iosr-Jm   Volume-12 ~ Issue-6 ~ Nov-Dec 2016

Abstract: In this paper an attempt is made to study about compactness and connectedness in rough topological spaces. Also separation axioms and in rough topological spaces are discussed..

Keywords - Rough set, Rough Topological spaces, Rough compactness, Rough Connectedness, and separations in rough topological spaces.

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Abstract: Daily water level data of the Brahmaputra of Dibrugarh gauge station in Assam has been obtained from Central Water Commission (CWC), Govt. of India. This study is aimed to explore the statistical probability distribution of the extreme water levels of the Brahmaputra in Dibrugarh, Assam. Descriptive statistics and six probability distributions, viz., Generalized Extreme Value, Generalized Logistic, Gumbel Max, Logistic, Log Logistic and Lognormal have been proposed and ranked using Akaike Information Criterion (AIC). Parameters of the distribution are estimated using the Maximum Likelihood Estimation (MLE) method.

Keywords: Extreme water level, probability distribution, AIC

[1] Compendium of Environment Statistics, Central Statistical Organization, Department of Statistics, Ministry of Planning and Programme Implementation, Govt. of India Publication, New Delhi, 1997, pp. 115–120
[2] Khan, M., (2013): Frequency Analysis of Flood Flow at Garudeshwar Station in Narmada River, Gujarat, India. Universal Journal of Environmental Research and Technology, eISSN : 2249 0256 , Volume 3, Issue 6, 2013, pp: 677-684
[3] Izinyon, O.C., Ihimekpen, N. and Igbinoba, G.F. (2011): Flood Frequency Analysis of Ikpoba River Catchment at Benin City Using Log Pearson Type III Distribution. Journal of Emerging Trends in Engineering and Applied Sciences (JETEAS) 2(1). Scholarlink Research Institute Journals, 2011 (ISSN: 2141-7016) pp :50-55

[4] Nooijen, R.R.P.V., Gubareva, T. and Kolechkina, A.G. (2010): A Comparison of Fitting Methods and Tests for Several Distributions on Hydrological Data. International Workshop: ADVANCES IN STATISTICAL HYDROLOGY. May 23-25, 2010 Taormina, Italy

Abstract: Generalist species Predator – Prey Model and Maximum sustainable Yield have been discussed in this study. Both prey and predator populations are considered to follow logistic law of growth. The model possibly concerns with the prey population as Tilapia fish and the predator population as Whale fish. Furthermore, intra – specific competition among predator population is also included........

Keywords - Generalist species predator prey model, global stability, Lyapunov function, perturbation analysis, Prey harvesting, Predator harvestin

[1]. Paritosh Bhattacharya, Maximum sustainable yield policy in prey predator system – A study, 2nd international conference on computing communication and sensor network (CCSN – 2013) proceeding published by International journal of computer application (IJCA).
[2]. Dawed, M.Y., Koya, P. R., and Goshu, A. T. "Mathematical modeling of population growth: The case of Logistic and Von Bertalanffy models", Open Journal of Modelling and Simulation, Vol. 2 (2014), 113-126. http://dx.doi.org/10.4236/ojmsi.2014.24013
[3]. HARALD E.KROGSTAD*, MOHAMMED YIHA DAWED AND TADELE TESFA TEGEGNE,
[4]. Alternative analysis of the Michaelis – Menten equations, Teaching Mathematics and its Applications, Advance Access published June 23, 2011, Published by Oxford University Press on behalf of The Institute of Mathematics and its Applications.
[5]. Christina Kuttler, Mathematical Ecology, summer semester, 2010.

Abstract: In this paper, we introduce the notion of cubic ideals of -near-rings which is a combination of an interval-valued fuzzy set and a fuzzy set. Interval-valued fuzzy set is another generalization of fuzzy sets that was introduced by Lofti Asker Zadeh. In order to obtain cubic sub Γ-near-ring, cubic ideals of Γ-near-rings, direct product of cubic ideals in Γ-near-rings is also a cubic ideal, intersection of any family of cubic ideals of Γ-near-ring is also a cubic ideal of Γ-near-ring, cubic level set on Γ-near- ring and strongest cubic relation on Γ-near-ring........

Keywords - Cubic ideal, cubic homomorphism, ideal, near-ring, Γ-near-ring

[1]. L. A. Zadeh, Fuzzy sets, Information and Computation, 8, 1965, 338-353.
[2]. L. A. Zadeh, The concept of a linguistic variable and its application to approximate reasoning I, Information Sciences, 8, 1975, 1-24.
[3]. A. Rosenfeld, Fuzzy groups, Journal of Mathematical Analysis and Applications, 35, 1971, 512-517.
[4]. S. Abou-Zaid, On fuzzy subnear-rings and ideals, Fuzzy Sets and Systems, 44, 1991, 139-146.
[5]. Y. B. Jun and K. H. kim, Interval-valued fuzzy R-subgroup of near-rings, Indian Journal of Pure and Applied Mathematics, 33(1), 2002, 71-80.

Abstract: In this paper more general deterministic sex – structured HIV/AIDS model is proposed. The effects of Homosexuality (MSM) and Heterosexuality on the dynamics of the HIV/AIDS are studied. The epidemic threshold is known as a reproduction number. In this study it is classified as basic and partial reproduction numbers. The basic reproduction number is constructed considering both the heterosexuality and homosexuality. The partial reproduction number is constructed by considering only one of the heterosexuality and homosexuality. The basic reproduction number is an algebraic composition of the partial reproduction numbers. It is found that both heterosexuality and homosexuality have their own influences on the dynamics of the epidemic.

Keywords: HIV/AIDS; Homosexual (MSM); Heterosexual; Disease free equilibrium; local stability; reproduction number; partial reproduction number; sex structured model

[1]. Emilia Vynnycky, Richard White, An introduction to infectious diseases modeling; Oxford university press,2010 ISBN 978-0-19-856-576-5
[2]. European Study Group on Heterosexual; Transmission of HIV Comparison of female to male and male to female transmission of HIV in 563 stable couples; BMJ Vol(304):1992
[3]. Hellen Namawejje, Livingstone S.Luboobi, Dmitrykuznetsov and Eric Wobudeya. Bifurcation Analysis of model for the effect of vaccination on the transmission dynamics of Rotavirus Disease. Asian Journal of Mathematics and applications Vol(4):2015
[4]. Ying-Hen Hsieh. A two-sex model for treatment of HIV/AIDS and behavior change in a population of varying sizeurdi. IMA Journal of Mathematics Applied in medicine and Biology vol. (13):151-173, 1996
[5]. Issa Shabani and S. Massawe, Modeling the effect of screening on the spread of HIV infection in a population with variable inflow of infective immigrants. Scientific research and essays, Vol. 20, 4397-4405, 2011

Abstract: In this paper we have introduced the concept of regular weakly generalized locally closed sets in ideal topological spaces. Properties and characterizations are discussed

Keywords: Irwg-lc set, Irwglc* set, Irwglc** set.

[1]. Arochiarani. I, Balachandran. K and Ganster. M, Regular generalized locally closed sets and RGL-continuous functions, Indian J. pure appl. Math. 28(5), 661-669, 1997.
[2]. Dotchev.J, Ganster. M, Rose.D, Ideal reslivability. Topology and its applications, 93(1):(1999), 1-16
[3]. Kuratowski.K , Topology, Vol I, Academic Press, New Yprk, 1966.
[4]. Navaneethakrishnan.M and Sivaraj. D, Generalized locally closed sets in Ideal topological spaces, Bulletin of the Allahabad Mathematical Society, Golden Jubilee year Volume 2008.
[5]. Sakthi Sathya.B,Murugesan.S, Regular presemi I locally closed sets in ideal topological spaces, Asian Journal of current Engineering and Maths, Oct(2013) 312-315.

Abstract: The article reveals some new properties of odd numbers by means of valuated binary tree. It first systematically investigates properties of valuated binary subtrees, including calculation law of nodes, symmetric law of nodes and their common divisors as well as duplication and transition law of a subtree, then it digs out several new properties of the odd numbers that are bigger than 1. The new properties claim that, in an odd valuated binary subtree the sum of nodes on every level and the sum of nodes in the first finite.........

Keywords: Odd numbers, Integer division, Multiple

[1] WANG Xingbo. Valuated Binary Tree: A New Approach in Study of Integers, International Journal of Scientific and Innovative
Mathematical Research (IJSIMR), Volume 4, Issue 3, March 2016, PP 63-67
[2] WANG Xingbo. Analytic Formulas for Computing LCA and Path in Complete Binary Trees, International Journal of Scientific and
Innovative Mathematical Research (IJSIMR)

Abstract: One branch of science in mathematics were taught junior high school students is Geometry. Students are required to be able to visualize and manipulate an object in their minds in solving geometry problems. For example, if students are asked to find a shaded area of a flat object, the students should be able to imagine how the shape of the object and determine how to proceed. Some studies show that students still have difficulty in finding a way to solve the problem of geometry................

Keywords: Spatial reasoning, problem geometry

[1]. Guven, B ; Kosa, T. (2008). The Effect Of Dynamic Geometry Software On Student Mathematics Teachers Spatial Visualization
Skill. The Turkish Online Journal of Education Technology. ISSN : 1303-6521 articel 11, 7 (4).
[2]. Hudojo, Herman. (2003). Pengembangan Kurikulum dan pembelajaran matematika. Malang: Universitas Negeri Malang
[3]. National Council of Teacher of Mathematics. (2000). Principles and Standards for School Mathematics . (V. N. Reston, Ed.)
[4]. National Council of Teacher Of Mathematics. (2006). Curriculum Focal Points For Prekindergarten Through Grade 8
Mathematics (A Quest For Coherence, Reston VA: Autor ed.).
[5]. National Research Council. (2006). Paying Attention to Spasial reasoning (Support Document for Paying Attention to Mathematics
Education). (K.-1. N. Press., Ed.) Washington, DC.

Abstract: A subset D of is an independent set if no two vertices in D are adjacent. A dominating set D which is also an independent dominating set. An independent dominating set D of vertex set is called independent equitable cototal dominating set, if it satisfied the following condition..............

Keywords: Domination number, Equitable domination number, Cototal domination number, independent equitable cototal domination number

[1] B. Basavanagoud and S. M. Hosamani, Degree equitable connected domination in graphs, ADMS, 5(1), 2013, 1-11
[2] C.Berge, Theory of graphs and its Applications (Mehtuen. London, 1962)
[3] E. J. Cockayne and S. T. Hedetniemi, Towards a theory of domination in graphs. Networks 7, 1977,247-261.
[4] F. Harary, Graph Theory, Addison-Wesley, Reading, Mass, 1969.
[5] T. W. Haynes, S.T. Hedetniemi, and P.J.Slater, Fundamentals of domination in graphs, Marcel Dekker, Inc, New York, 1998.

Abstract: In this paper we will present some properties of generalized k-Fibonacci sequence U kU U U q U kq k n k n k n k k     , 2 , 1 , ,0 ,1 , , by matrix methods (Multiplication and Addition of Matrices) such as the nth power for the matrix representation of generalized k-Fibonacci sequence, Cassini's Identity of generalized k-Fibonacci sequence and some identities will be presented on the relations between k-Fibonacci and generalized k-Fibonacci sequence.

Keywords: k-Fibonacci numbers, Generalized k-Fibonacci numbers, Cassini's identity and Matrix methods.

[1] A. Borges, P. Catarino, A. P. Aires, P. Vasco and H. Campos, Two-by-two matrices involving k-Fibonacci and k-Lucas sequences,
Applied Mathematical Sciences, 8 (34), 2014, 1659-1666.
[2] A. D. Godase and M. B. Dhakne, On the properties of Generalized k- Fibonacci Like sequence using matrices, Indian Journal in
Number Theory, 1, 2014.
[3] B. Demirturk, Fibonacci and Lucas sums by matrix methods, International Mathematical Forum, 5 (3), 2013, 99-107.
[4] C. Bolat and H. Kose, On the properties of k-Fibonacci Numbers, Int. J. Contemp. Math. Sciences, 5 (22), 2010, 1097-1105.
[5] F. Koken and D. Bozkurt, On the Jacobsthal numbers by matrix methods, Int. J. Contemp. Math. Sciences, 3 (13), 2010, 605-614

Abstract: A (p,q) graph G(V,E) is said to be a prime difference speed sequence graph if there exists a bijection f: V(G) → { 0, 1, 2, …q2 } such that the induced mapping f: E(G) →{Δi(x)}/ i=1, 2, 3, …n}defined by f(uv) = |f(u) – f(v) |is a bijection. Here Δm(x) = (Δ mxk) = |(xk – xk+m)| and (x) is the Lucas sequence . The function f is called a prime difference speed sequence graph. In this paper we prove that the path graph, the fan graph, star graph, cycle graph, wheel graph and various types of graph are prime difference speed sequence graph

Keywords: Graph Labeling , Prime Labeling , Difference speed sequence graphs, Lucas numbers.

[1]. J.A.Bondy and U.S.R.Murthy, 1976, Graph Theory with application, London: Macmillan.
[2]. J.A.Gallian, A Dynamic survey of graph labeling, Electronic journal of combinatorics.
[3]. NarsinghDeo, Graph theory with applications to Engineering and Computer Science.
[4]. K. Indirani, On "Rate sequence spaces", thesis submitted to Mother Teresa Women's University.
[5]. R.B.Gnanajothi, Topics in Graph Theory

Abstract: The Generalized Parikh vectors and the Generalized Parikh matrices have been studied to give a better numerical representation of words & 2D binary arrays. Algorithms to find these Generalized Parikh matrices of binary words and 2D binary arrays are given in the paper. Also some conditions related to the commutativity of the product of these Generalized Parikh matrices have been discussed.

Keywords: Parikh vectors, Parikh matrices, binary words, 2D binary arrays, Generalized Parikh vectors, Generalized Parikh matrices, path automaton.

[1] R.J. Parikh, On Context free languages, J. Assoc. Comput. Mach., 13, 1966, 570-581.
[2] A. Mateescu, A. Salomaa, K. Salomaa and S. Yu, A sharpening of the Parikh mapping, Theoretical Informatics Appl., 35, 2001, 551-564
[3] K.G. Subramanian, Ang Miin Huey and Atulya K Nagar, Parikh matrices, International Journal of Foundations of Computer Science, 20(2), 2009.
[4] R. Sironmoney and V. Rajkumar Dare, On generalization of the Parikh vector for finite and infinite words, Lecture Notes in Computer Science, 206 (Springer Verlag, 1985), 290-302.
[5] Huldah Samuel, On Generalized Parikh matrices for finite and infinite words, International Journal of Computer Applications, 68(15), 2013, 37-39.

Abstract: In this paper, we investigate some geometric properties of the Hurwitz set which corresponds to the set of stable monic polynomials in a parameter space. We firstly consider the segment stability. After we study properties of rays in the Hurwitz sets, which corresponds with inclusion or non-inclusion of certain rays in the Hurwitz sets.

Keywords: Hurwitz polynomials, monic polynomials, ray properties, segment stability

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Abstract: The purpose of this research article is to study about intuitionistic α-open sets and discuss interior and closure properties of intuitionistic sets

[1]. Andrijevic D, Some Properties of the Topology of α Sets, Mat. Vesnik 36(1984),1-10.
[2]. Andrijevic D, Semi Preopen Sets, Mat. Vesnik 38(1986), 24-32.
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Abstract: In this paper, a new class of sets called D α-closed sets in supra topological spaces are introduced and studied. Also we introduce supra D α-continuous function, totally supra D α -continuous and supra contra D α-continuous function in supra topology spaces and some of its properties are studied.

[1]. Andrijevic D. Some properties of the topology of α sets.Mat Vesnik 1984;36:1-10.
[2]. Devi, S.Sampathkumar and M.caldas, On supra α open sets and -continuous , General Math, 16(2008),77-84
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