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Communication Lower Bounds Using Directional Derivatives
Journal of the ACM, 2013We study the set disjointness problem in the most powerful model of bounded-error communication, the k -party randomized number-on-the-forehead model. We show that set disjointness requires Ω(√n/2 k k ) bits of communication, where n
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Directional Derivatives of Marginal Functions
2002Let X = R n , Y = R m and let U be a compact set in Y. We consider the functions $$\begin{array}{*{20}{c}} {\varphi \left( x \right) = \inf \left\{ {f\left( {x,y} \right)\left| {y \in U} \right.} \right\},} \\ {\Phi \left( x \right) = \sup \left\{ {f\left( {x,y} \right)\left| {y \in U} \right.} \right\},} \end{array}$$ where f : X × Y → R is ...
Bernd Luderer +2 more
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Liénard’s Generalisation: A Direct Derivation
Resonance, 2018In this pedagogical article, we elucidate the direct derivation of total power emitted by an accelerating charged particle, known as Lienard’s generalisation, using differentiation under integral sign technique.
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Image derived directional microphones
The Journal of the Acoustical Society of America, 1992Second-order gradient directional microphones, both toroidal and unidirectional, derived using a first-order gradient sensor and an acoustically reflecting surface are disclosed. The sensor is positioned with its axis illustratively orthogonal to and suspended a few centimeters from a large acoustically reflecting surface. The resulting sensor image is
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