Current Issue : April-June Volume : 2025 Issue Number : 2 Articles : 5 Articles
The article is devoted to completing the proof of the inconsistency of set theory. In this article and in the two preceding ones, all steps of the proof are based on generally accepted informal set-theoretic reasoning, but consider the prohibitions that were included in axiomatic set theories in order to overcome the difficulties encountered by the naive Cantor set theory. Therefore, in fact, the articles are about proving the inconsistency of existing axiomatic set theories, in particular, the ZFC theory....
This paper investigates the connections between ring theory, module theory, and graph theory through the graph G(R) of a ring R. We establish that vertices of G(R) correspond to modules, with edges defined by the vanishing of their tensor product. Key results include the graph’s connectivity, a diameter of at most 3, and a girth of at most 7 when cycles are present. We show that the set of modules S (R) is empty if and only if R is a field, and that for semisimple rings, the diameter is at most 2. The paper also discusses module isomorphisms over subrings and localization, as well as the inclusion of G(T ) within G(R) for a quotient ring T, highlighting that the reverse inclusion is not guaranteed. Finally, we provide an example illustrating that a non-finitely generated module M does not imply M ⊗M = 0 . These findings deepen our understanding of the interplay among rings, modules, and graphs....
The energy sector is the second largest emitter of greenhouse (GHG) gases in Kenya, emitting about 31.2% of GHG emissions in the country. The aim of this study was to model Kenya’s GHG emissions by the energy sector using ARIMA models for forecasting future values. The data used for the study was that of Kenya’s GHG emissions by the energy sector for the period starting from 1970 to 2022 obtained for the International Monetary Fund (IMF) database that was split into training and testing sets using the 80/20 rule for modelling purposes. The best specification for the ARIMA model was identified using Akaike Information Criterion (AIC), root mean squared error (RMSE), mean absolute error (MAE), mean absolute percentage error (MAPE) and mean absolute scaled error (MASE). ARIMA (1, 1, 1) was identified as the best model for modelling Kenya’s GHG emissions and forecasting future values. Using this model, Kenya’s GHG emissions by the energy sector were forecasted to increase to a value of about 43.13 million metric tons of carbon dioxide equivalents by 2030. The study, therefore, recommends that Kenya should accelerate the adjustment of industry structure and improve the efficient use of energy, optimize the energy structure and accelerate development and promotion of energy-efficient products to reduce the emission of GHGs by the country’s energy sector....
The polystyrene (PS) materials tend to yellow over time. The yellowing phenomenon is an indicator of the material’s reduced performance and structural integrity. In the natural environment, sunlight is a major contributor to the yellowing, and elevated temperatures can accelerate the chemical reactions that lead to yellowing. The natural environmental factors are difficult to control, making it challenging to predict the yellowing process accurately. In this paper, we established a model to quantify the relationship between the yellowing index and key factors, solar radiation and temperature, from outdoor monitored climatic data. The model is trained and tested by the datasets collected from atmospheric exposure test stations located in Guangzhou and Qionghai. Same kinds of PS materials were exposed to external natural environments at the stations for one year. The parameters were estimated by least squares method. The results indicated that the model fits training and testing datasets well with R2 of 0.980 and 0.985, respectively....
Stopping sets are useful for analyzing the performance of a linear code under an iterative decoding algorithm over an erasure channel. In this paper, we consider stopping sets of one-point algebraic geometry codes defined by a hyperelliptic curve of genus g = 2 defined by the plane model y2 = f (x), where the degree of f (x) was 5. We completely classify the stopping sets of the one-point algebraic geometric codes C = CΩ(D,mP∞) defined by a hyperelliptic curve of genus 2 with m ≤ 4. For m = 3, we proved in detail that all sets S ⊆ {1, 2, . . . , n} of a size greater than 3 are stopping sets and we give an example of sets of size 2, 3 that are not....
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