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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. 

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. 

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 were 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. 

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 

Abstract We present cosmological results from the measurement of baryon acoustic oscillations (BAO) in galaxy, quasar and Lyman-αforest tracers from the first year of observations from the Dark Energy Spectroscopic Instrument (DESI), to be released in the DESI Data Release 1. DESI BAO provide robust measurements of the transverse comoving distance and Hubble rate, or their combination, relative to the sound horizon, in seven redshift bins from over 6 million extragalactic objects in the redshift range 0.1 <z< 4.2. To mitigate confirmation bias, a blind analysis was implemented to measure the BAO scales. DESI BAO data alone are consistent with the standard flat ΛCDM cosmological model with a matter density Ω_m=0.295±0.015. Paired with a baryon density prior from Big Bang Nucleosynthesis and the robustly measured acoustic angular scale from the cosmic microwave background (CMB), DESI requiresH₀=(68.52±0.62) km s^-1Mpc^-1. In conjunction with CMB anisotropies fromPlanckand CMB lensing data fromPlanckand ACT, we find Ω_m=0.307± 0.005 andH₀=(67.97±0.38) km s^-1Mpc^-1. Extending the baseline model with a constant dark energy equation of state parameterw, DESI BAO alone requirew=-0.99^+0.15_-0.13. In models with a time-varying dark energy equation of state parametrised byw₀andw_a, combinations of DESI with CMB or with type Ia supernovae (SN Ia) individually preferw₀> -1 andw_a< 0. This preference is 2.6σfor the DESI+CMB combination, and persists or grows when SN Ia are added in, giving results discrepant with the ΛCDM model at the 2.5σ, 3.5σor 3.9σlevels for the addition of the Pantheon+, Union3, or DES-SN5YR supernova datasets respectively. For the flat ΛCDM model with the sum of neutrino mass ∑m_νfree, combining the DESI and CMB data yields an upper limit ∑m_ν< 0.072 (0.113) eV at 95% confidence for a ∑m_ν> 0 (∑m_ν> 0.059) eV prior. These neutrino-mass constraints are substantially relaxed if the background dynamics are allowed to deviate from flat ΛCDM.