Ein Gitterpunktproblem im dreidimensionalen hyperbolischen Raum

Ohne Zusammenfassung     

Pinning of an interface by a weak potential

We prove that in a two-dimensional Gaussian SOS model with a small attractive potential the height of the interface remains bounded no matter how small the potential is; this is in sharp contrast with the free situation in which the interface height diverges logarithmically in the thermodynamic limit.     

Normal forms and versal deformations of linear Hamiltonian systems

Equivalence classes of time independent, linear, real Hamiltonian systems can be identified, up to canonical transformations, with the orbits of the adjoint action of the real symplectic group on its Lie algebra. A new set of representatives, also called normal forms, for these orbits is given. Versal deformations of systems in normal form are constructed. Applications of versal deformations to the study of bifurcations of linear systems with small codimension are indicated.     

Yrast levels of 220Ra populated in the 208Pb(14C, 2n) reaction

Yrast states in the nucleus ²²⁰Ra were studied by means of the ²⁰⁸Pb(¹⁴C, 2n) reaction at 61 and 64 MeV. A staggering sequence of levels of positive and negative parity has been observed up to spin and parity I^π = 16⁺ (18 ⁺) and from I^π = 5^? to I^π = 17^?, respectively. These states are connected by strong E1 transitions competing with the stretched E2 transitions, the $\text{B(}\text{E}\text{1)}\text{B(}\text{E}\text{2)}$ ratio being ~ 10 ^?6 fm^?2. The ratio of the excitation energy of the 4⁺ state to that of the 2⁺ state is close to the vibrational limit. The moment of inertia associated with the negative-parity yrast states is slightly increasing with the rotational frequency ω. It is considerably higher than that of the positive-parity states at lower spins, the difference decreasing monotonically with increasing ω. The data are discussed with reference to the octupole vibrational picture as well as to the results of recent models predicting reflection-asymmetric shapes in the Ra-Th region.     

Fluctuation susceptibility relations for classical spin systems

We prove identities between integrated Ursell functions and derivatives of the pressure in the thermodynamic limit, for multicomponent classical spin systems which obey the Lee-Yang theorem and some form of Gaussian domination, when the susceptibility is finite (T>T _c). Following Refs. 3 and 4, we view the moment generating function of the magnetization as the inverse of an infinitely divisible characteristic function. Fluctuation susceptibility relations of all orders then follow by bounding the corresponding cumulants, taken in zero external field. High-order cumulants are bounded in terms of the susceptibility using Gaussian and Simon's inequalities for short-range interactions.     

Beltrami's solutions of general equilibrium equations in continuum mechanics

M. Gurtin has proved that the Beltrami representation, $\mathbf{S}=\mathrm{rot}\mathrm{rot}\mathbf{A}$, of a smooth, divergence-free stress tensor in a smooth domain, is verified if and only if S is self-equilibrated. Here, Gurtin's conditions are extended to the case of a bounded domain with a Lipschitz-continuous boundary, for a tensor field $\mathbf{S}\in L^2(\Omega ;M_{\mathrm{sym}}^3)$. We apply this result to obtain an extension of the Saint Venant's equations of compatibility to non necessarily simply-connected domains. To cite this article: G. Geymonat, F. Krasucki, C. R. Acad. Sci. Paris, Ser. I 342 (2006).     

Search for neutral, long-lived particles decaying into two muons in pp[over] collisions at sqrt[s]=1.96 TeV

We present a search for a neutral particle, pair produced in pp[over] collisions at sqrt[s]=1.96 TeV, which decays into two muons and lives long enough to travel at least 5 cm before decaying. The analysis uses approximately 380 pb(-1) of data recorded with the D0 detector. The background is estimated to be about one event. No candidates are observed, and limits are set on the pair-production cross section times branching fraction into dimuons + X for such particles. For a mass of 10 GeV and lifetime of 4x10(-11) s, we exclude values greater than 0.14 pb (95% C.L.). These results are used to limit the interpretation of NuTeV's excess of dimuon events.