Complex Phenomenon Research Articles

THEORETICAL REFLECTION ON THE CONCEPT OF PERCEIVED QUALITY FROM AN ARCHITECTURAL PERSPECTIVE

This paper is dedicated to exploring the subjective dimension of architectural quality, emphasizing the importance of understanding how individuals perceive architectural structures and spaces. To fully grasp this perception, it is essential to examine the multifaceted elements that capture the observer's attention, including the style, scale, form, color palette, and spatial organization of the building. Each of these factors contributes to the way a structure is experienced and interpreted, either in isolation or as part of an integrated whole. The combination of these elements can provoke a wide array of responses, ranging from aesthetic appreciation to emotional reaction, and thus, architectural design becomes a dynamic process that engages various facets of human experience. This paper aims to contribute to the body of knowledge surrounding architectural quality. The insights gained through this exploration hold the potential to inform and inspire design practices that foster greater aesthetic, functional, and emotional resonance with the individuals who engage with these spaces. Given the diverse and individualized nature of these responses, it is crucial to consider perception as a complex phenomenon in itself, one that not only encompasses sensory input but also emotional, cognitive, social, and cultural factors that influence how a building is perceived. Understanding this phenomenon allows architects and designers to identify the specific qualities that may enhance the effectiveness of their designs.

Most Cited Publications on Root Resorption of Permanent Teeth

Introduction: Root resorption of permanent teeth is a complex phenomenon, often presenting clinical challenges. The aim was to identify and analyze the most cited publications related to root resorption of permanent teeth. Method: A bibliographic search of all citations related to root resorption of permanent teeth published in scientific journals. Only publications with 100 citations or more were included, divided into four categories: experimental and review studies related to external or internal root resorption. A descriptive statistical analysis was conducted, including standard deviation and margin of error. Results: Sixty-nine (0.49%) publications, 48 experimental, and 21 review studies met the inclusion criteria. Of the 48 most cited experimental research publications, 48 (100%) pertained to external root resorption. Of the 21 most cited review publications, 19 (90.48%) pertained to external root resorption, and 2 (9.52%) to internal root resorption.

THE MULTILINGUAL BRAIN: UNVEILING COGNITIVE AND NEURAL DYNAMICS IN LANGUAGE LEARNING

In today's world, where multilingualism has become the norm and monolinguals are in the minority, academic research has been slow to adapt to this reality. This phenomenon, which highlights the human brain's ability to master multiple languages whether it be the native language (L1), a second language (L2), or even a third language (L3) calls for a reevaluation of traditional paradigms. This study aims to challenge conventional approaches in cognitive linguistics, particularly those related to language acquisition, language choice, and the underlying cerebral processes. The research questions addressed include: how individuals navigate between multiple languages in various cognitive and social contexts, and what are the implications for our understanding of human cognitive abilities? The methodology employed combines experimental analyses using brain imaging, psycholinguistic testing, and sociolinguistic surveys of multilingual speakers. The findings reveal that bilingualism and multilingualism not only enhance cognitive flexibility but also improve problem-solving abilities and adaptability in multicultural environments. In conclusion, this study demonstrates that multilingualism is not merely the acquisition of multiple linguistic systems, but a complex phenomenon that impacts cognition, social interactions, and brain structures. By redefining our understanding of cognitive and linguistic processes, this research proposes new paradigms for studying language in a globalized context.

FEATURES OF THE CONCEPT AND CONTENT OF PUBLIC SECURITY

The article analyzes the concept of public security in relation to such categories as «security», «national security», «state security», «security of society», «public order». An analysis of the scientific literature on this problem shows that in modern science there are two main approaches to understanding the phenomenon of «public security». Representatives of the first approach define public security as a social state, namely as a state of protection of the vital interests of the individual, society and the state from internal and external threats. Representatives of the second approach understand public security as a system of social relations that develop in the process of protecting the vital interests of the individual, society and the state from internal and external threats. Based on a thorough analysis of the concepts available in modern science, the author's definition of public security was formed. The important role and significance of public security in the existence of a modern state and society is emphasized, since it is this category that is the most relevant model for regulating social relations by maintaining law and order in society and the state. It is noted that public security should be considered from different points of view. First of all, as a concept that helps to reveal the meaning of the concept of security and its derivatives, as a certain state of protection of society and the state. It is emphasized that this aspect is the most important condition for establishing and maintaining law and order. It is substantiated that the use of the concept of public security leads to the emergence of certain concepts and strategies that also require thorough analysis and are a reflection of the relationship and interdependence between the development and security of society. The author draws special attention to the similarity of such concepts as public and national security. Most modern studies emphasize the fact that public security is one of the types of national security, since national security is a complex security concept and phenomenon in the context of increasing internal and external threats to the modern world.

Insights using Hamilton-Crosser model in Williamson hybrid nanofluids with homogeneous-heterogeneous reactions and diagonal electromagnetic effects

The study of Carboxymethyl Cellulose (CMC)-based Williamson hybrid nanofluids offers a significant leap in fluid dynamics and thermal management systems. This research investigates the flow characteristics over a porous, horizontally stretched cylindrical surface, incorporating complex phenomena such as Hall current, ion slip, diagonal magnetic fields, suction, velocity slip and thermal slip. A unique aspect is the inclusion of uniform and exponentially space-dependent heat sources, critical for advanced thermal transport processes. Using the Hamilton-Crosser model for accurate thermophysical properties and the Runge-Kutta-Fehlberg method for numerical analysis, the study examines the impact of varying hybrid nanoparticle concentrations (4% to 20%) on flow behaviour. The findings reveal that nanoparticles enhance viscosity, significantly increasing skin friction and momentum transfer, even as factors like the Weissenberg number, Hall current and ion slip mitigate these effects. The study emphasises the thermal management advantages of Carboxymethyl Cellulose-based Williamson hybrid nanofluids, especially when heat sources and homogeneous-heterogeneous reactions are involved. Notable differences are observed between pure Carboxymethyl Cellulose-based Williamson fluids and their hybrid nanofluid counterparts, particularly in velocity, temperature distribution and reaction dynamics. These results are promising for practical applications such as magnetic drug targeting, porous heat exchangers, magnetohydrodynamic systems and electronic cooling. The research underscores the potential of Carboxymethyl Cellulose-based Williamson hybrid nanofluids to enhance energy efficiency and reliability in industrial processes, making them pivotal for future developments in heat management technologies.

Insights to the Transition Regimes of Flow-Induced Vibration for Three Tandem Cylinders

Flow-induced vibration (FIV) is a complex phenomenon influenced by the interplay between flow dynamics and structural vibrations. Traditionally, it has been perceived as a threat to structures, but FIV has recently emerged as a promising method for highly efficient energy harvesting. This study focuses on the FIV of three tandem cylinders with varying spacing ratios (L/D) ranging from 1.3 to 4.0 with Reynold number Re of 5800-70000. Three distinct vibration states are identified: separated vortex-induced vibration (VIV) and wake-induced galloping (WIG) at L/D =1.3, continuous VIV-WIG at L/D =1.5, and partially separated VIV-WIG at L/D =2.0. To assess the coupling strength between the cylinders, the concept of vibration coherence is introduced and quantitatively analyzed. For L/D < 2, strong coherence is observed at the natural frequency ({f_{n), resulting in equal interference between the tandem cylinders across all reduced velocities. Conversely, for L/D >= 2, coherence becomes apparent at the vortex shedding frequency (f_v and 2 f_v), indicating linear interference with the reduced velocity. The transaction between the regimes is also accompanied with phase change. The establishment of these regimes, characterized by quantitative coherence, enhances our understanding of FIV in tandem cylinders, facilitating the efficient design of process industrial structures.

UNDERSTANDING RINGING IN THE EARS: A COMPREHENSIVE GUIDE TO TINNITUS

Tinnitus, commonly known as ringing in the ears, is a prevalent auditory condition affecting millions globally, with symptoms ranging from mild annoyance to severe disruption of daily life. Despite its widespread occurrence, tinnitus remains a complex phenomenon with diverse etiologies, including auditory system dysfunction, neurological disorders, and psychological stress. This article provides a comprehensive overview of tinnitus, focusing on its underlying mechanisms, classification, and associated risk factors. Furthermore, it examines current diagnostic tools and treatment modalities, including pharmacological therapies, sound therapy, cognitive-behavioural interventions, and emerging technologies such as neuromodulation. By synthesizing the latest research, this guide aims to enhance understanding among healthcare practitioners and offer practical strategies for effective management. The article concludes with a discussion of future directions in tinnitus research and therapy development

ALGORITHMIC THINKING IN HIGHER EDUCATION: DETERMINING OBSERVABLE AND MEASURABLE CONTENT

Nowadays algorithmic thinking, as a key demand and the main requirement of technology-based society, extensively expands outwards the computer science area and rapidly becomes a meaningful instrumentality for effective realization of any information activities with or without ICT. This instrumentality creates new opportunities and possibilities for improvement of the effectiveness of any educational professional activities in the higher education context by creating problem-solving algorithms completely within the ICT area, as well as non-ICT-based algorithms that provide clear technological step-by-step instructions for solving a diversity of educational problems. Although attention to algorithmic thinking as scientific phenomenon is increasing, the studies aimed at determining the algorithmic thinking content in observable and measurable statements have not been conducted yet and its great potential is still undiscovered. The purpose of this study is to identify, clarify, and categorize algorithmic thinking content in observable and measurable knowledge, skills, and abilities statements (KSAs). The study is a mixed-methods type of development research carried out in 4 stages: 1) extraction of the KSA statements from the extant scientific literature related to algorithmic thinking; 2) design of The Algorithmic Thinking Content Survey (ATCS) based on the five steps Universal Sequence of an Algorithm Development (USAD); 3) administration of the ATCS on a wide variety of educational professionals (N = 117); 4) data analysis aimed to obtain the content of algorithmic thinking in observable and measurable KSA statements. The design of the ATCS is also based on algorithmic thinking as a complex phenomenon that integrates five types of thinking: abstract, logical, figurative, conceptual, and constructive. The administration of the ATCS involved 117 experts – educational professionals (11 professors who teach courses concerning algorithms and computer science, 23 practicing teachers of informatics, 35 students in the 3rd year of Informatics teacher training program, and 48 master students of informatics). Expert validation of algorithmic thinking content in knowledge, skills, and abilities statements was obtained through the Likert scale. One hundred KSA statements of algorithmic thinking content were obtained (32 statements of knowledge, 38 statements of skills, and 30 statements of abilities).

«Bribe» and «gift» in Russia of the Petrine Era in interdisciplinary discourse

The article is devoted to the study of the phenomenon of bribery in the Peter the Great era through the prism of interdisciplinary research: closely related methods of cultural anthropology, linguo-semiotics, linguistics proper, historical semantics and historical-legal approach. Such methodological synthesis is aimed at studying the words that marked the phenomena defined by the author as private rewards of officials. Private rewards of officials are a complex social phenomenon that cannot be reduced to the modern concept of a bribe. The combination of methods of philological, historical and legal sciences allowed us to obtain a more subtle optics of its study, to see how the evolution and criminalization of ancient practices of gift exchange and tribute took place in the context of the emerging modern state, on the one hand, and how difficult it was for the legal concept of a bribe to mature as a criminal variety of such rewards, on the other.

Typical forms of counteraction to the investigation of criminal offences related to interference with the activities of public authorities

The article substantiates the position that counteraction to an investigation is a complex phenomenon which may encompass various forms of behaviour implemented by interested parties with the aim of preventing detection of a criminal offence, and making it impossible to fulfil the tasks of criminal proceedings. It is found that during the investigation of criminal offences related to interference with the activities of representatives of public authorities, suspects most often implement the following forms of behaviour as ways to counteract the investigation: 1) refuse to testify; 2) give false testimony; 3) hide from pre-trial investigation authorities; 4) fail to appear when summoned by the investigator, prosecutor, investigating judge; 5) exert influence on the victim, witnesses, refuse to provide biological samples, handwriting, voice samples, etc. It is established that other interested persons at the stage of pre-trial investigation of criminal offences of the type under study most often implement the following forms of behaviour to counteract the investigation: exerting influence on participants to criminal proceedings; implementation of actions to conceal crimes, including: staging, falsification, disguise, destruction, etc.; giving false testimony; disclosure of the secret of pre-trial investigation; refusal to provide biological samples or samples of handwriting, voice, etc.; delaying the pre-trial proceedings, delaying the pre-trial investigation, for example, by ignoring the investigator's calls, prolonged familiarisation with the criminal proceedings; failure to appear when summoned; failure to fulfil procedural obligations acquired in connection with obtaining the relevant procedural status in criminal proceedings; hiding from the pre-trial investigation authorities, etc. It is also emphasised that the prospects for further research should be to identify effective ways to overcome the following forms of resistance to investigation.

Decoding the physicochemical basis of resurrection: the journey of lichen Flavoparmelia caperata through prolonged water scarcity to full rehydration

Desiccation tolerance is a complex phenomenon observed in the lichen Flavoparmelia ceparata. To understand the reactivation process of desiccated thalli, completely dried samples were rehydrated. The rehydration process of this lichen occurs in two phases. The first phase, characterized by rapid rehydration, involves the conversion of non-functional reaction centers (RCs) into functional PSII RCs, and the accumulation of ROS along with the increment in SOD antioxidant enzyme. These coordinated mechanisms initiate the light reaction of photosynthesis by forming active light-harvesting complexes (LHCs). This adaptation ensures efficient recovery, as evidenced by specific energy fluxes (ABS/RC, TR/RC, ET/RC, and DI/RC), phenomenological fluxes (ABS/CS, TR/CS, ET/CS, and DI/CS), quantum efficiencies (ФP0, ФE0, and ФD0), primary and secondary photochemistry, photochemical and non-photochemical quenching, and performance index, highlighting the essential role of rapid water uptake in restoring turgor pressure for cell structure and function maintenance. The interconnected network of antioxidant defenses, including catalase (CAT) and peroxidase (POD), underscores the plant's ability to cope with oxidative stress during resilience. The acid phosphomonoesterase (PME) enzymatic activity corresponds to its role in releasing phosphate for essential cellular functions and post-rehydration thallus growth. The activity of CAT, GPOD, and PME signifies the gradual reactivation of lichen F. caperata. Moreover, the investigation into chlorophyll a fluorescence emphasizes the efficient reactivation of the photosynthetic process in F. caperata. In conclusion, lichen F. caperata demonstrates significant potential for desiccation tolerance through the rapid transformation of chloroplasts, chlorophylls, and PSII RCs from their inactive to active states upon rehydration. This research not only enhances our understanding of desiccation tolerance in resurrection plants but also highlights the importance of lichens, particularly F. caperata, as valuable models for studying plant resilience in challenging environments.

The Influences of Social Scientific Disciplines on the Interdisciplinarity of Public Administration Science

Public administration is a dynamic discipline that has evolved throughout history under the influence of various scientific fields, primarily social sciences. Its roots trace back to ancient civilizations, and it has significantly developed over centuries. As a scientific discipline and a complex social phenomenon, public administration encompasses sociological, political, legal, organizational, and other characteristics. The emergence and functioning of public administration as a crucial state instrument for law enforcement and ensuring social stability have been significantly influenced by numerous scientific disciplines, particularly political science, law, sociology, economics, and psychology. These disciplines provided the initial impetus and later momentum for the development of specific public administration concepts. Key theoretical approaches to studying public administration emphasize the importance of organizational structures and functionality within social systems. Understanding the historical and theoretical foundations of administration is essential for addressing contemporary challenges and opportunities in public administration. The aim of this paper is to highlight the influences of some key social and technological disciplines on the development of public administration, focusing on understanding how historical changes have shaped modern practices.

Water demand prediction in agriculture, construction industry, and residential sectors using a machine learning model relying on the concept of knowledge management

In contemporary times, the focus of water resource management has shifted from constructing novel water supply systems to the proficient management and utilization of pre-existing systems. Knowledge management is one of the most powerful tools in management science, which is very useful for identifying experimental solutions to this issue. Owing to the fact that machine learning techniques provide ideas for predicting complex phenomena, this study employed the ANFIS model to predict water demand in agriculture, construction, and residential sectors in Mecca Province, Saudi Arabia. Data spanning from 2000 to 2021 was utilized for this purpose. To achieve enough data, the Diz method is utilized for the seasonalization of annual data. The present study assessed and compared the efficacy of water recycling as a means to enhance productivity in the agriculture, construction, and residential sectors in response to water demand management. The findings indicate that the implementation of a water management and recycling strategy can potentially lead to a reduction of 4%, 6%, and 0.8% in water consumption by the agriculture, construction, and residential sectors respectively, by the year 2025. In the absence of management techniques and productivity measures aligned with projected water demand in 2025, the annual consumption levels for the agriculture, construction, and residential sectors are estimated to increase by 20.0, 0.5, and 1.0 MCM, respectively.

Exploring phase transitions in CdSe: a machine learning and swarm intelligence approach

The phase transition of cadmium selenide (CdSe) from wurtzite to rocksalt structure has been the subject of extensive research. In this study, we present a novel approach combining machine learning potentials with swarm intelligence-based pathway sampling to elucidate the complex phase transition mechanisms in CdSe. We developed an accurate machine-learning (ML) potential for CdSe, validated against density functional theory calculations, achieving mean absolute errors (MAEs) of 1.8 meV/atom for energies and 33 meV/Å for forces. This potential was integrated with the pathway sampling via swarm intelligence and graph theory (PALLAS) method to explore the potential energy landscape and identify low-energy transition pathways. Our simulations revealed a complex network of transition pathways, and we discovered a multi-step transition mechanism involving an unexpected zinc blende intermediate phase, which appears to play a crucial role in facilitating the transition between wurtzite and rocksalt structures. This finding provides new insights into the structural flexibility of CdSe and offers an explanation for experimentally observed phenomena such as wurtzite/zinc blende coexistence in nanostructures. Our approach not only advances the fundamental understanding of phase transitions in CdSe but also establishes a powerful computational framework for exploring complex materials phenomena, opening new avenues for materials design and discovery in semiconductor systems.

Особенности правового режима недвижимого имущества членов семьи

Introduction. The Russian lawmakers do not endow immovable property of family members with independent features of objectness, however, in family relations the realisation of rights to such property has a certain specificity, which is evident in the peculiarities of its purchasing and saling, realisation of the rights of the owner, as well as of the persons residing with him, restrictions of rights, protection measures, and the procedure for termination of rights. The purpose of the article is to develop theoretical provisions regarding the legal status of immovable property of family members, as well as practical recommendations aimed at further improvement of the current legislation. Methods. The research is based on the integrated use of dialectical method, which made it possible to reveal the peculiarities of the legal status of immovable property of family members, due to the identified specificity of the object and subject composition of relations, as well as the systematic approach, through which the legal status of immovable property of family members was analysed as a complex legal phenomenon, representing a set of legal means. Results. The legal status of immovable property of family members requires a systematic approach in ensuring the property interests of family members as a civil-law community, as well as public interests aimed at protecting the family, protecting the interests of particular family members unable to meet their own housing needs, and includes a set of legal means on the basis of which it is possible to own, use and dispose of a particular real property object.

The functional heterogeneity of non-suicidal self-injury: insights from latent profile analysis

BackgroundThe functional aspects of non-suicidal self-injury (NSSI) among adolescents represent a complex phenomenon requiring deeper understanding. While research has identified various NSSI functions, including emotional regulation, attention-seeking, and social avoidance, the field lacks comprehensive analysis of how these functions cluster into distinct profiles. Understanding these functional profiles is crucial for developing targeted interventions.MethodA cross-sectional study of 1,783 adolescents (1,464 girls, 318 boys) aged 12–18 years was conducted across 14 psychiatric or general hospitals in nine Chinese provinces. Participants completed the Functional Assessment of Self-Mutilation (FASM), which assesses 22 distinct NSSI functions across three primary dimensions: emotional regulation, attention-seeking, and social avoidance. Additional measures included the Patient Health Questionnaire (PHQ-9) for depression and Generalized Anxiety Disorder Scale (GAD-7) for anxiety symptoms. Latent profile analysis was employed to identify distinct patterns in NSSI functions, with model selection based on fit indices including AIC, BIC, entropy, and LMRT.ResultsLatent profile analysis revealed four distinct functional profiles: low attention-seeking-high social avoidance (LA-HS, 19.7%), high attention-seeking-high social avoidance (HA-HS, 9.5%), low attention-seeking and social avoidance (LA-LS, 57.8%), and high attention-seeking-low social avoidance (HA-LS, 13.0%). The HA-HS profile demonstrated the most severe clinical presentation, showing significantly elevated scores in NSSI frequency (M = 26.160, SD = 9.771), anxiety (GAD-7: M = 16.265, SD = 4.951), and depression (PHQ-9: M = 20.612, SD = 6.003). The LA-HS profile showed the second-highest severity (NSSI: M = 25.800, SD = 10.058; GAD-7: M = 14.775, SD = 5.376; PHQ-9: M = 19.966, SD = 5.938). Both profiles also demonstrated significantly higher rates of suicidal ideation (HA-HS: 77.6%; LA-HS: 79.2%) compared to other profiles.ConclusionsOur findings reveal distinct patterns in how adolescents utilize NSSI functionally, particularly regarding attention-seeking and social avoidance dimensions. These functional profiles show meaningful associations with psychological outcomes, suggesting that understanding NSSI functions, rather than just behaviors, may be crucial for assessment and intervention. The identification of these distinct functional profiles among Chinese adolescents highlights the importance of function-specific approaches in clinical assessment and treatment planning.

Psychoneural reduction revised: The case of suicidality in bipolar disorder.

This paper uses suicidality in bipolar disorder (BD) to illustrate that multidimensional frameworks account for complex phenomena with cognitive, psychological, socioenvironmental and physiological components better than their reductionist counterparts. We challenge level-based reductionist models that regard a particular dimension as fundamental. To comprehensively understand complex psychiatric phenomena, multidimensional models that acknowledge the heterogeneity of aetiological factors, rather than homogenising them under a single dimension, must be utilised. Multidimensional models allow a better understanding of the individual context under which a psychiatric phenomenon arises, and the interrelationships between its different aetiological dimensions. Suicidality in BD is used as a case study because it particularly highlights the interplay between biological, psychological, sociocultural and experiential factors. The multidimensional nature of suicidality is reflected by the heterogeneous strategies by which it is managed. Although similar to suicidality in other contexts, in BD suicidality has distinctive structural characteristics that emphasise its multidimensionality. Consequently, investigating suicidality in BD yields claims generalisable to suicidality as a whole alongside novel insights on BD-specific features. For instance, suicidality in BD has physiological causal factors, e.g., genetic predisposition and aggravation by symptomatic periods. However, its other features underscore the causal roles of cognitions. In persons with BD, suicidality can persist beyond depression and is sometimes experienced during mania, possibly due to suicidal ideation persisting beyond symptomatic periods. This indicates the need to account for cognitive or psychological causal factors. Models of suicidality in BD typically adopt a non-level-based, non-reductionist approach, reflected in the diverse clinical strategies for managing suicidality in BD.

Schadenfreude: A Conceptual Review

Individuals can exhibit different reactions in the face of others' misfortunes. These reactions sometimes manifest as sharing in the sadness, while at other times, they can manifest as a hidden or overt form of joy. Schadenfreude, a term of German origin, is an emotional expression primarily corresponding to reactions of the second type. Schadenfreude denotes the inner satisfaction or joy felt in response to someone else's failure, misfortune, or pain. In this manuscript, the concept of "malicious joy” is identified as the Turkish equivalent of schadenfreude and is used interchangeably throughout the manuscript. The sensation of malicious joy is a complex phenomenon that affects individuals' internal psychological processes and external expressions, and its exploration can contribute to the literature. Therefore, the main objective of this manuscript is to provide both theoretical and practical perspectives on malicious joy, contributing to the existing knowledge in the field. The manuscript focuses on the definition of malicious joy, its causes, relevant psychosocial factors, and its effects on mental health. Malicious joy arises from three main reasons: justice-based, comparison-based, and intergroup phenomena, namely rejoicing in someone else's sorrow. Emotional and social factors such as lack of empathy, jealousy, competitiveness, and social comparison are discussed for their role in the emergence of malicious joy. Additionally, studies on malicious joy and measurement tools used in its assessment are examined. Finally, the necessity for further research on malicious joy is emphasized.

Conservation Law Analysis in Numerical Schema for a Tumor Angiogenesis PDE System

Tumor angiogenesis, the formation of new blood vessels from pre-existing vasculature, is a crucial process in cancer growth and metastasis. Mathematical modeling through partial differential equations helps to understand this complex biological phenomenon. Here, we provide a conservation properties analysis in a tumor angiogenesis model describing the evolution of endothelial cells, proteases, inhibitors, and extracellular matrix. The adopted approach introduces a numerical framework that combines spatial and time discretization techniques. Here, we focus on maintaining solution accuracy while preserving physical quantities during the simulation process. The method achieved second-order accuracy in both space and time discretizations, with conservation errors showing consistent convergence as the mesh was refined. The numerical schema demonstrates stable wave propagation patterns, in agreement with experimental observations. Numerical experiments validate the approach and demonstrate its reliability for long-term angiogenesis simulations.

The Role of Virtue Epistemology in Resolving Internal-External Debates Taking the Sosa Virtue Perspective as an Example

In the development of contemporary epistemology, the evolving research focus of virtue epistemology has shifted towards the rational virtue that generates knowledge, thereby deepening our understanding of the essence of knowledge. Sosa's moral perspective is particularly prominent, skillfully blending the essence of internalism and externalism. Sosa not only retained the emphasis of internalism on the "controllability" of the internal state of the knower, but also absorbed the viewpoint of externalism that emphasizes the close connection between knowledge and the external world. This dual perspective of internal and external cultivation not only enhances the inclusiveness of its theory, but also significantly improves its ability to explain complex knowledge phenomena, opening up new avenues for resolving the long-standing internal and external disputes. Furthermore, Sosa's holistic approach fosters a comprehensive view of epistemic virtue, seamlessly integrating personal introspection with environmental interaction, thereby enriching contemporary debates and fostering a deeper, more nuanced understanding of knowledge acquisition.