Mixed-integer convex model for VAr expansion planning

This paper presents a mixed-integer convex-optimization-based approach for optimum investment reactive power sources in transmission systems. Unlike some convex-optimization techniques for the reactive power planning solution, in the proposed approach the taps settings of under-load tap-changing of transformers are modeled as a mixed-integer linear set equations. Are also considered the continuous and discrete variables for the existing and new capacitive and reactive power sources. The problem is solved for three significant demand scenarios (low demand, average demand and peak demand). Numerical results are presented for the CIGRE-32 electric power system.

Magnetic flux quantum in a Superconducting concave/convex disk

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

A forgotten little chapter on isoperimetric inequalities. On the fraction of a convex and closed plane area lying outside a circle with which it shares a diameter

[EN]Often some interesting or simply curious points are left out when developing a theory. It seems that one of them is the existence of an upper bound for the fraction of area of a convex and closed plane area lying outside a circle with which it shares a diameter, a problem stemming from the theory of isoperimetric inequalities. In this paper such a bound is constructed and shown to be attained for a particular area. It is also shown that convexity is a necessary condition in order to avoid the whole area lying outside the circle

Confidence Bands for Convex Median Curves using Sign-Tests

Suppose that one observes pairs (x1,Y1), (x2,Y2), ..., (xn,Yn), where x1 < x2 < ... < xn are fixed numbers while Y1, Y2, ..., Yn are independent random variables with unknown distributions. The only assumption is that Median(Yi) = f(xi) for some unknown convex or concave function f. We present a confidence band for this regression function f using suitable multiscale sign tests. While the exact computation of this band seems to require O(n4) steps, good approximations can be obtained in O(n2) steps. In addition the confidence band is shown to have desirable asymptotic properties as the sample size n tends to infinity.

Marshall's Lemma for Convex Density Estimation

Marshall's (1970) lemma is an analytical result which implies root-n-consistency of the distribution function corresponding to the Grenander (1956) estimator of a non-decreasing probability density. The present paper derives analogous results for the setting of convex densities on [0,\infty).