3,701 research outputs found
Bounded Imaginary Powers of Differential Operators on Manifolds with Conical Singularities
We study the minimal and maximal closed extension of a differential operator
A on a manifold B with conical singularities, when A acts as an unbounded
operator on weighted L^p-spaces over B, 1 < p < \infty. Under suitable
ellipticity assumptions we can define a family of complex powers A^z. We also
obtain sufficient information on the resolvent of A to show the boundedness of
the purely imaginary powers. Examples concern unique solvability and maximal
regularity for the solution of the Cauchy problem for the Laplacian on conical
manifolds as well as certain quasilinear diffusion equations.Comment: 27 pages, 3 figures (revised version 23/04/'02
Realizations of Differential Operators on Conic Manifolds with Boundary
We study the closed extensions (realizations) of differential operators
subject to homogeneous boundary conditions on weighted L_p-Sobolev spaces over
a manifold with boundary and conical singularities. Under natural ellipticity
conditions we determine the domains of the minimal and the maximal extension.
We show that both are Fredholm operators and give a formula for the relative
index.Comment: 41 pages, 1 figur
On the Fredholm property of bisingular pseudodifferential operators
For operators belonging either to a class of global bisingular
pseudodifferential operators on or to a class of bisingular
pseudodifferential operators on a product of two closed smooth
manifolds, we show the equivalence of their ellipticity (defined by the
invertibility of certain associated homogeneous principal symbols) and their
Fredholm mapping property in associated scales of Sobolev spaces. We also prove
the spectral invariance of these operator classes and then extend these results
to the even larger classes of Toeplitz type operators.Comment: 21 pages. Expanded sections 3 and 4. Corrected typos. Added
reference
Negative Giant Longitudinal Magnetoresistance in NiMnSb/InSb: An interface effect
We report on the electrical and magneto-transport properties of the contact
formed between polycrystalline NiMnSb thin films grown using pulsed laser
deposition (PLD) and n-type degenerate InSb (100) substrates. A negative giant
magnetoresistance (GMR) effect is observed when the external magnetic field is
parallel to the surface of the film and to the current direction. We attribute
the observed phenomenon to magnetic precipitates formed during the magnetic
film deposition and confined to a narrow layer at the interface. The effect of
these precipitates on the magnetoresistance depends on the thermal processing
of the system.Comment: 14 pages, 4 figure
On the Structure of the Observable Algebra of QCD on the Lattice
The structure of the observable algebra of lattice
QCD in the Hamiltonian approach is investigated. As was shown earlier,
is isomorphic to the tensor product of a gluonic
-subalgebra, built from gauge fields and a hadronic subalgebra
constructed from gauge invariant combinations of quark fields. The gluonic
component is isomorphic to a standard CCR algebra over the group manifold
SU(3). The structure of the hadronic part, as presented in terms of a number of
generators and relations, is studied in detail. It is shown that its
irreducible representations are classified by triality. Using this, it is
proved that the hadronic algebra is isomorphic to the commutant of the triality
operator in the enveloping algebra of the Lie super algebra
(factorized by a certain ideal).Comment: 33 page
The impact of competition on management quality: evidence from public hospitals
We analyse the causal impact of competition on managerial quality and hospital performance. To address the endogeneity of market structure we analyse the English public hospital sector where entry and exit are controlled by the central government. Because closing hospitals in areas where the governing party is expecting a tight election race (âmarginalsâ) is rare due to the fear of electoral defeat, we can use political marginality as an instrumental variable for the number of hospitals in a geographical area. We find that higher competition results in higher management quality, measured using a new survey tool, and improved hospital performance. Adding a rival hospital increases management quality by 0.4 standard deviations and increases survival rates from emergency heart attacks by 9.7%. We confirm the robustness of our IV strategy to âhidden policiesâ that could be used in marginal districts to improve hospital management and to changes in capacity that may follow from hospital closure
A Factorization Algorithm for G-Algebras and Applications
It has been recently discovered by Bell, Heinle and Levandovskyy that a large
class of algebras, including the ubiquitous -algebras, are finite
factorization domains (FFD for short).
Utilizing this result, we contribute an algorithm to find all distinct
factorizations of a given element , where is
any -algebra, with minor assumptions on the underlying field.
Moreover, the property of being an FFD, in combination with the factorization
algorithm, enables us to propose an analogous description of the factorized
Gr\"obner basis algorithm for -algebras. This algorithm is useful for
various applications, e.g. in analysis of solution spaces of systems of linear
partial functional equations with polynomial coefficients, coming from
. Additionally, it is possible to include inequality constraints
for ideals in the input
The Complex Langevin method: When can it be trusted?
We analyze to what extent the complex Langevin method, which is in principle
capable of solving the so-called sign problems, can be considered as reliable.
We give a formal derivation of the correctness and then point out various
mathematical loopholes. The detailed study of some simple examples leads to
practical suggestions about the application of the method.Comment: 14 pages, including several eps figures and tables; clarification and
minor corrections added, to appear in PR
Universality Class of Models
We point out that existing numerical data on the correlation length and
magnetic susceptibility suggest that the two dimensional model with
standard action has critical exponent , which is inconsistent with
asymptotic freedom. This value of is also different from the one of the
Wess-Zumino-Novikov-Witten model that is supposed to correspond to the
model at .Comment: 8 pages, with 3 figures included, postscript. An error concerning the
errors has been correcte
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