Mathematics and Computational Sciences
https://mcs.qut.ac.ir/
Mathematics and Computational Sciencesendaily1Tue, 04 Apr 2023 00:00:00 +0430Tue, 04 Apr 2023 00:00:00 +0430Polynomial collocation method for initial value problem of mixed integro-differential equations
https://mcs.qut.ac.ir/article_703978.html
This paper presents the development and implementation of a numerical method forthe solution of one dimensional Mixed Fredholm Volterra Intergro-Differential Equations(MFVIDEs). The new technique transformed MFVIDEs into an integral equation whichis then approximated using a polynomial collocation method. Standard collocation pointsare then used to convert the problem into a system of algebraic equations. Some numericalexamples are used to test the efficiency and accuracy of the method. The results showthat the new method is efficient, accurate and easy to implement.An extension of Lagrange interpolation formula and its applications
https://mcs.qut.ac.ir/article_703977.html
In this work, a new type of interpolation formulas is introduced. These formulas can be an extension of the Lagrange interpolation formula. The error of this new type of interpolation is calculated. In order to display efficiency of the proposed formulas, three numerical examples are presented.On $\partial-$locally compact space
https://mcs.qut.ac.ir/article_705143.html
The aim of this paper is to introduce and give preliminary investigation of $\partial-$locally compact spaces. Locally compactness and $\partial-$locally compactness are independent of each other. Every locally compact Hausdorff space is $\partial-$locally compact. But the converse is not true even though it be Hausdorff. $\partial-$locally compactness is a topological property. $\partial-$locally compactness is not preserved by the product topology.A Linear Mathematical Model for the Transmission Dynamics of Diabetes Mellitus
https://mcs.qut.ac.ir/article_705144.html
Diabetes mellitus is a global health problem, escalating at a disturbing rate dueto unbalanced lifestyles and some underlying health issues. In this work, a system offirst-order linear ordinary differential equations as well as numerical simulations wereemployed to gain insight into the dynamics of the disease. The theoretical outcomeof the analysis was derived in terms of the model parameters while computer simula-tion was used to assess the behaviour of the model in terms of the parameters values.Both the theoretical and numerical studies of the model revealed lifestyles and ef-fective treatment as the parameters to be targeted for effective reduction in bothdiabetes prevalence and mortality. It is therefore concluded that diabetes prevalenceand mortality reduction is a function of adjustment in unbalanced lifestyles as wellas improvement in diabetes treatment.Numerical modelling of double integration with different data spacing: A Python-based approach
https://mcs.qut.ac.ir/article_703976.html
In this article, an attempt has been made to model the process of double integration for different data spacing. The trapezoidal rule has been used to perform integration, whereas Newton's divided difference handles the inconsistent data points. The whole process of numerical integration has been automated in Python programming language. The developed code is tested against two example problems, and the results obtained agree with the one shown in the literature.Improving augmented reality with the help of deep learning methods in the tourism industry
https://mcs.qut.ac.ir/article_705129.html
From an economic point of view, the tourism industry has a special place. Especially in the single-product economy of Iran, it can be used as the best and most optimal alternative to oil. Augmented reality technology is one of the world&#039;s newest and most up-to-date applied technologies, highly regarded today. This research focuses on augmented reality and its patterns. This research aims to investigate and develop a practical pattern identification of augmented reality (ar) and its tracking in the tourism industry. Designs are provided by capturing the position and orientation of the device and its location using sensors and Computer vision with screen technology (augmented reality guide). A guide is designed, implemented, and evaluated as an augmented reality application on a mobile phone. The proposed solution has been using deep learning in marker identification. The deep learning architecture used is Yolo, and the proposed method&#039;s marker identification results have an accuracy of 68.73 mapsApproximate solutions of Klein-Gordon equation with equal vector and scalar modified Mobius square plus Kratzer potentials with centrifugal term.
https://mcs.qut.ac.ir/article_703308.html
In this study, we present the analytical solutions of Klein-Gordon equation with modified Mobius square plus Kratzer potential. The energy spectrum and wave functions are obtained via the parametric Nikiforov-Uvarov (NU) method by assuming equal scalar and vector potential. The non relativistic limit is obtained and numerical results are presented. In addition, the energy eigenvalues are obtained for special cases of this potential. Our results show that energy decreases with the screening parameter.Numerical solution to Volterra integro-differential equations using collocation approximation
https://mcs.qut.ac.ir/article_703306.html
This paper considers the collocation method for the numerical solution of the Volterra integro- differential equation using polynomial basis functions. The modeled equation was converted into a linear algebraic system of equations and matrix inversion was employed to solve the algebraic equation. We substitute the result of algebraic into the approximate solution to obtain the numerical result. Some numerical problems are solved to show the method's efficiency and consistency.On a fractional differential equation with fractional boundary conditions
https://mcs.qut.ac.ir/article_703307.html
In this article, we study a new nonlinear Langevin equation of two fractional orders with fractional boundary value conditions which is a generalization of previous Langevin equations. Based on Banach and Schauder fixed point theorems, the existence and uniqueness of solutions of this equation are investigated. Moreover, our hypotheses are simpler than similar works.Numerical solution of eight order boundary value problems using Chebyshev polynomials
https://mcs.qut.ac.ir/article_703309.html
First-kind Chebyshev polynomials are used as the basis functions in this study to present the approximations to the eighth-order boundary-value problems. The problem is reduced using the suggested approach into a set of linear algebraic equations, which are then solved to determine the unknown constants. To demonstrate the application and effectiveness of the strategy, analytical results are provided using tables and graphs for three examples. The results obtained using the proposed method reveal that it is simple and outperforms comparable solutions in the literature.Facial recognition system using eigenfaces and PCA
https://mcs.qut.ac.ir/article_703305.html
Face recognition is an essential field of image processing and computer vision. In this paper, we have developed a facial recognition system that can detect and recognize the face of a person by comparing the characteristics, and features of the face to those of known faces. Our approach considers the face recognition problem as an intrinsically two-dimensional recognition problem rather than requiring recovery of three-dimensional geometry, considering that eigenvectors generally describe human faces in the face space. The system works by projecting face images onto a feature space that spans the significant variations among known face images that are called eigenvectors (or principal components of the face set). Our technique can learn and recognize new faces in an unsupervised style&mdash;this approach is based on eigenfaces and principal component analysis (PCA).Linear programming for instant complimentary food formulations among Tanzanian infants aged 6 to 23 months
https://mcs.qut.ac.ir/article_703304.html
It is challenging to follow all nutritional requirements simultaneously. A good mathematical tool for converting nutrient-based suggestions into realistically nutritionally ideal food combinations integrating locally accessible foods is the diet optimization model. The objective of this study is to design a linear programming model that figures out how many grams of each food type need to be mixed to produce an instant meal complement for infants between the ages of 6 and 23 months. The mathematical model developed computes the grams of each food type &ndash; Quelea mixed with either Green Banana or White Rice or Irish Potato and Onions, Tomatoes, Carrots and Green bell Pepper. When those foods were combined, an instant food complement will be created and entirely satisfy the preset needs of malnourished infants. Thus, Tanzanian public health technologists and nutritionists may apply the linear programming approach explored in this study to create new ready-to-use food formulations.Approximation of inverse source problem for time fractional pseudo-parabolic equation in $L^p$
https://mcs.qut.ac.ir/article_703893.html
In this work, we focus on the final value problem of an inverse problem for the pseudo-parabolic equation. This study aims to provide a regularization method for this equation, once the measurement data are obtained at the final time in $L^{r}(0,\pi)$. We obtain an approximated solution using the Fourier method and the final input data $L^{r}(0,\pi)$ for $r \neq 2$. Using embedding between $L^{r}(0,\pi)$ and Hilbert scales $\mathcal{H}^{\rho}(0,\pi)$, this study is the error between the exact and regularized solutions to be estimated in $L^{r}(0,\pi)$.