Search Results (390)

A geodesic or geodetic line on a sphere is called the orthodrome. Research has shown that the orthodrome can be defined in a large number of ways. This article provides an overview of various definitions of the orthodrome. We recall the definitions of the orthodrome according to the greats of geodesy, such as Bessel and Helmert. We derive the equation of the orthodrome in the geographic coordinate system and in the Cartesian spatial coordinate system. A geodesic on a surface is a curve for which the geodetic curvature is zero at every point. Equivalent expressions of this statement are that at every point of this curve, the principal normal vector is collinear with the normal to the surface, i.e., it is a curve whose binormal at every point is perpendicular to the normal to the surface, and that it is a curve whose osculation plane contains the normal to the surface at every point. In this case, the well-known Clairaut equation of the geodesic in geodesy appears naturally. It is found that this equation can be written in several different forms. Although differential equations for geodesics can be found in the literature, they are solved in this article, first, by taking the sphere as a special case of any surface, and then as a special case of a surface of rotation. At the end of this article, we apply calculus of variations to determine the equation of the orthodrome on the sphere, first in the Bessel way, and then by applying the Euler–Lagrange equation. Overall, this paper elaborates a dozen different approaches to orthodrome definitions. 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

Background/Objectives: Non-enhanced computed tomography of the kidneys, ureters and bladder (NECT KUB) is the initial imaging modality for suspected nephroureterolithiasis. However, for alternative diagnoses, NECT may not be the ideal technique. Our institution changed the protocol for this cohort from NECT to intravenous contrast-enhanced CT (CECT) KUB. We aimed to retrospectively compare the rate of alternative diagnosis seen and the rates of calculus detection in CECT versus NECT KUB as a means of assessing performance. Our secondary aim was to compare the radiation dose between CECT and NECT KUB. Methods: Patients referred from the emergency department with suspected nephroureterolithiasis who underwent NECT and CECT KUB over two years were included. Key performance metrics included calculus detection rate, alternative findings, and negative studies. The metrics were compared between genders and age groups. Categorical variables were analysed using Chi-squared or Fisher’s Exact Test and continuous with T-testing. Results: A total of 423 patients had CT KUB imaging (209 NECT, 214 CECT). The incidence of alternative findings in the NECT group was 23% and 40% in CECT (p < 0.001). There were 48 findings (13 major, 11 moderate and 24 minor) in NECT studies and 85 findings (23 major, 43 moderate and 19 minor) in CECT (p < 0.001). Major diagnoses ranged from acute emergencies to more indolent findings, including suspicious nodules/masses. The calculus detection rate (NECT 56%, CECT 54%, p = 0.643) and negative studies (NECT 28%, CECT 22%, p = 0.168) did not significantly differ between protocols. CECT had a mean effective dose of 8.71 ± 2.58 mSv representing 2.4 times the exposure of NECT (p < 0.001). Conclusions: CECT is associated with a greater alternative diagnosis rate with similar calculus detection rates compared to NECT KUB, suggesting superior performance. However, CECT exposes patients to significantly greater levels of ionizing radiation. 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

Background: Intracranial atherosclerotic stenosis (ICAS) is a significant cause of ischemic stroke worldwide, with high recurrence rates despite optimal medical therapy. While endovascular stenting has been proposed as an adjunctive treatment, its clinical benefit remains controversial as a first line therapy. Objective: To evaluate the efficacy and safety of stenting plus medical therapy (STN+MT) compared to medical therapy alone (MT) in patients with symptomatic ICAS through a systematic review and meta-analysis of randomized controlled trials (RCTs). Methods: We systematically searched PubMed, Web of Science, the Cochrane Library, Embase, Scopus, and EBSCO for RCTs comparing STN+MT with MT in adult patients with symptomatic ICAS. Primary outcomes included transient ischemic attack (TIA), stroke, intracerebral hemorrhage (ICH), and death at 30 days and 1 year. Pooled risk ratios with 95% confidence intervals were calculated using random-effects or fixed-effects models as appropriate. Meta-regression was conducted to assess effect modification by study-level characteristics. Results: Four trials comprising 990 patients were included. STN+MT was associated with significantly higher 30-day risk of stroke and ICH compared to MT alone. No significant differences in TIA, stroke, ICH, or death were found at 1 year. Meta-regression revealed no significant effect modifiers, suggesting consistent findings across subgroups. Conclusions: Our meta-analysis consolidates the evidence that intracranial stenting as a first line therapy offers no significant advantage over medical therapy in preventing stroke in symptomatic ICAS, while it does pose added early risks. This holds true across different trials, patient demographics, and clinical scenarios examined. The consistency of this message across multiple RCTs provides a high level of evidence to guide practice. At present, aggressive medical therapy alone should be the default management for most patients. Endovascular intervention should be reserved for clinical trial settings or carefully selected salvage cases, until and unless new evidence emerges to change the risk–benefit calculus such as the promising use of balloon angioplasty in the BASIS trial. Full article

Most studies on relationships between humans and nonhuman animals focus on the benefits of the relationship to humans, the potential detriment or stress to animals, or how humans can better improve husbandry or handling practices in the domestic setting. By comparing existing research in human working relationships and friendships with animal friendships and studies on human–animal interactions, this paper proposes a new framework of an Interspecies Relational Theory that provides approaches for identifying, developing, and maintaining different levels of relationships between humans and nonhuman species. The framework is broken into three stages aligned with existing research in human levels of trust ranging from strategic/calculus-based to working/knowledge/information-based to friendship/affect-based. These levels are also aligned with stages of Maslow’s Hierarchy. The suggested framework can help provide insight into both human and animal perspectives of the human–animal relationship in a variety of veterinary and animal-assisted settings. Full article

In the new context of information sharing to reshape the supply chain’s interruption risk propagation mechanism, this paper focuses on the interruption risk propagation and resilience of the supply chain of emergency medical supplies in the background of emergencies. Firstly, an emergency supply chain’s risk propagation model under information sharing is proposed by combining the information sharing mechanism with the supply chain’s risk propagation theory. Secondly, an interruption risk propagation model for the supply chain of emergency medical supplies based on a Bayesian Network is constructed, and the do-calculus technique is introduced to transform the intervention effect of information sharing into the quantification of the supply chain’s risk probability. Thirdly, a system dynamics method is used to construct a supply chain model for emergency medical supplies, which takes into account different interruption scenarios caused by emergencies and evaluates the supply chain’s resilience through the key variable “demand fulfillment rate” in the model. The results of the study indicate that the impact of different types of interruption scenarios on supply chain resilience varies significantly. Information sharing can effectively reduce the negative impact of interruption risk. This study provides theoretical basis and practical guidance for improving the resilience of the supply chain of emergency medical supplies, which is of great significance for maintaining social stability and promoting the sustainable development of the public health system. Full article

Objectives: The purpose of the study is to evaluate the diagnostic accuracy of artificial intelligence (AI) software in detecting a common set of periodontal and restorative conditions, including marginal bone loss, dental caries, periapical lesions, calculus, endodontic treatment, crowns, restorations, and open crown margins, using intraoral periapical radiographs. Additionally, the study will assess how this AI software influences the diagnostic accuracy of dentists with varying levels of experience in identifying these conditions. Methods: A total of three hundred digital IOPARs representing 1030 teeth were selected based on predetermined selection criteria. The parameters assessed included (a) calculus, (b) periapical radiolucency, (c) caries, (d) marginal bone loss, (e) type of restorative (filling) material, (f) type of crown retainer material, and (g) detection of open crown margins. Two oral radiologists performed the initial diagnosis of the selected radiographs and independently labeled all the predefined parameters for the provided IOPARs under standardized conditions. This data served as reference data. A pre-trained AI-based computer-aided detection (“CADe”) software (Second Opinion^®, version 1.1) was used for the detection of the predefined features. The reports generated by the AI software were compared with the reference data to evaluate the diagnostic accuracy of the AI software. In the second phase of the study, thirty dental interns and thirty dental specialists were randomly selected. Each participant was randomly assigned five IOPARs and was asked to detect and diagnose the predefined conditions. Subsequently, all the participants were requested to reassess the IOPARs, this time with the assistance of the AI software. All the data was recorded using a self-designed Performa. Results: The sensitivity of the AI software in detecting caries, periapical lesions, crowns, open crown margins, restoration, endodontic treatment, calculus, and marginal bone loss was 91.0%, 86.6%, 97.1%, 82.6%, 89.3%, 93.4%, 80.2%, and 91.1%, respectively. The specificity of the AI software in detected caries, periapical lesions, crowns, open crown margins, restoration, endodontic treatment, calculus, and marginal bone loss was 87%, 98.3%, 99.6%, 91.9%, 96.4%, 99.3%, 97.8%, and 93.1%, respectively. The differences between the AI software and radiologist diagnoses of caries, periapical lesions, crowns, open crown margins, restoration, endodontic treatment, calculus, and marginal bone loss were statistically significant (all p values < 0.0001). The results showed that the diagnostic accuracy of operators (interns and specialists) with AI software revealed higher accuracy, sensitivity, and specificity in detecting caries, PA lesions, restoration, endodontic treatment, calculus, and marginal bone loss compared to that without using AI software. There were variations in the improvements in the diagnostic accuracy of interns and dental specialists. Conclusions: Within the limitations of the study, it can be concluded that the tested AI software has high accuracy in detecting the tested dental conditions in IOPARs. The use of AI software enhanced the diagnostic capabilities of dental operators. The present study used AI software to detect a clinically useful set of periodontal and restorative conditions, which can help dental operators in fast and accurate diagnosis and provide high-quality treatment to their patients. Full article

In this work, we apply fractional calculus to study quantum cosmology. Specifically, our Wheeler-DeWitt (WDW) equation includes a Friedman-Robertson-Walker (FRW) geometry, a radiation fluid, a positive cosmological constant ($\mathsf{\Lambda }$), and an ad-hoc potential. We employ the Riesz fractional derivative, which introduces a parameter $\alpha$, where $1<\alpha \le 2$, in the WDW equation. We investigate numerically the tunneling probability for the Universe to emerge using a suitable WKB approximation. Our findings are as follows. When we decrease the value of $\alpha$, the tunneling probability also decreases, suggesting that if fractional features could be considered to ascertain among different early universe scenarios, then the value $\alpha =2$ (meaning strict locality and standard cosmology) would be the most likely. Finally, our results also allow for an interesting discussion between selecting values for $\mathsf{\Lambda }$ (in a non-fractional conventional set-up) versus balancing, e.g., both $\mathsf{\Lambda }$ and $\alpha$ in the fractional framework. Full article

Automatic differentiation (AD) is a general method for computing exact derivatives in complex sensitivity analyses and optimisation tasks, particularly when closed-form solutions are unavailable and traditional analytical or numerical methods fall short. This paper introduces a vectorised formulation of AD grounded in matrix calculus. It aligns naturally with the matrix-oriented style prevalent in statistics, supports convenient implementations, and takes advantage of sparse matrix representation and other high-level optimisation techniques that are not available in the scalar counterpart. Our formulation is well-suited to high-dimensional statistical applications, where finite differences (FD) scale poorly due to the need to repeat computations for each input dimension, resulting in significant overhead, and is advantageous in simulation-intensive settings—such as Markov Chain Monte Carlo (MCMC)-based inference—where FD requires repeated sampling and multiple function evaluations, while AD can compute exact derivatives in a single pass, substantially reducing computational cost. Numerical studies are presented to demonstrate the efficacy and speed of the proposed AD method compared with FD schemes. Full article

This research introduces an innovative fractal–fractional synergy framework for multiscale analysis of stress field dynamics in geo-energy systems. By integrating fractional calculus with multiscale fractal dimension analysis, we develop a coupled approach examining stress redistribution patterns across different geological scales. The methodology combines fractal characterization of rock mechanical parameters with fractional-order stress gradient modeling, validated through integrated analysis of core testing, well logging, and seismic inversion data. Our fractal–fractional operators enable simultaneous characterization of stress memory effects and scale-invariant fracture propagation patterns. Key insights reveal the following: (1) Non-monotonic variations in rock mechanical properties (fractal dimension D = 2.31–2.67) correlate with oil–water ratio changes, exhibiting fractional-order transitional behavior. (2) Critical stress thresholds (12.19–25 MPa) for fracture activation follow fractional power-law relationships with fracture orientation deviations. (3) Fracture network evolution demonstrates dual-scale dynamics—microscale tip propagation governed by fractional stress singularities (order α = 0.63–0.78) and macroscale expansion obeying fractal growth patterns (Hurst exponent H = 0.71 ± 0.05). (4) Multiscale modeling reveals anisotropic development with fractal dimension increasing by 18–22% during multi-well fracturing operations. The fractal–fractional formalism successfully resolves the stress-shadow paradox while quantifying water channeling risks through fractional connectivity metrics. This work establishes a novel paradigm for coupled geomechanical–fluid dynamics analysis in complex reservoir systems. Full article

The complexity of mathematical formulas in scientific documents makes efficient formula similarity computation a critical task in information retrieval. Approaches based on text or structure matching cannot fully capture the inherent semantic and hierarchical properties of formulas. Although large language models (LLM) made significant progress in formula similarity comparison, the linear processing may ignore the structure information of formulas. In contrast, GNN excel at modeling the structure relationships of formulas, but still face challenges in accurately defining nodes and edges in a formula tree, especially in distinguishing between nodes at different levels and modeling edge relationships. In this paper, we propose a formula-structure-embedding based GNN (FSCMGNN), and it is integrated with formula structure embedding, structure standardization and attention mechanism. The model is designed for semantic equivalence comparison. Experimental results show that the model outperforms existing models in formula equivalence determination in calculus. Full article

This study focuses on optimizing the thermal performance of hydrogen turbine blades through a sensitivity analysis using generalized fractional calculus. The approach is designed to capture the transient temperature dynamics and optimize thermal profiles by analyzing the influence of a fractional-order parameter on the system’s behavior. The model was implemented in Python, using Monte Carlo simulations to evaluate the impact of the parameter on the temperature evolution in different thermal regimes. Three distinct regions were identified: the Quasi-Uniform Region (where fractional effects are negligible), the Sub-Classical Region (characterized by delayed thermal behavior), and the Super-Classical Region (exhibiting enhanced heat accumulation). Regression analyses reveal quadratic and cubic dependencies of blade temperature on the fractional-order parameter, confirming the robustness of the model with R² values greater than 0.96. The study highlights the potential of using fractional calculus to optimize the thermal response of turbine blades, helping to identify the most suitable parameters for faster stabilization and efficient heat management in hydrogen turbines. Furthermore, it was found that by adjusting the fractional-order parameter, the system can be optimized to reach equilibrium more rapidly while achieving higher temperatures. Importantly, the equilibrium is not altered but rather accelerated based on the chosen parameter, ensuring a more efficient thermal stabilization process. Full article

This study investigates extremal solutions for fractional-order delayed difference equations, utilizing the Caputo nabla operator to establish mild lower and upper approximations via discrete fractional calculus. A new approach is employed to demonstrate the uniform convergence of the sequences of lower and upper approximations within the monotone iterative scheme using the summation representation of the solutions, which serves as a discrete analogue to Volterra integral equations. This research highlights practical applications through numerical simulations in discrete bidirectional associative memory neural networks. Full article