--- _id: '217' abstract: - lang: eng text: We show that the number of nontrivial rational points of height at most B, which lie on the cubic surface x1 x2 x3 = x4 (x1 + x2 + x3)2, has order of magnitude B (log B)6. This agrees with Manin's conjecture. acknowledgement: EPSRC 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 citation: ama: Browning TD. The density of rational points on a certain singular cubic surface. Journal of Number Theory. 2005;119(2):242-283. doi:10.1016/j.jnt.2005.11.007 apa: Browning, T. D. (2005). The density of rational points on a certain singular cubic surface. Journal of Number Theory. Elsevier. https://doi.org/10.1016/j.jnt.2005.11.007 chicago: Browning, Timothy D. “The Density of Rational Points on a Certain Singular Cubic Surface.” Journal of Number Theory. Elsevier, 2005. https://doi.org/10.1016/j.jnt.2005.11.007. ieee: T. D. Browning, “The density of rational points on a certain singular cubic surface,” Journal of Number Theory, vol. 119, no. 2. Elsevier, pp. 242–283, 2005. ista: Browning TD. 2005. The density of rational points on a certain singular cubic surface. Journal of Number Theory. 119(2), 242–283. mla: Browning, Timothy D. “The Density of Rational Points on a Certain Singular Cubic Surface.” Journal of Number Theory, vol. 119, no. 2, Elsevier, 2005, pp. 242–83, doi:10.1016/j.jnt.2005.11.007. short: T.D. Browning, Journal of Number Theory 119 (2005) 242–283. date_created: 2018-12-11T11:45:16Z date_published: 2005-12-27T00:00:00Z date_updated: 2021-01-12T06:55:45Z day: '27' doi: 10.1016/j.jnt.2005.11.007 extern: 1 intvolume: ' 119' issue: '2' month: '12' page: 242 - 283 publication: Journal of Number Theory publication_status: published publisher: Elsevier publist_id: '7695' quality_controlled: 0 status: public title: The density of rational points on a certain singular cubic surface type: journal_article volume: 119 year: '2005' ... --- _id: '2307' abstract: - lang: eng text: The human norepinephrine (NE) transporter (hNET) attenuates neuronal signaling by rapid NE clearance from the synaptic cleft, and NET is a target for cocaine and amphetamines as well as therapeutics for depression, obsessive-compulsive disorder, and post-traumatic stress disorder. In spite of its central importance in the nervous system, little is known about how NET substrates, such as NE, 1-methyl-4-tetrahydropyridinium (MPP+), or amphetamine, interact with NET at the molecular level. Nor do we understand the mechanisms behind the transport rate. Previously we introduced a fluorescent substrate similar to MPP+, which allowed separate and simultaneous binding and transport measurement (Schwartz, J. W., Blakely, R. D., and DeFelice, L. J. (2003) J. Biol. Chem. 278, 9768-9777). Here we use this substrate, 4-(4-(dimethylamino)styrl)-N-methyl-pyridinium (ASP+), in combination with green fluorescent protein-tagged hNETs to measure substrate-transporter stoichiometry and substrate binding kinetics. Calibrated confocal microscopy and fluorescence correlation spectroscopy reveal that hNETs, which are homo-multimers, bind one substrate molecule per transporter subunit. Substrate residence at the transporter, obtained from rapid on-off kinetics revealed in fluorescence correlation spectroscopy, is 526 μs. Substrate residence obtained by infinite dilution is 1000 times slower. This novel examination of substrate-transporter kinetics indicates that a single ASP + molecule binds and unbinds thousands of times before being transported or ultimately dissociated from hNET. Calibrated fluorescent images combined with mass spectroscopy give a transport rate of 0.06 ASP +/hNET-protein/s, thus 36,000 on-off binding events (and 36 actual departures) occur for one transport event. Therefore binding has a low probability of resulting in transport. We interpret these data to mean that inefficient binding could contribute to slow transport rates. author: - first_name: Joel full_name: Schwartz, Joel W last_name: Schwartz - first_name: Gaia full_name: Gaia Novarino id: 3E57A680-F248-11E8-B48F-1D18A9856A87 last_name: Novarino orcid: 0000-0002-7673-7178 - first_name: David full_name: Piston, David W last_name: Piston - first_name: Louis full_name: DeFelice, Louis J last_name: Defelice citation: ama: Schwartz J, Novarino G, Piston D, Defelice L. Substrate binding stoichiometry and kinetics of the norepinephrine transporter. Journal of Biological Chemistry. 2005;280(19):19177-19184. doi:10.1074/jbc.M412923200 apa: Schwartz, J., Novarino, G., Piston, D., & Defelice, L. (2005). Substrate binding stoichiometry and kinetics of the norepinephrine transporter. Journal of Biological Chemistry. American Society for Biochemistry and Molecular Biology. https://doi.org/10.1074/jbc.M412923200 chicago: Schwartz, Joel, Gaia Novarino, David Piston, and Louis Defelice. “Substrate Binding Stoichiometry and Kinetics of the Norepinephrine Transporter.” Journal of Biological Chemistry. American Society for Biochemistry and Molecular Biology, 2005. https://doi.org/10.1074/jbc.M412923200. ieee: J. Schwartz, G. Novarino, D. Piston, and L. Defelice, “Substrate binding stoichiometry and kinetics of the norepinephrine transporter,” Journal of Biological Chemistry, vol. 280, no. 19. American Society for Biochemistry and Molecular Biology, pp. 19177–19184, 2005. ista: Schwartz J, Novarino G, Piston D, Defelice L. 2005. Substrate binding stoichiometry and kinetics of the norepinephrine transporter. Journal of Biological Chemistry. 280(19), 19177–19184. mla: Schwartz, Joel, et al. “Substrate Binding Stoichiometry and Kinetics of the Norepinephrine Transporter.” Journal of Biological Chemistry, vol. 280, no. 19, American Society for Biochemistry and Molecular Biology, 2005, pp. 19177–84, doi:10.1074/jbc.M412923200. short: J. Schwartz, G. Novarino, D. Piston, L. Defelice, Journal of Biological Chemistry 280 (2005) 19177–19184. date_created: 2018-12-11T11:56:54Z date_published: 2005-05-13T00:00:00Z date_updated: 2021-01-12T06:56:40Z day: '13' doi: 10.1074/jbc.M412923200 extern: 1 intvolume: ' 280' issue: '19' month: '05' page: 19177 - 19184 publication: Journal of Biological Chemistry publication_status: published publisher: American Society for Biochemistry and Molecular Biology publist_id: '4619' quality_controlled: 0 status: public title: Substrate binding stoichiometry and kinetics of the norepinephrine transporter type: journal_article volume: 280 year: '2005' ... --- _id: '2335' abstract: - lang: eng text: This book contains a unique survey of the mathematically rigorous results about the quantum-mechanical many-body problem that have been obtained by the authors in the past seven years. It addresses a topic that is not only rich mathematically, using a large variety of techniques in mathematical analysis, but is also one with strong ties to current experiments on ultra-cold Bose gases and Bose-Einstein condensation. The book provides a pedagogical entry into an active area of ongoing research for both graduate students and researchers. It is an outgrowth of a course given by the authors for graduate students and post-doctoral researchers at the Oberwolfach Research Institute in 2004. The book also provides a coherent summary of the field and a reference for mathematicians and physicists active in research on quantum mechanics. alternative_title: - Oberwolfach Seminars article_processing_charge: No author: - first_name: Élliott full_name: Lieb, Élliott last_name: Lieb - first_name: Robert full_name: Seiringer, Robert id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 - first_name: Jan full_name: Solovej, Jan last_name: Solovej - first_name: Jakob full_name: Yngvason, Jakob last_name: Yngvason citation: ama: 'Lieb É, Seiringer R, Solovej J, Yngvason J. The Mathematics of the Bose Gas and Its Condensation. Vol 34. Basel ; Berlin: Birkhäuser Verlag; 2005. doi:10.1007/b137508' apa: 'Lieb, É., Seiringer, R., Solovej, J., & Yngvason, J. (2005). The Mathematics of the Bose gas and its Condensation (Vol. 34). Basel ; Berlin: Birkhäuser Verlag. https://doi.org/10.1007/b137508' chicago: 'Lieb, Élliott, Robert Seiringer, Jan Solovej, and Jakob Yngvason. The Mathematics of the Bose Gas and Its Condensation. Vol. 34. Basel ; Berlin: Birkhäuser Verlag, 2005. https://doi.org/10.1007/b137508.' ieee: 'É. Lieb, R. Seiringer, J. Solovej, and J. Yngvason, The Mathematics of the Bose gas and its Condensation, vol. 34. Basel ; Berlin: Birkhäuser Verlag, 2005.' ista: 'Lieb É, Seiringer R, Solovej J, Yngvason J. 2005. The Mathematics of the Bose gas and its Condensation, Basel ; Berlin: Birkhäuser Verlag, VIII, 203p.' mla: Lieb, Élliott, et al. The Mathematics of the Bose Gas and Its Condensation. Vol. 34, Birkhäuser Verlag, 2005, doi:10.1007/b137508. short: É. Lieb, R. Seiringer, J. Solovej, J. Yngvason, The Mathematics of the Bose Gas and Its Condensation, Birkhäuser Verlag, Basel ; Berlin, 2005. date_created: 2018-12-11T11:57:03Z date_published: 2005-01-01T00:00:00Z date_updated: 2021-12-22T08:04:00Z day: '01' doi: 10.1007/b137508 extern: '1' external_id: arxiv: - cond-mat/0610117 intvolume: ' 34' language: - iso: eng main_file_link: - open_access: '1' url: http://arxiv.org/abs/cond-mat/0610117 month: '01' oa: 1 oa_version: Preprint page: VIII, 203 place: Basel ; Berlin publication_identifier: isbn: - 978-3-7643-7336-8 publication_status: published publisher: Birkhäuser Verlag publist_id: '4591' quality_controlled: '1' status: public title: The Mathematics of the Bose gas and its Condensation type: book user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9 volume: 34 year: '2005' ... --- _id: '2336' abstract: - lang: eng text: |2- Now that the low temperature properties of quantum-mechanical many-body systems (bosons) at low density, ρ, can be examined experimentally it is appropriate to revisit some of the formulas deduced by many authors 4–5 decades ago, and to explore new regimes not treated before. For systems with repulsive (i.e. positive) interaction potentials the experimental low temperature state and the ground state are effectively synonymous — and this fact is used in all modeling. In such cases, the leading term in the energy/particle is 2πħ2 aρ/m where a is the scattering length of the two-body potential. Owing to the delicate and peculiar nature of bosonic correlations (such as the strange N 7/5 law for charged bosons), four decades of research failed to establish this plausible formula rigorously. The only previous lower bound for the energy was found by Dyson in 1957, but it was 14 times too small. The correct asymptotic formula has been obtained by us and this work will be presented. The reason behind the mathematical difficulties will be emphasized. A different formula, postulated as late as 1971 by Schick, holds in two dimensions and this, too, will be shown to be correct. With the aid of the methodology developed to prove the lower bound for the homogeneous gas, several other problems have been successfully addressed. One is the proof by us that the Gross-Pitaevskii equation correctly describes the ground state in the ‘traps’ actually used in the experiments. For this system it is also possible to prove complete Bose condensation and superfluidity as we have shown. On the frontier of experimental developments is the possibility that a dilute gas in an elongated trap will behave like a one-dimensional system; we have proved this mathematically. Another topic is a proof that Foldy’s 1961 theory of a high density Bose gas of charged particles correctly describes its ground state energy; using this we can also prove the N 7/5 formula for the ground state energy of the two-component charged Bose gas proposed by Dyson in 1967. All of this is quite recent work and it is hoped that the mathematical methodology might be useful, ultimately, to solve more complex problems connected with these interesting systems. alternative_title: - Mathematical Physics Studies 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 - first_name: Jakob full_name: Yngvason, Jakob last_name: Yngvason citation: ama: 'Lieb É, Seiringer R, Solovej J, Yngvason J. The quantum-mechanical many-body problem: The Bose gas. In: Benedicks M, Jones P, Smirnov S, Winckler B, eds. Perspectives in Analysis. Vol 27. Springer; 2005:97-183. doi:10.1007/3-540-30434-7_9' apa: 'Lieb, É., Seiringer, R., Solovej, J., & Yngvason, J. (2005). The quantum-mechanical many-body problem: The Bose gas. In M. Benedicks, P. Jones, S. Smirnov, & B. Winckler (Eds.), Perspectives in Analysis (Vol. 27, pp. 97–183). Springer. https://doi.org/10.1007/3-540-30434-7_9' chicago: 'Lieb, Élliott, Robert Seiringer, Jan Solovej, and Jakob Yngvason. “The Quantum-Mechanical Many-Body Problem: The Bose Gas.” In Perspectives in Analysis, edited by Michael Benedicks, Peter Jones, Stanislav Smirnov, and Björn Winckler, 27:97–183. Springer, 2005. https://doi.org/10.1007/3-540-30434-7_9.' ieee: 'É. Lieb, R. Seiringer, J. Solovej, and J. Yngvason, “The quantum-mechanical many-body problem: The Bose gas,” in Perspectives in Analysis, vol. 27, M. Benedicks, P. Jones, S. Smirnov, and B. Winckler, Eds. Springer, 2005, pp. 97–183.' ista: 'Lieb É, Seiringer R, Solovej J, Yngvason J. 2005.The quantum-mechanical many-body problem: The Bose gas. In: Perspectives in Analysis. Mathematical Physics Studies, vol. 27, 97–183.' mla: 'Lieb, Élliott, et al. “The Quantum-Mechanical Many-Body Problem: The Bose Gas.” Perspectives in Analysis, edited by Michael Benedicks et al., vol. 27, Springer, 2005, pp. 97–183, doi:10.1007/3-540-30434-7_9.' short: É. Lieb, R. Seiringer, J. Solovej, J. Yngvason, in:, M. Benedicks, P. Jones, S. Smirnov, B. Winckler (Eds.), Perspectives in Analysis, Springer, 2005, pp. 97–183. date_created: 2018-12-11T11:57:04Z date_published: 2005-01-01T00:00:00Z date_updated: 2021-01-12T06:56:52Z day: '01' doi: 10.1007/3-540-30434-7_9 editor: - first_name: Michael full_name: Benedicks, Michael last_name: Benedicks - first_name: Peter full_name: Jones, Peter W last_name: Jones - first_name: Stanislav full_name: Smirnov, Stanislav last_name: Smirnov - first_name: Björn full_name: Winckler, Björn last_name: Winckler extern: 1 intvolume: ' 27' main_file_link: - open_access: '1' url: http://arxiv.org/abs/math-ph/0405004 month: '01' oa: 1 page: 97 - 183 publication: Perspectives in Analysis publication_status: published publisher: Springer publist_id: '4590' quality_controlled: 0 status: public title: 'The quantum-mechanical many-body problem: The Bose gas' type: book_chapter volume: 27 year: '2005' ... --- _id: '2359' abstract: - lang: eng text: The validity of substituting a c-number z for the k = 0 mode operator a0 is established rigorously in full generality, thereby verifying one aspect of Bogoliubov's 1947 theory. This substitution not only yields the correct value of thermodynamic quantities such as the pressure or ground state energy, but also the value of |z|2 that maximizes the partition function equals the true amount of condensation in the presence of a gauge-symmetry-breaking term. This point had previously been elusive. author: - first_name: Élliott full_name: Lieb, Élliott H last_name: Lieb - first_name: Robert full_name: Robert Seiringer id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 - first_name: Jakob full_name: Yngvason, Jakob last_name: Yngvason citation: ama: Lieb É, Seiringer R, Yngvason J. Justification of c-number substitutions in bosonic hamiltonians. Physical Review Letters. 2005;94(8). doi:10.1103/PhysRevLett.94.080401 apa: Lieb, É., Seiringer, R., & Yngvason, J. (2005). Justification of c-number substitutions in bosonic hamiltonians. Physical Review Letters. American Physical Society. https://doi.org/10.1103/PhysRevLett.94.080401 chicago: Lieb, Élliott, Robert Seiringer, and Jakob Yngvason. “Justification of C-Number Substitutions in Bosonic Hamiltonians.” Physical Review Letters. American Physical Society, 2005. https://doi.org/10.1103/PhysRevLett.94.080401. ieee: É. Lieb, R. Seiringer, and J. Yngvason, “Justification of c-number substitutions in bosonic hamiltonians,” Physical Review Letters, vol. 94, no. 8. American Physical Society, 2005. ista: Lieb É, Seiringer R, Yngvason J. 2005. Justification of c-number substitutions in bosonic hamiltonians. Physical Review Letters. 94(8). mla: Lieb, Élliott, et al. “Justification of C-Number Substitutions in Bosonic Hamiltonians.” Physical Review Letters, vol. 94, no. 8, American Physical Society, 2005, doi:10.1103/PhysRevLett.94.080401. short: É. Lieb, R. Seiringer, J. Yngvason, Physical Review Letters 94 (2005). date_created: 2018-12-11T11:57:12Z date_published: 2005-03-04T00:00:00Z date_updated: 2021-01-12T06:57:00Z day: '04' doi: 10.1103/PhysRevLett.94.080401 extern: 1 intvolume: ' 94' issue: '8' main_file_link: - open_access: '1' url: http://arxiv.org/abs/math-ph/0412023 month: '03' oa: 1 publication: Physical Review Letters publication_status: published publisher: American Physical Society publist_id: '4566' quality_controlled: 0 status: public title: Justification of c-number substitutions in bosonic hamiltonians type: journal_article volume: 94 year: '2005' ...