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Pro-Lie Groups: A survey with Open Problems
A topological group is called a pro-Lie group if it is isomorphic to a closed
subgroup of a product of finite-dimensional real Lie groups. This class of
groups is closed under the formation of arbitrary products and closed subgroups
and forms a complete category. It includes each finite-dimensional Lie group,
each locally compact group which has a compact quotient group modulo its
identity component and thus, in particular, each compact and each connected
locally compact group; it also includes all locally compact abelian groups.
This paper provides an overview of the structure theory and Lie theory of
pro-Lie groups including results more recent than those in the authors'
reference book on pro-Lie groups. Significantly, it also includes a review of
the recent insight that weakly complete unital algebras provide a natural
habitat for both pro-Lie algebras and pro-Lie groups, indeed for the
exponential function which links the two. (A topological vector space is weakly
complete if it is isomorphic to a power of an arbitrary set of copies of
. This class of real vector spaces is at the basis of the Lie theory of
pro-Lie groups.) The article also lists 12 open questions connected with
pro-Lie groups.Comment: 19 page
AGRICULTURAL ECONOMICS PROGRAMS AT 1890 INSTITUTIONS: CURRENT STATUS AND FUTURE DIRECTIONS
Teaching/Communication/Extension/Profession,
Pool boiling from rotating and stationary spheres in liquid nitrogen
Results are presented for a preliminary experiment involving saturated pool boiling at 1 atm from rotating 2 and 3 in. diameter spheres which were immersed in liquid nitrogen (LN2). Additional results are presented for a stationary, 2 inch diameter sphere, quenched in LN2, which were obtained utilizing a more versatile and complete experimental apparatus that will eventually be used for additional rotating sphere experiments. The speed for the rotational tests was varied from 0 to 10,000 rpm. The stationary experiments parametrically varied pressure and subcooling levels from 0 to 600 psig and from 0 to 50 F, respectively. During the rotational tests, a high speed photographic analysis was undertaken to measure the thickness of the vapor film surrounding the sphere. The average Nusselt number over the cooling period was plotted against the rotational Reynolds number. Stationary sphere results included local boiling heat transfer coefficients at different latitudinal locations, for various pressure and subcooling levels
Nonmeasurable subgroups of compact groups
In 1985 S.~Saeki and K.~Stromberg published the following question: {\it Does
every infinite compact group have a subgroup which is not Haar measurable?} An
affirmative answer is given for all compact groups with the exception of some
metric profinite groups known as strongly complete. In this spirit it is also
shown that every compact group contains a non-Borel subgroup
The weights of closed subgroups of a locally compact group
Let be an infinite locally compact group and a cardinal
satisfying for the weight of . It is
shown that there is a closed subgroup of with . Sample
consequences are:
(1) Every infinite compact group contains an infinite closed metric subgroup.
(2) For a locally compact group and a cardinal satisfying
\aleph_0\le\aleph\le \lw(G), where \lw(G) is the local weight of , there
are either no infinite compact subgroups at all or there is a compact subgroup
of with .
(3) For an infinite abelian group there exists a properly ascending
family of locally quasiconvex group topologies on , say,
(\tau_\aleph)_{\aleph_0\le \aleph\le \card(G)}, such that
.
Items (2) and (3) are shown in Section 5
Adaptation and Innovation in Wage Payment Systems in Canada, by Jack Chernik, Study no 5, Task Force on Labour Relations, Ottawa, Privy council office, 1970, 130 pp.
Steven H. London, Elvira R. Tarr and Joseph F. Wilson, eds. The Re-Education of the American Working Class
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