Shankar Pariyar, Bishnu P. Lamichhane, Jeevan Kafle
In this work, we investigate the dynamics of pollutant dispersion using a one-dimensional time-fractional advection-diffusion equation with the Caputo fractional derivative to predict air pollution levels. The focus is on pollutants such as NH3, CO, and CO2, Dirichlet boundary conditions applied in homogeneous and heterogeneous environments. Numerical simulations are performed using the Grünwald–Letnikov method to discretize the fractional derivative, and analytical solutions are obtained through eigenfunction expansion. Results demonstrate that both numerical and analytical approaches accurately capture pollutant behavior, graphical visualizations illustrate concentration profiles and the impact of varying diffusivities. This work enhances the understanding of contaminant dispersion by addressing complex boundary conditions, integrating variable diffusivity, and employing fractional time derivatives. The combination of these methodologies highlights the benefits of using fractional models while visual analysis underscores their utility for improved pollution control and environmental management.
Examining the dynamic interplay of muscle contributions to postural stability enhances our understanding of the neuromuscular mechanisms underlying balance control. This study examined the similarity in shape (using cross-correlation analysis) between seven individual lower limb electromyographic (EMG) signals and center-of-pressure (COP) displacements (i.e., EMG–COP correlation) in 20 young adults (25.2 ± 4.0 years) performing bipedal balance tasks on both stable and multi-axially unstable surfaces, testing the effects of four factors—leg dominance, surface stability, sway direction, and foot position—on individual EMG–COP correlations. The results revealed significant effects of leg dominance (<i>p</i> = 0.004), surface stability (<i>p</i> ≤ 0.001), and sway direction (<i>p</i> ≤ 0.001) on specific muscles. Notably, balancing on the non-dominant leg resulted in a stronger correlation between tibialis anterior activity and postural sway compared to the dominant leg. On a stable surface, postural sway showed stronger correlations with the rectus femoris, semitendinosus, biceps femoris, gastrocnemius medialis, and soleus muscles than on an unstable surface. Additionally, anteroposterior postural sway exhibited a greater correlation with semitendinosus and tibialis anterior activity compared to mediolateral sway. These findings underscore the importance of specific muscles in maintaining bipedal balance, with implications for improving balance performance across various populations.
This work examines the behavior of fields near corners under various boundary conditions (BCs), focusing on singularities arising from fully constrained and relaxed BCs. We analyze this behavior across diverse physical systems governed by similar equations, including electromagnetism, superconductivity, and two-phase fluid flow. The corner geometry presents a challenge due to potentially diverging field solutions as the corner is approached (r→ 0). This motivates the investigation of relaxed BCs, which regularize the field by introducing a characteristic length (Ls) that relates the field’s value to its normal derivative at the boundary.We explore both single-medium (single-phase) and double-medium (two-phase) systems. While prior research has addressed relaxed BCs in specific contexts, their application to corners, particularly in diverse physical systems, remains under-explored. We develop a series solution method to analyze the field behavior near the corner under different BCs. Concrete examples illustrate the theoretical framework, examining both fully constrained and relaxed scenarios. The implications of this work extend to fields such as fluid mechanics, electromagnetism, and heat transfer.
Martin Straka, Christian Höhne, Christian Koglin
et al.
Most flow metering methods used in industrial applications produce results sensitive to the local velocity profile. In response, manufacturers often implement correction algorithms; however, these are rarely supported by rigorous uncertainty evaluations. This paper presents a Reynolds number-dependent velocity profile correction, applicable under fully developed flow conditions and for the Reynolds-dependent part of the correction in disturbed flows, demonstrated on the example of an ultrasonic clamp-on flow meter. Measurement uncertainties are evaluated and propagated through a regression model using Monte Carlo simulation, in compliance with the Guide to the Expression of Uncertainty in Measurement (GUM). Special care is taken to assess the validity range and impact of assuming fully developed flow conditions at the test rig. A validation case demonstrates the reliability of the correction algorithm and its associated uncertainty within the tested conditions. The proposed approach is applicable to other meter types and can be extended to corrections for specific flow disturbances.
We present a kernel compensation method for Maxwell eigenproblem for photonic crystals to avoid the infinite-dimensional kernels that cause many difficulties in the calculation of energy gaps. The quasi-periodic problem is first transformed into a periodic one on the cube by the Floquet-Bloch theory. Then the compensation operator is introduced in Maxwell's equation with the shifted curl operator. The discrete problem depends on the compatible discretization of the de Rham complex, which is implemented by the mimetic finite difference method in this paper. We prove that the compensation term exactly fills up the kernel of the original problem and avoids spurious eigenvalues. Also, we propose an efficient preconditioner and its FFT and multigrid solvers, which allow parallel computing. Numerical experiments for different three-dimensional lattices are performed to validate the accuracy and effectiveness of the method.
Contemporary anarchism centers around three tenets: (1) a constant challenge of and resistance to all forms of domination, (2) so-called "prefigurative politics", in which all decisions are made in a manner that is consistent with a set of non-hierarchical values such as equality, decentralization and voluntary cooperation, (3) a focus on diversity and open-endedness (Gordon, 2008). Within this philosophy the notion of end goals becomes moot; progress, then, is measured by process, in which the values of diversity, pluralism, cooperation, autonomy and experimentation are celebrated. In this perspective piece we propose anarchism as a philosophical framework to address the perceived cognitive dissonances of the current undergraduate mathematics curriculum. Are learning outcomes appropriate in an anarchist approach to education? How can we address the power dynamics of grading and assessment? How can assessment be done in the context of a process-based and horizontal approach that celebrates diversity and autonomy? Should grades be used, and if so, how could they be assigned non-hierarchically? At its core, anarchism aims at aligning thoughts and actions, and we argue that an anarchist viewpoint on undergraduate mathematics addresses the cognitive dissonances that currently plague our curriculum. We propose food for thought for individual instructors' practice, including ideas for incremental and large-scale changes.
Simone Simionato dos Santos, Circe Mary Silva da Silva
Este estudo é um recorte da pesquisa de Doutorado do Programa de Pós-Graduação em Ensino de Ciências e Matemática da Rede Amazônica - REAMEC, que tem por objetivo identificar os saberes matemáticos integrantes da formação de normalistas na Escola Normal de Cuiabá em Mato Grosso, entre 1910 e 1937. Neste trabalho, procuramos identificar a qual tipo de escola de formação de professores o poder público de Mato Grosso aspirava e que conteúdos matemáticos os professores deveriam conhecer para ingressar em tal instituição. Entre as diferentes fontes que produziram a fundamentação historiográfica para realizar o estudo, foram consultados jornais e periódicos que circularam na época em Mato Grosso, assim como as mensagens do governador. Como método de análise, utilizamos a Análise de Discurso, a partir de unidades significantes, contemplando o cenário histórico da Escola Normal de Cuiabá, como instituição em Mato Grosso que formou professores para o ensino primário. Identificamos algumas unidades significantes como ‘Missão Paulista’, ‘A Escola é o Mestre’; ‘Feminilização do Magistério’, ‘O Magistério é Sacerdócio’ e ‘Indícios de uma Matemática a conhecer’ – como referência para a cultura escolar da Escola Normal de Cuiabá. Concluímos que essas fontes trazem indícios do que a sociedade local esperava da Escola Normal e dos futuros professores, assim como evidenciaram a importância dessa instituição para o Estado no início do século XX. Em relação à matemática, foi possível identificar quais os conhecimentos exigidos para o ingresso no curso, assim como os prescritos no programa oficial.
Special aspects of education, Applied mathematics. Quantitative methods
The accurate and efficient recognition of gym workout activities using wearable sensors holds significant implications for assessing fitness levels, tailoring personalized training regimens, and overseeing rehabilitation progress. This study introduces CNN-ResBiGRU, a novel deep learning architecture that amalgamates residual and hybrid methodologies, aiming to precisely categorize gym exercises based on multimodal sensor data. The primary goal of this model is to effectively identify various gym workouts by integrating convolutional neural networks, residual connections, and bidirectional gated recurrent units. Raw electromyography and inertial measurement unit data collected from wearable sensors worn by individuals during strength training and gym sessions serve as inputs for the CNN-ResBiGRU model. Initially, convolutional neural network layers are employed to extract unique features in both temporal and spatial dimensions, capturing localized patterns within the sensor outputs. Subsequently, the extracted features are fed into the ResBiGRU component, leveraging residual connections and bidirectional processing to capture the exercise activities’ long-term temporal dependencies and contextual information. The performance of the proposed model is evaluated using the Myogym dataset, comprising data from 10 participants engaged in 30 distinct gym activities. The model achieves a classification accuracy of 97.29% and an F1-score of 92.68%. Ablation studies confirm the effectiveness of the convolutional neural network and ResBiGRU components. The proposed hybrid model uses wearable multimodal sensor data to accurately and efficiently recognize gym exercise activity.
Andrea Tonini, Francesco Regazzoni, Matteo Salvador
et al.
Cardiocirculatory mathematical models serve as valuable tools for investigating physiological and pathological conditions of the circulatory system. To investigate the clinical condition of an individual, cardiocirculatory models need to be personalized by means of calibration methods. In this study we propose a new calibration method for a lumped-parameter cardiocirculatory model. This calibration method utilizes the correlation matrix between parameters and model outputs to calibrate the latter according to data. We test this calibration method and its combination with L-BFGS-B (Limited memory Broyden - Fletcher - Goldfarb - Shanno with Bound constraints) comparing them with the performances of L-BFGS-B alone. We show that the correlation matrix calibration method and the combined one effectively reduce the loss function of the associated optimization problem. In the case of in silico generated data, we show that the two new calibration methods are robust with respect to the initial guess of parameters and to the presence of noise in the data. Notably, the correlation matrix calibration method achieves the best results in estimating the parameters in the case of noisy data and it is faster than the combined calibration method and L-BFGS-B. Finally, we present real test case where the two new calibration methods yield results comparable to those obtained using L-BFGS-B in terms of minimizing the loss function and estimating the clinical data. This highlights the effectiveness of the new calibration methods for clinical applications.
Abstract Water inrush disaster seriously affects the safety of karst tunnel construction. It’s essential to assess the risk level of water inrush in karst tunnels accurately, and take some effective countermeasures to reduce the damage to the project. We integrates the variable weight theory and cloud model theory to construct the VW&ICM calculation model to evaluate the risk of construction of karst tunnels. First, we select the index factors that affect the risk of water inrush from karst tunnels. Secondly, according to the theory of variable weight, we construct the zoning variable weight model, and the normalization criterion of the data from index factors is established. Thirdly, according to the attribute mathematic theory, we select the numerical characteristics of the improved cloud model, and the normal cloud generator is used to establish the point membership function. Finally, the risk index data is brought into the variable weight vector function and the point membership function to obtain the variable weight vector W and the membership degree matrix R. The risk overall evaluation vector B is further calculated, and the membership degree fluctuation is comprehensively analyzed according to the principle of maximum membership degree. The scope determines the risk of water inrush from karst tunnels. Finally, calculate the variable weight vector W and the membership matrix R, and the overall risk evaluation vector B is further integrated by W and R. According to the max-subjection principle and the fluctuation rule of membership, we get the risk level of water inrush in karst tunnel. The VM&ICM not only can quantitatively evaluate risk by considering the uncertainty of risk assessment and the influence of indicator size on weight, but also can make an analysis of the reliability to make the assessment result more convincing. The model makes improvement in weakening the influence of subjective factors on assessment results and in allocating the weight of indicators. A simple and practical software package is developed, which greatly improves the computational efficiency of VW&ICM method. The VW&ICM calculation model is applied to the risk assessment of water inrush for karst tunnels, and the results are basically consistent with the on-site construction situation.
An one-fold Darboux transformation for the Lotka–Volterra lattice system is first established using a proper gauge transformation matrix. Then, as a result of the N times one-fold Darboux transformation, the corresponding N-fold Darboux transformation of the Lotka–Volterra lattice system is presented, and two exact solution are obtained by the resulting Darboux transformation. Hereafter, its the corresponding iso-spectral integrable lattice family is derived. Using the trace identity, bi-Hamiltonian structure of the Lotka–Volterra integrable family is established, and its Liouville integrability is proven.
The tessellation problem is interesting to study, especially when it is associated with mathematical concepts. In this study, a graph coloring technique will be applied to solve the problem of wallpaper tessellation decoration. The main objective of this study is to improve students' meta-literacy abilities when applying coloring techniques in completing tessellation wallpaper decorations in RBL-STEM learning. RBL is a learning model that stands for Research-Based Learning. This model is now becoming the focus of attention of learning practitioners, while the STEM approach is an approach that involves four studies in the field of science, namely science, technology, engineering, and mathematics. The method used in this study is a mixed method, a combination of quantitative and qualitative. Quantitative methods were used to analyze the significant differences in the students' meta-literacy learning achievement between the control and experimental classes. In contrast, the qualitative method was used to analyze the results of in-depth interviews, a triangulation process from the quantitative research results. The results of this study indicate that there is a significant difference in meta-literacy ability between the control class (the class that applies RBL-STEM but without using the learning materials developed by the researcher) and the experimental class (the class that applies RBL-STEM using the learning materials developed by the researcher). The independent sample t-test on the post-test learning outcomes of meta-literacy abilities on Sig (2 Tailed) showed a significant difference of 0.013 < 0.05. Furthermore, the data on the meta-literacy ability of students showed that as much as 10% of students have the poor meta-literacy ability, 17% of students have fair meta-literacy ability, 26% of students have the good meta-literacy ability, 32% of students have very good meta-literacy ability and 15% of students have the excellent meta-literacy ability. Based on this research result, to improve the students' meta-literacy, we need to implement the learning method which fosters the research activity in the classroom and brings the real-life phenomenon in the classroom. The integration of RBL and STEM is one of the novel breakthroughs.
This paper introduced a comparison method for three explicitly defined intermediate encoding methods in generative design for two-dimensional soft robotic units. This study evaluates a conventional genetic algorithm with full access to removing elements from the design domain using an implicit random encoding layer, a Lindenmayer system encoding mimicking biological growth patterns and a compositional pattern producing network encoding for 2D pattern generation. The objective of the optimisation problem is to match the deformation of a single actuator unit with a desired target shape, specifically uni-axial elongation, under internal pressure. The study results suggest that the Lindenmayer system encoding generates candidate units with fewer function evaluations than the traditional implicitly encoded genetic algorithm. However, the distribution of constraint and internal energy is similar to that of the random encoding, and the Lindenmayer system encoding produces a less diverse population of candidate units. In contrast, despite requiring more function evaluations than the Lindenmayer System encoding, the Compositional Pattern Producing Network encoding produces a similar diversity of candidate units. Overall, the Compositional Pattern Producing Network encoding results in a proportionally higher number of high-performing units than the random or Lindenmayer system encoding, making it a viable alternative to a conventional monolithic approach. The results suggest that the compositional pattern producing network encoding may be a promising approach for designing soft robotic actuators with desirable performance characteristics.
This work constructs the first-ever sixth-order exponential Runge--Kutta (ExpRK) methods for the time integration of stiff parabolic PDEs. First, we leverage the exponential B-series theory to restate the stiff order conditions for ExpRK methods of arbitrary order based on an essential set of trees only. Then, we explicitly provide the 36 order conditions required for sixth-order methods and present convergence results. In addition, we are able to solve the 36 stiff order conditions in both their weak and strong forms, resulting in two families of sixth-order parallel stages ExpRK schemes. Interestingly, while these new schemes require a high number of stages, they can be implemented efficiently similar to the cost of a 6-stage method. Numerical experiments are given to confirm the accuracy and efficiency of the new schemes.
We introduce a proof-theoretic approach to showing nondefinability of second-order intuitionistic connectives by quantifier-free schemata. We apply the method to prove that Taranovsky's "realizability disjunction" connective does not admit a quantifier-free definition, and use it to obtain new results and more nuanced information about the nondefinability of Kreisel's and Połacik's unary connectives. The finitary and combinatorial nature of our method makes it resilient to changes in metatheory, and suitable even for settings with axioms that are explicitly incompatible with classical logic. Furthermore, the problem-specific subproofs arising from this approach can be readily transcribed into univalent type theory and verified using the Agda proof assistant.
Analysing several characteristic mathematical models: natural and real numbers, Euclidean geometry, group theory, and set theory, I argue that a mathematical model in its final form is a junction of a set of axioms and an internal partial interpretation of the corresponding language. It follows from the analysis that (i) mathematical objects do not exist in the external world: they are imagined objects, some of which, at least approximately, exist in our internal world of activities or we can realize or represent them there; (ii) mathematical truths are not truths about the external world but specifications (formulations) of mathematical conceptions; (iii) mathematics is first and foremost our imagined tool by which, with certain assumptions about its applicability, we explore nature and synthesize our rational cognition of it.
Abstract Threaded fasteners naturally tend to loosen under vibration, impact, or alternating thermal load. Various anti-loosening methods or strategies are widely applied for preventing loosening, including a few anti-loosening designs and anti-loosening structures. In this review, a variety of influencing factors that improved the anti-loosening ability and helped guide the anti-loosening designs of threaded fasteners are summarized. Second, the anti-loosening structures are classified into two categories, that is, conventional and new-style anti-loosening structures. The former refers to widely used structures in engineering applications, while the latter refers to novel structures not available in the markets. The research on the evaluation and comparison of various conventional anti-loosening structures in terms of preventing loosening is summarized in detail and the new-style anti-loosening structures from five different aspects are also surveyed based on different structural characteristics. In the future, the effects of combined factors on loosening should be considered to achieve optimal anti-loosening designs. More quantitative research on the mathematical relationship between the anti-loosening performance of conventional structures and structural parameters must be conducted. Furthermore, novel structures with excellent abilities to prevent loosening are needed, and issues of difficulties in installation and disassembly, low strength at thread, large deformation, and temperature dependence also need to be addressed.
The fields of electronics and information technology have witnessed rapid development during the last decades, providing significant technical support to the field of biological sciences. Radio-Frequency Identification (RFID) technology has been used to automate the monitoring of animal location and behaviors in a wide range of vertebrate and invertebrate species, including social insects such as ants and honey bees (<i>Apis mellifera</i> L.). This technology relies on electromagnetic fields to identify and track transponders attached to objects automatically. Implementing new technologies to serve research purposes could be time consuming and require technical expertise from entomologists and researchers. Herein, we present a detailed description on how to harness RFID technology to serve honey bee research effectively. We describe how to build and operate a 32-antenna RFID system used to monitor various honey bee behaviors such as foraging, robbing, and queen and drone mating, which can be used in other social insects as well. Preliminary data related to queen nuptial flights were obtained using this unit and presented in this study. Virgin queens labeled with ≈5 mg transponders performed multiple (one to four) nuptial/orientation flights a day (9 a.m. to 5 p.m.) ranging from 8 to 145 s each. Contrary to virgin queens, no hive exit was recorded for mated queens. At full capacity, this unit can monitor up to 32 honey bee colonies concurrently and is self-sustained by a solar panel to work in remote areas. All materials, hardware, and software needed to build and operate this unit are detailed in this study, offering researchers and beekeepers a practical solution and a comprehensive source of information enabling the implementation of RFID technology in their research perspective.