Motivated by the fact that bounded variation (often discontinuous) functions frequently appear when studying integral equations that describe physical phenomena, we focus on the existence of bounded variation solution...
Motivated by the fact that bounded variation (often discontinuous) functions frequently appear when studying integral equations that describe physical phenomena, we focus on the existence of bounded variation solutions for Urysohn integral measure driven equations. Due to numerous applications of Urysohn integral equations in various domains, problems of this kind have been extensively studied in literature, under more restrictive assumptions. Our approach concerns the framework of Kurzweil-Stieltjes integration, which allows the occurrence of high oscillatory features on the right hand side of the equation. A discussion about interesting consequences of our main result (given by particular cases of the measure driving the equation) is presented. Finally, we show the generality of our results by investigating two examples of impulsive type problems (from both theoretical and numerical perspective) and giving an application in electronics industry concerning polarization properties of ferroelectric materials.
A sciencedepartment on the campus of the University of Illinois has received numerous national awards for excellence in undergraduate teaching. The secret to their success? For nearly two decades, they have collabora...
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A sciencedepartment on the campus of the University of Illinois has received numerous national awards for excellence in undergraduate teaching. The secret to their success? For nearly two decades, they have collaboratively used evidence-based instructional practices (EBIP) in their introductory level courses. Despite these successes and efforts to spread their EBIP, no other departments followed this department's lead. Then, suddenly six years ago, many instructors from other departments began adopting EBIP in their classrooms. This article asks what was the catalyst for this change? Why had previous attempts at institutional change failed? The authors answer these questions by analyzing their efforts to transform the teaching practices in large-enrollment science and engineering introductory courses on their campus.
Research software has become a central asset in academic research. It optimizes existing and enables new research methods, implements and embeds research knowledge, and constitutes an essential research product in its...
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Self-driving labs (SDLs) combine fully automated experiments with artificial intelligence (AI) that decides the next set of experiments. Taken to their ultimate expression, SDLs could usher a new paradigm of scientifi...
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