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It is proved that the total length of any set of countably many rectifiable curves whose union meets all straight lines that intersect the unit square U is at least 2.00002. This is the first improvement on the lower bound of 2 known since 1964. A similar ...
Nowadays, massive amounts of point cloud data can be collected thanks to advances in data acquisition and processing technologies such as dense image matching and airborne LiDAR scanning. With the increase in volume and precision, point cloud data offers a ...
An ordinary circle of a set P of n points in the plane is defined as a circle that contains exactly three points of P. We show that if P is not contained in a line or a circle, then P spans at least ordinary circles. Moreover, we determine the exact minimu ...
This paper aims at understanding the adhesion mechanics of a pressure-controlled adhesive thin elastomeric membrane for soft robotic gripping on non-planar, curved surfaces. The adhesive elastic membrane is lined with gecko-inspired microfiber arrays and c ...
Nature and technical applications abound with thin viscous flows, ranging from the lava flow on volcanoes to the lubricating layer around confined bubbles in the microchannels of Lab-on-a-Chip devices. Countless are the examples where coating flows arise i ...
We present a set of tools to assess the capabilities of LISA to detect and reconstruct the spectral shape and amplitude of a stochastic gravitational wave background (SGWB). We first provide the LISA power-law sensitivity curve and binned power-law sensiti ...
Deployable structures are physical mechanisms that can easily transition between two or more geometric configurations; such structures enable industrial, scientific, and consumer applications at a wide variety of scales. This paper develops novel deployabl ...
Nitrate is one of the most abundant inorganic water-soluble ions in fine particulate matter (PM2.5). However, the formation mechanism of nitrate in the ambient atmosphere, especially the impacts of its semivolatility and the various existing forms of nitro ...
Ongoing advances in imaging techniques create new demands regarding the analysis of images in medicine and biology. Image segmentation is a key step of many image analysis pipelines and its proper execution is a particularly challenging task. This thesis i ...
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Building-specific loss assessment methodologies utilize component fragility curves to compute the expected losses in the aftermath of earthquakes. Such curves are not available for steel columns assuming they remain elastic due to capacity design considera ...