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Grünbaum introduced measures of symmetry for convex bodies that measure how far a given convex body is from a centrally symmetric one. Here, we introduce new measures of symmetry that measure how far a given convex body is from one with " enough symmetries ". To define these new measures of symmetry, we use affine covariant points. We give examples of(More)
We elaborate on the use of shadow systems to prove a particular case of the conjectured lower bound of the volume product P(K) = min z∈int(K) |K|||K z |, where K ⊂ R n is a convex body and K z = {y ∈ R n : (y − z) · (x − z) 1 for all x ∈ K} is the polar body of K with respect to the center of polarity z. In particular, we show that if K ⊂ R 3 is the convex(More)
We report on the development of a three-axis absolute vector magnetometer suited for mobile operation in the Earth's magnetic field. It is based on low critical temperature dc superconducting quantum interference devices (LTS dc SQUIDs) with sub-micrometer sized cross-type Josephson junctions and exhibits a white noise level of about 10 fT/Hz(1/2). The(More)
Three different methods are presented to subtract thermal drifts and low frequency noise from the signal of infrared arrays: first dead pixels with open Indium bumps, second the reference output as implemented on the Hawaii2 multiplexer and third dark pixels to emulate reference cells having a capacity connected to the gate of the unit cell FET. The third(More)
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