rss_2.0International Journal of Mathematics and Computer in Engineering FeedSciendo RSS Feed for International Journal of Mathematics and Computer in Engineering Journal of Mathematics and Computer in Engineering Feed the complex version of the Cahn–Hilliard–Oono type equation for long interactions phase separation<abstract> <title style='display:none'>Abstract</title> <p>This paper focuses on the complex version of the Cahn-Hilliard-Oono equation with Neumann boundary conditions, which captures long-range nonlocal interactions in the phase separation process. The first part of the paper establishes the well-posedness of the corresponding stationary problem associated with the equation. Subsequently, a numerical model is constructed using a finite element discretization in space and a backward Euler scheme in time. We demonstrate the existence of a unique solution to the stationary problem and obtain error estimates for the numerical solution. This, in turn, serves as proof of the convergence of the semi-discrete scheme to the continuous problem. Finally, we establish the convergence of the fully discrete problem to the semi-discrete formulation.</p> </abstract>ARTICLEtrue by nonlinear Meyer-König and Zeller operators based on -integers<abstract> <title style='display:none'>Abstract</title> <p>In this paper, we introduce the nonlinear Meyer-König and Zeller operators based on q-integers. Firstly, we describe the q-Meyer-König and Zeller operators of max-product type. Then, we give an error estimation for the q-Meyer-König and Zeller operators of max-product kind by using modulus of continuity.</p> </abstract>ARTICLEtrue some plant communities in a region of Türkiye via fuzzy similarity<abstract> <title style='display:none'>Abstract</title> <p>In this study, the results obtained from forest vegetation via the research project on plant sociology which conducted in Black Sea region of Türkiye is evaluated with the help of fuzzy similarity measures approach. Via this project, the plant sociology in an area which has not been studied in Black Sea region of Türkiye is performed to investigate the plant communities and ecological and sociological relationships with each other. The similarity relations among the plant communities and relevés (sampling areas) which they covered are investigated. The issue of fuzzy similarity of sets and elements in sets is studied. According to this point of view, the fuzzy similarity among the plant communities and among the relevés is introduced. This joint study is carried out in a fuzzy environment, considering the classical results found in the project in question to be obtained in more detail for application. It is also understood that such studies can only be the best performed with an interdisciplinary working group.</p> </abstract>ARTICLEtrue fractional factors in fuzzy graphs-II<abstract> <title style='display:none'>Abstract</title> <p>The fractional factor implicates the characteristics of fractional flow in network data transmission, and it is a crucial tool for analyzing network information transfer. When there is uncertainty information in the network, the corresponding network graph should be characterized by fuzzy graphs, in which the vertex membership function (MF) describes the uncertainty of sites, and the edge membership reveals the uncertainty of channels. The previous work introduced the concept of fuzzy fractional factor (FFF) on fuzzy graphs, but the correlated concepts are still open on other fuzzy graph classes. In order to overcome this defect, in this contribution, the concept of fuzzy fractional factor is extended to intuitionistic fuzzy graph, Pythagorean fuzzy graph, and picture fuzzy graph. Sign-alternating walk and increasing walk are extended to the corresponding settings, and the transformation operations are re-defined in light of various situations. By means of constructive approaches, the corresponding theoretical results are further generalized in these settings, which characterizes the existence of (resp. maximum) fuzzy fractional factors in different kinds of fuzzy graphs.</p> </abstract>ARTICLEtrue results for generalized Hurwitz-Lerch Zeta functions using laplace transform<abstract> <title style='display:none'>Abstract</title> <p>Fractional Kinetic equations (FKEs) including a wide variety of special functions are widely and successfully applied in describing and solving many important problems of physics and astrophysics. In this present work, the solutions of a FKEs of the generalized Hurwitz-Lerch Zeta function using the Laplace transform are derived and examined.</p> </abstract>ARTICLEtrue analysis and invariant solutions of generalized coupled Zakharov-Kuznetsov equations using optimal system of Lie subalgebra<abstract> <title style='display:none'>Abstract</title> <p>This research focuses on the examination of nonlinear evolution equations, with a specific emphasis on the generalized coupled Zakharov-Kuznetsov (CZK) equations serving as a primary example. Given the wide application of classical Lie symmetry methods in this field, our study employs a Lie symmetry analysis to investigate the CZK equations, as detailed in this research. Our methodology involves the construction of a nine-dimensional optimal system by leveraging the fundamental elements of the Lie algebra. Subsequently, we apply similarity reductions to the equations using each subalgebra. The resulting invariant solutions find diverse applications within the realm of physics and can also be adapted to solve a broad range of related nonlinear evolution equations. We meticulously validate all these solutions through a straightforward verification process. To enhance our comprehension of the physical implications of these solutions, we employ Mathematica simulations to visually represent various solution scenarios. Additionally, to preserve conservation laws, we incorporate Ibragimov’s novel conservation law theorem as a crucial component of our analysis.</p> </abstract>ARTICLEtrue coupled non-linear higher order BVPs using improved shooting method<abstract> <title style='display:none'>Abstract</title> <p>The focus of this paper is to use better algorithms for obtaining refined initial guesses with shooting method to solve the coupled boundary value problems. Boundary value problem is formulated as a system of equations i.e. initial value problems with one unknown initial conditions. The purpose of this work is to propose a new efficient initial guess algorithms rather than conventional Newton method to meet the adjoint terminal conditions, rapidly. The efficiency and accuracy of Shooting method is enhanced by improving initial guess and then solving the problem iteratively.</p> </abstract>ARTICLEtrue hierarchy of double, quadruple and octuple primes<abstract> <title style='display:none'>Abstract</title> <p>In this paper double, quadruple and octuple primes are discussed. Computational and theoretical properties as well as examples of quadruple and octuple primes are presented, where the octuple primes in most cases have primes between the defining quadruples although the existence of a pure quadruple prime has also been demonstrated computationally. The possibility of sixtentuple primes is also briefly discussed.</p> </abstract>ARTICLEtrue novel approach for Benjamin-Bona-Mahony equation via ultraspherical wavelets collocation method<abstract> <title style='display:none'>Abstract</title> <p>We develop a precise and efficient ultraspherical wavelet method for a famous Benjamin-Bona-Mahony (BBM) mathematical model. The suggested technique uses the collocation method and ultraspherical wavelets. The proposed scheme is applied to linear and nonlinear BBM equations to inspect the proposed technique’s efficiency and accuracy. This practical approach’s effectiveness has been verified. Moreover, the method based on the ultraspherical wavelets is simple, accurate, fast, flexible, and convenient. The results are analyzed using tables and graphs and compared with other methods in the literature. As we know, Many PDEs don’t have exact solutions, and some semi-analytical methods work based on controlling parameters, but this is a controlling parameter-free technique. Also, it is pretty simple to implement and consumes less time to execute the programs. The recommended wavelet-based numerical approach is interesting, productive, and efficient. The proposed technique’s convergence analysis is presented through the theorem.</p> </abstract>ARTICLEtrue of the stress-strain relations for viscoanelastic media and the heat equation in irreversibile thermodynamic with internal variables<abstract> <title style='display:none'>Abstract</title> <p>By using a procedure of classical irreversible thermodynamics with internal variables (CIT-IV), some possible interactions among heat conduction and viscous-anelastic flows for rehological media are studied. By introducing as a tensor ɛ <sup>(1)</sup> <sub>αβ</sub> which is contribution to inelastic strain and an vectorial internal variable ξ, which influence thermal and diffusion phenomena, phenomenological equation for these variables are derived. A general vector, <italic>J</italic>, is introduced which assumes the role of heat flux and it is shown that, in isotropic media, <italic>J</italic> can be composed of two parts and this allows to obtain a heat equation that generalizes both the Fourier equation and the Maxwell-Cattaneo-Vernotte (M-C-V) equation. A general temperature equation for viscoanelastic media is obtained.</p> </abstract>ARTICLEtrue the complex properties of the first equation of the Kadomtsev-Petviashvili hierarchy<abstract> <title style='display:none'>Abstract</title> <p>This work studies the first equation of the Kadomtsev-Petviashvili (KP) hierarchy. The sine-Gordon expansion method (SGEM) and the rational SGEM (RSGEM) are applied to the governing model. RSGEM is the developed version of SGEM. New complex travelling wave solutions, logarithmic and complex function properties are obtained. Several simulations such as 2D, 3D and contour surfaces of the obtained results are plotted. Physical meanings of these solutions are also reported. Strain conditions are also extracted.</p> </abstract>ARTICLEtrue forecast models using hybrid intelligent methods<abstract> <title style='display:none'>Abstract</title> <p>The aim of this study is to forecast the revenue of a seller taking part in an online e-commerce marketplace by using hybrid intelligent methods to help the seller build a solid financial plan. For this purpose, three different approaches are applied in order to accurately forecast the revenue. In the first approach, after applying simple preprocessing steps on the dataset, forecast models are developed with Random Forest (RF). In the second approach, Isolation Forest (IF) is used to detect outliers on the dataset, and minimum Redundancy Maximum Relevance (mRMR) is utilized to select the features that affect the quality of revenue forecast, correctly. In the last approach, a feature selection process is performed first and then the Density-Based Spatial Clustering and Application with Noise (DBSCAN) is used to cluster the dataset. After these processes are carried out, forecast models are developed with RF. The dataset used includes the daily revenue of a seller with several other features. Mean Absolute Percent Error (MAPE) is used for evaluating the performance of the forecast models.</p> </abstract>ARTICLEtrue numerical approach for an epidemic SIR model via Morgan-Voyce series<abstract> <title style='display:none'>Abstract</title> <p>This study presents the problem of spreading non fatal disease in a population by using the Morgan-Voyce collocation method. The main aim of this paper is to find the exact solutions of the SIR model with vaccination. The problem may be modelled mathematically with a nonlinear system of ordinary differential equations. The presented method reduces the problem into a nonlinear algebraic system of equations by using unknown coefficient Morgan-Voyce polynomials and expanding approximate solutions. Morgan-Voyce polynomials are used. These unknown coefficients are calculated via the collocation method and matrix operation derivations. Two examples are given to show the feasibility of the method. To calculate the solutions, MATLAB R2021a is used. Additionally, comparing our method to the Homotopy perturbation method (HPM) and the Laplace Adomian decomposition method (LADM) proves the accuracy of the solution. The method studied can be seen as effective from these comparisons. So, it is essential to find solutions for the governing model. The study will contribute to literature since we also discuss the vaccination situation. The results of this study are valuable for controlling an epidemic.</p> </abstract>ARTICLEtrue closed form solutions of some nonlinear pseudo-parabolic models via a new extended direct algebraic method<abstract> <title style='display:none'>Abstract</title> <p>Our investigation delves into a specific category of nonlinear pseudo-parabolic partial differential equations (PDEs) that emerges from physical models. This set of equations includes the one-dimensional (1D) Oskolkov equation, the Benjamin-Bona-Mahony-Peregrine-Burgers (BBMPB) equation, the generalized hyperelastic rod wave (HERW) equation, and the Oskolkov Benjamin Bona Mahony Burgers (OBBMB) equation. We employ the new extended direct algebraic (NEDA) method to tackle these equations. The NEDA method serves as a powerful tool for our analysis, enabling us to obtain solutions grounded in various mathematical functions, such as hyperbolic, trigonometric, rational, exponential, and polynomial functions. As we delve into the physical implications of these solutions, we uncover complex structures with well-known characteristics. These include entities like dark, bright, singular, combined dark-bright solitons, dark-singular-combined solitons, solitary wave solutions, and others.</p> </abstract>ARTICLEtrue determination from periocular images using deep learning based EfficientNet architecture<abstract> <title style='display:none'>Abstract</title> <p>In this study, we obtain a sex prediction algorithm based on CNN in two ways - building a red Convolutional Neural Network (CNN) model from scratch and via transfer learning. We built a model from scratch and compared it with fine-tuned EfficientNetB1. We use these models for gender determination using periocular images and compare the two models depending on the accuracy of the models. The CNN model proposed from scratch yields an accuracy of 94.46% while the fine-tuned EfficientNetB1 yields an accuracy of 97.94% . This paper is one of the first works in determining gender from periocular images in the visible spectrum using a CNN model built from the outset.</p> </abstract>ARTICLEtrue modeling using deep learning for the classification of grape-type dried fruits<abstract> <title style='display:none'>Abstract</title> <p>Dried grapes (or Raisins) are among the most frequently grown and consumed cereal crops worldwide. They are also an important source of nutrition and nourishment in a variety of countries including Türkiye, the United States, Greece, etc. In addition to that, raisins consist of 15% water, 79% carbs (including 4% fiber), 3% protein, and very little fat. In our study, there were a total of 900 raisin grains used, with 450 pieces from each type: Kecimen and Besni raisin. Seven morphological features were taken from these images after going through several steps of pre-processing. Since machine learning algorithms can analyze large datasets quickly, automatic classification is made possible. With enough training and testing, machine learning models can attain a high degree of precision in classifying raisin grains. They are able to detect variations in size, shape, color, and texture that would be difficult for humans to detect consistently. Eleven machine learning and five different types of artificial intelligence have been used to classify these features. As part of this study, we look into different machine learning and deep learning methods: GaussianNB, Decision Tree, K-Nearest Neighbor, Random Forest, Support vector machine (SVM), XGBoost, LightGBM, and AdaBoost, Logistic Regression, Artificial Neural Network and Deep Learning Network. Study efficacy is evaluated using standard metrics as F1 score and ROC area under the curve (AUC). Using the caret, H2O, neuralnet, and keras packages, AdaBoost and LightGBM, two of the fourteen models, achieve an accuracy of 90.30% and 98.40%, respectively, and a ROC curve score of around 90%.</p> </abstract>ARTICLEtrue second order numerical method for singularly perturbed Volterra integro-differential equations with delay<abstract> <title style='display:none'>Abstract</title> <p>This study deals with singularly perturbed Volterra integro-differential equations with delay. Based on the properties of the exact solution, a hybrid difference scheme with appropriate quadrature rules on a Shishkin-type mesh is constructed. By using the truncation error estimate techniques and a discrete analogue of Grönwall’s inequality it is proved that the hybrid finite difference scheme is almost second order accurate in the discrete maximum norm. Numerical experiments support these theoretical results and indicate that the estimates are sharp.</p> </abstract>ARTICLEtrue fractional calculus findings associated with the product of incomplete ℵ-function and Srivastava polynomials<abstract> <title style='display:none'>Abstract</title> <p>The generalized fractional calculus operators introduced by Saigo and Maeda in 1996 will be examined and further explored in this paper. By combining an incomplete ℵ-function with a broad category of polynomials, we create generalized fractional calculus formulations. The findings are presented in a concise manner that are helpful in creating certain lists of fractional calculus operators. The derived outcomes of a generic nature may yield results in the form of various special functions and in the form of different polynomials as special instances of the primary findings.</p> </abstract>ARTICLEtrue of differential equations using linearly independent Hosoya polynomials of trees<abstract> <title style='display:none'>Abstract</title> <p>We present an algorithm for the result of differential equations (DEs) by using linearly independent Hosoya polynomials of trees. With the newly adopted strategy, the desired outcome is expanded in the form of a collection of continuous polynomials over an interval. Nevertheless, compared to other methods for solving differential equations, this method’s precision and effectiveness relies on the size of the collection of Hosoya polynomials, and the process is easier. Excellent agreement between the exact and approximate solutions is obtained when the current scheme is used to crack linear and nonlinear equations. Potentially, this method could be used in more intricate systems for which there are no exact solutions.</p> </abstract>ARTICLEtrue text to threats: A language model approach to software vulnerability detection<abstract> <title style='display:none'>Abstract</title> <p>In the rapidly-evolving landscape of software development, the detection of vulnerabilities in source code has become of paramount importance. Our study introduces a novel knowledge distillation (KD) technique aimed at enhancing vulnerability detection in software codebases. Using benchmark datasets such as SARD, SeVC, Devign, and D2A, we assess the prowess of the KD method when applied to different classifiers, specifically GPT2, CodeBERT, and LSTM. The empirical results are revealed a marked improvement in the performance of these classifiers upon the implementation of the KD technique, particularly with the GPT-2 model demonstrating the most promising outcomes. This work underscores the potential of integrating transformer-based learning models, like GPT-2, with knowledge distillation for more efficient and accurate vulnerability detection.</p> </abstract>ARTICLEtrue