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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 ...
In this note, we study certain sufficient conditions for a set of minimal klt pairs ( X, triangle) with kappa ( X, triangle) = dim( X ) - 1 to be bounded. ...
Conceived by Switzerland’s Ecole Polytechnique Fédérale de Lausanne, Clip-Air proposes a plane with a single flying wing encompassing the airframe, cockpit, and three engines, attached to a maximum of three interchangeable capsules a more flexible and effi ...
Crank arrangement (1) for driving a pin-driven two degrees? of freedom mechanical oscillator (5), comprising:- a crank element (7) arranged to be rotationally driven about an axis of rotation (19) by means of a mechanical source of energy (M),- a crank slo ...
Modifying the moduli of supporting convexity and supporting smoothness, we introduce new moduli for Banach spaces which occur, for example, as lengths of catheti of right-angled triangles (defined via so-called quasiorthogonality). These triangles have two ...
We prove that for any triangle-free intersection graph of n axis-parallel line segments in the plane, the independence number alpha of this graph is at least alpha n/4+ohm(root n). We complement this with a construction of a graph in this class satisfying ...
Conjugated polymers and small molecules are a promising class of semiconducting materials for application in macroelectronic and energy conversion devices. The development of high performance devices employing this class of semicrystalline materials ultima ...
A graph G is a diameter graph in R-d if its vertex set is a finite subset in R-d of diameter 1 and edges join pairs of vertices a unit distance apart. It is shown that if a diameter graph G in R-4 contains the complete subgraph K on five vertices, then any ...
Shape-changing robots adapt their own morphology to address a wider range of functions or environments than is possible with a fixed or rigid structure. Akin to biological organisms, the ability to alter shape or configuration emerges from the underlying m ...
We study time and space equivariant wave maps from M×R→S2, where M is dieomorphic to a two dimensional sphere and admits an action of SO(2) by isometries. We assume that metric on M can be written as $dr^2+f^2(r)d\theta ...
