5,885 research outputs found
Providing Access to Safe Water: Lessons Learned from Two Decades of Philanthropic Investment in the Rural Poor
The Conrad N. Hilton Foundation has been a leading U.S. funder for increasing safe water access for over 20 years. The author reflects on that history to describe valuable lessons, especially on partnership (in the context of West Africa Water Initiative), and how to think strategically in the long- and short-term about efficient and sustainable WASH funding
Periodicity in the cohomology of symmetric groups via divided powers
A famous theorem of Nakaoka asserts that the cohomology of the symmetric
group stabilizes. The first author generalized this theorem to non-trivial
coefficient systems, in the form of -modules over a field, though
one now obtains periodicity of the cohomology instead of stability. In this
paper, we further refine these results. Our main theorem states that if is
a finitely generated -module over a noetherian ring
then admits the structure of a
-module, where is the divided power algebra over
in a single variable, and moreover, this -module is
"nearly" finitely presented. This immediately recovers the periodicity result
when is a field, but also shows, for example, how the torsion
varies with when . Using the theory of connections
on -modules, we establish sharp bounds on the period in the case
where is a field. We apply our theory to obtain results on the
modular cohomology of Specht modules and the integral cohomology of unordered
configuration spaces of manifolds.Comment: Fixed some minor mistakes and expanded the section on configuration
space
A comprehensive class of harmonic functions defined by convolution and its connection with integral transforms and hypergeometric functions
For given two harmonic functions and with real coefficients in
the open unit disk , we study a class of harmonic functions
satisfying \RE \frac{(f*\Phi)(z)}{(f*\Psi)(z)}>\alpha \quad (0\leq
\alpha <1, z \in \mathbb{D}); * being the harmonic convolution. Coefficient
inequalities, growth and covering theorems, as well as closure theorems are
determined. The results obtained extend several known results as special cases.
In addition, we study the class of harmonic functions that satisfy \RE
f(z)/z>\alpha . As an application, their
connection with certain integral transforms and hypergeometric functions is
established.Comment: 14pages, 1 figur
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