73,404 research outputs found
The contribution of modern psychology to the understanding of the problem of moral and religious development in the realm of religious education
Thesis (M.A.)--Boston Universit
Gr\"obner bases of syzygies and Stanley depth
Let F. be a any free resolution of a Z^n-graded submodule of a free module
over the polynomial ring K[x_1, ..., x_n]. We show that for a suitable term
order on F., the initial module of the p'th syzygy module Z_p is generated by
terms m_ie_i where the m_i are monomials in K[x_{p+1}, ..., x_n]. Also for a
large class of free resolutions F., encompassing Eliahou-Kervaire resolutions,
we show that a Gr\"obner basis for Z_p is given by the boundaries of generators
of F_p. We apply the above to give lower bounds for the Stanley depth of the
syzygy modules Z_p, in particular showing it is at least p+1. We also show that
if I is any squarefree ideal in K[x_1, ..., x_n], the Stanley depth of I is at
least of order the square root of 2n.Comment: 13 page
The Maximal C*-Algebra of Quotients as an Operator Bimodule
We establish a description of the maximal C*-algebra of quotients of a unital
C*-algebra as a direct limit of spaces of completely bounded bimodule
homomorphisms from certain operator submodules of the Haagerup tensor product
labelled by the essential closed right ideals of into .
In addition the invariance of the construction of the maximal C*-algebra of
quotients under strong Morita equivalence is proved.Comment: 8 pages; submitte
The symplectic and algebraic geometry of Horn's problem
Horn's problem was the following: given two Hermitian matrices with known
spectra, what might be the eigenvalue spectrum of the sum? This linear algebra
problem is exactly of the sort to be approached with the methods of modern
Hamiltonian geometry (which were unavailable to Horn). The theorem linking
symplectic quotients and geometric invariant theory lets one also bring
algebraic geometry and representation theory into play. This expository note is
intended to elucidate these connections for linear algebraists, in the hope of
making it possible to recognize what sort of problems are likely to fall to the
same techniques that were used in proving Horn's conjecture.Comment: 16 pages, 1 figure; expository conference paper (second version has
inessential cosmetic changes
- …