iosr-Jm   Volume-15 ~ Issue-6 ~ Nov – Dec 2019

Abstract: This paper deals with a necessary and sufficient condition for the completeness of a uniform group of continuous functions from a topological spaces to a Housdorff complete uniform group. We also defined on the
completion of abelian or non- abelianHousdorff uniform group of functions.

Key Word: Topological space, Housdorff space, Uniform group, uniformity

[1]. Coth, E. : "Completeness and Compactness in linear topological spaces‟, Frans, Amer, MathSoz., 79 (1955) 256-280.
[2]. James, I. M. : Topological and uniform spaces; springer verlag. Berlin 1987
[3]. Isbll, J. R. : Uniform spaces, Amer Math Soz. Survey providence, 1964
[4]. Kelley, J. L. : General Topology, Van Nostrand, New-York, 1955.
[5]. Jha, K. K. : Advanced general topological, Nav Bharat Prakashan 1977.

Abstract: A graph G = (V, E) with p vertices is said to admit prime labeling if its vertices can be labeled with distinct positive integers not exceed p such that the label of each pair of adjacent vertices are relatively prime. A graph which admits prime labeling is called a prime graph. In this paper, we investigate prime labeling of Spliting graph of star K1,n .We also present an algorithm which enable us to find the chromatic number of Spl(K1,n)..

Key Word: Star Graph, Split Graph, Graph Labeling, Prime Labeling

[1]. J. A. Bondy and U. S. R Murthy, "Graph Theory and Applications", (North – Holland), New York (1976).
[2]. Tout, A. N. Dabboucy and K. Howalla, "Prime labeling of graphs", Nat Acad. Sci Letters, 11 (1982) 365-368.
[3]. J. A. Gallian, "A dynamic survey of Graph Labeling", The Electronic Journal of Combinatories, 16 # DS6, 2017.
[4]. Dr. V. Ganesan et al "Prime Labeling of Split graph of path graph Pn", International Journal of Applied and Advanced Scientific Research (IJAASR) volume 3, issue 2, 2018.
[5]. Dr. V. Ganesan and S. Lavanya "Prime labeling of Split graph of cycle Cn"..

Abstract: In this note, we review the work of Abubakar et al [1] and correct the value of the population growth rate which was wrongly calculated. We examine the difference between the new and the old population
projection growth by finding the absolute percentage error as presented in Table 2 and graphically in Figure 1.

Keywords: Census, Malthusian law, mathematical modeling, Population, Projection, Birth and Death rate

[1]. Abubakar, Y.A., Audu,, P.M. and Aisha, H.S. (2017). Mathematical modeling for population and management: A case study of Niger state. International Journal of Science and Research, 13(5), 51-57. http://dx.doi.org/10.9790/5728-1305035157.
[2]. Adegbile, I.O. (1975). Eighty Nigerians and their future: a commentary on the 1973 census. Africa to day, 22(1), 63-65.
[3]. Adeline, I.A., and Eme, O.I. (2015). Census politics in Nigeria: An examination of 2006 population cencus. Journal of Policy and Development Studies, 9(3), 47-72.[4]. Aluko, S.A. (1965). How many Nigerians? An Analysis of Nigeria's Census Problems, 1901-1963.The Journal of Modern African Studies, 3(3), 371-392.
[5]. Compbell, I. (1976). The Nigerian census: An essay in civil-militaryb relation. The Journal of Commonwealth and Comparative Politics, 4(3), 242-254..

Abstract: In the paper, we give characterizations of semi-states on residuated lattices, and discuss relations between Rl -morphism and semi-states on residuated lattices. Then we discuss the relations between maps defined by a frame. Finally, Using conanical frame on residuated lattices, we discuss the relations between state operator and the binary relation of Rl -morphisms.

Key Word: residuated lattice · state operator · frame

[1]. Chang CC (1958) Algebraic analysis of many-valued logic. Trans Am Math Soc 88: 467-490
[2]. Ciungu LC (2008) Bosbach and Rieˇcan states on residu- ated lattices. J Appl Funct Anal 2: 175-188
[3]. Gierz G, Hofmann KH, Keimel K, Lawson JD, Mislove M, Scott DS (2003) Continuous Lattices and Domains. Cambridge University Press, Cambridge
[4]. H´ajek P (1998) Metamathematics of fuzzy Logic, Trends in Logic-Studia Logica Library 4. Kluwer Academic Pub- lishers, Dordrecht
[5]. H¨ohle U (1995) Commutative residuated l -monoids. In H¨ohle, U and Klement, E. (eds), Non-Classical Logics and their Applications to Fuzzy Subsets. Kluwer, Dordrecht.