Volume-6 , Issue-1 , Feb 2019, ISSN 2348-4519 (Online) Go Back

• Open Access   Article

  A Shift-Dependent Generalized Doubly Truncated (Interval) Information Measure and its Properties

  Bilal Ahmad Bhat, M.A.K. Baig

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.6 , Issue.1 , pp.282-293, Feb-2019

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i1.282293

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  Abstract
  In the present article, we develop a two parametric shift-dependent generalized interval information (uncertainty) measure. In this new measure, the length of the observed random variable is set as the weight function and hence it is also known as length-biased shift-dependent uncertainty measure. Some significant characterization results of this measure are focused. For the measure, several momentous properties are also explored. Finally, we present some upper and lower bounds of this particular measure.

  Key-Words / Index Term
  Shift-dependent generalized entropy, Lifetime distributions, Shift-dependent generalized interval entropy, Characterization results

  References
  [1] C. E. Shannon, “A mathematical theory of communications”, Bell System Technical Journal, 27, pp. 379-423, 1948.
  [2] N. Ebrahimi, “How to measure uncertainty in the residual lifetime distribution”, Sankhya Series A, 58, pp. 48-56, 1996.
  [3] S. M. Sunoj, P. G. Sankaran and S. S. Maya, “Characterizations of life distributions using conditional expectations of doubly (interval) truncated random variables”, Communications in Statistics—Theory and Methods, 38 (9), pp. 1441–1452, 2009.
  [4] M. Belis and S. Guiasu, “A quantitative-qualitative measure of information in cybernetic systems”, IEEE Transactions on Information Theory, IT, 4, pp. 593–594, 1968.
  [5] Di Crescenzo and M. Longobardi, “On weighted residual and past entropies”, Scientiae Mathematicae Japonicae, 64, pp. 255–266, 2006.
  [6] F. Misagh and G. H. Yari “On weighted interval entropy”, Statistics and Probability Letters, 81, pp. 188–194, 2011.
  [7] M. Mirali and S. Baratpour, “Dynamic version of weighted cumulative residual entropy”, Communications in Statistics-Theory and Methods, 46, 2017.
  [8] F. Misagh, Y. Panahi, G. H.Yari and R. Shahi, “Weighted cumulative entropy and its estimation”, In Quality and Reliability (ICQR), IEEE International conference, pp. 477-480, 2011.
  [9] S. Kayal, “On weighted generalized cumulative residual entropy”, Springer Science+Business Media New York, pp. 1-17, 2017.
  [10] R. S. Nair, E. I. A. Sathar and G. Rajesh, “A study on dynamic weighted failure entropy of order ”, American Journal of Mathematical and Management Sciences, 36(2), pp. 137-149, 2017.
  [11] M. Nourbakhsh and G. Yari, “Weighted Renyi’s entropy for lifetime distributions”, Communications in Statistics-Theory and Methods, doi: 10.1080 /03610926.2016.1148729, 2016.
  [12] Y. Shiwei and H. Ting-Zhu, “Exponential weighted entropy and exponential weighted mutual information”, Neurocomputing, 249, pp. 86–94, 2017.
  [13] H. Khammar and S. M. A. Jahanshahi, “On weighted cumulative residual Tsallis entropy and its dynamic version”, Physica A, 491, pp. 678–692, 2018.
  [14] S. Yasaei Sekeh, G. R. Mohtashami Borzadaran and , A. H. Rezaei Roknabadi, “Some results based on weighted dynamic entropies”, Rend. Sem. Mat. Univ. Politec. Torino, Vol. 70, 4, pp. 369 – 382, 2012.
  

  Citation
  Bilal Ahmad Bhat, M.A.K. Baig, "A Shift-Dependent Generalized Doubly Truncated (Interval) Information Measure and its Properties," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.6, Issue.1, pp.282-293, 2019

• Open Access   Article

  A Test Based on Half Range for Nonparametric Regression

  S. V. Bhat, B. Deshpande

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.6 , Issue.1 , pp.294-302, Feb-2019

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i1.294302

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  Abstract
  A test is proposed for testing parametric regression against nonparametric regression using variable Nadaraya-Watson (NW) estimator based on half range along with its variant, deploying integrated squared error (ISE). We discuss the properties of the proposed test. The performance of the tests is computed in terms of empirical power and compared with the test based on NW estimator. The application of the test is illustrated through real data.

  Key-Words / Index Term
  Nonparametric regression, Pilot density,Kkernel function, L2-distance, Wild bootstrap,Cconsistency

  References
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  [5] E. Mammen, “When Does Bootstrap Work: Asymptotic Results and Simulations”, Lecture Notes in Statistics, Vol. 77, Springer, Berlin, 1992.
  [6] G. S. Watson, “Smooth Regression Analysis”, Sankhya Series A, Vol. 26, pp. 359-372, 1964.
  [7] H. L. Koul, P. Ni, “Minimum distance regression model checking”, Journal of Statistical Planning and Inference, Vol. 119, No. 1, pp. 109-141, 2004.
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  [9] J. Hart, “Nonparametric smoothing and lack-of-fit tests”, Springer Science & Business Media, 2013.
  [10] K. H. Aljuhani, Turk Al, “Modification of the adaptive Nadaraya-Watson kernel regression estimator”, Scientific Research and Essays, Vol. 9, No. 22, pp. 966-971, 2014.
  [11] P. de Jong, “A central limit theorem for generalized quadratic forms”, Probability Theory Related Fields Vol. 75, No. 2, pp. 261-277, 1987.
  [12] S. Demir, Ö Toktamiş, “On the adaptive Nadaraya-Watson kernel regression estimators”, Hacettepe Journal of Mathematics and Statistics, Vol. 39, No. 3, pp. 429-437, (2010).
  [13] V. B., Joshi, B. Deshpande, “A New Modification to the Adaptive Nadaraya-Watson Kernel Regression Estimator”, Advances and Applications in Statistics, Vol. 49, No. 4, pp. 245-256, 2016.
  [14] W. Gonzalez-Manteiga, R. M. Crujeiras, “An updated review of Goodness-of-Fit tests for regression models”, Test, Vol. 22, No. 3, pp. 361-411, 2013.
  [15] W. Härdle, “Applied Nonparametric Regression”, Cambridge Universiy Press, Cambridge, 1990.
  [16] W. Härdle, E., Mammen, “Comparing nonparametric versus parametric regression fits”, Annals of Statistics, Vol. 21, No. 4, pp. 1926-1947, 1993.
  [17] W. Stute, “Nonparametric model checks for regression”, Annals of Statistics, Vol. 25, No. 2, pp. 613-641, 1997.
  [18] W.K. Härdle, M. Müller, S. Sperlich, A. Werwatz, “Nonparametric and Semiparametric Models”, Springer, Berlin , 2004.
  

  Citation
  S. V. Bhat, B. Deshpande, "A Test Based on Half Range for Nonparametric Regression," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.6, Issue.1, pp.294-302, 2019

• Open Access   Article

  Equitable Edge Coloring of Strong Product of Cycle, Complete Graphs

  S. Manimaran, S. Moidheen Aliyar, K. Manikandan

  Survey Paper | Isroset-Journal (IJSRMSS)

  Vol.6 , Issue.1 , pp.303-306, Feb-2019

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i1.303306

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  Abstract
  An edge coloring of graph G is equitable if for each vertex v of G, the number of edges of any one color incident with v differs from the number of edges of any other color incident with v by at most one. In this paper, we obtain the exact expressions for the equitable edge coloring of strong product of C_(n ) K_m.

  Key-Words / Index Term
  Equitable edge coloring, Product graph, Cycle, Complete graph

  References
  [1] Erdős, Paul (1964), "Problem 9", in Fieldler, M., Theory of Graphs and its Applications, Prague: Czech Acad. Sci. Publ., p. 159.
  [2] M.A. Gang, M.A. Ming, “The equitable total chromatic number of some join graphs”, open journal of Applied Sciences (2012).
  [3] R. P. Gupta, "The Chromatic Index and the Degree of a Graph", Not. Amer. Math. Soc. 13, 719, 1966.
  [4] A. Hajnal, and E. Szemer´edi, (1970) “Proof of a conjecture of P. Erd˝os”, In Combinatorial Theory and its Application (P. Erd˝os, A. R´enyi, and V. T. S´os, eds), North-Holland, London, pp. 601–623.
  [5] R. Hammack, W. Imrich and S. Klavzar, “Handbook of Product Graphs”, CRC Press, Taylor & Francis Group, Boca Raton, 2011
  [6] H. A. Kierstead, A. V. Kostochka, (2008), "A short proof of the Hajnal-Szemerédi theorem on equitable colouring", Combinatorics, Probability and Computing, 17 (2): 265–270.
  [7] S. Mohan, J. Geetha, K. somasundaram, “Total coloring of certain classes of product graphs”, Electronic notes in Disc. Math. 53(2016), 173-180.
  [8] G. Sabidussi, “Graph Multiplication”, Math. Z. 1960, 72, 446-457.
  [9] P. Seymour (1974), "Problem section", in McDonough, T. P.; Mavron, Eds., V. C., Combinatorics: Proceeding of the British Combinatorial Conference 1973, Cambridge, UK: Cambridge Univ. Press, pp. 201–202.
  [10] S. Skiena, "Edge Colorings" §5.5.4 in Implementing Discrete Mathematics: Combinatorics and Graph Theory with Mathematica.Reading, MA: Addison-Wesley, p. 216, 1990.
  [11] V. G. Vizing, “On an Estimate of the Chromatic Class of a p-Graph” [Russian]. Diskret Analiz 3, 23-30, 1964.
  [12] V. G. Vizing, “The Cartesian product of graphs” Vyc. Sis. 1963, 9, 30-43.
  

  Citation
  S. Manimaran, S. Moidheen Aliyar, K. Manikandan, "Equitable Edge Coloring of Strong Product of Cycle, Complete Graphs," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.6, Issue.1, pp.303-306, 2019

• Open Access   Article

  HIGHER ORDER LP-DERIVATIVE, LP –CONTINUITY AND LP –BOUNDEDNESS OF COMPLEX VALUED FUNCTION

  T. K. Garai

  Survey Paper | Isroset-Journal (IJSRMSS)

  Vol.6 , Issue.1 , pp.307-310, Feb-2019

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i1.307310

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  Abstract
  Higher order Lp-derivative of Complex valued functions is defined. It is shown that this derivative is more general than ordinary derivative. Also Lp-Continuity and Lp-boundedness is studied for these type of functions and it is proved that LP-continuity and LP-boundedness are more general than the ordinary continuity and ordinary boundedness.

  Key-Words / Index Term
  Lp-derivative, Lp-Continuous, Lp-boundedness

  References
  [1] A.P.Calderon and A.Zygmund, "Local Properties of Solutions of Elliptic partial differential equations", Studia Math, 20(1961), 171-225.
  [2] M.J.Evans, "Lp-derivatives and Approximate Peano Derivative", Trans.Am. Math.Soc, 165(1972), 381-388.
  [3] S.N.Mukhopadhyay, "Higher Order Derivative", Chapman and Hall/CRC, Monographs and Surveys in Pure and Applied Mathematics, 144(2012)
  [4] A.Zygmund,"Trignometric Series ". Volume-1, Cambridge University Press, 1959.
  

  Citation
  T. K. Garai, "HIGHER ORDER LP-DERIVATIVE, LP –CONTINUITY AND LP –BOUNDEDNESS OF COMPLEX VALUED FUNCTION," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.6, Issue.1, pp.307-310, 2019

• Open Access   Article

  One Dimensional Numerical Study of Advection Diffusion of Calcium in a Hepatocyte Cell

  Y.D. Jagtap, N. Adlakha

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.6 , Issue.1 , pp.311-316, Feb-2019

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i1.311316

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  Abstract
  In a human body, in almost all types of cells, the calcium plays a vital role in chemical signalling required for communication and maintenance of structure and functions of a cell. Almost all chemicals and proteins are produced in liver therefore, it is also known as body`s chemical factory. The calcium regulates all vital functions of a hepatocyte cell. The calcium concentration is tightly regulated by various processes like diffusion and advection in cytosol, binding with buffers etc. In this paper an unsteady state numerical approach is prefer to investigate the effect of advection and diffusion of calcium in a hepatocyte cell. The initial and boundary conditions are formulated according to physiology of a hepatocyte cell. The finite volume approach is used for simulation on MATLAB to obtain numerical results. The results are used to analyze the effect of advection, diffusion and buffer concentration on calcium profiles in a hepatocyte cell.

  Key-Words / Index Term
  Calcium, Advection, Diffusion, Hepatocyte cell, Finite Volume Method

  References
  [1] G .Dupont, S. Stephanne, C. Clair, T. Tordjmann, L. Combettes, “Hierarchical organization of calcium signals in hepatocytes: from experiments to models”, Biochimica et Biophysica Acta (BBA)-Molecular Cell Research, Vol. 1498, Issue.2, pp.134-152, 2000.
  [2] I. Garcin, T. Tordjmann, “Calcium signalling and liver regeneration”, International journal of hepatology, Vol. 2012, pp.1-6, 2012.
  [3] G.D. Smith, J. Wagner, J. Keizer, “Validity of the rapid buffering approximation near a point source of calcium ions”, Biophysical Journal, Vol. 70, Issue.6, pp.2527-2539, 1996.
  [4] A Jha, N. Adlakha, “Analytical solution of two dimensional unsteady state problem of calcium diffusion in a neuron cell”, Journal of medical imaging and health informatics, Vol. 4, Issue.4, pp.547-553, 2014.
  [5] S. Tewari, K.R. Pardasani, “Finite element model to study two dimensional unsteady state cytosolic calcium diffusion in presence of excess buffers, IAENG International Journal of Applied Mathematics”, Vol. 40, Issue.3, pp.108-112, 2010.
  [6] B.K. Jha, N. Adlakha, M.N. Mehta, “Two-dimensional finite element model to study calcium distribution in astrocytes in presence of vgcc and excess buffer”, Int. J. Model. Simul. Sci. Comput, Vol. 4, Issue.2, pp.1250030, 2012.
  [7] B.K. Jha, N. Adlakha, M.N. Mehta, “Two-dimensional finite element model to study calcium distribution in astrocytes in presence of excess buffer”, International Journal of Biomathematics, Vol. 7, Issue.3, pp.1450031, 2014.
  [8] K . Pathak, N. Adlakha, “Finite element model to study two dimensional unsteady state calcium distribution in cardiac myocytes”, Alexandria Journal of Medicine, Vol. 52, Issue.3, pp.261-268, 2016.
  [9] K. B. Pathak, N. Adlakha, “Finite Element Model to Study One Dimensional Calcium Dyanmics in Cardiac Myocytes”, Journal of Multiscale Modelling, Vol. 6, Issue.2, pp.1550003, 2015.
  [10] M. Kotwani, N. Adlakha, “Modeling of endoplasmic reticulum and plasma membrane Ca 2+ uptake and release fluxes with excess buffer approximation (EBA) in fibroblast cell”, International Journal of Computational Materials Science and Engineering, Vol. 6, Issue.1, pp.1550004, 2017.
  [11] M. Kotwani, N. Adlakha, M.N. Mehta, “Numerical model to study calcium diffusion in fibroblasts cell for one dimensional unsteady state case” , Applied Mathematical Sciences, Vol. 6, Issue.102, pp.5063-5072, 2012.
  [12] Y. D. Jagtap, N. Adlakha, “Finite volume simulation of two dimensional calcium dynamics in a hepatocyte cell involving buffers and fluxes” Communications in Mathematical Biology and Neuroscience. Vol. 2018, pp.1-6, 2018.
  [13] N. Manhas, K.R. Pardasani, “Mathematical model to study IP3 dynamics dependent calcium oscillations in pancreatic acinar cells”, Journal of Medical Imaging and Health Informatics, Vol. 4, Issue.6, pp.874-880, 2014.
  [14] N. Manhas, K.R. Pardasani, “Modelling mechanism of calcium oscillations in pancreatic acinar cells”, Journal of bioenergetics and biomembranes, Vol. 46, Issue.5, pp.403-420, 2014.
  [15] N. Manhas, K.R. Pardasani, J. Sneyd , “Modelling the transition from simple to complex Ca2+ oscillations in pancreatic acinar cells”, Journal of biosciences, Vol. 39, Issue.3, pp.463-484, 2014.
  [16] P. A. Naik, K.R. Pardasani, “One Dimensional Finite Element Model to Study Calcium Distribution in Oocytes in Presence of VGCC, RyR and Buffers”, J. Medical Imaging Health Informatics, Vol. 5, Issue.3, pp.471-476, 2015.
  [17] P. A. Naik, K.R. Pardasani, “One dimensional finite element method approach to study effect of ryanodine receptor and serca pump on calcium distribution in oocytes”, Journal of Multiscale Modelling, Vol. 5, Issue.2, pp.1350007, 2013.
  [18] S. Panday, K.R. Pardasani, “Finite element model to study effect of advection diffusion and Na+/Ca2+ exchanger on Ca2+ distribution in Oocytes”, Journal of medical imaging and health informatics, Vol. 3, Issue.3, pp.374-379, 2013.
  [19] S. Panday, K.R. Pardasani, “Finite element model to study the mechanics of calcium regulation in oocyte”, Journal of Mechanics in Medicine and Biology, Vol. 14, Issue.2, pp.145002223, 2014.
  [20] A. P. Thomas, D. C. Renard, T. A. Rooney, “Spatial and temporal organization of calcium signalling in hepatocytes” Cell Calcium, Vol. 12, Issue. -2-3, pp.111-126, 1991.
  [21] L. D. Gaspers, A. P. Thomas, “Calcium signaling in liver” Cell calcium, Vol. 38, Issue.3, pp.329-342, 2005.
  [22] B. K. Jha, N. Adlakha, M. N. Mehta, “Finite Volume Model to Study The Effect of Voltage Gated Ca2+ Channel on Cytosolic Calcium Advection Diffusion” International Journal of Mathematical, Computational, Physical, Electrical and Computer Engineering, Vol. 8, Issue.8, pp.1379-1383, 2011.
  [23] K. B. Pathak, N. Adlakha, “Finite Element Simulation of Advection Diffusion of Calcium in Myocyes Involving Influx and Excess Buffer” Advances in Computational Sciences and Technology, Vol. 10, Issue.1, pp.11-23, 2017.
  [24] G. D. Smith, “Analytical steady-state solution to the rapid buffering approximation near an open Ca2+channel” Biophysical Journal, Vol.71, Issue.6, pp.3064-3072, 1996.
  [25] C. Fall, “Computational cell biology”, Interdisciplinary Applied Mathematics: V. Springer-Verlag New York Incorporated, pp.173-176, 2002.
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  [27] H. K. Versteeg, W. Malalasekera, “An introduction to computationnal Fluid Dynamics, The finite volume method”, Longman, Londres, pp.243-266, 1995.
  

  Citation
  Y.D. Jagtap, N. Adlakha, "One Dimensional Numerical Study of Advection Diffusion of Calcium in a Hepatocyte Cell," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.6, Issue.1, pp.311-316, 2019

• Open Access   Article

  CASP for Truncated Exponentiated Weibull Distribution Based on CUSUM Schemes and its Optimization

  M. C. Chandra Prasad, P. Mohammed Akhtar, B. Sainath

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.6 , Issue.1 , pp.317-322, Feb-2019

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i1.317322

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  Abstract
  Acceptance Sampling plan is a procedure employed mainly either to accept or reject the lots for finished goods. It is one of the Statistical tool helps in the improvement of the quality of the product but not to control. There are several techniques developed in order to improve and control the quality of a product under the assumption that variable with regard to the quality characteristic is distributed according to certain probability law. In the present paper, we assume that variable under study follows the Truncated Exponentiated Weibull Distribution and its Optimization of CASP-CUSUM Schemes. Critical comparison made based on the obtained numerical results.

  Key-Words / Index Term
  CASP–CUSUM Schemes, O C Curve, Optimal Truncated Point, Truncated Exponentiated Weibull Distribution

  References
  [1]. Akhtar, P. Md. and Sarma. K.L.A.P.(2004). “Opimization of CASP-CUSUM Schemes based on Truncated Gamma Distribution”. Bulletin of Pure and applied sciences, Vol-23E (No.2):215-223.
  [2] Narayana Muthy, B. R, Akhtar, P. Md and Venkataramudu, B.(2012) “Optimization of CASP- CUSUM Schemes based on Truncated Log-Logistic Distribution”. Bulletin of Pure and Applied Sciences, Vol-31E (Math&Stat.): Issue (No.2) pp243-255.
  [3] B.Sainath, P.Mohammed Akhtar, G.Venkatesulu, and Narayana Muthy, B. R, (2016) “CASP CUSUM Schemes based on Truncated Burr Distribution using Lobatto Integration Method”. IOSR Journal of Mathematics (IOSR-JM), Vol-12, Issue 2, pp54-63.
  [4]. Venkatesulu.G, Akhtar.P.Md, Sainath.B, Narayana Murthy B.R.(2017), “Truncated Gompertz Distribution and its Optimization of CASP-CUSUM Schemes” Journal of Research in applied Mathematics, Vol-3, Issue7, pp:19-28.
  [5]. Mudholkar, G.S., Srivastava, D.K., (1993), “Exponentiated Weibull for analyzing Bath tub Failure rate data”, IEEE Transactions and Reliability,Vol.42 (2), pp.15-18.
  [6]. Beattie, B.W.(1962). “A Continuous Acceptance Sampling procedure based upon a cumulative Sums Chart for a number of defective”. Applied Statistics, Vol. 11 (No.2): pp: 137-147.
  [7]. Kakoty, S and Chakravaborthy, A.B., (1990), “A Continuous Acceptance Sampling Plan for Truncated Normal distribution based on Cumulative Sums”, Journal of National Institution for Quality and Reliability, Vol.2 (No.1): 15-18.
  

  Citation
  M. C. Chandra Prasad, P. Mohammed Akhtar, B. Sainath, "CASP for Truncated Exponentiated Weibull Distribution Based on CUSUM Schemes and its Optimization," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.6, Issue.1, pp.317-322, 2019

• Open Access   Article

  Application of Fixed Point Theorems for Digital Contractive Type Mappings in Digital Metric Space

  Neena Gupta, Amardeep Singh, Geeta Modi

  Survey Paper | Isroset-Journal (IJSRMSS)

  Vol.6 , Issue.1 , pp.323-327, Feb-2019

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i1.323327

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  Abstract
  In this paper we introduce a notion and define a contractive type mapping for digital metric spaces. We prove some fixed point theorems in digital metric space by using contractive type mapping. We obtain Banach contraction principle in digital metric space. The purpose of this paper is to associate fixed point theory and digital images. This shows an application of fixed point theory in digital metric space.

  Key-Words / Index Term
  digital image, digital metric space, Banach contraction principle, finite sequence, increasing sequence, decreasing sequence, θ-contractive.

  References
  [1] Banach S,“Sur les operations dans les ensembles abstraits et leurs applications aux equations integrals”,Fund. Math., No. 3, pp. 133–181, 1922.
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  [5] Boxer L, “Digitally Continuous Functions”,Pattern Recognition Letters, 15, pp. 833- 839, 1994.
  [6] Boxer L, “A Classical Constructions for The Digital Fundamental Group”, J.Math. Imaging Vis., 10, pp. 51-62,1999.
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  [9] Ege O, Karaca I, “Applications of The Lefschetz Number to Digital Images”,Bull. Belg. Math. Soc. Simon Stevin,21,pp.823-839,2014.
  [10] Ege O, Karaca I, “Banach Fixed Point Theorem for Digital Images”, J. Nonlinear Sci. Appl. 8, pp. 237-245, 2015.
  [11] Ege O, Karaca I, “Lefschetz Fixed Point Theorem for Digital Images”,Fixed Point Theory, Appl., 13 pages, 2013.
  [12] Han S.E,“Non-Product property of the digital fundamental group”, Inform. Sci., 171, pp. 73-91, 2005.
  [13] Rosenfeld A, “Digital Topology”,Amer. Math. Monthly, 86, pp. 76-87,1979.
  [14] Han S. E, “Banach fixed point Theorem from the viewpoint of digital topology”, J. Nonlinear sci. Appl., 9, pp. 895-905, 2016.
  [15] Sridevi K., M. V. R. Kameshwari And D. M. K. Kiran,“Fixed Point Theorem for Digital Contractive Type Mappings in Digital Metric Space” International
  Journal of Mathematics Trends and Technology, Vol. 48, No. 3, pp. 159-167, 2017
  

  Citation
  Neena Gupta, Amardeep Singh, Geeta Modi, "Application of Fixed Point Theorems for Digital Contractive Type Mappings in Digital Metric Space," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.6, Issue.1, pp.323-327, 2019

• Open Access   Article

  Fixed Point Theorems for sub sequential continuous maps in Intuitionistic Fuzzy metric space using implicit Relation

  Rekha Agrawal, R.S. Chandel, Hasan Abbas

  Survey Paper | Isroset-Journal (IJSRMSS)

  Vol.6 , Issue.1 , pp.328-331, Feb-2019

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i1.328331

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  Abstract
  In this paper we prove fixed point theorem for two pair of sub sequential continuous and compatible mapping satisfying an implicit relation in Intuitionistic fuzzy metric space.

  Key-Words / Index Term
  Fixed point ,Intuitionistic fuzzy metric space, Compatible mapping, Sub-compatible mapping , I mplicit relation

  References
  [1] L.A. Zadeh, "Fuzzy sets", Infor. and Control. Vol. 8,
  pp.338-353, 1965.
  [2] Kramosil and J. Michalek, "Fuzzy metric and statistical metric spaces" ,Kybennetica, Vol. 11,Issue.5, pp. 336-344, 1975 .
  [3] A George and P. Veeramani, "On some results in fuzzy metric spacesˮ ,Fuzzy sets and System Vol. 64 ,pp.395 - 399, 1994.
  [4] G. Jungck, "Compatible mapping and common fixed points", International Journal of Mathematics and Mathematicl Sciences ,Vol .9 ,Issue. 4,pp.771-779 ,1986
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  Citation
  Rekha Agrawal, R.S. Chandel, Hasan Abbas, "Fixed Point Theorems for sub sequential continuous maps in Intuitionistic Fuzzy metric space using implicit Relation," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.6, Issue.1, pp.328-331, 2019

• Open Access   Article

  Comparative CFD analysis of heat sink with horizontal and vertical orientation

  Mimansha Agrawal, Tushar Choudhary

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.6 , Issue.1 , pp.332-335, Feb-2019

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i1.332335

  Abstract

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  References

  Citation

  Abstract
  In order to dissipate excessive heat generated within electrical circuit boards heat sinks are conventionally being used. Heat sink facilitates high performance, safe, long life and makes reliable electronic devices. Heat sinks are generally available in different shapes and sizes. In this paper rectangular shaped heat sink, where natural and forced convection is examined at different orientation of sink, i.e. horizontal and vertical has been taken. The complete analysis has been carried out by using software, where the CAD model of heat sink has been modeled in Solid works and the CAD model is imported to finite element tool i.e. ANSYS fluent where the governing equations are solved for given boundary condition. During analysis the overall heat transfer has been examined and the results have been compared with other published work. Form the result it has been observed that the heat transfer within heat sink at different orientation is quite different.

  Key-Words / Index Term
  Heat Sink, CFD, Heat Transfer

  References
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  Citation
  Mimansha Agrawal, Tushar Choudhary, "Comparative CFD analysis of heat sink with horizontal and vertical orientation," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.6, Issue.1, pp.332-335, 2019