39,692 research outputs found
The transverse index theorem for proper cocompact actions of Lie groupoids
Given a proper, cocompact action of a Lie groupoid, we define a higher index
pairing between invariant elliptic differential operators and smooth groupoid
cohomology classes. We prove a cohomological index formula for this pairing by
applying the van Est map and algebraic index theory. Finally we discuss in
examples the meaning of the index pairing and our index formula.Comment: 29 page
The index of geometric operators on Lie groupoids
We revisit the cohomological index theorem for elliptic elements in the
universal enveloping algebra of a Lie groupoid previously proved by the
authors. We prove a Thom isomorphism for Lie algebroids which enables us to
rewrite the "topological side" of the index theorem. This results in index
formulae for Lie groupoid analogues of the familiar geometric operators on
manifolds such as the signature and Dirac operator expressed in terms of the
usual characteristic classes in Lie algebroid cohomology.Comment: 15 page
Quantization of Whitney functions
We propose to study deformation quantizations of Whitney functions. To this
end, we extend the notion of a deformation quantization to algebras of Whitney
functions over a singular set, and show the existence of a deformation
quantization of Whitney functions over a closed subset of a symplectic
manifold. Under the assumption that the underlying symplectic manifold is
analytic and the singular subset subanalytic, we determine that the Hochschild
and cyclic homology of the deformed algebra of Whitney functions over the
subanalytic subset coincide with the Whitney--de Rham cohomology. Finally, we
note how an algebraic index theorem for Whitney functions can be derived.Comment: 10 page
Generalized linear isotherm regularity equation of state applied to metals
A three-parameter equation of state (EOS) without physically incorrect
oscillations is proposed based on the generalized Lennard-Jones (GLJ) potential
and the approach in developing linear isotherm regularity (LIR) EOS of Parsafar
and Mason [J. Phys. Chem., 1994, 49, 3049]. The proposed (GLIR) EOS can include
the LIR EOS therein as a special case. The three-parameter GLIR, Parsafar and
Mason (PM) [Phys. Rev. B, 1994, 49, 3049], Shanker, Singh and Kushwah (SSK)
[Physica B, 1997, 229, 419], Parsafar, Spohr and Patey (PSP) [J. Phys. Chem. B,
2009, 113, 11980], and reformulated PM and SSK EOSs are applied to 30 metallic
solids within wide pressure ranges. It is shown that the PM, PMR and PSP EOSs
for most solids, and the SSK and SSKR EOSs for several solids, have physically
incorrect turning points, and pressure becomes negative at high enough
pressure. The GLIR EOS is capable not only of overcoming the problem existing
in other five EOSs where the pressure becomes negative at high pressure, but
also gives results superior to other EOSs.Comment: 9 pages, 3 figure
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