In this study, we present a comparative analysis of gradient descent-based optimizers frequently used in Convolutional Neural Networks (CNNs), including SGD, mSGD, RMSprop, Adadelta, Nadam, Adamax, Adam, and the recent EVE optimizer. To explore the interaction between optimization strategies and activation functions, we systematically evaluate all combinations of these optimizers with four activation functions—ReLU, LeakyReLU, Tanh, and GELU—across three benchmark image classification datasets: CIFAR-10, Fashion-MNIST (F-MNIST), and Labeled Faces in the Wild (LFW). Each configuration was assessed using multiple evaluation metrics, including accuracy, precision, recall, F1-score, mean absolute error (MAE), and mean squared error (MSE). All experiments were performed using k-fold cross-validation to ensure statistical robustness. Additionally, two-way ANOVA was employed to validate the significance of differences across optimizer–activation combinations. This study aims to highlight the importance of jointly selecting optimizers and activation functions to enhance training dynamics and generalization in CNNs. We also consider the role of critical hyperparameters, such as learning rate and regularization methods, in influencing optimization stability. This work provides valuable insights into the optimizer–activation interplay and offers practical guidance for improving architectural and hyperparameter configurations in CNN-based deep learning models.

In this paper, we investigate the Sombor index of the zero-divisor graph of ℤ _n which is denoted by Γ(ℤ _n ) for n ∈ { p ^α , pq, p ² q, pqr } where p, q and r are distinct prime numbers. Moreover, we introduce an algorithm which calculates the Sombor index of Γ(ℤ _n ). Finally, we give Sombor index of product of rings of integers modulo n .

Classification, a data mining technique, has been applied on the financial parameters used in the Altman Z-Score formulas for a certain number of selected firms in manufacturing industry. The Altman Z-Score is used to estimate a firm's financial difficulties. The Z-Score value shows whether the financial position of the firm is good, moderate or risky. In this study, KNN and Naive Bayes algorithms are used as classification methods. The Z-Score values of all firms are calculated and a certain number of data for all three types are selected and taught to the system as learning data. Algorithms are run on the financial parameters in the Z-Score formulas of companies not taught to the system. Over all data, The KNN and Naive Bayes algorithms achieve 84–88% and 75–86% success, respectively. This study, where data mining techniques are applied on a finance model and successful results are achieved, will contribute to the application of different technologies in many different analysis processes of the financial sector.