iosr-Jm   Volume-17 ~ Issue-2 ~ Mar. – Apr. 2021

Abstract: Starting with an infinite set of nonlinear equations for the Li-Keiper coefficients, we first specify a lower bound emerging from the infinite set and give a characterization of it. Then, we propose a possible new upper and lower bound for the coefficients in few of the partitions occurring in the cluster functions furnishing in a nonlinear way the coefficients. A numerical experiment up to n=15 confirms the proposed bounds and an experiment, i.e. the counting of the zeros in the binary representation of an integer for a constant related to the Glaisher-Kinkelin constant is also given up to n=32.

Keywords: Li-Keiper coefficients and an Infinite set of nonlinear Equations, partition function, partitions, Bell Numbers, upper and lower bounds, Glaisher-Kinkelin constant, Riemann Wave Background, Riemann Hypothesis.

[1]. D. Merlini, M. Sala, N. Sala: "A possible Non Negative lower bound on the Li-Keiper coefficients", IOSR Journal of Mathematics, Vol.15 Issue 6 (Ser. IV). pp. 01-16 (2019).
[2]. D. Merlini, M. Sala, N. Sala: "The binomials coefficients in the Riemann Wave Background: a possible proof of the Riemann Hypothesis", IOSR Journal of Mathematics, Vol.16, Ser. III (2020), pp. 22-36
[3]. D. Merlini, M. Sala, N. Sala: "Primitive Riemann Wave at Re(s)=0.9 and Application of Gauss-Lucas Theorem", Chaos and Complexity Letters, Vol. 14, Issue 1 (2020), NOVA SCIENCE, New-York, pp. 3-32.
[4]. K. Maslanka: "Effective method for computing Li's coefficients and their properties" Arxiv: math/0402168v5 (2004).
[5]. D. Merlini, M. Sala, N. Sala: "Spin system on a hexagon and Riemann hypothesis", IOSR Journal of Mathematics, Vol. 16, Issue 5 (Ser. II) (2020), pp.14-24.

Abstract: The agricultural sector of Fars province plays a substantial role in ensuring food security, production, and employment in Iran. Unfortunately, in recent decade wide areas of the province have been affected by drought phenomenon. Due to interdependence drought characteristics and the existence of ungagged areas, in this research, a regional bivariate analysis is proposed for meteorological drought analysis. The cluster analysis and the L-moments method is used to identify homogenous regions of Fars. For meteorological drought analysis of the monthly rainfall series, standardized precipitation index method is used and the crucial drought characteristics, namely drought duration and severity, are determined. Marginal probability distributions of these characteristics are identified by fitting Gamma and Exponential distributions. Three types of bivariate copulas (i.e., Frank, Clayton, and Gumbel–Hougaard) are evaluated for modeling......

Keywords: copula functions, l- moment method, Regional bivariate frequency analysis, Water-Supply

[1]. Aissia, M. Ben, Chebana, F., Ouarda, T. B. M. J., Bruneau, P., & Barbet, M. (2015). Bivariate index-flood model : case study in Québec , Canada, 60(2).
[2]. Bazrafshan, J., Hejabi, S., & Rahimi, J. (2014a). Drought monitoring using the multivariate standardized precipitation index (MSPI). Water Resources Management, 28(4), 1045–1060.
[3]. Bazrafshan, J., Hejabi, S., & Rahimi, J. (2014b). Drought Monitoring Using the Multivariate Standardized Precipitation Index (MSPI). Water Resources Management, 28(4), 1045–1060. https://doi.org/10.1007/s11269-014-0533-2
[4]. Chebana, F., & Ouarda, T. B. M. J. (2009). Index flood-based multivariate regional frequency analysis. Water Resources Research, 45(10), 1–15. https://doi.org/10.1029/2008WR007490
[5]. Deheuvels, P. (1979). La fonction de dependence empirique et ses proprietes, Un test non parametrique d'independance. Bulletin de La Classe Des Sciences, Academie Royale de Belgique, 5e Serie, 65, 274–292.

Abstract: In the presented article, we generalize the positive linear operator which is Kantorovich type with beta bases given by Dhawal. J. Bhatt et al. recently. We introduce the real positive parameters to generalize the operator, then prove uniform convergence for the sequence of this newly defined operators with the help of Korovkin's theorem. We estimate central and pointwise moments and also the rate of convergence through modulus of continuity. We have shown its asymptotic behaviors in terms of Voronovskaya type asymptotic formula. MSC(2020) : 41A36 ,41A10 ,47A58.

Keywords: Kantorovich operator, Beta bases, rate of convergence, Voronovskaya type asymptotic formula, modulus of continuity.

[1]. Bernstein, S.N, Demonstration du theoreme de Weierstrass fondee sur le calcul des probabilites, Communications of the Kharkov Mathematical Society no.13 (2) ,1-2(1912)
[2]. Kantorovich ,L.V. : Sur certains developments suivant les polynomes de la forme de S . Bernstein ,I,II. C.R. Acad Sci .USSR 20, 563-568(1930)
[3]. Korovkin ,P.P : On convergence of linear positive operators in the space of continuous functions. Dokl .Akad. Nauk 90,961-964(1953)
[4]. Aniol, G.: On the rate of pointwise convergence of the Kantorovich-type operators, Fasciculi Mathematici, 29 ,5-15 (1999)
[5]. Dogru, O. et al. : Approximation by Kantorovich type generalization of Meyer-Konig and Zeller operators ,Glasnik matematicki 36(2),311-318(2001)

Abstract: There are many problems of modeling process. Multicollinearity phenomenon one is happened when there are high collinearity between the independent variables. It makes hard to interpret the coefficients, and reduces the power of the model. In this paper, we tried to solve this problem using two methods. The first one used the ridge Regression model (RRM). It is compared with a traditional linear regression model (LRM). The second one modified the original dataset by differencing (using the function "diffM" in "MTS" package), and scaling (using the function "scale" in "base" package) processes. We supposed three cases of the independent variables for this justify this purpose. Independent, Dependent, and Combination linear cases. The simulation study is used to generate the dataset, with 500 observation for each variable, using R program. The "MASS" and the "ridg" packages, and their functions "lm.ridge", "check_collinearity()", and "Linear.Ridge" all are used to determine the variance inflation factor (VIF) for each independent variable to know whether the Multicollinearity is absent or.......

Keywords: Linear Regression Model; Ridge Regression Model; Ridge parameter; Multicollinearity; MASS package; Generate dataset.

[1]. S. Abubakari, Principal components to overcome multicollinearity problem, Oradea J. Busi. Econom. 4(1) (2019), 79-91.
[2]. R. B. Francoeur, Could sequential residual centering resolve low sensitivity in moderated regression? Simulations and cancer
symptom clusters, Open J. Statist. 03(06) (2013), 24-44.
[3]. G. James, D. Witten, T. Hastie and R. Tibshirani, eds., An Introduction to Statistical Learning: with Applications in R, Springer,
New York, 2013.
[4]. R. McElreath, Statistical Rethinking: A Bayesian Course with Examples in R and Stan, 2nd Edition, Chapman & Hall/CRC, 2020.
[5]. M. O'Brien, A Caution regarding rules of thumb for variance inflation factors, Quality & Quantity 41(5) (2007), 673-
690.doi:10.1007/s11135-006-9018-6.

Abstract: In this paper, we studied the theory of fuzzy rings, the concept of fuzzy ring with operators, fuzzy ideal and anti-fuzzy ideal with operators, fuzzy homomorphism with operators etc., and their some elementary properties.

Keywords: Fuzzy rings, fuzzy ring with operators, fuzzy ideal with operators, anti-fuzzy ideal, and homomorphism.

[1]. W.J.Liu, Fuzzy invariant subgroups and fuzzy ideals, Fuzzy sets and systems 8 (1982), 133-139.
[2]. Y.C.Ren, Fuzzy ideals and quotient rings, Fuzzy Math 4 (1985), 19 – 26.
[3]. T.K.Mukharjee and M.K.Sen, on fuzzy ideals of ring I, Fuzzy sets and systems 21 (1987), 99 – 104.
[4]. W.X.Gu, S.Y.Li and D.G.Chen, Fuzzy groups with operators, Fuzzy sets and systems 66 (1994), 363 – 371.
[5]. Q.Y.Xiong, Modern algebra, (Science and technology Publication, Shanghai,1978)

Abstract: This study is part of a larger study which explores the classroom students' contributions as implicative to their learning abilities in secondary school Mathematics. For this part, it uses both qualitative and quantitative research design of two teaching strategies on Sequence and Series (Arithmetic & Geometric Progression) in Mathematics. The qualitative method examines the students' contributions via the use of videotape and transcription. The quantitative part uses quasi-experimental research design of a pre-test and a post-test control group 2x3x2 factorial. Kuder- Richardson formula 21 (K-R, 21) method is used to determine the reliability of the instrument and the process returns reliability coefficients of 0.85 and 0.72 for pretest and posttest respectively.....

Keywords: students' contributions, learning abilities, Mathematics education

[1]. Afthina, H., Mardiyana&Pramudya, I. (2017). Think Pair Share Using Realistic Mathematics Education Approach in Geometry Learning. International Conference on Mathematics and Science Education (ICMScE.doi :10.1088/1742-6596/895/1/012025
[2]. Belhu, H. S. (2017). Factors Affecting Learning Mathematics in the Case Assosa University Collage of Natural Science. International Journal of Education, Culture and Society. Vol. 2, No. 1, pp. 6-12. doi: 10.11648/j.ijecs.20170201.12
[3]. Brodie, K. (2007a), Teaching with conversations: Beginnings and endings. For the Learning of Mathematics 27, 1. FLM Publishing Association, Edmonton, Alberta, Canada
[4]. Brodie, K. (2007b), Dialogue in mathematics classrooms: beyond question-and- answer methods https://www.researchgate.net/publication/266070649 Article in Pythagoras·October2007DOI:10.4102/pythagoras.v0i66.75
[5]. Brodie, K. (2008) Describing Teacher Change: Interactions between teacher moves and Learner contributions. In J..F. Matos, P. Valero & K. Yasukawa (Eds.). Proceedings of the Fifth International Mathematics Education and Society Conference. Lisbon