Vafa-Witten Estimates for Compact Symmetric Spaces

We give an optimal upper bound for the first eigenvalue of the untwisted Dirac operator on a compact symmetric space G/H with rk G-rk H\le 1 with respect to arbitrary Riemannian metrics. We also prove a rigidity statement.Comment: LaTeX, 11 pages. V2: Rigidity statement added, minor changes. To appea

Minimal immersions of closed surfaces in hyperbolic three-manifolds

We study minimal immersions of closed surfaces (of genus $g \ge 2$) in hyperbolic 3-manifolds, with prescribed data $(\sigma, t\alpha)$, where $\sigma$ is a conformal structure on a topological surface $S$, and $\alpha dz^2$ is a holomorphic quadratic differential on the surface $(S,\sigma)$. We show that, for each $t \in (0,\tau_0)$ for some $\tau_0 > 0$, depending only on $(\sigma, \alpha)$, there are at least two minimal immersions of closed surface of prescribed second fundamental form $Re(t\alpha)$ in the conformal structure $\sigma$. Moreover, for $t$ sufficiently large, there exists no such minimal immersion. Asymptotically, as $t \to 0$, the principal curvatures of one minimal immersion tend to zero, while the intrinsic curvatures of the other blow up in magnitude.Comment: 16 page

Gravity coupled with matter and foundation of non-commutative geometry

We first exhibit in the commutative case the simple algebraic relations between the algebra of functions on a manifold and its infinitesimal length element $ds$. Its unitary representations correspond to Riemannian metrics and Spin structure while $ds$ is the Dirac propagator ds = \ts \!\!---\!\! \ts = D^{-1} where $D$ is the Dirac operator. We extend these simple relations to the non commutative case using Tomita's involution $J$. We then write a spectral action, the trace of a function of the length element in Planck units, which when applied to the non commutative geometry of the Standard Model will be shown (in a joint work with Ali Chamseddine) to give the SM Lagrangian coupled to gravity. The internal fluctuations of the non commutative geometry are trivial in the commutative case but yield the full bosonic sector of SM with all correct quantum numbers in the slightly non commutative case. The group of local gauge transformations appears spontaneously as a normal subgroup of the diffeomorphism group.Comment: 30 pages, Plain Te

A characterization of quadric constant mean curvature hypersurfaces of spheres

Let $\phi:M\to\mathbb{S}^{n+1}\subset\mathbb{R}^{n+2}$ be an immersion of a complete $n$-dimensional oriented manifold. For any $v\in\mathbb{R}^{n+2}$, let us denote by $\ell_v:M\to\mathbb{R}$ the function given by $\ell_v(x)=\phi(x),v$ and by $f_v:M\to\mathbb{R}$, the function given by $f_v(x)=\nu(x),v$, where $\nu:M\to\mathbb{S}^{n}$ is a Gauss map. We will prove that if $M$ has constant mean curvature, and, for some $v\ne{\bf 0}$ and some real number $\lambda$, we have that $\ell_v=\lambda f_v$, then, $\phi(M)$ is either a totally umbilical sphere or a Clifford hypersurface. As an application, we will use this result to prove that the weak stability index of any compact constant mean curvature hypersurface $M^n$ in $\mathbb{S}^{n+1}$ which is neither totally umbilical nor a Clifford hypersurface and has constant scalar curvature is greater than or equal to $2n+4$.Comment: Final version (February 2008). To appear in the Journal of Geometric Analysi

Equivariant geometric K-homology for compact Lie group actions

Let G be a compact Lie-group, X a compact G-CW-complex. We define equivariant geometric K-homology groups K^G_*(X), using an obvious equivariant version of the (M,E,f)-picture of Baum-Douglas for K-homology. We define explicit natural transformations to and from equivariant K-homology defined via KK-theory (the "official" equivariant K-homology groups) and show that these are isomorphism.Comment: 25 pages. v2: some mistakes corrected, more detail added, Michael Walter as author added. To appear in Abhandlungen aus dem Mathematischen Seminar der Universit\"at Hambur

Discovery of Calcium, Indium, Tin, and Platinum Isotopes

Currently, twenty-four calcium, thirty-eight indium, thirty-eight tin and thirty-nine platinum isotopes have been observed and the discovery of these isotopes is discussed here. For each isotope a brief synopsis of the first refereed publication, including the production and identification method, is presented.Comment: to be published in At. Data Nuclear Data Tables, This updated paper combines manuscripts: 1004.4934 (Calcium), 1004.5266 (Indium), 1003.5127 (Tin), and 1006.4033 (Platinum

The effect of warming climate on nutrient and solute export from the Greenland Ice Sheet

Glacial meltwater runoff is likely an important source of limiting nutrients for downstream primary producers. This has particular significance for regions surrounding the Greenland Ice Sheet, which discharges >400 km3 of meltwater annually. The Arctic is warming rapidly but the impact of higher discharge on nutrient export is unknown. We present four years of hydrological and geochemical data from a large Greenland Ice Sheet catchment that includes the two highest melt years on record (2010, 2012). Measurements reveal significant variation in dissolved solute (major ion) and estimated dissolved macronutrient (nitrogen, phosphorus and silica) fluxes, with increases in higher melt years. Labile particulate macronutrients dominate nutrient export, accounting for ~50 % of nitrogen and >80 % of both phosphorus and silica. The response of ice sheet nutrient export to enhanced melting is largely controlled by particle bound nutrients, the future supply of which is uncertain. We propose that the Greenland Ice Sheet provides an underappreciated and annually dynamic source of nutrients for the polar oceans, with changes in meltwater discharge likely to impact marine primary productivity in future decades

Characterization of and structural insight into struvite-K, MgKPO4·6H2O, an analogue of struvite

Struvite-K (MgKPO4·6H2O) is a magnesium potassium phosphate mineral with naturally cementitious properties, which is finding increasing usage as an inorganic cement for niche applications including nuclear waste management and rapid road repair. Struvite-K is also of interest in sustainable phosphate recovery from wastewater and, as such, a detailed knowledge of the crystal chemistry and high-temperature behavior is required to support further laboratory investigations and industrial applications. In this study, the local chemical environments of synthetic struvite-K were investigated using high-field solid-state 25Mg and 39K MAS NMR techniques, alongside 31P MAS NMR and thermal analysis. A single resonance was present in each of the 25Mg and 39K MAS NMR spectra, reported here for the first time alongside the experimental and calculated isotropic chemical shifts, which were comparable to the available data for isostructural struvite (MgNH4PO4·6H2O). An in situ high-temperature XRD analysis of struvite-K revealed the presence of a crystalline–amorphous–crystalline transition that occurred between 30 and 350 °C, following the single dehydration step of struvite-K. Between 50 and 300 °C, struvite-K dehydration yielded a transient disordered (amorphous) phase identified here for the first time, denoted δ-MgKPO4. At 350 °C, recrystallization was observed, yielding β-MgKPO4, commensurate with an endothermic DTA event. A subsequent phase transition to γ-MgKPO4 was observed on further heating, which reversed on cooling, resulting in the α-MgKPO4 structure stabilized at room temperature. This behavior was dissimilar from that of struvite exposed to high temperature, where NH4 liberation occurs at temperatures >50 °C, indicating that struvite-K could potentially withstand high temperatures via a transition to MgKPO4

Search for a W' boson decaying to a bottom quark and a top quark in pp collisions at sqrt(s) = 7 TeV

Results are presented from a search for a W' boson using a dataset corresponding to 5.0 inverse femtobarns of integrated luminosity collected during 2011 by the CMS experiment at the LHC in pp collisions at sqrt(s)=7 TeV. The W' boson is modeled as a heavy W boson, but different scenarios for the couplings to fermions are considered, involving both left-handed and right-handed chiral projections of the fermions, as well as an arbitrary mixture of the two. The search is performed in the decay channel W' to t b, leading to a final state signature with a single lepton (e, mu), missing transverse energy, and jets, at least one of which is tagged as a b-jet. A W' boson that couples to fermions with the same coupling constant as the W, but to the right-handed rather than left-handed chiral projections, is excluded for masses below 1.85 TeV at the 95% confidence level. For the first time using LHC data, constraints on the W' gauge coupling for a set of left- and right-handed coupling combinations have been placed. These results represent a significant improvement over previously published limits.Comment: Submitted to Physics Letters B. Replaced with version publishe

Search for the standard model Higgs boson decaying into two photons in pp collisions at sqrt(s)=7 TeV

A search for a Higgs boson decaying into two photons is described. The analysis is performed using a dataset recorded by the CMS experiment at the LHC from pp collisions at a centre-of-mass energy of 7 TeV, which corresponds to an integrated luminosity of 4.8 inverse femtobarns. Limits are set on the cross section of the standard model Higgs boson decaying to two photons. The expected exclusion limit at 95% confidence level is between 1.4 and 2.4 times the standard model cross section in the mass range between 110 and 150 GeV. The analysis of the data excludes, at 95% confidence level, the standard model Higgs boson decaying into two photons in the mass range 128 to 132 GeV. The largest excess of events above the expected standard model background is observed for a Higgs boson mass hypothesis of 124 GeV with a local significance of 3.1 sigma. The global significance of observing an excess with a local significance greater than 3.1 sigma anywhere in the search range 110-150 GeV is estimated to be 1.8 sigma. More data are required to ascertain the origin of this excess.Comment: Submitted to Physics Letters