iosr-Jm   Volume-10 ~ Issue-3 ~ May-June 2014

Abstract: In this paper, a bivariate stochastic model for cancer growth within a specific organ during chemotherapy is developed using the birth, death and migration processes based on pathophysiology and genetic programs of cancerous cell. Joint probability functions and statistical properties of the model are derived with the formulated stochastic differential equations. Model behaviour was analysed with numerical data.
Keywords: Stochastic Modelling, Cancer Growth within Organ, Chemotherapy, Generalized Poisson Processes, Differential- difference equations

[1] Iwata K, Kawasaki K, Shigesasa N (2000) A dynamical model for the growth and size distribution of multiple metastasis tumors.
Jounal. Theor. Biol., 203: 177-186
[2] Pinho S T R, Freedman H I, Nani F (2002) A Chemotherapy model for the treatment of cancer with metastasis. Mathematical and
Computer Modelling, 36: 773-803

[3] Srinivasa Rao K, Tirupathi Rao P (2004) A Stochastic Model for Cancer Cell Growth under Chemotherapy. Assam Statistical Review. 18(1): 81-101
[4] Srinivasa Rao K, Tirupathi Rao P (2004) Stochastic Model for Mutant Cell Growth with Inactivation of Allele Genes. Journal of Statistical Theory and Applications. 3(1): 75-85
[5] Tirupathi Rao P, Madhavi K, Masthan Babu S K (2011) Bivariate Stochastic Modeling for Mutant Cell Growth under Chemotherapy. International Journal of Mathematics and applications. 4(1): 1-12

Abstract: In this paper we study Molodtsov's notion of Fuzzy Soft Sets considering the fact that the parameters(which are words or sentences) are mostly fuzzy hedges or fuzzy parameters. We discuss and study the properties and structural characteristics of fuzzy soft groups and normal fuzzy soft groups. Then we define the left coset, right coset and middle coset of a fuzzy soft group and prove some important results on them. Finally we present factor group of a fuzzy soft group.
Keywords: Fuzzy Soft Group, Fuzzy Soft Set, Normal Fuzzy soft group, Cosets of a Fuzzy soft Group, Factor Group of a Fuzzy soft Group

[1]. H.J. Zimmerman, Fuzzy set theory and its applications, Kluwer Academic Publishers(Boston), 1996.
[2]. K. Atanassov, "Intuitionistic fuzzy sets, " Fuzzy sets and systems, no.20, pp.87-96, 1986
[3]. W.L. Gan and D.J. Buehrer, "Vague Sets," IEEE Transactions Systems, Man and Cybernetics, Vol.23, no.2, pp.610- 614, 1993.
[4]. Z. Pawlak, "Rough Sets," International Journal of Information and computer science, no.11, pp.341-356,
[5]. 1982
[6]. D. Molodtsov, "Soft set theory-first results" Computer and Mathematics with application, no.37, pp.19-31,
[7]. 1999
[8]. P. K. Maji, R. Biswas and A.R. Roy, "Fuzzy Soft sets," The journal of fuzzy mathematics, Vol.3, no.9,
[9]. pp.589-602,2001

Abstract: It is universally accepted that 3.14159265358… as the value of . It is thought an approximation, at its last decimal place. It is a transcendental number and squaring a circle is an unsolved problem with this number. A new, exact, algebraic number
14 2 4  = 3.14644660942… is derived and verified with a proof that is followed for Pythagorean theorem. It is proved here squaring of circle and rectification of circumference of a circle are possible too.
Keywords: Pythagorean thorem, circle, square, .

1. Squares 1 = ABCD, 2 = BZTC
2. Side = diameter of the inscribed circle = 1
3. KP = Parallel side to the side DC
4. OM = ON = radius ½
5. MON = triangle; MN = hypotenuse =
2
2
6. DK = KM = NP = PC =
KP MN
2

Abstract: Measuring the quality on quantitative formats is the most essential task where the attention of researchers is strongly desired. Modelling the scaling measures based on various formats is highly essential to explore several statistical devices. In this paper we have developed some stochastic models for the scaling measures similar to Likert's format. Bivariate stochastic processes in the context of spreadsheet experimentation were considered to develop these models. Mathematical formulae for several statistical measures of decision scores are derived for multiple choice decision items. The modelling is extended to formulate optimization programming problems with the objectives of maximising the expected decision score and also to minimise the volatility in decision score. The decision parameters namely, number of optimal decision assignments can be derived through the developed Non-Linear Programming Problem (NLPP). Sensitivity analysis is carried out with reference to optimal managerial decision scores.
Key Words: Stochastic modelling, optimisation programming, decision scores, scaling measures, bivariate stochastic process.

[1]. D Mather (1999), A framework for building spreadsheet based decision models; Journal of the Operational Research Society (1999) 50, 70-74.
[2]. Richard W.Kaz, Marc B. Carlange (1996), "Mixtures of stochastic processes: application to statistical downscaling"; Climate Research, Vol. 7: 185-193, 1996.
[3]. Thin-Yin Leong, Michelle L. F. Cheong (2008), "Teaching Business Modeling Using Spreadsheets" INFORMS Transactions on Education 9(1), pp. 20–34.
[4]. Tirupathi Rao Padi (2013), Stochastic Modeling on Likert‟s Scaling Measures; International Journal of Applied Mathematics & Statistical Sciences; Vol. 2(5); 19-32
[5]. Tirupathi Rao Padi, Kiran Kumar Paidipati and C. Umasanker (2013), Stochastic Programming for Optimal Decision Making through Scaling Measures; International Journal of Management & Information Technology; Vol. 6(1); 665-671.
[6]. Yuh-Yuan Guh, Rung-Wei Po, Kuo-Ren Lou (2009), "An Additive Scale Model for the Analytic Hierarchy Process"; International Journal of Information and Management Sciences; Vol. 20(2009), PP: 71-88

Abstract: We present a general stability concept of linear evolution operators which are defined on a Hilbert space. The stability concept include situations among which are non-uniform stability and non-uniform exponential stability.

Keywords: Banach space, evolution, operator, stability

[1]. P. Preda, D. R. Latcu, and C. Preda, On uniform and non-uniform exponential stability for evolutionary processes, AnaleleUnivers.Din Timisoara, Vol.XL, fascu 2, 2002.
[2]. R. Datko, Uniform asymptotic stability of evolutionary process in a Banach space, SIAM J. Math. Analysis, 3(1973), 428-445.
[3]. C. Buse, On non-uniform exponential stability of evolutionary process, Rend. Sem. Mat. Univ. Pol. Torino, Vol. 52, 4(1994).
[4]. A. Ichikawa, Equivalence of Lp stability and exponential stability for a class of non-linear sem-igroups, Nonlinear Analysis Theory, Methods and Applications 8, 9(1984).
[5]. J. L. Megan and C. Buse, On uniform exponential dichotomy of observable evolution operators, Rend. Sem. Mat. Univers.Politee. Torino, 50, 2(1992), 183-194.

Abstract: Human emotions are a complex manifestation of natural phenomena. However, these emotions to some extent can be mathematically expressed in form of simple equations. We have observed games and events and the reaction of the crowds to a particular situation. We find some events interesting and some dull. This subjective feeling has been mathematically expressed in form of an equation and termed as' Excitement'. A numerical factor is obtained, the magnitude of which gives the degree of excitement.
Key-words: Biased, Depression, Event, Excitement, Impulse, Un-biased

[1]. This is an independent theory and therefore there are no references

Abstract:This paper is based on bio heat transfer equation and demonstrates its application in solving one dimensional physiological heat distribution problems pertaining to limbs. The biological properties are assumed to vary along the radial direction. The dermal region is made up of three layers, namely epidermis dermis, and subcutaneous tissues. The model incorporates significant variations of physical and physiological parameters like blood mass flow rate, rate of metabolic heat generation, and thermal conductivity in each layer. Numerical results have been obtained for various cases of practical interest.

Keywords: Rate of metabolism 1, blood mass flow rate 2, thermal conductivity 3, heat generation 4, finite element method 5.

[1]. W.Perl Heat and matter distribution in body tissue and determination of tissue blood flow by local clearance methods" journal of theoretical biology 2(3),1962,201-235.
[2]. Perl,W. and Hirsch, R.L. ,Local blood flow in kidney tissue by heat clearance method, J. Theoret.Biol. 10(2), 1966, 251-280
[3]. Cooper, T.E. and Trezek, G.J.,A Probe technique for determining the thermal conductivity of tissues, J. Heat transfer, ASME 94 , 133-140,1972,a.
[4]. Cooper, J.E. and Trezek, G.T.,on the freezing of tissues, J. Heat transfer , ASME, 94,251-253,1972,b.
[5]. Patterson, A.M., Measurement of temperature profiles in human Skin, S.Afr J. Sci, 72, 78-79,1976
[6]. MONTAGNA, W. The Structure and Function of Skin.., Academic Press (1962).

Abstract: In this paper, we investigated the hydromagnetic steady flow of a viscous conducting fluid in a two-dimensional uniform width linearly diverging channel. For this investigation the effect of an externally applied homogeneous magnetic field on the development of velocity profiles and internal flow separation in the diverging channel are observed. The solution for the flow governing non-linear differential equation is found using perturbation method together with Pade´ approximation technique. The investigation results reveal that the requirement of flow Reynolds number for the development of internal flow separation increases with an increase in magnetic field intensity. Furthermore, the behavior of velocity profiles under the effect of magnetic field is discussed.
Keywords: Linear diverging channel, internal flow separation, magnetic field, Pade´ approximants

[1]. Baker Jr., G. A. 1975. Essentials of Pade´ Approximants, Academic Press, New York.
[2]. Makinde, O.D. 1995. Laminer flow in a channel of varying width with permeable boundaries, Rom. J. Phys. 40:403-417.
[3]. Makinde, O.D. and P. Mhone. 2006. Hydromagnetic effects on internal flow separation in a diverging channel, Rom. J. Phys. 51:959 966, Nos. 9-10.
[4]. Moreau, R. 1990. Magnetohydrodynamics, Kluwer Academic Publishers, Dordrecht.
[5]. Rao, A.R. and K.S. Deshikachar. 1986. MHD Oscillatory flow of blood through channels of variable cross section, Int. J. Engng. Sci. 24(10):1628-1628.

Abstract: Let G be the nonempty graph. The Jump graph J[G] of G is the graph whose vertices are edges of G, and where two vertices of J[G] are adjecent if and only if they are not adjacent in G, equivalently , the Jump graph J[G] is the complément of line graph L[G]. In [2] the authors have obtained Hamiltonian Jump graphs. In this paper we charecterised Hamiltonian laceability of Jump graph and also explore the Laceability in jump graph of Star, Friendship and Ladder graphs.
Keywords : Connected Graph, Jump graph, Friendship graph, Ladder graph,Hamiltonian-t*-laceable Graph

[1]. G.Chartrand, H.Hevia, E.B.M. Schultz, Sub graph distance graphs defined byEdge transfers, Discrete math. 170(1997)63-79.
[2]. Bayindureng Wu, Jixiang Meng, Hamiltonian Jump graphs, Discrete mathematics 289(2004)95-106.
[3]. Girisha.A and R.Murali, Hamiltonian laceability in a class of 4-Regular Graphs, IOSR Journal of Mathematics, Volume 4, Issue 1 (Nov.- Dec. 2012), pp 07-12.
[4]. G.Manjunath, R.Murali and S.K.Rajendra, Hamiltonian Laceability in the Modified Brick Product of Odd Cycles, International Journal of Graph Theory, submitted.
[5]. G.Manjunath and R.Murali, Hamiltonian Laceability in the Brick Product C(2n+1,1,r) Publish research paper in International Journal of Graph Theory(GBS Publishers), submitted.