iosr-Jm   Volume-10 ~ Issue-5 ~ Sep-Oct 2014

Abstract: A fuzzy graph can be obtained from two given fuzzy graphs using alpha product, beta product and
gamma product. In this paper, we find the degree of an edge in fuzzy graphs formed by these operations in terms
of the degree of edges and vertices in the given fuzzy graphs in some particular cases.
Key Words: Alpha product, Beta product, Gamma product, Degree of a vertex, Degree of an edge.
AMS Mathematics Subject Classification (2010): 03E72, 05C72, 05C76

[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.

Abstract: In this paper new oscillation criteria for the second order neutral difference equation of the form
r(n)x(n)  p(n)x( (n)) q(n)x( (n))v(n)x((n)) = 0
are presented. Gained results are based on the new comparison theorems, that enable us to reduce the problem of
the oscillation of the second order equation to the oscillation of the first order equation. Obtained comparison
principles essentially simplify the examination of the studied equations. We cover all possible cases when
arguments are delayed, advanced or mixed.

[1]. Agarwal R.P., Difference Equation and Inequalities, Marcel Dekker, New York (1992).
[2]. Andercon., C.H., Differential-Difference equations of advanced type, Ph.D., Dissertation, University of Missouvi, Columbia, 1968,
Absracted in the Amer.Math.Soc. 14(1967), 938.
[3]. Cheng S.S and Lin.Y.Z., Complete characterizations of an oscillatory neutral difference equation, Jour.Math.Anal.Appl.221(1998),
73-91.
[4]. Cheng S.S., Yan.T.C and Li.H.J., Oscillation criteria for second order difference equation Funk. Ekrac. 54 (1991) 223-239.
[5]. Cooke K.L., and Wiener.J., An equation alternately of retarded and advanced type, Proc.Amer.Math.Soc. 99(1987), 726-732.
[6]. Elaydi S.N., An Introduction to Difference Equations, Springer-Verlag, New York, 1995

Abstract: The aim of this note is to give an explicit formula for the number of subgroups of finite nonmetacyclic 2-groups having no elementary abelian subgroup of order 8.

Keywords: Centralproducts, cyclic subgroups, dihedral groups, finite nonmetacyclic 2-groups, number of subgroups.

[1]. M. Tarnauceanu, Counting subgroups for a class of finite nonabelian p-groups. AnaleleUniversitaatii de Vest, TimisoaraSeriaMatematica – Informatica XLVI, 1, (2008), 147-152.
[2]. G. Bhowmik, Evaluation of the divisor function of matrices, ActaArithmetica 74(1996), 155 – 159.
[3]. M. EniOluwafe, Counting subgroups of nonmetacyclic groups of typeD2n−1×C2,n≥3, submitted.
[4]. B. Huppert, Endlichegruppen I, II (Springer-Verlag, Berlin, 1967).
[5]. M. Suzuki, Group theory I, II (Springer-Verlag, Berlin, 1982, 1986).
[6]. H. Zassenhaus, Theory of groups (Chelsea, New York, 1949).

Abstract: In this paper, Manpower System of an organization with two groups is considered. Breakdown occurs in the two groups of the Manpower System due to attrition process. Group A consists of employees other than top management level executives; group B consists of top management level executives. In this model group A is exposed to Cumulative Shortage Process (CSP) due to attrition and group B has an Erlang phase 2 distribution. Joint Laplace transform of Time to Recruit , Recruitment time and sales time has been found. Their expectations are presented with numerical illustrations.

Keywords: Manpower system, attrition, shortage, cumulative shortage process, Erlang Phase two distributions.

[1]. D.J. Bartholonew, The statistical approach to manpower planning, Statistician, 20 (1971), 3-26
[2]. D.J. Bartholomew, A.F. Forbes, Statistical Techniques for Manpower Planning, John Wiley and Sons (1979)
[3]. J.D. Esary, A.W. Marshall, F. Proschan, Shock models and wear processes, Ann. Probability, 1, No. 4 (1973), 627-649
[4]. D.P. Gaver, Point Process Problems in Reliability Stochastic Point Processes (Ed. P.A.W. Lewis). Wiley-Interscience, New York
(1972), 774-800
[5]. R.C. Grinold, K.J. Marshall, Manpower Planning Models, New York (1977).
[6]. G.W. Lesson, Wastage and promotion in desired manpower structures, J. Opl. Res. Soc., 33 (1982), 433-442

Abstract: In sample surveys, stratified sampling is useful if the strata weights are known for each stratum. If they are not known double sampling may be used by selecting a large preliminary sample to estimate the strata weights. Then a stratified sample may be selected independently or from the initial sample. If the problem of non-response is also present then the strata are to be virtually divided into two disjoint and exhaustive groups of respondents and non-respondents. A subsamples from non-respondents is then selected and second more extensive attempt is to be group is to be made for obtaining the required information. The problem of obtaining a compromise allocation for first and second phase of sampling is the formulated as a multi-objective non-linear programming problem that minimizes the sum of variances of the stratified sample mean subject to the non-linear cost constraint. The formulated problem is solved using fuzzy programming and fuzzy goal programming based on piecewise linear approximation. A numerical example is presented to illustrate the computational details.

Keywords: Non-response, Multivariate Stratified Sampling, Multiobjective Integer non-linear programming problem, Fuzzy Programming, Travel cost

[1]. Cochran, W.G.: Sampling Techniques. John Wiley, New York, 1977.
[2]. Sukhatme, P.V., Sukhatme, B.V., Sukhatme, S., Asok, C.: Sampling Theory of Surveys with Applications. Iowa State University Press, Iowa, U.S.A. and Indian Society of Agricultural Statistics, New Delhi, India, 1984.
[3]. Geary, R.C.: Sampling methods applied to Irish agricultural statistics. Technical Series, Central Statistical office, Dublin, 1949.
[4]. Dalenius, T.: Sampling in Sweden: Contributions to the Methods and Theories of Sample Survey Practice. Almqvist and Wiksell, Stockholm, 1957.
[5]. Ghosh, S.P.: A note on stratified random sampling with multiple characters. Calcutta Statist. Assoc. Bull. 8, 81–89, 1958.

Abstract: The purpose of this paper is to use mathematical model to determine the minimum power needed to sustain flight. We considered, parasitic power, minimum velocity and lift power so as to get the minimum power needed to sustain flight and our general model is of the form, 𝑃𝑇=𝑃𝐿+𝑃𝑝.We efficiently utilized the Newton's laws of motion, Bernoulli's principle, and the Lift coefficient approach method for determining lift, in achieving this model.

Key words: Lift coefficient, parasitic power, Minimum velocity, Lift power, Minimum power, and Newton's laws.

[1] Anthony, J. (2010), Aerodynamics inverse design and shape optimization via control theory, Standard University.

[2] Gareth, H. (2010), Future aircraft fuel efficiency, Qinetic.

[3] Hurt H. Jr.(1965) aerodynamics for navel aviators, navel air system.

[4] Kelvin, P. (2009) Mathematical modeling of aircraft consumption,Eastern Washington University, Cheney.

[5] Mao, S. (2004) a computational study of the aerodynamic forces and power requirements dragonfly, China eijing University.

[6] Paul, G. (2011) flight path to sustainable aviation CSIRO, Australia

Abstract: In this paper developed a mathematical model of the spread of dengue hemorrhagic fever (DHF) SIR type, where SIR is an abbreviation of susceptible (S), infected (I) and recovered (R). Results of analysis and simulation obtained two fixed points, namely the disease-free quilibrium and endemic equilibrium. Human population, mosquitoes and mosquito eggs stable around the disease-free quilibrium when ℛ0<1 and stable around the endemic equilibrium point when ℛ0>1. Increased of mosquitoes mortality rate can reduce the value of the basic reproduction number.

Keywords : mathematical models, basic reproductive number, disease-free quilibrium, endemic equilibrium, numerical simulations

[1] Amaku M, Coutinho FAB, Raimundo SM, Lopez LF, Burattini MN, Massad E, A Comparative Analysis of the Relative Efficacy of Vektor-Control Strategies Against Dengue Fever, Biomedical, DOI 10.1007/s11538-014-9939-5, 2013.

[2] Burattini MN, Chen M, Chow A, Coutinho FAB, Goh KT, Lopez LF, MA S, Massad E, Modelling the control strategies against dengue in Singapore, Epidemiol Infect, 2007, doi: 10.1017/S0950268807008667.

[3] Jones JH, 2007. Note on ℛ0, 2007, Stanford.Department of Anthropological Sciences Stanford University.

[4] Jumadi, Model matematika penyebaran penyakit demam berdarah dengue, 2007, Bogor: Institut Pertanian Bogor.

[5] Massad E, Coutinho FA, Lopez LF, da Silva DR, Modeling the Impact of Global Warming on Vektor-Borne Infections, ScienceDirect, 8(2), 2011, 169-199

Abstract: Malaria is a deadly disease transmitted to humans through the bite of infected female mosquitoes .It can also be transmitted from an infected mother (congenitally) or through blood transfusion. In this paper, we discussed the transmission of malaria featuring in the framework of an SIRS-SI model with treatments are given to humans and mosquitoes. We here utilized the use of vaccines, the use of anti-malarial drugs, and the use of spraying as treatment efforts. A stability analysis was then performed and numerical simulation was provided to clarify the result. It is shown that treatments affect the dynamics of human and mosquito populations. In addition, we proposed the Homotopy Analysis Method (HAM) to construct the approximate solution of the model.

Keywords: HAM, Malaria model, SIRS-SI model, Stability analysis, Treatment

[1] Laarabi H, Labriji EH, Rachik M, Kaddar A. 2012. Optimal control of an epidemic model with a saturated incidence rate. Modelling and Control. Vol.17, No.4, pp. 448-459.
[2] Agusto FB, Marcus N, Okosun KO. 2012. Application of optimal control to the epidemiology of malaria. Electronic Journal of Differential Equation. Vol. 2012, No.81, pp. 1-22.
[3] Abdullahi MB, Hasan YA, Abdullah FA. 2013. A mathematical model of malaria and the effectiveness of drugs. Applied Mathematical Sciences. Vol. 7, 2013, No. 62, pp. 3079-3095.
[4] Mandal S, Sarkar RR, Sinha S. 2011. Mathematical models of malaria - a review. Malaria Journal. Vol. 10, pp. 1-19.
[5] Schwartz L, Brown GV, Genton B, Moorthy VS. 2012. A review malaria vaccine clinical projects based on the rainbow table. Malaria Journal. 11:11

Abstract: Human is the most significant creature on the earth having various complex biological structures. Skin the foremost and important organ of the body with many different functions is always a center of attraction for medical scientist. Protecting the skin is important. If the skin is unable to function properly, it will affect the entire parts of the body. Pathogens will enter the body cause harm to the internal environment and hence the different systems in our body may not be able to function properly. Thermoregulation due to skin plays an important role to maintain body core temperature. Any disorder in skin causes various disorderly idiosyncrasies. Present study deals with the thermal regulation in human tissues in wounding to healing process. All physiological essential factors responsible for healing are taken into consideration for real case studies. All estimations are based on bio-heat equation associated with bio physical and biochemical reactions. The present study deals with the theoretical model for the estimation of temperature variation in the human peripheral region. The study involves the essential factors responsible for the temperature distribution, the central blood flow, the heat transfer coefficient due to exchange of the temperature between the atmospheric temperatures and human periphery. The effect of the atmospheric temperature has been analyzed theoretically.

[1]. R. A. Clark, K. Ghosh amd M. G. Tonnesen, (2007), Tissue Engineering for Cutaneous Wounds. The Journal of Investigative Dermatology,127:1018-1029.
[2] E. Proksch, J. M. Brandner and J. M. Jensen, (2008). The Skin: An Indispensable Barrier. Exp Dermatol, 17(12):1063-72.

[3] D. G. MacLellan, Chronic wound management, Professor of Surgery, Canberra Hospital, Canberra.

[4] Jo Trim, Monitoring Temperature, Nurse times, 101(20): 30.

[5] Pennes, H. H., (1948), Analysis of Tissues and Arterial Blood Temperature in the Resting Forearm, Journal of Applied Physiology, 1, 93-122.

[6] Perl, W., (1962), An extension of the diffusion equation include clearance by capillary blood flow, Annals of the New York Academy Sci. 108 (92).

Abstract: In this paper we use fractional differential operators , ,
n
k x D  and x D
 to derive a number of key
formulas of multivariable H-function. We use the generalized Leibnitz's rule for fractional derivatives in order
to obtain one of the aforementioned formulas, which involve a product of two multivariable's H-function. It is
further shown that ,each of these formulas yield interesting new formulas for certain multivariable hyper
geometric function such as generalized Lauricella function (Srivastava-Dauost)and Lauriella hyper geometric
function some of these application of the key formulas provide potentially useful generalization of known result
in the theory of fractional calculus.
Key words: Fractional differential operator, multivariable H-function.
AMS subject classification 2000 MSC: 26a3333c40

[1]. Eredlyi A. et.al: Tables of Integral Transform, vol.2 Mc Graw Hill ,NY/Toronto/London (1954)
[2]. Lavoie J. L, Osler and Tremblay R: Fractional Derivatives and Special Functions SIAM, Rev.18(1976),240-268
[3]. Samko, S.G. Kilbas,A. A. and Maricev,O.L.: Integrals and Derivatives of Fractional order some of their
Applications,Nauka,Tekhnika Minsk(1987) in Russian
[4]. Nishimoto,K: Fractional Calculus Vol.1-4 Descrates Press ,Koriyama ,(1984,1987,1989,and 1991)
[5]. Oldham K.B.and Spanier.J: The Fractional Calculus, Acadmic Press NY/London,(1974)
[6]. Srivastava, H.M. and Panda R: Some expansion theorems and generating relations for the H-Function of several Complex variable
I and II, Comment.math, univ.st.paul, 24. (1975) Fasc.2, 119-137; ibid25 (1976), Fasc.2, 167-197