Qom University of Technology Mathematics and Computational Sciences 2717-2708 4 1 2023 03 01 Numerical solution to Volterra integro-differential equations using collocation approximation 1 8 703306 10.30511/mcs.2023.1978083.1099 EN Ganiyu Ajileye Department of Mathematics and Statistics, Federal University Wukari, Taraba State, Nigeria Sikiru A Amoo Department of Mathematics and Statistics, Federal University Wukari, Taraba State Journal Article 2022 12 04 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. https://mcs.qut.ac.ir/article_703306_902e36cd9368322687846123d4dad4e1.pdf
Qom University of Technology Mathematics and Computational Sciences 2717-2708 4 1 2023 03 01 On a fractional differential equation with fractional boundary conditions 9 17 703307 10.30511/mcs.2023.1987591.1106 EN Yasser Khalili Department of Basic Sciences, Sari Agricultural Sciences and Natural Resources University, 578 Sari, Iran, Milad Yadollahzadeh Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar 47416- 95447, Iran Journal Article 2023 01 16 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. https://mcs.qut.ac.ir/article_703307_542cf67a044ea0d396efa264e3b32ec3.pdf
Qom University of Technology Mathematics and Computational Sciences 2717-2708 4 1 2023 03 01 Numerical solution of eight order boundary value problems using Chebyshev polynomials 18 28 703309 10.30511/mcs.2023.1988829.1108 EN Musiliu Tayo Raji Department of Mathematics, Federal University of Agriculture, Abeokuta, Ogun State, Nigeria Christie Yemisi Ishola Department of Mathematics, National Open University of Nigeria Jabi, Abuja, Nigeria Olayemi Olutola Babalola Department of Mathematics and Statistics, Osun State College of Technology Esa Oke, Osun State, Nigeria Tawakalt Abosede Ayoola Department of Mathematics, Osun State University, Osogbo, Nigeria Nasiru Muhammed Momoh Department of Mathematics, Federal University of Technology Minna, Niger State, Nigeria. Olumuyiwa James Peter Department of Mathematical and Computer Sciences, University of Medical Sciences, Ondo City, Ondo State 0000-0001-9448-1164 Journal Article 2023 01 30 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. https://mcs.qut.ac.ir/article_703309_1ba6efe1fb096ae97b9033d5aa0c5642.pdf
Qom University of Technology Mathematics and Computational Sciences 2717-2708 4 1 2023 03 01 Facial recognition system using eigenfaces and PCA 29 35 703305 10.30511/mcs.2023.562662.1085 EN Hamid Reza Yazdani Iran University of Science and Technology, School of Mathematics, Tehran, Iran. 0000-0002-3556-4864 Ali Reza Shojaeifard Department of Mathematics and Statistics, Imam Hossein Comprehensive University, Tehran, Iran. Journal Article 2022 09 26 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—this approach is based on eigenfaces and principal component analysis (PCA). https://mcs.qut.ac.ir/article_703305_7e75d542da4fecc5c1c0dabc92143cea.pdf
Qom University of Technology Mathematics and Computational Sciences 2717-2708 4 1 2023 03 01 Linear programming for instant complimentary food formulations among Tanzanian infants aged 6 to 23 months 36 44 703304 10.30511/mcs.2023.561478.1080 EN Halidi Ally Lyeme Department of Mathematics, Faculty of Science, Muslim University of Morogoro, Morogoro, Tanzania 0000-0002-6139-3739 Leonard Katalambula bDepartment of Public Health and Community Nursing, University of Dodoma Journal Article 2022 09 04 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 – 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. https://mcs.qut.ac.ir/article_703304_8761d102a88c6195b0975132af94dc8f.pdf
Qom University of Technology Mathematics and Computational Sciences 2717-2708 4 1 2023 03 01 Approximation of inverse source problem for time fractional pseudo-parabolic equation in $L^p$ 45 57 703893 10.30511/mcs.2023.1990393.1111 EN Phong Thanh Tran Division of Applied Mathematics, Thu Dau Mot University, Binh Duong Province, Vietnam Long Dinh Le Division of Applied Mathematics, Science and Technology Advanced Institute Van Lang University, Ho Chi Minh City, Viet Nam Faculty of Applied Technology, School of Technology, Van Lang University, Ho Chi Minh City, Vietnam 0000-0001-8805-4588 Journal Article 2023 02 24 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 $L^{r}(0,\pi)$. https://mcs.qut.ac.ir/article_703893_d21afa1d1e996a0c865b31213980d906.pdf