--- _id: '2090' author: - first_name: Bernd full_name: Bernd Bickel id: 49876194-F248-11E8-B48F-1D18A9856A87 last_name: Bickel orcid: 0000-0001-6511-9385 - first_name: Tim full_name: Weyrich, Tim last_name: Weyrich - first_name: Wojciech full_name: Matusik, Wojciech last_name: Matusik - first_name: Hanspeter full_name: Pfister, Hanspeter last_name: Pfister - first_name: Craig full_name: Donner, Craig last_name: Donner - first_name: Chien full_name: Tu, Chien last_name: Tu - first_name: Janet full_name: McAndless, Janet M last_name: Mcandless - first_name: Jinho full_name: Lee, Jinho last_name: Lee - first_name: Addy full_name: Ngan, Addy last_name: Ngan - first_name: Henrik full_name: Jensen, Henrik W last_name: Jensen - first_name: Markus full_name: Groß, Markus S last_name: Groß citation: ama: 'Bickel B, Weyrich T, Matusik W, et al. Processing and editing of faces using a measurement-based skin reflectance model. In: ACM; 2006. doi:10.1145/1179849.1180059' apa: 'Bickel, B., Weyrich, T., Matusik, W., Pfister, H., Donner, C., Tu, C., … Groß, M. (2006). Processing and editing of faces using a measurement-based skin reflectance model. Presented at the SIGGRAPH: Special Interest Group on Computer Graphics and Interactive Techniques, ACM. https://doi.org/10.1145/1179849.1180059' chicago: Bickel, Bernd, Tim Weyrich, Wojciech Matusik, Hanspeter Pfister, Craig Donner, Chien Tu, Janet Mcandless, et al. “Processing and Editing of Faces Using a Measurement-Based Skin Reflectance Model.” ACM, 2006. https://doi.org/10.1145/1179849.1180059. ieee: 'B. Bickel et al., “Processing and editing of faces using a measurement-based skin reflectance model,” presented at the SIGGRAPH: Special Interest Group on Computer Graphics and Interactive Techniques, 2006.' ista: 'Bickel B, Weyrich T, Matusik W, Pfister H, Donner C, Tu C, Mcandless J, Lee J, Ngan A, Jensen H, Groß M. 2006. Processing and editing of faces using a measurement-based skin reflectance model. SIGGRAPH: Special Interest Group on Computer Graphics and Interactive Techniques.' mla: Bickel, Bernd, et al. Processing and Editing of Faces Using a Measurement-Based Skin Reflectance Model. ACM, 2006, doi:10.1145/1179849.1180059. short: B. Bickel, T. Weyrich, W. Matusik, H. Pfister, C. Donner, C. Tu, J. Mcandless, J. Lee, A. Ngan, H. Jensen, M. Groß, in:, ACM, 2006. conference: name: 'SIGGRAPH: Special Interest Group on Computer Graphics and Interactive Techniques' date_created: 2018-12-11T11:55:39Z date_published: 2006-07-01T00:00:00Z date_updated: 2021-01-12T06:55:15Z day: '01' doi: 10.1145/1179849.1180059 extern: 1 month: '07' publication_status: published publisher: ACM publist_id: '4945' quality_controlled: 0 status: public title: Processing and editing of faces using a measurement-based skin reflectance model type: conference 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: '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: '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: '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: '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' ... --- _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 orcid: 0000-0002-8314-0177 - 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. Unknown. 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. Unknown, 2006. 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. Unknown, 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: 2021-01-12T06:55:41Z 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 orcid: 0000-0002-8314-0177 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. Instytut Matematyczny. 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. Instytut Matematyczny, 2006. 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. Instytut Matematyczny, 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: 2021-01-12T06:55:49Z 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: 2021-01-12T06:56:51Z 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: 2021-01-12T06:56:51Z 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. World Scientific Publishing. https://doi.org/10.1142/S0129055X06002632 chicago: Seiringer, Robert. “A Correlation Estimate for Quantum Many-Body Systems at Positive Temperature.” Reviews in Mathematical Physics. World Scientific Publishing, 2006. 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. World Scientific Publishing, 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: 2021-01-12T06:57:02Z 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. Springer. https://doi.org/10.1007/s00220-005-1433-3 chicago: Seiringer, Robert. “The Thermodynamic Pressure of a Dilute Fermi Gas.” Communications in Mathematical Physics. Springer, 2006. 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. Springer, 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: 2021-01-12T06:57:02Z 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. Springer. 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. Springer, 2006. 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. Springer, 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: 2021-01-12T06:57:03Z 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. In: 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: 2021-01-12T06:57:03Z 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. In: 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: 2021-01-12T06:57:04Z 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. In: 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: 2021-01-12T06:57:21Z 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: '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. SIAM. 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. SIAM, 2006. 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. SIAM, 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: 2021-01-12T06:57:26Z 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: 2021-01-12T06:57:27Z 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: '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. Springer. 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. Springer, 2006. 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. Springer, 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: 2021-01-12T06:57:26Z 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' ...