---
_id: '213'
abstract:
- lang: eng
text: For any integers d,n ≥2, let X ⊂ Pn be a non‐singular hypersurface of degree
d that is defined over the rational numbers. The main result in this paper is
a proof that the number of rational points on X which have height at most B is
O(Bn − 1 + ɛ), for any ɛ > 0. The implied constant in this estimate depends
at most upon d, ɛ and n. 2000 Mathematics Subject Classification 11D45 (primary),
11G35, 14G05 (secondary).
acknowledgement: EPSRC grant number GR/R93155/01
author:
- first_name: Timothy D
full_name: Timothy Browning
id: 35827D50-F248-11E8-B48F-1D18A9856A87
last_name: Browning
- first_name: Roger
full_name: Heath-Brown, Roger
last_name: Heath Brown
- first_name: Jason
full_name: Starr, Jason M
last_name: Starr
citation:
ama: Browning TD, Heath Brown R, Starr J. The density of rational points on non-singular
hypersurfaces, II. *Proceedings of the London Mathematical Society*. 2006;93(2):273-303.
doi:https://doi.org/10.1112/S0024611506015784
apa: Browning, T. D., Heath Brown, R., & Starr, J. (2006). The density of rational
points on non-singular hypersurfaces, II. *Proceedings of the London Mathematical
Society*, *93*(2), 273–303. https://doi.org/10.1112/S0024611506015784
chicago: 'Browning, Timothy D, Roger Heath Brown, and Jason Starr. “The Density
of Rational Points on Non-Singular Hypersurfaces, II.” *Proceedings of the London
Mathematical Society* 93, no. 2 (2006): 273–303. https://doi.org/10.1112/S0024611506015784.'
ieee: T. D. Browning, R. Heath Brown, and J. Starr, “The density of rational points
on non-singular hypersurfaces, II,” *Proceedings of the London Mathematical
Society*, vol. 93, no. 2, pp. 273–303, 2006.
ista: Browning TD, Heath Brown R, Starr J. 2006. The density of rational points
on non-singular hypersurfaces, II. Proceedings of the London Mathematical Society.
93(2), 273–303.
mla: Browning, Timothy D., et al. “The Density of Rational Points on Non-Singular
Hypersurfaces, II.” *Proceedings of the London Mathematical Society*, vol.
93, no. 2, John Wiley and Sons Ltd, 2006, pp. 273–303, doi:https://doi.org/10.1112/S0024611506015784.
short: T.D. Browning, R. Heath Brown, J. Starr, Proceedings of the London Mathematical
Society 93 (2006) 273–303.
date_created: 2018-12-11T11:45:14Z
date_published: 2006-09-01T00:00:00Z
date_updated: 2019-04-26T07:22:08Z
day: '01'
doi: https://doi.org/10.1112/S0024611506015784
extern: 1
intvolume: ' 93'
issue: '2'
month: '09'
page: 273 - 303
publication: Proceedings of the London Mathematical Society
publication_status: published
publisher: John Wiley and Sons Ltd
publist_id: '7698'
quality_controlled: 0
status: public
title: The density of rational points on non-singular hypersurfaces, II
type: journal_article
volume: 93
year: '2006'
...
---
_id: '2134'
abstract:
- lang: eng
text: Predissociation of the N+2 C 2Σ+u(v') vibrational levels with v' ≥ 3 was observed
via dispersed C 2Σ+u → X 2Σ+g fluorescence in the spectral range of 165–208 nm
after resonant 1s−1π*(vr) excitation of N2 and its subsequent autoionization into
the N+2 C state. This range is dominated by lines in atomic nitrogen, by overlapped
C 2Σ+u(v') → X 2Σ+g(v'') vibrational band sequences with Δv = const and broad
unresolved band systems (D, (2))2Πg(v') → A2Πu(v'') in the N+2 molecular ion.
With very high fluorescence resolution of about 0.1 nm FWHM individual C 2Σ+u(v')
→ X 2Σ+g(v'') vibrational bands have been resolved. Calculation of the observed
fluorescence spectra by taking into account predissociation and molecular rotation
describes well the shape of both individual vibrational bands C 2Σ+u(v') → X 2Σ+g(v'')
and the whole band system.
acknowledgement: This work has been supported by the Deutsche Forschungsgemeinschaft
(DFG) and by the Bundesministerium für Bildung und Forschung (BMBF) (Förderkennzeichen
05 ES3XBA/5 and IB/DLR RUS 02/037). The cooperation between the groups at the universities
of Kaiserslautern and Rostov-on-Don was supported by the Alexander-von-Humboldt
Foundation within the framework of an institute partnership with funds from BMBF
author:
- first_name: Arno
full_name: Ehresmann, Arno
last_name: Ehresmann
- first_name: Lutz
full_name: Werner, Lutz
last_name: Werner
- first_name: Stefan
full_name: Klumpp, Stefan
last_name: Klumpp
- first_name: Ph
full_name: Demekhin, Ph V
last_name: Demekhin
- first_name: Mikhail
full_name: Mikhail Lemeshko
id: 37CB05FA-F248-11E8-B48F-1D18A9856A87
last_name: Lemeshko
orcid: 0000-0002-6990-7802
- first_name: V.
full_name: Sukhorukov, V. L
last_name: Sukhorukov
- first_name: Karl
full_name: Schartner, Karl H
last_name: Schartner
- first_name: Hans
full_name: Schmoranzer, Hans P
last_name: Schmoranzer
citation:
ama: 'Ehresmann A, Werner L, Klumpp S, et al. Predissociation of the N+2(C 2Σ+u)
state observed via C 2Σ+u → X 2Σ+g fluorescence after resonant 1s−1π* excitation
of N2 molecule. *Journal of Physics B: Atomic, Molecular and Optical Physics*.
2006;39(6):L119-L126. doi:10.1088/0953-4075/39/6/L03'
apa: 'Ehresmann, A., Werner, L., Klumpp, S., Demekhin, P., Lemeshko, M., Sukhorukov,
V., … Schmoranzer, H. (2006). Predissociation of the N+2(C 2Σ+u) state observed
via C 2Σ+u → X 2Σ+g fluorescence after resonant 1s−1π* excitation of N2 molecule.
*Journal of Physics B: Atomic, Molecular and Optical Physics*, *39*(6),
L119–L126. https://doi.org/10.1088/0953-4075/39/6/L03'
chicago: 'Ehresmann, Arno, Lutz Werner, Stefan Klumpp, Ph Demekhin, Mikhail Lemeshko,
V. Sukhorukov, Karl Schartner, and Hans Schmoranzer. “Predissociation of the N+2(C
2Σ+u) State Observed via C 2Σ+u → X 2Σ+g Fluorescence after Resonant 1s−1π* Excitation
of N2 Molecule.” *Journal of Physics B: Atomic, Molecular and Optical Physics*
39, no. 6 (2006): L119–26. https://doi.org/10.1088/0953-4075/39/6/L03.'
ieee: 'A. Ehresmann *et al.*, “Predissociation of the N+2(C 2Σ+u) state observed
via C 2Σ+u → X 2Σ+g fluorescence after resonant 1s−1π* excitation of N2 molecule,”
*Journal of Physics B: Atomic, Molecular and Optical Physics*, vol. 39, no.
6, pp. L119–L126, 2006.'
ista: 'Ehresmann A, Werner L, Klumpp S, Demekhin P, Lemeshko M, Sukhorukov V, Schartner
K, Schmoranzer H. 2006. Predissociation of the N+2(C 2Σ+u) state observed via
C 2Σ+u → X 2Σ+g fluorescence after resonant 1s−1π* excitation of N2 molecule.
Journal of Physics B: Atomic, Molecular and Optical Physics. 39(6), L119–L126.'
mla: 'Ehresmann, Arno, et al. “Predissociation of the N+2(C 2Σ+u) State Observed
via C 2Σ+u → X 2Σ+g Fluorescence after Resonant 1s−1π* Excitation of N2 Molecule.”
*Journal of Physics B: Atomic, Molecular and Optical Physics*, vol. 39, no.
6, IOP Publishing Ltd., 2006, pp. L119–26, doi:10.1088/0953-4075/39/6/L03.'
short: 'A. Ehresmann, L. Werner, S. Klumpp, P. Demekhin, M. Lemeshko, V. Sukhorukov,
K. Schartner, H. Schmoranzer, Journal of Physics B: Atomic, Molecular and Optical
Physics 39 (2006) L119–L126.'
date_created: 2018-12-11T11:55:54Z
date_published: 2006-03-28T00:00:00Z
date_updated: 2020-07-14T12:45:29Z
day: '28'
doi: 10.1088/0953-4075/39/6/L03
extern: 1
intvolume: ' 39'
issue: '6'
month: '03'
page: L119 - L126
publication: 'Journal of Physics B: Atomic, Molecular and Optical Physics'
publication_status: published
publisher: IOP Publishing Ltd.
publist_id: '4900'
quality_controlled: 0
status: public
title: Predissociation of the N+2(C 2Σ+u) state observed via C 2Σ+u → X 2Σ+g fluorescence
after resonant 1s−1π* excitation of N2 molecule
type: journal_article
volume: 39
year: '2006'
...
---
_id: '2142'
abstract:
- lang: eng
text: Fluorescence from fragments formed after the de-excitation of the N*2(1s−1π*)
resonance has been measured in the spectral range of 135–190 nm. This range is
dominated by lines in atomic nitrogen and lines formed by overlapping C2Σ+u(v')
→ X2Σ+g(v'') bands with Δv = const in the N+2 molecular ion which result from
the spectator Auger decays of the N*2(1s−1π*(vr)) resonances. Ab initio calculations
of the corresponding potential curves and transition probabilities showed that
the observed irregular intensity dependence of the C2Σ+u(v') → X2Σ+g(v'')(Δv =
const) fluorescence lines on the vibrational quantum number vr is due to transitions
between vibrational levels during the reaction N2(v0 = 0)→ N*2(1s−1π*(vr)) Longrightarrow
C2Σ+u(v') → X2Σ+g(v'').
author:
- first_name: Arno
full_name: Ehresmann, Arno
last_name: Ehresmann
- first_name: Lutz
full_name: Werner, Lutz
last_name: Werner
- first_name: Stefan
full_name: Klumpp, Stefan
last_name: Klumpp
- first_name: S
full_name: Lucht, S
last_name: Lucht
- first_name: Hans
full_name: Schmoranzer, Hans P
last_name: Schmoranzer
- first_name: Sascha
full_name: Mickat, Sascha
last_name: Mickat
- first_name: Rüdiger
full_name: Schill, Rüdiger H
last_name: Schill
- first_name: Karl
full_name: Schartner, Karl H
last_name: Schartner
- first_name: Philipp
full_name: Demekhin, Philipp
last_name: Demekhin
- first_name: Mikhail
full_name: Mikhail Lemeshko
id: 37CB05FA-F248-11E8-B48F-1D18A9856A87
last_name: Lemeshko
orcid: 0000-0002-6990-7802
- first_name: Victor
full_name: Sukhorukov, Victor L
last_name: Sukhorukov
citation:
ama: 'Ehresmann A, Werner L, Klumpp S, et al. Studying the N+2(C2Σ+u → X2Σ+g) fluorescence
excited via the 1s−1π* resonance. *Journal of Physics B: Atomic, Molecular and
Optical Physics*. 2006;39(2):283-304. doi:10.1088/0953-4075/39/2/006'
apa: 'Ehresmann, A., Werner, L., Klumpp, S., Lucht, S., Schmoranzer, H., Mickat,
S., … Sukhorukov, V. (2006). Studying the N+2(C2Σ+u → X2Σ+g) fluorescence excited
via the 1s−1π* resonance. *Journal of Physics B: Atomic, Molecular and Optical
Physics*, *39*(2), 283–304. https://doi.org/10.1088/0953-4075/39/2/006'
chicago: 'Ehresmann, Arno, Lutz Werner, Stefan Klumpp, S Lucht, Hans Schmoranzer,
Sascha Mickat, Rüdiger Schill, et al. “Studying the N+2(C2Σ+u → X2Σ+g) Fluorescence
Excited via the 1s−1π* Resonance.” *Journal of Physics B: Atomic, Molecular
and Optical Physics* 39, no. 2 (2006): 283–304. https://doi.org/10.1088/0953-4075/39/2/006.'
ieee: 'A. Ehresmann *et al.*, “Studying the N+2(C2Σ+u → X2Σ+g) fluorescence
excited via the 1s−1π* resonance,” *Journal of Physics B: Atomic, Molecular
and Optical Physics*, vol. 39, no. 2, pp. 283–304, 2006.'
ista: 'Ehresmann A, Werner L, Klumpp S, Lucht S, Schmoranzer H, Mickat S, Schill
R, Schartner K, Demekhin P, Lemeshko M, Sukhorukov V. 2006. Studying the N+2(C2Σ+u
→ X2Σ+g) fluorescence excited via the 1s−1π* resonance. Journal of Physics B:
Atomic, Molecular and Optical Physics. 39(2), 283–304.'
mla: 'Ehresmann, Arno, et al. “Studying the N+2(C2Σ+u → X2Σ+g) Fluorescence Excited
via the 1s−1π* Resonance.” *Journal of Physics B: Atomic, Molecular and Optical
Physics*, vol. 39, no. 2, IOP Publishing Ltd., 2006, pp. 283–304, doi:10.1088/0953-4075/39/2/006.'
short: 'A. Ehresmann, L. Werner, S. Klumpp, S. Lucht, H. Schmoranzer, S. Mickat,
R. Schill, K. Schartner, P. Demekhin, M. Lemeshko, V. Sukhorukov, Journal of Physics
B: Atomic, Molecular and Optical Physics 39 (2006) 283–304.'
date_created: 2018-12-11T11:55:57Z
date_published: 2006-01-28T00:00:00Z
date_updated: 2020-07-14T12:45:29Z
day: '28'
doi: 10.1088/0953-4075/39/2/006
extern: 1
intvolume: ' 39'
issue: '2'
month: '01'
page: 283 - 304
publication: 'Journal of Physics B: Atomic, Molecular and Optical Physics'
publication_status: published
publisher: IOP Publishing Ltd.
publist_id: '4882'
quality_controlled: 0
status: public
title: Studying the N+2(C2Σ+u → X2Σ+g) fluorescence excited via the 1s−1π* resonance
type: journal_article
volume: 39
year: '2006'
...
---
_id: '2144'
abstract:
- lang: eng
text: 'Temperature dependent preedge and extended x-ray absorption fine structure
measurements at the Zr K edge for the perovskite-type zirconates Pb Zr0.515 Ti0.485
O3 (PZT), PbZr O3 (PZ), and BaZr O3 are performed. To carry out a more accurate
study of the weak reconstruction of the local atomic structure we employed a combination
of two techniques: (i) analysis of the preedge fine structure, and (ii) analysis
of the Fourier transform of the difference between χ (k) functions obtained at
different temperatures. A detailed investigation of local atomic structure in
the cubic phase for all the crystals is also performed. It is shown that neither
the displacive nor the order-disorder model can describe correctly the changes
of local atomic structure during phase transitions in PZ and PZT. A spherical
model describing the local atomic structure of perovskite-type crystals suffering
structural phase transitions is proposed.'
acknowledgement: The studies were supported by the Russian Ministry of Science and
Education Grant No. R662. E.N. acknowledges partial support from the French Government
*CNOUS.
author:
- first_name: Rostislav
full_name: Vedrinskiǐ, Rostislav V
last_name: Vedrinskiǐ
- first_name: Elena
full_name: Nazarenko, Elena S
last_name: Nazarenko
- first_name: Mikhail
full_name: Mikhail Lemeshko
id: 37CB05FA-F248-11E8-B48F-1D18A9856A87
last_name: Lemeshko
orcid: 0000-0002-6990-7802
- first_name: Vivian
full_name: Nassif, Vivian M
last_name: Nassif
- first_name: Olivier
full_name: Proux, Olivier
last_name: Proux
- first_name: Alexander
full_name: Novakovich, Alexander A
last_name: Novakovich
- first_name: Yves
full_name: Joly, Yves
last_name: Joly
citation:
ama: Vedrinskiǐ R, Nazarenko E, Lemeshko M, et al. Temperature dependent XAFS studies
of local atomic structure of the perovskite-type zirconates. *Physical Review
B - Condensed Matter and Materials Physics*. 2006;73(13). doi:10.1103/PhysRevB.73.134109
apa: Vedrinskiǐ, R., Nazarenko, E., Lemeshko, M., Nassif, V., Proux, O., Novakovich,
A., & Joly, Y. (2006). Temperature dependent XAFS studies of local atomic
structure of the perovskite-type zirconates. *Physical Review B - Condensed
Matter and Materials Physics*, *73*(13). https://doi.org/10.1103/PhysRevB.73.134109
chicago: Vedrinskiǐ, Rostislav, Elena Nazarenko, Mikhail Lemeshko, Vivian Nassif,
Olivier Proux, Alexander Novakovich, and Yves Joly. “Temperature Dependent XAFS
Studies of Local Atomic Structure of the Perovskite-Type Zirconates.” *Physical
Review B - Condensed Matter and Materials Physics* 73, no. 13 (2006). https://doi.org/10.1103/PhysRevB.73.134109.
ieee: R. Vedrinskiǐ *et al.*, “Temperature dependent XAFS studies of local
atomic structure of the perovskite-type zirconates,” *Physical Review B - Condensed
Matter and Materials Physics*, vol. 73, no. 13, 2006.
ista: Vedrinskiǐ R, Nazarenko E, Lemeshko M, Nassif V, Proux O, Novakovich A, Joly
Y. 2006. Temperature dependent XAFS studies of local atomic structure of the perovskite-type
zirconates. Physical Review B - Condensed Matter and Materials Physics. 73(13).
mla: Vedrinskiǐ, Rostislav, et al. “Temperature Dependent XAFS Studies of Local
Atomic Structure of the Perovskite-Type Zirconates.” *Physical Review B - Condensed
Matter and Materials Physics*, vol. 73, no. 13, American Physical Society,
2006, doi:10.1103/PhysRevB.73.134109.
short: R. Vedrinskiǐ, E. Nazarenko, M. Lemeshko, V. Nassif, O. Proux, A. Novakovich,
Y. Joly, Physical Review B - Condensed Matter and Materials Physics 73 (2006).
date_created: 2018-12-11T11:55:58Z
date_published: 2006-04-17T00:00:00Z
date_updated: 2020-07-14T12:45:29Z
day: '17'
doi: 10.1103/PhysRevB.73.134109
extern: 1
intvolume: ' 73'
issue: '13'
month: '04'
publication: Physical Review B - Condensed Matter and Materials Physics
publication_status: published
publisher: American Physical Society
publist_id: '4881'
quality_controlled: 0
status: public
title: Temperature dependent XAFS studies of local atomic structure of the perovskite-type
zirconates
type: journal_article
volume: 73
year: '2006'
...
---
_id: '215'
abstract:
- lang: eng
text: For any n≥3, let F ∈ Z[X0,...,Xn ] be a form of degree d *≥5 that defines
a non-singular hypersurface X ⊂ Pn . The main result in this paper is a proof
of the fact that the number N (F ; B) of Q-rational points on X which have height
at most B satisfiesN (F ; B) = Od,ε,n (Bn −1+ε ), for any ε > 0. The implied
constant in this estimate depends at most upon d, ε and n. New estimates are also
obtained for the number of representations of a positive integer as the sum of
three dth powers, and for the paucity of integer solutions to equal sums of like
polynomials.*
author:
- first_name: Timothy D
full_name: Timothy Browning
id: 35827D50-F248-11E8-B48F-1D18A9856A87
last_name: Browning
- first_name: Roger
full_name: Heath-Brown, Roger
last_name: Heath Brown
citation:
ama: Browning TD, Heath Brown R. The density of rational points on non-singular
hypersurfaces, I. *Bulletin of the London Mathematical Society*. 2006;38(3):401-410.
doi:10.1112/S0024609305018412
apa: Browning, T. D., & Heath Brown, R. (2006). The density of rational points
on non-singular hypersurfaces, I. *Bulletin of the London Mathematical Society*,
*38*(3), 401–410. https://doi.org/10.1112/S0024609305018412
chicago: 'Browning, Timothy D, and Roger Heath Brown. “The Density of Rational Points
on Non-Singular Hypersurfaces, I.” *Bulletin of the London Mathematical Society*
38, no. 3 (2006): 401–10. https://doi.org/10.1112/S0024609305018412.'
ieee: T. D. Browning and R. Heath Brown, “The density of rational points on non-singular
hypersurfaces, I,” *Bulletin of the London Mathematical Society*, vol. 38,
no. 3, pp. 401–410, 2006.
ista: Browning TD, Heath Brown R. 2006. The density of rational points on non-singular
hypersurfaces, I. Bulletin of the London Mathematical Society. 38(3), 401–410.
mla: Browning, Timothy D., and Roger Heath Brown. “The Density of Rational Points
on Non-Singular Hypersurfaces, I.” *Bulletin of the London Mathematical Society*,
vol. 38, no. 3, Wiley-Blackwell, 2006, pp. 401–10, doi:10.1112/S0024609305018412.
short: T.D. Browning, R. Heath Brown, Bulletin of the London Mathematical Society
38 (2006) 401–410.
date_created: 2018-12-11T11:45:15Z
date_published: 2006-12-23T00:00:00Z
date_updated: 2019-04-26T07:22:09Z
day: '23'
doi: 10.1112/S0024609305018412
extern: 1
intvolume: ' 38'
issue: '3'
month: '12'
page: 401 - 410
publication: Bulletin of the London Mathematical Society
publication_status: published
publisher: Wiley-Blackwell
publist_id: '7697'
quality_controlled: 0
status: public
title: The density of rational points on non-singular hypersurfaces, I
type: journal_article
volume: 38
year: '2006'
...
---
_id: '216'
abstract:
- lang: eng
text: For any N ≥ 2, let Z ⊂ ℙN be a geometrically integral algebraic variety of
degree d. This article is concerned with the number Nz(B) of ℚ-rational points
on Z which have height at most B. For any ε > 0, we establish the estimate
NZ(B) = O d,ε,N(Bdim Z+ε), provided that d ≥ 6. As indicated, the implied constant
depends at most on d, ε, and N.
author:
- first_name: Timothy D
full_name: Timothy Browning
id: 35827D50-F248-11E8-B48F-1D18A9856A87
last_name: Browning
- first_name: Roger
full_name: Heath-Brown, Roger
last_name: Heath Brown
- first_name: Per
full_name: Salberger, Per
last_name: Salberger
citation:
ama: Browning TD, Heath Brown R, Salberger P. Counting rational points on algebraic
varieties. *Duke Mathematical Journal*. 2006;132(3):545-578. doi:10.1215/S0012-7094-06-13236-2
apa: Browning, T. D., Heath Brown, R., & Salberger, P. (2006). Counting rational
points on algebraic varieties. *Duke Mathematical Journal*, *132*(3),
545–578. https://doi.org/10.1215/S0012-7094-06-13236-2
chicago: 'Browning, Timothy D, Roger Heath Brown, and Per Salberger. “Counting Rational
Points on Algebraic Varieties.” *Duke Mathematical Journal* 132, no. 3 (2006):
545–78. https://doi.org/10.1215/S0012-7094-06-13236-2.'
ieee: T. D. Browning, R. Heath Brown, and P. Salberger, “Counting rational points
on algebraic varieties,” *Duke Mathematical Journal*, vol. 132, no. 3, pp.
545–578, 2006.
ista: Browning TD, Heath Brown R, Salberger P. 2006. Counting rational points on
algebraic varieties. Duke Mathematical Journal. 132(3), 545–578.
mla: Browning, Timothy D., et al. “Counting Rational Points on Algebraic Varieties.”
*Duke Mathematical Journal*, vol. 132, no. 3, Unknown, 2006, pp. 545–78,
doi:10.1215/S0012-7094-06-13236-2.
short: T.D. Browning, R. Heath Brown, P. Salberger, Duke Mathematical Journal 132
(2006) 545–578.
date_created: 2018-12-11T11:45:15Z
date_published: 2006-04-15T00:00:00Z
date_updated: 2019-04-26T07:22:09Z
day: '15'
doi: 10.1215/S0012-7094-06-13236-2
extern: 1
intvolume: ' 132'
issue: '3'
month: '04'
page: 545 - 578
publication: Duke Mathematical Journal
publication_status: published
publisher: Unknown
publist_id: '7696'
quality_controlled: 0
status: public
title: Counting rational points on algebraic varieties
type: journal_article
volume: 132
year: '2006'
...
---
_id: '218'
abstract:
- lang: eng
text: This paper is concerned with the average order of certain arithmetic functions,
as they range over the values taken by binary forms.
author:
- first_name: Régis
full_name: de la Bretèche, Régis
last_name: De La Bretèche
- first_name: Timothy D
full_name: Timothy Browning
id: 35827D50-F248-11E8-B48F-1D18A9856A87
last_name: Browning
citation:
ama: De La Bretèche R, Browning TD. Sums of arithmetic functions over values of
binary forms. *Acta Arithmetica*. 2006;125(3):291-304. doi:10.4064/aa125-3-6
apa: De La Bretèche, R., & Browning, T. D. (2006). Sums of arithmetic functions
over values of binary forms. *Acta Arithmetica*, *125*(3), 291–304.
https://doi.org/10.4064/aa125-3-6
chicago: 'De La Bretèche, Régis, and Timothy D Browning. “Sums of Arithmetic Functions
over Values of Binary Forms.” *Acta Arithmetica* 125, no. 3 (2006): 291–304.
https://doi.org/10.4064/aa125-3-6.'
ieee: R. De La Bretèche and T. D. Browning, “Sums of arithmetic functions over values
of binary forms,” *Acta Arithmetica*, vol. 125, no. 3, pp. 291–304, 2006.
ista: De La Bretèche R, Browning TD. 2006. Sums of arithmetic functions over values
of binary forms. Acta Arithmetica. 125(3), 291–304.
mla: De La Bretèche, Régis, and Timothy D. Browning. “Sums of Arithmetic Functions
over Values of Binary Forms.” *Acta Arithmetica*, vol. 125, no. 3, Instytut
Matematyczny, 2006, pp. 291–304, doi:10.4064/aa125-3-6.
short: R. De La Bretèche, T.D. Browning, Acta Arithmetica 125 (2006) 291–304.
date_created: 2018-12-11T11:45:16Z
date_published: 2006-01-01T00:00:00Z
date_updated: 2019-04-26T07:22:09Z
day: '01'
doi: 10.4064/aa125-3-6
extern: 1
intvolume: ' 125'
issue: '3'
month: '01'
page: 291 - 304
publication: Acta Arithmetica
publication_status: published
publisher: Instytut Matematyczny
publist_id: '7694'
quality_controlled: 0
status: public
title: Sums of arithmetic functions over values of binary forms
type: journal_article
volume: 125
year: '2006'
...
---
_id: '2333'
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
- first_name: Jan
full_name: Solovej, Jan P
last_name: Solovej
citation:
ama: 'Lieb É, Seiringer R, Solovej J. Ground-state energy of a dilute Fermi gas.
In: Vol 412. American Mathematical Society; 2006:239-248. doi:10.1090/conm/412'
apa: Lieb, É., Seiringer, R., & Solovej, J. (2006). Ground-state energy of a
dilute Fermi gas (Vol. 412, pp. 239–248). Presented at the Differential Equations
and Mathematical Physics, American Mathematical Society. https://doi.org/10.1090/conm/412
chicago: Lieb, Élliott, Robert Seiringer, and Jan Solovej. “Ground-State Energy
of a Dilute Fermi Gas,” 412:239–48. American Mathematical Society, 2006. https://doi.org/10.1090/conm/412.
ieee: É. Lieb, R. Seiringer, and J. Solovej, “Ground-state energy of a dilute Fermi
gas,” presented at the Differential Equations and Mathematical Physics, 2006,
vol. 412, pp. 239–248.
ista: Lieb É, Seiringer R, Solovej J. 2006. Ground-state energy of a dilute Fermi
gas. Differential Equations and Mathematical Physics, Contemporary Mathematics,
vol. 412. 239–248.
mla: Lieb, Élliott, et al. *Ground-State Energy of a Dilute Fermi Gas*. Vol.
412, American Mathematical Society, 2006, pp. 239–48, doi:10.1090/conm/412.
short: É. Lieb, R. Seiringer, J. Solovej, in:, American Mathematical Society, 2006,
pp. 239–248.
conference:
name: Differential Equations and Mathematical Physics
date_created: 2018-12-11T11:57:03Z
date_published: 2006-01-01T00:00:00Z
date_updated: 2020-07-14T12:45:39Z
day: '01'
doi: 10.1090/conm/412
extern: 1
intvolume: ' 412'
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/math-ph/0507049
month: '01'
oa: 1
page: 239 - 248
publication_status: published
publisher: American Mathematical Society
publist_id: '4593'
quality_controlled: 0
status: public
title: Ground-state energy of a dilute Fermi gas
type: conference
volume: 412
year: '2006'
...
---
_id: '2334'
author:
- first_name: Robert
full_name: Robert Seiringer
id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
last_name: Seiringer
orcid: 0000-0002-6781-0521
- first_name: Élliott
full_name: Lieb, Élliott H
last_name: Lieb
- first_name: Jakob
full_name: Yngvason, Jakob
last_name: Yngvason
citation:
ama: 'Seiringer R, Lieb É, Yngvason J. One-dimensional behavior of dilute, trapped
Bose gases in traps. In: Zambrini J, ed. World Scientific Publishing; 2006. doi:10.1007/s00220-003-0993-3'
apa: 'Seiringer, R., Lieb, É., & Yngvason, J. (2006). One-dimensional behavior
of dilute, trapped Bose gases in traps. In J. Zambrini (Ed.). Presented at the
ICMP: International Congress on Mathematical Physics, World Scientific Publishing.
https://doi.org/10.1007/s00220-003-0993-3'
chicago: Seiringer, Robert, Élliott Lieb, and Jakob Yngvason. “One-Dimensional Behavior
of Dilute, Trapped Bose Gases in Traps.” edited by Jean Zambrini. World Scientific
Publishing, 2006. https://doi.org/10.1007/s00220-003-0993-3.
ieee: 'R. Seiringer, É. Lieb, and J. Yngvason, “One-dimensional behavior of dilute,
trapped Bose gases in traps,” presented at the ICMP: International Congress on
Mathematical Physics, 2006.'
ista: 'Seiringer R, Lieb É, Yngvason J. 2006. One-dimensional behavior of dilute,
trapped Bose gases in traps. ICMP: International Congress on Mathematical Physics'
mla: Seiringer, Robert, et al. *One-Dimensional Behavior of Dilute, Trapped Bose
Gases in Traps*. Edited by Jean Zambrini, World Scientific Publishing, 2006,
doi:10.1007/s00220-003-0993-3.
short: R. Seiringer, É. Lieb, J. Yngvason, in:, J. Zambrini (Ed.), World Scientific
Publishing, 2006.
conference:
name: 'ICMP: International Congress on Mathematical Physics'
date_created: 2018-12-11T11:57:03Z
date_published: 2006-03-07T00:00:00Z
date_updated: 2020-07-14T12:45:39Z
day: '07'
doi: 10.1007/s00220-003-0993-3
editor:
- first_name: Jean
full_name: Zambrini, Jean-Claude
last_name: Zambrini
extern: 1
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/math-ph/0305025
month: '03'
oa: 1
publication_status: published
publisher: World Scientific Publishing
publist_id: '4592'
quality_controlled: 0
status: public
title: One-dimensional behavior of dilute, trapped Bose gases in traps
type: conference
year: '2006'
...
---
_id: '2363'
abstract:
- lang: eng
text: ' We prove that the Gross-Pitaevskii equation correctly describes the
ground state energy and corresponding one-particle density matrix of rotating,
dilute, trapped Bose gases with repulsive two-body interactions. We also show
that there is 100% Bose-Einstein condensation. While a proof that the GP equation
correctly describes non-rotating or slowly rotating gases was known for some time,
the rapidly rotating case was unclear because the Bose (i.e., symmetric) ground
state is not the lowest eigenstate of the Hamiltonian in this case. We have been
able to overcome this difficulty with the aid of coherent states. Our proof also
conceptually simplifies the previous proof for the slowly rotating case. In the
case of axially symmetric traps, our results show that the appearance of quantized
vortices causes spontaneous symmetry breaking in the ground state. '
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. Derivation of the Gross-Pitaevskii equation for rotating
Bose gases. *Communications in Mathematical Physics*. 2006;264(2):505-537.
doi:10.1007/s00220-006-1524-9
apa: Lieb, É., & Seiringer, R. (2006). Derivation of the Gross-Pitaevskii equation
for rotating Bose gases. *Communications in Mathematical Physics*. Springer.
https://doi.org/10.1007/s00220-006-1524-9
chicago: Lieb, Élliott, and Robert Seiringer. “Derivation of the Gross-Pitaevskii
Equation for Rotating Bose Gases.” *Communications in Mathematical Physics*.
Springer, 2006. https://doi.org/10.1007/s00220-006-1524-9.
ieee: É. Lieb and R. Seiringer, “Derivation of the Gross-Pitaevskii equation for
rotating Bose gases,” *Communications in Mathematical Physics*, vol. 264,
no. 2. Springer, pp. 505–537, 2006.
ista: Lieb É, Seiringer R. 2006. Derivation of the Gross-Pitaevskii equation for
rotating Bose gases. Communications in Mathematical Physics. 264(2), 505–537.
mla: Lieb, Élliott, and Robert Seiringer. “Derivation of the Gross-Pitaevskii Equation
for Rotating Bose Gases.” *Communications in Mathematical Physics*, vol.
264, no. 2, Springer, 2006, pp. 505–37, doi:10.1007/s00220-006-1524-9.
short: É. Lieb, R. Seiringer, Communications in Mathematical Physics 264 (2006)
505–537.
date_created: 2018-12-11T11:57:13Z
date_published: 2006-01-01T00:00:00Z
date_updated: 2020-07-14T12:45:40Z
day: '01'
doi: 10.1007/s00220-006-1524-9
extern: 1
intvolume: ' 264'
issue: '2'
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/math-ph/0504042
month: '01'
oa: 1
page: 505 - 537
publication: Communications in Mathematical Physics
publication_status: published
publisher: Springer
publist_id: '4561'
quality_controlled: 0
status: public
title: Derivation of the Gross-Pitaevskii equation for rotating Bose gases
type: review
volume: 264
year: '2006'
...
---
_id: '2364'
abstract:
- lang: eng
text: We present an inequality that gives a lower bound on the expectation value
of certain two-body interaction potentials in a general state on Fock space in
terms of the corresponding expectation value for thermal equilibrium states of
non-interacting systems and the difference in the free energy. This bound can
be viewed as a rigorous version of first-order perturbation theory for many-body
systems at positive temperature. As an application, we give a proof of the first
two terms in a high density (and high temperature) expansion of the free energy
of jellium with Coulomb interactions, both in the fermionic and bosonic case.
For bosons, our method works above the transition temperature (for the non-interacting
gas) for Bose-Einstein condensation.
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. A correlation estimate for quantum many-body systems at positive
temperature. *Reviews in Mathematical Physics*. 2006;18(3):233-253. doi:10.1142/S0129055X06002632
apa: Seiringer, R. (2006). A correlation estimate for quantum many-body systems
at positive temperature. *Reviews in Mathematical Physics*, *18*(3),
233–253. https://doi.org/10.1142/S0129055X06002632
chicago: 'Seiringer, Robert. “A Correlation Estimate for Quantum Many-Body Systems
at Positive Temperature.” *Reviews in Mathematical Physics* 18, no. 3 (2006):
233–53. https://doi.org/10.1142/S0129055X06002632.'
ieee: R. Seiringer, “A correlation estimate for quantum many-body systems at positive
temperature,” *Reviews in Mathematical Physics*, vol. 18, no. 3, pp. 233–253,
2006.
ista: Seiringer R. 2006. A correlation estimate for quantum many-body systems at
positive temperature. Reviews in Mathematical Physics. 18(3), 233–253.
mla: Seiringer, Robert. “A Correlation Estimate for Quantum Many-Body Systems at
Positive Temperature.” *Reviews in Mathematical Physics*, vol. 18, no. 3,
World Scientific Publishing, 2006, pp. 233–53, doi:10.1142/S0129055X06002632.
short: R. Seiringer, Reviews in Mathematical Physics 18 (2006) 233–253.
date_created: 2018-12-11T11:57:14Z
date_published: 2006-04-01T00:00:00Z
date_updated: 2020-07-14T12:45:40Z
day: '01'
doi: 10.1142/S0129055X06002632
extern: 1
intvolume: ' 18'
issue: '3'
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/math-ph/0601051
month: '04'
oa: 1
page: 233 - 253
publication: Reviews in Mathematical Physics
publication_status: published
publisher: World Scientific Publishing
publist_id: '4562'
quality_controlled: 0
status: public
title: A correlation estimate for quantum many-body systems at positive temperature
type: journal_article
volume: 18
year: '2006'
...
---
_id: '2365'
abstract:
- lang: eng
text: We consider a gas of fermions with non-zero spin at temperature T and chemical
potential μ. We show that if the range of the interparticle interaction is small
compared to the mean particle distance, the thermodynamic pressure differs to
leading order from the corresponding expression for non-interacting particles
by a term proportional to the scattering length of the interparticle interaction.
This is true for any repulsive interaction, including hard cores. The result is
uniform in the temperature as long as T is of the same order as the Fermi temperature,
or smaller.
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. The thermodynamic pressure of a dilute fermi gas. *Communications
in Mathematical Physics*. 2006;261(3):729-757. doi:10.1007/s00220-005-1433-3
apa: Seiringer, R. (2006). The thermodynamic pressure of a dilute fermi gas. *Communications
in Mathematical Physics*, *261*(3), 729–757. https://doi.org/10.1007/s00220-005-1433-3
chicago: 'Seiringer, Robert. “The Thermodynamic Pressure of a Dilute Fermi Gas.”
*Communications in Mathematical Physics* 261, no. 3 (2006): 729–57. https://doi.org/10.1007/s00220-005-1433-3.'
ieee: R. Seiringer, “The thermodynamic pressure of a dilute fermi gas,” *Communications
in Mathematical Physics*, vol. 261, no. 3, pp. 729–757, 2006.
ista: Seiringer R. 2006. The thermodynamic pressure of a dilute fermi gas. Communications
in Mathematical Physics. 261(3), 729–757.
mla: Seiringer, Robert. “The Thermodynamic Pressure of a Dilute Fermi Gas.” *Communications
in Mathematical Physics*, vol. 261, no. 3, Springer, 2006, pp. 729–57, doi:10.1007/s00220-005-1433-3.
short: R. Seiringer, Communications in Mathematical Physics 261 (2006) 729–757.
date_created: 2018-12-11T11:57:14Z
date_published: 2006-02-01T00:00:00Z
date_updated: 2020-07-14T12:45:40Z
day: '01'
doi: 10.1007/s00220-005-1433-3
extern: 1
intvolume: ' 261'
issue: '3'
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/math-ph/0412086
month: '02'
oa: 1
page: 729 - 757
publication: Communications in Mathematical Physics
publication_status: published
publisher: Springer
publist_id: '4563'
quality_controlled: 0
status: public
title: The thermodynamic pressure of a dilute fermi gas
type: journal_article
volume: 261
year: '2006'
...
---
_id: '2366'
abstract:
- lang: eng
text: Inequalities are derived for power sums of the real part and the modulus of
the eigenvalues of a Schrödinger operator with a complex-valued potential.
author:
- first_name: Rupert
full_name: Frank, Rupert L
last_name: Frank
- first_name: Ari
full_name: Laptev, Ari
last_name: Laptev
- 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: Frank R, Laptev A, Lieb É, Seiringer R. Lieb-Thirring inequalities for Schrödinger
operators with complex-valued potentials. *Letters in Mathematical Physics*.
2006;77(3):309-316. doi:10.1007/s11005-006-0095-1
apa: Frank, R., Laptev, A., Lieb, É., & Seiringer, R. (2006). Lieb-Thirring
inequalities for Schrödinger operators with complex-valued potentials. *Letters
in Mathematical Physics*, *77*(3), 309–316. https://doi.org/10.1007/s11005-006-0095-1
chicago: 'Frank, Rupert, Ari Laptev, Élliott Lieb, and Robert Seiringer. “Lieb-Thirring
Inequalities for Schrödinger Operators with Complex-Valued Potentials.” *Letters
in Mathematical Physics* 77, no. 3 (2006): 309–16. https://doi.org/10.1007/s11005-006-0095-1.'
ieee: R. Frank, A. Laptev, É. Lieb, and R. Seiringer, “Lieb-Thirring inequalities
for Schrödinger operators with complex-valued potentials,” *Letters in Mathematical
Physics*, vol. 77, no. 3, pp. 309–316, 2006.
ista: Frank R, Laptev A, Lieb É, Seiringer R. 2006. Lieb-Thirring inequalities for
Schrödinger operators with complex-valued potentials. Letters in Mathematical
Physics. 77(3), 309–316.
mla: Frank, Rupert, et al. “Lieb-Thirring Inequalities for Schrödinger Operators
with Complex-Valued Potentials.” *Letters in Mathematical Physics*, vol.
77, no. 3, Springer, 2006, pp. 309–16, doi:10.1007/s11005-006-0095-1.
short: R. Frank, A. Laptev, É. Lieb, R. Seiringer, Letters in Mathematical Physics
77 (2006) 309–316.
date_created: 2018-12-11T11:57:15Z
date_published: 2006-09-01T00:00:00Z
date_updated: 2020-07-14T12:45:40Z
day: '01'
doi: 10.1007/s11005-006-0095-1
extern: 1
intvolume: ' 77'
issue: '3'
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/math-ph/0605017
month: '09'
oa: 1
page: 309 - 316
publication: Letters in Mathematical Physics
publication_status: published
publisher: Springer
publist_id: '4560'
quality_controlled: 0
status: public
title: Lieb-Thirring inequalities for Schrödinger operators with complex-valued potentials
type: journal_article
volume: 77
year: '2006'
...
---
_id: '2368'
abstract:
- lang: eng
text: The recent experimental success in creating Bose-Einstein condensates of alkali
atoms, honored by the Nobel prize awards in 2001 [1,5], led to renewed interest
in the mathematical description of interacting Bose gases.
alternative_title:
- LNP
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. Dilute, trapped Bose gases and Bose-Einstein condensation. In:
Dereziński J, Siedentop H, eds. *Large Coulomb Systems*. Vol 695. Springer;
2006:249-274. doi:10.1007/3-540-32579-4_6'
apa: Seiringer, R. (2006). Dilute, trapped Bose gases and Bose-Einstein condensation.
In J. Dereziński & H. Siedentop (Eds.), *Large Coulomb Systems* (Vol.
695, pp. 249–274). Springer. https://doi.org/10.1007/3-540-32579-4_6
chicago: Seiringer, Robert. “Dilute, Trapped Bose Gases and Bose-Einstein Condensation.”
In *Large Coulomb Systems*, edited by Jan Dereziński and Heinz Siedentop,
695:249–74. Springer, 2006. https://doi.org/10.1007/3-540-32579-4_6.
ieee: R. Seiringer, “Dilute, trapped Bose gases and Bose-Einstein condensation,”
in *Large Coulomb Systems*, vol. 695, J. Dereziński and H. Siedentop, Eds.
Springer, 2006, pp. 249–274.
ista: Seiringer R. 2006. Dilute, trapped Bose gases and Bose-Einstein condensation.
Large Coulomb Systems. , LNP, vol. 695. 249–274.
mla: Seiringer, Robert. “Dilute, Trapped Bose Gases and Bose-Einstein Condensation.”
*Large Coulomb Systems*, edited by Jan Dereziński and Heinz Siedentop, vol.
695, Springer, 2006, pp. 249–74, doi:10.1007/3-540-32579-4_6.
short: R. Seiringer, in:, J. Dereziński, H. Siedentop (Eds.), Large Coulomb Systems,
Springer, 2006, pp. 249–274.
date_created: 2018-12-11T11:57:15Z
date_published: 2006-01-01T00:00:00Z
date_updated: 2020-07-14T12:45:40Z
day: '01'
doi: 10.1007/3-540-32579-4_6
editor:
- first_name: Jan
full_name: Dereziński, Jan
last_name: Dereziński
- first_name: Heinz
full_name: Siedentop, Heinz
last_name: Siedentop
extern: 1
intvolume: ' 695'
month: '01'
page: 249 - 274
publication: Large Coulomb Systems
publication_status: published
publisher: Springer
publist_id: '4558'
quality_controlled: 0
status: public
title: Dilute, trapped Bose gases and Bose-Einstein condensation
type: book_chapter
volume: 695
year: '2006'
...
---
_id: '2369'
abstract:
- lang: eng
text: One of the most remarkable recent developments in the study of ultracold Bose
gases is the observation of a reversible transition from a Bose Einstein condensate
to a state composed of localized atoms as the strength of a periodic, optical
trapping potential is varied. In [1] a model of this phenomenon has been analyzed
rigorously. The gas is a hard core lattice gas and the optical lattice is modeled
by a periodic potential of strength λ. For small λ and temperature Bose- Einstein
condensation (BEC) is proved to occur, while at large λ BEC disappears, even in
the ground state, which is a Mott-insulator state with a characteristic gap. The
inter-particle interaction is essential for this effect. This contribution gives
a pedagogical survey of these results.
alternative_title:
- LNP
author:
- first_name: Michael
full_name: Aizenman, Michael
last_name: Aizenman
- 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: Jan
full_name: Solovej, Jan P
last_name: Solovej
- first_name: Jakob
full_name: Yngvason, Jakob
last_name: Yngvason
citation:
ama: 'Aizenman M, Lieb É, Seiringer R, Solovej J, Yngvason J. Bose-Einstein condensation
as a quantum phase transition in an optical lattice. In: Asch J, Joye A, eds.
*Mathematical Physics of Quantum Mechanics*. Vol 690. Springer; 2006:199-215.
doi:10.1007/b11573432'
apa: Aizenman, M., Lieb, É., Seiringer, R., Solovej, J., & Yngvason, J. (2006).
Bose-Einstein condensation as a quantum phase transition in an optical lattice.
In J. Asch & A. Joye (Eds.), *Mathematical Physics of Quantum Mechanics*
(Vol. 690, pp. 199–215). Springer. https://doi.org/10.1007/b11573432
chicago: Aizenman, Michael, Élliott Lieb, Robert Seiringer, Jan Solovej, and Jakob
Yngvason. “Bose-Einstein Condensation as a Quantum Phase Transition in an Optical
Lattice.” In *Mathematical Physics of Quantum Mechanics*, edited by Joachim
Asch and Alain Joye, 690:199–215. Springer, 2006. https://doi.org/10.1007/b11573432.
ieee: M. Aizenman, É. Lieb, R. Seiringer, J. Solovej, and J. Yngvason, “Bose-Einstein
condensation as a quantum phase transition in an optical lattice,” in *Mathematical
Physics of Quantum Mechanics*, vol. 690, J. Asch and A. Joye, Eds. Springer,
2006, pp. 199–215.
ista: Aizenman M, Lieb É, Seiringer R, Solovej J, Yngvason J. 2006. Bose-Einstein
condensation as a quantum phase transition in an optical lattice. Mathematical
Physics of Quantum Mechanics. , LNP, vol. 690. 199–215.
mla: Aizenman, Michael, et al. “Bose-Einstein Condensation as a Quantum Phase Transition
in an Optical Lattice.” *Mathematical Physics of Quantum Mechanics*, edited
by Joachim Asch and Alain Joye, vol. 690, Springer, 2006, pp. 199–215, doi:10.1007/b11573432.
short: M. Aizenman, É. Lieb, R. Seiringer, J. Solovej, J. Yngvason, in:, J. Asch,
A. Joye (Eds.), Mathematical Physics of Quantum Mechanics, Springer, 2006, pp.
199–215.
date_created: 2018-12-11T11:57:16Z
date_published: 2006-01-01T00:00:00Z
date_updated: 2020-07-14T12:45:40Z
day: '01'
doi: 10.1007/b11573432
editor:
- first_name: Joachim
full_name: Asch, Joachim
last_name: Asch
- first_name: Alain
full_name: Joye, Alain
last_name: Joye
extern: 1
intvolume: ' 690'
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/cond-mat/0412034
month: '01'
oa: 1
page: 199 - 215
publication: Mathematical Physics of Quantum Mechanics
publication_status: published
publisher: Springer
publist_id: '4559'
quality_controlled: 0
status: public
title: Bose-Einstein condensation as a quantum phase transition in an optical lattice
type: book_chapter
volume: 690
year: '2006'
...
---
_id: '2416'
alternative_title:
- Algorithms and Combinatorics
author:
- first_name: Jørgen
full_name: Bang-Jensen, Jørgen
last_name: Bang Jensen
- first_name: Bruce
full_name: Reed, Bruce
last_name: Reed
- first_name: Bruce
full_name: Schacht, Bruce
last_name: Schacht
- first_name: Robert
full_name: Šámal, Robert
last_name: Šámal
- first_name: Bjarne
full_name: Toft, Bjarne
last_name: Toft
- first_name: Uli
full_name: Uli Wagner
id: 36690CA2-F248-11E8-B48F-1D18A9856A87
last_name: Wagner
orcid: 0000-0002-1494-0568
citation:
ama: 'Bang Jensen J, Reed B, Schacht B, Šámal R, Toft B, Wagner U. On six problems
posed by Jarik Nešetřil. In: *Topics in Discrete Mathematics*. Vol 26. Springer;
2006:613-627. doi:10.1007/3-540-33700-8_30'
apa: Bang Jensen, J., Reed, B., Schacht, B., Šámal, R., Toft, B., & Wagner,
U. (2006). On six problems posed by Jarik Nešetřil. In *Topics in Discrete Mathematics*
(Vol. 26, pp. 613–627). Springer. https://doi.org/10.1007/3-540-33700-8_30
chicago: Bang Jensen, Jørgen, Bruce Reed, Bruce Schacht, Robert Šámal, Bjarne Toft,
and Uli Wagner. “On Six Problems Posed by Jarik Nešetřil.” In *Topics in Discrete
Mathematics*, 26:613–27. Springer, 2006. https://doi.org/10.1007/3-540-33700-8_30.
ieee: J. Bang Jensen, B. Reed, B. Schacht, R. Šámal, B. Toft, and U. Wagner, “On
six problems posed by Jarik Nešetřil,” in *Topics in Discrete Mathematics*,
vol. 26, Springer, 2006, pp. 613–627.
ista: Bang Jensen J, Reed B, Schacht B, Šámal R, Toft B, Wagner U. 2006. On six
problems posed by Jarik Nešetřil. Topics in Discrete Mathematics. , Algorithms
and Combinatorics, vol. 26. 613–627.
mla: Bang Jensen, Jørgen, et al. “On Six Problems Posed by Jarik Nešetřil.” *Topics
in Discrete Mathematics*, vol. 26, Springer, 2006, pp. 613–27, doi:10.1007/3-540-33700-8_30.
short: J. Bang Jensen, B. Reed, B. Schacht, R. Šámal, B. Toft, U. Wagner, in:, Topics
in Discrete Mathematics, Springer, 2006, pp. 613–627.
date_created: 2018-12-11T11:57:32Z
date_published: 2006-01-01T00:00:00Z
date_updated: 2019-04-26T07:22:12Z
day: '01'
doi: 10.1007/3-540-33700-8_30
extern: 1
intvolume: ' 26'
month: '01'
page: 613 - 627
publication: Topics in Discrete Mathematics
publication_status: published
publisher: Springer
publist_id: '4509'
quality_controlled: 0
status: public
title: On six problems posed by Jarik Nešetřil
type: book_chapter
volume: 26
year: '2006'
...
---
_id: '2429'
abstract:
- lang: eng
text: 'We show, with an elementary proof, that the number of halving simplices in
a set of n points in 4 in general position is O(n4-2/45). This improves the previous
bound of O(n4-1/134). Our main new ingredient is a bound on the maximum number
of halving simplices intersecting a fixed 2-plane. '
author:
- first_name: Jiří
full_name: Matoušek, Jiří
last_name: Matoušek
- first_name: Micha
full_name: Sharir, Micha
last_name: Sharir
- first_name: Shakhar
full_name: Smorodinsky, Shakhar
last_name: Smorodinsky
- first_name: Uli
full_name: Uli Wagner
id: 36690CA2-F248-11E8-B48F-1D18A9856A87
last_name: Wagner
orcid: 0000-0002-1494-0568
citation:
ama: Matoušek J, Sharir M, Smorodinsky S, Wagner U. K-sets in four dimensions. *Discrete
& Computational Geometry*. 2006;35(2):177-191. doi:10.1007/s00454-005-1200-4
apa: Matoušek, J., Sharir, M., Smorodinsky, S., & Wagner, U. (2006). K-sets
in four dimensions. *Discrete & Computational Geometry*, *35*(2),
177–191. https://doi.org/10.1007/s00454-005-1200-4
chicago: 'Matoušek, Jiří, Micha Sharir, Shakhar Smorodinsky, and Uli Wagner. “K-Sets
in Four Dimensions.” *Discrete & Computational Geometry* 35, no. 2 (2006):
177–91. https://doi.org/10.1007/s00454-005-1200-4.'
ieee: J. Matoušek, M. Sharir, S. Smorodinsky, and U. Wagner, “K-sets in four dimensions,”
*Discrete & Computational Geometry*, vol. 35, no. 2, pp. 177–191, 2006.
ista: Matoušek J, Sharir M, Smorodinsky S, Wagner U. 2006. K-sets in four dimensions.
Discrete & Computational Geometry. 35(2), 177–191.
mla: Matoušek, Jiří, et al. “K-Sets in Four Dimensions.” *Discrete & Computational
Geometry*, vol. 35, no. 2, Springer, 2006, pp. 177–91, doi:10.1007/s00454-005-1200-4.
short: J. Matoušek, M. Sharir, S. Smorodinsky, U. Wagner, Discrete & Computational
Geometry 35 (2006) 177–191.
date_created: 2018-12-11T11:57:37Z
date_published: 2006-02-01T00:00:00Z
date_updated: 2019-04-26T07:22:12Z
day: '01'
doi: 10.1007/s00454-005-1200-4
extern: 1
intvolume: ' 35'
issue: '2'
month: '02'
page: 177 - 191
publication: Discrete & Computational Geometry
publication_status: published
publisher: Springer
publist_id: '4495'
quality_controlled: 0
status: public
title: K-sets in four dimensions
type: journal_article
volume: 35
year: '2006'
...
---
_id: '2430'
abstract:
- lang: eng
text: We consider an online version of the conflict-free coloring of a set of points
on the line, where each newly inserted point must be assigned a color upon insertion,
and at all times the coloring has to be conflict-free, in the sense that in every
interval I there is a color that appears exactly once in I. We present deterministic
and randomized algorithms for achieving this goal, and analyze their performance,
that is, the maximum number of colors that they need to use, as a function of
the number n of inserted points. We first show that a natural and simple (deterministic)
approach may perform rather poorly, requiring Ω(√̃) colors in the worst case.
We then derive two efficient variants of this simple algorithm. The first is deterministic
and uses O(log 2 n) colors, and the second is randomized and uses O(log n) colors
with high probability. We also show that the O(log 2 n) bound on the number of
colors used by our deterministic algorithm is tight on the worst case. We also
analyze the performance of the simplest proposed algorithm when the points are
inserted in a random order and present an incomplete analysis that indicates that,
with high probability, it uses only O(log n) colors. Finally, we show that in
the extension of this problem to two dimensions, where the relevant ranges are
disks, n colors may be required in the worst case.
author:
- first_name: Ke
full_name: Chent, Ke
last_name: Chent
- first_name: Amos
full_name: Fiat, Amos
last_name: Fiat
- first_name: Haim
full_name: Kaplan, Haim
last_name: Kaplan
- first_name: Meital
full_name: Levy, Meital B
last_name: Levy
- first_name: Jiří
full_name: Matoušek, Jiří
last_name: Matoušek
- first_name: Elchanan
full_name: Mossel, Elchanan
last_name: Mossel
- first_name: János
full_name: Pach, János
last_name: Pach
- first_name: Micha
full_name: Sharir, Micha
last_name: Sharir
- first_name: Shakhar
full_name: Smorodinsky, Shakhar
last_name: Smorodinsky
- 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: Chent K, Fiat A, Kaplan H, et al. Online conflict-free coloring for intervals.
*SIAM Journal on Computing*. 2006;36(5):1342-1359. doi:10.1137/S0097539704446682
apa: Chent, K., Fiat, A., Kaplan, H., Levy, M., Matoušek, J., Mossel, E., … Welzl,
E. (2006). Online conflict-free coloring for intervals. *SIAM Journal on Computing*,
*36*(5), 1342–1359. https://doi.org/10.1137/S0097539704446682
chicago: 'Chent, Ke, Amos Fiat, Haim Kaplan, Meital Levy, Jiří Matoušek, Elchanan
Mossel, János Pach, et al. “Online Conflict-Free Coloring for Intervals.” *SIAM
Journal on Computing* 36, no. 5 (2006): 1342–59. https://doi.org/10.1137/S0097539704446682.'
ieee: K. Chent *et al.*, “Online conflict-free coloring for intervals,” *SIAM
Journal on Computing*, vol. 36, no. 5, pp. 1342–1359, 2006.
ista: Chent K, Fiat A, Kaplan H, Levy M, Matoušek J, Mossel E, Pach J, Sharir M,
Smorodinsky S, Wagner U, Welzl E. 2006. Online conflict-free coloring for intervals.
SIAM Journal on Computing. 36(5), 1342–1359.
mla: Chent, Ke, et al. “Online Conflict-Free Coloring for Intervals.” *SIAM Journal
on Computing*, vol. 36, no. 5, SIAM, 2006, pp. 1342–59, doi:10.1137/S0097539704446682.
short: K. Chent, A. Fiat, H. Kaplan, M. Levy, J. Matoušek, E. Mossel, J. Pach, M.
Sharir, S. Smorodinsky, U. Wagner, E. Welzl, SIAM Journal on Computing 36 (2006)
1342–1359.
date_created: 2018-12-11T11:57:37Z
date_published: 2006-01-01T00:00:00Z
date_updated: 2019-04-26T07:22:12Z
day: '01'
doi: 10.1137/S0097539704446682
extern: 1
intvolume: ' 36'
issue: '5'
month: '01'
page: 1342 - 1359
publication: SIAM Journal on Computing
publication_status: published
publisher: SIAM
publist_id: '4490'
quality_controlled: 0
status: public
title: Online conflict-free coloring for intervals
type: journal_article
volume: 36
year: '2006'
...
---
_id: '2431'
abstract:
- lang: eng
text: We prove an upper bound, tight up to a factor of 2, for the number of vertices
of level at most t in an arrangement of n halfspaces in R , for arbitrary n and
d (in particular, the dimension d is not considered constant). This partially
settles a conjecture of Eckhoff, Linhart, and Welzl. Up to the factor of 2, the
result generalizes McMullen's Upper Bound Theorem for convex polytopes (the case
ℓ = O) and extends a theorem of Linhart for the case d ≤ 4. Moreover, the bound
sharpens asymptotic estimates obtained by Clarkson and Shor. The proof is based
on the h-matrix of the arrangement (a generalization, introduced by Mulmuley,
of the h-vector of a convex polytope). We show that bounding appropriate sums
of entries of this matrix reduces to a lemma about quadrupels of sets with certain
intersection properties, and we prove this lemma, up to a factor of 2, using tools
from multilinear algebra. This extends an approach of Alon and Kalai, who used
linear algebra methods for an alternative proof of the classical Upper Bound Theorem.
The bounds for the entries of the h-matrix also imply bounds for the number of
i-dimensional faces, i > 0, at level at most ℓ. Furthermore, we discuss a connection
with crossing numbers of graphs that was one of the main motivations for investigating
exact bounds that are valid for arbitrary dimensions.
alternative_title:
- IEEE Conference Proceedings
author:
- first_name: Uli
full_name: Uli Wagner
id: 36690CA2-F248-11E8-B48F-1D18A9856A87
last_name: Wagner
orcid: 0000-0002-1494-0568
citation:
ama: 'Wagner U. On a geometric generalization of the Upper Bound Theorem. In: IEEE;
2006:635-645. doi:10.1109/FOCS.2006.53'
apa: 'Wagner, U. (2006). On a geometric generalization of the Upper Bound Theorem
(pp. 635–645). Presented at the FOCS: Foundations of Computer Science, IEEE. https://doi.org/10.1109/FOCS.2006.53'
chicago: Wagner, Uli. “On a Geometric Generalization of the Upper Bound Theorem,”
635–45. IEEE, 2006. https://doi.org/10.1109/FOCS.2006.53.
ieee: 'U. Wagner, “On a geometric generalization of the Upper Bound Theorem,” presented
at the FOCS: Foundations of Computer Science, 2006, pp. 635–645.'
ista: 'Wagner U. 2006. On a geometric generalization of the Upper Bound Theorem.
FOCS: Foundations of Computer Science, IEEE Conference Proceedings, 635–645.'
mla: Wagner, Uli. *On a Geometric Generalization of the Upper Bound Theorem*.
IEEE, 2006, pp. 635–45, doi:10.1109/FOCS.2006.53.
short: U. Wagner, in:, IEEE, 2006, pp. 635–645.
conference:
name: 'FOCS: Foundations of Computer Science'
date_created: 2018-12-11T11:57:37Z
date_published: 2006-06-08T00:00:00Z
date_updated: 2019-04-26T07:22:12Z
day: '08'
doi: 10.1109/FOCS.2006.53
extern: 1
month: '06'
page: 635 - 645
publication_status: published
publisher: IEEE
publist_id: '4489'
quality_controlled: 0
status: public
title: On a geometric generalization of the Upper Bound Theorem
type: conference
year: '2006'
...
---
_id: '7326'
abstract:
- lang: eng
text: 'Often the properties of a single cell are considered as representative for
a complete polymer electrolyte fuel cell stack or even a fuel cell system. In
some cases this comes close, however, in many real cases differences on several
scales become important. Cell interaction phenomena in fuel cell stacks that arise
from inequalities between adjacent cells are investigated in detail experimentally.
For that, a specialized 2-cell stack with advanced localized diagnostics was developed.
The results show that inequalities propagate by electrical coupling, inhomogeneous
cell polarization and inducing in-plane current in the common bipolar plate. The
effects of the different loss-mechanisms are analyzed and quantified. '
article_processing_charge: No
author:
- first_name: Felix N.
full_name: Büchi, Felix N.
last_name: Büchi
- first_name: Stefan Alexander
full_name: Freunberger, Stefan Alexander
id: A8CA28E6-CE23-11E9-AD2D-EC27E6697425
last_name: Freunberger
orcid: 0000-0003-2902-5319
- first_name: Marco
full_name: Santis, Marco
last_name: Santis
citation:
ama: 'Büchi FN, Freunberger SA, Santis M. What is learned beyond the scale of single
cells? In: *ECS Transactions*. Vol 3. ECS; 2006:963-968. doi:10.1149/1.2356215'
apa: 'Büchi, F. N., Freunberger, S. A., & Santis, M. (2006). What is learned
beyond the scale of single cells? In *ECS Transactions* (Vol. 3, pp. 963–968).
Cancun, Mexico: ECS. https://doi.org/10.1149/1.2356215'
chicago: Büchi, Felix N., Stefan Alexander Freunberger, and Marco Santis. “What
Is Learned beyond the Scale of Single Cells?” In *ECS Transactions*, 3:963–68.
ECS, 2006. https://doi.org/10.1149/1.2356215.
ieee: F. N. Büchi, S. A. Freunberger, and M. Santis, “What is learned beyond the
scale of single cells?,” in *ECS Transactions*, Cancun, Mexico, 2006, vol.
3, no. 1, pp. 963–968.
ista: Büchi FN, Freunberger SA, Santis M. 2006. What is learned beyond the scale
of single cells? ECS Transactions. ECS Meeting vol. 3. 963–968.
mla: Büchi, Felix N., et al. “What Is Learned beyond the Scale of Single Cells?”
*ECS Transactions*, vol. 3, no. 1, ECS, 2006, pp. 963–68, doi:10.1149/1.2356215.
short: F.N. Büchi, S.A. Freunberger, M. Santis, in:, ECS Transactions, ECS, 2006,
pp. 963–968.
conference:
end_date: 2006-11-03
location: Cancun, Mexico
name: ECS Meeting
start_date: 2006-10-29
date_created: 2020-01-15T12:22:44Z
date_published: 2006-11-03T00:00:00Z
date_updated: 2020-01-26T15:46:17Z
day: '03'
doi: 10.1149/1.2356215
extern: '1'
intvolume: ' 3'
issue: '1'
language:
- iso: eng
month: '11'
oa_version: None
page: 963-968
publication: ECS Transactions
publication_status: published
publisher: ECS
quality_controlled: '1'
status: public
title: What is learned beyond the scale of single cells?
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 3
year: '2006'
...