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In this note we provide two special examples of non-injective polynomial maps from $\mathbb{R}^2$ to $\mathbb{R}^2$ with non-vanishing Jacobian: the first one is surjective, the second one has non-dense image.

Blockchain technologies for rewards in education are gaining attraction as a promising approach to motivate student learning and promote academic achievement. By providing tangible rewards for educational attainment and engagement, such as digital tokens, educators can motivate learners to take a more active role in their learning and increase their sense of ownership and responsibility for their academic outcomes. In this context, this work proposes the Software Engineering Skill (SES) token as a way of rewarding students in order to improve their experiences in Software Engineering Education (SEE). We performed a proof of concept and conclude that SES token can be deployed in a platform to support SEE., Comment: 6 pages

The Metaverse is a network of eXtended Reality applications (XR apps) connected to each other, over the Internet infrastructure, allowing network users, systems, and devices to access them. It is very challenging to implement solutions for XR apps, due to the combination of complex concerns that should be addressed: multiple users with non-traditional input and output devices, different hardware platforms that should be addressed, forceful interactive rates, and experimental interaction techniques, among other issues. Therefore, this work aims to present a Software Product Line (SPL)-based approach to support the development of Web XR apps. More specifically, we define a features model that represents similarities and variables (domain analysis); we defined a core composed of generic and reusable software artifacts (domain project); and we developed an interface to support the instantiation of a Web XR app family, named MetaSee Features Model Editor (domain implementation). This approach integrates with a component of the MetaSEE architecture (Metaverse for Software Engineering Education). A preliminary assessment found that Features Model has conceptual consistency from the point of view of the complexity of Web XR Apps multimodal interaction. As future work, features model and artifacts will be increased with improvements and an evaluation with a significant number of participants will be made.

Contribution: This secondary study examines the literature on immersive learning frameworks and reviews their state of the art. Frameworks have been categorized according to their purpose. In addition, the elements that compose them were also categorized. Some gaps were identified and proposed as a research roadmap. Background: Immersive technologies for education have been used for some years. Despite this, there are few works that aim to support the development and use of virtual environments for immersive learning. Research Questions: This systematic review has the following main research question: What is the state of the art of immersive learning frameworks? In order to answer this question, secondary research questions were defined: 1) what definitions of immersive learning were adopted in primary studies? 2) what are the purposes of use by the frameworks? 3) what are the elements that compose the frameworks? 4) what are the methods used to validate the frameworks? Methodology: As per the systematic review guidelines, this study followed a rigorous and replicable process for collecting and analyzing data. From 1721 articles identified in the search engines, 15 were selected after the inclusion and exclusion criteria. Findings: Most frameworks are models that investigate the causal relationship between immersive learning factors that influence learning outcomes. Although this theoretical aspect is important for the advancement of research, the area still lacks more practical frameworks that address more technical details and support development, as well as the use of immersive virtual environments by teachers and instructors., Comment: 12 pages, 2 figures, 6 tables

There is a wealth of data on air pollution within several users' reach, including modelled concentrations and depositions as well as observations from air quality stations. However, data integration to perceive spatial and temporal trends at the national level is a complex undertaking. The difficulties are mainly related to the data sources (many files with a lot of information and in different formats). In addition, the processing of this data is time-consuming and impractical when the time period under analysis increases. Furthermore,the processing of spatial-temporal data requires the use of multiple specific tools, such as geographic information systems software and statistical, which are not readily accessible to non-specialised users. The proposed solution is to develop libraries that are responsible for aggregating different types of data related with pollution. In addition to allowing the integration of different data, the libraries are also the basis for developing web applications. The libraries allow the collection of data made available by the Portuguese Environment Agency (APA) and official modelling results for Europe. The applications developed will extend the libraries to allow data processing and representation through Dashboards. These Dashboards provide access to non-specialised users, namely regarding the trends of pollutants in each region. The implemented libraries allow the development of projects that would need access to the same data sources. These Dashboards allow for simplified access to data and for studies that have so far been beyond the reach of researchers.

In this short note we provide the example with the lowest degree known so far of a non-injective local polynomial diffeomorphism $F=(p,q):\mathbb{R}^2 \to \mathbb{R}^2$. In our example $p$ has degree $10$ and $q$ has degree $15$, rather than $10$ and $25$, respectively, known up to now as the smallest degrees for the coordinates of $F$. Our construction was based on S. Pinchuk celebrated counterexample to the real Jacobian conjecture., Comment: 4 pages

Switched server systems are mathematical models of manufacturing, traffic and queueing systems that have being studied since the early 1990s. In particular, it is known that typically the dynamics of such systems is asymptotically periodic: each orbit of the system converges to one of its finitely many limit cycles. In this article, we provide an explicit example of a switched server system with exotic behavior: each orbit of the system converges to the same Cantor attractor. To accomplish this goal, we bring together recent advances in the understanding of the topological dynamics of piecewise contractions and interval exchange transformations with flips. The ultimate result is a switched server system whose Poincare map is semiconjugate to a minimal and uniquely ergodic interval exchange transformation with flips., Comment: 22 pages, 3 figures