3,981 research outputs found
Global surfaces of section in the planar restricted 3-body problem
The restricted planar three-body problem has a rich history, yet many
unanswered questions still remain. In the present paper we prove the existence
of a global surface of section near the smaller body in a new range of energies
and mass ratios for which the Hill's region still has three connected
components. The approach relies on recent global methods in symplectic geometry
and contrasts sharply with the perturbative methods used until now.Comment: 11 pages, 1 figur
Harmonic Maa{\ss}-Jacobi forms of degree 1 with higher rank indices
We define and investigate real analytic weak Jacobi forms of degree 1 and
arbitrary rank. En route we calculate the Casimir operator associated to the
maximal central extension of the real Jacobi group, which for rank exceeding 1
is of order 4. In ranks exceeding 1, the notions of H-harmonicity and
semi-holomorphicity are the same.Comment: 28 page
Measuring a Light Neutralino Mass at the ILC: Testing the MSSM Neutralino Cold Dark Matter Model
The LEP experiments give a lower bound on the neutralino mass of about 46 GeV
which, however, relies on a supersymmetric grand unification relation. Dropping
this assumption, the experimental lower bound on the neutralino mass vanishes
completely. Recent analyses suggest, however, that in the minimal
supersymmetric standard model (MSSM), a light neutralino dark matter candidate
has a lower bound on its mass of about 7 GeV. In light of this, we investigate
the mass sensitivity at the ILC for very light neutralinos. We study slepton
pair production, followed by the decay of the sleptons to a lepton and the
lightest neutralino. We find that the mass measurement accuracy for a few-GeV
neutralino is around 2 GeV, or even less if the relevant slepton is
sufficiently light. We thus conclude that the ILC can help verify or falsify
the MSSM neutralino cold dark matter model even for very light neutralinos.Comment: 7 pages, 1 figure; references adde
Oxy-functionalization of nucleophilic rhenium(I) metal carbon bonds catalyzed by selenium(IV)
We report that SeO_2 catalyzes the facile oxy-functionalization of (CO)_5Re(I)-Me^(δ−) with IO_4− to generate methanol. Mechanistic studies and DFT calculations reveal that catalysis involves methyl group transfer from Re to the electrophilic Se center followed by oxidation and subsequent reductive functionalization of the resulting CH_3Se(VI) species. Furthermore, (CO)_3Re(I)(Bpy)-R (R = ethyl, n-propyl, and aryl) complexes show analogous transfer to SeO_2 to generate the primary alcohols. This represents a new strategy for the oxy-functionalization of M−R^(δ−) polarized bonds
The random case of Conley's theorem
The well-known Conley's theorem states that the complement of chain recurrent
set equals the union of all connecting orbits of the flow on the compact
metric space , i.e. , where
denotes the chain recurrent set of , stands for
an attractor and is the basin determined by . In this paper we show
that by appropriately selecting the definition of random attractor, in fact we
define a random local attractor to be the -limit set of some random
pre-attractor surrounding it, and by considering appropriate measurability, in
fact we also consider the universal -algebra -measurability besides -measurability, we are able to obtain
the random case of Conley's theorem.Comment: 15 page
Existence and stability of viscoelastic shock profiles
We investigate existence and stability of viscoelastic shock profiles for a
class of planar models including the incompressible shear case studied by
Antman and Malek-Madani. We establish that the resulting equations fall into
the class of symmetrizable hyperbolic--parabolic systems, hence spectral
stability implies linearized and nonlinear stability with sharp rates of decay.
The new contributions are treatment of the compressible case, formulation of a
rigorous nonlinear stability theory, including verification of stability of
small-amplitude Lax shocks, and the systematic incorporation in our
investigations of numerical Evans function computations determining stability
of large-amplitude and or nonclassical type shock profiles.Comment: 43 pages, 12 figure
Probing the time dependence of dark energy
A new method to investigate a possible time-dependence of the dark energy
equation of state is proposed. We apply this methodology to two of the most
recent data sets of type Ia supernova (Union2 and SDSS) and the baryon acoustic
oscillation peak at . For some combinations of these data, we show
that there is a clear departure from the standard CDM model at
intermediary redshifts, although a non-evolving dark energy component () cannot be ruled out by these data. The approach developed here may be
useful to probe a possible evolving dark energy component when applied to
upcoming observational data.Comment: 6 pages, 3 figures, LaTe
Differential operators on supercircle: conformally equivariant quantization and symbol calculus
We consider the supercircle equipped with the standard contact
structure. The conformal Lie superalgebra K(1) acts on as the Lie
superalgebra of contact vector fields; it contains the M\"obius superalgebra
. We study the space of linear differential operators on weighted
densities as a module over . We introduce the canonical isomorphism
between this space and the corresponding space of symbols and find interesting
resonant cases where such an isomorphism does not exist
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