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• Open Access   Article

  Efficient Class of Combined Ratio Type Estimators for Estimating the Population Mean under Non-response

  Zakir Hussain Wani, S.E.H. Rizvi, Manish Sharma, M. Iqbal Jeelani Bhat

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.8 , Issue.6 , pp.1-6, Dec-2021

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  Abstract
  In this paper, we investigate the issue of non-response in two different instances for estimating the population mean in stratified random sampling. Case I occurs when non-response is observed on both the study variable Y and the auxiliary variable X, and the population mean ( ) of the auxiliary variable is known; case II occurs when non-response is observed on the study variable Y, information on the auxiliary variable X is obtained from all sample units, and the population mean ( ) of the auxiliary variable X is known. We propose a class of combined ratio-type estimators that utilize known values of population characteristics of auxiliary variable such as coefficient of variation, kurtosis, skewness, standard deviation, median, mid-range, and correlation coefficient. The properties of the proposed estimators are obtained up to the first order of approximation. It has been shown empirically that the proposed estimators perform better than the existing estimators in terms of mean square errors.

  Key-Words / Index Term
  Ratio estimator, Auxiliary variable, Bias, Mean square error, Relative efficiency

  References
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  Citation
  Zakir Hussain Wani, S.E.H. Rizvi, Manish Sharma, M. Iqbal Jeelani Bhat, "Efficient Class of Combined Ratio Type Estimators for Estimating the Population Mean under Non-response," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.8, Issue.6, pp.1-6, 2021

• Open Access   Article

  Analysis of the Students’ Level of Problem-Solving Skills in Mathematics: Basis for an Intervention Program

  A.G. Vasquez, M.S. Garcellano

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.8 , Issue.6 , pp.7-12, Dec-2021

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  Abstract
  Problem-solving is one of the two goals of Mathematics in Philippine basic education. In 2018, the country joined for the first time in the Programme for International Student Assessment (PISA) conducted by the Organization for Economic Co-operation and Development (OECD), which manifested that the Philippines ranked second-lowest in Mathematics out of the 79 member and partner countries, scoring 353 below the average of 489 points. This low level of students’ Mathematical problem-solving skills paved the way for this research to be coursed through, involving 53 students of the Narra National High School – Science, Technology, and Engineering (STE) program. A Convergent Parallel Mixed Methods design was utilized in this study, where the data collection method included a problem-solving test and an interview. It found out that the students’ level of problem-solving skills is Working towards Mastery and that their gender and parents’ educational attainment profile do not significantly affect their problem-solving skills. This study suggested that to improve the level of problem-solving skills of the students; it is vital to strengthen the integration of Polya’s method in teaching lessons about problem-solving; conduct an intervention program in the form of remedial and peer tutoring; enrich students vocabulary skills and intensify the reading skills of the students since problem sets in Mathematics involve reading comprehension skills.

  Key-Words / Index Term
  Intervention program, Polya, Problem-solving skills

  References
  [1] Department of Education, Philippines.
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  Citation
  A.G. Vasquez, M.S. Garcellano, "Analysis of the Students’ Level of Problem-Solving Skills in Mathematics: Basis for an Intervention Program," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.8, Issue.6, pp.7-12, 2021

• Open Access   Article

  Application of Successive Linearisation Method on Mixed Convection from an Exponentially Stretching Surface with Magnetic Field Effect

  A.A. Khidir, W.I. Alfaifi

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.8 , Issue.6 , pp.13-19, Dec-2021

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  Abstract
  In this paper, a numerical solution has been obtained to solve the problem of the MHD boundary layer flow of heat and mass transfer with magnetic field effect. The partial differential equations governing the problem consideration were to a system of boundary value problem of ordinary differential equations by using a similarity transformation. The transformed governing equations in the present study were solved numerically by using the successive linearization method (SLM). The Velocity, temperature and concentration profiles are considered as exponential function. The effect of magnetic field parameter M on the flow profiles were obtained and discussed as well as the numerical values of the skin friction and the rate of heat transfer are entered in tables and compared with other study in the literature. The accuracy of the obtained solution has been checked using comparison with previously published work and excellent agreement is observed. It has been found that in the magnetic field reduced the Velocity of the fluid , whereas the temperature and concentration in fluid is enhanced.

  Key-Words / Index Term
  Mixed convection; Boundary layer flow; Exponentially stretching surface; Successive linearisation method

  References
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  Citation
  A.A. Khidir, W.I. Alfaifi, "Application of Successive Linearisation Method on Mixed Convection from an Exponentially Stretching Surface with Magnetic Field Effect," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.8, Issue.6, pp.13-19, 2021

• Open Access   Article

  Conformable Fractional Reduced Differential Transform Method for Solving Linear and Nonlinear Time-Fractional Swift-Hohenberg (S-H) Equation

  S.S. Omorodion

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.8 , Issue.6 , pp.20-29, Dec-2021

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  Abstract
  In this paper, we present the conformable fractional reduced differential transform method (CFRDTM) for finding the exact and approximate analytical solution for the time-fractional Swift-Hohenberg (S-H) equations with initial value. The S-H equation was first proposed in 1977 by J.B. Swift and P.C. Hohenberg to study the thermal fluctuations on a fluid near the Rayleigh-Benard convective instability. To demonstrate the efficiency and applicability of the proposed method, we considered linear and nonlinear time-fractional S-H equations with and without dispersive terms. Results are calculated and presented through 2D/3D graphical representations. The obtained results show that the CFRDTM is effective and simple in constructing the exact and approximate analytical solutions for the time fractional S-H equations, and it may also find wide application in other complicated fractional partial differential equations that originate in the areas of engineering and science.

  Key-Words / Index Term
  Conformable Derivative, Conformable Fractional Reduced Differential Transform Method, Fractional Calculus, Time-Fractional Swift-Hohenberg Equation

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  Citation
  S.S. Omorodion, "Conformable Fractional Reduced Differential Transform Method for Solving Linear and Nonlinear Time-Fractional Swift-Hohenberg (S-H) Equation," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.8, Issue.6, pp.20-29, 2021

• Open Access   Article

  Some New Classes of Graceful Lobsters

  Dedas Mishra, Amaresh Chandra Panda, Subarna Bhattacharjee

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.8 , Issue.6 , pp.30-39, Dec-2021

  Abstract

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  Abstract
  It is readily found that a lobster L contains a unique path, say P = x_0 x_1?x_n called as the central path of L such that each vertex x_i,0

  Key-Words / Index Term
  graceful labeling, lobster, central path odd, even and pandent branches

  References
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  [6] S. L. Zhao, “All Trees of Diameter Four are Graceful,” Ann. New York Acad. Sci., Vol. 576, pp. 700 – 706, 1989.
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  [9] D. Morgan, “All Lobsters with Perfect Matching are Graceful”, Electron. Notes Discrete Math., Vol. 1, pp. 6, 2002.
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  [11] D. Mishra, P. Panigrahi, “Some Graceful Lobsters with All Three Types of branches Incident on the Vertices of the Central Path”, Computers and Mathematics with Applications, Vol. 50, Issue. 4, pp. 367-380, 2005.
  [12] D. Mishra and P. Panigrahi, “Graceful Lobster Obtained by Component Moving of Diamater Four Trees”, Ars Combinatoria, Vol. 89, pp. 129-147, 2006.
  [13] D. Mishra and P. Panigrahi, “Some Graceful Lobsters with Both Odd and Even Degree Vertices on Central Path”, Utilitus Mathematics, Vol.74, pp.155-177, 2007.
  [14] D. Mishra and P. Panigrahi, “Some Graceful Lobsters with All Three Types of Branches Incident on the Vertices of the Central Path”, Computers and Mathematics with Applications, Vol. 56, pp. 1382 – 1394, 2008.
  [15] D.Mishra and P. Panigrahi, “Graceful Lobsters Obtained from Diameter Four Trees Using Partitioning Technique”, Ars Combinatoria, Vol. 87 , pp. 291 – 320, 2008.
  [16] D. Mishra and P. Panigrahi, “A New Class of Graceful Lobsters Obtained from Diameter Four Trees,” Utilitus Mathematica, Vol. 80 pp. 183 – 209, 2009.
  [17] D. Mishra and P. Panigrahi, “Some New Classes of Graceful Lobsters Obtained from Diameter Four Trees”, Mathematica Bohemica, Vol. 135, No. 3, pp. 257 – 278, 2010.
  [18] D. Mishra and P. Panigrahi, “Some New Classes of Graceful Lobsters Obtained by Applying Inverse And Component Moving Transformations”, International Journal of Mathematics Trends and Technology (IJMTT), Vol.1, Issue – 2, pp. 6 – 16, 2011.
  [19] P. Panigrahi and D. Mishra, “Graceful Lobsters Obtained from Diameter Four Trees Using Partitioning Technique”, ARS Combinatoria, Vol. 87, pp. 291- 320, 2008.
  [20] P. Panigrahi and D.Mishra, “Larger Graceful and Interlaced Lobster Obtained by Joining Smaller Ones”, South East Asian Bulletin of Mathematics, Vol. 33, pp. 509-525, 2009.
  [21] D. Mishra, A. C. Panda, and R. B. Dash, “A Class of Graceful Lobsters with Even Number of Branches Incident on the Central Path”, International Journal of Mathematical Sciences and Applications, Vol. 1, No. 2, pp. 463 – 472, 2011.
  [22] D. Mishra and A. C. Panda, “Some New Graceful Generalized Classes of Lobsters”, International Journal of Pure and Applied Mathematics (IJPAM), ISSN: 1311-8080, Volume – 91, Issue. 1, pp. 57 – 76, 2014.
  [23] D. Mishra and A. C. Panda, “Some New Family of Graceful Lobsters”, Advances and Applications in Discrete Mathematics (AADM), Volume 14, Issue. 1, pp. 1-24, 2014.
  [24] D. Mishra and S. Bhattacharjee, “Some New Classes of Lobsters Exhibiting Graceful Labeling”, Global Journal of Pure and Applied Mathematics, Volume 11, No- 2, pp. 909 – 930, 2015.
  [25] D. Mishra, S. K. Rout, P. C. Nayak, “Some New Graceful Lobsters with Pendant Vertices with Central Paths”, Indian Journal of Science and technology, Vol 10, Issue. 6, pp. 1-9, 2017.
  [26] G. Sethuraman and J. Jesintha, “A New Class of Graceful Lobsters”, J. .Combin. Math. Combin. Computing, Vol. 67, pp.99-109, 2008.
  [27] S. Ghosh, “On Certain Classes of Graceful Lobsters,” Ars Combin., Vol. 136, pp. 67 – 96, 2018.
  [28] D. Mishra, S. K. Rout, S. Bhattacharjee, “Some New Classes of K-Distance Trees with Alpha Labeling,” International Journal of Scientific Research in Mathematical and Statistical Sciences, E-ISSN: 2348-4519, Vol 7, Issue 4, pp. 26 - 34 , 2020.
  [29] J. Jeba Jesintha, R. Jayaglory, G. Bhabita, Odd Graceful Labelling of the Union of Cycle and Lobsters, International Journal of Computer Sciences and Engineering, Vol.-7, Special Issue, 5,pp. 59-63, 2019.

  Citation
  Dedas Mishra, Amaresh Chandra Panda, Subarna Bhattacharjee, "Some New Classes of Graceful Lobsters," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.8, Issue.6, pp.30-39, 2021

• Open Access   Article

  Evaluation of Average Outgoing Quality (AOQ) for Reliability Acceptance Sampling Plan Based on the Exponentiated Rayleigh Distribution

  B. Jabir

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.8 , Issue.6 , pp.40-45, Dec-2021

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  Abstract
  Quality of the product plays vital role in acceptance sampling plan and the quality of the lot is determined by using average outgoing quality (AOQ) which is the expected quality of lots after the application of sampling inspecting. This paper introduces the designing of Average Outgoing Quality (AOQ) and Average Outgoing Quality Limit (AOQL) in Reliability acceptance sampling plan for life test is follows Exponentiated Rayleigh distribution. The procedure for designing a single sampling plan indexed through the Average Outgoing Quality (AOQ) is stated. A statistical software(R) is used to simulate the procedure developed and graphs are constructed for the selection of AOQ values for a sampling plan under the Exponentiated Rayleigh model.

  Key-Words / Index Term
  Acceptance sampling, Life test, Exponentiated Rayleigh distribution, Probability of acceptance, Average Outgoing quality (AOQ), Average Outgoing Quality Limit (AOQL).

  References
  [1] B. Epstein.,“Truncated life tests in the exponential case,” Annals of Mathematical Statistics, vol. 25, pp. 555–564,1954.
  [2] Sobel M, Tischendrof J.,”Acceptance sampling with new life test objectives, in Proceedings of 5th National Symposium on Reliability and Quality Control”,pp.108-118,1959
  [3] Goode HP, Kao JHK.,”Sampling plans based on the Weibull distribution, Proceedings of the Seventh National Symposium on Reliability and Quality Control”, Philadelphia,pp.24-40,1961
  [4] Gupta SS, Groll PA.,”Gamma distribution in acceptance sampling based on life test, Journal of American Statistical Association”, pp.56:942-970. 1961.
  [5] Kantam RRL, Rosaiah K, Srinivasa Rao G., “Acceptance sampling based on life test: log-logistic model, Journal of Applied Statistics”,28(1),pp.121-128,2001.
  [6] Baklizi A, El Masri AEK. Acceptance sampling plans based on truncated life tests in the Birnbaum Saunders model, Risk Analysis,vol.4,pp.24:453-1457, 2004.
  [7] G. Srinivasa Rao and R. R. L. Kantam.,“Acceptance sampling plans from truncated life tests based on log-logistic distribution for percentiles,” Economic Quality Control,vol.25, no.2, pp.153– 167,2010.
  [8] K. Rosaiah and R.R.L. Kantam.Acceptance Sampling Based on the Inverse Rayleigh Distribution, Economic Quality Control, Vol 20, No. 2, 277 – 286, 2005.
  [9] Rao, G.S., Kantam, R.R.L., Rosaiah, K. and Reddy, J.P.,”Acceptance sampling plans for percentiles based on the Inverse Rayleigh Distribution”. Electronic Journal of Applied Statistical Analysis, 5(2), 164-177, 2012.
  [10] K.Pradeepa Veerakumari & P. Ponneeswari, “Designing of Acceptance Sampling Plan for life tests based on Percentiles of Exponentiated Rayleigh Distribution”International Journal of Current Engineering and Technology, E-ISSN 2277-4106,P-ISSN 2347-5161.
  [11] Soundararajan,V.,”Single sampling attributes plan indexed by AQL & AOQL”., Journal of Quality Technology,13,pp.195-200.1981.

  Citation
  B. Jabir, "Evaluation of Average Outgoing Quality (AOQ) for Reliability Acceptance Sampling Plan Based on the Exponentiated Rayleigh Distribution," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.8, Issue.6, pp.40-45, 2021

• Open Access   Article

  Dio- Triples Involving Pentagonal Pyramidal Numbers

  C. Saranya, E. Mahalakshmi

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.8 , Issue.6 , pp.46-48, Dec-2021

  Abstract

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  Abstract
  We scrutinize for three particular polynomials with integer coefficients to such an extent that the result of any two numbers expanded by a non-zero number (or polynomials with number coefficients) is an ideal square.

  Key-Words / Index Term
  Diophantine triples, Pentagonal Pyramidal number, Polynomials & Perfect square

  References
  [1] R.D.Carmichael, “History of Theory of numbers and Diophantine Analysis”, Dover Publication, New york, 1959.
  [2] L.J.Mordell, “Diophantine equations”, Academic press, London, 1969.
  [3] T.Nagell, “Introduction to Number theory”, Chelsea publishing company, New york, 1981.
  [4] L.K.Hua, “Introduction to the Theory of Numbers”, Springer-Verlag, Berlin-New york, 1982.
  [5] Oistein Ore, “Number theory and its History”, Dover publications, New york, 1988.
  [6] H.John, Conway and Richard K.Guy, “The Book of Numbers”, Springer-verlag, New york, 1995.
  [7] Y.Fujita , “The extendability of Diphantine pairs ”, Journal of Number Theory, 128, 322-353, 2008.
  [8] M.A. Gopalan and V.Pandichelvi , “On the extendability of the Diophantine triple involving Jacobsthal numbers ”, International Journal of Mathematics & Applications, 2(1), 1-3, 2009.
  [9] G.Janaki and S.Vidhya, “Construction of the diophantine triple involving stella octangula number, Journal of Mathematics and Informatics, vol.10, Special issue, 89-93, Dec 2017.
  [10] G.Janaki and C.Saranya, “Special Dio 3-tuples for pentatope number”, Journal of Mathematics and Informatics, vol.11, Special issue, 119-123, Dec 2017.
  [11] G.Janaki and C.Saranya, “Construction of The Diophantine Triple involving Pentatope Number”, International Journal for Research in Applied Science & Engineering Technology, vol.6, Issue III, March 2018.
  [12] C.Saranya, and G.Janaki., “Some Non-extendable Diophantine Triples involving centered square numbers”, International Journal of Scientific Research in Mathematical and Statistical Sciences, vol 6, Issue 6, 105-107, 2019
  [13] Saranya C., and Janaki G, “Half companion sequences of special dio 3-tuples involving centered square numbers”, International Journal for Recent Technology and Engineering, vol.8, issue 3, 3843-3845, 2019.

  Citation
  C. Saranya, E. Mahalakshmi, "Dio- Triples Involving Pentagonal Pyramidal Numbers," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.8, Issue.6, pp.46-48, 2021

• Open Access   Article

  Intuitionistic Fuzzy Soft (T,S)-Normed Relations

  T. PortiaSamathanam, G. Subbiah, M. Navaneethakrishnan

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.8 , Issue.6 , pp.49-55, Dec-2021

  Abstract

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  Abstract
  In this article, we study soft equivalence relation, soft congruence relation on a group G by using (T,S)-norms. We investigate fuzzy soft normal subgroups of subgroups, direct product of fuzzy soft normal subgroups and their properties will be discussed. Also, the image and pre-image of them will be investigated by using group homomorphism.

  Key-Words / Index Term
  Fuzzy subset, (T,S) -norm, fuzzy soft subgroup, homomorphism, normal subgroup, projection, relation, (T,S)-fuzzy soft equivalence relation, direct product.

  References
  [1] Atanassov. K, “Intuitionistic fuzzy sets”, Fuzzy sets and Systems, 20, 87-96, 1986.
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  [10]Beg.I and Ashraf.S, “Fuzzy Relations”, Lambert Academic Publisher, Germany, 2009.
  [11]Cross.V.V and Sudkamp.T.A, “Similarity and Compatibility in Fuzzy Set Theory”, Springer-Verlag, Heidelberg 2002.
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  [18]Kumar.I.J, Saxena. P. K. and Yadava.P, “Fuzzy normal subgroups and fuzzy quotients”, Fuzzy Sets and Systems 46, 121-132, 1992.
  [19]Kuroki.N, “Fuzzy congruence’s and Fuzzy normal subgroups”, Inform. Sci. 60, 247-361, 1992.
  [20]Li.H.X and Yen.V.C., “Fuzzy Sets and Fuzzy Decision-Making”, CRC Press. Inc., London, 1995.
  [21]Malik.D.S and Mordeson.J.N, “A note on fuzzy relations and fuzzy groups”, Inform. Sci. 56, 193-198, 1991.
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  [24]V.Vanitha,G.Subbiah and M.Navaneethakrishnan, “Flexible fuzzy softification of group structures”, International Journal of Scientific Research in Mathematical and Statistical sciences (ISROSET), vol.5(4), 389-394, 2018.
  [25]T.PortiaSamathanam,G.Subbiah and M.Navaneethakrishnan, “Certain structures of Q-Fuzzy soft ideals of near-ring”, International Journal of Scientific Research in Mathematical and Statistical sciences (ISROSET), vol.6(4), , 44-48, 2019.
  [26]Poincare.H, La Science et “Hypotheses, Flammarion”, Paris, 1902.
  [27]Rasuli.R, “Fuzzy Ideals of Subtraction Semi groups with Respect to A t-norm and A t-conorm”, The Journal of Fuzzy Mathematics Los Angeles, 24 (4), 881-892, 2016.
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  [29]Zadeh.L.A, “Fuzzy sets”, Information and control, 8 pp 338-353, 1965.

  Citation
  T. PortiaSamathanam, G. Subbiah, M. Navaneethakrishnan, "Intuitionistic Fuzzy Soft (T,S)-Normed Relations," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.8, Issue.6, pp.49-55, 2021