50,962 research outputs found
Modular frames for Hilbert C*-modules and symmetric approximation of frames
We give a comprehensive introduction to a general modular frame construction
in Hilbert C*-modules and to related modular operators on them. The Hilbert
space situation appears as a special case. The reported investigations rely on
the idea of geometric dilation to standard Hilbert C*-modulesover unital
C*-algebras that admit an orthonormal Riesz basis. Interrelations and
applications to classical linear frame theory are indicated. As an application
we describe the nature of families of operators {S_i} such that SUM_i
S*_iS_i=id_H, where H is a Hilbert space. Resorting to frames in Hilbert spaces
we discuss some measures for pairs of frames to be close to one another. Most
of the measures are expressed in terms of norm-distances of different kinds of
frame operators. In particular, the existence and uniqueness of the closest
(normalized) tight frame to a given frame is investigated. For Riesz bases with
certain restrictions the set of closetst tight frames often contains a multiple
of its symmetric orthogonalization (i.e. L\"owdin orthogonalization).Comment: SPIE's Annual Meeting, Session 4119: Wavelets in Signal and Image
Processing; San Diego, CA, U.S.A., July 30 - August 4, 2000. to appear in:
Proceedings of SPIE v. 4119(2000), 12 p
Stronger Partnerships for Safer Food: An Agenda for Strengthening State and Local Roles in the Nation's Food Safety System
Examines federal, state, and local agencies' responsibilities, strengths, and weaknesses in ensuring food safety. Recommends systemwide reforms to enhance state and local roles and improve surveillance, outbreak response, and regulation and inspection
On the general position subset selection problem
Let be the maximum integer such that every set of points in
the plane with at most collinear contains a subset of points
with no three collinear. First we prove that if then
. Second we prove that if
then , which implies all previously known lower bounds on and
improves them when is not fixed. A more general problem is to consider
subsets with at most collinear points in a point set with at most
collinear. We also prove analogous results in this setting
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