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• Open Access   Article

  Role of Epidemic Model to Control Drinking Problem

  Ankit Agrawal, Abha Tenguria, Geeta Modi

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.5 , Issue.4 , pp.324-337, Aug-2018

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i4.324337

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  Abstract
  In this paper, we have developed a non-linear mathematical model of alcohol abuse with non-linear incidence rate proposed by Anderson and May [1] which consists of four compartments corresponding to four population classes, namely, non- drinkers , heavy drinkers , drinkers in treatment and temporarily recovered class . The basic properties and sensitivity analysis of the system are discussed. Next, Basic reproduction number is calculated. The local and global stability of the drinking-free (problem free) equilibrium and the endemic equilibrium of the model are discussed. The local asymptotical stability of equilibrium is verified by analyzing the eigenvalues and using the Routh-Hurwitz criterion. Also discuss the global asymptotical stability of the drinking-free equilibrium by using LaSalle’s invariance principle and endemic equilibrium by autonomous convergence theorem. The stability analysis of the model shows that the system is locally asymptotically stable at drinking-free equilibrium when . When , endemic equilibrium exists and the system becomes locally asymptotically stable at and becomes unstable. Finally, numerical findings by using actual data of my village are illustrated through computer simulations using MATLAB software, which show the reducing the contact rate between the non-drinkers and heavy drinkers, increasing the number of drinkers that go into treatment and awareness combating the drinking epidemic.

  Key-Words / Index Term
  epidemic, treatment, awareness effect, drinking-free and endemic equilibrium, local and global stability

  References
  [1] Adu, K. I. et. al.: "Mathematical Model of Drinking Epidemic", British Journal of Mathematics & Computer Science 22 (5), pp. 1–10, 2017.
  [2] Anderson, R. M. and May, R. M.: "Regulation and Stability of host-parasite Population Interactions: I. Regulatory processes", The Journal of Animal Ecology, 47 (1), pp. 219–247, 1978.
  [3] Driessche, Van. Den. and Watmough, P. J.: "Reproduction Numbers and Sub-threshold Endemic Equilibria for Compartmental Models of Disease Transmission", Mathematical Bioscience, 180 (1-2), pp. 29–48, 2002.
  [4] Gorman, D. M. et. al.: "Agent-Based Modeling of Drinking Behavior: a Preliminary Model and Potential Applications to Theory and Practice", American Public Health Association, 96 (11), pp. 2055–2060, 2006.
  [5] Huo, H. F. and Song, N. N.: "Global Stability for a Binge Drinking Model with Two Stages", Discrete Dynamics Nature and Society, 2012, pp. 1–15, 2012.
  [6] Kot, M.: "Elements of Mathematical Biology", Cambridge University Perss: Cambridge, pp. 453, 2001.
  [7] Li, M. Y. and Muldowney, J. S.: "A Geometric Approach to Global Stability Problem", SIAM Journal on Mathematical Analysis, 27,(4), pp. 1070–1083, 1996.
  [8] Lee, S. et. al: "Optimal Control Intervention Strategies in Low-and High Risk Problem Drinking Populations", Socio-Economic Planning Sciences, 44(4), pp. 258–265, 2010.
  [9] Manthey, J. L. et. al.: "Campus Drinking: An Epidemiological Model", Journal of Biological Dynamics, 2 (3), pp. 346–356, 2008.
  [10] Mubayi, A. et. al.: "The Impact of Relative Residence Times on the Distribution of Heavy Drinkers in Highly Distinct Environments", Socio-Economic Planning Sciences, 44 (1), pp. 45–56, 2010.
  [11] Mulone, G. and Straughan, B.: "Modeling Binge Drinking", International Journal of Biomathematics, 5(1), pp. 1–14, 2012.
  [12] Orford, J. et. al.: "University Student Drinking: The Role of Motivational and Social Factors", Drugs: Education, Prevention and Policy, 11(5), PP. 407–421, 2004.
  [13] Sharma, S., and Samanta, G. P.: "Drinking as an epidemic: A mathematical Model with Dynamics Behavior", Journal of Applied Mathematics & Informatics, 31(1-2), pp. 1–25, 2013.
  [14] Sharma, S. and Samanta, G. P.: "Analysis of a Drinking Epidemic Model", International Journal of Dynamics and Control, 3 (3), pp. 288–305, 2015.
  [15] Wiggins, S.: "Introduction to Applied Nonlinear Dynamical Systems and Chaos", Texts in Applied Mathematics (2nd edition), Springer-Verlag, New York, 2003.
  [16] Xiang, H., Song, N. and Huo, H. F.: "Modelling Effects of Public Health Educational Campaigns on Drinking Dynamics", Journal of Biological Dynamics, 10 (1), pp. 164–178, 2016.
  [17] Xiang, H., Zhu, C. C. and Huo, H. F.: "Modelling the Effect of Immigration on Drinking Behaviour", Journal of Biological Dynamics, 11(1), pp. 275-298, 2017.
  

  Citation
  Ankit Agrawal, Abha Tenguria, Geeta Modi, "Role of Epidemic Model to Control Drinking Problem," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.4, pp.324-337, 2018

• Open Access   Article

  Economic Design and Evaluation of Feasible Cost Model for Attribute Sampling Tightened-Normal-Tightened Plan

  M. Kokila, K. Pradeepa Veerakumari

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.5 , Issue.4 , pp.338-349, Aug-2018

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i4.338349

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  Abstract
  Tightened-normal-tightened (TNT) plans are the most useful plans in compliance sampling especially for safety related products. In this scenario the acceptance number zero is desirable. This paper provides the feasible costs model considering the stochastic transition of states while inspecting or in various costs involved in the destructive and non-destructive testing. It reveals the cost behavior with respect to plan parameters through sensitivity analysis and cost curves deals with determining the optimal plan parameters for certain attribute sampling schemes.

  Key-Words / Index Term
  TNT plan, Destructive testing, Non-destructive testing, Optimal inspection plan, Compliance sampling, Sampling plan

  References
  [1]. S. Balamurali, C.H. Jun, “A new system of skip-lot sampling plans having a provision for reducing normal inspection”,.Applied Stochastic Models in Business and Industry, Vol. 27, pp.348–363, 2011.
  [2]. T.W. Calvin, “TNT zero acceptance number sampling”, American Society for Quality Control Technical Conference Transactions, Philadelphia: PA. 1977.
  [3]. C.H. Chen, C.Y. Chou, C.C. Kan, “Modified economic production and raw material model with quality loss for conforming product”, Journal of Industrial and Production Engineering, Vol. 32, pp.196–203, 2015.
  [4]. A.J. Duncan, “Quality Control and Industrial Statistics”, Richard D. Irwin, Homewood, Illinois, USA: pp. 7-8, 1986.
  [5]. M. S. Fallahnezhad, M. Aslam, “A new economical design of acceptance sampling models using Bayesian inference”, Accred Qual Assur, Vol. 18, pp. 187-195, 2013.
  [6]. K. Govindaraju, K. Subramani, “Selection of Tightened-Normal-Tightened system for given values of Acceptable quality level and Limiting quality level”, Journal of Applied Statistics, Vol. 19, Issue. 2, pp. 241-250, 1992.
  [7]. A. Hald, “Statistical Theory of Sampling Inspection by attributes”, Probability and Mathematical Statistics, A series of Monographs and Textbooks, Academic press, London: pp.5-12, 1981.
  [8]. J.I.S. Hsu, “A cost model for skip-lot destructive sampling”, IEEE Transactions on Reliability, Vol. R-26, Issue. 1, pp.70-72, 1977.
  [9]. J.I.S. Hsu, “A cost model for skip-lot non-destructive sampling”, IEEE Transactions on Reliability, Vol. R-28, Issue. 4, pp.289-291, 1979.
  [10]. MIL-STD 105D, “Sampling Procedures and Tables for Inspection by attributes”. U.S. Government Printing Office, Washington, D.C., US, 1963.
  [11]. K. Pradeepa Veerakumari, M. Kokila, “Economic Design of Skip-Lot Sampling Plan of Type (SkSP-2) in Reducing Inspection for Destructive sampling”, International Journal of Pure and Applied Mathematics, Vol. 117, Issue. 12, pp. 101 -111, 2018.
  [12]. K. Pradeepa Veerakumari, M. Kokila, “Economic scheme for designing Skip lot sampling plans involving Cost functions using Graphical Evaluation Review Technique”, International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol. 5, Issue. 3, pp. 1-5, 2018.
  [13]. S.M. Ross, Stochastic processes, 2nd edition. New York: Wiley. 1996.
  [14]. E.G. Schilling, D.V. Neubauer. Acceptance Sampling in Quality Control. BocaRaton: CRC Press. Marcel Dekker, New York: pp. 94-95, 2008.
  [15]. V. Soundararajan, S. D. Arumainaiyagam, “Quick Switching System for Costly and Destructive Testing”, Sankhya: The Indian Journal of Statistics, Series B-Part I, Vol. 54, Issue. 1, pp. 1-12, 1992.
  [16]. V. Soundararajan, R. Vijayaraghavan, “Construction and Selection of tightened-normal-tightened (TNT) plans”, Journal of Quality Technology, Vol. 22, Issue 2, pp. 146–153, 1990.
  [17]. K.K. Suresh, S. Balamurali, “Designing of Tightened-Normal-Tightened (TNT) plans indexed by MAPD”. Communication in Statistics – Theory and Methods, Vol.22, Issue 7, pp.2043-2056, 1993.
  [18]. D. Senthilkumar, D. Muthuraj, “Construction and selection of tightened–normal–tightened variables sampling scheme of type TNTVSS (n1, n2; k)”, Journal of Applied Statistics, Vol. 37, Issue 3, pp.375-390, 2010
  [19]. J.R. Singh, A. Sanvalia, “Single Sampling Plan for Variable Indexed by AQL and AOQL with Known Coefficient of Variation”, International Journal of Computer Sciences and Engineering, Vol. 5, Issue. 10, pp. 20-25.2017.
  [20]. R.S. Walse, G.D. Kurundkar, P. U. Bhalchandra, “A Review: Design and Development of Novel Techniques for Clustering and Classification of Data”, International journal of scientific research in Computer science and Engineering, Vol. 6, Issue. 1, pp.19-22.
  [21]. Training Course series No.9, “Non-destructive Testing: A Guidebook for Industrial Management and Quality Control Personnel”, International Atomic Energy Agency, Vienna: pp.125-150, 1999.
  

  Citation
  M. Kokila, K. Pradeepa Veerakumari, "Economic Design and Evaluation of Feasible Cost Model for Attribute Sampling Tightened-Normal-Tightened Plan," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.4, pp.338-349, 2018

• Open Access   Article

  Generalized Ratio-Cum-Product Estimator for Estimating Population Mean in Systematic Sampling

  Rafia Jan, Asra Nazir, Showkat Maqbool and T. R. Jan

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.5 , Issue.4 , pp.350-353, Aug-2018

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i4.350353

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  Abstract
  This manuscript suggests a generalized class of ratio-cum-product estimator in systematic sampling. The Mean Square Error (MSE) of the suggested class and mathematical conditions have been also derived to prove the efficiency of proposed estimators. The results are justified numerically.

  Key-Words / Index Term
  Auxiliary variate; Bias; Efficiency; Mean Squared Error.

  References
  [1] W. G. Madow and L. H. Madow, “On the theory of systematic sampling”, Ann. Math. Statist., Vol. 15, pp. 1-24, 1944.
  [2] D. B. Lahiri, “On the question of bias of systematic sampling”, Proceedings of World Population Conference, 6, pp. 349-362, 1954.
  [3] W, Gautschi, “Some remarks on systematic sampling”, Ann. Math. Statist.,Vol. 28, pp. 385-394, 1957.
  [4] J. Hajeck, “Optimum strategy and other problems in probability sampling”, Casopis pro Pestovani Matematiky, Vol. 84, pp. 387–423, 1959.
  [5] W. G. Cochran, “Relative efficiency of systematic and stratified random samples for a certain class of population”, Ann. Math. Statist., Vol. 17, pp. 164–177, 1946.
  [6] K. S. Kushwaha and H. P. Singh, “Class of almost unbiased ratio and product estimators in systematic sampling” Jour. Ind. Soc. Ag. Statistics, Vol. 41 Issue 2, pp. 193–205, 1989.
  [7] Banarasi, S. N. S. Kushwaha, and K. S. Kushwaha, “A class of ratio, product and difference (RPD) estimators in systematic sampling”, Microelectron. Reliab., Vol. 33 Issue 4, pp. 455–457, 1993.
  [8] R. Singh, and H. P. Singh “Almost unbiased ratio and product type estimators in systematic sampling”, Questiio, Vol. 22 Issue 3, pp. 403-416, 1998.
  [9] R. Singh, S. Malik, and V. K. Singh. “An improved estimator in systematic sampling”, Jour. of Scie. Res., Vol. 56, pp. 177-182, 2012.
  [10] A. K. P. C. Swain, “The use of systematic sampling ratio estimate” J. Ind. Statist. Assoc., Vol. 2, pp.160–164, 1964.
  [11] N. D. Shukla, “Systematic sampling and product method of estimation”, In Proceedings of all India Seminar on Demography and Statistics. B.H.U. Varanasi: India, 1971.
  [12] H. P. Singh, and N. K. Jatwa, “A class of exponential type estimators in systematic sampling”, Eco. Qulty. Control., Vol. 27, pp. 195–208, 2016.
  [13] H. P. Singh, R, S. Solanki and A. K. Singh, “A generalized ratio-cum-product estimator for estimating the finite population mean in survey sampling”, Commun. Stat. Theory Methods Vol. 45 Issue 1, pp. 158–172, 2016.
  [14] R. Tailor, N. K. Jatwa and H. P. Singh, “A ratio-cum-product estimator of finite population mean in systematic sampling”, Statistics in Transition, Vol. 14, Issue 3, pp. 391–398, 2013.
  

  Citation
  Rafia Jan, Asra Nazir, Showkat Maqbool and T. R. Jan, "Generalized Ratio-Cum-Product Estimator for Estimating Population Mean in Systematic Sampling," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.4, pp.350-353, 2018

• Open Access   Article

  Weighted Ratio-cum-Product Estimator for Finite Population Mean

  K.B. Panda and M. Sen

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.5 , Issue.4 , pp.354-358, Aug-2018

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i4.354358

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  Abstract
  We have, in this paper, proposed a new ratio-cum-product estimator of finite population mean using information on two auxiliary variates. The bias and mean squared error of the proposed estimator, up to the first order of approximation have been derived. The proposed estimator, under optimal weights, is shown to be superior to the competing estimators. Empirical investigations have been carried out in support of the theoretical findings.

  Key-Words / Index Term
  Auxiliary variable, Ratio-cum-product estimator

  References
  [1] Goodman, L.A., On exact variance of products. Amer. Stat. Asso.55, 708-713, (1960).
  [2] Hansen, M.H. et. al: Sample surveys Methods and Theory. Vol.I Wiley, New York,(1953).
  [3] Koop, J.C., “On an identity for the variance of a ratio of two random variables.” Jour. Roy. Stat. Soc. Series B,26(3), 484-486, (1964).
  [4] Murthy, M.N., Product method of estimation.Sankhya, Series A, Vol.26, 69-74, (1964).
  [5] Olkin, I, Multivariate ratio method of estimation for finite populations. Biometrika, 45, 154-65. (1958).
  [6] Singh, M.P: On the estimation of ratio and product of population parameters. Sankhya, B,27,321-28, (1965).
  [7] Singh, M.P., Efficient use of systematic sampling in ratio and product estimation, Metrika113, 199-205, (1966).
  [8] Singh, M.P., Multivariate product method of estimation for finite populations.,J. Indian Soc. Agri. Statist., 19,1-10, (1967).
  [9] Singh, M.P.: Ratio cum Product Method of Estimation, Metrika, Vol.12, Issue 1, pp34-42, (1967).
  [10] Singh, M.P., 1969. Comparison of some ratio-cum-product estimators. Sankhya, series B, 31, 375-378.
  

  Citation
  K.B. Panda and M. Sen, "Weighted Ratio-cum-Product Estimator for Finite Population Mean," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.4, pp.354-358, 2018

• Open Access   Article

  Constructing Spanning Tree in Banking Sector Problem Using Different Types of Algorithms

  M. Vijaya and B. Mohanapriyaa

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.5 , Issue.4 , pp.359-370, Aug-2018

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i4.359370

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  Abstract
  Fuzzy graphs are used as device for modeling and description of the real world. Network systems such are Banking, Transport, water, electricity, internet, work operations schemes in the process of production, construction etc…. Banking system keeps the day by day tally record as a complete banking. It can keep the information of account type, account opening form, deposit, with drawl and searching the transaction. The working of banking account system and cover the basic functionality of a bank account management system. The main focus is to a systematic study of algorithms. Basic banking itself needs to be supported by innovative strategies, in order to improve the reach and reduce the operating cost of the banks. Infrastructure sharing amongst banks and organizations will help in lowering the in commission cost and thus the cost benefit can be transferred to customers. Greater use of technology should be made by the banks to improve their reach, speed of processing, as well as to cut down the operating cost. An illustrative example is included to demonstrate the proposed algorithm. This paper is designed to find a key application of the fund available for investment for the customer to the bank using Nearest Neighbor Algorithm, Repeated Nearest Neighbor Algorithm, Cheapest Link Algorithm and Kruskal`s Algorithm to a randomly weighted fuzzy graph. These algorithm continuously increases the size of a fuzzy tree, one edge at a time, starting with a fuzzy tree consisting of a single vertex, until it spans all vertices of the fuzzy graph.

  Key-Words / Index Term
  Fuzzy Spanning Tree-Nearest Neighbor Algorithm-Repeated Nearest Neighbor Algorithm-Cheapest Link Algorithm-Kruskal’s Algorithm

  References
  [1]. A.NAGOORGANI and V.T.CHANDRASEKARAN: A First Look at Fuzzy Graph Theory Allied Publishers Pvt. Ltd.
  [2]. A.NAGOORGANI and V.T.CHANDRASEKARAN: An Algorithm on domination Number of a graph, International Journal of Mathematics and Computer Science, Lebanon, 2(2007), no.3,231-235.
  [3]. DR.G,NIRMALA and K.UMA: Fizzy Shortest Route Algorithm For Telephone Line Connection, International Journal of Scientific and Research Publication, Volume 2, Issue 8, August2012.
  [4]. H.J.ZIMMERMANN: Fuzzy set theory and its Application. Allied Publishers Limited, 1996.
  [5]. L.A.ZADEH: Fuzzy logic and the calculi of fuzzy rules and fuzzy graphs, a précis, Multi. Val. Logic, 1:1-38, 1996.
  [6]. CHRISTOFIDES, N: Graph Theory: an algorithm approach. Academic Press, London, 1975.
  [7]. HALPERN.J, MAIMAON.O: Algorithm for the m-center problems; a survey. European J. Operational Res. 10, 1982, 90-99.
  [8]. T.N. Chuang, J.Y.Kung, The fuzzy shortest path length and the corresponding shortest path in a network, Computers & Operations Research 32 (2005) 1409-1428.
  [9]. C.lin, M.S. Chern, The fuzzy shortest path problem and its most vital arcs, Fuzzy Sets and Systems 58 (1993) 343-353.
  

  Citation
  M. Vijaya and B. Mohanapriyaa, "Constructing Spanning Tree in Banking Sector Problem Using Different Types of Algorithms," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.4, pp.359-370, 2018

• Open Access   Article

  The Mersenne Meet Matrices on A –Sets

  N. Elumalai, R. Kalpana

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.5 , Issue.4 , pp.371-373, Aug-2018

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i4.371373

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  Abstract
  A recursive structure theorem for Mersenne meet matrices on A-sets is verified and a recursive formula for det (Mersenne meet matrix) and for inverse of (Mersenne meet matrix) on A-sets is also verified. The recursive formulae also yield explicit formulae, e.g. the known determinant and inverse formulae on chains and a-sets.

  Key-Words / Index Term
  Meet Matrices, Mersenne Meet Matrices, a- Set, A-Set

  References
  [1] P. Haukkanen, “On meet matrices on posets”, Linear
  Algebra Appl. 249: 111-123 ,1996.
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  158: 77-97 ,1991.
  [3] B. Wang, “Explicit Expressions of Smith`s Determinant
  on a Poset”, Acta Math Sin.(Engl. Ser.), 17(1): 161-168,
  2001.
  [4] I. Korkee and P. Haukkanen, “Bounds for determinants of
  meet matrices associated with incidence functions”,
  Linear Algebra Appl. 329(1-3): 77-88 ,2001.
  [5] I. Korkee and P. Haukkanen, “On meet matrices with
  respect to reduced, extended and exchanged sets”, JP J.
  Algebra Number Theory Appl., 4(3),559-575 ,2004.
  [6] I. Korkee, “On meet and join matrices on A-sets and
  Related Sets”, Notes on Number theory and Discrete
  Mathematics, 10(3):57-67,2004.
  [7] S. Beslin and S. Ligh, “GCD-closed sets and the
  determinants of GCD matrices”, Fibonacci Quart.,
  30: 157-160 ,1992.
  [8] P. Haukkanen, J.Wang and J. SillanpÄaÄa, “On Smith`s
  Determinant”, Linear Algebra Appl 258: 251-269 , 1997.
  [9] [P. Haukkanen and J. SillanpÄaÄa, “Some analogues of
  Smith`s determinant”, Linear an Multilinear Algebra
  41: 233-244 ,1996.
  [10] I. Korkee and P. Haukkanen, “On meet and join matrices
  associated with incidence functions”.Linear Algebra
  Appl., 372: 127-153 , 2003.
  [11] M. Aigner, “Combinatorial Theory”. Springer-Verlag,
  1979.
  [12] G. Birkhof, “Lattice Theory”. American Mathematical
  Society Colloquium Publication, 25,Rhode Island, 1984.
  [13] R. A. Horn, C. R. Johnson, “Matrix Analysis”, Cambridge
  University Press, New York ,1985.
  [14] I. Korkee, “ A note on meet and join matrices and their
  special cases GCUD and LCUM Matrices”, Int. J. Pure
  Appl. Math.1-11
  [15] F. Zhang, “Matrix theory”. Basic results and techniques,
  Universitext, Springer-Verlag, New York, 1999.
  [16] Parthajit Roy, Swati Adhikari and J. K. Mandal, “A
  Shortest Path Similarity Matrix based Spectral
  Clustering”, International Journal of Computer
  Sciences and Engineering 4(1) , 2015.
  

  Citation
  N. Elumalai, R. Kalpana, "The Mersenne Meet Matrices on A –Sets," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.4, pp.371-373, 2018

• Open Access   Article

  On m-independence in Graphs

  D. K. Thakkar and Neha P. Jamvecha

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.5 , Issue.4 , pp.374-379, Aug-2018

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i4.374379

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  Abstract
  In this paper, we have defined the concepts of m-independent set, maximal m-independent set and maximum m-independent set. In order to define these concepts we have used the notion of m-adjacent vertices. Adjacent vertices are always m-adjacent vertices. This notion also gives rise to a concept called m-domination in graphs. We prove that a set is maximal m-independent set if and only if it is a minimal m-dominating set. We define m-independence number of a graph to be the maximum cardinality of an m-independent set. We prove a necessary and sufficient condition under which the m-independence number decreases when a vertex is removed from the graph. Further, we have also introduced a new operation in graph called m-removal of a vertex. The subgraph obtained by m-removing a vertex is a subgraph of the subgraph obtained by removing the vertex from the graph. We prove that a vertex is an isolated vertex if and only if the m-independence number of the graph decreases when the vertex is m-removed from the graph. Some related examples have been given to illustrate these concepts.

  Key-Words / Index Term
  m-independent set, maximal m-independent set, maximum m-independent set, m-independence number, m-dominating set, minimal m-dominating set, m-removal of a vertex

  References
  [1] D. K. Thakkar and Neha P. Jamvecha, “About m-domination number of Graphs” (communicated).
  [2] D. K. Thakkar and Neha P. Jamvecha, “A New Variant of Edge Stability in Graphs”, International Journal of Pure and Engineering Mathematics, Vol.5, Issue.3, pp.87-97, 2017.
  [3] R. Laskar and K. Peters, “Vertex and edge domination parameters in graphs”, Congressus Numerantium, Vol.48, pp.291-305, 1985.
  [4] E. Sampathkumar, and P. S. Neeralagi, “The neighbourhood number of a graph”, Journal of Pure and Applied Mathematics, Vol.16, Issue.2, pp.126-136, 1985.
  [5] E. Sampathkumar, and S. S. Kamath, “Mixed Domination in Graphs”, The Indian Journal of Statistics, 1992.
  [6] T. W. Haynes, S. T. Hedetniemi and P. J. Slater, “Domination in Graphs Advanced Topics”, Marcel Dekker, Inc., New-York, 1998.
  [7] T. W. Haynes, S. T. Hedetniemi, and P. J. Slater, “Fundamentals of domination in graphs”, Marcel Dekker, Inc., New-York, 1998.
  

  Citation
  D. K. Thakkar and Neha P. Jamvecha, "On m-independence in Graphs," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.4, pp.374-379, 2018

• Open Access   Article

  Numerical Approach for a Stable Solution of Fractional Order Calcium Diffusion Model

  S. Ruban Raj, Sheena Mathew, Tessy Tom

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.5 , Issue.4 , pp.380-383, Aug-2018

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i4.380383

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  Abstract
  Diffusion is one of the main carrying phenomena which is seen in signaling mechanisms of ions and molecules in living cells, such as neurons. Here we present a one dimensional fractional diffusion model of calcium dynamics in cylindrical dendrites with Dirichlet boundary conditions. Based on shifted Grunwald‐Letnikov definition of fractional derivatives, implicit finite difference scheme is used to approximate the solution. The numerical solutions are obtained by using MATLAB programme.

  Key-Words / Index Term
  Fractional Fick’s law, Fractional Differential equation, Grunwald‐Letnikov Derivative, Finite Difference Method, Calcium Diffusion.

  References
  [1] R.S. Zucker, N.Stockbridge , “Presynaptic calcium diffusion and the time courses of transmitter release and synaptic facilitation at the squid giant synapse”, Journal of Neuroscience, Vol.3, No.6, pp.1263‐1269 , 1983.
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  [3] Yu, B.Jiang, Xiaoyun, “A fractional anomalous diffusion model and numerical simulation for sodium ion transport in the intestinal wall”, Advances in Mathematical Physics, vol.2013, 2013 .
  [4] X. Y. Jiang, M. Y. Xu and H. T. Qi, “The fractional diffusion model with an absorption term and modified Fick’s law for non‐local transport processes”, Nonlinear Analysis: RealWorld Applications, vol.11, no.1, pp. 262‐269, 2010 .
  [5] M.ZecovÃ, J.TerpÃik, “Heat conduction modeling by using fractional‐ order derivatives”, Applied Mathematics and Computation, vol. 29, 2015 .
  [6] I.Podlubny. “Fractional differential equations”, Academic Press, San Diego, CA, 1999.
  [7]M.M.Meerschaert and C.Tadjeran, “Finite difference approximations for fractional advection‐dispersion flow equations”, Journal of Computational and Applied Mathematics, vol.172, pp.65‐77, 2004.
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  Citation
  S. Ruban Raj, Sheena Mathew, Tessy Tom, "Numerical Approach for a Stable Solution of Fractional Order Calcium Diffusion Model," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.4, pp.380-383, 2018

• Open Access   Article

  Fixed Point Theorem in Partial Metric Spaces

  R. Krishnakumar, R. Livingston

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.5 , Issue.4 , pp.384-388, Aug-2018

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i4.384388

  Abstract

  Full-Text HTML

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  Citation

  Abstract
  In this paper, we proved the common fixed point theorems for sequence of mappings in Partial Metric Spaces.

  Key-Words / Index Term
  Partial Metric Space, Complete Patial Metric Space, Coincidence Point, Weakly Compatible, Fixed Point.

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  Citation
  R. Krishnakumar, R. Livingston, "Fixed Point Theorem in Partial Metric Spaces," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.4, pp.384-388, 2018

• Open Access   Article

  Flexible Fuzzy Softification of Group Structures

  V. Vanitha, G. Subbiah, M. Navaneethakrishnan

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.5 , Issue.4 , pp.389-394, Aug-2018

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i4.389394

  Abstract

  Full-Text HTML

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  Citation

  Abstract
  In this paper, we introduce the concept of upper t-subgroups of a flexible fuzzy soft intersection group (FFSIG) and investigate various structures of flexible fuzzy soft intersection groups related to upper t- subgroups with suitable example.

  Key-Words / Index Term
  soft set, fuzzy soft set, soft int-group, upper t-subgroup, flexible fuzzy set, inclusion, relative complement

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  Citation
  V. Vanitha, G. Subbiah, M. Navaneethakrishnan, "Flexible Fuzzy Softification of Group Structures," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.4, pp.389-394, 2018