Search Results (540)

The formation mechanism of Virtual Reality (VR) Immersive Experience (VRIE) is notably complex; this study aimed to dynamically decode its underlying drivers by innovatively integrating Flow Theory and Privacy Calculus Theory, focusing on Perceptual-Interactive Fidelity (PIF), Consumer Willingness to Immerse in Technology (CWTI), and the applicability of Loss Aversion Theory. To achieve this, we analyzed approximately 30,000 user reviews from Amazon using Latent Semantic Analysis (LSA) and regression analysis. The findings reveal that user attention’s impact on VRIE is non-linear, suggesting an optimal threshold, and confirm PIF as a central influencing mechanism; furthermore, CWTI significantly moderates users’ privacy calculus, thereby affecting VRIE, while Loss Aversion Theory showed limited explanatory power in the VR context. These results provide a deeper understanding of VR user behavior, offering significant theoretical guidance and practical implications for future VR system design, particularly in strategically balancing user cognition, PIF, privacy concerns, and individual willingness. Full article

Background/Objectives: Quality of life (QOL) is a multifaceted concept involving a variety of factors which define the overall well-being of individuals. Food security, which implies a resilient food system, is one factor that is central to the calculus of the QOL status of a community considering that food is a staple of life. Advancing food security as a strategy for attaining sustained improvement in community QOL hinges on recognizing that food security is embedded in a matrix of other factors that work with it to generate the QOL the community experiences. The lived experience of the community defines the community’s QOL value matrix and the relative position of food security in that value matrix. Our thesis is that the role of food security in the lived experience of low-income communities depends on the position food security is accorded relative to other factors in the QOL value matrix of the community. Methods: This study employed a multimethod approach to define the QOL value matrix of low-income Guilford County residents, identifying the relative position of the value components and demographic segments based on priority ranking. First, an in-depth interview was conducted and then a telephone survey (280 sample) was used for collecting data. The ISAC Analysis Procedure and Best–Worst Scaling methods were used to identify and rank components of the QOL value matrix in terms of their relative impact on QOL. Results: The analysis revealed that spiritual well-being is the most important contributor to QOL, with a weight of 0.23, followed by access to health services (0.21) and economic opportunities (0.16), while food security has a moderate impact with 0.07. Conclusions: These findings emphasize the need for targeted policy interventions that consider the specific needs of different demographic segments to effectively improve QOL and inform the design of resilient food systems that reflect the lived experiences of low-income communities. Food security policies must be integrated with broader quality of life interventions, particularly for unemployed, low-educated, and single individuals, to ensure that a resilient food system effectively reduces inequities and address community-specific vulnerabilities. Full article

This study investigates how Greek professionals formulate upward requests and simultaneously manage rapport and workplace identity within hierarchical exchanges. The data comprise 400 written requests elicited through a discourse–completion task from 100 participants, supplemented by follow-up interviews. Integrating pragmatic perspectives on request mitigation with Spencer-Oatey’s Rapport-Management model and a social constructionist perspective on identity, the analysis reveals a distinctive “direct-yet-mitigated” style: syntactically direct head acts (typically want- or need-statements) various mitigating devices. This mitigation enables speakers to preserve superiors’ face, assert entitlement, and invoke shared corporate goals in a single move. Crucially, rapport work is intertwined with identity construction. Strategic oscillation between deference and entitlement projects four recurrent professional personae: the deferential subordinate, the competent and deserving employee, the cooperative team-player, and the rights-aware negotiator. Speakers shift among these personae to calibrate relational distance, demonstrating that rapport management functions not merely as a politeness calculus but as a resource for dynamic identity performance. This study thus bridges micro-pragmatic choices and macro social meanings, showing how linguistic mitigation safeguards interpersonal harmony while scripting desirable workplace selves. Full article

This paper introduces a novel class of analytic functions that integrates q-calculus, Janowski-type functions, and (a, b)-symmetrical functions. By exploring convolution operations and quantum calculus, we establish essential convolution conditions that lay the groundwork for subsequent research. Building on a new conceptual framework, we also define analogous neighborhoods for the classes ${\overline{\mathcal{F}}}_q^{a,b}(F,H)$ and investigate related neighborhood properties. These developments provide a deeper understanding of the structural and analytical behavior of these functions, opening up avenues for future study. Full article

The time-dependent creep behavior of coal is essential for assessing long-term structural stability and operational safety in deep coal mining. Therefore, this work develops a full-stage creep constitutive model. By integrating fractional calculus theory with statistical damage mechanics, a nonlinear fractional-order (FO) damage creep model is constructed through serial connection of elastic, viscous, viscoelastic, and viscoelastic–plastic components. Based on this model, both one-dimensional and three-dimensional (3D) fractional creep damage constitutive equations are acquired. Model parameters are identified using experimental data from deep coal samples in the mining area. The result curves of the improved model coincide with experimental data points, accurately describing the deceleration creep stage (DCS), steady-state creep stage (SCS), and accelerated creep stage (ACS). Furthermore, a sensitivity analysis elucidates the impact of model parameters on coal creep behavior, thereby confirming the model’s robustness and applicability. Consequently, the proposed model offers a solid theoretical basis for evaluating the sustained stability of deep coal mining and has great application potential in deep underground engineering. Full article

Integer-order models cannot characterize the dynamic behavior of the flexible two-link manipulator (FTLM) system accurately due to its viscoelastic characteristics and flexible oscillation. Hence, this paper proposes a fractional-order modeling method and identification algorithm for the FTLM system. Firstly, we exploit the memory and history-dependent properties of fractional calculus to describe the flexible link’s viscoelastic potential energy and viscous friction. Secondly, we establish a fractional-order differential equation for the flexible link based on the fractional-order Euler–Lagrange equation to characterize the flexible oscillation process accurately. Accordingly, we derive the fractional-order model of the FTLM system by analyzing the motor–link coupling as well as the symmetry of the system structure. Additionally, a system identification algorithm based on the multi-innovation integration operational matrix (MIOM) is proposed. The multi-innovation technique is combined with the least-squares algorithm to solve the operational matrix and achieve accurate system identification. Finally, experiments based on actual data are conducted to verify the effectiveness of the proposed modeling method and identification algorithm. The results show that the MIOM algorithm can improve system identification accuracy and that the fractional-order model can describe the dynamic behavior of the FTLM system more accurately than the integer-order model. Full article

This paper presents research on the origin, scope, evolution, and rationale of knowledge about polynomials in high school mathematics. Within the framework of the Anthropological Theory of the Didactic, Croatian high school curricula and textbooks were analyzed, and four models of knowledge to be taught were identified in the period following the formal abandonment of New Math principles. None of the identified models provides a unified discourse that integrates knowledge about polynomials transposed from scholarly domains of algebra and mathematical analysis. In relation to other curricular content the knowledge about polynomials has two-fold importance: (1) contributing to the development of various techniques related to high school algebra and calculus; (2) serving as a fundamental example in the formation of the notion of a function. Thus, the observed reduction in polynomial content over the analyzed period affects both practical and theoretical knowledge. The findings suggest that curricular changes have primarily focused on the selection of knowledge, with scarce adaptations of knowledge to be taught compared to the knowledge before each curricular change. This has led to a persistent gap between algebraic and analytical approaches to polynomials, potentially influencing the learned knowledge even among the highest-achieving students. Despite polynomials’ epistemological and didactical potential to bridge high school algebra and calculus, their restriction to specific forms of algebraic expressions and linear and quadratic functions contributes more to the fragmentation of high school mathematics. Full article

This paper examines a family of operators that combine the features of fractional-order and classical operators. Our goal is to obtain results on their invertibility in function spaces, based on their inherent improving properties. The class of proportional operators we study is extensive and includes both fractional-order and classical operators. This leads to interesting function spaces in which we obtain the right- and left-handed properties of invertibility. Thus, we extend and unify results concerning fractional-order and proportional operators. To confirm the relevance of our results, we have supplemented the paper with a series of results on the equivalence of differential and integral forms for various problems, including terminal value problems. Full article

Background/Objectives: Miscarriage is a common pregnancy complication that significantly impacts individuals’ health due to its physical and psychological effects. This study aimed to investigate the association between periodontal health and hematological parameters in women who experienced miscarriage before the 20th week of gestation, and to assess the potential predictive value of these parameters for miscarriage risk by comparing them with those of women with an uncomplicated pregnancy course. Methods: This study was a prospective case–control and cross-sectional study. It included a total of 82 participants, comprising 41 women with miscarriage and 41 healthy pregnant controls. The periodontal examinations included measurements of the Gingival Index (GI), Plaque Index (PI), Probing Depth (PD), Clinical Attachment Loss (CAL), and Simplified Calculus Index (SCI). Additionally, complete blood counts (CBCs) were obtained from all participants. Appropriate statistical analyses, including non-parametric, correlation, logistic regression, and ROC analyses, were conducted, with the significance level set at p < 0.05. Results: The primary outcome measure was CAL as an indicator of periodontal disease severity and its association with miscarriage risk. Additional outcomes included Plateletcrit (PCT), the Platelet Count (PLT), and the Neutrophil-to-Lymphocyte Ratio (NLR) to evaluate systemic inflammatory responses and their correlations with periodontal parameters. CAL was significantly elevated in the miscarriage group (p < 0.001) and emerged as the strongest predictor of miscarriage risk (OR = 0.0537, p < 0.001, AUC = 0.8691). PCT was significantly higher in the miscarriage group (p = 0.017) and positively correlated with the GI (p = 0.041), suggesting a link between systemic inflammation and periodontal health. Conclusions: Considering this study’s limitations, CAL was the strongest predictor of miscarriage, while PLT and PCT had some discriminative power. Collaboration between obstetricians and dentists can facilitate early diagnosis and intervention by promoting routine oral health check-ups before and during pregnancy. Additionally, integrating oral health assessments into prenatal care and developing public health policies could enhance access to dental services during both preconception and pregnancy periods. Full article

Medical images demand robust privacy protection, driving research into advanced image encryption (IE) schemes. However, current IE schemes still encounter certain challenges in both security and efficiency. Fractional-order Hopfield neural networks (HNNs) demonstrate unique advantages in IE. The introduction of fractional-order calculus operators enables them to possess more complex dynamical behaviors, creating more random and unpredictable keystreams. To enhance privacy protection, this paper introduces a high-performance medical IE scheme that integrates a novel 4D fractional-order HNN with a differentiated encryption strategy (MIES-FHNN-DE). Specifically, MIES-FHNN-DE leverages this 4D fractional-order HNN alongside a 2D hyperchaotic map to generate keystreams collaboratively. This design not only capitalizes on the 4D fractional-order HNN’s intricate dynamics but also sidesteps the efficiency constraints of recent IE schemes. Moreover, MIES-FHNN-DE boosts encryption efficiency through pixel bit splitting and weighted accumulation, ensuring robust security. Rigorous evaluations confirm that MIES-FHNN-DE delivers cutting-edge security performance. It features a large key space ($2^{383}$), exceptional key sensitivity, extremely low ciphertext pixel correlations (<0.002), excellent ciphertext entropy values (>7.999 bits), uniform ciphertext pixel distributions, outstanding resistance to differential attacks (with average NPCR and UACI values of $99.6096\%$ and $33.4638\%$, respectively), and remarkable robustness against data loss. Most importantly, MIES-FHNN-DE achieves an average encryption rate as high as 102.5623 Mbps. Compared with recent leading counterparts, MIES-FHNN-DE better meets the privacy protection demands for medical images in emerging fields like medical intelligent analysis and medical cloud services. Full article

This paper introduces a Gegenbauer-based fractional approximation (GBFA) method for high-precision approximation of the left Riemann–Liouville fractional integral (RLFI). By using precomputable fractional-order shifted Gegenbauer integration matrices (FSGIMs), the method achieves super-exponential convergence for smooth functions, delivering near machine-precision accuracy with minimal computational cost. Tunable shifted Gegenbauer (SG) parameters enable flexible optimization across diverse problems, while rigorous error analysis confirms rapid error decay under optimal settings. Numerical experiments demonstrate that the GBFA method outperforms MATLAB’s integral, MATHEMATICA’s NIntegrate, and existing techniques by up to two orders of magnitude in accuracy, with superior efficiency for varying fractional orders $0<\alpha <1$. Its adaptability and precision make the GBFA method a transformative tool for fractional calculus, ideal for modeling complex systems with memory and non-local behavior. Full article

A mathematical model of the anomalous diffusion of surfactant and the process of adsorption–desorption on an interface is analyzed using a fractional calculus approach. The model is based on time-fractional partial differential equations in the bulk phases and the corresponding time-fractional description of the flux bulk–interface. The general case, when the surfactant is soluble in both phases, is considered under the assumption that the adsorption–desorption process is diffusion-controlled. Some of the most popular kinetic models of Henry, Langmuir, and Volmer are considered. Applying the Laplace transform, the partial differential model is transformed into a single multi-term time-fractional nonlinear ordinary differential equation for the surfactant concentration on the interface. Based on existing analytical solutions of linear time-fractional differential equations, the exact solution in the case of the Henry model is derived in terms of multinomial Mittag–Leffler functions, and its asymptotic behavior is studied. Further, the fractional differential model in the general nonlinear case is rewritten as an integral equation, which is a generalization of the well-known Ward–Tordai equation. For computer simulations, based on the obtained integral equation, a predictor–corrector numerical technique is developed. Numerical results are presented and analyzed. Full article

Despite initial changes in respiratory illness epidemiology due to SARS-CoV-2, influenza activity has returned to pre-pandemic levels, highlighting its ongoing challenges. This paper investigates an influenza epidemic model using a Susceptible-Exposed-Infected-Recovered (SEIR) framework, extended with fuzzy Atangana–Baleanu–Caputo (ABC) fractional derivatives to incorporate uncertainty (via fuzzy numbers for state variables) and memory effects (via the ABC fractional derivative for non-local dynamics). We establish the theoretical foundation by defining the fuzzy ABC derivatives and integrals based on the generalized Hukuhara difference. The existence and uniqueness of the solutions for the fuzzy fractional SEIR model are rigorously proven using fixed-point theorems. Furthermore, we analyze the system’s disease-free and endemic equilibrium points under the fractional framework. A numerical scheme based on the fractional Adams–Bashforth method is used to approximate the fuzzy solutions, providing interval-valued results for different uncertainty levels. The study demonstrates the utility of fuzzy fractional calculus in providing a more flexible and potentially realistic approach to modeling epidemic dynamics under uncertainty. Full article

The two-parameter $(p,q)$-operators are a new family of operators in calculus that have shown their capabilities in modeling various systems in recent years. Following this path, in this paper, we present a new construction of the Langevin equation using two-parameter $(p,q)$-Caputo derivatives. For this new Langevin equation, equivalently, we obtain the solution structure as a post-quantum integral equation and then conduct an existence analysis via a fixed-point-based approach. The use of theorems such as the Krasnoselskii and Leray–Schauder fixed-point theorems will guarantee the existence of solutions to this equation, whose uniqueness is later proven by Banach’s contraction principle. Finally, we provide three examples in different structures and validate the results numerically. Full article

This study presents, for the first time, a new class of interval-valued superquadratic stochastic processes and examines their core properties through the lens of the center-radius total order relation on intervals. These processes serve as a powerful tool for modeling uncertainty in stochastic systems involving interval-valued data. By utilizing their intrinsic structure, we derive sharpened versions of Jensen-type and Hermite–Hadamard-type inequalities, along with their fractional extensions, within the framework of mean-square stochastic Riemann–Liouville fractional integrals. The theoretical findings are validated through extensive graphical representations and numerical simulations. Moreover, the applicability of the proposed processes is demonstrated in the domain of information theory by constructing novel stochastic divergence measures and Shannon’s entropy grounded in interval calculus. The outcomes of this work lay a solid foundation for further exploration in stochastic analysis, particularly in advancing generalized integral inequalities and formulating new stochastic models under uncertainty. Full article