@inproceedings{2077,
  abstract     = {We present an adaptive animation method for electrical discharges. Electrical discharges can be simulated using the dielectric breakdown model. Regular discretization of the governing Laplace equation leads to huge equation systems, and the computational cost of solving the equations quickly becomes prohibitive at high resolutions, especially for simulations in 3D. In contrast, our method discretizes the Laplace equation on an adaptive octree, reducing the size of the problem significantly, and making simulations of high resolution 3D datasets and even 3D animations feasible. In order to enhance realism for lightning animations, we propose a particle simulation that animates the residual positive charge. Thus, interaction of electrical discharges with their surroundings
can be simulated.},
  author       = {Bernd Bickel and Wicke, Martin and Gross, Markus},
  publisher    = {IOS Press},
  title        = {{Adaptive simulation of electrical discharges}},
  year         = {2006},
}

@inproceedings{2088,
  abstract     = {We have measured 3D face geometry, skin reflectance, and subsurface scattering using custom-built devices for 149 subjects of varying age, gender, and race. We developed a novel skin reflectance model whose parameters can be estimated from measurements. The model decomposes the large amount of measured skin data into a spatially-varying analytic BRDF, a diffuse albedo map, and diffuse subsurface scattering. Our model is intuitive, physically plausible, and - since we do not use the original measured data - easy to edit as well. High-quality renderings come close to reproducing real photographs. The analysis of the model parameters for our sample population reveals variations according to subject age, gender, skin type, and external factors (e.g., sweat, cold, or makeup). Using our statistics, a user can edit the overall appearance of a face (e.g., changing skin type and age) or change small-scale features using texture synthesis (e.g., adding moles and freckles). We are making the collected statistics publicly available to the research community for applications in face synthesis and analysis. },
  author       = {Weyrich, Tim and Matusik, Wojciech and Pfister, Hanspeter and Bernd Bickel and Donner, Craig and Tu, Chien and McAndless, Janet M and Lee, Jinho and Ngan, Addy and Jensen, Henrik W and Groß, Markus S},
  pages        = {1013 -- 1024},
  publisher    = {ACM},
  title        = {{Analysis of human faces using a measurement-based skin reflectance model}},
  doi          = {10.1145/1179352.1141987},
  year         = {2006},
}

@article{2089,
  abstract     = {We have measured 3D face geometry, skin reflectance, and subsurface scattering using custom-built devices for 149 subjects of varying age, gender, and race. We developed a novel skin reflectance model whose parameters can be estimated from measurements. The model decomposes the large amount of measured skin data into a spatially-varying analytic BRDF, a diffuse albedo map, and diffuse subsurface scattering. Our model is intuitive, physically plausible, and - since we do not use the original measured data - easy to edit as well. High-quality renderings come close to reproducing real photographs. The analysis of the model parameters for our sample population reveals variations according to subject age, gender, skin type, and external factors (e.g., sweat, cold, or makeup). Using our statistics, a user can edit the overall appearance of a face (e.g., changing skin type and age) or change small-scale features using texture synthesis (e.g., adding moles and freckles). We are making the collected statistics publicly available to the research community for applications in face synthesis and analysis.},
  author       = {Weyrich, Tim and Matusik, Wojciech and Pfister, Hanspeter and Bernd Bickel and Donner, Craig and Tu, Chien and McAndless, Janet M and Lee, Jinho and Ngan, Addy and Jensen, Henrik W and Groß, Markus S},
  journal      = {ACM Transactions on Graphics},
  number       = {3},
  pages        = {1013 -- 1024},
  publisher    = {ACM},
  title        = {{Analysis of human faces using a measurement-based skin reflectance model}},
  doi          = {10.1145/1141911.1141987},
  volume       = {25},
  year         = {2006},
}

@inproceedings{2090,
  author       = {Bernd Bickel and Weyrich, Tim and Matusik, Wojciech and Pfister, Hanspeter and Donner, Craig and Tu, Chien and McAndless, Janet M and Lee, Jinho and Ngan, Addy and Jensen, Henrik W and Groß, Markus S},
  publisher    = {ACM},
  title        = {{Processing and editing of faces using a measurement-based skin reflectance model}},
  doi          = {10.1145/1179849.1180059},
  year         = {2006},
}

@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},
}