72,926 research outputs found
PEO/CHCl3: Crystallinity of the polymer and vapor pressure of the solvent - Equilibrium and non-equilibrium phenomena -
Vapor pressures were measured for the system chloroform/polyethylene oxide
(peo, weight average molar mass = 1000 kg/mol) at 25 degrees centigrade as a
function of the weight fraction w of the polymer by means of a combination of
head space sampling and gas chromatography. The establishment of thermodynamic
equilibria was assisted by employing thin polymer films. The degrees of
crystallinity alpha of the pure peo and of the solid polymer contained in the
mixtures were determined via dsc. An analogous degree of polymer insolubility,
beta, was calculated from the vapor pressures measured in this composition
range. The experiments demonstrate that both quantities and their concentration
dependence are markedly affected by the particular mode of film preparation.
These non-equilibrium phenomena are discussed in terms of frozen local and
temporal equilibria, where differences between alpha and beta are attributed to
the occlusion of amorphous material within crystalline domains. Equilibrium
information was obtained from two sources, namely from the vapor pressures in
the absence of crystalline material (gas/liquid) and from the saturation
concentration of peo (liquid/solid). The thermodynamic consistency of these
data is demonstrated using a new approach that enables the modeling of
composition dependent interaction parameters by means of two adjustable
parameters only
Spherical Functions on Euclidean Space
We study special functions on euclidean spaces from the viewpoint of
riemannian symmetric spaces. Here the euclidean space where is
the semidirect product of the translation group with a closed
subgroup of the orthogonal group O(n). We give exact parameterizations of
the space of --spherical functions by a certain affine algebraic
variety, and of the positive definite ones by a real form of that variety. We
give exact formulae for the spherical functions in the case where is
transitive on the unit sphere in .Comment: 10 page
Stepwise Square Integrability for Nilradicals of Parabolic Subgroups and Maximal Amenable Subgroups
In a series of recent papers we extended the notion of square integrability,
for representations of nilpotent Lie groups, to that of stepwise square
integrability. There we discussed a number of applications based on the fact
that nilradicals of minimal parabolic subgroups of real reductive Lie groups
are stepwise square integrable. Here, in Part I, we prove stepwise square
integrability for nilradicals of arbitrary parabolic subgroups of real
reductive Lie groups. This is technically more delicate than the case of
minimal parabolics. We further discuss applications to Plancherel formulae and
Fourier inversion formulae for maximal exponential solvable subgroups of
parabolics and maximal amenable subgroups of real reductive Lie groups.
Finally, in Part II, we extend a number of those results to (infinite
dimensional) direct limit parabolics. These extensions involve an infinite
dimensional version of the Peter-Weyl Theorem, construction of a direct limit
Schwartz space, and realization of that Schwartz space as a dense subspace of
the corresponding space.Comment: The proof of Theorem 5.9 is improved, several statements are
clarified, and a certain number of typographical errors are correcte
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