Pub Date : 2024-02-15DOI: 10.3390/foundations4020010
Luca Fabbri
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.
{"title":"Dirac Field, van der Waals Gas, Weyssenhoff Fluid, and Newton Particle","authors":"Luca Fabbri","doi":"10.3390/foundations4020010","DOIUrl":"https://doi.org/10.3390/foundations4020010","url":null,"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 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.","PeriodicalId":81291,"journal":{"name":"Foundations","volume":"331 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140455421","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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.
{"title":"Visualizing Space–Time Multivariate Data Consisting of Discrete and Continuous Variables: A Method for the General Public","authors":"Chong-En Li, Bing-Wen Wu, Nae-Wen Kuo, Mei-Hua Yuan","doi":"10.3390/foundations4010007","DOIUrl":"https://doi.org/10.3390/foundations4010007","url":null,"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 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.","PeriodicalId":81291,"journal":{"name":"Foundations","volume":"528 ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140471488","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-01-30DOI: 10.3390/foundations4010006
Wanrong Hong, Sili Zhu, Jun Li
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.
{"title":"Data-Driven Field Representations and Measuring Processes","authors":"Wanrong Hong, Sili Zhu, Jun Li","doi":"10.3390/foundations4010006","DOIUrl":"https://doi.org/10.3390/foundations4010006","url":null,"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 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.","PeriodicalId":81291,"journal":{"name":"Foundations","volume":"67 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140484158","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-01-10DOI: 10.3390/foundations4010005
Manoj K. Singh, Ioannis K. Argyros, Samundra Regmi
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.
{"title":"A Study of Convergence of Sixth-Order Contraharmonic-Mean Newton’s Method (CHN) with Applications and Dynamics","authors":"Manoj K. Singh, Ioannis K. Argyros, Samundra Regmi","doi":"10.3390/foundations4010005","DOIUrl":"https://doi.org/10.3390/foundations4010005","url":null,"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 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.","PeriodicalId":81291,"journal":{"name":"Foundations","volume":"18 6","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139439062","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-01-03DOI: 10.3390/foundations4010004
Sheikh Zain Majid, M. Saeed, Umar Ishtiaq, Ioannis K. Argyros
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.
{"title":"The Development of a Hybrid Model for Dam Site Selection Using a Fuzzy Hypersoft Set and a Plithogenic Multipolar Fuzzy Hypersoft Set","authors":"Sheikh Zain Majid, M. Saeed, Umar Ishtiaq, Ioannis K. Argyros","doi":"10.3390/foundations4010004","DOIUrl":"https://doi.org/10.3390/foundations4010004","url":null,"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 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.","PeriodicalId":81291,"journal":{"name":"Foundations","volume":"48 16","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139451725","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-12-26DOI: 10.3390/foundations4010003
Rashed Hasan Ratul, Maliha Tasnim, Hwang-Cheng Wang, Rashadul Hasan Badhon, M. T. Kawser
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.
{"title":"The Potential Impact of a High-Frequency Telecommunication Network on Cognitive Functions: A Review","authors":"Rashed Hasan Ratul, Maliha Tasnim, Hwang-Cheng Wang, Rashadul Hasan Badhon, M. T. Kawser","doi":"10.3390/foundations4010003","DOIUrl":"https://doi.org/10.3390/foundations4010003","url":null,"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 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.","PeriodicalId":81291,"journal":{"name":"Foundations","volume":"10 17","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139157022","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-12-20DOI: 10.3390/foundations4010002
Petri P. Kärenlampi
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.
{"title":"Two Sets of Boundary Conditions in Cyclical Systems with Goodwill in Capitalization","authors":"Petri P. Kärenlampi","doi":"10.3390/foundations4010002","DOIUrl":"https://doi.org/10.3390/foundations4010002","url":null,"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 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.","PeriodicalId":81291,"journal":{"name":"Foundations","volume":"43 16","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138957380","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-12-19DOI: 10.3390/foundations4010001
Martin Bohner
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 [...]
{"title":"Updated Aims and Scope of Foundations","authors":"Martin Bohner","doi":"10.3390/foundations4010001","DOIUrl":"https://doi.org/10.3390/foundations4010001","url":null,"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 [...]","PeriodicalId":81291,"journal":{"name":"Foundations","volume":"123 9","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138959439","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-12-07DOI: 10.3390/foundations3040044
E. Papadaki, Theodoros G. Chatzimitakos, V. Athanasiadis, Dimitris Kalompatsios, Eleni Bozinou, P. Mitlianga, S. Lalas
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.
水源重金属污染是一个紧迫的环境问题。为此目的，正在使用各种程序来修复水，包括吸附。本研究的目的是探讨腐植酸(HAs)和黄腐酸(FAs)对水中金属的去除效果。具体来说，研究了HA和FA作为26种重金属、碱金属和碱土金属的吸附材料的潜力。HA和FA分别从希腊西马其顿Kozani的Mavropigi矿和South Field矿的褐煤样品中分离得到。实验采用未经pH调节的天然矿泉水进行，以便更好地了解实际样品的吸附效率。结果表明，与HAs相比，FAs能够吸收大部分被检测的金属。当两种来源的FAs均为900 ppm时，Ba(34.22-37.77%)、Ca(99.12-99.58%)和Sr(97.89-98.12%)等金属均被有效吸附，而任何来源的HAs均未被吸附(≤0.1%)。由于FA表面的官能团，它可以比HA去除更多的金属。同时，南田矿褐煤在较低浓度(300-600 ppm)下的吸附效率更高，而Mavropigi矿褐煤在较高浓度(900 ppm)下的吸附效率更高。例如，当使用300 ppm South Field矿的HAs时，Mo(62.84%)、Pb(56.81%)和U(49.22%)的去除率较高，而使用900 ppm Mavropigi矿的HAs时，As(49.90%)、Se(64.47%)和Tl(85.96%)的去除率较高。上述结果也反映在主成分分析中，表明金属参数在HA和FA参数附近或远处的分散取决于它们的吸附量。综上所述，HA和FA都可以有效地作为吸附材料去除水样中的金属。研究结果表明，为保护公众健康，在动态条件下对水中的金属进行修复具有潜在的应用前景。
{"title":"Assessment of Humic and Fulvic Acid Sorbing Potential for Heavy Metals in Water","authors":"E. Papadaki, Theodoros G. Chatzimitakos, V. Athanasiadis, Dimitris Kalompatsios, Eleni Bozinou, P. Mitlianga, S. Lalas","doi":"10.3390/foundations3040044","DOIUrl":"https://doi.org/10.3390/foundations3040044","url":null,"abstract":"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.","PeriodicalId":81291,"journal":{"name":"Foundations","volume":"103 8","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138590445","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-12-06DOI: 10.3390/foundations3040043
James Hoult, Yubin Yan
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 α∈ (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.
{"title":"Spatial Discretization for Stochastic Semilinear Superdiffusion Driven by Fractionally Integrated Multiplicative Space–Time White Noise","authors":"James Hoult, Yubin Yan","doi":"10.3390/foundations3040043","DOIUrl":"https://doi.org/10.3390/foundations3040043","url":null,"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 the Caputo sense with an order α∈ (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.","PeriodicalId":81291,"journal":{"name":"Foundations","volume":"36 5","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138595244","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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