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1.1 Independence, Spanning, and Dimension Definition 1 A (usually infinite) set of vectors S is a vector space if ∀x, y ∈ S, λ ∈ R, (a) x + y ∈ S (b) λx ∈ S, and (c) 0 ∈ S. Definition 2 A set of vectors x1, . . . , xk is said to be linearly dependent if there exists a vector λ 6= 0 such that ki=1 λix = 0. Otherwise, the set is linearly independent. Claim 1 If S is linearly dependent and S ⊂ T ,...
Efficient conversion of “mixing energy” to electricity through capacitive mixing (CapMix) has been limited by low energy recoveries, low power densities, and noncontinuous energy production resulting from intermittent charging and discharging cycles. We show here that a CapMix system based on a four-reactor process with flow electrodes can generate constant and continuous energy, providing a mo...
This Addendum provides a revised set of figures containing converged numerical data for total scattering cross section (TSCS), replacing the figures in our recent publication [Opt. Lett. 29, 1393 (2004)]. Due to the use of an overly large time step, our original TSCS data exhibited a systematic, nonphysical diminution above 150 THz for all cases studied. We have determined that numerical conver...
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