iosr-Jm   Volume-19 ~ Issue-5 ~ Sep. – Oct. 2023

Abstract : Response Surface Methodology (RSM) and Central Composite Design (CCD) is an important statistical tool for modeling and analysis of statistical problems where the response of interest is influenced by several variables with the objective of optimizing the response. The purpose of this study was to optimize oil extraction from mango seed using Response Surface Methodology. The experimental design for this study had three factors at five levels. Central Composite Design, is more useful methodology for modelling a second order model for a response variable in a full factorial design of experiments. This research optimized extraction of oil from mango seeds which are readily......

Key Word: Oil Production; Central Composite Design; Mango Seeds Oil, Optimization

[1]. Box, G. E. P., And K. B. Wilson. "On The Experimental Designs For Exploring Response Surfaces." Ann Math Stat 13 (1951): 1-45.
[2]. Box, G.E.P And Hunter, J.S (1957). Multi-Factorial Experimental Designs For Exploring Response Surfaces. Ann.Math.Statist.28 195-241
[3]. Emil Akbar, Zahira Yaakob; Siti Kartom Kamarudin, Manal Ismail And Jum'at Salimon (2009) Characteristic And Composition Of Jatropha Curcas Oil Seed From Malaysia And Its Potential As Biodiesel Feedstock
[4]. Karunanithi, B., Bogeshwaran, K., Tripuraneni, M., & Krishna Reddy, S. (2015). Extraction Of Mango Seed Oil From Mango Kernel. International Journal Of Engineering Research And Development, 11(11), 32-41.
[5]. Mas'ud, F., Mahendradatta, M., Laga, A., & Zainal, Z. (2017). Optimization Of Mango Seed Kernel Oil Extraction Using Response Surface Methodology. OCL, 24(5), D503

Abstract : We construct a new equivalent of the Riemann Hypothesis by means of the first coefficient  1 alone. Some comments are also specified for.......

Key Word: : Equivalents, Li Keiper coefficients, Partition Function, Riemann Hypothesis.

[1]. Patterson , S . J . (1988). An Introduction To The Theory Of The Riemann Zeta Function, Cambridge Studies In Advanced Mathematics ,
14. Cambridge University Press , Cambridge ,
[2]. Edwards , H . M . (2001). Riemann's Zeta Function. Reprint Of The 1974 Original [ Academic Press , New York ]. Dover Publications ,
Inc ., Mineola , NY
[3]. Titchmarsh , E . C . (1986). The Theory Of The Riemann Zeta Function, Second Edition. Edited And With A Preface By D . R . Heath
Brown . The Clar endon Press , Oxford University Press , New York
[4]. Broughan , K . ( Equivalents Of The Riemann Hypothesis : Volume 2, Analytic Equivalents Vol . 165). Cambridge University
Press
[5]. Matiyasevich , Y . (2014). Yet Another Representation For The Sum Of Reciprocals Of The Nontrivial Zeros Of The Riemann Zeta
Fun ction. Arxiv Preprint Arxiv:1410.7036

Abstract : In this paper I have proposed a new algorithm to solve minimization and maximization assignment problem which gives the optimal solution directly without any iteration contrary to previous methods such as Hungarian methods. This method can be applied for both balanced and unbalanced assignment problems without using dummy cells as in Hungarian method. By this new approach we acheive the goal with less number of computational steps. We also provide some examples to illustrate the proposed method.

Key Word: Assignment problems, Balanced and unbalanced assignment problems, Dummy cell, Hungarian method, Optimal solution

[1]. Basirzadeh, H. (2012). Ones assignment method for solving assignment problems. Applied Mathematical Sciences, 6(47):2345–2355.
[2]. Bazaraa, M. S., Jarvis, J. J., and Sherali, H. D. (2011). Linear programming and network flows. John Wiley & Sons.
[3]. Gamal, M. (2014). A note on ones assignment method. Applied Mathematical Sciences, 8(40):1979–1986.
[4]. Ghadle, K. and Muley, Y. (2013). Revised ones assignment method for solving assignment problem. Journal of Statistics and Mathematics, 4(1):147–150.
[5]. Gupta, R. (1992). Operations research. Krishna Prakashan Media.

Abstract : Electric networks must be watched over constantly. Placing phase measuring units (PMUs) at certain network sites can effectively carry out this monitoring. The PMUs must be used in the smallest possible number due to their high cost. The goal of the power domination problem is to determine the bare minimum of PMUs required to monitor a specific electric power system. Despite the NP-hardness of the power domination problem, closed formulas for the power domination number of specific networks, like rectangular meshes [4], have been discovered. We apply these findings to triangular grids in this paper.

Key Word: Power domination; triangular grid graph.

[1]. R. Akhtar, T. Jiang, D.Pritikin, Edge Bandwidth Of The Triangular Grid, The Elect.Journal Of Combinatorics 14 (2007) #R67.
[2]. R. Barrera And D. Ferrero. Power Domination In Cylinders, Tori And Generalized Petersen Graphs, Submitted To Networks, 2009
[3]. P. Dorbec, M. Mollard, S. Klavˇzar And S. ˇspacapan. Power Domination In Product Graphs, Siam J. Discrete Math. 22 (2008) No. 2, 554-567.
[4]. M. Dorfling And M. A. Henning. A Note On Power Domination In Grid Graphs, Discrete Appl. Math. 154 (2006) 1023-1027
[5]. T. W. Haynes, S. M. Hedetniemi, S. T. Hedetneimi And M. A. Henning, Domination In Graphs Applied To Electric Power Networks, Siam J. Discrete Math. 15(2002) 519-529.

Abstract : Background: Most of the classical distributions of count data available in the literature have a univariate weighted Poisson version. This family of weighted Poisson distributions is therefore very useful for dealing with all forms of dispersion as a function of the data. The bivariate case has also been studied by Elion et al, and Nganga et al.
Methods: In this paper, we propose the generalization of weighted Poisson distributions to n-variables by constructing its multivariate probability density via the product of conditional distributions. We also present the structure of its variance-covariance.......

Key Word: Weighted Poisson, dispersion index, marginal distribution, generalized linear model.

[1] R. A. Fisher, "The effect of methods of ascertainment upon the estimation of frequencies," Ann. Eugen., vol. 6, no. 1, pp. 13–25, 1934.
[2] C. R. Rao, "Weighted Distributions Arising Out of Methods of Ascertainment: What Population Does a Sample Represent?" in A Celebration of Statistics, A. C. Atkinson and S. E. Fienberg, Eds., New York, NY: Springer, 1985, pp. 543–569. doi: 10.1007/978-1-4613-8560-8_24.
[3] C. C. Kokonendji and M. Pérez-Casany, "A note on weighted count distributions," J Stat Theory Appl, vol. 11, no. 4, pp. 337–352, 2012.
[4] C. C. Kokonendji, D. Mizère, and N. Balakrishnan, "Connections of the Poisson weight function to overdispersion and underdispersion," J. Stat. Plan. Inference, vol. 138, no. 5, pp. 1287–1296, May 2008, doi: 10.1016/j.jspi.2007.05.028.
[5] B. Efron and R. Tibshirani, "Bootstrap Methods for Standard Errors, Confidence Intervals, and Other Measures of Statistical Accuracy," Stat. Sci., vol. 1, no. 1, pp. 54–75, Feb. 1986, doi: 10.1214/ss/1177013815.

Abstract : In this article we studied various polar plots 𝑟=1+2𝑚𝑐𝑜𝑠 (𝜃) . We consider only five cases 𝑚=0,𝑚=1; 𝑚=2,𝑚=3; 𝑚=4; and 𝑚=5. In the application part we established some designs with the help of these polar plots.

Key Word: Cartesian coordinate System, Polar Coordinate System, Polar Equation, Plotting.

[1] K. C. Moore, T. Paoletti, And S. Musgrave, "Complexities In Students' Construction Of The Polar Coordinate System," Journal Of Mathematical Behavior, Vol. 36, 2014, Doi: 10.1016/J.Jmathb.2014.10.001.
[2] S. Ichi Amari, "Information Geometry," International Statistical Review, Vol. 89, No. 2, 2021, Doi: 10.1111/Insr.12464.
[3] S. I. Amari, "Information Geometry And Its Applications," In Applied Mathematical Sciences (Switzerland), Vol. 194, 2016. Doi: 10.1007/978-4-431-55978-8.
[4] F. Nielsen, "The Many Faces Of Information Geometry," Notices Of The American Mathematical Society, Vol. 69, No. 01, 2022, Doi: 10.1090/Noti2403.
[5] F. Opitz, "Information Geometry And Its Applications," In European Microwave Week 2012: "Space For Microwaves", Eumw 2012, Conference Proceedings - 9th European Radar Conference, Eurad 2012, 2012.

Abstract : .....

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