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

Abstract: In this paper, we discuss iterated function systems with probabilities of generalized Cantor sets (IFSGCS) and show that these functions are non-expansiveness and asymptotically stable if the Markov operator has the corresponding property.

Keywords - Cantor set, Markov operator, iterated function system, non-expansiveness, asymptotically stable

[1]. Devaney R. L., A First Course in Chaotic Dynamical Systems, 2nd edition, Boston University, West Views Press, 1992.
[2]. Addison P. S., Fractals and Chaos, Institute of Physics, Bristol, 1997.
[3]. Islam M. J., Islam M. S., Generalized Cantor Set and its Fractal Dimension, Bangladesh J. Sci. Ind. Res. 46(4) (2011), 499-506.
[4]. Islam M. J., Islam M. S., Lebesgue Measure of Generalized Cantor Set, Annals of Pure & App. Math., 10(1), 75-87, 2015.
[5]. Islam M. J., Islam M. S., Invariant Measures for Iterated Function Systems of Generalized Cantor Sets, German J. Ad. Math. Sci.,
1(2) (2016), 31-47.

Abstract: This paper has been written more than twenty yearsago. exhibits a very short geomatric proof of the following fact for any..........

[1]. This colulbois free product profinite topology and finitely genrated sub group int J of algebra and computations 1 (2001), 171-184

Abstract: We study the asymptotic behaviour of solutions for a class of second order nonlinear difference equations. Using Bihari's inequality, we obtain conditions under which all solutions are asymptotic to anb as n, where a and b are real constants.

Keywords - Asymptotic behaviour, Bihari's inequality, second order nonlinear difference equations

[1]. Agarwal. R.P., Difference Equations and Inequalities Theory, Method and Applications, Marcel Dekker, New York, 1992.
[2]. Agarwal. R.P and Wong P.J.Y., Advanced Topics in Difference Equations, Kluwer Academic Publishers Group, Dordrecht, 1997.
[3]. Bellman. R., Stability Theory of Differential Equations, McGraw-Hill, London, 1953.
[4]. Bihari. I., A generalization of a lemma of Bellman and its application to uniqueness problems of differential equations, Acta. Math. Acad. Sci. Hung., 7 (1956), 83-94.
[5]. Cheng. S.S., Li. H.J, and Patula. W.T., Bounded and zero convergent solutions of second order difference equations, J. Math. Anal. Appl. 141 (1989), 463-484

Abstract: Zika fever has, in recent times, become a scourge to human. This is so especially because there is no specific treatment or vaccine currently available. However, we present a five compartmental mathematical model, which studies the dynamical spread of Zika fever within humans (host) and between humans and mosquitoes (vector).The mathematical analysis shows that the disease free and the endemic equilibrium point of the model exist. The model has disease free equilibrium point which is locally asymptotically stable (LAS........

Keywords - Zika fever, ZikV, Isolation, Critical points, Basic reproduction number, Stability

[1] Central for Disease Control and Prevention – CDC Zika virus Home (2016); "Symptoms, Diagnosis and Treatment of Zika virus", Retrieved April 29, 2016.

[2] Derrick, W.R., Grossman, S.I. (1976): Elementary Differential Equations with Applications; Addison-Wesley Pub. Co., USA.

[3] Dick, G.W.A.; Kitchen, S.F.; Haddow, A.J. (1952); "Zika virus (I): Isolations and Serological Specificity", Transaction of the Royal Society of Tropical Medicine and Hygiene, 46(5): 509-520.

[4] European Central for Disease Control and Prevention – CDC (2015); "Zika virus infection", Factsheet for Health Professionals.

[5] Kucharski, A.J.; Funk S.; Eggo, R.M.; Mallet, H.; Edmunds, W.J.; Nilles, E.J. (2016); "Transmission dynamics of Zika virus in Island populations: a modelling analysis of the 2013-14 French Polynesia outbreak", bioRxiv preprint

Abstract: In this study, non-Newtonian real number series were introduedand their convergence conditions were investigated

[1]. Grossman an katz r Non-Newtoine calculs lee press pigeon cove (1972) (Lovell Technological Institute)

Abstract: The aim of this paper is to find a formula that allows to find the infinite sum ofreciprocals of certain k–Fibonacci numbers whose subscripts are in linear form.Particularizing this formula, we are able to obtain other formulas previously foundby other authors for the case of both classical Fibonacci and Pell sequences.

Keywords: Binet identity, k–Fibonacci numbers, k–Lucas numbers.

[1] A.F. Horadam, A generalized Fibonacci sequence, Math. Mag. 68, (1961), 455-459.
[2] S. Vajda, Fibonacci & Lucas Numbers, and the Golden Section, Theory andApplications.( Ellis Horwood limited, 1989).
[3] V.E. Hoggat, Fibonacci and Lucas numbers, (Palo Alto, CA: Houghton-Mifflin, 1969).
[4] S. Falcon, A. Plaza, On the Fibonacci k-numbers,Chaos, Solit. & Fract. 32(5), (2007) 1615–24.
[5] S. Falcon, A. Plaza, The k-Fibonacci sequence and the Pascal 2-triangle, Chaos, Solit. & Fract. 33(1), (2007) 38–49.

Abstract: A mathematical model of HIV/AIDS was developed for a human population of five compartments. The dynamical systems theory was used to analyze the model. The steady states (equilibrium points) were determined. The stability of the steady states (equilibrium points) was established using Routh Hurtwitz criterion. It was shown that the model has two non-negative equilibra which are disease free equilibrium E0 (0,0,0,0) and endemic equilibrium EE (S*, I *, Ic*, IT* ,a* ) ........

Keywords: HIV/AIDS, Mathematical Model, Varying Population, Stability, Dynamical Systems Theory

[1] Aris, R. (1994) Mathematical Modeling Techniques New York, Dover.
[2] Basavarajaiah, D. M., Narasimhamuthy, B., Maheshappa, K., and Leelavathy, B. (2012) Mathematical Model Approach to
HIV/AIDS transmission from mother to child. Journal of Scientific and Technology Research; Vol. 1 Issue 9
[3] Beltrami, E. (1983) Mathematics for Dynamic Modeling; Academic Press Inc, New York
[4] Cooper, J. (2004): Modeling the spread of HIV in sub-Saharan Africa, Available online
http:/Newton.Dtc.ox.Ac:Uk/Cooper/HIV.Africa. pdf.
[5] Chukwu, M. and John, S. (2014): The spread of HIV in Africa; Nature, 51. (581-589).

Abstract: The objective of this paper is to analyze the effects of Soret, chemical reaction and radiation absorption on an unsteady MHD convective heat and mass transfer flow of a semi-infinite vertical moving in a porous medium with heat source and suction. The plate is assumed to move with a constant velocity in the fluid flow direction. The equations of continuity, momentum, energy and diffusion, which govern the flow field, are solved by using Galerkian finite element method. Numerical solutions of velocity, temperature and concentration profiles are discussed with the help of the graphs for different parameters.

Keywords: Vertical plate, MHD, Radiation, FEM, Chemical reaction, Nusselt number, Soret number.

[1] Dash, G.C and Das, S.S., "Hall effect on MHD flow along an accelerated porous flat plate with mass transfer and internal heat generation'', Math.Engg. Indust. , 7(4), pp.389-404, 1999.
[2] Satter,M.A.,"Free convection and mass transfer flow through a porous medium past an infinite vertical porous plate with time dependent temperature and concentration'', Ind.J.Pure Apple.Math.,23, pp.759-766, 1994.
[3] Achary.M.,Dadh, G.C. and Siggh,L.P., "Effect of chemical and thermal diffusin with Hall current on unsteady hydromagnetic flow near an infinite vertical porous plate", J.Phys.D Appl.Phys.28, pp. 2455-2464, 1995.
[4] Das, S.S. Shoo .S.K. and Dash. G.C "Numerical solution of mass transfer effects on unsteady flow past an accelerated vertical porous plate with suction,'' Bull.Malays MathScience Soc.(2), 29, pp.33-42, 2006.
[5] B.Vasu.,V. Ramchandra., N.Bhasker Reddy., "Radiation and and Mass Transfer effects on transient free convection flow of dissipative fluid past semi-infinite plate with uniform heat and mass flux", Journal of Applied mathematics and fluid Mechanics, 4(1), pp.15-26, 2006.

Abstract: Let M be a -ring and X be a left M-module, in this paper proved that every Jordan (,)-higher homomorphism from a -ring M into a prime left M - module X is either (,)-higher homomorphism or (,)-higher anti homomorphism.

Keywords: -ring, left M-module, homomorphism, Jordan homomorphism

[1] W.E.Barnes, "On The -Rings of Nobusawa", Pacific J.Math., Vol.18(3), pp.411-422 , (1966) .
[2] N. Jacobson and C.E. Rickart , " Jordan Homomorphisms of Rings", Trans. Amer.Math. Soc., Vol.69, pp.479-502,(1950) .
[3] F.R.Jarullah, "On (,)- Homomorphisms on prime -Rings " , M.Sc.Thesis, Department of Mathematics, college of Education,
Al-Mustansirya University,(2015) .
[4] A.C.Paul and A.K.Halder, "Jordan Left Derivations of Two Torsion Free M-modules", Journal of Physical Sciences, Vol.13,
pp.13-19, (2009).
[5] S.M. Salih, "On Prime-Rings with Derivations", Ph.D.Thesis, Department of Mathematics, College of Education, Al-Mustansiriya
University, (2010).

Abstract: In this paper, corruption is treated as an infection that spreads through social interactions. We developed and analyzed a new mathematical model of corruption in a population with constant recruitment rate, incorporating standard incidence rate, effort rate against corruption andeffect of the embarrassment faced by corrupt individuals due tosocial media freedom, which makes some corrupt individuals temporarily quit corruption. The effective reproduction number and its values are computed using four different control strategies. Results showed that if at least..............

Keywords: Corruption, Effective Reproductive Number, Mathematical Model, Recruitment Rate, Social Media.

[1] J. Gerring, and S. C. Thacker, Political Institutions and Corruption: The Role of Unitarianism and Parliamentarism. B.J.Pol.S. 34,
295 – 330. Cambridge University Press 2004.
[2] H. C. Black, Black's Law Dictionary. 10th ed. West Group, 2004, Retrieved from http://thelawdictionary.org/corruption/
[3] A. Hamilton, and J. Hudson, Bribery and Identity: Evidence from Sudan. Bath Economic Research Papers, No. 21/14, 2014.
[4] L. Diamond, Liberation Technology. Journal of Democracy, 2010, 21:69-83.
[5] N. Saleh, Egypt's Digital Activism and the Dictator's Dilemma: An Evaluation. Telecommunications P=olicy, 2012, 36:476-483.

Abstract: This paper present a single machine scheduling problem with common due date to minimize the earliness and tardiness (E/T). Earliness and tardiness are considered harmful to profitability. Earliness causes inventory carrying costs and possible loss of product quality, while tardiness causes loss of customer goodwill and delay of payment. Thus the scheduling problem of minimizing the total sum of earliness and tardiness with a common due date on a single machine is important task in scheduling problem and delivery of goods in production plants, and it is known to be NP- Hard problem. In this paper a heuristic algorithm is presented and can be performed manually for small systems and by using Java language for large systems

Keywords: Single machine scheduling, common due date, heuristic algorithms, earliness and tardiness.

[1] Abdelaziz Hamed and Bahrom Sanugi (2011) . "Neural Network and Scheduling" Germany : lap Lambert Academic publishing
[2] Abdelaziz Hamed (2002) . Application of neural network for solving Job scheduling problems. PhD thesis. UTM, Malaysia.
[3] Baker, K. and Scudder, G. (1989). "On the Assignment of Optimal Due Date." Journal of Operational Research Society. 40; 93-95.
[4] Baker, K. and Scudder, G. (1990). "Sequencing with Earliness and Tardiness Penalties: A review." Operations Research. 38; 22 - 36.
[5] Nordin Haji and Fatimah Said (2011) ). " Solving Single machine Scheduling problem with common due date. " Business Management Dynamics. 4; 63-72.

Abstract: In this paper we prove fixed point and common fixed point Theorem in non-expansive and existence mappings using Banach space for new rational expression. Which generalize the well known result

Keywords: Banach space, Common fixed point, fixed point, rational expression

[1] F.E., Browder. "Non-expansive non-linear operators in Banach space". Proc. Nat. Acad. Sci. U.S.A. vol-54,1965, pp-1041-1044.
[2] G., Emmanuele, "Fixed point theorems in complete metric space". Not linear Anal.vol 5, 1981, pp-287-292.
[3] Gohde Zum prizip dev kontraktiven abbildung. Math.Nachr. 30, 1965, 251-258.
[4] K., Goebel, "An elementary proof of the fixed theorem of Browder and Kirk". Michigan Math. J. vol 16, 1969, pp-381-383.
[5] K., Goebel, and E., Zlotkiewicz, "Some fixed point theorems in Banach spaces". Collq. Math. Vol 23, 1971, pp-103-106.

Abstract: In this paper, we prove common fixed point theorems for six mappings by using property satisfying contractive condition in intuitionistic fuzzy metric spaces

Keywords: Intuitionistic fuzzy metric spaces, property (E.A.).

[1] B. Schweizer, A. Sklar, Probabilistic Metric Spaces, North Holland, Amsterdam, 1983.
[2] C. Alaca, D. T¨urkoˇglu and C. Yildiz, Fixed points in intuitionistic fuzzy metric spaces, Chaos, Solitons Fractals, 29, No. 5 (2006), 1073-1078, doi: 10.1016/j.chaos.2005.08.066
[3] C. Alaca, I. Altun, D. T¨urkoˇglu, On compatible mappings of type (I) and (II) in intuitionistic fuzzy metric spaces, Commun. Korean Math. Soc., 23, No. 3 (2008), 427-446, doi: 10.4134/CKMS.2008.23.3.427 264 S. Manro, S.M. Kang
[4] D. T¨urkoˇglu, C. Alaca, Y.J. Cho, C. Yildiz, Common fixed point theorems in intuitionistic fuzzy metric spaces, J. Appl. Math Comput., 22, No. 1-2 (2006), 411-424, doi: 10.1007/BF02896489
[5] D. T¨urkoˇglu, C. Alaca, C. Yildiz, Compatible maps and compatible maps of type (α) and (β) in intuitionistic fuzzy metric spaces, Demonstratio Math., 39, No. 3 (2006), 671-684.

Abstract: Tilted and non tilted homogeneous plane symmetric C-field cosmological models are investigated. Using the method of Narlikar and Padmanabhan [4], the solutions have been presented when the creation field C is function of time t only. To get the deterministic model, we have assumed the supplementary conditions p   . The behaviour of different stages of the universe has been studied in non tilted models. We have also investigated the behaviours of some physical parameters

Keywords: Tilted models, Creation Field, Stiff Fluid.

[1] H.Bondi, T. Gold, (1948) Mon. Not. R. Astron. Soc. 108, 252 .
[2] F. Hoyle, J.V. Narlikar, (1963) Mach's principle and the creation of matter, Proc. Roy. Soc. Vol.273 A, pp.1-11 .
[3] J.V. Narlikar, (1973) Nature 242, 135 .
[4] J.V. Narlikar , T. Padmanabhan, (1985) Phys. Rev. D32, 1928 .
[5] S.Chatterjee, A. Banerjee, (2004) General Relativity Gravitation 36(2), 303-313.