iosr-Jm   Volume-15 ~ Issue-4 ~ July-August 2019

Abstract: In this paper, we shall introduce the concept of statistical convergence and statistical Cauchy of double sequence of functions in 2n-normed spaces. We shall also investigate some properties and establish relationships between these concept in 2n-normed spaces.

Key Word: Statistical convergence, Statistical Cauchy, Double Sequence, 2n-normed Spaces.

[1]. A GӦkhan, M. GűnGӦr and M. ET, statistical convergence of double sequence of real-valued functions,
[2]. Brono A. M., and Ali A. G. K. (2016),"λ_2-Statistical Convergence in 2n-normed Spaces",Far East journal of mathematical Science 99(10), 1551-1569.
[3]. Brono A. M., and Ali A. G. K. (2016),"A Matrix characterisation of CésaroC_11-statistical convergence Double Sequence"Far East Journal of Mathematical Sciences, 99(11), 1693-1702.
[4]. Brono A. M., and Ali A. G. K. (2016),"On Statistical Convergence of Double Sequences and Statistical Monotonicity",IOSR Journal of Mathematics, 12(1), 45-51.
[5]. Dundar E. and Altay B. (2015),"l_2-convergence of double sequence of functions",Electronic Journal of Mathematical Analysis and Application 3(1). 111-121.

Abstract: In this work, a class of new computational methods for solution of variable coefficients partial differential equation was developed at step numbers j = 3; resulting into a Trapezoidal rule spectral based computational scheme as reported in Lambert (1973). The accuracy, consistency, stability and convergence properties of these methods were determined. The methods were implemented on some sampled problems that involve both constant and, variable coefficients parabolic partial differential equations; and evaluated by comparing them with some existing difference methods. The results obtained are found to be more rapidly converging as the step lengths h and k approaches zeros. This work provides better alternative numerical solutions to a class of dynamical problems having time dependent boundary conditions. Higher ordered telegram parabolic partial differential equations with defined theoretical solutions to given boundary conditions can be solved directly using this method..

Key Word: Trigonometric Functions, Taylor Series Expansion, Time, Finite& Space Difference

[1]. Ademiluyi R. A. and Kayode S. J.(2001): 'Maximum Order Second Derivative Hybrid Multistep Methods for Integration of IVP in Ordinary Differential Equations' Journal of Nigerian Association of Mathematical Physics Vol. 5, pp254-262
[2]. Adoghe L. O. (2014): 'Numerical Algorithms for The Solution Of Third Order Ordinary Differential Equations' Ph. D Thesis, FUTA.(Unpublised)
[3]. Akinmoladun O. M. (2011) ''Numerical Methods for the Solutions of IVP with oscillatory solutions'' M. Tech. Thesis (Industrial Mathematics) FUTA, Nigeria. (Unpublished)
[4]. Akinmoladun O. M., Ademiluyi R.A., Abdrasid A. A. and D.A. Farinde (2013) ''Solutions of Second Order ODE with periodic solutions' published in International Journal for Science & Engineering Reseach (IJSER), USA. Vol. 4 issue 9, Sept. 2013, ISSN 2229 – 5518; pp2604-2612.
[5]. Akinfenwa O. A, Jato S. N. and Yao N. M (2011) 'A Continuous Hybrid Method for Solving Parabolic Partial Differential Equation' AMSE Journal, July,, 2011..

Abstract: We formulated a four compartmental model of Infectious Bursal Disease (IBD) for both the ordinary and control models. We first determined the basic Reproduction number and the existence of Steady (Equilibrium) states (disease-free and endemic). Conditions for the local stability of the disease-free and endemic steady states were determined. Further, the Global stability of the disease-free equilibrium (DFE) and endemic equilibrium were proved using Lyponav method. We went further to carry out the sensitivity analysis or parametric dependence on R0 and later formulated the optimal control problem. We finally looked at numerical Results on poultry productivity in the presence of Infectious Bursal Disease (IBD) and we drew six graphs to demonstrate this. From Figure 4.1 we observe that the number of birds at the early stage of the infection increases rapidly and drops.........

[1]. Abid, A. L. (2016). Optimal control of a SIR Epidemic Model with a saturated treatment; Journal of Applied Mathematics and Information Sciences, 10, No 11, 185 – 191.
[2]. Boot, H. J., Hoekwan A. J., Giekers A. I. (2005) The enhanced virulence of very virulent infectious Bursal Disease Virus partly determined by its B – Segment. Archive Virology, 150: 137 – 144.
[3]. Candelora, K. L., Spalding M. G., Sellers H. S. (2010). Survey for antibodies to Infectious BursalDisease Virus Sertyoe 2 in wild Turkeys and Sand hill cranes of Florida USA. Journal of Wild life Diseases 46(3) : 742-752. doi : 10.7589/0090-3558-46.3.742.
[4]. Chung-Chai, H., Tsan – Yuk L., Alexei D., Andrew R., Yiu – Fai L., Chai – Wai Y., Fanya Z., Pui Yi L., Patrick T., Frederick C. L. (2006). Phylogenetic Analysis reveals a correlation between the Expansion of very Virulent Infectious Bursal Disease Virus and reassortment of its Genome Segment. Journal of virology, Vol. 80, No. 17, pp 8503 – 8509.

[5]. Durairaj, V., Linnemann e., Icand A. H., Williams S. M., Sellers H. S., Mundt E. (2013). An in vivo experimental model to determine antigenic variations among Infectious Bursal Disease Virus. Journal of Avian Pathology 42(4) : 309 – 315. doi:10:1080/03079457-2013-793783

Abstract: This study examined the analysis of the relationship between co-curricular Activities (Sport) and Students achievement in senior secondary school Mathematics in the Southern part of Taraba state in North-East zone of Nigeria. The study adopted simple survey design. A review of related literature to the study was carried out. Data collected and collated were based on a set of Scales in the Questionnaire Mathematics-Sports- Related Scales (MSAS) consisting of ten (10) items and was administered to eighteen (18) public schools across the zone; three from.......

Keywords :Student`s Achievements; sports;Questionnaire;Spearman rank correlation; SPSS;

[1]. Adebayo, S.O. and Mukaila (2003) Learning Theories. London: Heinemann Educational Book Ltd.
[2]. Agbor, B. S. (1991) Games and Mathematics Achievement in Secondary School. An unpublished N.C.E. project submitted to cross River State College of Education, Akamkpa.
[3]. Akwo, S. A. (2006) Instructional Materials and Students Academic Achievement. An unpublished Bsc.ed project submitted to faculty of Education CRUTECH.
[4]. Ali, B. A. (1998) Introduction to Curriculum Research and Development. London: Heinemann Educational books Ltd.
[5]. Effiom, D. O. and Ejue, J. B. (2002) Handbook on Child Development Psychology. Calabar: Wusen Press Ltd.

Abstract: In this article, Modified Euler's Method and Runge- Kutta Methods have been used to find the numerical solutions of ordinary differential equations with initial value problems. By using MATLAB we determined the solutions of some numerical problems and at the same time calculated the exact analytic solution. Then, the numerical approximate solutions were compared with the exact solutions for validating the accuracy. We found that, the solution become more precise when the step size is very small. Here, the difference between the numerical approximate solutions and analytic solutions is the relative error. We found that, between the two proposed methods the relative error is nominal for Runge-Kutta fourth order method..

Keywords :Initial value problem, Modified Euler's method, Runge- Kutta method, Error analysis.

[1]. Shampine, L.F. and Watts, H.A. Comparing Error Estimators for Runge-Kutta Methods. Mathematics of Computation, 25, 445-455. http://dx.doi.org/10.1090/S0025-5718-1971- 0297138-9 (1971).
[2]. Eaqub Ali, S.M. A Text Book of Numerical Methods with Computer Programming. Beauty Publication, Khulna (2006).
[3]. Kockler, N. (1994) Numerical Method for Ordinary Systems of Initial value Problems. John Wiley and Sons, New York.
[4]. Lambert, J.D. Computational Methods in Ordinary Differential Equations. Wiley, New York (1973).
[5]. Gear, C.W. Numerical Initial Value Problems in Ordinary Differential Equations. Prentice-Hall, Upper Saddle River (1971)..

Abstract: In this chapter we have introduced two types of b# continuous mappings namely intuitionistic fuzzy almost b# continuous mappings and intuitionistic fuzzy almost contra b# continuous mappings. Also we have provided some interesting results based on these continuous mappings.

Keywords :Intuitionistic fuzzy sets, intuitionistic fuzzy topology, intuitionistic fuzzy almost b# continuous mapping.

[1]. Atanassov, K., Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20, 1986, 87- 96.
[2]. Coker, D., An introduction to intuitionistic fuzzy topological spaces, Fuzzy Sets and Systems, 88, 1997, 81 - 89.
[3]. Coker, D. and Demirci, M., On intuitionistic fuzzy points, Notes on Intuitionistic Fuzzy Sets, 1, 1995, 79-84.
[4]. Gomathi, G., and Jayanthi, D., Intuitionistic fuzzy b# continuous mapping, Advances in Fuzzy Mathematics, 13, 2018, 39 - 47.
[5]. Gomathi, G., and Jayanthi, D., b# Closed sets in Intuitionistic Fuzzy Topological Spaces, International Journal of Mathematical Trends and technology, 65, 2019, 22-26..

Abstract: The frequency of appearance of the Golden Ratio (Φ) in nature implies its importance as a cosmological constantand sign of beingfundamental characteristic of the Universe.Except than Leonardo Da Vinci's 'Monalisa' it appears on the sunflower seed head, flower petals, pinecones, pineapple, tree branches, shell, hurricane, tornado, ocean wave, and animal flight patterns. It is also very prominent on human body as it appears on human face, legs, arms, fingers, shoulder, height, eye-nose-lips, and all over DNA molecules and human brain as well. It is inevitable in ancient Egyptian pyramids and many of the proportions of the Parthenon. But very few of us are aware of the fact that it is part and parcel for constituting black hole's entropy equations,black hole's specific heat change equation,also it appears atKomar Mass equation ofblack holes and Schwarzschild–Kottler metric - for null-geodesics with maximal radial acceleration at the turning point of orbits [1, 2, 3, 4].But here in this paper the discussion is limited to the exhibition of mathematical aptitude of Golden Ratio a.k.a. the Devine Proportion

Keywords : Golden Ratio, Devine Proportion, Cosmological Constant, Fundamental Constantof Nature

[1]. C. Rovelli and F. Vidotto, "Covariant Loop Quantum Gravity", Cambridge University Press 1 edition, 2014
[2]. Klee Irwina, Marcelo M. Amaralab, Raymond Aschheima, Fang Fanga, "Quantum Walk on a Spin Network and theGolden Ratio as the Fundamental Constantof Nature", Minkowski Institute Press, Published on 29 April 2017
[3]. Salvatore Giandinoto,"Superluminal Transportation of High Energy Particles Through Wormholes Using the Phi-Based Solution to the Schrödinger Wave Equation, the theorem of Residues and the Cauchy Integral Formula", Journal Published on 2007
[4]. Norman Cr., Marco Ol. &VillanuevaJ. R., "The Golden Ratio in Schwarzschild–Kottler Black Holes", The European Physical Journal, Received: 16 January 2017 / Accepted: 27 January 2017 / Published online: 23 February 2017
[5]. Weblink: https://en.wikipedia.org/wiki/Golden_ratio; collected on 2019

Abstract: In the present work the model of the dynamics insulin-glucose is indicated for both a healthy person and a patient who has already contracted diabetes; the different types of diabetes are indicated as well as the symptoms that characterize it. It presents the model corresponding to the process of regeneration of diabetic foot tissues, distinguishing the case in which the tissues are added and when this process is decreasing; and a qualitative study of the solutions of the corresponding equations is made and conclusions are drawn regarding the future behavior of the process, indicating those cases when the process is irreversible and when the tissues are regenerated.

Keywords : Insulin, glucose, diabetic, hormones

[1]. Brazil. Epidemiological Bulletin Syphilis. Brasília: Ministry of Health, Department of Health Surveillance - Department of STD, AIDS and Viral Hepatitis, Year IV, n. 1, 2015.
[2]. Brazil. Ministry of Health. Health Surveillance Secretariat. National STD and AIDS Program. Manual of Control of Sexually Transmitted Diseases / Ministry of Health, Secretariat of Health Surveillance, National STD and AIDS Program. Brasilia: Ministry of Health.
[3]. Chaveco, A; Domínguez, S e GarcíasA.Mathematical modeling of the polymerization of hemoglobin S. LAP LAMBERT Academic Publishing. Germany. 2015.
[4]. D. Rodriguez1, M. Lacort2, R. Ferreira1, S. Sanchez1, E. Rodrigues2, Z. Ribeiro2, A. I. Ruiz2. "Modelofthe Dynamics Insulin-Glucose". InternationalJournalofInnovativeResearch in Electronicsand Communications. Volume 5, Issue 4, 2018, Page No: 1-8.
[5]. D. Rodríguez, M. Lacort, R. Ferreira, S. Sánchez, F. Chagas, Z. Ribeiro, A. I. Ruiz; "ModelofDynamicInsulin-Glucose in Diabetic". EJERS, EuropeanJournalofEngineeringResearchand Science. Vol. 4, No. 3, March 2019