Volume-8 , Issue-4 , Aug 2021, ISSN 2348-4519 (Online) Go Back

• Open Access   Article

  Without Using Pi, Area & Perimeter of Circle by Fulati - Suranjan Formulae

  Probir Roy

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.8 , Issue.4 , pp.1-9, Aug-2021

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  In this paper, an attempt has been taken to find out the Area and Circumference or Perimeter of Circle, without using Constant pi, by the Fulati-Suranjan formulae (up to two decimal places) along with a new constant, named Probir’s Constant denoted by the Bengali letter roshsho li-kar ?. To fulfill these purposes here, have been used some Theorems, Lemmas, Corollaries, the inner circle & the outer circle of the same square, also the inner square & the outer square of the same circle. It is noted that some of these theorem, lemma, and corollary are more or less discussed and proven formally or informally in various articles & online math portals. We think that the method established through this paper will be helpful for mathematics readers, especially those are students. It also seems that the concerned students can memorize and apply the formulas without using conventional constant pi.

  Key-Words / Index Term
  Archimedes, circle, area, pi, diameter, li-kar

  References
  [1]. Ravi P Agarwal, Hans Agarwal & Syamal K Sen, Birth, “Grown and computation of pi to the trillion digits,” Springer open, published on 11 April 2013.
  [2]. S.G Dani, “Cognition of the circle in ancient India,” arXiv:1703.0964, 5v1 [math.HO] 28 March 2017.
  [3]. Arthur E. Hallerberg, “Revealed yet rational values for pi nearly became law in an Indiana bill proposed by a country doctor in 1897,” Valparaiso University, Mathematics Magazine, vol 50, No. 3 (May 1977), pp. 136 – 140, published by Taylor & Francis Ltd. https://www.jstor.org/stable/2689499
  [4]. O.V VIJIMON, “A CIRCLE WITHOUT ?,” [ovvijimon@gmail.com], https://vixra.org/pdf/1308.0126v3.pdf
  [5]. Leon Cooper, “Historia Mathematica,” ELSEVIER, 38(2011), 455 – 484.
  [6]. RMP, “Circles: Problem 48 of the compares the area of a circle (approximated by an octagon) and its circumscribing square.”
  [7]. David Richeson, “Circular reasoning: Who first proved that c/d is a constant,” arXiv:1303.090, v2 [math.HO] 14 March 2013.
  [8]. Clement E. Falbo, “The golden ratio - A contrary Viewpoint,” The College Mathematics Journal, Vol 36, No. 2, p.127, March 2005.
  [9]. Wikipedia (Euclid), “Math begins from Pythagoras (Greek, 300BC), Axiomatic method (Euclid).”
  [10]. Book of Lemmas: Proposition 7, “Problem 646: Archimedes’, square and circle area,” WWW.GOGEOMETRY.COM, Land of the Incas.
  [11]. A. A. Halder, S. R. Pande, "Implementation of Iris Recognition Using Circular Hough Transform and Template Generation," International Journal of Computer Sciences and Engineering, Vol.8, Issue.1, pp.13-16, 2020.
  [12]. Vishal Verma, Anurag Sinha, "Manipulation of Email Data Using Machine Learning and Data Visualization," International Journal of Scientific Research in Computer Sciences and Engineering, Vol.8, Issue.5, pp.54-63, 2020.

  Citation
  Probir Roy, "Without Using Pi, Area & Perimeter of Circle by Fulati - Suranjan Formulae," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.8, Issue.4, pp.1-9, 2021

• Open Access   Article

  Some Special Operations and Related Results on Intuitionistic Fuzzy Sets

  Jaydip Bhattacharya

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.8 , Issue.4 , pp.10-13, Aug-2021

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  Operators are playing significant role in intuitionistic fuzzy set theory. There are several operators in literature which are introduced by the researchers. Similarly many operations are also defined time to time. In this paper some new operations are discussed and consequently some related results are established and proved. The main objective of this paper is to study those operations which are already available in the literature along with some newly defined operations and to explain their properties with respect to modal and other operators.

  Key-Words / Index Term
  Fuzzy sets, Intuitionistic fuzzy sets, Modal operators, Operations in intuitionistic fuzzy sets

  References
  [1] K.T. Atanassov, “Intuitionistic Fuzzy Sets,” VII ITKR’s Session, Sofia, 1983.
  [2] L.A.Zadeh, “Fuzzy sets,” Information and Control,Vol 8, pp 338-353, 1965.
  [3] K.T. Atanassov, “Intuitionistic Fuzzy Sets Past, Present and Future,” CLBME-Bulgarian Academy of Science, Sofia, 2003.
  [4] K.T. Atanassov, “Intuitionistic Fuzzy Sets,” Fuzzy Sets and Systems, Vol.20, pp 87-96,1986.
  [5] J. Bhattacharya, “A Few More on Intuitionistic Fuzzy Set,” Journal of Fuzzy set valued Analysis,Vol 3, pp 214-222, 2016.
  [6] K.T. Atanassov, “Some Operators in Intuitionistic Fuzzy Sets,” First Int. Conf. on IFS, Sofia, NIFS Vol 3 pp 28-33,1997.
  [7] K.T. Atanassov, “New Operations Defind Over Intuitionistic Fuzzy Sets,” Fuzzy Sets and Systems, Vol 61, 2 pp 137-142, 1994.

  Citation
  Jaydip Bhattacharya, "Some Special Operations and Related Results on Intuitionistic Fuzzy Sets," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.8, Issue.4, pp.10-13, 2021

• Open Access   Article

  High School Timetable Scheduling Vector Space Formulation

  A. Mozaffary, R. Shafaroudi

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.8 , Issue.4 , pp.14-17, Aug-2021

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  Timetable scheduling for high school is a challenging problem. Problem formulation is the first stage, and solving is the next. This problem is a NP-complete problem. An exact formulation for scheduling in a vector space is presented. With 6 constrains the condition and scope of a high school timetable is fully defined. The possibility of presenting a course (subject) in two or more days and also in several half-sessions is considered. Four constrains are linear and two of them that prevents conflictions between subjects are dot products of state vectors.Each session divided in two half-sections and the procedure has the ability to arrange sessions in continues and successive orders.

  Key-Words / Index Term
  timetable, scheduling, highschool, formulation, space vector

  References
  [1] Kristiansen, Simon; Stidsen, Thomas Riis, “A Comprehensive Study of Educational Timetabling - a Survey”, DTU Management Engineering,2013
  [2] A. Schaerf, “A Survey of Automated Timetabling”,Artificial Inteligence review, 1996
  [3] J.-C. R´egin, A ?ltering algorithm for constraints of di?erence in CSPs, Twelth National Conference on Arti?cial Intelligence,1994
  [4] Jean-Charles R´egin,”Generalized arc consistency for global cardinality constraint”, American Association for Artificial Intelligence (AAAI’96), 209-215, 1996
  [5] Pardalos,P.M.andM.G.C.Resende,”HandbookofAppliedOptimization.” Oxford University Press, USA,2002
  [6] N.M. Morade , "Reduction Method Using Minimum Supply And Demand Method to Find an Initial Basic Feasible Solution of Transportation Problem," International Journal of Computer Sciences and Engineering, Vol.7, Issue.1, pp.46-50, 2019.

  Citation
  A. Mozaffary, R. Shafaroudi, "High School Timetable Scheduling Vector Space Formulation," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.8, Issue.4, pp.14-17, 2021

• Open Access   Article

  New Iterative Method for Solving the Time Fractional Benjamin-Bona-Mahony-Burger Equation

  S.S. Omorodion

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.8 , Issue.4 , pp.18-25, Aug-2021

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  In this paper, we employed an iterative method called New Iterative Method (NIM) to obtain the approximate solution for time fractional Benjamin-Bona-Mahony-Burger (BBM-Burger) equation. The obtained approximate solution by NIM are calculated with MATLAB and compared with the exact analytical solutions as well as the Residual Power Series Method (RPSM) through different 2D/3D graphical representations and tables. The obtained results show that the NIM is an effective and straightforward method for solving the time fractional BBM-Burger equation and other nonlinear fractional partial differential equations arising in several areas of science and engineering.

  Key-Words / Index Term
  Time Fractional BBM-Burger Equation, Fractional Partial Differential Equations, New Iterative Method, Residual Power Series Method

  References
  [1] H. Bateman, “Some Recent Researches On the Motion of Fluids,” Monthly Weather Review, Vol. 43, Issue 4, pp.163-170, 1925.
  [2] G.B. Whitham, “Linear and Nonlinear Waves,” John Wiley & Sons, USA, pp.96-112, 2011.
  [3] J.M. Burgers, “A Mathematical Model Illustrating the Theory of Turbulence,” In Advances in applied mechanics, Vol.1, pp.171-199, 1948.
  [4] H. Brezis, F. Browder, “Partial differential equations in the 20th century,” Advances in Mathematics, Vol.135, Issue.1, pp.76–144, 1998.
  [5] A. D. Polyanin, V.F. Zaitsev, “Handbook of Nonlinear Partial Differential Equations,” Chapman & Hall/CRC, USA, pp.532-535, 2004.
  [6] W. Malfliet, “Solitary Wave Solutions of Nonlinear Wave Equations,” American Journal of Physics, Vol.60, Issue.7, pp.650–654, 1992.
  [7] P. G. Estévez, P.R. Gordoa, “Non-Classical Symmetries and The Singular Manifold Method,” Studies in Applied Mathematics, Vol .95, pp.73–113, 1995.
  [8] S. D. Liu, S. K. Liu, Q. X. Ye, “Explicit Traveling Wave Solutions of Nonlinear Evolution Equations”, Mathematics in Practice and Theory, Vol .28, Issue.4, pp.289–301, 1998.
  [9] A. M. Wazwaz, “Travelling Wave Solutions of Generalized Form of Burgers, Burgers – KdV and Burgers-Huxley Equations,” Applied Mathematics and Computation, Vol.169, Issue.1, pp.639–656, 2005.
  [10] T. B. Benjamin, J. L. Bona, J. J. Mahony, “Model Equations for Long Waves in Nonlinear Dispersive Systems,” Philosophical Transactions of the Royal Society of London, Vol.272, Issue.1220, pp.47–78, 1972.
  [11] C. I. Kondo, C. M. Webler, “The Generalized BBM-Burgers Equations: Convergence Results for Conservation Law with Discontinuous Flux Function,” Applicable Analysis, Vol.95, Issue.3, pp.503–523, 2016.
  [12] L. N. M. Tawfiq, Z. R. Yahya, “Using Cubic Trigonometric B-Spline Method to Solve BBM-Burger Equation,” In the Proceedings of the 2016 MDSG Conference, Malaysia, pp. 1-9, 2016.
  [13] M. Shakeel, Q. M. UI-Hassan, J. Ahmad, T. Naqvi, “Exact Solutions of the Time Fractional BBM-Burger Equation by Novel (G/G)-Expansion Method,” Advances in Mathematical Physics, Vol .2014, Article ID: 181594, 2014.
  [14] J. Zhang, Z. Wei, L. Yong, Y. Xiao, "Analytical Solution for the Time Fractional BBM-Burger Equation by Using Modified Residual Power Series Method," Complexity, vol. 2018, Article ID: 2891373, pp.1-11, 2018.
  [15] V. Daftardar – Gejjiand and H. Jafari, “An Iterative Method for Solving Nonlinear Functional Equations,” Journal of Mathematical Analysis and Applications, Vol.316, No.2, pp.753–763, 2006.
  [16] A. Mahdy, N. Mukhtar, “New Iterative Method for Solving Nonlinear Partial Differential Equations,” Journal of Progressive Research in Mathematics, Vol.11, No.3, pp.1701–1711, 2017.
  [17] M. Al - Luhaibi, “New Iterative Method for Fractional Gas Dynamics and Coupled Burger’ S Equations,” The Scientific World Journal, Vol .2015, Article ID: 153124, pp.1-8, 2015.
  [18] B. R. Sontakke, A. Shaikh, “Approximate Solutions of Time Fractional Kawahara and Modified Kawahara Equations by Fractional Complex Transform,” Communications in Numerical Analysis, Vol.2016, No.2, pp.218–229, 2016.
  [19] K. I. Falade, A.T. Tiamiyu, "Numerical Solution of Partial Differential Equations with Fractional Variable Coefficients Using New Iterative Method (NIM)," International Journal of Mathematical Sciences and Computing(IJMSC), Vol.6, No.3, pp.12-2, 2020.
  [20] S. Shiralashetti, S. I. Hanaji, “Taylor Wavelet Collocation Method for Benjamin–Bona–Mahony Partial Differential Equations,” Results in Applied Mathematics, Vol.9, Article ID: 100139, 2021.
  [21] H. Dehestani, Y. Ordokhani, M. Razzaghi, “Computational Method for Generalized Fractional Benjamin–Bona–Mahony–Burgers Equations Arising from The Propagation of Water Waves”, S?dhan? , Vol.45, pp.1-20, 2020.
  [22] M. Tarikul Islam, M. Ali Akbar, M. Abul Kalam Azad, “The Exact Traveling Wave Solutions to The Nonlinear Space-Time Fractional Modified Benjamin-Bona-Mahony Equation,” J. Mech. Cont.& Math. Sci., Vol.13, No.2, pp. 56-71.
  [23] S. Vong, P. Lyu “Unconditional Convergence in Maximum-Norm of a Second-Order Linearized Scheme for a Time-Fractional Burgers-Type Equation,” Journal of scientific computing, Vol.76, pp. 1252-1273, 2018.
  [24] Y. Wang, “A High-Order Linearized and Compact Difference Method for The Time-Fractional Benjamin–Bona–Mahony Equation,” Applied Mathematics Letters Vol.105, Article ID:106339, 2020.
  [25] A. Majeed, M. kamran, M. Abas, M. Yushalify, “An Efficient Numerical Scheme for The Simulation of Time-Fractional Nonhomogeneous Benjamin-Bona-Mahony-Burger Model,” Physica Scripta, Vol. 96, No.8 Article ID:084002, 2021.
  [26] A. S. Kumar, D. Kumar, “Fractional Modelling for BBM-Burger Equation by Using New Homotopy Analysis Transform Method,” Journal of the Association of Arab Universities for Basic and Applied Sciences, Vol. 16, No.1, pp.16–20, 2014.
  [27] I. Podlubny, “Fractional Differential Equations: An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of Their Solution and Some of Their Applications,” Vol., Academic Press, USA, 1999.
  [28] Y. Cherruault, “Convergence of Adomian`s method,” Kybernetes, Vol. 18, No.2, pp.31–38, 1989..
  [29] M. Shakeel, Q. Hassan, J. Ahmad, T. Naqvi, "Exact Solutions of the Time Fractional BBM-Burger Equation by Novel - Expansion Method," Advances in Mathematical Physics, Vol.2014, Article ID:181594, pp.1-14, 2014.

  Citation
  S.S. Omorodion, "New Iterative Method for Solving the Time Fractional Benjamin-Bona-Mahony-Burger Equation," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.8, Issue.4, pp.18-25, 2021

• Open Access   Article

  On Plurimum Discidium

  Ankush Kumar Parcha, Sahil Joon, Toyesh Prakash Sharma

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.8 , Issue.4 , pp.26-37, Aug-2021

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  Abstract
  This Paper deals with the divisions of really big numbers, some results will explain by using its proof, for example, method of mathematical induction, etc. for proving the theorems authors use the concept of exponents, limit, series, sequence etc. So, for understand the proof of the theorems this knowledge of Limits, Series, sequence etc required. The results that authors will introduce are really a difficult task to think because there required an assumption that such big numbers are exists may in future mathematicians take some actions to prove such numbers are existing one. The proof demands many steps and every one step of its open new doors to thing further as a result we discussed some results on behalf of which there some other generalizations will take place.

  Key-Words / Index Term
  Division, Bar, Very Big Numbers, Limit, continuous, sequence, increasing and decreasing etc.

  References
  [1] Class XI, Mathematics Textbook, National Council of Educational Research and Training (NCERT), Reprinted 2013 Edition-I Ch-5 “Complex Number and Quadratic Equations” ISBN-9788174504869, pp. 97.
  [2] Article on Wikipedia “Disquisitiones Arithmeticae” .
  [3] Class IX, Mathematics Textbook, National Council of Educational Research and Training (NCERT), Reprinted 2013 Edition-I Ch-1 “Number System” ISBN-9788174504890. pp. 10.
  [4] Article on Wolfram Alpha” Bar”
  [5] Article on Wikipedia “vinculum”.
  [6] I.A. Maron, “Problems Of Calculus In One Variabl”, Ch-3, Section 3.2 Classic text series-Arihant, ISBN-978-93-5176-259-1, pp. 124.

  Citation
  Ankush Kumar Parcha, Sahil Joon, Toyesh Prakash Sharma, "On Plurimum Discidium," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.8, Issue.4, pp.26-37, 2021

• Open Access   Article

  Stability and Consistency Analysis of FTCS Scheme for Unsteady Magnetohydrodynamic Fluid Flow over a Vertical Stretching Sheet

  A.O. Nyakebogo, J.M. Kerongo, R.K. Obogi

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.8 , Issue.4 , pp.38-43, Aug-2021

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  This paper analyzed the Forward Time Centered Space (FTCS) scheme for a two-dimensional fluid flow over a stretching surface. The fluid flow considered is unsteady, viscous and incompressible taking place under the influence of thermal radiation and variable viscosity in the presence of induced magnetic field. The partial differential equations considered, that is, the energy conservation and induction equations, cannot be solved using analytical methods. The finite difference numerical method has been used to discretize the partial differential equations to obtain a numerical scheme. The Forward Time and Central in Space (FTCS) scheme has been developed for the two governing equations. The Von-Neumann method is used to analyze for the stability of the FTCS scheme whereas the Taylor’s series expansion has been utilized in analyzing consistency. The energy conservation and the magnetic induction equations have been discretized to obtain the explicit scheme. It is observed that the FTCS scheme is conditionally stable for both equations while the consistency of both schemes is also confirmed from the analysis.

  Key-Words / Index Term
  Viscous dissipation, Magnetohydrodynamics, induced magnetic field, Von-Neumann analysis, FTCS scheme, amplification factor.

  References
  [1] L. Lapidus, “Parabolic Partial Differential Equations’’, Numerical Solution of Partial Differential Equations in Science and Engineering Lapidus/Numerical, 2011.
  [2] L. Lapidus and G.F. Pinder, “Numerical Solution of Partial Differential Equations in Science and Engineering.” John Wiley and Sons Inc, 1982.
  [3] J.M. McDonough, “Lectures on Computational Numerical Analysis of Partial Differential Equations”. University of Kentucky, 2008
  [4] F.T. Chan, “Stability Analysis of Finite Difference Schemes for the Advection-Diffusion Equation”. Numerical Analysis Project, Stanford University, California, 1984.
  [5] A.R. Appadu, “Numerical solution of the 1D Advection-Diffusion Equation Using Standard and Nonstandard Finite Difference Schemes.” Journal of Applied Mathematics, 2013.
  [6] T.M.A. Azad and L.S. Andallah, “Stability Analysis of Finite Difference Schemes for an Advection-diffusion Equation”. Bangladesh J. Sci. Ind. Res. Vol 29, issue 2, pp.143-151, 2016.
  [7] F. Sanjaya and S. Mungkasi, “A simple but Accurate Explicit Finite Difference Method for the Advection Equation.” International Conference on Science and Applied Science, series 909 (2017) 012038.
  [8] A.K. Tinega and C.O. Ndede, “Stability and Consistency Analysis for Central Difference Scheme for Advection Diffusion Partial Differential Equation”. International Journal of Science and Research (IJSR), Vol. 8 issue 7, pp. 1046-1049, 2017.
  [9] L.S. Andallah and M.R. Khatun, “Numerical Solution of Advection-Diffusion Equation Using Finite Difference Schemes.” Bangladesh J. Sci. Ind. Res. Vol. 55, issue 1, pp. 15-20, 2020.
  [10] Z. Liang, Y. Yan, and G. Gai, “A Dufort-Frankel Difference Scheme for Two-Dimensional Sine-Gordon Equation”. Discrete Dynamics in Nature and Society, 2014.
  [11] N.M.S. Nyachwaya, J.M. Okwoyo, J.O. Okelo and J.K. Sigey, “Finite Difference Solution of Seepage Equation: A Mathematical Model for Fluid Flow.” The SIJ Transactions on Computer Science Engineering and its Applications (CSEA), Vol. 2, issue 4, pp. 132-140, 2014, doaj.org
  [12] J.A. Mensah, F.O. Boateng and K. Bonsu, “Numerical Solution to Parabolic PDE Using Implicit Finite Difference Approach.” Mathematical Theory and Modeling, vol. 6, issue 8, pp.74-84, 2016.
  [13] A. Abdullah, “Simplified Von-Neumann Stability Analysis of Wave Equation Numerical Solution.” ARPN Journal of Engineering and Applied Sciences, Vol.14, issue 24, pp. 4164-4168, 2019.
  [14] E. Sousa “On the Edge of Stability Analysis.” Applied Numerical Mathematics, vol. 59 pp. 1322-1336, 2009
  [15] M.A. Ayanga, M.N. Kinyanjui, J.O. Okelo and J.K. Sigey, “Stability and Consistency Analysis for Implicit Scheme for MHD Stokes Free Convective Fluid Flow Model Equations Past an Infinite Vertical Porous Plate in a Variable Transverse Magnetic Field”. International Journal of Science and Research, Vol. 8, issue 1, pp. 1347-1351, 2019.
  [16] M.R. Murtaza, E.E. Tzirtzilakis and M. Ferdows, “Stability and Convergence Analysis of a Biomagnetic Fluid Flow over a Stretching Sheet in the Presence of a Magnetic Field”. Symmetry, Vol. 12, issue 2, pp. 253, 2020.
  [17] S. Shateyi and S.S. Motsa, “Variable Viscosity on Magnetohydrodynamic Fluid Flow and Heat Transfer over an Unsteady Stretching Surface with Hall Effect”. Boundary Value Problems, 2010
  [18] M.K. Prasad, S.H. Naveenkumar, C.S.K. Raju, and S.M. Upadhya, “Nonlinear Thermal Convection on Unsteady Thin Film Flow with Variable Properties.” Journal of Physics: Conference series, doi:10.1088/1742-6596/1427/1/012016, 2019
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  [25] S. Sungnul, B. Jitsom and M. Punpocha, “Numerical Solutions of the Modified Burger’s Equation Using FTCS Implicit Scheme, IAENG International Journal of Applied Mathematics, 48 pp. 53-61, 2018.
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  Citation
  A.O. Nyakebogo, J.M. Kerongo, R.K. Obogi, "Stability and Consistency Analysis of FTCS Scheme for Unsteady Magnetohydrodynamic Fluid Flow over a Vertical Stretching Sheet," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.8, Issue.4, pp.38-43, 2021

• Open Access   Article

  Solution to an Open Problem

  Toyesh Prakash Sharma

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.8 , Issue.4 , pp.44-46, Aug-2021

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  Abstract
  Today, with the help of this article, we will solve an open problem by using the concepts of calculus and formulated a new theorem that will be an answer to the open problem, the open problem is discussed below in Introduction Section. Although to understand the solution perfectly it must be knowing that knowledge of, Induction, Differentiation, product rule of differentiation, integration by parts, substitution in integration, and some other knowledge of calculus is required.

  Key-Words / Index Term
  Mathematical Induction, Substitution, integration, integration by parts, exponential functions, trigonometric functions, logarithmic function, algebric functions, product rule. Etc.

  References
  [1] Toyesh Prakash Sharma “A Generalization to ” Volume-7, Issue-6, pp.46-50, December (2020) International Journal of Scientific Research in Mathematical and Statistical Sciences (IJSRMSS).
  [2] Mathematics Textbook class XII, NCERT- Ch-7 integrals Ex-7.6. P.323-328. ISBN-81-7450-653-5.
  [3] Joseph Edwards: Integral Calculus for beginners, Ch IV “Integral by Parts. Publisher-arihant P 32 ISBN978-93-5094-145-4.
  [4] Article on Wikipedia- “Derivative”
  

  Citation
  Toyesh Prakash Sharma, "Solution to an Open Problem," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.8, Issue.4, pp.44-46, 2021

• Open Access   Article

  Comparison of Different Parametric Modelling for Child Dengue Patients: A Survival Approach

  V. Raghul Gandhi, R. Nandhinidevi, R. Reka, K. Saravanaraj, Saravanan G.

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.8 , Issue.4 , pp.47-53, Aug-2021

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  Abstract
  Survival Analysis is one of the important statistical procedures which are mainly used to analyze the time to event data in various fields such as Public Health, Medicine, Political Science, Biostatistics and Epidemiology etc. A Parametric and Non-Parametric method plays a vital role in building a survival model for many diseases. In this paper these parametric models were applied to the data of 109 child dengue patients. The primary goal of this paper is to study the parametric survival models such as Exponential distribution, Weibull distribution, Gompertz distribution and some life time distributions and distribution free Methods such as Kaplan Meier Estimator and Log-Rank test for the dengue data and to compare the best model among Parametric methods by using model measurement criterion as the best model fit is identified by smaller AIC, BIC value and Non Parametric methods is used to examine the survival curves of the Dengue patients. As a result, Logistic distribution is found to be best model. The Statistical Analysis is done by using Statistical software such as IBM SPSS Statistics 21 and R i386 3.6.3 language.

  Key-Words / Index Term
  Survival Analysis, Parametric methods, Distribution free methods, AIC and BIC.

  References
  [1] L. Handayani, M. Fatekurohman, and D. Anggraeni, “Survival Analysis in Patients with Dengue Hemorrhagic Fever (DHF) Using Cox Proportional Hazard Regression,” 2017.
  [2] D. Collett, Modelling survival data in medical research. CRC press, 2015.
  [3] E. T. Lee and J. Wang, Statistical methods for survival data analysis, vol. 476. John Wiley & Sons, 2003.
  [4] M. A. Pourhoseingholi, E. Hajizadeh, B. Moghimi Dehkordi, A. Safaee, A. Abadi, and M. R. Zali, “Comparing Cox regression and parametric models for survival of patients with gastric carcinoma,” Asian Pacific J. Cancer Prev., vol. 8, no. 3, p. 412, 2007.
  [5] V. Vallinayagam, S. Prathap, and P. Venkatesan, “Parametric regression models in the analysis of breast cancer survival data,” Int. J. Sci. Technol., vol. 3, no. 3, pp. 163–167, 2014.
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  Citation
  V. Raghul Gandhi, R. Nandhinidevi, R. Reka, K. Saravanaraj, Saravanan G., "Comparison of Different Parametric Modelling for Child Dengue Patients: A Survival Approach," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.8, Issue.4, pp.47-53, 2021