---
_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
orcid: 0000-0002-8314-0177
- 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*. John Wiley and Sons Ltd. 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*. John Wiley and Sons Ltd, 2006. 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. John Wiley and Sons Ltd, 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: 2021-01-12T06:55:29Z
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*. IOP Publishing
Ltd. 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*.
IOP Publishing Ltd., 2006. 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. IOP Publishing Ltd., 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: 2021-01-12T06:55:31Z
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*. IOP Publishing Ltd. 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*. IOP Publishing Ltd., 2006. 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. IOP Publishing Ltd., 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: 2021-01-12T06:55:34Z
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*. American Physical Society. 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*. American Physical Society,
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. American Physical Society,
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: 2021-01-12T06:55:34Z
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
orcid: 0000-0002-8314-0177
- 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*.
Wiley-Blackwell. 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*.
Wiley-Blackwell, 2006. 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. Wiley-Blackwell, 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: 2021-01-12T06:55:36Z
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'
...