iosr-Jm   Volume-11 ~ Issue-6 ~ Nov-Dec 2015

Abstract: Diabetic mellitus is a chronic disease of pancreatic origin which is not fully curable once a person becomes diabetic. This paper assumes that one organ A of a diabetic person is exposed to organ failure due to a two phase risk process and another organ B has a random failure time. Two models are treated. In model I, his hospitalization for diabetes starts when any one of the organs A or B fails or when prophylactic treatment starts after an exponential time. In model II, his hospitalization for diabetes starts when the two organs A and B are in failed state or when prophylactic treatment starts after an exponential time.

[1]. Bhattacharya S.K., Biswas R., Ghosh M.M., Banerjee., (1993), A Study of Risk Factors of Diabetes Mellitus, Indian Community Med., 18 (1993), p.7-13.
[2]. Foster D.W., Fauci A.S., Braunward E., Isselbacher K.J., Wilson J.S., Mortin J.B., Kasper D.L., (2002), Diabetes Mellitus, Principles of International Medicines,2, 15th edition p.2111-2126.
[3]. Kannell W.B., McGee D.L.,(1979), Diabetes and Cardiovascular Risk Factors- the Framingam Study, Circulation,59,p 8-13.
[4]. King H, Aubert R.E., Herman W.H., (1998), Global Burdon of Diabetes 1995-2025: Prevalence, Numerical Estimates and Projections, Diabetes Care 21, p 1414-1431.
[5]. King H and Rewers M.,(1993), Global Estimates for Prevalence of Diabetes Mellitus and Impaired Glucose Tolerance in Adults: WHO Ad Hoc Diabetes Reporting Group, Diabetes Care, 16, p157-177.
[6]. Usha K and Eswariprem., (2009), Stochastic Analysis of Time to Carbohydrate Metabolic Disorder, International Journal of Applied Mathematics,22,2, p317-330.

Abstract: In this paper we examine the existing definitions of deterministic chaos and the characterisation of its various ingredients. We then make use of some classical examples to provide cross links between the different chaotic behaviour of some simple but interesting maps which are then explained in a precise manner.

[1]. E. Akin, The general topology of dynamical systems, American Mathematical Society, Providence, R. I., 1993.
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[5]. P. Collet and J.P Eckmann, Iterated maps on the interval as Dynamical systems, Birkhauser, Basel, 1980.
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[7]. A. Fotiou "Deterministic chaos" M Sc Project, Queen Mary and Westfield College, University of London, 2005
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Abstract:In this work, we investigate the existence ,uniqueness and stability solution of non-linear differential equations with boundary conditions by using both method Picard approximation and Banach fixed point theorem which were introduced by [6] .These investigations lead us to improving and extending the above method. Also we expand the results obtained by [1] to change the non-linear
differential equations with initial condition to non-linear differential equations with boundary conditions.
Keywords: Picard approximation method, Banach fixed point theorem, existence, uniqueness, boundary conditions.

[1]. R. N. Butris, and Hasso,M.Sh." Existence of a solution for certain system nonlinear system of differential equation with boundary conditions ", J. Education and Science, Mosul, Iraq, vol.(33), (1998) ,99-108.
[2]. R. N. Butris, and Rafeq, A. Sh., Existence and Uniqueness Solution for Nonlinear Volterra Integral Equation, J. Duhok Univ. Vol. 14, No. 1, (Pure and Eng. Sciences),(2011),25-29.
[3]. R.N. Butris and D.S. Abdullah, Solution of integro-differential equation of the second order with the operators, International Journal of Innovative Science, Engineering & Technology, India, ( IJISET), 2(8) (2015), 937-953.
[4]. E. A . Coddington , An introduction to Ordinary Differential Equations ,Prentice-Hall,Inc.Englewood Cliffs,N.J., (1961), 292 pages.
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Abstract: The objective of the present analysis is to study the effect of overlapping stenosis on blood flow through an artery by taking the blood as Casson type non-Newtonian fluid. The expressions flux and resistance to flow have been studied here by assuming the stenosis is to be mild. The results are shown graphically for different values of yield stress, stenosis length, stenosis height and discussed.

Key Words: Stenosis, Casson fluid, resistance to flow, flux.

[1]. Young, D. F.: Effects of a time-dependency stenosis on flow through through a tube, J. Engg. Ind., Trans ASME, vol. 90, 248-254,
(1968).
[2]. Lee, J.S. and Fung, Y. C.: Flow in locally constricted tubes and low Reynolds number, J. Appl. Mech., Trans ASME, Vol. 37, 9-16,
(1970).
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Math. Biol.,Vol.42, 283-294, (1980).
[4]. Chaturani, P. and PonnalagarSamy, R.: Pulsatile flow of Casson's fluid through stenosed arteries with applications to blood flow,
Biorheol., vol. 23, 491-511, (1986).

Abstract: In this paper, we present the notions of cubic (weak) implicative hyper BCK-ideals of hyper BCK-algebras and then we present some results which characterize the above notions according to the level subsets. In addition, we obtain the relationship among these notions, cubic positive implicative hyper BCK-ideals of types-1, 2…8 and obtain some related results.AMS (2010): 06F35. Key words: Hyper BCK-algebras, cubic sets, cubic (weak) implicative hyper BCK-ideal.

[17]. Jun Y.B. and Xin X.L., Fuzzy hyper BCK-ideals of hyper BCK-algebras, Scientiae Mathematicae Japonica, 53(2) (2001), 353-360.
[18]. Jun Y.B. and Xin X.L., Roh E.H. and Zahedi M.M., Strong hyper BCK-idealsof hyper of hyper BCK-algebras, Scientiae Mathematicae Japonica, 51(3) (2000),493-498.
[19]. Jun Y.B., Zahedi M.M., Xin X.L. and Borzooei R.A., On hyper BCK-algebras,Italian J. of Pure and Applied Math. 8 (2000), 127-136.
[20]. Jun Y.B. and Lee K.J., Closed cubic ideals and cubic o-subalgebras in BCK/BCIalgebras,Applied Mathematical Sciences, 4(68) (2010), 3395-3402.
[21]. Jun Y.B., Kim C.S. and Yang K.O., Cubic sets, Ann. Fuzzy Math. Inform., 4(1)(2012), 83-98.

Abstract: The aim of this paper is to obtain the decomposition of nano continuity in nano topological spaces. 2010 AMS Subject Classi cation: 54B05, 54C05.

Keywords: nano-open sets, nano continuity.

1] Abd El-Monsef.M.E, E. F. Lashien and A. A. Nasef, 1992, On I-open sets and I-continuous functions, Kyungpook Math. J., 21-30.
[2] Ganster.M and Reily .I.L,1990, A Decomposition of Continuity,Acta Math.Hung , 299-301.
[3] Hatir.E,T. Noiri and S. Yuksel, A decomposition of continuity, Acta Math.Hung, No.1-2(1996), 145-150.
[4] Jingcheng Tong,1994, Expansion of open sets and Decomposition of continuous map-pings,Rendiconti del circolo Mathematico di palarmo,,volume 43,Issue 2, 303-308.
[5] Jingcheng Tong,1989, On decomposition of continuity in topological spaces, Acta Math. Hung,51-55.

Abstract:In this we defined certain analytic p-valent function with negative type denoted by 𝜏𝑝 . We obtained sharp results concerning coefficient bounds, distortion theorem belonging to the class 𝜏𝑝 .
Keywords: p-valent function, distortion theorem, convexity.

[1]. P. L. Duren, Univalent Functions, Grundlehren Math. Wiss., Vol. 259, Springer, New York 1983.
[2]. H. M. Srivastava, M. K. Aouf, A certain derivative operator and its applications to a new class of analytic and multivalent functions with negative coefficients, J. Math. Anal.Appl.171, (1992),1-13.
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Abstract: HIV/AIDS remains one of the leading causes of death in the world with its effects most devastating in Sub Saharan Africa due to its dual infection with opportunistic infections especially malaria and tuberculosis. This study presents a co infection deterministic model defined by a system of ordinary differential equations for HIV/AIDS, malaria and tuberculosis. The HIV/AIDS malaria co infection sub model is analyzed to determine the conditions for the stability of the equilibria points and assess the role of treatment and counseling in controlling the spread of the infections. This study shows that treatment of malaria a lone even in the absence of HIV/AIDS, may not eliminate malaria from the community therefore strategies for the reduction of malaria infections in humans should not only target malaria treatment but also the reduction of mosquito biting rate.

[1]. L. Abu-Raddad, P.Patnaik, and J. Kublin, "Dual infection with HIV and malaria fuels the spread of both diseases in Sub-Saharan Africa", Science, 314(5805), (2006), 1603-1606.

[2] E, Allman and J. Rhodes, "An introduction to Mathematical models in Biology", Cambridge University press: New York, (2004).

[3] R. Anderson and R. May, "Infectious Diseases of Humans: Dynamics and Control", Oxford University Press: United Kingdom, (1993).

[4] R. Audu, D. Onwujekwe, C. Onubogu, J. Adedoyin, N. Onyejepu, A. Mafe, J. Onyewuche, C. Oparaugo, C. Enwuru, M. Aniedobe, A. Musa, and E. Idigbe, "Impact of co infections of tuberculosis and malaria on the C D4+ cell counts of HIV patients in Nigeria", Annals of African Medicine, (2005), 4(1): 10-13.

[5] F. Baryama, and T. Mugisha, "Comparison of single - stage and staged progression models for HIV/AIDS models", International Journal of Mathematics and Mathematical sciences.(2007), 12(4):399 - 417.

[6] C. Bhunu, W. Garira and Z. Mukandavire, "Modeling HIV/AIDS and Tuberculosis Co infection", Bulletin of Mathematical Biology, (2009), 71: 17451780.

Abstract: In this article, we present Hillel Furstenberg's proof on the infinity of primes in a way that it can be read and understood even by a freshman of mathematics or engineering with no background in topology

[1] Ralph P. Grimaldi, Discrete and Combinatorial Mathematics- An Applied Introduction, Fifth Edition, Pearson (2004)

Abstract: This paper discusses the complex dynamical behaviour of a communicable disease in a plant-herbivore system with Allee effect. It is assumed that (a) Disease has no vertical transmission but it is untreatable and causes additional mortality in infected plant; (b) Allee effects built in the reproduction of susceptible plant while infected plant has no reproduction; (c) Herbivore captures susceptible and infected plant at the same rate but the consumption of infected plant hasless benefits or even causes harm to herbivore; (d) Disease transmission follows the law of mass action; (e) Two predation response functions of Holling-Type II are used for both healthy and infected plants. The feasibility and stability conditions of the equilibrium points of the system were analyzed.Finally we performed numerical simulations to verify the theoretical results and to investigate further the properties of the system. Keywords: Allee effect, Holling-Type II, susceptible plant -infective plant, vertical transmission, law of mass action, stability analysis.

[1] Allee, W.C., 1931. Animal Aggregations: A study in General Sociology. University of Chicago Press, Chicago.

[2] Asrul Sani, Edi Cahyono, Mukhsar, Gusti Arviana Rahman, Yuni Tri Hewindati, Faeldog, Farah Aini Abdullah, 2014. Dynamics of Disease spread in a predator-prey system. Advanced Studies in Biology, Volume -6 and Number 4, 169 - 179.

[3] Beltrami, E., 1989. Mathematics for dynamic modelling, Academic Press, New York

[4] Courchamp, F., Berec and Gascoigne, J., 2008. Allee effects in Ecology and Conservation. Oxford University Press, Oxford.

[5] Hadeler, K.P., Freedman, H.I., 1989. Predator - prey populations with parasitic infection. Journal of Mathematical Biology, 27, 609 -631.

[6] Lotka, A.J., 1925. Elements of physical biology, Williams and Wilkins (Baltimore)

[7] Md. Sabiar Rahman, Santabrata Chakravarty, 2013. A Predator - Prey model with disease in prey. Nonlinear Analysis: Modelling and Control, Volume 18, Number 2, 191 – 209.