Wikipedia:Reference desk/Archives/Mathematics/2013 September 3

= September 3 =

generalized eigenvalue maximization using convex feasibility
Find a family of convex functions $$\phi_t : \mathbb{S}^{k \times k} \times \mathbb{S}^{k \times k}_{++} \rightarrow \mathbb{R}$$ such that $$\sup_{u \in \mathbb{R}^k}\frac{u^TAu}{u^TBu} \le t \iff \phi_t(A,B) \le 0$$.

AnalysisAlgebra (talk) 04:27, 3 September 2013 (UTC)

capacitive vars
if a 1 kw motor operates at 80% power factor ,how many cap vars are required to increase the power factor to 90% ??cant seem to find the formoula?? — Preceding unsigned comment added by 204.152.90.10 (talk) 19:40, 3 September 2013 (UTC)
 * If this is a homework question, then it's probably intended that you work it out rather than look up a formula. I suggest you assume that either the current or the voltage is known: so (for example) assume that the voltage is V. Then work out:
 * What is the in-phase (with V) component of the current (we have the power remember)?
 * What is the magnitude of the current for 80% power factor?
 * What is the quadrature (to V) component of the current (Pythagoras may help you here)?
 * What would the quadrature current be if the power factor was actually 90%?
 * How much must you reduce the quadrature current to change the power factor from 80% to 90%
 * Remembering that the voltage was assumed to be V, how many volt-amps is that?

--catslash (talk) 21:20, 3 September 2013 (UTC)