Matematik Mühendisliği

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http://hdl.handle.net/11527/18049

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  • Öge
    A novel image denoising technique with Caputo type space–time fractional operators
    (Springer, 2024) Tanrıöver, Evren ; Kiriş, Ahmet ; Tunga, Burcu ; Tunga, M. Alper ; 0000-0003-4098-3155 ; 0000-0002-3687-6640 ; 0000-0001-7318-964X ; 0000-0003-3551-4549 ; Matematik Mühendisliği
    A novel image denoising model, namely Full Fractional Total Variation (TVFF), based on the Rudin-Osher-Fatemi (ROF) and the fractional total variation models is presented. The leading advantage of TVFF model is that it uses fractional derivatives with length scale parameters instead of ordinary derivatives with respect to both time and spatial variables in the diffusion equation. The Riesz–Caputo fractional derivative operator is used to disperse nonlocal influence throughout all directions, whereas the Caputo fractional derivative concept is employed for time fractional derivatives. Therefore, the influence of neighboring pixels is given greater weight compared to those situated farther away and this reflects the consideration behind denoising process better. Moreover, the numerical approach is constructed, and its stability and convergence properties are thoroughly examined. To show the superiority of our model, the denoised images are subjected to visual and numerical comparisons using metrics such as the Signal-to-Noise Ratio (SNR), the Structural Similarity Index Measure (SSIM) and the Edge-Retention Ratio (ERR). The performance of the TVFF method is evaluated under various types of noise, including Poisson, Speckle, and Salt & Pepper, and the results are compared with those obtained using Gauss and Median Filters. Furthermore, the proposed method is applied to both blind and synthetic images, thereby showcasing its versatility and applicability across diverse datasets. The outcomes showcase the substantial potential of our enhanced model as a versatile and efficient tool for image denoising.
  • Öge
    Buckling analysis of single-walled carbon nanotubes using the initial value method and approximate transfer matrix based on nonlocal elasticity theory
    (Wiley, 2024) Tepe, Ayşegül ; orcid.org/0000-0001-5612-3526 ; Mathematical Engineering
    In this study, a novel method is presented to analyze the buckling behavior of single-walled carbon nanotubes (SWCNTs) using the initial value method (IVM) in conjunction with the approximate transfer matrix, within the framework of nonlocal elasticity theory. The study aims to accurately approximate critical buckling load parameters under various boundary conditions, without encountering high computational requirements. IVM enables the computation of displacements and stress resultants along the entire beam from given initial conditions. The approximate transfer matrix is employed to analyze system states at different points through successive integration of solutions, generating the principal matrix needed for IVM and ensuring systematic and precise results that optimize the accuracy of the analysis. A convergence study confirms the effectiveness and precision of the proposed method, revealing a decrease in the critical buckling load parameters as the nonlocal parameter increases, applicable across all boundary conditions studied (simply supported, clamped–clamped, clamped–simply supported, and clamped-free). These results underscore the need to incorporate nonlocal effects for more accurate nanostructure mechanics predictions. The integration of IVM and the approximate transfer matrix provides a computationally efficient alternative to traditional numerical and semi-analytical methods, aiding researchers and engineers working with SWCNTs and other nanomaterials.
  • Öge
    Error analysis of the exponential wave integrator sine pseudo-spectral method for the higher-order Boussinesq equation
    (Springer, 2024) Çanak, Melih Cem ; Muslu, Gülçin M. ; 0009-0005-1699-5027 ; 0000-0003-2268-3992 ; Matematik Mühendisliği
    In this paper, we derive a new exponential wave integrator sine pseudo-spectral (EWI-SP) method for the higher-order Boussinesq equation involving the higher-order effects of dispersion. The method is fully-explicit and it has fourth order accuracy in time and spectral accuracy in space. We rigorously carry out error analysis and establish error bounds in the Sobolev spaces. The performance of the EWI-SP method is illustrated by examining the long-time evolution of the single solitary wave, single wave splitting, and head-on collision of solitary waves. Numerical experiments confirm the theoretical results.
  • Öge
    Machine learning based tomographic image reconstruction technique to detect hollows in wood
    (Springer, 2024) Yıldızcan, Ecem Nur ; Arı, Mehmet Erdi ; Tunga, Burcu ; Gelir, Ali ; Kurul, Fatih ; As, Nusret ; Dündar, Türker ; 0000-0001-6511-5587 ; 0000-0001-7659-6742 ; 0000-0001-7318-964X ; 0000-0001-6534-2253 ; Matematik Mühendisliği
    A new technique based on machine learning algorithms was introduced to detect internal wood defects. This technique relies on analyzing segmented propagation rays of stress waves and successfully generates the tomographic images of the defects by using the stress wave velocity. Utilizing a dual-stage methodology, the initial phase involves ray segmentation for the precise delineation of stress wave propagation, while the subsequent stage integrates advanced classification and clustering algorithms to facilitate the generation of tomographic images. This approach effectively tackles the inherent challenges associated with accurate segmentation and classification of stress wave velocity rays. The effectiveness of the proposed method was evaluated using both synthetic and experimental data. The results showed that the proposed method, when compared with some state-of-the-art methods, has a superior ability to accurately detect defective regions in the wood. The success of the proposed method is evaluated with four different evaluation metrics. It determined that over 90% success is achieved for all metrics. In comparison with related studies, it determined that the results are improved by 7–22% compared to the literature.
  • Öge
    Proceedings book of international workshop on theory of submanifolds
    (İstanbul Teknik Üniversitesi, 2017) Matematik Mühendisliği ; Mathematical Engineering ; Turgay, Nurettin Cenk ; Özkara Canfes, Elif ; Veken, Joeri Van Der ; Bejan, Cornelia-Livia
    Differential geometry is proving to be an increasingly powerful tool that improves its ties to other branches of mathematics such as analysis, topology, algebra, PDEs, and so on, as well as to theoretical physics research. The growing number of publications in the field of submanifolds was probably the main reason to organize the ”International Workshop on Theory of Submanifolds”, which took place at Istanbul Technical University, Turkey, from June 2 to June 4, 2016. One of the main features of the conference is the originality of its topic, being the only one focussing particularly on submanifold theory in the last few years. This is remarkable since submanifold theory is a very broad and omnipresent topic, going from surface theory in three-space, with applications in engineering and computer vision for example, to very abstract settings with high dimension and codimension, some of them appearing in modern physical theories. This volume, containing the proceedings of the above mentioned workshop, provides very recent results mainly on the theory of submanifolds, which the reader would be interested in getting acquainted with. The book is divided into three parts, each of them having a distinct editor. The first part contains surveys on submanifolds with certain properties, in particular on surfaces. Part two is the biggest one, and is devoted to the theory of submanifolds. The last part extends the main subject of the workshop toward some related topics, such as some geometrical structures which are extended from a manifold to the whole space containing the manifold (e.g. the total space of its cotangent bundle). The experience of the contributors to the Proceedings is illustrated by their publications in this field and the freshness of this conference was given mainly by the presence of many young mathematicians. The workshop was very successful, despite the critical period of this conference, where many participants had to cancel their participation for reasons beyond their control. All articles included here passed the usual referee process. Our warm thanks go to all those who contributed to this book by their work, to all participants of the workshop, to the referees of the Proceedings, to the host institution for organizing the conference and last but not least to our sponsors.
  • Öge
    SH waves in a weakly inhomogeneous half space with a nonlinear thin layer coating
    (Springer, 2024) Ahmetolan, Semra ; Demirci, Ali ; Peker-Dobie, Ayşe ; Özdemir, Neşe ; 0000-0003-1003-7918 ; 0000-0002-5228-7694 ; 0000-0002-9144-5691 ; Matematik Mühendisliği
    We investigate the self-modulation of Love waves propagating in a nonlinear half-space covered by a nonlinear layer. We assume that the constituent material of the layer is nonlinear, homogeneous, isotropic, compressible, and hyperelastic, whereas for the half-space, it is nonlinear, heterogeneous, compressible and a different hyperelastic material. By employing the nonlinear thin layer approximation, the problem of wave propagation in a layered half-space is reduced to the one for a nonlinear heterogeneous half-space with a modified nonlinear homogeneous boundary condition on the top surface. This new problem is analyzed by a relevant perturbation method, and a nonlinear Schrödinger (NLS) equation defining the self-modulation of waves asymptotically is obtained. The dispersion relation is derived for different heterogeneous properties of the half-space and the thin layer. Then the results of the thin layer approximation are compared with the ones for the finite layer obtained in Teymur et al. (Int J Eng Sci 85:150–162, 2014). The solitary solutions of the derived NLS equation are obtained for selected real material models. It has been discussed how these solutions are influenced by the heterogeneity of the semi-infinite space.
  • Öge
    Various optimized machine learning techniques to predict agricultural commodity prices
    (Springer, 2024) Sarı, Mustafa ; Duran, Serbay ; Kutlu, Hüseyin ; Güloğlu, Bülent ; Atik, Zehra ; Matematik Mühendisliği
    Recent increases in global food demand have made this research and, therefore, the prediction of agricultural commodity prices, almost imperative. The aim of this paper is to build efficient artificial intelligence methods to effectively forecast commodity prices in light of these global events. Using three separate, well-structured models, the commodity prices of eleven major agricultural commodities that have recently caused crises around the world have been predicted. In achieving its objective, this paper proposes a novel forecasting model for agricultural commodity prices using the extreme learning machine technique optimized with the genetic algorithm. In predicting the eleven commodities, the proposed model, the extreme learning machine with the genetic algorithm, outperforms the model formed by the combination of long short-term memory with the genetic algorithm and the autoregressive integrated moving average model. Despite the fluctuations and changes in agricultural commodity prices in 2022, the extreme learning machine with the genetic algorithm model described in this study successfully predicts both qualitative and quantitative behavior in such a large number of commodities and over such a long period of time for the first time. It is expected that these predictions will provide benefits for the effective management, direction and, if necessary, restructuring of agricultural policies by providing food requirements that adapt to the dynamic structure of the countries.