Journal Description
Foundations
Foundations
is an international, peer-reviewed, open access journal on mathematics, physics and chemistry published quarterly online by MDPI.
- Open Access free for readers, with article processing charges (APC) paid by authors or their institutions.
- Rapid Publication: manuscripts are peer-reviewed and a first decision is provided to authors approximately 23 days after submission; acceptance to publication is undertaken in 4.6 days (median values for papers published in this journal in the second half of 2023).
- Recognition of Reviewers: APC discount vouchers, optional signed peer review, and reviewer names published annually in the journal.
- Foundations is a companion journal of Molecules, Entropy and Mathematics.
Latest Articles
Minimal Conditioned Stiffness Matrices with Frequency-Dependent Path Following for Arbitrary Elastic Layers over Half-Spaces
Foundations 2024, 4(2), 205-224; https://doi.org/10.3390/foundations4020014 - 14 May 2024
Abstract
This paper introduces an efficient computational procedure for analyzing the propagation of harmonic waves in layered elastic media. This offers several advantages, including the ability to handle arbitrary frequencies, depths, and the number of layers above an elastic half-space, and efforts to follow
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This paper introduces an efficient computational procedure for analyzing the propagation of harmonic waves in layered elastic media. This offers several advantages, including the ability to handle arbitrary frequencies, depths, and the number of layers above an elastic half-space, and efforts to follow dispersion curves and flag up possible singularities are investigated. While there are inherent limitations in terms of computational accuracy and capacity, this methodology is straightforward to implement for studying free or forced vibrations and obtaining relevant response data. We present computations of wavenumber dispersion diagrams, phase velocity plots, and response data in both the frequency and time domains. These computational results are provided for two example cases: plane strain and axisymmetry. Our methodology is grounded in a well-conditioned dynamic stiffness approach specifically tailored for deep-layered strata analysis. We introduce an innovative method for efficiently computing wavenumber dispersion curves. By tracking the slope of these curves, users can effectively manage continuation parameters. We illustrate this technique through numerical evidence of a layer resonance in a real-life case study characterized by a fold in the dispersion curves. Furthermore, this framework is particularly advantageous for engineers addressing problems related to ground-borne vibrations. It enables the analysis of phenomena such as zero group velocity (ZGV), where a singularity occurs, both in the frequency and time domains, shedding light on the unique characteristics of such cases. Given the reduced dimension of the problem, this formulation can considerably aid geophysicists and engineers in areas such as MASW or SASW techniques.
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(This article belongs to the Section Physical Sciences)
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A Fundamental Duality in the Exact Sciences: The Application to Quantum Mechanics
by
David Ellerman
Foundations 2024, 4(2), 175-204; https://doi.org/10.3390/foundations4020013 - 11 May 2024
Abstract
There is a fundamental subsets–partitions duality that runs through the exact sciences. In more concrete terms, it is the duality between elements of a subset and the distinctions of a partition. In more abstract terms, it is the reverse-the-arrows of category theory that
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There is a fundamental subsets–partitions duality that runs through the exact sciences. In more concrete terms, it is the duality between elements of a subset and the distinctions of a partition. In more abstract terms, it is the reverse-the-arrows of category theory that provides a major architectonic of mathematics. The paper first develops the duality between the Boolean logic of subsets and the logic of partitions. Then, probability theory and information theory (as based on logical entropy) are shown to start with the quantitative versions of subsets and partitions. Some basic universal mapping properties in the category of are developed that precede the abstract duality of category theory. But by far the main application is to the clarification and interpretation of quantum mechanics. Since classical mechanics illustrates the Boolean worldview of full distinctness, it is natural that quantum mechanics would be based on the indefiniteness of its characteristic superposition states, which is modeled at the set level by partitions (or equivalence relations). This approach to interpreting quantum mechanics is not a jury-rigged or ad hoc attempt at the interpretation of quantum mechanics but is a natural application of the fundamental duality running throughout the exact sciences.
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(This article belongs to the Section Physical Sciences)
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Exchangeable Quantities and Power Laws: Τhe Case of Pores in Solids
by
Antigoni G. Margellou and Philippos J. Pomonis
Foundations 2024, 4(2), 156-174; https://doi.org/10.3390/foundations4020012 - 23 Apr 2024
Abstract
In this work we suggest that the common cause for the development of various power laws is the existence of a suitable exchangeable quantity between the agents of a set. Examples of such exchangeable quantities, leading to eponymous power laws, include money (Pareto’s
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In this work we suggest that the common cause for the development of various power laws is the existence of a suitable exchangeable quantity between the agents of a set. Examples of such exchangeable quantities, leading to eponymous power laws, include money (Pareto’s Law), scientific knowledge (Lotka’s Law), people (Auerbach’s Law), and written or verbal information (Zipf’s Law), as well as less common cases like bullets during deadly conflicts, recognition in social networks, heat between the atmosphere and sea-ice floes, and, finally, mass of water vapors between pores in solids. This last case is examined closely in the present article based on extensive experimental data. It is shown that the transferred mass between pores, which eventually grow towards a power law distribution, may be expressed using different parameters, either transferred surface area, or transferred volume, or transferred pore length or transferred pore anisotropy. These distinctions lead to different power laws of variable strength as reflected by the corresponding exponent. The exponents depend quantitatively on the spread of frequency distribution of the examined parameter and tend to zero as the spread of distribution tends to a single order of magnitude. A comparison between the energy and the entropy of different kinds of pore distributions reveals that these two statistical parameters are linearly related, implying that the system poise at a critical state and the exchangeable quantities are the most convenient operations helping to keep this balance.
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(This article belongs to the Section Chemical Sciences)
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On Mach’s Principle in Entropic Gravity
by
A. Schlatter and R. E. Kastner
Foundations 2024, 4(2), 146-155; https://doi.org/10.3390/foundations4020011 - 3 Apr 2024
Abstract
The question of where the inertial properties of matter come from has been open for a long time. Isaac Newton considered inertia an intrinsic property of matter. Ernst Mach held a different view whereby the inertia of a body comes from its interaction
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The question of where the inertial properties of matter come from has been open for a long time. Isaac Newton considered inertia an intrinsic property of matter. Ernst Mach held a different view whereby the inertia of a body comes from its interaction with the rest of the universe. This idea is known today as Mach’s principle. We discuss Mach’s principle based on transactional gravity, the recently developed connection of entropic gravity to the physics of quantum events, induced by transactions. It is shown that Mach’s principle holds and that there is a fundamental relation between the gravitational constant and the total mass in the causal universe. This relationship, derived by means of entropic principles, is rigorously proven.
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(This article belongs to the Section Physical Sciences)
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Dirac Field, van der Waals Gas, Weyssenhoff Fluid, and Newton Particle
by
Luca Fabbri
Foundations 2024, 4(2), 134-145; https://doi.org/10.3390/foundations4020010 - 28 Mar 2024
Abstract
This article considers the Dirac field in polar formulation and shows that when torsion is taken in effective approximation the theory has the thermodynamic properties of a van der Waals gas. It is then shown that in the limit of zero chiral angle
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This article considers the Dirac field in polar formulation and shows that when torsion is taken in effective approximation the theory has the thermodynamic properties of a van der Waals gas. It is then shown that in the limit of zero chiral angle the van der Waals gas reduces to a Weyssenhoff fluid, and in spinlessness regime the Weyssenhoff fluid further reduces to a Newton particle. This nesting of approximations allows us to interpret the various spinor quantities. We will see that torsion will provide a form of negative pressure, while the chiral angle will be related to a type of temperature.
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(This article belongs to the Section Physical Sciences)
Open AccessReview
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
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,
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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.
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(This article belongs to the Section Physical Sciences)
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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 - 8 Feb 2024
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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
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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 , 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, , to “monthly”, . 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.
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Open AccessArticle
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
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
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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.
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(This article belongs to the Section Mathematical Sciences)
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Open AccessReview
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
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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
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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.
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Open AccessArticle
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
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
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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.
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(This article belongs to the Section Mathematical Sciences)
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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 - 3 Jan 2024
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
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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.
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(This article belongs to the Section Mathematical Sciences)
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Open AccessReview
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
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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
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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.
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Open AccessArticle
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
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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
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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.
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Open AccessEditorial
Updated Aims and Scope of Foundations
by
Martin Bohner
Foundations 2024, 4(1), 1-2; https://doi.org/10.3390/foundations4010001 - 19 Dec 2023
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 [...]
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Assessment of Humic and Fulvic Acid Sorbing Potential for Heavy Metals in Water
by
Eirini S. Papadaki, Theodoros Chatzimitakos, Vassilis Athanasiadis, Dimitrios Kalompatsios, Eleni Bozinou, Paraskevi Mitlianga and Stavros I. Lalas
Foundations 2023, 3(4), 788-804; https://doi.org/10.3390/foundations3040044 - 7 Dec 2023
Cited by 1
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Pollution of water sources with heavy metals is a pressing environmental issue. To this end, various procedures are being used to remediate water, including sorption. The aim of this study was to investigate the effectiveness of humic acids (HAs) and fulvic acids (FAs)
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Pollution of water sources with heavy metals is a pressing environmental issue. To this end, various procedures are being used to remediate water, including sorption. The aim of this study was to investigate the effectiveness of humic acids (HAs) and fulvic acids (FAs) for the removal of metals from water. Specifically, HA and FA were examined for their potential to be used as sorbent materials for 26 heavy metals, alkali metals, and alkaline earth metals. HA and FA were isolated from lignite samples from two mines (Mavropigi mine and South Field mine, Kozani, West Macedonia, Greece). Experiments were carried out using natural mineral water without pH adjustment, so as to gain a better overview of the sorption efficiency in real-life samples. The results showed that FAs were able to sorb most of the examined metals compared to HAs. Several metals such as Ba (34.22–37.77%), Ca (99.12–99.58%), and Sr (97.89–98.12%) were efficiently sorbed when 900 ppm of FAs from both sources were used but were not sorbed by HAs from any source (≤0.1%). Due to the functional groups on the surface of FA, it is plausible to conclude that it can remove more metals than HA. Meanwhile, lignite from the South Field mine was found to be more efficient for the sorption efficiency in lower concentrations (300–600 ppm), whereas lignite from the Mavropigi mine was more effective in higher concentrations (900 ppm). For instance, higher removal rates were observed in Mo (62.84%), Pb (56.81%), and U (49.22%) when 300 ppm of HAs of South Field mine were used, whilst the employment of 900 ppm of HAs from Mavropigi mine led to high removal rates of As (49.90%), Se (64.47%), and Tl (85.96%). The above results were also reflected in a principal component analysis, which showed the dispersion of the metal parameters near to or far from the HA and FA parameters depending on their sorption capacity. Overall, both HA and FA could be effectively utilized as sorbent materials for metal removal from water samples. The results of the research indicate a potential application to the remediation of water from metals under dynamic conditions in order to protect public health.
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Open AccessArticle
Spatial Discretization for Stochastic Semilinear Superdiffusion Driven by Fractionally Integrated Multiplicative Space–Time White Noise
by
James A. Hoult and Yubin Yan
Foundations 2023, 3(4), 763-787; https://doi.org/10.3390/foundations3040043 - 6 Dec 2023
Abstract
We investigate the spatial discretization of a stochastic semilinear superdiffusion problem driven by fractionally integrated multiplicative space–time white noise. The white noise is characterized by its properties of being white in both space and time, and the time fractional derivative is considered in
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We investigate the spatial discretization of a stochastic semilinear superdiffusion problem driven by fractionally integrated multiplicative space–time white noise. The white noise is characterized by its properties of being white in both space and time, and the time fractional derivative is considered in the Caputo sense with an order ∈ (1, 2). A spatial discretization scheme is introduced by approximating the space–time white noise with the Euler method in the spatial direction and approximating the second-order space derivative with the central difference scheme. By using the Green functions, we obtain both exact and approximate solutions for the proposed problem. The regularities of both the exact and approximate solutions are studied, and the optimal error estimates that depend on the smoothness of the initial values are established.
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(This article belongs to the Special Issue Recent Advances in Fractional Differential Equations and Inclusions II)
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Common Fixed-Point Theorems for Families of Compatible Mappings in Neutrosophic Metric Spaces
by
Umar Ishtiaq, Khaleel Ahmad, Farhan Ali, Moazzama Faraz and Ioannis K. Argyros
Foundations 2023, 3(4), 738-762; https://doi.org/10.3390/foundations3040042 - 30 Nov 2023
Abstract
Sets, probability, and neutrosophic logic are all topics covered by neutrosophy. Moreover, the classical set, fuzzy set, and intuitionistic fuzzy set are generalized using the neutrosophic set. A neutrosophic set is a mathematical concept used to solve problems with inconsistent, ambiguous, and inaccurate
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Sets, probability, and neutrosophic logic are all topics covered by neutrosophy. Moreover, the classical set, fuzzy set, and intuitionistic fuzzy set are generalized using the neutrosophic set. A neutrosophic set is a mathematical concept used to solve problems with inconsistent, ambiguous, and inaccurate data. In this article, we demonstrate some basic fixed-point theorems for any even number of compatible mappings in complete neutrosophic metric spaces. Our primary findings expand and generalize the findings previously established in the literature.
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(This article belongs to the Section Mathematical Sciences)
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Relativistic Time-of-Arrival Measurements: Predictions, Post-Selection and Causality Problems
by
Charis Anastopoulos and Maria-Electra Plakitsi
Foundations 2023, 3(4), 724-737; https://doi.org/10.3390/foundations3040041 - 29 Nov 2023
Cited by 1
Abstract
We analyze time-of-arrival probability distributions for relativistic particles in the context of quantum field theory (QFT). We show that QFT leads to a unique prediction, modulo post-selection that incorporates properties of the apparatus into the initial state. We also show that an experimental
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We analyze time-of-arrival probability distributions for relativistic particles in the context of quantum field theory (QFT). We show that QFT leads to a unique prediction, modulo post-selection that incorporates properties of the apparatus into the initial state. We also show that an experimental distinction of different probability assignments is possible especially in near-field measurements. We also analyze causality in relativistic measurements. We consider a quantum state obtained by a spacetime-localized operation on the vacuum, and we show that detection probabilities are typically characterized by small transient non-causal terms. We explain that these terms originate from Feynman propagation of the initial operation, because the Feynman propagator does not vanish outside the light cone. We discuss possible ways to restore causality, and we argue that this may not be possible in measurement models that involve switching the field–apparatus coupling on and off.
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(This article belongs to the Section Physical Sciences)
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Open AccessReview
Ostrowski-Type Fractional Integral Inequalities: A Survey
by
Muhammad Tariq, Sotiris K. Ntouyas and Bashir Ahmad
Foundations 2023, 3(4), 660-723; https://doi.org/10.3390/foundations3040040 - 13 Nov 2023
Abstract
This paper presents an extensive review of some recent results on fractional Ostrowski-type inequalities associated with a variety of convexities and different kinds of fractional integrals. We have taken into account the classical convex functions, quasi-convex functions, -convex
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This paper presents an extensive review of some recent results on fractional Ostrowski-type inequalities associated with a variety of convexities and different kinds of fractional integrals. We have taken into account the classical convex functions, quasi-convex functions, -convex functions, s-convex functions, -convex functions, strongly convex functions, harmonically convex functions, h-convex functions, Godunova-Levin-convex functions, -convex functions, P-convex functions, m-convex functions, -convex functions, exponentially s-convex functions, -convex functions, exponential-convex functions, -convex functions, quasi-geometrically convex functions, -convex functions and n-polynomial exponentially s-convex functions. Riemann–Liouville fractional integral, Katugampola fractional integral, k-Riemann–Liouville, Riemann–Liouville fractional integrals with respect to another function, Hadamard fractional integral, fractional integrals with exponential kernel and Atagana-Baleanu fractional integrals are included. Results for Ostrowski-Mercer-type inequalities, Ostrowski-type inequalities for preinvex functions, Ostrowski-type inequalities for Quantum-Calculus and Ostrowski-type inequalities of tensorial type are also presented.
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(This article belongs to the Special Issue Recent Advances in Fractional Differential Equations and Inclusions II)
Open AccessArticle
Comparison between Two Competing Newton-Type High Convergence Order Schemes for Equations on Banach Spaces
by
Ioannis K. Argyros, Manoj K. Singh and Samundra Regmi
Foundations 2023, 3(4), 643-659; https://doi.org/10.3390/foundations3040039 - 30 Oct 2023
Abstract
We carried out a local comparison between two ninth convergence order schemes for solving nonlinear equations, relying on first-order Fréchet derivatives. Earlier investigations require the existence as well as the boundedness of derivatives of a high order to prove the convergence of these
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We carried out a local comparison between two ninth convergence order schemes for solving nonlinear equations, relying on first-order Fréchet derivatives. Earlier investigations require the existence as well as the boundedness of derivatives of a high order to prove the convergence of these schemes. However, these derivatives are not in the schemes. These assumptions restrict the applicability of the schemes, which may converge. Numerical results along with a boundary value problem are given to examine the theoretical results. Both schemes are symmetrical not only in the theoretical results (formation and convergence order), but the numerical and dynamical results are also similar. We calculated the convergence radii of the nonlinear schemes. Moreover, we obtained the extraneous fixed points for the proposed schemes, which are repulsive and are not part of the solution space. Lastly, the theoretical and numerical results are supported by the dynamic results, where we plotted basins of attraction for a selected test function.
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(This article belongs to the Special Issue Iterative Methods with Applications in Mathematical Sciences II)
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