---
_id: '208'
abstract:
- lang: eng
text: For any ε > 0 and any diagonal quadratic form Q ∈ ℤ[x 1, x 2, x 3, x 4]
with a square-free discriminant of modulus Δ Q ≠ 0, we establish the uniform estimate
≪ε B 3/2+ε + B 2+ε/Δ Q 1/6 for the number of rational points of height at most
B lying in the projective surface Q = 0.
author:
- first_name: Timothy D
full_name: Timothy Browning
id: 35827D50-F248-11E8-B48F-1D18A9856A87
last_name: Browning
citation:
ama: Browning TD. Counting rational points on diagonal quadratic surfaces. *Quarterly
Journal of Mathematics*. 2003;54(1):11-31. doi:10.1093/qjmath/54.1.11
apa: Browning, T. D. (2003). Counting rational points on diagonal quadratic surfaces.
*Quarterly Journal of Mathematics*, *54*(1), 11–31. https://doi.org/10.1093/qjmath/54.1.11
chicago: 'Browning, Timothy D. “Counting Rational Points on Diagonal Quadratic Surfaces.”
*Quarterly Journal of Mathematics* 54, no. 1 (2003): 11–31. https://doi.org/10.1093/qjmath/54.1.11.'
ieee: T. D. Browning, “Counting rational points on diagonal quadratic surfaces,”
*Quarterly Journal of Mathematics*, vol. 54, no. 1, pp. 11–31, 2003.
ista: Browning TD. 2003. Counting rational points on diagonal quadratic surfaces.
Quarterly Journal of Mathematics. 54(1), 11–31.
mla: Browning, Timothy D. “Counting Rational Points on Diagonal Quadratic Surfaces.”
*Quarterly Journal of Mathematics*, vol. 54, no. 1, Oxford University Press,
2003, pp. 11–31, doi:10.1093/qjmath/54.1.11.
short: T.D. Browning, Quarterly Journal of Mathematics 54 (2003) 11–31.
date_created: 2018-12-11T11:45:13Z
date_published: 2003-03-01T00:00:00Z
date_updated: 2019-04-26T07:22:07Z
day: '01'
doi: 10.1093/qjmath/54.1.11
extern: 1
intvolume: ' 54'
issue: '1'
month: '03'
page: 11 - 31
publication: Quarterly Journal of Mathematics
publication_status: published
publisher: Oxford University Press
publist_id: '7705'
quality_controlled: 0
status: public
title: Counting rational points on diagonal quadratic surfaces
type: journal_article
volume: 54
year: '2003'
...
---
_id: '2337'
alternative_title:
- Contemporary Mathematics
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
citation:
ama: 'Lieb É, Seiringer R. Bose-Einstein condensation of dilute gases in traps .
In: Karpeshina Y, Weikard R, Zeng Y, eds. Vol 327. American Mathematical Society;
2003:239-250. doi:10.1090/conm/327/05818'
apa: Lieb, É., & Seiringer, R. (2003). Bose-Einstein condensation of dilute
gases in traps . In Y. Karpeshina, R. Weikard, & Y. Zeng (Eds.) (Vol. 327,
pp. 239–250). Presented at the Differential Equations and Mathematical Physics,
American Mathematical Society. https://doi.org/10.1090/conm/327/05818
chicago: Lieb, Élliott, and Robert Seiringer. “Bose-Einstein Condensation of Dilute
Gases in Traps .” edited by Yulia Karpeshina, Rudi Weikard, and Yanni Zeng, 327:239–50.
American Mathematical Society, 2003. https://doi.org/10.1090/conm/327/05818.
ieee: É. Lieb and R. Seiringer, “Bose-Einstein condensation of dilute gases in traps
,” presented at the Differential Equations and Mathematical Physics, 2003, vol.
327, pp. 239–250.
ista: Lieb É, Seiringer R. 2003. Bose-Einstein condensation of dilute gases in traps
. Differential Equations and Mathematical Physics, Contemporary Mathematics, vol.
327. 239–250.
mla: Lieb, Élliott, and Robert Seiringer. *Bose-Einstein Condensation of Dilute
Gases in Traps *. Edited by Yulia Karpeshina et al., vol. 327, American Mathematical
Society, 2003, pp. 239–50, doi:10.1090/conm/327/05818.
short: É. Lieb, R. Seiringer, in:, Y. Karpeshina, R. Weikard, Y. Zeng (Eds.), American
Mathematical Society, 2003, pp. 239–250.
conference:
name: Differential Equations and Mathematical Physics
date_created: 2018-12-11T11:57:04Z
date_published: 2003-01-01T00:00:00Z
date_updated: 2020-07-14T12:45:39Z
day: '01'
doi: 10.1090/conm/327/05818
editor:
- first_name: Yulia
full_name: Karpeshina, Yulia
last_name: Karpeshina
- first_name: Rudi
full_name: Weikard, Rudi
last_name: Weikard
- first_name: Yanni
full_name: Zeng, Yanni
last_name: Zeng
extern: 1
intvolume: ' 327'
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/math-ph/0210028
month: '01'
oa: 1
page: 239 - 250
publication_status: published
publisher: American Mathematical Society
publist_id: '4589'
quality_controlled: 0
status: public
title: 'Bose-Einstein condensation of dilute gases in traps '
type: conference
volume: 327
year: '2003'
...
---
_id: '2354'
abstract:
- lang: eng
text: We investigate the ground state properties of a gas of interacting particles
confined in an external potential in three dimensions and subject to rotation
around an axis of symmetry. We consider the Gross-Pitaevskii (GP) limit of a dilute
gas. Analysing both the absolute and the bosonic ground states of the system,
we show, in particular, their different behaviour for a certain range of parameters.
This parameter range is determined by the question whether the rotational symmetry
in the minimizer of the GP functional is broken or not. For the absolute ground
state, we prove that in the GP limit a modified GP functional depending on density
matrices correctly describes the energy and reduced density matrices, independent
of symmetry breaking. For the bosonic ground state this holds true if and only
if the symmetry is unbroken.
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. Ground state asymptotics of a dilute, rotating gas. *Journal
of Physics A: Mathematical and Theoretical*. 2003;36(37):9755-9778. doi:10.1088/0305-4470/36/37/312'
apa: 'Seiringer, R. (2003). Ground state asymptotics of a dilute, rotating gas.
*Journal of Physics A: Mathematical and Theoretical*, *36*(37), 9755–9778.
https://doi.org/10.1088/0305-4470/36/37/312'
chicago: 'Seiringer, Robert. “Ground State Asymptotics of a Dilute, Rotating Gas.”
*Journal of Physics A: Mathematical and Theoretical* 36, no. 37 (2003): 9755–78.
https://doi.org/10.1088/0305-4470/36/37/312.'
ieee: 'R. Seiringer, “Ground state asymptotics of a dilute, rotating gas,” *Journal
of Physics A: Mathematical and Theoretical*, vol. 36, no. 37, pp. 9755–9778,
2003.'
ista: 'Seiringer R. 2003. Ground state asymptotics of a dilute, rotating gas. Journal
of Physics A: Mathematical and Theoretical. 36(37), 9755–9778.'
mla: 'Seiringer, Robert. “Ground State Asymptotics of a Dilute, Rotating Gas.” *Journal
of Physics A: Mathematical and Theoretical*, vol. 36, no. 37, IOP Publishing
Ltd., 2003, pp. 9755–78, doi:10.1088/0305-4470/36/37/312.'
short: 'R. Seiringer, Journal of Physics A: Mathematical and Theoretical 36 (2003)
9755–9778.'
date_created: 2018-12-11T11:57:10Z
date_published: 2003-09-19T00:00:00Z
date_updated: 2020-07-14T12:45:39Z
day: '19'
doi: 10.1088/0305-4470/36/37/312
extern: 1
intvolume: ' 36'
issue: '37'
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/math-ph/0306022
month: '09'
oa: 1
page: 9755 - 9778
publication: 'Journal of Physics A: Mathematical and Theoretical'
publication_status: published
publisher: IOP Publishing Ltd.
publist_id: '4572'
quality_controlled: 0
status: public
title: Ground state asymptotics of a dilute, rotating gas
type: journal_article
volume: 36
year: '2003'
...
---
_id: '2357'
abstract:
- lang: eng
text: 'The classic Poincaré inequality bounds the L q-norm of a function f in a
bounded domain Ω ⊂ ℝ n in terms of some L p-norm of its gradient in Ω. We generalize
this in two ways: In the first generalization we remove a set Τ from Ω and concentrate
our attention on Λ = Ω \ Τ. This new domain might not even be connected and hence
no Poincaré inequality can generally hold for it, or if it does hold it might
have a very bad constant. This is so even if the volume of Τ is arbitrarily small.
A Poincaré inequality does hold, however, if one makes the additional assumption
that f has a finite L p gradient norm on the whole of Ω, not just on Λ. The important
point is that the Poincaré inequality thus obtained bounds the L q-norm of f in
terms of the L p gradient norm on Λ (not Ω) plus an additional term that goes
to zero as the volume of Τ goes to zero. This error term depends on Τ only through
its volume. Apart from this additive error term, the constant in the inequality
remains that of the ''nice'' domain Ω. In the second generalization we are given
a vector field A and replace ∇ by ∇ + iA(x) (geometrically, a connection on a
U(1) bundle). Unlike the A = 0 case, the infimum of ∥(∇ + iA)f∥ p over all f with
a given ∥f∥ q is in general not zero. This permits an improvement of the inequality
by the addition of a term whose sharp value we derive. We describe some open problems
that arise from these generalizations.'
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. Poincaré inequalities in punctured domains.
*Annals of Mathematics*. 2003;158(3):1067-1080. doi:10.4007/annals.2003.158.1067
apa: Lieb, É., Seiringer, R., & Yngvason, J. (2003). Poincaré inequalities in
punctured domains. *Annals of Mathematics*, *158*(3), 1067–1080. https://doi.org/10.4007/annals.2003.158.1067
chicago: 'Lieb, Élliott, Robert Seiringer, and Jakob Yngvason. “Poincaré Inequalities
in Punctured Domains.” *Annals of Mathematics* 158, no. 3 (2003): 1067–80.
https://doi.org/10.4007/annals.2003.158.1067
.'
ieee: É. Lieb, R. Seiringer, and J. Yngvason, “Poincaré inequalities in punctured
domains,” *Annals of Mathematics*, vol. 158, no. 3, pp. 1067–1080, 2003.
ista: Lieb É, Seiringer R, Yngvason J. 2003. Poincaré inequalities in punctured
domains. Annals of Mathematics. 158(3), 1067–1080.
mla: Lieb, Élliott, et al. “Poincaré Inequalities in Punctured Domains.” *Annals
of Mathematics*, vol. 158, no. 3, Princeton University Press, 2003, pp. 1067–80,
doi:10.4007/annals.2003.158.1067
.
short: É. Lieb, R. Seiringer, J. Yngvason, Annals of Mathematics 158 (2003) 1067–1080.
date_created: 2018-12-11T11:57:11Z
date_published: 2003-11-01T00:00:00Z
date_updated: 2020-07-14T12:45:39Z
day: '01'
doi: '10.4007/annals.2003.158.1067 '
extern: 1
intvolume: ' 158'
issue: '3'
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/math/0205088
month: '11'
oa: 1
page: 1067 - 1080
publication: Annals of Mathematics
publication_status: published
publisher: Princeton University Press
publist_id: '4570'
quality_controlled: 0
status: public
title: Poincaré inequalities in punctured domains
type: journal_article
volume: 158
year: '2003'
...
---
_id: '2358'
abstract:
- lang: eng
text: A study was conducted on the one-dimensional (1D) bosons in three-dimensional
(3D) traps. A rigorous analysis was carried out on the parameter regions in which
various types of 1D or 3D behavior occurred in the ground state. The four parameter
regions include density, transverse, longitudinal dimensions and scattering length.
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. One-dimensional Bosons in three-dimensional
traps. *Physical Review Letters*. 2003;91(15):1504011-1504014. doi:10.1103/PhysRevLett.91.150401
apa: Lieb, É., Seiringer, R., & Yngvason, J. (2003). One-dimensional Bosons
in three-dimensional traps. *Physical Review Letters*, *91*(15), 1504011–1504014.
https://doi.org/10.1103/PhysRevLett.91.150401
chicago: 'Lieb, Élliott, Robert Seiringer, and Jakob Yngvason. “One-Dimensional
Bosons in Three-Dimensional Traps.” *Physical Review Letters* 91, no. 15
(2003): 1504011–14. https://doi.org/10.1103/PhysRevLett.91.150401.'
ieee: É. Lieb, R. Seiringer, and J. Yngvason, “One-dimensional Bosons in three-dimensional
traps,” *Physical Review Letters*, vol. 91, no. 15, pp. 1504011–1504014,
2003.
ista: Lieb É, Seiringer R, Yngvason J. 2003. One-dimensional Bosons in three-dimensional
traps. Physical Review Letters. 91(15), 1504011–1504014.
mla: Lieb, Élliott, et al. “One-Dimensional Bosons in Three-Dimensional Traps.”
*Physical Review Letters*, vol. 91, no. 15, American Physical Society, 2003,
pp. 1504011–14, doi:10.1103/PhysRevLett.91.150401.
short: É. Lieb, R. Seiringer, J. Yngvason, Physical Review Letters 91 (2003) 1504011–1504014.
date_created: 2018-12-11T11:57:12Z
date_published: 2003-10-10T00:00:00Z
date_updated: 2020-07-14T12:45:39Z
day: '10'
doi: 10.1103/PhysRevLett.91.150401
extern: 1
intvolume: ' 91'
issue: '15'
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/cond-mat/0304071
month: '10'
oa: 1
page: 1504011 - 1504014
publication: Physical Review Letters
publication_status: published
publisher: American Physical Society
publist_id: '4571'
quality_controlled: 0
status: public
title: One-dimensional Bosons in three-dimensional traps
type: journal_article
volume: 91
year: '2003'
...