---
_id: '2148'
abstract:
- lang: eng
  text: Despite the growing geological evidence that fluid boiling and vapour-liquid
    separation affect the distribution of metals in magmatic-hydrothermal systems
    significantly, there are few experimental data on the chemical status and partitioning
    of metals in the vapour and liquid phases. Here we report on an in situ measurement,
    using X-ray absorption fine structure (XAFS) spectroscopy, of antimony speciation
    and partitioning in the system Sb2O3-H2O-NaCl-HCl at 400°C and pressures 270–300
    bar corresponding to the vapour-liquid equilibrium. Experiments were performed
    using a spectroscopic cell which allows simultaneous determination of the total
    concentration and atomic environment of the absorbing element (Sb) in each phase.
    Results show that quantitative vapour-brine separation of a supercritical aqueous
    salt fluid can be achieved by a controlled decompression and monitoring the X-ray
    absorbance of the fluid phase. Antimony concentrations in equilibrium with Sb2O3
    (cubic, senarmontite) in the coexisting vapour and liquid phases and corresponding
    SbIII vapour-liquid partitioning coefficients are in agreement with recent data
    obtained using batch-reactor solubility techniques. The XAFS spectra analysis
    shows that hydroxy-chloride complexes, probably Sb(OH)2Cl0, are dominant both
    in the vapour and liquid phase in a salt-water system at acidic conditions. This
    first in situ XAFS study of element fractionation between coexisting volatile
    and dense phases opens new possibilities for systematic investigations of vapour-brine
    and fluid-melt immiscibility phenomena, avoiding many experimental artifacts common
    in less direct techniques.
author:
- first_name: Gleb
  full_name: Pokrovski, Gleb S
  last_name: Pokrovski
- first_name: Jacques
  full_name: Roux, Jacques L
  last_name: Roux
- first_name: Jean
  full_name: Hazemann, Jean L
  last_name: Hazemann
- first_name: Anastassia
  full_name: Borisova, Anastassia Y
  last_name: Borisova
- first_name: Anastasia
  full_name: Gonchar, Anastasia A
  last_name: Gonchar
- first_name: Mikhail
  full_name: Mikhail Lemeshko
  id: 37CB05FA-F248-11E8-B48F-1D18A9856A87
  last_name: Lemeshko
  orcid: 0000-0002-6990-7802
citation:
  ama: Pokrovski G, Roux J, Hazemann J, Borisova A, Gonchar A, Lemeshko M. In situ
    X-ray absorption spectroscopy measurement of vapour-brine fractionation of antimony
    at hydrothermal conditions. <i>Mineralogical Magazine</i>. 2008;72(2):667-681.
    doi:<a href="https://doi.org/10.1180/minmag.2008.072.2.667 ">10.1180/minmag.2008.072.2.667
    </a>
  apa: Pokrovski, G., Roux, J., Hazemann, J., Borisova, A., Gonchar, A., &#38; Lemeshko,
    M. (2008). In situ X-ray absorption spectroscopy measurement of vapour-brine fractionation
    of antimony at hydrothermal conditions. <i>Mineralogical Magazine</i>. Mineralogical
    Society. <a href="https://doi.org/10.1180/minmag.2008.072.2.667 ">https://doi.org/10.1180/minmag.2008.072.2.667
    </a>
  chicago: Pokrovski, Gleb, Jacques Roux, Jean Hazemann, Anastassia Borisova, Anastasia
    Gonchar, and Mikhail Lemeshko. “In Situ X-Ray Absorption Spectroscopy Measurement
    of Vapour-Brine Fractionation of Antimony at Hydrothermal Conditions.” <i>Mineralogical
    Magazine</i>. Mineralogical Society, 2008. <a href="https://doi.org/10.1180/minmag.2008.072.2.667
    ">https://doi.org/10.1180/minmag.2008.072.2.667 </a>.
  ieee: G. Pokrovski, J. Roux, J. Hazemann, A. Borisova, A. Gonchar, and M. Lemeshko,
    “In situ X-ray absorption spectroscopy measurement of vapour-brine fractionation
    of antimony at hydrothermal conditions,” <i>Mineralogical Magazine</i>, vol. 72,
    no. 2. Mineralogical Society, pp. 667–681, 2008.
  ista: Pokrovski G, Roux J, Hazemann J, Borisova A, Gonchar A, Lemeshko M. 2008.
    In situ X-ray absorption spectroscopy measurement of vapour-brine fractionation
    of antimony at hydrothermal conditions. Mineralogical Magazine. 72(2), 667–681.
  mla: Pokrovski, Gleb, et al. “In Situ X-Ray Absorption Spectroscopy Measurement
    of Vapour-Brine Fractionation of Antimony at Hydrothermal Conditions.” <i>Mineralogical
    Magazine</i>, vol. 72, no. 2, Mineralogical Society, 2008, pp. 667–81, doi:<a
    href="https://doi.org/10.1180/minmag.2008.072.2.667 ">10.1180/minmag.2008.072.2.667
    </a>.
  short: G. Pokrovski, J. Roux, J. Hazemann, A. Borisova, A. Gonchar, M. Lemeshko,
    Mineralogical Magazine 72 (2008) 667–681.
date_created: 2018-12-11T11:55:59Z
date_published: 2008-04-01T00:00:00Z
date_updated: 2021-01-12T06:55:36Z
day: '01'
doi: '10.1180/minmag.2008.072.2.667 '
extern: 1
intvolume: '        72'
issue: '2'
month: '04'
page: 667 - 681
publication: Mineralogical Magazine
publication_status: published
publisher: Mineralogical Society
publist_id: '4876'
quality_controlled: 0
status: public
title: In situ X-ray absorption spectroscopy measurement of vapour-brine fractionation
  of antimony at hydrothermal conditions
type: journal_article
volume: 72
year: '2008'
...
---
_id: '224'
abstract:
- lang: eng
  text: Let n ≥ 4 and let Q ∈ [X1, ..., Xn] be a non-singular quadratic form. When
    Q is indefinite we provide new upper bounds for the least non-trivial integral
    solution to the equation Q = 0, and when Q is positive definite we provide improved
    upper bounds for the greatest positive integer k for which the equation Q = k
    is insoluble in integers, despite being soluble modulo every prime power.
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: Rainer
  full_name: Dietmann, Rainer
  last_name: Dietmann
citation:
  ama: Browning TD, Dietmann R. On the representation of integers by quadratic forms.
    <i>Proceedings of the London Mathematical Society</i>. 2008;96(2):389-416. doi:<a
    href="https://doi.org/10.1112/plms/pdm032">10.1112/plms/pdm032</a>
  apa: Browning, T. D., &#38; Dietmann, R. (2008). On the representation of integers
    by quadratic forms. <i>Proceedings of the London Mathematical Society</i>. John
    Wiley and Sons Ltd. <a href="https://doi.org/10.1112/plms/pdm032">https://doi.org/10.1112/plms/pdm032</a>
  chicago: Browning, Timothy D, and Rainer Dietmann. “On the Representation of Integers
    by Quadratic Forms.” <i>Proceedings of the London Mathematical Society</i>. John
    Wiley and Sons Ltd, 2008. <a href="https://doi.org/10.1112/plms/pdm032">https://doi.org/10.1112/plms/pdm032</a>.
  ieee: T. D. Browning and R. Dietmann, “On the representation of integers by quadratic
    forms,” <i>Proceedings of the London Mathematical Society</i>, vol. 96, no. 2.
    John Wiley and Sons Ltd, pp. 389–416, 2008.
  ista: Browning TD, Dietmann R. 2008. On the representation of integers by quadratic
    forms. Proceedings of the London Mathematical Society. 96(2), 389–416.
  mla: Browning, Timothy D., and Rainer Dietmann. “On the Representation of Integers
    by Quadratic Forms.” <i>Proceedings of the London Mathematical Society</i>, vol.
    96, no. 2, John Wiley and Sons Ltd, 2008, pp. 389–416, doi:<a href="https://doi.org/10.1112/plms/pdm032">10.1112/plms/pdm032</a>.
  short: T.D. Browning, R. Dietmann, Proceedings of the London Mathematical Society
    96 (2008) 389–416.
date_created: 2018-12-11T11:45:18Z
date_published: 2008-03-01T00:00:00Z
date_updated: 2021-01-12T06:56:13Z
day: '01'
doi: 10.1112/plms/pdm032
extern: 1
intvolume: '        96'
issue: '2'
month: '03'
page: 389 - 416
publication: Proceedings of the London Mathematical Society
publication_status: published
publisher: John Wiley and Sons Ltd
publist_id: '7688'
quality_controlled: 0
status: public
title: On the representation of integers by quadratic forms
type: journal_article
volume: 96
year: '2008'
...
---
_id: '225'
abstract:
- lang: eng
  text: We revisit recent work of Heath-Brown on the average order of the quantity
    r(L1(x))⋯r(L4(x)), for suitable binary linear forms L1,...,L4, as x=(x1,x2) ranges
    over quite general regions in ℤ2. In addition to improving the error term in Heath-Browns
    estimate, we generalise his result to cover a wider class of linear forms.
acknowledgement: "EP/E053262/1\tEngineering and Physical Sciences Research Council"
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. Binary linear forms as sums of two squares.
    <i>Compositio Mathematica</i>. 2008;144(6):1375-1402. doi:<a href="https://doi.org/10.1112/S0010437X08003692">10.1112/S0010437X08003692</a>
  apa: De La Bretèche, R., &#38; Browning, T. D. (2008). Binary linear forms as sums
    of two squares. <i>Compositio Mathematica</i>. Cambridge University Press. <a
    href="https://doi.org/10.1112/S0010437X08003692">https://doi.org/10.1112/S0010437X08003692</a>
  chicago: De La Bretèche, Régis, and Timothy D Browning. “Binary Linear Forms as
    Sums of Two Squares.” <i>Compositio Mathematica</i>. Cambridge University Press,
    2008. <a href="https://doi.org/10.1112/S0010437X08003692">https://doi.org/10.1112/S0010437X08003692</a>.
  ieee: R. De La Bretèche and T. D. Browning, “Binary linear forms as sums of two
    squares,” <i>Compositio Mathematica</i>, vol. 144, no. 6. Cambridge University
    Press, pp. 1375–1402, 2008.
  ista: De La Bretèche R, Browning TD. 2008. Binary linear forms as sums of two squares.
    Compositio Mathematica. 144(6), 1375–1402.
  mla: De La Bretèche, Régis, and Timothy D. Browning. “Binary Linear Forms as Sums
    of Two Squares.” <i>Compositio Mathematica</i>, vol. 144, no. 6, Cambridge University
    Press, 2008, pp. 1375–402, doi:<a href="https://doi.org/10.1112/S0010437X08003692">10.1112/S0010437X08003692</a>.
  short: R. De La Bretèche, T.D. Browning, Compositio Mathematica 144 (2008) 1375–1402.
date_created: 2018-12-11T11:45:18Z
date_published: 2008-11-01T00:00:00Z
date_updated: 2021-01-12T06:56:17Z
day: '01'
doi: 10.1112/S0010437X08003692
extern: 1
intvolume: '       144'
issue: '6'
month: '11'
page: 1375 - 1402
publication: Compositio Mathematica
publication_status: published
publisher: Cambridge University Press
publist_id: '7687'
quality_controlled: 0
status: public
title: Binary linear forms as sums of two squares
type: journal_article
volume: 144
year: '2008'
...
---
_id: '2331'
abstract:
- lang: eng
  text: We present a review of recent work on the mathematical aspects of the BCS
    gap equation, covering our results of Ref. 9 as well our recent joint work with
    Hamza and Solovej and with Frank and Naboko, respectively. In addition, we mention
    some related new results.
author:
- first_name: Christian
  full_name: Hainzl, Christian
  last_name: Hainzl
- first_name: Robert
  full_name: Robert Seiringer
  id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
  last_name: Seiringer
  orcid: 0000-0002-6781-0521
citation:
  ama: 'Hainzl C, Seiringer R.  Spectral properties of the BCS gap equation of superfluidity.
    In: World Scientific Publishing; 2008:117-136. doi:<a href="https://doi.org/10.1142/9789812832382_0009">10.1142/9789812832382_0009</a>'
  apa: 'Hainzl, C., &#38; Seiringer, R. (2008).  Spectral properties of the BCS gap
    equation of superfluidity (pp. 117–136). Presented at the QMath: Mathematical
    Results in Quantum Physics, World Scientific Publishing. <a href="https://doi.org/10.1142/9789812832382_0009">https://doi.org/10.1142/9789812832382_0009</a>'
  chicago: Hainzl, Christian, and Robert Seiringer. “ Spectral Properties of the BCS
    Gap Equation of Superfluidity,” 117–36. World Scientific Publishing, 2008. <a
    href="https://doi.org/10.1142/9789812832382_0009">https://doi.org/10.1142/9789812832382_0009</a>.
  ieee: 'C. Hainzl and R. Seiringer, “ Spectral properties of the BCS gap equation
    of superfluidity,” presented at the QMath: Mathematical Results in Quantum Physics,
    2008, pp. 117–136.'
  ista: 'Hainzl C, Seiringer R. 2008.  Spectral properties of the BCS gap equation
    of superfluidity. QMath: Mathematical Results in Quantum Physics, 117–136.'
  mla: Hainzl, Christian, and Robert Seiringer. <i> Spectral Properties of the BCS
    Gap Equation of Superfluidity</i>. World Scientific Publishing, 2008, pp. 117–36,
    doi:<a href="https://doi.org/10.1142/9789812832382_0009">10.1142/9789812832382_0009</a>.
  short: C. Hainzl, R. Seiringer, in:, World Scientific Publishing, 2008, pp. 117–136.
conference:
  name: 'QMath: Mathematical Results in Quantum Physics'
date_created: 2018-12-11T11:57:02Z
date_published: 2008-08-01T00:00:00Z
date_updated: 2021-01-12T06:56:50Z
day: '01'
doi: 10.1142/9789812832382_0009
extern: 1
main_file_link:
- open_access: '1'
  url: http://arxiv.org/abs/0802.0446
month: '08'
oa: 1
page: 117 - 136
publication_status: published
publisher: World Scientific Publishing
publist_id: '4595'
quality_controlled: 0
status: public
title: ' Spectral properties of the BCS gap equation of superfluidity'
type: conference
year: '2008'
...
---
_id: '2332'
abstract:
- lang: eng
  text: We present a rigorous proof of the appearance of quantized vortices in dilute
    trapped Bose gases with repulsive two-body interactions subject to rotation, which
    was obtained recently in joint work with Elliott Lieb.14 Starting from the many-body
    Schrödinger equation, we show that the ground state of such gases is, in a suitable
    limit, well described by the nonlinear Gross-Pitaevskii equation. 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: Robert
  full_name: Robert Seiringer
  id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
  last_name: Seiringer
  orcid: 0000-0002-6781-0521
citation:
  ama: 'Seiringer R. Vortices and Spontaneous Symmetry Breaking in Rotating Bose Gases.
    In: World Scientific Publishing; 2008:241-254. doi:<a href="https://doi.org/10.1142/9789812832382_0017">10.1142/9789812832382_0017</a>'
  apa: 'Seiringer, R. (2008). Vortices and Spontaneous Symmetry Breaking in Rotating
    Bose Gases (pp. 241–254). Presented at the QMath: Mathematical Results in Quantum
    Physics, World Scientific Publishing. <a href="https://doi.org/10.1142/9789812832382_0017">https://doi.org/10.1142/9789812832382_0017</a>'
  chicago: Seiringer, Robert. “Vortices and Spontaneous Symmetry Breaking in Rotating
    Bose Gases,” 241–54. World Scientific Publishing, 2008. <a href="https://doi.org/10.1142/9789812832382_0017">https://doi.org/10.1142/9789812832382_0017</a>.
  ieee: 'R. Seiringer, “Vortices and Spontaneous Symmetry Breaking in Rotating Bose
    Gases,” presented at the QMath: Mathematical Results in Quantum Physics, 2008,
    pp. 241–254.'
  ista: 'Seiringer R. 2008. Vortices and Spontaneous Symmetry Breaking in Rotating
    Bose Gases. QMath: Mathematical Results in Quantum Physics, 241–254.'
  mla: Seiringer, Robert. <i>Vortices and Spontaneous Symmetry Breaking in Rotating
    Bose Gases</i>. World Scientific Publishing, 2008, pp. 241–54, doi:<a href="https://doi.org/10.1142/9789812832382_0017">10.1142/9789812832382_0017</a>.
  short: R. Seiringer, in:, World Scientific Publishing, 2008, pp. 241–254.
conference:
  name: 'QMath: Mathematical Results in Quantum Physics'
date_created: 2018-12-11T11:57:02Z
date_published: 2008-12-30T00:00:00Z
date_updated: 2021-01-12T06:56:50Z
day: '30'
doi: 10.1142/9789812832382_0017
extern: 1
main_file_link:
- open_access: '1'
  url: http://arxiv.org/abs/0801.0427
month: '12'
oa: 1
page: 241 - 254
publication_status: published
publisher: World Scientific Publishing
publist_id: '4594'
quality_controlled: 0
status: public
title: Vortices and Spontaneous Symmetry Breaking in Rotating Bose Gases
type: conference
year: '2008'
...
---
_id: '2374'
abstract:
- lang: eng
  text: A lower bound is derived on the free energy (per unit volume) of a homogeneous
    Bose gas at density Q and temperature T. In the dilute regime, i.e., when a3 1,
    where a denotes the scattering length of the pair-interaction potential, our bound
    differs to leading order from the expression for non-interacting particles by
    the term 4πa(2 2}-[ - c]2+). Here, c(T) denotes the critical density for Bose-Einstein
    condensation (for the non-interacting gas), and [ · ]+ = max{ ·, 0} denotes the
    positive part. Our bound is uniform in the temperature up to temperatures of the
    order of the critical temperature, i.e., T ~ 2/3 or smaller. One of the key ingredients
    in the proof is the use of coherent states to extend the method introduced in
    [17] for estimating correlations to temperatures below the critical one.
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. Free energy of a dilute Bose gas: Lower bound. <i>Communications
    in Mathematical Physics</i>. 2008;279(3):595-636. doi:<a href="https://doi.org/10.1007/s00220-008-0428-2">10.1007/s00220-008-0428-2</a>'
  apa: 'Seiringer, R. (2008). Free energy of a dilute Bose gas: Lower bound. <i>Communications
    in Mathematical Physics</i>. Springer. <a href="https://doi.org/10.1007/s00220-008-0428-2">https://doi.org/10.1007/s00220-008-0428-2</a>'
  chicago: 'Seiringer, Robert. “Free Energy of a Dilute Bose Gas: Lower Bound.” <i>Communications
    in Mathematical Physics</i>. Springer, 2008. <a href="https://doi.org/10.1007/s00220-008-0428-2">https://doi.org/10.1007/s00220-008-0428-2</a>.'
  ieee: 'R. Seiringer, “Free energy of a dilute Bose gas: Lower bound,” <i>Communications
    in Mathematical Physics</i>, vol. 279, no. 3. Springer, pp. 595–636, 2008.'
  ista: 'Seiringer R. 2008. Free energy of a dilute Bose gas: Lower bound. Communications
    in Mathematical Physics. 279(3), 595–636.'
  mla: 'Seiringer, Robert. “Free Energy of a Dilute Bose Gas: Lower Bound.” <i>Communications
    in Mathematical Physics</i>, vol. 279, no. 3, Springer, 2008, pp. 595–636, doi:<a
    href="https://doi.org/10.1007/s00220-008-0428-2">10.1007/s00220-008-0428-2</a>.'
  short: R. Seiringer, Communications in Mathematical Physics 279 (2008) 595–636.
date_created: 2018-12-11T11:57:17Z
date_published: 2008-05-01T00:00:00Z
date_updated: 2021-01-12T06:57:06Z
day: '01'
doi: 10.1007/s00220-008-0428-2
extern: 1
intvolume: '       279'
issue: '3'
main_file_link:
- open_access: '1'
  url: http://arxiv.org/abs/math-ph/0608069
month: '05'
oa: 1
page: 595 - 636
publication: Communications in Mathematical Physics
publication_status: published
publisher: Springer
publist_id: '4551'
quality_controlled: 0
status: public
title: 'Free energy of a dilute Bose gas: Lower bound'
type: journal_article
volume: 279
year: '2008'
...
---
_id: '2376'
abstract:
- lang: eng
  text: We derive upper and lower bounds on the critical temperature Tc and the energy
    gap Ξ (at zero temperature) for the BCS gap equation, describing spin- 1 2 fermions
    interacting via a local two-body interaction potential λV(x). At weak coupling
    λ 1 and under appropriate assumptions on V(x), our bounds show that Tc ∼A exp(-B/λ)
    and Ξ∼C exp(-B/λ) for some explicit coefficients A, B, and C depending on the
    interaction V(x) and the chemical potential μ. The ratio A/C turns out to be a
    universal constant, independent of both V(x) and μ. Our analysis is valid for
    any μ; for small μ, or low density, our formulas reduce to well-known expressions
    involving the scattering length of V(x).
author:
- first_name: Christian
  full_name: Hainzl, Christian
  last_name: Hainzl
- first_name: Robert
  full_name: Robert Seiringer
  id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
  last_name: Seiringer
  orcid: 0000-0002-6781-0521
citation:
  ama: Hainzl C, Seiringer R. Critical temperature and energy gap for the BCS equation.
    <i>Physical Review B - Condensed Matter and Materials Physics</i>. 2008;77(18).
    doi:<a href="https://doi.org/10.1103/PhysRevB.77.184517">10.1103/PhysRevB.77.184517</a>
  apa: Hainzl, C., &#38; Seiringer, R. (2008). Critical temperature and energy gap
    for the BCS equation. <i>Physical Review B - Condensed Matter and Materials Physics</i>.
    American Physical Society. <a href="https://doi.org/10.1103/PhysRevB.77.184517">https://doi.org/10.1103/PhysRevB.77.184517</a>
  chicago: Hainzl, Christian, and Robert Seiringer. “Critical Temperature and Energy
    Gap for the BCS Equation.” <i>Physical Review B - Condensed Matter and Materials
    Physics</i>. American Physical Society, 2008. <a href="https://doi.org/10.1103/PhysRevB.77.184517">https://doi.org/10.1103/PhysRevB.77.184517</a>.
  ieee: C. Hainzl and R. Seiringer, “Critical temperature and energy gap for the BCS
    equation,” <i>Physical Review B - Condensed Matter and Materials Physics</i>,
    vol. 77, no. 18. American Physical Society, 2008.
  ista: Hainzl C, Seiringer R. 2008. Critical temperature and energy gap for the BCS
    equation. Physical Review B - Condensed Matter and Materials Physics. 77(18).
  mla: Hainzl, Christian, and Robert Seiringer. “Critical Temperature and Energy Gap
    for the BCS Equation.” <i>Physical Review B - Condensed Matter and Materials Physics</i>,
    vol. 77, no. 18, American Physical Society, 2008, doi:<a href="https://doi.org/10.1103/PhysRevB.77.184517">10.1103/PhysRevB.77.184517</a>.
  short: C. Hainzl, R. Seiringer, Physical Review B - Condensed Matter and Materials
    Physics 77 (2008).
date_created: 2018-12-11T11:57:18Z
date_published: 2008-05-28T00:00:00Z
date_updated: 2021-01-12T06:57:06Z
day: '28'
doi: 10.1103/PhysRevB.77.184517
extern: 1
intvolume: '        77'
issue: '18'
main_file_link:
- open_access: '1'
  url: http://arxiv.org/abs/0801.4159
month: '05'
oa: 1
publication: Physical Review B - Condensed Matter and Materials Physics
publication_status: published
publisher: American Physical Society
publist_id: '4550'
quality_controlled: 0
status: public
title: Critical temperature and energy gap for the BCS equation
type: journal_article
volume: 77
year: '2008'
...
---
_id: '2377'
abstract:
- lang: eng
  text: We prove that the critical temperature for the BCS gap equation is given by
    T c = μ ( 8\π e γ-2+ o(1)) e π/(2μa) in the low density limit μ→ 0, with γ denoting
    Euler's constant. The formula holds for a suitable class of interaction potentials
    with negative scattering length a in the absence of bound states.
author:
- first_name: Christian
  full_name: Hainzl, Christian
  last_name: Hainzl
- first_name: Robert
  full_name: Robert Seiringer
  id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
  last_name: Seiringer
  orcid: 0000-0002-6781-0521
citation:
  ama: Hainzl C, Seiringer R. The BCS critical temperature for potentials with negative
    scattering length. <i>Letters in Mathematical Physics</i>. 2008;84(2-3):99-107.
    doi:<a href="https://doi.org/10.1007/s11005-008-0242-y">10.1007/s11005-008-0242-y</a>
  apa: Hainzl, C., &#38; Seiringer, R. (2008). The BCS critical temperature for potentials
    with negative scattering length. <i>Letters in Mathematical Physics</i>. Springer.
    <a href="https://doi.org/10.1007/s11005-008-0242-y">https://doi.org/10.1007/s11005-008-0242-y</a>
  chicago: Hainzl, Christian, and Robert Seiringer. “The BCS Critical Temperature
    for Potentials with Negative Scattering Length.” <i>Letters in Mathematical Physics</i>.
    Springer, 2008. <a href="https://doi.org/10.1007/s11005-008-0242-y">https://doi.org/10.1007/s11005-008-0242-y</a>.
  ieee: C. Hainzl and R. Seiringer, “The BCS critical temperature for potentials with
    negative scattering length,” <i>Letters in Mathematical Physics</i>, vol. 84,
    no. 2–3. Springer, pp. 99–107, 2008.
  ista: Hainzl C, Seiringer R. 2008. The BCS critical temperature for potentials with
    negative scattering length. Letters in Mathematical Physics. 84(2–3), 99–107.
  mla: Hainzl, Christian, and Robert Seiringer. “The BCS Critical Temperature for
    Potentials with Negative Scattering Length.” <i>Letters in Mathematical Physics</i>,
    vol. 84, no. 2–3, Springer, 2008, pp. 99–107, doi:<a href="https://doi.org/10.1007/s11005-008-0242-y">10.1007/s11005-008-0242-y</a>.
  short: C. Hainzl, R. Seiringer, Letters in Mathematical Physics 84 (2008) 99–107.
date_created: 2018-12-11T11:57:19Z
date_published: 2008-06-01T00:00:00Z
date_updated: 2021-01-12T06:57:07Z
day: '01'
doi: 10.1007/s11005-008-0242-y
extern: 1
intvolume: '        84'
issue: 2-3
main_file_link:
- open_access: '1'
  url: http://arxiv.org/abs/0803.3324
month: '06'
oa: 1
page: 99 - 107
publication: Letters in Mathematical Physics
publication_status: published
publisher: Springer
publist_id: '4548'
quality_controlled: 0
status: public
title: The BCS critical temperature for potentials with negative scattering length
type: journal_article
volume: 84
year: '2008'
...
---
_id: '2378'
abstract:
- lang: eng
  text: We derive a lower bound on the ground state energy of the Hubbard model for
    given value of the total spin. In combination with the upper bound derived previously
    by Giuliani (J. Math. Phys. 48:023302, [2007]), our result proves that in the
    low density limit the leading order correction compared to the ground state energy
    of a non-interacting lattice Fermi gas is given by 8πaσ uσ d , where σ u(d) denotes
    the density of the spin-up (down) particles, and a is the scattering length of
    the contact interaction potential. This result extends previous work on the corresponding
    continuum model to the lattice case.
author:
- first_name: Robert
  full_name: Robert Seiringer
  id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
  last_name: Seiringer
  orcid: 0000-0002-6781-0521
- first_name: Jun
  full_name: Yin, Jun
  last_name: Yin
citation:
  ama: Seiringer R, Yin J. Ground state energy of the low density hubbard model. <i>Journal
    of Statistical Physics</i>. 2008;131(6):1139-1154. doi:<a href="https://doi.org/10.1007/s10955-008-9527-x">10.1007/s10955-008-9527-x</a>
  apa: Seiringer, R., &#38; Yin, J. (2008). Ground state energy of the low density
    hubbard model. <i>Journal of Statistical Physics</i>. Springer. <a href="https://doi.org/10.1007/s10955-008-9527-x">https://doi.org/10.1007/s10955-008-9527-x</a>
  chicago: Seiringer, Robert, and Jun Yin. “Ground State Energy of the Low Density
    Hubbard Model.” <i>Journal of Statistical Physics</i>. Springer, 2008. <a href="https://doi.org/10.1007/s10955-008-9527-x">https://doi.org/10.1007/s10955-008-9527-x</a>.
  ieee: R. Seiringer and J. Yin, “Ground state energy of the low density hubbard model,”
    <i>Journal of Statistical Physics</i>, vol. 131, no. 6. Springer, pp. 1139–1154,
    2008.
  ista: Seiringer R, Yin J. 2008. Ground state energy of the low density hubbard model.
    Journal of Statistical Physics. 131(6), 1139–1154.
  mla: Seiringer, Robert, and Jun Yin. “Ground State Energy of the Low Density Hubbard
    Model.” <i>Journal of Statistical Physics</i>, vol. 131, no. 6, Springer, 2008,
    pp. 1139–54, doi:<a href="https://doi.org/10.1007/s10955-008-9527-x">10.1007/s10955-008-9527-x</a>.
  short: R. Seiringer, J. Yin, Journal of Statistical Physics 131 (2008) 1139–1154.
date_created: 2018-12-11T11:57:19Z
date_published: 2008-06-01T00:00:00Z
date_updated: 2021-01-12T06:57:07Z
day: '01'
doi: 10.1007/s10955-008-9527-x
extern: 1
intvolume: '       131'
issue: '6'
main_file_link:
- open_access: '1'
  url: http://arxiv.org/abs/0712.2810
month: '06'
oa: 1
page: 1139 - 1154
publication: Journal of Statistical Physics
publication_status: published
publisher: Springer
publist_id: '4549'
quality_controlled: 0
status: public
title: Ground state energy of the low density hubbard model
type: journal_article
volume: 131
year: '2008'
...
---
_id: '2379'
author:
- first_name: Rupert
  full_name: Frank, Rupert L
  last_name: Frank
- 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, Lieb É, Seiringer R. Hardy-Lieb-Thirring inequalities for fractional
    Schrödinger operators. <i>Journal of the American Mathematical Society</i>. 2008;21(4):925-950.
    doi:<a href="https://doi.org/10.1090/S0894-0347-07-00582-6">10.1090/S0894-0347-07-00582-6</a>
  apa: Frank, R., Lieb, É., &#38; Seiringer, R. (2008). Hardy-Lieb-Thirring inequalities
    for fractional Schrödinger operators. <i>Journal of the American Mathematical
    Society</i>. American Mathematical Society. <a href="https://doi.org/10.1090/S0894-0347-07-00582-6">https://doi.org/10.1090/S0894-0347-07-00582-6</a>
  chicago: Frank, Rupert, Élliott Lieb, and Robert Seiringer. “Hardy-Lieb-Thirring
    Inequalities for Fractional Schrödinger Operators.” <i>Journal of the American
    Mathematical Society</i>. American Mathematical Society, 2008. <a href="https://doi.org/10.1090/S0894-0347-07-00582-6">https://doi.org/10.1090/S0894-0347-07-00582-6</a>.
  ieee: R. Frank, É. Lieb, and R. Seiringer, “Hardy-Lieb-Thirring inequalities for
    fractional Schrödinger operators,” <i>Journal of the American Mathematical Society</i>,
    vol. 21, no. 4. American Mathematical Society, pp. 925–950, 2008.
  ista: Frank R, Lieb É, Seiringer R. 2008. Hardy-Lieb-Thirring inequalities for fractional
    Schrödinger operators. Journal of the American Mathematical Society. 21(4), 925–950.
  mla: Frank, Rupert, et al. “Hardy-Lieb-Thirring Inequalities for Fractional Schrödinger
    Operators.” <i>Journal of the American Mathematical Society</i>, vol. 21, no.
    4, American Mathematical Society, 2008, pp. 925–50, doi:<a href="https://doi.org/10.1090/S0894-0347-07-00582-6">10.1090/S0894-0347-07-00582-6</a>.
  short: R. Frank, É. Lieb, R. Seiringer, Journal of the American Mathematical Society
    21 (2008) 925–950.
date_created: 2018-12-11T11:57:19Z
date_published: 2008-01-01T00:00:00Z
date_updated: 2021-01-12T06:57:07Z
day: '01'
doi: 10.1090/S0894-0347-07-00582-6
extern: 1
intvolume: '        21'
issue: '4'
main_file_link:
- open_access: '1'
  url: http://arxiv.org/abs/math/0610593
month: '01'
oa: 1
page: 925 - 950
publication: Journal of the American Mathematical Society
publication_status: published
publisher: American Mathematical Society
publist_id: '4546'
quality_controlled: 0
status: public
title: Hardy-Lieb-Thirring inequalities for fractional Schrödinger operators
type: journal_article
volume: 21
year: '2008'
...
---
_id: '2380'
abstract:
- lang: eng
  text: The Bardeen-Cooper-Schrieffer (BCS) functional has recently received renewed
    attention as a description of fermionic gases interacting with local pairwise
    interactions. We present here a rigorous analysis of the BCS functional for general
    pair interaction potentials. For both zero and positive temperature, we show that
    the existence of a non-trivial solution of the nonlinear BCS gap equation is equivalent
    to the existence of a negative eigenvalue of a certain linear operator. From this
    we conclude the existence of a critical temperature below which the BCS pairing
    wave function does not vanish identically. For attractive potentials, we prove
    that the critical temperature is non-zero and exponentially small in the strength
    of the potential.
author:
- first_name: Christian
  full_name: Hainzl, Christian
  last_name: Hainzl
- first_name: Eman
  full_name: Hamza, Eman
  last_name: Hamza
- 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: Hainzl C, Hamza E, Seiringer R, Solovej J. The BCS functional for general pair
    interactions. <i>Communications in Mathematical Physics</i>. 2008;281(2):349-367.
    doi:<a href="https://doi.org/10.1007/s00220-008-0489-2">10.1007/s00220-008-0489-2</a>
  apa: Hainzl, C., Hamza, E., Seiringer, R., &#38; Solovej, J. (2008). The BCS functional
    for general pair interactions. <i>Communications in Mathematical Physics</i>.
    Springer. <a href="https://doi.org/10.1007/s00220-008-0489-2">https://doi.org/10.1007/s00220-008-0489-2</a>
  chicago: Hainzl, Christian, Eman Hamza, Robert Seiringer, and Jan Solovej. “The
    BCS Functional for General Pair Interactions.” <i>Communications in Mathematical
    Physics</i>. Springer, 2008. <a href="https://doi.org/10.1007/s00220-008-0489-2">https://doi.org/10.1007/s00220-008-0489-2</a>.
  ieee: C. Hainzl, E. Hamza, R. Seiringer, and J. Solovej, “The BCS functional for
    general pair interactions,” <i>Communications in Mathematical Physics</i>, vol.
    281, no. 2. Springer, pp. 349–367, 2008.
  ista: Hainzl C, Hamza E, Seiringer R, Solovej J. 2008. The BCS functional for general
    pair interactions. Communications in Mathematical Physics. 281(2), 349–367.
  mla: Hainzl, Christian, et al. “The BCS Functional for General Pair Interactions.”
    <i>Communications in Mathematical Physics</i>, vol. 281, no. 2, Springer, 2008,
    pp. 349–67, doi:<a href="https://doi.org/10.1007/s00220-008-0489-2">10.1007/s00220-008-0489-2</a>.
  short: C. Hainzl, E. Hamza, R. Seiringer, J. Solovej, Communications in Mathematical
    Physics 281 (2008) 349–367.
date_created: 2018-12-11T11:57:20Z
date_published: 2008-07-01T00:00:00Z
date_updated: 2021-01-12T06:57:08Z
day: '01'
doi: 10.1007/s00220-008-0489-2
extern: 1
intvolume: '       281'
issue: '2'
main_file_link:
- open_access: '1'
  url: http://arxiv.org/abs/math-ph/0703086
month: '07'
oa: 1
page: 349 - 367
publication: Communications in Mathematical Physics
publication_status: published
publisher: Springer
publist_id: '4547'
quality_controlled: 0
status: public
title: The BCS functional for general pair interactions
type: journal_article
volume: 281
year: '2008'
...
---
_id: '2381'
abstract:
- lang: eng
  text: We determine the sharp constant in the Hardy inequality for fractional Sobolev
    spaces. To do so, we develop a non-linear and non-local version of the ground
    state representation, which even yields a remainder term. From the sharp Hardy
    inequality we deduce the sharp constant in a Sobolev embedding which is optimal
    in the Lorentz scale. In the appendix, we characterize the cases of equality in
    the rearrangement inequality in fractional Sobolev spaces.
author:
- first_name: Rupert
  full_name: Frank, Rupert L
  last_name: Frank
- 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, Seiringer R. Non-linear ground state representations and sharp Hardy
    inequalities. <i>Journal of Functional Analysis</i>. 2008;255(12):3407-3430. doi:<a
    href="https://doi.org/10.1016/j.jfa.2008.05.015">10.1016/j.jfa.2008.05.015</a>
  apa: Frank, R., &#38; Seiringer, R. (2008). Non-linear ground state representations
    and sharp Hardy inequalities. <i>Journal of Functional Analysis</i>. Academic
    Press. <a href="https://doi.org/10.1016/j.jfa.2008.05.015">https://doi.org/10.1016/j.jfa.2008.05.015</a>
  chicago: Frank, Rupert, and Robert Seiringer. “Non-Linear Ground State Representations
    and Sharp Hardy Inequalities.” <i>Journal of Functional Analysis</i>. Academic
    Press, 2008. <a href="https://doi.org/10.1016/j.jfa.2008.05.015">https://doi.org/10.1016/j.jfa.2008.05.015</a>.
  ieee: R. Frank and R. Seiringer, “Non-linear ground state representations and sharp
    Hardy inequalities,” <i>Journal of Functional Analysis</i>, vol. 255, no. 12.
    Academic Press, pp. 3407–3430, 2008.
  ista: Frank R, Seiringer R. 2008. Non-linear ground state representations and sharp
    Hardy inequalities. Journal of Functional Analysis. 255(12), 3407–3430.
  mla: Frank, Rupert, and Robert Seiringer. “Non-Linear Ground State Representations
    and Sharp Hardy Inequalities.” <i>Journal of Functional Analysis</i>, vol. 255,
    no. 12, Academic Press, 2008, pp. 3407–30, doi:<a href="https://doi.org/10.1016/j.jfa.2008.05.015">10.1016/j.jfa.2008.05.015</a>.
  short: R. Frank, R. Seiringer, Journal of Functional Analysis 255 (2008) 3407–3430.
date_created: 2018-12-11T11:57:20Z
date_published: 2008-12-15T00:00:00Z
date_updated: 2021-01-12T06:57:08Z
day: '15'
doi: 10.1016/j.jfa.2008.05.015
extern: 1
intvolume: '       255'
issue: '12'
main_file_link:
- open_access: '1'
  url: http://arxiv.org/abs/0803.0503
month: '12'
oa: 1
page: 3407 - 3430
publication: Journal of Functional Analysis
publication_status: published
publisher: Academic Press
publist_id: '4543'
quality_controlled: 0
status: public
title: Non-linear ground state representations and sharp Hardy inequalities
type: journal_article
volume: 255
year: '2008'
...
---
_id: '2382'
abstract:
- lang: eng
  text: We show that the Lieb-Liniger model for one-dimensional bosons with repulsive
    δ-function interaction can be rigorously derived via a scaling limit from a dilute
    three-dimensional Bose gas with arbitrary repulsive interaction potential of finite
    scattering length. For this purpose, we prove bounds on both the eigenvalues and
    corresponding eigenfunctions of three-dimensional bosons in strongly elongated
    traps and relate them to the corresponding quantities in the Lieb-Liniger model.
    In particular, if both the scattering length a and the radius r of the cylindrical
    trap go to zero, the Lieb-Liniger model with coupling constant g ∼ a/r 2 is derived.
    Our bounds are uniform in g in the whole parameter range 0 ≤ g ≤ ∞, and apply
    to the Hamiltonian for three-dimensional bosons in a spectral window of size ∼
    r -2 above the ground state energy.
author:
- first_name: Robert
  full_name: Robert Seiringer
  id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
  last_name: Seiringer
  orcid: 0000-0002-6781-0521
- first_name: Jun
  full_name: Yin, Jun
  last_name: Yin
citation:
  ama: Seiringer R, Yin J. The Lieb-Liniger model as a limit of dilute bosons in three
    dimensions. <i>Communications in Mathematical Physics</i>. 2008;284(2):459-479.
    doi:<a href="https://doi.org/10.1007/s00220-008-0521-6">10.1007/s00220-008-0521-6</a>
  apa: Seiringer, R., &#38; Yin, J. (2008). The Lieb-Liniger model as a limit of dilute
    bosons in three dimensions. <i>Communications in Mathematical Physics</i>. Springer.
    <a href="https://doi.org/10.1007/s00220-008-0521-6">https://doi.org/10.1007/s00220-008-0521-6</a>
  chicago: Seiringer, Robert, and Jun Yin. “The Lieb-Liniger Model as a Limit of Dilute
    Bosons in Three Dimensions.” <i>Communications in Mathematical Physics</i>. Springer,
    2008. <a href="https://doi.org/10.1007/s00220-008-0521-6">https://doi.org/10.1007/s00220-008-0521-6</a>.
  ieee: R. Seiringer and J. Yin, “The Lieb-Liniger model as a limit of dilute bosons
    in three dimensions,” <i>Communications in Mathematical Physics</i>, vol. 284,
    no. 2. Springer, pp. 459–479, 2008.
  ista: Seiringer R, Yin J. 2008. The Lieb-Liniger model as a limit of dilute bosons
    in three dimensions. Communications in Mathematical Physics. 284(2), 459–479.
  mla: Seiringer, Robert, and Jun Yin. “The Lieb-Liniger Model as a Limit of Dilute
    Bosons in Three Dimensions.” <i>Communications in Mathematical Physics</i>, vol.
    284, no. 2, Springer, 2008, pp. 459–79, doi:<a href="https://doi.org/10.1007/s00220-008-0521-6">10.1007/s00220-008-0521-6</a>.
  short: R. Seiringer, J. Yin, Communications in Mathematical Physics 284 (2008) 459–479.
date_created: 2018-12-11T11:57:21Z
date_published: 2008-12-01T00:00:00Z
date_updated: 2021-01-12T06:57:08Z
day: '01'
doi: 10.1007/s00220-008-0521-6
extern: 1
intvolume: '       284'
issue: '2'
main_file_link:
- open_access: '1'
  url: http://arxiv.org/abs/0709.4022
month: '12'
oa: 1
page: 459 - 479
publication: Communications in Mathematical Physics
publication_status: published
publisher: Springer
publist_id: '4544'
quality_controlled: 0
status: public
title: The Lieb-Liniger model as a limit of dilute bosons in three dimensions
type: journal_article
volume: 284
year: '2008'
...
---
_id: '2383'
abstract:
- lang: eng
  text: We study the relativistic electron-positron field at positive temperature
    in the Hartree-Fock approximation. We consider both the case with and without
    exchange terms, and investigate the existence and properties of minimizers. Our
    approach is non-perturbative in the sense that the relevant electron subspace
    is determined in a self-consistent way. The present work is an extension of previous
    work by Hainzl, Lewin, Séré and Solovej where the case of zero temperature was
    considered.
author:
- first_name: Christian
  full_name: Hainzl, Christian
  last_name: Hainzl
- first_name: Mathieu
  full_name: Lewin, Mathieu
  last_name: Lewin
- first_name: Robert
  full_name: Robert Seiringer
  id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
  last_name: Seiringer
  orcid: 0000-0002-6781-0521
citation:
  ama: Hainzl C, Lewin M, Seiringer R. A nonlinear model for relativistic electrons
    at positive temperature. <i>Reviews in Mathematical Physics</i>. 2008;20(10):1283-1307.
    doi:<a href="https://doi.org/10.1142/S0129055X08003547">10.1142/S0129055X08003547</a>
  apa: Hainzl, C., Lewin, M., &#38; Seiringer, R. (2008). A nonlinear model for relativistic
    electrons at positive temperature. <i>Reviews in Mathematical Physics</i>. World
    Scientific Publishing. <a href="https://doi.org/10.1142/S0129055X08003547">https://doi.org/10.1142/S0129055X08003547</a>
  chicago: Hainzl, Christian, Mathieu Lewin, and Robert Seiringer. “A Nonlinear Model
    for Relativistic Electrons at Positive Temperature.” <i>Reviews in Mathematical
    Physics</i>. World Scientific Publishing, 2008. <a href="https://doi.org/10.1142/S0129055X08003547">https://doi.org/10.1142/S0129055X08003547</a>.
  ieee: C. Hainzl, M. Lewin, and R. Seiringer, “A nonlinear model for relativistic
    electrons at positive temperature,” <i>Reviews in Mathematical Physics</i>, vol.
    20, no. 10. World Scientific Publishing, pp. 1283–1307, 2008.
  ista: Hainzl C, Lewin M, Seiringer R. 2008. A nonlinear model for relativistic electrons
    at positive temperature. Reviews in Mathematical Physics. 20(10), 1283–1307.
  mla: Hainzl, Christian, et al. “A Nonlinear Model for Relativistic Electrons at
    Positive Temperature.” <i>Reviews in Mathematical Physics</i>, vol. 20, no. 10,
    World Scientific Publishing, 2008, pp. 1283–307, doi:<a href="https://doi.org/10.1142/S0129055X08003547">10.1142/S0129055X08003547</a>.
  short: C. Hainzl, M. Lewin, R. Seiringer, Reviews in Mathematical Physics 20 (2008)
    1283–1307.
date_created: 2018-12-11T11:57:21Z
date_published: 2008-11-01T00:00:00Z
date_updated: 2021-01-12T06:57:09Z
day: '01'
doi: 10.1142/S0129055X08003547
extern: 1
intvolume: '        20'
issue: '10'
main_file_link:
- open_access: '1'
  url: http://arxiv.org/abs/0802.4054
month: '11'
oa: 1
page: 1283 - 1307
publication: Reviews in Mathematical Physics
publication_status: published
publisher: World Scientific Publishing
publist_id: '4545'
quality_controlled: 0
status: public
title: A nonlinear model for relativistic electrons at positive temperature
type: journal_article
volume: 20
year: '2008'
...
---
_id: '2415'
alternative_title:
- Contemporary Mathematics
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. k-Sets and k-facets. In: Goodman J, Pach J, Pollack R, eds. <i>Surveys
    on Discrete and Computational Geometry: Twenty Years Later</i>. Vol 453. American
    Mathematical Society; 2008:443-514. doi:<a href="https://doi.org/10.1090/conm/453">10.1090/conm/453</a>'
  apa: 'Wagner, U. (2008). k-Sets and k-facets. In J. Goodman, J. Pach, &#38; R. Pollack
    (Eds.), <i>Surveys on Discrete and Computational Geometry: Twenty Years Later</i>
    (Vol. 453, pp. 443–514). American Mathematical Society. <a href="https://doi.org/10.1090/conm/453">https://doi.org/10.1090/conm/453</a>'
  chicago: 'Wagner, Uli. “K-Sets and k-Facets.” In <i>Surveys on Discrete and Computational
    Geometry: Twenty Years Later</i>, edited by Jacob Goodman, János Pach, and Richard
    Pollack, 453:443–514. American Mathematical Society, 2008. <a href="https://doi.org/10.1090/conm/453">https://doi.org/10.1090/conm/453</a>.'
  ieee: 'U. Wagner, “k-Sets and k-facets,” in <i>Surveys on Discrete and Computational
    Geometry: Twenty Years Later</i>, vol. 453, J. Goodman, J. Pach, and R. Pollack,
    Eds. American Mathematical Society, 2008, pp. 443–514.'
  ista: 'Wagner U. 2008.k-Sets and k-facets. In: Surveys on Discrete and Computational
    Geometry: Twenty Years Later. Contemporary Mathematics, vol. 453, 443–514.'
  mla: 'Wagner, Uli. “K-Sets and k-Facets.” <i>Surveys on Discrete and Computational
    Geometry: Twenty Years Later</i>, edited by Jacob Goodman et al., vol. 453, American
    Mathematical Society, 2008, pp. 443–514, doi:<a href="https://doi.org/10.1090/conm/453">10.1090/conm/453</a>.'
  short: 'U. Wagner, in:, J. Goodman, J. Pach, R. Pollack (Eds.), Surveys on Discrete
    and Computational Geometry: Twenty Years Later, American Mathematical Society,
    2008, pp. 443–514.'
date_created: 2018-12-11T11:57:32Z
date_published: 2008-01-01T00:00:00Z
date_updated: 2021-01-12T06:57:21Z
day: '01'
doi: 10.1090/conm/453
editor:
- first_name: Jacob
  full_name: Goodman, Jacob E
  last_name: Goodman
- first_name: János
  full_name: Pach, János
  last_name: Pach
- first_name: Richard
  full_name: Pollack, Richard
  last_name: Pollack
extern: 1
intvolume: '       453'
month: '01'
page: 443 - 514
publication: 'Surveys on Discrete and Computational Geometry: Twenty Years Later'
publication_status: published
publisher: American Mathematical Society
publist_id: '4510'
quality_controlled: 0
status: public
title: k-Sets and k-facets
type: book_chapter
volume: 453
year: '2008'
...
---
_id: '2432'
abstract:
- lang: eng
  text: We study the disk containment problem introduced by Neumann-Lara and Urrutia
    and its generalization to higher dimensions. We relate the problem to centerpoints
    and lower centerpoints of point sets. Moreover, we show that for any set of n
    points in ℝd, there is a subset A ⊆ S of size [d+3/2] such that any ball containing
    A contains at least roughly 4/5ed 3n points of S. This improves previous bounds
    for which the constant was exponentially small in d. We also consider a generalization
    of the planar disk containment problem to families of pseudodisks.
alternative_title:
- LNCS
author:
- first_name: Shakhar
  full_name: Smorodinsky, Shakhar
  last_name: Smorodinsky
- first_name: Marek
  full_name: Sulovský, Marek
  last_name: Sulovský
- first_name: Uli
  full_name: Uli Wagner
  id: 36690CA2-F248-11E8-B48F-1D18A9856A87
  last_name: Wagner
  orcid: 0000-0002-1494-0568
citation:
  ama: 'Smorodinsky S, Sulovský M, Wagner U. On center regions and balls containing
    many points. In: Vol 5092. Springer; 2008:363-373. doi:<a href="https://doi.org/10.1007/978-3-540-69733-6_36">10.1007/978-3-540-69733-6_36</a>'
  apa: 'Smorodinsky, S., Sulovský, M., &#38; Wagner, U. (2008). On center regions
    and balls containing many points (Vol. 5092, pp. 363–373). Presented at the COCOON:
    Conference on Computing and Combinatorics, Springer. <a href="https://doi.org/10.1007/978-3-540-69733-6_36">https://doi.org/10.1007/978-3-540-69733-6_36</a>'
  chicago: Smorodinsky, Shakhar, Marek Sulovský, and Uli Wagner. “On Center Regions
    and Balls Containing Many Points,” 5092:363–73. Springer, 2008. <a href="https://doi.org/10.1007/978-3-540-69733-6_36">https://doi.org/10.1007/978-3-540-69733-6_36</a>.
  ieee: 'S. Smorodinsky, M. Sulovský, and U. Wagner, “On center regions and balls
    containing many points,” presented at the COCOON: Conference on Computing and
    Combinatorics, 2008, vol. 5092, pp. 363–373.'
  ista: 'Smorodinsky S, Sulovský M, Wagner U. 2008. On center regions and balls containing
    many points. COCOON: Conference on Computing and Combinatorics, LNCS, vol. 5092,
    363–373.'
  mla: Smorodinsky, Shakhar, et al. <i>On Center Regions and Balls Containing Many
    Points</i>. Vol. 5092, Springer, 2008, pp. 363–73, doi:<a href="https://doi.org/10.1007/978-3-540-69733-6_36">10.1007/978-3-540-69733-6_36</a>.
  short: S. Smorodinsky, M. Sulovský, U. Wagner, in:, Springer, 2008, pp. 363–373.
conference:
  name: 'COCOON: Conference on Computing and Combinatorics'
date_created: 2018-12-11T11:57:38Z
date_published: 2008-01-01T00:00:00Z
date_updated: 2021-01-12T06:57:27Z
day: '01'
doi: 10.1007/978-3-540-69733-6_36
extern: 1
intvolume: '      5092'
month: '01'
page: 363 - 373
publication_status: published
publisher: Springer
publist_id: '4482'
quality_controlled: 0
status: public
title: On center regions and balls containing many points
type: conference
volume: 5092
year: '2008'
...
---
_id: '2497'
abstract:
- lang: eng
  text: Cyclic nucleotide phosphodiesterase 10A (PDE10A) is a member of phosphodiesterase
    families that degrade cAMP and/or cGMP in distinct intracellular sites. PDE10A
    has a dual activity on hydrolysis of both cAMP and cGMP, and is prominently expressed
    in the striatum and the testis. Previous studies suggested that PDE10A is involved
    in regulation of locomotor activity and potentially related to psychosis, but
    concrete physiological roles of PDE10A remains elusive yet. In this study, we
    genetically inactivated PDE10A2, a prominent isoform of PDE10A in the brain, in
    mice, and demonstrate that PDE10A2 deficiency results in increased social interaction
    without any major influence on different other behaviors, along with increased
    levels of striatal cAMP. We also demonstrate that PDE10A2 is selectively distributed
    in medium spiny neurons, but not interneurons, of the striatal complex. Thus,
    our results establish a physiological role for PDE10A2 in regulating cAMP pathway
    and social interaction, and suggest that cAMP signaling cascade in striatal medium
    spiny neurons might be involved in regulating social interaction behavior in mice.
author:
- first_name: Hiromi
  full_name: Sano, Hiromi
  last_name: Sano
- first_name: Yumiko
  full_name: Nagai, Yumiko
  last_name: Nagai
- first_name: Tsuyoshi
  full_name: Miyakawa, Tsuyoshi
  last_name: Miyakawa
- first_name: Ryuichi
  full_name: Ryuichi Shigemoto
  id: 499F3ABC-F248-11E8-B48F-1D18A9856A87
  last_name: Shigemoto
  orcid: 0000-0001-8761-9444
- first_name: Mineto
  full_name: Yokoi, Mineto
  last_name: Yokoi
citation:
  ama: Sano H, Nagai Y, Miyakawa T, Shigemoto R, Yokoi M. Increased social interaction
    in mice deficient of the striatal medium spiny neuron-specific phosphodiesterase
    10A2. <i>Journal of Neurochemistry</i>. 2008;105(2):546-556. doi:<a href="https://doi.org/10.1111/j.1471-4159.2007.05152.x">10.1111/j.1471-4159.2007.05152.x</a>
  apa: Sano, H., Nagai, Y., Miyakawa, T., Shigemoto, R., &#38; Yokoi, M. (2008). Increased
    social interaction in mice deficient of the striatal medium spiny neuron-specific
    phosphodiesterase 10A2. <i>Journal of Neurochemistry</i>. Wiley-Blackwell. <a
    href="https://doi.org/10.1111/j.1471-4159.2007.05152.x">https://doi.org/10.1111/j.1471-4159.2007.05152.x</a>
  chicago: Sano, Hiromi, Yumiko Nagai, Tsuyoshi Miyakawa, Ryuichi Shigemoto, and Mineto
    Yokoi. “Increased Social Interaction in Mice Deficient of the Striatal Medium
    Spiny Neuron-Specific Phosphodiesterase 10A2.” <i>Journal of Neurochemistry</i>.
    Wiley-Blackwell, 2008. <a href="https://doi.org/10.1111/j.1471-4159.2007.05152.x">https://doi.org/10.1111/j.1471-4159.2007.05152.x</a>.
  ieee: H. Sano, Y. Nagai, T. Miyakawa, R. Shigemoto, and M. Yokoi, “Increased social
    interaction in mice deficient of the striatal medium spiny neuron-specific phosphodiesterase
    10A2,” <i>Journal of Neurochemistry</i>, vol. 105, no. 2. Wiley-Blackwell, pp.
    546–556, 2008.
  ista: Sano H, Nagai Y, Miyakawa T, Shigemoto R, Yokoi M. 2008. Increased social
    interaction in mice deficient of the striatal medium spiny neuron-specific phosphodiesterase
    10A2. Journal of Neurochemistry. 105(2), 546–556.
  mla: Sano, Hiromi, et al. “Increased Social Interaction in Mice Deficient of the
    Striatal Medium Spiny Neuron-Specific Phosphodiesterase 10A2.” <i>Journal of Neurochemistry</i>,
    vol. 105, no. 2, Wiley-Blackwell, 2008, pp. 546–56, doi:<a href="https://doi.org/10.1111/j.1471-4159.2007.05152.x">10.1111/j.1471-4159.2007.05152.x</a>.
  short: H. Sano, Y. Nagai, T. Miyakawa, R. Shigemoto, M. Yokoi, Journal of Neurochemistry
    105 (2008) 546–556.
date_created: 2018-12-11T11:58:01Z
date_published: 2008-04-01T00:00:00Z
date_updated: 2021-01-12T06:57:50Z
day: '01'
doi: 10.1111/j.1471-4159.2007.05152.x
extern: 1
intvolume: '       105'
issue: '2'
month: '04'
page: 546 - 556
publication: Journal of Neurochemistry
publication_status: published
publisher: Wiley-Blackwell
publist_id: '4404'
quality_controlled: 0
status: public
title: Increased social interaction in mice deficient of the striatal medium spiny
  neuron-specific phosphodiesterase 10A2
type: journal_article
volume: 105
year: '2008'
...
---
_id: '1717'
abstract:
- lang: eng
  text: 'Two key processes are in the basis of morphogenesis: the spatial allocation
    of cell types in fields of naïve cells and the regulation of growth. Both are
    controlled by morphogens, which activate target genes in the growing tissue in
    a concentration-dependent manner. Thus the morphogen model is an intrinsically
    quantitative concept. However, quantitative studies were performed only in recent
    years on two morphogens: Bicoid and Decapentaplegic. This review covers quantitative
    aspects of the formation and precision of the Decapentaplegic morphogen gradient.
    The morphogen gradient concept is transitioning from a soft definition to a precise
    idea of what the gradient could really do.'
acknowledgement: This work was supported by the University of Geneva, Max Planck Society,
  VW, EU, SNF, and HFSP
author:
- first_name: Anna
  full_name: Anna Kicheva
  id: 3959A2A0-F248-11E8-B48F-1D18A9856A87
  last_name: Kicheva
  orcid: 0000-0003-4509-4998
- first_name: Marcos
  full_name: González-Gaitán, Marcos A
  last_name: González Gaitán
citation:
  ama: Kicheva A, González Gaitán M. The Decapentaplegic morphogen gradient a precise
    definition. <i>Current Opinion in Cell Biology</i>. 2008;20(2):137-143. doi:<a
    href="https://doi.org/10.1016/j.ceb.2008.01.008">10.1016/j.ceb.2008.01.008</a>
  apa: Kicheva, A., &#38; González Gaitán, M. (2008). The Decapentaplegic morphogen
    gradient a precise definition. <i>Current Opinion in Cell Biology</i>. Elsevier.
    <a href="https://doi.org/10.1016/j.ceb.2008.01.008">https://doi.org/10.1016/j.ceb.2008.01.008</a>
  chicago: Kicheva, Anna, and Marcos González Gaitán. “The Decapentaplegic Morphogen
    Gradient a Precise Definition.” <i>Current Opinion in Cell Biology</i>. Elsevier,
    2008. <a href="https://doi.org/10.1016/j.ceb.2008.01.008">https://doi.org/10.1016/j.ceb.2008.01.008</a>.
  ieee: A. Kicheva and M. González Gaitán, “The Decapentaplegic morphogen gradient
    a precise definition,” <i>Current Opinion in Cell Biology</i>, vol. 20, no. 2.
    Elsevier, pp. 137–143, 2008.
  ista: Kicheva A, González Gaitán M. 2008. The Decapentaplegic morphogen gradient
    a precise definition. Current Opinion in Cell Biology. 20(2), 137–143.
  mla: Kicheva, Anna, and Marcos González Gaitán. “The Decapentaplegic Morphogen Gradient
    a Precise Definition.” <i>Current Opinion in Cell Biology</i>, vol. 20, no. 2,
    Elsevier, 2008, pp. 137–43, doi:<a href="https://doi.org/10.1016/j.ceb.2008.01.008">10.1016/j.ceb.2008.01.008</a>.
  short: A. Kicheva, M. González Gaitán, Current Opinion in Cell Biology 20 (2008)
    137–143.
date_created: 2018-12-11T11:53:38Z
date_published: 2008-04-01T00:00:00Z
date_updated: 2021-01-12T06:52:44Z
day: '01'
doi: 10.1016/j.ceb.2008.01.008
extern: 1
intvolume: '        20'
issue: '2'
month: '04'
page: 137 - 143
publication: Current Opinion in Cell Biology
publication_status: published
publisher: Elsevier
publist_id: '5412'
quality_controlled: 0
status: public
title: The Decapentaplegic morphogen gradient a precise definition
type: journal_article
volume: 20
year: '2008'
...
---
_id: '1719'
abstract:
- lang: eng
  text: We study the mechanics of tissue growth via cell division and cell death (apoptosis).
    The rearrangements of cells can on large scales and times be captured by a continuum
    theory which describes the tissue as an effective viscous material with active
    stresses generated by cell division. We study the effects of anisotropies of cell
    division on cell rearrangements and show that average cellular trajectories exhibit
    anisotropic scaling behaviors. If cell division and apoptosis balance, there is
    no net growth, but for anisotropic cell division the tissue undergoes spontaneous
    shear deformations. Our description is relevant for the study of developing tissues
    such as the imaginal disks of the fruit fly Drosophila melanogaster, which grow
    anisotropically.
author:
- first_name: Thomas
  full_name: Bittig, Thomas
  last_name: Bittig
- first_name: Ortrud
  full_name: Wartlick, Ortrud
  last_name: Wartlick
- first_name: Anna
  full_name: Anna Kicheva
  id: 3959A2A0-F248-11E8-B48F-1D18A9856A87
  last_name: Kicheva
  orcid: 0000-0003-4509-4998
- first_name: Marcos
  full_name: González-Gaitárr, Marcos
  last_name: González Gaitárr
- first_name: Frank
  full_name: Julicher, Frank
  last_name: Julicher
citation:
  ama: Bittig T, Wartlick O, Kicheva A, González Gaitárr M, Julicher F. Dynamics of
    anisotropic tissue growth. <i>New Journal of Physics</i>. 2008;10. doi:<a href="https://doi.org/10.1088/1367-2630/10/6/063001">10.1088/1367-2630/10/6/063001</a>
  apa: Bittig, T., Wartlick, O., Kicheva, A., González Gaitárr, M., &#38; Julicher,
    F. (2008). Dynamics of anisotropic tissue growth. <i>New Journal of Physics</i>.
    IOP Publishing Ltd. <a href="https://doi.org/10.1088/1367-2630/10/6/063001">https://doi.org/10.1088/1367-2630/10/6/063001</a>
  chicago: Bittig, Thomas, Ortrud Wartlick, Anna Kicheva, Marcos González Gaitárr,
    and Frank Julicher. “Dynamics of Anisotropic Tissue Growth.” <i>New Journal of
    Physics</i>. IOP Publishing Ltd., 2008. <a href="https://doi.org/10.1088/1367-2630/10/6/063001">https://doi.org/10.1088/1367-2630/10/6/063001</a>.
  ieee: T. Bittig, O. Wartlick, A. Kicheva, M. González Gaitárr, and F. Julicher,
    “Dynamics of anisotropic tissue growth,” <i>New Journal of Physics</i>, vol. 10.
    IOP Publishing Ltd., 2008.
  ista: Bittig T, Wartlick O, Kicheva A, González Gaitárr M, Julicher F. 2008. Dynamics
    of anisotropic tissue growth. New Journal of Physics. 10.
  mla: Bittig, Thomas, et al. “Dynamics of Anisotropic Tissue Growth.” <i>New Journal
    of Physics</i>, vol. 10, IOP Publishing Ltd., 2008, doi:<a href="https://doi.org/10.1088/1367-2630/10/6/063001">10.1088/1367-2630/10/6/063001</a>.
  short: T. Bittig, O. Wartlick, A. Kicheva, M. González Gaitárr, F. Julicher, New
    Journal of Physics 10 (2008).
date_created: 2018-12-11T11:53:39Z
date_published: 2008-06-03T00:00:00Z
date_updated: 2021-01-12T06:52:44Z
day: '03'
doi: 10.1088/1367-2630/10/6/063001
extern: 1
intvolume: '        10'
month: '06'
publication: New Journal of Physics
publication_status: published
publisher: IOP Publishing Ltd.
publist_id: '5411'
quality_controlled: 0
status: public
title: Dynamics of anisotropic tissue growth
type: journal_article
volume: 10
year: '2008'
...
---
_id: '1749'
abstract:
- lang: eng
  text: Scanning probe microscopy; Semiconductor quantum dots; Composition gradients;
    Composition profiles; Nanotomography; Single quantum dots; Strained sige/si; Three-dimensional
    (3D); Wet-chemical etchings; X-ray scattering measurements; quantum dot; methodology;
    nanotechnology; optical tomography; scanning probe microscopy; three dimensional
    imaging; Imaging, Three-Dimensional; Materials Testing; Microscopy, Scanning Probe;
    Nanotechnology; Quantum Dots; Tomography,
acknowledgement: This work was supported by the BMBF (No. 03N8711) and the EU project
  D-DotFET (No. 012150)
author:
- first_name: Armando
  full_name: Rastelli, Armando
  last_name: Rastelli
- first_name: Mathieu
  full_name: Stoffel, Mathieu
  last_name: Stoffel
- first_name: Ângelo
  full_name: Malachias, Ângelo S
  last_name: Malachias
- first_name: Tsvetelina
  full_name: Merdzhanova, Tsvetelina
  last_name: Merdzhanova
- first_name: Georgios
  full_name: Georgios Katsaros
  id: 38DB5788-F248-11E8-B48F-1D18A9856A87
  last_name: Katsaros
- first_name: Klaus
  full_name: Kern, Klaus
  last_name: Kern
- first_name: Till
  full_name: Metzger, Till H
  last_name: Metzger
- first_name: Oliver
  full_name: Schmidt, Oliver G
  last_name: Schmidt
citation:
  ama: Rastelli A, Stoffel M, Malachias Â, et al. Three-dimensional composition profiles
    of single quantum dots determined by scanning-probe-microscopy-based nanotomography.
    <i>Nano Letters</i>. 2008;8(5):1404-1409. doi:<a href="https://doi.org/10.1021/nl080290y">10.1021/nl080290y</a>
  apa: Rastelli, A., Stoffel, M., Malachias, Â., Merdzhanova, T., Katsaros, G., Kern,
    K., … Schmidt, O. (2008). Three-dimensional composition profiles of single quantum
    dots determined by scanning-probe-microscopy-based nanotomography. <i>Nano Letters</i>.
    American Chemical Society. <a href="https://doi.org/10.1021/nl080290y">https://doi.org/10.1021/nl080290y</a>
  chicago: Rastelli, Armando, Mathieu Stoffel, Ângelo Malachias, Tsvetelina Merdzhanova,
    Georgios Katsaros, Klaus Kern, Till Metzger, and Oliver Schmidt. “Three-Dimensional
    Composition Profiles of Single Quantum Dots Determined by Scanning-Probe-Microscopy-Based
    Nanotomography.” <i>Nano Letters</i>. American Chemical Society, 2008. <a href="https://doi.org/10.1021/nl080290y">https://doi.org/10.1021/nl080290y</a>.
  ieee: A. Rastelli <i>et al.</i>, “Three-dimensional composition profiles of single
    quantum dots determined by scanning-probe-microscopy-based nanotomography,” <i>Nano
    Letters</i>, vol. 8, no. 5. American Chemical Society, pp. 1404–1409, 2008.
  ista: Rastelli A, Stoffel M, Malachias Â, Merdzhanova T, Katsaros G, Kern K, Metzger
    T, Schmidt O. 2008. Three-dimensional composition profiles of single quantum dots
    determined by scanning-probe-microscopy-based nanotomography. Nano Letters. 8(5),
    1404–1409.
  mla: Rastelli, Armando, et al. “Three-Dimensional Composition Profiles of Single
    Quantum Dots Determined by Scanning-Probe-Microscopy-Based Nanotomography.” <i>Nano
    Letters</i>, vol. 8, no. 5, American Chemical Society, 2008, pp. 1404–09, doi:<a
    href="https://doi.org/10.1021/nl080290y">10.1021/nl080290y</a>.
  short: A. Rastelli, M. Stoffel, Â. Malachias, T. Merdzhanova, G. Katsaros, K. Kern,
    T. Metzger, O. Schmidt, Nano Letters 8 (2008) 1404–1409.
date_created: 2018-12-11T11:53:48Z
date_published: 2008-05-01T00:00:00Z
date_updated: 2021-01-12T06:52:57Z
day: '01'
doi: 10.1021/nl080290y
extern: 1
intvolume: '         8'
issue: '5'
month: '05'
page: 1404 - 1409
publication: Nano Letters
publication_status: published
publisher: American Chemical Society
publist_id: '5374'
quality_controlled: 0
status: public
title: Three-dimensional composition profiles of single quantum dots determined by
  scanning-probe-microscopy-based nanotomography
type: journal_article
volume: 8
year: '2008'
...
