Volume-9 , Issue-6 , Dec 2022, ISSN 2348-4519 (Online) Go Back

• Open Access   Article

  Classification of Iris Flower Dataset using Different Algorithms

  S.A. Mithy, S. Hossain, S. Akter, U. Honey, S.B. Sogir

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.9 , Issue.6 , pp.1-10, Dec-2022

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  Abstract
  The Iris dataset is one of the most famous dataset containing data on four attributes named as Sepal.length, Sepal.width, Petal.length, Petal.width and three classes or subspecies named as Sentosa,Versicolor and Virginic each class has 50 samples. The measurement of four attributes in CM (centimeters). This data set was developed by Ronald Fisher in 1936. This is available on UCI data set. In this study we want to show that how to solve the classification problem using some algorithms like K-means clustering, Random Forest decision, SVM, Logistic Regression, KNN, K-medoids. In addition, we also worked on four features to a advanced feature. The scikit tool we use for implementation. In this study applies classification and regression algorithms on the iris dataset by discovering and analyzing the patterns.

  Key-Words / Index Term
  Iris dataset, Logistic Regression, k-nearest neighbors, Support Vector Machine, Random Forest, K-means clustering, K-medoids.

  References
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  Citation
  S.A. Mithy, S. Hossain, S. Akter, U. Honey, S.B. Sogir, "Classification of Iris Flower Dataset using Different Algorithms," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.9, Issue.6, pp.1-10, 2022

• Open Access   Article

  Exact Solutions of the (3+1) Generalized Fractional Nonlinear Wave Equation with Gas Bubbles

  U.A. Muhammad, A. Salisu

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.9 , Issue.6 , pp.11-24, Dec-2022

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  Abstract
  This article investigates exact desolate wave blend (solutions) for the fractional (3+1) generalized computational (nonlinear) wave equation (identification) with gas bubbles. Liquids with gas bubbles mainly arise in manifold or crowded applications like science, engineering, nature, and physics. We explored this model using some well-known ansatz techniques and the sine-cosine procedure. These procedure or methods yield different periodic and hyperbolic desalate wave blend (solutions). Moreover, solving the (3+1) Aspect (dimensional) generalized fractional nonlinear wave equation with gas bubbles is equivalent to solving many physical models, such as the (2+1)-dimensional Kadomtsev-Petviashvil model with gloomy despair, the (3+1)-dimensional Kadomtsev-Petviashvili model, the (3+1) dimensional(aspect) nonlinear waves with bubble liquid mixture, and other special cases of the considered model. Finally, we conspiracy both 2D and 3D as well as the curve plots to understand the physical application of the considered model using maple.

  Key-Words / Index Term
  Wave equation; gas bubbles; ansatz technique; sine-cosine method, desolate wave blend (solutions)

  References
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  Citation
  U.A. Muhammad, A. Salisu, "Exact Solutions of the (3+1) Generalized Fractional Nonlinear Wave Equation with Gas Bubbles," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.9, Issue.6, pp.11-24, 2022

• Open Access   Article

  On The Existence of Common Fixed Point in a Complete Metric Space Using Integral Type Contraction Conditions

  Mainak Mitra, Jigmi Dorjee Bhutia, Kalishankar Tiwary

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.9 , Issue.6 , pp.25-35, Dec-2022

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  Abstract
  The main objective of this paper is to introduce two new fixed point theorems involving more than one functions. Here in this article we will use some integral type contraction conditions and choose some suitable control functions to establish our result. We’ll further prove show that our result is a generalization of the result of Gupta et. al. which was introduced in 2020. Moreover we’ll see that our result will generate some other contraction conditions that will assure the existence of common fixed points.

  Key-Words / Index Term
  Almost Altering Distance, C-Class Function, Common Fixed Point, Compatible Mapping, Integral Type Contraction,Metric Space, Ultra Altering Distance.

  References
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  Citation
  Mainak Mitra, Jigmi Dorjee Bhutia, Kalishankar Tiwary, "On The Existence of Common Fixed Point in a Complete Metric Space Using Integral Type Contraction Conditions," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.9, Issue.6, pp.25-35, 2022

• Open Access   Article

  Article on the applications of the Jensen’s Inequality in Alternative proofs and Problems

  Toyesh Prakash Sharma

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.9 , Issue.6 , pp.36-42, Dec-2022

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  Abstract
  Since as it is mentioned in the title that through this article there, we will deal with various applications of the classic Jensen’s Inequality more clearly Weighted Jensen’s Inequality of both kinds of a convex function and concave function. Under the title applications, we will mainly discuss two aspects of it which are the application of Jensen inequality in proving well-known inequalities such as AM-GM inequality, GM-HM inequality, Cauchy-Schwarz Inequality, Nesbitt’s inequality, weighted AM-GM inequality, Power Mean Inequality etc. and another aspect is the application of Jensen’s Inequality in solving and simplifying problems proposals published in different journals on the basis of it there are example problems for readers.

  Key-Words / Index Term
  Jensen’s Inequality, Concave function, convex function, Weighted Jensen’s Inequality etc.

  References
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  Citation
  Toyesh Prakash Sharma, "Article on the applications of the Jensen’s Inequality in Alternative proofs and Problems," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.9, Issue.6, pp.36-42, 2022

• Open Access   Article

  A Purview and the inter-relations of “Fuzzy Sets, Intuitionistic Fuzzy Sets, Rough Sets, and their Extensions”

  Babita Mishra

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.9 , Issue.6 , pp.43-49, Dec-2022

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  Abstract
  The handling of uncertainty and vagueness is a very tough task for any decision-making body. It is not possible to mathematically formulate a realistic problem by ignoring the terms like uncertain and vague. Therefore taking into consideration such types of linguistic variables, it is an essential tool for any decision-maker to handle such types of situations by using “fuzzy sets, intuitionistic fuzzy sets, rough sets, etc.” In this paper, I would like to define fuzzy sets and how gradually all the extensions or purview as a “rough set, type-2 fuzzy set, and intuitionistic fuzzy sets” are developed have been discussed. The outline of this paper includes historical development, definitions, and the relevance of the topic through real-world examples. The most important feature of this paper is to incorporate the same example in different extensions to understand the difference and needs of the extensions. Also, the inter-relations of all the sets (cited above) have been discussed.

  Key-Words / Index Term
  Fuzzy sets, Rough set, Type-2 fuzzy set, Intuitionistic fuzzy sets, Uncertainty, Vagueness

  References
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  Citation
  Babita Mishra , "A Purview and the inter-relations of “Fuzzy Sets, Intuitionistic Fuzzy Sets, Rough Sets, and their Extensions”," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.9, Issue.6, pp.43-49, 2022

• Open Access   Article

  D-Optimal Design of Experiment for Bivariate Logistic Model Using Various Algorithms

  Kupolusi Joseph Ayodele

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.9 , Issue.6 , pp.50-55, Dec-2022

  Abstract

  Full-Text HTML

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  Abstract
  The optimality of a design can be obtained through various methods in practice. A set of values to locate support points to maximize the determinant of information matrix is sought through this method. Three methods are proposed in this study to finding optimality of a design for binary response variable of quadratic logistic regression model. The methods are namely grid search, Sobol sequence and Halton sequence that were considered to determine most efficient method through design efficiency and prediction error variance (PEV). The suggested design methods were evaluated and compared in simulation study of 10000 runs. The grid search approach outperformed the other two methods with the smaller value of PEV. The lower the PEV of a design, the better its performance for prediction.

  Key-Words / Index Term
  optimal design, general equivalence theorem, algorithms, quadratic logistic model

  References
  [1] Adebola, F.B., Fasoranbaku, O.A. & Kupolusi, J.A. On prediction error variance to determining optimal design of experiment for two variable quadratic logistic models.
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  [4] Fornius, E. F. Sequential Designs for Binary Data with the Purpose to Maximize the
  Probability of Response. Communications in Statistics - Simulation and Computation. 2008
  [5] Hovav A. Dror & David M Steinberg. Robust Experimental Design for Multivariate
  Generalized Linear Models , Technometrics. 2006
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  [7] Myers, R. H., D. C. Montgomery, G. G. Vining and T. J. Robinson. Generalized Linear Models with Applications in Engineering and the Sciences. 2nd edition Wiley, New York. 2010
  [8] Nelder, J.A. and Wedderburn, R.W.M. Generalized Linear Models. Journal of the Royal Statistical Society. Series A 135, 370-384. 1972

  Citation
  Kupolusi Joseph Ayodele, "D-Optimal Design of Experiment for Bivariate Logistic Model Using Various Algorithms," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.9, Issue.6, pp.50-55, 2022

• Open Access   Article

  Generalized Logarithmic Ratio and Product-Type Estimators in Simple Random Sampling (SRS)

  Nikita, S. Malik

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.9 , Issue.6 , pp.56-60, Dec-2022

  Abstract

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  Abstract
  The present study deals with a modified logarithmic ratio and product-type estimators in simple random sampling (SRS). The bias and mean square error (MSE) expressions based on the proposed estimator were obtained up to the first order of approximation. The proposed logarithmic ratio and product-type estimators outperform the classic simple mean, ratio, and product-type estimators. Some numerical datasets are used to illustrate and validate the theoretical results.

  Key-Words / Index Term
  Logarithmic ratio; Product-type estimators; Bias; Mean square error; Efficiency

  References
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  Citation
  Nikita, S. Malik, "Generalized Logarithmic Ratio and Product-Type Estimators in Simple Random Sampling (SRS)," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.9, Issue.6, pp.56-60, 2022

• Open Access   Article

  Matrix Modelling of Extended Generalized Fibonacci Polynomial

  Vaishali Billore, Naresh Patel

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.9 , Issue.6 , pp.61-64, Dec-2022

  Abstract

  Full-Text HTML

  References

  Citation

  Abstract
  In this paper, We Introduced Extended Generalized Fibonacci Polynomials. Further, described the matrix modelling of Extended Generalized Fibonacci Polynomial, Classical Fibonacci Polynomial, Lucas Polynomial, Pell Polynomial, Pell-Lucas Polynomial, Vieta Polynomial and Vieta-Lucas Polynomial.

  Key-Words / Index Term
  Extended Gibonacci Polynomial, Fibonacci Polynomial, Lucas Polynomial, Vieta Polynomial.

  References
  [1] T. Koshy, Fibonacci and Lucas number with application, Volume II, Wiley Hoboken, new Jersey, 2019.
  [2] T. Koshy, Fibonacci and Lucas Numbers with Applications, Toronto, New York, NY, USA, 2001.
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  [5] Alexandru Lupas, A Guide of Fibonacci and Lucas Polynomial, Octagon Mathematics Magazine, Vol.7, Issue.1, pp.2-12, 1999.
  [6] Christian Berg, Fibonacci numbers and orthogonal polynomials, Arab Journal of Mathematical Sciences, 17, pp.75-88, 2011.
  [7] S. Falcon and A. Plaza, On k-Fibonacci sequences and polynomials and their derivatives, Chaos, Solitons and Fractals, 39, pp.1005-1019, 2009.
  [8] K. Kaygisiz and A. Sahin, New Generalizations of Lucas Numbers, Gen. Math. Notes, Vol.10, Issue.1, pp.63-77, 2012.
  [9] V. Billore and N. Patel, Extended Gibonacci Polynomial with Determinant Identities, Design Engineering, 8, pp.7201–7209, 2021.
  [10] V. Kaladevi and C. Dhevaki, Matrix Modelling of 2 - (MY)^p sequence, Bulletin of Pure and Applied Sciences, Vol.31, Issue.2, pp.175-179, 2012.
  [11] V. Kaladevi and C. Dhevaki, Matrix Modelling of Generalized Fibonacci Like Polynomials, Bulletin of Pure and Applied Sciences, Vol.33, Issue.2, pp.95-103, 2014.
  [12] V. Kaladevi and C. Dhevaki, Matrix Modelling of Pell-Lucas-Kala Polynomials, Bulletin of Pure and Applied Sciences, Vol.33, Issue.2, pp.157-160, 2014.

  Citation
  Vaishali Billore, Naresh Patel, "Matrix Modelling of Extended Generalized Fibonacci Polynomial," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.9, Issue.6, pp.61-64, 2022