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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 $\sup _{u\in \mathbb {R} ^{k}}{\frac {u^{T}Au}{u^{T}Bu}}\leq t\iff \phi _{t}(A,B)\leq 0$ .

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

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)[reply]

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)[reply]