iosr-Jm   Volume-14 ~ Issue-1 ~ Jan-Feb 2018

Abstract: In this paper we extend to infinite triangular arrays the concept of triangular domino systems and triangular tiling systems which recognize infinite triangular arrays and show that the class of -triangular array languages recognized by triangular domino systems is same as the class of -triangular array languages recognized by triangular tiling systems. Also we introduce triangular Wang systems and prove that the class of -triangular languages obtained by triangular Wang systems is the same as the class of recognizable -triangular languages.

Keywords: Infinite triangular domino systems,Wang recognizable infinite triangular array languages, labelled
triangular Wang tile.

[1]. Ahmed Saoudi,Takashi Yokomoni,Learning "Local and Recognizable Omega languages and Monadic Logic Programs", proceedings of the first European conference on computational learning theory,pages 157-169,October 1994, Royal Holloay Univ of Londan,United Kingdom.
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[3]. V.Devi Rajaselvi, T.Kalyani, D.G.Thomas "HRL-Local infinite triangular picture languages" Published in Brazillian Archives of Biology and Technology" vol. 59, n.spe. 2 e16161076,January-December 2016,ISSN 1678-4324.
[4]. V.Devi Rajaselvi, T.Kalyani, D.G.Thomas, "Domino Recognizability of triangular picture languages", International Journal of Computer Applications Vol.57, No.15, (ISSN 0975-8887), Nov-2012.
[5]. Prophetis L.De and S.Varricchio.Recognizability of rectangular pictures by Wang systems.Journal of Automata,Languages and Combinatorics,4:269-288,1997.

Abstract: Cholera is an infection of the small intestine of humans caused by a gram negative bacterium called Vibrio cholerae. It is spread through eating food or drinking water contaminated with faeces from an infected person. It causes rapid dehydration and general body imbalance, and can lead to death since untreated individuals suffer severely from diarrhoea and vomiting. In this paper we formulate a mathematical model to assess the role of rehydration and antibiotic treatment on reduction of cholera mortality. All solutions in our model are positive and bounded hence well posed. The stability analysis of the model has been done. Numerical simulation shows that rehydration and administration of antibiotics play a major role in reducing cholera deaths.

Keywords: Cholera Disease, Role of Rehydration and Antibiotic treatment.

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Abstract: An analysis of complex functions and mapping that are holomorphic in nature are studied and discussed in this paper through Riemann surfaces, which involves Riemann Mapping theorem and Caratheodory's theorem. Furthermore Montel's theorem, Runge's theorem and Mergelyan's theorem over the holomorphic nature is studied with its basic properties and developed in this paper. To enhance the reliability over the nature of holomorphism the metrics of Riemann surface and conformal maps of plane to disk is analyzed and studied in this paper.

Keywords: Holomorphic functions, Conformal mapping, Riemann mappings, Riemann surface and Holomorphic open sets.

[1]. Carl Friedrich Gauss (1831) "The geometric representation of complex numbers since 1796, submitted his ideas to the Royal Society of Gottingen.

[2]. Carathéodory, C. (1954), Theory of functions of a complex variable, Vol. 2, translated by F. Steinhardt, Chelsea

[3]. John B. Conway (1978). Functions of One Complex Variable I. Springer-Verlag. ISBN 0-387-90328-3.

[4]. Carathéodory, C. (1998), Conformal representation (reprint of the 1952 second edition), Dover, ISBN 0-486-40028-X.

[5]. Pommerenke, C. (1992), Boundary behaviour of conformal maps, Grundlehren der Mathematischen Wissenschaften, 299, Springer, ISBN 3-540-54751-7.

Abstract: To study problems in geometry the technique known as Differential geometry is used. Through which in calculus, linear algebra and multi linear algebra are studied from theory of plane and space curves and of surfaces in the three-dimensional Euclidean space formed the basis for development of differential geometry during the 18th century and the 19th century. Since the late 19th century, differential geometry has grown into a field concerned more generally with the geometric structures on differentiable manifolds. The differential geometry of surfaces captures many of the key ideas and techniques characteristic of this field..

Keywords: Curvature Manifolds, Riemannian geometry and surface of revolutions.

[1]. Hestenes, David (2011). "The Shape of Differential Geometry in Geometric Calculus" (PDF). In Dorst, L.; Lasenby, J. Guide to Geometric Algebra in Practice. Springer Verlag. pp. 393–410. There is also a pdf available of a scientific talk on the subject.

[2]. Calavi and Roselicht ―complex analytic manifolds without countable base, Proc. Amer. Math. Soc (1953)pg335-340.

[3]. Manton, Jonathan H. (2005). "On the role of differential geometry in signal processing". doi:10.1109/ICASSP.2005.1416480.

[4]. Love, David J.; Heath, Robert W., Jr. (October 2003). "Grassmannian Beamforming for Multiple-Input Multiple-Output Wireless Systems" (PDF). IEEE Transactions on Information Theory. 49 (10): 2735–2747. doi:10.1109/TIT.2003.817466.

[5]. Micheli, Mario (May 2008). The Differential Geometry of Landmark Shape Manifolds: Metrics, Geodesics, and Curvature(PDF) (Ph.D.)..

Abstract: Many reasonable optimization problems include mathematical models of complex true wonders. This paper discusses some aspects of modeling that impact the execution of optimization methods. Information and guidance are given concerning the development of smooth models, the change of an optimization problem starting with one class then onto the next, scaling, detailing of imperatives, and techniques for exceptional sorts of models. The improved mathematical models and algorithms of vertical alignment by set forms of the course design are advertised. The issue is settled in a few phases in interrelation with other plan issues. The first algorithm of plunge is given for solving the emerging problem of nonlinear programming. Basic components of limitations are utilized thus it is not required to comprehend any frameworks of linear equations.

Keywords: Mathematical Modeling, Optimization Problem, performance, information, models, techniques, algorithms, nonlinear programming, linear equations..

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[2] V. S. Mikhalevich, V. I. Bykov and A. N. Sibirko, "The Problem of Designing Optimum Longitudinal Profile of the Road," Transportation Building, Moscow, 1975.

[3] Anonym, "The Use of Mathematical Optimization Techniques and Computer Engineering at the Longitudinal Profile of the Railways," Proceedings of the All-Union Scientific Research Institute of Transport Engineering, Transport, Moscow, 1977.

[4] F. Gill and W. Murray, "Numerical Methods for Constrained Optimization," Mir, Moscow, 1977.

[5] M. Aoki, "Introduction to Optimization Methods," Nauka, Moscow, 1977.

Abstract: In this paper, we construct the irreducible character table for symmetric group𝑆6following the same procedure used by Rao and Shankar (2016), in constructing irreducible character of 𝑆5 i.eusing the permutation module and the semi-standard young tableau x

[1]. A.G. Rao , N.R. Shankar, Characters of Permutation Group of Degree n Using SpechtModule and Semi Standard Young Tableaux. International journal of computer Application,147(2016) 0975 - 8887.
[2]. B.K. Mihsin, Decomposition Symmetric Group S5 to Character Table Subgroup by Using

[3]. Young Subgroup ofType S3S2 and S2S2S1, International Advanced Research Journal in Science, Engineering and Technology 3(4) (2016) ISSN(online) 2393-8021, ISSN(Print) 2394-1588.
[4]. B.K. Mihsin,H.B. Ameen, Construction of character table of symmetric group S4 by using permutation module,journal of karbala university,volume.11 No.2 Scientific.(2013)
[5]. D.E.Knuth, Permutations, Matrices And Generalized Young Tableaux, Pacific journal of mathematics. volume 34,No. 3 (1970).
[6]. E.Oucherlony,On Young TableauInvolutions and Patterns in Permutations. MatematiskainstitutionenLinköping Universitet, SE-581 83Linköping, Sweden.(2005).

Abstract: This paper investigates a reduction from boundary value problems to initial value problems. Shooting and Finite difference methods were used in the numerical solutions of two-point boundary value problems. Problems with and without exact solutions were considered. It showed the rate, efficiency and efficacy of convergence for two point Boundary Value Problems. The difficulty in providing exact solutions to two point boundary value problems via analytical methods necessitated the study. It was observed that the shooting method provides a better result than the finite difference method in solving two point boundary value problems (ODEs) with Dirichlet boundary conditions. The study further revealed other integrating factors adopted.

Keywords: BVP, Shooting method, Finite difference method, MATLAB, MAPLE, Euler's method, Trapezoidal method, Classical RK4,Embedded RK23

[1]. Bogacki P. and Shampine L"A 3(2) pair of Runge-Kutta formulas". Appl. Math. . Vol. 2 (1989), pages 321-325.

[2]. Burrage, K. "Special Family of Runge-Kutta Methods," (1978), Ell 18 22-41

[3]. Butcher J. C. "The Numerical Analysis of Ordira y Differential Equations, Runge-Kutta and General Linear Methods" Wiley, Chichester, New York. (1987),

[4]. Butcher, J. C. "A Multistep Generalization of R-K Method 3 with Four or Five stages", Journal of tlw ACM 14, (1967), 84-99. [5]. Causon M. and Mingham G. "Introduction to Finite Difference Methods for partial Differential Equations Ventus publishing" (2010), Aps ISBN 978-87-7681-642-1..

Abstract: Robust regression model has proved to provide efficiency in presence of errors with heavy tailed distribution. The application of the robust regression has gained a lot of application because of its indiscriminate in either parametric or non-parametric methods. This paper examines application of modified weighting method to a cross national regression analysis of election data in Africa countries. Data for analysis was obtained from African Social Survey(ASS)2002/2003 , the data covered 48 countries though only 29 countries were used because of comparability of survey questions. The results obtained reveals 𝑋𝑤𝑥2to be higher for the weights within-country. The paper does not observe clearly the effects expected from misspecification might simply mean that the model is adequately............

Keywords: Robut regression model, Election survey. design weights, within the country weights RK23

[1]. Fieldhouse, E, Tranmer, M., and Rusell, A (2007). Electoral participation of youngpeopleinEurope.
[2]. Hosmer,D.W.andLemeshow,S.(1980)Goodness-of-fittestsforthemultiple 1. logistics regression model
[3]. Thompson, M. E. (2008). International Surveys, Motives and methodologies.
[4]. African Social Survey (2004). ASS Round one 2002/2003
[5]. Graubard,B.I.,Korn,E.L.andMidthane,D.(1997).Testinggoodness-of-fit forlogisticregressionwithSurveydata..

Abstract: In this work we study the relationship between rough sets concept and image classification and explores the effectiveness of rough sets theory in image classification by using the change of rough sets theory to improve image classification model. Rough sets theory is used for classification rules extraction.

Keywords: Rough Set. Change of topologies, Image Classification

[1]. Fibak, Jan, et al. "Rough sets based decision algorithm for treatment of duodenal ulcer by HSV." Biological Sciences 34 (1986): 227-249.Hunt, E. B.: Concept formation. John Wiley and Stom, New York, (1974).
[2]. Pawlak, Zdzislaw, and W. Marek. "Rough sets and information systems." ICS. PAS. Reports 441 (1981): 481-485.
[3]. Martize, P.: Pawlak and topological rough sets in terms of multifunction, GlassnikMathemticki, vol. 31 (51), 159-178, (1996).
[4]. Nowak, R., R. Slowinski, and J. Stefanowski. "Rough Sets based diagnostic classifier of reducers." Maintenance Management International (1990).
[5]. Orłowska, Ewa S. Logic of vague concepts: applications of rough sets. Polish Academy of Sciences [PAS]. Institute of Computer Science, 1982..

Abstract: In this paper, a compartmental model approach was used in formulating a model to investigate the effects of social media on academic performance of students in higher institution. The total population is sub divided in to five compartments which are: social media non users class, less active users class, active users class, high performance class and low performance class. Two equilibria (Media Free Equilibrium MFE and Media Addiction Equilibrium Points AEP) were obtained and analyzed. The basic reproduction number was obtained and the stability analysis of the MFE reveals that, the MFE is locally asymptotically stable if is greater than unity and unstable otherwise. The AEP exists whenever . A numerical solution of the model was obtained and it shows that there is a significant effects of social media on academic performance of students in higher institution which proved the local stability analysis of the MFE.

Keywords: Compartmental model, Social media, Equilibrium point, Basic reproduction number, Local Stability.

[1]. A. Karpinski A description of Facebook Use and Academic Performance Among Undergraduate and Graduate Students. Annual Meeting of the American Educational Research Association, San Diego, Calif. (2009).
[2]. S. Edith, L.Victor The Effect of Social Network on Student's Academic Performance and Non-cognitive Behavioral Outcome, University of Warwick. (2014).
[3]. B. Gonxhe, The Impact of Social Media on Higher Education in Kosovo: The Student's Perspective, Academic Journal of Interdisciplinary Studies, 3 (2). (2014).
[4]. M. Munienge, Claver N., Kikunga M., The Effect of Social Media on Student's Engagement and Collaboration in Higher Education: A Case Study of the Use of Facebook at a South African University , Journal of communication, (2014) 5(2): 115-125. [5]. A. Adebiyi, M. Akinbode, S. Okuboyejo, G. Agboola, A. Oni,. Social Networking and Students' Academic Performance: bThe Role of Attention Deficit, Predictors of Behavior and Academic Competence, International Conference on African Development Issues (2015)..