TY - JOUR
AB - 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).
AU - Timothy Browning
AU - Heath-Brown, Roger
AU - Starr, Jason M
ID - 213
IS - 2
JF - Proceedings of the London Mathematical Society
TI - The density of rational points on non-singular hypersurfaces, II
VL - 93
ER -
TY - JOUR
AB - 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.
AU - Ehresmann, Arno
AU - Werner, Lutz
AU - Klumpp, Stefan
AU - Demekhin, Ph V
AU - Mikhail Lemeshko
AU - Sukhorukov, V. L
AU - Schartner, Karl H
AU - Schmoranzer, Hans P
ID - 2134
IS - 6
JF - Journal of Physics B: Atomic, Molecular and Optical Physics
TI - 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
VL - 39
ER -
TY - JOUR
AB - 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'').
AU - Ehresmann, Arno
AU - Werner, Lutz
AU - Klumpp, Stefan
AU - Lucht, S
AU - Schmoranzer, Hans P
AU - Mickat, Sascha
AU - Schill, Rüdiger H
AU - Schartner, Karl H
AU - Demekhin, Philipp
AU - Mikhail Lemeshko
AU - Sukhorukov, Victor L
ID - 2142
IS - 2
JF - Journal of Physics B: Atomic, Molecular and Optical Physics
TI - Studying the N+2(C2Σ+u → X2Σ+g) fluorescence excited via the 1s−1π* resonance
VL - 39
ER -
TY - JOUR
AB - 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.
AU - Vedrinskiǐ, Rostislav V
AU - Nazarenko, Elena S
AU - Mikhail Lemeshko
AU - Nassif, Vivian M
AU - Proux, Olivier
AU - Novakovich, Alexander A
AU - Joly, Yves
ID - 2144
IS - 13
JF - Physical Review B - Condensed Matter and Materials Physics
TI - Temperature dependent XAFS studies of local atomic structure of the perovskite-type zirconates
VL - 73
ER -
TY - JOUR
AB - 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.*
AU - Timothy Browning
AU - Heath-Brown, Roger
ID - 215
IS - 3
JF - Bulletin of the London Mathematical Society
TI - The density of rational points on non-singular hypersurfaces, I
VL - 38
ER -