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.

Abstract: Analogy is an effective thinking method to explore problems, solve problems and discover problems, and in mathematics, it is an important means to discover concepts, methods, theorems and formulas. Transformation is an important method to explore and prove new proposition and to make mathematical creations. Pursuing analogy and transformation in depth is very beneficial to the study of mathematics. Complex analysis is based on real analysis, so, many concepts, properties, definitions and methods for dealing with problems are similar. Based on the complex functions, we discuss the embodiment of analogy and transformation in complex analysis from several aspects, in this paper..

Key Word: analogy, transformation, complex variable functions

[1]. Morris Kline. Mathematical thought from ancient to modern times. Oxford University Press; New Ed, 1990.
[2]. L R Novick，K J Holyoak. Mathematical Problem Solving by Analogy. Journalof Experimental, Psychology:LearningMemoryand Cognition，1991，17:398-415.
[3]. P.A. Alexander, C.S. White,M. Daugherty, Analogical reasoning and early mathematics learning.In L.D.English (Ed.)，Mathematical reasoning ：Analogies ，metaphors，and images 1995:117-147.
[4]. G Polya，How to solve it. Princeton Princeton University Press: Peprint, 2014.
[5]. Lyn D. English，Patrick V. Sharry. Analogical reasoning and the development of algebraic abstraction. Educational studies in mathematics.1996,30(2): 135-157

Abstract: To investigate vibration of a simplified human thoracic aorta and its natural frequencies DMV(Donnell MushtariVlsasov) theory is used in present study. The theoretical analysis is presented to calculate natural frequencies and variation in length of thoracic aorta with respect to age of human being.The results show that the first natural frequency of thoracic aorta is near about 1.2 hertz, which corresponds to the natural heart beat rate(1.2 beat per second).

[1]. Anooshiravan F., Pouria O. Free Vibration Analysis of Circular Cylindrical Shells: Comparison of Different Shell Theories. International Journal of Mechanics and Applications ,2012; 2(5): 74-80.
[2]. Arnett DK, Evans GW, Riley WA. Arterial stiffness: a new cardiovascular risk factor? Am J Epidemiol 1994; 140: 669–682.
[3]. Charles T. Dotter, Aortic Length: Angiocardiographic Measurements, American Heart Association, 1950;2:915-920.
[4]. Choung C J, Fung Y C on residual stress in arteries, Journal of Biomechanical engineering, 1986,108:189-192.
[5]. Delfino A, StergiopulosN,Moore J E, Meister JJ. Residual strain effects on the stress field in a thick wall finite element model of the human carotid bifurcation. Journal of Biomechanics, 1997, 30(8):777-786.

Abstract: The object of this paper is to study non-invariant hypersurfaces of a nearly Kenmotsu manifold equipped with (f, g, u, v, λ)- structure. Some properties obeyed by this structure are obtained. The necessary and sufficient conditions also have been obtained for totally umbilical non-invariant hypersurfaces with (f, g, u, v, λ)- structure of nearly Kenmotsu manifold to be totally geodesic. The second fundamental form of a non-invariant hypersurfaces of a nearly Kenmotsu manifold with (f, g, u, v, λ)- structure has been traced under the condition when f is parallel.

Keywords and Phrases: Nearly Kenmotsu Manifold, totally geodesic, totally umbilical..

[1]. S. I. Goldberg, and K. Yano, Non-invariant Hypersurfaces of Almost Contact Manifolds, J. of Math. Soc. Japan, 22 (1970) 25-35.[2]. K. Yano and M. Okumura, On ( 𝑓 ,𝑔,𝑢,𝑣,𝜆 ) − Structures, Kodai Math. Sem. Rep., 22(1970) 401-423.
[3]. K. Yano and M. Okumura, Invariant Submanifolds with ( 𝑓 ,𝑔,𝑢,𝑣,𝜆 ) − Structures, Kodai Math. Sem. Rep., 24 (1972) 75-90.
[4]. D. E. Blair, and G. D. Ludden, Hypersurfaces in Almost Contact Manifold, Tohoku Math. J., 22 (1969) 354-362.
[5]. R. Prasad, On Non-invariant Hypersurfaces of Trans- Sasakian Manifold, J. Inter. Acad.Phys. Sci.

Abstract: Here the order statistics of new distribution[1]with the recurrence relation for single and product moments have been studied.Some statistical properties have been studied with Residual entropy and Past residual entropy.

Keywords: Order statistics, Single Moments, Joint Moments, Residual entropy, Past Residual entropy.

[1]. Dwivedi S.,Siddiqui S.A. Dwivedi P. and Siddiqui I.,"Study of a new power function as a Faliure model:Its statistical and Mathematical properties",Bulletin of Mathematics and Statistical Research,Vol 7,Issue-2,2348- 0580(2019).
[2]. B. C. Arnold ,N. Blakrishan and N. H. Nagraja, A rst course in order Statistics, John Wiley and Sons, New York, 1992.
[3]. H. A. David and H. N. Nagaraja, Order Statistics. Third Edition, John Willey and Sons, New York (2003).
[4]. N. Ebrahimi, How to measure uncertainty in the residual lifetime distribution, Sankhya Ser. A 58 4856(1996).
[5]. N. Ebrahimi, E. S. Soo and H. Zahedi, Information properties of order statistics and spacings, Information Theory, IEEE Transactions on 50 1777183(2004)..

Abstract: In this paper......

Keywords: African......

[1]. R. M. Anderson, R. M. May, Infectious disease of humans: dynamics and control, Oxford University Press, Oxford, London (1991).
[2]. M.B.Barongo, R.P.Bishop, E.M. Fvre, D.L. Knobel, A.Ssematimba, A mathematical model that simulates control options for African swine fever virus (ASFV), PLoS One, 11 (7) (2016) e0158658.
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