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• Open Access   Article

  Fixed Point Theorem in Generalized Fuzzy Metric Space Using Kannan-Type Mappings

  Geetanjali Sharma, Richa Gupta, Pankaj Tiwari, Akshay Sharma

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.6 , Issue.2 , pp.310-314, Apr-2019

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i2.310314

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  Abstract
  In this paper, we extend generalized Kannan-type mappings in generalized fuzzy metric space. Then, we prove a fixed point of this kind of mapping in generalized Kannan-type mappings in generalized fuzzy metric space, which generalize the well known results.

  Key-Words / Index Term
  Common fixed points, Metric space, t-norm, Generalized Fuzzy metric space, Kannan-type mappings, Generalized Kannan-type mappings

  References
  [1] A. Branciari, “A fixed point theorem of Banach-Caccioppoli type on a class of generalized metric spaces”, Publ. Math. Debrecen, (1-2), pp. 31-37, 2000.
  [2] A. George and P. Veeramani, “On some results in metric spaces”, Fuzzy Set and System., 64, pp. 395-399, 1994.
  [3] Binayak S. Choudhury and Kirshnapada Das, “Fixed point of generalized Kannan-type mappings in generalized menger spaces”, Commun. Korean. Math. Soc., (4) 24, pp. 529-537, 2009.
  [4] Binayak S. Choudhury and Kirshnapada Das, “Cyclic contraction result in 2- menger space”, Bull.of Int. Mathematical Virtual Institute, (2), pp. 223-234, 2012.
  [5] Cho, et al., “Coupled coincidence point theorems in (Intuitionistic) fuzzy normed spaces”, Journal of Inequalities and Applications, 1(104), 2013.
  [6] C. Dibari and C. Vetro, “Fixed points attractors and weak fuzzy contractive mappings in a fuzzy metric space”, J. Fuzzy Math, 13, pp. 973-982, 2005.
  [7] I. Kramosil and J. Michalek, “Fuzzy metrics and statistical metric spaces”, Kybernetika, 11, pp. 336-344, 1975.
  [8] J. O. Olaleru, G. A. Okeke and H. Akewe, “Coupled Fixed Point Theorems for Generalized ϕ-mappings satisfying Contractive Condition of Integral Type on Cone Metric Spaces”, International Journal of Mathematical Modeling & Computations, 2(2), pp. 87-98, 2012.
  [9] K. Menger, “Statistical metrics”, Proc. Nat. Acad. Sci. U.S.A, 28, pp. 535-537, 1942.
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  [11] M. Grabiec, “Fixed point in fuzzy metric spaces”, Fuzzy Set and System., 27, pp. 385-389, 1988.
  [12] M. Sanei, R. Dehghan and A. Mahmoodi Rad,“The Identification by Using Fuzzy Numbers”, IJM2C, 1, pp. 51-59, 2012.
  [13] P. Das and L. Kanta Dey, “A fixed point theorem in generalized metric spaces”, Soochow Journal of mathematics, 1, pp. 33-39, 2007.
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  [15] R. Chugh and S. Kumar, “Weakly compatible maps in generalized fuzzy metric spaces”, J. Analysis, 10, pp. 65-74, 2002.
  [16] R. Kannan, “Some result on fixed points”, Bull. Calcutta Math. Soc., 60, pp. 71-76, 1968.
  [17] Z. K. Deng, “Fuzzy pseudo-metric spaces”, J. Math. Anal. Appl., 86, pp. 74-95,1982.
  

  Citation
  Geetanjali Sharma, Richa Gupta, Pankaj Tiwari, Akshay Sharma, "Fixed Point Theorem in Generalized Fuzzy Metric Space Using Kannan-Type Mappings," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.6, Issue.2, pp.310-314, 2019

• Open Access   Article

  Stability Analysis of Dengue Epidemic Model with Vertical Transmission Function

  Lakhan Nagar, V. K. Gupta, S. K. Tiwari

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.6 , Issue.2 , pp.315-324, Apr-2019

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i2.315324

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  In this paper, we consider a mathematical model to investigate the dynamics of spread of Dengue fever in both human and mosquito population. We find equilibrium of the model and basic re-production number. We also derive the necessary condition of the model are locally asymptotically stable, globally asymptotically stable or unstable. Global stability of the model is provided by constructing a Lyapunov function. We consider epidemic model with vertical transmission in mosquito population and shows that increases as p increases.

  Key-Words / Index Term
  Epidemic Model, Saturated Incidence rate, Basic Reproduction number, Stability

  References
  [1] M. Derouich , A. Boutayeb and E.H. Twizell, “A Model of Dengue Fever”, Biomedical engineering online,Brunel, vol. 2, pp. 1-10,2003.
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  [3] N. Nuraini, E. Soewono, K.A. Sidarto, “Mathematical model of dengue disease transmission with severe DHF Compartment”, Bulletin of the Malaysian Mathematical Sciences Society, vol. 30(2), pp. 143-157,2007.
  [4] P. Pongsumpun , “Transmission model for dengue disease with and without the effect of extrinsic incubation period”, KMITL Sci. Tech. J. Thailand , pp. 74-82, 2006.57, 2007.
  [5] G.R. Phaijoo , D.B. Gurung , “Mathematical model on analysis of awareness in controlling dengue disease”, International Journal of Advanced Research, vol. 4(7) ,pp. 999-1006, 2016.
  [6] G.R. Phaijoo , D.B. Gurung , “Mathematical study of biting rates of mosquitoes in transmission of dengue disease”, Journal of Science , Engineering and Technology ,pp. 25-33,2015.
  [7] Van den Driessche, andJ. Watmough , “Reproduction number and sub threshold endemic equilibria for compartmental models of disease transmission”, mathematical Bioscience, pp.1679-1684, 2007.
  [8] S. Gakkhar , N.K. Chavda , “Impact of awareness on the spread of dengue infection in human population”, Applied mathematics,vol. 4(8), pp. 142-147,2013.
  [9] E. Soewono, A.K. Supriatna , “A two-dimensional model for the transmission of dengue fever disease”,Bulletin of the Malaysian Mathematical Sciences Society, pp.49-57, 2005.
  

  Citation
  Lakhan Nagar, V. K. Gupta, S. K. Tiwari, "Stability Analysis of Dengue Epidemic Model with Vertical Transmission Function," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.6, Issue.2, pp.315-324, 2019

• Open Access   Article

  Multicriterion Fuzzy Decision Making in Irrigation Planning

  Rajkumar, S. Udayakumar

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.6 , Issue.2 , pp.325-333, Apr-2019

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i2.325333

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  Relative importance or weight of criterion indicate the main concern assigned to the condition by the decision-maker while ranking the alternatives in a multicriterion decision making (MCDM) environment. Multicriterion decision making (MCDM) has emerged as an effective methodology due to its ability to merge quantitative and qualitative criteria selection of the best option. Concurrently, fuzzy logic is in advance significance due to its flexibility in managing imprecise individual data. In the present study two fuzzy logic-based MCDM methods, namely similarity analysis (SA) and Decision analysis (DA), are adopted and developed as a fuzzy decision system(FUDS) and applied to a case study of the Aringar Anna Sugar Project(AASP),Thanjavur,Tamilnadu,India,for selecting the best-performing irrigation subsystem. It is found that both SA and DA recommended the same irrigation subsystem as the most excellent. It is fulfilled that application of fuzzy logic methodology for real-world decision-making problems is create to be efficient.

  Key-Words / Index Term
  Multi criteria decision making, Fuzzy logic, FUDS, SA,DA

  References
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  [8] Raju KS. 1995. Studies on multicriterion decision making methods and management of irrigation systems. Unpublished doctoral dissertation, India Institute of Technology, Kharagpur, India.
  [9] Raju KS. Duckstein L. 2002. Multicriterion analysis for ranking an irrigation system: an India case study. Journal of Decision Systems 11:499-511.
  [10] Raju KS. Nagesh Kumar D. 1999.Multicriterion decision making in irrigation development strategies. Journal of Agricultural Systems 62:117-129.
  [11] Ross TJ. 1995. Fuzzy logic with Engineering Applications. McGraw-Hill. Inc: New York, USA.
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  [14] Bui, T.X., (1987) Coop: A Group Decision Support System for Cooperative Multiple Criteria Group Decision Making, Spinger-Verlag, Berlin.
  [15] Keeney, R.L., and H. Raffia, (1976) Decision with Multiple Objectives: Preferences and Value Tradeoffs, Wiley, New York.
  [16] Keeney, R.L., and E.F. Wood, (1977) An Illustrative Example of the Use of Multi-Attribute Utility Theory for Water Resource Planning, Water Resources Research, 13(4), pp. 705-712.
  [17] Mareschal, B., (1986) Stochastic Multicriteria Decision Making and Uncertainty, European Journal of Operational Research, 26, pp. 58-64.
  [18] Raju, K.S., (1995) Studies on Multicriterion Decision making Techniques and Management of Irrigation System, PhD thesis, Indian Institute of Technology, Kharagpur.
  [19] Raju, K.S. and C.R.S. Pillai, (1999) Multicriterion Decision Making in Performance Evaluation of an Irrigation System, European Journal of Operational Research, 112(3), pp. 479-488.al of FUDS.
  

  Citation
  Rajkumar, S. Udayakumar, "Multicriterion Fuzzy Decision Making in Irrigation Planning," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.6, Issue.2, pp.325-333, 2019

• Open Access   Article

  A Generalized Hybrid Steepest Descent Method for Variational Inequality Problem

  Poonam Mishra, Shailesh Dhar Diwan

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.6 , Issue.2 , pp.334-338, Apr-2019

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i2.334338

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  Abstract
  Variational inequalities are used as models for sovinga large number of problems in mathematical, physical, economics, optimization,finance and engineering. The fixed point formulation of any variational inequality problem can be formulated as a fixed point problem and is useful for existence of solution of the variational inequality problem as well as it also provides the facility to develop algorithms for approximation of solution of VI problem. A lot of research has been carried out to approximate solution of a variational inequality problem. In this paper, we propose to investigate a generalized hybrid steepest descent method and develop a convergence theory for solving variational inequality problem over the fixed point set of a mapping which is not necessarily Lipschitz continuous.Our result extends and generalizes many known results in recent history

  Key-Words / Index Term
  minimization problem; Fixed point; Hybrid steepest descent method; Monotone variational inequality;Nearly asymptotically nonexpansive mapping., strongly asymptotically nonexpansive mapping

  References
  [1] R.P. Agarwal, D. O’Regan, D.R. Sahu, Fixed Point Theory for Lipschitzian-type Mappings with Applications, Springer-Verlag New York, 1st edition, 2009.
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  [6] N. Buong, L.T. Duong, An explicit iterative algorithm for a class of variational inequalities in hilbert spaces, J. Optim.Theory Appl. 151 (2011), 513-524.
  [7] N. Buong, V.X. Quynh, N.T.T. Thuy, A steepest-descent krasnoselŁkii–mann algorithm for a class of variational inequalitiesin banach spaces, J. Fixed Point Theory Appl. 18 (2016), 519-532.
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  [10] Q.H. Ansari D.R. Sahu, J.C. Yao, The prox-tikhonov-like forward-backward method and applications, Taiwanese J. Math.19 (2015), 481-503.
  [11] J. Eckstein, D.P. Bertsekas, On the douglasachford splitting method and the proximal point algorithm for maximal monotoneoperators, Math. Program. 55 (1992), 293-318.
  [12] A.A. Goldstein, On steepest descent, J. Sco. Industrial Appl. Math. Series A: Control 3 (1965), 147-151.
  [13] R.T. Rockafellar. Monotone operators and the proximal point algorithm, SIAM J. Control Optim. 14 (1976), 877-898.
  [14] D.R. Sahu. Fixed points of demicontinuous nearly lipschitzian mappings in banach spaces, Comment.Math.Univ. Carolin46 (2005), 653-666.
  [15] D.R. Sahu, Q.H. Ansari, J.C. Yao, Convergence of inexact mann iterations generated by nearly nonexpansive sequencesand applications, Numer. Funct.Anal.Optim. 37 (2016), 1312-1338.
  [16] D.R. Sahu, N.C. Wong, J.C. Yao, A unified hybrid iterative method for solving variational inequalities involving generalizedpseudocontractive mappings, SIAM J. Control Optim. 50 (2012), 2335-2354.
  [17] D.R. Sahu, H.K. Xu, J.C. Yao, Asymptotically strict pseudocontractive mappings in the intermediate sense, NonlinearAnal. 70 (2009), 3502-3511.
  [18] D.R. Sahu, Q.H. Ansari, J.C. Yao, A unified hybrid iterative method for hierarchical minimization problems, J. Comput.Appl. Math. 253 (2013), 208-221.
  [19] D.R. Sahu, N.C. Wong, J.C. Yao, A generalized hybrid steepest-descent method for variational inequalities in banachspaces, Fixed Point Theory Appl. 2011 (2011), 1-28.
  [20] N. Shahzad, H. Zegeye, Strong convergence of an implicit iteration process for a finite family of generalized asymptoticallyquasi-nonexpansive maps, Appl. Math. Comput. 189 (2007), 1058-1065.
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  [26] I. Yamada, The hybrid steepest descent method for the variational inequality problem over the intersection of fixed pointsets of nonexpansive mappings, Inherently parallel algorithms in feasibility and optimization and their applications, 8:473–504, 2001.
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  [28] H. Zhou, P. Wang, A simpler explicit iterative algorithm for a class of variational inequalities in hilbert spaces, J. Optim.Theory Appl. 161 (2014), 716-727.
  

  Citation
  Poonam Mishra, Shailesh Dhar Diwan, "A Generalized Hybrid Steepest Descent Method for Variational Inequality Problem," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.6, Issue.2, pp.334-338, 2019

• Open Access   Article

  A New Generalization of One Parameter Quasi Exponential Distribution: Properties and Applications

  Anwar Hassan, Nazima Akhter, Bilal Ahmad Para

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.6 , Issue.2 , pp.339-354, Apr-2019

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i2.339354

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  Abstract
  In this article, we have introduced a new generalization of one parameter quasi exponential distribution using weighting technique. Important mathematical and statistical properties of the distribution have been derived and discussed. The expression for stochastic ordering, reliability measures and order statistics has been obtained. Maximum likelihood method of estimation along with Monte Carlo simulation has been discussed. Finally, real data set is analyzed to investigate the suitability of the proposed distribution in modeling lifetime data.

  Key-Words / Index Term
  Quasi Exponential Distribution, Moments, Stochastic Ordering, Order Statistics, MLE, Lifetime Data

  References
  [1]. Ajami, M., & Jahanshahi, S. M. (2017). Parameter Estimation in Weighted Rayleigh Distribution. Journal of Modern Applied Statistical Methods, 16(2), 256-276. doi:10.22237/jmasm/1509495240
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  [5]. Gove, H. J (2003).Estimation and application of size-biased distributions in forestry, In Modeling Forest systems, A.Amaro,D. Reed and P.Soares CAB International Wallingford UK,201-212
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  [7]. Hassan, A., Dar, S. A., & Para, B. A. (2018), On three Parameter Weighted Quasi Akash Distribution: Properties and Applications, IOSR Journal of Engineering (IOSRJEN), 08(11), 01-10.
  [8]. Hassan, A., Wani, S.A., & Para, B. A. (2018). On three Parameter Weighted Quasi Lindley Distribution: Properties and Applications, International Journal of Scientific Research in Mathematical and Statistical Sciences, 5(5), pp. 210-224 DOI: https://doi.org/10.26438/ijsrmss/v5i5.210224.
  [9]. Jing (2010). Weighted Inverse Weibull and Beta-Inverse Weibull Distribution, Georgia Southern University Digital Commons@Georgia Southern.
  [10]. Para, B.A., & Jan, T. R. (2018). On three Parameter Weighted Pareto Type II Distribution: Properties and Applications in Medical Sciences. Applied Mathematics and Information Sciences Letters, 6 (1), 13-26.
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  [13]. Taillie, C., Patil, G.P. and Hennemuth, R. (1995). Modelling and analysis of recruitment distributions. Ecological and Environmental Statistics, 2(4), 315-329.
  [14]. Van Deusen, P.C. (1986). Fitting assumed distributions to horizontal point sample diameters. Forest Science, 32, 146-148.
  [15]. Warren, W. (1975). Statistical distributions in forestry and forest products research. In: Patil, G.P., Kotz, S. and Ord, J.K. (eds) Statistical Distributions in Scientific Work, Vol. 2. D. Reidel, Dordrecht, The Netherlands, pp. 369-384.
  

  Citation
  Anwar Hassan, Nazima Akhter, Bilal Ahmad Para, "A New Generalization of One Parameter Quasi Exponential Distribution: Properties and Applications," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.6, Issue.2, pp.339-354, 2019

• Open Access   Article

  On Asymptotic Testing of the Parameters of Two Pareto Distributions

  M.B. Bhatt, S.R. Patel, P. Nandy

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.6 , Issue.2 , pp.355-358, Apr-2019

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i2.355358

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  Abstract
  Considering two independent Pareto distributions we have obtained the asymptotic tests for the parameters in this article. After getting the distribution of the sum of the transformed variables, the conditional distribution of complete sufficient statistic of interest has been obtained by fixing the sum of the transformed variables. This conditional distribution is used to obtain the tests for testing. (i) one parameter is larger than the other and (ii) equality of both parameters. Further the power functions of the asymptotic tests have been derived and some power points have been presented.

  Key-Words / Index Term
  Asymptotic Distributions, Asymptotic tests, ParetoDistributions, Conditional tests

  References
  [1] A. H. Bayoud, and A. O. Kittaneh “Testing of equality of Two Exponential Distributons ”, Communication in Statistics-simulation and Computation, Vol.47, Issue.7, pp.2249-2256, 2016.
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  [6] Handa, at el, “Test of equality of two exponential distributions with common known coefficient of variation”, Communication in Statistics-Theory and Methods , Vol.34. No.11, pp.2147-2155, 2005.
  [7] M.B. Bhatt, “Ph.D. thesis. Library Sardar Patel Univresity”, Vallabh Vidyanagar , 388120, India.
  [8] M.B. Bhatt, and S.R. Patel, “Asymptotic Distribution for the order statistic of a truncated one-parameter family of distributions”, Communication in Statistics-Theory and Methods, Vol.28, Issue.8, pp.1823-1855, 1999.
  [9] M.B. Bhatt, and S.R. Patel, “Asymptotic test for parameters of two power function distrubutions,” Research and Review joutnal of ststistics , Vol.7, Issue.1, pp.17-21, 2018.
  

  Citation
  M.B. Bhatt, S.R. Patel, P. Nandy, "On Asymptotic Testing of the Parameters of Two Pareto Distributions," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.6, Issue.2, pp.355-358, 2019

• Open Access   Article

  Effects of Heat absorption and porosity of the medium on MHD flow past an oscillating vertical plate in the presence of Hall current

  U.S. Rajput, Neetu Kanaujia

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.6 , Issue.2 , pp.359-365, Apr-2019

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i2.359365

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  Abstract
  The present study is carried out to examine the effects of heat absorption and porosity of the medium on flow model. In the study of motivated by several important problems like maintenance and secular variation of earth`s magnetic field, the internal rotation rate of sun, the structure of rotating magnetic stars, the planetary and solar dynamo problems. The model consists of an unsteady flow of a viscous, incompressible and electrically conducting fluid. The flow is along an impulsively started oscillating vertical plate with variable mass diffusion. The magnetic field is applied perpendicular to the plate. The fluid model under consideration has been solved by Laplace transform technique. The numerical data obtained are discussed with the help of graphs and table. The effects of velocity and skin fraction are studied for different parameters like phase angle, thermal Grashof number, mass Grashaf number, the permeability of the medium, heat absorption and rotation parameter.

  Key-Words / Index Term
  MHD flow, mass diffusion, Hall current and porous media

  References
  [1] Garg B P “Combined effects of thermal radiations and Hall current on moving vertical porous plate in a rotating system with variable temperature”. Int. J. Pure Appl. Math. 81:335-345, 2012.
  [2] Reddy G V R, Reddy K J and Lakshmi R “Radiation and mass transfer effects on nonlinear MHD boundary layer flow of liquid metal over a porous stretching surface embedded in porous medium with heat generation”. WSEAS Transactions on. Fluid Mechanics. 10: 01-12, 2015.
  [3] Seth G S, Sharma R and Hussain S M “Hall effects on unsteady MHD natural convection flow of a heat absorbing fluid past an accelerated moving vertical plate with ramped temperature”. EJER. 19:19-32, 2014.
  [4] Ramireddy A, Reddy J P, Sandeep N M and Sugunamma V “Effect of Nonlinear Thermal Radiation on MHD Chemically Reacting Maxwell Fluid Flow Past a Linearly Stretching Sheet”. Appl. Appl. Math.12: 259-274, 2017.
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  [ [12] Hossain M A and Rashi, Hall Effect on Hydromagnetic Free-convection flows along aporous Flat Plate with Mass Transfer’. Journal of the Physical Society of Japan, vol. 56(1), pp. 97-104, 1987.
  [[13] Ramamohan Reddy L, Raju M C, Raju G S S and Ibrahim S M, “Chemical reaction and thermal radiation effects on MHD micro polar fluid past a stretching sheet embedded in a non- Darcian porous medium”, Journal of computational and applied research in mechanical engineering, vol. 6, page, no 2, pp. 27- 46, 2017.
  [[14] Sattar M A, “Free convection and mass transfer flow through a porous medium past an infinite vertical porous plate with Time dependent temperature and concentration”, Indian j. Pure appl. Math., 23, 759–766, 1994 .
  [[15] Hayat, T, Wang Y and Hutter K Hall effects on the unsteady hydro magnetic oscillatory flow of a second-grade fluid. Int. J. Non-linear Mech. 39, 1027-1037, 2004.
  [[16] Seth G S, Sharma R, and Hussain S M, “Hall effects on unsteady MHD natural convection flow of a heat absorbing fluid past an accelerated moving vertical plate with ramped temperature”, Emirates Journal for Engineering Research, 19 (2), pp.19-32, 2014.
  [17] Kim J Y “Heat and mass transfer in MHD micro polar flow over a vertical moving porous plate in a porous medium”. Transport in porous Media, vol. 56, pp.17-37, 2004.
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  Citation
  U.S. Rajput, Neetu Kanaujia, "Effects of Heat absorption and porosity of the medium on MHD flow past an oscillating vertical plate in the presence of Hall current," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.6, Issue.2, pp.359-365, 2019

• Open Access   Article

  Heat Transfer Due to MHD Flow of a Second Grade Fluid over a Permeable Stretching Sheet through the Porous Medium With non-uniform heat source/sink

  Anant Kumar Kulkarni, M. Subhas Abel

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.6 , Issue.2 , pp.366-382, Apr-2019

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i2.366382

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  Abstract
  An analysis is carried out to study the heat transfer characteristics of a second grade non-Newtonian fluid flow over a stretching sheet through the porous medium under the influence of external magnetic field. The stretching sheet is assumed to be permeable and hence suction effect is taken into account. The effects of viscous dissipation, non-uniform heat source/sink on heat transfer are addressed. The basic boundary layer equations for momentum and heat transfer, which are non-linear partial differential equations, are converted into non-linear ordinary differential equations using a similarity transformation. Analytical solutions are obtained for the resulting boundary value problems. The effects of suction parameter, magnetic parameter, porous parameter, Prandtl number, Eckert number, non-uniform heat source/sink parameters on the heat transfer are shown in several plots. Analytical expressions for the wall frictional drag coefficient and non-dimensional wall temperature gradient are obtained and are tabulated for various values of the governing parameters.

  Key-Words / Index Term
  stretching sheet, second grade fluid, porous medium, non-uniform heat source/sink, suction

  References
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  Citation
  Anant Kumar Kulkarni, M. Subhas Abel, "Heat Transfer Due to MHD Flow of a Second Grade Fluid over a Permeable Stretching Sheet through the Porous Medium With non-uniform heat source/sink," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.6, Issue.2, pp.366-382, 2019

• Open Access   Article

  A Deterministic Inventory Model with Weibull Deterioration and Quadratic Demand Rate under Trade Credit

  S. D. Rohida, U. B. Gothi

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.6 , Issue.2 , pp.383-393, Apr-2019

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i2.383393

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  Abstract
  In this research paper, we have analysed a deterministic inventory model follows two parameter Weibull distribution for deteriorating items with Quadratic demand rate under trade credit. The study has two main purposes: firstly, to establish the mathematical model of an inventory system under the given condition, and secondly to demonstrate that the optimal solution not only exists but is also feasible. The derived model is then illustrated by a numerical example and its sensitivity analysis is carried out. A supplier offers a credit limit to the customers during which there is no interest charged but after the expiry of a prescribed time limit, the supplier will charge some interest. However, the customer usually has the reserve capital to make the payment at the beginning but decides to take the benefit of the credit limit.

  Key-Words / Index Term
  Deterioration, Quadratic Demand, Two Parameter Weibull Distribution, Trade Credit

  References
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  [3] Bhojak, A. and Gothi, U. B., “An EOQ model with time dependent demand and Weibull distributed deterioration.”, International Journal of Engineering Research and Technology (IJERT), Vol. 4. No. 09, pp. 109-115, 2015.
  [4] Bhojak, A. and Gothi, U. B., “EPQ model with time dependent IHC and Weibull distributed deterioration under shortages.”, International Journal of Innovative Research in Science, Engineering and Technology, Vol. 4, No. 11, pp. 10748-10757, 2015.
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  [6] Chatterji, D. and Gothi, U.B., “An EPQ model for two - parameter Weibully deteriorated items with exponential demand rate and completely backlogged shortages.”, International Journal of Computer Science Trends and Technology, Vol. 3, No. 6, pp. 38-47, 2015.
  [7] Chen, L. H., &Kang, F. S., “Integrated inventory models considering permissible delay in payment and variant pricing strategy.”, Applied Mathematical Modelling, Vol. 34, pp. 36-46, 2010.
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  [9] Chung- Yuan Dye, “A deteriorating inventory model with stock-dependent demand and partial backlogging under conditions of permissible delay in payments.”, Operational research, Vol.39. No.3 & 4, pp. 189-201, 2002.
  [10] Chun-Tao, C., Liang-Yuh, O., & Jinn-Tsair T., “An EOQ model for deteriorating items under supplier credits linked to order quantity.”, Applied Mathematical Modelling, Vol.27. No.12, pp. 983-996,2003.
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  [13] Ghosh, S. K., & Chaudhuri, K. S., “An order- level inventory model for a deteriorating item with Weibull Deterioration, Time-quadratic demand and shortages.”, Advanced Modelling and Optimization, Vol. 6. No.1, pp. 21-35, 2004.
  [14] Gothi U.B., & Parmar, K. C., “order level lot size inventory model for deteriorating items under quadratic demand with time dependent IHC and partial backlogging.”, Research Hub - International Multidisciplinary Research Journal, Vol.2. No.2, 2015.
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  [16] Jamal, A. M. M., Sarkar, B. R., Wang, S., “An ordering policy for deteriorating items with allowable shortage and permissible delay in payment.”, Journal of Operational Research Society, Vol. 48. No.8, pp. 826-833, 1997.
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  Citation
  S. D. Rohida, U. B. Gothi, "A Deterministic Inventory Model with Weibull Deterioration and Quadratic Demand Rate under Trade Credit," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.6, Issue.2, pp.383-393, 2019

• Open Access   Article

  Multiple Intruder Locating Dominating Sets

  K. Venugopal, K. A. Vidya

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.6 , Issue.2 , pp.394-398, Apr-2019

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i2.394398

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  Abstract
  Safeguarding of facilities has been at a major focus in graph theoretical research which has led to a surge of various parameters of locating dominating sets in graphs. However, in all those parameters, a single intruder is assumed to be present in a network. In this paper, we introduce Multiple Intruder Locating Dominating (MILD) sets where one is interested in finding the presence as well as the locations of intruders at multiple (possibly all) locations in a network. The number of vertices in the smallest MILD set of a graph G is called its MILD number, denoted by MILD(G). For a simple connected graph of order n, the MILD number lies between n/2 and n-1, both inclusive. The graphs which attain these bounds are characterized.

  Key-Words / Index Term
  Domination, Locating Domination, Multiple intruder locating domination

  References
  [1] B. Chaluvaraju, K. A. Vidya, “Generalized perfect domination in graphs”, Journal of Combinatorial Optimization, Vol.27, Issue.2, pp.292-301, 2014.
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  [3] Frank Harary, “Graph theory”, Narosa Publications, 1988.
  [4] T. W. Haynes, S. T. Hedetniemi, P. J. Slater, “Fundamentals of domination in graphs”, CRC Press, 1998.
  [5] T. W. Haynes, S. T. Hedetniemi, P. J. Slater, “Domination in graphs: advanced topics”, Monographs and textbooks in pure and applied mathematics, Vol.209, 1998.
  [6] S. J. Seo, P. J. Slater, “Open neighborhood locating-dominating sets”, Australasian Journal of Combinatorics, Vol.46, pp.109-120, 2010.
  [7] S. J. Seo, P. J. Slater, “Open-independent, open-locating-dominating sets”, Electronic Journal of Graph Theory and Applications, Vol.5, Issue 2, pp.179-193, 2017.
  [8] P. J. Slater, “Domination and location in acyclic graphs”, Networks, Vol.17, pp.55–64, 1987.
  [9] P. J. Slater, “Dominating and reference sets in a graph”, Journal of Mathematical and Physical Sciences, Vol.22, pp.445–455, 1988.
  [10] P. J. Slater, “Locating dominating sets and locating-dominating sets”, Graph Theory, Combinatorics and Applications: Proceedings of the Seventh Quadrennial International Conference on the Theory and Applications of Graphs, Vol.2, pp.1073-1079, 1995.
  [11] P. J. Slater, “Fault-tolerant locating-dominating sets”, Discrete Mathematics, Vol.249, Issue 1-3, pp.179-189, 2002.
  [12] D. K. Thakkar, S.M. Badiyani, "Independent Roman Domination Number of Graphs", International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.2, pp.29-34, 2018
  [13] D. B. West, “Introduction to graph theory”, Prentice hall Upper Saddle River, 2001.
  

  Citation
  K. Venugopal, K. A. Vidya, "Multiple Intruder Locating Dominating Sets," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.6, Issue.2, pp.394-398, 2019