@article{209,
author = {Timothy Browning and Heath-Brown, Roger},
journal = {Inventiones Mathematicae},
number = {3},
pages = {553 -- 573},
publisher = {Unknown},
title = {{Equal sums of three powers}},
doi = {10.1007/s00222-004-0360-9},
volume = {157},
year = {2004},
}
@article{2308,
abstract = {It is widely believed that the inflammatory events mediated by microglial activation contribute to several neurodegenerative processes. Alzheimer's disease, for example, is characterized by an accumulation of β-amyloid protein (Aβ) in neuritic plaques that are infiltrated by reactive microglia and astrocytes. Although Aβ and its fragment 25-35 exert a direct toxic effect on neurons, they also activate microglia. Microglial activation is accompanied by morphological changes, cell proliferation, and release of various cytokines and growth factors. A number of scientific reports suggest that the increased proliferation of microglial cells is dependent on ionic membrane currents and in particular on chloride conductances. An unusual chloride ion channel known to be associated with macrophage activation is the chloride intracellular channel-1 (CLIC1). Here we show that Aβ stimulation of neonatal rat microglia specifically leads to the increase in CLIC1 protein and to the functional expression of CLIC1 chloride conductance, both barely detectable on the plasma membrane of quiescent cells. CLIC1 protein expression in microglia increases after 24 hr of incubation with Aβ, simultaneously with the production of reactive nitrogen intermediates and of tumor necrosis factor-α (TNF-α). We demonstrate that reducing CLIC1 chloride conductance by a specific blocker [IAA-94 (R(+)-[(6,7-dichloro-2-cyclopentyl-2,3-dihydro-2-methyl-1-oxo-1H-inden-5yl)-oxy] acetic acid)] prevents neuronal apoptosis in neurons cocultured with Aβ-treated microglia. Furthermore, we show that small interfering RNAs used to knock down CLIC1 expression prevent TNF-α release induced by Aβ stimulation. These results provide a direct link between Aβ-induced microglial activation and CLIC1 functional expression.},
author = {Gaia Novarino and Fabrizi, Cinzia and Tonini, Raffaella and Denti, Michela A and Malchiodi, Albedi F and Lauro, Giuliana M and Sacchetti, Benedetto and Paradisi, Silvia and Ferroni, Arnaldo and Curmi, Paul M G and Breit, Samuel N and Mazzanti, Michele},
journal = {Journal of Neuroscience},
number = {23},
pages = {5322 -- 5330},
publisher = {Society for Neuroscience},
title = {{Involvement of the intracellular ion channel CLIC1 in microglia-mediated β-amyloid-induced neurotoxicity}},
doi = {10.1523/JNEUROSCI.1170-04.2004},
volume = {24},
year = {2004},
}
@article{2355,
abstract = {The BMV conjecture for traces, which states that Tr exp(A - λB) is the Laplace transform of a positive measure, is shown to be equivalent to two other statements: (i) The polynomial λ → Tr(A + λB) p has only non-negative coefficients for all A, B ≥ 0, p ∈ ℕ and (ii) λ → Tr(A + λB)-p is the Laplace transform of a positive measure for A, B ≥ 0, p > 0.},
author = {Lieb, Élliott H and Robert Seiringer},
journal = {Journal of Statistical Physics},
number = {1-2},
pages = {185 -- 190},
publisher = {Springer},
title = {{ Equivalent forms of the Bessis-Moussa-Villani conjecture}},
doi = {10.1023/B:JOSS.0000019811.15510.27},
volume = {115},
year = {2004},
}
@article{2356,
abstract = {Recent experimental and theoretical work has shown that there are conditions in which a trapped, low-density Bose gas behaves like the one-dimensional delta-function Bose gas solved years ago by Lieb and Liniger. This is an intrinsically quantum-mechanical phenomenon because it is not necessary to have a trap width that is the size of an atom - as might have been supposed - but it suffices merely to have a trap width such that the energy gap for motion in the transverse direction is large compared to the energy associated with the motion along the trap. Up to now the theoretical arguments have been based on variational - perturbative ideas or numerical investigations. In contrast, this paper gives a rigorous proof of the one-dimensional behavior as far as the ground state energy and particle density are concerned. There are four parameters involved: the particle number, N, transverse and longitudinal dimensions of the trap, r and L, and the scattering length a of the interaction potential. Our main result is that if r/L → 0 and N → ∞ the ground state energy and density can be obtained by minimizing a one-dimensional density functional involving the Lieb-Liniger energy density with coupling constant ∼ a/r 2. This density functional simplifies in various limiting cases and we identify five asymptotic parameter regions altogether. Three of these, corresponding to the weak coupling regime, can also be obtained as limits of a three-dimensional Gross-Pitaevskii theory. We also show that Bose-Einstein condensation in the ground state persists in a part of this regime. In the strong coupling regime the longitudinal motion of the particles is strongly correlated. The Gross-Pitaevskii description is not valid in this regime and new mathematical methods come into play.},
author = {Lieb, Élliott H and Robert Seiringer and Yngvason, Jakob},
journal = {Communications in Mathematical Physics},
number = {2},
pages = {347 -- 393},
publisher = {Springer},
title = {{One-dimensional behavior of dilute, trapped Bose gases}},
doi = {10.1007/s00220-003-0993-3},
volume = {244},
year = {2004},
}
@article{2360,
abstract = {An optical lattice model developed that is similar to the Bose-Hubbard model to describe the transition between Bose-Einstein condensation (BEC) and a Mott insulator state was analyzed. It was found that the system was a hard core lattice gas at half of the maximum density and the optical lattice was modeled by a periodic potential of strength λ. It was also observed that the interparticle interaction was essential for this transition that occurred even in the ground state. The results show that all the essential features could be proved rigorously such as the existence of BEC for small λ and its suppression for a large λ.},
author = {Aizenman, Michael and Lieb, Élliott H and Robert Seiringer and Solovej, Jan P and Yngvason, Jakob},
journal = {Physical Review A - Atomic, Molecular, and Optical Physics},
number = {2},
pages = {023612 -- 1--0236121--2},
publisher = {American Physical Society},
title = {{Bose-Einstein quantum phase transition in an optical lattice model}},
doi = {10.1103/PhysRevA.70.023612},
volume = {70},
year = {2004},
}