Highlighted Articles Published by ITU's Department of Mathematics Engineering in 2025-2026
The ITU Department of Mathematics Engineering has experienced a remarkable academic year, defined by significant academic achievements and groundbreaking research. Faculty members and students have been recognized for their pivotal contributions to advancing mathematical knowledge, securing publications in prestigious journals, and engaging in high-impact interdisciplinary projects. These accomplishments underscore the department’s unwavering dedication to excellence in both research and education. By fostering a collaborative and innovative academic environment, ITU Mathematics Engineering continues to push the boundaries of theoretical and applied mathematics. Looking ahead, the department is eager to build on this momentum, driving further innovation and addressing complex challenges across diverse fields.
Solving Baer wave equation reduced to three-parameter eigenvalue problem by dynamic thread-based computing
The article titled “Solving Baer wave equation reduced to three-parameter eigenvalue problem by dynamic thread-based computing”, by Prof. Dr. Ahmet Duran (corresponding author) from ITU Department of Mathematics Engineering, Hayati Ünsal Özer (a Ph.D. student of Prof. Dr. A. Duran) from ITU and YTU, Mehmet Tunçel from ITU AI and Data Science Research Center and Texas A&M at Qatar, and Fatih Said Duran from ITU and MEF University, was published in The Journal of Supercomputing-Springer.
Real-time computation of eigenvalues is very important in science and engineering. This is possible via memory-efficient, scalable, robust, and high-performance algorithms when we take advantage of supercomputing. Baer wave equation arises from applying the separation of variables to the Helmholtz equation. When the Baer wave equation is discretized, a three-parameter eigenvalue problem is obtained. In this study, the authors consider the computationally challenging problem of finding eigenvalue tuples in a three-parameter eigenvalue problem reduced from the Baer wave equation. They solve this problem using a fused parameter optimization algorithm by implementing a dynamic thread-based computation in C and MATLAB. They achieved scaled speed-up for the dense coefficient matrices of the problem from the Baer wave equation to run up to 64 threads in their C implementation. To the best of their knowledge, this is the first study to solve the three-parameter eigenvalue problem using parallel thread-based computing.
To access the full article, https://doi.org/10.1007/s11227-025-08152-3
A SMOTE–ViT Framework for Advanced Soil Classification on a Self-Generated Geotechnical Image Database
The article titled “A SMOTE–ViT Framework for Advanced Soil Classification on a Self-Generated Geotechnical Image Database”, authored by Atousa Zohouri Rad, Ahmet Topal, and Burcu Tunga from the Department of Mathematics Engineering, Faculty of Science and Letters, Istanbul Technical University, and Müge Balkaya from the Department of Civil Engineering, Faculty of Civil Engineering, Istanbul Technical University, was published in Applied Sciences, an MDPI journal.
Accurate soil type classification is a fundamental requirement in geotechnical and construction engineering, as it directly influences site investigation, design decisions, and construction performance. However, conventional laboratory-based soil characterization methods are often time-consuming, labor-intensive, and resource-intensive. To address these limitations, this study investigates the potential of deep learning-based image analysis techniques for high-accuracy automated soil classification using a self-generated image dataset specifically designed for geotechnical applications.
Unlike many existing studies that primarily focus on agricultural soils, this research targets site-relevant soil mixtures commonly encountered in geotechnical and construction engineering. A novel image database was developed using four primary soil constituents—gravel, sand, silt, and clay. Six representative geotechnical samples were systematically combined to produce 80 distinct ternary soil mixtures, creating a comprehensive dataset that reflects the complexity of real-world soil compositions. To mitigate the effects of class imbalance within the multi-component dataset, the Synthetic Minority Oversampling Technique (SMOTE) was employed, ensuring a more balanced representation of all mixture classes and improving model robustness.
The proposed classification framework is based on a Vision Transformer (ViT) architecture, which leverages self-attention mechanisms to capture both fine-grained textural characteristics and long-range spatial dependencies within soil images. This capability enables the model to effectively distinguish subtle differences among complex soil mixtures that may be difficult to identify through conventional image-processing approaches.
Experimental results demonstrate the effectiveness of the SMOTE–ViT framework, achieving an overall classification accuracy of 95.83% while maintaining high precision and recall across diverse ternary compositions. The model exhibited strong performance in differentiating between individual soil mixture classes, highlighting its potential as a reliable tool for automated geotechnical soil characterization.
Beyond its classification capability, the proposed approach offers practical advantages for engineering applications by providing a scalable, rapid, and high-precision alternative to traditional laboratory procedures. Furthermore, it has the potential to contribute to environmental sustainability and green construction practices. By enabling efficient in situ soil assessment, the framework can reduce the need for extensive physical sampling, laboratory testing, and transportation logistics, thereby lowering resource consumption, operational costs, and the carbon footprint associated with conventional soil investigation workflows.
To see the full article, https://doi.org/10.3390/app16094063
Rationality and Rivalry: A Game-Theoretic Analysis of the Turkey-Greece Aegean Dispute
The article titled “Rationality and Rivalry: A Game-Theoretic Analysis of the Turkey-Greece Aegean Dispute”, authored by Prof. Dr. Burhaneddin İzgi from the ITU Department of Mathematics Engineering and Assist Prof. Dr. Murat Özkaya from the Çanakkale Onsekiz Mart University (a former Ph.D. student of Prof. Dr. İzgi), was published in MGIMO Review of International Relations.
In this article, the authors examine the enduring Aegean dispute between Türkiye and Greece, a longstanding interstate rivalry centered on competing claims over maritime zones, national airspace, and the demilitarized status of Aegean islands, islets, and rocks. Despite periodic crises, such as the Kardak/Imia incident, the conflict has generally remained below the threshold of open warfare. The study explains this pattern through a game-theoretic framework that models the strategic interaction between the two states.
The authors construct a sequential game in which both Türkiye and Greece are assumed to be rational actors. Each state can choose among three strategic options: aggressive, passive-aggressive, or passive behavior. A decision tree illustrates the sequence of choices and the corresponding payoffs, while backward induction is used to identify the equilibrium outcome. The model demonstrates that both sides are most likely to adopt passive-aggressive strategies because this option maximizes potential benefits while minimizing the risks of direct military escalation.
As a result, the dispute is characterized by recurring but controlled actions, such as naval deployments, airspace violations, maritime incidents, and symbolic demonstrations of resolve. These activities allow both governments to defend their national claims and maintain credibility without provoking a full-scale confrontation. The findings suggest that the persistence of the dispute is driven by incentives to maintain a state of managed tension rather than pursue either outright escalation or complete accommodation, thereby explaining the stability of this low-intensity rivalry in the Aegean.
To see the full article, https://doi.org/10.24833/2071-8160-2025-6-105-7-22
Keen model with a delayed Phillips curve
A research article entitled “Keen model with a delayed Phillips curve” was published in Physica D: Nonlinear Phenomena in 2026. The study was authored by Ayşe Tiryakioğlu, Şeyma Gönül, and Cihangir Özemir from the Department of Mathematics, Faculty of Science and Letters, Istanbul Technical University.
The article focuses on a modified version of the Keen macroeconomic model, which is based on Hyman Minsky’s Financial Instability Hypothesis. Minsky argued that financial crises are not external or accidental events, but rather natural outcomes of the capitalist economic system. The Keen model provides a mathematical framework for this idea by describing the interactions between wage share, employment rate, and debt dynamics.
In this study, the classical Keen model is extended by introducing a time delay into the Phillips curve, which represents the relationship between wage dynamics and employment. The motivation behind this modification is that wage adjustments and employment-related responses in real economies do not always occur instantaneously. Instead, such mechanisms may involve delayed effects, and these delays can significantly alter the long-term behavior of the system.
The analysis shows that the model may have an equilibrium point that is stable in the absence of delay. However, when the delay parameter exceeds a critical threshold, the equilibrium can lose its stability. In this case, a Hopf bifurcation occurs, leading to a transition from stable economic behavior to oscillatory dynamics. From an economic perspective, this means that an economy predicted to return to equilibrium in the non-delayed model may instead exhibit persistent cycles when delayed responses are taken into account.
The study contributes to the literature on nonlinear dynamical systems and mathematical economics by demonstrating that delay effects can play a decisive role in macroeconomic stability.
In particular, it shows that the inclusion of delayed mechanisms may change the qualitative predictions of a model, transforming stable behavior into periodic fluctuations. These findings emphasize the importance of considering time-dependent responses in the mathematical modeling of economic systems.
To see the full article, https://doi.org/10.1016/j.physd.2026.135221
Analysis of Operator Splitting Methods for the Dispersive-Fisher Equation
Dr. Fatma Zürnacı Yetiş from the Department of Mathematics Engineering at Istanbul Technical University, in collaboration with Prof. Muaz Seydaoğlu from Muş Alparslan University has published a research article entitled “Analysis of Operator Splitting Methods for the Dispersive-Fisher Equation” in the Journal of Mathematical Analysis and Applications.
The study investigates operator splitting methods, a powerful approach for the numerical solution of complex nonlinear partial differential equations. The basic idea behind these methods is to split a complicated problem into simpler sub-problems that can be treated separately. These methods have been widely used for the numerical simulation of reaction-diffusion systems, dispersive wave equations, Burgers-type equations, and many other time-dependent evolution problems. Focusing on the third-order dispersive-Fisher equation, the authors decompose the original problem into simpler linear and nonlinear sub-problems and analyze two operator splitting techniques: the Lie-Trotter and Strang methods. A major contribution of the work is the rigorous convergence analysis of these numerical schemes. By employing the differential theory of operators in Banach spaces together with Lie commutator estimates and numerical quadrature error analysis, the study derives local error bounds and establishes corresponding global error estimates through the classical Lady Windermere’s fan argument. The theoretical analysis proves first-order convergence for the Lie-Trotter method and second-order convergence for the Strang splitting method under suitable regularity assumptions. The paper also includes numerical results demonstrating that the observed convergence rates are in excellent agreement with the theoretical analysis. Beyond its specific application to the dispersive-Fisher equation, the study provides a mathematical framework that can serve as a foundation for future investigations of operator splitting techniques applied to more general nonlinear evolution equations. By combining rigorous theoretical analysis with numerical verification, this work contributes to the development of reliable and efficient computational methods for challenging nonlinear partial differential equations and advances ongoing research in numerical analysis and scientific computing.
To see the full article, https://doi.org/10.1016/j.jmaa.2025.130382
A novel computational strategy for solving electrohydrodynamic flow problem
The article titled “A novel computational strategy for solving electrohydrodynamic flow problem”, authored by Soner Aydınlık and Ahmet Kırış from the Department of Mathematics, Faculty of Science and Letters, Istanbul Technical University, together with Pradip Roul from the Department of Mathematics, Visvesvaraya National Institute of Technology (VNIT), India, was published in Soft Computing, a Springer journal.
Electrohydrodynamic flow describes the motion of ionized fluids under the influence of electric fields and plays an important role in many engineering applications, including dielectric pumps, inkjet technologies, microfluidic devices, electrospray systems, and biomedical technologies. Accurate prediction of such flows is essential for improving the design and performance of these systems.
The study focuses on a challenging nonlinear mathematical model that describes the velocity distribution of an ionized fluid inside a cylindrical conduit. Because of the singular and nonlinear nature of the governing equations, obtaining accurate numerical solutions can be computationally demanding. To address this challenge, the researchers developed a novel numerical approach based on a Smooth Composite Chebyshev Finite Difference Method.
Unlike conventional numerical techniques, the proposed method combines high-order accuracy with smooth transitions between computational subdomains. This feature enables the algorithm to achieve highly accurate solutions while maintaining computational efficiency. The researchers also conducted detailed convergence and error analyses to verify the reliability and stability of the proposed framework.
The performance of the new method was evaluated through extensive numerical experiments and compared with several existing techniques reported in the literature. The results demonstrated smaller residual errors and competitive computational times, confirming the effectiveness of the proposed approach.
In addition to methodological developments, the study examined how two important physical parameters—the Hartmann number and the nonlinearity parameter—affect the velocity of electrohydrodynamic flow. The results showed that increasing the Hartmann number generally increases the fluid velocity, whereas stronger nonlinear effects reduce it.
Beyond its contribution to numerical analysis, the proposed framework provides a reliable computational tool for studying electrohydrodynamic systems and may support future developments in fluid mechanics, microfluidics, energy technologies, and electrically driven flow applications.
To access the full article, https://doi.org/10.1007/s00500-025-10852-0
Comparative analysis of beam responses via Hencky and fractional models under different mass distributions
The article titled “Comparative analysis of beam responses via Hencky and fractional models under different mass distributions”, authored by Soner Aydınlık and Ahmet Kırış from the Department of Mathematics Engineering, Faculty of Science and Letters, Istanbul Technical University, together with Wojciech Sumelka from Poznan University of Technology, was published in Mechanics Research Communications, an Elsevier journal.
Accurate prediction of structural vibrations is essential for the design of engineering systems ranging from bridges and aerospace structures to advanced materials and microscale devices. However, conventional models often have difficulty representing the influence of internal microstructures on mechanical behavior.
The researchers focused on Hencky-type beam models, which describe a beam as a sequence of rigid segments connected by rotational springs. Three different mass configurations were examined: masses concentrated at the joints, masses located at the midpoints of the segments, and masses distributed continuously along the beam. The study showed that these different mass arrangements significantly influence vibration characteristics, affecting both natural frequencies and wave propagation characteristics.
To capture these effects, the team developed fractional continuum models based on the symmetric Caputo fractional derivative. Unlike classical beam theories, the proposed approach incorporates nonlocal interactions, allowing the influence of neighboring regions within the structure to be considered. The fractional model parameters were calibrated directly from the behavior of the corresponding discrete systems, establishing a strong link between microstructural properties and continuum-scale responses.
The results demonstrated that the proposed framework reproduces the vibration and dispersion characteristics of microstructured beams more accurately than widely used classical nonlocal models. In particular, the fractional approach provided improved agreement with the discrete beam models over a broader frequency range, where conventional methods often lose accuracy.
Beyond its scientific contribution, the study highlights the potential of fractional mechanics as a practical tool for engineering applications. The developed framework may support future advances in smart materials, metamaterials, lightweight structures, vibration-sensitive components, and microscale mechanical devices. By improving the representation of scale-dependent effects, the proposed methodology contributes to the development of more reliable predictive models for next-generation engineering systems.
To access the full article, https://doi.org/10.1016/j.mechrescom.2025.104511
Incorporating robust transition probabilities into MCMC for initial value problems with variable coefficients in modelling
The article titled “Incorporating robust transition probabilities into MCMC for initial value problems with variable coefficients in modelling”, by Prof. Dr. Murat Sarı from the Department of Mathematics Engineering, Faculty of Science and Letters, Istanbul Technical University, and Zeinab Hassanzadeh from the Department of Computer Engineering, Faculty of Engineering and Architecture, Istanbul Gelişim University, was published in Physica Scripta.
Numerical methods are essential for solving complex scientific and engineering problems, especially when physical models lead to large-scale systems of linear algebraic equations or initial value problems with variable coefficients. While deterministic solvers such as Krylov subspace and conjugate gradient methods perform well for structured systems, they often face limitations in sparse, high-dimensional, or uncertain models, including higher computational cost, slower convergence, and reduced stability.
This study proposes a newly constructed Markov Chain Monte Carlo method to overcome these challenges. The method introduces optimized transition probability matrices, adaptive stopping criteria, and variance reduction techniques to improve accuracy while reducing computational effort. By minimizing probable error and requiring fewer stochastic samples, the approach enhances convergence efficiency and reliability.
One of the main strengths of the proposed method is its scalability. Numerical experiments involving coefficient matrices of various sizes, including matrices up to order 5000, show that the stochastic approach can effectively handle sparse and complex structures commonly encountered in physical modelling. The results also indicate that the OMC transition probability matrix outperforms the AOMC matrix in terms of required sample size, CPU time, accuracy, and theoretical consistency.
The method is particularly suitable for parallel computing because stochastic samples can be simulated independently. This makes it promising for large-scale simulations, big-data environments, and computationally intensive applications. Overall, the study provides a strong theoretical and practical foundation for using scalable stochastic methods in the simulation of complex physical phenomena.
To access the full article, https://doi.org/10.1088/1402-4896/ae2bb2
Effects of Contact Tracing and Isolation Policies on Epidemic Dynamics
The article titled “Effects of Contact Tracing and Isolation Policies on Epidemic Dynamics”, by Esra Özge Asan and Murat Sarı from the Department of Mathematical Engineering, Faculty of Science and Letters, Istanbul Technical University, Hüseyin Tunç from the Department of Biostatistics and Medical Informatics, School of Medicine, Bahçeşehir University, and Seyfullah Enes Kotil from the Department of Molecular Biology and Genetics, Faculty of Arts and Sciences, Boğaziçi University, was published in International Journal of Applied and Computational Mathematics, Springer.
Compartmental models are widely used to understand epidemic dynamics, estimate transmission potential, and support evidence-based public health decisions. During the COVID-19 pandemic, such models played a central role in evaluating intervention strategies including social distancing, quarantine, isolation, and contact tracing. Among the most important epidemiological indicators is the basic reproduction number, which reflects the expected number of secondary infections generated by one infectious individual in a fully susceptible population.
This study investigates how early contact tracing and isolation policies may affect the estimation of the basic reproduction number. Using a Susceptible–Exposed–Presymptomatic–Asymptomatic–Symptomatic–Reported model, the authors develop an integro-differential framework that incorporates contact tracing and isolation effects without adding unnecessary structural complexity. This approach enables a clearer relationship between the exponential growth rate and the basic reproduction number under intervention policies.
The study analyses early epidemic dynamics across 32 European countries by using confirmed case data and contact tracing information. The results show that models neglecting contact tracing and isolation may systematically underestimate the basic reproduction number. The findings also indicate that contact tracing efficiency and the exponential growth rate are key drivers of epidemic progression.
Long-term simulations further demonstrate that higher contact tracing efficiency can substantially reduce epidemic peaks and final epidemic size. When presymptomatic transmission is significant, effective tracing and timely isolation become especially important for shortening epidemic duration. Overall, the study provides a refined modelling framework for assessing epidemic control strategies and highlights the importance of accurately incorporating intervention effects into reproduction number estimation.
To access the full article, https://doi.org/10.1007/s40819-026-02114-w
Deterministic, Stochastic, and Mean-Field PDE Models in Neuroscience
The article titled “Deterministic, stochastic, and mean-field PDE models in neuroscience”, authored by Coşkun Çetin from the Department of Mathematics and Statistics, California State University, Sacramento, Jose Roberto Castilho Piqueira from Escola Politécnica, Universidade de São Paulo, together with Burhaneddin İzgi, Ayşe Peker-Dobie, and Semra Ahmetolan from the Department of Mathematics Engineering, Faculty of Science and Letters, Istanbul Technical University, and Murat Özkaya from the Department of Business, Faculty of Political Sciences, Çanakkale Onsekiz Mart University, was published in Frontiers in Computational Neuroscience.
The study brings together deterministic, stochastic, and mean-field differential equation approaches used to model brain activity across different scales, from the behavior of a single neuron to large neuronal populations and whole-brain networks.
The article discusses the role of these models in understanding neuronal excitability, firing patterns, synaptic variability, neural noise, and collective brain dynamics. It also examines numerical solution methods and current research topics such as parameter estimation, data assimilation, control-oriented modeling, and the integration of mathematical models with machine learning methods.
The study aims to support efforts to link cellular-level mechanisms with population-level brain activity and to help researchers select appropriate mathematical modeling tools in computational neuroscience.
To access the full article, https://doi.org/10.3389/fncom.2026.1762692
Lie Symmetry Structure of Nonlinear Wave Equations in Dimensional Space-Time
A research article entitled “Lie Symmetry Structure of Nonlinear Wave Equations in Dimensional Space-Time” was published in International Jouurnal of Thereotical Physics in 2026. The study was authored by Faruk Güngör (Prof. Emeritus) and Cihangir Özemir, both from the Department of Mathematics, Faculty of Science and Letters, Istanbul Technical University.
The article studies Lie point symmetry structure of generalized nonlinear wave equations with an arbitrary nonlinear source term in an arbitrary physical dimension. The equivalence groups of this class and its subclass where the first order derivatives are absent in the nonlinearity are determined. Then, the symmetry group as a special case of the equivalence transformation is obtained from the invariance requirement of the nonlinearity. As an application, the authors solve this condition for some specific cases of the nonlinearity to build physically important equations like conformally-invariant nonlinear wave and Euler–Poisson–Darboux equation. Canonical forms for allowable symmetries are also studied.
The main contribution of this article lies in the fact that no previous study in the literature has investigated nonlinear source functions at the level of generality considered here. Existing results are confined to much more restrictive classes of nonlinearities and are far from covering the broad framework addressed in the present work.
To access the full article, https://doi.org/10.1007/s10773-025-06219-8
Improving traceability query in blockchain-based food supply chain systems using NLP and B+ tree indexing
The article titled “Improving traceability query in blockchain-based food supply chain systems using NLP and B+ tree indexing”, authored by Ilyas Ziaya, Brahim Farou, Zineddine Kouahla, and Hamid Seridi from the Department of Computer Science and Labstic Laboratory, 8 May 1945 University, Algeria, together with Muhammet Kurulay from the Department of Mathematical Engineering, Istanbul Technical University, was published in Knowledge and Information Systems, a Springer journal.
Food supply chains have increasingly adopted blockchain technology due to its critical role in ensuring food safety and providing consumers with traceability and transparency of food products. Existing blockchain-based traceability systems often rely on complementary technologies such as QR codes, RFID, and barcodes to facilitate tracking and data retrieval. However, these systems face significant challenges in managing large-scale, complex traceability queries. Moreover, their query time performance tends to degrade as the volume of data and the size of the blockchain ledger grow, since the search must be performed sequentially across blocks especially in complex food supply chains. To address these limitations, we propose a novel blockchain-based traceability system that integrates a natural language processing (NLP) model and B+ tree indexing technique. This integration ensures accurate data responses and optimizes traceability queries within the blockchain ledger. The system was simulated using the hyperledger fabric framework, with various scenarios tested based on different data and block sizes, and the experimental results demonstrate a significant improvement in complex traceability range queries, achieving an average reduction of 68.32% compared to native blockchain-based methods with sequential search and scanning of all blocks in the ledger.
To access the full article, https://doi.org/10.1007/s10115-026-02715-3
An accurate and effective computational method to solve brain tumor problems: a Jacobian-free Newton Krylov method with an innovative preconditioning strategy II
The article titled “An accurate and effective computational method to solve brain tumor problems: a Jacobian-free Newton Krylov method with an innovative preconditioning strategy II”, by Ece Hazal Korkmaz, Samet Y. Kadıoğlu, and Ersin Özuğurlu from the Department of Mathematical Engineering, Faculty of Science and Letters, Istanbul Technical University, was published in Computational and Applied Mathematics, Springer.
We explore the application of sophisticated mathematical and computational models to simulate the interplay between radiotherapy, chemotherapy, and glioma progression, aiming to develop optimized treatment strategies. By employing the Jacobian-free Newton Krylov method and an innovative physics-based preconditioning technique, we demonstrate computational accuracy and efficiency that improve treatment optimization. Our findings emphasize the potential of these models to enhance therapeutic outcomes for GBM patients.
The computational results also suggest that the hyperfractionated therapy significantly improves patient outcomes as compared to traditional treatment. Regarding the computational aspects, we confirmed theoretical second-order accuracy through a numerical convergence study, validating the reliability of our code and providing evidence that the JFNK method consistently converges all nonlinearities in the physical system as anticipated. Moreover, an efficiency analysis comparing our novel preconditioning approach with established techniques such as incomplete lower-upper (ILU) methods showed that the new preconditioner outperforms in terms of reducing nonlinear and linear iterations and lowering CPU time.
To access the full article, https://doi.org/10.1007/s40314-025-03406-5
B-Doped ZnO Nanoparticles: Defect Chemistry, Tensile Strain, and Tunable Optical Response
The article titled “B-Doped ZnO Nanoparticles: Defect Chemistry, Tensile Strain, and Tunable Optical Response”, co-authored by Ersin Özuğurlu from the Department of Mathematics, Faculty of Science and Letters, Istanbul Technical University, together with Lütfi Arda, Merve Mine Şeker Perez, and İlke Taşçıoğlu, was published in Inorganics, an MDPI journal.
In this study, Zn0.95B0.05O nanoparticles synthesized via the sol–gel method exhibited a single-phase wurtzite structure, and their crystal integrity was confirmed by XRD. Analysis of line broadening revealed that the average crystallite size was in the range of 32.37–39.63 nm, while the microstrain was on the order of 2 × 10−4. Moreover, the positive slopes in the Williamson–Hall plots indicated that tensile stresses were dominant.
Optical measurements using the Kubelka–Munk/Tauc approach yielded a band gap of Eg = 3.216 eV, which represents a slight narrowing compared to pure ZnO. This result supports the conclusion that B3+→Zn2+ substitution increases the density of edge states and enhances the band-tailing effect. Indeed, the Urbach energy (Eu = 184–193 meV) is consistent with short range bond distortions and localization effects. Refractive index values calculated from five different n(Eg) models ranged between 2.05 and 2.71, confirming the material’s potential for ptoelectronic applications within the wide band gap/high refractive index window.
Gaussian deconvolution of the PL spectrum revealed that the violet (Zni) and blue (VZn) bands were dominant, while the red (Oi) contribution was relatively limited. This defect chemistry indicates an enrichment of zinc vacancy/interstitial centers as an inevitable consequence of charge compensation and size mismatch. ESR measurements exhibited a single, broad, and intense resonance line (g = 2.294, ΔHpp ≈ 120.7 mT), suggesting the predominance of paramagnetic defect centers and a high defect density.
Because B doping in ZnO efficiently affects the crystal–chemical defect landscape while subtly changing band-edge states and optical constants, it has potential use in transparent conducting films, electron transport layers in organic photovoltaics (OPVs), and UV photo detection.
To see the full article, https://doi.org/10.3390/inorganics14020060
Structural Features, Defect-Related Photoluminescence, and Optical Constants of Mg-Doped ZnO Thin Films
The article titled “Structural Features, Defect-Related Photoluminescence, and Optical Constants of Mg-Doped ZnO Thin Films”, authored by Lütfi Arda from Bahçeşehir University, Ersin Özuğurlu from the Department of Mathematics, Faculty of Science and Letters, Istanbul Technical University, together with İlke Taşçıoğlu from the Faculty of Engineering and Natural Sciences, Istanbul Topkapı University, was published in Crystals, an MDPI journal.
Optical constants were accurately extracted using a double-facet-coated substrate (DFCS) model, combined with nonlinear curve fitting using the Nelder–Mead optimization algorithm.
This study on Zn1−xMgxO thin films shows that sol–gel-derived Mg-doped ZnO thin films with composition-dependent stress states, defect states, and tunable optical properties are promising candidates for UV photodetectors, optical coatings, and transparent optoelectronic devices.
Using the sol–gel dip-coating method, Zn1−xMgxO (x = 0.00–0.05) thin films were successfully deposited on soda–lime glass substrates with a single-phase wurtzite structure and strong (002) preferred orientation. Mg incorporation was found to modify the microstructure, defect-related emission, and optical response of the films. All samples exhibited high visible transparency (70–80%) together with a composition-dependent blue shift and bandgap widening (3.27–3.326 eV). The optical constants were successfully extracted using the DFCS-based nonlinear fitting approach, which provides a more realistic optical analysis for dip-coated double-facet films. Photoluminescence and Urbach-energy results further showed that defect states and band-tail behavior are strongly influenced by Mg-induced lattice distortion. Compared with previous sol–gel Zn1−xMgxO studies, the main contribution of this work is the combined treatment of structural evolution, defect-related photoluminescence, and DFCS-based optical constants within a single framework. These findings indicate that Zn1−xMgxO thin films are promising for UV-selective transparent optoelectronic coatings.
To see the full article, https://doi.org/10.3390/cryst16050291
Shielding efficiency of iron doped tincal: A first-principles study
The article titled “Shielding efficiency of iron doped tincal: A first-principles study”, authored by İzzet Paruğ Duru from Gedik University, Ersin Özuğurlu from the Department of Mathematics Engineering, Faculty of Science and Letters, Istanbul Technical University, together with Lütfi Arda from Bahçeşehir University, was published in Physica B: Condensed Matter, an Elsevier journal.
For many years, there has been interest in the idea of shielding to reduce undesired radiation across a wide spectrum, particularly in relation to security and health. The theoretical calculation of the shielding efficiency (SE) of Fe-doped tincal nanoparticles using DFT and a proven methodology is the main subject of this study. The GGA with the Koelling-Harmon relativistic correction and the PBEsol functional was used in the computations. Both the FM and AFM states of the dopant were taken into account when treating the Fe-doped tincal structures. The most advantageous condition was determined to be AFM. Furthermore, unlike raw tincal, which has a broad bandgap, the doped structure shows conductive conductivity.
For incoming photons, the materials under investigation have almost the same shielding efficiency (SE) along the [010] and [100] projections. However, they vary along the [001] projection. This suggests that the in-plane and out-of-plane shielding efficiency exhibit optical anisotropy, a property that is similarly impacted by the dopant configurational variations.
Comparing the FM and AFM states, the SE of the AFM state is wider throughout the spectrum than that of the FM state. For photon energies between 15 and 20 eV, the highest SE is noted. For all configurations taken into consideration, the Fe-B interchanged tincal structures show comparatively low shielding efficiency. Moreover, these materials' major shielding properties are limited to the extreme ultraviolet (EUV) spectrum. Total shielding efficiency is between -0.6 and -0.8 for the FM phase, while the AFM phase provides higher values, which are between -0.6 and -1.4.
To see the full article, https://doi.org/10.1016/j.physb.2026.418810
Modeling Opinion Polarization: Can We Control Public Discourse?
The article titled “Modeling Opinion Polarization: Can We Control Public Discourse?”, authored by ITU Department of Mathematics Engineering faculty members Assoc. Prof. Dr. Ali Demirci, Assoc. Prof. Dr. Ayşe Peker-Dobie, and Dr. Sevgi Harman, was published in Frontiers in Physics.
In this novel study, the researchers propose an epidemiologically inspired model to analyze the evolution of public opinion and the dynamics of polarization. Unlike traditional approaches, this framework classifies the population into five distinct groups: Susceptible, Exposed, Positive, Negative, and Mixed-Emotion communicators. This model uniquely incorporates a time-dependent control function to simulate engagement surges driven by external events. By focusing on short intervention windows, this research demonstrates how targeted strategies can effectively steer public discourse. A derived basic reproduction number serves as a critical threshold, determining whether opposing groups persist or fade away. Ultimately, this study offers powerful theoretical tools for evaluating how platform algorithms and governmental interventions can be leveraged to mitigate or amplify polarization in digital environments.
To access the full article, https://doi.org/10.3389/fphy.2025.1626026.
Machine Learning Tree Trimming for Faster Markov Reward Game Solutions
The article titled “Machine Learning Tree Trimming for Faster Markov Reward Game Solutions”, authored by Prof. Dr. Burhaneddin İzgi from the ITU Department of Mathematics Engineering, Dr. Murat Özkaya from the Canakkale Onsekiz Mart University (a Ph.D. student of Prof. Dr. İzgi), Assoc. Prof. Dr. Nazım Kemal Üre from the ITU Department of Artificial Intelligence and Data Engineering, and Professor Matjaz Perc from the University of Maribor, was published in Journal of Computational Science.
In this research, the authors address the high computational burden of existing iterative algorithms for solving Markov Reward Games (MRGs). To overcome these challenges, this paper introduces a novel neural network architecture designed to solve MRGs with large state-action sets by effectively trimming the decision tree. This framework utilizes a holistic matrix norm-based solution method to generate training datasets, employing a unique vectorization process to adapt payoff and transition matrices. By treating the problem as a classification task, the model identifies optimal paths by distinguishing between rewarding and non-rewarding branches. The results reveal that this system efficiently predicts optimal strategies, achieving F1-scores exceeding 0.97. Ultimately, this study proposes a powerful architecture for solving MRGs in real-time, significantly enhancing their practicality for complex, real-world applications.
To access the full article, https://doi.org/10.1016/j.jocs.2025.102726.
The Copositive Range
The article titled “The Copositive Range”, authored by ITU Department of Mathematics Engineering member Dr. Nurhan Çolakoğlu, in collaboration with Dr. Seong Jun Park and Dr. Michael Tsatsomeros from the Washington State University, was published in Electronic Journal of Linear Algebra.
This study aims to advance the theory, detection, and categorization of copositive matrices by introducing a novel concept: the “Copositive Range”. Motivated by the classical numerical range, this research defines the copositive range for a matrix as the set . While copositivity, first introduced by Motzkin in 1952, plays a crucial role in reformulating nonconvex mixed quadratic programs and solving Linear Complementarity Problems (LCP), effective characterization remains a challenge. This paper addresses that gap by extending the numerical range concept specifically to non-negative vectors. Ultimately, this work provides a unified framework that bridges theoretical matrix analysis with practical applications in differential equations and theoretical economics.
To access the full article, https://doi.org/10.13001/ela.2025.9741.
Bifurcation Structure and Stability of Solitary Waves in Nonlinear Optical Systems
The article titled “Bifurcation Structure and Stability of Solitary Waves in the Cubic–Quintic Nonlinear Schrödinger Equation with Self-Steepening”, authored by ITU Department of Mathematics Engineering faculty members Res. Assist. Eril Güray Çelik and Prof. Dr. Nalan Antar, was published in European Physical Journal Plus.
This study presents a comprehensive analysis of the bifurcation structure and stability of solitary waves governed by the cubic-quintic nonlinear Schrödinger equation with self-steepening in a symmetric double-well potential. The research specifically investigates how higher-order effects, specifically self-steepening and quintic nonlinearity, influence localized states in nonlinear optical systems.
The investigation examines two primary regimes. In the focusing-defocusing regime, the interplay between cubic focusing and quintic defocusing generates a complex bifurcation landscape, including supercritical pitchfork, double-pitchfork, and saddle-node bifurcations. This analysis reveals that increasing the self-steepening parameter compresses unstable regions and reduces multistability, effectively eliminating upper solution branches. In contrast, the fully focusing regime exhibits a more robust structure characterized by a single supercritical pitchfork bifurcation that remains qualitatively unchanged under parameter variations.
A notable methodological innovation of this work is the first application of the pseudospectral renormalization (PSR) method to construct bifurcation diagrams in cubic-quintic systems. By combining PSR for solution computation with Fourier collocation for stability analysis, this study provides critical theoretical insights into how higher-order nonlinearities dictate symmetry breaking and stability in externally confined nonlinear environments.
To access the full article, https://doi.org/10.1140/epjp/s13360-025-07053-x.
Optimizing Treatment of Brain Cancer Through Mathematics
The study titled "An accurate and effective computational method to solve brain tumor problems: a Jacobian-free Newton Krylov method with an innovative preconditioning strategy II", authored by ITU Department of Mathematics Engineering faculty members Res. Assist. Ece Hazal Korkmaz, Prof. Dr Samet Yücel Kadıoğlu and Prof. Dr. Ersin Özuğurlu, was published in Computational and Applied Mathematics.
Glioblastoma multiforme (GBM) is one of the most aggressive brain cancers, and even combined surgery, radiotherapy, and temozolomide chemotherapy often fail to halt its progression. In this study, Korkmaz, Kadıoğlu, and Özuğurlu investigate how mathematical modeling and high-performance computation can contribute to more effective treatment strategies.
They construct a reaction–diffusion model that captures the proliferation and invasive spread of GBM cells, then incorporate detailed representations of radiotherapy and chemotherapy to examine how different treatment schedules reshape tumor evolution. Rather than producing a single simulation, the objective is to identify dosing patterns and timing strategies capable of measurably extending survival.
The primary obstacle is computational: realistic tumor geometries and months-long treatment windows generate large, nonlinear systems. To overcome this, the authors use a Jacobian-free Newton–Krylov method supported by a physics-based preconditioner that targets the stiffest components of the model. This approach significantly reduces iteration counts and computation time, enabling high-resolution simulations that would otherwise be infeasible.
The resulting model reproduces clinically consistent behavior, such as untreated tumors reaching lethal size within roughly a year, and shows that hyperfractionated radiotherapy—delivering two smaller fractions per day—can outperform conventional single-fraction protocols. By enabling rapid evaluation of alternative treatment regimens, this work provides a computational framework that may support future patient-specific optimization of GBM therapy.
To access the full article, https://doi.org/10.1007/s40314-025-03406-5.
Processing and Analysis of Quadratic Spectrum Approximation for Three Bounded Operators via Generalized ν-Convergence
The article titled "Processing and Analysis of Quadratic Spectrum Approximation for Three Bounded Operators via Generalized ν-Convergence", authored by ITU Department of Mathematics Engineering member Prof. Dr. Muhammed Kurulay, in collaboration with S. Kamouche, H. Guebbai and M. Ghiat (Universite 8 Mai 1945 Guelma, University of Blida), was published in Lobachevskii Journal of Mathematics.
The purpose of this paper is to demonstrate the efficacy of the generalized quadratic spectrum approximation in addressing the issue of spectral pollution that arises in the approximation of unbounded operator spectra. To achieve this, the authors investigate key analytical properties of the generalized quadratic resolvent function, such as holomorphicity and Fréchet differentiability, which are essential for developing the numerical framework. Furthermore, they extend the concept of ν-convergence, originally introduced for the classical spectrum, to establish property U convergence, a novel approach that effectively mitigates spectral pollution. This extension provides a more robust framework for addressing spectral contamination. To illustrate the practical applicability of the method, the authors focus on the quadratic pencil of Schrödinger's operator. By combining the finite differences method with the generalized quadratic spectral approximation, they estimate the eigenvalues of the selected operator. Extensive numerical experiments have been conducted to validate the efficiency and accuracy of the approach. The results confirm the effectiveness of the method in resolving spectral pollution and demonstrate its capability to deliver precise eigenvalue approximations. These findings highlight the potential of this technique for broader applications in spectral analysis.
To access the full article, https://doi.org/10.1134/S1995080225605806.
Effects of Surface Roughness on Generalised Rayleigh Waves in Elastic Waveguides
The article titled "Effects of Surface Roughness on Generalised Rayleigh Waves in Elastic Waveguides", authored by ITU Department of Mathematics Engineering members Tuğçe Sezer, Prof. Dr. Semra Ahmetolan, Assoc. Prof. Dr. Ayşe Peker-Dobie, and Assoc. Prof. Dr. Ali Demirci, was published in Wave Motion.
This work examines the propagation of Rayleigh surface waves in an elastic half-space covered by a layer with spatially varying surface corrugation. The mathematical model is established within the framework of two-dimensional linear elasticity, considering general roughness profiles for both the upper free surface and the interface of the layer. A perturbation method is employed to derive analytical expressions for the displacement fields, and dispersion relations are obtained by enforcing the relevant boundary and continuity conditions. The influence of surface corrugation parameters on phase velocity and wave propagation is examined numerically for periodic roughness profiles using selected real material models. The results demonstrate that both the amplitude and geometric characteristics of the surface irregularities have a pronounced impact on the dispersion behaviour of Rayleigh waves. These findings provide new insights into wave propagation in layered elastic media with irregular boundaries and may inform future applications in wave-based sensing, nondestructive evaluation, and acoustic material design.
To access the full article, https://doi.org/10.1016/j.wavemoti.2025.103658.
Mathematical Modeling on the Strategies of Imperfect Vaccination, Quarantine, and Natural Immunity
The study titled “Mathematical Modeling on the Strategies of Imperfect Vaccination, Quarantine, and Natural Immunity in a Future Epidemic”, derived from the master’s thesis of Seda Çelik under the supervision of ITU Department of Mathematics Engineering member Assoc. Prof. Dr. Saadet S. Özer, was published in Mathematical Methods in the Applied Sciences.
A mathematical analysis is being conducted to determine the extent to which contact measures such as masks and social distancing should be balanced with vaccine efficacy, vaccination rates, natural immunity, and quarantine in order to mitigate a future pandemic. A method is being formulated to answer the question of what should be implemented, when, and how.
Understanding epidemic dynamics is vital for global health security. A recent study, authored by Seda Çelik and Saadet S. Özer, investigates the complexities of pandemic management. Originating from a master's thesis and published in the Q1 journal Mathematical Methods in the Applied Sciences (Volume 48, Issue 11), this research offers a mathematical approach to optimizing control strategies for future outbreaks. The core challenge addressed is how to balance non-pharmaceutical interventions such as masks and social distancing with medical countermeasures like imperfect vaccination and quarantine. The researchers aimed to formulate a method to answer "what should be implemented, when, and how" to mitigate pandemics effectively, considering variables like natural immunity. The authors developed a system of nonlinear ordinary differential equations to model the population, categorizing individuals into nonvaccinated, vaccinated, exposed, quarantined, infected, and recovered groups. The study goes beyond the standard basic reproduction number calculating specific reproduction numbers for vaccination and quarantine to assess control efficacy. Through rigorous analysis, the study proves that the disease-free equilibrium is locally asymptotically stable if . Furthermore, global asymptotic stability is achieved under specific conditions where for a positive real . These theoretical results were validated through sensitivity analysis and numerical simulations. The findings provide a scientific basis for policymakers to balance lockdown policies, contact rates, and vaccine efficiency. By simulating strategies from the onset of an outbreak, including periods without vaccines, the study outlines how natural immunity and quarantine rates can be leveraged to control future pandemics.
To access the full article, https://doi.org/10.1002/mma.10980.