van Heuvelen and X. Zou. (2001). Multiple representations of workenergy processes. Am. J. Phys. 69_2_, 184–193 __.
[5] American Association for the Advancement of Science (AAAS). (1989). Project 2061: Science for all Americans. Washington, DC: National Academy Press.

Abstract: The purpose of this study is to modeling the growth of the tumor volume in the rats. Using the SAEM algorithm in R and non-linear mixed model for a longitudinal data to predict future tumor volume in the rats.

Keywords: Nonlinear mixed effects model; Breast cancer; SAEM algorithm; Longitudinal Data.

[1]. E. Comets, A. Lavenu , M. Lavielle (2017). Parameter Estimation in Nonlinear Mixed Effect Models Using saemix, an R Implementation of the SAEM Algorithm. Journal of Statistical Software. doi:10.18637/jss.v080.i03.
[2]. E. Comets, A. Lavenu , M. Lavielle (2017). saemix: Stochastic Approximation Expectation Maximization (SAEM) Algorithm. R package version 2.1, URL https://CRAN.R-project. org/package=saemix.
[3]. H.Akaike, (1974). A new look at the statistical model identification. IEEE Trans. Autom. Control, 19(6), 716--723.
[4]. G. Schwarz, (1978). Estimating the dimension of a model. Ann. Statist., 6(2), 461--464.
[5]. E.Escrich , M. Solanas , M. C. Ruiz de Villa, R. Ribalta Muntané Segura (1994) Experimental diets for the study of lipid influence on the induced mammary carcinoma in rats: I-diet definition. International Journal In Vivo Research, 8: 1007-1012..

Abstract: If after 374 years the famous theorem of Fermat-Wiles was demonstrated in 110 pages by A. Wiles [4], the puspose of this article is to give a simple demonstration and deduce a proof of the Beal conjecture. Résumé : Si après 374 ans le célèbre théorème de Fermat-Wiles a été démontré en 110 pages par A. Wiles [4], le but de cet article est de donner une simple démonstration et d'en déduire une preuve de la conjecture de Beal.

Keywords: Fermat, Fermat-Wiles theorem, Fermat's great theorem.

[1]. https://en.wikipedia.org/wiki/Beal conjecture .
[2]. https://en.wikipedia.org/wiki/Fermat last theorem.
[3]. M. Mghiar , la preuve de la conjecture abc, iosr journal of mathematics (iosr-jm), e-issn: 2278-5728, p-issn: 2319-765x. volume 14,
issue 4 ver. i (jul - aug 2018), pp 22-26.
[4]. Andrew Wiles, Modular elliptic curves and Fermat's last Theorem, Annal of mathematics, volume 10,142, pages 443-551, septemberdecember,
1995...

Abstract: We consider a class of generalized trigonometric functions given by the divergent trigonometric series; coefficients of these series have a certain order of growth. These functions have no values in usual sense and manifest themselves only as convolution with the test functions. Classes of test functions are formed by even periodical functions that are either defined by chosen Fourier coefficients or have certain differential properties. The operations of differentiation and integration of these generalized trigonometric functions are considered. The class of generalized trigonometric functions of zero order with coefficients forming N - periodical sequences is investigated in details. Such functions under certain conditions that are received in this paper have interpolating properties. The results of calculations for the test example are given; these results are well correlated to those predicted by theory.

Keywords: generalized trigonometric functions, test functions, divergent trigonometric series, convolution, have interpolation

[1]. Hardy G. H. Divergent Series. – Oxford, 1949.
[2]. Denysiuk V. P. Trigonometric series and splines. – К.: "NAU", 2017. – 212 p. (Ukrainian).
[3]. Scwartz L. Méthodes mathématiques pour les sciences physiques. – Hermann, 115, Boulevard Saint-Germain, Paris VI, 1961. –
412p...

Abstract: This paper present a numerical algorithm for the linear one-dimensional wave equation. In this method a finite difference approach had been used to describe the time derivative while quintic spline is used as an interpolation function in the space dimension. We discuss the accuracy of the method by expanding the equation based on Taylor series and minimizing the error. The proposed method was eight-order accuracy in space and fourth-order accuracy in time variables. From the computational point of view, the solution obtained by this method is in excellent agreement with those obtained by previous works and also it is efficient to use. Numerical examples are given to show the applicability and efficiency of the method.

[1]. Saadatmandi and M. Dehghan, Numerical Solution of the One-Dimensional Wave Equation with An integral Condition, Numerical
Methods for Partial Differential Equations, Vol, 23, no.2, pp. 282-292, 2007.
[2]. J. Rashidinia, R. Jalilian, and V. Kazemi, "Spline methods for the solutions of hyperbolic equations," Applied Mathematics and
Computation, vol. 190, no. 1, pp. 882 – 886, 2007.
[3]. R. K. Mohanty and V. Gopal, "High accuracy cubic spline finite difference approximation for the solution of one-space dimensional
non- linear wave equations," Applied Mathematics and Computation, vol. 218, no. 8, pp. 4234 – 4244, 2011.
[4]. Ryo, Fast decay of solutions for linear wave equations with dissipation localized near infinity in an exterior domain, J. Differential
Equations, 188 (2) (2003) 390-405.
[5]. Rashidinia J. and Mohsenyzadeha, Numerical Solution of One-Dimensional Heat and Wave Equation by Non-Polynomial Quintic
Spline, International Journal of Mathematical Modelling & Computations Vol. 05, No. 04, ( 2015), 291- 305.

Abstract: In this paper, we formulate a multi – group model of the Coccidiosis disease with eight (8) compartments. The susceptible birds are divided into two groups, latently infected birds are divided into three groups, infected birds are divided into two groups according to infectivity and the recovered birds. A deterministic model was formulated and analyzed using methods from dynamical systems theory. Conditions for the stability of the disease-free and endemic steady states were determined.............

Keywords: Coccidiosis Disease, Stability Analysis, Optimal Control, Sensitivity Index

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Abstract: Symmetric Methods are of much current interest due to their efficiency when solving stiff systems and the possibility to use them as basic methods for extrapolation processes. In this paper, we extend of the Symmetric Implicit Runge-Kutta Nyström Type Method (SIRKNTM) for the integration of first order ODEs to a SIRKNTM for Direct Integration of Two-Point Boundary Value Problem (BVPs).The theory of Nyström method was adopted in the formulation of the method. The method has an implicit structure for efficient implementation and produces simultaneously approximation of the solution of Two-Point Boundary Value Problem (BVPs). The proposed method was tested with Numerical experiment to illustrate its efficiency and the method can be extended to solve higher order differential equations.

[1]. Agam S.A and Badmus A.M (2010), Improved Runge-Kutta Nyström Method for Second Order Ordinary Differential Equations J. of Research in Physical Science, 6, No 1, 71-76.
[2]. Butcher J.C and Hojjat G. (2005) Second Derivative Methods with Runge-Kutta Stability, Num alg, 40, 415-429.
[3]. Yusuph Y. and Onumanyi P (2002) New Multiple Finite Difference Method through Multi –Step Collocation for y"= f (x,y), Abacus, 29; 92-96.
[4]. Z .A. Adegboye and R.Kehinde (2016) Super Runge-Kutta Nyström method for direct Integration of third order ordinary differential equations. The Journal of Mathematical Scences of Nigeria,NMC Abuja Nigeria,Vol 4,847-856.
[5]. Zamurat A. Adegboye, Okeowo G.F and Isiyaku Aliyu(2014) Explicit Runge-Kutta Type Method For Direct Solution Of Linear Third Order Boundary Value Problems. The Nigerian Association of Mathematical Physics, Vol.28(2),121-128.

Abstract: Recent studies on urban economics and real estate theory have highlighted how investment can affect real estate values. In addition, city residents pay more attention to the quality of their living space. The rate of crime, air quality, access to employment centers or highways are just some of the parameters that can influence the housing and location options and hence land use, mobility and the economy of the citizens concerned. Several are the interested citizens who choose to invest either by risking or by dragging on only some parameters, without thoroughly scrutinizing all available ones. The legitimate question that arises here is whether a citizen who is interested in investing is in a position to make a rational decision when he receives a large amount of data and has limited time. A second question is whether this decision could have taken a model of mechanical learning..................

Keywords: Artificial Neural Networks, Bounded Rationality, Linear Models, Elastic Net.

[1]. P. Argyrakis, (2001), Neural Networks and Applies, Greek Open University , pages 192
[2]. D. Graupe, (2013), Principles of Artificial Neural Networks.3rd Edition, World Scientific Publishers,
[3]. Auer, Peter; Harald Burgsteiner; Wolfgang Maass (2008). "A learning rule for very simple universal approximators consisting of a single layer of perceptrons". Neural Networks. 21 (5): 786–795. doi:10.1016/j.neunet.2007.12.036.
[4]. https://en.wikipedia.org/wiki/Feedforward_neural_network (date of access: 1/10/2018)
[5]. Simon, Herbert A. (1997). Administrative Behavior: a Study of Decision-Making Processes in Administrative Organizations (4th ed.). New York: Free Press.
[6]. David Rettinger, Reid Hastie, (2001), Content Effects on Decision Making, Organizational Behavior and Human Decision Processes 85(2), pp 336-359

Abstract: Similar to the notion of ⊕-stabilizers in MV-algebras, the present paper introduce the notion of boosters. Then some elementary properties of principle boosters and boosters are presented, and a principle booster is proved to an MV-filter. According to the properties of of principle boosters, we prove that the set of all principle boosters is a complete distributive lattice.

Keywords: MV-algebra, booster, principle booster, MV-filters.

[1]. P. Hájek, Metamathematics of fuzzy logic, Springer Science & Business Media, 2013.
[2]. C.C. Chang, Algebraic analysis of many valued logics, Transactions of The American Mathematical Society, 88(2), 1958, 467-
490.
[3]. C. Lele and J. B. Nganou, MV-algebras derived from ideals in BL-algebras, Fuzzy sets and Systems, 218, 2013, 103-113.
[4]. J. Rachůnek, D. Šalounová, Ideals and involutive filters in generalizations of fuzzy structures, Fuzzy Sets and Systems, 311, 2017,
70-85.

Abstract: A right near-ring N is called Quasi-weak commutative if xyz = yxz[3].A right near-ring N is called quasi weak m- power commutative if xm y z = ymxz for all x,y,z ∈ N,where m ≥1 is a fixed integer [5].An algebra A over a commutative ring R is called scalar quasi-weak commutative if for every x,y,z ∈ A there exists α = α (x,y,z) ∈ R depending on x,y,z such that xyz = α yxz. An algebra A over a commutative ring R is called scalar quasi-weak m - power commutativity if for every x,y,z ∈ A,there exists a scalar α ∈ R depending on x,y,z such that xm y z = α ymxz [8]. In this paper,the concept of scalar quasi-weak m-power commutativity is generalized as scalar quasi- weak commutative (m,n) power commutativity and prove many results.

[1]. R.Coughlin and M.Rich,On Scalar dependent algebras,J.Math 24(1972),696-702.
[2]. R.Coughlin,K.Kleinfield and M.Rich,Scalars dependent algebras,Proc.Amer.Math.Soc,39(1973), 69-73.
[3]. G.Gopalakrishnamoorthy,M.Kamaraj and S.Geetha,On quasi-weak commutative Near- rings, International Journal of Mathematics Research,Vol5(5),(2013),431-440.
[4]. G.Gopalakrishnamoorthy,S.Geetha and S.Anitha,On quasi-weak commutative Near-rings-II,Malaya Journal of Mathematik,Vol3(3),(2015),327-337.
[5]. G.Gopalakrishnamoorthy and S.Geetha,On (m,n) – Power Commutativity of rings and Scalar (m,n) – Power Commutativity of Algebras,Jour. of Mathermatical Sciences ,Vol 24(3),2013, 97-110.

Abstract: The proxy signature, a variant of the ordinary digital signature, has been an active research topic in recent years; it has many useful applications, including distributed systems and grid computing. In an ordinary proxy signature scheme any one can verify the validity of a proxy signature produced by the proxy signer on behalf of original signer. But public verifiability of proxy signature is not desirable in some applications where the signed message is sensitive to the signature receiver, for example signatures on medical records, tax information. To meet this requirement, the concept of directed proxy signature was introduced. A directed proxy signature scheme is a kind of signature scheme in which the verification ability is controlled by the proxy signer. Although many identity-based proxy..........

[1]. Diffe, W., Hellman, M.E., New directions in cryptography. IEEE Transactions in Information Theory, vol. 22, pp. 644-654, 1976.
[2]. Shamir, A., Identity-based Cryptosystems and Signature Schemes. In: Blakley G. R., Chaum D. (Eds.) Advances in Cryptology,
Crypto'84, Springer, Berlin, Heidelberg, LNCS 196, pp. 47-53, 1984,.
[3]. Neuman, B.C., Proxy-based authorization and accounting for distributed systems. In: Proceedings of the 13th International
Conference on Distributed Computing Systems, pp. 283–291, 1993.
[4]. Foster, I., Kesselman, C., Tsudik, G., Tuecke, S., A security architecture for computational grids. In: Proceeding of the 5th ACM
conference on Computers and Communication Security, pp. 83–92, 1998.
[5]. Kim, H., Baek, J., Lee, B., Kim, K., Secret computation with secrets for mobile agent using one-time proxy signatures. In:
Proceedings of the Cryptography and Information Security (CIS'01), pp. 845–850, 2001..

Abstract: Pipelines are used to convey fluid materials not only in the industrial process but also in the place of residence and agriculture. Pipes are simple and convenient to use. But the numerical modeling and estimation of flows inside pipes is challenging. Due to this, the investigation of flow behaviors of fluid through pipes is absolutely fascinating for researchers. We have met with various pipe flow analysis at the literature which have been conducted with laboratory experimental techniques. Bend pipe is often used in pipe line transportation, fluid flow velocity and pressure change dramatically when passing through the bend pipe, therefore the bend pipe influences the efficiency of pipeline.........

Keywords: No-slip conditions, Reynolds number, Steady, Laminar, incompressible, CFD simulation, bend pipe, FLUENT.

[1]. V. M. Soundalgekar and V. G. Divekar, "Laminar Flow through bend pipe with Small Suction," Publication de l'Institute Mathematique, Nouvelle Serie, Vol. 16, No. 30, pp. 147-157, 1993.
[2]. D. Bhandari and Dr. S. Singh "Analysis of fully developed laminar flow in a bend pipe using computational fluid dynamics," International Journal of Engineering Research and Technology, vol. 1, no. 5, pp. 1-8, 2012.
[3]. M. Sahu, Kishanjit Kumar Khatua, Kanhu Charan Patra and T. Naik, "Developed laminar flow in pipe using computational fluid dynamics," International R &D Conference on Development and Management of Water and Energy Resources, Bhubaneswar, India, 4-6 February 2009.
[4]. H. Phan, L.Wen, H. Zhang," Numerical simulation and analysis of gas liquid flow in a T-junction micro channel," Advances in Mechanical Engineering, (2012), ID 231675.
[5]. H. Shamloo, B. Pirzadeh, "Investigation of characteristics of separation zones in T-junction channels," WSEAS transactions on Mathematics, vol. 7, pp. 303-312, 2012..