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 $\phi$ on the compact metric space $X$, i.e. $X-\mathcal{CR}(\phi)=\bigcup [B(A)-A]$, where $\mathcal{CR}(\phi)$ denotes the chain recurrent set of $\phi$, $A$ stands for an attractor and $B(A)$ is the basin determined by $A$. 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 $\omega$-limit set of some random pre-attractor surrounding it, and by considering appropriate measurability, in fact we also consider the universal $\sigma$-algebra $\mathcal F^u$-measurability besides $\mathcal F$-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 $w$ 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 $z = 0.35$. For some combinations of these data, we show that there is a clear departure from the standard $\Lambda$CDM model at intermediary redshifts, although a non-evolving dark energy component ($dw/dz = 0$) 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 $S^{1|1}$ equipped with the standard contact structure. The conformal Lie superalgebra K(1) acts on $S^{1|1}$ as the Lie superalgebra of contact vector fields; it contains the M\"obius superalgebra $osp(1|2)$. We study the space of linear differential operators on weighted densities as a module over $osp(1|2)$. 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