iosr-Jm   Volume-11 ~ Issue-4 ~ July-Aug 2015

Abstract: In the present paper we have formulated the renal blood flow along the capillaries in case of renal disease kidney infection (UTI) keeping in the view the nature of renal circulatory system in human body. Earlier researchers like Dr. V. Upadhyay and Dr. P.N.Pandey had assumed the blood flow has two phased, one of which is that of red blood cells and other is plasma. According to Fahreaus- Lindqvist affect the blood flow in two separated layers while passing through capillaries. The plasma layer which flows along the surface of the capillaries contains almost no blood cells. The second layer the core layer containing blood cells which float in plasma along the axis of capillary.

[1]. Joao Paulo Zambon, Renata S Magalhaes, Inkap ko, Christina L Ross, Giuseppe Orlando, Andrea Peloso, AnthonyAtala, James J yoo; Research Paper; Kidney regeneration:Where we are and future perspectives; World Journal of Nephrology ; 6 August ; 3(3); 24-30; 2014
[2]. Julian Brown, Todd A Briscoe, Richard Harding, Megan L Cock, Jhon F Bertram and Jane M Black; Research paper; Glomerular number and capillary dimensions in the normal Lamb kidney; Image Anal stercol; Accepted October 10; 157-164; 2002
[3]. Omran Bakoush, Diagnostic and Prognostic value of Proteinuria in Chronic renal diseases; clinical studies; Department of Nephrology, Faculty of medicine; University hospital in Lund , Sweden; 2004
[4]. Neelam Bajpai, V. Upadhyay, P.N. Pandey ; Research Paper; A mathematical model on the two phase renal systolic blood flow in renal aryerioles with special reference to Kidney Infection (UTI); International Journal of Engineering research & Development; Volume 5, Issue 5, PP. 23-30; December 2012.

Abstract: In this paper, we introduce a dual purely Rickart modules as a dual concept of purely Rickart modules and a proper generalization to dual Rickart modules. Some characterizations are studied. It's shown that a ring R is dual purely Rickart if and only if R is von Neumann regular ring if and only if R is d-Rickart ring. Also, a ring R is a dual purely Rickart ring if and only all R-modules are dual purely Rickart module. In principal right ideal ring R, a ring R is a field if and only if all R-modules are dual purely Rickart. Furthermore, we give a counter example to show that the endomorphism ring of the dual purely Rickart module is not necessarily dual purely Rickart ring. More than, the relation among known modules and dual purely Rickart modules are investigated.

Keywords: Dual purely Rickart modules , purely Rickart, Rickart modules, regular rings, regular modules.

[1]. S. AL-Saadi and T. Arif (2014), Purely Rickart module, International J. of Algebra, Vol. 8, no. 18, 873 – 881.
[2]. N. M. Al-Thani (1997), Pure Baer injective modules, Int. J. Math. Sci., Vol. 20, No.3, 529-538.
[3]. D.J. Fieldhous, Purity and flatness (1967), PhD. Thesis, McGill University.
[4]. A. Hattori (1960), Foundation of a torsion theory for modules over general rings, Nagoya Math. J., Vol. 17, pp.147-158.
[5]. G. Lee; S.T. Rizvi; C.S. Roman (2010) Rickart modules, Comm. Algebra,38(11), 4005-4027
[6]. G.Lee, S.T. Rizvi and C. Roman, (2011) Dual Rickart Modules, Comm. Algebra 39, 4036-4058.
[7]. S. Maeda (1960), On a ring whose principal right ideals generated by idempotent form a lattice. J. Sci. Hiroshima Univ. Ser. A, 24:509-525.

Abstract: In this paper, we investigate the numerical solution of fractional integro-differential equations by comparison between He's variational iteration method and taylor expansion method. The fractional derivative is described in the Caputo sense. Some numerical examples are presented to illustrate the methods. Keywords - Fractional integro-differential equations, He's variational iteration method, Taylor expansion method, Caputo fractional derivative, Riemann-Liouville.

[1] A. Arikoglu, I. Ozkol, Solution of fractional integro-differential equations by using fractional differential transform, Chaos, Solutions and Fractals, 40 (2009) 521-529.
[2] Adam Loverro, Fractional calculus: History, Definitions and Application for the Engineer. (2004).
[3] E. A. Rawashdeh, Legendre Wavelet method for fractional integro-differential equations, Applied Mathematics Sciences.5 (2011) 2467-2474.
[4] E. A. Rawashdeh, Numerical of fractional integro-differential equations by collocation method, Appl. Math. Comput. 176 (2006) 1-6.
[5] Eke A. N. and Jackreece P. C, Taylor series expansion of nonlinear integro differential equations, American Journal of Scientific and Industrial Research, 2011.

Abstract: In this paper, nd 2 -Highly irregular fuzzy graphs and nd 2 -Highly totally irregular fuzzy graphs are defined. Comparative study between nd 2 -Highly irregular fuzzy graph and nd 2 -Highly totally irregular fuzzy graph is done. Property of nd 2 -Highly irregular fuzzy graph and nd 2 -Highly totally irregular fuzzy graph are discussed. nd 2 -Highly irregularity on fuzzy graphs whose underlying graphs are cycle n c , a Barbell graph n m B , , Sub ( ) n,m B are studied.

keywords: degree of a vertex in fuzzy graph, irregular fuzzy graph, highly irregular fuzzy graph, highly totally irregular fuzzy graph.

[1]. Y. Alavi, G.Chartrand, F.R.K. Chung, P. Erdos, R.L. Graham, Ortrud R. Oellermann, Highly irregular graphs, J. Graph Theory,
11(2), (1987), 235-249.
[2]. Alison Northup, A Study of semiregular graphs,Bachelors thesis, Stetson university (2002).
[3]. G.S. Bloom, J.K. Kennedy, L.V. Quintas, Distance degree regular graphs, The Theory and Applications of Graphs, Wiley, New
York, (1981), 95-108.
[4]. P.Bhattacharya, Some remarks on Fuzzy Graphs, Pattern Recognition Lett 6(1987), 297-302.

Abstract: In this paper we consider an integrated inventory control system that consists of a Manufacturer (MF), single Warehouse (WH), one Distribution Centre (DC) and n identical Retailers. The Demands occurring during the stock out periods are backlogged up to a specified quantity 'b' at DC. The optimization criterion is to minimize the total cost rate incurred at all the location subject to the performance level constrains. The steady state probability distribution and the operating characteristics are obtained explicitly. The required algorithm is designed and it is executed using MATLAB. Numerical example with sensitivity analysis is provided to illustrate the proposed model.

[1]. Antony Svoronos and Paul Zipkin, Evaluation of One-for-One Replenishment Policies for Multiechelon Inventory Systems, Management Science, 37(1): 68-83, 1991.
[2]. Axsäter, S. (1990). Simple solution procedures for a class of two-echelon inventory problems. Operations research, 38(1), 64-69.
[3]. Bakthavachalam.R, Navaneethakrishnan. S, Elango.C,(2012) A Modified (Q, r) Policy for Stochastic Inventory Control Systems in Supply Chain. Proceeding of International Conference on Advances in Computing," Advances in Intelligent and Soft Computing",Springer, 247-255.
[4]. Benita, Beamon, M. Supply Chain Design and Analysis: Models and Methods. International Journal of Production Economics.Vol.55, No.3, pp.281 294, 1998.
[5]. Cinlar. E, Introduction to Stochastic Processes. Prentice Hall, Englewood Cliffs, NJ, 1975.

Abstract: The temperature distribution in human head (cranium) regulate variety of biological mechanism. Human head (cranium) is a very complex structure and abnormality in temperature of various layer of human head (cranium) play important role for treatment of diseases like tumor, cancer, hyperthermia, hypothermia etc. Here, a finite element model has been developed to study the temperature distribution of human head (cranium) with ten layers namely brain, skull, fat-layer, reticular region, papillary region, stratum germinativum, stratum spinosum, stratum granulosum, stratum lucidum and stratum corneum in presence of tumor in the reticular region. Appropriate boundary conditions have been framed and finite element method is used to obtain temperature values in one dimension.

[1] H. Wang, B Wang, K. P. Normoyle, K. Jackson, K. Spitler, M. F. Sharrock, C. M. Miller, C. Best, D. Llano, and R. Du. "Brain temperature and its fundamental properties: a review for clinical neuroscientists." Frontiers in neuroscience 8 (2014).
[2] M. A. Khanday "Theoretical approach to study the thermal stress on human brain tissue in hypothermic conditions." Int. J. Adv. Comput. Math. Sci 4, no. 2: 181-187 (2013).
[3] S. A. Bernard, T. W. Gray, M. D. Buist, B. M. Jones, W. Silvester, G. Gutteridge, Treatment of comatose survivors of out-of-hospital cardiac arrest with induced hypothermia. N. Engl. J. Med. 346, 557–563 10.1056/NEJMoa003289 (2002)
[4] G. L. Clifton, A. Valadka, D. Zygun, C. S. Coffey, P. Drever, S. Fourwinds, Very early hypothermia induction in patients with severe brain injury (the National Acute Brain Injury Study: Hypothermia II): a randomised trial. Lancet Neurol. 10, 131–139 10.1016/S1474-4422(10)70300-8 (2011)
[5] J. F. Patton, "The Effects of Acute Cold Exposure on Exercise Performance." The Journal of Strength & Conditioning Research 2, no. 4: 72-78 (1988).

Abstract: In this project we tried to cover the possible aspects of mathematical control theory, especially Left invariant optimal control on the very important physical Group \"Schrodinger Lie Group\". Here we tried to restrict our-selves only in the mathematical aspects, as a result we concluded thestability factors of Schrodinger Lie Group at various equilibrium states. However this group is related to many physical phenomenon, which are interesting to physicist .We hope our study will be lead to a small step towards such type of investigation.

[1]. Remsing, C.C., Optimal Control and Hamilton-Poisson Formalism, Int. J. Pure Appl. Math., V59,N1, pp. 11-17, 1/10
[2]. M. L. Curtis, Matrix Groups, Springer-Verlag, New York Inc., 1984.
[3]. Juan M. Romero, Ulises Lavana, Elio Martnez , "Schrdinger group and quantum nance", General Physics 1304.4995v1.
[4]. N. E. Leonard, Averaging and motion constant of systems on Lie groups, Ph. D. Thesis, University of Maryland, College Park. M. D., 1994.
[5]. M. Puta, Hamiltonian Mechanical Systems and Geometric Quantiza-tion, Math. and Appl., 260, Kluwer Academic Publishers, 1993.

Abstract: In non- preemptive single machine scheduling problems, processing of a job cannot be temporarily interrupted. In classic scheduling, it was assumed that the machines are always ready to work. So, we need not considered maintenance time for calculations. Single machine, no common due dates, earliness /lateness machine problem and fuzzy environment closely models the situation faced by 'Just in Time' manufacturing In this paper, we propose more than one jobs to be processed on Single Machine Scheduling Problem (SMSP) involving fuzzy processing time and fuzzy due dates. Result shows that the developed average high ranking method performs well to minimize the total penalty with single machine system.-

[1] Baker, K.S and G.D.Scudder (1990), "Sequencing with earliness and tardiness penalties". A Review - Operation Research, 38. 22-36 [2] Chong T.C.E,(1995), "Optimal due date determination and sequence of n – jobs on asingle machine" Journal. Op. Res. Soc. 35, (5) pp-433 [3] Conway, R. W (1965), "Priority dispatching and job lateness in a jobshop".Journal. Ind Engg. 16, 228-237

[4] Mohd. Ikram (1986), "On minimization of lateness coast function and determination of optimal due date in two machines scheduling problem" Pure and applied Mathematika Sciences vol 1-2.

[5]. J. K. Sharama (2007), Operations Research Theory & Applications.Macmillan India Ltd, Third edition.

[6]. XIE Yuan et al (2005), Single Machine Scheduling with Fuzzy Due Dates and Fuzzy Precedence. Journal of Shanghai University (English Edition), 9(5) PP-

[7]. Ishubuchi H.T.Murtha and K.H.Lee (1996), Formulation of Fuzzy Flow shop Scheduling with Fuzzy Processing Time, Proceeding of IEEE International Conference of Fuzzy System. pp 199-205.

Abstract: Some rings have properties that differ radically from usual number theoretic problems. This fact forces to define what is called Radical of a ring. In Radical theory ideas of Homomorphism and the concept of Semi-simple ring is required where Zorn's Lemma and also ideas of axiom of choice is very important. Jacobson radical of a ring R consists of those elements in R which annihilates all simple right R-module. Radical properties based on the notion of nilpotence do not seem to yield fruitful results for rings without chain condition. It was not until Perlis introduced the notion of quasi-regularity and Jacobson used it in 1945, that significant chainless results were obtained.

Keywords: Commutativity, Ideal, Jacobson Radical, Simple ring, Quasi- regular.

[1]. C. Musili, Introduction to Rings and Modules, University of Hyderabad, Norsha publishing house, (1999).24-26.
[2]. D.W. Henderson, A short proof of Wedderburn's theorem, Amer. Math. Monthly 72 (1965). 385-386
[3]. N. J. Divinsky, Ring and Radical, University of British Columbia, University of Toronto press, (1965). 91-115.
[4]. J.W.Wamsley, On a condition for commutativity of rings, J. LONDON MATH Soc.(2), 4 (1971).331-332

Abstract: In this paper, we determined that the alpha product, beta product and gamma product of two edge regular fuzzy graphs need not be edge regular and that if these operations of two fuzzy graphs are edge regular, then 1 G (or) 2 G need not be edge regular. A necessary and sufficient condition for alpha product and gamma product of two fuzzy graphs to be edge regular fuzzy graph is determined.
Key Words: Alpha product, Beta product, Gamma product, Regular fuzzy graph, Edge regular fuzzy graph.

[1]. S. Arumugam and S. Velammal, Edge domination in graphs, Taiwanese Journal of Mathematics, Vol.2, No.2, 1998, 173 – 179.
[2]. J.N. Mordeson and C.S. Peng, Operations on fuzzy graphs, Information Sciences, Volume 79, Issues 3 – 4, 1994, 159 – 170.
[3]. A. Nagoor Gani and B. Fathima Kani, Degree of a vertex in alpha, beta and gamma product of fuzzy graphs, Jamal Academic
Research Journal (JARJ), Special issue, 2014, 104 – 114.
[4]. A. Nagoor Gani and B. Fathima Kani, Beta and gamma product of fuzzy graphs, International Journal of Fuzzy Mathematical
Archive, Volume 4, Number 1, 2014, 20 – 36.
[5]. A. Nagoor Gani and K. Radha, The degree of a vertex in some fuzzy graphs, International Journal of Algorithms, Computing and
Mathematics, Volume 2, Number 3, 2009, 107 – 116.