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Theoretical study of polar and global ozone changes using a coupled radiative-dynamical 2-D model
An existing 2-D model has recently been updated to incorporate ozone-temperature feedbacks with more comprehensive radiative transfer calculations and more detailed temperature data input. Researchers address the following issues: (1) given the observed temperature changes for the past eight years, quantitatively how much ozone change can be produced by the dynamical effect of the temperature change over the Arctic and Antarctic; (2) how much of the reported change in globally averaged ozone can be accounted for by temperature changes; (3) the role of the diabatic circulation changes in the lower stratosphere in determining the timing of the polar spring maximum and minimum; and (4) the role of the seasonal change in the diabatic circulation in causing the fall minimum over the Arctic and Antarctic
A further extension of R\"odl's theorem
Fix and a nonnull graph . A well-known theorem of R\"odl
from the 80s says that every graph with no induced copy of contains a
linear-sized -restricted set , which means
induces a subgraph with maximum degree at most in
or its complement. There are two extensions of this result:
quantitatively, Nikiforov (and later Fox and Sudakov) relaxed the
condition "no induced copy of " into "at most induced copies of for some depending on and
"; and
qualitatively, Chudnovsky, Scott, Seymour, and Spirkl recently
showed that there exists depending on and such that
is -restricted, which means has a partition into at
most subsets that are -restricted.
A natural common generalization of these two asserts that every graph
with at most induced copies of is
-restricted for some depending on and
. This is unfortunately false, but we prove that for every
, and still exist so that for every , every
graph with at most induced copies of has an
-restricted induced subgraph on at least
vertices. This unifies the two aforementioned theorems, and is optimal up to
and for every value of .Comment: 11 pages, revised according to the referees' comment
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