---
_id: '3508'
abstract:
- lang: eng
text: A method of automatic conversion of a physical object into a three-dimensional
digital model. The method acquires a set of measured data points on the surface
of a physical model. From the measured data points, the method reconstructs a
digital model of the physical object using a Delaunay complex of the points, a
flow strcuture of the simplicies in the Delaunay complex and retracting the Delaunay
complex into a digital model of the physical object using the flow structure.
The method then outputs the digital model of the physical object.
author:
- first_name: Herbert
full_name: Herbert Edelsbrunner
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Ping
full_name: Fu, Ping
last_name: Fu
citation:
ama: Edelsbrunner H, Fu P. Methods of generating three-dimensional digital models
of objects by wrapping point cloud data points. 2002. doi:US 6,377,865 B1
apa: Edelsbrunner, H., & Fu, P. (2002). Methods of generating three-dimensional
digital models of objects by wrapping point cloud data points. Elsevier. https://doi.org/US 6,377,865 B1
chicago: Edelsbrunner, Herbert, and Ping Fu. “Methods of Generating Three-Dimensional
Digital Models of Objects by Wrapping Point Cloud Data Points.” Elsevier, 2002.
https://doi.org/US 6,377,865 B1.
ieee: H. Edelsbrunner and P. Fu, “Methods of generating three-dimensional digital
models of objects by wrapping point cloud data points.” Elsevier, 2002.
ista: Edelsbrunner H, Fu P. 2002. Methods of generating three-dimensional digital
models of objects by wrapping point cloud data points.
mla: Edelsbrunner, Herbert, and Ping Fu. *Methods of Generating Three-Dimensional
Digital Models of Objects by Wrapping Point Cloud Data Points*. Elsevier, 2002,
doi:US 6,377,865 B1.
short: H. Edelsbrunner, P. Fu, (2002).
date_created: 2018-12-11T12:03:42Z
date_published: 2002-04-01T00:00:00Z
date_updated: 2019-04-26T07:22:29Z
day: '01'
doi: US 6,377,865 B1
extern: 1
main_file_link:
- open_access: '0'
url: http://www.google.com/patents/US6377865.pdf
month: '04'
publication_status: published
publisher: Elsevier
publist_id: '2879'
quality_controlled: 0
status: public
title: Methods of generating three-dimensional digital models of objects by wrapping
point cloud data points
type: patent
year: '2002'
...
---
_id: '3533'
abstract:
- lang: eng
text: 'Information in neuronal networks is thought to be represented by the rate
of discharge and the temporal relationship between the discharging neurons. The
discharge frequency of neurons is affected by their afferents and intrinsic properties,
and shows great individual variability. The temporal coordination of neurons is
greatly facilitated by network oscillations. In the hippocampus, population synchrony
fluctuates during theta and gamma oscillations (10-100 ms scale) and can increase
almost 10-fold during sharp wave bursts. Despite these large changes in excitability
in the sub-second scale, longer-term (minute-scale) firing rates of individual
neurons are relatively constant in an unchanging environment. As a result, mean
hippocampal output remains stable over time. To understand the mechanisms responsible
for this homeostasis, we address the following issues: (i) Can firing rates of
single cells be modified? (ii) Once modified, what mechanism(s) can maintain the
changes? We show that firing rates of hippocampal pyramidal cells can be altered
in a novel environment and by Hebbian pairing of physiological input patterns
with postsynaptic burst discharge. We also illustrate a competition between single
spikes and the occurrence of spike bursts. Since spike-inducing (suprathreshold)
inputs decrease the ability of strong (''teaching'') inputs to induce a burst
discharge, we propose that the single spike versus burst competition presents
a homeostatic regulatory mechanism to maintain synaptic strength and, consequently,
firing rate in pyramidal cells.'
author:
- first_name: György
full_name: Buzsáki, György
last_name: Buzsáki
- first_name: Jozsef L
full_name: Jozsef Csicsvari
id: 3FA14672-F248-11E8-B48F-1D18A9856A87
last_name: Csicsvari
orcid: 0000-0002-5193-4036
- first_name: George
full_name: Dragoi, George
last_name: Dragoi
- first_name: Kenneth
full_name: Harris, Kenneth D
last_name: Harris
- first_name: D.
full_name: Henze,D.
last_name: Henze
- first_name: Hajima
full_name: Hirase, Hajima
last_name: Hirase
citation:
ama: Buzsáki G, Csicsvari JL, Dragoi G, Harris K, Henze D, Hirase H. Homeostatic
maintenance of neuronal excitability by burst discharges in vivo. *Cerebral
Cortex*. 2002;12(9):893-899. doi:10.1093/cercor/12.9.893
apa: Buzsáki, G., Csicsvari, J. L., Dragoi, G., Harris, K., Henze, D., & Hirase,
H. (2002). Homeostatic maintenance of neuronal excitability by burst discharges
in vivo. *Cerebral Cortex*. Oxford University Press. https://doi.org/10.1093/cercor/12.9.893
chicago: Buzsáki, György, Jozsef L Csicsvari, George Dragoi, Kenneth Harris, D.
Henze, and Hajima Hirase. “Homeostatic Maintenance of Neuronal Excitability by
Burst Discharges in Vivo.” *Cerebral Cortex*. Oxford University Press, 2002.
https://doi.org/10.1093/cercor/12.9.893.
ieee: G. Buzsáki, J. L. Csicsvari, G. Dragoi, K. Harris, D. Henze, and H. Hirase,
“Homeostatic maintenance of neuronal excitability by burst discharges in vivo,”
*Cerebral Cortex*, vol. 12, no. 9. Oxford University Press, pp. 893–899,
2002.
ista: Buzsáki G, Csicsvari JL, Dragoi G, Harris K, Henze D, Hirase H. 2002. Homeostatic
maintenance of neuronal excitability by burst discharges in vivo. Cerebral Cortex.
12(9), 893–899.
mla: Buzsáki, György, et al. “Homeostatic Maintenance of Neuronal Excitability by
Burst Discharges in Vivo.” *Cerebral Cortex*, vol. 12, no. 9, Oxford University
Press, 2002, pp. 893–99, doi:10.1093/cercor/12.9.893.
short: G. Buzsáki, J.L. Csicsvari, G. Dragoi, K. Harris, D. Henze, H. Hirase, Cerebral
Cortex 12 (2002) 893–899.
date_created: 2018-12-11T12:03:50Z
date_published: 2002-09-01T00:00:00Z
date_updated: 2021-01-12T07:44:08Z
day: '01'
doi: 10.1093/cercor/12.9.893
extern: 1
intvolume: ' 12'
issue: '9'
month: '09'
page: 893 - 899
publication: Cerebral Cortex
publication_status: published
publisher: Oxford University Press
publist_id: '2851'
quality_controlled: 0
status: public
title: Homeostatic maintenance of neuronal excitability by burst discharges in vivo
type: journal_article
volume: 12
year: '2002'
...
---
_id: '3621'
abstract:
- lang: eng
text: In 1991, Barton and Turelli developed recursions to describe the evolution
of multilocus systems under arbitrary forms of selection. This article generalizes
their approach to allow for arbitrary modes of inheritance, including diploidy,
polyploidy, sex linkage, cytoplasmic inheritance, and genomic imprinting. The
framework is also extended to allow for other deterministic evolutionary forces,
including migration and mutation. Exact recursions that fully describe the state
of the population are presented; these are implemented in a computer algebra package
(available on the Web at http://helios.bto.ed.ac.uk/evolgen). Despite the generality
of our framework, it can describe evolutionary dynamics exactly by just two equations.
These recursions can be further simplified using a "quasi-linkage equilibrium"
(QLE) approximation. We illustrate the methods by finding the effect of natural
selection, sexual selection, mutation, and migration on the genetic composition
of a population.
author:
- first_name: Mark
full_name: Kirkpatrick, Mark
last_name: Kirkpatrick
- first_name: Toby
full_name: Johnson, Toby
last_name: Johnson
- first_name: Nicholas H
full_name: Nicholas Barton
id: 4880FE40-F248-11E8-B48F-1D18A9856A87
last_name: Barton
orcid: 0000-0002-8548-5240
citation:
ama: Kirkpatrick M, Johnson T, Barton NH. General models of multilocus evolution.
*Genetics*. 2002;161(4):1727-1750.
apa: Kirkpatrick, M., Johnson, T., & Barton, N. H. (2002). General models of
multilocus evolution. *Genetics*. Genetics Society of America.
chicago: Kirkpatrick, Mark, Toby Johnson, and Nicholas H Barton. “General Models
of Multilocus Evolution.” *Genetics*. Genetics Society of America, 2002.
ieee: M. Kirkpatrick, T. Johnson, and N. H. Barton, “General models of multilocus
evolution,” *Genetics*, vol. 161, no. 4. Genetics Society of America, pp.
1727–1750, 2002.
ista: Kirkpatrick M, Johnson T, Barton NH. 2002. General models of multilocus evolution.
Genetics. 161(4), 1727–1750.
mla: Kirkpatrick, Mark, et al. “General Models of Multilocus Evolution.” *Genetics*,
vol. 161, no. 4, Genetics Society of America, 2002, pp. 1727–50.
short: M. Kirkpatrick, T. Johnson, N.H. Barton, Genetics 161 (2002) 1727–1750.
date_created: 2018-12-11T12:04:17Z
date_published: 2002-08-01T00:00:00Z
date_updated: 2021-01-12T07:44:43Z
day: '01'
extern: 1
intvolume: ' 161'
issue: '4'
main_file_link:
- open_access: '1'
url: http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1462196/
month: '08'
oa: 1
page: 1727 - 1750
publication: Genetics
publication_status: published
publisher: Genetics Society of America
publist_id: '2762'
quality_controlled: 0
status: public
title: General models of multilocus evolution
type: journal_article
volume: 161
year: '2002'
...
---
_id: '2340'
abstract:
- lang: eng
text: |2
Recent experimental breakthroughs in the treatment of dilute Bose gases have renewed interest in their quantum mechanical description, respectively in approximations to it. The ground state properties of dilute Bose gases confined in external potentials and interacting via repulsive short range forces are usually described by means of the Gross-Pitaevskii energy functional. In joint work with Elliott H. Lieb and Jakob Yngvason its status as an approximation for the quantum mechanical many-body ground state problem has recently been rigorously clarified. We present a summary of this work, for both the two-and three-dimensional case.
alternative_title:
- 'Operator Theory: Advances and Applications'
author:
- first_name: Robert
full_name: Robert Seiringer
id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
last_name: Seiringer
orcid: 0000-0002-6781-0521
citation:
ama: 'Seiringer R. Bosons in a trap: Asymptotic exactness of the Gross-Pitaevskii
ground state energy formula. In: Demuth M, Schultze B, eds. Vol 126. Birkhäuser;
2001:307-314. doi:10.1007/978-3-0348-8231-6'
apa: 'Seiringer, R. (2001). Bosons in a trap: Asymptotic exactness of the Gross-Pitaevskii
ground state energy formula. In M. Demuth & B. Schultze (Eds.) (Vol. 126,
pp. 307–314). Presented at the PDE: Partial Differential Equations and Spectral
Theory, Birkhäuser. https://doi.org/10.1007/978-3-0348-8231-6'
chicago: 'Seiringer, Robert. “Bosons in a Trap: Asymptotic Exactness of the Gross-Pitaevskii
Ground State Energy Formula.” edited by Michael Demuth and Bert Schultze, 126:307–14.
Birkhäuser, 2001. https://doi.org/10.1007/978-3-0348-8231-6.'
ieee: 'R. Seiringer, “Bosons in a trap: Asymptotic exactness of the Gross-Pitaevskii
ground state energy formula,” presented at the PDE: Partial Differential Equations
and Spectral Theory, 2001, vol. 126, pp. 307–314.'
ista: 'Seiringer R. 2001. Bosons in a trap: Asymptotic exactness of the Gross-Pitaevskii
ground state energy formula. PDE: Partial Differential Equations and Spectral
Theory, Operator Theory: Advances and Applications, vol. 126, 307–314.'
mla: 'Seiringer, Robert. *Bosons in a Trap: Asymptotic Exactness of the Gross-Pitaevskii
Ground State Energy Formula*. Edited by Michael Demuth and Bert Schultze, vol.
126, Birkhäuser, 2001, pp. 307–14, doi:10.1007/978-3-0348-8231-6.'
short: R. Seiringer, in:, M. Demuth, B. Schultze (Eds.), Birkhäuser, 2001, pp. 307–314.
conference:
name: 'PDE: Partial Differential Equations and Spectral Theory'
date_created: 2018-12-11T11:57:05Z
date_published: 2001-01-01T00:00:00Z
date_updated: 2021-01-12T06:56:53Z
day: '01'
doi: 10.1007/978-3-0348-8231-6
editor:
- first_name: Michael
full_name: Demuth, Michael
last_name: Demuth
- first_name: Bert
full_name: Schultze, Bert-Wolfgang
last_name: Schultze
extern: 1
intvolume: ' 126'
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/math-ph/0010006
month: '01'
oa: 1
page: 307 - 314
publication_status: published
publisher: Birkhäuser
publist_id: '4586'
quality_controlled: 0
status: public
title: 'Bosons in a trap: Asymptotic exactness of the Gross-Pitaevskii ground state
energy formula'
type: conference
volume: 126
year: '2001'
...
---
_id: '2341'
abstract:
- lang: eng
text: We study the ground state properties of an atom with nuclear charge Z and
N bosonic "electrons" in the presence of a homogeneous magnetic field
B. We investigate the mean field limit N→∞ with N / Z fixed, and identify three
different asymptotic regions, according to B≪Z2,B∼Z2,andB≫Z2 . In Region 1 standard
Hartree theory is applicable. Region 3 is described by a one-dimensional functional,
which is identical to the so-called Hyper-Strong functional introduced by Lieb,
Solovej and Yngvason for atoms with fermionic electrons in the region B≫Z3 ; i.e.,
for very strong magnetic fields the ground state properties of atoms are independent
of statistics. For Region 2 we introduce a general magnetic Hartree functional,
which is studied in detail. It is shown that in the special case of an atom it
can be restricted to the subspace of zero angular momentum parallel to the magnetic
field, which simplifies the theory considerably. The functional reproduces the
energy and the one-particle reduced density matrix for the full N-particle ground
state to leading order in N, and it implies the description of the other regions
as limiting cases.
author:
- first_name: Bernhard
full_name: Baumgartner, Bernhard
last_name: Baumgartner
- first_name: Robert
full_name: Robert Seiringer
id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
last_name: Seiringer
orcid: 0000-0002-6781-0521
citation:
ama: Baumgartner B, Seiringer R. Atoms with bosonic "electrons"
in strong magnetic fields. *Annales Henri Poincare*. 2001;2(1):41-76. doi:10.1007/PL00001032
apa: Baumgartner, B., & Seiringer, R. (2001). Atoms with bosonic "electrons"
in strong magnetic fields. *Annales Henri Poincare*. Birkhäuser. https://doi.org/10.1007/PL00001032
chicago: Baumgartner, Bernhard, and Robert Seiringer. “Atoms with Bosonic "Electrons"
in Strong Magnetic Fields.” *Annales Henri Poincare*. Birkhäuser, 2001. https://doi.org/10.1007/PL00001032.
ieee: B. Baumgartner and R. Seiringer, “Atoms with bosonic "electrons"
in strong magnetic fields,” *Annales Henri Poincare*, vol. 2, no. 1. Birkhäuser,
pp. 41–76, 2001.
ista: Baumgartner B, Seiringer R. 2001. Atoms with bosonic "electrons"
in strong magnetic fields. Annales Henri Poincare. 2(1), 41–76.
mla: Baumgartner, Bernhard, and Robert Seiringer. “Atoms with Bosonic "Electrons"
in Strong Magnetic Fields.” *Annales Henri Poincare*, vol. 2, no. 1, Birkhäuser,
2001, pp. 41–76, doi:10.1007/PL00001032.
short: B. Baumgartner, R. Seiringer, Annales Henri Poincare 2 (2001) 41–76.
date_created: 2018-12-11T11:57:06Z
date_published: 2001-02-01T00:00:00Z
date_updated: 2021-01-12T06:56:54Z
day: '01'
doi: 10.1007/PL00001032
extern: 1
intvolume: ' 2'
issue: '1'
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/math-ph/0007007
month: '02'
oa: 1
page: 41 - 76
publication: Annales Henri Poincare
publication_status: published
publisher: Birkhäuser
publist_id: '4585'
quality_controlled: 0
status: public
title: Atoms with bosonic "electrons" in strong magnetic fields
type: journal_article
volume: 2
year: '2001'
...
---
_id: '2345'
abstract:
- lang: eng
text: We give upper bounds for the number of spin-1/2 particles that can be bound
to a nucleus of charge Z in the presence of a magnetic field B, including the
spin-field coupling. We use Lieb's strategy, which is known to yield Nc < 2Z
+ 1 for magnetic fields that go to zero at infinity, ignoring the spin-field interaction.
For particles with fermionic statistics in a homogeneous magnetic field our upper
bound has an additional term of the order of Z × min {(B/Z3)2/5, 1 + | 1n(B/Z3)|2}.
author:
- first_name: Robert
full_name: Robert Seiringer
id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
last_name: Seiringer
orcid: 0000-0002-6781-0521
citation:
ama: 'Seiringer R. On the maximal ionization of atoms in strong magnetic fields.
*Journal of Physics A: Mathematical and General*. 2001;34(9):1943-1948. doi:10.1088/0305-4470/34/9/311'
apa: 'Seiringer, R. (2001). On the maximal ionization of atoms in strong magnetic
fields. *Journal of Physics A: Mathematical and General*. IOP Publishing
Ltd. https://doi.org/10.1088/0305-4470/34/9/311'
chicago: 'Seiringer, Robert. “On the Maximal Ionization of Atoms in Strong Magnetic
Fields.” *Journal of Physics A: Mathematical and General*. IOP Publishing
Ltd., 2001. https://doi.org/10.1088/0305-4470/34/9/311.'
ieee: 'R. Seiringer, “On the maximal ionization of atoms in strong magnetic fields,”
*Journal of Physics A: Mathematical and General*, vol. 34, no. 9. IOP Publishing
Ltd., pp. 1943–1948, 2001.'
ista: 'Seiringer R. 2001. On the maximal ionization of atoms in strong magnetic
fields. Journal of Physics A: Mathematical and General. 34(9), 1943–1948.'
mla: 'Seiringer, Robert. “On the Maximal Ionization of Atoms in Strong Magnetic
Fields.” *Journal of Physics A: Mathematical and General*, vol. 34, no. 9,
IOP Publishing Ltd., 2001, pp. 1943–48, doi:10.1088/0305-4470/34/9/311.'
short: 'R. Seiringer, Journal of Physics A: Mathematical and General 34 (2001) 1943–1948.'
date_created: 2018-12-11T11:57:07Z
date_published: 2001-03-09T00:00:00Z
date_updated: 2021-01-12T06:56:55Z
day: '09'
doi: 10.1088/0305-4470/34/9/311
extern: 1
intvolume: ' 34'
issue: '9'
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/math-ph/0006002
month: '03'
oa: 1
page: 1943 - 1948
publication: 'Journal of Physics A: Mathematical and General'
publication_status: published
publisher: IOP Publishing Ltd.
publist_id: '4580'
quality_controlled: 0
status: public
title: On the maximal ionization of atoms in strong magnetic fields
type: journal_article
volume: 34
year: '2001'
...
---
_id: '2346'
abstract:
- lang: eng
text: By means of a generalization of the Fefferman - de la Llave decomposition
we derive a general lower bound on the interaction energy of one-dimensional quantum
systems. We apply this result to a specific class of lowest Landau band wave functions.
author:
- first_name: Christian
full_name: Hainzl, Christian
last_name: Hainzl
- first_name: Robert
full_name: Robert Seiringer
id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
last_name: Seiringer
orcid: 0000-0002-6781-0521
citation:
ama: Hainzl C, Seiringer R. Bounds on one-dimensional exchange energies with application
to lowest Landau band quantum mechanics. *Letters in Mathematical Physics*.
2001;55(2):133-142. doi:10.1023/A:1010951905548
apa: Hainzl, C., & Seiringer, R. (2001). Bounds on one-dimensional exchange
energies with application to lowest Landau band quantum mechanics. *Letters
in Mathematical Physics*. Springer. https://doi.org/10.1023/A:1010951905548
chicago: Hainzl, Christian, and Robert Seiringer. “Bounds on One-Dimensional Exchange
Energies with Application to Lowest Landau Band Quantum Mechanics.” *Letters
in Mathematical Physics*. Springer, 2001. https://doi.org/10.1023/A:1010951905548.
ieee: C. Hainzl and R. Seiringer, “Bounds on one-dimensional exchange energies with
application to lowest Landau band quantum mechanics,” *Letters in Mathematical
Physics*, vol. 55, no. 2. Springer, pp. 133–142, 2001.
ista: Hainzl C, Seiringer R. 2001. Bounds on one-dimensional exchange energies with
application to lowest Landau band quantum mechanics. Letters in Mathematical Physics.
55(2), 133–142.
mla: Hainzl, Christian, and Robert Seiringer. “Bounds on One-Dimensional Exchange
Energies with Application to Lowest Landau Band Quantum Mechanics.” *Letters
in Mathematical Physics*, vol. 55, no. 2, Springer, 2001, pp. 133–42, doi:10.1023/A:1010951905548.
short: C. Hainzl, R. Seiringer, Letters in Mathematical Physics 55 (2001) 133–142.
date_created: 2018-12-11T11:57:07Z
date_published: 2001-02-01T00:00:00Z
date_updated: 2021-01-12T06:56:56Z
day: '01'
doi: 10.1023/A:1010951905548
extern: 1
intvolume: ' 55'
issue: '2'
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/cond-mat/0102118
month: '02'
oa: 1
page: 133 - 142
publication: Letters in Mathematical Physics
publication_status: published
publisher: Springer
publist_id: '4581'
quality_controlled: 0
status: public
title: Bounds on one-dimensional exchange energies with application to lowest Landau
band quantum mechanics
type: journal_article
volume: 55
year: '2001'
...
---
_id: '2347'
abstract:
- lang: eng
text: We consider the ground state properties of an inhomogeneous two-dimensional
Bose gas with a repulsive, short range pair interaction and an external confining
potential. In the limit when the particle number N is large but ρ̄a2 is small,
where ρ̄ is the average particle density and a the scattering length, the ground
state energy and density are rigorously shown to be given to leading order by
a Gross-Pitaevskii (GP) energy functional with a coupling constant g ∼ 1/| 1n(ρ̄a2)|.
In contrast to the 3D case the coupling constant depends on N through the mean
density. The GP energy per particle depends only on Ng. In 2D this parameter is
typically so large that the gradient term in the GP energy functional is negligible
and the simpler description by a Thomas-Fermi type functional is adequate.
author:
- first_name: Élliott
full_name: Lieb, Élliott H
last_name: Lieb
- first_name: Robert
full_name: Robert Seiringer
id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
last_name: Seiringer
orcid: 0000-0002-6781-0521
- first_name: Jakob
full_name: Yngvason, Jakob
last_name: Yngvason
citation:
ama: Lieb É, Seiringer R, Yngvason J. A rigorous derivation of the Gross-Pitaevskii
energy functional for a two-dimensional Bose gas. *Communications in Mathematical
Physics*. 2001;224(1):17-31. doi:10.1007/s002200100533
apa: Lieb, É., Seiringer, R., & Yngvason, J. (2001). A rigorous derivation of
the Gross-Pitaevskii energy functional for a two-dimensional Bose gas. *Communications
in Mathematical Physics*. Springer. https://doi.org/10.1007/s002200100533
chicago: Lieb, Élliott, Robert Seiringer, and Jakob Yngvason. “A Rigorous Derivation
of the Gross-Pitaevskii Energy Functional for a Two-Dimensional Bose Gas.” *Communications
in Mathematical Physics*. Springer, 2001. https://doi.org/10.1007/s002200100533.
ieee: É. Lieb, R. Seiringer, and J. Yngvason, “A rigorous derivation of the Gross-Pitaevskii
energy functional for a two-dimensional Bose gas,” *Communications in Mathematical
Physics*, vol. 224, no. 1. Springer, pp. 17–31, 2001.
ista: Lieb É, Seiringer R, Yngvason J. 2001. A rigorous derivation of the Gross-Pitaevskii
energy functional for a two-dimensional Bose gas. Communications in Mathematical
Physics. 224(1), 17–31.
mla: Lieb, Élliott, et al. “A Rigorous Derivation of the Gross-Pitaevskii Energy
Functional for a Two-Dimensional Bose Gas.” *Communications in Mathematical
Physics*, vol. 224, no. 1, Springer, 2001, pp. 17–31, doi:10.1007/s002200100533.
short: É. Lieb, R. Seiringer, J. Yngvason, Communications in Mathematical Physics
224 (2001) 17–31.
date_created: 2018-12-11T11:57:08Z
date_published: 2001-11-01T00:00:00Z
date_updated: 2021-01-12T06:56:56Z
day: '01'
doi: 10.1007/s002200100533
extern: 1
intvolume: ' 224'
issue: '1'
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/cond-mat/0005026
month: '11'
oa: 1
page: 17 - 31
publication: Communications in Mathematical Physics
publication_status: published
publisher: Springer
publist_id: '4579'
quality_controlled: 0
status: public
title: A rigorous derivation of the Gross-Pitaevskii energy functional for a two-dimensional
Bose gas
type: journal_article
volume: 224
year: '2001'
...
---
_id: '2348'
abstract:
- lang: eng
text: This paper concerns the asymptotic ground state properties of heavy atoms
in strong, homogeneous magnetic fields. In the limit when the nuclear charge Z
tends to ∞ with the magnetic field B satisfying B ≫ Z4/3 all the electrons are
confined to the lowest Landau band. We consider here an energy functional, whose
variable is a sequence of one-dimensional density matrices corresponding to different
angular momentum functions in the lowest Landau band. We study this functional
in detail and derive various interesting properties, which are compared with the
density matrix (DM) theory introduced by Lieb, Solovej and Yngvason. In contrast
to the DM theory the variable perpendicular to the field is replaced by the discrete
angular momentum quantum numbers. Hence we call the new functional a discrete
density matrix (DDM) functional. We relate this DDM theory to the lowest Landau
band quantum mechanics and show that it reproduces correctly the ground state
energy apart from errors due to the indirect part of the Coulomb interaction energy.
author:
- first_name: Christian
full_name: Hainzl, Christian
last_name: Hainzl
- first_name: Robert
full_name: Robert Seiringer
id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
last_name: Seiringer
orcid: 0000-0002-6781-0521
citation:
ama: Hainzl C, Seiringer R. A discrete density matrix theory for atoms in strong
magnetic fields. *Communications in Mathematical Physics*. 2001;217(1):229-248.
doi:10.1007/s002200100373
apa: Hainzl, C., & Seiringer, R. (2001). A discrete density matrix theory for
atoms in strong magnetic fields. *Communications in Mathematical Physics*.
Springer. https://doi.org/10.1007/s002200100373
chicago: Hainzl, Christian, and Robert Seiringer. “A Discrete Density Matrix Theory
for Atoms in Strong Magnetic Fields.” *Communications in Mathematical Physics*.
Springer, 2001. https://doi.org/10.1007/s002200100373.
ieee: C. Hainzl and R. Seiringer, “A discrete density matrix theory for atoms in
strong magnetic fields,” *Communications in Mathematical Physics*, vol. 217,
no. 1. Springer, pp. 229–248, 2001.
ista: Hainzl C, Seiringer R. 2001. A discrete density matrix theory for atoms in
strong magnetic fields. Communications in Mathematical Physics. 217(1), 229–248.
mla: Hainzl, Christian, and Robert Seiringer. “A Discrete Density Matrix Theory
for Atoms in Strong Magnetic Fields.” *Communications in Mathematical Physics*,
vol. 217, no. 1, Springer, 2001, pp. 229–48, doi:10.1007/s002200100373.
short: C. Hainzl, R. Seiringer, Communications in Mathematical Physics 217 (2001)
229–248.
date_created: 2018-12-11T11:57:08Z
date_published: 2001-02-01T00:00:00Z
date_updated: 2021-01-12T06:56:56Z
day: '01'
doi: 10.1007/s002200100373
extern: 1
intvolume: ' 217'
issue: '1'
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/math-ph/0010005
month: '02'
oa: 1
page: 229 - 248
publication: Communications in Mathematical Physics
publication_status: published
publisher: Springer
publist_id: '4578'
quality_controlled: 0
status: public
title: A discrete density matrix theory for atoms in strong magnetic fields
type: journal_article
volume: 217
year: '2001'
...
---
_id: '2419'
abstract:
- lang: eng
text: For an absolutely continuous probability measure μ. on ℝd and a nonnegative
integer k, let S̃k(μ, 0) denote the probability that the convex hull of k + d
+ 1 random points which are i.i.d. according to μ contains the origin 0. For d
and k given, we determine a tight upper bound on S̃k(μ, 0), and we characterize
the measures in ℝd which attain this bound. As we will see, this result can be
considered a continuous analogue of the Upper Bound Theorem for the maximal number
of faces of convex polytopes with a given number of vertices. For our proof we
introduce so-called h-functions, continuous counterparts of h-vectors of simplicial
convex polytopes.
author:
- first_name: Uli
full_name: Uli Wagner
id: 36690CA2-F248-11E8-B48F-1D18A9856A87
last_name: Wagner
orcid: 0000-0002-1494-0568
- first_name: Emo
full_name: Welzl, Emo
last_name: Welzl
citation:
ama: Wagner U, Welzl E. A continuous analogue of the Upper Bound Theorem. *Discrete
& Computational Geometry*. 2001;26(2):205-219. doi:10.1007/s00454-001-0028-9
apa: Wagner, U., & Welzl, E. (2001). A continuous analogue of the Upper Bound
Theorem. *Discrete & Computational Geometry*. Springer. https://doi.org/10.1007/s00454-001-0028-9
chicago: Wagner, Uli, and Emo Welzl. “A Continuous Analogue of the Upper Bound Theorem.”
*Discrete & Computational Geometry*. Springer, 2001. https://doi.org/10.1007/s00454-001-0028-9.
ieee: U. Wagner and E. Welzl, “A continuous analogue of the Upper Bound Theorem,”
*Discrete & Computational Geometry*, vol. 26, no. 2. Springer, pp. 205–219,
2001.
ista: Wagner U, Welzl E. 2001. A continuous analogue of the Upper Bound Theorem.
Discrete & Computational Geometry. 26(2), 205–219.
mla: Wagner, Uli, and Emo Welzl. “A Continuous Analogue of the Upper Bound Theorem.”
*Discrete & Computational Geometry*, vol. 26, no. 2, Springer, 2001,
pp. 205–19, doi:10.1007/s00454-001-0028-9.
short: U. Wagner, E. Welzl, Discrete & Computational Geometry 26 (2001) 205–219.
date_created: 2018-12-11T11:57:33Z
date_published: 2001-01-01T00:00:00Z
date_updated: 2021-01-12T06:57:22Z
day: '01'
doi: 10.1007/s00454-001-0028-9
extern: 1
intvolume: ' 26'
issue: '2'
month: '01'
page: 205 - 219
publication: Discrete & Computational Geometry
publication_status: published
publisher: Springer
publist_id: '4506'
quality_controlled: 0
status: public
title: A continuous analogue of the Upper Bound Theorem
type: journal_article
volume: 26
year: '2001'
...