Background As aging populations continue to grow, smart home technologies—such as smart locks—have become increasingly essential to support older adults’ independent living. Long-term use remains a challenge, however, with most studies focusing on initial adoption rather than sustained engagement. Methods In this study, we examined the key factors related to older adults’ continuance intention toward smart locks, applying a socio-technical framework that integrated the Expectation-Confirmation Model of Information Systems (ECM-IS), the Task-Technology Fit (TTF) model, and external variables, including privacy and security, trust, and habit. We analyzed survey data from 422 Chinese participants aged 55 and older using Partial Least Squares Structural Equation Modeling (PLS-SEM) and Importance-Performance Matrix Analysis (IPMA). Results The model explained 71.6% of the variance in continuance intention (R2 = 0.716) and showed strong predictive relevance (Q2 = 0.623). Trust and perceived usefulness were positively related to continuance intention, followed by satisfaction. Task-technology fit and confirmation were significantly associated with perceived usefulness and satisfaction. Habit and privacy and security were not significant with respect to continuance intention. Conclusions These findings provide theoretical and practical insight for designing age-inclusive, trust-enhancing smart locks that better support older adults’ needs in post-adoption contexts.
The widespread availability of generative artificial intelligence tools poses new challenges for school mathematics education, particularly regarding the formative role of traditional mathematical tasks. In post-AI educational contexts, many activities can be solved automatically, without engaging students in interpretation, decision-making, or mathematical validation processes. This study analyzes a secondary school classroom experience in which open mathematical tasks are implemented as a didactic response to this scenario, aiming to sustain students' mathematical activity. Adopting a qualitative and descriptive-interpretative approach, the study examines the forms of mathematical work that emerge during task resolution, mediated by the didactic regulation device COMPAS. The analysis is structured around four analytical axes: open task design in post-AI contexts, students' mathematical agency, human-AI complementarity, and modeling and validation practices. The findings suggest that, under explicit didactic regulation, students retain epistemic control over mathematical activity, even in the presence of generative artificial intelligence.
We introduce determinantal sieving, a new, remarkably powerful tool in the toolbox of algebraic FPT algorithms. Given a polynomial $P(X)$ on a set of variables $X=\{x_1,\ldots,x_n\}$ and a linear matroid $M=(X,\mathcal{I})$ of rank $k$, both over a field $\mathbb{F}$ of characteristic 2, in $2^k$ evaluations we can sieve for those terms in the monomial expansion of $P$ which are multilinear and whose support is a basis for $M$. Alternatively, using $2^k$ evaluations of $P$ we can sieve for those monomials whose odd support spans $M$. Applying this framework, we improve on a range of algebraic FPT algorithms, such as: 1. Solving $q$-Matroid Intersection in time $O^*(2^{(q-2)k})$ and $q$-Matroid Parity in time $O^*(2^{qk})$, improving on $O^*(4^{qk})$ over general fields (Brand and Pratt, ICALP 2021) 2. Long $(s,t)$-Path in $O^*(1.66^k)$ time, improving on $O^*(2^k)$, and Rank $k$ $(S,T)$-Linkage in so-called frameworks in $O^*(2^k)$ time, improving on $O^*(2^{|S|+O(k^2 \log(k+|\mathbb{F}|))})$ over general fields (Fomin et al., SODA 2023). 3. Many instances of the Diverse X paradigm, finding a collection of $r$ solutions to a problem with a minimum mutual distance of $d$ in time $O^*(2^{r(r-1)d/2})$, improving solutions for $k$-Distinct Branchings from time $2^{O(k \log k)}$ to $O^*(2^k)$ (Bang-Jensen et al., ESA 2021), and for Diverse Perfect Matchings from $O^*(2^{2^{O(rd)}})$ to $O^*(2^{r^2d/2})$ (Fomin et al., STACS 2021). Here, all matroids are assumed to be represented over fields of characteristic 2. Over general fields, we achieve similar results at the cost of using exponential space by working over the exterior algebra. For a class of arithmetic circuits we call strongly monotone, this is even achieved without any loss of running time. However, the odd support sieving result appears to be specific to working over characteristic 2.
Starting from Greg Moore's description about Physical Mathematics, a framework is proposed in order to understand it, based on Gilles Châtelet's philosophy. It will be argued that Châtelet's ideas of inverting, splitting, augmenting and virtuality are crucial in the discussion about the nature of Physical Mathematics. Along this line, it will be proposed that mirror symmetry is a natural study case to test Châtelet's ideas in this context. This should be considered as a first step in a long term project aiming to study the relations among mathematics, physics and philosophy in the construction of a global understanding of the structure of the universe, as it was envisioned by Grothendieck in the late 80's of the last century and it was started to be developed independently by Châtelet in the beginning of the 90's. The main suggestion of the essay is that it is in the relations between mathematics, physics and philosophy that new knowledge arises.
Phuong-Nam Nguyen, Quang Nguyen-The, An Vu-Minh
et al.
ChatGPT, an Artificial Intelligence model, has the potential to revolutionize education. However, its effectiveness in solving non-English questions remains uncertain. This study evaluates ChatGPT's robustness using 586 Korean mathematics questions. ChatGPT achieves 66.72% accuracy, correctly answering 391 out of 586 questions. We also assess its ability to rate mathematics questions based on eleven criteria and perform a topic analysis. Our findings show that ChatGPT's ratings align with educational theory and test-taker perspectives. While ChatGPT performs well in question classification, it struggles with non-English contexts, highlighting areas for improvement. Future research should address linguistic biases and enhance accuracy across diverse languages. Domain-specific optimizations and multilingual training could improve ChatGPT's role in personalized education.
Jessica Rodrigues Esteves, Jorge C. S. Cardoso, Berenice Santos Gonçalves
The growing popularity of immersive virtual reality (iVR) technologies has opened up new possibilities for learning English. In the literature, it is possible to find several studies focused on the design, development, and evaluation of immersive virtual reality applications. However, there are no studies that systematize design recommendations for immersive virtual reality applications for English learning. To fill this gap, we present a systematic review that aims to identify design recommendations for immersive virtual reality English learning applications. We searched the ACM Digital Library, ERIC, IEEE Xplore, Scopus, and Web of Science (1 January 2010 to April 2023) and found that 24 out of 847 articles met the inclusion criteria. We identified 18 categories of design considerations related to design and learning and a design process used to create iVR applications. We also identified existing trends related to universities, publications, devices, human senses, and development platforms. Finally, we addressed study limitations and future directions for designing iVR applications for English learning.
Najwan Alsadat, Mohammed Elgarhy, Amal S. Hassan
et al.
In this article, we provide a new three-parameter model derived from the newly reduced Cauchy power-G family and linked to the linear failure rate model. The truncated Cauchy power linear failure rate (TCPLFR) is the name given to this distribution. The TCPLFR distribution also contains the truncated Cauchy power Rayleigh distribution and the truncated Cauchy power exponential distribution as sub-models. The TCPLFR distribution has rising, falling, and U-shaped hazard rate functions. The distribution characteristics of the TCPLFR are presented. To compute the population parameters’ point and estimated confidence intervals, the maximum likelihood approach is employed. We explore the behavior of the maximum likelihood estimates as well as the estimated confidence intervals for the model parameters using Monte Carlo simulation. To demonstrate the significance and flexibility of the TCPLFR distribution, the Akaike information criterion (D1), Bayesian information criterion (D2), consistent Akaike information criterion (D3), Hannan–Quinn information criterion (D4), and Kolmogorov–Smirnov (D5) statistic with its p-value (D6) were employed. According to a real-world data analysis, the truncated Cauchy power linear failure rate distribution outperforms alternative models with two, three, and four parameters.
Abbirami Balachandran, Sy Bing Choi, Morak-Młodawska Beata
et al.
1. Diabetic chronic wounds, mainly foot ulcers, constitute one of the most common complications of poorly managed diabetes mellitus. The most typical reasons are insufficient glycemic management, latent neuropathy, peripheral vascular disease, and neglected foot care. In addition, it is a common cause of foot osteomyelitis and amputation of the lower extremities. Patients are admitted in larger numbers attributable to chronic wounds compared to any other diabetic disease. In the United States, diabetes is currently the most common cause of non-traumatic amputations. Approximately five percent of diabetics develop foot ulcers, and one percent require amputation. Therefore, it is necessary to identify sources of lead with wound-healing properties. Redox imbalance due to excessive oxidative stress is one of the causes for the development of diabetic wounds. Antioxidants have been shown to decrease the progression of diabetic neuropathy by scavenging ROS, regenerating endogenous and exogenous antioxidants, and reversing redox imbalance. Matrix metalloproteinases (MMPs) play vital roles in numerous phases of the wound healing process. Antioxidant and fibroblast cell migration activity of <i>Marantodes pumilum</i> (MP) crude extract has previously been reported. Through their antioxidant, epithelialization, collagen synthesis, and fibroblast migration activities, the authors hypothesise that naringin, eicosane and octacosane identified in the MP extract may have wound-healing properties. 2. The present study aims to identify the bioactive components present in the dichloromethane (DCM) extract of <i>M. pumilum</i> and evaluate their antioxidant and wound healing activity. Bioactive components were identified using LCMS, HPTLC and GCMS. Excision wound on STZ-induced diabetic rat model, human dermal fibroblast (HDF) cell line and colorimetric antioxidant assays were used to evaluate wound healing and antioxidant activities, respectively. Molecular docking and pkCMS software would be utilised to predict binding energy and affinity, as well as ADME parameters. 3. Naringin (NAR), eicosane (EIC), and octacosane (OCT) present in MP displayed antioxidant action and wound excision closure. Histological examination HDF cell line demonstrates epithelialization, collagen production, fibroblast migration, polymorphonuclear leukocyte migration (PNML), and fibroblast movement. The results of molecular docking indicate a substantial attraction and contact between MMPs. pkCMS prediction indicates inadequate blood-brain barrier permeability, low toxicity, and absence of hepatotoxicity. 4. Wound healing properties of (NEO) naringin, eicosane and octacosane may be the result of their antioxidant properties and possible interactions with MMP.
The paper continues the consideration of Hilbert mathematics to mathematics itself as an additional “dimension” allowing for the most difficult and fundamental problems to be attacked in a new general and universal way shareable between all of them. That dimension consists in the parameter of the “distance between finiteness and infinity”, particularly able to interpret standard mathematics as a particular case, the basis of which are arithmetic, set theory and propositional logic: that is as a special “flat” case of Hilbert mathematics. The following four essential problems are considered for the idea to be elucidated: Fermat’s last theorem proved by Andrew Wiles; Poincaré’s conjecture proved by Grigori Perelman and the only resolved from the seven Millennium problems offered by the Clay Mathematics Institute (CMI); the four-color theorem proved “machine-likely” by enumerating all cases and the crucial software assistance; the Yang-Mills existence and mass gap problem also suggested by CMI and yet unresolved. They are intentionally chosen to belong to quite different mathematical areas (number theory, topology, mathematical physics) just to demonstrate the power of the approach able to unite and even unify them from the viewpoint of Hilbert mathematics. Also, specific ideas relevant to each of them are considered. Fermat’s last theorem is shown as a Gödel insoluble statement by means of Yablo’s paradox. Thus, Wiles’s proof as a corollary from the modularity theorem and thus needing both arithmetic and set theory involves necessarily an inverse Grothendieck universe. On the contrary, its proof in “Fermat arithmetic” introduced by “epoché to infinity” (following the pattern of Husserl’s original “epoché to reality”) can be suggested by Hilbert arithmetic relevant to Hilbert mathematics, the mediation of which can be removed in the final analysis as a “Wittgenstein ladder”. Poincaré’s conjecture can be reinterpreted physically by Minkowski space and thus reduced to the “nonstandard homeomorphism” of a bit of information mathematically. Perelman’s proof can be accordingly reinterpreted. However, it is valid in Gödel (or Gödelian) mathematics, but not in Hilbert mathematics in general, where the question of whether it holds remains open. The four-color theorem can be also deduced from the nonstandard homeomorphism at issue, but the available proof by enumerating a finite set of all possible cases is more general and relevant to Hilbert mathematics as well, therefore being an indirect argument in favor of the validity of Poincaré’s conjecture in Hilbert mathematics. The Yang-Mills existence and mass gap problem furthermore suggests the most general viewpoint to the relation of Hilbert and Gödel mathematics justifying the qubit Hilbert space as the dual counterpart of Hilbert arithmetic in a narrow sense, in turn being inferable from Hilbert arithmetic in a wide sense. The conjecture that many if not almost all great problems in contemporary mathematics rely on (or at least relate to) the Gödel incompleteness is suggested. It implies that Hilbert mathematics is the natural medium for their discussion or eventual solutions.
It is nowadays common to consider that proof must be part of the learning of mathematics from Kindergarten to University1. As it is easy to observe, looking back to the history of mathematical curricula, this has not always been the case either because following an old pedagogical tradition of rote learning proof was reduced to the formalism of a text and deprived from its meaning or, despiteits acknowledged presence anywhere in mathematics, proof did not get the status of something to learn for what it is. On the long way from its absence as such in the past to its contemporary presence as a content to be taught at all grades, proof has had to go through a process of didactical transposition to satisfy a number of different constraints either of an epistemic, didactical, logical ormathematical nature. I will follow a chronological order to outline the main features of this process with the objective to better understand the didactical problem that our current research is facing.
In the study reported on here, the effects of science centres on the perceptions of secondary school students towards the nature of science were examined. The study group consisted of 16 students aged 13 and 14 of which 7 were female and 9 male. In this study, a total of 4 trips were arranged to the science centre twice a month for 2 months. Students attended different workshops, planetariums and exhibitions on each trip to the science centre they attended. The activities that students attended during these trips were independent of the school curriculum. The data were obtained in the spring of 2019. This study was experimental research. Mixed method was used as the research model and the concurrent triangulation pattern was used as the design. The Scientific Knowledge Scale, the Questionnaire for Scientific Knowledge and semi-structured interviews were used as data collection tools, which were administered to students before and after the activities. In data analysis, qualitative data were analysed using content analysis. Quantitative data were analysed using the SPSS program. As a result of the research, it was determined that science centres caused an increase in students’ scores and levels of scientific knowledge and an improvement in their views on the nature of science.
In order to study the driving effect of industrial product design, a method based on the application of 3D simulation technology in industrial product design technology was proposed. This method introduces the information about the change in industrial product design in industrial enterprises and analyzes the application of 3D simulation technology in industrial product design by taking DIALux, industrial robot, and resource information search system as examples. The results show that the application of 3D simulation system needs to be combined with industrial software, and the development of industrial software business mainly based on 3D simulation technology is emphasized so that the business revenue of enterprises increases from 709 million yuan in 2029 to 1.385 billion yuan in 2021, with a compound growth rate of 25.01%, which has achieved good economic benefits. 3D simulation technology plays an important role in promoting the development of industrial product design technology. It is necessary to actively promote the integration between 3D simulation technology and industrial software.
Francesco Carnazza, Federico Carollo, Dominik Zietlow
et al.
Full information about a many-body quantum system is usually out-of-reach due to the exponential growth—with the size of the system—of the number of parameters needed to encode its state. Nonetheless, in order to understand the complex phenomenology that can be observed in these systems, it is often sufficient to consider dynamical or stationary properties of local observables or, at most, of few-body correlation functions. These quantities are typically studied by singling out a specific subsystem of interest and regarding the remainder of the many-body system as an effective bath. In the simplest scenario, the subsystem dynamics, which is in fact an open quantum dynamics, can be approximated through Markovian quantum master equations. Here, we formulate the problem of finding the generator of the subsystem dynamics as a variational problem, which we solve using the standard toolbox of machine learning for optimization. This dynamical or ‘Lindblad’ generator provides the relevant dynamical parameters for the subsystem of interest. Importantly, the algorithm we develop is constructed such that the learned generator implements a physically consistent open quantum time-evolution. We exploit this to learn the generator of the dynamics of a subsystem of a many-body system subject to a unitary quantum dynamics. We explore the capability of our method to recover the time-evolution of a two-body subsystem and exploit the physical consistency of the generator to make predictions on the stationary state of the subsystem dynamics.
Toposes can be pictured as mathematical universes. Besides the standard topos, in which most of mathematics unfolds, there is a colorful host of alternate toposes in which mathematics plays out slightly differently. For instance, there are toposes in which the axiom of choice and the intermediate value theorem from undergraduate calculus fail. The purpose of this contribution is to give a glimpse of the toposophic landscape, presenting several specific toposes and exploring their peculiar properties, and to explicate how toposes provide distinct lenses through which the usual mathematical objects of the standard topos can be viewed.
In this paper we give a brief overview of the geometry of involute gears, from a mathematical more than an engineering perspective. We also list some of the many variant geared mechanisms and discuss some of our 3D printed mechanisms.
In the Soviet Union a reform movement in mathematics education was triggered by Andrey Kolmogorov in the 1970s, and followed by a counter-reform. This movement was rooted in the very different socioeconomic conditions of that time and place, and followed a strategy with very significant contrasts to similar programs in the USA, England, or France. This provides an interesting case study which may illuminate the way such movements arise and succeed or fail, and, at the social level, certain fundamental commonalities of constraints as well as significant differences according to local conditions. We shall show that the principal reasons of the failure of the Kolmogorov reform were political: (1) The reform ignored the reality of the socio-economic conditions of the country; (2) The human factor was ignored, and very little attention was given to professional development and retraining of, and methodological help to, the whole army of teachers; (3) An attempt to transfer mathematical content and methods from the highly successful advanced extension stream for mathematically strong and highly engaged children to mainstream education was an especially grievous error.
Nurhikmah H., Hamsu Abdul Gani, Muh. Putra Pratama
et al.
Teachers still use a semi-conventional evaluation process. Namely, the exam process is carried out by utilizing social media to send students' exam results manually on paper. This kind of evaluation process is less effective and efficient, both in terms of time, the method used and examining exam results which takes a long time and is inaccurate. This study aims to develop a Computer Based Test based on Android. This research method is Research and Development, which is focused on developing a Computer Based Test based on smartphones, especially Android. The development model used refers to the Alessi and Trollip development model. The research subjects were 30 students and 1 mathematics teacher. The instrument used to collect data is a questionnaire. Data collection techniques used are observation, interviews, questionnaires or questionnaires, tests, and documentation. The technique used to analyze the data is descriptive qualitative and quantitative analysis. The results of the study were the results of validation by material experts obtained an average score of 3.7 (very valid). By media, experts obtained an average score of 3.8 (very valid) so that the Computer Based Test could be tested in the field to determine the practicality where the practicality level met criteria with efficient results. This means that it can be stated that the Android-based Computer Based Test is efficient in the evaluation/exam process on mathematics subjects. Based on the feasibility test of the Computer Based Test, it can be concluded that the use of the Computer Based Test is feasible to be used as a medium for evaluating learning in mathematics subjects.
The propagation of optical solitons in optical fibers with the generalized Kudryashov’s refractive index is described by a high order nonlinear Schrödinger equation. The main feature is that the amplitude and width of the pulse can be changed with arbitrary power. By trial equation method, a series of propagation patterns of optical waves are obtained. In addition, the graphs of two-dimensional and three-dimensional solutions are illustrated, and then the existence of all those patterns of optical waves is proved.
Inese Polaka, Danute Razuka-Ebela, Jin Young Park
et al.
Abstract Background The amount of available and potentially significant data describing study subjects is ever growing with the introduction and integration of different registries and data banks. The single specific attribute of these data are not always necessary; more often, membership to a specific group (e.g. diet, social ‘bubble’, living area) is enough to build a successful machine learning or data mining model without overfitting it. Therefore, in this article we propose an approach to building taxonomies using clustering to replace detailed data from large heterogenous data sets from different sources, while improving interpretability. We used the GISTAR study data base that holds exhaustive self-assessment questionnaire data to demonstrate this approach in the task of differentiating between H. pylori positive and negative study participants, and assessing their potential risk factors. We have compared the results of taxonomy-based classification to the results of classification using raw data. Results Evaluation of our approach was carried out using 6 classification algorithms that induce rule-based or tree-based classifiers. The taxonomy-based classification results show no significant loss in information, with similar and up to 2.5% better classification accuracy. Information held by 10 and more attributes can be replaced by one attribute demonstrating membership to a cluster in a hierarchy at a specific cut. The clusters created this way can be easily interpreted by researchers (doctors, epidemiologists) and describe the co-occurring features in the group, which is significant for the specific task. Conclusions While there are always features and measurements that must be used in data analysis as they are, the use of taxonomies for the description of study subjects in parallel allows using membership to specific naturally occurring groups and their impact on an outcome. This can decrease the risk of overfitting (picking attributes and values specific to the training set without explaining the underlying conditions), improve the accuracy of the models, and improve privacy protection of study participants by decreasing the amount of specific information used to identify the individual.
Computer applications to medicine. Medical informatics, Analysis