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

• Open Access   Article

  On The Equivalence of Categories of A^H-Semimodules and A#H-Semimodules

  M. Devendran, V. Selvan

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.6 , Issue.6 , pp.79-86, Dec-2019

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  Abstract
  In this paper, we have introduced two functors between the category of A^H- semimodules and the category of A#H- semimodules, where A is a H-semimodule semialgebra over a Hopf algebra. Further, assuming H as a finite dimensional semisimple Hopf algebra we have established a categorical equivalence between these two categories.

  Key-Words / Index Term
  Semialgebra, Smash product, Hopf algebra, Natural transformation, equivalent categories

  References
  [1] Miriam Cohen and Davida Fishman, Hopf Algebra Actions, Journal of Algebra, 100, 363-379(1986).
  [2] M.Devendran, V.Selvan, Hopf Algebra Actions on Semialgebras, Journal of combinatorics, information and system sciences Vol.42(2017), No.1-2, 33-50.
  [3] Jonathan S Golan, Semiring and their Applications, Kluwer Academic Publishers, 1999.
  [4] Saunders Maclane, Categories for working mathematicians, Graduate text in mathematics, Springer, 1971.
  [5] Y.Katsov, Tensor products and injective envelopes of semimodules over additively regular semirings, Algebra Colloquium 4(2)(1997)121-131.
  [6] V.Selvan, M.Devendran, Morita equivalence between H-fixed semialgebra and smash product semialgebra, Journal of combinatorics, information and system sciences, Vol.43 (2018), No.1-4, pages 57-77.
  [7] R.P.Sharma, Anu, N.Singh, Partial group action on semialgebras, Asian-Eur.J.Math. 5(4)2012, Act1250060, 20pp.
  [8] M.Sweedler, Hopf Algebra, Benjamin, New York, 1969.

  Citation
  M. Devendran, V. Selvan, "On The Equivalence of Categories of A^H-Semimodules and A#H-Semimodules," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.6, Issue.6, pp.79-86, 2019

• Open Access   Article

  The Derivation and Choice of Appropriate Test Statistic (Z, t, F and Chi-Square Test) in Research Methodology

  Teshome Hailemeskel Abebe

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.6 , Issue.6 , pp.87-95, Dec-2019

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  Abstract
  This paper aims to choose an appropriate test statistic for research methodology. Specifically, it tries to explore the concept of statistical hypothesis test, derivation of the test statistic and identify their application on research methodology. It also try to show the basic formulating and testing of hypothesis using test statistic since choosing appropriate test statistic is the most important tool of research. Among the common statistical tests: Z-test, Student’s t-test, F test (like ANOVA), and Chi square test were identified. In testing the mean of a population or comparing the means from two continuous populations, the z-test and t-test were used, while the F test is used for comparing more than two means and equality of variance. The chi-square test was used for testing independence, goodness of fit and population variance of single sample in categorical data. Therefore, choosing an appropriate test statistic gives valid results about hypothesis testing.

  Key-Words / Index Term
  Test Statistic, Z-test, Student’s t-test, F test (like ANOVA), Chi-square test, Research Methodology

  References
  [1] David, J. Pittenger, "Hypothesis Testing as a Moral Choice", Ethics & Behavior, Vol. 11, Issue. 2, PP.151-162, 2001, DOI: 10.1207/S15327019EB1102_3.
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  [3] Joginder Kaur, "Techniques Used in Hypothesis Testing in Research Methodology A Review", International Journal of Science and Research (IJSR), ISSN (Online): 2319-7064 Index Copernicus Value: 6.14 | Impact Factor: 4.438, 2013.
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  Citation
  Teshome Hailemeskel Abebe, "The Derivation and Choice of Appropriate Test Statistic (Z, t, F and Chi-Square Test) in Research Methodology," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.6, Issue.6, pp.87-95, 2019

• Open Access   Article

  Union of Fuzzy Normal Semi- “N” Groups and Anti- Fuzzy Normal Semi- “N” Groups (for n= 1,2,….n)

  N. Deepica

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.6 , Issue.6 , pp.96-104, Dec-2019

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i6.96104

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  Abstract
  In this paper, definition of Fuzzy normal semigroup, definition of Fuzzy normal semi bi-group, definition of Fuzzy normal semi tri-group, definition of Fuzzy normal semi – Quadratic group, definition of fuzzy normal semi- Pentant group and definition of Fuzzy normal semi –N groups are invented. Moreover, some properties and theorems of union in fuzzy normal based on these have been invented.

  Key-Words / Index Term
  Union of Fuzzy subsets, Fuzzy Normal semigroup, Fuzzy Normal semi-bigroup, Fuzzy Normal semi-trigroup , Fuzzy Normal semi – Quadratic group, Fuzzy Normal semi - Pendant group and Fuzzy Normal semi –N groups

  References
  [1]. Dr. S.Chandrasekaran, N. Deepica “Relation between Fuzzy subgroups and Anti- Fuzzy subgroups“ , IJIRST –International Journal for Innovative Research in Science & Technology| Volume 5 , Issue 9 , pp.1-5, February 2019 .
  [2]. Dr. S. Chandrasekaran, N.Deepica “Union of Fuzzy Sub-Quadradicgroups , Fuzzy Sub - Pendantgroups and Fuzzy Sub- N groups” - International Journal of Scientific Research in Science, Engineering and Technology (IJSRSET),Volume 6, Issue 1, page number : 303-311, January-February 2019.
  [3]. Dr. S.Chandrasekaran, N. Deepica “Algebraic Structure of Union of Fuzzy(Anti-Fuzzy)Normal Subgroups, Fuzzy(Anti-Fuzzy) Normal Sub – Bigroups And Soon Fuzzy (Anti-Fuzzy) Normal Sub – N groups “- International Journal of Scientific Research in Science, Engineering and Technology (IJSRSET), Volume 6 , Issue 1, page number: 312-322, January-February 2019.
  [4]. Dr.S.Chandrasekaran, N. Deepica, " Connectedness and Compactness of Fuzzy (Anti - Fuzzy) Subgroups and Fuzzy (Anti - Fuzzy) Normal Sub groups", International Journal of Scientific Research in Science, Engineering and Technology (IJSRSET), Volume 6 , Issue 1, page number : 392-401, January-February 2019.
  [5]. Dr.S. Chandrasekaran ,N. Deepica “Union of Anti - Fuzzy Sub - Quadradic groups , Anti - Fuzzy Sub - Pendant groups and Anti- Fuzzy Sub - N groups” , - International Research Journal of Pure Algebra - / IRJPA- 9(3), March-2019.,Page number : 1-11.
  [6]. N.Duraimanickam, N.Deepica –
  “Algebraic structure of union of fuzzy subgroups and fuzzy sub –bigroups” – National Conference on Emerging Trends in Mathematics - 2017 On 28th July 2017 - Organized by PG and Research Department of Mathematics, A. V. V. M. Sri Pushpam College (Autonomous), Poondi , Thanjavur (Dt.), Tamilnadu. - International journal of current Research and Modern education – Special issues , July – 2017 , ISSN: 2455-5428. Page Number : 95-99.
  [7]. N. Duraimanickam, N. Deepica–“Algebraic structure of union of fuzzy sub - trigroups and fuzzy sub –N groups”–International Journal of Advanced Research Publications, Volume 1, Issue 5, November 2017, Page Number : 374-378
  [8]. N. Duraimanickam, N. Deepica –Algebraic structure of union of Anti-fuzzy subgroups and Anti-fuzzy
  sub –bigroups and Anti- fuzzy
  Sub-trigroups”– In the Proceeding of the 2017 National Conference on Emerging Trends in Mathematical Techniques(NCETMT2017), Organized by PG Department of Mathematics, Sengamala Thayaar Educational Trust Women’s College Mannargudi , Tiruvarur (Dt.), Tamilnadu , India . Page Number : 56 - 64 .
  
  [9]. S.Arumugam,A.Thangapandi Isaac.-ModernAlgebra-SciTech Publications (India) Pvt. Ltd.(2003) .
  [10]. R. Muthuraj, M. Rajinikannan , M.S. Muthuraman – A Study on Anti- Fuzzy Sub –bigroup – International Journal of Computer Applications Volume 2 –No.1,May 2010 (0975- 8887) .
  [11]. S. Nanda, N.R .Das. - Fuzzy Mathematical concepts. - Narosa Publishing House Pvt. Ltd. (2010).
  [12]. G . Nirmala, S. Suganthi - Fuzzy Sub - Trigroup – Trilevel Properties.- International Journal of Scientific and Research Publications,Volume 2, Issue 6, June 2012.
  [13]. G . Nirmala, S. Suganthi - - Fuzzy Sub-Trigroup – Characteristics.-International Journal of Scientific and Research, Volume: 2, Issue: 11, November 2013.
  [14]. W.B .Vasanthakandasamy - Smarandache Fuzzy Algebra.

  Citation
  N. Deepica, "Union of Fuzzy Normal Semi- “N” Groups and Anti- Fuzzy Normal Semi- “N” Groups (for n= 1,2,….n)," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.6, Issue.6, pp.96-104, 2019

• Open Access   Article

  Some Non-Extendable Diophantine Triples Involving Centered Square Numbers

  C. Saranya, G. Janaki

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.6 , Issue.6 , pp.105-107, Dec-2019

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  Abstract
  In this paper, we accomplish three non-extendable Diophantine triples of the form {a, b, 2(a+b-Square of the difference of the ranks)} involving centered square numbers with property D(-Square of the difference of the ranks).

  Key-Words / Index Term
  Diophantine Triples, Centered Square Number, Non-extendability

  References
  [1] Carmichael, R.D. “History of Theory of numbers and Diophantine Analysis”, Dover Publication, Newyork, 1959
  [2] Mordell, L.J. “Diophantine equations”, Academic press, London, 1969
  [3] Nagell, T. “Introduction to Number theory”, Chelsea publishing company, Newyork, 1981
  [4] Hua, L.K. “Introduction to the Theory of Numbers”, Springer-Verlag, Berlin-Newyork, 1982
  [5] Oistein Ore, “Number theory and its History”, Dover publications, Newyork, 1988
  [6] Fujita, Y. “The extendability of Diphantine pairs ”, Journal of Number Theory, 128, 322-353, 2008
  [7] Gopalan, M.A. and Pandichelvi, V., “On the extendability of the Diophantine triple involving Jacobsthal numbers ”, International Journal of Mathematics & Applications, 2(1), 1-3, 2009
  [8] Janaki, G. and Saranya, C., “Special Dio 3-tuples for pentatope number”, Journal of Mathematics and Informatics, vol.11, Special issue, 119-123, 2017
  [9] Janaki, G. and Saranya, C., “Construction of the Diophantine Triple involving Pentatope Number”, International Journal for Research in Applied Science & Engineering Technology, vol.6, issue III, 2317-2319, 2018
  [10] Saranya, C. and G.Janaki, G., “Integer triples comprising of Jarasandha numbers in Arithmetic progression & Geometric progression”, International Journal of Research and Analytical Reviews, vol.6, issue 1, 751-752, 2019
  [11] Gopalan, M.A, Vidhyalakshmi, S. and Thiruniraiselvi, N., “Some non-extendable diophantine triples in special number patterns”, International Journal of Innovative research and Review, Vol. 2 (3), pp.1-7, 2014

  Citation
  C. Saranya, 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, pp.105-107, 2019

• Open Access   Article

  A New Modified Product Estimator for Estimation of Population Mean when Median of the Auxiliary Variable is known

  M. Zahid Hasan, M. Ali Hossian, M. Sultana, K. Fatema, M. Murad Hossain

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.6 , Issue.6 , pp.108-113, Dec-2019

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i6.108113

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  Abstract
  In the present paper, it has been proposed a new modified product estimator of population mean when the median of the auxiliary variable is known. The paper clearly states those product estimators are used when correlation between study variable and auxiliary variable is negative. Then we have defined the proposed estimator and derived bias, mean square error of the same. A theoretical analysis from comparison shows improved performance in our proposed estimator. Further from numerical study the calculated mean square error and bias stamps the performance. The paper ends by showing high rations of the existing estimator to the proposed one.

  Key-Words / Index Term
  Auxiliary Variable, Bias, Mean Squared Error, Modified Product Estimator, Simple Random Sampling

  References
  [1] Subramani, J. A new median based ratio estimator for estimation of the finite population mean. Statistics in Transition. New Series, 17(4), 591-604, 2016
  [2] Subramani, J. A new modified ratio estimator for estimation of population mean when median of the auxiliary variable is known. Pakistan Journal of Statistics and Operation Research, 9(2), 137-145, 2013
  [3] Subramani, J., & Kumarapandiyan, G. Estimation of population mean using known correlation coefficient and median. Journal of Statistical Theory and Applications, 13(4), 333-343, 2014
  [4] Subramani, J., & Kumarap, G. Modified ratio estimators for population mean using function of quartiles of auxiliary variable. Bonfring International Journal of Industrial Engineering and Management Science, 2(2), 19-23, 2012
  [5] Shittu, O. I., & Adepoju, K. A. On the efficiency of modified ratio estimator based on linear combination of kurtosis, median and quartile deviation. International Journal of Modern Mathematical Sciences, 11(2), 103-107, 2014
  [6] Subramani, J., & Prabavathy, G. Median based modified ratio estimators with known quartiles of an auxiliary variable. Journal of Modern Applied Statistical Methods, 13(1), 15, 2014
  [7] Subramani, J., & Kumarapandiyan, G. Estimation of population mean using known median and co-efficient of skewness. American Journal of Mathematics and Statistics, 2(5), 101-107, 2012
  [8] Subramani, J., & Prabavathy, G. MEDIAN BASED MODIFIED RATIO ESTIMATORS WITH KNOWN SKEWNESS AND CORRELATION COEFFICIENT FOR THE ESTIMATION OF FINITE POPULATION MEAN. Journal of Reliability and Statistical Studies, 8(1), 2015
  [9] Kumar, S. An estimator of the mean estimation of study variable using median of auxiliary variable. Sri Lankan Journal of Applied Statistics, 16(2), 2015
  [10] Subramani, J., & Kumarapandiyan, G. Estimation of population mean using co-efficient of variation and median of an auxiliary variable. International Journal of Probability and Statistics, 1(4), 111-118, 2012
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  [12] Singh, S. Advanced Sampling Theory With Applications: How Michael"" Selected"" Amy (Vol. 2). Springer Science & Business Media, 2003
  [13] Yadav, S. K., Gupta, S., Mishra, S. S., & Shukla, A. K. Modified Ratio and Product Estimators for Estimating Population Mean in Two-Phase Sampling. American Journal of Operational Research, 6(3), 61-68, 2016
  [14] Sukhatme, P. V. Sampling theory of surveys with applications. The Indian Society Of Agricultural Statistics; New Delhi, 1957
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  [17] Md. Zahid Hasan, Ali Hasan, A New Regression Type Estimator and its Industrial Application, Conference paper, 1st national Conference on Application of Statistics on Sustainable Development Goals, Tangail, Bangladesh, 2018

  Citation
  M. Zahid Hasan, M. Ali Hossian, M. Sultana, K. Fatema, M. Murad Hossain, "A New Modified Product Estimator for Estimation of Population Mean when Median of the Auxiliary Variable is known," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.6, Issue.6, pp.108-113, 2019