1,242 research outputs found
A trace formula and high energy spectral asymptotics for the perturbed Landau Hamiltonian
A two-dimensional Schr\"odinger operator with a constant magnetic field
perturbed by a smooth compactly supported potential is considered. The spectrum
of this operator consists of eigenvalues which accumulate to the Landau levels.
We call the set of eigenvalues near the 'th Landau level an 'th
eigenvalue cluster, and study the distribution of eigenvalues in the 'th
cluster as . A complete asymptotic expansion for the eigenvalue
moments in the 'th cluster is obtained and some coefficients of this
expansion are computed. A trace formula involving the first eigenvalue moments
is obtained.Comment: 23 page
Hardy-Carleman Type Inequalities for Dirac Operators
General Hardy-Carleman type inequalities for Dirac operators are proved. New
inequalities are derived involving particular traditionally used weight
functions. In particular, a version of the Agmon inequality and Treve type
inequalities are established. The case of a Dirac particle in a (potential)
magnetic field is also considered. The methods used are direct and based on
quadratic form techniques
Traces, extensions and co-normal derivatives for elliptic systems on Lipschitz domains
This is the post-print version of the article. The official published version can be accessed from the link below - Copyright @ 2011 ElsevierFor functions from the Sobolev space H^s(\OmegaĀ), 1/2 < s < 3/2 , definitions of non-unique generalized and unique canonical co-normal derivative are considered, which are related to possible extensions of a partial differential operator and its right hand side from the domainĀ, where they are prescribed, to the domain boundary, where they are not. Revision of the boundary value problem settings, which makes them insensitive to the generalized co-normal derivative inherent non-uniqueness are given. It is shown, that the canonical co-normal derivatives, although deĀÆned on a more narrow function class than the generalized ones, are continuous extensions of the classical co-norma derivatives. Some new results about trace operator estimates and Sobolev spaces haracterizations, are also presented
Control theory for principled heap sizing
We propose a new, principled approach to adaptive heap sizing based on control theory. We review current state-of-the-art heap sizing mechanisms, as deployed in Jikes RVM and HotSpot. We then formulate heap sizing as a control problem, apply and tune a standard controller algorithm, and evaluate its performance on a set of well-known benchmarks. We find our controller adapts the heap size more responsively than existing mechanisms. This responsiveness allows tighter virtual machine memory footprints while preserving target application throughput, which is ideal for both embedded and utility computing domains. In short, we argue that formal, systematic approaches to memory management should be replacing ad-hoc heuristics as the discipline matures. Control-theoretic heap sizing is one such systematic approach
Autoimmune (auto-inflammatory) syndrome induced by adjuvants (ASIA) - Animal models as a proof of concept
ASIA syndrome, 'Autoimmune (Auto-inflammatory) Syndromes Induced by Adjuvants' includes at least four conditions which share a similar complex of signs and symptoms and have been defined by hyperactive immune responses: siliconosis, macrophagic myofasciitis syndrome, Gulf war syndrome and post-vaccination phenomena. Exposure to adjuvants has been documented in these four medical conditions, suggesting that the common denominator to these syndromes is a trigger entailing adjuvant activity. An important role of animal models in proving the ASIA concept has been established. Experimentally animal models of autoimmune diseases induced by adjuvants are currently widely used to understand the mechanisms and etiology and pathogenesis of these diseases and might thus promote the development of new diagnostic, predictive and therapeutic methods. In the current review we wish to unveil the variety of ASIA animal models associated with systemic and organ specific autoimmune diseases induced by adjuvants. We included in this review animal models for rheumatoid arthritis-like disease, for systemic lupus erythematosus-like disease, autoimmune thyroid disease-like disease, antiphospholipid syndrome, myocarditis and others. All these models support the concept of ASIA, as the Autoimmune (Auto-inflammatory) Syndrome Induced by Adjuvants. Ā© 2013 Bentham Science Publishers
On the existence of effective potentials in time-dependent density functional theory
We investigate the existence and properties of effective potentials in
time-dependent density functional theory. We outline conditions for a general
solution of the corresponding Sturm-Liouville boundary value problems. We
define the set of potentials and v-representable densities, give a proof of
existence of the effective potentials under certain restrictions, and show the
set of v-representable densities to be independent of the interaction.Comment: 13 page
Wave operator bounds for 1-dimensional Schr\"odinger operators with singular potentials and applications
Boundedness of wave operators for Schr\"odinger operators in one space
dimension for a class of singular potentials, admitting finitely many Dirac
delta distributions, is proved. Applications are presented to, for example,
dispersive estimates and commutator bounds.Comment: 16 pages, 0 figure
Morse homology for the heat flow
We use the heat flow on the loop space of a closed Riemannian manifold to
construct an algebraic chain complex. The chain groups are generated by
perturbed closed geodesics. The boundary operator is defined in the spirit of
Floer theory by counting, modulo time shift, heat flow trajectories that
converge asymptotically to nondegenerate closed geodesics of Morse index
difference one.Comment: 89 pages, 3 figure
The Hartree limit of Born's ensemble for the ground state of a bosonic atom or ion
The non-relativistic bosonic ground state is studied for quantum N-body
systems with Coulomb interactions, modeling atoms or ions made of N "bosonic
point electrons" bound to an atomic point nucleus of Z "electron" charges,
treated in Born--Oppenheimer approximation. It is shown that the (negative)
ground state energy E(Z,N) yields the monotonically growing function (E(l N,N)
over N cubed). By adapting an argument of Hogreve, it is shown that its limit
as N to infinity for l > l* is governed by Hartree theory, with the rescaled
bosonic ground state wave function factoring into an infinite product of
identical one-body wave functions determined by the Hartree equation. The proof
resembles the construction of the thermodynamic mean-field limit of the
classical ensembles with thermodynamically unstable interactions, except that
here the ensemble is Born's, with the absolute square of the ground state wave
function as ensemble probability density function, with the Fisher information
functional in the variational principle for Born's ensemble playing the role of
the negative of the Gibbs entropy functional in the free-energy variational
principle for the classical petit-canonical configurational ensemble.Comment: Corrected version. Accepted for publication in Journal of
Mathematical Physic
Stability Of contact discontinuity for steady Euler System in infinite duct
In this paper, we prove structural stability of contact discontinuities for
full Euler system
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