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Foundations, Volume 4, Issue 1 (March 2024) – 9 articles

Cover Story (view full-size image): Foundations is an international, peer-reviewed, open access journal on mathematics, physics and chemistry published quarterly online by MDPI. Our aim is to provide an advanced forum for scientists to share their research or ideas to promote the innovation of fundamental research related to natural sciences and high technologies. The journal welcomes all related studies within the scope, whether they be original research articles, reviews, communications, perspectives, opinions, or protocols. There is no restriction on the maximum length of the papers. A full account of the research must be provided so that the results can be reproduced. Electronic files or software which provide full details of the calculations, proofs, and experimental procedures can be deposited as supplementary material if unable to be published in the normal way. View this paper
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20 pages, 3166 KiB  
Review
Review of the Uses of Acoustic Emissions in Monitoring Cavitation Erosion and Crack Propagation
by Ismael Fernández-Osete, David Bermejo, Xavier Ayneto-Gubert and Xavier Escaler
Foundations 2024, 4(1), 114-133; https://doi.org/10.3390/foundations4010009 - 24 Feb 2024
Viewed by 676
Abstract
Nowadays, hydropower plants are being used to compensate for the variable power produced by the new fluctuating renewable energy sources, such as wind and solar power, and to stabilise the grid. Consequently, hydraulic turbines are forced to work more often in off-design conditions, [...] Read more.
Nowadays, hydropower plants are being used to compensate for the variable power produced by the new fluctuating renewable energy sources, such as wind and solar power, and to stabilise the grid. Consequently, hydraulic turbines are forced to work more often in off-design conditions, far from their best efficiency point. This new operation strategy increases the probability of erosive cavitation and of hydraulic instabilities and pressure fluctuations that increase the risk of fatigue damage and reduce the life expectancy of the units. To monitor erosive cavitation and fatigue damage, acoustic emissions induced by very-high-frequency elastic waves within the solid have been traditionally used. Therefore, acoustic emissions are becoming an important tool for hydraulic turbine failure detection and troubleshooting. In particular, artificial intelligence is a promising signal analysis research hotspot, and it has a great potential in the condition monitoring of hydraulic turbines using acoustic emissions as a key factor in the digitalisation process. In this paper, a brief introduction of acoustic emissions and a description of their main applications are presented. Then, the research works carried out for cavitation and fracture detection using acoustic emissions are summarised, and the different levels of development are compared and discussed. Finally, the role of artificial intelligence is reviewed, and expected directions for future works are suggested. Full article
(This article belongs to the Section Physical Sciences)
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23 pages, 5485 KiB  
Article
Are There Dragon Kings in the Stock Market?
by Jiong Liu, Mohammadamin Dashti Moghaddam and Rostislav A. Serota
Foundations 2024, 4(1), 91-113; https://doi.org/10.3390/foundations4010008 - 08 Feb 2024
Viewed by 379
Abstract
In this study, we undertake a systematic study of historic market volatility spanning roughly five preceding decades. We focus specifically on the time series of the realized volatility (RV) of the S&P500 index and its distribution function. As expected, the largest values of [...] Read more.
In this study, we undertake a systematic study of historic market volatility spanning roughly five preceding decades. We focus specifically on the time series of the realized volatility (RV) of the S&P500 index and its distribution function. As expected, the largest values of RV coincide with the largest economic upheavals of the period: Savings and Loan Crisis, Tech Bubble, Financial Crisis and Covid Pandemic. We address the question of whether these values belong to one of the three categories: Black Swans (BS), that is, they lie on scale-free, power-law tails of the distribution; Dragon Kings (DK), defined as statistically significant upward deviations from BS; or Negative Dragons Kings (nDK), defined as statistically significant downward deviations from BS. In analyzing the tails of the distribution with RV>40, we observe the appearance of “potential” DK, which eventually terminate in an abrupt plunge to nDK. This phenomenon becomes more pronounced with the increase in the number of days over which the average RV is calculated—here from daily, n=1, to “monthly”, n=21. We fit the entire distribution with a modified Generalized Beta (mGB) distribution function, which terminates at a finite value of the variable but exhibits a long power-law stretch prior to that, as well as a Generalized Beta Prime (GB2) distribution function, which has a power-law tail. We also fit the tails directly with a straight line on a log-log scale. In order to ascertain BS, DK or nDK behavior, all fits include their confidence intervals and p-values are evaluated for the data points to check whether they can come from the respective distributions. Full article
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11 pages, 2238 KiB  
Article
Visualizing Space–Time Multivariate Data Consisting of Discrete and Continuous Variables: A Method for the General Public
by Chong-En Li, Bing-Wen Wu, Nae-Wen Kuo and Mei-Hua Yuan
Foundations 2024, 4(1), 80-90; https://doi.org/10.3390/foundations4010007 - 31 Jan 2024
Viewed by 609
Abstract
Visualizing multivariate data can be challenging, especially for the general public. The difficulties extend beyond determining how to present the data; they also involve comprehension. Early literature has identified various methods, including Chernoff’s face, but these methods often have significant drawbacks, making them [...] Read more.
Visualizing multivariate data can be challenging, especially for the general public. The difficulties extend beyond determining how to present the data; they also involve comprehension. Early literature has identified various methods, including Chernoff’s face, but these methods often have significant drawbacks, making them challenging to interpret. Subsequently, other techniques, such as scatterplots, parallel coordinate plots, and dynamic graphics, have been introduced. However, many of these methods can be intricate to create and interpret, particularly when visualizing high-dimensional data. Additionally, simultaneously representing discrete aspects (including “space”) and continuous aspects (including “time”) presents another challenge. This study proposes a novel approach named the “Δ table” (delta table), which transforms space–time multivariate data consisting of discrete and continuous variables into a tabular format. The Δ table is believed to be more user-friendly for the general public, which is its most significant advantage compared to previous methods. Finally, we used a case study of the decoupling of the world’s developed, newly industrialized, and developing economies in recent decades as an example of an attempt to apply the Δ table. Full article
(This article belongs to the Section Mathematical Sciences)
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19 pages, 734 KiB  
Review
Data-Driven Field Representations and Measuring Processes
by Wanrong Hong, Sili Zhu and Jun Li
Foundations 2024, 4(1), 61-79; https://doi.org/10.3390/foundations4010006 - 30 Jan 2024
Viewed by 627
Abstract
Natural mathematical objects for representing spatially distributed physical attributes are 3D field functions, which are prevalent in applied sciences and engineering, including areas such as fluid dynamics and computational geometry. The representations of these objects are task-oriented, which are achieved using various techniques [...] Read more.
Natural mathematical objects for representing spatially distributed physical attributes are 3D field functions, which are prevalent in applied sciences and engineering, including areas such as fluid dynamics and computational geometry. The representations of these objects are task-oriented, which are achieved using various techniques that are suitable for specific areas. A recent breakthrough involves using flexible parameterized representations, particularly through neural networks, to model a range of field functions. This technique aims to uncover fields for computational vision tasks, such as representing light-scattering fields. Its effectiveness has led to rapid advancements, enabling the modeling of time dependence in various applications. This survey provides an informative taxonomy of the recent literature in the field of learnable field representation, as well as a comprehensive summary in the application field of visual computing. Open problems in field representation and learning are also discussed, which help shed light on future research. Full article
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14 pages, 452 KiB  
Article
A Study of Convergence of Sixth-Order Contraharmonic-Mean Newton’s Method (CHN) with Applications and Dynamics
by Manoj K. Singh, Ioannis K. Argyros and Samundra Regmi
Foundations 2024, 4(1), 47-60; https://doi.org/10.3390/foundations4010005 - 10 Jan 2024
Viewed by 593
Abstract
We develop the local convergence of the six order Contraharmonic-mean Newton’s method (CHN) to solve Banach space valued equations. Our analysis approach is two fold: The first way uses Taylor’s series and derivatives of higher orders. The second one uses only the first [...] Read more.
We develop the local convergence of the six order Contraharmonic-mean Newton’s method (CHN) to solve Banach space valued equations. Our analysis approach is two fold: The first way uses Taylor’s series and derivatives of higher orders. The second one uses only the first derivatives. We examine the theoretical results by solving a boundary value problem also using the examples relating the proposed method with other’s methods such as Newton’s, Kou’s and Jarratt’s to show that the proposed method performs better. The conjugate maps for second-degree polynomial are verified. We also calculate the fixed points (extraneous). The article is completed with the study of basins of attraction, which support and further validate the theoretical and numerical results. Full article
(This article belongs to the Section Mathematical Sciences)
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15 pages, 398 KiB  
Article
The Development of a Hybrid Model for Dam Site Selection Using a Fuzzy Hypersoft Set and a Plithogenic Multipolar Fuzzy Hypersoft Set
by Sheikh Zain Majid, Muhammad Saeed, Umar Ishtiaq and Ioannis K. Argyros
Foundations 2024, 4(1), 32-46; https://doi.org/10.3390/foundations4010004 - 03 Jan 2024
Viewed by 830
Abstract
Inrecent years, there has been a notable increase in utilising multiple criteria decision-making (MCDM) methods in practical problem solving. The advancement of enhanced decision models with greater capabilities, coupled with technologies like geographic information systems (GIS) and artificial intelligence (AI), has fueled the [...] Read more.
Inrecent years, there has been a notable increase in utilising multiple criteria decision-making (MCDM) methods in practical problem solving. The advancement of enhanced decision models with greater capabilities, coupled with technologies like geographic information systems (GIS) and artificial intelligence (AI), has fueled the application of MCDM techniques across various domains. To address the scarcity of irrigation water resources in Bortala, Northwest China, the selection of a dam site has been approached using a hybrid model integrating a multipolar Fuzzy set and a plithogenic Fuzzy hypersoft set along with a GIS. This study considered criteria such as a geological layer, slope, soil type, and land cover. Four potential and reasonably suitable dam locations were identified using a dam construction suitability map developed for Bortala. Ultimately, we showcased the benefits of the innovative method, emphasizing an open, transparent, and science-based approach to selecting optimal dam sites through local studies and group discussions. The results highlight the effectiveness of the hybrid approach involving a fuzzy hypersoft set and plithogenic multipolar fuzzy hypersoft set in addressing the challenges of dam site selection. Full article
(This article belongs to the Section Mathematical Sciences)
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18 pages, 2108 KiB  
Review
The Potential Impact of a High-Frequency Telecommunication Network on Cognitive Functions: A Review
by Rashed Hasan Ratul, Maliha Tasnim, Hwang-Cheng Wang, Rashadul Hasan Badhon and Mohammad Tawhid Kawser
Foundations 2024, 4(1), 14-31; https://doi.org/10.3390/foundations4010003 - 26 Dec 2023
Viewed by 868
Abstract
The latest cellular technology, known as 5G-NR, is intended to significantly speed up and improve the effectiveness of wireless systems. A revolution in the telecom industry has been sparked by the widespread use of and increased reliance on cellular communication technology. Moreover, 5G [...] Read more.
The latest cellular technology, known as 5G-NR, is intended to significantly speed up and improve the effectiveness of wireless systems. A revolution in the telecom industry has been sparked by the widespread use of and increased reliance on cellular communication technology. Moreover, 5G and B5G technologies are expected to utilize an even higher-frequency range to achieve faster data transmission and lower latency communication. Consequently, while transmitting signals across various types of equipment and infrastructure, the general public is exposed to much higher frequencies of electromagnetic radiation. The increasing need for 5G NR base stations (gNodeB) has heightened public anxiety over potential negative health impacts. This study reviews recent research on the effects of electromagnetic waves on humans, particularly focusing on how these effects influence cognitive functions. Most research to date has not found significant differences in cognitive performance due to ubiquitous mobile communications. However, current research has largely been limited to 4G technologies, and the health effects of exposure to 5G user equipment (UE) and base stations in higher-frequency bands remain unexplored. If subsequent research suggests that exposure to high-frequency wireless networks significantly impacts cognitive functions, the deployment and acceptance of these technologies may face challenges and constraints. Therefore, such investigations are crucial for determining whether next-generation technologies pose no risk to individuals. Full article
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11 pages, 3191 KiB  
Article
Two Sets of Boundary Conditions in Cyclical Systems with Goodwill in Capitalization
by Petri P. Kärenlampi
Foundations 2024, 4(1), 3-13; https://doi.org/10.3390/foundations4010002 - 20 Dec 2023
Viewed by 494
Abstract
Mathematical analysis is conducted on cyclical systems with goodwill in capitalization. Proportional goodwill vanishes with vanishing tangible value. Correspondingly, periodic boundary condition does not enable commercial utilization of the goodwill. Abandoning the periodic boundary condition enables commercial utilization of the goodwill. Even if [...] Read more.
Mathematical analysis is conducted on cyclical systems with goodwill in capitalization. Proportional goodwill vanishes with vanishing tangible value. Correspondingly, periodic boundary condition does not enable commercial utilization of the goodwill. Abandoning the periodic boundary condition enables commercial utilization of the goodwill. Even if a physical system is periodic, an agent can abandon the corresponding boundary condition by divesting. Example cases are shown in terms of boreal forestry systems. Full article
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2 pages, 133 KiB  
Editorial
Updated Aims and Scope of Foundations
by Martin Bohner
Foundations 2024, 4(1), 1-2; https://doi.org/10.3390/foundations4010001 - 19 Dec 2023
Viewed by 542
Abstract
Foundations published its inaugural issue in 2021, establishing itself as a new international open access, peer-reviewed, multidisciplinary journal of science and techonology, covering mathematics, physics, chemistry, biology, engineering, earth sciences, materials, information sciences, and medical sciences [...] Full article
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