@article{213,
abstract = {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).},
author = {Timothy Browning and Heath-Brown, Roger and Starr, Jason M},
journal = {Proceedings of the London Mathematical Society},
number = {2},
pages = {273 -- 303},
publisher = {John Wiley and Sons Ltd},
title = {{The density of rational points on non-singular hypersurfaces, II}},
doi = {https://doi.org/10.1112/S0024611506015784},
volume = {93},
year = {2006},
}
@article{2134,
abstract = {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.},
author = {Ehresmann, Arno and Werner, Lutz and Klumpp, Stefan and Demekhin, Ph V and Mikhail Lemeshko and Sukhorukov, V. L and Schartner, Karl H and Schmoranzer, Hans P},
journal = {Journal of Physics B: Atomic, Molecular and Optical Physics},
number = {6},
pages = {L119 -- L126},
publisher = {IOP Publishing Ltd.},
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}},
doi = {10.1088/0953-4075/39/6/L03},
volume = {39},
year = {2006},
}
@article{2142,
abstract = {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 = {Ehresmann, Arno and Werner, Lutz and Klumpp, Stefan and Lucht, S and Schmoranzer, Hans P and Mickat, Sascha and Schill, Rüdiger H and Schartner, Karl H and Demekhin, Philipp and Mikhail Lemeshko and Sukhorukov, Victor L},
journal = {Journal of Physics B: Atomic, Molecular and Optical Physics},
number = {2},
pages = {283 -- 304},
publisher = {IOP Publishing Ltd.},
title = {{Studying the N+2(C2Σ+u → X2Σ+g) fluorescence excited via the 1s−1π* resonance}},
doi = {10.1088/0953-4075/39/2/006},
volume = {39},
year = {2006},
}
@article{2144,
abstract = {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.},
author = {Vedrinskiǐ, Rostislav V and Nazarenko, Elena S and Mikhail Lemeshko and Nassif, Vivian M and Proux, Olivier and Novakovich, Alexander A and Joly, Yves},
journal = {Physical Review B - Condensed Matter and Materials Physics},
number = {13},
publisher = {American Physical Society},
title = {{Temperature dependent XAFS studies of local atomic structure of the perovskite-type zirconates}},
doi = {10.1103/PhysRevB.73.134109},
volume = {73},
year = {2006},
}
@article{215,
abstract = {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 = {Timothy Browning and Heath-Brown, Roger},
journal = {Bulletin of the London Mathematical Society},
number = {3},
pages = {401 -- 410},
publisher = {Wiley-Blackwell},
title = {{The density of rational points on non-singular hypersurfaces, I}},
doi = {10.1112/S0024609305018412},
volume = {38},
year = {2006},
}
@article{216,
abstract = {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 = {Timothy Browning and Heath-Brown, Roger and Salberger, Per},
journal = {Duke Mathematical Journal},
number = {3},
pages = {545 -- 578},
publisher = {Unknown},
title = {{Counting rational points on algebraic varieties}},
doi = {10.1215/S0012-7094-06-13236-2},
volume = {132},
year = {2006},
}
@article{218,
abstract = {This paper is concerned with the average order of certain arithmetic functions, as they range over the values taken by binary forms.},
author = {de la Bretèche, Régis and Timothy Browning},
journal = {Acta Arithmetica},
number = {3},
pages = {291 -- 304},
publisher = {Instytut Matematyczny},
title = {{Sums of arithmetic functions over values of binary forms}},
doi = {10.4064/aa125-3-6},
volume = {125},
year = {2006},
}
@inproceedings{2333,
author = {Lieb, Élliott H and Robert Seiringer and Solovej, Jan P},
pages = {239 -- 248},
publisher = {American Mathematical Society},
title = {{Ground-state energy of a dilute Fermi gas}},
doi = {10.1090/conm/412},
volume = {412},
year = {2006},
}
@inproceedings{2334,
author = {Robert Seiringer and Lieb, Élliott H and Yngvason, Jakob},
editor = {Zambrini, Jean-Claude},
publisher = {World Scientific Publishing},
title = {{One-dimensional behavior of dilute, trapped Bose gases in traps}},
doi = {10.1007/s00220-003-0993-3},
year = {2006},
}
@misc{2363,
abstract = { 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 = {Lieb, Élliott H and Robert Seiringer},
booktitle = {Communications in Mathematical Physics},
number = {2},
pages = {505 -- 537},
publisher = {Springer},
title = {{Derivation of the Gross-Pitaevskii equation for rotating Bose gases}},
doi = {10.1007/s00220-006-1524-9},
volume = {264},
year = {2006},
}
@article{2364,
abstract = {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 = {Robert Seiringer},
journal = {Reviews in Mathematical Physics},
number = {3},
pages = {233 -- 253},
publisher = {World Scientific Publishing},
title = {{A correlation estimate for quantum many-body systems at positive temperature}},
doi = {10.1142/S0129055X06002632},
volume = {18},
year = {2006},
}
@article{2365,
abstract = {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 = {Robert Seiringer},
journal = {Communications in Mathematical Physics},
number = {3},
pages = {729 -- 757},
publisher = {Springer},
title = {{The thermodynamic pressure of a dilute fermi gas}},
doi = {10.1007/s00220-005-1433-3},
volume = {261},
year = {2006},
}
@article{2366,
abstract = {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 = {Frank, Rupert L and Laptev, Ari and Lieb, Élliott H and Robert Seiringer},
journal = {Letters in Mathematical Physics},
number = {3},
pages = {309 -- 316},
publisher = {Springer},
title = {{Lieb-Thirring inequalities for Schrödinger operators with complex-valued potentials}},
doi = {10.1007/s11005-006-0095-1},
volume = {77},
year = {2006},
}
@inbook{2368,
abstract = {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.},
author = {Robert Seiringer},
booktitle = {Large Coulomb Systems},
editor = {Dereziński, Jan and Siedentop, Heinz},
pages = {249 -- 274},
publisher = {Springer},
title = {{Dilute, trapped Bose gases and Bose-Einstein condensation}},
doi = {10.1007/3-540-32579-4_6},
volume = {695},
year = {2006},
}
@inbook{2369,
abstract = {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.},
author = {Aizenman, Michael and Lieb, Élliott H and Robert Seiringer and Solovej, Jan P and Yngvason, Jakob},
booktitle = {Mathematical Physics of Quantum Mechanics},
editor = {Asch, Joachim and Joye, Alain},
pages = {199 -- 215},
publisher = {Springer},
title = {{Bose-Einstein condensation as a quantum phase transition in an optical lattice}},
doi = {10.1007/b11573432},
volume = {690},
year = {2006},
}
@inbook{2416,
author = {Bang-Jensen, Jørgen and Reed, Bruce and Schacht, Bruce and Šámal, Robert and Toft, Bjarne and Uli Wagner},
booktitle = {Topics in Discrete Mathematics},
pages = {613 -- 627},
publisher = {Springer},
title = {{On six problems posed by Jarik Nešetřil}},
doi = {10.1007/3-540-33700-8_30},
volume = {26},
year = {2006},
}
@article{2429,
abstract = {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 = {Matoušek, Jiří and Sharir, Micha and Smorodinsky, Shakhar and Uli Wagner},
journal = {Discrete & Computational Geometry},
number = {2},
pages = {177 -- 191},
publisher = {Springer},
title = {{K-sets in four dimensions}},
doi = {10.1007/s00454-005-1200-4},
volume = {35},
year = {2006},
}
@article{2430,
abstract = {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 = {Chent, Ke and Fiat, Amos and Kaplan, Haim and Levy, Meital B and Matoušek, Jiří and Mossel, Elchanan and Pach, János and Sharir, Micha and Smorodinsky, Shakhar and Uli Wagner and Welzl, Emo},
journal = {SIAM Journal on Computing},
number = {5},
pages = {1342 -- 1359},
publisher = {SIAM},
title = {{Online conflict-free coloring for intervals}},
doi = {10.1137/S0097539704446682},
volume = {36},
year = {2006},
}
@inproceedings{2431,
abstract = {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.},
author = {Uli Wagner},
pages = {635 -- 645},
publisher = {IEEE},
title = {{On a geometric generalization of the Upper Bound Theorem}},
doi = {10.1109/FOCS.2006.53},
year = {2006},
}
@inproceedings{7326,
abstract = {Often the properties of a single cell are considered as representative for a complete polymer electrolyte fuel cell stack or even a fuel cell system. In some cases this comes close, however, in many real cases differences on several scales become important. Cell interaction phenomena in fuel cell stacks that arise from inequalities between adjacent cells are investigated in detail experimentally. For that, a specialized 2-cell stack with advanced localized diagnostics was developed. The results show that inequalities propagate by electrical coupling, inhomogeneous cell polarization and inducing in-plane current in the common bipolar plate. The effects of the different loss-mechanisms are analyzed and quantified. },
author = {Büchi, Felix N. and Freunberger, Stefan Alexander and Santis, Marco},
booktitle = {ECS Transactions},
location = {Cancun, Mexico},
number = {1},
pages = {963--968},
publisher = {ECS},
title = {{What is learned beyond the scale of single cells?}},
doi = {10.1149/1.2356215},
volume = {3},
year = {2006},
}