Analele Universității ”Dunărea de Jos” din Galați. Fascicula II, Matematică, fizică, mecanică teoretică / Annals of the ”Dunarea de Jos” University of Galati. Fascicle II, Mathematics, Physics, Theoretical Mechanics

Cuprins

*** *** — Mon, 29 Dec 2025 10:34:10 +0200

***

Implicitly defined V-harmonic maps

Monica Alice Aprodu — Mon, 12 Jan 2026 09:48:11 +0200

We extend the method of constructing harmonic morphisms via implicitly defined maps to the generalized context of -harmonicity. We prove that if a map satisfies specific holomorphic and -harmonic conditions, the local solutions to the implicit equation defined by are -harmonic pseudo-horizontally homothetic (PHH) maps.

Analytical solutions in solving the parabolic partial differential equation using separation of variables and Fourier series

Gabriel Bercu, Stefanut Ciochină — Mon, 12 Jan 2026 09:53:37 +0200

In this paper we present the analytical solution of a one-dimensional (1D) parabolic differential equation (PDE), encountered in many engineering studies under the name of the heat equation. To solve the equation, we use the method of separation of variables together with Fourier series. After applying the separation of variables, the initial equation decomposes into two ordinary differential equations (ODE). The equations obtained correspond to the spatial (x) and temporal (t) components. The spatial solution, for the first equation, is expressed by sinusoidal functions corresponding to the eigenfunctions, and the temporal component, for the second equation, has a characteristic exponential dependence. The determination of the Fourier series coefficients is based on the initial condition. Thus, we constructed an exact solution in the form of convergent series. The method used in solving the equation, together with the boundary conditions and initial conditions, can be used as a reference for validating numerical methods or practical experiments performed in the laboratory.

Urban noise pollution in a medium-sized city from Romania

Mon, 12 Jan 2026 10:06:41 +0200

This research examines urban noise pollution in Galati, Romania, focusing on sound intensity measurements across six strategic locations. The study investigates noise levels during weekends at different moments (morning and afternoon), to assess varying patterns of anthropogenic activities. Measurements revealed that the Harbor area maintained the lowest noise pollution levels, while the Ring Road consistently showed extremely high sound levels, often exceeding acceptable limits. The research identified road traffic as the primary contributor to noise pollution, with construction activities significantly impacting local areas, where heavy machinery was used. Quantitative analysis demonstrated that most studied locations exceeded the 55 dB threshold considered acceptable for residential areas, with particularly concerning levels during peak traffic hours. The study encompassed 15 days of measurements, strategically selecting Friday, Saturday, and Sunday to capture the gradual decrease in anthropogenic activities throughout the weekend. Results indicate a clear correlation between traffic patterns, urban planning, and noise pollution levels, with the highest readings recorded during Friday evening rush hours. The findings suggest an urgent need for traffic management solutions and stricter enforcement of construction noise regulations to mitigate the growing urban noise pollution problem, which affects approximately over a hundred million people worldwide.

Developing computational thinking through playful activities in lower secondary education

Mon, 12 Jan 2026 10:23:48 +0200

This paper presents a theoretical analysis of methods for developing computational thinking in middle school students through the use of playful activities integrated into mathematics teaching. Computational thinking represents a set of essential cognitive skills for problem-solving, with transversal applicability across STEM fields. The paper highlights how playful activities can support the development of computational thinking in middle school students (grades 5 and 6), with a focus on mathematics instruction. Computational thinking is a key 21st-century skill that helps students approach complex problems and develop logical and algorithmic strategies.

The study presents concrete examples of activities carried out during Code Week, such as “Pete the Cat Calculates Gauss’s Sum” and “Draw Geometric Shapes with Code – Mathematics Comes to Life in Scratch!”, demonstrating how both digital and non-digital games can be integrated into mathematics lessons to stimulate understanding of concepts, as well as students’ motivation and creativity. The study emphasizes the importance of playful approaches in fostering curiosity, intrinsic motivation, and creativity, providing methodological guidance for designing educational activities centered on active and collaborative learning. The conclusions underline the necessity of intentionally integrating educational games into the process of developing computational skills in the context of mathematics teaching at the middle school level.

On units with complex Galois conjugates of equal absolute value

Ștefan - Alexandru Deaconu — Mon, 12 Jan 2026 10:43:24 +0200

We investigate the following question:

Given a number field K with s real embeddings and 2t complex ones has a group of units such that all elements in U have all its complex conjugates of same absolute value, does it follow that t = 1?

This fact has an interesting implication in complex hermitian geometry, namely it describes all Oeljeklaus–Toma manifolds carrying locally conformally Kähler structures. We prove that the stated question has an affirmative answer under a (relatively mild) condition on K, namely that for some finitely may extensions L of it, L has finitely many units lying on some specific circle.

Algorithmic paradigms in Big Data

Corina Dima — Mon, 12 Jan 2026 10:48:36 +0200

The gigantic increase in the volume of data that needs to be stored, transmitted and processed in recent years has led to the emergence of a new category of algorithms designed specifically for what is called Big Data. Today's information is too large, too diverse and requires real-time transmission to be manipulated by classical techniques. This has led to a complete rethinking of algorithmic paradigms. In this paper we present the MapReduce paradigms, streaming algorithms, approximate structures, algorithms for large graphs, dimensionality reduction, distributed machine learning. For a better understanding we have added comparisons, intuitive explanations, mathematical formulas and pseudocode.

Romania's climate dynamics and future projections

Mon, 12 Jan 2026 12:46:04 +0200

Climate change is a hot topic these days in all countries around the world. Although Romania has taken important steps to combat climate change, continued efforts are needed to implement existing policies for monitoring and forecasting climate parameters, as well as to raise population awareness. In this paper, several climatic parameters are analyzed, such as mean annual air temperature, average minimum and maximum temperatures per month, mean temperature during the vegetation season, annual amount of precipitation, amount of precipitation per month and amount of precipitation during the vegetation season. Climatic parameters were studied over four periods: 1901-1930, 1931-1960, 1961-1990 and 1991-2023. Temperatures were also estimated until the year 2100. Projected future temperatures were estimated by combining data found in the current databases and Representative Concentration Pathways (RCP) projection data. Some ecoclimatic indices were calculated, such as De Martonne aridity index and the Lang rainfall index. To achieve the objectives of this study, the following databases were used: World Bank Climate Knowledge Portal, European Environment Agency (EEA), Our World in Data, European Drought Observatory (EDO), European Climate Assessment & Dataset.

Engaging and collaborative teaching methods

Adrian Ștefan Gheorghiță — Mon, 12 Jan 2026 12:52:34 +0200

The paper highlights the importance of combining traditional teaching with digital methods to stimulate students' logical thinking, creativity, and autonomy.

ATR-FTIR investigation of plastics in cosmetics, personal-care products and biodegradable materials

Steluta Gosav, Antoaneta Ene — Mon, 12 Jan 2026 12:59:51 +0200

This paper presents the relevance of ATR-FTIR technique in the investigation of the presence of synthetic plastics in selected beauty and consumer goods. In the first step, we performed a vibrational analysis of different types of synthetic plastic consumer goods, i.e. PET, PP, PS, PE, HDPE and LDPE. Thus, we identified the vibrational assignments of each IR absorption band, as well as the quality of the plastic consumer goods samples. Secondly, we investigated from point of view of the presence of plastics, some personal care products and cosmetics, i.e, a lipstick, a bio sunscreen emulsion for children, a sunscreen emulsion for adults, a toothpaste sample, a blush and five shampoo samples, using their ATR-FTIR spectra and the characteristic IR absorption bands of the analyzed synthetic plastics.

The influence of the environment of origin and histopathological structure on the evolution and prognosis of patients with prostate adenocarcinoma

Mihai Grecu, Aurelia Romila, Marius Moroianu, Ioana Maier, Adrian Maier — Mon, 12 Jan 2026 13:14:28 +0200

Adenocarcinoma is an increasingly common pathology in men, especially with advancing age. Currently, there are many treatment regimens that can lead to the cure of these patients. However, there are a number of factors that influence the evolution of these patients: comorbidities, age, environment of origin, histopathological nature, presence or absence of metastases. In a study conducted on 101 patients, it has been observed that, besides the presence or absence of metastases and the age that impacts the evolution of any oncologic pathology, the prognosis of these patients is greatly influenced by the environment of origin and the histopathological nature.

Mathematics –

Aurora Olivia Mironescu — Mon, 12 Jan 2026 13:28:42 +0200

In this study there are presented a few practical mathematical applications. How to achieve interdisciplinarity between high school and other subject that are found in the students’ curriculum. I consider that it is an essential condition of modern education, therefore contributing to the development of integrated skills (transversal or key) which prepare students for the real and professional life.

A survey on the use of vision transformer and custom-built CNN for classifying ultrasound images of breast tissue

Mihai Grecu, Simona Moldovanu — Mon, 12 Jan 2026 13:33:30 +0200

Recently, the scientific community has focused on developing convolutional neural network (CNN) algorithms to enhance the ability of medical tools to diagnose breast cancer. This study aims to evaluate a powerful new deep learning technique based on Vision Transformers (ViT), which involves pre-processing images by dividing them into patches, and a custom-built CNN. The performance of both CNNs were tested using the following class combinations: healthy/benign, healthy/malignant, benign/ malignant, and healthy/benign/malignant. The images utilized in the classification process were sourced from the BUS-BRA dataset available on Kaggle. We observed that ViT demonstrated improved performance when the benign class was included in the classification. Although the obtained accuracy is modest, it is noteworthy that in this relatively unexplored field, the classification accuracy between benign and malignant classes was 78%, and 75% for the benign class and healthy patients when the ViT was used.

Study of urban heat islands through first-order models.

Mon, 12 Jan 2026 14:16:59 +0200

The urban heat island is the phenomenon by which cities become suggestively heater due to the absorption and holding of heat by built issues. The study of urban heat islands is a present subject in Romania as well. In this paper, we present a procedure for noticing climate change using extreme values of air temperature by using first order model. The modeling urban heat islands (UHI) was achieved by using ArcGIS tools. In the case of this paper, we conducted a data collection covering the period 2017 -2024, regarding the temperature in 8 monitoring stations of National Air Quality Network (.calitateaer.ro): Gl-2, GL-3, GL-4, BR-2, BR-3, BR-4, GL-5 and BR-5. The used algorithm includes: multivariate analysis - based on the ANOVA method, clustering - to group the stations according to thermal behavior. Using spatial interpolation procedures based on methods such as IDW or Kriging to create thermal maps, we managed to obtain a zonal classification.

Influence of deposition temperature on the surface morphology and optical spectra of Sb2O3 thin films

Mon, 12 Jan 2026 14:37:06 +0200

Sb₂O₃ thin films were deposited by vacuum thermal evaporation technique at substrate temperature 298 K and 498 K. The surface morphology was investigated by atomic force microscopy (AFM) and vertical scanning interferometry (VSI). The optical transmission and reflection spectra of the Sb₂O₃ thin films were recorded in the spectral range 190-1100 nm. From these spectra, the absorption coefficient and the band gap energy of the investigated thin films were calculated.