iosr-Jm   Volume-15 ~ Issue-2 ~ March-April 2019

Abstract: In this paper, we consider a multilane fluid dynamic traffic flow model for three lanes based on a linear velocity-density relationship which yields a non-linear first order system of hyperbolic partial differential equation as an IBVP. Due to the complexity of findings the analytical solution of the model, we investigate numerical solution by finite difference method. For numerical solution, we present the finite difference discretization of the model analogous to the second order Lax-Wendroff difference scheme and report on the
stability and efficiency of the scheme by performing numerical experiments. The computed result satisfies some well known qualitative behaviors of the numerical solution based on artificial initial and boundary data.........

Key Word: Multilane traffic flow model, Non-linear PDE and Numerical Simulation.

[1]. Nicola Bellomo, Marcello Delitala, and V. Coscia, "On the Mathematical Theory of vehicular Traffic Fluid Dynamic and Kinetic Modeling", Mathematical Models and Methods in Applied Sciences Vol. 12, No. 12 (2002) 1801-1843.
[2]. Bretti, G., Natalini, R. and Piccoli, B. (2007) "A Fluid-Dynamic Traffic Model on Road Networks", Comput Methods Eng., CIMNE, Barcelona, Spain.Vol-14:139-172.
[3]. Klar, A., Kuhene, R.D. and Wegener, R. "Mathematical Models for Vehicular Traffic" Technical University of Kaiserlautern, Germany.
[4]. Dong NGODUY, "Macroscopic Discontinuity Modeling for Multi class Multilane Traffic Flow Operations", Master of Science in Engineering Thesis, Delft University of Technology, Netherland, 2006.
[5]. V. I. Shvetsov, "Mathematical Modeling of Traffic Flows, Automation and Remote Control", Vol.64, No. 11, pp. 1651-1689, 2003

Abstract: The purpose of this paper is to introduce and study about neutrosophic regular 𝛼 generalized closed sets in neutrosophic topological spaces. Some interesting propositions based on this set are presented and established with suitable examples. Their properties are discussed. Mathematics Subject Classification (2010): 54A40, 03E72.

Keywords: Neutrosophic sets, neutrosophic topology, neutrosophic regular 𝛼 generalized closed sets.

[1]. Atanassov, K., Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 1986,87-96.
[2]. Chang, C., Fuzzy topological spaces, J.Math.Anal.Appl., 1968,182-190.
[3]. Coker, D., An Introduction to Intuitionistic fuzzy topological spaces, Fuzzy Sets and Systems,1997,81-89.
[4]. Floretin Smarandache., Neutrosophic set: A generalization of Intuitionistic fuzzy set, Jour. of Defense Resources Management, 2010,107-116.
[5]. Ishwarya, P., and Bageerathi, K., On Neutrosophic semi-open sets in neutrosophic topological spaces, International Jour. of Math. Trends and Tech.2016, 214-223.

Abstract: In this paper we have introduced weakly generalized continuous mappings in neutrosophic topological spaces and analyzed some of their properties. We have discussed some characterizations of weakly generalized continuous mappings in neutrosophic topological spaces. Mathematics Subject Classification (2010): 54A40, 03E72.

Keywords: Neutrosophic sets, neutrosophic topology, neutrosophic weakly generalized closed sets, neutrosophic weakly generalized open sets, neutrosophic weakly generalized continuous mappings, neutrosophic weakly generalized irresolute mappings.

[1]. Abinaya, S and Jayanthi, D, Weakly generalized closed sets in neutrosophic topological spaces (submitted).
[2]. Atanassov, K., Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 1986, 87-96.
[3]. Atanassov, K., (1999) Interval valued intuitionistic fuzzy sets, in: Intuitionistic Fuzzy sets. Studies in fuzziness and soft computing, vol 35. Physica, Heidelberg.
[4]. Chang, C., Fuzzy topological spaces, J.Math.Anal.Appl., 1968,182-190.
[5]. Coker, D., An Introduction to Intuitionistic fuzzy topological spaces, Fuzzy Sets and Systems,1997,81-89.

Abstract: In this paper, game theory is applied to the selling decision to establish that shopkeepers are locked in "prisoner's dilemma" and one shot game over the decision. Individual rationality has pushed both shopkeepers in a duopoly market to adopt a dominating strategy, leading to several full-fledged and limited wars. However, collective rationality brings about peace as a Pareto-optimal solution under game theory. An attempt has also been made to show how two shopkeepers can mitigate their dilemma by using the strategies meant for mitigating the prisoner's dilemma in game theory.

Keywords: Duopoly, prisoner's dilemma, one shot game, revenue, game value.v.

[1]. D. G. Rand, M. A. Nowak (2013), Human Cooperation, Trends Cogn. Sci. 17(8), 413-425.
[2]. R. M. Dawes, R. Thaler (1988), Anomalies: Cooperation, J. Econ. Perspectives 2, 187–197.
[3]. B. Rockenbach, M. Milinski (2006), The efficient interaction of indirect reciprocity and costly punishment, Nature 444(7120), 718-723.
[4]. M. A. Nowak (2006), Evolutionary dynamics, Harvard University Press.
[5]. M. Perc, J. J. Jordan, D. G. Rand, Z. Wang, S. Boccaletti, A. Szolnoki (2017), Statistical physics of human cooperation, Phys. Rep. 687 1-51. doi:10.1016/j.physrep.2017.05.004.

Abstract: A direct sum of simple modules is being splited by every module. There are different kind of rings but special case has been raised in Principal Ideal Domain(PID). PID is considered like as semisimple rings that is splited a direct sum. In fact while the integer Z and the ring of polynomial k[x] may look like as different rings initially but these are very analogous for being both PIDs.

Keywords: Semisimple Ring ,Principal Ideal Domain, Principal Ideal, Integral Domain, Direct Sum.

[1]. Waffle, Principal Ideal Domain, Mathcamp 2009, P: 1-9.
[2]. A.W Chatters "Rings which are nearly principal Ideal Domain." Glasgow Math. J.40(1998):343-351.
[3]. From Google Wikipedia.
[4]. Thomas William Hungerford, "On the structure of Principal Ideal Rings." PJ of Mathematics, vol25, No.3,1968.

Abstract: In this paper, we shall introduce the extension of recently introduced concepts of Wijsman I−lacunary statistical convergence of order 𝛼 and Wijsman strongly 𝐼−lacunary statistical convergence of order 𝛼 to double sequences.

Keywords: 𝐼2 −convergence, Wijsman convergence, lacunary double sequences. 2010 Mathematics subject classification: Primary 40F05, 40J05, 40G05

[1]. A. M. Brono, A. G. K. Ali and M. T. Bukar, 𝐼2−statistical and 𝐼2−lacunary statistical convergence for double sequence of order 𝛼. IOSR Journal of Mathematics, 13(2017), 107-112.
[2]. H. Cakalli, On statistical convergence in topological groups. Pure Appl. Math. Sci. 43(1996), 27–31.
[3]. H. Cakalli and P. Das, Fuzzy compactness via summability. Journal of Applied Mathematics, 22(2009), 1665-1669. [4]. L. Cheng, G. Lin, Y. Lan and H. Liu, Measure Theory of Statistical Convergence. Science in China Series A-Math. (2008) 51: 2285.
[5]. J. Connor, and M. A. Swardson, Strong integral summability and stone-chech compactification of the half-line. Pacific Journal of Mathematics. 157(1993), 201-224..

Abstract: We shall in analogy to the recently introduced notion of 𝐼𝜆−statistical convergence of order 𝛼; introduce and study, 𝐼𝜆2−statistical convergence for double sequence of order 𝛼 in topological groups and also establish some inclusion theorems

Keywords: Filter, 𝐼2-Statistical Convergence, Double sequences, Topological groups. 2010 Mathematics subject classification: Primary 40F05, 40J05, 40G05

[1]. A. M. Brono and A. G. K. Ali, 𝜆2−Statistical convergence in 2n-normed spaces. Far East Journal of Mathematical Sciences, 99(2016), 1551-1569.
[2]. A. M. Brono, A. G. K. Ali and M. T. Bukar, 𝐼2−statistical and 𝐼2−lacunary statistical convergence for double sequence of order 𝛼. IOSR Journal of Mathematics, 13(2017), 107-112.
[3]. H. Cakalli. On statistical convergence in topological groups, Pure and Applied Mathematical Sciences, 43(1996), 27-31.
[4]. H. Cakalli, A study on statistical convergence. Funct. Anal. Approx. Comput., 1(2009), 19-24.
[5]. A. Caserta, G. Di Maio and Lj. D. R. Ko𝑐 inac, Statistical convergence in function spaces, Abstr. Appl. Anal. (2011)..

Abstract: The Weyl group, W of G is defined as NG(T )/CG(T ), where NG(T ) is the normalizer of T in G and CG(T ) is the centralizer. This group is a finite group which can be regard as permutation groups on certain relevant sets of points in Z, see ([4],[5]). In this paper we defined a special way of denoting to write the Weyl elements for the group SO(2n; C).

[1]. F. Abu-Shoga. Combinatorial geometry of flag domains in G=B, PhD thesis, Ruhr Univer-sity Bochum, 2017.
[2]. F. Abu-Shoga. Combinatorial geometry of flag domains in G=Q. Preprint in preparation.
[3]. V. Lakshmibai, Geometry of G=P X: The Group SO(2n) and the Involution . Journal of Algebra 130, pages 122-165, 1990.
[4]. A. W. Knapp. Lie Groups Beyond an Introduction. Progress in Mathematics. Birkhauser Boston, Boston, 2 edition, 2002.
[5]. J. Humphreys. Linear Algebraic Groups, Volume 21 of Graduate Texts in Mathematics, Springer, 1975..

Abstract: Several people presented solutions to the Birkhoff's problem "Develop a common abstraction which includes Boolean algebras (rings) and lattice ordered groups as special cases". Many common abstractions namely dually residuated lattice ordered semi groups, lattice ordered groups, DRℓ - groups, lattice ordered rings are presented in [6], [4], [3] and [2] respectively. The objective of this paper is to introduce Characterization Theorem for commutative lattice ordered ring or commutative ℓ-ring which is an abstraction between Boolean algebra and lattice ordered group

[1]. BIRKHOFF, G., - Lattice Theory, Amer. Math. Soc. Colloq. Publ. XXV, Providance R.I, Third Edition, Third printing, 1979.
[2]. JOHNSON, D.G., - A Structure Theory for a class of Lattice Ordered Rings, Acta Math. 104 (1960), 163 – 215.
[3]. NATARAJAN, R. DRℓ - group, Acta Ciencia Indica and - Vol XXIXM, No4. 823 -830, 2003 JAYALAKSHMI, M. (MR 2064351)
[4]. RAMA RAO, V.V., - On a common abstraction of Boolean rings and lattice ordered groups I, Monatshefte fur Mathematik, 73 (1969), 411 – 421.
[5]. RANGA RAO, P., - Lattice ordered semi rings, Mathematics Seminar notes, 9 (1981), 119 – 149

Abstract: Universal portfolios generated by the f-divergences have been proposed recently. The f-divergence of Csiszar is generated by a non-negative convex function on the positive axis. In this paper, the pseudo f-divergence is defined for two types of convex functions not satisfying the usual requirements. The first type is a non-negative function convex on a subset of the positive axis and the second is a function convex on the positive axis but non-negative on a subset of the axis. Five portfolios are selected from the local stock exchange for the empirical study of the generated universal portfolio. High investment returns are observed for some of the selected portfolios, indicating the suitability of practical usage

Keywords-Pseudo𝑓-divergence, universal portfolio, convex function, investment

[1]. T. M. Cover and E. Ordentlich, Universal portfolios with side information, IEEE Transactions on Information Theory, vol.42, no.2, pp.348-363, Mar. 1996.
[2]. C. P. Tan, Performance bounds for the distribution-generated universal portfolios, Proc. 59thISI World Statistics Congress, Hong Kong, 5327-5332, 2013.
[3]. D. P. Helmbold, R. E. Shapire, Y. Singer and M. K. Warmuth, On-line portfolio selection using multiplicative updates, Mathematical Finance, vol.8, no.4, pp.325-347, Oct. 1998.
[4]. C. P. Tan and K. S. Kuang, Universal Portfolios Generated by the 𝑓 and Bregman Divergences, IOSR Journal of Mathematics, 14, 19-25, 2018.
[5]. L. Pardo, Statistical Inference Based on Divergence Measures, FL: CRC Press, Boca Rotan, p. 29, 2006.

Abstract: The purpose of this study focused on exploring and determining an effective and plausible mathematical growth model for prediction of future Population size of United Republic of Tanzania for the next two censuses of 2022 and 2032.Tanzania's Population is growing faster as science and Technology growing which become a burden to Government budget in allocation of the limited resources available. The Exponential, Logistic growth model and Method of Least square (MLS) were employed by using previous census data from 1980 to 2016 inclusive and analyzed by using MATLAB (R2017a) software. The study determined that Logistic model is more effective and reliable with Average relative error of 0.72%, carrying Capacity (K) of 728133426 and vital coefficients of r=0.032 and 𝑟𝐾=4.39479892796461×10−11.These plausible parameters used to predict Tanzania's Population to be 667853660 and 88896969 in 2022 and 2032 respectively.

Keywords-modeling, estimation, model fitting, parameters, prediction, mathematical models

[1]. Venkatesha.P,G.BlessySachy Eunice et al Mathematical modelling of Population growth International Journal of Science,Engineering and Management (IJSEM) vol2.issue 11,November 2017
[2]. Hironmoy Mondol,Uzzwal Kumar mallick,Md.H.A.Biswas Mathematical model- ing and predicting the current trends of human population growth in Bangladesh Advances in modelling and Analysis A vol.55,No.2,June 2018,pp. 62-69
[3]. Yahaya,Ahmad Abubakar,Philip Moses Audu and Hassan Sheikh Aisha Math- ematical modelling for population projection and management:A case study Of Niger stateIOSR Journal of Mathematics (IOSR-JM)e-ISSN:2278-5728,p- ISSN:2319-765X.volume 13,issue 5 ver III(sep-oct.2017),pp 51-57
[4]. Abdelrahim.M.Zabadi,Ramiz Assef, Mohammad Kanan A mathematical and statistical approach for predicting the population GrowthWWJMRD2017;3(7):50-59
[5]. Sintayehu Agegnehu Matintu mathematical model of Ethiopia's population growth Journal of Natural science Research ISSN 2224-3186 vol.6,No.17 2016.