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    A note on complex combined boundary value problem for the nonhomogeneous tri-analytic equation
    (Soc Paranaense Matematica, 2024) Karaca, Bahriye
    In this paper, a combination of boundary value problems for the nonhomogeneous analytic equations have been studied. The aim of this paper is to find a solution for the Schwarz-(Dirichlet-Neumann) problem and obtain its solvability conditions.
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    Boundary value problems for bi-polyanalytic functions on the upper half plane
    (Taylor & Francis Ltd, 2025) Karaca, Bahriye
    In this study, explicit solutions for certain boundary value problems in the upper half-plane are obtained. Various types of boundary conditions are examined in detail, and their effects on the solutions are analyzed. The solution methodology relies on higher-order Cauchy-Pompeiu representations, which are used to address boundary value problems for bi-polyanalytic functions and inhomogeneous Cauchy-Riemann equations. In this context, the solutions obtained extend classical boundary value problems, including the Schwarz, Dirichlet and Neumann problems, providing a more general framework for analyzing these equations.
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    Impact of nitro substituents on dopamine sensing and nanostructure morphology: A machine learning approach for PANI:2-and 3-Nitro-1H-Pyrrole nanocomposite sensors
    (Electrochemical Soc Inc, 2024) Gursu, Gamze; Yildiz, Dilber Esra; Tasaltin, Nevin; Baytemir, Gulsen; Karakus, Selcan; Karaca, Bahriye; Akarsu, Canan Hazal
    In this study, we explore the effects of nitro substituents on the morphology and dopamine (DOP) sensing performance of polyaniline (PANI) nanocomposites (NCs). The novelty of the study is the unique integration of 2-nitro-1H-pyrrole (D9A) and 3-nitro-1H-pyrrole (D9B) into PANI to develop advanced non-enzymatic voltammetric sensors, combined with machine learning for DOP sensitivity and morphology analysis. Structural and morphological insights were obtained through comprehensive characterization techniques including H-1 NMR, 13C NMR, Fourier transform infrared spectroscopy, scanning electron microscopy, and artificial intelligence-enhanced SEM analysis. The PANI: D9B NCs sensor demonstrated superior DOP detection in the range of 0.625-5 mu M, with exceptional sensitivity (329.72 mu A mu M-1 cm-2) and an ultra-low limit of detection of 0.078 mu M. Its rapid sensing capability within 1 min indicates potential for use in biomedical diagnostics. In contrast, the PANI NCs sensor exhibited lower sensitivity, which was linked to higher Zreel values and space charge effects. To further enhance DOP prediction accuracy, we employed machine learning (ML) models-ANN, SVM, XGBoost, and Linear Regression-to analyze sensor outputs, with a focus on feature extraction and multivariate data analysis. Our combined approach provides a robust framework for optimizing nitro-substituted PANI NCs for high-performance sensing applications.
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    Schwarz problem for model partial differential equations with one complex variable
    (Sakarya University, 2024) Karaca, Bahriye
    This paper investigates the Schwarz problem. Initially, the focus lies on analyzing the problem for the first, second orders. Subsequently, attention shifts towards studying the same problem for equations of higher order. In the realm of second-order equations, the Schwarz problem is specifically examined for some operators; Laplace, Bitsadze and its complex conjugate. The findings demonstrate that the Schwarz problem for an n-order equation, when equipped with solely one boundary condition, exhibits an infinite number of solutions. However, by incorporating additional boundary conditions, it becomes feasible to obtain a unique solution for problem concerning n-order equations, effectively rendering it a well-posed problem. © 2024, Sakarya University. All rights reserved.