Matrix Science Mathematic (MSMK)

A CONDITIONAL MARGINAL APPROACH IN MULTIVARIATE POISSON REGRESSION MODEL

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msmk.02.2024.74.77

ABSTRACT

A CONDITIONAL MARGINAL APPROACH IN MULTIVARIATE POISSON
REGRESSION MODEL

Journal: Matrix Science Mathematic (MSMK)
Author: Janardan Mahanta, Soma Chowdhury Biswas

This is an open access article distributed under the Creative Commons Attribution License CC BY 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited

DOI: 10.26480/msmk.02.2024.74.77

In recent times, the conditional marginal modeling approach has emerged as a new area in longitudinal studies; a new multivariate Poisson regression model has been proposed for count data, the model’s validity was assessed using simulation techniques, followed by fitting the model to real data from the Health and Retirement Study, and the correlation coefficients of the response variable’s impact among the first, second, and third follow-up were estimated.
Pages 74-77
Year 2024
Issue 2
Volume 8

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msmk.01.2024.24.26

ABSTRACT

FIBONACCI SEQUENCES AND IT’S COMPLETENESS

Journal: Matrix Science Mathematic (MSMK)
Author: Nand Kishor Kumar

This is an open access article distributed under the Creative Commons Attribution License CC BY 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited

DOI: 10.26480/msmk.01.2024.24.26

This paper attempts to describe the Fibonacci numbers, their qualities, completeness, and mathematical completeness; the Fibonacci sequence may be seen in a number of stunning natural events; as a result, this paper begins by introducing the Fibonacci sequence and then goes on to discuss some of its properties; the Fibonacci sequence is mathematically complete, as well as having natural and artistic manifestations; the series itself is infinite, and any positive integer may be expressed as the sum of individual Fibonacci numbers; the Fibonacci sequence and golden ratio act as testimonies; the Fibonacci sequence, which has ancient mathematical foundations, continues to fascinate our minds and show subtle patterns in a variety of fields; as we interpret the complexities of these mathematical masterworks, we develop a better understanding of how mathematics and the world around us.
Pages 24-26
Year 2024
Issue 1
Volume 8

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msmk.02.2024.69.73

ABSTRACT

ON FUNCTIONAL SERIES WITH APPLICATIONS TO ROOT FINDING TECHNIQUES AND TO ORDINARY DIFFERENTIAL EQUATIONS

Journal: Matrix Science Mathematic (MSMK)
Author: Mehmet Pakdemirli

This is an open access article distributed under the Creative Commons Attribution License CC BY 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited

DOI: 10.26480/msmk.02.2024.69.73

The approximate equivalence of functions is defined with respect to Taylor series expansions first. Based on the approximate equivalence, approximation of a given function with other functional series is discussed. The theory is first applied to root finding iteration algorithms. Then the solution of ordinary differential equations is treated as the next application. Several numerical sample problems are considered. It is shown that the formalism can be effectively used in determining the roots of algebraic equations or finding the solutions of differential equations. To increase the precision of the solutions, higher order approximations should be taken.
Pages 69-73
Year 2024
Issue 2
Volume 8

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msmk.02.2024.35.41

ABSTRACT

ON LOGISTIC GROWTH MODELS BY USING THE FRACTIONAL CAPUTO-FABRIZIO DERIVATIVE

Journal: Matrix Science Mathematic (MSMK)
Author: M.O. Aibinu, F.M. Mahomed

This is an open access article distributed under the Creative Commons Attribution License CC BY 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited

DOI: 10.26480/msmk.02.2024.35.41

This paper considers the conventional logistic model and how to obtain the solutions of fractional differential equations. It examines using a hybrid of Sumudu transform method, which is an approximate analytical method for solving fractional differential equations that are associated with time delay. Furthermore, the paper introduces the fractional Caputo-Fabrizio derivative and proportional time delay into the conventional logistic model to propose a general and more logistic model for the population growth. The paper considers different cases of the newly introduced general logistic model and using a hybrid of Sumudu transform method, their solutions were obtained. Using MATLAB, it displays and compares the behaviour of different cases of the general logistic model with fractional Caputo-Fabrizio derivative and proportional time delay.
Pages 35-41
Year 2024
Issue 2
Volume 8

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msmk.01.2024.20.23

ABSTRACT

BERNOULLI COLLOCATION FOR SOLVING TWO-POINT BVP IN MODELLING VISCOELASTIC FLOWS

Journal: Matrix Science Mathematic (MSMK)
Author: Mohamed El-Gamel, Mahmoud Abd El Hady

This is an open access article distributed under the Creative Commons Attribution License CC BY 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited

DOI: 10.26480/msmk.01.2024.20.23

Bernoulli bases are developed to approximate the solutions of two-point BVP in modelling viscoelastic flows in which the shifted Chebyshev collocation points are used as collocation nodes. Properties of Bernoulli bases are then used to reduce the two-point BVP in modelling viscoelastic flows to systems of nonlinear algebraic equations. The results show the agreement between the exact solutions and the approximate solutions. Form the numerical results we see that the proposed method gives accurate results.
Pages 20-23
Year 2024
Issue 1
Volume 8

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msmk.02.2024.59.68

ABSTRACT

DERIVATION AND IMPLEMENTATION OF A-STABLE DIAGONALLY IMPLICIT HYBRID BLOCK METHOD FOR THE NUMERICAL INTEGRATION OF STIFF ORDINARY DIFFERENTIAL EQUATIONS

Journal: Matrix Science Mathematic (MSMK)
Author: Alhassan B., Musa H., Yusuf H., Adamu A., Bello A., Hamisu A

This is an open access article distributed under the Creative Commons Attribution License CC BY 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited

DOI: 10.26480/msmk.02.2024.59.68

A new 2-point hybrid block method for the numerical solution of first-order stiff systems of ordinary differential equations in initial value problems with optimal stability property is presented. The necessary and sufficient conditions for the convergence of the proposed implicit block numerical scheme for solving stiff ODEs are established. The stability and convergence analysis of the method show that it is consistent, zero-stable, and convergent. The absolute stability region of the method is plotted, indicating that the method is A-stable. The method is implemented in Microsoft Dev C++ environment using the C programming language and Newton’s iteration, and some selected first-order stiff initial value problems are solved. The numerical results obtained for the proposed method are compared with the existing fifth order fully implicit 2-point block backward differentiation formula and 2-point block backward differentiation formula with two off-step points methods. The comparison reveals that the new method outperforms both methods in terms of accuracy but are competing in terms of computation time as we reduce the step size. It is evident that the method converges faster.
Pages 59-68
Year 2024
Issue 2
Volume 8

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msmk.02.2024.53.58

ABSTRACT

THE VISUAL WEIGHING METHOD OF MINING DUMP ATRUCK BASED ON RESNET

Journal: Matrix Science Mathematic (MSMK)
Author: Kai Bai, Likun Zhao, Wenqing Che, Beijun Guo, and Zhanlong Li

This is an open access article distributed under the Creative Commons Attribution License CC BY 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited

DOI: 10.26480/msmk.02.2024.53.58

Intelligent weighing systems play a significant role in guiding coal production and assisting production decisions. However, the traditional weighing method not only cannot guarantee efficiency, but also is prone to artificial fraud, causing economic losses to enterprises. In view of the needs of industrial production, this paper studies a visual weighing method for mining dump trucks with ResNet deep learning network as the core. Firstly, the collected dataset is processed by the Resize function and the Blend function, and then the ResNet neural network is trained with the processed dataset, and finally the cross-entropy loss function and Adam optimization strategy are used to improve the recognition accuracy. The results show that the final recognition accuracy is 60%.
Pages 53-58
Year 2024
Issue 2
Volume 8

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msmk.02.2024.42.52

ABSTRACT

A NEW TYPE OF OPERATION FOR SOFT SETS: SOFT BINARY PIECEWISE STAR OPERATION

Journal: Matrix Science Mathematic (MSMK)
Author: Aslıhan Sezgin, Eda Yavuz

This is an open access article distributed under the Creative Commons Attribution License CC BY 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited

DOI: 10.26480/msmk.02.2024.42.52

Soft set theory gained popularity as a cutting-edge approach to handling uncertainty-related problems and modeling uncertainty when it was introduced by Molodtsov in 1999. It may be applied in a variety of contexts, both theoretical and practical. This paper introduces a new soft set operation called the “soft binary piecewise star operation.” Its basic algebraic characteristics are thoroughly examined. Moreover, this operation’s distributions over various soft set operations are obtained. We prove that the soft binary piecewise star operation is a commutative semigroup under certain conditions and is also a right-left system. Furthermore, we show that the collection of soft sets over the universe, along with the soft binary piecewise star operation and some other types of soft sets, form many important algebraic structures, such as semirings and near-semirings, by considering the algebraic properties of the operation and its distribution rules together.
Pages 42-52
Year 2024
Issue 2
Volume 8

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msmk.02.2024.31.37

ABSTRACT

ON LOGISTIC GROWTH MODELS BY USING THE FRACTIONAL CAPUTO-FABRIZIO DERIVATIVE

Journal: Matrix Science Mathematic (MSMK)
Author: M.O. Aibinu, F.M. Mahomed

This is an open access article distributed under the Creative Commons Attribution License CC BY 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited

DOI: 10.26480/msmk.02.2024.31.37

This paper considers the conventional logistic model and how to obtain the solutions of fractional differential equations. It examines using a hybrid of Sumudu transform method, which is an approximate analytical method for solving fractional differential equations that are associated with time delay. Furthermore, the paper introduces the fractional Caputo-Fabrizio derivative and proportional time delay into the conventional logistic model to propose a general and more logistic model for the population growth. The paper considers different cases of the newly introduced general logistic model and using a hybrid of Sumudu transform method, their solutions were obtained. Using MATLAB, it displays and compares the behaviour of different cases of the general logistic model with fractional Caputo-Fabrizio derivative and proportional time delay.
Pages 31-37
Year 2024
Issue 2
Volume 8

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msmk.02.2024.28.34

ABSTRACT

GENERALIZATION OF BURR DISTRIBUTION AND INTRODUCTION OF A NEW FAMILY OF STATISTICAL DISTRIBUTIONS

Journal: Matrix Science Mathematic (MSMK)
Author: Iravani Hossein, Yari Gholamhossein

This is an open access article distributed under the Creative Commons Attribution License CC BY 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited

DOI: 10.26480/msmk.02.2024.28.34

The family of Burr distributions consists of twelve different distributions that result from solving a differential equation. This family is part of the family of continuous distributions and its applications have been investigated in various topics such as survival function, simulation problems, and economic and insurance analyses. Since the flexibility of the generalized distributions is often greater than the distribution itself, the generalization of the distributions of this family is of great interest. Also, due to the diversity of the distribution type, various generalizations of the Burr distribution have been presented. Regarding the importance of generalized distributions in this family, it is enough that the family of Burr distributions can be considered a parametric generalized family. In this article, it is intended to present a generalization of the Burr distribution, which results in the special case of the type II Burr distribution; In this way, we add a parameter in the type II Burr distribution structure and by changing this parameter, we reach different Burr distributions, including the type II Burr distribution. The mentioned parameter along with other distribution parameters is estimated by the maximum likelihood method.
Pages 28-34
Year 2024
Issue 2
Volume 8

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