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  1. Existence and uniqueness results for solutions of stochastic differential equations (SDEs) under exceptionally weak conditions are well known in the case where the diffusion coeffcient is nondegenerate. Here, existence and uniqueness of strong solutions is obtained in the case of degenerate SDEs in a class that is motivated by diffusion representations for solutions of Schrödinger initial value problems. In such examples, the dimension of the range of the diffusion coeffcient is exactly half that of the state. In addition to this degeneracy, two types of discontinuities and singularities in the drift are allowed, where these are motivated by the structure of the Coulomb potential. The first type consists of discontinuities that may occur on a possibly high-dimensional manifold. The second consists of singularities that may occur on a smoothly parameterized curve.
  2. Metacognition is the understanding of your own knowledge including what knowledge you do not have and what knowledge you do have. This includes knowledge of strategies and regulation of one’s own cognition. Studying metacognition is important because higher-order thinking is commonly used, and problem-solving skills are positively correlated with metacognition. A positive previous disposition to metacognition can improve problem-solving skills. Metacognition is a key skill in design and manufacturing, as teams of engineers must solve complex problems. Moreover, metacognition increases individual and team performance and can lead to more original ideas. This study discusses the assessment of metacognitive skills in engineering students by having the students participate in hands-on and virtual reality activities related to design and manufacturing. The study is guided by two research questions: (1) do the proposed activities affect students’ metacognition in terms of monitoring, awareness, planning, self-checking, or strategy selection, and (2) are there other components of metacognition that are affected by the design and manufacturing activities? The hypothesis is that the participation in the proposed activities will improve problem-solving skills and metacognitive awareness of the engineering students. A total of 34 undergraduate students participated in the study. Of these, 32 were male and 2 weremore »female students. All students stated that they were interested in pursuing a career in engineering. The students were divided into two groups with the first group being the initial pilot run of the data. In this first group there were 24 students, in the second group there were 10 students. The groups’ demographics were nearly identical to each other. Analysis of the collected data indicated that problem-solving skills contribute to metacognitive skills and may develop first in students before larger metacognitive constructs of awareness, monitoring, planning, self-checking, and strategy selection. Based on this, we recommend that the problem-solving skills and expertise in solving engineering problems should be developed in students before other skills emerge or can be measured. While we are sure that the students who participated in our study have awareness as well as the other metacognitive skills in reading, writing, science, and math, they are still developing in relation to engineering problems.« less
  3. Familiarity with manufacturing environments is an essential aspect for many engineering students. However, such environments in real world often contain expensive equipment making them difficult to recreate in an educational setting. For this reason, simulated physical environments where the process is approximated using scaled-down representations are usually used in education. However, such physical simulations alone may not capture all the details of a real environment. Virtual reality (VR) technology nowadays allows for the creation of fully immersive environments, bringing simulations to the next level. Using rapidly advancing gaming technology, this research paper explores the applicability of creating multiplayer serious games for manufacturing simulation. First, we create and validate a hands-on activity that engages groups of students in the design and assembly of toy cars. Then, a corresponding multiplayer VR game is developed, which allows for the collaboration of multiple VR users in the same virtual environment. With a VR headset and proper infrastructure, a user can participate in a simulation game from any location. This paper explores whether multiplayer VR simulations could be used as an alternative to physical simulations.
  4. Problem-solving is an iterative process that requires brainstorming, analysis of the problem, development and testing of solutions. It relies on under-standing what is known and what is unknown about the problem. That knowledge of the knowns and unknowns is called metacognition. Today’s engineers must understand their own metacognition and that of other team members to derive the best solutions for engineering problems given the different constraints. Engineers working in design and manufacturing fields confront challenges due to a lack of important metacognitive understanding of their own and their team’s problem-solving skills. This research suggests measuring metacognition within teams by using manufacturing simulations with virtual reality and eye tracking
  5. Abstract The prediction of reactor antineutrino spectra will play a crucial role as reactor experiments enter the precision era. The positron energy spectrum of 3.5 million antineutrino inverse beta decay reactions observed by the Daya Bay experiment, in combination with the fission rates of fissile isotopes in the reactor, is used to extract the positron energy spectra resulting from the fission of specific isotopes. This information can be used to produce a precise, data-based prediction of the antineutrino energy spectrum in other reactor antineutrino experiments with different fission fractions than Daya Bay. The positron energy spectra are unfolded to obtain the antineutrino energy spectra by removing the contribution from detector response with the Wiener-SVD unfolding method. Consistent results are obtained with other unfolding methods. A technique to construct a data-based prediction of the reactor antineutrino energy spectrum is proposed and investigated. Given the reactor fission fractions, the technique can predict the energy spectrum to a 2% precision. In addition, we illustrate how to perform a rigorous comparison between the unfolded antineutrino spectrum and a theoretical model prediction that avoids the input model bias of the unfolding method.