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Keywords = Hölder law

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24 pages, 478 KiB  
Article
Addressing Maintenance Challenges and Reputational Risks in Spanish Real Estate: A Strategic Role for Facility Managers
by Luis Eduardo Bardón Rubio and Antonio Eduardo Humero Martín
Urban Sci. 2025, 9(7), 250; https://doi.org/10.3390/urbansci9070250 - 1 Jul 2025
Viewed by 328
Abstract
This study addresses a critical deficiency in real estate management by examining how contractual arrangements between property owners and facility managers (FMs) can mitigate reputational damage arising from third-party liability incidents. While Spanish regulations impose comprehensive conservation and maintenance duties on property owners, [...] Read more.
This study addresses a critical deficiency in real estate management by examining how contractual arrangements between property owners and facility managers (FMs) can mitigate reputational damage arising from third-party liability incidents. While Spanish regulations impose comprehensive conservation and maintenance duties on property owners, current contractual frameworks inadequately protect owners from reputational risks when damages occur due to FMs’ negligence or operational failures. This conceptual study employs a systematic analysis of 16 Spanish regulations governing real estate conservation and maintenance duties, complemented by an examination of the statutory contract law and a Strengths, Weaknesses, Opportunities, and Threats (SWOT) analysis to evaluate the proposed solutions. The analysis reveals four distinct liability attribution blocks, ranging from quasi-objective owner liability to full objective installation holder liability. Current service contracts between owners and FMs provide insufficient reputational protection, as civil liability remains with the property owners regardless of the FMs’ performance. This study identifies specific contractual mechanisms—combining statutory work contracts with representative mandates and installation ownership transfers—that effectively redirect tort liability from owners to FMs. While this study focuses on Spanish regulatory frameworks as a methodologically necessary foundation for theoretical development, the conceptual framework provides transferable mechanisms for adaptation to other civil law jurisdictions. This study constitutes the first comprehensive analysis bridging legal architecture and facility management to propose novel liability transfer mechanisms within established frameworks. Full article
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30 pages, 291 KiB  
Article
Rethinking Trademark Dilution in Jordan: Addressing Ambiguities and Aligning with Global Standards
by Shatha Majid Shannag and Subhajit Basu
Laws 2025, 14(3), 36; https://doi.org/10.3390/laws14030036 - 25 May 2025
Viewed by 1360
Abstract
This paper critically analyses the application of the trademark dilution doctrine under Jordanian trademark law, exposing fundamental deficiencies arising from statutory ambiguity and inconsistent judicial interpretation. The indeterminate definition of a “well-known” trademark in the second section has led to an indiscriminate classification [...] Read more.
This paper critically analyses the application of the trademark dilution doctrine under Jordanian trademark law, exposing fundamental deficiencies arising from statutory ambiguity and inconsistent judicial interpretation. The indeterminate definition of a “well-known” trademark in the second section has led to an indiscriminate classification of foreign marks as inherently well-known, resulting in courts extending automatic dilution protection without a rigorous evidentiary assessment. This practice fosters an implicit presumption favouring foreign trademark holders, potentially disadvantaging domestic marks that may not receive commensurate protection, thereby undermining the principle of equitable trademark enforcement. This paper argues for a systematic recalibration of Jordan’s dilution framework. A comparative analysis of the well-established dilution doctrines in the United States and European Union identifies jurisprudential best practices that could enhance the doctrinal coherence and judicial application of dilution protection in Jordan. Furthermore, drawing on the WIPO Joint Recommendation as a normative foundation, the paper proposes legal reforms to rectify inconsistencies, ensuring a more balanced and principled approach to trademark dilution. We argue that aligning Jordan’s legal framework with international standards strengthens the discourse on harmonising intellectual property law and ensuring equitable trademark protection in emerging markets. Full article
39 pages, 488 KiB  
Article
The Local Times for Additive Brownian Sheets and the Intersection Local Times for Independent Brownian Sheets
by Mingjie Liang and Chenfang Lin
Mathematics 2025, 13(9), 1425; https://doi.org/10.3390/math13091425 - 26 Apr 2025
Viewed by 330
Abstract
A new class of Gaussian random fields is introduced in this article, described as additive Brownian sheets (ABSs), which can be regarded as a type of generalized Brownian sheet encompassing Brownian motions, Brownian sheets, and additive Brownian motions. The existence, joint continuity and [...] Read more.
A new class of Gaussian random fields is introduced in this article, described as additive Brownian sheets (ABSs), which can be regarded as a type of generalized Brownian sheet encompassing Brownian motions, Brownian sheets, and additive Brownian motions. The existence, joint continuity and the Hölder law of the local times for ABSs are derived under certain conditions, and some results of the intersection local times for two independent Brownian sheets are also given as special cases. Furthermore, the intersection local times for two independent Brownian sheets in a Hida distribution is proved through white noise analysis, and the Wiener chaos expansion of the intersection local times is expressed in terms of S-transform. Additionally, the large deviations for the intersection local time of two independent Brownian sheets are established. The multi-parameter Gaussian random fields have become a core tool for complex system analysis due to their flexible multidimensional modeling capabilities. With the improvement of computational efficiency and interdisciplinary integration, the ABS constructed in this article will unleash greater potential in fields such as metaverse simulation, financial mathematics, climate science, precision medicine, quantum physics, and string theory. Full article
(This article belongs to the Special Issue Mathematical Analysis: Theory, Methods and Applications)
16 pages, 3378 KiB  
Article
Multifractal Analysis of Neuronal Morphology in the Human Dorsal Striatum: Age-Related Changes and Spatial Differences
by Zorana Nedeljković, Bojana Krstonošić, Nebojša Milošević, Olivera Stanojlović, Dragan Hrnčić and Nemanja Rajković
Fractal Fract. 2024, 8(9), 514; https://doi.org/10.3390/fractalfract8090514 - 30 Aug 2024
Viewed by 1134
Abstract
Multifractal analysis offers a sophisticated method to examine the complex morphology of neurons, which traditionally have been analyzed using monofractal techniques. This study investigates the multifractal properties of two-dimensional neuron projections from the human dorsal striatum, focusing on potential morphological changes related to [...] Read more.
Multifractal analysis offers a sophisticated method to examine the complex morphology of neurons, which traditionally have been analyzed using monofractal techniques. This study investigates the multifractal properties of two-dimensional neuron projections from the human dorsal striatum, focusing on potential morphological changes related to aging and differences based on spatial origin within the nucleus. Using multifractal spectra, we analyzed various parameters, including generalized dimensions and Hölder exponents, to characterize the neurons’ morphology. Despite the detailed analysis, no significant correlation was found between neuronal morphology and age. However, clear morphological differences were observed between neurons from the caudate nucleus and the putamen. Neurons from the putamen displayed higher morphological complexity and greater local homogeneity, while those from the caudate nucleus exhibited more scaling laws and higher local heterogeneity. These findings suggest that while age may not significantly impact neuronal morphology in the dorsal striatum, the spatial origin within this brain region plays a crucial role in determining neuronal structure. Further studies with larger samples are recommended to confirm these findings and to explore the full potential of multifractal analysis in neuronal morphology research. Full article
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10 pages, 3271 KiB  
Article
Effects of the Space Holder Shape on the Pore Structure and Mechanical Properties of Porous Cu with a Wide Porosity Range
by Jian Xiao, Yanping He, Wenjun Ma, Yiheng Yue and Guibao Qiu
Materials 2024, 17(12), 3008; https://doi.org/10.3390/ma17123008 - 19 Jun 2024
Cited by 2 | Viewed by 1088
Abstract
Porous copper (Cu), with varying porosities, has been made using carbamide as a space holder through the powder metallurgy route. Two shapes of carbamide particles were used, (i) needlelike and (ii) spherical, in order to investigate the effect of the space holder shape [...] Read more.
Porous copper (Cu), with varying porosities, has been made using carbamide as a space holder through the powder metallurgy route. Two shapes of carbamide particles were used, (i) needlelike and (ii) spherical, in order to investigate the effect of the space holder shape on the pore structure and mechanical properties of porous Cu. The compressive deformation behavior of porous Cu was studied under a compression test. The pores’ structural characteristics and mechanical properties of the porous Cu varied significantly with the shape of the space holder. Although the effect of the space holder shape on the porosity was not regular, the effect on the mechanical properties was regular. The stress increased monotonically with the increase in the strain, and strain hardening occurred at the plastic yield stage. The elastic modulus and yield strength followed the power law, with the relative density irrespective of the space holder shape. The empirical constants associated with different empirically developed power law relations were different, according to the shape of space holder. A quantitative relationship between the elastic modulus and yield strength and the spacer content was obtained to control the mechanical properties of the present porous Cu or other porous metals and metal foams using the well-known space holder method. Full article
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17 pages, 3768 KiB  
Article
A Study on Yield Criteria Influence on Anisotropic Behavior and Fracture Prediction in Deep Drawing SECC Steel Cylindrical Cups
by Quy-Huy Trieu, The-Thanh Luyen, Duc-Toan Nguyen and Ngoc-Tam Bui
Materials 2024, 17(12), 2872; https://doi.org/10.3390/ma17122872 - 12 Jun 2024
Cited by 3 | Viewed by 1520
Abstract
The deep drawing process, a pivotal technique in sheet metal forming, frequently encounters challenges such as anisotropy-induced defects. This study comprehensively investigates the influence of various yield criteria on the anisotropic behavior and fracture prediction in SECC steel cylindrical cups. It integrates Hill’48R, [...] Read more.
The deep drawing process, a pivotal technique in sheet metal forming, frequently encounters challenges such as anisotropy-induced defects. This study comprehensively investigates the influence of various yield criteria on the anisotropic behavior and fracture prediction in SECC steel cylindrical cups. It integrates Hill’48R, Hill’48S, and von Mises yield criteria in conjunction with Swift’s hardening law to evaluate material behavior under complex stress states. Experimental and numerical simulations assess the anisotropy effects across multiple orientations (0°, 45°, and 90°), revealing intricate relationships between stress criteria and material response. The findings indicate significant discrepancies between isotropic and anisotropic models in predicting fracture heights, emphasizing the importance of selecting appropriate yield criteria. Notably, the von Mises criterion results in lower fracture heights, suggesting higher susceptibility to fractures, while the Hill’48R model aligns closely with experimental data, validated through variations in punch corner radius and blank holder force parameters, with a maximum deviation of 3.23%. Hill’48S displays moderate plastic deformation characteristics. Full article
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16 pages, 2671 KiB  
Article
Advancing Thrombosis Research: A Novel Device for Measuring Clot Permeability
by Elia Landi, Marco Mugnaini, Tunahan Vatansever, Ada Fort, Valerio Vignoli, Elvira Giurranna, Flavia Rita Argento, Eleonora Fini, Giacomo Emmi, Claudia Fiorillo and Matteo Becatti
Sensors 2024, 24(12), 3764; https://doi.org/10.3390/s24123764 - 9 Jun 2024
Cited by 3 | Viewed by 2033
Abstract
Thromboembolism, a global leading cause of mortality, needs accurate risk assessment for effective prophylaxis and treatment. Current stratification methods fall short in predicting thrombotic events, emphasizing the need for a deeper understanding of clot properties. Fibrin clot permeability, a crucial parameter in hypercoagulable [...] Read more.
Thromboembolism, a global leading cause of mortality, needs accurate risk assessment for effective prophylaxis and treatment. Current stratification methods fall short in predicting thrombotic events, emphasizing the need for a deeper understanding of clot properties. Fibrin clot permeability, a crucial parameter in hypercoagulable states, impacts clot structure and resistance to lysis. Current clot permeability measurement limitations propel the need for standardized methods. Prior findings underscore the importance of clot permeability in various thrombotic conditions but call for improvements and more precise, repeatable, and standardized methods. Addressing these challenges, our study presents an upgraded, portable, and cost-effective system for measuring blood clot permeability, which utilizes a pressure-based approach that adheres to Darcy’s law. By enhancing precision and sensitivity in discerning clot characteristics, this innovation provides a valuable tool for assessing thrombotic risk and associated pathological conditions. In this paper, the authors present a device that is able to automatically perform the permeability measurements on plasma or fibrinogen in vitro-induced clots on specific holders (filters). The proposed device has been tailored to distinguish clot permeability, with high precision and sensitivity, between healthy subjects and high cardiovascular-risk patients. The precise measure of clot permeability represents an excellent indicator of thrombotic risk, thus allowing the clinician, also on the basis of other anamnestic and laboratory data, to attribute a risk score to the subject. The proposed instrument was characterized by performing permeability measurements in plasma and purified fibrinogen clots derived from 17 Behcet patients and 15 sex- and age-matched controls. As expected, our results clearly indicate a significant difference in plasma clot permeability in Behcet patients with respect to controls (0.0533 ± 0.0199 d vs. 0.0976 ± 0.0160 d, p < 0.001). This difference was confirmed in the patient’s vs. control fibrin clots (0.0487 ± 0.0170 d vs. 0.1167 ± 0.0487 d, p < 0.001). In conclusion, our study demonstrates the feasibility, efficacy, portability, and cost-effectiveness of a novel device for measuring clot permeability, allowing healthcare providers to better stratify thrombotic risk and tailor interventions, thereby improving patient outcomes and reducing healthcare costs, which could significantly improve the management of thromboembolic diseases. Full article
(This article belongs to the Special Issue Metrology for Industry 4.0 & IoT 2023)
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21 pages, 315 KiB  
Article
“We Cannot Go There, They Cannot Come Here”: Dispersed Care, Asian Indian Immigrant Families and the COVID-19 Pandemic
by Rianka Roy, Bandana Purkayastha and Elizabeth Chacko
Soc. Sci. 2024, 13(5), 252; https://doi.org/10.3390/socsci13050252 - 6 May 2024
Cited by 2 | Viewed by 2619
Abstract
The COVID-19 pandemic disrupted families and displaced individuals. For migrant workers, these disruptions and displacements exacerbated the state-imposed constraints on family formation. But how did high-skilled and high-wage immigrants, presumably immune from these challenges, provide care to and receive care from families during [...] Read more.
The COVID-19 pandemic disrupted families and displaced individuals. For migrant workers, these disruptions and displacements exacerbated the state-imposed constraints on family formation. But how did high-skilled and high-wage immigrants, presumably immune from these challenges, provide care to and receive care from families during the pandemic? Based on 33 in-depth interviews with high-skilled Asian Indian immigrants in the USA during the pandemic, we note disruptions in their care to and from families. These disruptions reveal a persistent pattern of dispersion in immigrant families which leads to what we call “dispersed care.” By “dispersed care” we identify the effects of various state-imposed immigration laws and policies, which force immigrants to divide and allocate care among multiple fragments of their families in home and host countries. Dispersed care affects immigrant workers’ professional output, forcing them to make difficult choices between their career and care commitments. To unsettle the assumed homogeneity of high-skilled “Asian Indians,” we choose participants at diverse intersections of their migration pathways—naturalized US citizens, permanent US residents, and temporary visa holders or nonimmigrants. While naturalized US citizens and permanent residents have better resources to maintain transnational family ties than nonimmigrants, all of them face the intersectional challenges of dispersed care. Full article
21 pages, 11289 KiB  
Article
Research on Numerical Simulation Methods for Reservoirs of Loose Sandstone Considering the Equilibrium Time of Vertical Seepage Flow
by Shuozhen Wang, Qing You, Ruichao Zhang, Chunlei Yu, Shuoliang Wang, Congcong Li and Xiao Zhuo
Processes 2024, 12(4), 733; https://doi.org/10.3390/pr12040733 - 4 Apr 2024
Viewed by 1430
Abstract
Due to their high porosity and permeability characteristics, reservoirs of loose sandstone have great development potential. Under weak dynamic conditions, the vertical migration and mass exchange of oil–water two-phase fluids in loose sandstone reservoirs occur very easily. The phenomenon of vertical seepage flow [...] Read more.
Due to their high porosity and permeability characteristics, reservoirs of loose sandstone have great development potential. Under weak dynamic conditions, the vertical migration and mass exchange of oil–water two-phase fluids in loose sandstone reservoirs occur very easily. The phenomenon of vertical seepage flow equilibrium has a significant impact on the distribution of oil–water two-phase fluids in the reservoir. However, existing mainstream numerical simulators cannot accurately describe the phenomenon of vertical migration of oil–water two-phase fluids under weak dynamic conditions. In this study, using 3D printing technology, multiple transparent rock core holders were constructed to conduct experiments on the vertical seepage flow equilibrium time of different viscosities and contents of crude oil under different permeabilities of rock cores. Through the analysis and regression of experimental results, a predictive formula for the vertical seepage flow equilibrium time of loose sandstone reservoirs was established. Based on the time-prediction discriminant formula, a multi-scale numerical simulation method for vertical seepage flow equilibrium was constructed. A comparison between the new method and experimental results showed that the numerical simulation method, considering vertical seepage flow equilibrium, is closer to experimental phenomena than traditional numerical simulation methods. This indicates that the method can more accurately reveal the characteristics and distribution laws of the vertical seepage flow of oil–water two-phase fluids in loose sandstone reservoirs. Full article
(This article belongs to the Special Issue New Insight in Enhanced Oil Recovery Process Analysis and Application)
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11 pages, 1101 KiB  
Article
Account Information and Payment Initiation Services and the Related AML Obligations in the Law of the European Union
by Michał Grabowski
FinTech 2024, 3(1), 173-183; https://doi.org/10.3390/fintech3010011 - 4 Mar 2024
Viewed by 2506
Abstract
The Second Payment Services Directive introduced new services into the European Union legal system—Payment Initiation and Account Information Services. These services are based on payment accounts already opened and maintained for customers by the Account Servicing Payment Service Provider (bank, payment institution, electronic [...] Read more.
The Second Payment Services Directive introduced new services into the European Union legal system—Payment Initiation and Account Information Services. These services are based on payment accounts already opened and maintained for customers by the Account Servicing Payment Service Provider (bank, payment institution, electronic money institution). The Account Services Payment Service provider performs AML/CFT verification of the account holder and applies customer due diligence measures to the account holder, such as identifying beneficial owners, obtaining information on the purpose and intended nature of the business relationship, and ongoing monitoring of the business relationship. Payment Initiation and Account Information services are therefore provided to a previously verified client and based on the payment account currently maintained for him. European Union law does not clearly specify whether a Third-Party Service Provider offering Payment Initiation or Account Information Services is obliged to re-apply financial security measures to customers. The aim of this article was to perform a legal analysis of the regulations and soft law acts in force in the European Union and to answer the question. The purposive (teleological) and linguistic–logical (grammatical) methods of interpretation of regulations were used for the analysis. The structure of the legal system of the European Union as a civil law (code law) system was taken into account. This article shows that in the current legal situation, there is no doubt that Third-Party Service Providers are obliged entities in terms of AML/CFT law and are obliged to apply the AML/CFT to customers using Payment Initiation and Account Information services. However, the degree to which customer due diligence measures have to be applied varies depending on the adopted model of providing Payment Initiation and Account Information services. Third-Party Service Providers will be obliged to apply financial security measures in cases where the relationship between the customer and the service providers will have a continuing character. In the case of occasional provision of services, when the transaction value does not exceed a certain threshold, the supplier may only perform simplified customer verification. In particular, this applies to Payment Initiation service models, where the Payment Initiation Service Provider works for merchants, enabling them to accept payments for goods and services sold. In such a model, the Service Provider has a continuous relationship with the merchant but only performs an occasional transaction for the user. The analysis also allowed for the conclusion that European Union law, including that in the draft phase, does not regulate in a sufficiently precise manner when a given model of Account Services and Payment Initiation Services may be treated as based on an occasional transaction. This made it possible to formulate a de lege ferenda request to include this issue in the proposal for an EU Regulation on the prevention of the use of the financial system for the purposes of money laundering or terrorist financing. Full article
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28 pages, 9015 KiB  
Article
Collaboration and Competition: A Social Network Analysis of Thailand’s Music Industry
by Wichaya Peechapat and Nattapong Puttanapong
Economies 2024, 12(2), 45; https://doi.org/10.3390/economies12020045 - 12 Feb 2024
Viewed by 5749
Abstract
This study quantitatively investigates the collaborative framework and competitive landscape of Thailand’s evolving music industry, driven by technological progress and changing consumer preferences. By examining data obtained from Thailand’s Department of Intellectual Property, specifically 138,868 songs, it explores the complex network of relationships [...] Read more.
This study quantitatively investigates the collaborative framework and competitive landscape of Thailand’s evolving music industry, driven by technological progress and changing consumer preferences. By examining data obtained from Thailand’s Department of Intellectual Property, specifically 138,868 songs, it explores the complex network of relationships among music creators, artists, and various rights-holders, including those associated with recording, music, melodies, and lyrics. Utilizing social network analysis, this research uncovers a power law distribution in these networks, reflecting a scale-free market configuration. This characteristic is marked by a few dominant players exercising considerable market influence, contrasted with numerous less-interconnected participants. This investigation notes regular patterns of collaboration between artists and different rights-holders. Furthermore, the network of music creators displays small-world properties, with short collaborative distances fostering efficient information exchange and creative synergy. Crucially, this study identifies key influential players instrumental in directing the industry’s major trends, highlighting their role in market concentration. These significant findings will provide critical evidence for informing future policy development aimed at improving efficiency and equity in the digital content industries. Full article
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13 pages, 1251 KiB  
Article
Propensity for Self-Employment in a Model of Occupational Choice: Evidence from a Cohort of Recent University Graduates in Spain
by Manuel Salas-Velasco
Sustainability 2023, 15(4), 3400; https://doi.org/10.3390/su15043400 - 13 Feb 2023
Cited by 5 | Viewed by 3225
Abstract
This paper presents a microeconomic analysis of the occupational choices that individuals make after graduating from higher education. Specifically, a binomial logit model of the self-employment decision, which can be seen as a special case of a model of utility maximization, is estimated [...] Read more.
This paper presents a microeconomic analysis of the occupational choices that individuals make after graduating from higher education. Specifically, a binomial logit model of the self-employment decision, which can be seen as a special case of a model of utility maximization, is estimated for a large, nationally representative sample of Spanish bachelor’s degree holders. The estimation of the logit model allows one to analyze the influence of the university degree and individual sociodemographic characteristics on the probability of becoming self-employed five years after graduation. Results show that graduates in Odontology, Physiotherapy, Architecture, Law, Fine Arts, Pharmacy, and Psychology are the most likely to become self-employed. Surprisingly, financially literate individuals (economics and finance-related undergraduate degree holders) are less likely to start their own businesses. The paper also shows that women are less likely to be self-employed than men, but those graduates whose mothers obtained a university degree have an increased likelihood of being self-employed. The paper highlights the need for career guidance for undergraduates contemplating a career in self-employment. Full article
(This article belongs to the Section Economic and Business Aspects of Sustainability)
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21 pages, 4181 KiB  
Article
Seafood Sustainability Supply Chain Trends and Challenges in Japan: Marine Stewardship Council Fisheries and Chain of Custody Certificates
by Minako Iue, Mitsutaku Makino and Misuzu Asari
Sustainability 2022, 14(20), 13523; https://doi.org/10.3390/su142013523 - 19 Oct 2022
Cited by 10 | Viewed by 6201
Abstract
In Japan, fisheries’ product has decreased since the 1980s, and the government amended the fisheries law in 2020 to shift to managed fisheries. However, awareness of seafood sustainability is still low. This study identifies the reason for the low awareness and states the [...] Read more.
In Japan, fisheries’ product has decreased since the 1980s, and the government amended the fisheries law in 2020 to shift to managed fisheries. However, awareness of seafood sustainability is still low. This study identifies the reason for the low awareness and states the necessary actions to increase sustainable seafood consumption. The proactive stakeholders in seafood supply were surveyed to determine the current status of sustainable seafood sales. Marine Stewardship Council-certified fishers and MSC’s Chain-of-Custody certification holders answered the questionnaires. Fishers showed a positive attitude, citing proactive sales channel expansions and contributions to sustainability. Distributors were primarily passive, mainly because they obtained the certification at the request of their clients, and about half of them did not disseminate information between consumers and suppliers. Both fishers and distributors expect the government to promote campaigns and education. The stages of the awareness of producers, intermediary trade, and retailers are different and did not align. Therefore, if the supply chain stakeholders proactively educate themselves, choose sustainable products from the fishers, and pass the sustainability information to the consumers, sustainable seafood consumption would progress. Full article
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11 pages, 4295 KiB  
Article
Averaging Principle for a Class of Time-Fractal-Fractional Stochastic Differential Equations
by Xiaoyu Xia, Yinmeng Chen and Litan Yan
Fractal Fract. 2022, 6(10), 558; https://doi.org/10.3390/fractalfract6100558 - 30 Sep 2022
Cited by 4 | Viewed by 1774
Abstract
In this paper, we study a class of time-fractal-fractional stochastic differential equations with the fractal–fractional differential operator of Atangana under the meaning of Caputo and with a kernel of the power law type. We first establish the Hölder continuity of the solution of [...] Read more.
In this paper, we study a class of time-fractal-fractional stochastic differential equations with the fractal–fractional differential operator of Atangana under the meaning of Caputo and with a kernel of the power law type. We first establish the Hölder continuity of the solution of the equation. Then, under certain averaging conditions, we show that the solutions of original equations can be approximated by the solutions of the associated averaged equations in the sense of the mean square convergence. As an application, we provide an example with numerical simulations to explore the established averaging principle. Full article
(This article belongs to the Special Issue New Trends in Fractional Stochastic Processes)
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14 pages, 2784 KiB  
Article
A Deep-Learning Method for the Classification of Apple Varieties via Leaf Images from Different Growth Periods in Natural Environment
by Junkang Chen, Junying Han, Chengzhong Liu, Yefeng Wang, Hangchi Shen and Long Li
Symmetry 2022, 14(8), 1671; https://doi.org/10.3390/sym14081671 - 11 Aug 2022
Cited by 15 | Viewed by 2589
Abstract
With the continuous innovation and development of technologies for breeding varieties of fruits, there are more than 8000 varieties of apples in existence. The accurate identification of apple varieties can promote the healthy and stable development of the global apple industry and protect [...] Read more.
With the continuous innovation and development of technologies for breeding varieties of fruits, there are more than 8000 varieties of apples in existence. The accurate identification of apple varieties can promote the healthy and stable development of the global apple industry and protect the breeding property rights of rights-holders. To avoid economic losses due to the improper identification of varieties at the seedling-procurement stage, this paper proposes the classification of varieties using images of apple leaves in conjunction with the network models of traditional classification methods, supplemented with deep-learning methods, such as AlexNet, VGG, and ResNet, to account for their shortcomings in robustness and generalizability. We used the Multi-Attention Fusion Convolutional Neural Network (MAFNet) classification method for apple leaf images. The convolutional block distribution pattern of [2,2,2,2] is used to drive the feature extraction layer to have a symmetric structure. According to the characteristics of the dataset, the model is based on the ResNet model to optimize the feature extraction module and integrate a variety of attention mechanisms to achieve the weight distribution of channel features, reduce the interference information before and after feature extraction, complete the accurate extraction of image features, from low-dimensional to high-dimensional, and finally obtain the apple classification results through the Softmax function. The experiments were conducted on a mixture of leaves from 30 apple varieties at 2 growth stages: tender and mature. A total of 14,400 images were used for training, 2400 for validation, and 7200 for testing. The model’s classification accuracy was 98.14%, which improved the accuracy and reduced the classification imputation time as compared with the previous model. Among them, the accuracy rate of “Red General”, “SinanoGold”, and “Jonagold” reached 100%, and the accuracy rate of the bud variant of the Fuji line (“Fuji 2001”, “Red General”, “Yanfu 0”. and “Yanfu 3”) also had an accuracy rate of over 90%. The method proposed in this paper not only significantly improves the classification accuracy of apple cultivars, but it also achieves this with a low cost and a high efficiency level, providing a new way of thinking and an essential technical reference for apple cultivar identification by growers, operators, and law enforcement supervisors in the production practice. Full article
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