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The Georgian Government's Goldilocks Problem
The Georgian government will likely continue to complain that their opposition is either too weak or too strong and, unlike Goldilocks, never find the one that is just right for them
Relevance, Choices, and the Goldilocks Problem
Ms. Whisner ponders a core question in answering reference queries: How can we know whether what we find is relevant to what the questioner wants? Her article provides criteria to consider and some guidelines for choosing sources in response to a query
Goldilocks domains, a weak notion of visibility, and applications
In this paper we introduce a new class of domains in complex Euclidean space,
called Goldilocks domains, and study their complex geometry. These domains are
defined in terms of a lower bound on how fast the Kobayashi metric grows and an
upper bound on how fast the Kobayashi distance grows as one approaches the
boundary. Strongly pseudoconvex domains and weakly pseudoconvex domains of
finite type always satisfy this Goldilocks condition, but we also present
families of Goldilocks domains that have low boundary regularity or have
boundary points of infinite type. We will show that the Kobayashi metric on
these domains behaves, in some sense, like a negatively curved Riemannian
metric. In particular, it satisfies a visibility condition in the sense of
Eberlein and O'Neill. This behavior allows us to prove a variety of results
concerning boundary extension of maps and to establish Wolff-Denjoy theorems
for a wide collection of domains.Comment: 36 pages. v2: minor changes, final version to appear in Advances in
Mathematic
Is the Sun Lighter than the Earth? Isotopic CO in the Photosphere, Viewed through the Lens of 3D Spectrum Synthesis
We consider the formation of solar infrared (2-6 micron) rovibrational bands
of carbon monoxide (CO) in CO5BOLD 3D convection models, with the aim to refine
abundances of the heavy isotopes of carbon (13C) and oxygen (18O,17O), to
compare with direct capture measurements of solar wind light ions by the
Genesis Discovery Mission. We find that previous, mainly 1D, analyses were
systematically biased toward lower isotopic ratios (e.g., R23= 12C/13C),
suggesting an isotopically "heavy" Sun contrary to accepted fractionation
processes thought to have operated in the primitive solar nebula. The new 3D
ratios for 13C and 18O are: R23= 91.4 +/- 1.3 (Rsun= 89.2); and R68= 511 +/- 10
(Rsun= 499), where the uncertainties are 1 sigma and "optimistic." We also
obtained R67= 2738 +/- 118 (Rsun= 2632), but we caution that the observed
12C17O features are extremely weak. The new solar ratios for the oxygen
isotopes fall between the terrestrial values and those reported by Genesis
(R68= 530, R6= 2798), although including both within 2 sigma error flags, and
go in the direction favoring recent theories for the oxygen isotope composition
of Ca-Al inclusions (CAI) in primitive meteorites. While not a major focus of
this work, we derive an oxygen abundance of 603 +/- 9 ppm (relative to
hydrogen; 8.78 on the logarithmic H= 12 scale). That the Sun likely is lighter
than the Earth, isotopically speaking, removes the necessity to invoke exotic
fractionation processes during the early construction of the inner solar
system
"Goldilocks and the Three Bears"
Unlike the Papa, Mama, and Baby Bears faced by the storybook Goldilocks, our Goldilocks faced three ferocious grizzlies: a cascading, global financial crisis; global deflation and excess capacity (or insufficient demand); and a domestic fiscal surplus in conjunction with record private deficits.
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