307 research outputs found
Maximum Coronal Mass Ejection Speed as an Indicator of Solar and Geomagnetic Activities
We investigate the relationship between the monthly averaged maximal speeds
of coronal mass ejections (CMEs), international sunspot number (ISSN), and the
geomagnetic Dst and Ap indices covering the 1996-2008 time interval (solar
cycle 23). Our new findings are as follows. (1) There is a noteworthy
relationship between monthly averaged maximum CME speeds and sunspot numbers,
Ap and Dst indices. Various peculiarities in the monthly Dst index are
correlated better with the fine structures in the CME speed profile than that
in the ISSN data. (2) Unlike the sunspot numbers, the CME speed index does not
exhibit a double peak maximum. Instead, the CME speed profile peaks during the
declining phase of solar cycle 23. Similar to the Ap index, both CME speed and
the Dst indices lag behind the sunspot numbers by several months. (3) The CME
number shows a double peak similar to that seen in the sunspot numbers. The CME
occurrence rate remained very high even near the minimum of the solar cycle 23,
when both the sunspot number and the CME average maximum speed were reaching
their minimum values. (4) A well-defined peak of the Ap index between 2002 May
and 2004 August was co-temporal with the excess of the mid-latitude coronal
holes during solar cycle 23. The above findings suggest that the CME speed
index may be a useful indicator of both solar and geomagnetic activities. It
may have advantages over the sunspot numbers, because it better reflects the
intensity of Earth-directed solar eruptions
Applications of the Fixed Point Theorem for group actions on buildings to algebraic groups over polynomial rings
We apply the Fixed Point Theorem for the actions of finite groups on
Bruhat-Tits buildings and their products to establish two results concerning
the groups of points of reductive algebraic groups over polynomial rings in one
variable, assuming that the base field is of characteristic zero. First, we
prove that for a reductive -group , every finite subgroup of is
conjugate to a subgroup of . This, in particular, implies that if is
a finite extension of the -adic field , then the group
has finitely many conjugacy classes of finite subgroups, which is a
well-known property for arithmetic groups. Second, we give a give a short proof
of the theorem of Raghunathan-Ramanathan about -torsors over the affine
line.Comment: Corrections and clarifications based on referee's feedbac
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