v.12 n.1 February

Static, Spherically Symmetric, Anisotropic Stars in General Relativity

Stefan Bernhard Rüster

Parana J. Sci. Educ., v.12, n.1, (1-4),  February 3, 2026.

DOI:  10.5281/zenodo.18457251

Abstract

This work investigates the structure of static, spherically symmetric stellar objects considering pressure anisotropy within the framework of General Relativity. A novel theoretical approach is presented in which the thermodynamic pressure of an Equation of State (EoS) is consistently identified with the tangential pressure. This assignment is derived from the fundamental property of the EoS as a relation characterized by the absence of pressure gradients in its reference state, which remains preserved in the tangential plane of the stellar configuration due to spherical symmetry. The radial pressure, in contrast, acts as a dynamical response to gravitational equilibrium. The field equations are formulated including a cosmological constant, and a detailed theoretical scheme for determining the metric functions as well as the mass and pressure profiles is derived. With regard to numerical integration, the adaptation of the internal solution to the external Kottler spacetime using an auxiliary metric and the subsequent rescaling procedure are explained. Finally, the physical viability of the resulting model is discussed, emphasizing that the use of a realistic EoS for the tangential component inherently ensures the stability of the configuration as a direct consequence of the relativistic field equations.

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On Ekeland Variational Principle in Asymmetric b-Metric Spaces

Anas Yusuf and Junaidu Nafiu Mallam

Parana J. Sci. Educ., v.12, n.1, (5-11),  February 3, 2026.

DOI:  10.5281/zenodo.18457309

Abstract

This paper extends the Ekeland Variational Principle (EVP) to the setting of asymmetric b-metric spaces, which generalize both asymmetric metric and b-metric spaces. By distinguishing forward, backward and bi- completeness, we establish corresponding forward, backward and bi-complete version of EVP. Examples are provided to demonstrate that forward and backward principles may yield different minimizers while the bi-complete EVP reduces to the classical EVP when symmetry holds. As an application, we obtain a forward and backward Cartisi-type fixed point theorem. These results broaden the scope of EVP and offer a new tools for optimization and fixed-point theory in asymmetric frameworks.

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Machine Learning Based Classification for Alzheimer's Disease Using EEG Signal

Abdulfatah Kalaje and Hasan Demir

Parana J. Sci. Educ., v.12, n.1, (12-23),  February 3, 2026.

DOI:  10.5281/zenodo.18457352

Abstract

Alzheimer’s disease (AD) is neurodegenerative disorder that affects memory, cognition, and behavior, representing the most common cause of dementia with old people. Alzheimer’s disease detection was performed using convolutional neural networks (CNNs) applied to electroencephalogram (EEG) signals, where the features were extracted from signal transformation coefficients. The EEG dataset collected from 48 participants, divided into two groups: Alzheimer’s disease patients and healthy controls. Several signal transformation techniques were compared, including the fast Fourier transform (FFT), short-time Fourier transform (STFT), synchrosqueezed Fourier transform (SSFT), continuous wavelet transform (CWT), discrete wavelet transform (DWT) for 1D and 2D, and synchrosqueezed wavelet transform (SSWT), to determine the most effective approach for EEG-based classification. Experimental results demonstrated that the STFT method provided the highest performance, achieving superior accuracy, precision, sensitivity, specificity, and F1-score for Alzheimer’s disease detection.

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